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  <updated>2026-03-25T15:16:45.000Z</updated>
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  <author>
    <name>秉</name>
    
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  <entry>
    <title>仲春夜行记</title>
    <link href="https://blog.si-on.top/2026/walking2freedom/"/>
    <id>https://blog.si-on.top/2026/walking2freedom/</id>
    <published>2026-03-25T15:16:45.000Z</published>
    <updated>2026-03-25T15:16:45.000Z</updated>
    
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       });    }    function createLegacyMidi(audio, visualObj) {        var options = clonePlainObject(config.options);        var animateOptions = createLegacyAnimateOptions();        if (animateOptions) {            options.animate = animateOptions;            options.animate.target = visualObj;        }        options.inlineControls = options.inlineControls || {};        options.inlineControls.startPlaying = !!config.autoplay;        ABCJS.renderMidi(config.audioId, abcString, options);    }    function createSynthAudio(audio, visualObj, state) {        state.control = new ABCJS.synth.SynthController();        state.synth = new ABCJS.synth.CreateSynth();        audio.innerHTML = '';        state.control.load(audio, createCursorControl(state), getInlineControlOptions());        applyInlineControlText(audio);        return state.synth.init({ visualObj: visualObj })            .then(function () {                return state.control.setTune(visualObj, false, getAudioOptions());            })            .then(function () {                bindAutoplayOnFirstGesture(state);            });    }    function initAudio(audio, visualObj, state) {        if (!config.midi) {            audio.innerHTML = '';            return Promise.resolve();        }        if (ABCJS.synth && ABCJS.synth.SynthController && ABCJS.synth.CreateSynth) {            return createSynthAudio(audio, visualObj, state);        }        if (typeof ABCJS.renderMidi === 'function') {            createLegacyMidi(audio, visualObj);            return Promise.resolve();        }        audio.innerHTML = '';        return Promise.resolve();    }    function renderAbc(paper) {        paper.innerHTML = '';        return ABCJS.renderAbc(config.paperId, abcString, getRenderOptions());    }    function setup() {        var paper = document.getElementById(config.paperId);        var audio = document.getElementById(config.audioId);        if (!paper || !audio || paper.dataset.abcjsRendered === 'true') return;        paper.dataset.abcjsRendered = 'true';        var state = {            currentEvent: null,            touchedElements: [],            control: null,            synth: null,            autoplayBound: false        };        try {            var tunes = renderAbc(paper);            if (!tunes || !tunes[0]) {                paper.dataset.abcjsRendered = 'false';                return;            }            initAudio(audio, tunes[0], state).catch(function (error) {                paper.dataset.abcjsRendered = 'false';                resetAnimationState(state);                console.error('abcjs audio init failed:', error);            });        } catch (error) {            paper.dataset.abcjsRendered = 'false';            resetAnimationState(state);            console.error('abcjs render failed:', error);        }    }    if (config.midi && config.css) {        loadStyleOnce(config.css);    }    loadScriptOnce(config.scriptId, config.js)        .then(setup)        .catch(function (error) {            console.error('abcjs script load failed:', error);        });})();</script><blockquote><center>自其不变者而观之，不变者变，自其变者而观之，变者不变。</center><p align="right">——仲春夜行中的Sion</p></blockquote><p>春寒料峭已经过去，润而暖的空气再一次蒸熏大地。然而我却感到没有一丝春意，心中亦如寒冬的深夜般渴望一个盛夏的多云傍晚。</p><p>举目四望，春分的枯草是冬至的枯草，一成不变，秋分的樟树亦是夏至的樟树，一成也不变。明月却稍黯淡了些，海风也寡淡了一些。倒不是说此地没有分明的四季，而是我目之所及处，草木常绿，倒不是说这明月清风有大变化，而是我目之所及处，风滞星稀。</p><p>不该变的变了，该变的却没有变，哈哈，世上恐怕再没有比这更滑稽之事了。</p><p>闭眼，在盲道上行走，前方寂寞敞亮，我无所惧。只觉着，随着步子的上下起伏，有碎碎月火、星火、灯火透过树影，在眼帘之外摇曳，投射着深红的影，惨绿的影，它们织在一起不停地摇动。我睁眼欲辨，眼前却是树穿过灯，灯穿过树，那种摇曳感荡然无存。</p><p>大脑弥补了太多，它知道这闪烁与摇曳对于我的行走，对于我的呼吸，对于我的生存是毫无意义的，数年的经验也更坚定了这一点，于是它习得了(选择遗忘)。而后者，即这种实感，已经越来越难以捉摸了，只有偶尔关闭感官的片刻，沉入雾霭之中，才能略略觉察一二。</p><p>循着灯火行走，逐渐接近道路尽头，我想要抓住一个略微积极的念头，作为历来夜行的团圆结局，我苦苦地抓，往树上，往楼房上，往柏油路上，我迫切地要抓住那么一个事物，或者一个事件，只要稍微触动下心绪，定就会引发一个圆满的结束，然而没有。</p><p>那触动还没抓到，道路已经走到尽头。我忙不迭地停住，或许我可以就此止步，或许也可以回头再走，或许我原地转圈，就这一点而言，这个选择定然决然必然地不受所有的自然规律、道德法则所约束。</p><p>我往前迈了一步，这一步，是自由的一步。(史诗bgm响起)</p><p>唔，那下一步呢？同理，也可以是自由的一步，或者一圈、一跃、一言、一篆、一影、一隅…</p><blockquote><p>🤖：结尾仓促，略显中二。</p></blockquote>]]></content>
    
    
    <summary type="html">仲春夜行，走路碎碎念。</summary>
    
    
    
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    <category term="✒️随笔" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%E2%9C%92%EF%B8%8F%E9%9A%8F%E7%AC%94/"/>
    
    
    <category term="情绪" scheme="https://blog.si-on.top/tags/%E6%83%85%E7%BB%AA/"/>
    
    <category term="格物" scheme="https://blog.si-on.top/tags/%E6%A0%BC%E7%89%A9/"/>
    
    <category term="审视" scheme="https://blog.si-on.top/tags/%E5%AE%A1%E8%A7%86/"/>
    
  </entry>
  
  <entry>
    <title>溶剂上石机理：高分子的溶解性分析</title>
    <link href="https://blog.si-on.top/2026/Toner2Stone/"/>
    <id>https://blog.si-on.top/2026/Toner2Stone/</id>
    <published>2026-03-23T06:23:49.000Z</published>
    <updated>2026-03-23T06:23:49.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><blockquote><center>石性稳定且无事，溶剂挥发最毒人。</center><p align="right">——Sion</p></blockquote><p>根据<a href="/2026/lp1_202601">上周定下的计划</a>，从本周开始，就要在业余时间用更多的时间去研究篆刻了。就目前阶段的熟练度而言，印稿设计是一个很主观的过程，自我感觉倒还好，然而刀法的运用上就明显感觉到吃力，每次刻完后都不很满意。为了训练刀法，就必须要舍弃浪费时间的设计过程，“依式填篆”地多描几方古印，于是乎，转印上石再一次被提上了日程。</p><p>所谓转印上石是指<strong>将篆刻作者设计的印章样稿显现于印面之上</strong><sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>的方法，属于篆刻技法中比较偏门的一种，在浩大的期刊网络中仅仅发现了一篇某小学教师讨论转印上石的文章。转印上石大体分为两种：书稿法和渡稿法。</p><p>书稿法，即将印稿以手写的方式书写到印面上。最简单直接是方法是<strong>反写上石</strong>——直接拿用毛笔将印稿反写于印面之上。然而对于临摹古印来说，这样操作难度非常大，不仅其临摹的效果难以保证，还需要有一定的书法、美术功底。需要“视正书反”，一般爱好者大多数只能查反字字典、对着镜子反写，再不然就是照一张透亮的薄纸，描摹然后反过来描一遍，或者直接用相机拍下来，后期镜像处理一下印稿再比着描。现代还有另一种间接的书稿法，即<strong>复写纸上石</strong>——“将一层复写纸覆于石上，再覆印稿于其上，固定好以后，用硬笔将印稿复写于石上”。效果相较于手写好一些，但是复写的时候，印稿也会出现移位的现象。</p><p>反书上石虽然便捷，但需要深厚的书法基础做支撑。对篆刻初学者而言难度极大，且 不便修改，水印上石法则极大地降低了难度，一直以来 颇为篆刻家高度重视并被广泛传承使用”<sup class="footnote-ref"><a href="#fn1" id="fnref1:1">[1:1]</a></sup>。一但涉及到了人工操作，质量终究是不能得到保证的，我需要精准的500dpi以上的超级精准复刻！这就不得不提到渡稿法了。</p><p>所谓<strong>渡稿</strong>亦即大家常说的<strong>水印上石法</strong>“，是利用墨溶于水的特性，将事先写在纸上的印稿润湿过渡到印面之上。就我本人的实践而言，常规的操作是：</p><ol><li>在一张连史纸/拷贝纸上面用毛笔或签字笔对着印稿描摹</li><li>用水打湿此纸，贴到印面上</li><li>叠放几张吸水的纸巾或宣纸，然后用指甲盖或牙刷把、梳子、耳机盒、手机壳等等圆滑坚硬的物体再三按压表面</li><li>最后揭开纸张，印面就会残留一些笔墨的痕迹，这时如果再用浓墨勾画一下就很清楚了。</li></ol><p>这种转印的方法自二十世纪初便有记录，取材方便，无毒无害，但转印效果其实不是非常清楚，受到纸张水分、墨汁扩散效果等等的影响，对于一些精细的印稿，几乎毫无用武之地了。</p><p>水印上石的改良版便是用洗甲水、香蕉水、风油精代替水来上石（简称<strong>溶剂上石</strong>，也是本文的主要讨论内容），需要事先把印稿用常见的激光打印机打出来，将印稿贴到石上，滴几滴洗甲水，按压，过一段时间俟其挥发后，撕掉印纸，印稿便印了上去，因为这种方法可以完全避免墨痕的扩散，其效果极佳，简直如同打印到石头上的一样。效果虽然好，但因其气味刺鼻难闻，含有丙酮、乙酸乙酯等等💀有毒物质，对皮肤还有一定的腐蚀性，长期使用对身体不好，我也只是曾经练手的时候才用了几次。“其实，水印上石法也就是印刷技术中所讲的<strong>湿转印</strong>，<u>湿转印就是指在油墨和染料的转印过程中需要借助一定的介质来促进转印膜的脱离和转印</u>，根据转印过程中浸渍的介质不同湿转印分为水转印和溶剂转印两种转印方式<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>。 其中传统的水印上石即为水转印，而香蕉水、洗甲水、风油精等上石法即为<strong>溶剂转印</strong>”<br><img src="/images/20260106/%E4%B8%8A%E7%9F%B3-20260323220632789.webp" alt></p><hr><p>昨晚(2026/3/22)准备刻下印，又一次试验了一下洗甲水上石，发现同样的操作，上石的效果并不是很好，不知是洗甲水过期，还是印稿打印太久，碳粉老化。而后便想，能否有一安全无害的方法，不是用洗甲水，而是用其他的溶剂也能实现转印上石的效果？洗甲水上石的机理是什么？碳粉不是无机物吗？怎么可能跟洗甲水有反应？在查阅各方资料后，终于找到了答案。</p><h2 id="溶剂上石之机理"><a class="markdownIt-Anchor" href="#溶剂上石之机理"></a> 溶剂上石之机理</h2><div class="tip bolt"><p>太长不看版：打印机的碳粉，实际是大量的有机合成树脂，属于极性高分子，可以溶解于洗甲水中的丙酮等溶度与之接近的有机溶剂里。</p></div><h3 id="激光打印墨粉之组成"><a class="markdownIt-Anchor" href="#激光打印墨粉之组成"></a> 激光打印墨粉之组成</h3><p><img src="/images/20260106/%E9%AB%98%E5%88%86%E5%AD%90%E7%9A%84%E6%BA%B6%E8%A7%A3%E6%80%A7%E5%88%86%E6%9E%90-20260323161427601.webp" alt><br><img src="/images/20260106/%E9%AB%98%E5%88%86%E5%AD%90%E7%9A%84%E6%BA%B6%E8%A7%A3%E6%80%A7%E5%88%86%E6%9E%90-20260323160753514.webp" alt="A4纸上放大83.3倍看到的字体，可见边缘有细小的碳粉颗粒"></p><p>墨粉又叫碳粉、色粉、色调剂等，英文名称是toner，主要用于静电复印和激光打印等技术中的粉末状墨，它的主要成分是以树脂、碳黑、磁性氧化铁、电荷控制微粒、 硅粒（润滑剂）、增塑剂（热融塑料）等为原料，它是一种高技术复合的产物，简言之，<strong>墨粉就是一种被染了色的热熔性树脂</strong>。</p><p>单组分墨粉的组成如下：</p><ol><li>树脂（占比60%）：由化学性能稳定的合成树脂组成，如<strong>苯丙树脂，聚酯树脂，酚醛树脂</strong>等，墨粉可以简单理解为，将完成染色的树脂，通过加 压、加热的过程完成在纸张上的显影。因此，树脂的质量很大程度上直 接决定了墨粉的质量。一款优良的墨粉，首先其使用树脂不仅要具备较 好的粘合性能、热塑性、电性能其次要有较稳定的化学性能，并且能够 与其他助剂相容性好，最后要具有可行的生产成本。<sup class="footnote-ref"><a href="#fn3" id="fnref3">[3]</a></sup></li><li>染料：使树脂具有成像功能，通常使用<strong>碳黑</strong>进行上色，根据添 加比例的不同调整颜色的深浅，通常占比为10%</li><li>磁粉：通常只有单组分墨粉使用，为避免显影过程中带电量低， 通过添加磁粉形成磁穗增加动力，便于用磁辊传输，磁粉多为磁体矿或者化学生产的<strong>磁性粉末</strong>。</li><li>电荷调节剂：显影过程需要树脂具有一定的电性能，但树脂本身并没有带电性能，通过电荷调节剂，控制树脂的带电量、电荷分布曲 线、带电速度，起到墨粉带电性能的作用，一般只占主体成分5%，通常使用季铵盐、金属偶氮络合物、水杨酸衍生<strong>金属络合物</strong>等</li><li>辅助添加剂：与电荷调节剂共同改变墨粉的带电量，同时起到 防沾辊，改善流动性的作用，通常为<strong>二氧化硅</strong>、<strong>氧化铝</strong>、<strong>氧化钛</strong>等。</li><li>脱模剂：通常使用<strong>低分子蜡</strong>，用于防止墨粉在加热后附着在定 影辊上的状况。</li></ol><h3 id="树脂溶解之机理"><a class="markdownIt-Anchor" href="#树脂溶解之机理"></a> 树脂溶解之机理</h3><p>可见树脂是墨粉的主要组成部分，那墨粉怎么会被洗甲水溶解呢？理科的同学肯定已经猜到了，没错，这就是高中化学里讲的相似相溶原理，然而仅仅这个词还不足以精确地解读这个现象，相似相溶的机理用科学的方式究竟怎样解释呢？为此我找来了一本复旦大学出版的《高分子物理(第三版)》一书，<s>因为</s>虽然本专业开设过《物理化学》一门课，这些知识看起来还算有些<s>熟悉</s>陌生。</p><p>树脂属于一种极性高分子聚合物，由于聚合物结构的复杂性——分子量大而且具有多分散性，分子的形状有线型、支化和交联的不同，高分子的聚集态又有非晶态与晶态之分，因此聚合物的溶解现象比小分子物质的溶解要复杂得多。</p><p>首先，高分子与溶剂分子的尺寸相差悬殊，两者的分子运动速度也差别很大，溶剂分子能比较快地渗透进入聚合物，而高分子向溶剂的扩散却非常慢。这样，聚合物的溶解过程要经过两个阶段，先是溶剂分子渗入聚合物内部，使聚合物体积膨胀，称为溶胀；然后才是高分子均匀分散在溶剂中，形成完全溶解的分子分散的均相体系。对于交联的聚合物，在与溶剂接触时也会发生溶胀，但因有交联的化学键束缚，不能再进一步使交联的分子拆散，只能停留在溶胀阶段，不会溶解。</p><p>非晶态聚合物的分子堆砌比较松散，分子间的相互作用较弱，因此溶剂分子比较容易渗入聚合物内部使之溶胀和溶解。晶态聚合物由于分子排列规整，堆砌紧密，分子间相互作用力很强，以致溶剂分子渗入聚合物内部非常困难，因此晶态聚合物的溶解比非晶态聚合物要困难得多。</p><p>溶解的过程是溶质分子与溶剂分子相互混合的过程，可以发生回合的必要条件是吉布斯自由能的变化<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>F</mi><mi>M</mi></msub><mo>&lt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\Delta F_M &lt; 0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>，（即混合热<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>H</mi><mi>M</mi></msub></mrow><annotation encoding="application/x-tex">\Delta H_M</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>减去温度乘以混合熵<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>S</mi><mi>M</mi></msub></mrow><annotation encoding="application/x-tex">\Delta S_M</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>（溶解趋于混乱，总是大于零）的总和小于0）：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>F</mi><mi>M</mi></msub><mo>=</mo><mi mathvariant="normal">Δ</mi><msub><mi>H</mi><mi>M</mi></msub><mo>−</mo><mi>T</mi><mi mathvariant="normal">Δ</mi><msub><mi>S</mi><mi>M</mi></msub><mo>&lt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\Delta F_M = \Delta H_M - T\Delta S_M &lt;0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span></span></p><p>对于极性聚合物，溶解时放热，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>H</mi><mi>M</mi></msub><mo>&lt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\Delta H_M &lt;0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>，体系自由能必定减低，可以自发进行。而对于非极性聚合物，溶解一般是吸热的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>H</mi><mi>M</mi></msub><mo>&gt;</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\Delta H_M &gt;0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>，那么就需要加热到一定温度会在减小混合热才能进行，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>H</mi><mi>M</mi></msub></mrow><annotation encoding="application/x-tex">\Delta H_M</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>越小，越有利于反应。非极性聚合物与溶剂互相混合时的混合热计算公式为：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>H</mi><mi>M</mi></msub><mo>=</mo><msub><mi>V</mi><mi>M</mi></msub><msub><mi>ϕ</mi><mn>1</mn></msub><msub><mi>ϕ</mi><mn>2</mn></msub><mo stretchy="false">[</mo><mo stretchy="false">(</mo><mi mathvariant="normal">Δ</mi><msub><mi>E</mi><mn>1</mn></msub><mi mathvariant="normal">/</mi><msub><mi>V</mi><mn>1</mn></msub><msup><mo stretchy="false">)</mo><mrow><mn>1</mn><mi mathvariant="normal">/</mi><mn>2</mn></mrow></msup><mo>−</mo><mo stretchy="false">(</mo><mi mathvariant="normal">Δ</mi><msub><mi>E</mi><mn>2</mn></msub><mi mathvariant="normal">/</mi><msub><mi>V</mi><mn>2</mn></msub><msup><mo stretchy="false">)</mo><mrow><mn>1</mn><mi mathvariant="normal">/</mi><mn>2</mn></mrow></msup><msup><mo stretchy="false">]</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\Delta H_M =V_M \phi_1\phi_2[(\Delta E_1/V_1)^{1/2}-(\Delta E_2/V_2)^{1/2}]^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.188em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">ϕ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">ϕ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">[(</span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">/</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1/2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.188em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0576em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord">/</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1/2</span></span></span></span></span></span></span></span></span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></p><p>令内聚能密度的平方根用<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>δ</mi></mrow><annotation encoding="application/x-tex">\delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span></span></span></span>(这便是溶度参数，单位为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathcolor="blue"><mi>c</mi><mi>a</mi><msup><mi>l</mi><mrow><mn>1</mn><mi mathvariant="normal">/</mi><mn>2</mn></mrow></msup><mo>⋅</mo><mi>c</mi><msup><mi>m</mi><mrow><mo>−</mo><mn>3</mn><mi mathvariant="normal">/</mi><mn>2</mn></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">\color{blue}cal^{1/2}\cdot cm^{-3/2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.888em;"></span><span class="mord mathnormal" style="color:blue;">c</span><span class="mord mathnormal" style="color:blue;">a</span><span class="mord" style="color:blue;"><span class="mord mathnormal" style="margin-right:0.01968em;color:blue;">l</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style="color:blue;"><span class="mord mtight" style="color:blue;"><span class="mord mtight" style="color:blue;">1/2</span></span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin" style="color:blue;">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.888em;"></span><span class="mord mathnormal" style="color:blue;">c</span><span class="mord" style="color:blue;"><span class="mord mathnormal" style="color:blue;">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style="color:blue;"><span class="mord mtight" style="color:blue;"><span class="mord mtight" style="color:blue;">−</span><span class="mord mtight" style="color:blue;">3/2</span></span></span></span></span></span></span></span></span></span></span></span>)表示，即<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>δ</mi><mo>=</mo><mo stretchy="false">(</mo><mi mathvariant="normal">Δ</mi><mi>E</mi><mi mathvariant="normal">/</mi><mi>V</mi><msup><mo stretchy="false">)</mo><mrow><mn>1</mn><mi mathvariant="normal">/</mi><mn>2</mn></mrow></msup></mrow><annotation encoding="application/x-tex">\delta =(\Delta E/V)^{1/2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.138em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">Δ</span><span class="mord mathnormal" style="margin-right:0.05764em;">E</span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.888em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1/2</span></span></span></span></span></span></span></span></span></span></span></span>，则上述溶解度（Hildebrand）公式为:</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>H</mi><mi>M</mi></msub><mo>=</mo><msub><mi>V</mi><mi>M</mi></msub><msub><mi>ϕ</mi><mn>1</mn></msub><msub><mi>ϕ</mi><mn>2</mn></msub><mo stretchy="false">(</mo><msub><mi>δ</mi><mn>1</mn></msub><mo>−</mo><msub><mi>δ</mi><mn>2</mn></msub><msup><mo stretchy="false">)</mo><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">\Delta H_M =V_M \phi_1\phi_2(\delta_1-\delta_2)^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.22222em;">V</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.2222em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">ϕ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal">ϕ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.1141em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></p><p>（此处需要区分极性聚合物与非极性聚合物）可见<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>H</mi><mi>M</mi></msub></mrow><annotation encoding="application/x-tex">\Delta H_M</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>的大小取决于两种介质溶度参数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>δ</mi></mrow><annotation encoding="application/x-tex">\delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span></span></span></span>的差异，差异越小，吉布斯自由能<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>F</mi><mi>M</mi></msub></mrow><annotation encoding="application/x-tex">\Delta F_M</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">F</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>越低，反映越容易进行。根据手册可以查到。</p><p>然而现实情况总是多种多样的，不同厂商的墨粉、洗甲水的溶度各异，查手册显然是行不通的，那除此之外，我们该如何测量溶度呢？一种简单的方法是粘度法：我们假定高分子的溶度参数与某种溶剂的溶度参数相等（此时<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><msub><mi>H</mi><mi>M</mi></msub><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">\Delta H_M=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord">Δ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:-0.0813em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">M</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0</span></span></span></span>），那么高分子在溶剂中完全溶解，会全部“舒展”开来，此时溶液的粘度最大，如果未完全溶解，则粘度偏小。粘度最大的混合溶液里的溶质便是高分子的溶度。【此处可以进行试验，用不同碳粉+洗甲水，找一个测粘度的仪器，待完善】。</p><p>除了试验外，我们也可以用一些材料属性上的方法来判断，有如下三种<sup class="footnote-ref"><a href="#fn4" id="fnref4">[4]</a></sup>：</p><ol><li>极性相近原则：溶质和溶剂的极性越接近，两者越容易互溶。如树脂和丙酮都是极性物质两者很容易互溶，而非极性的橡胶与极性的水显然不能互溶。</li><li>溶质浓度参数接近原则。有时候，我们会发现明明溶度很接近的两种物质，却并不能很好互溶，这是因为溶度其实是由三种由分子间作用力反应的子参数决定的，分别是色散力浓度参数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>δ</mi><mi>d</mi></msub></mrow><annotation encoding="application/x-tex">\delta_d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>、极性浓度参数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>δ</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">\delta_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9805em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span>和氢键浓度参数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>δ</mi><mi>h</mi></msub></mrow><annotation encoding="application/x-tex">\delta_h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，用公式表示如下：</li></ol><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>δ</mi><mi>t</mi></msub><mo>=</mo><mo stretchy="false">(</mo><msubsup><mi>δ</mi><mi>d</mi><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>δ</mi><mi>p</mi><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>δ</mi><mi>h</mi><mn>2</mn></msubsup><msup><mo stretchy="false">)</mo><mrow><mn>1</mn><mi mathvariant="normal">/</mi><mn>2</mn></mrow></msup></mrow><annotation encoding="application/x-tex">\delta_t=(\delta_d^2+\delta_p^2+\delta_h^2)^{1/2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1141em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.453em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.2472em;vertical-align:-0.3831em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.453em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3831em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.188em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.453em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">h</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.938em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1/2</span></span></span></span></span></span></span></span></span></span></span></span></span></p><p>对于极性高分子–溶剂的溶液体系，不仅要求两者的溶度参数接近，且要求两者的溶度子参数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>δ</mi><mi>d</mi></msub></mrow><annotation encoding="application/x-tex">\delta_d</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">d</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>δ</mi><mi>p</mi></msub></mrow><annotation encoding="application/x-tex">\delta_p</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9805em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>δ</mi><mi>h</mi></msub></mrow><annotation encoding="application/x-tex">\delta_h</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">h</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>也分别接近。<br>3. 溶剂化原则：极性高分子溶解在极性溶剂中的过程，本质上是🤯含亲电基团(如-CH2-CH-的第二个氢键带正电，有吸引电子的特点)或亲核基团的<u>极性溶剂分子</u>与含高分子的<u>含亲电基团或亲核基团</u>相互吸引产生溶剂化作用，使高分子溶解。</p><hr><p>我们不可能一下子就找到两个溶度完全一样的溶质与溶剂，对于溶度不太接近的溶剂，我们可以通过配比来得到一个混合溶度的溶剂，其混合公式如下（其中<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ϕ</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\phi_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal">ϕ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>δ</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\delta_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>为溶剂组元各自的体积分数与溶度）</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>δ</mi><mrow><mi>m</mi><mi>i</mi><mi>x</mi></mrow></msub><mo>=</mo><munderover><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><msub><mi>ϕ</mi><mi>i</mi></msub><msub><mi>δ</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\delta_{mix}=\sum_{i=1}^{n}\phi_i\delta_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8444em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">mi</span><span class="mord mathnormal mtight">x</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.9291em;vertical-align:-1.2777em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.6514em;"><span style="top:-1.8723em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.05em;"><span class="pstrut" style="height:3.05em;"></span><span><span class="mop op-symbol large-op">∑</span></span></span><span style="top:-4.3em;margin-left:0em;"><span class="pstrut" style="height:3.05em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2777em;"><span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal">ϕ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p><p>经过比对分析，估测墨粉的溶度在10左右，已经下单一瓶乳酸乙酯与乙醚，准备混合出一个合适的转印溶剂，具体试验结果等快递到了再做，过两天更新此文。</p><h2 id="附一常见高分子溶度表"><a class="markdownIt-Anchor" href="#附一常见高分子溶度表"></a> 附一：常见高分子溶度表</h2><p><img src="/images/20260106/%E4%B8%8A%E7%9F%B3-20260323224424658.webp" alt></p><p><img src="/images/20260106/%E4%B8%8A%E7%9F%B3-20260323224448265.webp" alt></p><h2 id="附二激光打印之过程"><a class="markdownIt-Anchor" href="#附二激光打印之过程"></a> 附二：激光打印之过程</h2><ol><li>充电过程：硒鼓表面通过充电装置的作用，使其充满静电，充电工作完成；<sup class="footnote-ref"><a href="#fn5" id="fnref5">[5]</a></sup></li><li>曝光过程：在螺旋转动部件的作用下，硒鼓就会转动，而且因为硒鼓的表面是充满静电的，所以当其转动到发射激光束的位置时，打印机的中央处理器就会接收由计算机传送过来的二进制数据信息，并且将其输出为打印数据。这时激光扫描系统就会调制出激光，而且是根据黑白位图的原理，通过控制激光二极管的打开与关闭，一个一直在高速旋转的多棱角会不断发射、聚焦、校正这些被调制过的激光束，从而使硒鼓表面形成带有字符图文信息的信号，至此，曝光工作完成，硒鼓表面的潜像就出现了；</li><li>显影过程：硒鼓是一直在旋转的，当其转动到显影部件的时候，显影棍是充满着与硒鼓表面相反电极的静电，由于在摩擦作用下，被吸附在显影辊上的碳粉也带有与硒鼓表面相反电极的静电，同时因为较大电势差的存在，硒鼓表面未形成字符图文信息信号的地方就仍会带着高静电，所以带有静电的碳粉就会根据“异性相吸”的原理从显影辊上被吸附到硒鼓的表面。至此，显影工作完成，图像已在硒鼓的表面显现出来；</li><li><strong>转印过程</strong>：硒鼓仍然在不停地旋转，当显影工作完成后，搓纸部件也开始工作，将纸张从纸盒里面带到转印辊下面，而<u>转印辊上是带有与硒鼓表面碳粉电极相 反的电流，因此纸张上也有与转印辊电极相同、与硒鼓表面碳粉电极相反的静电，所 以刚才还被吸附在硒鼓表面的碳粉，也是通过“异性相吸”的原理，被吸引、转移、 吸附在纸张上</u>，至此，转印工作完成；</li><li>分离过程：因为纸张张力的作用，以及分离部件的帮助下，纸张就会与硒 鼓分离，完成分离工作；</li><li>定影过程：转动部件会带动纸张不断运动，然后到达定影部件，定影部件 是一个可以产生高温高压的的装置，因此碳粉就可以在其作用之下，碳粉就会在纸张 上凝固，形成字符图文信息，至此，定影工作完成，纸张被传送到激光打印机外；</li><li>清洗过程：在转动部件的带动下，硒鼓一直旋转，并且到达清洗部件，清 洗部件会将硒鼓表面剩余的碳粉和静电全部清洗，清洗干净后，清洗工作完成。蓄贾 可以准备开始下一激光打印循环工作过程。激光打印机内部技术部件工作原理如图<br><img src="/images/20260106/%E9%AB%98%E5%88%86%E5%AD%90%E7%9A%84%E6%BA%B6%E8%A7%A3%E6%80%A7%E5%88%86%E6%9E%90-20260323155342500.webp" alt="激光打印机原理"></li></ol><a class="btn-beautify orange block right outline" href="https://js.design/f/RzqI5O?mode=design&p=nR2eB4NCBM" title="封面设计稿"><i class="fas fa-panorama"></i><span>封面设计稿</span></a><hr class="footnotes-sep"><section class="footnotes"><ol class="footnotes-list"><li id="fn1" class="footnote-item"><p>沈天者.印稿上石方法新探[J].中国书法,2018,(12):180-182.DOI:10.3969/j.issn.1003-1782.2018.12.037. <a href="#fnref1" class="footnote-backref">↩︎</a> <a href="#fnref1:1" class="footnote-backref">↩︎</a></p></li><li id="fn2" class="footnote-item"><p>王晶晶，《热转印纸转移层和油墨吸收层结构与印 刷性能的研究》，山东轻工业学院，二〇一一年硕士学位论文 <a href="#fnref2" class="footnote-backref">↩︎</a></p></li><li id="fn3" class="footnote-item"><p>石成龙.墨粉用功能树脂的制备与性能[D].武汉工程大学,2024. <a href="#fnref3" class="footnote-backref">↩︎</a></p></li><li id="fn4" class="footnote-item"><p>《高分子物理》<a href="https://mooc1.chaoxing.com/mooc-ans/course/portal/u0xIe2LgeoUVt13_ZuXtXg==">超星视频</a>，高华 <a href="#fnref4" class="footnote-backref">↩︎</a></p></li><li id="fn5" class="footnote-item"><p>吴慧婷.几种激光打印墨粉的主要成分分析及其在司法鉴定中的应用[D].广东工业大学,2018.DOI:10.7666/d.D01524375. <a href="#fnref5" class="footnote-backref">↩︎</a></p></li></ol></section>]]></content>
    
    
    <summary type="html">对于洗甲水、风油精等溶剂转印上石的原理分析，以及配置完美转印水的思路。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/Toner2Stone.svg" type="image"/>
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
    <category term="⚙️工程机械" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%9A%99%EF%B8%8F%E5%B7%A5%E7%A8%8B%E6%9C%BA%E6%A2%B0/"/>
    
    <category term="🧪化学" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%9A%99%EF%B8%8F%E5%B7%A5%E7%A8%8B%E6%9C%BA%E6%A2%B0/%F0%9F%A7%AA%E5%8C%96%E5%AD%A6/"/>
    
    
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    <category term="上石" scheme="https://blog.si-on.top/tags/%E4%B8%8A%E7%9F%B3/"/>
    
  </entry>
  
  <entry>
    <title>LP1：窒陬记</title>
    <link href="https://blog.si-on.top/2026/lp1_202601/"/>
    <id>https://blog.si-on.top/2026/lp1_202601/</id>
    <published>2026-03-21T16:48:11.000Z</published>
    <updated>2026-04-05T15:21:22.037Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script>        <div id="aplayer-DsXCRwOz" class="aplayer aplayer-tag-marker" style="margin-bottom: 20px;">            <pre class="aplayer-lrc-content"></pre>        </div>        <script>          var ap = new APlayer({            element: document.getElementById("aplayer-DsXCRwOz"),            narrow: false,            autoplay: false,            showlrc: false,            music: {              title: "LP1：窒陬记",              author: "秉蕳",              url: "/music/podcast/lp1.mp3",              pic: "/images/Cover/podcast/lp1.png",              lrc: ""            }          });          window.aplayers || (window.aplayers = []);          window.aplayers.push(ap);        </script><ol><li>(01:12) 本月两次旅游的经历</li><li>(23:35) 阅读记录转移，阅读推荐</li><li>(35:42) 杂谈，思考、计划（专科、软考、B证）</li><li>(53:00) 对未来自己的话<br><img src="/images/20260106/lp1-20260322004842500.webp" alt="人众看山"><br><img src="/images/20260106/lp1-20260322004755141.webp" alt="山口"></li></ol><p><img src="/images/20260106/lp1-20260322004816764.webp" alt="油菜花田"></p><h2 id="注本系列文章命名说明"><a class="markdownIt-Anchor" href="#注本系列文章命名说明"></a> 注：本系列文章命名说明</h2><p>本文为月度日志的总结，命名方式上取《尔雅·释天第八》中的月份别称来命名，丙午年即“柔兆敦牂”，文章标题取月名的天干别称+月份的别称，如庚寅正月则为窒陬记。</p><table><thead><tr><th style="text-align:center">天干</th><th style="text-align:center">甲</th><th style="text-align:center">乙</th><th style="text-align:center">丙</th><th style="text-align:center">丁</th><th style="text-align:center">戊</th><th style="text-align:center">己</th><th style="text-align:center">庚</th><th style="text-align:center">辛</th><th style="text-align:center">壬</th><th style="text-align:center">癸</th></tr></thead><tbody><tr><td style="text-align:center">太岁名</td><td style="text-align:center">阏逢</td><td style="text-align:center">旃蒙</td><td style="text-align:center">柔兆</td><td style="text-align:center">强圉</td><td style="text-align:center">着雍</td><td style="text-align:center">屠维</td><td style="text-align:center">上章</td><td style="text-align:center">重光</td><td style="text-align:center">玄黓</td><td style="text-align:center">昭阳</td></tr></tbody></table><table><thead><tr><th style="text-align:center">地支</th><th style="text-align:center">寅</th><th style="text-align:center">卯</th><th style="text-align:center">辰</th><th style="text-align:center">巳</th><th style="text-align:center">午</th><th style="text-align:center">未</th><th style="text-align:center">申</th><th style="text-align:center">酉</th><th style="text-align:center">戌</th><th style="text-align:center">亥</th><th style="text-align:center">子</th><th style="text-align:center">丑</th></tr></thead><tbody><tr><td style="text-align:center">太岁名</td><td style="text-align:center">摄提格</td><td style="text-align:center">单阏</td><td style="text-align:center">执徐</td><td style="text-align:center">大荒落</td><td style="text-align:center">敦牂</td><td style="text-align:center">协洽</td><td style="text-align:center">涒滩</td><td style="text-align:center">作噩</td><td style="text-align:center">阉茂</td><td style="text-align:center">大渊献</td><td style="text-align:center">困敦</td><td style="text-align:center">赤奋若</td></tr></tbody></table><table><thead><tr><th style="text-align:center">天干</th><th style="text-align:center">甲</th><th style="text-align:center">乙</th><th style="text-align:center">丙</th><th style="text-align:center">丁</th><th style="text-align:center">戊</th><th style="text-align:center">己</th><th style="text-align:center">庚</th><th style="text-align:center">辛</th><th style="text-align:center">壬</th><th style="text-align:center">癸</th></tr></thead><tbody><tr><td style="text-align:center">月阳</td><td style="text-align:center">毕</td><td style="text-align:center">橘</td><td style="text-align:center">修</td><td style="text-align:center">圉</td><td style="text-align:center">厉</td><td style="text-align:center">则</td><td style="text-align:center">窒</td><td style="text-align:center">塞</td><td style="text-align:center">终</td><td style="text-align:center">极</td></tr></tbody></table><table><thead><tr><th style="text-align:center">月份</th><th style="text-align:center">正月</th><th style="text-align:center">二月</th><th style="text-align:center">三月</th><th style="text-align:center">四月</th><th style="text-align:center">五月</th><th style="text-align:center">六月</th><th style="text-align:center">七月</th><th style="text-align:center">八月</th><th style="text-align:center">九月</th><th style="text-align:center">十月</th><th style="text-align:center">十一月</th><th style="text-align:center">十二月</th></tr></thead><tbody><tr><td style="text-align:center">月名</td><td style="text-align:center">陬</td><td style="text-align:center">如</td><td style="text-align:center">寎</td><td style="text-align:center">余</td><td style="text-align:center">皋</td><td style="text-align:center">且</td><td style="text-align:center">相</td><td style="text-align:center">壮</td><td style="text-align:center">玄</td><td style="text-align:center">阳</td><td style="text-align:center">辜</td><td style="text-align:center">涂</td></tr></tbody></table><div class="tag link"><a class="link-card" title="👉订阅《虚言》" href="https://blog.si-on.top/audio.xml/"><div class="left"><img src="/images/avator/ava_Lee.svg"></div><div class="right"><p class="text">👉订阅《虚言》</p><p class="url">https://blog.si-on.top/audio.xml/</p></div></a></div><span class="p center small">Nothing Words</span><span class="p center logo large">虚言</span>  ]]></content>
    
    
    <summary type="html">丙午庚寅正月记：老君山、东钱湖旅游杂感、阅读记录工具、下阶段计划、对自己的话</summary>
    
    
    <content src="https://blog.si-on.top/images/Cover/podcast/lp1.png" type="image"/>
    
    
    <cover src="https://blog.si-on.top/images/Cover/podcast/lp1w.png" type="image"/>
    
    
    <category term="播客" scheme="https://blog.si-on.top/categories/%E6%92%AD%E5%AE%A2/"/>
    
    
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    <category term="生活" scheme="https://blog.si-on.top/tags/%E7%94%9F%E6%B4%BB/"/>
    
  </entry>
  
  <entry>
    <title>皆得其宜？</title>
    <link href="https://blog.si-on.top/2026/ThisIsFine/"/>
    <id>https://blog.si-on.top/2026/ThisIsFine/</id>
    <published>2026-03-17T14:29:47.000Z</published>
    <updated>2026-03-17T14:29:47.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><blockquote><center>万物皆得其宜，六畜皆得其长，群生皆得其命。</center><p align="right">——《荀子·王制》</p></blockquote><p><img src="/images/20260106/893609d71506d2777e62bdaadcb6f181-800-403.webp" alt="This is fine (by K.C. Green)"></p><h2 id="阅读始末"><a class="markdownIt-Anchor" href="#阅读始末"></a> 阅读始末</h2><p>上个月月底，摸鱼读了篇Zotero里订阅的期刊，那文章<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>把这本『签名收藏家』解读到了吓人的高度，提到了鲍德里亚、哈贝马斯、禅宗、反对现代文化等等，这些都是我从23年至今所喜欢的主题，一文浏览罢便不由得心里痒痒，想要读一读原著。媒介上，首选还是电子版，但因为书比较老，2008年出版的，主流的资源网站里能找到的都是些影印的pdf，下了一本，真是看瞎我老眼。遂网购了一本二手的。</p><p>从3.1号开始读，到3.15号上午读完，磕磕绊绊，花费了半个月之久。速度相较于23年耒耨期的疯狂阅读差远了，但不是说过了三年，我退化迟钝了，而是这书…哇呀呀呀，一言难尽呐～(京剧唱白拖长腔调)，这是一本如果是看电子版不到半个小时就会删掉但因为买了纸质书不得不读终于读出来一点意思的书。</p><p>因为曾经有过多次写阅读笔记翻车的痛苦经历，从本书开始，阅读相关的内容将以书本与个人的感应、旧有思想体系构筑为主而不是文本分析、内容汇总等惯有的形式，因为后者完全可以从读前言后记、做些阅读分析的功课，甚至AI总结得到，但前者确实独属于我自己的——自身的经历与书中某些文字发生了共振，诱发了进一步的思考，这才是让我跟书的“感情基础”，如果淡化这种感情，那样的读书笔记纵然写得怎样精致，也终是淡如白水。(然后我为了这篇笔记准备了四天，也就是19天读完)。</p><p>简单介绍下，『签名收藏家』(The autograph man) 是英国作家扎迪·史密斯的第二本小说。主角华裔犹太人亚历克斯·李·坦德姆幼时丧父，在朋友的影响下成为了一名专门收集倒卖名人签名的签名收藏家。故事主要围绕他追求圈内最稀有的明星凯蒂·亚历山大签名，在苦苦写信十三年后得到签名后，从伦敦坐飞机出发纽约寻找凯蒂，解救凯蒂，反思自身职业意义、与朋友关系的故事。穿插了很多犹太教的东西、意识流式的片段也比较多，内容形式上有创新，有很多文本之外的图形、冷幽默等等。说实话，如果让我推荐的话，那么这本书最好还是不要读，琐碎的东西太多，核心的思想可能聊聊几句话而已。</p><h2 id="现代宜居"><a class="markdownIt-Anchor" href="#现代宜居"></a> 现代宜居</h2><p>“但是大家不是已经拥有一切了吗？他们还缺什么呢？地球上的每样东西都是为每个人定做的。每个人都能收到所有的电视节目，看到几乎所有的电影，听到百分之八十的音乐。… 而那些没有人想要的东西在哪里呢？亚历克斯时不时地能看到或者听到些不是给任何人准备的东西，但是没过多久这些东西就会又变成像是为谁准备的，花点广告费，就会撒向全世界，变得和每个人相关了。剩下了谁在制作和任何人都无关的东西呢？只有亚历克斯。只有他。《犹太性和异族性》就不是给任何一个人写的。你可以管这本书本叫一场新的艺术运动的开端，可悲的是当一场新的艺术运动扑面而来时，却没有人能意识到。没有人在为《犹太性和异族性》而等待。没有人想要它。它还没有写完。一旦它写完了，他就会知道的。”</p><p>书中对主角自己杜撰的小书着墨甚多，这孤独的小书，或许是代表了一种对世界的主流意识形态的反抗。这种心态，与我折腾些没有意义的东西时的心态有相似之处。篆刻，在汉朝都进入顶峰，风格流派研究成形了，现在却想在学习的过程中整出来个自己的风格来，可真是不自量力地可笑。至于表达呢？一旦涉及某些意义的东西，稍微个人化一点，就都没人看的，说到底，就是没人在乎你到底想要构建什么玩意儿，内心的真实感觉什么。有时候即便出于儒家入世的执念，不愿孤芳自赏，而把它堂而皇之地晾晒出来，然后呢，不也是晾晒出来的孤芳罢了，气息甚至不会扩散毫厘。</p><p>现代人的爱好，是被精确调制的。</p><p>大家都在追求大家想追求的东西，什么美食了、咖啡了、大众的小众音乐、旅游、养娃恋爱结婚升学就业生老病死人生经历了、新潮的技术了，等等等等，你如果不涉及这种东西，就是要冷落的，小众的小众，没人喜闻乐见。</p><p>书中描写主角在坐飞机时看到附赠的小包裹时的反应(P232)，令我心中一动——现代人的生活不就是这样吗？一切都是预设的，界面上圆润的图标、无衬线字体、单调的颜色、简单到愚蠢的按钮，一切一切，表面堂而皇之地冠以以人为本的名义，却不一点都考虑人，塑造着预设的欲望，一刻也不停的异化着人，同化着人！</p><p>后面这段飞机上场景的审视，尤其令人深思，简直就是把我许久以来想说但找不到合适方式表达的东西给说出来了！扎迪·史密斯(本书作者)，你他娘的写得可真好！</p><p>“这架飞机上的一切都是一个界面，就像是他电脑里的Windows系统，这架飞机上的一切都与飞行无关，就像是他的电脑与信息处理无关一样。有的只是异常漂亮的画面。有的只是我们彼此讲述着的、动人的、分散注意力的故事。要是亚历克斯的身子再向走道里靠一些的话，就会看到惊人的一幕：他要享有的私人经历在视线所及的任何地方都被复制了。相同的饭菜、相同的碎片（失踪的袜子、坏了的圆珠笔、弄皱的毯子、就要裂开的塑料水杯）、相同的躺下的姿势、相同的电视屏幕、上面相同的父亲和儿子在玩接球游戏、相同的对于个人空间的警觉。在这个情景中，离开界面、越过白线都是不可想象的。这是英雄的行为——或者是疯子的行为。”</p><p><img src="/images/20260106/IMG_20240820_130111.jpg" alt="2024.8.20 C城一新装修好的居民楼"><br>决定离开这个界面，做出上述“英雄的行为”，几乎是举步维艰的。大多数时候，人们都是潜移默化的被界面带走了节奏。</p><p>听歌是个爱好吗？<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>我不知道，但大家都说要喜欢听歌，不听便落后了，要挨打啊，要成了异己啊，所以我也听歌。</p><p>听歌是个爱好吗？我不确定，但大家都在晒宝藏歌单，捧小众歌手，听小众歌单，我若不喜欢点什么，便土气了，便要为人所不屑啊，所以我也爱好听歌。</p><p>听歌是个爱好吗？我略有犹豫，但大家都说“生活不可一日不放歌！”、“耳机就是我的命根子！”、“不听歌，毋宁死！”，我若一日不听歌，便成了活死人了，要被边缘化啊，所以我也喜欢听歌。</p><p>或许，身处这种被塑造的环境里，才是现代人真实的触手可及的桃花源，至于人本身的意义，唔，除了康德，还有谁去真正关心呢？</p><h2 id="其他收获与书摘"><a class="markdownIt-Anchor" href="#其他收获与书摘"></a> 其他收获与书摘</h2><p>一书读罢，书中最值得学习的莫过于一些细节描写的手法了，可见作者对生活的观察程度之细腻。这里将一些精辟的小句子摘录出来，以供日后写作借鉴。</p><p>“这阵嘟嘟声让亚历克斯有了种怯场的感觉。他大概是唯一一个会因此而感到怯场的人。他对作秀嗤之以鼻。一个人如果可以成功地对着机器留言，那么他肯定有演员的素质。”</p><p>从微小的动作细节中放大心理，进而表现出人的态度。这段描写咱家尤其喜欢，因为去年年中第一次录播客时也有类似的感觉，点下录音按钮后总觉得不是很自在，说话都不怎么利索，心里想的绝妙的念头，形成文字/语音后，总觉得那么干瘪无力，一想到别人会听到，便更加语无伦次了，最后索性由着性子随便说，后面剪辑的时候再把好的部分挑出来(这大概就是“作秀”吧💀)。</p><p>下面这段是描写路人看到主角喝中药汤剂后的反应，从动作映射到心理，写的也是相当很细腻。</p><p>“亚历克斯叹口气，打开瓶子猛喝了一大口，药味刺得眼睛直流泪。左首的一个女人并没有让他把瓶盖盖上，而是像个异族人那样，比手划脚了一番——看了看手表，做出一副坐过了站的样子，微微喘了口气，踮着脚站起来——然后在下一站停靠时从座位上走出来，离开了这节车厢。半分钟后，亚历克斯在紧邻的车厢里又看到了她，她被挤在一个很胖的男人和一个修女中间。对于这种不露痕迹的善举，亚历克斯异常地感动。”</p><hr><p>此外还有一些精辟的句子，读起来都是很有感觉的，如下：</p><p>在你自己的城市里，夜间乘车出行就意味着在一个沉闷的盒子里思索。在其他城市，它就只是出行。灯光不够亮，你无法欣赏街景。什么都看不见，除非你站在某物的脚下或者紧挨着它——没有风景，只有轮廓在你眼前显形。街灯是不间断的一长条。城里来往的出租车像是一条血液供给线，把醉醺醺的人运到酒吧里去。</p><p>秃鹫过去尝尝围绕着村庄的周围盘旋，现在是电话交换机和卫星在干这样的事情。电话里若是有人死了，会发生什么呢？</p><p>1969年以后的电影我都看不下去。它们让我恶心，我喜欢老的。…大概是因为他们就演出他们自己，他们演出了自己的本质。</p><p>真正的美是神性在尘世间的体现。一块刚刚休整过的草地。一道峡谷。人行道上的一条裂缝。</p><p>音乐有太多触角，无边无际，无法掌控。</p><p>运气是对世界的一种羞辱。</p><p>当他收拾行装离开伦敦的时候，他不仅像每个人那样带上了衣服和必需品，而且还把胳膊放在桌上伸直，然后把桌上的所有东西都扫进了一个手提的厚纸袋里，现在他把袋子里的所有东西都倒在酒店床上，想要把这些东西放到房间的各个角落。这就是挪人不挪窝的旅行。</p><p>想一想一位艺术品修补者把一张人像上的涂料剥下来，想要找到下面的人像。你因为某种不恰当的好奇心——可能会找到别的人像——毁了一张很好的图画。这是一种永无休止的替代—都是因为你不知道该如何正确对待它们。</p><p><img src="/images/20260106/IMG_20260319_202932.jpg" alt="做的小笔记"></p><hr class="footnotes-sep"><section class="footnotes"><ol class="footnotes-list"><li id="fn1" class="footnote-item"><p>王爱菊,刘馨雅.《签名收藏家》中拟真世界的后世俗建构[J].当代外国文学,2026,47(01):47-53.DOI:10.16077/j.cnki.issn1001-1757.2026.01.009. <a href="#fnref1" class="footnote-backref">↩︎</a></p></li><li id="fn2" class="footnote-item"><p>此段节来自23年年末的残篇『党同伐异新解』 <a href="#fnref2" class="footnote-backref">↩︎</a></p></li></ol></section>]]></content>
    
    
    <summary type="html">『签名收藏家』读后感与由此触发的一些切身的杂感。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/20260106/IMG_20240820_130111.jpg" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="📖涵泳" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%F0%9F%93%96%E6%B6%B5%E6%B3%B3/"/>
    
    
    <category term="批判性思考" scheme="https://blog.si-on.top/tags/%E6%89%B9%E5%88%A4%E6%80%A7%E6%80%9D%E8%80%83/"/>
    
    <category term="阅读" scheme="https://blog.si-on.top/tags/%E9%98%85%E8%AF%BB/"/>
    
    <category term="理性" scheme="https://blog.si-on.top/tags/%E7%90%86%E6%80%A7/"/>
    
  </entry>
  
  <entry>
    <title>金属清洗笔记</title>
    <link href="https://blog.si-on.top/2026/MetalCleaningEvaluation/"/>
    <id>https://blog.si-on.top/2026/MetalCleaningEvaluation/</id>
    <published>2026-03-02T03:51:34.000Z</published>
    <updated>2026-03-02T03:51:34.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><blockquote><p>本文参考自《金属清洗与防锈》王恒，P163（2.6 清洗效果评价方法）（pdf文件实际第175页）</p></blockquote><h2 id="清洗效果评定检测方法"><a class="markdownIt-Anchor" href="#清洗效果评定检测方法"></a> 清洗效果评定检测方法</h2><h3 id="定性评价方法"><a class="markdownIt-Anchor" href="#定性评价方法"></a> 定性评价方法</h3><p>（1）直接检测 直接检测包括：目视观察法、擦拭法、水膜湿润法、接触角法、硫酸铜法、荧光检测法、放射性示踪检测法、有机碳含量测定等。</p><ol><li>擦拭法：用干燥、清洁、不起毛的布或有一定强度的白纸，在工件表面擦拭，根据布或纸的脏污程度判断表面清洁度。</li><li><strong>水膜湿润法</strong>：将清洗后的工件浸泡在水中，然后将工件表面沾与水面垂直方向提出，10s后观察，若工件表面均匀沾满水膜，表明清洗干净；若工件表面出现水珠，则表明未清洗干净。对于大型工件水平面的清洗，则是将工件表面倾斜，与地平面呈30°角，使表面过剩的水流滴，静置30s后观察，若表面无水珠则表示基本清洗干净。</li><li>喷雾法：用喷雾器按150~300mm间距，把染色的微粒状水滴喷射到清洗后干燥的工件表面上，通过形成水滴的情况判断清洁度。清洗干净的表面，喷雾后30s，微粒状水滴会在表面上均匀地润湿铺展，覆盖面大，而且干燥后凝聚水膜周边呈规则的圆形0</li><li>荧光法：经清洗的工件表面，用紫外线发射器照射（此乃利用油污等物质在紫外线作用下能发光），然后用光电管观察表面的发光量，由此间接评定表面的清洗质量。</li><li>乙醇蒸发法：经清洗的工件表面，滴入一滴乙醇，观察蒸发后是否有白色残留物。</li><li>验油试纸法</li></ol><p>直接检测比较直观，多数只限于工件在加工过程中定性检测，以确保最后部件、产品的清洁度。所以都未具有相关标准。</p><h3 id="定量评价方法"><a class="markdownIt-Anchor" href="#定量评价方法"></a> 定量评价方法</h3><ol><li>重量法，清洗前后重量变化</li><li>接触角法：测量水滴与工件表面的夹角大小</li></ol><p>清洗脱脂液组成、指标、检测方法</p><h2 id="金属清洗剂检验分析方法"><a class="markdownIt-Anchor" href="#金属清洗剂检验分析方法"></a> 金属清洗剂检验分析方法</h2><h3 id="预试验的准备可省略"><a class="markdownIt-Anchor" href="#预试验的准备可省略"></a> 【预】试验的准备(可省略)</h3><p>(1) <strong>试片的打磨和清洗</strong><br>用铺平的 220 号砂纸，将试片打磨光亮，打磨方向要<strong>平行于试片长边</strong>，打磨好的试片先用脱脂纱布或脱脂棉擦净，吊挂在 S 形钩上，浸入无水乙醇中，再用镊子夹脱脂棉纱布或脱脂棉擦洗。然后把试片移至丙酮或 30~60℃石油醚中漂洗，用热风吹干，把干净试片用 S 形钩吊挂在试片架上备用。</p><p>(2) <strong>试液的制备</strong><br>用于腐蚀性、防锈性、耐水分及挥发物、高低温稳定性和漂洗性等实验的试液，用蒸馏水或去离子水（新煮沸冷却过的）按 3%（质量分数）浓度配制。</p><p>用于净洗力和消泡性试验的试液用 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>250</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow><annotation encoding="application/x-tex">250 \times 10^{-6}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">250</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">6</span></span></span></span></span></span></span></span></span></span></span></span> 硬水（含无水氯化钙 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.16</mn><mtext> </mtext><mtext>g/L</mtext></mrow><annotation encoding="application/x-tex">0.16\,\text{g/L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0.16</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">g/L</span></span></span></span></span>，硫酸镁 (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mtext>MgSO</mtext><mn>4</mn></msub><mo>⋅</mo><msub><mtext>H</mtext><mn>2</mn></msub><mtext>O</mtext></mrow><annotation encoding="application/x-tex">\text{MgSO}_4\cdot \text{H}_2\text{O}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9275em;vertical-align:-0.2441em;"></span><span class="mord"><span class="mord text"><span class="mord">MgSO</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.207em;"><span style="top:-2.4559em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2441em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord text"><span class="mord">H</span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord text"><span class="mord">O</span></span></span></span></span>) <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.247</mn><mtext> </mtext><mtext>g/L</mtext></mrow><annotation encoding="application/x-tex">0.247\,\text{g/L}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0.247</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">g/L</span></span></span></span></span>）按 3%（质量分数）配制。</p><h3 id="ph值测量方法"><a class="markdownIt-Anchor" href="#ph值测量方法"></a> PH值测量方法</h3><p>用PH试纸或PH计，或酸碱中和滴定法。</p><h3 id="净洗力试验方法"><a class="markdownIt-Anchor" href="#净洗力试验方法"></a> 净洗力试验方法</h3><p>(1) <strong>仪器和设备</strong><br>S 形挂钩、试片架、搅拌机（摆动频率 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>40</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>次/min</mtext></mrow><annotation encoding="application/x-tex">(40 \pm 2)\,\text{次/min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">40</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord cjk_fallback">次</span><span class="mord">/min</span></span></span></span></span>，摆动距离 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>50</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>mm</mtext></mrow><annotation encoding="application/x-tex">(50 \pm 2)\,\text{mm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">50</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span></span></span></span>）、恒温烘箱、水浴能控温 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>60</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(60 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">60</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span>。</p><p>(2) <strong>人工油污的配制</strong><br>人工油污的成分质量分数如下：</p><ul><li>石油磺酸钠 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">8\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">8%</span></span></span></span></li><li>羊毛脂皂 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3.5</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">3.5\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">3.5%</span></span></span></span></li><li>羊毛脂 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">2\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">2%</span></span></span></span></li><li>工业凡士林 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>30</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">30\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">30%</span></span></span></span></li><li>L-AN22 号机油 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>34.5</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">34.5\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">34.5%</span></span></span></span></li><li>L-AN46 号机油 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>12</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">12\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">12%</span></span></span></span></li><li>钠基润滑脂 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">2\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">2%</span></span></span></span></li><li>氧化铝 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">8\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">8%</span></span></span></span></li></ul><p>配制时，将工业凡士林、22 号机油、46 号机油混合物，加热到 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>120</mn><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">120\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">120</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 左右待溶解均匀，倒入羊毛脂皂、石油磺酸钠、钠基润滑脂和羊毛脂，搅拌均匀至室温，储存于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mo>∼</mo><mn>10</mn><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">5\sim10\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 冰箱或干燥器中备用。</p><p>(3) <strong>人工油污的涂覆</strong><br>试验用的不锈钢片，与试片架一起置于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>40</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(40 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">40</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 烘箱中干燥 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>30</mn><mtext> </mtext><mtext>min</mtext></mrow><annotation encoding="application/x-tex">30\,\text{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">min</span></span></span></span></span> 后，移入干燥器中，冷却后称重，直至 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>±</mo><mn>0.2</mn><mtext> </mtext><mtext>mg</mtext></mrow><annotation encoding="application/x-tex">\pm 0.2\,\text{mg}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">±</span><span class="mord">0.2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mg</span></span></span></span></span>。将称量后的试片平放在干净的滤纸上，用小刮刀取人工油污，均匀地涂覆在试片一面上的规定部位，并将试片两侧和底边多余的油污用滤纸擦去，称重。油污涂覆量应控制在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.08</mn><mo>∼</mo><mn>0.19</mn><mtext> </mtext><mtext>g</mtext></mrow><annotation encoding="application/x-tex">0.08\sim0.19\,\text{g}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.08</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0.19</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">g</span></span></span></span></span> 之间。</p><p>(4) <strong>摇洗</strong><br>在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>500</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">500\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span> 烧杯或搪瓷药物缸中，倒入 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>400</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">400\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span> 清洗液，然后将烧杯放置在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>60</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(60 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">60</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 水浴锅上。将待涂油的试片夹持在搅拌机的搅拌架上，使试片表面垂直于摆动方向。在清洗液中浸泡 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mtext>min</mtext></mrow><annotation encoding="application/x-tex">3\,\text{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">min</span></span></span></span></span>，立即开动搅拌机搅拌 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mtext> </mtext><mtext>min</mtext></mrow><annotation encoding="application/x-tex">3\,\text{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">min</span></span></span></span></span>。搅拌结束后，连同挂钩取出试片，在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>60</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(60 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">60</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span>、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>400</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">400\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span> 蒸馏水中搅拌 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>30</mn><mtext> </mtext><mtext>s</mtext></mrow><annotation encoding="application/x-tex">30\,\text{s}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">s</span></span></span></span></span>，挂于试架上，放入 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>40</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(40 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">40</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 的恒温烘箱中干燥 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mtext>h</mtext></mrow><annotation encoding="application/x-tex">2\,\text{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">h</span></span></span></span></span>，冷却至室温称重。</p><p>(5) <strong>净洗力 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span></span></span></span> (%) 计算</strong></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>X</mi><mo>=</mo><mfrac><mrow><msub><mi>m</mi><mn>1</mn></msub><mo>−</mo><msub><mi>m</mi><mn>2</mn></msub></mrow><mrow><msub><mi>m</mi><mn>1</mn></msub><mo>−</mo><msub><mi>m</mi><mn>0</mn></msub></mrow></mfrac><mo>×</mo><mn>100</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">X = \frac{m_1 - m_2}{m_1 - m_0} \times 100\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0963em;vertical-align:-0.836em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.2603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.836em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">100%</span></span></span></span></span></p><p>式中<br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">X</span></span></span></span> —— 净洗力%；<br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">m_0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> —— 试片质量g；<br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">m_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> —— 涂覆油污试片清洗前的质量g；<br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>m</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">m_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> —— 涂覆油污试片清洗后的质量g。</p><p>(6) <strong>结果评定</strong><br>三片试片平行试验所得的净洗力值中，应至少有两片的数值相差不超过 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">3\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">3%</span></span></span></span>，否则应重新试验，取平均值作为测定结果。</p><h3 id="防锈性试验方法"><a class="markdownIt-Anchor" href="#防锈性试验方法"></a> 防锈性试验方法</h3><p>(1) <strong>仪器</strong><br>包括恒温水浴锅、恒温干燥箱、湿热器、不锈钢挂钩。</p><p>湿热器：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ϕ</mi><mn>300</mn><mtext> </mtext><mtext>mm</mtext></mrow><annotation encoding="application/x-tex">\phi 300\,\text{mm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">ϕ</span><span class="mord">300</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span></span></span></span> 玻璃干燥器，底部盛放密度为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1.083</mn><mo>∼</mo><mn>1.084</mn><mtext> </mtext><msup><mtext>g/cm</mtext><mn>3</mn></msup></mrow><annotation encoding="application/x-tex">1.083\sim1.084\,\text{g/cm}^3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1.083</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.204em;vertical-align:-0.25em;"></span><span class="mord">1.084</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord text"><span class="mord">g/cm</span></span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.954em;"><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">3</span></span></span></span></span></span></span></span></span></span></span>（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>25</mn><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">25\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span>）甘油-水溶液，滑板上放置一个挂试片的架子。</p><p>(2) <strong>金属试片的材质和规格</strong></p><ul><li>45 号钢 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mn>25</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mo stretchy="false">(</mo><mn>3</mn><mo>∼</mo><mn>5</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>mm</mtext></mrow><annotation encoding="application/x-tex">50\,\text{mm} \times 25\,\text{mm} \times (3\sim5)\,\text{mm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">3</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span></span></span></span></li><li>Z30 一级铸件 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mn>25</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mo stretchy="false">(</mo><mn>3</mn><mo>∼</mo><mn>5</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>mm</mtext></mrow><annotation encoding="application/x-tex">50\,\text{mm} \times 25\,\text{mm} \times (3\sim5)\,\text{mm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">3</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span></span></span></span></li><li>H62 黄铜 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mn>25</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mo stretchy="false">(</mo><mn>3</mn><mo>∼</mo><mn>5</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>mm</mtext></mrow><annotation encoding="application/x-tex">50\,\text{mm} \times 25\,\text{mm} \times (3\sim5)\,\text{mm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">3</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span></span></span></span></li><li>LY12 硬铝 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mn>25</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mo stretchy="false">(</mo><mn>3</mn><mo>∼</mo><mn>5</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>mm</mtext></mrow><annotation encoding="application/x-tex">50\,\text{mm} \times 25\,\text{mm} \times (3\sim5)\,\text{mm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">3</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span></span></span></span></li></ul><p>(3) <strong>试验步骤</strong><br>将盛有 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>400</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">400\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">400</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span> 清洗液的烧杯放入恒温水浴锅中，加热至 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>80</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(80 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">80</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span>，把试液放入到清洗液中 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>30</mn><mtext> </mtext><mtext>s</mtext></mrow><annotation encoding="application/x-tex">30\,\text{s}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">s</span></span></span></span></span>，提出，用滤纸吸净试片上下端及孔眼的液体，垂直悬挂在试片上。将挂有试片的架子放在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>40</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(40 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">40</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 烘箱中，干燥 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>15</mn><mtext> </mtext><mtext>min</mtext></mrow><annotation encoding="application/x-tex">15\,\text{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">min</span></span></span></span></span>。干燥后，将试片移入已预先在烘箱中恒温至 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>35</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(35 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">35</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span>，相对湿度为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>90</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">90\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">90%</span></span></span></span> 的湿热器中。放置 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>24</mn><mtext> </mtext><mtext>h</mtext></mrow><annotation encoding="application/x-tex">24\,\text{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">24</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">h</span></span></span></span></span>，烘箱温度始终保持 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>35</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(35 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">35</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span>。试验结束后，对 45 号钢片、Z30 铸件片取出检查外观。对 H62 黄铜片、LY12 铝片先用蒸馏水漂洗，吹干后，再检查外观。</p><p>(4) <strong>结果评定</strong><br>参见腐蚀试验中的外观评级标准表。</p><h3 id="腐蚀性试验方法"><a class="markdownIt-Anchor" href="#腐蚀性试验方法"></a> 腐蚀性试验方法</h3><p>(1) <strong>仪器及材料</strong><br>分析天平、恒温干燥箱、金属试片（规格：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mn>25</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mo stretchy="false">(</mo><mn>3</mn><mo>∼</mo><mn>5</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>mm</mtext></mrow><annotation encoding="application/x-tex">50\,\text{mm} \times 25\,\text{mm} \times (3\sim5)\,\text{mm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">3</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span></span></span></span>）、广口瓶（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>500</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">500\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span>）。</p><p>(2) <strong>试验步骤</strong><br>将打磨、清洗后 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn></mrow><annotation encoding="application/x-tex">3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">3</span></span></span></span> 块同材质的试片，分别在分析天平上称重（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">P_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 准确到 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.1</mn><mtext> </mtext><mtext>mg</mtext></mrow><annotation encoding="application/x-tex">0.1\,\text{mg}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">0.1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mg</span></span></span></span></span>），然后挂于广口瓶中，试片不得互相接触。把 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">3\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">3%</span></span></span></span> 的清洗液预热至 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>70</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(70 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">70</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span>，常温清洗剂加热到 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>40</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(40 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">40</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span>，倒入广口瓶中，并使清洗液高于试片顶端约 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn><mtext> </mtext><mtext>mm</mtext></mrow><annotation encoding="application/x-tex">10\,\text{mm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">10</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span></span></span></span>，然后加盖，置于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>70</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(70 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">70</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 下（常温清洗剂为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>40</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(40 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">40</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span>）的恒温烘箱中。</p><p>试验时间：在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>70</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(70 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">70</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 时，有色金属为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mtext>h</mtext></mrow><annotation encoding="application/x-tex">2\,\text{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">h</span></span></span></span></span>，黑色金属为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mtext> </mtext><mtext>h</mtext></mrow><annotation encoding="application/x-tex">4\,\text{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">h</span></span></span></span></span>；在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>40</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(40 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">40</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 时，有色金属为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mtext> </mtext><mtext>h</mtext></mrow><annotation encoding="application/x-tex">4\,\text{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">h</span></span></span></span></span>，黑色金属为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>8</mn><mtext> </mtext><mtext>h</mtext></mrow><annotation encoding="application/x-tex">8\,\text{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">8</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">h</span></span></span></span></span>。趁热取出试片，经蒸馏水漂洗后，再用无水乙醇清洗 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span></span></span></span> 次，立即吹风晾干，与新打磨的试片对比检查外观。再次称重（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">P_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>）。</p><p>(3) <strong>试验结果评定</strong></p><p>① 计算失重量</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>G</mi><mo>=</mo><msub><mi>P</mi><mn>1</mn></msub><mo>−</mo><msub><mi>P</mi><mn>2</mn></msub><mspace width="1em"><mo stretchy="false">(</mo><mtext>mg</mtext><mo stretchy="false">)</mo></mspace></mrow><annotation encoding="application/x-tex">G = P_1 - P_2 \quad (\text{mg})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:1em;"></span><span class="mopen">(</span><span class="mord text"><span class="mord">mg</span></span><span class="mclose">)</span></span></span></span></span></p><p>② 腐蚀外观按评级标准评定（见下表）。</p><table><thead><tr><th style="text-align:center">级别</th><th style="text-align:center">试片外观</th><th style="text-align:center">失重量 /mg</th></tr></thead><tbody><tr><td style="text-align:center">0 级</td><td style="text-align:center">表面无腐蚀点，无明显变色</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&lt;</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">&lt;2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span></span></span></span></td></tr><tr><td style="text-align:center">1 级</td><td style="text-align:center">表面无腐蚀点，轻微变色或失光</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&lt;</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">&lt;2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&lt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span></span></span></span></td></tr><tr><td style="text-align:center">2 级</td><td style="text-align:center">表面明显变色或失光</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&gt;</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">&gt;2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span></span></span></span></td></tr><tr><td style="text-align:center">3 级</td><td style="text-align:center">表面有明显腐蚀点</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>&gt;</mo><mn>2</mn></mrow><annotation encoding="application/x-tex">&gt;2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">&gt;</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2</span></span></span></span></td></tr></tbody></table><p>(4) <strong>去除腐蚀产物的方法</strong></p><p>① 45 号钢、Z30 一级铸铁和 H62 黄铜，在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>25</mn><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">25\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 下，全浸在加有 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.5</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">0.5\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">0.5%</span></span></span></span> 硫脲的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>25</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">25\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">25%</span></span></span></span> 硫酸溶液中 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mtext>min</mtext></mrow><annotation encoding="application/x-tex">2\,\text{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">min</span></span></span></span></span> 取出，用新煮过的冷蒸馏水冲洗，再在蒸馏水中用毛刷洗。再经冲洗，用丙酮或无水乙醇脱水，热风吹干，冷却后，称重（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>P</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">P_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>）。</p><p>③ 由于在除锈液中处理时会对金属基体造成腐蚀，所以要按同样试验方法，用清洁试片做空白试验，得到金属基体的腐蚀失质量 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>P</mi></mrow><annotation encoding="application/x-tex">\Delta P</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Δ</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span></span></span></span>。</p><p>④ 计算腐蚀失质量</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>G</mi><mo>=</mo><msub><mi>P</mi><mn>1</mn></msub><mo>−</mo><mo stretchy="false">(</mo><msub><mi>P</mi><mn>2</mn></msub><mo>+</mo><mi mathvariant="normal">Δ</mi><mi>P</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">G = P_1 - (P_2 + \Delta P)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">Δ</span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mclose">)</span></span></span></span></span></p><p>式中<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi></mrow><annotation encoding="application/x-tex">G</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span></span></span></span>——腐蚀失质量，mg。</p><h3 id="消泡性能试验方法"><a class="markdownIt-Anchor" href="#消泡性能试验方法"></a> 消泡性能试验方法</h3><p>(1) <strong>试验步骤</strong><br>在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>100</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">100\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span> 的具塞量筒中，装入 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">50\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span> <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">3\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">3%</span></span></span></span> 的清洗液，上下激烈摇晃 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mtext>min</mtext></mrow><annotation encoding="application/x-tex">1\,\text{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">min</span></span></span></span></span>，其上下摇晃的距离为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>0.33</mn><mtext> </mtext><mtext>m</mtext></mrow><annotation encoding="application/x-tex">0.33\,\text{m}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.33</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">m</span></span></span></span></span>，其摇晃速度大致为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>100</mn><mo>∼</mo><mn>120</mn><mtext> </mtext><mtext>次/min</mtext></mrow><annotation encoding="application/x-tex">100\sim120\,\text{次/min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">100</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">120</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord cjk_fallback">次</span><span class="mord">/min</span></span></span></span></span>。</p><p>摇晃完毕后，将清洗液在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>15</mn><mo>∼</mo><mn>35</mn><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">15\sim35\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">15</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">35</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 下静止 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mtext> </mtext><mtext>min</mtext></mrow><annotation encoding="application/x-tex">5\,\text{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">min</span></span></span></span></span>，观察泡沫消失情况。<br><img src="/images/20260106/%E9%87%91%E5%B1%9E%E6%B8%85%E6%B4%97-20260302164906437.webp" alt="新旧清洗剂对比（30℃左右）"><br>(2) <strong>判断结果</strong><br>若泡沫在液面上残留的泡沫体积，振荡法测定消泡性在室温下进行，当温度偏低时，由于清洗液的黏度加大，影响了消泡性能。可以预先将试液加热至 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>30</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(30 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">30</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span>，摇晃后静置 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mtext> </mtext><mtext>min</mtext></mrow><annotation encoding="application/x-tex">5\,\text{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">min</span></span></span></span></span> 观察时间，将量筒放入同样温度的水浴或恒温干燥箱中保温。</p><h3 id="水分及挥发物试验方法"><a class="markdownIt-Anchor" href="#水分及挥发物试验方法"></a> 水分及挥发物试验方法</h3><p>于已称重的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>9</mn><mtext> </mtext><mtext>cm</mtext></mrow><annotation encoding="application/x-tex">9\,\text{cm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">cm</span></span></span></span></span> 的培养皿下盖中，准确称量清洗剂样品约 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>2</mn><mtext> </mtext><mtext>g</mtext></mrow><annotation encoding="application/x-tex">2\,\text{g}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8389em;vertical-align:-0.1944em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">g</span></span></span></span></span>（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>G</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">G_0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">G</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>）。在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>150</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(150 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">150</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 烘箱内烘干 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>4</mn><mtext> </mtext><mtext>h</mtext></mrow><annotation encoding="application/x-tex">4\,\text{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">h</span></span></span></span></span>。取出加上盖放入玻璃干燥器内，冷却到室温（约 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>20</mn><mtext> </mtext><mtext>min</mtext></mrow><annotation encoding="application/x-tex">20\,\text{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">20</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">min</span></span></span></span></span>），去掉上盖后称重（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>G</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">G_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">G</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>），按式 (10-2) 计算水分及挥发物含量（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo separator="true">,</mo><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">x, \%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9444em;vertical-align:-0.1944em;"></span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">%</span></span></span></span>）。</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>x</mi><mo>=</mo><mfrac><mrow><msub><mi>G</mi><mn>1</mn></msub><mo>−</mo><msub><mi>G</mi><mn>2</mn></msub></mrow><msub><mi>G</mi><mn>0</mn></msub></mfrac><mo>×</mo><mn>100</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">x = \frac{G_1 - G_2}{G_0} \times 100\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.1963em;vertical-align:-0.836em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">G</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">G</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">G</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.836em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">100%</span></span></span></span></span></p><p>式中<br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>G</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">G_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">G</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>——试验前容器和样品总质量g；<br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>G</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">G_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">G</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>——试验后容器和样品总质量g；<br><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>G</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">G_0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">G</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>——取样质量g。</p><h3 id="高-低温稳定性试验方法"><a class="markdownIt-Anchor" href="#高-低温稳定性试验方法"></a> 高、低温稳定性试验方法</h3><p>(1) <strong>仪器及材料</strong><br>低温冰箱、恒温水浴、具塞量筒。</p><p>(2) <strong>试验步骤</strong></p><p>① <strong>高温试验</strong>：将 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">50\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span> 清洗剂原液或 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>50</mn><mo>±</mo><mn>5</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>g</mtext></mrow><annotation encoding="application/x-tex">(50 \pm 5)\,\text{g}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">50</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">g</span></span></span></span></span> 清洗剂容量入 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">50\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span> 具塞量筒中，加塞后放入 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>60</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(60 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">60</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 的水浴中。水面应没过量筒 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>30</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">30\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">30</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span> 刻度处以上。<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>6</mn><mtext> </mtext><mtext>h</mtext></mrow><annotation encoding="application/x-tex">6\,\text{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">h</span></span></span></span></span> 后，取出量筒。冷却到室温，检查。</p><p>② <strong>低温试验</strong>：将经过高温试验无异常现象的试样（若有异常现象另取新样），放置在冰箱中，于 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mo>−</mo><mn>18</mn><mo>±</mo><mn>1</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(-18 \pm 1)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">−</span><span class="mord">18</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 保持 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mtext>h</mtext></mrow><annotation encoding="application/x-tex">1\,\text{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">h</span></span></span></span></span>。取出量筒，待试液回复至室温并保持 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mtext> </mtext><mtext>h</mtext></mrow><annotation encoding="application/x-tex">1\,\text{h}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">h</span></span></span></span></span> 后（若是液体试样尚需倾斜 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn></mrow><annotation encoding="application/x-tex">5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">5</span></span></span></span> 次），进行观察。</p><p>③ <strong>结果评价</strong>：检查经高、低温试验后的液体水基清洗剂是否均匀、透明，有无混浊或分层现象，有无沉淀或絮状物出现；膏状清洗剂有无分层或相分离现象。</p><h3 id="漂洗性能试验"><a class="markdownIt-Anchor" href="#漂洗性能试验"></a> 漂洗性能试验</h3><p>(1) <strong>仪器及材料</strong><br>电热吹风机、摆洗机、金属试片 45 号钢片，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mn>25</mn><mtext> </mtext><mtext>mm</mtext><mo>×</mo><mo stretchy="false">(</mo><mn>3</mn><mo>∼</mo><mn>5</mn><mo stretchy="false">)</mo><mtext> </mtext><mtext>mm</mtext></mrow><annotation encoding="application/x-tex">50\,\text{mm} \times 25\,\text{mm} \times (3\sim5)\,\text{mm}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">50</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">25</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">3</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mm</span></span></span></span></span>。</p><p>(2) <strong>试验步骤</strong><br>将 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>3</mn></mrow><annotation encoding="application/x-tex">3</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">3</span></span></span></span> 片试片用不锈钢挂钩挂好，全浸在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>60</mn><mo>±</mo><mn>5</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(60 \pm 5)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">60</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>500</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">500\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span> 的清洗 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5</mn><mtext> </mtext><mtext>min</mtext></mrow><annotation encoding="application/x-tex">5\,\text{min}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6679em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">min</span></span></span></span></span>，取出后将试片呈 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>45</mn><mo>∘</mo></msup></mrow><annotation encoding="application/x-tex">45^\circ</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6741em;"></span><span class="mord">4</span><span class="mord"><span class="mord">5</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6741em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∘</span></span></span></span></span></span></span></span></span></span></span> 角放置，到晾干为止。常温清洗剂在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>30</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(30 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">30</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 下浸渍。将晾干的试片用金属钩固定在摆洗机试片上，全浸在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>60</mn><mo>±</mo><mn>5</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(60 \pm 5)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">60</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">5</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 的 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>500</mn><mtext> </mtext><mtext>mL</mtext></mrow><annotation encoding="application/x-tex">500\,\text{mL}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">500</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord text"><span class="mord">mL</span></span></span></span></span> 的蒸馏水中，立刻摆洗 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn></mrow><annotation encoding="application/x-tex">10</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">10</span></span></span></span> 次（往返为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> 次）。无摆洗机时，可按摆洗机的摆距、摆频、人工摆洗；常温型的在 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">(</mo><mn>30</mn><mo>±</mo><mn>2</mn><mo stretchy="false">)</mo><mtext> </mtext><mi mathvariant="normal">°</mi><mtext>C</mtext></mrow><annotation encoding="application/x-tex">(30 \pm 2)\,\degree\text{C}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span class="mord">30</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">2</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord">°</span><span class="mord text"><span class="mord">C</span></span></span></span></span> 下摆洗。取出用热风吹干试片，吹干时试片呈 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>45</mn><mo>∘</mo></msup></mrow><annotation encoding="application/x-tex">45^\circ</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6741em;"></span><span class="mord">4</span><span class="mord"><span class="mord">5</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.6741em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mbin mtight">∘</span></span></span></span></span></span></span></span></span></span></span> 角。</p><p>(3) <strong>结果评价</strong><br>检查试片表面有无清洗剂残留物。再在试片上滴 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span></span></span></span> 滴无水乙醇，乙醇挥发后，再检查试片有无白色残留物。若乙醇挥发后留有圈痕，需要用空白试片滴乙醇进行对照试验。</p><a class="btn-beautify orange block right outline" href="https://js.design/f/YdotUf" title="封面设计稿"><i class="fas fa-panorama"></i><span>封面设计稿</span></a>]]></content>
    
    
    <summary type="html">金属清洗评定以及金属清洗剂检验分析方法（备忘）</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/MetalCleaningEvaluation.png" type="image"/>
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
    <category term="⚙️工程机械" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%9A%99%EF%B8%8F%E5%B7%A5%E7%A8%8B%E6%9C%BA%E6%A2%B0/"/>
    
    
    <category term="不累计字数标记" scheme="https://blog.si-on.top/tags/%E4%B8%8D%E7%B4%AF%E8%AE%A1%E5%AD%97%E6%95%B0%E6%A0%87%E8%AE%B0/"/>
    
    <category term="工" scheme="https://blog.si-on.top/tags/%E5%B7%A5/"/>
    
  </entry>
  
  <entry>
    <title>播客解蔽</title>
    <link href="https://blog.si-on.top/2026/Podcast2Podcast/"/>
    <id>https://blog.si-on.top/2026/Podcast2Podcast/</id>
    <published>2026-02-27T14:50:33.000Z</published>
    <updated>2026-02-27T14:50:33.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p>尽管大学时候很热衷听播客，知识、成长、阅读、音乐之类信息的摄入确然可以帮助一个人更快地成长，然而23年年末以来至今，我都几乎在刻意回避这种媒介，浅意识里隐约觉得这里头有一些与我相悖的东西，此论当时在<a href="/2024/script4mored2read/">『把喜欢的播客打印出来！』</a>一文中有过分析。对播客的回避，大概也是那时节开始的。</p><p>算到今日，对播客这媒介的否定，也已过了两年。在这期间，从对听播客的热情逐渐消淡，到自己在博客里借助插件实验了一个<a href="/2025/ep1_Expression">小播客</a><sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>，再到去年在骑行途中偶然用AI听了一篇期刊<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>生成的播客，再到去年年底EZFM停播后陷入一段声音空洞的焦虑期，这期间对播客这一媒介的观点有了新的思考。</p><p>结果就是现在的我，从某个角度上，又能接受播客这种媒介<sup class="footnote-ref"><a href="#fn3" id="fnref3">[3]</a></sup>了。通过控制源头，按法兰克福学派的那套框架的阐述来说<sup class="footnote-ref"><a href="#fn4" id="fnref4">[4]</a></sup>，我能掌控住这种意识形态<sup class="footnote-ref"><a href="#fn5" id="fnref5">[5]</a></sup>了，不再让它作妖。</p><p>这观点最开始，源自一些很杂乱的思考，很个人化的体验，概括来讲就是一个词——“弃人牙慧情结”。</p><h2 id="弃人"><a class="markdownIt-Anchor" href="#弃人"></a> 弃人</h2><p>“当看到别人在做某件事后，即便自己正在做或者打算想做，现在也不再会当着面去做。”</p><p>“看到别人做某件事，自己受到了触发，因而也想表达一些东西，或者也去做这些东西。要么换一个触发源不在地方去做，要么就强烈压制住这种欲望。”</p><p>“看到一个见解/想法，即便自己想不到，也绝不会把这种见解看做自己的。要么通过批判(除了一些大略不变的真理，大多数东西都是可批判，可发展的)整出来一个新的，要么刻意忽视，直至把它忘掉。”</p><p>“在一个地方说了一句话，即便在另外一个地方说会有更多的价值，也不愿意再去重复。”</p><p>“自己偶然间产生了某种想法，经年累月之后，这种想法如果既没有在行动上得到运用，本身也没有新的发展，是不会再去利用它的。如果利用，那就算是嫖窃旧我，自挖己坟，内心不得安宁。”</p><p>这一些念头，不好统一分类，一直在四处游荡。去年年中读康德的时候，曾与Z君讨论过一次这个观点，结论是我妄自菲薄。后面再想想，似乎、大概、可能、或许确实是我妄自菲薄，那我为什么会妄自菲薄呢？思来想去，用“<u>弃人牙慧</u>”一词来描述其中的一部分甚为恰当。这个约略可以描述为“独创性情结”的东西实在不好解释。或许是人的一种天性？！想要与众不同，不随波逐流，体现独特价值？！</p><p>玩梗、追风、meme、社评、历史、伶化(当把别的价值观强加到自身，做违真心却不违心的非强迫性寻求阶级上升的表演，来自年初研究某个问题所臆造的一个词)，这些内在的关联大抵都是拾人牙慧。不可否认，这些东西绝对有利于拉平人们的认知，提高社会规范的适用范围，但绝对不会有利于面向时空/意义的纵向的发展。此情绪的存在，或许会让人变得孤僻，但在一定程度上抵抗所谓社会规范的“侵蚀”。同样不可不中庸——为了不拾人牙慧，强制否定一切，也就走上极端了<sup class="footnote-ref"><a href="#fn6" id="fnref6">[6]</a></sup>。</p><p>保持自己思想的独立性，因为这是一切的前提，如果不能保持独立，那么与他人灵魂的附庸毫无差异。播客，虽披着知识传播的外衣，但其本质与短视频、拍快照者<sup class="footnote-ref"><a href="#fn7" id="fnref7">[7]</a></sup>的作品无异。想让我异化，想让我接受所藏掖着的意识形态，嘿嘿，门儿都没有！</p><h2 id="物它"><a class="markdownIt-Anchor" href="#物它"></a> 物它</h2><p>在<a href="/2023/key4read">电子阅读新语</a>中开篇“源头”一节中曾提到过信息来源的关键——要关注来源，通过筛选来源，让源头的活水潺潺流动，进而才能冲刷出更宽阔的河流来。</p><p>在这个时代（盗版资源盛行也是这时代的一个部分），信息的来源都极其方便了。我们只需要掌握一点点技巧，就可以筛选出各种优质来源，然而如何消化它，就显得比较棘手了。不妨以核桃为例：比如你要吃个核桃，得先找个门把核桃壳夹裂吧(祖传夹核桃法)，还要用手把果壳一个个掰掉把果仁从中取出来吧，取出来果仁还没完，又得把果仁中间的分心木去掉，再有挑剔者，甚至要把果仁上的种皮给剥了去最后才吃到里面的果仁。如果遇到某些山核桃难剥的，脾气暴躁的，有时甚至连壳嚼碎咽下。打开果壳，摄取知识也是需要下一点功夫的。<br><img src="/images/20260106/20191231190904_dhmmi.jpeg" alt></p><p>然而大家都说，现在有AI(LLM)了，<strong>人家不仅把果仁完完全全取出来，还顺手给它用糖炒一炒，给你放到盘子里，在旁边点缀一些小花喂到你嘴边，更有甚者，还给你造几个新品种的外国五颜六色的核桃来</strong>。</p><p>然而我却觉得恐惧。</p><p>我并不期待它能给我造一个新核桃来，我也不愿意它给我造出来别的什么花样。我的目的就是他娘滴干干净净的核桃仁！不要在旁边点缀小花，上点味道，可能有些人喜欢那种味道，但是它毕竟不是原味儿，说不定其中就有一些变异的转基因核桃。<u>你吃完之后明明中了毒也茫然不知道怎么回事</u>。</p><p>想要干干净净的核桃仁，那该怎么办呢？</p><p>得拿出来祖师爷留下的『南华真经』里的绝招了！</p><p><strong>物它</strong></p><p><img src="/images/20260106/%E6%92%AD%E5%AE%A2%E8%A7%A3%E8%94%BD-20260227234759770.webp" alt></p><p>套用庄子老祖师爷的话，这就叫物AI而不物于AI，驱使AI，而不被AI驱使。我们的目的就是要把它做成一个工具，不要让其越殂代疱，让它回归到一个工具上。</p><p>期刊上的文字是相对可信的，经过审查翻版的图书是整个人类文明中最靠谱的东西。平时有时间，我就会精心筛选一些来源，备一些核桃(现在放到zotero里一个名叫『日至』的分类里了)。但是一到看书的时候就犯了难，人是不能久坐的，人的注意力是总是不能一直集中的。所以这些东西常常被埋没掉，有很多特别有意思的东西，常常因为没有时间去看而被荒废掉。现在我发现可以用AI把这个东西直接做成一集二三十分钟短短的播客。在我看累的时候，走路、吃饭、洗衣服、篆刻、打字的时候，把那些想看的东西都放里面，生成音频听，后面再觉得有必要了，再进行精读，这样两不相误。一来篇幅较短，AI播客观点是否准确与否，一看便知，二来AI还没有往里面掺杂意识形态的能力，也没有什么可担心的。<sup class="footnote-ref"><a href="#fn8" id="fnref8">[8]</a></sup></p><p>播客最原始的目的就是让知识更好的传播，它就是一个媒介，一个介质，从这头到那头的一个桥梁。</p><p>播客是一个工具！</p><p>让播客重新成为一个工具！</p><a class="btn-beautify orange block right outline" href="https://js.design/f/fCMYt9?mode=design&p=uRfz-9I1F8" title="封面设计稿"><i class="fas fa-panorama"></i><span>封面设计稿</span></a><hr class="footnotes-sep"><section class="footnotes"><ol class="footnotes-list"><li id="fn1" class="footnote-item"><p>不多时，因为语言表达不畅、录音场地限制，热情逐渐褪去 <a href="#fnref1" class="footnote-backref">↩︎</a></p></li><li id="fn2" class="footnote-item"><p>去年五月份到八月份左右热衷于研究康德，与做播客几乎是同时期，播客文件夹里至今还有准备录一期康德，所写的脚本、音频的残篇断简。 <a href="#fnref2" class="footnote-backref">↩︎</a></p></li><li id="fn3" class="footnote-item"><p>“大众媒介乍看是一种传播信息和提供娱乐的工具 但实质上不发挥思想引导、政治控制等功能 的大众媒介在现代社会是不存在的” <a href="#fnref3" class="footnote-backref">↩︎</a></p></li><li id="fn4" class="footnote-item"><p>邵培仁, 和李梁. 《媒介即意识形态——论法兰克福学派的媒介控制思想》. 浙江大学学报(人文社会科学版), 期 1, 2001年, 页 99～106. <a href="#fnref4" class="footnote-backref">↩︎</a></p></li><li id="fn5" class="footnote-item"><p>“在经典的马克思主义理论中 意识形态是指由占统治地位的政治力量维持的 一套骗人的思想 而科学则必须用来发现真理并战胜虚妄的意识形态” <a href="#fnref5" class="footnote-backref">↩︎</a></p></li><li id="fn6" class="footnote-item"><p>此部分为2025.12.16日，所撰的残篇《论弃人牙慧》inassimilable，行文思路会有跳跃，望读者见谅。 <a href="#fnref6" class="footnote-backref">↩︎</a></p></li><li id="fn7" class="footnote-item"><p>威廉·弗鲁塞尔一书中对被摄影装置控制，成为装置一部分的摄影者的定义 <a href="#fnref7" class="footnote-backref">↩︎</a></p></li><li id="fn8" class="footnote-item"><p>（快十二点半了，时间不够了，容我先草草收个尾） <a href="#fnref8" class="footnote-backref">↩︎</a></p></li></ol></section>]]></content>
    
    
    <summary type="html">让播客回归播客！</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/podcast2podcast.png" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="🪶杂谈" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%F0%9F%AA%B6%E6%9D%82%E8%B0%88/"/>
    
    
    <category term="批判性思考" scheme="https://blog.si-on.top/tags/%E6%89%B9%E5%88%A4%E6%80%A7%E6%80%9D%E8%80%83/"/>
    
    <category term="播客" scheme="https://blog.si-on.top/tags/%E6%92%AD%E5%AE%A2/"/>
    
    <category term="剖析" scheme="https://blog.si-on.top/tags/%E5%89%96%E6%9E%90/"/>
    
  </entry>
  
  <entry>
    <title>卖个破绽</title>
    <link href="https://blog.si-on.top/2026/HeyMyDefectOverHere/"/>
    <id>https://blog.si-on.top/2026/HeyMyDefectOverHere/</id>
    <published>2026-02-26T14:22:48.000Z</published>
    <updated>2026-02-26T14:22:48.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><blockquote><center>将欲歙之，必固张之。将欲弱之，必固强之。将欲废之，必固兴之。将欲取之，必固与之。是谓微明。柔弱胜刚强。</center><p align="right">——《道德经》</p></blockquote><p>近日在读水浒，发现人物打斗到难分难解时总出来一个词叫做——<strong>卖个破绽</strong>。显然这不是说角色把破得露出烂棉絮的衣服卖给了对方，而是一个动作（废话）。一般角色在做了这个动作之后，局势就会发生较大的转变。如：</p><blockquote><p>史进、陈达两个斗了多时，只见战马咆哮，踢起手中军器；枪刀来往，各防架隔遮拦。两个斗到间深里，史进<strong>卖个破绽</strong>，让陈达把枪望心窝里搠来，史进却把腰一闪，陈达和枪攧入怀里来。史进轻舒猿臂，款扭狼腰，只一挟，把陈达轻轻摘离了嵌花鞍，款款揪住了线搭膊，只一丢，丢落地。那匹战马拨风也似去了。</p><p align="right">——《第二回·王教头私走延安府 九纹龙大闹史家村》</p></blockquote><blockquote><p>崔道成和丘道人两个，又并了十合之上。智深一来肚里无食，二来走了许多路途，三者当不的他两个生力，只得卖个破绽，拖了禅杖便走。两个撚着朴刀，直杀出山门外来。</p><p align="right">——《第六回·九纹龙剪径赤松林鲁智深火烧瓦罐寺》</p></blockquote><p>那这个词的具体动作含义是什么呢？</p><p>根据语境来推测，大概是角色故意做了一个虚假的动作，比如故意呆住、把腿或手臂伸到自己明显招架不住的夸张幅度，让对手感觉自己在这里忘记防备了，于是诱惑对方就往这个没有防备的地方攻击，然后对方砍过来之前自己就及时收手，好让对方打空，从而让自己有一次喘息的机会，进而利用这个机会进行反击或者逃走。</p><p>但这只是主观推测臆想，还是查一些资料吧。</p><p>找到王资鑫前辈所撰的闲文《<u>卖个破绽的心理轨迹——先与后夺法</u>》 ，里面从力学、哲学、心理学三个层间来解读，写得着实精彩，<s>抄</s>摘录几段如下：</p><blockquote><p>“破绽”者，对敌是攻击之天赐空当，对己则是防守薄弱环节。傅、张在毫无外力的威逼或利诱下，完全自愿地自“卖”破绽，自讨苦吃，倒不是风格高尚，而是大有深意，因为天下没有无缘无故的自戕性命的笨蛋。观察傅、张二将，战不十合便走此险棋，显然为图速战速决。如果双方深沟高垒、坚壁自守，谁都极力隐藏庐山真面貌，谁都不先使出撒手锏，必然耗力费神，而破绽一露，则大不相同了，对手必定见空就补，见空就插，也必定亮出看家本领，暴露真实意图，就像带有阴阳电荷的两片云层相遇，立刻发响声，立刻爆火花，是雌是雄立见分晓。</p></blockquote><div class="tip warning"><p>作者引出了一些生活上的例子，这是写作时很难得的触类旁通的体验。笔者俺每每有这种感觉时，总是欢欣雀跃一阵子，恨不得立时把它写出来，然而真正着手去写，却发现很是单调，无非A情况与B有一种潜在的相同模式，可以通过A来理解B，B去理解A。而作者这段将其做一个例子用，来引出后面道理，如此便显得触动不那么空洞，这是我辈需要学习的地方——不是得了一个妙语，妙悟就要立马表达的，可以先放在那里，等到适当的时机，掺杂着别的好东西一起或盘托出。</p></div><blockquote><p>“ 🐦麻雀起飞时，不是先双爪蹬地，而是身体下蹲，紧接着才伸腿使力蹬地，在给地面一个向下的作用力的同时，也获得了地面给自己的向上的反作用力，于是乎，麻雀飞上天空。麻雀如此，所有飞禽走兽莫不如此，人的走、跳、跑、翻……也不例外。麻雀起飞面对的对手是地面，要离地面而去（飞起），却先表现为接近地面（下蹲），这与技击时要“夺”对手，却要先“与”对手（表现为卖个破绽）大致相似。 ”</p></blockquote><blockquote><p>《老子》第三十六章说过：“将欲歙之，必固张之。将欲弱之，必固强之。将欲废之，必固兴之。将欲取之，必固与之。是谓微明。柔弱胜刚强。”就是说，将要收敛它，必须暂且扩张它；将要削弱它，必须暂且增强它；将要废弃它，必须暂且兴起它；将要夺取它，必须暂且拿给它。老子认为，这是一个预见——柔弱必定胜刚强。</p></blockquote><p>尽管里头”权术“的味道太浓了，但从”欲擒故纵“这里，可以提炼出一个模型：A与B是对立的，想要得到A，就先要B。由此确实能联想到许多东西来。如：</p><ul><li>骑自行车时的转弯动作：想要往左转，必须要向往右边扭动下</li><li>晚上想要睡得舒坦，白日就要累一点</li><li>想要躺平，就不能躺平</li><li>想要细细品味好吃的食物，就不能经常吃它。</li><li>”想要破坏一首歌的感受，就把改成起床铃“（每天都听，自然就烦了）</li><li>想要失败，就要先成功一下</li><li>想要活着，就要先”死“一回</li></ul><hr><p>（下面对搏击的心理写的如此之细腻，这个前辈，莫非还是个练家子（学过武术）。）</p><blockquote><p>先与后夺，与其说是一场力量、技巧、速度的比赛，倒不如说是一场精神、思想、意识的较量。傅佥擒王真，张飞擒严颜，实际也是一场心理大战。 当傅与王、张与严交手时，双方都把心理活动逼上了电闪雷鸣的闪爆点。傅、张能取胜，从心理意义说，首先具有自觉而敏锐的攻防感觉。在双方对垒中，通过对手身体的任何一个部位的攻防作用于己方感觉器官，人脑中就产生了对这些劲力的针对性的反映，这就叫做攻防感觉。谁能较快而又较准地获得攻防感觉，谁就能占有战斗主动权。而获得这一感觉的基础，便是双方接触（表现为王真向傅佥刺枪，严颜向张飞砍刀）——而傅佥、张飞正是为了获得接触、获得感觉，才“卖个破绽”。在傅佥、张飞，这一感觉过程有三个阶段：</p><ol><li>第一阶段：审敌阶段。首先，傅、张卖个破绽，引王、严攻击自己，人体表面（外感受器）开始接受作用于它的进攻力量的方向、大小（即刺激物），双方对峙，依靠感觉摸底。在这阶段中，傅、张即依靠视觉了解对手神态、体型、实力、攻防路线及出手动向；又通过听觉，凭借对手出击引起振动所发出的声波，作用于自己的听觉分析器，从而掌握进攻的力度、力点和方向；特别依靠体测及神遇将对手攻防意图打探清楚。</li><li>第二阶段：决策阶段。当王真挺枪来刺和严颜一刀砍来时，来自外周的神经兴奋传入傅、张的中枢。傅、张将对手的攻防虚实强弱种种情况所带来的神经冲动进行综合分析，据此确定应付措施及战胜对手的方法。</li><li>第三阶段：致胜阶段。返回信息，转入进攻，傅佥、张飞都闪过进攻，并撞将人去，在曲横闪战中，主动地引导对方形成被动局势，一举生擒了对手。</li></ol><p>当然，傅、张取胜的心理活动，除了他们具有对王、严个别属性和部分的反映——攻防感觉之外，还具有对王、严攻防各个部分和属性的整体反映——攻防知觉：这是指搏斗中的奥妙无穷、瞬息万变的双方复杂态势所构成的反射活动。应当指出，傅、张要比王、严知觉主体优良得多，反映清晰得多，所以格斗信心强烈得多，态度也主动得多。 也许，当王真、严颜被活捉时，他们那戴着头盔的大脑还不曾反应过来：怎么好端端地捕捉个“破绽”，一家伙捅去，却反倒束手被擒呢？</p></blockquote><p><img src="/images/20260106/%E6%86%A8%E8%B1%86%E7%9A%84%E7%A0%B4%E7%BB%BD.gif" alt="拥有强大格斗信念的憨豆先生"></p><a class="btn-beautify orange block right outline" href="https://js.design/f/tYN1SG?p=73ZSynI6MW&mode=design" title="封面设计稿"><i class="fas fa-panorama"></i><span>封面设计稿</span></a>]]></content>
    
    
    <summary type="html">欲擒之，故纵之，欲亡之，故兴之。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/HeyMyDefectOverHere.png" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="🪶杂谈" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%F0%9F%AA%B6%E6%9D%82%E8%B0%88/"/>
    
    
    <category term="文言" scheme="https://blog.si-on.top/tags/%E6%96%87%E8%A8%80/"/>
    
    <category term="训诂" scheme="https://blog.si-on.top/tags/%E8%AE%AD%E8%AF%82/"/>
    
    <category term="触类" scheme="https://blog.si-on.top/tags/%E8%A7%A6%E7%B1%BB/"/>
    
  </entry>
  
  <entry>
    <title>MetaBase笔记</title>
    <link href="https://blog.si-on.top/2026/Metabase/"/>
    <id>https://blog.si-on.top/2026/Metabase/</id>
    <published>2026-02-26T06:57:00.000Z</published>
    <updated>2026-04-05T15:21:22.005Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p>近日在研究数据可视化，扒拉了一些BI工具，找来找去，陷入选择困难症。最后发现Metabase安装很方便——直接用java便可以运行。便快速上手，用了几天，感觉良好，有深入学习的必要，特意撰写此文，边学边用。</p><p>之前也有用过其他的一些数据可视化工具，如厂内MES系统的<strong>Ureport2</strong>，帆软的<strong>finerepport</strong>，因为其定位都是做报表，也就意味着<strong>需要对展示数据的细节进行巨细无遗的全面控制</strong>才能整出来一个结果。这类软件很相近（一丘之貉般的繁琐），大概的步骤都是：</p><ol><li>在数据库管理软件(如DBeaver)里测试SQL，</li><li>SQL没问题了再放到报表的模型里，并按照其语法规则配置可控的查询参数；</li><li>在报表引擎的界面上逐个单元格地配置字段、格式、字体、大小。如果需要进行一些图表的展示，还需要控制表的位置，定义各个轴的参数，维护一套配色规则等等，</li><li>最后点击渲染。如果报错，就必须回头重新配置报表，往往配置好一个完美的报表需要好几天的时间。</li></ol><table><thead><tr><th><img src="/images/20260106/MetaBase-20260226160827748.webp" alt="配置SQL语句"></th><th><img src="/images/20260106/MetaBase-20260226153658622.webp" alt="配置扇形图"></th></tr></thead></table><p>尽管磕磕拌拌地也能做出来想要的效果，但是对于一些简单的数据分析、监控来说，就非常烦人了。如果说时间就是生命，那操作这些报表引擎简直就是在割腕自杀，发明这类报表的人就是在谋财害命，让使用报表的同志们把热情消弭于各种本该自动化的调整、点击中。虽说对于开发项目初期那些大型报表来说，能熟练运用这类引擎的话效率也蛮高的，然而因为诸多的反人类设计，这类引擎的学习曲线也比较陡峭，通常熟练起来之后报表也基本都做完了（亲身体验），只能做些锦上添花的小修改，让人暗叹英雄无用武之地。</p><p>而MetaBase的话，就…好呗。</p><p>最突出的优势是它将SQL编辑器与数据可视化很好地集成在了一起。内置的SQL编辑器有语法高亮，搜索替换、快捷键、语法纠错，自动填充，数据表字段建议等等<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>。在进行一些即时的分析，挖掘一些如工艺参数关系、产量情况等的情形下，非常之方便。</p><p>因为MetaBase的文档比较<s>垃圾</s>偏向说明，一些操作细节上的疑难，自己摸索<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>搞不出来的，完全可以去查阅学习，但对于一些提纲挈领的思路，文档就显得模模糊糊，一些名词翻译或者定义本身就有问题，让人丈二和尚摸不着头脑，这便本文的目标——对MetaBase进行一个全局的审视。</p><h2 id="通览"><a class="markdownIt-Anchor" href="#通览"></a> 通览</h2><p><img src="/images/20260106/MetaBase-20260226164130879.webp" alt></p><ol><li>问题（Question）这其实就是一个将SQL查询与可视化结合在一起的功能，是MetaBase最为基础的组成部分。有各种可视化、查询结果导出、问题提醒。其本身也有一个版本记录功能，出岔子后可以向前复原历史版本的记录。向外可以嵌入到其他地方，放置到仪表盘中。</li></ol><p><code>问题</code>的编辑方式有两种，一种是写SQL，适用于从头写的原始SQL；一种是用图形化界面进行配置，适合于一些已经初步整理的视图。</p><p><code>问题</code>的储存方式也有两种，一种是传统的将其放到一个文件夹里（这里叫做“<code>集合</code>”），然后在各个地方复用；另一种是将其储存到仪表盘里，那就只能在仪表盘的界面里看到点进去编辑。后者适合那些临时的小指标，没有整理归类的必要直接写在仪表里。<img src="/images/20260106/MetaBase-20260226161524107.webp" alt="快速可视化"><br>界面最下面正中便是基本的两部分——查询结果与可视化。</p><p>左侧的可视化有基本的表格（相较于查询结果表，有更多自定义的部分，如控制显示、用条件格式）、柱状图、折线图、饼图、组合图、散点图、也有复杂一点的桑基图、瀑布图、地图、漏斗图等。配置的方式大同小异，都是点击左侧<code>可视化|⚙</code>的可视化，选择图表类型，然后点击<code>⚙</code>配置各个坐标轴的参数、系列、颜色、线宽、格式等等。</p><div class="tip sync"><p>图表有一个很人性化的设计——可以自动保存历史每种可视化的配置。比如你费了一些功夫绘制了一个折线图，又想绘制成柱状图看看效果，这时候可视化直接点击到柱状图进行配置（系统会根据前一个折线的配置给你生成一个差不多的柱状图，而不需要从头配置）。当感觉柱状图效果不怎样时，点击回到折线图里，折线图的配置也不会丢失。这个非常细节的设计极其好用。</p></div><p>右侧显示查询的行数、查询耗时、查询结果/图表的导出。</p><hr><h2 id="其他"><a class="markdownIt-Anchor" href="#其他"></a> 其他</h2><h3 id="安装"><a class="markdownIt-Anchor" href="#安装"></a> 安装</h3><ol><li>Metabase<a href="https://www.metabase.com/start/oss/">安装</a>：下载<a href="https://www.metabase.com/start/oss/jar">JAR</a>文件，安装<a href="https://www.oracle.com/java/technologies/javase/jdk21-archive-downloads.html">jdk</a>，运行<code>java --add-opens java.base/java.nio=ALL-UNNAMED -jar metabase.jar</code>,访问<code>http://localhost:3000/</code></li><li>SQLite<a href="https://www.runoob.com/sqlite/sqlite-installation.html">安装</a>：<a href="https://sqlite.org/download.html">下载</a>sqlite-dll与sqlite-tools，解压到一个文件夹，添加环境变量。终端输入<code>sqlite3</code>进入交互命令模式，找个合适位置，创建数据库<code>.open ku.db</code>，同时随便创建一个表(Metabase连接时，如果是空数据库，会报错连不上)</li></ol><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">CREATE TABLE</span> demo(</span><br><span class="line">   ID <span class="type">INT</span> <span class="keyword">PRIMARY KEY</span>     <span class="keyword">NOT NULL</span></span><br><span class="line">);</span><br></pre></td></tr></table></figure><ol start="3"><li>连接SQLite：假设我在此处创建了一个数据库<code>D:/BI/ku.db</code>，那么可以通过<code>jdbc:sqlite:///D:/BI/ku.db</code>链接来在MetaBase中配置此数据库<sup class="footnote-ref"><a href="#fn3" id="fnref3">[3]</a></sup><br><img src="/images/20260106/MetaBase-20260115164347354.webp" alt="连接示例"></li></ol><h3 id="配置"><a class="markdownIt-Anchor" href="#配置"></a> 配置</h3><p>Metabase支持各种数据库，配置起来也比较方便，<a href="https://www.metabase.com/docs/v0.58/databases/connecting">文档</a>写的很细，在此不再赘叙。</p><table><thead><tr><th><img src="/images/20260106/MetaBase-20260226164419172.webp" alt="配置sqlite"></th><th><img src="/images/20260106/MetaBase-20260226164407357.webp" alt="配置mysql"></th></tr></thead></table><h3 id="邮箱提醒"><a class="markdownIt-Anchor" href="#邮箱提醒"></a> 邮箱提醒</h3><p>参照文档，配置SMTP等邮箱服务，写SQL查询，创建警报，出现预期的不良值时自动触发，发送到自己账号的邮箱里。</p><table><thead><tr><th><img src="/images/20260106/MetaBase-20260226165314524.webp" alt></th><th><img src="/images/20260106/MetaBase-20260226165243966.webp" alt></th></tr></thead></table><div class="tip bolt"><p>如果是用的QQ邮箱，在微信里配置一下名为”QQ邮箱提醒“的服务，就可以收到实时的提醒了</p></div><p><img src="/images/20260106/MetaBase-20260226165748321.webp" alt></p><h3 id="问题记录"><a class="markdownIt-Anchor" href="#问题记录"></a> 问题记录</h3><h3 id="忘记账号且忘记密码怎么办"><a class="markdownIt-Anchor" href="#忘记账号且忘记密码怎么办"></a> 忘记账号且忘记密码怎么办？</h3><p>metabase本身的数据是存储在H2数据库中的，可以通过一些数据库管理软件来读取之，比如利用我手头的DBeaver，就可以这样做：</p><ol><li>停止metabase服务，不然后面访问其数据库时会因为同时访问而报错。</li><li>在DBeaver中新建一个H2(<u>Embedded V.2)</u>数据库连接，连接时选中<code>metabase.jar</code>同级目录下的<code>metabase.db.mv.db</code>文件实体。<br><img src="/images/20260106/MetaBase-20260127162257436.webp" alt="DBeaver新建连接时注意选择这个V2版本的H2"></li><li>执行如下SQL语句，或者直接点开<code>public</code>数据库下的<code>core_user</code>表单可以查到管理员的账号邮箱<br><img src="/images/20260106/MetaBase-20260226150039610.webp" alt></li></ol><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">SELECT</span> id, email, first_name, last_name </span><br><span class="line"><span class="keyword">FROM</span> core_user </span><br><span class="line"><span class="keyword">WHERE</span> is_superuser <span class="operator">=</span> <span class="literal">TRUE</span>;</span><br></pre></td></tr></table></figure><ol start="3"><li>最后执行密码重置命令，会得到一个【token】，而后访问<code>http://localhost:3000/auth/reset_password/【这个Token】</code>即可重置密码</li></ol><figure class="highlight shell"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">java --add-opens java.base/java.nio=ALL-UNNAMED -jar metabase.jar reset-password thebesthumanever@exmaple.com</span><br></pre></td></tr></table></figure><hr class="footnotes-sep"><section class="footnotes"><ol class="footnotes-list"><li id="fn1" class="footnote-item"><p>如果可以像Dbeaver一样点表名跳转表单详情等一些功能的话就更完美了（有空去提个issue） <a href="#fnref1" class="footnote-backref">↩︎</a></p></li><li id="fn2" class="footnote-item"><p>Metabase的页面很直观，大多数时候直接就可以上手，不需要学习 <a href="#fnref2" class="footnote-backref">↩︎</a></p></li><li id="fn3" class="footnote-item"><p>注意：空库有概率出现【Metabase 已尝试，但无法连接 Failed to connect to Database】的报错，随便建个表即可 <a href="#fnref3" class="footnote-backref">↩︎</a></p></li></ol></section>]]></content>
    
    
    <summary type="html">Metabase工具使用心得</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/metabasenote.svg" type="image"/>
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
    <category term="⌨️软件编程" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%8C%A8%EF%B8%8F%E8%BD%AF%E4%BB%B6%E7%BC%96%E7%A8%8B/"/>
    
    <category term="BI" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%8C%A8%EF%B8%8F%E8%BD%AF%E4%BB%B6%E7%BC%96%E7%A8%8B/BI/"/>
    
    
  </entry>
  
  <entry>
    <title>动量</title>
    <link href="https://blog.si-on.top/2026/MV/"/>
    <id>https://blog.si-on.top/2026/MV/</id>
    <published>2026-02-23T08:53:56.000Z</published>
    <updated>2026-02-23T08:53:56.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p><img src="/images/20260106/%E5%8A%A8%E9%87%8F-20260226110613940.webp" alt></p><p>当你在冬日的太阳底下沐浴阳光，天空似乎静止不动，一切——山、树、风、雀——都在静止。忽一阵无名风起，推着兴致涌上心头，便准备迈开脚步出门，方才迈开第一步，便觉着思绪迅速流转，再走两步，天空开始流动了，万物也开始呼吸了，连光线都跟随着步伐轻轻地跳起来，山、树影晃动，鸟雀鸣唱，流水潺潺，仿佛这世界是正因你的活动才凭空造出来如此多的变化来。</p><p>相较于静坐，我更多欢喜走动，绝非是那些所谓“运动有助身心健康”、“自由其精神，野蛮其体魄”之类宣传的鼓动，而是在于一种很微妙的物理上的体验。</p><p>近来在坐车时察觉到这一体验，发现当车在运动时，心情会活跃一点，当车停滞在路口时，便要低落紧绷一点。有人说这是对目的地的渴望所致，距离目标越近一分，便会多一分的欢喜。然而有时，我确实是漫无目的地在闲逛散步，根本没有目的地，同样也会有这种体验，走起路来比坐在椅子上歇息，心思更活跃一点。对于这一体验，推测是上古时期，人类为了生存必须要不停地走动觅食，在走动时候又或多或少会发现高山大泽、找到野菜野果、遇见毒蛇野兽，体验着种种恐惧与狂喜，而静止在原地是无法体验的。渐渐地，经过几千万年的进化，人逐渐将在活动时体会到的那种向前动的、起起伏伏的惯性与那种活跃的情绪连接起来。</p><p>这种颠簸的惯性体验，跟物理学取类比象一下，不妨叫做“动量”吧。由此，便可以看出来一些“道理”来：</p><p>动量的直接来源是势，可以重力势，也可以是运动势。所谓重力势，就是一种静止很长时间后酝酿的势能，比如上了一周班，沉默了很长时间，很自然的，在某些时候就想把郁积许久的冲动给释放出来，于是就去爬山了，旅游了，做些燃烧生命的运动了；运动势则是之前势能没有消耗尽，就在这样的惯性下继续运动，比如之前没有完成的目标，很多年来一直念念不忘，便不可停止地继续运动下去。运动的时候会有阻力，在与外界不停刃靡的过程中，动量终究是会消弭于无形中的，这也是热情必须添柴加火否则就很容易消散的一种解释。</p><p>如果动量指代朝着一个方向的运动，那么自身在运动过程中对周遭或自身各个角度的审视观察就可以类比做角动量。好比打水漂，如果动量的方向不仅仅是直线，而且自身还有一个自旋的角动量，那么就可以飞行地更远，甚至打出来令人拍案称奇的几十漂（实际试验过）。在形状合适的情况下，自旋越强，甚至能产生向上的升力来抵抗自由落体，这样就抛得越发远了。</p>]]></content>
    
    
    <summary type="html">关于惯性体验的一篇随笔</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/mv.svg" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="✒️随笔" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%E2%9C%92%EF%B8%8F%E9%9A%8F%E7%AC%94/"/>
    
    
  </entry>
  
  <entry>
    <title>随机的殇</title>
    <link href="https://blog.si-on.top/2026/fear2farewell/"/>
    <id>https://blog.si-on.top/2026/fear2farewell/</id>
    <published>2026-01-21T12:11:42.000Z</published>
    <updated>2026-01-21T12:11:42.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p>生活着，或许多少都会留意身边的人吧。在一个个的集合里，有的人来，有的人走，有的人来了便不愿走，有的人走了又回来，有的人终于来了，有的人终于走了。</p><p>变动，每每都会在心里荡起一阵涟漪，有时我想，是不是因为恐惧失去，才犹豫开始，进而错过了开始，终于永远失去。然而一但开始，却发现并非总是想象的开始，当失去了想象的开始，却又并非悲意难平。</p><p>大人总说，生活就是这样，来来往往，离散聚合，如池中浮萍一般。唔！浮萍为何这样？这样又是到底怎样？</p><p>是不同集合的引力斥力？是社会学规律？或许有，但决计不单单是沙里淘金，也不单单是优胜劣汰、前浪后浪。我看到的，就那样，嗯…自然而然地，毫无征兆地出现，又毫无理由地，无可驳辩地消失，而后，又稀里糊涂地出现。绝非几个小时的电影，几页妙语所能描刻。</p><p>如一个旋律，不，旋律尚且可以品味琢磨；如窗外飞来一只麻雀，不，麻雀尚且有百科全书记载其种群的生老病死，地域分布；如一声痴笑，不，痴笑尚且可以解析出其心理脉络，哀乐喜愁。</p><p>此物无可比拟。</p><p>此物竟不可比拟！</p><p>“并非我不爱你，而是这方土地，而是这意识形态，总之，我要离去，并永远爱你。”</p><p>“并非我不恨你，而是这方土地，而是这社会规范，总之，我在这里，永远地缠绕在你身边。记住，我每天都会恶心你。”</p><p>“并非我爱你或恨你或漠视你，而是我碰巧结识你，你碰巧结识我，或许，… 我终于需要结识你，你终于需要结识我。”</p><p>啊，深刻的随机性，或言荒谬，唔~ 绝伦的荒谬！</p><p>随便吧，莫顾他人熙来攘往，且自迎风嘿嘿哭，嘿嘿笑。</p><p><img src="/images/20260106/IMG_20240914_203846.jpg" alt></p>]]></content>
    
    
    <summary type="html">周遭人事变动有感。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/20260106/IMG_20240914_203846.jpg" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="🪶杂谈" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%F0%9F%AA%B6%E6%9D%82%E8%B0%88/"/>
    
    
    <category term="剖析" scheme="https://blog.si-on.top/tags/%E5%89%96%E6%9E%90/"/>
    
    <category term="意识流" scheme="https://blog.si-on.top/tags/%E6%84%8F%E8%AF%86%E6%B5%81/"/>
    
  </entry>
  
  <entry>
    <title>MDX+HEXO初试</title>
    <link href="https://blog.si-on.top/2026/newage4hexo/"/>
    <id>https://blog.si-on.top/2026/newage4hexo/</id>
    <published>2026-01-09T15:00:00.000Z</published>
    <updated>2026-04-05T15:21:22.029Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p>今日发现了一个<a href="https://github.com/Bryan0324/hexo-renderer-mdx">hexo-renderer-mdx</a>渲染插件，可以直接对mdx文件进行渲染，而且与md的渲染器可以共存。查阅了mdx的文档，它的一大特性就是支持JavaScript，比如大括号中的表达式（<code>&#123;1 + 1&#125;</code>）和ESM（<code>import</code>和<code>export</code>）（引入插件、变量、函数等）。发觉这其中有许多可玩的东西，几乎是敞开了一个面向前端的大门。鄙人虽玩这个hexo博客五六年了，对于前端的了解也仅限于html+css+一点点js，完全没有接触过react/vue等前端框架。mdx的出现让我有机会可以在博客中直接使用jsx语法，从而可以使用react/vue等前端框架的组件。</p><p>今日便开始尝试一番。之前用LaTeX比较久，很是享受那些自定义指令的功能——临时定义一个样式，然后便<code>\lalala()</code>重复利用起来，巨方便。通过mdx来执行jsx代码，便可以实现这种梦寐以求的效果。借由jsx还可以直接进行计算，比如输入<code>&#123;Math.PI&#125;</code> 得到<!-- -->3.141592653589793</p><p>用作自定义块也很方便，比如我有时候需要输入一些不好打的或者经常使用的文字，比如站点名，我的笔名、座右铭等，那么我便可以提前定义到一个字符上，然后在需要的地方直接调用。在做了如下的定义之后便可以这样写——本站名为<code>&#123;blog&#125;</code> ，站长<code>&#123;me&#125;</code>,近来的座右铭“<code>&#123;motto&#125;</code>”出自《荀子·解蔽篇》，意思是要沉心静气，专一学问。</p><!-- --><pre><code class="language-js">export const blog = &#x27;子虚栈&#x27;export const me = &#x27;秉蕳&#x27;export const motto = &#x27; 虚一而静，浊明外景。&#x27;</code></pre><blockquote><p>本站名为<!-- -->子虚栈<!-- --> ，站长<!-- -->秉蕳<!-- -->，近来的座右铭“ <!-- --> 虚一而静，浊明外景。<!-- --> ”出自《荀子·解蔽篇》，意思是要沉心静气，专一学问。</p></blockquote><p><abbr title="妙妙妙啊，这里还能放隐藏彩蛋。"><strong>很好玩吧</strong></abbr>。经过测试，mdx插件目前基本支持md语法，但代码不高亮、数学公式不能渲染，或许需要引用一些组件什么的，等下再摸索。</p><p><img src="/images/20250610/hexo-quickest-20260109224238126.webp" alt="图片测试：J君养的宠物可达鸭"></p><p>接下来，开始学习点React，希望能做出来类似duckquill主题作者主页那样的效果。</p><h2>MDX 试验区</h2><!-- --><!-- --><!-- --><span style="background:linear-gradient(90deg, #FF0000, #FF7F00, #FFFF00, #00FF00, #0000FF, #4B0082, #9400D3);background-size:200% 100%;-webkit-background-clip:text;-webkit-text-fill-color:transparent;background-clip:text;color:transparent;font-size:1.8em;font-weight:normal;animation:gradientMove 6s ease infinite;padding:2px 0;display:inline-block">彩虹文字效果</span><span style="background:linear-gradient(90deg, #FF00FF, #00FFFF, #00FF00, #FFFF00);background-size:200% 100%;-webkit-background-clip:text;-webkit-text-fill-color:transparent;background-clip:text;color:transparent;font-size:1em;font-weight:normal;animation:gradientMove 1.5s ease infinite;padding:2px 0;display:inline-block">霓虹灯闪烁效果</span>]]></content>
    
    
    <summary type="html">进入hexo博客异世界的大门。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/bg.svg" type="image"/>
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
    <category term="⌨️软件编程" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%8C%A8%EF%B8%8F%E8%BD%AF%E4%BB%B6%E7%BC%96%E7%A8%8B/"/>
    
    <category term="hexo" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%8C%A8%EF%B8%8F%E8%BD%AF%E4%BB%B6%E7%BC%96%E7%A8%8B/hexo/"/>
    
    
    <category term="hexo" scheme="https://blog.si-on.top/tags/hexo/"/>
    
    <category term="mdx" scheme="https://blog.si-on.top/tags/mdx/"/>
    
  </entry>
  
  <entry>
    <title>乙巳大雪摄影小结</title>
    <link href="https://blog.si-on.top/2025/photography:202512/"/>
    <id>https://blog.si-on.top/2025/photography:202512/</id>
    <published>2025-12-21T15:21:02.000Z</published>
    <updated>2025-12-21T15:21:02.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><h2 id="乙巳大雪摄影小结"><a class="markdownIt-Anchor" href="#乙巳大雪摄影小结"></a> 乙巳大雪摄影小结</h2><p>反观博客今年的内容，写得简直七零八碎不成系统，全都是稀碎，这一点长毛象贡献了不少功劳，它夺去了我的表达欲！</p><p>人非自动化工具，表达欲一但宣泄，是不会立马恢复的，往往要经历长达一周的琐碎与鸡毛蒜皮才能酝酿起来。</p><p>即时的表达，即时的反馈，已经让表达的回环压缩到小时级，也就是说这样的表达会在几小时后腐朽！好短视！我说怎么一直活在过去俩仨月，原来是这样的表达训练了我，异化了我！</p><p>要抵抗异化！要直抒胸臆，要革命到底，要坚持革命浪漫主义！</p><p>从本文开始，至少每一个节气，本栈都会以某种载体写一篇小结，总结这段时间所做的一些东西，以及一些可能有用的念头。本次就以影像为载体吧:</p><p><img src="/images/20250610/IMG_20251207_225910.jpg" alt="大雪节气印"></p><p>此次小结时间所选取的摄影作品跨度为最近一月，拍摄地点主要包括</p><ol><li>绍兴，城区—鲁迅故居—大禹陵—会稽山(11.30)</li><li>杭州，西湖—云栖竹径—五云山—九溪—贵人阁(12.14)</li><li>慈溪，杭州湾新区(12.22等)</li></ol><p>题材分为抽象(主要风格)、人文(关注本地人)、风景(登高望远所见)、微观凝视(植物特写)。</p><h3 id="抽象"><a class="markdownIt-Anchor" href="#抽象"></a> 抽象</h3><h4 id="山阴道上"><a class="markdownIt-Anchor" href="#山阴道上"></a> 山阴道上</h4><p>徒步去会稽山，路边一白墙的裂缝，很有木版画的味道<br><img src="/images/20250610/DSC_2235_1%20(1).jpg" alt></p><h4 id="秋色卡"><a class="markdownIt-Anchor" href="#秋色卡"></a> 秋色卡</h4><p><img src="/images/20250610/DSC_2917%20(1).jpg" alt></p><h4 id="失修"><a class="markdownIt-Anchor" href="#失修"></a> 失修</h4><p>富北村徒步所见，残缺更有动感！<br><img src="/images/20250610/DSC_3002_1%20(1).jpg" alt></p><h4 id="赤枫"><a class="markdownIt-Anchor" href="#赤枫"></a> 赤枫</h4><p>西冷印舍院里所摄，当天见到很多人导出拍枫叶，只有这个地方还算清净，调整好曝光了几次(旁边一幅世界各地印章演变的科普图值的细看。)</p><p><img src="/images/20250610/DSC_2618_2%20(1).jpg" alt><br><img src="/images/20250610/DSC_2589%20(1).jpg" alt></p><h4 id="会稽山南"><a class="markdownIt-Anchor" href="#会稽山南"></a> 会稽山南</h4><p>为了爬到快稽山看日落，四点上山，四点半登顶，看了半个小时的群山。<br><img src="/images/20250610/DSC_2296_1.jpg" alt></p><h4 id="打开天窗"><a class="markdownIt-Anchor" href="#打开天窗"></a> 打开天窗</h4><p>路边一化工厂的简易棚，窗户毫不客气地选择与地面倾斜。<br><img src="/images/20250610/DSC_2947.jpg" alt></p><h4 id="飞鹤"><a class="markdownIt-Anchor" href="#飞鹤"></a> 飞鹤</h4><p><img src="/images/20250610/DSC_3038_1.jpg" alt></p><h4 id="建兰"><a class="markdownIt-Anchor" href="#建兰"></a> 建兰</h4><p>新买的建兰，叶艺确实好看<br><img src="/images/20250610/DSC_2414_1%20(2).jpg" alt></p><h4 id="横切"><a class="markdownIt-Anchor" href="#横切"></a> 横切</h4><p><img src="/images/20250610/DSC_2109_1.jpg" alt></p><h4 id="一城"><a class="markdownIt-Anchor" href="#一城"></a> 一城</h4><p>杭州城远景<br><img src="/images/20250610/DSC_2559_2.jpg" alt></p><h4 id="一湖"><a class="markdownIt-Anchor" href="#一湖"></a> 一湖</h4><p><img src="/images/20250610/DSC_2568_1%20(1).jpg" alt></p><h4 id="秋楝"><a class="markdownIt-Anchor" href="#秋楝"></a> 秋楝</h4><p><img src="/images/20250610/DSC_3020%20(1).jpg" alt></p><h4 id="日落西山"><a class="markdownIt-Anchor" href="#日落西山"></a> 日落西山</h4><p>贵人亭看日落<br><img src="/images/20250610/DSC_2846_2.jpg" alt></p><h4 id="勿近"><a class="markdownIt-Anchor" href="#勿近"></a> 勿近</h4><p>九溪山路上，消防水池上的警戒线<br><img src="/images/20250610/DSC_2690_1%20(1).jpg" alt></p><h4 id="凝视"><a class="markdownIt-Anchor" href="#凝视"></a> 凝视</h4><p>路边非常机灵的某种鸦<br><img src="/images/20250610/DSC_3048.jpg" alt></p><h3 id="人文"><a class="markdownIt-Anchor" href="#人文"></a> 人文</h3><h4 id="修复"><a class="markdownIt-Anchor" href="#修复"></a> 修复</h4><p>绿化带边种植植物的工人<br><img src="/images/20250610/DSC_2859_2.jpg" alt></p><h4 id="虚钓"><a class="markdownIt-Anchor" href="#虚钓"></a> 虚钓</h4><p>苏堤上拿着虚拟路亚竿健身的大爷<br><img src="/images/20250610/DSC_2532_2.jpg" alt></p><h4 id="刚决以进"><a class="markdownIt-Anchor" href="#刚决以进"></a> 刚决以进</h4><p>路边偶遇的老人<br><img src="/images/20250610/DSC_1747_2.jpg" alt></p><h4 id="菜农"><a class="markdownIt-Anchor" href="#菜农"></a> 菜农</h4><p><img src="/images/20250610/DSC_2087_2.jpg" alt></p><h4 id="有利位置"><a class="markdownIt-Anchor" href="#有利位置"></a> 有利位置</h4><p>桥边大胆的钓鱼人<br><img src="/images/20250610/DSC_2078_2.jpg" alt></p><h4 id="修复-2"><a class="markdownIt-Anchor" href="#修复-2"></a> 修复</h4><p>绍兴城区的河面清洁工<br><img src="/images/20250610/DSC_2202_2.jpg" alt></p><h3 id="微观凝视"><a class="markdownIt-Anchor" href="#微观凝视"></a> 微观凝视</h3><p><img src="/images/20250610/DSC_2965.jpg" alt><br><img src="/images/20250610/DSC_2878_1%20(1).jpg" alt><br><img src="/images/20250610/DSC_2922.jpg" alt><br><img src="/images/20250610/DSC_2949_1.jpg" alt><br><img src="/images/20250610/DSC_1951_2.jpg" alt><br><img src="/images/20250610/DSC_2722_1.jpg" alt><br><img src="/images/20250610/DSC_2959.jpg" alt><br><img src="/images/20250610/DSC_2421_3%20(1).jpg" alt><br><img src="/images/20250610/DSC_2801_1.jpg" alt><br><img src="/images/20250610/DSC_2964%20(1).jpg" alt><br><img src="/images/20250610/DSC_2880_1.jpg" alt><br><img src="/images/20250610/DSC_2997_1%20(1).jpg" alt><br><img src="/images/20250610/DSC_2920.jpg" alt><br><img src="/images/20250610/DSC_2553_2.jpg" alt><br><img src="/images/20250610/DSC_2210.jpg" alt></p><h3 id="风景"><a class="markdownIt-Anchor" href="#风景"></a> 风景</h3><p><img src="/images/20250610/DSC_2808_1%20(1).jpg" alt><br><img src="/images/20250610/DSC_2997_1%20(1)%201.jpg" alt><br><img src="/images/20250610/DSC_2268_2.jpg" alt><br><img src="/images/20250610/DSC_2252_3.jpg" alt><br><img src="/images/20250610/DSC_2248_3.jpg" alt><br><img src="/images/20250610/DSC_2226_3.jpg" alt><br><img src="/images/20250610/DSC_2210%201.jpg" alt><br><img src="/images/20250610/DSC_2181_1.jpg" alt><br><img src="/images/20250610/DSC_2180_2.jpg" alt><br><img src="/images/20250610/DSC_1912.jpg" alt><br><img src="/images/20250610/DSC_2464.jpg" alt><br><img src="/images/20250610/DSC_2833_2.jpg" alt></p>]]></content>
    
    
    <summary type="html">乙巳大雪摄影小结</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/20250610/DSC_2235_1%20(1).jpg" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="周记" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%E5%91%A8%E8%AE%B0/"/>
    
    
    <category term="摄影" scheme="https://blog.si-on.top/tags/%E6%91%84%E5%BD%B1/"/>
    
  </entry>
  
  <entry>
    <title>字母雕刻笔记</title>
    <link href="https://blog.si-on.top/2025/NoteOfLetterCarvingInStone/"/>
    <id>https://blog.si-on.top/2025/NoteOfLetterCarvingInStone/</id>
    <published>2025-11-27T11:28:30.000Z</published>
    <updated>2025-11-27T11:28:30.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><blockquote><center>他山之石，可以攻玉。</center></blockquote><p><img src="/images/Cover/NoteOfLetterCarvingInStone.svg" alt></p><p>篆刻，作为一门小众的爱好，其入门的方法几乎与书法一样——依靠不断的临摹。篆界最标准的风格就是秦汉印了，在秦汉时期那个篆刻的黄金时代，作为身份的证明，王公大臣，大小官职无不人手一印，印章的管理又极为严苛，官员死后印章都要上交。在现今留存后世的印章中，一大部分就是为了殉葬而草草刻的印。又因为中国人好古的传统，到了近代，篆刻的发展也没有因为西学东渐而受到太大的影响，除了几位风格独特的名家外，篆刻已然同书法一样，风格固化、评价标准固化，而且字体难以辨识，几近成了中老年闲人打发时间的玩意儿了。传说当初从河图洛书里，古人得到灵感开始了文字、八卦与篆刻，而今纷繁的造物也不比当时少，为何不可再次向外取法呢？</p><p>今日办理的无线电台呼号下来了，打算刻一方呼号印。呼号由六位字母+数字组成，这就涉及到一个新领域——字母的刻法。</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mi>B</mi><mi>G</mi><mn>5</mn><mi>G</mi><mi>E</mi><mi>R</mi></mstyle></mrow><annotation encoding="application/x-tex">\Large BG5GER</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.984em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.05017em;">B</span><span class="mord mathnormal sizing reset-size6 size8">G</span><span class="mord sizing reset-size6 size8">5</span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.05764em;">GE</span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.00773em;">R</span></span></span></span></span></p><p>网上查了很多资料，含有字母的篆刻作品凤毛麟角，大多是被看作“一个妙手偶得的小创意”，严肃的刻法鲜有人研究。于是转而向英语世界查询，关键词“letter curving”，果然在“影子图书馆”里搜到了一些资料，其中最为详尽的莫过于这本Tom Perkins所撰的 <em>The Art Of Letter Carving In Stone</em>，浏览罢，越发觉得书中有许多可以借用的方法，因而做此文来记录一些关键的内容。</p><p>书中分十一个章节，有背景、工具、石材、刻法、风格（罗马体、意大利体、字母与章法）、风格演绎、墓石、铭文布局方法等。本文重点关注有关风格三个章节，希望能对后来人篆刻英文字母的场景有所帮助吧。</p><blockquote><center>Our aim should be, I think, to make letters live... that men themselves may have more life.（斯人之志，在乎文字。其字不灭，其人存焉。）</center><p align="right">——Edward Johnston</p></blockquote><hr><table><thead><tr><th style="text-align:center"><img src="/images/20250610/%E8%A5%BF%E6%B4%8B%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251127203912727.webp" alt></th><th style="text-align:center"><img src="/images/20250610/%E8%A5%BF%E6%B4%8B%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251127205915382.webp" alt></th><th><img src="/images/20250610/%E8%A5%BF%E6%B4%8B%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251127205934785.webp" alt></th></tr></thead></table><h2 id="实践"><a class="markdownIt-Anchor" href="#实践"></a> 实践</h2><p>因为印面太小(不好画线)，印石太硬(不好下刀)，第一次尝试，刻地跟狗一样。<br><img src="/images/20250610/IMG_20251201_190211.jpg" alt="失败品(此印面已经磨平!)"><br><img src="/images/20250610/IMG_20251207_233736.jpg" alt></p><p><img src="/images/20250610/IMG_20251208_124337%201.jpg" alt></p><p><img src="/images/20250610/IMG_20251208_185822.jpg" alt></p><h2 id="历史"><a class="markdownIt-Anchor" href="#历史"></a> 历史</h2><p>在工业革命后，手工艺，在世界各地都会迟早会被大机器所取代，刻字亦是如此，得益于的诸多能工巧匠的努力，刻字得以在二十世纪艰难地传承下去。英国的刻字业比较发达，很多手工艺人都来自英国。</p><p>Eric Gill派。祖师Gill，师从Edward Jhonson，一开始是采用凿边的方式刻字，后面全部使用铅笔勾线而后描刻，其助手、后辈多沿用其风格。作为大师级人物。盖尔对制作行为的评论很有意义，他认为创作本身并不是达尔文式的生存竞争，而是对世界的爱。在此引述：</p><blockquote><p>…the most important motive for man’s activity in doing or making are neither animal instincts nor caprice. We hold that love is more important and not merely prettier than instinct. Upon such a ground and from such a place of vantage we survey the works of men. We see all things as evidence of love. We make what we love – in accordance with our love so we make. A pair of scissors, no less than a cathedral or a symphony is evidence  of what we hold good and therefore lovely, and owes its being to love.（…人类做事或做人的最重要动机既不是动物的本能，也不是任性。我们认为，爱比本能更重要，而不仅仅是漂亮。在这样的基础上，从这样的视角出发，我们审视人类的作品。我们将万物视为爱的证据。我们创造我们所爱–根据我们的爱，我们创造。一把剪刀，不亚于一座大教堂或一首交响乐，都是我们所认为的美好事物的证据，因此是可爱的，它的存在归功于爱。）</p></blockquote><p>下面几位实验性大师作品<br><img src="/images/20250610/%E8%A5%BF%E6%B4%8B%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251127205955249.webp" alt><br><img src="/images/20250610/%E8%A5%BF%E6%B4%8B%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251127210217229.webp" alt><br><img src="/images/20250610/%E8%A5%BF%E6%B4%8B%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251127210306482.webp" alt></p><h2 id="工具"><a class="markdownIt-Anchor" href="#工具"></a> 工具</h2><p>同咱们篆刻一样，刻字的工具也非常简单，不过是刻刀变成了凿子，又多了一个木槌。<br><img src="/images/20250610/%E8%A5%BF%E6%B4%8B%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251127210952279.webp" alt></p><ol><li>刻字槌。重约一斤左右，手柄材质白蜡木，头部用圆形铸铁做成。刻如花岗岩等硬质石头时槌子越重越方便，也可用回火马氏体钢。刻时用边缘敲击凿子。</li><li>凿子。分钢凿与钨凿，前者适合砂岩、石灰岩，后者适合花岗岩、大理石。还有如上图右侧的爪凿，用来给石面上增加质感。</li><li>画架。用来放置石板。</li></ol><table><thead><tr><th><img src="/images/20250610/%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251127224121547.webp" alt></th><th><img src="/images/20250610/%E8%A5%BF%E6%B4%8B%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251127212217566.webp" alt></th></tr></thead></table><h2 id="石材"><a class="markdownIt-Anchor" href="#石材"></a> 石材</h2><p>英国四面环海，所取之石多来自地下的岩层，其质地较硬，难以用类似我国篆刻的方法来人力操刀手工刻制，所以采用了凿+槌的方法。主要石材按照岩石大类来分有</p><ol><li>Sedimentary（沉积岩）“<u>沉积岩由海床的水载沉积物和钙质沉积物堆积而成。</u>各种石灰岩，如波特兰石灰岩、德比郡霍普顿伍德地区的石灰岩以及牛津郡的蓝霍恩顿石灰岩都适合雕刻。约克石、苏格兰和坎布里亚红砂岩等砂岩类型也很适合。个别采石场也会推荐其他适合字母雕刻的石灰岩和砂岩，但在订购不熟悉的石材之前，最好先获取少量样本进行雕刻尝试，并说明是字母雕刻所需的石材，因为沉积岩的质量可能会有很大差异。”</li><li>Metamorphic （变质岩）“<u>变质岩是地表下经过高温或高压作用的沉积岩</u>。威尔士的蓝黑色板岩相对较软，非常耐用，可以雕刻出非常精细的字母。坎布里亚蓝黑色板岩和迷人的绿色板岩通常带有天然斑纹，也适合雕刻字母。绿色板岩比威尔士蓝黑色板岩更硬一些，初学者可能不太适合。德拉博尔板岩产自康沃尔郡，尤其是较小尺寸的板岩：除了天然巨石外，请查看是否有较大尺寸的板岩可用于字母雕刻。也有进口板岩，但其中一些在室外会漂白成浅灰颜色，因此最好注意这一点。以及来着意大利的白色大理石”</li><li>Igneous（火成岩）“火成岩是由地表下或地表上凝固的熔融物质形成的。其中，花岗岩是用于字母雕刻的主要岩石，主要产自康沃尔、威尔士和苏格兰等地，但也有许多种类的花岗岩是进口的。花岗岩是一种非常坚硬的和耐用的岩石。它需要专门用于非常坚硬岩石的凿子，不建议初学者使用。”</li></ol><h2 id="刻法"><a class="markdownIt-Anchor" href="#刻法"></a> 刻法</h2><p>书中文字毕竟局限，在看了一些视频后，对字母雕刻法有了直观的理解。</p><p>西洋字母雕刻中，首先是用在石头上勾线，用篆刻的术语就来说是上石。他们一般使用铅笔，将所需要的字母轮廓给画出来，也有用复写纸描摹现成字体的。其字母轮廓一般是衬线(Serif)字，横向拉伸，纵向压缩。</p><p>下一步自然就是上手刻制了。原文大意如下：</p><blockquote><p>“通过凿头有节奏地敲击石模，凿子在石料中舒适地向前移动，而不会卡住。这种无障碍的移动是通过找到正确的角度来实现的，首先是凿柄的整个长度与石材表面的角度，其次是凿刃与石材表面的角度。凿柄与石材表面的夹角应该较浅。如果角度太陡，凿刃可能会卡在石材上；如果角度太浅，凿子可能会在石材上打滑。凿子边缘与石材表面的角度应为 45 度左右，这与 90 度截面的 V 形切割所需的角度一致。”<br>“从一个行程的一端到另一端的雕刻被称为 “经过(‘<strong>pass’</strong>)”，要雕刻一个完整的 V 形截面，必须在行程的两侧交替经过若干次。用凿子轻轻敲击凿头的规律性动作会在石头上留下一个个小台阶、其规律性将反映出攻丝的规律性。通过小幅度、有规律的连续敲击可以最大限度地控制凿子，每次敲击的距离大约为 10 毫米（3⁄8 英寸）。”<br>“一旦你能通过追切相当成功地刻画出一个形状，就可以尝试劈切(Chopping)技术了。这样可以更快、更有效地从 V 形切割中取出更多的石材。凿柄的整个长度与石材表面的夹角比凿刻要陡。为了形成 90 度的 V 形截面，凿子边缘与石材表面的夹角仍然约为 45 度，并斜向下进入 V 形切口的底部。然后在整个雕刻过程中重复这一动作，与凿刻法一样，在 V 形切口的两侧交替进行。”</p></blockquote><p>类比篆刻刀法。其步骤相当于先进行一次沿着笔画方向的冲刀，而后用细碎的切刀，沿着冲刀的两侧往中间切，最后用冲刀把切刀的痕迹给冲平，来获得一个完美的刻痕。西洋字母雕刻是直接展示用的，因而对刻痕的要求也很高，不像篆刻只看铃印效果，哪管刻痕怎样<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>。<br><img src="/images/20250610/%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251127223754451.webp" alt></p><h2 id="风格"><a class="markdownIt-Anchor" href="#风格"></a> 风格</h2><p>西洋字母就26个，笔画很少，风格变化也不大。设计师甚至可以精心定义每一个字母的大小比例，每一根线的粗细，这是依托汉字的篆刻所远远无法想象的。</p><p>其风格主要有罗马体与意大利体：</p><h3 id="罗马字"><a class="markdownIt-Anchor" href="#罗马字"></a> 罗马字</h3><p>罗马大写字在现在叫做Trajan，其设计师是Carol Twombly，灵感取自罗马遗迹<strong>图拉真柱</strong>，是一个非常之经典的字体。奇怪的是，这罗马帝国的柱子是公元113年立起来的，而这个时间刚好是我国的汉朝，也就是篆刻最为兴盛的时期。似乎这个时期大家都在玩石刻，或许是铁器时代的一个潮流吧。<img src="/images/20250610/%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251127225917720.webp" alt="中西历史时期对照表(节选)（陈会林编制）">如前所述，罗马字的设计要求非常严苛。字母形状和比例、字干宽度与字母高度之间的关系（简称字重）、字干、粗斜线和细斜线以及曲线之间的相对宽度等等都有明确的要求。</p><ol><li>字重：一般而言，以字母“I”的宽长比来判定，其宽为一，其长越小，则字越重，其长越长则，字越轻。大写字宽长比一般在<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo>:</mo><mn>8</mn></mrow><annotation encoding="application/x-tex">1:8</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">8</span></span></span></span>到<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo>:</mo><mn>10</mn></mrow><annotation encoding="application/x-tex">1:10</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">10</span></span></span></span>，小写字母在<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo>:</mo><mn>5</mn></mrow><annotation encoding="application/x-tex">1:5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">5</span></span></span></span>到<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo>:</mo><mn>6</mn></mrow><annotation encoding="application/x-tex">1:6</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">:</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">6</span></span></span></span>左右。如果刻制在对比度较低的石面上时，应适当增加字重。</li><li>字宽：字母主体部分的宽度，如字母&quot;a&quot;</li><li>弧度：字母最厚处的弧形部分通常比字干的中部重一些。笔直的字干中部由于略微凹陷，比顶部和底部窄一些。字母最薄部分的弧度是渐变的，通常比半个字杆宽度要薄一些。</li><li>竖画：“粗竖画的顶部和底部巧妙地向外延伸，并以水平方向绘制的细衬线作为末端。如下图所示，这些衬线形状微妙–粗画底部的水平衬线两侧略微抬离基线，中间略微抬起，呈双椭圆形。粗画顶部的衬线也遵循同样的概念，两侧向顶线略微倾斜，中间略微倾斜，形成双椭圆形。</li><li>衬线：字母横画的衬线大部分是垂直的，或者微微翘起。<img src="/images/20250610/%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251128212924136.webp" alt="衬线的细节"><br>下面是各部分字体详细的介绍，第一组：</li></ol><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mi>H</mi><mtext> </mtext><mi>T</mi><mtext> </mtext><mi>U</mi><mtext> </mtext><mi>X</mi><mtext> </mtext><mi>Y</mi><mtext> </mtext><mi>N</mi><mtext> </mtext><mi>Z</mi><mtext> </mtext><mi>A</mi><mtext> </mtext><mi>V</mi></mstyle></mrow><annotation encoding="application/x-tex">\Large H\ T\ U\ X\ Y\ N\ Z\ A\ V</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.984em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.08125em;">H</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.13889em;">T</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.10903em;">U</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.07847em;">X</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.22222em;">Y</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.10903em;">N</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.07153em;">Z</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8">A</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.22222em;">V</span></span></span></span></span></p><p>为了方便起见，这组字母可以称为矩形字母，因为它们可以拼成一个矩形，矩形的面积与相同高度的圆的面积相同。从圆的两边向内测量字母高度的十分之一，就可以得到这个矩形。如字母的高度为 4 厘米，那么矩形的宽度就是 3.2 厘米。适合填入矩形的字母是 “H”、“T”、“U”、“X”、“Y”、&quot;N &quot;和 “Z”。A &quot;和 &quot;V &quot;的宽度比矩形稍宽，但没有包含圆形的正方形宽。为确保准确性，所有第 1 组字母最初都应按图示绘制矩形和圆形辅助线。其字干的宽度约为长度的八分之一，两侧略微有凹陷。<br><img src="/images/20250610/%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251128202948863.webp" alt></p><ul><li>字母 &quot;H &quot;的绘制方法是先画左横线，再画右横线，记住中间要比两端稍细，最后加上上下锯齿。一般的光学原理是，如果要在中间高度显示某物，就必须将其略微抬高，因此 &quot;H &quot;横线的底边要放在中心线上。水平笔画的宽度约为垂直笔画的一半。<br><img src="/images/20250610/%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251128205056544.webp" alt></li><li>T：字母 &quot;T &quot;的词干与 &quot;I &quot;相同，通常画在顶部横线之前，宽度与 &quot;H &quot;相同（忽略 &quot;H &quot;的衬线）。有时，<u>&quot;T &quot;的横线会从顶线向下略微移动</u>，以在视觉上弥补横线过长的缺陷，并防止其看起来比其他字母高。横线两端的衬线或多或少保持垂直，在横线下方衬线突起多于上方。</li><li>U：字母 &quot;U &quot;的宽度与 &quot;H &quot;相同。中点处的弧底厚度约为半个竖画宽度甚至更小，然后逐渐向两侧加宽，直至整个竖画宽度。底部弧线应始终略微穿过底线，以防止字母看起来比其他字母短。与 &quot;H &quot;一样，两个垂直笔画的顶部也要用衬线来修饰。</li><li>X：字母 &quot;X &quot;的底部宽度与 &quot;H &quot;相同，但上半部分略微压缩（非常小），从而为字母的下半部分创造了更多的空间，以防止字母看起来头重脚轻。这与提高 &quot;H &quot;横画高度（在中线之上）的原理相同，&quot;X &quot;交叉的横线也刚刚超过字母高度的一半。粗笔画通常先画，宽度与粗竖画相同。两端微微外撇，最后画上细细的横衬线。注意粗细对角线与底层矩形的起止位置。细对角线的宽度约为竖画的一半，两端微微外扩，以细衬线结束。<br><img src="/images/20250610/%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251128210727166.webp" alt></li><li>Y：字母 &quot;Y &quot;的顶部宽度与 &quot;H &quot;相同，V 部分与笔杆的交界处位于高度中间。重要的是要确保对角线笔画与两侧的笔杆连接在同一高度。从 &quot;Y &quot;开始，将短的垂直笔杆画到高度的中心，在底部稍稍外扩，最后在底部画上与 &quot;I &quot;相同的细衬线。然后绘制粗细对角线，分别为一个茎宽和半个茎宽，并在两端巧妙地外撇，最后以细的横衬线收尾。</li><li>N：字母 &quot;N &quot;的宽度与 &quot;H &quot;相同，不同之处在于竖线较窄，约为粗杆宽度的一半。先画左竖，再画右竖。注意它们略微凹陷，在中间高度处最细，最后是精细的横向衬线。粗对角线的宽度与粗画相同。对角线与垂直支撑的底部连接处有一个轻微的剪切点。重要的是要保持窄度，略小于细竖杆的宽度。</li><li>Z：字母 &quot;Z &quot;的底部宽度与 &quot;H &quot;相同，顶部略微位于矩形内。粗对角线的宽度相当于粗画，通常首先绘制，然后绘制顶部横线，宽度约为粗画的一半。横线的开口端巧妙地外撇，最后画上细小、略微倾斜、接近垂直的衬线。然后完成下横线的绘制，末端略微外扩，最后使用精细、略微倾斜的衬线，衬线可以尽量伸出矩形之外–注意底角的微妙圆角。</li><li>A：字母 &quot;A &quot;的底部比 &quot;H &quot;略宽，与 &quot;H &quot;不同的是，横线从中间向下移动，以平衡上下的空间。从左边的细对角线开始，宽度约为半个粗杆，然后是粗对角线，宽度为一个粗杆。两条对角线都向底部略微外扩，并以精细的横向衬线收尾。注意 &quot;A &quot;字的凿顶。最后，绘制横条，横条宽度为粗杆宽度的一半，位于中心下方。</li><li>V：字母 &quot;V &quot;的顶端宽度与 &quot;A &quot;的底端宽度相同，刚好伸出矩形之外。首先绘制粗对角线，宽度为粗竖线宽度。然后绘制细对角线，宽度为粗竖线的一半，两条对角线的笔画都在开口处巧妙地外撇，最后以细横线结束。注意底部交界处的窄凿尾，以及底部内侧略微偏离中心。</li></ul><p>第二组：O &quot;和 &quot;Q &quot;的外轮廓是略微扁平的圆形；“C”、&quot;G &quot;和 &quot;D &quot;的字母宽度比整个圆形小大约一个粗横宽。</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mi>O</mi><mtext> </mtext><mi>Q</mi><mtext> </mtext><mi>C</mi><mtext> </mtext><mi>G</mi><mtext> </mtext><mi>D</mi></mstyle></mrow><annotation encoding="application/x-tex">\Large O\ Q\ C\ G\ D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.264em;vertical-align:-0.28em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.02778em;">O</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8">Q</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.07153em;">C</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8">G</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.02778em;">D</span></span></span></span></span></p><p><img src="/images/20250610/%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251128211145353.webp" alt></p><ul><li>Q与O：字母 &quot;O &quot;和 &quot;Q &quot;从绘制外轮廓开始。重要的是，这两个字母要稍微切断上下两条线，使它们看起来与字母表的其他部分高度一致。因此，字母顶部和底部的弧形部分与上下线相切是一个普遍原则。虽然这些字母的外轮廓简单地按照圆形绘制会更容易，但将侧面稍稍削平会大大加强字母的形式。画完外轮廓后，再画内轮廓：这是一个略微方正的椭圆形，这样做是为了给字母制造垂直压力。也就是说，笔画最细的部分正好在垂直上方，而最粗的部分则在字母中间高度水平相对。在弧形字母上，笔画最粗的部分与粗干顶部或底部的宽度有关且相似，而不是粗干中部的宽度，后者更窄。弧形笔画最细处的宽度略小于粗画的一半。确保所有的曲线都由粗到细巧妙地渐变。对于 &quot;Q &quot;尾，在字母中间垂直画一条线。在与字母外轮廓相交处，从基线向下 25 度画一条线，然后在其上方再画一条线，宽度约为粗杆的一半，在与字母主体相接处略微变细，在尾部开口处略微外扩，在底部形成一条柔和的曲线。</li><li>C：与 &quot;O &quot;和 &quot;Q &quot;一样，字母 &quot;C &quot;的外轮廓线也是先画出来的，它是一个略微扁平的圆，略微穿过顶线和基线。在这种情况下，&quot;C &quot;的整体宽度是距圆形右边缘不到一个粗画宽，距圆形左边缘 2 毫米。内部方形椭圆的垂直轴与 &quot;O &quot;和 &quot;Q &quot;相同，最细的部分垂直排列，并向开口端微微外扩，最后形成细密的垂直衬线。要注意的是，底部的开口端在下侧变软，并在顶部稍稍停止。曲线的厚度与 &quot;O &quot;和 &quot;Q &quot;相同，顶部和底部的曲线同样被削平。</li><li>G：字母 &quot;G &quot;的宽度和形状与 &quot;C &quot;相同，只是多了一个竖杆。它的宽度和形状与粗竖杆的顶部相同，其高度是字母高度的一半或略低于一半。竖画的右侧与 &quot;G &quot;顶部曲线的末端垂直对齐。注意结尾处的低点，靠近底线，即底部曲线和<strong>竖画</strong>的交汇处。</li><li>D：字母 &quot;D &quot;的宽度与 &quot;C &quot;和 &quot;G &quot;相同，字母右侧距离圆圈右边缘 2 毫米，字母左侧距离圆圈左边缘不到一个粗杆宽度。先画出字杆，然后画出曲线的外轮廓，将曲线与圆稍稍拉平。最后绘制内曲线，与 “O”、“Q”、&quot;C &quot;和 &quot;G &quot;一样保持垂直压力，曲线宽度与这组字母中的其他字母相同。注意曲线在内侧底部与字母杆相接处的弧形连接，但在字母内侧顶部没有弧形连接。</li></ul><p>第三组：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mi>E</mi><mtext> </mtext><mi>F</mi><mtext> </mtext><mi>L</mi><mtext> </mtext><mi>P</mi><mtext> </mtext><mi>R</mi><mtext> </mtext><mi>B</mi><mtext> </mtext><mi>S</mi></mstyle></mrow><annotation encoding="application/x-tex">\Large E\ F\ L\ P\ R\ B\ S</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.984em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.05764em;">E</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.13889em;">F</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8">L</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.13889em;">P</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.00773em;">R</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.05017em;">B</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.05764em;">S</span></span></span></span></span></p><ul><li>字母 &quot;E &quot;是顶部半正方形的宽度，中臂稍短，底臂稍长。先画竖干，后画横基臂。底部笔画在紧靠竖画下方的基线上方略有移动，并在其开口端略微穿过基线，在该处将底角磨圆。衬线略微向右倾斜。中臂的下划线位于中线上，上划线高于中线半个粗杆宽度，中臂向开口端略微外扩，最后是一条细细的竖衬线。上臂的上部笔画是直的，上臂的下部笔画向上臂的开口端稍稍外扩，最后是一条向下突出的细竖衬线。所有横臂约为半个粗杆宽。</li><li>字母 &quot;F &quot;与 &quot;E &quot;相似，只是下臂位置降低了半个水平臂的厚度。这略微增加了顶部空间，以平衡开放的底部空间。  字母’L’的阀杆和底臂与’E’相同。</li><li>字母 &quot;P &quot;先画出柄，然后画出碗的外侧，碗的外侧比半圆略宽，比圆形略扁。碗底低于字母高度的中部。接着画碗的内侧，笔画保持垂直。碗的弧形笔画最宽处的厚度与笔杆顶端的厚度相同；碗的细横与 &quot;E &quot;的臂部厚度相同（即笔杆竖向宽度的一半或略少）。确保弧线由粗到细的微妙渐变，弧线在距离主茎不远处的一点结束。</li><li>字母 &quot;R &quot;与 &quot;P &quot;一样，先画出茎，然后画出碗的外轮廓，比例与 &quot;P &quot;相同。碗的内轮廓与 &quot;P &quot;一样，也有垂直应力。碗与杆的连接处有一个横向构件，厚度约为粗杆的一半，其上部笔画位于字母高度的中线上，下部笔画位于粗杆宽度的一半或稍小的下方（即与上部横向构件的厚度相同）。对于 &quot;R &quot;的尾部，从碗的边缘到基线画一条垂直线，然后用一条线连接到笔杆的左上角。这就是 &quot;R &quot;尾的下笔。上部笔画是一个竖画宽，尾部向开口端略微外扩，下部巧妙地呈圆形，最后以细横衬线收尾。注意尾部内侧没有衬线。</li><li>字母 &quot;B &quot;也是先绘制其横画，然后绘制顶部碗圆弧的外侧（与 &quot;P &quot;和 &quot;R &quot;的形状相同，但要小一些–适合半正方形的宽度。然后用垂直压力绘制内轮廓。B &quot;上圆弧的厚度和渐变与 &quot;P &quot;和 &quot;R &quot;有关。注意中横的下笔在字高的中线上，上笔略高于半个竖画宽。B &quot;下粗茎的内侧弧线与半格的宽度相吻合，外侧轮廓的绘制是为了使碗的弧形笔画的最大厚度与上碗的宽度相同。请注意 &quot;D &quot;的微妙弧度，在底横的上撇与茎相交处。三条横线的厚度相同，大约是半个竖画宽。</li><li>字母 &quot;S &quot;和 &quot;B &quot;一样，上半部分的空间略小于下半部分。对角线是一个竖画宽，在顶部和底部逐渐变细为水平曲线，略小于半个竖画宽，并巧妙地向开口的两端延伸。两端以垂直衬线收尾（从上臂下降，从下臂上升）。上臂和下臂分别略微穿过顶线和基线，以使 &quot;S &quot;看起来与其他字母高度一致。S &quot;在右侧垂直排列，而在左侧，尾部略微超出顶部。</li><li>字母 &quot;K &quot;与第 3 组中的其他字干不同，因为它的右侧与半方格的左侧边缘重合，使得 &quot;K &quot;比这一组中的其他字母宽一些。先画字干，再画粗对角线（宽度为一个粗字干），其上部笔画的起笔刚好触及字干高度的一半。尾部超出半个正方形，底部呈非常巧妙的圆角，最后是一条细细的横衬线，仅向笔画右侧延伸。字母顶部的细对角线画在最后，宽度是粗杆的一半。它的右侧笔画刚好伸出半方格的右上角。细对角线的末端是一条向左延伸的细横衬线，再稍稍向右延伸。第四组：</li></ul><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mstyle mathsize="1.44em"><mi>M</mi><mtext> </mtext><mi>W</mi><mtext> </mtext><mi>I</mi><mtext> </mtext><mi>J</mi></mstyle></mrow><annotation encoding="application/x-tex">\Large M\ W\ I\ J</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.984em;"></span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.10903em;">M</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.13889em;">W</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.07847em;">I</span><span class="mspace sizing reset-size6 size8"> </span><span class="mord mathnormal sizing reset-size6 size8" style="margin-right:0.09618em;">J</span></span></span></span></span></p><ul><li>字母 &quot;M &quot;以正方形开头。标出基线和顶线的中点。画粗对角线（一个竖画宽），从正方形左上角内半茎宽的左边笔画开始，一直画到底线中点。然后绘制细对角线（半竖画宽），从正方形右上角内侧半茎宽处开始。注意，V 字形的内点将位于中心的右侧。从正方形的左上角内侧（粗斜线的起点）到左下角，绘制细的左支撑（半个竖画宽）–它向底部略微外扩，以细的横衬线结束。最后，绘制右侧的粗支撑，宽度与粗对角线相同（即粗杆宽度）。它在右上方刚好伸出正方形外，在右下方稍稍外扩，最后以细横衬线结束。需要注意的是，粗细笔画都有微妙的凹陷，就像竖茎一样，顶部的横衬线也没有凸出 V 字段。底部的两个计数器（字形内部的空白处，可以是 &quot;B &quot;中的封闭式，也可以是 &quot;C &quot;中的半开放式）的宽度应相等。</li><li>字母 &quot;W &quot;的起笔是一个圆形和周围的正方形，并将其分成四等分的竖条。画出的 &quot;V &quot;是前三部分的宽度，粗笔画是一个粗杆的宽度，顶部以细横线结束。然后画出宽度为粗杆一半的细对角线。基点被剪掉。为了画出 &quot;W &quot;的第二个 “V”，在主方格的右边再加上两条竖线，这样整个图的宽度就变成了六个相等的部分。粗对角线的左侧从第三部分的一半开始，一直延伸到第四部分的末端。第二个 &quot;V &quot;字的细对角线（不包括衬线）的顶端大约从第六部分顶端的一半处开始。确保两条粗对角线宽度相同且平行，两条细对角线宽度相同且平行。顶部中心剪切点要比底部两个剪切点宽。</li><li>字母 &quot;I &quot;是一个简单的字干，与该字母表中所有粗字干一样，两端微微外撇，从而产生一个轻微的凹面，在 &quot;腰部 &quot;形成一个微妙的收窄。顶部和底部的细横衬线呈微妙的弧形</li><li>字母’J’的宽度与’I’相同，但在底部变细至半个竖画宽，刚好穿过基线，并向开口端稍稍外扩，最后呈现出与’S’底部类似的细竖衬线。在第二个 &quot;J &quot;的例子中，茎干逐渐变细，直至远远低于基线。</li></ul><p><img src="/images/20250610/%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251128213602783.webp" alt="小写示例"><br><img src="/images/20250610/%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251128213800994.webp" alt="数字示例"></p><h3 id="意大利体"><a class="markdownIt-Anchor" href="#意大利体"></a> 意大利体</h3><p>从略</p><h2 id="其他"><a class="markdownIt-Anchor" href="#其他"></a> 其他</h2><p><img src="/images/20250610/%E5%AD%97%E6%AF%8D%E9%9B%95%E5%88%BB%E7%AC%94%E8%AE%B0-20251128213942703.webp" alt="各种衬线设计"></p><hr class="footnotes-sep"><section class="footnotes"><ol class="footnotes-list"><li id="fn1" class="footnote-item"><p>白文大多不管，有些朱文的刻痕也是会考究一点的。 <a href="#fnref1" class="footnote-backref">↩︎</a></p></li></ol></section>]]></content>
    
    
    <summary type="html">关于西洋字母雕刻工艺的粗浅研究</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/NoteOfLetterCarvingInStone.svg" type="image"/>
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
    <category term="✂️手工制作" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%9C%82%EF%B8%8F%E6%89%8B%E5%B7%A5%E5%88%B6%E4%BD%9C/"/>
    
    
  </entry>
  
  <entry>
    <title>mysql子查询</title>
    <link href="https://blog.si-on.top/2025/sql_subquery_in_a_nutshell/"/>
    <id>https://blog.si-on.top/2025/sql_subquery_in_a_nutshell/</id>
    <published>2025-11-19T07:43:53.000Z</published>
    <updated>2025-11-19T07:43:53.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p>厂内MES系统上线前后，因为开发人员紧缺，作为关键用户之一，也跟着学了一些SQL，开发维护了一些报表。今日遇到一个棘手的连接，在此记录一下。</p><h2 id="问题分析"><a class="markdownIt-Anchor" href="#问题分析"></a> 问题分析</h2><p>系统中数据库里几个关键的表如下，其中<u>数据收集结果</u>与<u>工单工序的出料</u>通过前者的<code>so_router_step_out_id</code>与后者的<code>id</code>进行连接。</p><ol><li>数据收集结果(data_collection_result)<ol><li>操作条件(dcr_operation_condition)</li><li>尺寸检验(dcr_operation_condition)</li><li>表面缺陷(dcr_surface_defect)</li><li>过程检验(dcr_process_inspect)</li><li>加工记录(dcr_process_record)</li></ol></li><li>工单(so)<ol><li>工单工序(so_router_step)<ol><li>进料(so_router_step_in)</li><li>出料(so_router_step_out)</li><li>退料(so_router_step_rp)</li></ol></li><li>销售订单行(so_sale_order_item)</li><li>成品要求(so_final_req)</li></ol></li></ol><p>每次工序进行一次生产后，会记录以上数据，现在需要计算一个折合产量的指标，要求如下：</p><ul><li>一次产出合宽(<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>W</mi><mi>t</mi></msub></mrow><annotation encoding="application/x-tex">W_t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>)：根据工单&gt;工单工序&gt;出料(多行)里的宽度（<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>W</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">W_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>）与限重次数(<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>C</mi><mi>k</mi></msub></mrow><annotation encoding="application/x-tex">C_k</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0715em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>)计算：通过不同限重来划分一次产出，计算一次产出下宽度的合宽(<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>k</mi></msubsup><msub><mi>W</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\sum_{i=1}^k W_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2887em;vertical-align:-0.2997em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.989em;"><span style="top:-2.4003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>)</li><li>连接(<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi><mi>o</mi><mi>n</mi><mi>n</mi><mi>e</mi><mi>c</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">Connect</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">C</span><span class="mord mathnormal">o</span><span class="mord mathnormal">nn</span><span class="mord mathnormal">ec</span><span class="mord mathnormal">t</span></span></span></span>)：将合宽返回到出料，作为一个属性加入到出料料行中</li></ul><h2 id="相关笔记"><a class="markdownIt-Anchor" href="#相关笔记"></a> 相关笔记</h2><p>经过查阅资料，发现SQL中可以通过子查询(Subquery)来实现类似的需求。子查询就是在正常查询的基础上嵌套一层，从该层里面进行查询。子查询时会先执行内层括号里的语句而后才执行外层的语句。这种方法原则上没有上限，可以无限嵌套🪆，然而套娃层数越多，查询效率越低。</p><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">select</span> a,</span><br><span class="line"><span class="keyword">from</span> (</span><br><span class="line"><span class="keyword">select</span> A1</span><br><span class="line"><span class="keyword">from</span> source</span><br><span class="line"><span class="keyword">where</span> a <span class="operator">&gt;</span> <span class="number">0</span>) <span class="keyword">as</span> <span class="keyword">table</span></span><br></pre></td></tr></table></figure><p><img src="/images/20250610/mysql%E5%AD%90%E8%BF%9E%E6%8E%A5-20251119180254204.webp" alt><br>根据子查询返回结果的行数，可以分为两种方式：标量子查询与关联子查询。</p><h3 id="标量子查询"><a class="markdownIt-Anchor" href="#标量子查询"></a> 标量子查询</h3><p>顾名思义，这个查询方式的特点就是返回一个唯一的结果，适用于返回诸如平均值、合格率、求和等数据集合的唯一值。因为是返回的唯一值，因而可以用到常数、列名等地方，来进一步的筛选。比如，用子查询查出来平均值，然后用Where语句去筛选出来大于小于平均值的数据，也可以用Group by、Havingf、Oeder by等语句里。</p><p>比如这是从14:00至今(19:00)，F产线出料的宽度值</p><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">SELECT</span> </span><br><span class="line">o.width</span><br><span class="line"><span class="keyword">FROM</span> so_router_step_out o</span><br><span class="line"><span class="keyword">where</span> o.start_date_time_lt <span class="operator">&gt;</span> <span class="string">&#x27;2025-11-19 14:00&#x27;</span></span><br><span class="line"><span class="keyword">GROUP</span> <span class="keyword">BY</span> o.id</span><br></pre></td></tr></table></figure><figure class="highlight txt"><figcaption><span>output</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br></pre></td><td class="code"><pre><span class="line">633</span><br><span class="line">600</span><br><span class="line">482</span><br><span class="line">612</span><br><span class="line">612</span><br><span class="line">612</span><br><span class="line">612</span><br><span class="line">612</span><br><span class="line">598</span><br><span class="line">482</span><br><span class="line">605</span><br><span class="line">617</span><br></pre></td></tr></table></figure><p>取大于平均值的数据，就可以这样操作：</p><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">SELECT</span> </span><br><span class="line">o.width</span><br><span class="line"><span class="keyword">FROM</span> so_router_step_out o</span><br><span class="line"><span class="keyword">where</span> o.start_date_time_lt <span class="operator">&gt;</span> <span class="string">&#x27;2025-11-19 14:00&#x27;</span> </span><br><span class="line"><span class="keyword">and</span></span><br><span class="line"> o.width <span class="operator">&gt;</span> </span><br><span class="line">(</span><br><span class="line"><span class="keyword">select</span> </span><br><span class="line"><span class="built_in">avg</span>(width) </span><br><span class="line"><span class="keyword">from</span> so_router_step_out </span><br><span class="line"><span class="keyword">where</span> start_date_time_lt <span class="operator">&gt;</span> <span class="string">&#x27;2025-11-19 14:00&#x27;</span> </span><br><span class="line">)</span><br><span class="line"><span class="keyword">GROUP</span> <span class="keyword">BY</span> o.id</span><br></pre></td></tr></table></figure><figure class="highlight txt"><figcaption><span>output</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line">633</span><br><span class="line">600</span><br><span class="line">612</span><br><span class="line">612</span><br><span class="line">612</span><br><span class="line">612</span><br><span class="line">612</span><br><span class="line">598</span><br><span class="line">605</span><br><span class="line">617</span><br></pre></td></tr></table></figure><h3 id="关联子查询"><a class="markdownIt-Anchor" href="#关联子查询"></a> 关联子查询</h3><p>标量子查询只能范围唯一的值，如果我们想要返回多个值，比如不同钢种的宽度平均值。就必须用到关联子查询了，还以今天14:00至今(19:20)，F产线出料的宽度值以及钢种的信息为例：</p><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">SELECT</span> </span><br><span class="line">o.width,</span><br><span class="line">o.steel_grade</span><br><span class="line"><span class="keyword">FROM</span> so_router_step_out o</span><br><span class="line"><span class="keyword">where</span> o.start_date_time_lt <span class="operator">&gt;</span> <span class="string">&#x27;2025-11-19 14:00&#x27;</span> </span><br><span class="line"><span class="keyword">GROUP</span> <span class="keyword">BY</span> o.id</span><br><span class="line"><span class="comment">-- 输出结果</span></span><br><span class="line"><span class="comment">-- 638301不锈钢</span></span><br><span class="line"><span class="comment">-- 603301不锈钢</span></span><br><span class="line"><span class="comment">-- 633301不锈钢</span></span><br><span class="line"><span class="comment">-- 600301B不锈钢</span></span><br><span class="line"><span class="comment">-- 482737复合性不锈钢</span></span><br><span class="line"><span class="comment">-- 612304不锈钢</span></span><br><span class="line"><span class="comment">-- 612304不锈钢</span></span><br><span class="line"><span class="comment">-- 612304不锈钢</span></span><br><span class="line"><span class="comment">-- 612304不锈钢</span></span><br><span class="line"><span class="comment">-- 612304不锈钢</span></span><br><span class="line"><span class="comment">-- 598301不锈钢</span></span><br><span class="line"><span class="comment">-- 482737复合性不锈钢</span></span><br><span class="line"><span class="comment">-- 605304不锈钢</span></span><br><span class="line"><span class="comment">-- 617301不锈钢</span></span><br><span class="line"><span class="comment">-- 616304不锈钢</span></span><br><span class="line"><span class="comment">-- 338304不锈钢</span></span><br><span class="line"><span class="comment">-- 331304不锈钢</span></span><br><span class="line"><span class="comment">-- 338304不锈钢</span></span><br><span class="line"><span class="comment">-- 331304不锈钢</span></span><br><span class="line"><span class="comment">-- 338304不锈钢</span></span><br><span class="line"><span class="comment">-- 331304不锈钢</span></span><br></pre></td></tr></table></figure><p>各个钢种的平均宽度如下：</p><figure class="highlight sql"><figcaption><span>平均值计算</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">select</span></span><br><span class="line"><span class="built_in">avg</span>(o1.width),</span><br><span class="line">o1.steel_grade</span><br><span class="line"><span class="keyword">from</span></span><br><span class="line">so_router_step_out <span class="keyword">as</span> o1</span><br><span class="line"><span class="keyword">where</span></span><br><span class="line">start_date_time_lt <span class="operator">&gt;</span> <span class="string">&#x27;2025-11-19 14:00&#x27;</span></span><br><span class="line"><span class="keyword">group</span> <span class="keyword">by</span></span><br><span class="line">o1.steel_grade</span><br><span class="line"><span class="comment">-- 600.0000301B不锈钢</span></span><br><span class="line"><span class="comment">-- 617.8000301不锈钢</span></span><br><span class="line"><span class="comment">-- 483.6923304不锈钢</span></span><br><span class="line"><span class="comment">-- 482.0000737复合性不锈钢</span></span><br></pre></td></tr></table></figure><p>这是使用标量子查询是会报错的，我们就必须采用关联子查询，与前者不同的是，关联子查询通过一个类似于<code>join</code>语句写法的<code>where</code>语句，将内层与外层的信息连接在一起，比如下例中内外层的<code>steel_grade</code>就是一个连接条件，（注意连接条件一定要写在内层中，写在外层的话作用域就变了，不会起效果。）</p><figure class="highlight sql"><figcaption><span>关联子查询</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">SELECT</span> </span><br><span class="line">o.width,</span><br><span class="line">o.steel_grade</span><br><span class="line"><span class="keyword">FROM</span> so_router_step_out o</span><br><span class="line"><span class="keyword">where</span> o.start_date_time_lt <span class="operator">&gt;</span> <span class="string">&#x27;2025-11-19 14:00&#x27;</span> <span class="keyword">and</span> o.width <span class="operator">&gt;=</span> </span><br><span class="line">(</span><br><span class="line"><span class="keyword">select</span></span><br><span class="line"><span class="built_in">avg</span>(o1.width)</span><br><span class="line"><span class="keyword">from</span></span><br><span class="line">so_router_step_out <span class="keyword">as</span> o1</span><br><span class="line"><span class="keyword">where</span></span><br><span class="line">start_date_time_lt <span class="operator">&gt;</span> <span class="string">&#x27;2025-11-19 14:00&#x27;</span> </span><br><span class="line"><span class="keyword">and</span></span><br><span class="line">o1.steel_grade <span class="operator">=</span> o.steel_grade</span><br><span class="line"><span class="keyword">group</span> <span class="keyword">by</span></span><br><span class="line">o1.steel_grade</span><br><span class="line">)</span><br><span class="line"><span class="keyword">GROUP</span> <span class="keyword">BY</span> o.id</span><br><span class="line"></span><br><span class="line"><span class="comment">-- 638301不锈钢</span></span><br><span class="line"><span class="comment">-- 633301不锈钢</span></span><br><span class="line"><span class="comment">-- 600301B不锈钢</span></span><br><span class="line"><span class="comment">-- 482737复合性不锈钢</span></span><br><span class="line"><span class="comment">-- 612304不锈钢</span></span><br><span class="line"><span class="comment">-- 612304不锈钢</span></span><br><span class="line"><span class="comment">-- 612304不锈钢</span></span><br><span class="line"><span class="comment">-- 612304不锈钢</span></span><br><span class="line"><span class="comment">-- 612304不锈钢</span></span><br><span class="line"><span class="comment">-- 482737复合性不锈钢</span></span><br><span class="line"><span class="comment">-- 605304不锈钢</span></span><br><span class="line"><span class="comment">-- 616304不锈钢</span></span><br></pre></td></tr></table></figure><p>从实际的作用来看，关联子查询与group by的作用是相近的，都是通过一些方法对数据进行了切分。</p><h2 id="问题解决"><a class="markdownIt-Anchor" href="#问题解决"></a> 问题解决</h2><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">select</span></span><br><span class="line">i.id,</span><br><span class="line">o.width <span class="keyword">as</span> widthtotal</span><br><span class="line"><span class="keyword">from</span> so_router_step m</span><br><span class="line"><span class="keyword">left</span> <span class="keyword">join</span> so_router_step_in i <span class="keyword">on</span> i.detail_table_id <span class="operator">=</span> m.id </span><br><span class="line"><span class="keyword">left</span> <span class="keyword">join</span> so_router_step_out o <span class="keyword">on</span> o.detail_table_id <span class="operator">=</span> m.id</span><br><span class="line"><span class="keyword">where</span> m.resource <span class="operator">=</span> <span class="string">&#x27;740755479873064960&#x27;</span> </span><br><span class="line"><span class="keyword">group</span> <span class="keyword">by</span> i.id </span><br></pre></td></tr></table></figure><p>通过限重次数(xz_times)与进料id进行分组计算，通内层关联子查询连接合宽，然后借由限重与id两者连接到外层。如果为NULL则返回原有宽度(CASE)实现。</p><figure class="highlight sql"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">SELECT</span> </span><br><span class="line">    i.id <span class="keyword">AS</span> 进料id,</span><br><span class="line">    o.id <span class="keyword">AS</span> 出料id,</span><br><span class="line">    o.sfc <span class="keyword">AS</span> 出料钢卷号,</span><br><span class="line">    o.batch <span class="keyword">AS</span> 出料批次号,</span><br><span class="line">    o.xz_times <span class="keyword">AS</span> 限重次数,</span><br><span class="line">    o.width <span class="keyword">AS</span> 出料宽度,</span><br><span class="line">    <span class="keyword">CASE</span> </span><br><span class="line">        <span class="keyword">WHEN</span> o.xz_times <span class="keyword">IS</span> <span class="keyword">NULL</span> <span class="keyword">THEN</span> o.width</span><br><span class="line">        <span class="keyword">ELSE</span> (</span><br><span class="line">            <span class="keyword">SELECT</span> <span class="built_in">SUM</span>(o2.width) </span><br><span class="line">            <span class="keyword">FROM</span> so_router_step_out o2</span><br><span class="line">            <span class="keyword">JOIN</span> so_router_step_in i2 <span class="keyword">ON</span> i2.detail_table_id <span class="operator">=</span> o2.detail_table_id</span><br><span class="line">            <span class="keyword">WHERE</span> i2.id <span class="operator">=</span> i.id <span class="keyword">AND</span> o2.xz_times <span class="operator">=</span> o.xz_times</span><br><span class="line">        )</span><br><span class="line">    <span class="keyword">END</span> <span class="keyword">AS</span> 一次产出合宽</span><br><span class="line"><span class="keyword">FROM</span> so_router_step m</span><br><span class="line"><span class="keyword">LEFT</span> <span class="keyword">JOIN</span> so_router_step_in i <span class="keyword">ON</span> i.detail_table_id <span class="operator">=</span> m.id </span><br><span class="line"><span class="keyword">LEFT</span> <span class="keyword">JOIN</span> so_router_step_out o <span class="keyword">ON</span> o.detail_table_id <span class="operator">=</span> m.id</span><br><span class="line"><span class="keyword">WHERE</span> m.resource <span class="operator">=</span> <span class="string">&#x27;740755479873064960&#x27;</span> </span><br><span class="line"><span class="keyword">GROUP</span> <span class="keyword">BY</span> o.id</span><br><span class="line"><span class="keyword">ORDER</span> <span class="keyword">BY</span> i.id, o.xz_times;</span><br></pre></td></tr></table></figure><h2 id="in与exist的区别"><a class="markdownIt-Anchor" href="#in与exist的区别"></a> in与exist的区别</h2><ol><li><code>IN</code> 的子查询是独立的，无法引用外部表的列</li><li><code>EXISTS</code>可以做<strong>关联子查询</strong></li><li>当你需要在子查询中关联外部表时，就应该用 <code>EXISTS</code> 或 <code>JOIN</code></li></ol>]]></content>
    
    
    <summary type="html">sql子查询相关笔记以及合宽问题的解决。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/subquery.svg" type="image"/>
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
    <category term="⌨️软件编程" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%8C%A8%EF%B8%8F%E8%BD%AF%E4%BB%B6%E7%BC%96%E7%A8%8B/"/>
    
    <category term="SQL" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%8C%A8%EF%B8%8F%E8%BD%AF%E4%BB%B6%E7%BC%96%E7%A8%8B/SQL/"/>
    
    
    <category term="现学现卖" scheme="https://blog.si-on.top/tags/%E7%8E%B0%E5%AD%A6%E7%8E%B0%E5%8D%96/"/>
    
  </entry>
  
  <entry>
    <title>业余无线电笔记</title>
    <link href="https://blog.si-on.top/2025/ham_note/"/>
    <id>https://blog.si-on.top/2025/ham_note/</id>
    <published>2025-10-17T15:27:56.000Z</published>
    <updated>2026-03-05T07:15:56.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><blockquote><ol class="series-items"><li><a href="/2025/ham_note/" title="业余无线电笔记">业余无线电笔记</a></li><li><a href="/2026/Antenna_DIY/" title="天线制作笔记">天线制作笔记</a></li></ol></blockquote><details class="folding-tag" green><summary> ✍文章痕迹 </summary>              <div class="content">              <div class="timeline  green"><div class="timeline-item headline">        <div class="timeline-item-title">          <div class="item-circle"><p>写作时间线</p></div>        </div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-10-07</p></div>        </div>        <div class="timeline-item-content"><blockquote><p><a href="https://corner.si-on.top/notes/adk91356m5oi0016"> 偶然间翻到了本《业余无线电通信》，看书里一步步介绍业余无线电从民国发展到现在，蛮激动的，有空也整一个玩儿。</a></p></blockquote></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-10-13</p></div>        </div>        <div class="timeline-item-content"><p>绘制封面《<a href="https://corner.si-on.top/notes/adsmo0g7qn0l004r">秉台</a>》<br><img src="/images/Cover/humnote.svg" alt></p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-10-21</p></div>        </div>        <div class="timeline-item-content"><p>业余无线电操作证考试<a href="https://corner.si-on.top/notes/ae43i9kwxhw3001l">报名成功</a>，11-16考试，正式开始撰写此文。</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-10-30</p></div>        </div>        <div class="timeline-item-content"><p>刷完683道题</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-11-9</p></div>        </div>        <div class="timeline-item-content"><p><s>参考<a href="https://github.com/jks-liu/zhihu/blob/master/ham-license-type-a.md">此文章</a>，进行笔记初次汇总</s> （此笔记错漏颇多，放弃之）</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-11-13</p></div>        </div>        <div class="timeline-item-content"><p>购买泉盛UV-K5</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-11-15</p></div>        </div>        <div class="timeline-item-content"><p>下午14:57 完成全部草稿撰写。</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-11-16</p></div>        </div>        <div class="timeline-item-content"><p>下午13:40，结束考试(估计是满分40)<br><img src="/images/20250610/Screenshot_2025-11-16-23-33-21-350_com.microsoft.emmx-edit.jpg" alt></p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-11-20</p></div>        </div>        <div class="timeline-item-content"><p>成绩合格，本文进入实践阶段。在群友帮助下，初次设置好丰山中继，并收到回波。<br>(报考B证日期在5.20日)</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-11-21</p></div>        </div>        <div class="timeline-item-content"><p>操作证下来了，晚上提交了电台登记~~“子虚站”~~(被打回去修改成“田欣洋的电台”)</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-11-22 20:00~21:20</p></div>        </div>        <div class="timeline-item-content"><p>第一次守听本地台网点名活动</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-11-28</p></div>        </div>        <div class="timeline-item-content"><p><a href="https://www.qrz.com/db/BG5GER">申请</a><a href="http://QRZ.COM">QRZ.COM</a></p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-11-29</p></div>        </div>        <div class="timeline-item-content"><ul><li>收到操作证卡片</li><li>首次参与宁波周六例行的台网点名活动。</li></ul></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-12-8 刻呼号印</p></div>        </div>        <div class="timeline-item-content"><p><img src="/images/20250610/IMG_20251208_185822.jpg" alt></p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-12-9</p></div>        </div>        <div class="timeline-item-content"><p><a href="https://forum.hamcq.cn/u/9553">注册</a>Hamcq社区</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2026-2-5</p></div>        </div>        <div class="timeline-item-content"><p>提交年报：C:\Users\siont_bhvhgz1\OneDrive\Public\DOCS\业余无线电</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2026-3-5</p></div>        </div>        <div class="timeline-item-content"><p>购买RTL-SDR V4，成功配置好RTL-SDR收听到广播，完善笔记。</p></div>      </div></div><div class="markmap-container" style="height:300px">  <svg data="{&quot;type&quot;:&quot;root&quot;,&quot;depth&quot;:0,&quot;content&quot;:&quot;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[0,1]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%A5%94%E5%AD%90%E6%97%A0%E7%BA%BF%E7%94%B5%E6%8A%98%E8%85%BE%E5%BA%8F\&quot;&gt;楔子🦂：无线电折腾序&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[1,2]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%AE%9E%E8%B7%B5%E7%AF%87\&quot;&gt;实践篇&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[2,3]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E8%AE%BE%E5%A4%87%E9%80%89%E8%B4%AD\&quot;&gt;设备选购&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[3,4]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%9F%BA%E6%9C%AC%E6%93%8D%E4%BD%9C\&quot;&gt;基本操作&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[4,5]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%AE%88%E5%90%AC%E6%93%8D%E4%BD%9C\&quot;&gt;守听操作&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[5,6]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%B5%8B%E8%AF%95%E4%B8%AD%E7%BB%A7\&quot;&gt;测试中继&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[6,7]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E4%B8%AD%E7%BB%A7%E5%8F%B0%E7%82%B9%E5%90%8D\&quot;&gt;中继台点名&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[7,8]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E8%AE%BE%E8%AE%A1\&quot;&gt;设计&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[8,9]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%91%BC%E5%8F%B7%E5%8D%B0%E5%AE%8C%E6%88%90\&quot;&gt;呼号印（完成）&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[9,10]},&quot;content&quot;:&quot;&lt;a href=\&quot;#qsl%E5%8D%A1%E7%89%87%E6%9C%AA%E5%AE%8C%E6%88%90\&quot;&gt;QSL卡片（未完成）&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[10,11]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%80%9A%E8%81%94%E6%97%A5%E5%BF%97\&quot;&gt;通联日志&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[11,12]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E8%BD%AF%E4%BB%B6%E5%AE%9A%E4%B9%89%E6%97%A0%E7%BA%BF%E7%94%B5\&quot;&gt;软件定义无线电&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[12,13]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%A0%91%E8%8E%93%E9%85%8D%E9%85%8D%E7%BD%AErtl-sdr\&quot;&gt;树莓配配置RTL-SDR&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[13,14]},&quot;content&quot;:&quot;&lt;a href=\&quot;#windows%E4%B8%8A%E9%85%8D%E7%BD%AErtl-sdr\&quot;&gt;Windows上配置RTL-SDR&lt;/a&gt;&quot;,&quot;children&quot;:[]}]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[14,15]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%BA%94%E8%AF%95%E7%AF%87%E6%97%A0%E7%BA%BF%E7%94%B5%E7%AE%A1%E7%90%86%E7%9B%B8%E5%85%B3%E6%B3%95%E8%A7%84\&quot;&gt;应试篇：无线电管理相关法规&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[15,16]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%97%A0%E7%BA%BF%E7%94%B5%E5%8F%B0%E7%9B%B8%E5%85%B3\&quot;&gt;无线电台相关&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[16,17]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E7%AD%89%E7%BA%A7%E8%AF%81%E7%85%A7%E4%B8%9A%E4%BD%99%E6%97%A0%E7%BA%BF%E7%94%B5%E5%8F%B0%E6%93%8D%E4%BD%9C%E6%8A%80%E6%9C%AF%E8%83%BD%E5%8A%9B%E9%AA%8C%E8%AF%81%E8%AF%81%E4%B9%A6\&quot;&gt;等级证照(业余无线电台操作技术能力验证证书)&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[17,18]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%91%BC%E5%8F%B7%E7%9B%B8%E5%85%B3\&quot;&gt;呼号相关&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[18,19]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%97%A0%E7%BA%BF%E7%94%B5%E9%80%9A%E4%BF%A1%E8%A7%84%E5%AE%9A\&quot;&gt;无线电通信规定&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[19,20]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%A2%91%E6%AE%B5%E5%88%92%E5%88%86\&quot;&gt;频段划分&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[20,21]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E4%B8%9A%E5%8A%A1%E9%A2%91%E6%AE%B5%E8%AE%B0%E5%BF%86%E4%B8%93%E9%A2%98\&quot;&gt;业务频段记忆专题&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[21,22]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%A2%91%E6%AE%B5%E5%8D%A0%E7%94%A8%E4%B8%93%E9%A2%98%E6%9C%80%E5%90%8E%E6%AD%BB%E8%83%8C\&quot;&gt;频段占用专题（最后死背）&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[22,23]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E8%A7%84%E5%AE%9A%E4%B8%8E%E5%A4%84%E7%BD%9A\&quot;&gt;规定与处罚&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[23,24]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%9B%B6%E7%A2%8E\&quot;&gt;零碎&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[24,25]},&quot;content&quot;:&quot;&lt;a href=\&quot;#q%E7%AE%80%E8%AF%AD%E4%B8%93%E9%A2%98\&quot;&gt;Q简语专题&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[25,26]},&quot;content&quot;:&quot;&lt;a href=\&quot;#cq\&quot;&gt;CQ&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[26,27]},&quot;content&quot;:&quot;&lt;a href=\&quot;#qsl%E5%8D%A1%E7%89%87\&quot;&gt;QSL卡片&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[27,28]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E7%BC%A9%E7%95%A5%E8%AF%AD\&quot;&gt;缩略语&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[28,29]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%BA%94%E8%AF%95%E7%AF%87-%E6%8A%80%E6%9C%AF%E7%9B%B8%E5%85%B3\&quot;&gt;应试篇 技术相关&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[29,30]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E8%AE%A1%E7%AE%97%E4%B8%93%E9%A2%98\&quot;&gt;计算专题&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[30,31]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E4%BF%A1%E5%8F%B7%E8%AE%A1%E7%AE%97215\&quot;&gt;信号计算2.15&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[31,32]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E7%81%B5%E6%95%8F%E5%BA%A6%E8%AE%A1%E7%AE%97\&quot;&gt;灵敏度计算&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[32,33]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%95%9C%E5%83%8F%E5%B9%B2%E6%89%B0%E8%AE%A1%E7%AE%97%E6%AD%A3%E8%B4%9F%E4%B8%AD%E9%A2%91\&quot;&gt;镜像干扰计算(正负中频)&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[33,34]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%A4%A9%E7%BA%BF%E5%8A%9F%E7%8E%87%E8%AE%A1%E7%AE%97\&quot;&gt;天线功率计算&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[34,35]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%8F%AF%E7%94%A8%E9%A2%91%E7%8E%87%E5%8C%BA%E9%97%B4%E8%AE%A1%E7%AE%97\&quot;&gt;可用频率区间计算&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[35,36]},&quot;content&quot;:&quot;&lt;a href=\&quot;#dbm%E4%B8%8E%E5%8A%9F%E7%8E%87%E7%9A%84%E6%8D%A2%E7%AE%97\&quot;&gt;dbm与功率的换算：&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[36,37]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%AF%94%E8%BE%83%E4%B8%93%E9%A2%98\&quot;&gt;比较专题&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[37,38]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%8F%91%E5%B0%84\&quot;&gt;发射&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[38,39]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%A4%A9%E7%BA%BF\&quot;&gt;天线&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[39,40]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E7%A1%AC%E4%BB%B6\&quot;&gt;硬件&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[40,41]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%94%B6%E5%8F%91%E4%BF%A1%E6%9C%BA\&quot;&gt;收发信机&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[41,42]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%A6%88%E7%BA%BF%E4%B8%8E%E5%90%8C%E8%BD%B4%E7%94%B5%E7%BC%86\&quot;&gt;馈线与同轴电缆&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[42,43]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E8%B0%83%E5%88%B6%E5%99%A8%E6%B7%B7%E9%A2%91%E5%99%A8%E4%B8%8E%E6%BB%A4%E6%B3%A2%E5%99%A8\&quot;&gt;调制器、混频器与滤波器&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[43,44]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%9E%81%E5%8C%96%E6%96%B9%E5%BC%8F\&quot;&gt;极化方式&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[44,45]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E4%BF%A1%E5%8F%B7%E5%B9%B2%E6%89%B0%E4%B8%8E%E8%B6%85%E8%B7%9D%E7%A6%BB%E4%BC%A0%E6%92%AD\&quot;&gt;信号干扰与超距离传播&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[45,46]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%80%89%E6%8B%A9%E6%80%A7%E6%8C%87%E6%A0%87\&quot;&gt;选择性指标&lt;/a&gt;&quot;,&quot;children&quot;:[]}]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[46,47]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%BA%94%E8%AF%95%E7%AF%87%E6%97%A0%E7%BA%BF%E7%94%B5%E7%B3%BB%E7%BB%9F%E5%8E%9F%E7%90%86\&quot;&gt;应试篇：无线电系统原理&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[47,48]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E7%94%B5%E5%AD%90%E7%9B%B8%E5%85%B3\&quot;&gt;电子相关&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[48,49]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E4%B8%8E%E4%B8%9A%E4%BD%99%E6%97%A0%E7%BA%BF%E7%94%B5%E5%8F%B0%E6%9C%89%E5%85%B3%E7%9A%84%E5%AE%89%E5%85%A8%E9%98%B2%E6%8A%A4%E6%8A%80%E6%9C%AF\&quot;&gt;与业余无线电台有关的安全防护技术&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[49,50]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E7%94%B5%E7%A3%81%E5%85%BC%E5%AE%B9%E6%8A%80%E6%9C%AF%E4%BB%A5%E5%8F%8A%E5%B0%84%E9%A2%91%E5%B9%B2%E6%89%B0%E7%9A%84%E9%A2%84%E9%98%B2%E5%92%8C%E6%B6%88%E9%99%A4\&quot;&gt;电磁兼容技术以及射频干扰的预防和消除&lt;/a&gt;&quot;,&quot;children&quot;:[]}]}],&quot;payload&quot;:{}}"/></div>              </div>            </details><h2 id="楔子无线电折腾序"><a class="markdownIt-Anchor" href="#楔子无线电折腾序"></a> 楔子🦂：无线电折腾序</h2><p>吴道一在民国刊物《无线电》的发刊词中写道：“致知格物，扶幽阐微，科学家之目标；而无线电之运用，则今日成功之片段，出没穹苍大地，驰骋万里长空，目视之无形，而可借以传影，耳听之无声，而可借以传音，手触之无物，而可借以传力，所得之结果，一则维妙维肖，纤屑毕陈，一则不即不离，真伪莫辨，一则能大能小，操纵自如；以之宣扬文化，则人众从风，以之表演艺术，则万目共睹，以之控制机械，则得心应手。故有识之士，知其需要，仅次於粟帛水火，而宏用伟功，不胜枚举，遂相率殚精竭虑，潜心研究，期使诞生廿余年之事业，发扬光大，上阐造化之枢机，下慰众生之愿望。”</p><p>每一次呼叫都期待着回应。无线电，其趣味性远不同于摄影、篆刻、阅读之类，后者偏向内在，可独乐可众乐，前者则非众乐不可。它作为一种交流的手段，天生存在着交流的特点。如果玩下去，就意味着不断地与其他人进行交流，不管你有怎样的设备、天线，自制的、网购的、开源的、打印的等等等等折腾地怎样花哨，一但按下PPT键/电键后，所有的信息依托着电磁波传出去。如果没有远方的人反馈这个信号，就意味着没有闭环，看不到结果，是很烦人的。交流是及其重要的一部分，这也是Ham社区比其他爱好者社区更活跃、持久的原因所在。</p><p>这个集社交、手工、电气，乃至天气（大气波导）、太阳黑子活动（突发E层传播）、地理、攀岩、应急救援通信于一身的玩意儿，怎不值得一玩儿哩。</p><h2 id="实践篇"><a class="markdownIt-Anchor" href="#实践篇"></a> 实践篇</h2><h3 id="设备选购"><a class="markdownIt-Anchor" href="#设备选购"></a> 设备选购</h3><p>人类的肢体实在有限，折腾任何一门兴趣，贯注任何一种热情，除了少数借助体力、脑力得以自洽的之外，其余大多都是要借助于各种各样的工具。作为肢体的延展，工具越发成为人类存在最不可缺之物，如摄影离不开<a href="/2024/note4camera">相机镜头</a>、篆刻离不开<a href="/2024/tracting">石头刻刀</a>、涂鸦离不开<a href="/2023/Tuuuuuuu_001">喷漆</a>，对于无线电而言，其借助的工具则是一台趁手的电台了。</p><p>荀子言“学莫便乎近其人”，作为该领域的新手，得到设备方面经验最快的方法，自然也就是了解老手的经验了，听其口传，察其“身”授，然后再自己做总结、选择、实际使用。在查找资料、选购设备的过程中，首先是看了<a href="https://bg2fnv.top/">@BG2FNV</a>的<a href="https://www.bilibili.com/video/BV1SgZHYZEbP">《无线电入门II：设备推荐》</a>一视频，其中对手台的厂商、型号、数字标准都做了详尽的说明，很有帮助，让我大概锁定了设备的价格区间与型号。尽管在前人的帮助下避免了一部分弯路，但在购置之前，仍然不可避免地陷入了选择的漩涡。功能上的变动带来价格的差距几乎令人咂舌，同所有的工具一样，电台设备的价格与功能似乎也没有上限：</p><blockquote><p>“ 一开始只是想买个机器玩玩，看经典的宝锋 UV-5R 不错，才几十块钱有人说宝锋指标不好，不如上更经典的泉盛 UV-K6，也就一百块钱<br>…<br>有人说 891 毕竟是短波，A 证不能玩，而且操作反人类，不如来个全波段的 ICOM IC-705，找个代购也就 7000 多，于是入手了一台 UV 段的 ICOM IC-9700 和短波的 ICOM IC-7760，加上天线和配件一共才几万块钱，真不错”    — @<a href="https://forum.hamcq.cn/d/5275">BG4LZP的贴文</a></p></blockquote><p>在仔细考量本次业余无线电热情的持久程度、设备的吃灰概率后，入了一个大众的、性价比较高的、可玩性还行的泉盛UV-K6。这个设备非常热门，各种折腾教程层出不穷，甚至有爱好者专门搭建的<a href="https://k5.vicicode.com/">网站</a>，让我感觉它在手台中的地位几乎相当于阅读器中的Kindle。本文封面是在备考过程中绘制的，原型便是此设备。然而不巧的是，笔者买的是今年的新版本(京东官方140)，新版换了芯片，只有旧版本的固件才能刷机😭，如此便让可玩性降低了一大截。友台有157从拼多多购得加内存的改装版，建议直接买改装好的，可玩性更多。</p><p><img src="/images/20250610/%E4%B8%9A%E4%BD%99%E6%97%A0%E7%BA%BF%E7%94%B5%E8%83%BD%E5%8A%9B%E9%AA%8C%E8%AF%81%E8%80%83%E8%AF%95%E7%AC%94%E8%AE%B0(%E6%96%B0%E9%A2%98%E5%BA%93)-20251115220440718.webp" alt="黑色版泉盛UV-K6，原装天线"></p><h3 id="基本操作"><a class="markdownIt-Anchor" href="#基本操作"></a> 基本操作</h3><h4 id="守听操作"><a class="markdownIt-Anchor" href="#守听操作"></a> 守听操作</h4><ol><li>BR5AC(145.58 -0.6 发射亚音 88.5) 余姚丰山</li><li><a href="https://forum.hamcq.cn/d/6300">BR5AO</a>(145.22 -0.6 C4FM 收发亚音88.5)嘉兴</li><li><a href="https://forum.hamcq.cn/d/7367">BR5AQ</a>(145.28 -0.6 发射亚音88.5)宁波</li><li><a href="https://forum.hamcq.cn/d/6200/7">BR5AI</a>(145.40 -0.6 C4FM 收发亚音88.5)杭州</li><li>BR4AA(145.775 -0.6 C4FM 收发亚音88.5)上海</li><li>112.300 摩斯密码重复发hsn，VOR信标台</li></ol><p>11/22晚上，第一次守听到爱好者们所谓的周六晚八点“台网点名”活动，扫到有两个台在进行，因为异常传播（当时开始起雾、气温骤降）的缘故，许多杭州、上海的Ham也通过余姚中继145.58进行了通联。(实际上平常也能收到上海的信号，只不过这一次比平常多了一点，也许并不是异常传播。)</p><p>参与的时候挺过瘾的，一开始在楼上，后来太冷，便下楼骑车去，路上把手台夹在心口相机包斜挎包的袋上，听着电波里不断交流声，面对着路边熟悉的景物，产生了异样的感觉——原来在我感官触及不到的维度，一直有事情在发生。</p><p><img src="/images/20250610/%E4%B8%9A%E4%BD%99%E6%97%A0%E7%BA%BF%E7%94%B5%E7%AC%94%E8%AE%B0-20251122234438354.webp" alt="11/22日 20:00（UTC 12:00）异常传播"></p><h4 id="测试中继"><a class="markdownIt-Anchor" href="#测试中继"></a> 测试中继</h4><p>在配置好发射亚音后，短暂按下PTT键，如果联通到中继，则会在松下PTT键后，收到一个短暂的噪音，这就是所谓的“回波”，这个操作黑话叫做“掐”。</p><h3 id="中继台点名"><a class="markdownIt-Anchor" href="#中继台点名"></a> 中继台点名</h3>        <div id="aplayer-ORtBpTNj" class="aplayer aplayer-tag-marker" style="margin-bottom: 20px;">            <pre class="aplayer-lrc-content"></pre>        </div>        <script>          var ap = new APlayer({            element: document.getElementById("aplayer-ORtBpTNj"),            narrow: false,            autoplay: false,            showlrc: false,            music: {              title: "BG5GER的首次通联",              author: "秉蕳",              url: "https://cloud.si-on.top/api/raw/?path=/Podcast/first_bg5ger.mp3",              pic: "/images/avator/serif-dark.png",              lrc: ""            }          });          window.aplayers || (window.aplayers = []);          window.aplayers.push(ap);        </script><p><img src="/images/20250610/%E4%B8%9A%E4%BD%99%E6%97%A0%E7%BA%BF%E7%94%B5%E7%AC%94%E8%AE%B0-20251129233154477.webp" alt="https://forum.hamcq.cn/d/7633"></p><h3 id="设计"><a class="markdownIt-Anchor" href="#设计"></a> 设计</h3><h4 id="呼号印完成"><a class="markdownIt-Anchor" href="#呼号印完成"></a> 呼号印（完成）</h4><p>为了刻制此印，专门研究了英文字母雕刻的<a href="/2025/NoteOfLetterCarvingInStone">资料</a>。</p><p><img src="/images/20250610/IMG_20251201_190211.jpg" alt="失败品(此印面已经磨平!)"><br><img src="/images/20250610/IMG_20251207_233736.jpg" alt="灵感来源"></p><p><img src="/images/20250610/IMG_20251208_124337%201.jpg" alt="粗刻"></p><p><img src="/images/20250610/IMG_20251208_185822.jpg" alt="精刻·最终成品"></p><h4 id="qsl卡片未完成"><a class="markdownIt-Anchor" href="#qsl卡片未完成"></a> QSL卡片（未完成）</h4><table><thead><tr><th>应当包含</th><th>备注</th><th>实例</th></tr></thead><tbody><tr><td>自己呼号</td><td>英文字母（固定）</td><td>BG5AAA</td></tr><tr><td>对方呼号</td><td>英文字母</td><td>BG5BBB</td></tr><tr><td>日期(DATE)</td><td>年月日</td><td>2025/11/20</td></tr><tr><td>时间(TIME)</td><td>时间(UTC)</td><td>21:13</td></tr><tr><td>地址(ZONE)</td><td>地址(ITU)</td><td>PN00AA</td></tr><tr><td>频率(FREQ)</td><td>数字</td><td>145.500</td></tr><tr><td>模式(MODE)</td><td>英文字母</td><td>FM/SSB/CW/FT8</td></tr><tr><td>信号报告(RST)</td><td>数字</td><td>59/559</td></tr><tr><td>设备(RIG)</td><td>中英混合</td><td>泉盛uv-K6</td></tr><tr><td>功率(WATTS)</td><td>数字</td><td>10</td></tr><tr><td>天线(ANT)</td><td>中英混合</td><td>原装天线</td></tr></tbody></table><p><img src="/images/20250610/%E4%B8%9A%E4%BD%99%E6%97%A0%E7%BA%BF%E7%94%B5%E8%83%BD%E5%8A%9B%E9%AA%8C%E8%AF%81%E8%80%83%E8%AF%95%E7%AC%94%E8%AE%B0(%E6%96%B0%E9%A2%98%E5%BA%93)-20251120225553468.webp" alt="初版"></p><h4 id="通联日志"><a class="markdownIt-Anchor" href="#通联日志"></a> 通联日志</h4><p>2025/12/9 与BG5GGT进行通联，老鹰771天线，uvk6，</p><h3 id="软件定义无线电"><a class="markdownIt-Anchor" href="#软件定义无线电"></a> 软件定义无线电</h3><h4 id="树莓配配置rtl-sdr"><a class="markdownIt-Anchor" href="#树莓配配置rtl-sdr"></a> 树莓配配置RTL-SDR</h4><p>参考<a href="https://luarvique.github.io/ppa/">OpenWebRX+ Package Repository 官网教程</a>，在树莓派debian12(代号：bookworm)里添加gpg公钥与软件源，直接安装<code>sudo apt install openwebrx</code>即可，安装完成后会增加682MB的储存空间（2026.3.4）。安装很顺利，没有遇到网络卡顿的情况。但内网穿透的时候，遇到了<strong>r.x.si-on.top</strong> 使用不受支持的协议。ERR_SSL_VERSION_OR_CIPHER_MISMATCH的报错。软件实际体验下来效果很差，倒不如一些有UI的软件。</p><blockquote><p>Linux查询操作系统版本的命令<code>lsb_release -a</code></p></blockquote><h4 id="windows上配置rtl-sdr"><a class="markdownIt-Anchor" href="#windows上配置rtl-sdr"></a> Windows上配置RTL-SDR</h4><p>跟C语言系编程语言的命名类似，SDR软件的命名有<code>SDR++</code>、<code>SDR#</code>(SDR Sharp)等等，软件大同小异，而在windows上使用RTL-SDR最关键的是安装驱动。</p><p>根据网上的教程，大多是通过使用一个名为<a href="https://zadig.akeo.ie/">zadig</a>的工具来安装。步骤如下：</p><ol><li>将RTL-SDR的硬件安装好，连接到电脑上的USB口，打开zadig软件</li><li>按照下图安装（注意选择<code>Bulk-In,Interface(Interface 0)</code>），两三分钟即可安装好<br><img src="/images/20260106/Pasted%20image%2020260305145335.png" alt></li><li>设备管理器中验证( <kbd>🪟</kbd> + <kbd>X</kbd>  ，打开设备管理器)，看到<strong>其他设备</strong>、<strong>通用串行总线设备</strong>下面有一个有个附带⚠️<code>Bulk-In,Interface</code>的设备即代表安装完成<br><img src="/images/20260106/%E4%B8%9A%E4%BD%99%E6%97%A0%E7%BA%BF%E7%94%B5%E7%AC%94%E8%AE%B0-20260305145804010.webp" alt></li></ol><p>安装完成后，打开任意SDR软件，选择RTL-SDR USB设备即可开始收听。</p><div class="tip warning"><p>注意，绝大多数SDR软件的增益设置都很小，需要调整后才能听到声音。<br><img src="/images/20260106/%E4%B8%9A%E4%BD%99%E6%97%A0%E7%BA%BF%E7%94%B5%E7%AC%94%E8%AE%B0-20260305150540395.webp" alt="SDR++ 界面中调整增益到44.5dB"><br><img src="/images/20260106/%E4%B8%9A%E4%BD%99%E6%97%A0%E7%BA%BF%E7%94%B5%E7%AC%94%E8%AE%B0-20260305150750165.webp" alt="SDR # 中调整RF增益到48dB"></p></div><hr><h2 id="应试篇无线电管理相关法规"><a class="markdownIt-Anchor" href="#应试篇无线电管理相关法规"></a> 应试篇：无线电管理相关法规</h2><table><thead><tr><th style="text-align:center">法律</th><th style="text-align:center">特点</th><th style="text-align:center">制定机构</th><th style="text-align:center">巧记</th></tr></thead><tbody><tr><td style="text-align:center"><a href="http://www.gov.cn/zhengce/content/2016-11/25/content_5137687.htm">《中华人民共和国无线电管理条例》</a></td><td style="text-align:center">无线电管理的行政法规</td><td style="text-align:center">国务院和中央军委</td><td style="text-align:center">国力</td></tr><tr><td style="text-align:center"><a href="http://www.gov.cn/flfg/2012-11/08/content_2260255.htm">《业余无线电台管理办法》</a><sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup></td><td style="text-align:center">业余无线<u>电台</u>的管理文件</td><td style="text-align:center"><strong>工业与信息部</strong></td><td style="text-align:center">公办，431（2024年3月1日施行）</td></tr><tr><td style="text-align:center">《<a href="http://www.srrc.org.cn/article23480.aspx">中华人民共和国无线电频率划分规定</a>》</td><td style="text-align:center">对无线电管理术语进行定义</td><td style="text-align:center">–</td><td style="text-align:center">区分各种主要次要业务，其特点是频率上的划分。</td></tr><tr><td style="text-align:center">《中华人民共和国刑法》</td><td style="text-align:center">针对擅自使用无线电频率的处罚定义</td><td style="text-align:center"></td><td style="text-align:center"></td></tr><tr><td style="text-align:center">《中华人民共和国民法典》</td><td style="text-align:center">“无线电频谱资源属于  国家所有”</td><td style="text-align:center"></td><td style="text-align:center"></td></tr></tbody></table><table><thead><tr><th>名词</th><th>定义</th><th>巧记</th></tr></thead><tbody><tr><td>划分</td><td>将某个特定的频段列入频率划分表,规定该频段可在指定的条件下供一种或多种地面或空间无线电通信业务或射电天文业务使用</td><td>频率划分规定了各个业务的使用范围</td></tr><tr><td>分配</td><td>将无线电频率或频道规定由一个或多个部门,在指定的区域内供地面或空间无线电通信  业务在指定条件下使用</td><td>按需分配到部门</td></tr><tr><td>指配</td><td>将无线电频率或频道批准给无线电台在规定条件下使用</td><td>最终指定到电台</td></tr></tbody></table><h3 id="无线电台相关"><a class="markdownIt-Anchor" href="#无线电台相关"></a> 无线电台相关</h3><div class="tip warning"><p>按照《业余无线电台管理办法》的规定向无线电管理机构提出申请,取得业余无线电台执照是合法设置、使用业余电台的必要步骤。</p></div><p>业余无线电台是指为开展业余业务(含卫星业余业务)使用的一个或者多个发信机、收  信机,或者发信机与收信机的组合(包括附属设备)。目的是<strong>用于相互通信、技术研究和自我训练</strong>。申请条件：</p><ul><li>不论是单位还是个人，申请电台时<strong>无需</strong>复印件</li><li>独立操作具有发信功能业余无线电台的年龄条件是：具备《业余无线电台操作证书》者操作业余无线电台不受年龄限制。</li><li>申请设置、使用具有发信功能的业余无线电台的年龄条件是: 未成年人可以申请设置、使用规定条件内的业余无线电台。(可以使用A证的uv段，但是即便有了B证也不能设HF段)</li><li>设置、使用有固定台址的业余无线电台,应当向<strong>电台所在地的省、自治区、直辖市无线电管理机构</strong>申请，没有固定台址，经地所在的省，自治区，直辖市无线电管理机构申请</li><li>一个电台可以包含多个收发信机，但视为一个业余电台,指配一个电台呼号,但所有设备均应经过核定并将参数载入电台执照。</li></ul><p>设置无线电台，要满足：</p><ol><li>使用的无线电发射设备依法取得型号核准</li><li>型号核准证载明的频率范围包含业余业务频段</li><li>使用的自制、改装、拼装等未取得型号核准的无线电发射设备需要<ol><li>符合国家标准和国家无线  电管理规定</li><li>其无线电发射频率范围仅限于业余业务频段</li></ol></li></ol><div class="tip warning"><p>“<s>已取得型号核准证,但自行更换设备操作软件将频率范围扩展到业余业务频段的无线电发射设备</s>”是不行的，因为原有频段含有非业余业务的，操作时存在风险。</p></div><div class="tip bolt"><p><strong>自制</strong>、<strong>改装、拼装</strong>等未取得型号核准的无线电发射：</p><ul><li>符合国家标准和国家无线电管理规定，具体如下：<ul><li>业余无线电设备射频技术要求及测试方法》(GB/T 32658-2016)</li><li>《短波单边带通信设备通用规范》(GB/T 16946-2017)</li></ul></li><li>发射频率范围仅限于业余业务频段</li><li>自制业余无线电发射设备,在经无线电检测机构检验合格并取得电台执照之前,应在调  测时在设备的天线端口连接假负载</li><li>由 220 伏交流市电供电的设备,安全措施应至少包括:在交流电源入口的火线中串联一个保险丝</li><li>无线电管理机构开展对该设备进行技术检测时，不收费</li></ul></div><h3 id="等级证照业余无线电台操作技术能力验证证书"><a class="markdownIt-Anchor" href="#等级证照业余无线电台操作技术能力验证证书"></a> 等级证照(业余无线电台操作技术能力验证证书)</h3><table><thead><tr><th style="text-align:center">等级</th><th style="text-align:center">可使用的频率范围</th></tr></thead><tbody><tr><td style="text-align:center">A</td><td style="text-align:center">30~3000MHZ，功率小于25W</td></tr><tr><td style="text-align:center">B(A证6个月)</td><td style="text-align:center">&lt;30MHZ,功率小于15W；&gt;30MHZ,功率小于25W</td></tr><tr><td style="text-align:center">C(B证18个月)</td><td style="text-align:center">&lt;30MHZ,功率小于1000W；&gt;30MHZ,功率小于25W</td></tr></tbody></table><ul><li>15W以上短波，需要国家无线电管理机构做出许可决定，可委托省、自治区、直辖市无线电管理机构进行技术检验</li><li>C类考试只能由国家无线电管理机构去认证</li><li>考试不收费</li></ul><table><thead><tr><th style="text-align:center">等级</th><th style="text-align:center">电台设置的频率范围</th></tr></thead><tbody><tr><td style="text-align:center">A</td><td style="text-align:center">VHF/UHF，功率小于25W</td></tr><tr><td style="text-align:center">B</td><td style="text-align:center">VHF/UHF，功率小于25W; HF 功率小于15W(未成年人不可以);LF(eirp)功率小于1W</td></tr><tr><td style="text-align:center">C</td><td style="text-align:center">VHF/UHF，功率小于25W(特殊情况下可以大于25W); HF 功率小于1000W;</td></tr></tbody></table><ul><li>证照内容全选<ul><li>电台设置、使用人，操作技术能力类别、编号</li><li>电台呼号、台址/设置区域、使用频率、发射功率</li><li>执照编号、颁发日期、有效期、发证机关，以及特别规定事项</li><li>业余中继台、业余信标台执照还应当载明工作模式等事项</li></ul></li><li>有效期5年</li><li>有效期满前30天要申请更换</li><li>注销：要去作出许可决定的无线电管理机构注销</li><li>终止使用电台的，要办理注销手续，60个工作日内拆除电台</li></ul><h3 id="呼号相关"><a class="markdownIt-Anchor" href="#呼号相关"></a> 呼号相关</h3><table><thead><tr><th style="text-align:center">前缀</th><th style="text-align:center">电台种类</th><th style="text-align:center">分区</th><th style="text-align:center">后缀</th></tr></thead><tbody><tr><td style="text-align:center">B</td><td style="text-align:center">G</td><td style="text-align:center">5</td><td style="text-align:center">ABC</td></tr><tr><td style="text-align:center">国际电信联盟（ITU）分配</td><td style="text-align:center">各种各样</td><td style="text-align:center">空间信号是1</td><td style="text-align:center">双字母、三字母组成，数字保留</td></tr></tbody></table><ul><li>有号不再发新号,注销后一年以后才会重新分配新号</li><li>鼓励技术手段自动报号</li><li>比赛、活动时，可临时使用其他呼号</li><li>无线电管理机构颁发业余无线电台执照,应当同时向申请人核发业余无线电台呼号</li><li>呼号构成、电台呼号第二部分种类，题目全选<ul><li>字母S、T、Y、Z以及其他字母序列的业余无线电台呼号由国家无线电管理机构保留</li><li>字母R用于业余中继台和业余信标台呼号</li><li>字母G、H、I、D、A、B、C、E、F、K、L用于一般业余无线电台呼号</li><li>字母J用于空间业余无线电台呼号</li></ul></li></ul><table><thead><tr><th style="text-align:center">分区</th><th style="text-align:center">地址</th></tr></thead><tbody><tr><td style="text-align:center">1</td><td style="text-align:center">北京</td></tr><tr><td style="text-align:center">2</td><td style="text-align:center">辽宁、吉林、黑龙江</td></tr><tr><td style="text-align:center">3</td><td style="text-align:center">天津、河北、山西、内蒙</td></tr><tr><td style="text-align:center">4</td><td style="text-align:center">上海、江苏、山东</td></tr><tr><td style="text-align:center">5</td><td style="text-align:center">浙江、江西、福建</td></tr><tr><td style="text-align:center">6</td><td style="text-align:center">河南、安徽、湖北</td></tr><tr><td style="text-align:center">7</td><td style="text-align:center">湖南、广东、广西、海南</td></tr><tr><td style="text-align:center">8</td><td style="text-align:center">重庆、四川、云南、贵州</td></tr><tr><td style="text-align:center">9</td><td style="text-align:center">陕西、甘肃、宁夏、青海</td></tr><tr><td style="text-align:center">0</td><td style="text-align:center">新疆、西藏</td></tr></tbody></table><h3 id="无线电通信规定"><a class="markdownIt-Anchor" href="#无线电通信规定"></a> 无线电通信规定</h3><ul><li>业余电台应该记载：DATE、TIME、FREQ、MODE、CALL、RST</li><li>RST中的R表示信号的可辨识度</li><li>在突发重大自然灾害等紧急情况下,业余无线电台的通信内容可以涉及应急救援相关部门交办的任务呼叫对方的操作：先叫出对方的名字，然后报出自己的呼号</li></ul><p>为在世界范围内划分无线电频率,国际电信联盟《无线电规则》规定了如下区域划分：</p><ol><li><strong>欧</strong>洲、俄罗斯亚洲部分、蒙古及部分西北亚国家为一区</li><li>南北<strong>美</strong>洲为二区</li><li><strong>亚</strong>洲(除俄  罗斯、蒙古和部分西北亚洲国家)和大洋洲为三区</li></ol><h3 id="频段划分"><a class="markdownIt-Anchor" href="#频段划分"></a> 频段划分</h3><p>无线电波是指频率为 3,000GHz 以下的在空间传播的电磁波。</p><table><thead><tr><th style="text-align:center">波段</th><th style="text-align:center">3~30</th><th style="text-align:center">30~300</th><th style="text-align:center">300~3000</th><th style="text-align:center">3~30</th><th style="text-align:center">30~300</th><th style="text-align:center">300~3000</th><th style="text-align:center">3~30</th><th style="text-align:center">30~300</th><th>300~</th></tr></thead><tbody><tr><td style="text-align:center">单位</td><td style="text-align:center"><span 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xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>H</mi><mi>z</mi></mrow><annotation encoding="application/x-tex">MHz</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>H</mi><mi>z</mi></mrow><annotation encoding="application/x-tex">MHz</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>M</mi><mi>H</mi><mi>z</mi></mrow><annotation encoding="application/x-tex">MHz</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.10903em;">M</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi><mi>H</mi><mi>z</mi></mrow><annotation encoding="application/x-tex">GHz</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi><mi>H</mi><mi>z</mi></mrow><annotation encoding="application/x-tex">GHz</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span></td><td><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>G</mi><mi>H</mi><mi>z</mi></mrow><annotation encoding="application/x-tex">GHz</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">G</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span></td></tr><tr><td style="text-align:center">英文</td><td style="text-align:center">VLF</td><td style="text-align:center">LF</td><td style="text-align:center">MF</td><td style="text-align:center">HF</td><td style="text-align:center">VHF</td><td style="text-align:center">UHF</td><td style="text-align:center">SHF</td><td style="text-align:center">EHF</td><td>THF</td></tr><tr><td style="text-align:center">中文</td><td style="text-align:center">超低频</td><td style="text-align:center">低频</td><td style="text-align:center">中频</td><td style="text-align:center">高频</td><td style="text-align:center">甚高频</td><td style="text-align:center">特高频</td><td style="text-align:center">超高频</td><td style="text-align:center">极高频</td><td>至高频</td></tr><tr><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center"></td><td style="text-align:center">米波</td><td style="text-align:center">分米波</td><td style="text-align:center">厘米波</td><td style="text-align:center"></td><td></td></tr></tbody></table><div class="tip "><p>波段划分以10的倍数来划分，只用记住高频HF是3~30$MHz$即可，后面高频段可以巧记为&quot;(VUSE)Why You See 神塔超级&quot;。</p></div><h4 id="业务频段记忆专题"><a class="markdownIt-Anchor" href="#业务频段记忆专题"></a> 业务频段记忆专题</h4><div class="tip "><ul><li>长波的一般专用与主要，短波次要居多</li></ul></div><div class="tip "><ul><li>专用7倍：专用的选7与7的倍数有关的</li><li>主要1835：1835各种变体</li><li>唯一生一世：</li><li>次要1357</li></ul></div><table><thead><tr><th>描述</th><th>频段</th><th>提示</th></tr></thead><tbody><tr><td>业余业务与卫星业余业务专用</td><td>7MHz、14MHz、21MHz、28MHz、47GHz</td><td>专用7倍</td></tr><tr><td>业余业务与卫星业余业务主要（30MHZ以下）</td><td>1.8MHz、3.5MHz、14.25MHz、18.068MHz、24.89MHz</td><td>主要1835</td></tr><tr><td>业余业务与卫星业余业务主要（30MHZ以上）</td><td>50MHz、144MHz</td><td>主要我零落一世</td></tr><tr><td>业余业务与卫星业余业务唯一主要</td><td>3 个, 144-146MHz</td><td>唯一生一世</td></tr><tr><td>业余业务与卫星业余业务唯一主要（最高）</td><td>248-250GHz</td><td>最唯一的二百五</td></tr><tr><td>业余业务与卫星业余业务次要</td><td>135.7kHz、5351.5KHz、10.1MHz、430MHz</td><td>次要1357</td></tr></tbody></table><table><thead><tr><th>描述</th><th>频段</th><th>提示</th></tr></thead><tbody><tr><td>WARC-76</td><td>10.1-10.15MHz、18.068-18.168MHz、24.89-24.99MHz</td><td>我靠10086（筛选中间项目18.068）</td></tr><tr><td>IARU</td><td>14.100MHz、18.110MHz、21.150MHz、24.930MHz、28.200MHz</td><td>哎呦10011（前几位组合成10011）</td></tr><tr><td>40米，ITU1、2、3分区</td><td>7.0-7.2MHz、7.0-7.3MHz、7.0-7.2MHz,专用</td><td>232，欧洲1区与亚洲3区相同</td></tr><tr><td>160米</td><td>1800-2000kHz,主要业务</td><td>主要18</td></tr><tr><td>80米</td><td>3.5-3.9MHz,主要业务</td><td>主要35</td></tr><tr><td>20米</td><td>14-14.25MHz 为专用,14.25-14.35 为主要业务</td><td>主要35（选题目中含主要，35的）</td></tr><tr><td>15米</td><td>21-21.45MHz,专用</td><td>专用7倍，21、14（合起来）</td></tr><tr><td>10米</td><td>28-29.7MHz,专用</td><td>专用7倍，含有专用与7</td></tr><tr><td>6米</td><td>50-54MHz,主要业务</td><td>主要我5零落一世4</td></tr><tr><td>2米</td><td>144-148MHz;其中 144-146MHz 为唯一主要业务,146-148MHz 为与其他业务共同作 为主要业务</td><td>最长的</td></tr><tr><td>0.7米</td><td>430-440MHz,次要业务</td><td>宇宙波段430，无线电定位和航空无线电导航</td></tr></tbody></table><h4 id="频段占用专题最后死背"><a class="markdownIt-Anchor" href="#频段占用专题最后死背"></a> 频段占用专题（最后死背）</h4><p>144 和 430MHz 频段业余中继台  的上下行频差分别为:0.6MHz与5MHz<br>14MHZ USB 通话：14.100-14.350 MHz 上边带（438）430MHz（70cm）划分给卫星业余业务的：431.9-432.240MHz与435-438MHz</p><p>留给卫星的：</p><table><thead><tr><th>频段</th><th>频率范围</th></tr></thead><tbody><tr><td>10米段</td><td>29.3MMz 至 29.51MHz</td></tr><tr><td>144MHz段</td><td>145.8MHz 至 146MHz</td></tr><tr><td>430MHz</td><td>435MHz 至 438MHz</td></tr></tbody></table><h3 id="规定与处罚"><a class="markdownIt-Anchor" href="#规定与处罚"></a> 规定与处罚</h3><p>无线电管制（限制或者禁止业余无线电台(站)的使用,以及对特定的无线电频率实施技术阻断等）</p><ul><li>在全国范围内或者跨省、自治区、直辖市实施,由国务院和中央军事委员会决定</li><li>在省、自治区、直辖市范围内实施,由省、自治区、直辖市人民政府和相关军区决定</li></ul><table><thead><tr><th>违反治安管理规定相关</th></tr></thead><tbody><tr><td>违反无线电管制命令和无线电管制指令的,由国家无线电管理机构或者省、自治区、直辖市无线电管理机构处罚，违反治安管理规定者由公安机关处罚。</td></tr><tr><td><strong>违反《中华人民共和国无线电管理条例》的，构成违反治安管理行为的,依法给予治安管理处罚，构成犯罪的,依法追究刑事责任</strong></td></tr><tr><td>违反国家规定,故意干扰无线电业务正常进行的,或者对正常运行的无线电台(站)产生有害干扰,经有关主管部门指出后,拒不采取有效措施消除的,处五日以上十日以下拘留;  情节严重的,处十日以上十五日以下拘留</td></tr></tbody></table><div class="tip "><p>擅自使用无线电频率，擅自设台的处罚最严重，罚钱多，还入刑法。</p></div><table><thead><tr><th>情形</th><th>处罚</th><th>巧记</th></tr></thead><tbody><tr><td>业余电台违反无线电管制命令和无线电管制指令</td><td>责令改正;拒不改正的,关闭、查封、暂扣或者拆除相关设备；情节严重的,吊销电台执照；违反治安管理规定的,由公安机关处罚</td><td>改正，暂扣，吊销</td></tr><tr><td>对未经许可擅自使用无线电频率的</td><td>由无线电管理机构责令改正,没收从事违法活动的设备和违法所得,可以并处 5 万元以下的罚款；拒不改正的,并处 5 万元以上 20 万元以下的罚款</td><td>没收5；5-20</td></tr><tr><td>对擅自设置、使用业余无线电台的</td><td>由无线电管理机构责令改正,没收从事违法活动的设备和违法所得,可以并处 5 万元以下的罚款；拒不改正的,并处 5 万元以上 20 万元以下的罚款（利用诈骗的直接20万到50万罚款）</td><td>没收5；5-20</td></tr><tr><td>业余电台干扰无线电业务正常进行的</td><td>由无线电管理机构责令改正,拒不改正的,没收产生有害干扰的设备,并处 5 万元以上  20 万元以下的罚款,吊销无线电台执照</td><td>改正；没收5-20</td></tr><tr><td>业余电台对船舶、航天器、航空器、铁路机车专用无线电导航、遇险救助和安全通信等  涉及人身安全的无线电频率产生有害干扰的</td><td>处 20 万元以上 50 万元以下的罚款</td><td>20-50</td></tr><tr><td>研制、生产、销售和维修大功率无线电发射设备,未采取有效措施抑制电波发射的,</td><td>由无线电管理机构责令改正;拒不改正的,没收从事违法活动的设备,并处 3 万元以上  10 万元以下的罚款；造成严重后果的,并处 10 万元以上 30 万元以下的罚款</td><td>改正；没收3-10，严重10-30</td></tr><tr><td>境外组织或者个人在我国境内进行电波参数测试或者电波监测的,</td><td>由无线电管理机构责令改正;拒不改正的,没收从事违法活动的设备,并处 3 万元以上  10 万元以下的罚款；造成严重后果的,并处 10 万元以上 30 万元以下的罚款</td><td>改正；没收3-10，严重10-30</td></tr><tr><td>向境外组织或者个人提供涉及国家安全的境内电波参数资料的</td><td>由无线电管理机构责令改正;拒不改正的,没收从事违法活动的设备,并处 3 万元以上  10 万元以下的罚款；造成严重后果的,并处 10 万元以上 30 万元以下的罚款</td><td>改正；没收3-10，严重10-30</td></tr><tr><td>生产或者进口在国内销售、使用的无线电发射设备未取得型号核准的</td><td>由无线电管理机构责令改正,处 5 万元以上 20 万元以下的罚款；拒不改正的,没收未取得型号核准的无线电发射设备,并处 20 万元以上 100 万元以下的  罚款</td><td>改正5-20；没收20-100</td></tr></tbody></table><table><thead><tr><th>情形</th><th>处罚</th><th>巧记</th></tr></thead><tbody><tr><td>不按照业余无线电台执照规定的许可事项和要求设置、使用业余无线电台的</td><td>由无线电管理机构责令改正,没收违法所得,可以并处 3 万元以下的罚款；造成严重后果的,吊销无线电台执照,并处 3 万元以上 10 万元以下的罚款</td><td>没收3，3-10</td></tr><tr><td>故意收发业余无线电台执照许可事项之外的无线电信号,传播、公布或者利用无意接收  的信息</td><td>由无线电管理机构责令改正,没收违法所得,可以并处 3 万元以下的罚款；造成严重后果的,吊销无线电台执照,并处 3 万元以上 10 万元以下的罚款</td><td>没收3，3-10</td></tr><tr><td>擅自编制、使用业余无线电台呼号</td><td>由无线电管理机构责令改正,没收违法所得,可以并处 3 万元以下的罚款；造成严重后果的,吊销无线电台执照,并处 3 万元以上 10 万元以下的罚款</td><td>没收3，3-10</td></tr><tr><td>销售依照本条例第四十四条的规定应当取得型号核准的无线电发射设备未向无线电管理  机构办理销售备案的,</td><td>由无线电管理机构责令改正；拒不改正的,处 1 万元以上 3 万元以下的罚款</td><td>改正；1-3</td></tr><tr><td>隐瞒有关情况、提供虚假材料或者虚假承诺申请业余无线电台设置、使用许可</td><td>无线电管理机构不予许可,并给予警告</td><td>不罚钱</td></tr><tr><td>以欺骗、贿赂等不正当手段取得业余无线电台执照的</td><td>无线电管理机构依法给予行政处罚；构成犯罪的,依法追究刑事责任</td><td>不罚钱</td></tr></tbody></table><p>总体国家安全观：（十九大后注意政治，记住政治作为根本）</p><ol><li>以人民安全为宗旨，</li><li>,以政治安全为根本,</li><li>以经济安全为基础,</li><li>以军事、文化、社会安全为保障</li></ol><h3 id="零碎"><a class="markdownIt-Anchor" href="#零碎"></a> 零碎</h3><hr><p>业余业务（包括卫星业余业务）用于：<strong>业余无线电爱好者进行自我训练、相互通信和技术研究</strong>。业余业务不可以在其他业务通信。业余无线电爱好者系指经正式批准的、对无线电技术有兴趣的人，其兴趣纯系个人爱好而不涉及谋取利润。</p><p>协调国际无线电管理的国际组织是：国际电信联盟。</p><p>无线电通信是指利用无线电波进行的符号、信号、文字、图像、声音或其他信息的传输、  发射或接收。</p><p>地面无线电通信(terrestrial radio communication)航空通信属于地面无线电通信。</p><h3 id="q简语专题"><a class="markdownIt-Anchor" href="#q简语专题"></a> Q简语专题</h3><table><thead><tr><th style="text-align:center">R系列（状态）</th><th style="text-align:center">含义</th><th style="text-align:center">巧记</th></tr></thead><tbody><tr><td style="text-align:center">QRN</td><td style="text-align:center">天电干扰</td><td style="text-align:center">nature 干扰</td></tr><tr><td style="text-align:center">QRM</td><td style="text-align:center">旁台干扰</td><td style="text-align:center">man 干扰</td></tr><tr><td style="text-align:center">QRO</td><td style="text-align:center">信号不好，询问是否增加功率</td><td style="text-align:center">左眼流泪的眼睛</td></tr><tr><td style="text-align:center">QRP</td><td style="text-align:center">信号良好（CW559，FM55），可否降低功率</td><td style="text-align:center">吐舌，挑衅性降功率</td></tr><tr><td style="text-align:center">QRQ</td><td style="text-align:center">加快速度</td><td style="text-align:center">Quickly 快点</td></tr><tr><td style="text-align:center">QRS</td><td style="text-align:center">放慢速度</td><td style="text-align:center">Slowly 慢点</td></tr><tr><td style="text-align:center">QRT</td><td style="text-align:center">关机</td><td style="text-align:center">“T”断头路，下车</td></tr><tr><td style="text-align:center">QRU</td><td style="text-align:center">结束联络寒暄语，还有什么信息要说吗？</td><td style="text-align:center">RUOK“Are you OK”</td></tr><tr><td style="text-align:center">QRV</td><td style="text-align:center">邀请</td><td style="text-align:center">InVent 邀请</td></tr><tr><td style="text-align:center">QRZ</td><td style="text-align:center">重发信号</td><td style="text-align:center">This is BG1ZZZ</td></tr></tbody></table><table><thead><tr><th style="text-align:center">S系列（动作）</th><th style="text-align:center">含义</th><th style="text-align:center">巧记</th></tr></thead><tbody><tr><td style="text-align:center">QSA</td><td style="text-align:center">发送信号</td><td style="text-align:center">愤怒小鸟，红鸟“Ah Hengniya”</td></tr><tr><td style="text-align:center">QSB</td><td style="text-align:center">信号是否衰落</td><td style="text-align:center">Birdge 如鸟飞起落下</td></tr><tr><td style="text-align:center">QSD</td><td style="text-align:center">发报是否有问题：键盘、字母手法</td><td style="text-align:center">手法有问题，你这个沙雕</td></tr><tr><td style="text-align:center">QSL</td><td style="text-align:center">对方电台确认收妥自己发出的消息</td><td style="text-align:center">QSL卡片</td></tr><tr><td style="text-align:center">QSO</td><td style="text-align:center">我可直接通联</td><td style="text-align:center">瞪大眼睛苦苦等待的人</td></tr><tr><td style="text-align:center">QSP</td><td style="text-align:center">转信至xxx电台</td><td style="text-align:center">Please 帮忙转信下呗</td></tr><tr><td style="text-align:center">QSX</td><td style="text-align:center">帮忙守听</td><td style="text-align:center">我在沙县小吃等你</td></tr><tr><td style="text-align:center">QSY</td><td style="text-align:center">改频</td><td style="text-align:center">换个频道，See you soon</td></tr></tbody></table><table><thead><tr><th style="text-align:center">其他系列</th><th style="text-align:center">含义</th><th style="text-align:center">巧记</th></tr></thead><tbody><tr><td style="text-align:center">QTH</td><td style="text-align:center">电台位置</td><td style="text-align:center">hello there</td></tr></tbody></table><h4 id="cq"><a class="markdownIt-Anchor" href="#cq"></a> CQ</h4><blockquote><p>孙悟空，我叫你一声你敢答应吗？</p></blockquote><table><thead><tr><th>术语</th><th>解释</th></tr></thead><tbody><tr><td>CQ</td><td>非特指地呼叫任何一部国内和国外业余电台</td></tr></tbody></table><ul><li>发起CQ：呼叫 CQ 并报出己方呼号。清晰起见,可重复一两次 CQ 并对呼号进行字母拼读</li><li>回复CQ：出对方的呼号并报出自己的呼号。清晰起见,可重复关键内容或进行字母拼读</li></ul><h4 id="qsl卡片"><a class="markdownIt-Anchor" href="#qsl卡片"></a> QSL卡片</h4><p>意义：</p><ol><li>确认本地、国内,甚至世界范围内的无线电联络</li><li>掌握包括自制发射机在内的本台设备的运作表现</li><li>申请奖状,证明自己在通信、技术等领域的努力</li><li>纯粹收集,欣赏,展示来自世界各地的 QSL 卡片</li></ol><p>包含的内容：</p><ol><li>联络双方的电台呼号</li><li>双方信号报告和联络时间</li><li>操作方式及联络频率</li><li>操作员签章、本台通信地址</li></ol><p>如果所交换的 QSL 卡片并非用作通联或收听证明,则应在通信方式一栏填写“现场交流”  或“Eyeball QSO”等字样。不应赠送空白卡片</p><hr><h3 id="缩略语"><a class="markdownIt-Anchor" href="#缩略语"></a> 缩略语</h3><table><thead><tr><th>缩略语</th><th>含义</th><th>缩略语</th><th>含义</th><th>缩略语</th><th>含义</th></tr></thead><tbody><tr><td>AGN</td><td>再一次</td><td>AHR</td><td>另一个</td><td>ARDF</td><td>业余无线电测向</td></tr><tr><td>HST</td><td>快速收发报</td><td>K</td><td>完成发送并守听</td><td>KN</td><td>完成发送并听对方</td></tr><tr><td>QSL管理局</td><td>BURO</td><td>CK</td><td>检查</td><td>DX</td><td>远距离</td></tr><tr><td>ES</td><td>和</td><td>FB</td><td>太棒了</td><td>FREQ</td><td>频率</td></tr><tr><td>GM</td><td>早上好</td><td>GA</td><td>下午好</td><td>GE</td><td>晚上好</td></tr><tr><td>GN</td><td>晚安</td><td>GL</td><td>祝你好运</td><td>HNY</td><td>新年快乐</td></tr><tr><td>HPE</td><td>希望去做</td><td>HPI</td><td>幸福</td><td>GLD</td><td>高兴</td></tr><tr><td>GND</td><td>地面</td><td>GMT</td><td>格林尼治时间</td><td>MNY TNX</td><td>非常感谢</td></tr><tr><td>NW</td><td>现在</td><td>OM</td><td>老伙计</td><td>OP</td><td>操作员</td></tr><tr><td>PSE/PLS</td><td>请</td><td>TNX/TKS</td><td>谢谢</td><td>TU</td><td>谢谢你</td></tr><tr><td>UR</td><td>你的</td><td>WL</td><td>将要</td><td>R</td><td>收到</td></tr><tr><td>SAE</td><td>写好地址的信封</td><td>SASE</td><td>写好地址贴邮票信封</td><td>SRI</td><td>对不起</td></tr><tr><td>TEMP</td><td>温度</td><td>YL</td><td>女士</td><td>XYL</td><td>妻子</td></tr><tr><td>EL/ELE/ELS</td><td>天线振子</td><td></td><td></td><td></td><td></td></tr></tbody></table><p>AMSAT：美国的业余无线电卫星公司,是一个专注于实验卫星的设计、制造、运行和推进空间教  育的非营利性志愿者组织<br><img src="/images/20250610/%E4%B8%9A%E4%BD%99%E6%97%A0%E7%BA%BF%E7%94%B5%E8%83%BD%E5%8A%9B%E9%AA%8C%E8%AF%81%E8%80%83%E8%AF%95%E7%AC%94%E8%AE%B0(%E6%96%B0%E9%A2%98%E5%BA%93)-20251115145246036.webp" alt><br>OSCAR：“搭载有业余无线电装置的地球轨道卫星”的英文缩写我国发射的第一颗业余卫星的发射年份、名称、国际 OSCAR 系列号和转发器模式分别2009 年,希望一号(XW-1),HO68,V/U(J)（汶川地震之后那年）</p><p>EME通信试验的最佳时机是：月亮处于近地点：操作时前置放大器尽量安装在靠近天线的地方,信号特别微弱时对放大器进行冷却以降低热噪声</p><p>FT4通信方式，6米适合流星余迹散射通信。（飞天(FT)流星🌠666）</p><table><thead><tr><th>简写</th><th>含义</th></tr></thead><tbody><tr><td>DCS</td><td>亚音</td></tr><tr><td>CTCSS</td><td>数字亚音降噪技术</td></tr><tr><td>PTT</td><td>按键发射,有信号(一般为对地接通)时发射机由等待转为发射</td></tr><tr><td>SQL(收发信机面板上)</td><td>静噪控制,用来调整静噪阈值的大小。</td></tr></tbody></table><h2 id="应试篇-技术相关"><a class="markdownIt-Anchor" href="#应试篇-技术相关"></a> 应试篇 技术相关</h2><h3 id="计算专题"><a class="markdownIt-Anchor" href="#计算专题"></a> 计算专题</h3><h4 id="信号计算215"><a class="markdownIt-Anchor" href="#信号计算215"></a> 信号计算2.15</h4><p>dBi：待测天线最大辐射方向上的辐射功率密度与<strong>理想点源天线</strong>对应值之比的 dB 值<br>dBd：待测天线最大辐射方向上的辐射功率密度与<strong>半波长偶极天线</strong>对应值之比的 dB 值</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>0</mn><mi>d</mi><mi>B</mi><mi>d</mi><mo>=</mo><mn>2.15</mn><mi>d</mi><mi>B</mi><mi>i</mi></mrow><annotation encoding="application/x-tex">0dBd = 2.15 dBi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">0</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">2.15</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mord mathnormal">i</span></span></span></span></span></p><blockquote><p>1dBd=3.15dBi，6.15dBi的功率为3.15dBi的二倍（加三乘二）</p></blockquote><h4 id="灵敏度计算"><a class="markdownIt-Anchor" href="#灵敏度计算"></a> 灵敏度计算</h4><p>当输出信号满足规定质量标准时,在输入阻抗为 50 欧的某接收机天线输入端口测得最小电压值及对应的灵敏度：</p><table><thead><tr><th style="text-align:center">最小电压</th><th style="text-align:center">灵敏度指标1</th><th style="text-align:center">灵敏度指标2</th><th style="text-align:center">灵敏度指标3</th></tr></thead><tbody><tr><td style="text-align:center">1μV</td><td style="text-align:center">2μV</td><td style="text-align:center"><strong>-107dBm</strong></td><td style="text-align:center">6dBμV</td></tr><tr><td style="text-align:center">0.5μV</td><td style="text-align:center">1μV</td><td style="text-align:center"><strong>-113dBm</strong></td><td style="text-align:center">0dBμV</td></tr></tbody></table><p>影响灵敏度的主要因素是：机内噪声</p><p>信噪比：有用信号功率对噪声功率的比值静噪灵敏度：能够使静噪电路退出静噪状态的射频信号最小输入电平。</p><p>噪声系数Fn(1)：接收机输入端信噪比 Si/Ni 对输出端信噪比 So/No 的比值。Fn 一定大于 1;在同样的灵敏度下,Fn 越接近 1 越好</p><p>噪声指数 NF(0)：接收机输入端信噪比 Si/Ni 对输出端信噪比 So/No 的比值的对数形式。NF 一定大于 0;在同样的灵敏度下,NF 越接近 0 越好</p><p>等效噪声温度 Te(0°K) 的意义是: 收机的内部噪声功率等于一个接在天线输入端的优质匹配电阻在产生相同的热噪声功  率时该电阻所具有的绝对温度</p><h4 id="镜像干扰计算正负中频"><a class="markdownIt-Anchor" href="#镜像干扰计算正负中频"></a> 镜像干扰计算(正负中频)</h4><p>超外差式收信机所收信号的频率要比本振频率低(或高)一个中频。然而,比本振频率  高(或低)一个中频的另一个遥相对应的信号也可能经混频窜入中频通道,形成“镜像频率  干扰”或“镜频干扰”。如果某对讲机的技术规格书给出的 VHF 接收机第一中频为 45.05MHz,  那么在 145.00MHz 收到的镜频干扰可能来自:</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>f</mi><mrow><mi>m</mi><mi>i</mi><mi>r</mi><mi>r</mi><mi>o</mi><mi>r</mi></mrow></msub><mo>=</mo><mi>f</mi><mo>±</mo><msub><mi>f</mi><mrow><mi>m</mi><mi>i</mi><mi>d</mi><mi>d</mi><mi>l</mi><mi>e</mi></mrow></msub></mrow><annotation encoding="application/x-tex">f_{mirror}=f\pm f_{middle}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em;"><span style="top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">mi</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span><span class="mord mathnormal mtight" style="margin-right:0.02778em;">or</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">±</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.1076em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">mi</span><span class="mord mathnormal mtight">dd</span><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span><span class="mord mathnormal mtight">e</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></span></p><div class="tip bolt"><p>简单成狗了🐕。</p></div><h4 id="天线功率计算"><a class="markdownIt-Anchor" href="#天线功率计算"></a> 天线功率计算</h4><p><strong>发射机效率：输出到天线系统的信号功率与发射机所消耗的电源功率之比</strong></p><p>若一部业余无线电台的工作电压为直流 13.8 伏,FM 方式的射频输出功率为 N 瓦,电源  效率约为 80%,则发射时的工作电流约为:</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>η</mi><mo>=</mo><mfrac><msub><mi>W</mi><mi>r</mi></msub><msub><mi>W</mi><mi>p</mi></msub></mfrac></mrow><annotation encoding="application/x-tex">\eta=\frac{W_r}{W_p}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">η</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.3324em;vertical-align:-0.9721em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">p</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em;">r</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.9721em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>I</mi><mo>=</mo><mfrac><mi>P</mi><mi>U</mi></mfrac><mo>=</mo><mfrac><mrow><mi>N</mi><mo>×</mo><msup><mi>η</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></mrow><mi>U</mi></mfrac><mo>=</mo><mfrac><mrow><mn>1.25</mn><mi>N</mi></mrow><mn>13.8</mn></mfrac><mo>=</mo><mn>0.09058</mn><mo stretchy="false">(</mo><mi>A</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">I=\frac{P}{U}=\frac{N\times \eta^{-1}}{U}=\frac{1.25N}{13.8}=0.09058(A)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">U</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.13889em;">P</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.415em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.07em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">U</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4461em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span><span class="mbin mtight">×</span><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03588em;">η</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8913em;"><span style="top:-2.931em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">1</span></span></span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2173em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8723em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">13.8</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1.25</span><span class="mord mathnormal mtight" style="margin-right:0.10903em;">N</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">0.09058</span><span class="mopen">(</span><span class="mord mathnormal">A</span><span class="mclose">)</span></span></span></span></p><h4 id="可用频率区间计算"><a class="markdownIt-Anchor" href="#可用频率区间计算"></a> 可用频率区间计算</h4><ol><li>FM（调频）发射带宽包含上下的范围，如20kHz代表可达到+10kHz与-10kHz，再考虑频率容限即可计算。</li></ol><blockquote><p>在 70 厘米波段中,爱好者经常在 438-440MHz 展开话音通信。这也是 IARU 第 3 区波  段规划中的一个多模式共用细分频段。假设一部业余电台正以 FM 方式在该频段参与通联,  发射带宽小于 20kHz 并且频率容限优于±2kHz,则该电台的主载波设置范围可以是:从 438.012MHz 至 439.988MHz</p></blockquote><ol start="2"><li>USB上边带模式，只发生边带之上的，计算时下限只考虑频率容限即可</li></ol><blockquote><p>在 70 厘米波段中,爱好者经常在 438-440MHz 展开话音通信。这也是 IARU 第 3 区波  段规划中的一个多模式共用细分频段。假设一部业余电台正以 USB 方式在该频段参与通联,  发射带宽小于 3kHz 并且频率容限优于±2kHz,则该电台的主载波设置范围可以是:  从 438.002MHz 至 439.995MHz</p></blockquote><h4 id="dbm与功率的换算"><a class="markdownIt-Anchor" href="#dbm与功率的换算"></a> dbm与功率的换算：</h4><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>1</mn><mi>d</mi><mi>B</mi><mi>m</mi><mo>=</mo><mn>10</mn><mi>l</mi><mi>g</mi><mo stretchy="false">(</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>∗</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></mfrac><mi>W</mi><mo stretchy="false">)</mo><mo>=</mo><mn>30</mn><mi>W</mi></mrow><annotation encoding="application/x-tex">1dBm=10 lg(\frac{1}{1*10^{-3}}W)=30W</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">1</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord">10</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">3</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">30</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>1</mn><mi>d</mi><mi>B</mi><mi>μ</mi><mo>=</mo><mn>10</mn><mi>l</mi><mi>g</mi><mo stretchy="false">(</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mo>∗</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></mrow></mfrac><mi>W</mi><mo stretchy="false">)</mo><mo>=</mo><mn>60</mn><mi>W</mi></mrow><annotation encoding="application/x-tex">1dBμ=10 lg(\frac{1}{1*10^{-6}}W)=60W</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">1</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.05017em;">B</span><span class="mord mathnormal">μ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord">10</span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">∗</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7401em;"><span style="top:-2.989em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">6</span></span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">60</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>l</mi><mi>g</mi><mn>2</mn><mo>=</mo><mn>0.301029995664</mn></mrow><annotation encoding="application/x-tex">lg2=0.301029995664</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.01968em;">l</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord">2</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.301029995664</span></span></span></span></span></p><p>瓦数每增大一倍，dbm增加3</p><h3 id="比较专题"><a class="markdownIt-Anchor" href="#比较专题"></a> 比较专题</h3><ul><li>串联电感后的发射效率：顶部&gt;中部&gt;底部</li><li>如果某话音发射机在不同调制方式下的峰值输出功率相同,则在无语音输入时,实际射  频输出功率由大到小可以排序为: FM,AM,SSB</li><li>如果用两手分别接触电压有效值相同但频率不同的电路的两个端点,则所受安全威胁由  大到小可以排序为: 工频交流电、HF 射频交流电、UHF 射频交流电</li></ul><p>越大越好</p><ol><li>信噪比</li></ol><p>越小越好<br>1. 通带矩形系数<br>2. 灵敏度指标的数值越小,接收微弱信号的能力越强</p><p>越1越好</p><ol><li>噪声系数Fn</li><li>驻波比(SWR)</li></ol><h3 id="发射"><a class="markdownIt-Anchor" href="#发射"></a> 发射</h3><table><thead><tr><th style="text-align:center">调整方式</th><th style="text-align:center">含义</th></tr></thead><tbody><tr><td style="text-align:center">AM</td><td style="text-align:center">幅度调制(调幅)</td></tr><tr><td style="text-align:center">FM</td><td style="text-align:center">频率调制(调频)</td></tr><tr><td style="text-align:center">PM</td><td style="text-align:center">相位调制(调相)</td></tr></tbody></table><p>SSB(单边带调制)发射带宽较FM窄，与周边电台的频率间隔至少应该是2~3kHz。用于</p><ul><li><p>长距离VHF、UHF（上边带）</p></li><li><p>HF语音通联（14MHz以上，上边带）</p></li><li><p>7MHz以下用下边带</p></li><li><p>10.1MHz用下边带,10.1MHz以上用上边带<br>FM用于VHF与UHF本地通联。<br>FM无法同时守听多个信号</p></li><li><p>无论是 FM 还是 SSB 调制,向发射机的话筒输入端施加 10 倍于规定输入电压的音频信  号,最可能的结果是：信号失真。大量的谐波和互调产物还可能促使发射带宽增加,通信质量下降。</p></li><li><p>CW（等幅电报）拥有最窄的发射带宽。带外发射：由于调制过程而产生的、刚超出<strong>必要</strong>带宽的一个或多个频率的发射,但杂散发射除外</p></li></ul><p>HF：通信依靠电离层的反射</p><p>发射类别的编码由三个字符构成：第一位表示主载波调制方式，第二位标识调制信号特性，第三位体现传输信息类型。例如’A0A’表示双边带调幅电话通信，'F2D’代表调频编码数字传输系统。</p><ol><li>主载波调制分类<ul><li>未调制载波（N型）</li><li>调幅（A型）包含双边带、单边带等子类</li><li>调频（F型）涵盖宽带、窄带调制</li><li>脉冲调制（P型）包含脉宽、脉位调制等形态</li><li>单边带制（J型）主载波为调制的发射</li></ul></li><li>信号特性分类<ul><li>无调制信号（0型）</li><li>单信道模拟信息（1型）</li><li>单信道数字信息（2型）</li><li>多信道复合信息（3型）</li></ul></li><li>信息类型分类<ul><li>电报（人工收发）（A型）</li><li>电报（自动接收）（B型）</li><li>传真（C型）</li><li>数据传输（D型）</li><li>电话<sup class="footnote-ref"><a href="#fn2" id="fnref2">[2]</a></sup>（E型）</li><li>电视（F型）</li></ul></li></ol><blockquote><p>（字母越往后越高级，仅仅记住尾缀E代表电话、F代表电视，A代表电报就足以做对所有题目）</p></blockquote><table><thead><tr><th>方法</th><th>发射类型</th><th>解释</th></tr></thead><tbody><tr><td>CW(等幅电报)</td><td>A1A</td><td>调幅；单信道；电报</td></tr><tr><td>单边带话</td><td>J3E</td><td>单边带；多信道；图像传输</td></tr><tr><td>SSTV、ATV</td><td>F3F</td><td>调频；多信道；电视</td></tr><tr><td>调频话</td><td>F2E</td><td>调频；单信道数字；电话</td></tr></tbody></table><ul><li>YSF：是数字语音和数据传输相互融合的一种通信方式，该方式为业余无线电通信广为采用，具备通过中继台转发进行通信的能力，调制方式为 C4FM。(<u>巧记：约瑟夫不用宽带，不选含带宽的选项</u>)</li><li>Icom D-STAR System：卫星，全选</li><li>FreeDV：为爱好者提供一种传输带宽较窄,完全适合 HF 的数字语音方式 ，为爱好者提供探索数字通信原理和语音处理技术的可能性，在遵循开源许可协议的前提下可用来研发自己的业余无线电装备。（DV音色不好）</li><li>DATV（数字业余电视）是将数字音视频压缩编码实验用于实时图像通信的一种方式。通  过卫星转发器进行 DATV 联络时,爱好者们普遍选用 DVB-S2 协议,调制方式可以是：QPSK、8PSK、16APSK、32APSK</li><li>用 DRM 协议进行数字慢扫描电视(DSSTV)通信时,爱好者总是倾向于通过单边带  而非调频话方式来传输在音频范围内生成的 DSSTV 基带。主要原因是：单边带方式完整保留 DSSTV 的基带特性,利于衰落信道中的差错控制。（为什么单边带好，因为单边带好，顺着问题找答案）</li></ul><h3 id="天线"><a class="markdownIt-Anchor" href="#天线"></a> 天线</h3><blockquote><p>理想点源天线：存在于理论中的一种小到一个点,可将发射机输出的全部射频能量都转化为各向同性且  均匀辐射的电磁波的假想天线;用作比较实际天线辐射性能的一种全向基准天线。</p></blockquote><table><thead><tr><th style="text-align:center">简称</th><th style="text-align:center">全称</th></tr></thead><tbody><tr><td style="text-align:center">DP</td><td style="text-align:center">偶极天线</td></tr><tr><td style="text-align:center">GP</td><td style="text-align:center">垂直接地天线</td></tr><tr><td style="text-align:center">VER</td><td style="text-align:center">垂直天线</td></tr><tr><td style="text-align:center">LW</td><td style="text-align:center">长线天线</td></tr><tr><td style="text-align:center">YAGI</td><td style="text-align:center">八木天线</td></tr><tr><td style="text-align:center">BEAM</td><td style="text-align:center">定向天线</td></tr><tr><td style="text-align:center">I</td><td style="text-align:center">理想点源天线</td></tr></tbody></table><ul><li>水平<strong>E</strong>极化偶极天线：通过该天线发射的电磁波,电场平行于地面，该天线水平面上的(E 面)方向图呈“8”字展开</li><li>垂直<strong>H</strong>极化天线：该天线发射垂直极化波,电场与地面垂直；垂直天线是全向天线,其 H 面方向图是全向的</li></ul><p>橡胶天线：就电台的一般持握方式而言,电波的垂直极化分量要强一些，相对于全尺寸天线,“橡胶天线”的发射与接收增益都低一些</p><p>驻波比(SWR):连接到传输线终端的负载阻抗与传输线自身的特性阻抗相匹配的程度,负载与传输线完美匹配时,传输线之中没有驻波,因此驻波比为 1:1,如果负载与传输线不匹配,传向负载的部分能量会沿传输线返回始端.越趋近于1:1,其能量可以更有效地用于传输信号射频。</p><ul><li><p>数发射机都在 SWR 超过一定值时降低输出功率。这是为了保护发射机中的功率半导体器件</p></li><li><p>SSB测量SWR不稳定，要用CW模式进行测量。</p></li><li><p>发射天线的作用是：把发射机输出的射频信号转化为无线电波；</p></li><li><p>接收天线的作用是：把空间的无线电波转化为接收机中的射频电信号。</p></li></ul><p>天线增益（<u>相对值</u>）：待测天线最大辐射方向上的辐射功率密度与基准天线对应值的比值；与参考天线相比,被测天线在某个方向上使信号增强的程度天线加载：为天线振子串联电感线圈,延长振子的电气长度</p><p>自制业余无线电发射设备,在经无线电检测机构检验合格并取得电台执照之前,应在调  测时在设备的天线端口连接(或在串联必要的仪表之后连接)：假负载</p><h3 id="硬件"><a class="markdownIt-Anchor" href="#硬件"></a> 硬件</h3><h4 id="收发信机"><a class="markdownIt-Anchor" href="#收发信机"></a> 收发信机</h4><p>收发信机是<strong>一种组合了接收机和发射机的无线电通信设备</strong></p><ul><li>一个可以工作的无线电接收系统至少应该包含<strong>接受天线和解调器</strong>。（如晶体管收音机）</li><li>一个可以工作的无线电发射系统至少应该包含<strong>射频振荡器、调制器和发射天线</strong></li><li>业余无线电收发信机所用的直流电源线要尽量短粗是为了减少发信时电源线的压降。</li></ul><p>单工操作(simplex operation)是指:在一条电信通路的两个方向上交替进行传输的一种工作方式。下列通信采用单工操作方式:两台由 PTT 键转换收发状态的业余对讲机之间的通信。</p><p>双工操作(duplex operation)是指:一条电信通路的两个方向能同时进行传输的工作方  式。下列通信采用双工操作方式:由一台连续工作的 430MHz 接收机和一台 144MHz 发信机组成的地面业余电台与业余卫  星之间的通信。</p><p>半双工操作(semi-duplex operation)是指:电路的一端用单工操作,另一端用双工操  作的一种工作方式。下列通信采用半双工操作方式:一台业余中继台与一台由 PTT 键转换收发状态的业余对讲机之间的通信</p><table><thead><tr><th style="text-align:center">缩写</th><th style="text-align:center">全称/说明</th><th style="text-align:center">功能描述</th></tr></thead><tbody><tr><td style="text-align:center">PTT</td><td style="text-align:center">按键发射</td><td style="text-align:center"></td></tr><tr><td style="text-align:center">DTMF</td><td style="text-align:center">双音多频编码</td><td style="text-align:center">由8个音调频率中的两个频率组合成的控制信号，代表16种状态之一，用于遥控和传输数字等简单字符</td></tr><tr><td style="text-align:center">NFM</td><td style="text-align:center">窄带调频</td><td style="text-align:center">适用于信道带宽25kHz/12.5kHz的通信信号</td></tr><tr><td style="text-align:center">WFM</td><td style="text-align:center">宽带调频</td><td style="text-align:center">适用于接收信道带宽180kHz左右的广播信号</td></tr><tr><td style="text-align:center">VOL</td><td style="text-align:center">音量控制</td><td style="text-align:center">用来调整接收机放出的声音大小</td></tr><tr><td style="text-align:center">VOX</td><td style="text-align:center">发信机声控</td><td style="text-align:center">接入后将根据对话筒有无语音输入的判别自动控制收发转换</td></tr><tr><td style="text-align:center">NB</td><td style="text-align:center">“抑噪”</td><td style="text-align:center">切除高于平均信号的大幅度突发脉冲噪声。可用于火花塞辐射脉冲干扰</td></tr><tr><td style="text-align:center">MODE</td><td style="text-align:center">工作模式切换</td><td style="text-align:center">用来切换工作方式，比如FM、LSB、USB和CW等</td></tr><tr><td style="text-align:center">PRE</td><td style="text-align:center">收信机前置放大器</td><td style="text-align:center">在接收微弱信号时接入（此时某些技术指标可能低于额定值）</td></tr><tr><td style="text-align:center">ATT</td><td style="text-align:center">收信机输入衰减器</td><td style="text-align:center">在接收大信号时接入，使信号不致过大而使前级电路过载</td></tr><tr><td style="text-align:center">AT/TUNE</td><td style="text-align:center">自动天线调谐</td><td style="text-align:center">对天线电路的电压驻波比进行检测并进行自动补偿，以维持最小驻波比</td></tr><tr><td style="text-align:center">DC</td><td style="text-align:center">直接变换</td><td style="text-align:center">接收到的射频信号在解调之前不做频率变换</td></tr></tbody></table><p>使用射频/中频增益和音频增益分开控制的通信接收机进行收听时,可以这样设置: 信号特弱时尽量把射频/中频增益开到最大,信号特强时尽量把音频增益开到最大,然后  从低到高调整另一个增益以得到适当的音量。（信号弱开射频增益）</p><p>ALC：发信自动电平控制,对射频输出电平进行检测并反馈控制,以维持其在适当限度之内（防止过驱动导致调制失真或引发电路故障）即使打开了发射机的 ALC,将话筒的增益调得过高仍可能导致:发出的信号市镇；使用单边带收发信机发送 AFSK 信号时需要关闭 ALC，因为ALC 增加 AFSK 信号的失真,抬升误码率。</p><p>PROC：发信语音压缩,对音频输入电平进行检测并反馈控制,以使包络幅度较小语音获得提升。</p><ul><li>发信时,若话音压缩调整不当可能带来什么问题? 可能产生很多互调成分,影响对方收信时的辨识度</li><li>用单边带收发信机发送 AFSK 信号时应关闭语音压缩功能，语音压缩可能导致信号的包络畸变,破坏基带特征,抬升误码率</li></ul><p><strong>在电缆外面穿套铁氧体磁环</strong>可以减小话筒或耳机用音频电缆可能感生的射频电流?</p><p>AGC：收信机自动增益控制,对中频级信号电平进行检测并反馈控制,防止电路过载。当有用微弱信号和强干扰同时出现时要关闭AGC；接收 FM/FSK/PSK 等包络幅度恒定的信号时选择较短的AGC时间常数；接收 SSB 和 AM 等正常信号的包络幅度不断变化的信号选择较大的AGC时间常数。</p><p>静噪：信噪比达不  到一定水平时自动关闭音频输出</p><ul><li>SQL：静噪控制,用来调整静噪阈值的大小</li><li>作用：在没有信号的情况下关闭音频输出,避免播放刺耳的噪声</li><li>需要聆听非常微弱的 FM 信号时应如何设置收发信机的静噪?关闭静噪或将阈值设为 0,使接收机的音频输出不受限制。</li><li>Digital Coded Squelch：DCS数字亚音</li><li>CTCSS：亚音调静噪,即从 67-250.3Hz 的 38 个亚音调频率中选取一个作为选通信号,代表 38  种状态之一,接收机没有收到特定的选通信号时自动关闭音频输出</li></ul><h4 id="馈线与同轴电缆"><a class="markdownIt-Anchor" href="#馈线与同轴电缆"></a> 馈线与同轴电缆</h4><p>馈线：同轴电缆：</p><ul><li>最适合的同轴电缆特性阻抗为50欧姆</li><li>优点：因为它易于使用,与架设环境之中其他物体间的互耦也很低</li><li>关键电气参数：特性阻抗、指定频率下每百米的传输损耗。</li><li>如果其信号频率升高，则其传输损耗增加。</li><li>外皮需要防紫外线的原因是：如果电缆护套被紫外线破坏,电缆就会<u>受潮</u>损坏</li><li>空气介质同轴电缆需要特别措施来<u>防止湿气渗透</u>。</li><li>馈线损耗会导致：发信功率降低、收信信噪比下降（信号不失真）</li><li>对于 400MHz 或更高频率的信号,应当优先选用的同轴电缆连接器是:N 型连接器</li><li>对于HF 和 VHF 通信系统，多使用M型同轴电缆连接器</li></ul><h4 id="调制器-混频器与滤波器"><a class="markdownIt-Anchor" href="#调制器-混频器与滤波器"></a> 调制器、混频器与滤波器</h4><p>调制器的作用：以原始调制信号控制射频载波的幅度、频率和相位参数。接收机调制器的作用是：从接收到的已调射频信号中分离出原始调制信号。接收机前置放大器的主要作用是:降低接收机内部噪声的影响。选用解调器的主要应考因素是:尽量忠实地还原原始调制信号</p><p>亚音频静噪系统(CTCSS)所用的声调大体位于音频中的什么范围?67-250.3Hz</p><p>混频器：</p><ol><li>频率变换。将信号的原始频率变换成另一个频率</li><li>中频频率高于输入频率的为上变频方式；中频频率低于输入频率的为下变频方式</li></ol><p>中频滤波器所抑制的干扰是临近频率干扰，描述了接收机抗拒邻近频率干扰能力的指标是中频选择性。在超外差式业余收发信机中,负责抑制镜像频率干扰的部件是: 变频级之前的波段预选滤波器</p><hr><p>“通带矩形系数”或“通带形状系数”通常是用来描述<strong>带通滤波器频率特性曲线两侧斜坡的陡峭程度</strong>。陡峭程度越小，机对邻近频道干扰的抑制能力越强。</p><hr><p>用设置在 NFM 方式的对讲机接收 WFM 信号,效果为:可以听到信号。如果调制信号幅度较大或音调较高,会听到明显的非线性失真。</p><p>用设置在 WFM 方式的对讲机接收 NFM 信号,效果为:可以正常听到信号,只是声音比较小。</p><hr><p>哪种电路可以解调 FM 信号?鉴频器（对调频信号进行解调的过程称为鉴频）哪种电路可以解调 AM 信号?检波器（对调幅信号进行解调的过程称为检波）</p><h4 id="极化方式"><a class="markdownIt-Anchor" href="#极化方式"></a> 极化方式</h4><p>使用同样的天线进行通信，极化保持一致，效果更好：一级：1/2 波长水平偶极天线、1/2 波长垂直偶极天线、二级：左旋圆极化天线、右旋圆极化天线。</p><p>左旋圆极化天线与水平偶极天线互相通信的效果相当于两个水平/垂直偶极天线的通信。左旋圆极化天线与右旋圆极化天线的通信效果差</p><p>顺时针、左旋发射天线左旋，接收天线最佳极化方式也是指向发射点的左旋圆极化。</p><ul><li>卫星采用右旋圆极化，从北向南飞行，天线始终指向地球南极，如果地面上某业余电台采用极化卫星天线追踪该卫星，则该台所用天线的最佳极化方式是：卫星过顶前为右旋，过顶后为右旋。</li><li>卫星采用偶极天线，接收天线可以采用指向卫星的右旋或左旋圆极化天线。</li></ul><h4 id="信号干扰与超距离传播"><a class="markdownIt-Anchor" href="#信号干扰与超距离传播"></a> 信号干扰与超距离传播</h4><p>多径传播对 UHF 或 VHF 波段数据通信的影响是: 可能使误码率上升</p><p>用 VSB 方式进行 ATV 通信时,即使信号相对较强,有时所收图像的边缘也有重影。  这是因为:  多径传播。来自不同路径的信号到达接收天线的时延不同,造成重影；发射天线的 VSWR 过高。如果信号在馈线中多次往返于发射机和天线,会造成重影。</p><p>决定超短波视距传播距离极限的主要因素是：发射天线和接收天线距地面的相对高度。</p><ul><li>有时,相隔数百千米的业余电台可以实现 VHF/UHF 超视距直接联络。可能的原因是:号的传播路径中出现了大气波导现象（由大气高空逆温导致）</li><li>有时,我们可以在 6 米或 2 米业余波段中收到上千千米外的“超视距传播”信号：突发 E 层的传播</li><li>有时,VHF/UHF 业余波段中可能出现远达 500 千米的“超视距传播”信号。这与下列哪  种现象密切相关?对流层散射</li></ul><h4 id="选择性指标"><a class="markdownIt-Anchor" href="#选择性指标"></a> 选择性指标</h4><table><thead><tr><th style="text-align:center">指标</th><th style="text-align:center">反应的特性</th></tr></thead><tbody><tr><td style="text-align:center">信道带宽、信道选择性和信道滤波器的矩形系数</td><td style="text-align:center">接收机抗拒工作频率附近干扰信号的能力</td></tr><tr><td style="text-align:center">带内波动和信道带宽</td><td style="text-align:center">接收机接收 SSB 话音信号时的频响均匀程度</td></tr><tr><td style="text-align:center">前端带宽</td><td style="text-align:center">接收机抗拒相距工作频率较远的强干扰信号的能力</td></tr><tr><td style="text-align:center">镜像抑制比</td><td style="text-align:center">接收机抗拒相距工作频率两倍于中频的强干扰信号的能力</td></tr></tbody></table><h2 id="应试篇无线电系统原理"><a class="markdownIt-Anchor" href="#应试篇无线电系统原理"></a> 应试篇：无线电系统原理</h2><p>无线电波范围：3000GHZ以下的</p><ul><li>发射类别：与定义无关的不选，含“只”的不选*</li><li>（AM）单边带发射：只发射一个边带的调幅发射</li></ul><h3 id="电子相关"><a class="markdownIt-Anchor" href="#电子相关"></a> 电子相关</h3><hr><p>音频：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>16</mn><mi>H</mi><mi>z</mi><mo>∼</mo><mn>20</mn><mi>k</mi><mi>H</mi><mi>z</mi></mrow><annotation encoding="application/x-tex">16Hz\sim 20 kHz</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">16</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">∼</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord">20</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mord mathnormal" style="margin-right:0.08125em;">H</span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span></span></span></span></p><p>“击穿”是指施加于绝缘介质上的电压高于一定值时,部分介质突然变成导体,导致介质的电阻陡然下降的一种现象。</p><p>业余无线电设备中的射频部件积灰或受潮后,即使没有击穿或漏电,也可能因绝缘体的物理性质发生改变而意外产生<strong>介质损耗</strong>。</p><blockquote><p>介质损耗：绝缘材料在电场作用下，由于介质电导和介质极化的滞后效应，在其内部引起的能量损耗。</p></blockquote><hr><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>c</mi><mo>=</mo><mi>λ</mi><mo>×</mo><mi>f</mi></mrow><annotation encoding="application/x-tex">c =\lambda\times f</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">c</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.0833em;"></span><span class="mord mathnormal">λ</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span></span></span></span></span></p><ul><li>“电动势”(V): 电子器件或装置将某种形式的能量转化为电能的能力。电源两端电动势的方向为:从电源负极到正极。</li><li>”电压“(V)：加在电路两端的电源驱动电子流动的力量大小。电压方向为从电源正极到负极。</li><li>”电流“(A)：单位时间内流过电路的电子数量</li><li>”电阻“(Ω)：电路从一点到另一点阻碍电流通过的能力大小</li><li>“电源”：一种将某种形式的能量转化为电能的供电装置。常见的有开关电源、线性电源、蓄电池。<ul><li>用蓄电池为电台供电时,应如何估算电池供电的时长?：用电池的标称安时数除以收发信机的平均工作电流</li><li>电源的内阻使电源的实际输出电压降低（电源分压）</li></ul></li><li>”功率“(W)：电流在单位时间内所做的功</li><li>”阻抗“(Ω)：电路从一点到另一点对交流电流阻碍作用的统称</li></ul><table><thead><tr><th>类别</th><th>标准阻抗（Ω）</th></tr></thead><tbody><tr><td>无线电通信及相关测试设备</td><td>50</td></tr><tr><td>电视设备</td><td>75</td></tr><tr><td>音频设备</td><td>600</td></tr></tbody></table><ul><li>正弦交流电的电压、电流的峰值（Peak Value）是指从零点算起的最大值。设备传输接口标准阻抗：</li><li>正弦交流电的电压、电流的峰-峰值（Peak-to-Peak Value）是指从负半周峰值到正半周峰值之间的差值</li><li>任意交流电压的有效值（RMS voltage）是指：在同一电阻上可以转换出与该交流电压效果相同的热量的直流电压</li><li>直流电路欧姆定律：</li></ul><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>R</mi><mo>=</mo><mfrac><mi>U</mi><mi>I</mi></mfrac></mrow><annotation encoding="application/x-tex">R=\frac{U}{I}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0463em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3603em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">I</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">U</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>P</mi><mo>=</mo><msup><mi>I</mi><mn>2</mn></msup><mi>R</mi><mo>=</mo><mfrac><msup><mi>U</mi><mn>2</mn></msup><mi>R</mi></mfrac></mrow><annotation encoding="application/x-tex">P=I^2 R=\frac{U^2}{R}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">P</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8641em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07847em;">I</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.1771em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.4911em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.10903em;">U</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><hr><p>计量单位：分厘毫3微6纳9皮12飞15，千3兆6吉9太12</p><p>“有些收发信机会在 13.8V 直流电源插座附近安装一个标有数字的复位按钮。其作用是：当设备过流时切断电源；当电源极性接反时切断电源。</p><hr><ul><li><p>用万用表的直流电压档测量<strong>正负对称的方波电压</strong>(占空比为 1:1)。所得读数为0</p></li><li><p>如果用磁电式万用表的交流电压档测量正负对称的方波电压(占空比为 1:1),其指针所示的电压读数:大于该电压的峰值（表头按 <code>平均值 × 1.11</code> 来显示“有效值”）</p></li><li><p>用指针式万用表的直流电压档测量最小值为 0 的方波电压(占空比为 1:1),得到的读数  是该电压的:峰值的 1/2,亦为有效值</p></li><li><p>用万用表的电阻档测量一个电路。最开始,电表指示电路的阻值很小。但是随着测量时  间的延长,测量值却变得越来越大（电阻指针左边是极大值）。这是因为：这个电路两端可能存在一个很大的电容</p></li><li><p>测量一个电解电容器是否完好应当使用:指针式万用表的电阻档；数字万用表的电容测试档(如果仪表具备该功能)</p></li><li><p>用指针式万用电表的电阻档测量一个常用元件,表笔第一次连接时表针挥动了一下,但  很快回到零点。断开表笔重新连接,表针却不再有任何指示。正确的推论是:该元件可能是一个电解电容器.</p></li><li><p>指针式万用表的电压档有个“欧姆/伏(每伏欧姆)”指标。越大的每伏欧姆数越说明:测量电压时电表对电路工作状态的影响小</p></li><li><p>用数字万用表的直流电压档测量电路两点间某个等幅音频信号的电压,发现读数不为零。  交换两支表笔之后再测,所得读数的极性反转。正确推论：音频信号上叠加有直流成分。直流档只会影响直流分量。</p></li></ul><h3 id="与业余无线电台有关的安全防护技术"><a class="markdownIt-Anchor" href="#与业余无线电台有关的安全防护技术"></a> 与业余无线电台有关的安全防护技术</h3><p>业余无线电发射设备的下列指标必须符合国家的相关规定:  <strong>频率容限和杂散域发射功率</strong>。（为了防止主要攻略发射其他波段造成干扰）</p><p>业余电台的无线电发射设备应符国家规定的下列主要技术指标：符合频率容限、符合杂散发射最大允许功率电平。</p><p>频率容限是指：</p><ul><li>发射所占频段的<strong>中心频率</strong>偏离指配频率的最大容许偏差，</li><li>发射的<strong>特征频率</strong>偏离参考频率的最大容许偏差</li><li>单位是：百万分之几Hz<br>杂散域发射是指：（<u>在带内</u>）</li></ul><ol><li>必要带宽之外的一个或多个频率的发射,其发射电平可降低而不致影响相应信息的传输</li><li>杂散发射包括谐波发射、寄生发射</li><li>杂散发射包括互调产物、变频产物功率的单位</li></ol><ul><li>绝对功率：dBm</li><li>低于载波发射功率的分贝值 dBc</li><li>低于 PEP 发射功率的相对值 dB<br>业余无线电专用发射设备必须满足的主要技术指标要求包括：频率容限与杂散辐射<strong>不超过</strong>限值，发射频率不超过国家规定的业余业务和卫星业余业务。</li></ul><p>按照国家标准 GB8702-2014《电磁环境控制限值》,从电磁环境保护管理角度,向没有  屏蔽空间发射电磁场可以免于管理的有:</p><ol><li>频率范围为0.1-3MHz，等效辐射功率小于300W的无线电通信设施（设备）</li><li>频率范围为3MHz-300GHz，等效辐射功率小于100W的无线电通信设施（设备）</li></ol><ul><li>根据国家标准 GB8702-2014《电磁环境控制限值》,公众曝露是指：公众所受的全部电场、磁场、电磁场照射。</li><li>为什么我国《电磁环境控制限值》标准中的照射限值伴随频率有所不同?：人体对某些特定波长的电磁波有更多的吸收</li><li>电路接触点打火会产生减幅波辐射</li><li>空中的VHF和UHF属于<strong>非电离辐射</strong></li></ul><h3 id="电磁兼容技术以及射频干扰的预防和消除"><a class="markdownIt-Anchor" href="#电磁兼容技术以及射频干扰的预防和消除"></a> 电磁兼容技术以及射频干扰的预防和消除</h3><p>传统防雷装置的主要组成部分：接闪器(避雷针)、引下线、接地体。</p><ul><li>防雷接地的作用是：把接闪器引入的雷击电流有效地泄入大地</li><li>接地体的要求：要有单独的接地体,接地电阻要小,接闪器到接地体之间的引下线应尽量<strong>短而粗</strong><ul><li><strong>镀银软铜丝编织扁带</strong>最适宜连接天线、塔架和入室馈线等处的各个接地部件。</li></ul></li><li>对于一般建筑物,单支避雷针的保护范围至多能为在避雷针顶点至地面之间,由 60 米半径滚球曲线所构成的空间</li><li>在为同轴馈线安装避雷器时应当注意<strong>将所有避雷器的地线接到同一个金属条带上,然后将条带可靠连到室外的接地处</strong></li></ul><hr><p>考虑实际工作环境必然存在一定的湿度,则根据 GB/T 3805-2008《特低电压 ELV 限值》  在潮湿条件下的限值,当人体握紧某个带电零件时,零件与人体间的电压不可高于: 交流16V，直流33V</p><p>假如接触电压相同,则触及带有射频电压(例如,频率不低于 LF)的裸露导线与触及带  有直流或交流 50Hz 电压的裸露导线相比,人体所受的安全威胁有什么不同?致死风险有所下降,但是灼伤皮肤或深层皮下组织的风险显著上升。</p><p>使用普通 12 伏铅酸蓄电池为电台供电存在什么潜在风险?如果通风不良,会有爆炸性气体（氢气）聚集，快速充电会释放氢气。</p><p>电台室如遇电气设备、电线电缆或者电源装置失火,正确的处置应当为: 立即切断所有供电,使用二氧化碳灭火器或干粉灭火器</p><hr class="footnotes-sep"><section class="footnotes"><ol class="footnotes-list"><li id="fn1" class="footnote-item"><p>新规定于2024/3/1起实行。 <a href="#fnref1" class="footnote-backref">↩︎</a></p></li><li id="fn2" class="footnote-item"><p><a href="https://dovesky.com/275.html">备考B证-无线电发射类型 - DoveSky|BG8LNG</a> <a href="#fnref2" class="footnote-backref">↩︎</a></p></li></ol></section>]]></content>
    
    
    <summary type="html">自2025.10以来，关于业余无线电的相关学习、考试与实践记录。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/humnote.svg" type="image"/>
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
    <category term="⚙️工程机械" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%9A%99%EF%B8%8F%E5%B7%A5%E7%A8%8B%E6%9C%BA%E6%A2%B0/"/>
    
    <category term="📻无线电" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%9A%99%EF%B8%8F%E5%B7%A5%E7%A8%8B%E6%9C%BA%E6%A2%B0/%F0%9F%93%BB%E6%97%A0%E7%BA%BF%E7%94%B5/"/>
    
    
    <category term="奇技淫巧" scheme="https://blog.si-on.top/tags/%E5%A5%87%E6%8A%80%E6%B7%AB%E5%B7%A7/"/>
    
    <category term="技能" scheme="https://blog.si-on.top/tags/%E6%8A%80%E8%83%BD/"/>
    
    <category term="电工学" scheme="https://blog.si-on.top/tags/%E7%94%B5%E5%B7%A5%E5%AD%A6/"/>
    
  </entry>
  
  <entry>
    <title>EP4：有纸化生活</title>
    <link href="https://blog.si-on.top/2025/ep4_PaPerPen/"/>
    <id>https://blog.si-on.top/2025/ep4_PaPerPen/</id>
    <published>2025-09-14T14:48:11.000Z</published>
    <updated>2026-04-05T15:21:22.037Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p>你是否天天与消费主义斗智斗勇，评测，拆箱、生产力…是否在商品挑逗下，一次次几乎被它击溃，然而倔强地一再进行反思，心中默想是必须吗？可替代吗？钱有必要存着吗？有必要花吗？</p><p>不可否认，装置能赋予极大的自由，然而这自由终究不过是装置自己的，那不决是人的自由。人的自由只需要一丁点工具，给肢体一丁点延伸。如果用奥卡姆剃刀给这一丁点装置不断去除非必须的部分，最后留下的不可再简的实体，不过就是纸与笔而已。笔代表时间，纸代表时间的痕迹，在时间中审视时间的痕迹就是在迭代。由此即可涌现出一切文明的造物。</p>        <div id="aplayer-QaaqooXv" class="aplayer aplayer-tag-marker" style="margin-bottom: 20px;">            <pre class="aplayer-lrc-content"></pre>        </div>        <script>          var ap = new APlayer({            element: document.getElementById("aplayer-QaaqooXv"),            narrow: false,            autoplay: false,            showlrc: false,            music: {              title: "EP4：有纸化生活",              author: "秉蕳",              url: "/music/podcast/ep4.mp3",              pic: "/images/Cover/podcast/ep4.png",              lrc: ""            }          });          window.aplayers || (window.aplayers = []);          window.aplayers.push(ap);        </script><p><img src="/images/Cover/podcast/ep4.png" alt></p><ol><li>00:10 关于播客停止五个月的简要说明：维护草稿时间太久以至于新念头浮现使就念头遗忘，</li><li>03:12 压制购买平板设备消费欲望的经历，关于阅读与绘画的两个需求投射到平板上。</li><li>08:32 下单前的最后挣扎，外出散步时对设备进行审视。自己的工具理性其实根深蒂固，对他的批判只是浮于表面</li><li>11:40 对现有工具进行追根溯源，找到它最原始的形貌。</li><li>12:40 当红电子数码设备的根源都可以抽象到纸与笔之中。</li><li>14:55 (上述)工具的本质是人类借由输出的反馈进行迭代的载体，表达迭代的过程（很奇妙）。追寻工具最原始形貌——纸与笔，纸笔的优势。</li><li>18:39 有纸化生活初次尝试的体验。写字比输入法的好处——没有重复，顺畅表达。</li><li>20:40 (自我小批评)，大懒虫就是我</li></ol><p>纸笔乃是人类文明的根基！不要屏幕，心里要更多的纸！不要装置，心里要更多的字！</p><div class="tag link"><a class="link-card" title="👉订阅《虚言》" href="https://blog.si-on.top/audio.xml/"><div class="left"><img src="/images/avator/ava_Lee.svg"></div><div class="right"><p class="text">👉订阅《虚言》</p><p class="url">https://blog.si-on.top/audio.xml/</p></div></a></div><span class="p center small">Nothing Words</span><span class="p center logo large">虚言</span>  ]]></content>
    
    
    <summary type="html">扔开设备，拿起纸笔吧！</summary>
    
    
    <content src="https://blog.si-on.top/images/Cover/podcast/ep4.png" type="image"/>
    
    
    <cover src="https://blog.si-on.top/images/Cover/podcast/ep4W.png" type="image"/>
    
    
    <category term="播客" scheme="https://blog.si-on.top/categories/%E6%92%AD%E5%AE%A2/"/>
    
    
    <category term="podcast" scheme="https://blog.si-on.top/tags/podcast/"/>
    
    <category term="批判性思考" scheme="https://blog.si-on.top/tags/%E6%89%B9%E5%88%A4%E6%80%A7%E6%80%9D%E8%80%83/"/>
    
  </entry>
  
  <entry>
    <title>格风吹草木</title>
    <link href="https://blog.si-on.top/2025/TheShakeOfWind/"/>
    <id>https://blog.si-on.top/2025/TheShakeOfWind/</id>
    <published>2025-09-01T13:25:43.000Z</published>
    <updated>2025-09-01T13:25:43.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><blockquote><center>上而无极、太极，下而至于一草、一木、一昆虫之微，亦各有理。一书不读，则阙了一书道理; 一事不穷，则阙了一事道理; 一物不格，则阙了一物道理。须着逐一件与他理会过。</center><p align="right">——《朱子语录》</p></blockquote><hr><p>午间回宿舍抽闲读了几页判断力批判，概念越发繁复，便合上kindle。抬眼眺向窗外：几棵芦苇被风吹拂，在有节奏地晃动，周遭低矮的垂柳，杂草也在摇动，再看向远处，路旁的行道树也在以树干为单位地晃动着，树叶婆娑，尽管隔着窗子，也仍看到那沙沙声。看着看着，逐渐产生了一种愉悦的感觉。</p><p>前不久<a href="/2025/oh_my_hand">说过</a>要留意一些没有意义的东西，这晃动多半是没有意义的(在此不论及由此而产生的发电机的灵感)，那么为何风吹树叶摇动能让我感觉到愉悦呢？纵然这感觉不可名状，为了名状它，当分析一二再说。</p><p>风、木、树叶摇动都是自然的造物与自然的因果，它们的存在具有一种不容置疑的合理，用判断力批判中的解读来说就是自然形式合目的性——“这种合目的性，只与对象对于主体认识能力的适应性相关，因而具有形式上普遍引起愉快的特点。”想当初王阳明格竹致疾，却什么也没格到，就是他心性还没达到可以认识竹的能力(无论是理性还是感性)，不仅得不到愉悦，得不到竹的道理，反而充满了痛苦。</p><p>风吹动树叶，树叶摇动，满足对常识的判断。且不论这判断是否严密，且不考虑树木的高度、树杈的分布，树叶的形状对摇动产生怎样怎样的影响。</p><p>因为树叶动了，单单树叶被风吹产生摇动这简单判断的本身的验证，就会造成一种愉悦。况且如果不止是一片叶子，一棵树，而是一万片叶子，无穷多的树木，都在风的吹拂下摇动，不停的验证着这个判断。这种无数次多验证带来的近乎知性的东西，会带来一种更深的愉悦，可谓致知了。</p><p>这树叶摇动毕竟是“向外求理”纯粹的他律，这愉悦之感必然也需要“逐物而返”回归内在。天地同心一理，我心中某个地方定然也有风吹树叶摇动的沙沙声，这沙沙声响，定然也唤起了另一些想法，念头。外界的摇动与内在的摇动忙碌地呼应着，而我只是默默地看着，想着，只感一愉悦。</p><hr><p>按: 格物致知，经世致用，这将是未来日子里实践的新原则。康德哲学这一套东西确实繁琐地厉害，晚上在桥头读了个把小时，几乎无所收获，更何谈经世致用，枉费了我几个小时的精力。不若把笔记完善好后就此作罢算了。</p>]]></content>
    
    
    <summary type="html">对无用之物进行审视。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/20250610/IMG_20220909_175525.jpg" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="🪶杂谈" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%F0%9F%AA%B6%E6%9D%82%E8%B0%88/"/>
    
    
    <category term="情绪" scheme="https://blog.si-on.top/tags/%E6%83%85%E7%BB%AA/"/>
    
    <category term="格物" scheme="https://blog.si-on.top/tags/%E6%A0%BC%E7%89%A9/"/>
    
  </entry>
  
  <entry>
    <title>W山游记</title>
    <link href="https://blog.si-on.top/2025/Travel_of_the_W/"/>
    <id>https://blog.si-on.top/2025/Travel_of_the_W/</id>
    <published>2025-08-31T14:31:04.000Z</published>
    <updated>2025-08-31T17:31:04.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><div class="tip sync"><p>匆忙写就，文白混乱，词句不通，有待润色。</p></div><p>岁在乙巳，时值处暑，金风未至，暑热依然。周末方醒，忽生登W山(五磊)之念想。W山距撇室<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>东南七十余里，过附海、观海、绕杜湖，又盘山十里方至。所行不远，时间可贵，欣然规往，且行且谋之。</p><p>九时起身，乘公车走，换乘二车，无缝衔接，约十时许至观城。备水储粮，决意游山整日，傍晚且归。绕杜湖行，未及山脚，已见山来。是日天朗云清，云汽弥漫缀乎群山之中，海云之白、远山之青、天光之蓝、湖色之碧，杂然乎一目之中，心游世界，顿失其所在。十一时，至山脚。</p><p>山有溪，藏云其名也，自山巅小池出，绕乱石，冲泥沙，成小潭，蜿蜒而下。沿溪有步道，余携相机，拾阶而上，且行且玩，且赏且拍。</p><p>溪侧有茂林古竹，密而不乱，两岸枝干，交叠溪上。日色下照，光影明灭，斑驳石中。</p><p>行走间，忽见蓝影翩翩溪流上，余甚为惊讶，追逐而行，欲拍之。少顷，蓝影止于一突兀石上，吾缓慢凑近，调整参数，摄以特写，定睛看，乃一蓝色蟌䗓，其体碧绿，其翅翠蓝，世间竟有如此华丽之虫，相较之下，往日所见之蓝色摩萝叶甲也顿失趣味。</p><p>蟌䗓忽游走，溪水自流深。</p><p>下小潭，见虎斑小鱼、河虾三五只游荡溪石间，上有水黾。日光下澈，水黾之影投射水底，如微型黑洞；溪流击石，波晕散漫。时鱼、黾之动，虾、影之慢，杂糅一处，动静相宜，可爱有趣，甚觉快哉。</p><p>复登高，稍行百十阶，已觉酷热非常，汗如雨下，上衣几乎湿透。强行至山顶空石处，解衣赤背，晒衣石上。于石荫处歇息，瞭远山，观C城，看积云。归寺中拍照，无非飞檐走壁，古树老僧，川蜀游人而已，略知。</p><p>下午二时，到山门，忽雷声大作，未闻如此响动，如在头顶。始知所处愈高，所闻愈响。少顷，烈雨如注，止于庙门避雨。阵雨初歇，趁凉爽，复登顶，然岩上水汽蒸发，白气阵阵，燥热非常，又赤背晒衣石上😂。四时许，山风大作，暴雨欲来，狼狈下山归家。</p><hr><p>所摄一二，罗列于下<br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011901147.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011857058.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011638701.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011926940.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011915138.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011908759.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011758939.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011816277.webp" alt></p><p><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011833707.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011751512.webp" alt></p><p><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011708144.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011825074.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011726420.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011733615.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011740351.webp" alt><br><img src="/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011807228.webp" alt></p><hr class="footnotes-sep"><section class="footnotes"><ol class="footnotes-list"><li id="fn1" class="footnote-item"><p>出租屋之名号，甲辰八月初次租房，命名点室，取自《平面国》中的点国，乙巳雨水搬至此处，房间略大，名以撇. <a href="#fnref1" class="footnote-backref">↩︎</a></p></li></ol></section>]]></content>
    
    
    <summary type="html">二游W山，胡乱记之。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/20250610/W%E5%B1%B1%E6%B8%B8%E8%AE%B0-20250901011833707.webp" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="✒️随笔" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%E2%9C%92%EF%B8%8F%E9%9A%8F%E7%AC%94/"/>
    
    
    <category term="情绪" scheme="https://blog.si-on.top/tags/%E6%83%85%E7%BB%AA/"/>
    
    <category term="文言" scheme="https://blog.si-on.top/tags/%E6%96%87%E8%A8%80/"/>
    
    <category term="旅游" scheme="https://blog.si-on.top/tags/%E6%97%85%E6%B8%B8/"/>
    
  </entry>
  
  <entry>
    <title>巨人的荷塘</title>
    <link href="https://blog.si-on.top/2025/LotusPond@Giant/"/>
    <id>https://blog.si-on.top/2025/LotusPond@Giant/</id>
    <published>2025-08-21T03:46:00.000Z</published>
    <updated>2025-08-21T03:46:00.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p>从围墙翻将进去，迎面是几亩方塘，中间一道绿油油的小路把池塘分成整齐的两块。<br><img src="/images/20250610/DSC_9204.jpg" alt></p><p>靠东边的塘中是一块斑驳的荷田，临近处暑，荷叶却已然憔悴了不少，枯萎正不知不觉间从荷塘深处蔓延开来。荷花也开的不甚齐整，这朵正含苞待放，下旁却已经有旁处飘来的落花；而那朵花开殆尽的枯萎莲蓬正兀自飘摇零落着，一边却有咄咄逼人的尖尖角露将出来。生老病死，荷花的一生，此刻竟全在一处了。</p><p><img src="/images/20250610/DSC_9210.jpg" alt><br><img src="/images/20250610/DSC_9203.jpg" alt></p><p>塘边则尽是些狗尾草、山柳菊，田菁之类的野草🌿，偶有一两株细长的稗子从绿意里伸将出来，在发红的日光下摇曳着微粉的须芒。花草个个争先恐后，都要在这有限的时间里放出光来。<img src="/images/20250610/DSC_9241.jpg" alt><img src="/images/20250610/DSC_9251.jpg" alt><br>暮色将至，蚊虫开始活动，蜻蜓也随之忙碌起来，大的，小的，红的，蓝的，不住得在塘中盘旋，绕得我眼花缭乱，乃至走了大半圈池塘，才发现了一只停住的蜻蜓。本想寻点惬意，体会下“小荷才露尖尖角，早有蜻蜓立上头”的松弛，这哪儿会有？闲不了一点儿，这群造物，分明都是些亡命之徒，这会儿哪怕两只蜻蜓飞的太快，互相撞架摔进水里也不是什么奇怪事。<img src="/images/20250610/DSC_9220.jpg" alt><br>还没转多久，日头就已经落下，傍晚光线变化大的快门参数不好调整，便收起了相机，张望着信步走起来。因为背着书包的缘故，背上早已汗津津的，衣服粘在皮肤上不甚自在。再者怕待久了守门人会忽然从某个地方钻出来找我麻烦，便趁着暮色，急匆匆地翻出去了。</p>]]></content>
    
    
    <summary type="html">乙巳年处暑前二日，在路边某无名荷塘观景后的随笔。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/20250610/DSC_9203.jpg" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="✒️随笔" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%E2%9C%92%EF%B8%8F%E9%9A%8F%E7%AC%94/"/>
    
    
    <category term="即兴" scheme="https://blog.si-on.top/tags/%E5%8D%B3%E5%85%B4/"/>
    
  </entry>
  
  <entry>
    <title>小心王二麻子</title>
    <link href="https://blog.si-on.top/2025/Top_secret_cannot_let_WangerMathy_know/"/>
    <id>https://blog.si-on.top/2025/Top_secret_cannot_let_WangerMathy_know/</id>
    <published>2025-08-15T14:39:04.000Z</published>
    <updated>2025-08-15T14:39:04.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p>传说在有穷国的乌有地，有两大门派，一派以张三为首的张派，师法天地，一派是李四为首的李派，师法本心。两派虽在世界本源的问题上相争千年，但却从未发生过冲突，反而在互相的责难中共同进步。</p><p>一年春天，几十个来自无穷国的以王二麻子为首的王派闯入乌有地，自称有统一张、李两派分歧的方法，只要两个门派将自己的思想完全阐述，便可在百日之内给出一个统一理论。两派闻听这外来的和尚竟有如此大能耐，便纷纷向它述说自己门派的奥秘。</p><p>在经过王派子弟三个多月的调研，眼看着就要到第一百天了，忽然王派的人踪影全无，如同凭空蒸发一样，连个毛都没有。</p><p>人们诧异、失望、而后平静下来继续生活，继续争辩。</p><p>第二年秋天，一位云游四海的老者回到乌有地，向众人谈起外界A国、B国的种种见闻，人们不禁唏嘘起这些国家百姓的苦痛来。谈话间老者说在M国有一个学派，徒众甚广，几乎遍布列国，老者仔细听过他们几次演说，其主张与本地的张、李两派几近相同，在根本问题是只是用一个机能属性之类的模糊字眼连接两者，糊弄过去，但因其一些思想（仍是抄来的）甚是切实理性，而广受欢迎。人们便向老者谈及两年前王派的那场闹剧，当谈及王二麻子的长相时，老者一个激灵，啊呀一声，气愤填膺指着M国的方向怒骂道“王二麻子，盗我乌有地百年基业而只字不提出处，真欺世盗名，鳖孙儿子也！”</p><p>当学派的掌门人张三、李四秘密调查本地与外地的情况后，发现每当乌有地有研究新内容，不出三日，在外界便有雷同的述说，他们终于明白：乌有地存在一个王派特务的地下据点！</p><p>自此，张李两派，人人自危，不再进行广泛地讨论，宁愿沉默也不愿思辨成果被王二麻子这群鳖孙们盗了去。</p><p>然而，当主动沉默还没满一月，张李两派，便都觉得在没有对立门派的责难下，在自己内部开展的思辨活动变得越发偏执。师法天地的张派内部甚至分化成了诸多小派，比如张派为本，李派为用的张李派、主张实践为目的的行字张、主张认识为目的的知字张，还有一群年长者组成的原旨张派等等等等，小派系之间纷争不断，早已没了乌有地那种平和的氛围。</p><p>在冬至日，张三、李四秘密会见，交换意见后纷纷表示两派必须进行定期的信息交流，否则乌有地不日就将陷入如同外界战国一般的地狱景象。然而信息传递又不可避免地会被王二麻子渗透的特务看到，必须进行加密。</p><p>乌有地的技术远没有外界发达，简单的加密手段很容易就被王二麻子破译掉。</p><p>这年九月十五，阳历是西方的万圣节，当各派长老苦于没有合适的加密手段茶饭不思，一筹莫展之时，打乌有溪对岸走来三个人，三人自称叫作瑞娃子，沙弥儿和阿地蛮，提出了一种名为RSA的异世界超级加密方法。长老们在研习了其中机理后，纷纷满意的点了点头。下面是瑞娃子给长老们讲解加密操作时的讲义，暂摘录在此：</p><h2 id="密学第三次实操指导"><a class="markdownIt-Anchor" href="#密学第三次实操指导"></a> 密学·第三次实操指导</h2><h3 id="gpg加密"><a class="markdownIt-Anchor" href="#gpg加密"></a> GPG加密</h3><figure class="highlight bash"><figcaption><span>张三生成自己的公私钥，将公钥分发出去</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line">gpg --batch --generate-key &lt;&lt;<span class="string">EOF</span></span><br><span class="line"><span class="string">Key-Type: RSA</span></span><br><span class="line"><span class="string">Key-Length: 2048</span></span><br><span class="line"><span class="string">Name-Real: Zhang San</span></span><br><span class="line"><span class="string">Name-Email: Zhang3@nowhere.Land</span></span><br><span class="line"><span class="string">Expire-Date: 0</span></span><br><span class="line"><span class="string">%no-protection</span></span><br><span class="line"><span class="string">EOF</span></span><br><span class="line">gpg --<span class="built_in">export</span> -a <span class="string">&quot;Zhang San&quot;</span> &gt; 张三RSA.pub</span><br><span class="line">gpg --export-secret-key -a <span class="string">&quot;Zhang San&quot;</span> &gt; 张三RSA.priv</span><br></pre></td></tr></table></figure><figure class="highlight bash"><figcaption><span>李四生成自己的公私钥，也将公钥分发出去</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line">gpg --batch --generate-key &lt;&lt;<span class="string">EOF</span></span><br><span class="line"><span class="string">Key-Type: RSA</span></span><br><span class="line"><span class="string">Key-Length: 2048</span></span><br><span class="line"><span class="string">Name-Real: Li Si</span></span><br><span class="line"><span class="string">Name-Email: Li4@nowhere.Land</span></span><br><span class="line"><span class="string">Expire-Date: 0</span></span><br><span class="line"><span class="string">%no-protection</span></span><br><span class="line"><span class="string">EOF</span></span><br><span class="line">gpg --<span class="built_in">export</span> -a <span class="string">&quot;Li Si&quot;</span> &gt; 李四RSA.pub</span><br><span class="line">gpg --export-secret-key -a <span class="string">&quot;Li Si&quot;</span> &gt; 李四RSA.priv</span><br></pre></td></tr></table></figure><figure class="highlight bash"><figcaption><span>张三操作，通过李四公开的公钥，加密张派机密文件给李四</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"># 导入李四的公钥</span></span><br><span class="line">gpg --import 李四RSA.pub</span><br><span class="line"></span><br><span class="line"><span class="comment"># 用李四公钥加密文件</span></span><br><span class="line">gpg --encrypt --recipient Li4@nowhere.Land --output 张派顶级机密.txt 张派绝密.txt</span><br></pre></td></tr></table></figure><figure class="highlight shell"><figcaption><span>李四操作，利用私钥解密上述文件</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta prompt_"># </span><span class="language-bash">李四导入自己的私钥</span></span><br><span class="line">gpg --import 李四RSA.priv</span><br><span class="line"><span class="meta prompt_"></span></span><br><span class="line"><span class="meta prompt_"># </span><span class="language-bash">解密文件</span></span><br><span class="line">gpg --decrypt --output 张派绝密.txt 张派顶级机密.txt</span><br></pre></td></tr></table></figure><h3 id="openssl"><a class="markdownIt-Anchor" href="#openssl"></a> OpenSSL</h3><figure class="highlight shell"><figcaption><span>张三生成自己的公私钥，将公钥分发出去</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">openssl genrsa -out 张三RSA.priv 2048</span><br><span class="line">openssl rsa -in 张三RSA.priv -pubout -out 张三RSA.pub</span><br></pre></td></tr></table></figure><figure class="highlight shell"><figcaption><span>李四生成自己的公私钥，也将公钥分发出去</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">openssl genrsa -out 李四RSA.priv 2048</span><br><span class="line">openssl rsa -in 李四RSA.priv -pubout -out 李四RSA.pub</span><br></pre></td></tr></table></figure><figure class="highlight shell"><figcaption><span>张三操作，通过李四公开的公钥，加密张派机密文件给李四</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">openssl rsautl -encrypt -pubin -inkey 李四RSA.pub -in 张派绝密.txt -out 张派顶级机密.txt</span><br></pre></td></tr></table></figure><figure class="highlight shell"><figcaption><span>李四操作，利用私钥解密上述文件</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">openssl rsautl -decrypt -inkey 李四RSA.priv -in 张派顶级机密.txt -out 张派绝密.txt</span><br></pre></td></tr></table></figure><h3 id="openssh"><a class="markdownIt-Anchor" href="#openssh"></a> OpenSSH</h3><p>SSH的定位是安全通信，没有文件加密的功能，在这里提一下吧，如果想要用ssh的公私钥进行加密，需要用<code>ssh-keygen</code>将其转换成openSSL支持的PEM格式。<code>ssh-keygen -f 李四RSA.pub -e -m pem &gt; 李四RSA_pem.pub</code></p><p>SSH默认输出的公私钥明灭是：私钥名自定义，公钥在私钥名基础上加<code>.pub</code>后缀</p><figure class="highlight shell"><figcaption><span>张三生成公私钥</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">ssh-keygen -t rsa -b 2048 -C &quot;Zhang3@nowhere.Land&quot; -f 张三RSA -N &quot;&quot;</span><br></pre></td></tr></table></figure><p>执行操作后就会产生名为<code>张三RSA</code>的私钥与<code>张三RSA.pub</code>的公钥。</p><figure class="highlight shell"><figcaption><span>李四生成公私钥</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">ssh-keygen -t rsa -b 2048 -C &quot;Li4@nowhere.Land&quot; -f 李四RSA -N &quot;&quot;</span><br></pre></td></tr></table></figure><hr><p>在经过瑞娃子，沙弥儿和阿地蛮三位异人的耐心指导下，张李两派通过非对称加密的方法成功地恢复了乌有地往日的平静，各派系内部的争论也以在外派帮助下转移到自身的完善为终。</p><p>就这样，又过了一千年。</p><p>一天夏天，量子计算机研究的风声从外地传到了乌有地，当技术部门评定该技术会破解旧有的RSA所依赖的加密算法，所有历史文件都有可能被王二麻子破解后，人们有一次陷入恐慌。<strong>乌有地标准与技术研究所</strong>（NIST：Nowhereland Institute of Standards and Technology）当即令开发人员着手研究抗量子算法Dilithium，并逐渐弃用旧有算法，同时销毁历史文件。</p><p>四个月后，抗量子算法研究成功，以下是加密通信变动的内容</p><h2 id="抗量子算法加密示例"><a class="markdownIt-Anchor" href="#抗量子算法加密示例"></a> 抗量子算法加密示例</h2><h3 id="gpg"><a class="markdownIt-Anchor" href="#gpg"></a> GPG</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"># 需要编译支持PQC的GPG分支（如pqc-gpgme）</span></span><br><span class="line"><span class="comment"># 生成CRYSTALS-Dilithium（NIST选定PQC算法）密钥</span></span><br><span class="line">gpg --batch --generate-key &lt;&lt;<span class="string">EOF</span></span><br><span class="line"><span class="string">Key-Type: DILITHIUM5</span></span><br><span class="line"><span class="string">Name-Real: Zhang San</span></span><br><span class="line"><span class="string">Name-Email: Zhang3@nowhere.Land</span></span><br><span class="line"><span class="string">Expire-Date: 0</span></span><br><span class="line"><span class="string">%no-protection</span></span><br><span class="line"><span class="string">EOF</span></span><br></pre></td></tr></table></figure><h3 id="openssh-2"><a class="markdownIt-Anchor" href="#openssh-2"></a> openSSH</h3><figure class="highlight bash"><figcaption><span>需要OpenSSH 9.0+</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"># 生成NTRU Prime抗量子密钥（x25519-ntruprime）</span></span><br><span class="line">ssh-keygen -t x25519-ntruprime-sntrup761 -C <span class="string">&quot;Zhang3@nowhere.Land&quot;</span> -f 张三NTRU</span><br></pre></td></tr></table></figure><h3 id="openssh-3"><a class="markdownIt-Anchor" href="#openssh-3"></a> openSSH</h3><figure class="highlight bash"><figcaption><span>需要OpenSSL 3.2+</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment"># 生成CRYSTALS-Kyber（NIST选定KEM方案）</span></span><br><span class="line">openssl genpkey -algorithm kyber768 -out 张三Kyber.priv</span><br><span class="line">openssl pkey -<span class="keyword">in</span> 张三Kyber.priv -pubout -out 张三Kyber.pub</span><br><span class="line"></span><br></pre></td></tr></table></figure>]]></content>
    
    
    <summary type="html">一定不能让这帮家伙知道。</summary>
    
    
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
    <category term="⌨️软件编程" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%8C%A8%EF%B8%8F%E8%BD%AF%E4%BB%B6%E7%BC%96%E7%A8%8B/"/>
    
    
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  </entry>
  
  <entry>
    <title>手</title>
    <link href="https://blog.si-on.top/2025/oh_my_hand/"/>
    <id>https://blog.si-on.top/2025/oh_my_hand/</id>
    <published>2025-08-04T14:57:14.000Z</published>
    <updated>2025-08-04T14:57:14.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p>今晚按照前日定下的计划，练了练MIDI琴，这是自三月份弃置以后，第二次进行积极地练习。大概是第一次热情褪去的同时，也褪去了对新鲜工具那种包裹着贪念的欲望，这第二次似乎能更客观而冷静地进行学习了。之前总想着能弹一首完整的曲子Show出来因而不重视练习，直接拿复杂的谱去弹，虽然费老大劲弹出个大概来，但也仅此而已。热情褪去，一切都变得无趣。</p><p>与之前所有的计划都不同，本次的练习有着一个抽象的目的——从实践中审视工具。古往今来对于工具那么多凛冽入骨的批判思考对实践的帮助委实不大，唯有在亲身实践中审视而得来的才真正为自己所有。</p><div class="abc-music-sheet">X: 4T: 练习一M: 4/4 L: 1/4Q: 1/4=140K: CV: 1  name=&quot;右手&quot;| cdec | dedz | efgf| edcz| \V: 2  name=&quot;左手&quot;| CDEC | DEDz | EFGF | EDCz| \</div><p>在对上面的《练习一》这首曲子：1231 2320 3454 3210 (简谱)进行将近一个小时的不断地重复练习后，发现手指敲击的准确度明显提高，甚至不需要思考，只需要就那样地子按下去。结束后，发觉手腕发酸，筋肉记忆建立的过程是这般痛苦的吗？稍歇片刻，又尝试双手弹奏，一开始是很恐惧的(高中看金庸武侠中左右互搏的神功，后左手画圆，右手画方尝试失败带来的心理阴影)，仍耐着性子按下去，不多时，这种筋肉记忆自然也建立起来了，后面几乎能很顺畅地弹奏下去。</p><h2 id="功用"><a class="markdownIt-Anchor" href="#功用"></a> 功用</h2><p>练习结束后出去超市买水，看着手投影到地上的影子，便下意识对这手审视起来——这手竟然能做这么多事情，写字，画画，骑车，搬砖，锄地，三百六十行，十八般武艺，样样都是直接或间接地依靠手去执行的。我用右手模仿着刚才弹琴的指法，看着它，赞叹它的能力如此之强。又跟着步伐，有节奏地用手甩几个很酷的手势。</p><h2 id="目的"><a class="markdownIt-Anchor" href="#目的"></a> 目的</h2><p>在路边，我看到一个花盆。花盆的顶部有一个边沿(就是顶部直径大于盆体向外突出的部分)，这个边缘存在的目的是什么呢？它设计成这样必然是为了方便搬运或者吊装，这个结构作为最终的结果，其与需求/原因是一脉相承的。</p><p>快走进超市时，当花盆的这个念头对应到手上时，我的眼光突然发生变化，周围一切的一切都变得陌生起来。门口这个垃圾桶是为手设计的，这个女士开的轿车的方向盘是为手设计的，这个师傅骑的电动车的把手，手刹也是的。</p><p>走进超市，哇！超市这个门把手也是为手设计的！这边冰柜里的饮料瓶、瓶盖也是，还有这个辣条的包装、那个小推车、称重的称、筷子、刀子、笔…哇奥，我一抬头，全都是以手为目的的！</p><p>我拿了瓶水走出超市。回头瞥了一眼超市——它的目的呢？</p><p>是人！<strong>整个人类文明都是以人为目的</strong>！生产是为了人，消费是为了人，工业发展是为了人，环境保护也是为了人。城市存在的目的是为了人，所有的衣食住行、声色犬马，理性感性、认识实践都是以人为目的。</p><p>我审视这个略显仓促的答案——从人出发得到的对目的的寻求竟然又归为自身，原因与目的竟然是一个东西，形成了一个闭环。推而广之那宇宙的目的呢？从它的角度来说，它脱离了人，不与一切有任何一点点价值判断的关联。它的目的难道也是他自己本身——宇宙存在的意义就是宇宙？！</p><p>我讨厌闭环，衔尾蛇，这是无聊且无益的一个象征。如果一个一个原因产生了一个目的，而这两者最终竟然是一样的东西，那么这个过程到底产生了什么呢？那么人类跟人类存在是没有区别的吗？这中间应当有一个别的新东西，然而我现在找不到。如果不去查资料的话，单就个人实践而言，应当去<strong>审视那些无用之物</strong>，那些从现在过去乃至未来都绝对对人毫无意义价值的东西。</p><h2 id="异化"><a class="markdownIt-Anchor" href="#异化"></a> 异化</h2><p>在回去的路上我又一次摆弄自己的手。我意识到：我竟然能够控制它！不需要思考就能控制它。</p><p>“别的手指不动，把食指使劲地向上拉。”我在潜意识里这样命令道，它果然这样向上指着，我感受到指根的韧带在拉伸。</p><p>“再来！别的手指不动，把无名指像食指一样使劲地向上拉。”我在又命令道，然而它不能，只略微的抬了一点点。</p><p>我意识到这个作为工具的手是有局限的，每个手指的灵活性都有所不同，难怪那会儿在弹奏的时候总想用食指去代替无名指击键。然后就对这双手产生了一种异样的感觉——这双手真是我的吗？我的定义是包括了手的我吗？没有了手，我是不是我呢？没有了四肢，没有了大脑，那我是不是我呢？太玄了，这个想法就此搁置，不想了，等日后读闲书时候(也可能是我之前已经看到的想法在内心里扎根后形成的，然而我却并没有意识到它究竟来自哪里)，留意一下有没有跟这个想法有联系的地方？</p>]]></content>
    
    
    <summary type="html">关于作为工具的手的审视</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/20240609/%E7%94%B5%E5%AD%90%E7%BB%98%E7%94%BB%E7%BB%83%E4%B9%A0-20240630003903580.webp" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="🪶杂谈" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%F0%9F%AA%B6%E6%9D%82%E8%B0%88/"/>
    
    
    <category term="审视" scheme="https://blog.si-on.top/tags/%E5%AE%A1%E8%A7%86/"/>
    
    <category term="意义" scheme="https://blog.si-on.top/tags/%E6%84%8F%E4%B9%89/"/>
    
  </entry>
  
  <entry>
    <title>Oxygen Pro Mini 使用手册</title>
    <link href="https://blog.si-on.top/2025/Oxygen%20Pro%20Mini%20User%20Guide/"/>
    <id>https://blog.si-on.top/2025/Oxygen%20Pro%20Mini%20User%20Guide/</id>
    <published>2025-08-03T15:53:33.000Z</published>
    <updated>2025-08-04T03:34:33.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><div class="tip home"><p>近日在审视哈贝马斯工具理性批判后形成了一系列模糊的形而下学观点，就在这个燥热的八月，借助二月份一时冲动购置的却即将吃灰的设备进行一次试验性的实践。</p></div><details class="folding-tag" green><summary> ✍文章痕迹 </summary>              <div class="content">              <div class="timeline  green"><div class="timeline-item headline">        <div class="timeline-item-title">          <div class="item-circle"><p>写作时间线</p></div>        </div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-02-25</p></div>        </div>        <div class="timeline-item-content"><p>初次撰写此文</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-08-03</p></div>        </div>        <div class="timeline-item-content"><p>在ai辅助下，完成此文</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-08-04</p></div>        </div>        <div class="timeline-item-content"><p>实践后，按照自己易于理解的风格进行重整。</p></div>      </div></div>              </div>            </details><div class="markmap-container" style="height:300px">  <svg data="{&quot;type&quot;:&quot;root&quot;,&quot;depth&quot;:0,&quot;content&quot;:&quot;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[0,1]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E7%AE%80%E4%BB%8B\&quot;&gt;简介&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[1,2]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%8C%85%E8%A3%85%E7%9B%92%E5%86%85%E5%AE%B9\&quot;&gt;包装盒内容&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[2,3]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%94%AF%E6%8C%81\&quot;&gt;支持&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[3,4]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E8%AE%BE%E7%BD%AE\&quot;&gt;设置&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[4,5]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E8%BF%9E%E6%8E%A5\&quot;&gt;连接&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[5,6]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%90%8E%E9%9D%A2%E6%9D%BF\&quot;&gt;后面板&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[6,7]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%88%9D%E5%A7%8B%E8%AE%BE%E7%BD%AE\&quot;&gt;初始设置&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[7,8]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%88%9D%E5%A7%8B%E8%AE%BE%E7%BD%AE---daw-%E8%AE%BE%E7%BD%AE\&quot;&gt;初始设置 - DAW 设置&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[8,9]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%88%9D%E5%A7%8B%E8%AE%BE%E7%BD%AE---%E8%99%9A%E6%8B%9F%E4%B9%90%E5%99%A8--%E6%8F%92%E4%BB%B6%E8%AE%BE%E7%BD%AE\&quot;&gt;初始设置 - 虚拟乐器 / 插件设置&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[9,10]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%88%9D%E5%A7%8B%E8%AE%BE%E7%BD%AE---%E7%A1%AC%E4%BB%B6%E5%90%88%E6%88%90%E5%99%A8\&quot;&gt;初始设置 - 硬件合成器&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[10,11]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%AE%89%E8%A3%85%E9%9A%8F%E9%99%84%E8%BD%AF%E4%BB%B6\&quot;&gt;安装随附软件&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[11,12]},&quot;content&quot;:&quot;&lt;a href=\&quot;#daw-%E5%92%8C%E8%99%9A%E6%8B%9F%E4%B9%90%E5%99%A8\&quot;&gt;DAW 和虚拟乐器&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[12,13]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%A2%84%E8%AE%BE%E7%BC%96%E8%BE%91%E5%99%A8\&quot;&gt;预设编辑器&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[13,14]},&quot;content&quot;:&quot;&lt;a href=\&quot;#mpc-beats\&quot;&gt;MPC Beats&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[14,15]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E8%AE%BE%E7%BD%AE%E9%94%AE%E7%9B%98%E7%9A%84%E6%93%8D%E4%BD%9C%E6%A8%A1%E5%BC%8F\&quot;&gt;设置键盘的操作模式&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[15,16]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%8A%9F%E8%83%BD\&quot;&gt;功能&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[16,17]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%89%8D%E9%9D%A2%E6%9D%BF%E7%90%B4%E9%94%AE--%E5%85%AB%E5%BA%A6--%E8%BD%AE\&quot;&gt;前面板(琴键 / 八度 / 轮)&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[17,27]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%9F%BA%E6%9C%AC%E6%A6%82%E5%BF%B5\&quot;&gt;基本概念&lt;/a&gt;&lt;br&gt;\n- &lt;a href=\&quot;#%E9%94%AE%E7%9B%98\&quot;&gt;键盘&lt;/a&gt;&lt;br&gt;\n- &lt;a href=\&quot;#%E5%85%AB%E5%BA%A6%E5%92%8C%E7%A7%BB%E8%B0%83\&quot;&gt;八度和移调&lt;/a&gt;&lt;br&gt;\n- &lt;a href=\&quot;#%E9%80%9F%E5%BA%A6%E6%8E%A7%E5%88%B6\&quot;&gt;速度控制&lt;/a&gt;&lt;br&gt;\n- &lt;a href=\&quot;#%E9%9F%B3%E7%AC%A6%E9%87%8D%E5%A4%8D--%E9%94%81%E5%AE%9A%E9%94%AE\&quot;&gt;音符重复 / 锁定键&lt;/a&gt;&lt;br&gt;\n- &lt;a href=\&quot;#%E9%A2%84%E8%AE%BE\&quot;&gt;预设&lt;/a&gt;&lt;br&gt;\n- &lt;a href=\&quot;#daw-%E5%92%8C%E9%A2%84%E8%AE%BE%E6%A8%A1%E5%BC%8F\&quot;&gt;DAW 和预设模式&lt;/a&gt;&lt;br&gt;\n- &lt;a href=\&quot;#shift-%E9%94%AE\&quot;&gt;Shift 键&lt;/a&gt;&lt;br&gt;\n- &lt;a href=\&quot;#%E8%BF%94%E5%9B%9E%E9%94%AE\&quot;&gt;返回键&lt;/a&gt;&lt;br&gt;\n- &lt;a href=\&quot;#%E7%BC%96%E7%A0%81%E5%99%A8%E5%92%8C%E7%BC%96%E7%A0%81%E5%99%A8%E9%94%AE\&quot;&gt;编码器和编码器键&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[27,28]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%A8%A1%E5%BC%8F%E9%94%AE\&quot;&gt;模式键&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[28,29]},&quot;content&quot;:&quot;&lt;a href=\&quot;#daw-%E6%A8%A1%E5%BC%8F\&quot;&gt;DAW 模式&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[29,30]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%A2%84%E8%AE%BE%E6%A8%A1%E5%BC%8F\&quot;&gt;预设模式&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[30,31]},&quot;content&quot;:&quot;&lt;a href=\&quot;#arp-%E5%92%8C-arp-%E9%94%81%E5%AE%9A%E6%8E%A7%E5%88%B6\&quot;&gt;ARP 和 ARP 锁定控制&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[31,32]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%99%BA%E8%83%BD%E5%92%8C%E5%BC%A6%E6%8E%A7%E5%88%B6\&quot;&gt;智能和弦控制&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[32,33]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%99%BA%E8%83%BD%E9%9F%B3%E9%98%B6%E6%8E%A7%E5%88%B6\&quot;&gt;智能音阶控制&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[33,34]},&quot;content&quot;:&quot;&lt;a href=\&quot;#daw-%E6%97%8B%E9%92%AE%E6%8E%A7%E5%88%B6\&quot;&gt;DAW 旋钮控制&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[34,35]},&quot;content&quot;:&quot;&lt;a href=\&quot;#daw-%E6%A8%A1%E5%BC%8F\&quot;&gt;DAW 模式&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[35,36]},&quot;content&quot;:&quot;&lt;a href=\&quot;#arp-%E6%97%8B%E9%92%AE%E6%8E%A7%E5%88%B6\&quot;&gt;ARP 旋钮控制&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[36,37]},&quot;content&quot;:&quot;&lt;a href=\&quot;#arp-%E6%97%8B%E9%92%AE%E6%8E%A7%E5%88%B6\&quot;&gt;ARP 旋钮控制&lt;/a&gt;&quot;,&quot;children&quot;:[]}]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[37,38]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%A2%84%E8%AE%BE%E7%BC%96%E8%BE%91%E6%A8%A1%E5%BC%8F\&quot;&gt;预设编辑模式&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[38,39]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%AD%98%E5%82%A8%E9%A2%84%E8%AE%BE\&quot;&gt;存储预设&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[39,40]},&quot;content&quot;:&quot;&lt;a href=\&quot;#daw-%E7%BC%96%E8%BE%91%E6%A8%A1%E5%BC%8F\&quot;&gt;DAW 编辑模式&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[40,41]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%AD%98%E5%82%A8%E7%94%A8%E6%88%B7-daw\&quot;&gt;存储用户 DAW&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[41,42]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%AB%98%E7%BA%A7%E8%AE%BE%E7%BD%AE\&quot;&gt;高级设置&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[42,43]},&quot;content&quot;:&quot;&lt;a href=\&quot;#arp-%E5%92%8C%E9%94%81%E5%AE%9A%E9%94%AE\&quot;&gt;ARP 和锁定键&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[43,44]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%99%BA%E8%83%BD%E5%92%8C%E5%BC%A6%E9%94%AE\&quot;&gt;智能和弦键&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[44,45]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%99%BA%E8%83%BD%E9%9F%B3%E9%98%B6%E9%94%AE\&quot;&gt;智能音阶键&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[45,46]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%85%A8%E5%B1%80%E8%AE%BE%E7%BD%AE%E8%8F%9C%E5%8D%95\&quot;&gt;全局设置菜单&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[46,47]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%99%84%E5%BD%95\&quot;&gt;附录&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[47,48]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%94%AE%E7%9B%98%E7%81%B5%E6%95%8F%E5%BA%A6\&quot;&gt;键盘灵敏度&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[48,49]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%89%93%E5%87%BB%E5%9E%AB%E7%81%B5%E6%95%8F%E5%BA%A6\&quot;&gt;打击垫灵敏度&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[49,50]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%89%93%E5%87%BB%E5%9E%AB-led-%E9%A2%9C%E8%89%B2%E5%88%97%E8%A1%A8\&quot;&gt;打击垫 LED 颜色列表&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[50,51]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%A2%84%E8%AE%BE%E5%88%97%E8%A1%A8\&quot;&gt;预设列表&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[51,52]},&quot;content&quot;:&quot;&lt;a href=\&quot;#daw-%E5%88%97%E8%A1%A8\&quot;&gt;DAW 列表&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[52,53]},&quot;content&quot;:&quot;&lt;a href=\&quot;#midi-%E7%AB%AF%E5%8F%A3\&quot;&gt;MIDI 端口&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[53,54]},&quot;content&quot;:&quot;&lt;a href=\&quot;#oxygen-pro-mini-%E8%BE%93%E5%87%BA%E7%AB%AF%E5%8F%A3\&quot;&gt;Oxygen Pro Mini 输出端口&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[54,55]},&quot;content&quot;:&quot;&lt;a href=\&quot;#oxygen-pro-mini-%E8%BE%93%E5%85%A5%E7%AB%AF%E5%8F%A3\&quot;&gt;Oxygen Pro Mini 输入端口&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[55,56]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%81%A2%E5%A4%8D%E5%87%BA%E5%8E%82%E8%AE%BE%E7%BD%AE\&quot;&gt;恢复出厂设置&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[56,57]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%8A%80%E6%9C%AF%E8%A7%84%E6%A0%BC\&quot;&gt;技术规格&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[57,58]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%95%86%E6%A0%87%E5%92%8C%E8%AE%B8%E5%8F%AF\&quot;&gt;商标和许可&lt;/a&gt;&quot;,&quot;children&quot;:[]}]}],&quot;payload&quot;:{}}"/></div><blockquote><center>工欲善其事，必先知其器。</center><p align="right">——秉蕳</p></blockquote><h2 id="序"><a class="markdownIt-Anchor" href="#序"></a> 序</h2><p>本文为Oxygen Pro Mini的使用心得笔记，主要内容参考自官方说明书：<a href="https://www.m-audio.com/support/downloads.html#oxypmini">Oxygen Pro Mini User Guide v1.2</a>。<br><img src="/images/blogimage/Oxygen-mini-web-4.png" alt></p><h2 id="功用概览"><a class="markdownIt-Anchor" href="#功用概览"></a> 功用概览</h2><h3 id="主面板"><a class="markdownIt-Anchor" href="#主面板"></a> 主面板</h3><p><img src="/images/20250610/OxygenPro_mini_keyboardmap.svg" alt><br>标注键盘的主面板示意图</p><ol><li><kbd>🎹键盘</kbd> ，此产品的琴键是半配重键盘。琴键是midi的主要部分，通过是。通过按住 Shift 并按 C2–Bb3 键可编辑和弦模式设置。有关此功能的更多信息，请参见 “基本概念”。</li><li>OCTAVE(八度键)：这些键可将琴键的音高范围上下调整一个八度。按住 Shift 并按这些键可将琴键的音高范围上下调整一个半音。键盘可以从默认八度范围向上调整最多 4 个八度或向下调整最多 3 个八度，从默认移调最多调整 12 个半音。要将Oxygen Pro Mini重置为其默认八度范围和移调（键盘上的F2-C5），请同时按下Octave-和Octave+按钮。</li><li>PITCH(音高滚轮)：从中心位置上下滚动这个滚轮，在弹奏时改变键盘的音高。调音的默认范围因软件合成器而异。滚轮安装在弹簧上，释放后将返回到初始中心位置。</li><li>MOD(自定义滚轮)：移动此轮可发送连续控制器数据 —— 默认是 <code>MIDI CC#01</code>（调制）。</li><li>DAW(宿主软件)/Preset(预设)\编辑 按钮：按此键可将 Oxygen Pro Mini 设置为 DAW 模式或预设模式。在 DAW 模式下，此键的 LED 会亮起。在预设模式下，此键的 LED 会熄灭。按住 Shift 并按此键可编辑预设或用户 DAW。编辑预设或用户 DAW 后，再次按此键可将更改保存到用户 DAW 或预设。按住该键可在显示屏上打开 DAW / 预设选择菜单。</li><li>显示屏：主显示屏显示上次使用控件的状态。在调整键盘上的控件时，使用此屏幕可监视参数级别。此外，使用显示器和选择/滚动旋钮来查看和编辑键盘设置。</li><li>(选择/滚动旋钮)：如果进入了显示屏的某个编辑菜单，转动此旋钮可更改设置 / 参数，按下旋钮可确认选择。如果您没有查看任何编辑菜单，转动旋钮和按下旋钮将分别作为单独的MIDI控件。当使用DAW操作时，分配的控制将是预先确定的。在选择预设或用户DAW的情况下操作时，可以编辑控件。</li><li>BACK(返回键)：如果进入了键盘的某个编辑模式，按此键将返回上一级菜单。在未进入任何编辑模式时，在 DAW 模式下，此键将发送单独的 MIDI、Mackie 或 Mackie/HUI 消息。在预设模式下，当选中预设 1 - 14 时，此键将发送单独的用户可编辑 MIDI 消息。当使用DAW操作时，分配的控制将是预定的。在选择预设或用户DAW的情况下操作时，可以编辑控件。</li><li>Shift：在移动或按下键盘上的控件或按钮时按住Shift按钮以访问其辅助功能。</li><li><code>&lt;&lt;</code>(回退键)：根据DAW中的显示界面，此按钮将倒带打开的歌曲或在活动窗口中下移。某些DAW可能需要按下SHIFT按钮，并且&lt;&lt;按钮在活动窗口中向下移动。（在ableton中是将“播放线”移动1/4个位置），编辑预设或DAW名称时，按Shift按钮和Back按钮删除字母。</li><li><code>&gt;&gt;</code>(快进键)，同10</li><li>🔁 循环：按下此按钮可激活/停用DAW中的循环功能。</li><li>⏹️停止：按此按钮停止DAW中打开的歌曲。<ol><li>双击此按钮可停止打开的歌曲，并将播放头返回到歌曲的开头。</li><li>按Shift和此按钮发送MIDI紧急消息，关闭所有音符消息并将所有控件归零。</li></ol></li><li>▶️ 播放：按下此按钮在您的DAW中播放歌曲。</li><li>⏺️录制：按此按钮激活DAW中的录制。</li><li>BANK&lt;(存储键)：Bank &gt;、Bank &lt;键：在 DAW 模式或某个自定义预设下，使用这些键可切换当前选中的推子、旋钮、打击垫和功能键组。DAW 模式下共有 8 个组，预设模式下有 2 个组。按住 Shift 和 Bank&gt; 键可锁定 Shift 修饰符 ARP 旋钮控件。这在现场表演中更改 ARP 参数时很有用。要将旋钮或打击垫恢复到正常模式，请按住 Shift 键并按 Bank &gt; 键。</li><li>TEMPO(速度键)：点速度键：按此键可设置 Oxygen Pro Mini 的速度，或按住它打开显示屏上的速度编辑菜单，您可以使用选择 / 滚动编码器手动输入速度并选择将 Oxygen Pro Mini 的速度与 DAW 同步。速度设置会影响键盘的琶音器和音符重复功能。更多详情见 “基本概念” 部分。</li><li>NOTE REPEAT/ LATCH(音符重复)：音符重复 [锁定] 键：按此键可激活打击垫的音符重复功能。要锁定或解锁音符重复功能，请按住 Shift 然后按此键。有关音符重复的更多详情，请参见 “基本概念” 部分。</li><li>(八个)打击垫：使用这些速度敏感的打击垫发送MIDI音符开/关消息或执行其他MIDI分配（如果使用预设或用户DAW）。当音符重复处于活动状态时，使用选择/滚动编码器更改自动琶音器和键盘音符重复的当前时分设置。</li><li>PAD BANK 打击垫储存库：按此按钮切换到不同的Pad Bank。有两个打击垫库可用。</li><li>推子（四个）：向上/向下推动这些推子以执行其指定的控制。当使用DAW操作时，分配的控制将是预先确定的。在选择预设或DAW的情况下操作时，可以编辑控件。</li><li>旋钮：左/右转动这些旋钮以执行其指定的控制。当使用DAW操作时，分配的控制将是预先确定的。在选择预设或用户DAW的情况下操作时，可以编辑控件。请参阅“基本概念”部分，了解如何更改在DAW模式下操作并选择DAW时的旋钮。按住Shift键，同时转动旋钮1-4以编辑自动琶音器设置。</li><li>ARP/EDIT(琶音器/编辑)：按下这个按钮激活自动琶音器。按住Shift键并按下此按钮可编辑自动琶音器的设置。</li><li>LATCH(重复锁定)：按下此按钮可在实时(按住不停)和重复模式之间切换自动琶音器。</li><li>CHORD(和弦)：按下此按钮激活和弦模式。按住Shift键并按下此按钮可编辑和弦模式设置。</li><li>SCALE(缩放)：按此按钮激活缩放模式。按住Shift键并按下此按钮可编辑缩放模式设置。</li><li>按下 模式按钮（Mode Button） 可激活功能键（Function Buttons）的 次级模式。<ul><li>模式按钮亮起时：功能键将切换至 DAW 或 MIDI 控制功能。</li><li>模式按钮熄灭时：功能键将执行其面板印刷的默认功能。</li><li>当键盘设置为 DAW 模式 时，功能键可切换以下次级模式：<ul><li>Rec（录制）：控制 DAW 轨道的 录音启用（Record Arm）</li><li>Select（选择）：控制 DAW 轨道的 选择（Track Select）</li><li>Mute（静音）：控制 DAW 轨道的 静音（Mute）</li><li>Solo（独奏）：控制 DAW 轨道的 独奏（Solo）</li></ul></li><li>当键盘设置为 预设模式（Preset Mode） 时，功能键的次级模式为：<ul><li>MIDI：按钮将执行 自定义预设中预定义的 MIDI 控制功能。</li><li>模式按钮的 LED 指示灯 会显示当前激活的模式。</li></ul></li><li><strong>按住 Shift 并按下 Mode 按钮</strong>，即可进入键盘的 <strong>全局设置菜单（Global Settings Menu）</strong>。在全局设置菜单中，通过调整 <strong>BUTTON（按钮功能）</strong> 选项，您可以自定义 <strong>DAW 模式下功能键的控制功能</strong>，包括：<strong>Rec（录制启用）</strong>、<strong>Select（轨道选择）</strong>、<strong>Mute（静音）</strong>、- <strong>Solo（独奏）</strong></li></ul></li></ol><div class="tip warning"><p>（机翻待润色）推子和旋钮均采用&quot;软接管&quot;模式。这意味着当您切换控制组时，物理推子/旋钮必须移动到新选中软件控制的当前值位置才会生效。例如：若您在1号控制组移动了推子1，随后切换到2号控制组，此时物理推子1必须移动到软件推子5的当前值位置，才能开始控制软件推子5。此功能可确保您在切换控制组时，不会意外改变新控制组的参数值。当推子或旋钮需要移动至接管位置时，显示屏将出现方格纹数值提示条。</p></div><h3 id="后面板"><a class="markdownIt-Anchor" href="#后面板"></a> 后面板</h3><p><img src="/images/20250610/Oxygen%20Pro%20Mini%20%E4%BD%BF%E7%94%A8%E6%89%8B%E5%86%8C-20250803235435659.webp" alt></p><ol><li>USB：当连接到计算机时，USB端口为键盘供电并传输MIDI数据。</li><li>延音踏板插孔：此输入接受瞬时接触脚踏板（不包括在内）。当按下时，默认情况下，踏板将维持您正在播放的声音，而您不必将手指按在琴键上。延音踏板输入可以重新映射以执行自定义MIDI分配。</li><li>MIDI输出：使用1/8英寸TRS转5针MIDI电缆（单独出售）将此端口连接到硬件合成器或其他MIDI设备。(<u>请使用TRS 3.5 mm至5针DIN母A型电缆</u>)</li></ol><div class="tip warning"><p>注意：启动时，延音踏板的极性由键盘决定。当Oxygen Pro Mini键盘通电时，延音踏板被认为处于“向上”（关闭）位置。重要的是，在启动键盘之前，延音踏板不要处于向下位置，因为踏板将反向操作，当踏板未按下时，音符将延音。</p></div><h2 id="基本概念"><a class="markdownIt-Anchor" href="#基本概念"></a> 基本概念</h2><p>本节概述了一些基本概念，有助于您理解和使用 Oxygen Pro Mini 键盘。</p><ul><li>键盘</li><li>八度和移调</li><li>速度控制</li><li>音符重复 / 锁定键</li><li>预设</li><li>DAW 和预设模式</li><li>Shift 键</li><li>返回键</li><li>编码器和编码器键</li><li>模式键</li><li>ARP 和锁定控制</li><li>智能和弦控制</li><li>智能音阶控制</li><li>DAW 旋钮控制</li><li>ARP 旋钮控制每个部分都包含本指南其他相关部分的链接，建议您一并阅读。</li></ul><h4 id="键盘"><a class="markdownIt-Anchor" href="#键盘"></a> 键盘</h4><p>键盘具有 velocity 感应功能，可在 10 个八度范围内访问 127 个可用 MIDI 音符的全部范围。</p><p>按住 Shift 并按其中一个带标签的键，用户可以快速编辑和弦功能或更改全局通道。</p><h4 id="八度和移调"><a class="markdownIt-Anchor" href="#八度和移调"></a> 八度和移调</h4><p>通过使用琴键八度 –/+ 键，键盘可以访问 127 个可用 MIDI 音符的全部范围（10 个八度）。此外，您可以将键盘移调最多 12 个半音（1 个八度）。</p><p>要更改键盘的八度，请使用琴键八度 –/+ 键分别降低或升高八度。显示屏会暂时显示 “OCT” 和当前的八度偏移。</p><p>Oxygen Pro Mini 的键盘可以向下移 4 个八度或向上移 5 个八度。</p><p>要更改键盘的移调，请按住 Shift，然后使用琴键八度 –/+ 键分别降低或升高琴键 1 个半音。显示屏会暂时显示 “TRANS” 和当前的移调（-12 至 12）。</p><h4 id="速度控制"><a class="markdownIt-Anchor" href="#速度控制"></a> 速度控制</h4><p>要编辑速度键，请按速度键。您可以反复按速度键输入速度，或按住速度键进入速度编辑模式。进入速度编辑模式后，可以使用编码器滚动浏览可用的参数值。按下编码器选择要编辑的参数。</p><p>时钟源 “CLOCK”：选择速度是由键盘的内部速度发送还是与外部 DAW 同步。</p><p>可用值：内部、外部</p><p>BPM ###.：20.00 – 240.00</p><p>BPM .#：.0 – .9</p><p>注意：时钟消息在 Oxygen Pro Mini 的端口 1（Oxygen Pro ##/USB MIDI）上发送和接收。</p><h4 id="音符重复-锁定键"><a class="markdownIt-Anchor" href="#音符重复-锁定键"></a> 音符重复 / 锁定键</h4><p>按下并按住此键将激活打击垫的音符重复 / 滚动功能。如果同时按下 Shift 和此键，将激活音符重复键的锁定功能。</p><p>当音符重复激活时，选择 / 滚动编码器可用于更改琶音器和打击垫音符重复的当前时间分割设置：</p><ul><li>1/4</li><li>1/4T</li><li>1/8</li><li>1/8T</li><li>1/16</li><li>1/16T</li><li>1/32</li><li>1/32T<br>注意：您也可以使用 Shift 和 1/4、1/8、1/16 和 1/32 打击垫更改速度。要访问时间分割打击垫的三连音功能，请双击所需的时间分割打击垫。</li></ul><h4 id="预设"><a class="markdownIt-Anchor" href="#预设"></a> 预设</h4><p>预设是 Oxygen Pro Mini 控件、通道设置等的保存集合。您可以在 Oxygen Pro Mini 的内部存储器中存储多达 14 个预设，这样您就可以为每个虚拟乐器或项目 / 会话使用专用预设。</p><p>除了随附的 DAW 预设外，您还可以在 Oxygen Pro Mini 的内部存储器中存储自己的 DAW 预设，这样您就可以为数字音频工作站（DAW）创建和使用自己的专用 DAW 预设。</p><p>建议在 <a href="https://m-audio.com">m-audio.com</a> 上注册您的 Oxygen Pro Mini 并下载 Oxygen Pro 软件管理器。</p><p>在软件管理器中，您可以访问所有随附的软件以及 Oxygen Pro Mini 预设编辑器。预设编辑器为您提供了一种直观的可视化方式来编辑 Oxygen Pro Mini 控件发送到计算机的各种消息，而无需使用硬件界面。预设编辑器允许您从计算机保存和加载自定义预设。</p><p>要在 Oxygen Pro Mini 上选择预设，请在预设模式（键熄灭）下按住 DAW / 预设键，直到 OLED 上出现预设选择屏幕，然后转动编码器滚动到某个预设，再按下编码器选择所需的预设。</p><p>要在 Oxygen Pro Mini 上选择 DAW 预设，请在 DAW 模式（键亮起）下按住 DAW / 预设键，直到 OLED 上出现 DAW 预设选择屏幕，然后转动编码器滚动到某个 DAW 预设，再按下编码器选择所需的预设。</p><p>重要提示：如果在未保存预设的情况下关闭 Oxygen Pro Mini 键盘，您所做的任何分配或更改都将丢失。</p><h4 id="daw-和预设模式"><a class="markdownIt-Anchor" href="#daw-和预设模式"></a> DAW 和预设模式</h4><p>在将 Oxygen Pro Mini 键盘设置为与 DAW 配合使用后，就可以设置键盘的操作模式（预设或 DAW）了。通过选择操作模式，您可以在 DAW 模式激活时快速切换 Oxygen Pro Mini 控制 DAW 的控件，在预设模式激活时控制软合成器 / 虚拟乐器。</p><p>这两种操作模式决定了 MIDI 键盘可编辑控件的功能：</p><ul><li>DAW 模式：在 DAW 模式下，键盘的控件将映射到 DAW 中的推子、按钮、旋钮，在某些情况下还有打击垫。</li><li>预设模式：在预设模式下，键盘的控件将映射到所选虚拟乐器中的推子、按钮、旋钮和打击垫。键盘的可编辑控件可以设置为您自行设计的功能。您可以创建多个单独的预设映射，并将其保存到键盘的内部存储器中，以便日后加载。</li></ul><p>要将键盘设置为 DAW 模式，请按 DAW / 预设键。键的 LED 亮起表示已选择 DAW 模式。</p><p>要更改键盘要控制的 DAW：</p><ol><li>按住 DAW 键，在显示屏上打开 DAW 选择菜单。</li><li>转动选择 / 滚动编码器，在显示屏上循环浏览可用的 DAW。转动编码器时，当前选中的 DAW 会在显示屏上更新。“用户” 选项允许您将自定义 DAW 控件映射到键盘，详情见 “基本概念” 部分。</li><li>当显示屏上显示您想要的 DAW 时，按下选择 / 滚动编码器进行确认。</li></ol><p>注意：要退出 DAW 模式而不更改当前选中的 DAW，请按返回键。</p><p>大多数 DAW 会自动识别 Oxygen Pro Mini 键盘，并在 DAW 模式下自动将其控件配置为控制表面，在预设模式下配置为虚拟乐器控制器。</p><p>如果您的 DAW 未自动配置 Oxygen Pro Mini 键盘，请遵循《Oxygen Pro Mini DAW 设置指南》中的设置步骤。</p><p>要将键盘设置为预设模式，请按 DAW / 预设键。LED 熄灭表示已选择预设模式。</p><p>要更改当前选中的预设：</p><ol><li>按住预设键，在显示屏上打开预设选择菜单。</li><li>转动选择 / 滚动编码器，在显示屏上循环浏览可用的预设。转动编码器时，当前选中的预设会在显示屏上更新。</li><li>当显示屏上显示您想要的预设时，按下选择 / 滚动编码器进行确认。</li></ol><p>Oxygen Pro Mini 随附的所有虚拟乐器都有对应的预设。对于非随附的虚拟乐器，建议在您喜爱的 DAW 中使用 MPC Beats 作为插件包装器，并搭配 Oxygen Pro Mini 的 MPC PI 预设。MPC Beats 可作为插件包装器在所有主流 DAW 中打开，融合各种 DAW 的优势。这使您可以自由使用 MPC Beats 作为软合成器 / 虚拟乐器插件包装器，让 Oxygen Pro Mini 的所有控件自动映射到您喜爱的软合成器 / 虚拟乐器插件。</p><p>要下载随附的 MPC Beats 软件，请按照随附的软件下载卡上的说明操作。</p><h4 id="shift-键"><a class="markdownIt-Anchor" href="#shift-键"></a> Shift 键</h4><p>按住此键可启用键盘的 Shift 修饰符功能。</p><h4 id="返回键"><a class="markdownIt-Anchor" href="#返回键"></a> 返回键</h4><p>在键盘的任何可用编辑模式下，此键将发送返回上一级菜单的消息。在未进入任何编辑模式时，在 DAW 模式下，此键将发送单独的 MIDI、Mackie 或 Mackie/HUI 消息。在预设模式下，当选中预设 1 - 14 时，此键将发送单独的用户可编辑 MIDI 消息。</p><p>按住 Shift 并按此键，在保存用户预设名称或用户 DAW 名称时，将删除当前选中的字母。</p><h4 id="编码器和编码器键"><a class="markdownIt-Anchor" href="#编码器和编码器键"></a> 编码器和编码器键</h4><p>在键盘的任何可用编辑模式下，此编码器向左 / 向右转动时用于滚动浏览选项，按下时用于确认进入。在 DAW 模式下，此编码器将发送单独的上 / 下或左 / 右消息（取决于 DAW）和确认消息。在预设模式下，此编码器将发送与 DAW 编码器分配相同的消息，或发送程序或 CC 消息。</p><p>当音符重复激活时，编码器用于选择音符重复和 ARP 时间分割设置。</p><h3 id="模式键"><a class="markdownIt-Anchor" href="#模式键"></a> 模式键</h3><p>模式键的 LED 亮起表示推子键的次要功能已激活。次要功能取决于键盘所处的模式（DAW 或预设）以及全局功能中 “按钮” 的选择（录制、独奏、静音或选择）。在预设和 DAW 模式下，推子键的丝印选项始终可选择。在 DAW 模式下，推子键的丝印选项可选择，还有轨道录制（录音准备）、选择、静音和独奏选项。在预设模式下，推子键的丝印选项可选择，还有用户可编辑的 MIDI 消息。</p><h4 id="daw-模式"><a class="markdownIt-Anchor" href="#daw-模式"></a> DAW 模式</h4><ul><li><p>关闭 / 无 LED：推子键将激活以下选项：</p><ul><li>ARP 开 / 关、ARP 编辑进入 / 退出</li><li>ARP 锁定开 / 关</li><li>智能和弦开 / 关、和弦编辑进入 / 退出</li><li>智能音阶开 / 关、音阶编辑进入 / 退出</li></ul></li><li><p>录制 / 模式 LED 亮起：推子键将激活 DAW 中相关键当前通道的录音准备 MIDI、Mackie 或 Mackie/HUI 消息。</p></li><li><p>选择 / 模式 LED 亮起：推子键将激活 DAW 中相关键当前通道的轨道选择 MIDI、Mackie 或 Mackie/HUI 消息。</p></li><li><p>静音 / 模式 LED 亮起：推子键将激活 DAW 中相关键当前通道的静音 MIDI、Mackie 或 Mackie/HUI 消息。</p></li><li><p>独奏 / 模式 LED 亮起：推子键将激活 DAW 中相关键当前通道的独奏 MIDI、Mackie 或 Mackie/HUI 消息。</p></li></ul><h4 id="预设模式"><a class="markdownIt-Anchor" href="#预设模式"></a> 预设模式</h4><ul><li>关闭 / 无 LED：推子键将激活以下选项：<ul><li>ARP 开 / 关、ARP 编辑进入 / 退出</li><li>ARP 锁定开 / 关</li><li>和弦开 / 关、和弦编辑进入 / 退出</li><li>音阶开 / 关、音阶编辑进入 / 退出</li></ul></li><li>MIDI / 模式 LED 亮起：在工厂预设中，推子键将发送预设的 MIDI 消息；在用户预设中，推子键将发送任何用户可分配的 MIDI 消息。</li></ul><h3 id="arp-和-arp-锁定控制"><a class="markdownIt-Anchor" href="#arp-和-arp-锁定控制"></a> ARP 和 ARP 锁定控制</h3><p>在 Oxygen Pro Mini 上，按此键将激活键盘的内部琶音器。琶音器的速率基于当前的速度和时间分割设置 —— 速度设置可使用速度键编辑。按住音符重复键并转动编码器，或按住 Shift 键并按 5 - 8 号打击垫，可访问时间分割设置。</p><p>要激活 Oxygen Pro Mini 上的 ARP 锁定功能，请按 ARP 锁定键。如果 ARP 键激活，ARP 键将亮起，表示 ARP 已激活。如果 ARP 锁定激活，ARP 锁定键将亮起。</p><p>注意：您还可以将琶音器与当前速度的 BPM 设置或外部 MIDI 时钟源同步。在预设编辑模式下，选择 / 按速度键可编辑时钟源。琶音器功能在两种键盘模式（DAW、预设）下均可用。</p><h3 id="智能和弦控制"><a class="markdownIt-Anchor" href="#智能和弦控制"></a> 智能和弦控制</h3><p>在 Oxygen Pro Mini 上，按此键将激活键盘的内部智能和弦功能。根据全局设置菜单中的选择，智能和弦功能可以作用于在键盘或打击垫上演奏的音符。当智能和弦模式激活时，按一个键将演奏当前智能和弦编辑选项中选中的和弦。此功能在两种键盘模式（DAW、预设）下均可用。</p><h3 id="智能音阶控制"><a class="markdownIt-Anchor" href="#智能音阶控制"></a> 智能音阶控制</h3><p>在 Oxygen Pro Mini 上，按此键将激活键盘的内部智能音阶功能。当前音阶基于当前的智能音阶设置（在智能音阶编辑菜单中）。智能音阶功能仅作用于在键盘上演奏的音符。当智能音阶模式激活时，按键将只演奏当前调号和音阶选择中的音符。此功能在两种键盘模式（DAW、预设）下均可用。</p><h3 id="daw-旋钮控制"><a class="markdownIt-Anchor" href="#daw-旋钮控制"></a> DAW 旋钮控制</h3><p>使用 Shift 键和 1 - 3 号打击垫可以更改 DAW 模式下旋钮的功能。</p><h4 id="daw-模式-2"><a class="markdownIt-Anchor" href="#daw-模式-2"></a> DAW 模式</h4><ul><li>声像：将旋钮功能更改为控制 DAW 中的通道声像旋钮。</li><li>设备：将旋钮功能更改为控制 DAW 中当前选中通道的插件控件。注意：并非所有 DAW 都支持设备控制。</li><li>发送：将旋钮功能更改为控制 DAW 中当前选中通道的发送控件。注意：并非所有 DAW 都支持发送控制。</li></ul><h3 id="arp-旋钮控制"><a class="markdownIt-Anchor" href="#arp-旋钮控制"></a> ARP 旋钮控制</h3><p>使用 Shift 键和 1 - 4 号旋钮可以将旋钮功能更改为控制琶音器的功能。</p><h4 id="arp-旋钮控制-2"><a class="markdownIt-Anchor" href="#arp-旋钮控制-2"></a> ARP 旋钮控制</h4><ul><li>类型：更改 ARP 中音符的回放顺序。</li><li>八度：更改 ARP 的八度范围。</li><li>门限：更改 ARP 音符的长度。</li><li>摇摆：更改 ARP 速度的摇摆程度。注意：按住 Shift 和 Bank &gt; 键可以锁定和解锁 ARP 旋钮控件，使其始终激活。</li></ul><h2 id="预设编辑模式"><a class="markdownIt-Anchor" href="#预设编辑模式"></a> 预设编辑模式</h2><p>按住 Shift 键并按 DAW / 预设键，将进入预设或用户 DAW 编辑模式。按下编码器选择 “预设”，即可编辑预设控件。</p><p>默认要编辑的参数是当前预设的音高轮分配。但是，一旦移动或按下其他控件（例如 1 号旋钮），将激活该选中的控件进行编辑。</p><h3 id="存储预设"><a class="markdownIt-Anchor" href="#存储预设"></a> 存储预设</h3><ol><li>按住 Shift 和 DAW / 预设键进入编辑模式。OLED 的第一行会显示 “EDIT”，根据当前的 DAW / 预设模式选择，第二行会高亮显示 “预设” 或 “DAW”。注意：当 “预设” 或 “DAW” 高亮显示时，您可以转动编码器在编辑 DAW 模式和编辑预设模式之间切换，更改当前选择。</li><li>按下编码器进入 DAW 或预设编辑模式。</li><li>编辑控件。</li><li>按 DAW / 预设键。</li><li>显示屏会显示 “SAVE?”，并有以下选项可供选择：</li></ol><ul><li>取消：选择取消将恢复所有更改。</li><li>替换：选择替换将覆盖当前选中的预设。</li><li>另存为：选择 “是” 进行另存为，可选择预设的存储 “位置” 并编辑 / 更改预设的 “名称”。另存为屏幕中的最后一个选项是保存。在保存屏幕上按 “是” 将保存您的新预设。注意：编辑预设名称时，使用编码器滚动到要编辑的字母，然后按编码器选择当前字母。要删除预设名称中的字母，请按住 Shift 并按返回键。</li></ul><h2 id="daw-编辑模式"><a class="markdownIt-Anchor" href="#daw-编辑模式"></a> DAW 编辑模式</h2><p>按住 Shift 键并按 DAW / 预设键，将进入预设或用户 DAW 编辑模式。按下编码器选择 “DAW”，即可编辑 DAW 控件。默认要编辑的参数是当前用户 DAW 的推子 1 分配。但是，一旦移动或按下其他控件（例如 1 号旋钮），将激活该选中的控件进行编辑。</p><h3 id="存储用户-daw"><a class="markdownIt-Anchor" href="#存储用户-daw"></a> 存储用户 DAW</h3><ol><li>按住 Shift 和 DAW / 预设键进入编辑模式。OLED 的第一行会显示 “EDIT”，根据当前的 DAW / 预设模式选择，第二行会高亮显示 “预设” 或 “DAW”。注意：当 “预设” 或 “DAW” 高亮显示时，您可以转动编码器在编辑 DAW 模式和编辑预设模式之间切换，更改当前选择。</li><li>按下编码器进入 DAW 或预设编辑模式。</li><li>编辑控件。</li><li>按 DAW / 预设键。</li><li>显示屏会显示 “SAVE?”，并有以下选项可供选择：</li></ol><ul><li>取消：选择取消将恢复所有更改。</li><li>替换：选择替换将覆盖当前选中的预设。</li><li>另存为：选择 “是” 进行另存为，可编辑 / 更改 DAW 的 “名称”。另存为屏幕中的最后一个选项是保存。在保存屏幕上按 “是” 将保存您的新用户 DAW。</li></ul><p>注意：编辑 DAW 名称时，按住 Shift 键并使用编码器滚动到要编辑的字母，松开 Shift 键选择当前字母。要删除 DAW 名称中的字母，请按住 Shift 并按返回键。</p><h2 id="高级设置"><a class="markdownIt-Anchor" href="#高级设置"></a> 高级设置</h2><h3 id="arp-和锁定键"><a class="markdownIt-Anchor" href="#arp-和锁定键"></a> ARP 和锁定键</h3><p>按 ARP 键将激活键盘的内部琶音器。琶音器的速率基于当前的速度和时间分割设置 —— 速度设置可使用速度键编辑。按住 Shift 键并按 5 - 8 号打击垫（1/4、1/8、1/16、1/32），或按住音符重复键并转动编码器，可访问时间分割设置。要激活 ARP 锁定功能，请按 ARP 锁定键。如果 ARP 键激活，ARP 键将亮起，表示 ARP 已激活。如果 ARP 锁定激活，ARP 锁定键将亮起。注意：您还可以将琶音器与当前速度的 BPM 设置或外部 MIDI 时钟源同步。在预设编辑模式下，选择 / 按速度键可编辑时钟源。琶音器功能在两种键盘模式（DAW、预设）下均可用。注意：您可以通过双击时间分割打击垫将时间分割设置更改为三连音。例如，如果您希望琶音器演奏 1/16 音符三连音，可以双击 1/16 打击垫。1/16 打击垫会闪烁，表示三连音已激活。</p><p>要编辑琶音器，请按住 Shift 并按 ARP 键。</p><p>要编辑琶音器的类型，在 “类型” 选项中点击编码器，然后从菜单中选择所需的设置。该模式决定了琶音音符的回放方式：</p><ul><li>向上：音符从最低到最高发声。</li><li>向下：音符从最高到最低发声。</li><li>包含：音符从最低到最高，然后再向下。最低和最高音符在方向改变时会发声两次。</li><li>排除：音符从最低到最高，然后再向下。最低和最高音符在方向改变时只发声一次。</li><li>顺序：音符按按下的顺序发声。</li><li>随机：音符按随机顺序发声。</li><li>和弦：音符以和弦形式发声。</li></ul><p>要设置琶音器的八度范围，在 “八度” 选项中点击编码器，然后选择所需的值：1、2 或 3 个八度。八度范围决定了一次按键将在 ARP 中演奏多少个八度的音符。八度越多，一次按键演奏的音符就越多。要设置琶音器的门限，在 “门限” 选项中点击编码器，然后从 5 - 100 中选择所需的值。门限范围决定了 ARP 中音符的演奏时长。门限越短，音符越短。要设置琶音器的摇摆，在 “摇摆” 选项中点击编码器，然后选择 50% 到 75% 之间的所需设置。摇摆范围决定了与模式化音符的偏差程度。摇摆值越高，时间偏差越大。</p><p>选择 “通道”，设置 ARP 分割将发送到的通道。</p><h3 id="智能和弦键"><a class="markdownIt-Anchor" href="#智能和弦键"></a> 智能和弦键</h3><p>按此键将激活键盘的内部智能和弦功能。根据全局设置菜单中的选择，智能和弦功能可以作用于在键盘、打击垫上演奏的音符，或两者都作用。当智能和弦模式激活时，按一个键将演奏当前智能和弦编辑选项中选中的和弦。此功能在两种键盘模式（DAW、预设）下均可用。</p><p>要编辑智能和弦设置，请按住 Shift 并按和弦键。</p><p>模式：</p><ul><li>智能模式允许您选择歌曲的调（例如 C 大调）。当按下物理键盘上的某个键时，将在该调中演奏一个和弦。</li><li>自定义模式允许您输入自定义和弦。输入和弦后，按物理键盘上的某个键即可演奏该和弦。要创建自定义和弦，在自定义字段中按下编码器，然后使用编码器选择所需的音符，或按琴键输入您想要的音符。自定义和弦模式中有 6 个可用音符：<ul><li>音符 1：自定义和弦中的第一个音符。</li><li>音符 2：自定义和弦中的第二个音符。</li><li>音符 3：自定义和弦中的第三个音符。</li><li>音符 4：自定义和弦中的第四个音符。</li><li>音符 5：自定义和弦中的第五个音符。</li><li>音符 6：自定义和弦中的第六个音符。</li></ul></li><li>调：选择智能和弦所在的调。</li><li>类型：选择和弦将使用的音阶，大调或小调。</li><li>声部编排：这让您可以选择智能和弦模式中激活的指法。您也可以在按住 Shift 键的同时，使用键盘的琴键快速编辑参数。</li><li>通道：选择全局通道（全局）或特定通道（通道 1 - 16）。</li></ul><h3 id="智能音阶键"><a class="markdownIt-Anchor" href="#智能音阶键"></a> 智能音阶键</h3><p>按此键将激活键盘的内部智能音阶功能。当前音阶基于当前的智能音阶设置（在智能音阶编辑菜单中）。智能音阶功能仅作用于在键盘上演奏的音符。当智能音阶模式激活时，按键将只演奏当前调号和音阶选择中的音符。此功能在两种键盘模式（DAW、预设）下均可用。</p><p>要编辑智能音阶设置，请按住 Shift 并按音阶键。</p><ul><li>调：选择智能音阶所在的调。</li><li>音阶：选择智能音阶将使用的音阶。在 “音阶” 选项上按下编码器，然后选择您要应用的音阶：半音阶、大调、多利亚调式、弗里几亚调式、利底亚调式、混合利底亚调式、和声小调、洛克利亚调式、小调、旋律小调、大调五声音阶、小调五声音阶、布鲁斯音阶、变化属音、半全减音阶、全音音阶。</li><li>通道：选择全局通道（全局）或特定通道（通道 1 - 16）。</li></ul><h2 id="全局设置菜单"><a class="markdownIt-Anchor" href="#全局设置菜单"></a> 全局设置菜单</h2><p>使用显示屏上的全局设置菜单可以自定义键盘的一些默认控件。这些设置适用于 DAW 模式和预设模式下的键盘，在全局设置菜单中所做的任何更改在键盘关闭后都会保存。要进入全局设置菜单，请按住 Shift 并按模式键。使用选择 / 滚动编码器调整设置。</p><p>要退出全局设置菜单，请按返回键。可选择的全局设置如下：</p><ul><li><p>按钮：此按钮设置决定了在 DAW 模式下通道推子键将发送的消息。</p><ul><li>录制：选择此功能后，当模式键亮起时，按钮将发送通道录音准备消息。</li><li>独奏：选择此功能后，当模式键亮起时，按钮将发送通道独奏消息。</li><li>静音：选择此功能后，当模式键亮起时，按钮将发送通道静音消息。</li><li>轨道选择：选择此功能后，当模式键亮起时，按钮将发送轨道选择消息。</li></ul></li><li><p>全局 MIDI 通道（G. CHAN.）：从 1 - 16 中选择默认的全局 MIDI 通道，使键盘在该通道上发送 MIDI 音符和消息。</p></li><li><p>程序更改（PROG）：从 0 - 127 中选择程序更改编号，使键盘发送传出 MIDI 消息，以选择所连接的 MIDI 硬件上的 MIDI 程序或通过 USB 连接的软件上的 MIDI 程序。</p></li><li><p>银行 MSB（B. MSB）：发送 0 - 127 的银行选择消息，以访问对 MSB 消息有响应的 MIDI 硬件或软件上的音色。</p></li><li><p>银行 LSB（B. LSB）：发送 0 - 127 的银行选择消息，以访问对 LSB 消息有响应的 MIDI 硬件或软件上的音色。</p></li><li><p>键盘八度（KEY OCT.）：从 -4 到 +5 中选择键盘的八度范围。</p></li><li><p>键盘移调（K. TRANS）：从 -12 到 +12 中选择键盘的移调范围。</p></li><li><p>键盘灵敏度（K. SENS.）：从低、中、高、线性、固定 64、固定 100、固定 127 中选择琴键的灵敏度设置。</p></li><li><p>打击垫灵敏度（PD SENS.）：从低、中、高、线性、固定 64、固定 100、固定 127、从 64 到 127、固定 64、100 或 127、固定 32、64、100、127 中选择打击垫的灵敏度设置。</p></li><li><p>5 针 MIDI 输出消息 “MIDI OUT”：此字段决定后面板上的 5 针 MIDI DIN 连接器是否发送仅来自 Oxygen Pro Mini 的控件、打击垫和琴键的 MIDI 数据（琴键）、仅来自 USB 连接的电脑的 MIDI 数据（USB）、Oxygen Pro Mini 的控件、打击垫、琴键和所连接电脑的 MIDI 数据（琴键 / USB），或不发送任何 MIDI 数据（关闭）。</p></li><li><p>和弦模式：此字段决定和弦模式激活时，是对琴键、打击垫还是琴键和打击垫激活和弦模式。</p></li><li><p>MIDI 输出：选择是否将来自琴键和 / 或 USB 端口的 MIDI 数据发送到 MIDI 输出。可选择关闭、琴键、USB 或琴键和 USB。</p></li></ul><h2 id="附录"><a class="markdownIt-Anchor" href="#附录"></a> 附录</h2><h3 id="键盘灵敏度"><a class="markdownIt-Anchor" href="#键盘灵敏度"></a> 键盘灵敏度</h3><p>选择键盘力度曲线时，显示屏上会出现 K.SENS.。</p><table><thead><tr><th style="text-align:center">Oxygen Pro Mini 显示屏显示</th><th style="text-align:center">描述</th></tr></thead><tbody><tr><td style="text-align:center">低</td><td style="text-align:center">低灵敏度设置，适用于主要以低力度演奏音符的情况。</td></tr><tr><td style="text-align:center">中</td><td style="text-align:center">中灵敏度设置（默认），适用于以平均力度演奏的情况。</td></tr><tr><td style="text-align:center">高</td><td style="text-align:center">高灵敏度设置，适用于主要以高力度演奏音符的情况。</td></tr><tr><td style="text-align:center">线性</td><td style="text-align:center">线性曲线。音符的力度与施加的力度成正比。</td></tr><tr><td style="text-align:center">固定 64</td><td style="text-align:center">所有音符的力度固定为 64。</td></tr><tr><td style="text-align:center">固定 100</td><td style="text-align:center">所有音符的力度固定为 100。</td></tr><tr><td style="text-align:center">固定 127</td><td style="text-align:center">所有音符的力度固定为 127。</td></tr></tbody></table><h3 id="打击垫灵敏度"><a class="markdownIt-Anchor" href="#打击垫灵敏度"></a> 打击垫灵敏度</h3><p>选择打击垫力度曲线时，显示屏上会出现 PD.SENS.。</p><table><thead><tr><th style="text-align:center">Oxygen Pro Mini 显示屏显示</th><th style="text-align:center">描述</th></tr></thead><tbody><tr><td style="text-align:center">低</td><td style="text-align:center">低灵敏度设置，适用于主要以低力度演奏音符的情况。</td></tr><tr><td style="text-align:center">中</td><td style="text-align:center">中灵敏度设置（默认），适用于以平均力度演奏的情况。</td></tr><tr><td style="text-align:center">高</td><td style="text-align:center">高灵敏度设置，适用于主要以高力度演奏音符的情况。</td></tr><tr><td style="text-align:center">线性</td><td style="text-align:center">线性曲线。音符的力度与施加的力度成正比。</td></tr><tr><td style="text-align:center">固定 64</td><td style="text-align:center">所有音符的力度固定为 64。</td></tr><tr><td style="text-align:center">固定 100</td><td style="text-align:center">所有音符的力度固定为 100。</td></tr><tr><td style="text-align:center">固定 127</td><td style="text-align:center">所有音符的力度固定为 127。</td></tr><tr><td style="text-align:center">从 64 - 127</td><td style="text-align:center">所有音符的力度从 64 到 127，取决于施加的力度。</td></tr><tr><td style="text-align:center">固定 64、100、127</td><td style="text-align:center">所有音符的力度为 64、100 或 127，取决于施加的力度。</td></tr><tr><td style="text-align:center">固定 32、64、100、127</td><td style="text-align:center">所有音符的力度为 32、64、100 或 127，取决于施加的力度。</td></tr></tbody></table><h3 id="打击垫-led-颜色列表"><a class="markdownIt-Anchor" href="#打击垫-led-颜色列表"></a> 打击垫 LED 颜色列表</h3><p><img src="/images/20250610/Oxygen%20Pro%20Mini%20%E4%BD%BF%E7%94%A8%E6%89%8B%E5%86%8C-20250804112711638.webp" alt></p><table><thead><tr><th>名称</th><th>颜色</th></tr></thead><tbody><tr><td>OFF</td><td>LED 关闭</td></tr><tr><td>CHAR.</td><td>淡黄绿色</td></tr><tr><td>GREEN</td><td>绿色</td></tr><tr><td>AQUA</td><td>蓝绿色</td></tr><tr><td>CYAN</td><td>青色</td></tr><tr><td>AZURE</td><td>天蓝色</td></tr><tr><td>BLUE</td><td>蓝色</td></tr><tr><td>VIOLET</td><td>紫色</td></tr><tr><td>MAGENTA</td><td>品红色</td></tr><tr><td>ROSE</td><td>玫瑰红</td></tr><tr><td>RED</td><td>红色</td></tr><tr><td>ORANGE</td><td>橙色</td></tr><tr><td>YELLOW</td><td>黄色</td></tr><tr><td>WHITE</td><td>白色</td></tr></tbody></table><h3 id="预设列表"><a class="markdownIt-Anchor" href="#预设列表"></a> 预设列表</h3><ol><li>MPC Pl（MPC 插件）</li><li>Hybrid（Hybrid 3）</li><li>MiniGrd（MiniGrand）</li><li>Velvet</li><li>Xpand（Xpand!2）</li><li>Vacuum</li><li>Boom</li><li>DB33</li></ol><h3 id="daw-列表"><a class="markdownIt-Anchor" href="#daw-列表"></a> DAW 列表</h3><table><thead><tr><th>1.</th><th>Ableton（Ableton Live）</th><th>7.</th><th>Logic</th></tr></thead><tbody><tr><td>2.</td><td>MPC（MPC Beats）</td><td>8.</td><td>Reaper</td></tr><tr><td>3.</td><td>Pro Tools</td><td>9.</td><td>Reason</td></tr><tr><td>4.</td><td>Bitwig</td><td>10.</td><td>FL St.（FL Studio）</td></tr><tr><td>5.</td><td>Studio 1（Studio One）</td><td>11.</td><td>用户 DAW</td></tr><tr><td>6.</td><td>Cubase</td><td></td><td></td></tr></tbody></table><h3 id="midi-端口"><a class="markdownIt-Anchor" href="#midi-端口"></a> MIDI 端口</h3><h4 id="oxygen-pro-mini-输出端口"><a class="markdownIt-Anchor" href="#oxygen-pro-mini-输出端口"></a> Oxygen Pro Mini 输出端口</h4><table><thead><tr><th>消息</th><th>Windows 系统</th><th>macOS 系统</th></tr></thead><tbody><tr><td>预设模式控件、琴键、打击垫、时钟消息</td><td>Oxygen Pro ##</td><td>USB MIDI</td></tr><tr><td>DAW 模式控件、打击垫</td><td>MIDIOUT3（Oxygen Pro ##）</td><td>MACKIE/HUI</td></tr><tr><td>预设编辑器</td><td>MIDIOUT4（Oxygen Pro ##）</td><td>EDITOR</td></tr></tbody></table><h4 id="oxygen-pro-mini-输入端口"><a class="markdownIt-Anchor" href="#oxygen-pro-mini-输入端口"></a> Oxygen Pro Mini 输入端口</h4><table><thead><tr><th>消息</th><th>Windows 系统</th><th>macOS 系统</th></tr></thead><tbody><tr><td>时钟消息输入</td><td>Oxygen Pro ##</td><td>USB MIDI</td></tr><tr><td>5 针 MIDI DIN 输入</td><td>MIDIIN2（Oxygen Pro ##）</td><td>MIDI DIN</td></tr><tr><td>DAW LED 控制和 Mackie/HUI 心跳消息</td><td>MIDIIN3（Oxygen Pro ##）</td><td>MACKIE/HUI</td></tr><tr><td>预设编辑器</td><td>MIDIIN4（Oxygen Pro ##）</td><td>EDITOR</td></tr></tbody></table><h3 id="恢复出厂设置"><a class="markdownIt-Anchor" href="#恢复出厂设置"></a> 恢复出厂设置</h3><p>要将 Oxygen Pro Mini 的控件、预设和 DAW 恢复为出厂默认设置，请关闭 Oxygen Pro Mini，然后按住八度 + 和 - 键并打开 Oxygen Pro Mini。</p><h3 id="技术规格"><a class="markdownIt-Anchor" href="#技术规格"></a> 技术规格</h3><table><thead><tr><th>电源</th><th>通过 USB 端口供电</th></tr></thead><tbody><tr><td>MIDI 连接器</td><td>TRS 3.5 mm 转 5 针 DIN 母头 - A 型线缆</td></tr><tr><td>尺寸（宽 x 深 x 高）</td><td>15.8 英寸 x 7.52 英寸 x 2.56 英寸（401 毫米 x 190 毫米 x 60 毫米）</td></tr><tr><td>重量</td><td>2.65 磅 / 1.2 千克</td></tr></tbody></table>]]></content>
    
    
    <summary type="html">或许是国内唯一的Oxygen Pro Mini参考手册</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/20250610/OxygenPro_mini_keyboardmap.svg" type="image"/>
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
    <category term="⚙️工程机械" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%9A%99%EF%B8%8F%E5%B7%A5%E7%A8%8B%E6%9C%BA%E6%A2%B0/"/>
    
    
    <category term="音乐" scheme="https://blog.si-on.top/tags/%E9%9F%B3%E4%B9%90/"/>
    
    <category term="形而下学" scheme="https://blog.si-on.top/tags/%E5%BD%A2%E8%80%8C%E4%B8%8B%E5%AD%A6/"/>
    
  </entry>
  
  <entry>
    <title>池塘、鱼以及鱼食</title>
    <link href="https://blog.si-on.top/2025/fish4Showtify/"/>
    <id>https://blog.si-on.top/2025/fish4Showtify/</id>
    <published>2025-08-03T11:15:53.000Z</published>
    <updated>2025-08-03T11:15:53.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><div class="tip warning"><p>本文为四月份构思的《伶化》一文的补充内容，因其内容较为繁多，完成时间一直拖延，特将此部分较为有用内容先抽离出发布之。</p></div><div class="tip ban"><p>本文为临时性文章，将在《伶化》发布后删除，请勿保存此链接！</p></div><p>两年前<a href="https://sionreading.notion.site/79e0b8162e2a44b28551dcbd6f5d3029">阅读数字劳动</a>后，关于数媒平台的认识逐渐明朗起来，那种入骨的批判直接导致我这两年对自有<a href="/2024/firefish-the-slowest">独立平台</a>的折腾与实践。随着实践的深入，近来发觉在fediverse/自有平台、RSS介入这个框架之后，那种明朗变得模糊不定，因为有必要再进行一番审视。</p><h2 id="假设"><a class="markdownIt-Anchor" href="#假设"></a> 假设</h2><p>为方便讨论，本文遵循取象比类的东方传统，承接《<a href="/2023/key4read">电子阅读新语</a>》一文中鱼与鱼塘的比喻进行探讨，首先有如下抽取表象的定义：</p><ol><li>平台为池塘，用户为鱼，UGC内容为鱼食。</li><li>池塘不生产任何东西，只提供环境。</li><li>此池塘提供的环境与鱼食是鱼<strong>赖以生存</strong>的唯二之物。</li><li>鱼是此池塘鱼食的唯一生产者。</li><li>生产行为：鱼不会无所事事，会在环境中通过自发劳动来<strong>生产鱼食</strong>。(鱼食的生产过程是抽象自用户在平台里的促进劳动价值进行累计的一切可能，包括但不限于UGC(主要)、正向负向互动、浏览(次要)等</li><li>搬运加工行为：指鱼食实体被转换且成可批量复制的通用鱼食的行为。</li><li>吸引行为：鱼食会吸引更多的鱼。鱼食过多会产生剩余价值。</li></ol><p>有点抽象，那画个图吧：<br><img src="/images/20250610/fish_things.svg" alt></p><p>我的困惑有三：</p><ol><li>鱼与鱼食的关系究竟怎样？</li><li>如果把池塘私有化，那么生产的剩余价值到哪里去了？</li><li>池塘之间的行为是怎样的？在考虑搬运行为后，不同池塘间行为会产生怎样的变化？</li></ol><h2 id="论证"><a class="markdownIt-Anchor" href="#论证"></a> 论证</h2><h3 id="鱼与鱼食的关系"><a class="markdownIt-Anchor" href="#鱼与鱼食的关系"></a> 鱼与鱼食的关系</h3><p>我们不能发现，鱼直接而感性的欲望是鱼食，为此它会不惜一切代价去获得它。把吃的欲望看作目的，那么我们可以借用康德目的论的思路进行分析。在康德的目的论的范畴里，“一个对象的概念就它同时包含这个对象的现象性的根据而言，叫做目的”。这既是说，</p><ol><li>目的是事物自身所隐含的概念，此概念是造物的规定，鱼追逐鱼食乃是鱼本身的目的，因为没有鱼世态就无法生存，这也可看做是千万年演化的经验凝固成的法则；</li><li>事物作为自身的目的，从其结果上看是它自身的原因。即它所赖以构成或生成的原因，不是来自外部的，因与果相分离的。鱼的生存与消耗鱼食的目的是实质而客观的自然目的，且不仅仅局限于外在，因为我们的鱼是有思想的鱼，所以内在也必然囊括其中。所以，它的整个行为——生产鱼食、消耗鱼食都是互为目的与手段的。</li></ol><h3 id="鱼与池塘行为的合目的性"><a class="markdownIt-Anchor" href="#鱼与池塘行为的合目的性"></a> 鱼与池塘行为的合目的性</h3><p>这一部分是我较为困惑的，首先从《数字劳动》可以知：在传统的UGC平台中，如推特微博、油管B站中，平台从鱼生产鱼食、吸引鱼的整个过程中榨取剩余价值，这是毋庸置疑的。</p><p>然而把这个模型套用到其他地方，如搜索引擎的池塘(母池塘)里，那么问题成了池塘之间的竞争，因而必然导致池塘内鱼的行为的改变，在池塘的角度，鱼就不仅仅要生产鱼食，也要能帮助池塘在母池塘之中有更大的竞争力，这样才能吸引来更多的鱼。</p><p>我们假设所有平台(不包括那些池塘本身已经大到可以闭关自产自销的)都要在搜索引擎中获得一席之地，那么所有池塘(子池塘)都可被抽象成一条大鱼。子池塘的鱼的目的之上的、母池塘作为鱼的目的之下的关系显然又加深了一层，这两者是互相影响，只有子池塘的目的合乎母池塘的目的，母池塘才能更好地生产、获得母池塘的鱼食。<br><img src="/images/20250610/%F0%9F%90%9F-20250803204519249.webp" alt="池塘间的博弈"></p><p>对于一个体量小只有三五条鱼的池塘来说，自产自销的鱼食是不够吃的。要么这三五条鱼要在别的池塘里窜来窜去，要么这个池塘本身就要到别的母池塘里窜来窜去，要么就是这个池塘以及三五条鱼都一直忍受着这种饥饿，在痛苦的边缘挣扎，或者心灰意冷得死去，或者一直熬煎直到适应这种饥饿，在这种池塘获得一种超然的、摆脱感性了器官欲望的怡然自得。</p><h3 id="通用型鱼食的影响"><a class="markdownIt-Anchor" href="#通用型鱼食的影响"></a> 通用型鱼食的影响</h3><p>当一条鱼发现它生产的鱼食被复制到其他地方时， 它自然会愤懑不平，尤其是当此鱼食是一个独立的池塘生产的时候。然而这个通用型鱼食会带来实体鱼食的回馈，虽然鱼食可能并非等价，但总归是比原来多了，这个池塘又多了一个新的鱼食的来源。这个价值可看做是通过搬运信息差所产生的熵减的价值，搬运鱼食的劳动与生产鱼食劳动的价值是不可同日而语的，两者均有其价值。在此我不能明确地评判了。简而言之：</p><ol><li>当一个池塘的鱼食少于其中鱼所需要的鱼食时，鱼与池塘是欢迎这种搬运的；</li><li>当鱼食多于其所需要的鱼食时，则是抵触这种搬运的；</li><li>当鱼池塘有更高的价值与目的所在时，会对这种搬运采取更多复杂的态度与手段——或者更加公而开之，或者深深隐蔽起来，或者采取一种暧昧的态度。</li></ol><p><img src="/images/20250610/%E6%B6%B8%E8%BE%99%20(1).jpg" alt="《涸辙之鲋》"></p>]]></content>
    
    
    <summary type="html">关于用户、平台、创作内容之间思考。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/20250610/%E6%B6%B8%E8%BE%99%20(1).jpg" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="📖涵泳" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%F0%9F%93%96%E6%B6%B5%E6%B3%B3/"/>
    
    <category term="🗿伶化" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%F0%9F%93%96%E6%B6%B5%E6%B3%B3/%F0%9F%97%BF%E4%BC%B6%E5%8C%96/"/>
    
    
    <category term="批判性思考" scheme="https://blog.si-on.top/tags/%E6%89%B9%E5%88%A4%E6%80%A7%E6%80%9D%E8%80%83/"/>
    
    <category term="理性" scheme="https://blog.si-on.top/tags/%E7%90%86%E6%80%A7/"/>
    
    <category term="临时标记" scheme="https://blog.si-on.top/tags/%E4%B8%B4%E6%97%B6%E6%A0%87%E8%AE%B0/"/>
    
  </entry>
  
  <entry>
    <title>在这个疆场的那个地域的领域之内</title>
    <link href="https://blog.si-on.top/2025/field_limit/"/>
    <id>https://blog.si-on.top/2025/field_limit/</id>
    <published>2025-07-30T21:42:12.000Z</published>
    <updated>2025-07-30T23:07:12.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><blockquote><center>先天概念在多大的范围具有其运用，我们的认识能力根据原则的应用所达到的范围就有多大，从而哲学达到的范围就有多大。</center><p align="right">——康德</p></blockquote><p>假设存有一个僭妄于一切认识能力之上的疆场，在此疆场上所有可知以及不可知之物皆可从无限的方式任意逼近认识的地域，所有的认识都井然有序地存在，所有的存在都有其合乎理性、知性的意义。在此疆场之中，万物皆得其宜，六畜皆得其长，群生皆得其命。假设上述疆场的认识体系的为<strong>形而外学</strong>。<img src="/images/20250610/DSC_8143%20(1).jpg" alt><br>现以形而外学来审视形而内的认识:</p><p>所谓学习，无外乎<strong>开合与连结</strong>。把这些认识显现，而把那些隐没掉，有选择地进行涌现，就是开合。模仿外界的认识，把一些对象、范畴的关系强行放置到自己身上，就是连结。从形而外学来看，<strong>彼隐没掉的涌现、未进行连结的关系就是其永远失掉的不可认识之物，因而其认识定然是片面的且经验化的</strong>。当下所谓规范(包括人类理性的，心理的以及约定俗成的社会规范)皆是如此。</p><p>考虑到人非机器，不只进行简单的开合与连结，还会进行批判性的思考。从形而外学来看，这思考，也不过是另一种重复。</p><p>所谓思考，不过是<strong>有感而应的触动</strong>。这感，是先验的，因为没有先验的知识作为锚点是不可能进行思考的。这触动，自然就是在先验认识范围之内的(比如灵感爆发导致的新认识)。思考，归根到底也是<strong>旧认识的重新组合</strong>。感而应，应而再感，再感而又应，无穷无尽。在这过程中，看不出来有创造出纯粹的新东西。</p><blockquote><p>理性不可能超出经验的红线，去提供一个超验的知识。</p></blockquote><p>学而不思也好，思而不学也好，总归都是在规范之内进行迭代，形成一条不断延展的受到各种随机因素而变形的多股线，随机因素导致的价值观念、历史变化可以轻而易举地就将认识扰动到另一个方向。</p><p>线的尽头或许能抵达彼岸的疆场，也或许就这样永远飘荡在不断相对接近彼岸疆场的真空中，孤独，且空无一物。这线断了，折了，绕回去了缠成一团也完全可能。</p><p>唔，一条无限空间里的大蛇，吃尽一切可以看见的食物，拖着逐渐变长的身躯，随便爬向哪个地方。</p>]]></content>
    
    
    <summary type="html">悠悠沧溟，一斗折蛇行矣。</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/20250610/IMG_20250731_070625.jpg" type="image"/>
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="📖涵泳" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%F0%9F%93%96%E6%B6%B5%E6%B3%B3/"/>
    
    
    <category term="批判性思考" scheme="https://blog.si-on.top/tags/%E6%89%B9%E5%88%A4%E6%80%A7%E6%80%9D%E8%80%83/"/>
    
  </entry>
  
  <entry>
    <title>前端笔记101</title>
    <link href="https://blog.si-on.top/2025/Frontend101/"/>
    <id>https://blog.si-on.top/2025/Frontend101/</id>
    <published>2025-07-28T08:31:17.000Z</published>
    <updated>2026-04-05T15:21:22.029Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><blockquote><center>像骑自行车一样自然地设计网页。</center><p align="right">——Sion</p></blockquote><details class="folding-tag" green><summary> ✍文章痕迹 </summary>              <div class="content">              <div class="timeline  green"><div class="timeline-item headline">        <div class="timeline-item-title">          <div class="item-circle"><p>写作时间线</p></div>        </div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-01-？</p></div>        </div>        <div class="timeline-item-content"><p>某日打开github星标榜，发现storybook项目。</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-03-30</p></div>        </div>        <div class="timeline-item-content"><p>阅读《版式设计原理》</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-03-31</p></div>        </div>        <div class="timeline-item-content"><p>再次产生创建STUDIO网站的念头，初步想法是使用<code>React</code>进行构建</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-04-01~4-02</p></div>        </div>        <div class="timeline-item-content"><p>阅读《大前端三剑客——Vue+React+Flutter》，旋即弃置</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-06-09</p></div>        </div>        <div class="timeline-item-content"><ul><li>受两年前喜欢的hexo主题《Paper》作者影响，尝试学习Sigma</li><li>观看视频教程《<a href="https://www.bilibili.com/video/BV19TDGYWEp7">零基础学Figma</a>》[^2]</li></ul></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-06-10</p></div>        </div>        <div class="timeline-item-content"><ul><li>申请Sigma教育账号</li><li>阅读《<a href="https://weread.qq.com/web/reader/3ec32830813ab8e61g0151b8#outline?noScroll=1">《Figma UI设计技法与思维全解析》 </a>》</li></ul></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-06-14</p></div>        </div>        <div class="timeline-item-content"><p>意识到Figam的局限性——只是一个原型设计软件，开始接触react。</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-06-15</p></div>        </div>        <div class="timeline-item-content"><p>理性看待Figma。Figma可以作为指导性文件来勾勒整体的轮廓而后以此为基础进行开发，同时可以进行简单的封面制作。</p></div>      </div><div class="timeline-item">        <div class="timeline-item-title">          <div class="item-circle"><p>2025-07-25</p></div>        </div>        <div class="timeline-item-content"><p>因为MES系统维护需要，借阅《JavaScript 技术手册》，开始系统学习js。</p></div>      </div></div>              </div>            </details><div class="markmap-container" style="height:300px">  <svg data="{&quot;type&quot;:&quot;root&quot;,&quot;depth&quot;:0,&quot;content&quot;:&quot;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[0,1]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%86%99%E5%9C%A8%E5%BC%80%E5%A7%8B%E7%9A%84%E9%A2%84%E6%9C%9F\&quot;&gt;写在开始的预期&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[1,2]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E8%AE%BE%E8%AE%A1%E5%B7%A5%E5%85%B7\&quot;&gt;设计工具&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[2,3]},&quot;content&quot;:&quot;&lt;a href=\&quot;#figma\&quot;&gt;figma&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[3,4]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E9%97%AE%E9%A2%98\&quot;&gt;问题&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[4,5]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%89%8D%E7%AB%AF%E6%A1%86%E6%9E%B6\&quot;&gt;🕳前端框架&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[5,6]},&quot;content&quot;:&quot;&lt;a href=\&quot;#javascript\&quot;&gt;JavaScript&lt;/a&gt;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[6,7]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E5%9F%BA%E6%9C%AC%E7%B1%BB%E5%9E%8B%E4%B8%8E%E8%BF%90%E7%AE%97\&quot;&gt;基本类型与运算&lt;/a&gt;&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[7,8]},&quot;content&quot;:&quot;&lt;a href=\&quot;#%E6%B5%81%E7%A8%8B%E8%AF%AD%E6%B3%95%E4%B8%8E%E5%87%BD%E6%95%B0\&quot;&gt;流程语法与函数&lt;/a&gt;&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[8,9]},&quot;content&quot;:&quot;&lt;a href=\&quot;#css\&quot;&gt;css&lt;/a&gt;&quot;,&quot;children&quot;:[]}]}],&quot;payload&quot;:{}}"/></div><hr><p>平日走路、工作、骑车，脑海里或多或少会浮现出一些念头，可能是一个照片的绝妙机位，一个有趣的游戏原型，一段悦耳的节奏，可能是一幅以天空为背景的插画，也可能是对网站主页的一个构建。有人说这叫灵感，我却以为这是虚感，不过是一阵风吹来，恰到好处地拂动了脑海里几个不同的念头而已，在这感觉没有落地之前，是毫无意义的。那如何让这些念头变得有意义呢？我觉得要去培养，去一点一滴地呵护它，如同养一盆花一般，让慢慢地成长，才会赋予其意义。</p><p>本文动笔的契机就是许多个念头的累积让这颗种子发了芽，至于到底能不能长大开花，甚至结果，我也不管，当下哩，我就静静地看着它，想起来了就浇点水~</p><h2 id="写在开始的预期"><a class="markdownIt-Anchor" href="#写在开始的预期"></a> 写在开始的预期</h2><p>本次试验要做出来几个原型，大概有这些：</p><ul><li><p>星际牛仔片头设计<br><img src="/images/20250610/Studio101-20250610224520298.webp" alt></p></li><li><p>国画风格：留白——文本让位图像<br><img src="/images/20250610/Studio101-20250610224732504.webp" alt></p></li><li><p>45°布局：<br><img src="/images/20250610/Studio101-20250610224928980.webp" alt></p></li><li><p>90°布局：即直排版</p></li><li><p>社会主义革命和建设时期宣传海报风格的当代演绎<br><img src="/images/20250610/Studio101-20250610225102976.webp" alt></p></li><li><p>细朱文为主的拟物线条风格</p></li><li><p>图表，数据可视化相关。</p></li><li><p>个人主页、工作室主页、专题展示页（摄影、篆刻、绘画）</p></li></ul><h2 id="设计工具"><a class="markdownIt-Anchor" href="#设计工具"></a> 设计工具</h2><h3 id="figma"><a class="markdownIt-Anchor" href="#figma"></a> figma</h3><p>figma给我的初步观感：像做PPT一样设计网页。</p><div class="tip warning"><p>本文定位只是一个辅助学习用的很随便的草稿，非教程，非笔记</p></div><ul><li>我们可以通过多种方式去补足这些知识，​“三大构成”就是开始系统认知设计或者UI设计的第一步。​“三大构成”包含《<strong>平面构成</strong>》(The Plane Constitution)、​《<strong>色彩构成</strong>》(The ColorConstitution)和《<strong>立体构成</strong>》(Three-Dimensional Constitutes)，通过这三本书，我们可以在更高的理论层面来对设计有个系统的认知。</li><li>如果还有时间，伊顿的《设计与形态》​《康定斯基论点线面》​，福兰可·惠特福特的《包豪斯》也是非常适合设计师夯实基础的著作。</li></ul><p>与时下流行的Material Design不同（尽管我也觉得这种设计很美观），笔者本次实践主要目标是向前求索：<u>追寻、挖掘、表现古文古画古书上图像与符号的关联关系</u>。具体到就是（竖排版，模仿自然）。</p><ul><li><p>图形绘制能力是几乎所有设计师都必须具备的一项能力，如果说版式设计能力决定了UI设计师60%的能力要素，那么图形绘制能力则让你的技能分从60分精进到80分甚至更高。</p></li><li><p>UI设计师学习的工具有以下几类，首先是</p><ul><li>图形绘制工具，如Sketch（Windows下有Adobe XD）​、<strong>Figma</strong>、Photoshop，这也是当今设计师用得比较多的主流工具，从难易程度上来说，Sketch(XD)和Figma上手难度最低，操作最简单。</li><li>交互工具，在UI设计稿完成前，这类工具可以帮我们绘制低保真的线框图；而设计稿完成后，我们需要用这类工具将其处理成高保真演示原型。最常见的交互工具，可以统称为“连连看工具”​，只需按照页面的顺序，将点击区域及目标区域进行连接即可。目前大部分的设计工具都提供了此类连线功能，如Sketch、XD、Figma等。当然，也有更复杂的工具，<strong>如Flinto</strong>、Principle及一些在线设计工具（如墨刀）​，都可以完成从设计稿导入到连线导出，最终形成可以在手机上真实点击的效果，这类工具的特色是做出更接近手机真实动作效果的演示，比如论坛图、下拉刷新、页面滚动等。</li><li>进阶类的图形绘制工具，以Photoshop或者Adobe illustrator为代表。用以完成界面中的一些图形化设计工作，如插画、字体、Logo设计。</li><li>动效（微交互）效果的设计、3D视觉工具等。这类工具有Adobe的After Effect和Cinema 4D，通常学习成本较高，需要花费更多精力才能有所收获。<br><img src="/images/20250610/Studio101-20250610220737673.webp" alt="作者推荐的软件"></li></ul></li></ul><blockquote><p><img src="/images/20250610/Studio101-20250610220802742.webp" alt="linux设计老师傅（穷人版）的工具箱"></p></blockquote><blockquote><p>目前掌握程度简单自评：</p><div class="progress"><div class="progress-bar-animated progress-bar progress-bar-striped bg-yellow" style="width: 70%" aria-valuenow="70" aria-valuemin="0" aria-valuemax="100"><p>Adobeillustrator(3年+)</p></div></div> <div class="progress"><div class="progress-bar-animated progress-bar progress-bar-striped bg-blue" style="width: 60%" aria-valuenow="60" aria-valuemin="0" aria-valuemax="100"><p>Adobephotoshop(2年)</p></div></div> </blockquote><blockquote><p>清华大学出版社提供了第二章的<a href="http://tup.tsinghua.edu.cn/booksCenter/book_08986601.html">样章</a>，微信阅读排版不好，还是读这个舒服。</p></blockquote><blockquote><p>Figam中的Frame（画框）与html中的<code>&lt;iframe&gt;</code>内嵌框架元素标签有类似的含义.</p></blockquote><ul><li>Figma的交互设计比较有趣的一点就是,特定的工具只有在激活的时候才会出现,非激活状态或者不可用状态下是完全隐藏的。</li></ul><table><thead><tr><th style="text-align:center"><img src="/images/20250610/Studio101-20250610220840738.webp" alt></th><th style="text-align:center"><img src="/images/20250610/Studio101-20250610220400161.png" alt></th></tr></thead><tbody><tr><td style="text-align:center">figma可以创建文本样式与组件以便复用</td><td style="text-align:center">文本转化为矢量(Flatten Selection)进行编辑</td></tr></tbody></table><ul><li><p>导出内容：“①使用切片工具划定需要导出的内容；②选中某个图层，在右侧的属性检查器中，找到“Export”选项，并单击加号，设定导出倍数、后缀和图片格式。”<img src="/images/20250610/Studio101-20250610221253560.webp" alt></p></li><li><p>快捷键说明（基本与PPT一致）</p><ul><li><kbd>Ctrl</kbd> + <kbd>D</kbd> ：副本</li><li><kbd>Ctrl</kbd> + <kbd>G</kbd> ：编组</li><li><kbd>Ctrl</kbd> + +<kbd>Shift</kbd>+<kbd>G</kbd> ：取消编组</li><li>拖拽调整数值：与Blender类似</li><li>选择矢量图形，然后直接粘贴可以将图形贴到矢量图形中。</li></ul></li><li><p>创建蒙版步骤</p><ol><li>新建一个矢量图层，右键新建蒙版（mask）</li><li>此时左侧会生成一个蒙版组（Mask Group）</li><li>把图片放进蒙版组里面</li><li>（调整图片或者矢量图形可以得到不同的画面）</li></ol></li></ul><h3 id="问题"><a class="markdownIt-Anchor" href="#问题"></a> 问题</h3><ul><li>Figma对竖排没有支持，插件vertja的实现方式是文本框溢出，不能简单转换成css。</li></ul><h2 id="前端框架"><a class="markdownIt-Anchor" href="#前端框架"></a> 🕳前端框架</h2><h3 id="npm"><a class="markdownIt-Anchor" href="#npm"></a> Npm</h3><p>package.json的版本号写法：<br>1. <code>^</code>（插入符号，Caret）</p><ul><li><strong>含义</strong>：允许更新到当前主版本号下的最新版本（不破坏向后兼容性）。</li><li><strong>规则</strong>：<code>^x.y.z</code> 允许更新 <code>y</code> 和 <code>z</code>，但保持 <code>x</code> 不变。</li><li><strong>示例</strong>：<ul><li><code>^1.2.3</code> → 允许 <code>1.x.x</code>（如 <code>1.2.4</code>、<code>1.3.0</code>），但禁止 <code>2.0.0</code>。</li><li><code>^0.y.z</code>：因为主版本是 <code>0</code>（初始开发阶段），仅允许更新 <code>z</code>（如 <code>^0.1.2</code> → <code>0.1.x</code>）。<br>2. <strong><code>~</code>（波浪符号，Tilde）</strong></li></ul></li><li><strong>含义</strong>：允许更新到当前次版本号下的最新补丁版本（更保守）。</li><li><strong>规则</strong>：<code>~x.y.z</code> 仅允许更新 <code>z</code>，保持 <code>x</code> 和 <code>y</code> 不变。</li><li><strong>示例</strong>：<ul><li><code>~1.2.3</code> → 允许 <code>1.2.x</code>（如 <code>1.2.4</code>），但禁止 <code>1.3.0</code> 或 <code>2.0.0</code>。</li><li><code>~1.0.0</code> → 仅允许 <code>1.0.x</code>。</li></ul></li></ul><p>3. <strong>无符号（精确版本）</strong></p><ul><li>直接写 <code>x.y.z</code> 表示严格锁定该版本，不自动更新。</li></ul><p>4. <strong>其他符号</strong></p><ul><li><code>&gt;</code>、<code>&lt;</code>、<code>&gt;=</code>、<code>&lt;=</code>：指定版本范围。</li><li><code>*</code> 或 <code>x</code>：匹配任意版本（不推荐）。</li></ul><ol start="5"><li><strong>选取建议</strong></li></ol><ul><li><strong><code>^</code></strong>：默认行为（<code>npm install --save</code> 使用），平衡新功能和稳定性。</li><li><strong><code>~</code></strong>：更严格，适合需要最小化更新的场景。</li><li><strong>锁定文件</strong>：实际安装版本由 <code>package-lock.json</code> 或 <code>yarn.lock</code> 精确控制，确保团队一致性。</li></ul><h3 id="ng-zorro"><a class="markdownIt-Anchor" href="#ng-zorro"></a> NG-ZORRO</h3><p><a href="https://ng.ant.design/docs/introduce/zh">NG-ZORRO(Angular 组件库)</a></p><h3 id="ionic"><a class="markdownIt-Anchor" href="#ionic"></a> Ionic</h3><p><a href="https://ionicframework.cn/docs">Ionic 移动端框架</a></p><h3 id="javascript"><a class="markdownIt-Anchor" href="#javascript"></a> JavaScript</h3><div class="tip bell"><p>编程随感：<a href="https://si-on.top/channels/aai4qoz5o11lvkx1">https://si-on.top/channels/aai4qoz5o11lvkx1</a></p></div><div class="markmap-container" style="height:300px">  <svg data="{&quot;type&quot;:&quot;root&quot;,&quot;depth&quot;:0,&quot;content&quot;:&quot;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;bullet_list&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[0,5]},&quot;content&quot;:&quot;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[0,1]},&quot;content&quot;:&quot;变量与函数&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[1,2]},&quot;content&quot;:&quot;面向对象&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[2,3]},&quot;content&quot;:&quot;构造函数&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[3,4]},&quot;content&quot;:&quot;异步设计&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[4,5]},&quot;content&quot;:&quot;错误处理&quot;,&quot;children&quot;:[]}]},{&quot;type&quot;:&quot;bullet_list&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[5,12]},&quot;content&quot;:&quot;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[5,6]},&quot;content&quot;:&quot;应用&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[6,7]},&quot;content&quot;:&quot;浏览器&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[7,8]},&quot;content&quot;:&quot;DOM、事件与样式&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[8,9]},&quot;content&quot;:&quot;网络通信&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[9,10]},&quot;content&quot;:&quot;浏览器保存方案&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:4,&quot;payload&quot;:{&quot;lines&quot;:[10,11]},&quot;content&quot;:&quot;COOKIE&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:4,&quot;payload&quot;:{&quot;lines&quot;:[11,12]},&quot;content&quot;:&quot;Web Storage&quot;,&quot;children&quot;:[]}]}]}]},{&quot;type&quot;:&quot;bullet_list&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[12,14]},&quot;content&quot;:&quot;&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:2,&quot;payload&quot;:{&quot;lines&quot;:[12,13]},&quot;content&quot;:&quot;其他&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:3,&quot;payload&quot;:{&quot;lines&quot;:[13,14]},&quot;content&quot;:&quot;标准API&quot;,&quot;children&quot;:[]}]}]}],&quot;payload&quot;:{}}"/></div><p>JavaScript 常见的功能包括:</p><ul><li>以指定尺寸、位置和样式(比如是否有边框、菜单、工具栏等)打开新窗口；</li><li>提供用户友好的导航帮助,比如<strong>下拉菜单</strong>；</li><li><strong>检验 Web 表单输入的数据</strong>，在向 Web 服务器提交表单之前确保数据格式正确；</li><li><strong>在特定事件(比如鼠标光标经过页面元素之上)发生时,改变页面元素的外观与行为</strong>；（每次浏览器要加载和显示页面时,都需要解释(更专业的术语是“解析”)构成页面的  HTML 源代码。在解析过程中,浏览器建立一个内部模型来表示文档里的内容,这个模型就  是 DOM(Document Object Model)。在浏览器渲染页面的可见内容时,就会引用这个模型。可以使用 JavaScript 来访问  和编辑这个 DOM 的各个部分,从而改变页面的显示内容和用户交互的方式。）</li><li>检测和发现特定浏览器支持的高级功能,比如第三方插件,或是对新技术的原生支持。</li></ul><div class="tip bell"><p>“JavaScript 是一种解释型语言,不是 C++或 Java 那样的编译语言。JavaScript <strong>指令以纯文本形式传递给浏览器,然后依次解释执行</strong>。它们不必先“编译”成只有计算机处理器能够理解的机器码,这让JavaScript 程序很便于阅读,能够迅速  地进行编辑,然后在浏览器里重新加载页面就可以进行测试。”</p></div><p>html使用<code>&lt;script&gt;...&lt;/script&gt;</code>标签，可以在html代码中直接包含JavaScript语句，也可以在标签里定义一些特有的熟悉。对于 HTML4里，需要使用type属性：<code>&lt;script type=&quot;text/javascript&quot;&gt;</code>，在本栈的主题配置文件里，就存在这样的写法,</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line">- <span class="language-xml"><span class="tag">&lt;<span class="name">script</span> <span class="attr">src</span>=<span class="string">&quot;https://npm.elemecdn.com/echarts@4.9.0/dist/echarts.min.js&quot;</span>&gt;</span><span class="tag">&lt;/<span class="name">script</span>&gt;</span></span></span><br><span class="line">- <span class="language-xml"><span class="tag">&lt;<span class="name">script</span> <span class="attr">type</span>=<span class="string">&quot;text/javascript&quot;</span> <span class="attr">src</span>=<span class="string">&quot;https://fastly.jsdelivr.net/npm/echarts@5/dist/echarts.min.js&quot;</span>&gt;</span><span class="tag">&lt;/<span class="name">script</span>&gt;</span></span></span><br><span class="line">- <span class="language-xml"><span class="tag">&lt;<span class="name">script</span> <span class="attr">charset</span>=<span class="string">&quot;UTF-8&quot;</span> <span class="attr">id</span>=<span class="string">&quot;LA_COLLECT&quot;</span> <span class="attr">src</span>=<span class="string">&quot;//sdk.51.la/js-sdk-pro.min.js&quot;</span>&gt;</span><span class="language-handlebars"><span class="language-xml">&lt;/scri</span></span></span></span><br><span class="line"><span class="language-xml"><span class="language-handlebars"><span class="language-xml">- <span class="tag">&lt;<span class="name">script</span>&gt;</span><span class="language-javascript"> <span class="keyword">new</span> <span class="title class_">LingQue</span>.<span class="title class_">Monitor</span>().<span class="title function_">init</span>(&#123;<span class="attr">id</span>:<span class="string">&quot;3FTSzvJ4NLnOUYqy&quot;</span>,<span class="attr">sendSuspicious</span>:<span class="literal">true</span>&#125;);</span></span></span><span class="tag">&lt;/<span class="name">script</span>&gt;</span></span></span><br><span class="line"><span class="language-xml">- <span class="tag">&lt;<span class="name">script</span> <span class="attr">src</span>=<span class="string">&#x27;/js/mastodon-timeline.js&#x27;</span>&gt;</span><span class="tag">&lt;/<span class="name">script</span>&gt;</span></span></span><br><span class="line"><span class="language-xml">- <span class="tag">&lt;<span class="name">script</span> <span class="attr">src</span>=<span class="string">&#x27;/js/embed.js&#x27;</span>&gt;</span><span class="tag">&lt;/<span class="name">script</span>&gt;</span></span></span><br></pre></td></tr></table></figure><h4 id="dom"><a class="markdownIt-Anchor" href="#dom"></a> DOM</h4><blockquote><p>“浏览器每次加载和显示页面时,都在内存里创建页面及其全部元素的一个内部表示体系,  也就是 DOM。在 DOM 里,页面的元素具有一个逻辑化、层级化的结构,就像相互关联的父对象和子对象组成了一个树形的结构。这些对象及其相互关系构成了 Web 页面及显示页面的  浏览器的抽象模型。每个对象都有“属性”列表来描述它,而利用 JavaScript 可以使用一些  方法来操作这些属性。”</p></blockquote><p>DOM全称：Document Object Model，即文档对象模型，如上所述，它是浏览器解析渲染HTML源码过程中所用到的一个模型规则。DOM可以类比成康德哲学里的图式——连接感性直观与理性的中介。(W3C的目的是让DOM不仅应用于Web页面与Js，也能用于任何编程语言和XML。)</p><p>在浏览器的疆域里，DOM模型的框架是由许多对象进行表示的，最顶级的DOM对象是window，他是一切对象的父对象，示例如下：</p><div class="markmap-container" style="height:200px">  <svg data="{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:0,&quot;payload&quot;:{&quot;lines&quot;:[0,1]},&quot;content&quot;:&quot;Window&quot;,&quot;children&quot;:[{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[1,2]},&quot;content&quot;:&quot;Document&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[2,3]},&quot;content&quot;:&quot;location（URL的详细信息）&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[3,4]},&quot;content&quot;:&quot;history（浏览器以前访问的页面地址）&quot;,&quot;children&quot;:[]},{&quot;type&quot;:&quot;list_item&quot;,&quot;depth&quot;:1,&quot;payload&quot;:{&quot;lines&quot;:[4,5]},&quot;content&quot;:&quot;navigator（浏览器类型、版本兼容等）&quot;,&quot;children&quot;:[]}]}"/></div><p>以hexo官网为例，在<a href="https://learn.microsoft.com/zh-cn/microsoft-edge/devtools/console/">控制台</a>输入<code>window.location</code>后会显示如下信息：</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br></pre></td><td class="code"><pre><span class="line">1. Location &#123;ancestorOrigins: DOMStringList, href: &#x27;https://hexo.io/zh-cn/&#x27;, origin: &#x27;https://hexo.io&#x27;, protocol: &#x27;https:&#x27;, host: &#x27;hexo.io&#x27;&#125;</span><br><span class="line">2. ancestorOrigins: DOMStringList &#123;length: 0&#125;</span><br><span class="line">3. assign: ƒ assign()</span><br><span class="line">4. hash: &quot;&quot;</span><br><span class="line">5. host: &quot;hexo.io&quot;</span><br><span class="line">6. hostname: &quot;hexo.io&quot;</span><br><span class="line">7. href: &quot;https://hexo.io/zh-cn/&quot;</span><br><span class="line">8. origin: &quot;https://hexo.io&quot;</span><br><span class="line">9. pathname: &quot;/zh-cn/&quot;</span><br><span class="line">10. port: &quot;&quot;</span><br><span class="line">11. protocol: &quot;https:&quot;</span><br><span class="line">12. reload: ƒ reload()</span><br><span class="line">13. replace: ƒ replace()</span><br><span class="line">14. search: &quot;&quot;</span><br><span class="line">15. toString: ƒ toString()</span><br><span class="line">16. valueOf: ƒ valueOf()</span><br><span class="line">17. Symbol(Symbol.toPrimitive): undefined</span><br><span class="line">18. [[Prototype]]: Location</span><br></pre></td></tr></table></figure><p>有了树形结构，就可以通过线性的方式找到节点下任何一个对象，</p><ol><li><code>window.document.body</code>：HTML页面的<code>&lt;body&gt;</code>部分在DOM里就是document对象的一个子对象。类似的：<ol><li><code>window.document.domain</code>：HTML页面的domin</li><li><code>window.document.title</code>：HTML页面的<code>&lt;title&gt;...&lt;/title&gt;</code></li></ol></li><li><code>window.object.method</code>：不仅仅是对象甚至是属性或方法也可以通过这种方式进行表示。</li></ol><div class="tip "><p>window 对象永远包含当前浏览器窗口,所以使用 window.document 就可以访问当前文档。作为一种简化表示,使用 document 也能访问当前文档。<br>如果是打开了多个窗口,或是使用框架集,那么每个窗口或框架都有单独的 window  和 document 对象,为了访问其中的某一个文档,需要使用<u>相应的窗口名称和文档名称</u>。</p></div><h4 id="交互的方法"><a class="markdownIt-Anchor" href="#交互的方法"></a> 交互的方法</h4><ul><li><code>object.method</code></li></ul><ol><li>命令<code>window.alert()</code>，浏览器弹出一个包含“确定”按钮的窗口：</li></ol><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">&lt;script&gt;<span class="variable language_">window</span>.<span class="title function_">alert</span>(<span class="string">&quot;问世界好在&quot;</span>);&lt;/script&gt;</span><br><span class="line"><span class="comment">//alert(document.title)，浏览器将显示当前页面的标题，对象可以作为变量来进行操作。</span></span><br></pre></td></tr></table></figure><p>这是句点表示法的案例，调用了windows对象的alert()方法。在实际编写过程中，window作为DOM的最顶层，因而上述语句中的<code>window.</code>可以忽略掉。<br>2. <code>window.document.write(&quot;主页body啦啦啦&quot;)</code>，浏览器将页面全部内容覆写成<code>&lt;body&gt;主页body啦啦啦&lt;/body&gt;</code><br>3. <code>confirm()</code>,弹出一个模态对话框，向用户弹出一个选择的对话框，选择不同值，会返回不同值，也可以直接</p><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">var answer = confirm(&quot;你吃饭没有啊？&quot;);</span><br></pre></td></tr></table></figure><ol start="4"><li><code>prompt()</code>，弹出一个对话框，用户可以输入信息(第二个参数可以输入默认信息)。</li></ol><figure class="highlight plaintext"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><span class="line">whatmeal = prompt(&quot;吃啥饭？&quot;,&quot;面条儿&quot;)</span><br><span class="line">&#x27;煎饼&#x27;</span><br></pre></td></tr></table></figure><ol start="5"><li><code>getElementById()</code>：通过id调用DOM。如果想从 HTML 页面里选择具有某个特定 ID 的元素,我们只需要把相应元素的 ID 作为  参数来调用 document 对象的 getElementById()方法,它就会返回特定 ID 的页面元素所对应的 DOM 对象。比如调用hexo官网里id为<code>intro-feature-list</code>的部分</li></ol><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="variable language_">document</span>.<span class="title function_">getElementById</span>(<span class="string">&quot;intro-feature-list&quot;</span>)</span><br></pre></td></tr></table></figure><h4 id="脚本示例"><a class="markdownIt-Anchor" href="#脚本示例"></a> 脚本示例</h4><p>在Web页面里嵌入JavaScript有两种方法，第一种方法是直接包含在HTML文件里：</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line">&lt;script&gt;</span><br><span class="line">... <span class="title class_">Javascript</span> 语句 ...</span><br><span class="line">&lt;/script&gt;</span><br></pre></td></tr></table></figure><p>第二种方法是将js代码保存到单独的文件里，然后使用<code>&lt;script&gt;</code>元素的src（源）属性来指定文件名，从而把这个文件包含到页面里：</p><figure class="highlight js"><figcaption><span>如果不在同一文件夹内，要使用相对路径，或者用网络存到一个链接上。</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line">&lt;script src=<span class="string">&#x27;code.js&#x27;</span>&gt; &lt;/script&gt;</span><br></pre></td></tr></table></figure><p>值得注意的是：不能使用同一个<code>&lt;script&gt;</code>元素来包含外部 JavaScript 文件,同时包含 JavaScript 语句,因为如果利用<code>&lt;script&gt;</code>元素的 src 属性包含了外部 JavaScript 文件,就不能在<code>&lt;script&gt;</code>和 <code>&lt;/script&gt;</code>之间包含 JavaScript 语句了,而是这个区域必须为空。</p><div class="tip "><p>按照惯例,JavaScript 代码文件的名称扩展名是.js。但从实际情况来看,代码文  件的名称可以使用任何扩展名,浏览器都会把其中的内容当作 JavaScript 来解释。</p></div><p>JavaScript 语句必须包含在定义这些元素的 HTML 的后面。在代码读取和执行完毕之后,页  面呈现才会继续,直到页面完成。对于一些包含<a href="/#%E5%87%BD%E6%95%B0">函数</a>的js文件，最好是放在<code>&lt;head&gt;...&lt;/head&gt;</code>区域里，这样它会被首先加载，以后就可以在任何位置调用它了</p><h4 id="鼠标事件"><a class="markdownIt-Anchor" href="#鼠标事件"></a> 鼠标事件</h4><p>为了增加交互功能，我们需要知道用户在页面唯一的肢体延申——鼠标，在什么时间，存在于何处、在做什么等。这些基本因素我们称之为<code>event</code>(事件)。</p><ol><li>onClick：在点击之后执行此事件</li><li>onMouseOver：当鼠标进入页面的某个元素所占据的区域时，会触发此事件</li><li>onMouseOut：当鼠标离开页面的某个元素所占据的区域时，会触发此事件</li></ol><blockquote><p>利用 <code>onMouseOver</code> 和 <code>onMouseOut</code> 事件处理器可以在鼠标位于图像上方时改变图像的显  示方式。为此,当鼠标进入图像区域时,可以利用<code>onMouseOver</code> 改变<img>元素的 src 属性;  而当鼠标离开时,利用 <code>onMouseOut</code> 再把这个属性修改回来。</p></blockquote><h4 id="数据类型与运算"><a class="markdownIt-Anchor" href="#数据类型与运算"></a> 数据类型与运算</h4><ul><li>数字：<code>0xA</code>十六进制；<code>0b1010001</code>二进制；<code>0o4545</code>八进制；<code>8.848e3</code>、<code>8848000e-3</code>科学计数法(代表<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mstyle mathcolor="blue"><mn>8848000</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">\color{blue}8848000\times 10^{-3}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord" style="color:blue;">8848000</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin" style="color:blue;">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord" style="color:blue;">1</span><span class="mord" style="color:blue;"><span class="mord" style="color:blue;">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight" style="color:blue;"><span class="mord mtight" style="color:blue;"><span class="mord mtight" style="color:blue;">−</span><span class="mord mtight" style="color:blue;">3</span></span></span></span></span></span></span></span></span></span></span></span> )。js中可以表示的数字的最小值<code> Number.MIN_VALUE</code>是<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo>−</mo><msup><mn>2</mn><mn>53</mn></msup></mrow><annotation encoding="application/x-tex">-2^{53}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8974em;vertical-align:-0.0833em;"></span><span class="mord">−</span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">53</span></span></span></span></span></span></span></span></span></span></span></span>，最大值<code> Number.MAX_VALUE</code>是<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mn>2</mn><mn>53</mn></msup></mrow><annotation encoding="application/x-tex">2^{53}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8141em;"></span><span class="mord"><span class="mord">2</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">53</span></span></span></span></span></span></span></span></span></span></span></span>。</li></ul><blockquote><p><code>Number()</code>可以把数字的字符串转化成数字（在给 Number()传递某个值作为一个参数时,该函数将尽全力返回一个对等的数值。如果  它不能返回数值,将返回 NaN。），而<code>toString()</code>则可以将数字转化成字符串。</p></blockquote><figure class="highlight js"><figcaption><span>node 环境</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line">&gt; A=<span class="string">&#x27;0xB&#x27;</span></span><br><span class="line"><span class="string">&#x27;0xB&#x27;</span></span><br><span class="line">&gt; <span class="title class_">Number</span>(A)</span><br><span class="line"><span class="number">11</span></span><br></pre></td></tr></table></figure><p>js用 Number 对象来表示各种数值类型,包括整数和浮点数。通常,我们不需要  操心自己创建 Number 对象,因为 JavaScript 会将数值转换为 Number 类的一个实例。一些用法如下：</p><ol><li>number.isNaN()：检测是否非数值</li><li>number.isInteger()：检测是否是整数</li><li>Number.isFinite()：检测是否是无穷大。</li><li>Number.parseFloat()和 Number.parseInt()：将字符串解析成浮点数或者整数。</li></ol><ul><li>字符串，转义相关（超过<code>\uhhh</code>用<code>\u&#123;&#125;</code>，ES6新增特性）</li><li>布尔，<code>boolean</code></li><li>复合类型，<code>&#123;&#125;</code>，中间以逗号隔开，可以同时放置各种字段。使用点运算符来随时操作对象的特性(js的重要特点，这个写法太优雅了。)</li></ul><figure class="highlight js"><figcaption><span>复合类型</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br></pre></td><td class="code"><pre><span class="line">&gt; <span class="keyword">let</span> dog001 = &#123;<span class="attr">name</span>:<span class="string">&#x27;小黑&#x27;</span>, <span class="attr">color</span>: <span class="string">&#x27;black&#x27;</span>&#125;</span><br><span class="line"><span class="literal">undefined</span></span><br><span class="line">&gt; dog001.<span class="property">name</span></span><br><span class="line"><span class="string">&#x27;小黑&#x27;</span></span><br><span class="line">&gt; dog001.<span class="property">color</span></span><br><span class="line"><span class="string">&#x27;black&#x27;</span></span><br><span class="line">&gt; dog001.<span class="property">color</span> = ‘white’</span><br><span class="line"><span class="string">&#x27;white&#x27;</span></span><br><span class="line"></span><br><span class="line">&gt; <span class="keyword">delete</span> dog001.<span class="property">name</span></span><br><span class="line"><span class="literal">true</span></span><br><span class="line">&gt; dog001.<span class="property">name</span></span><br><span class="line"><span class="literal">undefined</span></span><br><span class="line">&gt; dog001</span><br><span class="line">&#123; <span class="attr">color</span>: <span class="string">&#x27;black&#x27;</span> &#125;</span><br></pre></td></tr></table></figure><ol start="5"><li>数组<code>[111,222,333,444]</code></li><li>变量声明（js变量对大小写敏感，因而可以用“骆驼大小写”的方式来编写一个更具可读性的变量，如GodIsDead💀）<ul><li><code>let</code>:变量。在区块<code>&#123;&#125;</code>作用域内有效，处于暂时性死区区块外无定义则会报错。</li><li><code>const</code>:常量，一次声明而后不能重新初始化、  重新声明或重新赋值。</li><li><code>var</code>:声明变量，在创建时便被初始化，被赋值为<code>undefined</code>，有提升行为（全局变量）：在未指定值之前，会被定义为<code>undefined</code></li></ul></li></ol><div class="tip "><p>undefined代表“值没有定义”的值,其在JavaScript中不是保留字，在函数中可以被拿来作为变量名称，但尽量不要用它。通过<code>void</code>可以在任何值或表达式前产生<code>undefined</code>。类似的还有<code>null</code>表示没有对象，令对象为<code>null</code>相当于给它置空。<code>NaN</code>:当结果无法运算时，便会产生此值。</p></div><ol start="7"><li>加减乘除运算：js中的数字是IEEE 754标准64位浮点数，使用分数以及指数来表示小数，然而有些小数无法用分数表示，这就导致比如0.3之类的数字会有浮点数误差。如果要避免需要用第三方库<code>bignumber.js</code>来解决<ol><li><code>*</code>：乘法</li><li><code>**</code>：指数</li><li><code>%</code>：取模</li><li><code>/</code>：除法</li><li><code>++</code>：自加操作</li><li><code>--</code>：自减操作</li><li><code>-= AnNobodyCareLittleNumber</code>：自减去一个数值</li></ol></li></ol><p>严格模式，ES5后新增，若误用了不好或早期规则含混不清的特性，就会报错。使用<code>use strict</code>来进入严格模式。<br>8. 比较运算：使用 <code>\===、!==</code> 来进行比较<br>9. 逻辑运算：<code>&amp;&amp;</code>、<code>||</code>、<code>!</code>这个返回值要研究研究。<br>1. <code>A &amp;&amp; B</code>：A为真，则不论B真假都返回B；A为假，则直接返回A<br>2. <code>A || B</code>：A为真，则不论B真假都返回A；A为假，则直接返回B。（可以看作默认返回值，输入A假，返回B作为默认值）<br>3. <code>!A</code>：A为真，返回<code>false</code>，A为假(0)，返回<code>true</code></p><figure class="highlight js"><figcaption><span>返回值为TRUE</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="number">0</span> || <span class="string">``</span> &amp;&amp; <span class="title class_">NaN</span> || !<span class="literal">undefined</span> || <span class="literal">null</span></span><br></pre></td></tr></table></figure><ol start="10"><li>条件运算：<code>表达式 ? 成立返回值 : 失败返回值</code>。可用于局部的判断语句，减少程序体量。</li></ol><h4 id="流程语法"><a class="markdownIt-Anchor" href="#流程语法"></a> 流程语法</h4><div class="tip "><p><code>break</code>可以离开switch、for、while、do…while的区块，break与continue可以搭配标签使用，离开整个区块。</p></div><ol><li>if分支判断：条件默认</li></ol><figure class="highlight js"><figcaption><span>单层判断</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">if</span>(条件)&#123;</span><br><span class="line">语句A;</span><br><span class="line">&#125;</span><br><span class="line"><span class="keyword">else</span>&#123;</span><br><span class="line">语句B;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure><figure class="highlight js"><figcaption><span>多层判断</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">if</span>(条件)&#123;</span><br><span class="line">语句A;</span><br><span class="line">&#125;</span><br><span class="line"><span class="keyword">else</span> <span class="keyword">if</span>(条件<span class="number">2</span>)&#123;</span><br><span class="line">语句C;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure><ol start="2"><li>Switch 复合分支,使用break进行结束跳转</li></ol><figure class="highlight js"><figcaption><span>switch</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">switch</span>(number)&#123;</span><br><span class="line"><span class="keyword">case</span> <span class="number">10</span>:</span><br><span class="line">score= <span class="string">&#x27;S&#x27;</span>;</span><br><span class="line"><span class="keyword">break</span>;</span><br><span class="line"><span class="keyword">case</span> <span class="number">9</span>:</span><br><span class="line">score= <span class="string">&#x27;A&#x27;</span>;</span><br><span class="line"><span class="keyword">break</span>;</span><br><span class="line"><span class="keyword">case</span> <span class="number">8</span>:</span><br><span class="line">score= <span class="string">&#x27;B&#x27;</span>;</span><br><span class="line"><span class="keyword">break</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure><ol start="3"><li>for 循环，先判断后执行循环语句</li></ol><figure class="highlight js"><figcaption><span>for</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">for</span>(<span class="keyword">let</span> number=<span class="number">1</span>; number&lt;<span class="number">10</span>; number++)&#123;</span><br><span class="line"><span class="variable language_">console</span>.<span class="title function_">log</span>(number);</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure><pre><code>1. `for of`，循环访问数组中(of)的值`for(let nuumber of [10,20,30])`2. `for in`，列举对象的特性名称，搭配`[]`运算符使用3. `for`循环分三部分，变量声明+循环退出条件+表达式，变量声明</code></pre><div class="tip "><p>js中<code>{}</code>表示对象，<code>[]</code>/<code>·</code>访问对象的属性。</p></div><ol start="4"><li>While循环，先循环语句后执行判断</li></ol><figure class="highlight js"><figcaption><span>while</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">do</span>&#123;</span><br><span class="line">语句;</span><br><span class="line">&#125;</span><br><span class="line"><span class="keyword">while</span>(条件表达式);</span><br></pre></td></tr></table></figure><h4 id="函数"><a class="markdownIt-Anchor" href="#函数"></a> 函数</h4><figure class="highlight js"><figcaption><span>函数</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">function</span> <span class="title function_">hello</span>(<span class="params"></span>) &#123;</span><br><span class="line"><span class="title function_">alert</span>(<span class="string">&quot;问世界好在&quot;</span>)</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure><p>在页面加载时,包含在函数定义区域内的代码不会执行,而是静静地等待,直到“调用”  的时候才会执行。</p><ol><li>声明函数<code>function</code>。如果没有return值，则返回undefined。函数名称必须以字母或下画线开头,可以包含字母、数字和下画线,不能包含空格、标  点符号和其他特殊字符。</li></ol><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">let</span> n1 = <span class="number">100</span></span><br><span class="line"><span class="keyword">let</span> n2 = <span class="number">200</span></span><br><span class="line"><span class="variable language_">console</span>.<span class="title function_">log</span>(<span class="title function_">max</span>(n1,n2));</span><br><span class="line"></span><br><span class="line"><span class="keyword">function</span> <span class="title function_">max</span>(<span class="params">n1,n2</span>)&#123;</span><br><span class="line">    <span class="keyword">return</span> n1 &gt; n2 ? <span class="attr">n1</span>:n2;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure><p>语句中如果不写分号结束，则js会以分行判断结束。</p><figure class="highlight js"><figcaption><span>辗转相除法</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">function</span> <span class="title function_">gcd</span>(<span class="params">m,n</span>)&#123;</span><br><span class="line">    <span class="keyword">if</span>(n ===<span class="number">0</span>)&#123;</span><br><span class="line">        <span class="keyword">return</span> m;</span><br><span class="line">    &#125;</span><br><span class="line">    <span class="keyword">return</span> <span class="title function_">gcd</span>(n,m%n);</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="keyword">let</span> m = <span class="number">999</span>;</span><br><span class="line"><span class="keyword">let</span> n = <span class="number">666</span>;</span><br><span class="line"><span class="keyword">let</span> r = <span class="title function_">gcd</span>(n,m);</span><br><span class="line"><span class="keyword">if</span>(r === <span class="number">1</span>)&#123;</span><br><span class="line">    <span class="variable language_">console</span>.<span class="title function_">log</span>(<span class="string">&#x27;互质&#x27;</span>);</span><br><span class="line">&#125;</span><br><span class="line"><span class="keyword">else</span> &#123;</span><br><span class="line">    <span class="variable language_">console</span>.<span class="title function_">log</span>(<span class="string">&#x27;最大公因子&#x27;</span>, r);</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure><p>如果函数只是在重复操作，那么其应用范围将大大受限，可以通过参数传递的方式来拓展其功能。用latex中的函数能更直观地理解,下面的2就是入参的个数，<code>#1</code>与<code>#2</code>为参数在函数内的值。</p><figure class="highlight tex"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">\newcommand</span>&#123;<span class="keyword">\hello</span>&#125;[2]&#123;</span><br><span class="line">hello，<span class="keyword">\textbf</span>&#123;<span class="params">#1</span>&#125;,<span class="keyword">\textit</span>&#123;<span class="params">#2</span>&#125;</span><br><span class="line">&#125;</span><br><span class="line"></span><br><span class="line"><span class="keyword">\hello</span>&#123;世界&#125;&#123;你好&#125;</span><br></pre></td></tr></table></figure><p>在javascript中，需要定义每一个函数的具体名称，并确保包含了与函数定义相匹配的参数数量,比如下面的求和函数，需要四个入参：</p><figure class="highlight js"><figcaption><span>➕</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">function</span> <span class="title function_">plus</span>(<span class="params">a,b,c,d</span>) &#123;</span><br><span class="line"><span class="title function_">alert</span>(a+b+c);</span><br><span class="line">&#125;</span><br><span class="line"><span class="title function_">plus</span>(<span class="number">1</span>,<span class="number">1</span>,<span class="number">2</span>,<span class="number">3</span>)</span><br></pre></td></tr></table></figure><p>对于简单的函数，可以采用匿名函数的写法：</p><figure class="highlight js"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">var</span> sayHello = <span class="keyword">function</span>(<span class="params"></span>) &#123; <span class="title function_">alert</span>(<span class="string">&quot;Hello&quot;</span>); &#125;;</span><br></pre></td></tr></table></figure><p>更简洁直观的写法是利用所谓的箭头函数=&gt;下面以上述加法函数为例：</p><figure class="highlight js"><figcaption><span>➕➕</span></figcaption><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><span class="line"><span class="comment">//写在一行</span></span><br><span class="line">plus = <span class="function">(<span class="params">a,b,c,d</span>) =&gt;</span> <span class="title function_">alert</span>(a+b+c+d); </span><br><span class="line"></span><br><span class="line"><span class="comment">//写在多行</span></span><br><span class="line">plus = <span class="function">(<span class="params">a,b,c,d</span>) =&gt;</span> &#123;</span><br><span class="line"><span class="keyword">let</span> dongdong = a+b;</span><br><span class="line"><span class="keyword">let</span> qiang = c+d;</span><br><span class="line"><span class="title function_">alert</span>(dongdong+qiang); </span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure><h3 id="浏览器相关"><a class="markdownIt-Anchor" href="#浏览器相关"></a> 浏览器相关</h3><p>js可以通过<code>window.history</code>来访问浏览器历史记录，<code>history</code>对象只有一个长度的属性，表示用户访问过的页面的数量，<code>history</code>对象有许多种方法：</p><ol><li><code>forward()</code>：相当于前进</li><li><code>backward()</code>：相当于后退</li><li><code>go(number)</code>：跳转到历史记录列表里相应匹配的URL里（或许可以实现无法后退的效果）</li></ol><p>通过<code>location</code>则可以“帮助”用户导航至新页面，<code>location.href = 'www.newpage.com'</code></p><h3 id="css"><a class="markdownIt-Anchor" href="#css"></a> css</h3><p>按钮背景动画：</p><figure class="highlight css"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br></pre></td><td class="code"><pre><span class="line"><span class="selector-class">.glowing-button</span><span class="selector-pseudo">::before</span>, <span class="selector-class">.glowing-button</span><span class="selector-pseudo">::after</span>, <span class="selector-class">.glowing-button-alt</span><span class="selector-pseudo">::before</span>, <span class="selector-class">.glowing-button-alt</span><span class="selector-pseudo">::after</span> &#123;</span><br><span class="line">    <span class="attribute">content</span>: <span class="string">&#x27;&#x27;</span>;</span><br><span class="line">    <span class="attribute">position</span>: absolute;</span><br><span class="line">    <span class="attribute">top</span>: <span class="number">0</span>;</span><br><span class="line">    <span class="attribute">left</span>: -<span class="number">100%</span>;</span><br><span class="line">    <span class="attribute">width</span>: <span class="number">200%</span>;</span><br><span class="line">    <span class="attribute">height</span>: <span class="number">100%</span>;</span><br><span class="line">    <span class="attribute">background</span>: <span class="built_in">radial-gradient</span>(circle, <span class="built_in">rgba</span>(<span class="number">255</span>, <span class="number">255</span>, <span class="number">255</span>, <span class="number">0.3</span>), <span class="built_in">rgba</span>(<span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>, <span class="number">0</span>));</span><br><span class="line">    <span class="attribute">transform</span>: <span class="built_in">rotate</span>(<span class="number">45deg</span>);</span><br><span class="line">    <span class="attribute">animation</span>: glow <span class="number">4s</span> linear infinite;</span><br></pre></td></tr></table></figure>]]></content>
    
    
    <summary type="html">Figma、js等前端相关的学习笔记</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/Frontend101.svg" type="image"/>
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
    <category term="⌨️软件编程" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%8C%A8%EF%B8%8F%E8%BD%AF%E4%BB%B6%E7%BC%96%E7%A8%8B/"/>
    
    <category term="前端" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%E2%8C%A8%EF%B8%8F%E8%BD%AF%E4%BB%B6%E7%BC%96%E7%A8%8B/%E5%89%8D%E7%AB%AF/"/>
    
    
  </entry>
  
  <entry>
    <title>九云坊专用程序学习笔记</title>
    <link href="https://blog.si-on.top/2025/jiu.yun.fang/"/>
    <id>https://blog.si-on.top/2025/jiu.yun.fang/</id>
    <published>2025-07-19T01:30:39.000Z</published>
    <updated>2025-07-19T01:30:39.000Z</updated>
    
    <content type="html"><![CDATA[<div class="hbe hbe-container" id="hexo-blog-encrypt" data-wpm="Oh, this is an invalid password. Check and try again, please." data-whm="OOPS, these decrypted content may changed, but you can still have a look.">  <script id="hbeData" type="hbeData" 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    <summary type="html">特殊软件学习笔记</summary>
    
    
    
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  </entry>
  
  <entry>
    <title>热传导（稳态）笔记</title>
    <link href="https://blog.si-on.top/2025/thermal-conduction/"/>
    <id>https://blog.si-on.top/2025/thermal-conduction/</id>
    <published>2025-07-02T07:52:26.000Z</published>
    <updated>2025-07-02T15:52:26.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><blockquote><p>本文为《<a href="/2025/Basic@Heat-transfer">传热学笔记</a>》的分支，在后期精简过程中会被清理合并。</p></blockquote><table><thead><tr><th style="text-align:center">介质</th><th style="text-align:center">传热机理</th></tr></thead><tbody><tr><td style="text-align:center">气体</td><td style="text-align:center">分子不规则运动</td></tr><tr><td style="text-align:center">导电固体</td><td style="text-align:center">自由电子运动</td></tr><tr><td style="text-align:center">不导电固体</td><td style="text-align:center">（声子）晶格结构振动</td></tr><tr><td style="text-align:center">液体</td><td style="text-align:center">综合气体与固体</td></tr></tbody></table><p>引入温度场：定义各个时刻物体中各点温度所组成的集合，物体的温度场时坐标与时间的函数：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo separator="true">,</mo><mi>z</mi><mo separator="true">,</mo><mi>τ</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">t=f(x,y,x,z,\tau)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.1132em;">τ</span><span class="mclose">)</span></span></span></span>，如果为稳态问题，则时间为定值，即<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo separator="true">,</mo><mi>y</mi><mo separator="true">,</mo><mi>x</mi><mo separator="true">,</mo><mi>z</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">t=f(x,y,x,z)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em;"></span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">y</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">x</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal" style="margin-right:0.04398em;">z</span><span class="mclose">)</span></span></span></span></p><h3 id="导热基本定律"><a class="markdownIt-Anchor" href="#导热基本定律"></a> 导热基本定律</h3><p>在导热过程中，单位时间内通过给定截面积的导热率量，正比于垂直于该截面方向上的温度变化率和截面面积，热量传递的方向与温度升高的方向相反。</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>Φ</mi><mo>=</mo><mo>−</mo><mi>λ</mi><mi>A</mi><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow><mrow><mi mathvariant="normal">∂</mi><mi>x</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\varPhi=-\lambda A \frac{\partial t}{\partial x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathit">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord">−</span><span class="mord mathnormal">λ</span><span class="mord mathnormal">A</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal">x</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>q</mi><mo>=</mo><mo>−</mo><mi>A</mi><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow><mrow><mi mathvariant="normal">∂</mi><mi>x</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">q= - A \frac{\partial t}{\partial x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord">−</span><span class="mord mathnormal">A</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal">x</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p>当物体的温度式三个坐标的函数时，热流密度式是矢量，上式为沿着x方向的矢量，傅里叶导热定律的一般数学表达式为：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>q</mi><mo>=</mo><mo>−</mo><mi>λ</mi><mi>g</mi><mi>r</mi><mi>a</mi><mi>d</mi><mtext> </mtext><mi>t</mi><mo>=</mo><mo>−</mo><mi>λ</mi><mfrac><mrow><mi mathvariant="normal">∂</mi><mi>t</mi></mrow><mrow><mi mathvariant="normal">∂</mi><mi>x</mi></mrow></mfrac><mi>n</mi></mrow><annotation encoding="application/x-tex">q= - \lambda grad\ t= - \lambda \frac{\partial t}{\partial x }n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord">−</span><span class="mord mathnormal">λ</span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">a</span><span class="mord mathnormal">d</span><span class="mspace"> </span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord">−</span><span class="mord mathnormal">λ</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal">x</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord" style="margin-right:0.05556em;">∂</span><span class="mord mathnormal">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal">n</span></span></span></span></span></p><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>g</mi><mi>r</mi><mi>a</mi><mi>d</mi><mtext> </mtext><mi>t</mi></mrow><annotation encoding="application/x-tex">grad\ t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">g</span><span class="mord mathnormal" style="margin-right:0.02778em;">r</span><span class="mord mathnormal">a</span><span class="mord mathnormal">d</span><span class="mspace"> </span><span class="mord mathnormal">t</span></span></span></span>为空间中某点的温度梯度，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">{n}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord"><span class="mord mathnormal">n</span></span></span></span></span> 为通过该点的等温线上的单位矢量。</p><h3 id="导热系数"><a class="markdownIt-Anchor" href="#导热系数"></a> 导热系数</h3><p>导热系数的数值取决于物质的种类和温度等因素。</p><p>导热系数小于0.08$W/(m\cdot K)$的材料被称为保温材料，如矿渣棉、硅藻土、岩棉板、膨胀珍珠岩、<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>S</mi><mi>i</mi><msub><mi>O</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">SiO_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord mathnormal" style="margin-right:0.05764em;">S</span><span class="mord mathnormal">i</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02778em;">O</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0278em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>气凝胶等。</p><p>降低导热系数的方法：使用空心结构（如将标准黏土砖从实心改成空心率为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>40</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">40\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">40%</span></span></span></span>的空心砖，其当量传热系数可以减少大约<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>50</mn><mi mathvariant="normal">%</mi></mrow><annotation encoding="application/x-tex">50\%</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8056em;vertical-align:-0.0556em;"></span><span class="mord">50%</span></span></span></span>左右）</p><p><img src="/images/20250610/%E7%83%AD%E4%BC%A0%E5%AF%BC%EF%BC%88%E7%A8%B3%E6%80%81%EF%BC%89-20250702234615923.webp" alt="导热微分方程笔记"></p><h3 id="目标案例"><a class="markdownIt-Anchor" href="#目标案例"></a> 目标案例</h3><p>现有一加热炉，炉壁由四层结构构成：最里层为厚65mm的耐火砖，第二层为65mm的隔热层（材质标注为聚轻球，不知道明确材质），第三层为70mm的保温棉，最外层为160mm的保温块（材质未知）。<br><img src="/images/20250610/%E6%B0%94%E7%82%89%E7%82%89%E5%A3%81%E7%BB%93%E6%9E%84.svg" alt></p><p>在炉内温度为1100摄氏度时，炉壁平均为65摄氏度，计算每平方米每小时的散热量。</p><p>【分析】：本问题忽略炉顶炉底，仅分析炉壁散热，可以简化为传热学中一维稳态导热问题中的多层平壁模型<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>（忽略各层间的接触热阻，层与层之间不发生温度降低），此模型求解计算时需要知道：</p><ol><li>各层的厚度：可在工程图中获得数据，</li><li>各层的导热系数：材料导热系数与温度有关，可假设一估计值，而后进行迭代求解。</li><li>最内最外层的温度：内层通过热电偶获得，外层通过测温仪测得。</li></ol><p>收集数据简单整理如下图：</p><p><img src="/images/20250610/%E6%B0%94%E7%82%89%E7%82%89%E5%A3%81%E6%B8%A9%E5%BA%A6%E5%88%86%E5%B8%83.svg" alt></p><p>【导热系数计算】：工程上材料的导热系数一般都是温度的函数，这就意味着需要知道温度才能求得导热系数，然而层间温度本身是未知的，甚至有些材料（如最外层的保温块）本身也是未知的。在这种情况下可通过迭代法求解：估计一个大概的导热系数，用此导热系数来估计出层间温度，与已知的最内侧、最外侧温度进行比较，偏差超过允许值则重新估计，进行迭代，直到逼近到合理数值。</p><ol><li>将温度分布看作线性——从炉内到炉外依次降低，来估计层间温度。即 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">Δ</mi><mi>t</mi><mo>=</mo><mfrac><mrow><msub><mi>t</mi><mn>0</mn></msub><mo>−</mo><msub><mi>t</mi><mn>4</mn></msub></mrow><mrow><mo>∑</mo><mi>δ</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>1100</mn><mo>−</mo><mn>65</mn></mrow><mrow><mn>65</mn><mo>+</mo><mn>65</mn><mo>+</mo><mn>70</mn><mo>+</mo><mn>160</mn></mrow></mfrac><mo>=</mo><mn>2.875</mn></mrow><annotation encoding="application/x-tex">\Delta t = \frac{t_0-t_4}{\sum \delta}=\frac{1100-65}{65+65+70+160}=2.875</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord">Δ</span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3607em;vertical-align:-0.52em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8407em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mop op-symbol small-op mtight" style="position:relative;top:0em;">∑</span><span class="mspace mtight" style="margin-right:0.1952em;"></span><span class="mord mathnormal mtight" style="margin-right:0.03785em;">δ</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.4101em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span><span class="mbin mtight">−</span><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.2484em;vertical-align:-0.4033em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">65</span><span class="mbin mtight">+</span><span class="mord mtight">65</span><span class="mbin mtight">+</span><span class="mord mtight">70</span><span class="mbin mtight">+</span><span class="mord mtight">160</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1100</span><span class="mbin mtight">−</span><span class="mord mtight">65</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4033em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">2.875</span></span></span></span>℃/mm</li><li>查询材料的导热系数经验计算公式，根据层间温度来估计导热系数：</li></ol><table><thead><tr><th style="text-align:center">材料层</th><th style="text-align:center">厚度(mm)</th><th style="text-align:center">材质</th><th style="text-align:center">参考导热系数λ₀ (W/m·K)</th><th style="text-align:center">温度系数b (K⁻¹)</th><th>估计层间温度</th></tr></thead><tbody><tr><td style="text-align:center">耐火砖</td><td style="text-align:center">65</td><td style="text-align:center">高铝耐火砖</td><td style="text-align:center">1.30</td><td style="text-align:center">0.0006</td><td>913.1°C</td></tr><tr><td style="text-align:center">聚轻球</td><td style="text-align:center">65</td><td style="text-align:center">轻质氧化铝球</td><td style="text-align:center">0.15</td><td style="text-align:center">0.0003</td><td>726.2°C</td></tr><tr><td style="text-align:center">保温棉</td><td style="text-align:center">70</td><td style="text-align:center">硅酸铝纤维棉</td><td style="text-align:center">0.08</td><td style="text-align:center">0.0001</td><td>525.0°C</td></tr><tr><td style="text-align:center">保温块</td><td style="text-align:center">160</td><td style="text-align:center">微孔硅酸钙板</td><td style="text-align:center">0.07</td><td style="text-align:center">0.0002</td><td>–</td></tr></tbody></table><p><img src="/images/20250610/%E7%83%AD%E4%BC%A0%E5%AF%BC%EF%BC%88%E7%A8%B3%E6%80%81%EF%BC%89-20250702225839009.webp" alt="查手册得到的耐火砖导热系数值"></p><p>按照思路撰写迭代程序：</p><figure class="highlight python"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span class="line">30</span><br><span class="line">31</span><br><span class="line">32</span><br><span class="line">33</span><br><span class="line">34</span><br><span class="line">35</span><br><span class="line">36</span><br><span class="line">37</span><br><span class="line">38</span><br><span class="line">39</span><br><span class="line">40</span><br><span class="line">41</span><br><span class="line">42</span><br><span class="line">43</span><br><span class="line">44</span><br><span class="line">45</span><br><span class="line">46</span><br><span class="line">47</span><br><span class="line">48</span><br><span class="line">49</span><br><span class="line">50</span><br><span class="line">51</span><br><span class="line">52</span><br><span class="line">53</span><br><span class="line">54</span><br><span class="line">55</span><br><span class="line">56</span><br><span class="line">57</span><br><span class="line">58</span><br><span class="line">59</span><br><span class="line">60</span><br><span class="line">61</span><br><span class="line">62</span><br><span class="line">63</span><br><span class="line">64</span><br><span class="line">65</span><br><span class="line">66</span><br><span class="line">67</span><br><span class="line">68</span><br><span class="line">69</span><br><span class="line">70</span><br><span class="line">71</span><br><span class="line">72</span><br><span class="line">73</span><br><span class="line">74</span><br><span class="line">75</span><br><span class="line">76</span><br><span class="line">77</span><br><span class="line">78</span><br><span class="line">79</span><br><span class="line">80</span><br><span class="line">81</span><br><span class="line">82</span><br><span class="line">83</span><br><span class="line">84</span><br><span class="line">85</span><br><span class="line">86</span><br><span class="line">87</span><br><span class="line">88</span><br><span class="line">89</span><br><span class="line">90</span><br></pre></td><td class="code"><pre><span class="line"><span class="keyword">import</span> numpy <span class="keyword">as</span> np</span><br><span class="line"></span><br><span class="line"><span class="keyword">def</span> <span class="title function_">calculate_lambda</span>(<span class="params">T, lambda0, b</span>):</span><br><span class="line">    <span class="keyword">return</span> lambda0 * (<span class="number">1</span> + b * T)</span><br><span class="line"></span><br><span class="line"><span class="keyword">def</span> <span class="title function_">solve_furnace_wall</span>(<span class="params">T_inner, T_outer, layers, tol=<span class="number">0.5</span>, max_iter=<span class="number">100</span></span>):</span><br><span class="line">    total_thickness = <span class="built_in">sum</span>(layer[<span class="number">0</span>] <span class="keyword">for</span> layer <span class="keyword">in</span> layers)</span><br><span class="line">    T_interfaces = [T_inner - (T_inner - T_outer) * <span class="built_in">sum</span>(layers[i][<span class="number">0</span>] <span class="keyword">for</span> i <span class="keyword">in</span> <span class="built_in">range</span>(j+<span class="number">1</span>)) / total_thickness</span><br><span class="line">                   <span class="keyword">for</span> j <span class="keyword">in</span> <span class="built_in">range</span>(<span class="number">3</span>)]</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">print</span>(<span class="string">&quot;初始界面温度估计:&quot;</span>, [<span class="string">f&quot;<span class="subst">&#123;t:<span class="number">.1</span>f&#125;</span>°C&quot;</span> <span class="keyword">for</span> t <span class="keyword">in</span> T_interfaces])</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">for</span> <span class="built_in">iter</span> <span class="keyword">in</span> <span class="built_in">range</span>(max_iter):</span><br><span class="line">        <span class="comment"># 计算各层平均温度和导热系数</span></span><br><span class="line">        T_avgs = []</span><br><span class="line">        lambdas = []</span><br><span class="line">        R_layers = []</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># 第一层：内壁到T2</span></span><br><span class="line">        T_avg1 = (T_inner + T_interfaces[<span class="number">0</span>]) / <span class="number">2</span></span><br><span class="line">        lambda1 = calculate_lambda(T_avg1, layers[<span class="number">0</span>][<span class="number">1</span>], layers[<span class="number">0</span>][<span class="number">2</span>])</span><br><span class="line">        R1 = layers[<span class="number">0</span>][<span class="number">0</span>] / lambda1</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># 第二层：T2到T3</span></span><br><span class="line">        T_avg2 = (T_interfaces[<span class="number">0</span>] + T_interfaces[<span class="number">1</span>]) / <span class="number">2</span></span><br><span class="line">        lambda2 = calculate_lambda(T_avg2, layers[<span class="number">1</span>][<span class="number">1</span>], layers[<span class="number">1</span>][<span class="number">2</span>])</span><br><span class="line">        R2 = layers[<span class="number">1</span>][<span class="number">0</span>] / lambda2</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># 第三层：T3到T4</span></span><br><span class="line">        T_avg3 = (T_interfaces[<span class="number">1</span>] + T_interfaces[<span class="number">2</span>]) / <span class="number">2</span></span><br><span class="line">        lambda3 = calculate_lambda(T_avg3, layers[<span class="number">2</span>][<span class="number">1</span>], layers[<span class="number">2</span>][<span class="number">2</span>])</span><br><span class="line">        R3 = layers[<span class="number">2</span>][<span class="number">0</span>] / lambda3</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># 第四层：T4到外壁</span></span><br><span class="line">        T_avg4 = (T_interfaces[<span class="number">2</span>] + T_outer) / <span class="number">2</span></span><br><span class="line">        lambda4 = calculate_lambda(T_avg4, layers[<span class="number">3</span>][<span class="number">1</span>], layers[<span class="number">3</span>][<span class="number">2</span>])</span><br><span class="line">        R4 = layers[<span class="number">3</span>][<span class="number">0</span>] / lambda4</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># 总热阻</span></span><br><span class="line">        R_total = R1 + R2 + R3 + R4</span><br><span class="line">        q = (T_inner - T_outer) / R_total</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># 更新界面温度</span></span><br><span class="line">        T2_new = T_inner - q * R1</span><br><span class="line">        T3_new = T2_new - q * R2</span><br><span class="line">        T4_new = T3_new - q * R3</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># 检查收敛</span></span><br><span class="line">        diff = <span class="built_in">max</span>(<span class="built_in">abs</span>(T2_new - T_interfaces[<span class="number">0</span>]), </span><br><span class="line">                  <span class="built_in">abs</span>(T3_new - T_interfaces[<span class="number">1</span>]), </span><br><span class="line">                  <span class="built_in">abs</span>(T4_new - T_interfaces[<span class="number">2</span>]))</span><br><span class="line">        </span><br><span class="line">        <span class="comment"># 更新界面温度</span></span><br><span class="line">        T_interfaces = [T2_new, T3_new, T4_new]</span><br><span class="line">        </span><br><span class="line">        <span class="built_in">print</span>(<span class="string">f&quot;迭代 <span class="subst">&#123;<span class="built_in">iter</span>+<span class="number">1</span>&#125;</span>: q = <span class="subst">&#123;q:<span class="number">.2</span>f&#125;</span> W/m², 界面温度: <span class="subst">&#123;T2_new:<span class="number">.1</span>f&#125;</span>°C, <span class="subst">&#123;T3_new:<span class="number">.1</span>f&#125;</span>°C, <span class="subst">&#123;T4_new:<span class="number">.1</span>f&#125;</span>°C&quot;</span>)</span><br><span class="line">        </span><br><span class="line">        <span class="keyword">if</span> diff &lt; tol:</span><br><span class="line">            <span class="built_in">print</span>(<span class="string">f&quot;收敛于 <span class="subst">&#123;<span class="built_in">iter</span>+<span class="number">1</span>&#125;</span> 次迭代&quot;</span>)</span><br><span class="line">            <span class="keyword">return</span> [lambda1, lambda2, lambda3, lambda4], q, T_interfaces</span><br><span class="line">    </span><br><span class="line">    <span class="keyword">raise</span> ValueError(<span class="string">f&quot;未在 <span class="subst">&#123;max_iter&#125;</span> 次迭代内收敛&quot;</span>)</span><br><span class="line"></span><br><span class="line"><span class="comment"># 输入参数</span></span><br><span class="line">T_inner = <span class="number">1100</span>  <span class="comment"># 炉内温度 (°C)</span></span><br><span class="line">T_outer = <span class="number">65</span>     <span class="comment"># 炉外温度 (°C)</span></span><br><span class="line"></span><br><span class="line"><span class="comment"># 各层参数 (厚度(m), λ₀(W/m·K), b(K⁻¹))</span></span><br><span class="line">layers = [</span><br><span class="line">    (<span class="number">0.065</span>, <span class="number">1.30</span>, <span class="number">0.0006</span>),    <span class="comment"># 耐火砖</span></span><br><span class="line">    (<span class="number">0.065</span>, <span class="number">0.15</span>, <span class="number">0.0003</span>),   <span class="comment"># 聚轻球（假设）</span></span><br><span class="line">    (<span class="number">0.070</span>, <span class="number">0.08</span>, <span class="number">0.0001</span>),   <span class="comment"># 保温棉</span></span><br><span class="line">    (<span class="number">0.160</span>, <span class="number">0.07</span>, <span class="number">0.0002</span>)    <span class="comment"># 保温块（假设）</span></span><br><span class="line">]</span><br><span class="line"></span><br><span class="line"><span class="comment"># 运行计算</span></span><br><span class="line"><span class="keyword">try</span>:</span><br><span class="line">    lambdas, q, T_interfaces = solve_furnace_wall(T_inner, T_outer, layers)</span><br><span class="line">    </span><br><span class="line">    <span class="built_in">print</span>(<span class="string">&quot;\n=== 最终结果 ===&quot;</span>)</span><br><span class="line">    <span class="built_in">print</span>(<span class="string">f&quot;热流密度 q = <span class="subst">&#123;q:<span class="number">.2</span>f&#125;</span> W/m²&quot;</span>)</span><br><span class="line">    <span class="built_in">print</span>(<span class="string">&quot;各层导热系数:&quot;</span>)</span><br><span class="line">    <span class="built_in">print</span>(<span class="string">f&quot;  1. 耐火砖: <span class="subst">&#123;lambdas[<span class="number">0</span>]:<span class="number">.4</span>f&#125;</span> W/(m·K)  (参考λ₀=1.30)&quot;</span>)</span><br><span class="line">    <span class="built_in">print</span>(<span class="string">f&quot;  2. 聚轻球: <span class="subst">&#123;lambdas[<span class="number">1</span>]:<span class="number">.4</span>f&#125;</span> W/(m·K)  (参考λ₀=0.15)&quot;</span>)</span><br><span class="line">    <span class="built_in">print</span>(<span class="string">f&quot;  3. 保温棉: <span class="subst">&#123;lambdas[<span class="number">2</span>]:<span class="number">.4</span>f&#125;</span> W/(m·K)  (参考λ₀=0.08)&quot;</span>)</span><br><span class="line">    <span class="built_in">print</span>(<span class="string">f&quot;  4. 保温块: <span class="subst">&#123;lambdas[<span class="number">3</span>]:<span class="number">.4</span>f&#125;</span> W/(m·K)  (参考λ₀=0.07)&quot;</span>)</span><br><span class="line">    <span class="built_in">print</span>(<span class="string">f&quot;界面温度: T2=<span class="subst">&#123;T_interfaces[<span class="number">0</span>]:<span class="number">.1</span>f&#125;</span>°C, T3=<span class="subst">&#123;T_interfaces[<span class="number">1</span>]:<span class="number">.1</span>f&#125;</span>°C, T4=<span class="subst">&#123;T_interfaces[<span class="number">2</span>]:<span class="number">.1</span>f&#125;</span>°C&quot;</span>)</span><br><span class="line">    </span><br><span class="line"><span class="keyword">except</span> ValueError <span class="keyword">as</span> e:</span><br><span class="line">    <span class="built_in">print</span>(e)</span><br></pre></td></tr></table></figure><p>运行结果：</p><figure class="highlight txt"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br></pre></td><td class="code"><pre><span class="line">初始界面温度估计: [&#x27;913.1°C&#x27;, &#x27;726.2°C&#x27;, &#x27;525.0°C&#x27;]</span><br><span class="line">迭代 1: q = 307.96 W/m², 界面温度: 1090.4°C, 983.3°C, 729.7°C</span><br><span class="line">迭代 2: q = 315.15 W/m², 界面温度: 1090.5°C, 986.3°C, 732.3°C</span><br><span class="line">迭代 3: q = 315.24 W/m², 界面温度: 1090.5°C, 986.3°C, 732.3°C</span><br><span class="line">收敛于 3 次迭代</span><br><span class="line"></span><br><span class="line">=== 最终结果 ===</span><br><span class="line">热流密度 q = 315.24 W/m²</span><br><span class="line">各层导热系数:</span><br><span class="line">  1. 耐火砖: 2.1543 W/(m·K)  (参考λ₀=1.30)</span><br><span class="line">  2. 聚轻球: 0.1967 W/(m·K)  (参考λ₀=0.15)</span><br><span class="line">  3. 保温棉: 0.0869 W/(m·K)  (参考λ₀=0.08)</span><br><span class="line">  4. 保温块: 0.0756 W/(m·K)  (参考λ₀=0.07)</span><br><span class="line">界面温度: T2=1090.5°C, T3=986.3°C, T4=732.3°C</span><br></pre></td></tr></table></figure><p>结果整理如下：</p><table><thead><tr><th style="text-align:center">材料层</th><th style="text-align:center">厚度(mm)</th><th style="text-align:center">迭代导热系数λ₀ (W/m·K)</th><th style="text-align:center">迭代层间温度</th></tr></thead><tbody><tr><td style="text-align:center">耐火砖</td><td style="text-align:center">65</td><td style="text-align:center">2.1543</td><td style="text-align:center">1090.5°C</td></tr><tr><td style="text-align:center">聚轻球</td><td style="text-align:center">65</td><td style="text-align:center">0.1967</td><td style="text-align:center">986.3°C</td></tr><tr><td style="text-align:center">保温棉</td><td style="text-align:center">70</td><td style="text-align:center">0.0869</td><td style="text-align:center">732.3°C</td></tr><tr><td style="text-align:center">保温块</td><td style="text-align:center">160</td><td style="text-align:center">0.0756</td><td style="text-align:center">–</td></tr></tbody></table><p>则总热阻为</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>R</mi><mrow><mi>t</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>l</mi></mrow></msub><mo>=</mo><mfrac><mn>0.065</mn><mn>2.1543</mn></mfrac><mo>+</mo><mfrac><mn>0.065</mn><mn>0.1967</mn></mfrac><mo>+</mo><mfrac><mn>0.070</mn><mn>0.0869</mn></mfrac><mo>+</mo><mfrac><mn>0.16</mn><mn>0.0756</mn></mfrac><mo>=</mo><mn>3.283</mn><msup><mi>m</mi><mn>2</mn></msup><mo>⋅</mo><mi>K</mi><mi mathvariant="normal">/</mi><mi>W</mi></mrow><annotation encoding="application/x-tex">R_{total}=\frac{0.065}{2.1543}+\frac{0.065}{0.1967}+\frac{0.070}{0.0869}+\frac{0.16}{0.0756}=3.283 m^2\cdot K/W</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">o</span><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">2.1543</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0.065</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0.1967</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0.065</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0.0869</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0.070</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0.0756</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">0.16</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8641em;"></span><span class="mord">3.283</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="mord">/</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span></span></span></span></span></p><p>热流密度为：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>q</mi><mo>=</mo><mfrac><mrow><mn>1100</mn><mo>−</mo><mn>65</mn></mrow><msub><mi>R</mi><mrow><mi>t</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>l</mi></mrow></msub></mfrac><mo>=</mo><mn>315.26</mn><mi>W</mi><mi mathvariant="normal">/</mi><msup><mi>m</mi><mn>2</mn></msup><mo>=</mo><mn>315.26</mn><mi>J</mi><mi mathvariant="normal">/</mi><mi>s</mi><mo>⋅</mo><msup><mi>m</mi><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow><annotation encoding="application/x-tex">q=\frac{1100-65}{R_{total}}=315.26 W/m^2 = 315.26 J/s\cdot m^{-2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.1574em;vertical-align:-0.836em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.00773em;">R</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0077em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">o</span><span class="mord mathnormal mtight">t</span><span class="mord mathnormal mtight">a</span><span class="mord mathnormal mtight" style="margin-right:0.01968em;">l</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1100</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">65</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.836em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.1141em;vertical-align:-0.25em;"></span><span class="mord">315.26</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord">/</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">315.26</span><span class="mord mathnormal" style="margin-right:0.09618em;">J</span><span class="mord">/</span><span class="mord mathnormal">s</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.8641em;"></span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span></span></span></p><p>则每平方米炉壁每小时散热：</p><ul><li>1134.85 kJ/(m²·h)（千焦）</li><li>0.3152 kWh/(m²·h)（换算成千瓦时）</li><li>0.0317Nm3/(m2⋅h)（换算成标准大气压下天然气消耗(35.8兆焦/方)）</li></ul><hr class="footnotes-sep"><section class="footnotes"><ol class="footnotes-list"><li id="fn1" class="footnote-item"><p>《传热学》P41 <a href="#fnref1" class="footnote-backref">↩︎</a></p></li></ol></section>]]></content>
    
    
    <summary type="html">稳态热传导学习笔记+实际案例分析计算</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/%E4%BC%A0%E7%83%AD%E5%AD%A6%E7%AC%94%E8%AE%B0.svg" type="image"/>
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
    <category term="📒课程笔记" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%F0%9F%93%92%E8%AF%BE%E7%A8%8B%E7%AC%94%E8%AE%B0/"/>
    
    <category term="传热学" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%F0%9F%93%92%E8%AF%BE%E7%A8%8B%E7%AC%94%E8%AE%B0/%E4%BC%A0%E7%83%AD%E5%AD%A6/"/>
    
    
    <category term="快餐" scheme="https://blog.si-on.top/tags/%E5%BF%AB%E9%A4%90/"/>
    
  </entry>
  
  <entry>
    <title>年中</title>
    <link href="https://blog.si-on.top/2025/01%E2%80%9306/"/>
    <id>https://blog.si-on.top/2025/01%E2%80%9306/</id>
    <published>2025-06-30T13:14:23.000Z</published>
    <updated>2025-06-30T13:14:23.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><blockquote><p>所见所期，不可不远且大，然行之亦须量力有渐。志大心劳，力小任重，弘而不毅，恐终败事<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>。</p></blockquote><h2 id="瞻顾"><a class="markdownIt-Anchor" href="#瞻顾"></a> 瞻顾</h2><p>兴趣A，断断续续自嗨而已，无所成就，少有满意的作品。大概是自我定位太高，像一条孤傲的猛虎，瞧不起陈旧的风格，对一些基本功不屑一顾。然而这基本功便是所谓专业的训练。此兴趣与个人心绪紧密结合，心绪没有波动的日子，也只能放在那里，拿起来又放下。</p><p>兴趣B的火焰，在设备买来的一个月之内，很快地灭掉了。一开始的的确确熟悉了一点点筋肉的技巧，还很高兴，甚至还能做些蹩脚的展示。随着之前累计的热情染料逐渐消耗殆尽，我却一直没有找到方向，一直没有找到那条属于我的路。导致火焰没有新的燃料便熄灭成死灰了。尽管我现在还不愿意承认火焰熄灭这个事实。</p><p>兴趣C，因为进入圈子门槛极低的缘故，使我在一次次反馈中持续的吞噬自由意志，几乎沦为C的奴隶。在5月份左右开始，对风格的形成有一点思考。这是一点点进步。</p><p>表达D，因为某些变动与自身习惯的不及时调整，导致源头变得干涸。D逐渐混乱、随意而抽象。</p><p>表达E，开了头，有了流，后面的路反而走不成了。</p><p>对于年初计划3点</p><ol><li>扬波鳞鳞(风扬起的波浪造成如鱼鳞似的光一般的招摇作态)</li><li>死水微澜(不够决然的否定)</li><li>冰泉冷涩(不够豁然的心境)</li></ol><p>有些进步: 1，在写计划某文章过程中，看书读书，体察实际后得到一定程度的反思。2，因为从未十分肯定过什么东西，否定总是持续进行的，一个理想化的目标应该定为决然的肯定。3， 努力压制，逐渐脱敏，豁然了些。</p><hr><h2 id="载驰"><a class="markdownIt-Anchor" href="#载驰"></a> 载驰</h2><p>后半年，需要做到:</p><ol><li>打磨基础理论，以加快学习掌握达以其他某领域一般水平的速度。</li><li>通览领域G，以从中完善对于G乃至X的看法。</li><li>把握后半年可能遇到的三四种随机某领域/某风格/某技术</li><li>【试验性】以<strong>风格形成</strong>为价值导向 发展ABCDE(A要注意关注核心操作，C信息容易过载，要及时去粗存精)</li><li>适当 开放/筛选/随机化 外界信息流，与外界互通有无，以抵抗自为师的负面影响。(受Z提醒)</li></ol><hr><p>备注:<br>A: ZuanK B: YinY C: Nyos D: XieZ E:Bok G: JiS phil X: phil Z:zsk</p><hr class="footnotes-sep"><section class="footnotes"><ol class="footnotes-list"><li id="fn1" class="footnote-item"><p>然观圣人之教（近乎完美的教学方法），循循有序，使人求之至小至近之中，博之文以开其讲学之端，约之礼(规范)以严其践履之实，使之得寸则守其寸，得尺则守其尺。如是久之，日滋月益，然后道之全体乃有所向望，而渐可识，有所循习，而渐可能，自是而往挽焉，孜孜斃而后已。而其所造之浅深，所就之广狭，亦非可以必诣而预期也。盖于此小差则心失其正，虽有仰高钻坚之志而反为谋利计功之私矣” <a href="#fnref1" class="footnote-backref">↩︎</a></p></li></ol></section>]]></content>
    
    
    <summary type="html">一般阶段性计划。</summary>
    
    
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="计划总结" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%E8%AE%A1%E5%88%92%E6%80%BB%E7%BB%93/"/>
    
    
  </entry>
  
  <entry>
    <title>浅论书写方式：提示词是书写的最终形式吗？</title>
    <link href="https://blog.si-on.top/2025/the_way_of_writing/"/>
    <id>https://blog.si-on.top/2025/the_way_of_writing/</id>
    <published>2025-06-29T14:49:26.000Z</published>
    <updated>2025-06-29T14:49:26.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p>近日对“迭代”一词有了极大的兴趣，除了编程上的妙用外，它甚至可以是解读世界的一把神器——“凡在天地间,无非迭代之理,造化与人事皆是。”</p><p>思考是一种基本的迭代，将色声香味触、图像、文本等接收到的信息而产生的念头进行重复审视，以得到新的或否定旧的，或强化现在的想法。书写则可看作是思考的迭代，将飘忽不定、图式而混乱的想法，通过逻辑的、线性的，颗粒化的文字符号表达出来。</p><p>书写本身又可借由誊写、修订、甚至传播、训练成语料库等方式进行迭代。管它迭代几次三番，以手稿、书本、大语言模型还是何种形式存乎于世，其最终目的都大相径庭——“生产信息，迭代下去，抵抗熵增，永久流传”使个体的自由意志与客体的无常荒谬相拮抗。</p><p>从流芳百世、遗臭万年的“百世”、“万年”可见，不朽大抵是以时间为标的物的。假设不考虑传播与复制，那么决定书写朽与不朽的关键点的便是书写方式了。下面以我所熟悉的几种书写方式及笔者的使用熟练程度为基础进行探讨。</p><ol><li>篆刻刀，结构简单，功能复杂。采用镌刻式书写，钢刀刻入石头表面2~3mm深，速度约10min/字，可承受风吹日晒雨淋火烧，可保存约上百年。</li><li>毛笔（软笔），结构复杂，功能简单。采用表面式书写，毛刷上的颜料液滴通过复杂物理化学作用吸附到另一表面，速度约10s/字，以纸张为媒介，可保存几十年。</li><li>钢笔（硬笔），结构相对于软笔更为复杂，不能写出粗细变化，功能上更为简单。采用表面式书写，颜料通过复杂精密机械结构恒流量地通过复杂物理化学作用吸附到另一表面，速度约2s/字，以纸张为媒介，可保存十几年。</li><li>文本编辑器，结构高度复杂（以操作系统为载体的软件）功能高度简单抽象（舍弃了实体，虚拟化到显示器上，有便捷的文本操作，样式设定等功能）。采用虚拟化书写，通过敲击键盘上特定规则按键的组合，将需要的文本写入到显示器上，速度约0.8s/字，以硬盘为媒介，可保存十年左右。</li><li>生成式文本，结构极度复杂（以操作系统上，通过海量语料训练的大语言模型软件为基础）功能极度简单。采用迭代的虚拟化书写，通过自然语言写出简短的提示词，不需要谋篇布局，即可在显示器上生成真正可读的文本，速度约0.001s/字，储存于硬盘的缓冲区，可保存30天（chatgpt为例）到180天（deepseek）左右。</li></ol><table><thead><tr><th>维度</th><th>篆刻刀</th><th>毛笔</th><th>钢笔</th><th>文本编辑器</th><th>生成式文本</th></tr></thead><tbody><tr><td><strong>中断频率</strong></td><td>每笔画</td><td>每字/词</td><td>每页</td><td>篇章级</td><td>仅复制时</td></tr><tr><td><strong>存续时长</strong></td><td>≈300年</td><td>≈50年</td><td>≈15年</td><td>≈10年</td><td>30-180天</td></tr><tr><td><strong>书写速度</strong></td><td>10min/字</td><td>10s/字</td><td>2s/字</td><td>0.8s/字</td><td>0.001s/字</td></tr><tr><td><strong>交互深度</strong></td><td>物理镌刻</td><td>表面渗透</td><td>表面附着</td><td>虚拟化</td><td>缓冲区暂存</td></tr></tbody></table><p>我们可以得到如下规律：书写越容易，信息消失越快。书写工具结构越简单，功能越复杂，对使用者要求越高。</p><p>下面再回到迭代，上文说过书写过程是思考的迭代，一个线性化过程。既然是线，就或多或少会发生间断，这种线性化过程中的间断，可看作作寓于书写父迭代之里的子迭代。</p><p>间断是一种反思，对书写行为的审视，如果失去这种审视，思维中的疯狂便会显露出来，吞噬书写，吞噬一切。</p><p>书写过程中同样如此，比如篆刻的回刀，软笔的吸墨，硬笔的换芯等等。在篆刻兴盛的秦汉，每刻一条线就要间断一次，惜字如金；到了软笔，几个字写完蘸墨一次，有时一个字都要推敲良久；在硬笔的时代，写完一页纸间断一次，鸿篇巨制已不罕见；到了文本编辑器，自动滚动换行，一篇一间断。进入提示词时代，只有复制时才会间断。</p><p>没有了间断，失去了好地狱，这里将充满抽象的狂欢以及泛滥的疯狂。</p><p>提示词的确是书写的最终形式。在此之后的在某个时间，书写将被收入联合国非物质文化遗产名录。</p>]]></content>
    
    
    <summary type="html">浅论书写方式。</summary>
    
    
    
    
    <category term="生活" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/"/>
    
    <category term="🪶杂谈" scheme="https://blog.si-on.top/categories/%E7%94%9F%E6%B4%BB/%F0%9F%AA%B6%E6%9D%82%E8%B0%88/"/>
    
    
  </entry>
  
  <entry>
    <title>传热学笔记</title>
    <link href="https://blog.si-on.top/2025/Basic@Heat-transfer/"/>
    <id>https://blog.si-on.top/2025/Basic@Heat-transfer/</id>
    <published>2025-06-24T07:52:26.000Z</published>
    <updated>2025-06-24T07:52:26.000Z</updated>
    
    <content type="html"><![CDATA[<link rel="stylesheet" class="aplayer-secondary-style-marker" href="/assets/css/APlayer.min.css"><script src="/assets/js/APlayer.min.js" class="aplayer-secondary-script-marker"></script><script class="meting-secondary-script-marker" src="/assets/js/Meting.min.js"></script><p>因工作需要计算某设备的散热，临时补课传热学。</p><h2 id="概览"><a class="markdownIt-Anchor" href="#概览"></a> 概览</h2><p>传热学就是研究温差引起的热能传递规律的科学。基本假设：所研究的物体中的温度、密度、速度、压力等物理参数都是空间的连续函数； 热量传递过程发生的时间远远大于物体内微观粒子在经受扰动后恢复平衡状态所需的时间。</p><p>热力学研究热量传递，传热学关注时间，单位时间内传递多少热能。</p><p>传热学主要研究的问题：</p><ol><li>强化传热（ heat enhancement ）。即在一定的条件（如一定的温差、体积、重量或泵功等）下增加所传递的热量。</li><li>削弱传热（ heat transfer reduction ），或称热绝缘。<strong>即在一定的温差下使热量的传递减到最小</strong>。（此部分与需求高度吻合）</li><li>温度控制（ temperature control ）。为使一些设备能安全经济地运行，或者为得到优质产品，要对热量传递过程中物体关键部位的温度进行控制。</li></ol><h3 id="热能传递三种方式"><a class="markdownIt-Anchor" href="#热能传递三种方式"></a> 热能传递三种方式</h3><p><strong>热传导</strong>：物体各部分之间不发生相对位移时，依靠分子、原子及自由电子等微观粒子的热运动而产生的热能传递称为热传导（ heat conduction ），简称导热。例如，固体内部热量从温度较高的部分传递到温度较低的部分，以及温度较高的固体把热量传递给与之接触的度较低的另一固体都是导热现象。</p><p>热传导的经验公式已经被总结成傅里叶定律(导热基本定律)——<u>单位时间内通过一维表面厚度的导热热量与当地温度变化率与平板面积A成正比</u>：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>Φ</mi><mo>=</mo><mo>−</mo><mi>λ</mi><mi>A</mi><mfrac><mrow><mi>d</mi><mi>t</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">\varPhi=-\lambda A \frac{dt}{dx}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathit">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord">−</span><span class="mord mathnormal">λ</span><span class="mord mathnormal">A</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>q</mi><mo>=</mo><mo>−</mo><mi>λ</mi><mfrac><mrow><mi>d</mi><mi>t</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac></mrow><annotation encoding="application/x-tex">q=-\lambda \frac{dt}{dx}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord">−</span><span class="mord mathnormal">λ</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">d</span><span class="mord mathnormal">t</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><ul><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>λ</mi><mo stretchy="false">(</mo><mi>W</mi><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><mi>m</mi><mo>⋅</mo><mi>K</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\lambda(W/(m\cdot K))</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">λ</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord">/</span><span class="mopen">(</span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="mclose">))</span></span></span></span>:热导率，比例系数，热物性参数。（与材料、材料本身温度有关）</li><li>”-“：表示热量传递方向与温度升高方向相反</li><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Φ</mi></mrow><annotation encoding="application/x-tex">\varPhi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathit">Φ</span></span></span></span>(<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>W</mi></mrow><annotation encoding="application/x-tex">W</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span></span></span></span>)：单位时间内通过某一给定面积的热量称为热流量</li><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi></mrow><annotation encoding="application/x-tex">q</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span></span></span></span>(<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>W</mi><mi mathvariant="normal">/</mi><msup><mi>m</mi><mn>2</mn></msup></mrow><annotation encoding="application/x-tex">W/m^2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord">/</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span></span></span></span>)：单位面积的热流量称为热流密度</li></ul><blockquote><p>积分处理：此公式为单位面积上的热量，如果是一个有厚度的薄板，需要沿厚度方向积分才能得到热流密度：<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>q</mi><mo>×</mo><msubsup><mo>∫</mo><mn>0</mn><mi>x</mi></msubsup><mi>d</mi><mi>δ</mi><mo>=</mo><mo>−</mo><mi>λ</mi><msubsup><mo>∫</mo><mrow><mi>t</mi><mn>1</mn></mrow><mrow><mi>t</mi><mn>2</mn></mrow></msubsup><mfrac><mrow><mi>d</mi><mi>t</mi></mrow><mrow><mi>d</mi><mi>x</mi></mrow></mfrac><mi>d</mi><mi>x</mi><mo>=</mo><mi>q</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">q\times \int_0^x d\delta=-\lambda \int_{t1}^{t2} \frac{dt}{dx} dx=qx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7778em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.2151em;vertical-align:-0.3558em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8593em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">x</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.3648em;vertical-align:-0.3558em;"></span><span class="mord">−</span><span class="mord mathnormal">λ</span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mop"><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0006em;">∫</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.009em;"><span style="top:-2.3442em;margin-left:-0.1945em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2579em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3558em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">d</span><span class="mord mathnormal mtight">x</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">d</span><span class="mord mathnormal mtight">t</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mord mathnormal">d</span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mord mathnormal">x</span></span></span></span></p></blockquote><hr><p><strong>热对流</strong>：热对流（ heat convection ）是指由于流体的宏观运动而引起的流体各部分之间发生相对位移，冷、热流体相互掺混所导致的热量传递过程。热对流仅能发生在流体中，而且由于流体中的分子同时在进行着不规则的热运动，因而热对流必然伴銪有热传导现象。工程上特别感兴趣的是流体流过一个物体表面时流体与物体表面间的热量传递过程，并称之为对流传热（ convective heat sfer ），以区别于一般意义上的热对流。对流分两种，一是自然对流（依靠密度），二是强制对流（依靠压力）。对流传热的基本公式为牛顿冷却公式<sup class="footnote-ref"><a href="#fn1" id="fnref1">[1]</a></sup>：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>q</mi><mo>=</mo><mi>h</mi><mo stretchy="false">(</mo><msub><mi>t</mi><mi>w</mi></msub><mo>−</mo><msub><mi>t</mi><mi>f</mi></msub><mo stretchy="false">)</mo><mo>=</mo><mi>h</mi><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">q=h(t_w-t_f)=h\Delta t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">h</span><span class="mord">Δ</span><span class="mord mathnormal">t</span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>Φ</mi><mo>=</mo><mi>h</mi><mi>A</mi><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow><annotation encoding="application/x-tex">\varPhi=hA\Delta t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathit">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">h</span><span class="mord mathnormal">A</span><span class="mord">Δ</span><span class="mord mathnormal">t</span></span></span></span></span></p><ul><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi><mo stretchy="false">(</mo><mi>W</mi><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><msup><mi>m</mi><mn>2</mn></msup><mo>⋅</mo><mi>K</mi><mo stretchy="false">)</mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">h(W/(m^2\cdot K))</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="mclose">))</span></span></span></span>:表面传热系数（对流换热系数）,与多种因素有关，取决于流体的物性、换热面形状、大小与布置、流速等。</li></ul><hr><p><strong>热辐射</strong>：物体通过电磁波来传递能量的方式称为辐射。物体会因各种原因发出辐射能，其中因热的原因而发出辐射能的现象称为热辐射。物体辐射能力与温度以及物体本身特性有关</p><blockquote><p>导热、对流这两种热量传递方式只在有物质存在的条件下才能实现，而热辐射可以在真空中传递。当两个物体被真空隔开时，例如地球与太阳之间，导热与对流都不会发生，只能进行辐射传热。辐射传热区别于导热、对流传热的另一为特点是，它不仅产生能量的转移，而且还伴随着能量形式的转换，即<u>发射时从热能转换为辐射能，而被吸收时又从辐射能转换为热能</u>。</p></blockquote><p><strong>黑体</strong>指能吸收投入其表面上的所有热辐射能量的物体（即热能与辐射能的转变效率为100%）。黑体<u>单位时间内发射的热辐射能量</u>由Stefan-Boltzmann定律（四次方定律）定义：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>Φ</mi><mo>=</mo><mi>A</mi><mi>σ</mi><msup><mi>T</mi><mn>4</mn></msup></mrow><annotation encoding="application/x-tex">\varPhi=A\sigma T^4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathit">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8641em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span></span></span></span></span></p><ul><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>T</mi></mrow><annotation encoding="application/x-tex">T</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.13889em;">T</span></span></span></span>：黑体的热力学温度，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>K</mi></mrow><annotation encoding="application/x-tex">K</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">K</span></span></span></span></li><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span></span></span></span>：黑体辐射常数，<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>5.67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup><mi>W</mi><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><msup><mi>m</mi><mn>2</mn></msup><mo>⋅</mo><msup><mi>K</mi><mn>4</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">5.67\times 10^{-8} W/(m^2\cdot K^{4})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7278em;vertical-align:-0.0833em;"></span><span class="mord">5.67</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">8</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></li><li><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span>：辐射表面积对于非黑体的一般物体辐射热流量计算需引入黑度<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ε</mi></mrow><annotation encoding="application/x-tex">\varepsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">ε</span></span></span></span>(值小于1，与物体及其表面状态有关)</li></ul><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>Φ</mi><mo>=</mo><mstyle mathcolor="blue"><mi>ε</mi></mstyle><mi>A</mi><mi>σ</mi><msup><mi>T</mi><mn>4</mn></msup></mrow><annotation encoding="application/x-tex">\varPhi={\color{blue} \varepsilon} A\sigma T^4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathit">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8641em;"></span><span class="mord"><span class="mord mathnormal" style="color:blue;">ε</span></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span></span></span></span></span></p><blockquote><p>一个简单的场景：一个表面积为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>A</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">A_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>、表面温度为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">T_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span> 、发射率为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>ε</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">\varepsilon_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">ε</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>的物体被包容在一个很大的表面温度为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>T</mi><mn>2</mn></msub></mrow><annotation encoding="application/x-tex">T_2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>的空腔内，此时该物体与空腔表面间的辐射换热量按下式计算。物体本身辐射向外的能量为 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Φ</mi><mtext>自</mtext></msub><mo>=</mo><msub><mi>A</mi><mn>1</mn></msub><msub><mi>σ</mi><mn>1</mn></msub><msubsup><mi>T</mi><mn>1</mn><mn>4</mn></msubsup></mrow><annotation encoding="application/x-tex">\varPhi_{\text{自}} =A_1 \sigma_1 T_1^4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathit">Φ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord cjk_fallback mtight">自</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0622em;vertical-align:-0.2481em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4519em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2481em;"><span></span></span></span></span></span></span></span></span></span>,外界向其表面辐射的能量（自身从外界接受的能量）为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Φ</mi><mtext>外</mtext></msub><mo>=</mo><msub><mi>A</mi><mn>1</mn></msub><msub><mi>σ</mi><mn>1</mn></msub><msubsup><mi>T</mi><mn>2</mn><mn>4</mn></msubsup></mrow><annotation encoding="application/x-tex">\varPhi_{\text{外}} =A_1 \sigma_1 T_2^4</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathit">Φ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord cjk_fallback mtight">外</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0622em;vertical-align:-0.2481em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4519em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2481em;"><span></span></span></span></span></span></span></span></span></span>。故最终的换热量为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>Φ</mi><mtext>换</mtext></msub><mo>=</mo><msub><mi>A</mi><mn>1</mn></msub><msub><mi>σ</mi><mn>1</mn></msub><mo stretchy="false">(</mo><msubsup><mi>T</mi><mn>1</mn><mn>4</mn></msubsup><mo>−</mo><msubsup><mi>T</mi><mn>2</mn><mn>4</mn></msubsup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\varPhi_{\text{换}} =A_1 \sigma_1 (T_1^4-T_2^4)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8333em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathit">Φ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3283em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord text mtight"><span class="mord cjk_fallback mtight">换</span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4519em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2481em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-2.4519em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2481em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></p></blockquote><p>下面是暖气片内热水传热到室内的传热过程示意图：</p><pre><code class="highlight mermaid">flowchart LR id1(热水) -- 对流传热 --&gt; id2(管子内壁) -- 导热 --&gt; id3(管子外壁) -- 对流传热及辐射传热 --&gt; id4(室内温度)</code></pre><p>【示例】一水平放置的蒸汽管道，其保温层外径<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>d</mi><mo>=</mo><mn>583</mn><mi>m</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">d=583 mm</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">d</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">583</span><span class="mord mathnormal">mm</span></span></span></span>，外表面实测平均温度为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>w</mi></msub><mo>=</mo><mn>48</mn></mrow><annotation encoding="application/x-tex">t_w=48</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7651em;vertical-align:-0.15em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">48</span></span></span></span>℃。空气温度为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>t</mi><mi>f</mi></msub><mo>=</mo><mn>23</mn></mrow><annotation encoding="application/x-tex">t_f=23</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9012em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">23</span></span></span></span>℃，此时空气与管道外表面间的自然对流传热的表面传热系数<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>h</mi><mo>=</mo><mn>3.42</mn><mi>W</mi><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><msup><mi>m</mi><mn>2</mn></msup><mo>⋅</mo><mi>K</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">h=3.42 W/(m^2\cdot K)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em;"></span><span class="mord mathnormal">h</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em;"></span><span class="mord">3.42</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em;"><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="mclose">)</span></span></span></span>，保温层外表面的发射率<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>ε</mi><mo>=</mo><mn>0.9</mn></mrow><annotation encoding="application/x-tex">\varepsilon=0.9</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em;"></span><span class="mord mathnormal">ε</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.6444em;"></span><span class="mord">0.9</span></span></span></span>。计算每米长度管道的总散热量。</p><details class="folding-tag"><summary> 🔦解决示例 </summary>              <div class="content">              <p>解：假设沿管子长度方向各给定参数都保持不变，过程为一个稳态过程，管道周围的其他固体表面温度等于空气温度。把每米长度上的散热量记作<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>q</mi><mn>1</mn></msub></mrow><annotation encoding="application/x-tex">q_1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>，散热量分两部分，一是自然对流散热，二是辐射散热。</p><ol><li>对流散热</li></ol><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>q</mi><mrow><mn>1</mn><mo separator="true">,</mo><mi>d</mi></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>π</mi><mi>d</mi><mi>h</mi><mi mathvariant="normal">Δ</mi><mi>t</mi></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>π</mi><mi>d</mi><mi>h</mi><mo stretchy="false">(</mo><msub><mi>t</mi><mi>w</mi></msub><mo>−</mo><msub><mi>t</mi><mi>f</mi></msub><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>3.14</mn><mo>×</mo><mn>0.583</mn><mi>m</mi><mo>×</mo><mn>3.42</mn><mi>W</mi><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><msup><mi>m</mi><mn>2</mn></msup><mo>⋅</mo><mi>K</mi><mo stretchy="false">)</mo><mo>×</mo><mo stretchy="false">(</mo><mn>48</mn><mtext>℃</mtext><mo>−</mo><mn>23</mn><mtext>℃</mtext><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>156.5</mn><mi>W</mi><mi mathvariant="normal">/</mi><mi>m</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">   \begin{aligned}   q_{1,d} &amp;= \pi d h \Delta t\\   &amp;= \pi d h(t_w-t_f)\\   &amp;= 3.14\times 0.583 m\times3.42 W/(m^2\cdot K)\times(48℃-23℃)\\   &amp;= 156.5 W/m   \end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:6.0241em;vertical-align:-2.7621em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.2621em;"><span style="top:-5.4221em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.9221em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-2.3979em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-0.8979em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.7621em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:3.2621em;"><span style="top:-5.4221em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="mord mathnormal">d</span><span class="mord mathnormal">h</span><span class="mord">Δ</span><span class="mord mathnormal">t</span></span></span><span style="top:-3.9221em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="mord mathnormal">d</span><span class="mord mathnormal">h</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-2.3979em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">3.14</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0.583</span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">3.42</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">48℃</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">23℃</span><span class="mclose">)</span></span></span><span style="top:-0.8979em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">156.5</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord">/</span><span class="mord mathnormal">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.7621em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><ol start="2"><li>辐射散热</li></ol><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mtable rowspacing="0.25em" columnalign="right left" columnspacing="0em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><msub><mi>q</mi><mrow><mn>1</mn><mo separator="true">,</mo><mi>f</mi></mrow></msub></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mi>π</mi><mi>d</mi><mi>σ</mi><mi>ε</mi><mo stretchy="false">(</mo><msubsup><mi>T</mi><mi>w</mi><mn>4</mn></msubsup><mo>−</mo><msubsup><mi>T</mi><mi>f</mi><mn>4</mn></msubsup><mo stretchy="false">)</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>3.14</mn><mo>×</mo><mn>0.583</mn><mi>m</mi><mo>×</mo><mn>5.67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>8</mn></mrow></msup><mi>W</mi><mi mathvariant="normal">/</mi><mo stretchy="false">(</mo><msup><mi>m</mi><mn>2</mn></msup><mo>⋅</mo><msup><mi>K</mi><mn>4</mn></msup><mo stretchy="false">)</mo><mo>×</mo><mn>0.9</mn><mo>×</mo><mo stretchy="false">[</mo><mo stretchy="false">(</mo><mn>48</mn><mo>+</mo><mn>273</mn><msup><mo stretchy="false">)</mo><mn>4</mn></msup><msup><mi>K</mi><mn>4</mn></msup><mo>−</mo><mo stretchy="false">(</mo><mn>23</mn><mo>+</mo><mn>273</mn><msup><mo stretchy="false">)</mo><mn>4</mn></msup><msup><mi>K</mi><mn>4</mn></msup><mo stretchy="false">]</mo></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="true"><mrow><mrow></mrow><mo>=</mo><mn>274.7</mn><mi>W</mi><mi mathvariant="normal">/</mi><mi>m</mi></mrow></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">   \begin{aligned}   q_{1,f} &amp;= \pi d \sigma \varepsilon(T_w^4-T_f^4)\\   &amp;= 3.14\times 0.583m\times 5.67\times 10^{-8} W/(m^2\cdot K^{4}) \times 0.9\times  [(48+273)^4K^4-(23+273)^4K^4]\\   &amp;= 274.7 W/m   \end{aligned}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:4.5713em;vertical-align:-2.0357em;"></span><span class="mord"><span class="mtable"><span class="col-align-r"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.5357em;"><span style="top:-4.6716em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.1243em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span><span style="top:-1.6243em;"><span class="pstrut" style="height:3em;"></span><span class="mord"></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.0357em;"><span></span></span></span></span></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:2.5357em;"><span style="top:-4.6716em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord mathnormal" style="margin-right:0.03588em;">π</span><span class="mord mathnormal">d</span><span class="mord mathnormal" style="margin-right:0.03588em;">σ</span><span class="mord mathnormal">ε</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.453em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.247em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.13889em;">T</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-2.453em;margin-left:-0.1389em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.3831em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span><span style="top:-3.1243em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">3.14</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0.583</span><span class="mord mathnormal">m</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">5.67</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">1</span><span class="mord"><span class="mord">0</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">−</span><span class="mord mtight">8</span></span></span></span></span></span></span></span></span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord">/</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">m</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span></span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">0.9</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">×</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">[(</span><span class="mord">48</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">273</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mopen">(</span><span class="mord">23</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord">273</span><span class="mclose"><span class="mclose">)</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8641em;"><span style="top:-3.113em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span></span></span></span></span><span class="mclose">]</span></span></span><span style="top:-1.6243em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mord">274.7</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord">/</span><span class="mord mathnormal">m</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:2.0357em;"><span></span></span></span></span></span></span></span></span></span></span></span></p><p>所以每米长管道的总散热量为：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><msub><mi>q</mi><mn>1</mn></msub><mo>=</mo><msub><mi>q</mi><mrow><mn>1</mn><mo separator="true">,</mo><mi>d</mi></mrow></msub><mo>+</mo><msub><mi>q</mi><mrow><mn>1</mn><mo separator="true">,</mo><mi>f</mi></mrow></msub><mo>=</mo><mn>431.2</mn><mi>W</mi><mi mathvariant="normal">/</mi><mi>m</mi></mrow><annotation encoding="application/x-tex">q_1=q_{1,d}+q_{1,f}=431.2 W/m</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:0.8694em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight">d</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:0.7167em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em;">q</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span><span class="mpunct mtight">,</span><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord">431.2</span><span class="mord mathnormal" style="margin-right:0.13889em;">W</span><span class="mord">/</span><span class="mord mathnormal">m</span></span></span></span></span></p><p>计算结果表明，对于表面温度为几十摄氏度的一类表面的散热问题，自然对流散热与辐射散热量具有相同的数量级，不能忽略（如两者有“远远大于”的情况可以忽略）。</p>              </div>            </details><h3 id="传热过程与传热系数"><a class="markdownIt-Anchor" href="#传热过程与传热系数"></a> 传热过程与传热系数</h3><p>以冷、热流体通过一块大平壁交换热量为例（稳态），整个过程中包含着串联着的三个环节：</p><ol><li>从热流体到壁面高温侧的热量传递</li><li>从壁面高温侧到壁面低温侧的热量传递,亦即穿过固体壁的导热</li><li>从壁面低温侧到冷流体的热量传递。由于是稳态过程,通过串联着的每个环节的热流量应该是相同的。设平壁表面积为<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal">A</span></span></span></span>,<br><img src="/images/20250610/MES%20%E6%93%8D%E4%BD%9C%E7%95%8C%E9%9D%A2%201.svg" alt></li></ol><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>Φ</mi><mo>=</mo><mi>A</mi><msub><mi>h</mi><mn>1</mn></msub><mo stretchy="false">(</mo><msub><mi>t</mi><msub><mi>t</mi><mn>1</mn></msub></msub><mo>−</mo><msub><mi>t</mi><msub><mi>w</mi><mn>1</mn></msub></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\varPhi = Ah_1(t_{t_1}-t_{w_1})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathit">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0001em;vertical-align:-0.2501em;"></span><span class="mord mathnormal">A</span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0001em;vertical-align:-0.2501em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.0269em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>Φ</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mi>λ</mi></mrow><mi>δ</mi></mfrac><mo stretchy="false">(</mo><msub><mi>t</mi><msub><mi>w</mi><mn>1</mn></msub></msub><mo>−</mo><msub><mi>t</mi><msub><mi>w</mi><mn>2</mn></msub></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\varPhi = \frac{A\lambda}{\delta}(t_{w_1}-t_{w_2}) </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathit">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mord mathnormal">λ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.0269em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0001em;vertical-align:-0.2501em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.0269em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>Φ</mi><mo>=</mo><mi>A</mi><msub><mi>h</mi><mn>2</mn></msub><mo stretchy="false">(</mo><msub><mi>t</mi><msub><mi>w</mi><mn>2</mn></msub></msub><mo>−</mo><msub><mi>t</mi><msub><mi>t</mi><mn>2</mn></msub></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\varPhi = Ah_2(t_{w_2}-t_{t_2})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathit">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0001em;vertical-align:-0.2501em;"></span><span class="mord mathnormal">A</span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.02691em;">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:-0.0269em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0001em;vertical-align:-0.2501em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p><p>更改成温压，经过换算可以得到</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>Φ</mi><mo>=</mo><mfrac><mrow><mi>A</mi><mo stretchy="false">(</mo><msub><mi>t</mi><msub><mi>t</mi><mn>1</mn></msub></msub><mo>−</mo><msub><mi>t</mi><msub><mi>t</mi><mn>2</mn></msub></msub><mo stretchy="false">)</mo></mrow><mrow><mfrac><mn>1</mn><msub><mi>h</mi><mn>1</mn></msub></mfrac><mo>+</mo><mfrac><mi>δ</mi><mi>λ</mi></mfrac><mo>+</mo><mfrac><mn>1</mn><msub><mi>h</mi><mn>2</mn></msub></mfrac></mrow></mfrac></mrow><annotation encoding="application/x-tex">\varPhi = \frac{A(t_{t_1} - t_{t_2})}{\frac{1}{h_1} + \frac{\delta}{\lambda} + \frac{1}{h_2}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathit">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.6422em;vertical-align:-1.2152em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.427em;"><span style="top:-2.2299em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">λ</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03785em;">δ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2806em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2501em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2152em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p>我们把式子化简，把不变的记作K，则可以得到：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>Φ</mi><mo>=</mo><mi>A</mi><mi>k</mi><mo stretchy="false">(</mo><msub><mi>t</mi><mrow><mi>f</mi><mn>1</mn></mrow></msub><mo>−</mo><msub><mi>t</mi><mrow><mi>f</mi><mn>2</mn></mrow></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\varPhi =Ak(t_{f1}-t_{f2})</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathit">Φ</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">−</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.0361em;vertical-align:-0.2861em;"></span><span class="mord"><span class="mord mathnormal">t</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3361em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10764em;">f</span><span class="mord mtight">2</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.2861em;"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span></span></p><p>上式被成为传热方程式（传热过程总是包含两个对流传热，因而把这一特殊的模型一般化了）。</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mi>K</mi><mo>=</mo><mfrac><mn>1</mn><mrow><mfrac><mn>1</mn><msub><mi>h</mi><mn>1</mn></msub></mfrac><mo>+</mo><mfrac><mi>δ</mi><mi>λ</mi></mfrac><mo>+</mo><mfrac><mn>1</mn><msub><mi>h</mi><mn>2</mn></msub></mfrac></mrow></mfrac></mrow><annotation encoding="application/x-tex">K=\frac{1}{\frac{1}{h_1} + \frac{\delta}{\lambda} + \frac{1}{h_2}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em;"></span><span class="mord mathnormal" style="margin-right:0.07153em;">K</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.5366em;vertical-align:-1.2152em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.2299em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">λ</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03785em;">δ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:1.2152em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p>其中K称为传热系数，表征传热过程强烈程度。等于组成传热过程诸串联环节的<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>1</mn><msub><mi>h</mi><mn>1</mn></msub></mfrac><mo>+</mo><mfrac><mi>δ</mi><mi>λ</mi></mfrac><mo>+</mo><mfrac><mn>1</mn><msub><mi>h</mi><mn>2</mn></msub></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{h_1} + \frac{\delta}{\lambda} + \frac{1}{h_2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.2902em;vertical-align:-0.4451em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.2251em;vertical-align:-0.345em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8801em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">λ</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.03785em;">δ</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:1.2902em;vertical-align:-0.4451em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight"><span class="mord mathnormal mtight">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3173em;"><span style="top:-2.357em;margin-left:0em;margin-right:0.0714em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size3 size1 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.143em;"><span></span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.4451em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>的倒数，换种表达方式就可以看到它与电学中的欧姆定律的相似性：</p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mn>1</mn><mi>k</mi></mfrac><mo>=</mo><mfrac><mn>1</mn><msub><mi>h</mi><mn>1</mn></msub></mfrac><mo>+</mo><mfrac><mi>δ</mi><mi>λ</mi></mfrac><mo>+</mo><mfrac><mn>1</mn><msub><mi>h</mi><mn>2</mn></msub></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{k}=\frac{1}{h_1} + \frac{\delta}{\lambda} + \frac{1}{h_2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.1574em;vertical-align:-0.836em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.836em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">λ</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:2.1574em;vertical-align:-0.836em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.836em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><p class="katex-block"><span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mfrac><mn>1</mn><mrow><mi>A</mi><mi>k</mi></mrow></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mi>A</mi><msub><mi>h</mi><mn>1</mn></msub></mrow></mfrac><mo>+</mo><mfrac><mi>δ</mi><mrow><mi>A</mi><mi>λ</mi></mrow></mfrac><mo>+</mo><mfrac><mn>1</mn><mrow><mi>A</mi><msub><mi>h</mi><mn>2</mn></msub></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{Ak}=\frac{1}{Ah_1} + \frac{\delta}{A\lambda} + \frac{1}{Ah_2}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.0074em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mord mathnormal" style="margin-right:0.03148em;">k</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="base"><span class="strut" style="height:2.1574em;vertical-align:-0.836em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.836em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:2.0574em;vertical-align:-0.686em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3714em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mord mathnormal">λ</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03785em;">δ</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.686em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="base"><span class="strut" style="height:2.1574em;vertical-align:-0.836em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.3214em;"><span style="top:-2.314em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathnormal">A</span><span class="mord"><span class="mord mathnormal">h</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em;"><span style="top:-2.55em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.677em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">1</span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.836em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></span></p><pre><code class="highlight mermaid">flowchart LR        tt1(热流体温度 t&lt;sub&gt;t1&lt;/sub&gt;) --&gt;|对流热阻 1/h&lt;sub&gt;1&lt;/sub&gt;| tw1(壁面温度 t&lt;sub&gt;w1&lt;/sub&gt;)        tw1 --&gt;|导热热阻 δ/λ| tw2(壁面温度 t&lt;sub&gt;w2&lt;/sub&gt;)        tw2 --&gt;|对流热阻 1/h&lt;sub&gt;2&lt;/sub&gt;| tt2(冷流体温度 t&lt;sub&gt;t2&lt;/sub&gt;)</code></pre><p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mfrac><mn>1</mn><mrow><mo stretchy="false">(</mo><mi>A</mi><mi>k</mi><mo stretchy="false">)</mo></mrow></mfrac></mrow><annotation encoding="application/x-tex">\frac{1}{(Ak)}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.3651em;vertical-align:-0.52em;"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em;"><span style="top:-2.655em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mopen mtight">(</span><span class="mord mathnormal mtight">A</span><span class="mord mathnormal mtight" style="margin-right:0.03148em;">k</span><span class="mclose mtight">)</span></span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist" style="height:0.52em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span>称为传热过程热阻，串联热阻叠加原则与电学中串联电阻叠加原则相对应,即:<strong>在一个串联的热量传递过程中,如果通过各个环不节的热流量相同,则各串联环节的总热阻等于各串联环节热阻之和</strong>。</p><h2 id="随记"><a class="markdownIt-Anchor" href="#随记"></a> 随记</h2><ol><li>对于目标问题，<ol><li>要考虑冬季夏季，炉体的散热效率。</li><li>考虑炉壁的散热与强度、承载能力。+</li></ol></li><li>思考左手拧开水杯盖子后，右手握住杯子的手感觉水杯表面温度升高的现象。<ul><li>怀疑是拿起杯子后，不小心扰动水杯，让水与杯壁形成了强制对流换热。</li></ul></li></ol><hr class="footnotes-sep"><section class="footnotes"><ol class="footnotes-list"><li id="fn1" class="footnote-item"><p>似乎并非牛顿本人提出 <a href="#fnref1" class="footnote-backref">↩︎</a></p></li></ol></section>]]></content>
    
    
    <summary type="html">传热学基本概念</summary>
    
    
    
    <cover src="https://blog.si-on.top/images/Cover/%E4%BC%A0%E7%83%AD%E5%AD%A6%E7%AC%94%E8%AE%B0.svg" type="image"/>
    
    
    <category term="学习" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/"/>
    
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    <category term="传热学" scheme="https://blog.si-on.top/categories/%E5%AD%A6%E4%B9%A0/%F0%9F%93%92%E8%AF%BE%E7%A8%8B%E7%AC%94%E8%AE%B0/%E4%BC%A0%E7%83%AD%E5%AD%A6/"/>
    
    
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