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id="tpnrxl7j" class="title"> <h3><a>分析分量法及導納圓分析法<small></small></a></h3> </div> <!-- 頁面標題結束 --> <hr class="featurette-divider"> <!-- 中部開始 --> <div id="tpnrxl7j" class="container"> <!-- 正文 --> <div id="tpnrxl7j" class="lead" id="print"> <p> <st1:chsdate year="1899" month="12" day="30" islunardate="False" isrocdate="False" w:st="on" style="line-height: 12pt; background-color: transparent;"><span id="tpnrxl7j" class="67"><span style="font-family: SimSun;">2.3.2</span></span></st1:chsdate><span id="tpnrxl7j" class="67" style="line-height: 12pt; background-color: transparent;">分析分量法</span></p> <p class="670" style="margin:0cm;margin-bottom:.0001pt;line-height:12.0pt; mso-line-height-rule:exactly;mso-pagination:lines-together;page-break-after: avoid;background:transparent"><a name="bookmark16"></a></p> <p class="MsoNormal" style="text-indent:36.0pt;mso-char-indent-count:3.0">由于試驗條件的關系，本文采用頻域識別的方法對機床的模態參數進行識別， 下面簡單介紹在頻域中的一些模態參數識別方法。</p> <p class="21" style="margin:0cm;margin-bottom:.0001pt;text-indent:32.0pt; line-height:21.35pt;mso-line-height-rule:exactly;background:transparent"><span id="tpnrxl7j" class="2">分量分析法就是將頻響函數分成實部和虛部分量進行分析，式</span><span id="tpnrxl7j" class="2Constantia2"><span lang="EN-US" style="font-size: 11pt;">(2-15)</span></span><span id="tpnrxl7j" class="2">是基本 公式，它是一種圖解法，即從曲線上直接找出有關參數。</span></p> <p class="21" style="margin:0cm;margin-bottom:.0001pt;text-indent:32.0pt; line-height:21.35pt;mso-line-height-rule:exactly;background:transparent"><span id="tpnrxl7j" class="2">由式</span><span id="tpnrxl7j" class="2Constantia2"><span lang="EN-US" style="font-size: 11pt;">(2-14)</span></span><span id="tpnrxl7j" class="2">可知，在某一頻率下的傳遞函數為各階模態傳遞函數的疊加。當 激振頻率</span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">w</span></span><span id="tpnrxl7j" class="2">趨近于第</span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">r</span></span><span id="tpnrxl7j" class="2">階模態的自然頻率時，則該階模態在傳遞函數中起主導作 用，稱為主導模態，在主導模態附近其它模態的影響比較小，特別是當模態密度 不是很大時，即各階模態相距較遠時，其它模態的傳遞函數數值很小，且曲線比 較平坦，幾乎不隨頻率而變化，因此其余模態的影響可用</span><span id="tpnrxl7j" class="2"><span style="font-family: 'Times New Roman';">•</span></span><span id="tpnrxl7j" class="2">復常數</span><span id="tpnrxl7j" class="211pt5"><span lang="EN-US" style="font-size: 11pt;">H<sub>c</sub></span></span><span id="tpnrxl7j" class="2">■來表示，當 </span><span id="tpnrxl7j" class="2105pt2"><span style="font-size: 10.5pt;">〇</span></span><span id="tpnrxl7j" class="2Constantia2"><span lang="EN-US" style="font-size: 11pt;">)</span></span><span id="tpnrxl7j" class="2">在以的鄰域內時</span><span id="tpnrxl7j" class="2105pt2"><span style="font-size: 10.5pt;">，</span></span><span id="tpnrxl7j" class="2105pt2"><span style="font-size: 10.5pt;">（</span></span><span id="tpnrxl7j" class="2Constantia2"><span lang="EN-US" style="font-size: 11pt;">2-15)</span></span><span id="tpnrxl7j" class="2">式可寫成</span></p> <p class="MsoNormal" style="text-indent:30.0pt;mso-char-indent-count:2.5">分量分析法在系統模態密度不高時，具有足夠的精度，但是由于它僅利用了 頻響函數曲線峰值點的信息來確定模態參數，當峰值點有誤差時，識別精度將會</p> <p class="MsoNormal">受到影響[38]。</p> <p class="620" align="left" style="margin-bottom: 3.3pt; line-height: 12pt; page-break-after: avoid; background: transparent;"><a name="bookmark17"></a><st1:chsdate year="1899" month="12" day="30" islunardate="False" isrocdate="False" w:st="on"><span id="tpnrxl7j" class="62"><span style="font-family: SimSun;">2.3.3</span></span></st1:chsdate><span id="tpnrxl7j" class="62">導納圓分析法</span></p> <p class="890" style="margin-top:0cm;text-align:justify;text-justify:inter-ideograph; text-indent:35.0pt;line-height:21.35pt;mso-line-height-rule:exactly;background: transparent"><span id="tpnrxl7j" class="89">這是一種比較經典的方法。許多動態信號分析儀在頻響函數測量后都能顯 示</span><span id="tpnrxl7j" class="89Constantia"><span lang="EN-US">Nyquist</span></span><span id="tpnrxl7j" class="89">圖，也就是導納圓圖，所以它也是比較直觀的方法。對單自由度 系統或模態耦合不很緊密的自由度系統，這種方法能取得比較滿意的結果。</span></p> <p class="890" style="margin-top:0cm;text-align:justify;text-justify:inter-ideograph; text-indent:35.0pt;line-height:21.35pt;mso-line-height-rule:exactly;background: transparent"><span id="tpnrxl7j" class="89">對具有結構阻尼的單自由度系統，其位移導納在復平面上構成一個圓。對粘 性阻尼單自由度系統，若阻尼系數較小，其頻響函數矢量端軌跡亦近似為圓。在 實際工程應用中，大多數結構都是多自由度系統，為此可在某階模態頻響函數共 振峰值附近選項取</span><span id="tpnrxl7j" class="89"><span style="font-family: SimSun;">6-10</span></span><span id="tpnrxl7j" class="89">個頻率點，即所謂截取某階模態為單模態系統，從而應用 導納圓理論。</span></p> <p class="890" style="margin-top:0cm;text-align:justify;text-justify:inter-ideograph; text-indent:28.0pt;line-height:21.35pt;mso-line-height-rule:exactly;background: transparent"><span id="tpnrxl7j" class="89">即使對于單自由度系統，由于模態測試等方面不可避免的誤差，頻響函數矢 端軌跡不一定都落在理論圓上。為此必須找出一個理論圓，使此圓上各相應點的 數值與實測值之間的誤差最小，即采取所謂曲線擬合法。</span><span id="tpnrxl7j" class="150pt"><span style="font-size: 12pt;"><o:p></o:p></span></span><br clear="ALL" /> <span id="tpnrxl7j" class="150pt"> 這里的討論只涉及到單一模態，實際上多自由度系統的導納圓由于各模態間 的疊加，會在多平面上產生平移或旋轉，且由于存在多個模態，同一測點上的頻 響函數會形成多個導納圓，它們不一定是完整的圓，而是幾個弧段，各階模態對 應有一個弧段，因此可根據第一個弧段擬合一個圓，然后根據各擬合圓，按單模 態的情況分別識別對應的模態參數。</span><o:p></o:p></p> <p class="150" style="text-align:justify;text-justify:inter-ideograph;text-indent: 28.0pt;line-height:21.85pt;mso-line-height-rule:exactly;background:transparent"><span id="tpnrxl7j" class="150pt">上面討論的是結構阻尼的情況，對于粘性阻尼，系統的頻響函數在復平面上 緩出</span><span id="tpnrxl7j" class="15TimesNewRoman"><span lang="EN-US">Nyquist</span></span><span id="tpnrxl7j" class="150pt">圖則不是一個圓，但在小阻尼或固有頻率附近，其</span><span id="tpnrxl7j" class="15TimesNewRoman"><span lang="EN-US">Nyquist</span></span><span id="tpnrxl7j" class="150pt">圖仍接近 于一個圓，因此對其各階固有頻率附近的頻響函數測量值，仍可按上述方法進行 參數識別。</span><o:p></o:p></p> <p class="150" style="margin-bottom:19.9pt;text-align:justify;text-justify:inter-ideograph; text-indent:28.0pt;line-height:21.85pt;mso-line-height-rule:exactly;background: transparent"><span id="tpnrxl7j" class="150pt">導納圓識別方法不僅利用頻響函數峰值點的信息，而且利用固有頻率附近很 多點的信息，即使沒有峰值信息，仍然可以求出固有頻率。這樣可避免峰值信息 誤差所造成的影響。但是該方法在模態密集時誤差較大，因為導納圓法仍然是建 立在主導模態基礎上的。</span></p> <p class="150" style="margin-bottom:19.9pt;text-align:justify;text-justify:inter-ideograph; text-indent:28.0pt;line-height:21.85pt;mso-line-height-rule:exactly;background: transparent"> </p> <p class="MsoNormal"><span style="font-size:9.0pt;font-family:宋體;mso-ascii-font-family: "Times New Roman";mso-hansi-font-family:"Times New Roman"">本文采摘自“</span><span lang="EN-US" style="font-size:9.0pt">VMC1060</span><span style="font-size:9.0pt; font-family:宋體;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman"">型立式加工中心試驗模態分析”，因為編輯困難導致有些函數、表格、圖片、內容無法顯示，有需要者可以在網絡中查找相關文章！本文由伯特利數控整理發表文章均來自網絡僅供學習參考，轉載請注明！</span><span lang="EN-US" style="font-size:9.0pt"> <o:p></o:p></span></p> <p class="150" style="margin-bottom:19.9pt;text-align:justify;text-justify:inter-ideograph; text-indent:28.0pt;line-height:21.85pt;mso-line-height-rule:exactly;background: transparent"><o:p></o:p></p></div> 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