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面包屑導航結束 --> <!-- 頁面標題開始 --> <div id="n1l1njb9b" class="title"> <h3><a>SV-41立式加工中心機主軸靜動態特性分析<small></small></a></h3> </div> <!-- 頁面標題結束 --> <hr class="featurette-divider"> <!-- 中部開始 --> <div id="n1l1njb9b" class="container"> <!-- 正文 --> <div id="n1l1njb9b" class="lead" id="print"> <p> 0引言<br /> 加工中心是我國裝備制造業的基礎，也是我國實現 工業2025的重要技術環節。加工中心設備性能好壞、加 工效率的高低與機床主軸的靜動態特性有重大的關系。 因此，對主軸系統進行靜動態分析就有很重要的意義。<br /> 1主軸靜力學分析<br /> 機床主軸抵抗靜態外力的衡量標準是靜剛度。一般 情況下，主軸的彎曲剛度比軸向剛度重要，通常用彎曲剛 度衡量主軸的靜剛度。主軸的彎曲剛度可以定義為:主軸 在徑向力作用下產生的單位徑向位移[1]。<br /> 1.1靜力分析的剛度方程<br /> 根據動力學問題單元構造的基本表達式[2]<br /> Meqe+ceq e+Keqe=p e， (D<br /> 可以得到某一系統的整體有限元方程，即<br /> Mq,+Cq,+Kq,=P,。 （2)<br /> 式中為節點位移矩陣；，為節點速度矩陣；，為節點加 速度矩陣;M為系統質量矩陣;C為系統阻尼矩陣陣;K為系 統剛度矩陣；，為系統外力矩陣。<br /> 由于靜力學情形時，與時間無關，則方程為<br /> Kq=P。 ⑶<br /> 這就是結構靜力分析的整體剛度方程。<br /> ANSYS分析得到主軸的靜態位移q，根據方程<br /> K=p， ⑷<br /> q<br /> 得出主軸的彎曲靜剛度。<br /> 基金項目：014年度內蒙古工業大學科學研究基金項目 (X201429)<br /> 1.2主軸有限元模型建立<br /> SV-41加工中心主軸是一種中空、多支撐的階梯軸。 軸承承受多種外力的作用，因此有非線性彈性形變，根據 有限元分析理論，建立主軸有限元模型時要做適當的簡 化。簡化角接觸球軸承為彈性支撐，忽略軸承角剛度只取 徑向剛度，將軸承模擬為徑向彈簧單元。不考慮軸承載荷 的影響，電機轉子假設為軸材料等效到主軸上'<br /> 根據上述模型簡化分析，選擇ANSYS中的solid187 單元模擬軸，選擇combin14彈簧-阻尼單元模擬軸承[4]。<br /> 利用SolidWorks軟件建立主軸三維模型，通過 ANSYS接口導人，進行必要簡化后選擇solid187單元選 項對主軸劃分網格，定義材料屬性，賦予主軸combin14 彈簧-阻尼單元，可得到主軸有限元模型，如圖1所示。<br /> 1.3靜態特性分析結果<br /> 選擇ANSYS的Static分析模塊，對主軸施加相應的 約束，在主軸前端施加徑向載荷2167N(通過切削力計算 得到)，ANSYS靜力分析得到主軸靜態變形圖(圖2所示）。<br /> 據圖2知主軸變形最大的部分出現在主軸前端，最 大靜態位移qDMX=2.89 ^m，主軸的彎曲靜剛度K=i =<br /> 2167<br /> 2.89<br /> =749.83 N/^m〇<br /> 2主軸動力學分析<br /> 加工中心主軸的動態特性很大程度上決定了加工中 心的加工質量和切削能力。主軸的動態性能是指主軸抵 抗受迫振動和自激振動的能力=]。受迫振動幅值與激振 力頻率相關，如果主軸的某階固有頻率與激振頻率相近 或相等，結果會使振幅劇增，主軸會發生共振現象。所以 主軸的各階固有頻率是評價動態特性的重要內容。<br /> 2.1動態特性數學模型<br /> 根據系統的整體有限元方程式(2)，考慮主軸系統自 由振動時，忽略系統的阻尼及外力影響，可以得到系統的 無阻尼自由振動方程<br /> Mq+Kq=0。 ⑶<br /> 該方程解的形式為簡諧振動形式<br /> q,=^-ei™'。 (6)<br /> 式(6)帶人式⑶有<br /> (K-«2M)q=0。 （7)<br /> 方程(7)有非零解的條件是<br /> I(K-M2M)I=0。 （8)<br /> 求得自然圓頻率~后可以得到對應的頻率/=+，再<br /> 2n<br /> 將其帶人式(7)可以得到對應于振動頻率的振型。<br /> 利用ANSYS進行模態分析，獲得主軸固有頻率和振 型，根據公式n=60/得到主軸臨界轉速。<br /> 2.2模態分析<br /> 模態分析是動力學分析的基礎，模態分析就是分析 結構的固有頻率與振型，所以主軸的模態分析是主軸動 態特性的首要分析問題。<br /> 在ANSYS軟件中，打開已建立好的主軸有限元模型 (圖1所示），選擇Modal分析模塊中的Block Lanczos模 態提取法獲得前八階固有頻率及振型，根據固有頻率得 到主軸臨界轉速(表1所示）。<br /> 據表1，主軸的一階、二階固有頻率值近似，視為式⑶ 的重根，同理，主軸的四階、五階固有頻率值近似，六階、 七階固有頻率值近似。主軸模態振型圖如圖3~圖10。<br /> 3結論<br /> 1) 利用ANSYS對主軸進行了靜態特性分析，計算出了 最大位移qDMX及彎曲剛度K該剛度完全滿足主軸削加工 的需要。機床在實際加工中，主軸前端會安裝軸頭、刀具 等，所以實際工作中剛度會高于計算值。如剛度不足，可以 通過重新選擇和配置軸承等方式改進主軸部件的結構。<br /> 2) 通過模態分析，得到了主軸前八階固有頻率和振型， 計算出主軸臨界轉速。SV-41加工中心機主油的最高轉速為12000r/min，遠低于H階臨界轉速15918.6r/min，可以保證主軸 在額定轉速附近工作不會發生共振，能夠保證加工中心 的加工精度。</p> <div> <table cellspacing="0" cellpadding="0" hspace="0" vspace="0" width="489" height="87"> <tbody> <tr> <td valign="top" align="left" height="87" style="padding-top:0cm;padding-right: 0cm;padding-bottom:0cm;padding-left:0cm"> <p class="MsoNormal" style="margin-top:0cm;margin-right:0cm;margin-bottom:.7pt; margin-left:102.0pt;line-height:10.0pt;mso-line-height-rule:exactly; mso-element:frame;mso-element-frame-width:367.2pt;mso-element-frame-height: 65.25pt;mso-element-wrap:none;mso-element-anchor-vertical:page;mso-element-anchor-horizontal: page;mso-element-left:63.5pt;mso-element-top:704.05pt;mso-height-rule:exactly"><span id="n1l1njb9b" class="530">表</span><span id="n1l1njb9b" class="53TimesNewRoman"><span style="font-size:10.0pt;mso-fareast-font-family: MingLiU">1</span></span><span id="n1l1njb9b" class="530">主軸前八階固有頻率與振型表</span></p> <p class="MsoNormal" style="margin-left:25.0pt;text-align:justify;text-justify: inter-ideograph;line-height:12.5pt;mso-line-height-rule:exactly;tab-stops: center 85.5pt 122.45pt 154.1pt 185.55pt 221.55pt 257.8pt 294.75pt 330.75pt right 365.55pt; mso-element:frame;mso-element-frame-width:367.2pt;mso-element-frame-height: 65.25pt;mso-element-wrap:none;mso-element-anchor-vertical:page;mso-element-anchor-horizontal: page;mso-element-left:63.5pt;mso-element-top:704.05pt;mso-height-rule:exactly"><span id="n1l1njb9b" class="370"><span style="font-size:8.0pt">項目 </span></span><span id="n1l1njb9b" class="3785pt"><span style="font-size:8.5pt">1</span></span><span id="n1l1njb9b" class="370"><span style="font-size:8.0pt">階 </span></span><span id="n1l1njb9b" class="3785pt"><span style="font-size:8.5pt">2</span></span><span id="n1l1njb9b" class="370"><span style="font-size:8.0pt">階 </span></span><span id="n1l1njb9b" class="3785pt"><span style="font-size:8.5pt">3</span></span><span id="n1l1njb9b" class="370"><span style="font-size:8.0pt">階 </span></span><span id="n1l1njb9b" class="3785pt"><span style="font-size:8.5pt">4</span></span><span id="n1l1njb9b" class="370"><span style="font-size:8.0pt">階 </span></span><span id="n1l1njb9b" class="3785pt"><span style="font-size:8.5pt">5</span></span><span id="n1l1njb9b" class="370"><span style="font-size:8.0pt">階 </span></span><span id="n1l1njb9b" class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family: MingLiU">6</span></span><span id="n1l1njb9b" class="370"><span style="font-size:8.0pt">階 </span></span><span id="n1l1njb9b" class="3785pt"><span style="font-size:8.5pt">7</span></span><span id="n1l1njb9b" class="370"><span style="font-size:8.0pt">階 </span></span><span id="n1l1njb9b" class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family: MingLiU">8</span></span><span id="n1l1njb9b" class="370"><span style="font-size:8.0pt">階 [</span></span><span id="n1l1njb9b" class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family:MingLiU">7</span></span><span id="n1l1njb9b" class="370"><span style="font-size:8.0pt">]</span></span></p> <p class="MsoNormal" style="margin-left:20.0pt;text-align:justify;text-justify: inter-ideograph;line-height:12.5pt;mso-line-height-rule:exactly;tab-stops: center 85.75pt 122.7pt 154.4pt 185.85pt 221.85pt 258.1pt 295.05pt 331.05pt; mso-element:frame;mso-element-frame-width:367.2pt;mso-element-frame-height: 65.25pt;mso-element-wrap:none;mso-element-anchor-vertical:page;mso-element-anchor-horizontal: page;mso-element-left:63.5pt;mso-element-top:704.05pt;mso-height-rule:exactly"><span id="n1l1njb9b" class="148pt"><span style="font-size:8.0pt">頻率</span></span><span id="n1l1njb9b" class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family: MingLiU">/Hz</span></span><span id="n1l1njb9b" class="140"><span style="font-size:8.5pt"> 265.31 265.39 1025.20 1468.90 1469.50 3291.60 3291.90 3751.70</span></span></p> <p class="MsoNormal" style="text-align:justify;text-justify:inter-ideograph; line-height:12.5pt;mso-line-height-rule:exactly;tab-stops:center 84.25pt 121.2pt 152.9pt 184.3pt 220.3pt 256.55pt 293.5pt 329.5pt; mso-element:frame;mso-element-frame-width:367.2pt;mso-element-frame-height: 65.25pt;mso-element-wrap:none;mso-element-anchor-vertical:page;mso-element-anchor-horizontal: page;mso-element-left:63.5pt;mso-element-top:704.05pt;mso-height-rule:exactly"><span id="n1l1njb9b" class="148pt"><span style="font-size:8.0pt">臨界轉速</span></span><span id="n1l1njb9b" class="140"><span style="font-size:8.5pt">/(</span></span><span id="n1l1njb9b" class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family:MingLiU">r</span></span><span id="n1l1njb9b" class="140"><span style="font-size:8.5pt">.</span></span><span id="n1l1njb9b" class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family: MingLiU">min<sup>—1</sup></span></span><span id="n1l1njb9b" class="148pt"><span style="font-size:8.0pt">) </span></span><span id="n1l1njb9b" class="140"><span style="font-size:8.5pt">15918.6 15923.4 61512.0 88134.0 88170.0 197496.0 197514.0 225102.0</span></span></p> <p class="MsoNormal" style="margin-left:25.0pt;text-align:justify;text-justify: inter-ideograph;line-height:8.0pt;mso-line-height-rule:exactly;tab-stops: 67.95pt;mso-element:frame;mso-element-frame-width:367.2pt;mso-element-frame-height: 65.25pt;mso-element-wrap:none;mso-element-anchor-vertical:page;mso-element-anchor-horizontal: page;mso-element-left:63.5pt;mso-element-top:704.05pt;mso-height-rule:exactly"><span id="n1l1njb9b" class="370"><span style="font-size:8.0pt">振型 </span></span><span id="n1l1njb9b" class="371pt"><span style="font-size:8.0pt">一階彎曲一階擺動扭轉二階彎曲地階擺動三階彎曲三階擺動軸向擺動</span></span></p> </td> </tr> </tbody> </table> </div> <p><!--[if !supportTextWrap]--><br clear="ALL" /> <!--[endif]--></p></div> <div id="n1l1njb9b" class="blank30"></div> <!-- tag --> <div id="n1l1njb9b" class="blank10"></div> 標簽： <a href='/index.php?case=tag&act=show&tag=%E5%8A%A0%E5%B7%A5%E4%B8%AD%E5%BF%83' target='_blank'>加工中心</a> <a href='/index.php?case=tag&act=show&tag=%E7%AB%8B%E5%BC%8F%E5%8A%A0%E5%B7%A5%E4%B8%AD%E5%BF%83' target='_blank'>立式加工中心</a> <!-- 分類 --> <div id="n1l1njb9b" class="blank10"></div> 分類： <a href='/bethel/type/jnc/type-1.html' target='_blank'>加工中心</a> <div id="n1l1njb9b" class="blank30"></div> <!--自動調用自定義字段--> <div 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