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class="title"> <h3><a>滾珠絲杠強度、剛度的校核<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> <span style="line-height: 14pt; text-indent: 0pt; font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">4.4</span><span style="line-height: 14pt; text-indent: 0pt; font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">滾珠絲杠強度、剛度的校核</span></p> <div id="n1l1njb9b" class="Section0"> <table cellpadding="0" cellspacing="0"> <tbody> <tr> <td width="103.333" height="0"> </td> </tr> <tr> <td><br /> </td> <td><span style="font-family: 宋體; font-size: 10.5pt; letter-spacing: 0pt; line-height: 11pt; text-align: justify; text-indent: 23pt;">1、滾珠絲杠強度的校核，實心滾珠絲杠</span></td> </tr> </tbody> </table> <table cellpadding="0" cellspacing="0"> <tbody> <tr> <td width="103.333" height="0"> </td> </tr> <tr> <td> </td> <td><span style="font-family: 宋體; font-size: 10.5pt; letter-spacing: 0pt; line-height: 11pt; text-indent: 0pt;">空心滾珠絲杠</span></td> </tr> </tbody> </table> <p class="NewStyle45" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:23.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; "><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">式中，^為絲杠的應力</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">，'</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">為絲杠的進給力，</span><span id="n1l1njb9b" class="19" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 10.5pt;">io</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">^, 4</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">為截面面積，</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">[</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt; vertical-align: super;">CT</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">]</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">為絲杠 的許用應力，</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">113</span><span id="n1l1njb9b" class="19" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 10.5pt;">MP</span><span id="n1l1njb9b" class="19" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 10.5pt; vertical-align: sub;">a</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">,</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">故無論空心/實心滾珠絲杠，其強度均遠小于許用強度。</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;"><o:p></o:p></span></p> <span style="font-family: 宋體; font-size: 10.5pt; letter-spacing: 0pt; text-align: justify; text-indent: 23pt;"><br /> 2、由于絲杠在切削時受到很大的橫向進給力，如果采用空心滾珠絲杠，其軸向 變形量可能很大；如果遠遠的大于采用空心滾珠絲杠補償的熱變形量，則開孔的大小 不能滿足軸向剛度要求。實心絲杠、空心滾珠絲杠的拉伸變形量分別為</span><br /> <p class="NewStyle45" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:23.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; "><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;"><o:p></o:p></span></p> <p class="NewStyle45" style="margin: 0pt; text-indent: 23pt; line-height: 22.1pt;"><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">與實心滾珠絲杠的熱變形量</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">（0.6</span><span id="n1l1njb9b" class="19" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 10.5pt;">mm</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">—</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">5.3</span><span id="n1l1njb9b" class="19" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 10.5pt;">mm</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">)</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">相比，其變形量可以忽略不計。 從空心絲杠的角度看，空心絲杠補償后的熱變形量在</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">0.06</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">左右，而進給力引起的變 形量在</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">0.04</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">左右，說明如果繼續進一步提高絲杠的定位精度，拉伸變形量也是一個 不可忽視的問題，需要同熱變形綜合考慮。</span></p> <span style="font-family: 宋體; font-size: 10.5pt; letter-spacing: 0pt; line-height: 22.1pt; text-indent: 0pt;">3、考慮到空心絲杠可能影響到扭轉剛度，故需要校核扭轉剛度 實心絲杠的扭轉角</span><br /> <p class="NewStyle45" style="margin-top:28.8500pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:23.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; "><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">由此可見，空心絲杠的扭轉角相比于實心滾珠絲杠的扭轉角變化不大，空心絲杠 對扭轉剛度的影響不大，可以忽略。</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;"><o:p></o:p></span></p> <p class="NewStyle45" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:23.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; "><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">從上面的校核可知，空性絲杠在強度、剛度等方面與實心滾珠絲杠很接近，這主 要是因為開孔在絲杠的中心處，對扭轉剛度的影響不大；而對于強度由于開孔的面積 很小，故對滾珠絲杠的強度的影響也很小。</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;"><o:p></o:p></span></p> <p class="NewStyle45" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:23.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; "><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">然而在滾珠的轉速加快時,反復的沖擊力會使滾珠絲杠的滾珠循環系統結構減弱， 往往造成循環系統中導珠器因沖擊疲勞而容易斷裂。</span></p> </div> <p><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;"><br clear="all" style="page-break-before:always;mso-break-type:section-break" /> </span></p> <p class="NewStyle44" style="margin: 0pt 0pt 8.55pt; text-indent: 0pt; page-break-after: avoid; line-height: 14pt;"><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">4.5</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">本章小結</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;"><o:p></o:p></span></p> <p class="NewStyle45" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:26.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; "><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">首先根據伺服系統的受力分析，分別建立了實心/空心滾珠絲杠伺服進給系統的 數學模型。空心滾珠絲杠開孔對伺服系統性能的影響有別于實心滾珠絲杠，故在此做 了對比研究。由于伺服進給系統作為一個機電一體化系統，系統的穩定性是前提。本 章不僅用開環伯德圖判斷了系統的穩定性，同時通過</span><span id="n1l1njb9b" class="19" style="font-family: 'Times New Roman'; letter-spacing: 0pt; font-size: 10.5pt;">Routh</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">判據，證明了系統是穩定 的。</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;"><o:p></o:p></span></p> <p class="NewStyle45" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:26.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; "><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">快速性是滾珠絲杠伺服進給系統的重要指標。本章分析了空心滾珠絲杠系統的快 速性較快些，并仿真驗證了空心滾珠絲杠的快速性稍快于實心滾珠絲杠的快速性。</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;"><o:p></o:p></span></p> <p class="NewStyle45" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:26.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; "><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;">在本章的最后部分校核了系統的強度和剛度，滿足滾珠絲杠的要求。</span><span style="font-family: 宋體; letter-spacing: 0pt; font-size: 10.5pt;"><br clear="all" style="page-break-before:always" /> </span></p> <p class="NewStyle45" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:26.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; "> </p> <p class="NewStyle45" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:26.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; "> </p> <p class="NewStyle45" style="margin-top:0.0000pt; margin-right:0.0000pt; margin-bottom:0.0000pt; margin-left:0.0000pt; text-indent:26.0000pt; mso-pagination:none; text-align:justify; text-justify:inter-ideograph; 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