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因此，对主轴系统进行静动态分析就有很重要的意义。<br /> 1主轴静力学分析<br /> 机床主轴抵抗静态外力的衡量标准是静刚度。一般 情况下，主轴的弯曲刚度比轴向刚度重要，通常用弯曲刚 度衡量主轴的静刚度。主轴的弯曲刚度可以定义为:主轴 在径向力作用下产生的单位径向位移[1]。<br /> 1.1静力分析的刚度方程<br /> 根据动力学问题单元构造的基本表达式[2]<br /> Meqe+ceq e+Keqe=p e， (D<br /> 可以得到某一系统的整体有限元方程，即<br /> Mq,+Cq,+Kq,=P,。 （2)<br /> 式中为节点位移矩阵；，为节点速度矩阵；，为节点加 速度矩阵;M为系统质量矩阵;C为系统阻尼矩阵阵;K为系 统刚度矩阵；，为系统外力矩阵。<br /> 由于静力学情形时，与时间无关，则方程为<br /> Kq=P。 ⑶<br /> 这就是结构静力分析的整体刚度方程。<br /> ANSYS分析得到主轴的静态位移q，根据方程<br /> K=p， ⑷<br /> q<br /> 得出主轴的弯曲静刚度。<br /> 基金项目：014年度内蒙古工业大学科学研究基金项目 (X201429)<br /> 1.2主轴有限元模型建立<br /> SV-41加工中心主轴是一种中空、多支撑的阶梯轴。 轴承承受多种外力的作用，因此有非线性弹性形变，根据 有限元分析理论，建立主轴有限元模型时要做适当的简 化。简化角接触球轴承为弹性支撑，忽略轴承角刚度只取 径向刚度，将轴承模拟为径向弹簧单元。不考虑轴承载荷 的影响，电机转子假设为轴材料等效到主轴上'<br /> 根据上述模型简化分析，选择ANSYS中的solid187 单元模拟轴，选择combin14弹簧-阻尼单元模拟轴承[4]。<br /> 利用SolidWorks软件建立主轴三维模型，通过 ANSYS接口导人，进行必要简化后选择solid187单元选 项对主轴划分网格，定义材料属性，赋予主轴combin14 弹簧-阻尼单元，可得到主轴有限元模型，如图1所示。<br /> 1.3静态特性分析结果<br /> 选择ANSYS的Static分析模块，对主轴施加相应的 约束，在主轴前端施加径向载荷2167N(通过切削力计算 得到)，ANSYS静力分析得到主轴静态变形图(图2所示）。<br /> 据图2知主轴变形最大的部分出现在主轴前端，最 大静态位移qDMX=2.89 ^m，主轴的弯曲静刚度K=i =<br /> 2167<br /> 2.89<br /> =749.83 N/^m〇<br /> 2主轴动力学分析<br /> 加工中心主轴的动态特性很大程度上决定了加工中 心的加工质量和切削能力。主轴的动态性能是指主轴抵 抗受迫振动和自激振动的能力=]。受迫振动幅值与激振 力频率相关，如果主轴的某阶固有频率与激振频率相近 或相等，结果会使振幅剧增，主轴会发生共振现象。所以 主轴的各阶固有频率是评价动态特性的重要内容。<br /> 2.1动态特性数学模型<br /> 根据系统的整体有限元方程式(2)，考虑主轴系统自 由振动时，忽略系统的阻尼及外力影响，可以得到系统的 无阻尼自由振动方程<br /> Mq+Kq=0。 ⑶<br /> 该方程解的形式为简谐振动形式<br /> q,=^-ei™'。 (6)<br /> 式(6)带人式⑶有<br /> (K-«2M)q=0。 （7)<br /> 方程(7)有非零解的条件是<br /> I(K-M2M)I=0。 （8)<br /> 求得自然圆频率~后可以得到对应的频率/=+，再<br /> 2n<br /> 将其带人式(7)可以得到对应于振动频率的振型。<br /> 利用ANSYS进行模态分析，获得主轴固有频率和振 型，根据公式n=60/得到主轴临界转速。<br /> 2.2模态分析<br /> 模态分析是动力学分析的基础，模态分析就是分析 结构的固有频率与振型，所以主轴的模态分析是主轴动 态特性的首要分析问题。<br /> 在ANSYS软件中，打开已建立好的主轴有限元模型 (图1所示），选择Modal分析模块中的Block Lanczos模 态提取法获得前八阶固有频率及振型，根据固有频率得 到主轴临界转速(表1所示）。<br /> 据表1，主轴的一阶、二阶固有频率值近似，视为式⑶ 的重根，同理，主轴的四阶、五阶固有频率值近似，六阶、 七阶固有频率值近似。主轴模态振型图如图3~图10。<br /> 3结论<br /> 1) 利用ANSYS对主轴进行了静态特性分析，计算出了 最大位移qDMX及弯曲刚度K该刚度完全满足主轴削加工 的需要。机床在实际加工中，主轴前端会安装轴头、刀具 等，所以实际工作中刚度会高于计算值。如刚度不足，可以 通过重新选择和配置轴承等方式改进主轴部件的结构。<br /> 2) 通过模态分析，得到了主轴前八阶固有频率和振型， 计算出主轴临界转速。SV-41加工中心机主油的最高转速为12000r/min，远低于H阶临界转速15918.6r/min，可以保证主轴 在额定转速附近工作不会发生共振，能够保证加工中心 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 class="530">表</span><span class="53TimesNewRoman"><span style="font-size:10.0pt;mso-fareast-font-family: MingLiU">1</span></span><span class="530">主轴前八阶固有频率与振型表</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 class="370"><span style="font-size:8.0pt">项目 </span></span><span class="3785pt"><span style="font-size:8.5pt">1</span></span><span class="370"><span style="font-size:8.0pt">阶 </span></span><span class="3785pt"><span style="font-size:8.5pt">2</span></span><span class="370"><span style="font-size:8.0pt">阶 </span></span><span class="3785pt"><span style="font-size:8.5pt">3</span></span><span class="370"><span style="font-size:8.0pt">阶 </span></span><span class="3785pt"><span style="font-size:8.5pt">4</span></span><span class="370"><span style="font-size:8.0pt">阶 </span></span><span class="3785pt"><span style="font-size:8.5pt">5</span></span><span class="370"><span style="font-size:8.0pt">阶 </span></span><span class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family: MingLiU">6</span></span><span class="370"><span style="font-size:8.0pt">阶 </span></span><span class="3785pt"><span style="font-size:8.5pt">7</span></span><span class="370"><span style="font-size:8.0pt">阶 </span></span><span class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family: MingLiU">8</span></span><span class="370"><span style="font-size:8.0pt">阶 [</span></span><span class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family:MingLiU">7</span></span><span 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 class="148pt"><span style="font-size:8.0pt">频率</span></span><span class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family: MingLiU">/Hz</span></span><span 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 class="148pt"><span style="font-size:8.0pt">临界转速</span></span><span class="140"><span style="font-size:8.5pt">/(</span></span><span class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family:MingLiU">r</span></span><span class="140"><span style="font-size:8.5pt">.</span></span><span class="14TimesNewRoman"><span lang="EN-US" style="font-size:9.0pt;mso-fareast-font-family: MingLiU">min<sup>—1</sup></span></span><span class="148pt"><span style="font-size:8.0pt">) </span></span><span 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 class="370"><span style="font-size:8.0pt">振型 </span></span><span class="371pt"><span style="font-size:8.0pt">一阶弯曲一阶摆动扭转二阶弯曲地阶摆动三阶弯曲三阶摆动轴向摆动</span></span></p> </td> </tr> </tbody> </table> </div> <p><!--[if !supportTextWrap]--><br clear="ALL" /> <!--[endif]--></p></div> <div class="blank30"></div> <!-- tag --> <div class="blank10"></div> 标签： <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> <!-- 分类 --> <div class="blank10"></div> 分类： <a href='/bethel/type/jnc/type-1.html' 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<p>宇匠数控 备注：为保证文章的完整度，本文核心内容由PDF格式显示，如未有显示请刷新或转换浏览器尝试，手机浏览可能无法正常使用！本文摘要：通过对混联五轴加工中心自适应深度学习控制方法的 研 究，可 知 此 方 法 的 创 新 之 处 在 于：１）建 立 了 机 床 的 运 动 学 … <a href="/bethel/5-aix/show-2965.html" target="_blank">[了解更多]</a></p> </div> <div class="news-list list-border list-border-w"> <div class="list-date"> <span>05</span> <p>2024-11</p> </div> <h4><a title="五轴加工中心和五轴钻攻中心在机测量探头补偿" href="/bethel/5-aix/show-2959.html" target="_blank">五轴加工中心和五轴钻攻中心在机测量探头补</a></h4> <p>在机测量技术由于其成本低、检测效率高、无需二次装夹等优势被广泛用于零件加工测量当中，使得五轴加工中心和五轴钻攻中心，同时又兼具测量功能。在机测量系统的构成如图1所示，硬件部分主要是由高精度探头、信号接收器、机床整个本体，软件部分由机床控制系统、测量软件等组成[8]。待零件加工完成… <a href="/bethel/5-aix/show-2959.html" target="_blank">[了解更多]</a></p> </div> <div class="news-list list-border list-border-w"> <div class="list-date"> <span>05</span> <p>2024-11</p> </div> <h4><a title="五轴加工中心进给系统动态误差影响因素" href="/bethel/5-aix/show-2958.html" target="_blank">五轴加工中心进给系统动态误差影响因素</a></h4> 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