Parameterization of Motorized Spindle and Multi-objective Optimization Combined with Response Surface Method
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摘要: 以某电主轴为对象，通过Solidworks对模型进行二次建模，导入到Workbench中并进行参数化传递。在完成静态和模态有限元分析的基础上，以电主轴的前后轴承组跨距、悬伸量、主轴前端半径、前端内孔半径为设计变量，以最大总体变形最小、1阶固有频率最大、质量最轻为优化目标，对设计参数进行敏感性分析，建立响应面优化模型并进行优化分析。优化结果表明，采用上述方法进行优化后，其静刚度提高了4.2%，1阶固有频率增大了7.4%，质量减少了5.3%，达到了最初的优化目的。Abstract: Taking a domestic motorized spindle as an object, the secondary finite element modeling of the model was carried out through SolidWorks, and then imported into the Workbench to be parameterized. On the basis of static and modal analysis, taking the span of front and rear bearing group, overhanging amount, front radius of spindle and inner hole radius of front end of motorized spindle as design variables, the sensitivity analysis of design parameters is carried out with minimum total deformation, maximum first natural frequency and lightest geometry mass as optimization objectives, and then response surface optimization model is established and optimized. The optimization results of motorized spindle show that the static stiffness increases by 4.2%, the first natural frequency increases by 7.4%, and the mass decreases by 5.3%, these improve mechanic performances of motorized spindle.
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表 1 尺寸参数、初始值及变化范围
mm 名称 轴承跨距L1 悬伸量L2 前端外半径D1 前端内半径D2 初始值 361.5 114 35 27 上限值 397.65 125.4 38.5 29.7 下限值 325.35 102.6 31.5 24.3 
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表 2 前6阶固有频率、振型及临界转速
阶数 固有频率/Hz 振型 临界转速/（r·min−1） 1 1048.7 弯曲 62922 2 1048.8 弯曲 62928 3 1876.4 摆动 112584 4 1876.8 摆动 112608 5 2668.3 扭转 160098 6 2668.5 扭转 160110
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表 3 优化后的3组候选点
参数名称 第1组 第2组 第3组 轴承跨距P1/mm 381.93 361.53 397.38 悬伸量P2/mm 110.79 105.43 107.34 前端外半径P3 /mm 32.725 32.764 32.902 前端内半径P4/mm 19.823 19.837 19.822 主轴前端变形量P6/μm 0.8477 0.84895 0.83836 1阶固有频率P7/Hz 1057.4 1057.2 1056.5 质量P8/kg 9.2346 9.2446 9.2823
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