高速球轴承?转子系统动态性能的分析与优化

Dynamic Performance Analysis and Optimization of High-Speed Rotor-Ball Bearing Systems

针对轴承刚度随转速呈非线性变化的特点,基于角接触球轴承拟静力学模型,考虑轴承内圈离心位移的影响,运用数值方法对轴承和轴承组的动刚度进行了计算。在此基础上,根据轴承-转子系统的有限元模型建立了动力学方程,并编制数值迭代程序求解其特征值,进而得到了系统的临界转速。由于转速对轴承(组)动刚度的影响,在每一次迭代计算中,需根据前次迭代计算出的临界转速求解前、后轴承(组)的动刚度,重建系统的有限元模型,因此结合Matlab优化工具箱,运用单纯形法对转子内径与轴承跨距进行了优化。分析结果表明:通过优化转子内径与轴承跨距,轴承-转子系统的一阶临界转速提高了7.65%,由于转速与内圈离心位移对轴承或轴承组动刚度的影响很大,因此在高速轴承-转子系统的动态分析中应考虑该影响因素。

Focusing on the nonlinearly changed dynamic stiffness of bearings with working speed,a numerical approach is presented to calculate the dynamic stiffness of a single bearing and a bearing group based on the ball bearing quasi-static model,the dynamic equation is established according to the finite element model of the rotor-ball bearing system,the eigenvalues then are obtained by numerical iteration and the critical speed is sought out.Due to the influence of speed on dynamic stiffness of bearings,the finite element model ought to be updated according to the calculated dynamic stiffness by last iteration.Combining the optimization toolbox of Matlab,the inner diameter of rotor and the bearing span are optimized by simplex method.The analysis results show that the stiffness of spindle bearings is obviously influenced by the working speed and inner ring centrifugation,which should be taken into consideration during the dynamic analysis of a high-speed rotor-ball bearing system,and the first critical speed of the rotor-ball bearing system increases by 7.65% after optimization.