不同支撑方式下的滚珠丝杠进给系统 横向振动特性分析

为研究滚珠丝杠进给系统的横向振动特性,文章采用假设模态法和拉格朗日能量法建立系统的横向振动动力学模型,利用丝杠边界条件推导丝杠横向振动的频率方程,并求解出假设模态函数;将所提出的数学模型与有限元方法进行对比分析,验证模型的正确性和精度范围,分析系统在两端弹性、固定-简支、两端固定3种支撑方式下的系统固有频率和模态振型的振动特性。结果表明:弹性支撑下,若将边界条件简化为固定支撑,会使频率计算结果偏大,且阶数越高,两者差距越大;丝杠横向模态振型的节点位置与节点数量会随着工作台位置变化而发生改变。文章分析结果对于理解并改善滚珠丝杠进给系统的横向振动有着一定的实际应用价值。

In order to study the lateral vibration characteristics of the ball screw feed system, the lateral vibration dynamical model of the system was established by using the assumed modal method and the Lagrangian energy method. The frequency equation of the lateral vibration of the screw was deduced by using the boundary conditions of the screw and the assumed modal function was solved. The proposed mathematical model was compared with the finite element method to verify the correctness and accuracy range of the model, and the characteristics of the natural frequency and vibration mode of the system with the three kinds of support modes, including elastic support at both ends, fixed-simple support, and fixed support at both ends, were analyzed. The results show that under elastic support, if the boundary conditions are simplified to the fixed support, it will result in an overestimation of the frequency, and the higher the order, the larger the difference between the two; under the three types of support, the node position and the number of nodes of the lateral vibration mode of the screw will vary with the table position. The results provide practical application value for understanding and improving the lateral vibration of the ball screw feed system.