应用有限单元法的机床进给系统轴扭特性分析

Axial and Torsional Characteristic Analysis of Feed Drive System of Machine Tools Based on the Finite Element Method

基于有限元法建立了考虑轴扭耦合的机床进给系统动力学方程,分析了工作台位置变化对其动态性能的影响。结果表明:第1、3阶固有频率为丝杠和工作台的轴向振动模态,第2阶为丝杠扭转振动模态。随着工作台位置变化,第1阶固有频率呈现先减后增的变化,最大值出现在丝杠端部,变化率达50.58%;第3阶固有频率为先增后减的变化规律,其中最大值出现在丝杠中部,变化率为10.3%;试验结果与计算结果相吻合;第2阶固有频率受工作台位置变化影响不大,验证试验结果与仿真结果相一致,证明这里的进给系统动力学模型具有较高的精度。

The finite element method was used to divide the feed system model into elements.Special elements include screw-bearing contact elements and screw-worktable contact element.The feed drive system dynamics equations with coupled axial and torsional are proposed based on the finite element method.The element mass matrix and element stiffness matrix are integrated by using transformation matrix,and the total mass matrix and stiffness matrix of feed system are obtained.The natural frequencies and modes of the system are solved by using MATLAB.The effect of the carriage position on the dynamic characteristics of the system is discussed.The results demonstrate that the first and third vibration modes are axial and the mode frequencies shift for different carriage position.The second one is torsional and the mode frequency almost does not vary.With the position change of the carriage,the first mode frequency decreases and then increases.The mode frequency maximum with the change rate of 50.58%is located at the two ends of the screw.The third mode frequency shows increases firstly and then decreases with the change rate of 10.3%,and the maximum locates in the middle of screw.The experimental results verify the numeric results,which proves that the dynamic model of feed system in this paper has a high accuracy.