车削工件扭转振动模态的时变特性研究

Research on time-varying characteristics of torsion vibration mode for cutting workpiece

基于车削加工过程中工件直径和转动惯量的时变特性,建立工件扭转自由振动的时变力学模型,导出工件扭转自振频率的时变方程,在Mathcad软件中求解时变方程得到其低阶自振频率;利用ANSYS软件进行模态分析,研究不同背吃刀量和进给速度对工件扭转自振频率及振型时变规律的影响。研究表明,有限元仿真结果与理论解答趋于一致;一阶扭转自振频率随车削时间呈对称的抛物线状分布,二阶自振频率随时间呈近似正弦分布。背吃刀量越大,自振频率时变曲线的幅值越大;进给速度越大,自振频率的时变周期越短。

Based on time-varying characteristics of the diameter and inertia moment for the workpiece in the cutting process, the time-varying mechanical model on torsion free vibration is established, and time-dependant equation of torsion natural frequency for workpiece is obtained and by Mathcad software the lower order natural frequency of workpiece is obtained by solving time-dependant equation. Using ANSYS the torsion vibration modal analysis for the workpiece is carried out and the effect of the different back cutting depth and feed rate on the time-varying laws of the natural vibration frequency and the vibration shape of the workpiece was studied. The study results show that time-varying torsion vibration frequency curves by theoretical calculation and finite element simulation are basically identical, and the first order torsion vibration frequency displays as a symmetric parabolic distribution with time, second-order vibration frequency displays as a sine distribution. The bigger the back cutting depth,the larger the amplitude of natural frequency curves, and the bigger the feed rate, the shorter the time-varying cycle of natural frequency.