拉拔自激振动方程及其数值算法分析

Analysis on drawing self-excited vibration equation and its numerical algorithm

针对拉拔加工过程中常发生“追逐”或“跳跃”现象并诱发产生振动的问题,根据丁文镜教授提出的机械系统追逐现象微分控制方程,建立了拉拔自激振动的时变质量非线性微分控制方程,并利用移位的Chebyshev多项式函数对建立的微分方程进行数值求解。另外,给出3个具体的工况模拟问题,每个问题分别考虑了不同的阻尼系数、刚度系数、变质量函数和摩擦力,并绘制了相应的无量纲位移图和相图,通过数值仿真研究了质量模块和摩擦力分别变化时对拉拔过程的影响。结果表明:摩擦力呈线性或者周期性等变化时,对拉拔过程的振动位移产生较大的影响,而质量模块变化不会对拉拔结果产生影响。

For the problem of vibration induced by“hunting”or“jumping”phenomenon in the process of drawing,the time-varying mass nonlinear differential control equation of self-excited vibration of drawing was established according to the differential control equation of hunting phenomenon proposed by Professor Ding Wenjing,and the differential equation was solved numerically by the shifted Chebyshev polynomial function.Then,three specific simulation problems of actual working conditions were given,and for each problem,different damping coefficients,stiffness coefficients,variable mass functions and friction forces were respectively considered.Furthermore,corresponding dimensionless displacement diagram and phase diagram were drawn,and the influences of mass module and friction force on the drawing process were studied by numerical simulation.The results show that when the friction force exhibits linear or periodic changes,it has a significant impact on the vibration displacement during the drawing process,while the change of mass module has not affect the drawing result.