基于初态激扰法的铁道车辆蛇行运动不稳定极限环求解

Unstable Limit Cycle Solution for Hunting Motion of Railway Vehicle Based on Initial State Excitation Method

针对铁道车辆蛇行运动分岔图中不稳定极限环通过整车动力学仿真求解困难的问题,提出直接积分求解不稳定极限环的方法——初态激扰法。该方法利用多体系统动力学软件Simpack建立高速列车动力学模型,采用Matlab软件对拟周期解进行动态加权调整后作为车辆系统主要部件的初始状态,在光滑轨道上时域积分获取刚体运动状态,在轮对横移幅值随运行速度变化的分岔图中绘制不稳定极限环及平衡点和稳定极限环,从而得到完整的车辆蛇行运动分岔图。以某高速列车为例,基于初态激扰法求解不同轮轨接触工况和抗蛇行减振器故障工况下蛇行运动分岔曲线。结果表明:新轮和磨耗轮工况的车辆蛇行运动分别对应Hopf亚临界分岔和超临界分岔行为,且磨耗轮工况下蛇行运动由亚临界分岔变为超临界分岔;不改变抗蛇行减振器阻尼仅减小卸荷力,对车辆Hopf分岔临界速度没有影响,但会降低车辆LPC (Limit Point Bifurcation of Circles)分岔临界速度并减小不稳定极限环的幅值,从而降低车辆横向稳定性。

Aiming at the difficulty in solving the unstable limit cycle through vehicle dynamics simulation in hunting motion bifurcation diagram of railway vehicles,the initial state excitation method was proposed to solve the unstable limit cycle by direct integration.In this method,the multi-body system dynamics simulation software Simpack was used to establish the dynamic model of high-speed train;and the quasi-periodic solution was dynamically weighted and adjusted by Matlab as the initial state of the main components of the vehicle system.The motion state of rigid body was obtained by time domain integration on the smooth track;then the unstable limit cycle,the equilibrium point and the stable limit cycle were drawn in the bifurcation diagram indicating the change in the lateral displacement amplitude of the wheelset along with the running speed;and the complete hunting motion bifurcation diagram of the vehicle was obtained.A high-speed train was taken as an example to solve the hunting motion bifurcation curves under different wheel-rail contact conditions and anti-hunting damper fault conditions based on the initial state excitation method.The results show that the vehicle hunting motions of the new wheel and the wear wheel correspond to Hopf subcritical bifurcation and supercritical bifurcation,respectively;and the hunting motion under wear wheel conditions changes from subcritical bifurcation to supercritical bifurcation.Making no change to the damping of anti-hunting damper will only reduce the unloading force,which does not affect the critical speed of vehicle Hopf bifurcation,but it will reduce the critical speed of vehicle LPC(Limit Point Bifurcation of Circle)bifurcation and the amplitude of the unstable limit cycle,so as to reduce the lateral stability of the vehicle.