轮轨集总参数简化模型稳定性与分岔研究

基于轮轨集总参数简化模型，采用Hertz非线性接触理论模拟轮轨接触力，导出轮轨耦合非线性动力学模型的状态方程。利用自适应变步长Runge-Kutta法求解状态方程，可得到轮轨系统各部件位移、速度、加速度等随车辆运行速度的变化规律及车辆失稳的临界速度。数值结果表明，该方法不仅可以得出系统的失稳临界速度，而且可以观察到各部件的振动情况和失稳形态。

Stability and Bifurcation Analysis of the Simplified Parameter-Lumped Model in Wheel-Rail System

Based on the simplified parameter-lumped dynamical model which dominates the vertical vibration of wheel-rail system, the state equations of the wheel-rail coupling nonlinear dynamic model are derived, in which the Hertz nonlinear contact force is adopted to simulate the wheel-rail interactions. The self-adapted Runge-Kutta method is used to solve the state equations. The change rule of the overall displacements, velocities and accelerations of all parts changed with the vehicle speed is investigated and the critical speed which describes the dynamic stability of vehicle system is obtained. The numerical results show that the method can not only obtain the critical speed, but also may have the overview of the vibration and instability of all parts.