轮对蛇行运动的相位同步模态分析

Phase Synchronization Modal Analysis of Wheelset Hunting Motion

基于单轮对蛇行运动模型,推导了考虑悬挂系统刚度和阻尼的系统特征根解析式,根据Routh-Hurwitz稳定性判据导出了轮对蛇行运动临界速度和频率公式。应用相位同步模态分析法,消除系统阻尼引起的相位差异,实现了轮对蛇行运动的非保守系统方程实模态解耦。研究表明,减小轮对质量、转动惯量及等效锥度,增大一系横向和纵向定位刚度及阻尼,增大轮径和接触点跨距能够提高蛇行临界速度,蠕滑系数降低不会降低蛇行临界速度;减小轮对质量和转动惯量,增大一系横向和纵向定位刚度,减小接触点跨距会增大临界速度对应的蛇行运动频率,悬挂系统阻尼对临界速度时的蛇行运动频率影响不大,而等效锥度、轮径和蠕滑系数对临界速度时的蛇行频率无影响。通过一系悬挂系统刚度优化可在理论上实现足够大的轮对蛇行运动临界速度。在任意运行速度时,均存在蛇行共振响应,响应幅值和频率随速度提高而增大。轮对蛇行运动中高阻尼模态在所有速度范围内均呈现过阻尼特征,轮对蛇行响应由低阻尼振动模态主导。

The analytic eigenvalue formula of the system characteristic equation is derived based on the hunting model of a single wheelset.The critical velocity for unstable wheelset hunting as well as the corresponding frequency are deduced according to the Routh-Hurwitz stability criteria.The phase synchronization modal analysis method is adopted to eliminate the phase difference caused by the system damping,and the real modal decoupling of the non-conservative system equations of wheelset hunting motion is realized.The research indicates that reducing the mass and moment of inertia of wheelset as well as the equivalent conicity,increasing the stiffness and the damping of primary suspension in lateral and longitudinal directions,increasing wheelset diameter and distance between two contact points can increase the critical hunting velocity.Reduction of creep coefficient will not reduce the critical velocity.The frequency corresponding to the critical hunting motion is increasing with the decreasement of the mass and moment of inertia of wheelset,the increasement of the stiffness of the primary suspension in lateral and longitudinal directions,and with the reduction of the distance between contact points.The influence of the suspension damping on the corresponding hunting frequency is not obvious.The equivalent conicity,wheel diameter and creep coefficient have no influence on the frequency for critical hunting.A large enough critical velocity can be achieved in theory by the optimizing the primary suspension stiffness.There is a hunting resonance response existed at any running speed.The resonance amplitude and frequency increase with the increasement of speed.The high-damping mode of wheelset hunting motion is actually an over-damped response,while the wheelset hunting motion is dominated by the low-damping vibration mode.