轮对系统随机动态分叉研究

Research on Stochastic Dynamical Bifurcation in Wheelset System

运用随机平均法对轮对系统的随机分叉行为进行研究,对比亚临界和超临界分叉2种典型轮对系统随机动态分叉的差异,分析动态分叉与Hopf分叉的区别,定义全局随机临界速度,提出新的失稳判定方法。结果表明,随机激扰对轮对系统的稳定性影响很大,在随机激扰的作用下,轮对系统的临界速度会随着随机激扰的强度增大而显著降低,当轮对仅受轨道随机激励时随机激扰对稳定性的影响不大,但遇到大风等强激扰环境时,随机激扰的影响将不可忽视。随机动态分叉点对应的速度可作为全局随机临界速度,且最大Lyapunov指数法可作为新的失稳判定方法。

The research on stochastic bifurcation of wheelset system was performed by using the stochastic averaging method.The difference between the stochastic dynamical bifurcation of two typical subcritical and supercritical bifurcation wheelset systems was investigated.Based on the analysis of the difference between stochastic dynamical bifurcation and Hopf bifurcation,the conception of global stochastic critical speed and a new instability criterion were proposed.The results show that the random excitation has a great influence on the stability of the wheelset system.Under the action of random excitation,the critical speed of the wheelset system significantly decreases with the increase of the intensity of random excitation.The influence of random excitation on stability is relatively small when the wheelset is only subjected to the track random excitation.However,the influence cann’t be ignored when the wheelset is under the strong excitation condition such as strong wind.The speed corresponding to the point of stochastic dynamical bifurcation can be regarded as the global stochastic critical speed,while the largest Lyapunov exponent method can be used as the new instability criterion method.