轮对非线性随机动力学模型稳定性及分岔研究

Research on Stability and Bifurcation of Nonlinear Stochastic Dynamic Model of Wheelset

针对轮对系统的随机动力学问题,综合考虑等效锥度和悬挂刚度的随机因素影响,建立含有陀螺效应的非线性轮轨接触关系的轮对模型,研究轮对系统随机稳定性和随机Hopf分岔。利用随机平均法将轮对系统转化为一维扩散过程,通过判定奇异边界的性态,得到轮对系统随机失稳条件和失稳临界速度。理论推导求得平稳概率密度和联合概率密度函数,分析概率密度函数拓扑结构演化,确定轮对系统随机Hopf分岔类型。探究随机因素对失稳临界速度和Hopf分岔域的影响,仿真结果验证了理论分析的正确性。结果表明,扩散过程的边界性态决定了轮对系统的随机稳定性,左边界特征标值cL=1是随机失稳的临界状态。考虑随机因素后,轮对系统的稳态概率密度函数随着分岔参数增加发生两次定性性态改变,分别对应轮对系统的随机D分岔和随机P分岔,且两种随机分岔的临界速度均随着随机参激强度的增大而减小。

Aiming at the stochastic dynamics of the wheelset system,considering the influence of the stochastic factors of the equivalent conicity and suspension stiffness,a wheelset model of nonlinear wheel-rail contact relationship with gyroscopic effect is established to investigate the stochastic stability and stochastic Hopf bifurcation of the wheelset system.The stochastic average method transforms the wheelset system into a one-dimensional diffusion process.By judging the behavior of the singular boundary,the stochastic instability conditions and critical speed of the wheelset system are obtained.The stationary probability density function and the joint probability density function are derived theoretically.The topological structure evolution of the probability density function is analyzed,and the type of stochastic Hopf bifurcation of the wheelset system is determined.The influence of stochastic factors on the critical speed of instability and the Hopf bifurcation region is explored.The simulation results verify the correctness of the theoretical analysis.The results reveal that the stochastic stability of the wheelset system is determined by the boundary behavior of the diffusion process,and the left boundary eigenvalue cL=1 is the critical state of stochastic instability.After considering the stochastic factors,the steady-state probability density function of the wheelset system has two qualitative changes with the increase of the bifurcation parameters,which correspond to the stochastic D bifurcation and stochastic P bifurcation of the wheelset system respectively,and the critical speeds of the two stochastic bifurcations decrease with the increase of the random parameter intensity.