Research on hunting stability and bifurcation characteristics of nonlinear stochastic wheelset system

A stochastic wheelset model with a nonlinear wheel-rail contact relationship is established to investigate the stochastic stability and stochastic bifurcation of the wheelset system with the consideration of the stochastic parametric excitations of equivalent conicity and suspension stiffness. The wheelset is systematized into a one-dimensional (1D) diffusion process by using the stochastic average method, the behavior of the singular boundary is analyzed to determine the hunting stability condition of the wheelset system, and the critical speed of stochastic bifurcation is obtained. The stationary probability density and joint probability density are derived theoretically. Based on the topological structure change of the probability density function, the stochastic Hopf bifurcation form and bifurcation condition of the wheelset system are determined. The effects of stochastic factors on the hunting stability and bifurcation characteristics are analyzed, and the simulation results verify the correctness of the theoretical analysis. The results reveal that the boundary behavior of the diffusion process determines the hunting stability of the stochastic wheelset system, and the left boundary characteristic value c(L) = 1 is the critical state of hunting stability. Besides, stochastic D-bifurcation and P-bifurcation will appear in the wheelset system, and the critical speeds of the two kinds of stochastic bifurcation decrease with the increase in the stochastic parametric excitation intensity.