Research On Bifurcation And Chaos Of Elastic Colliding Between Vehicle Wheel And Rail System

Wheelset as a key component of the running part of railway vehicles,the geometric relationship between wheel and rail is complex,and the impact vibration of wheel and rail has a great impact on the stability of vehicle operation,which will affect the driving safety when problems occur.Therefore,it is necessary to study the impact vibration characteristics of wheel-rail.This paper mainly studies the dynamic behavior characteristics of wheel-rail system under serpentine excitation.In this paper,taking the wheel and rail as the research object,the equivalent stiffness of the rail is obtained by static analysis of the rail by the finite element method,and the lateral and vertical motion of the wheelset is ignored without considering friction.It is considered that the lateral and vertical motion of the wheelset is weakly coupled,and different mechanical models are established to study the nonlinear dynamic characteristics between the wheel and rail.The analytical solution of the differential equation of motion is obtained,and the numerical solution of the system is obtained by using the fourth-order Runge-Kutta method.The dynamic characteristics of the simulation results are analyzed by bifurcation diagram,time history diagram,phase diagram,Poincare section diagram and frequency spectrum diagram of the system.It is found that Hopf bifurcation,Neimark-Sacker bifurcation,torus doubling,cataclysm and other roads leading to chaos have occurred in the wheel-rail system.Firstly,according to the contact relationship between free wheelset and track,the elastic impact vibration model of two-degree-of-freedom wheel-rail system is established.The nonlinear dynamic behavior of the system under frequency,vertical damping C2 and lateral stiffness K1 of primary suspension is simulated and analyzed.It is found that the two-degree-of-freedom wheel-rail elastic impact vibration system has bifurcation behaviors such as Hopf bifurcation,boundary shock and doubling bifurcation under the corresponding system parameters,which reveals the road to chaos.The system can directly enter chaos from three-periodic motion,and the wheel-rail system is sensitive to K1 lateral stiffness of primary suspension.Secondly,considering the influence of single-degree-of-freedom car body on wheel-rail relationship,the elastic impact vibration model of four-degree-of-freedom wheel-rail system is established,and the stability of wheel-rail system is analyzed by Floquet theory.The nonlinear dynamic behavior of the system under the frequency range and vertical damping C2 of the primary suspension is simulated and analyzed.It is found that the system mainly changes from single periodic motion to chaos after the smooth Hopf circle gradually expands.In addition,the vertical damping C2 of primary suspension will also have an impact on the lateral stability of wheel/rail.When the damping value is too small or too large,the wheel/rail system will enter a state of chaotic motion.Finally,considering the wheel-rail relationship between 1/4 vehicle and rail,the vibration model of elastic collision of 1/4 vehicle wheel-rail system is established.because the model is complex and comes from engineering practice,the simulation shows that the wheel-rail system has multiple ways to enter chaos,such as periodic transfer behavior,five-periodic motion,Neimark-Sacker bifurcation,Hopf bifurcation and torus doubling.In addition,the lateral stiffness of the primary suspension K1 will also have an impact on the lateral stability of the wheel/rail,and the speed of the wheelset converges rapidly with the increase of the stiffness.When the system parameters are returned to the original model,the simulation parameters of the vehicle wheel-rail system basically float near the set parameters.The research results have a certain guiding significance for reality.