Research On Non-smooth Dynamics Of Railway Vehicle Wheelset Systems

In recent years,the dynamics of non-smooth systems as a hot and challenge topic in the field of mathematics and engineering have received extensive attention.They have many special dynamics phenomena that are not found in smooth systems,such as stick-slip phenomena,grazing bifurcation,sliding bifurcation,corner-collision bifurcation,period-adding bifurcation,and new routes to chaos caused by these bifurcations,and so on.In this dissertation,the non-smooth factors of railway vehicle system are considered,mainly including,non-smooth yaw damper,flange impact,dry friction,non-smooth wheel/rail contact relation and so on.The bifurcation and chaos in railway wheelset system and their mechanism are studied by the theory of non-smooth dynamics,and the influence of parameters on the stability and dynamics of wheelset system is studied,which provides a theoretical basis for improving the stability and comfort of railway vehicle system and parameter optimization.The main work of this dissertation are as follows:1.Based on Kaller's linear creep theory,the differential equations of lateral motions of the wheelset system considering the non-smooth yaw damper are established.According to the center manifold and based on the symmetry of the system,the reduction equations of the railway wheelset system are obtained.Moreover,by constructing a Poincare map,a criterion for determining the type of the Hopf bifurcation for the system is given.And then,the Hopf bifurcation and the stability of the periodic solution for the railway wheelset system are analyzed.Based on the above model,considering the non-smooth factor of flange contact,the equations of lateral motions of the wheelset system are established.It is shown that the system exists generalized Hopf bifurcation and Hopf bifurcation at infinity,and the influences of the parameters on the critical velocity for the wheelset system is also discussed.2.Based on Johnson-Vermeulen's nonlinear creep theory,the equations of lateral motions of the wheelset system with flange contact are derived.Poincare mappings near the grazing trajectory are derived by the PDM(Poincaré-section discontinuity mapping)approach for the two classes of impact models.Then,we analyze and compare the near grazing dynamics of the two classes of models.It is shown that in the rigid impact model the stable periodic motion of the railway wheelset system translates into chaotic motion after the gazing bifurcation,while in the soft impact model a pitchfork bifurcation occurs and the system tends to the chaotic state through the period doubling bifurcation route.3.Based on Johnson-Vermeulen's nonlinear creep theory,the differential equations of lateral motions of the wheelset system considering the dry friction non-smooth factor are derived.The generalized Jacobi matrix of the dry friction wheelset system is constructed by the jump matrix,and the Floquet multipliers and Lyapunov exponents of the dry friction system are calculated.Then the type of bifurcation and the type of attractor for the system are determined.Moreover,the sliding bifurcation of the system is discussed by the non-smooth bifurcation theory,and the global dynamics of the railway wheelset system is discussed by the cell mapping method.In addition,the influences of the suspension parameters and contact parameters on the global dynamics are discussed.Furthermore,the influence of the two parameters on the dynamic response for the wheelset system is analyzed numerically.The results show that the system has abundant dynamics phenomena,including stick-slip phenomena,periodic motion,quasiperiodic motion and chaotic motion and so on.In addition,it is found that the system has a large number of coexistence of multiple attractors,including the coexistence of multiple periodic attractors,the coexistence of multiple periodic attractors and chaotic attractors,et.al.The routes to chaos for the wheelset system with dry friction damping mainly include quasi-periodic route,doubling and inverse doubling bifurcation route and periodic motion transitions directly into chaotic motion.4.The wheel/rail contact table is obtained by the program RSGEO and then a lateral dynamic model of railway wheelset considering the non-smooth wheel/rail contact relation is derived.The lateral motion stability,bifurcation and chaos of the wheelset system and the influences of suspension parameters on the stability of the system are analyzed numerically.It is shown that the system is particularly sensitive to initial disturbance,and there are typical hysteresis phenomena and jump phenomena.Both linear and nonlinear critical velocities increase with the increase of longitudinal and lateral spring stiffness,and the lateral spring stiffness has strong influence on the lateral stability of the system than the longitudinal spring stiffness.When the longitudinal spring stiffness is small,it has little effect on the lateral dynamics.However,when the order of magnitude for the longitudinal spring stiffness is approximate the lateral spring stiffness,it has a greater effect on the lateral dynamics of the wheelset system.With the increase of longitudinal stiffness,the chaotic motion interval of the system decreases.