Research On Symmetric/Asymmetric Bifurcation And Chaos Of Lateral Motion Of Railway Passegner Car System

This dissertation takes the railway passenger car system as research object, and studies such nonlinear dynamical behaviors as the symmetric/asymmetric bifurcation and chaos of lateral motion in vehicle system. The research shows that, due to some reasons such as the coupling of each degrees of freedom and nonlinear wheel/rail interaction forces, it is likely that some asymmetric bifurcation behaviors and chaotic motions occur in the vehicle running on the ideal straight and perfect track, or the vehicle running on the track with nonlinear wheel/rail contact relation or the asymmetric vehicle in curves.Based on the theoretic researches and engineering applications on the lateral motion stability, bifurcation and chaos and asymmetric vehicle system, Chapter One surveys the related achievements, recent development home and abroad, and the main problems in this area and illustrates the preparing work at the end of the chapter as well.Chapter Two studies the symmetric/asymmetric bifurcation behaviors and chaotic motions in a symmetric truck system running on the ideal straight and perfect track. The Hopf bifurcation point and the periodic solution branches are obtained with continuation method, in which the linear and nonlinear critical speeds are easily determined. Meanwhile,'the resultant bifurcation'method is put forward in order to display the possible symmetric/asymmetric dynamic features around track centerline, and the method is applied to analyze the real motion form and the state of symmetry in truck system. Research results show that there exists lots of symmetric/asymmetric motion forms, including the single period motion, period-doubling motion, chaotic motion and several period windows among them.Chapter Three focuses on the asymmetric bifurcation behaviors and their characteristics of a railway truck travelling on a curve with constant radius and superelevation. Because of the asymmetries of the whole system, the motion becomes fully asymmetric. To show the flange contact relation between wheels and rails and the asymmetric motion around track centerline, the'max-min amplitude bifurcation'method is brought forward, and the method is employed to construct the bifurcation diagram to show the motion form, the state of symmetry and the flange contact relation. It is shown not only the equilibrium position is off-centered around track centerline, but also the nonlinear critical speed is lower than the corresponding critical speed in straight track and the critical speed in curves is lowered with the decreasing of the curve radius.Chapter Four researches on the symmetric/asymmetric bifurcation and chaos of the truck model with symmetric and nonlinear wheel/rail contact relation. The system is symmetric around track centerline. Analysis on the critical speed shows that the nonlinear critical speed with nonlinear wheel/rail contact relation is lower than the ones with linear wheel/rail contact geometry relation. Thus the system is safe. Meanwhile, it is found that the results with nonlinear wheel/rail contact relation are more accordant with the results in operation and experiment through analysis of the influence of some parameters on the critical speed. Thus it is advised that considering the nonlinear wheel/rail contact relation as much as possible to study the dynamic features in railway vehicle dynamics. It is more convicing and more reasonable under this circumstance when the findings is used as the basis of design, experiment and operation. Moreover, analysis on bifurcation behaviors of the truck sytem with'increasing-decreasing speed' method shows that the jump from sub-critical bifurcation is not strikingly obvious in the system and the asymmetric motion forms also exist as well.Chapter Five represents studies on the symmetric/asymmetric bifurcation behaviors of a four-axle railway passenger car running on straight track with Vermeulen-Johnson creep force laws and flange force given by a piecewise linear function. The rule of symmetry-breaking is also discussed in this context. Research on the critical speed shows that the nonlinear critical speed in vehicle system is lower than the result in truck system, thus the results tend to be more convincing accordingly. Research on bifurcation and chaos shows that there exist several nonlinear dynamical phenomena, such as the coexistence of many symmetric/asymmetric periodic motions, quasi-periodic motions and chaotic motions. Furthermore, the study discusses the rule of symmetry-breaking of the vehicle system by applying the ramping method with slowly decreasing speed combined with the ramping method with slowly increasing speed. The results show that the motion may break symmetry though jump and becomes asymmetric, or undergo symmetry-breaking and symmetry-restoring processes repeatedly through many pitchfork bifurcations and finally the moiton becomes asymmetric.