【作者】 李悦；

【导师】 曹鸿钧；

【作者基本信息】 北京交通大学 ， 系统理论， 2024， 博士

【摘要】 随着高速铁路和磁悬浮列车的发展,高速车辆系统动力学受到广泛关注.运行稳定性是高速车辆系统的重要问题,直接影响车辆的最高运行速度、安全性以及乘坐舒适性.因此,深入研究高速车辆系统动力学对高速列车的发展具有重要的实际工程意义.本文研究两类高速车辆系统,包括具有轮轨接触的高速铁路车辆系统和悬浮在导轨上的磁悬浮车辆系统.根据研究重点和内容,分别建立高速铁路车辆的轮对横向运动模型、时滞轮对动力学模型、电机转向架横向运动模型和磁悬浮车辆垂向运动模型.应用微分方程定性理论、分岔理论、中心流形定理和规范型理论,分析高速车辆系统的稳定性和分岔等动力学行为.本文主要研究工作和相关结论如下:1.研究非线性轮轨接触关系下高速列车轮对系统的Hopf分岔和极限环分岔.首先,根据轮轨等效锥度实测数据拟合轮对横向位移小于3 mm时的两类等效锥度曲线,构造带有非线性等效锥度函数的轮对横向运动模型.其次,定性分析轮对系统平衡点的稳定性和Hopf分岔,推导Hopf分岔的规范型,计算第一Lyapunov系数,进而分析两种类型的等效锥度差异对高速列车轮对系统Hopf分岔性质的影响.结果表明,非线性等效锥度函数关于轮对横向位移的二阶导数在平衡点处取值的正负决定轮对系统的Hopf分岔类型.研究由Hopf分岔产生的极限环分岔,包括fold分岔、倍周期分岔、cusp分岔和fold-flip分岔,分别讨论以上分岔对极限环稳定性和轮对蛇行运动振幅的影响.2.研究带有横向和偏航阻尼器时滞的轮对系统的稳定性、Hopf分岔、周期和混沌振动.首先,建立具有横向和偏航阻尼器时滞的非线性轮对模型.其次,定性分析平衡点的局部稳定性,发现随着时滞的变化,轮对系统会经历稳定性开关.当时滞取临界值时,轮对系统发生Hopf分岔,导致平衡点的稳定性发生改变.应用规范型理论和中心流形定理研究Hopf分岔的性质.通过数值模拟发现,横向和偏航阻尼器时滞取值影响轮对蛇行运动振幅、周期和混沌振动,导致系统在周期和混沌状态之间切换,甚至出现轮对横向位移较大的不规则振动.3.研究高速列车电机转向架系统的双参数分岔.首先,建立含非线性等效锥度函数的电机转向架模型,以列车运行速度作为分岔参数,定性分析平衡点的稳定性和Hopf分岔.其次,以电机悬挂刚度和阻尼作为分岔参数,分析平衡点的双参数分岔,包括Bautin分岔和Hopf-Hopf分岔.研究Hopf分岔产生的极限环的余维1和余维2分岔,包括Neimark-Sacker分岔、fold分岔、cusp分岔、1:3共振和1:4共振.结果表明,fold分岔改变极限环的稳定性和分岔方向,cusp分岔改变fold分岔的类型.超临界的Neimark-Sacker分岔导致极限环产生稳定的环面,次临界的Neimark-Sacker分岔及其分岔曲线上的1:3共振和1:4共振点会导致电机转向架系统失稳.4.证明具有速度反馈信号时滞的磁悬浮车辆系统存在zero-Hopf分岔,推导zero-Hopf分岔的三次截断规范型.首先,考虑速度反馈信号时滞,建立具有非线性电磁力的时滞磁悬浮车辆模型.其次,定性分析平衡点的局部稳定性和Hopf分岔发生的条件.当时滞取临界值时,平衡点发生Hopf分岔,导致稳定性发生改变.此外,证明时滞磁悬浮车辆系统存在zero-Hopf分岔,应用中心流形定理和规范型理论推导zero-Hopf分岔的三次截断规范型.通过柱坐标变换,将规范型转化为含两个参数的平面系统,分析不同参数区域上系统的动力学行为.本文研究内容为提高高速铁路车辆和磁悬浮车辆系统的稳定性提供理论参考.更多还原

【Abstract】 With the development of high-speed railway and maglev train,the dynamics of highspeed vehicle systems has received extensive attention.Running stability is an important issue of high-speed vehicle system,which directly affects the maximum running speed,safety and ride comfort of the vehicle.Therefore,in-depth study of high-speed vehicle system dynamics has important practical engineering significance.In this dissertation,two classes of high-speed vehicle systems are studied,including high-speed railway vehicle systems with wheel-rail contact and a maglev vehicle system suspended on a guideway.According to the focus and content of the study,the lateral motion model of a wheelset,the wheelset dynamic model with time delays,the lateral motion model of motor bogies and the vertical motion model of maglev vehicles are established,respectively.The qualitative theory of differential equations,bifurcation theory,center manifold theorem and normal form theory are applied to analyze the stability and bifurcation of the high-speed vehicle systems.The main contents and conclusions of this dissertation are as follows:1.Hopf bifurcation and bifurcation of limit cycles of a high-speed railway wheelset under a nonlinear wheel-rail contact relationship are investigated.Firstly,the two types of equivalent conicity curves are fitted according to the measured data of the equivalent conicity,and the lateral motion model of the wheelset with a nonlinear equivalent conicity function is established.Secondly,the stability and Hopf bifurcation of the equilibrium of the wheelset system are qualitatively analyzed,the normal form of the Hopf bifurcation is derived,and the first Lyapunov coefficient is calculated to analyze the effect of the difference between the two types of equivalent conicity on the Hopf bifurcation of the wheelset system.Analytical studies reveal that the second-order derivative of the equivalent conicity function with respect to the lateral displacement of the wheelset at the equilibrium determines the Hopf bifurcation type.The limit cycle bifurcations caused by the Hopf bifurcation is analyzed,including the fold bifurcation,the period-doubling bifurcation,the cusp bifurcation,and the fold-flip bifurcation.The effects of the above bifurcations on the stability of the limit cycle and the hunting motion amplitude of the wheelset are discussed.2.The stability,Hopf bifurcation,periodic,and chaotic vibrations of a wheelset system with time delays in the lateral and yaw damper are investigated.Firstly,a nonlinear wheelset model is established with time delays in lateral and yaw damper.Secondly,the local stability at the equilibrium is analyzed qualitatively.It is found that the wheelset system undergoes stability switches as the time delay varies.When the time delays cross critical values,the wheelset system undergoes Hopf bifurcation and the equilibrium becomes unstable.Applying the normal form theory and the center manifold theorem,the properties of Hopf bifurcation are studied.Numerical results show that time delays in the lateral and yaw dampers not only affect the amplitude of the hunting motion of the wheelset but also the periodic and chaotic motions.If the time delays gradually increase,the wheelset will vibrate irregularly with large lateral displacements.3.The two-parameter bifurcation of a motor bogie system for high-speed trains is investigated.Firstly,a motor bogie model with a nonlinear equivalent conicity function is established.The running speed is chosen as the bifurcation parameter to qualitatively analyze the stability and Hopf bifurcation of the equilibrium.Secondly,the motor suspension stiffness and damping are chosen as the bifurcation parameters to analyze the two-parameter bifurcation at the equilibrium,including the Bautin bifurcation and the Hopf-Hopf bifurcation.The codimension 1 and codimension 2 bifurcations of the limit cycles generated by the Hopf bifurcation are investigated,including Neimark-Sacker bifurcation,fold bifurcation,cusp bifurcation,1:3 resonance,and 1:4 resonance.Analytical investigations reveal that the fold bifurcation influences the stability and bifurcation direction of the limit cycle,and the cusp bifurcation alters the fold bifurcation type.In addition,the subcritical Neimark-Sacker bifurcation produces an unstable torus,which will lead to the instability of the motor bogie.4.The existence of the zero-Hopf bifurcation of a maglev vehicle system with time delay in the speed feedback signal is investigated,and the truncated normal form of the zero-Hopf bifurcation is deduced.Firstly,considering the time delay in the speed feedback signal,a time delayed maglev vehicle model with nonlinear electromagnetic force is established.Secondly,the local stability of the equilibrium and the existence of Hopf bifurcation are qualitatively analyze.When the time delay crosses the critical value,the Hopf bifurcation occurs and the equilibrium becomes unstable.In addition,it is proved that there exists a zero-Hopf bifurcation in the time delayed maglev vehicle system,and the center manifold theorem and the normal form theory are applied to derive the truncated normal form of the zero-Hopf bifurcation.Using the cylindrical coordinate transformation,the normal form is transformed into a planar system with two free parameters,and the dynamics of the system in different parameter regions is analyzed.The research content of this dissertation provides theoretical references for improving the stability of high-speed railway vehicles and maglev vehicle systems.更多还原