轮对系统的Hopf分岔研究  

HOPF BIFURCATION STUDY OF WHEELSET SYSTEM

作　　者：武世江 张继业[1] 隋皓[1] 殷中慧 胥奇 Wu Shijiang;Zhang Jiye;Sui Hao;Yin Zhonghui;Xu Qi(State Key Laboratory of Traction Power,Southwest Jiaotong University,Chengdu 610031,China;School of Mechanics and Engineering,Southwest Jiaotong University,Chengdu 610031,China)

机构地区：[1]西南交通大学牵引动力国家重点实验室,成都610031 [2]西南交通大学力学与工程学院,成都610031

出　　处：《力学学报》2021年第9期2569-2581,共13页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家重点研发计划课题(2020YFA0710902);国家自然科学基金资助项目(12172308)。

摘　　要：针对轮对系统中的非线性动力学问题,本文基于Hopf分岔代数判据得到考虑陀螺效应的轮对系统Hopf分岔点解析表达式,即轮对系统蛇形失稳的线性临界速度解析表达式.基于分岔理论得到轮对系统的第一、第二Lyapunov系数表达式,并结合打靶法分别得到不同纵向刚度下,考虑陀螺效应与不考虑陀螺效应的轮对系统分岔图.通过对比有无陀螺效应的轮对系统分岔图发现,在同一纵向刚度下,考虑陀螺效应的轮对系统线性临界速度和非线性临界速度均大于不考虑陀螺效应的轮对系统,即陀螺效应可以提高轮对系统的运动稳定性.基于Bautin分岔理论,以纵向刚度和纵向速度作为参数,分别得到考虑陀螺效应和不考虑陀螺效应的轮对系统,从亚临界Hopf分岔到超临界Hopf分岔,再从超临界Hopf分岔到亚临界Hopf分岔的迁移机理拓扑图.通过对比有、无陀螺效应的轮对系统Bautin分岔拓扑图发现,陀螺效应将改变轮对系统的退化Hopf分岔点,但对于轮对系统Bautin分岔拓扑图的影响不大.Aiming at the problem of nonlinear dynamics in the wheelset system,this paper analyzes the Hopf bifurcation point of the system based on the Hopf bifurcation algebraic criterion of the wheel considering the gyroscopic action,that is,the expression of the linear critical speed of the serpentine instability of the wheelset system.Based on the bifurcation theory,the first and second Lyapunov coefficient expressions of the wheelset system are obtained.Combining with the shooting method,the bifurcation diagrams of the wheelset system with and without the gyroscopic action under different longitudinal stiffness are also obtained.Through comparison with the bifurcation diagrams of the wheelset system with and without gyroscopic action,it is found that under the same longitudinal stiffness,both the linear critical speed and the nonlinear critical speed of the wheelset system considering the gyroscopic action are greater than those of the wheelset system without considering the gyroscopic action,that is to say,the gyroscopic action can improve the motion stability of the wheelset system.Based on the Bautin bifurcation theory,this paper takes the longitudinal stiffness and longitudinal velocity as parameters.In this way,wheelset systems with and without gyroscopic action are obtained,as well as the topological diagrams of the migration mechanism from subcritical Hopf bifurcation to supercritical Hopf bifurcation,and then from supercritical Hopf bifurcation to subcritical Hopf bifurcation.By comparing the Bautin bifurcation topological diagrams of the wheelset system with and without gyroscopic action,it is found that the gyroscopic action will change the degenerate Hopf bifurcation of the wheelset system,which,however,has little action on the Bautin bifurcation topology of the wheelset system.

关 键 词：陀螺效应 HOPF 分岔代数判据 第一、第二Lyapunov 系数 退化Hopf 分岔 Bautin 分岔 

分 类 号：U270.11[机械工程—车辆工程]