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Wu Shijiang, Zhang Jiye, Sui Hao, Yin Zhonghui, Xu Qi. Hopf bifurcation study of wheelset system. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2569-2581. DOI: 10.6052/0459-1879-21-321
Citation: Wu Shijiang, Zhang Jiye, Sui Hao, Yin Zhonghui, Xu Qi. Hopf bifurcation study of wheelset system. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(9): 2569-2581. DOI: 10.6052/0459-1879-21-321

HOPF BIFURCATION STUDY OF WHEELSET SYSTEM

  • Received Date: June 30, 2021
  • Accepted Date: August 11, 2021
  • Available Online: August 12, 2021
  • 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.
  • [1]
    Knothe K, Stichel S. Rail Vehicle Dynamics. Germany: Springer, 2017
    [2]
    True H. Dynamics of a rolling wheelset. Applied Mechanics Reviews, 1993, 46(7): 438-444 doi: 10.1115/1.3120372
    [3]
    Wagner UV. Nonlinear dynamic behaviour of a railway wheelset. Vehicle System Dynamics, 2009, 47(5): 627-640 doi: 10.1080/00423110802331575
    [4]
    Zboinski K, Dusza M. Development of the method and analysis for nonlinear lateral stability of railway vehicles in a curverd track. Vehicle System Dynamics, 2006, 44: 147-157 doi: 10.1080/00423110600869644
    [5]
    Zboinski K, Dusza M. Bifurcation approach to the influence of rolling radius modelling and rail inclination on the stability of railway vehicles in a curved track. Vehicle System Dynamics, 2008, 46: 1023-1037 doi: 10.1080/00423110802037255
    [6]
    Zboinski K, Dusza M. Extended study of railway vehicle lateral stability in a curved track. Vehicle System Dynamics, 2011, 49(5): 789-810 doi: 10.1080/00423111003770447
    [7]
    Kim P, Jung J, Seok J. A parametric dynamic study on hunting stability of full dual-bogie railway vehicle. International Journal of Precision Engineering and Manufacturing, 2011, 12(3): 505-519 doi: 10.1007/s12541-011-0064-1
    [8]
    Park JH, Koh HI, Kim NP. Parametric study of lateral stability for a railway vehicle. Journal of Mechanical Science and Technology, 2011, 25(7): 1657-1666 doi: 10.1007/s12206-011-0421-0
    [9]
    张卫华, 沈志云. 车辆系统非线性运动稳定性研究. 铁道学报, 1993, 8(1): 29-34 (Zhang Weihua, Shen Zhiyun. Nonlinear stability analysis of railway vehicle system. Journal of The China Railway Society, 1993, 8(1): 29-34 (in Chinese)
    [10]
    张卫华, 宋绍南, 陈良麒. 车辆运动稳定性试验台试验及结果分析. 西南交通大学学报, 1998, 33(5): 485-489 (Zhang Weihua, Song Shaonan, Chen Liangqi. An experimental study on the stability of a vehicle tested on roller testing rig. Journal of Southwest Jiaotong University, 1998, 33(5): 485-489 (in Chinese)
    [11]
    曾京. 车辆系统的蛇行运动分岔及极限环的数值计算. 铁道学报, 1996, 18(3): 13-19 (Zeng Jing. Numerical calculation of bifurcation and limit loops for snaking motion of vehicle systems. Journal of The China Railway Society, 1996, 18(3): 13-19 (in Chinese) doi: 10.3321/j.issn:1001-8360.1996.03.003
    [12]
    张继业, 杨翊仁, 曾京. Hopf分岔的代数判据及其在车辆动力学中的应用. 力学学报, 2000, 32(5): 596-605 (Zhang Jiye, Yang Yiren, Zeng Jing. An algorithm criterion for Hopf bifurcation and its applications in vehicle dynamics. Chinese Journal of Theoretical and Applied Mechanics, 2000, 32(5): 596-605 (in Chinese) doi: 10.3321/j.issn:0459-1879.2000.05.011
    [13]
    舒仲周, 张继业, 曹登庆. 运动稳定性. 北京: 中国铁道出版社, 2001

    (Shu Zhongzhou, Zhang Jiye, Cao Dengqing. Stability of Motion. Beijing: China Railway Press, 2001(in Chinese))
    [14]
    黄世凯. 轮对运动稳定性的机理研究. [硕士论文]. 成都: 西南交通大学, 2013

    (Huang Shikai. The mechanism research on wheelset stability. [Master Thesis]. Chengdu: Southwest Jiaotong University, 2013 (in Chinese))
    [15]
    Hao D, Zeng J, Xie JH, et al. Bifurcation\instability forms of high speed railway vehicles. Science China Technological Sciences, 2013, 56(7): 1685-1696 doi: 10.1007/s11431-013-5254-x
    [16]
    董浩. 铁道车辆运动稳定性及分岔类型研究. [博士论文]. 成都: 西南交通大学, 2014

    (Dong Hao. Study on stability and bifurcation types of railway vehicles. [PhD Thesis]. Chengdu: Southwest Jiaotong University, 2014 (in Chinese))
    [17]
    高学军, 李映辉, 乐源. 延续算法在简单轨道客车系统分岔中的应用. 振动与冲击, 2012, 31(20): 177-182 (Gao Xuejun, Li Yinghui, Yue Yuan. Continuation method and its application in bifurcation of a railway passenger car system car system with simple rails. Journal of Vibration and Shock, 2012, 31(20): 177-182 (in Chinese)
    [18]
    Gao XJ, Li YH, Yue Y. The “resultant bifurcation diagram” method and its application to bifurcation behaviors of a symmetric railway bogie system. Nonlinear Dynamics, 2012, 70(1): 363-380 (in Chinese) doi: 10.1007/s11071-012-0460-9
    [19]
    Gao XJ, Li YH, Yue Y, et al. Symmetric/asymmetric bifurcation behaviours of a bogie system. Journal of Sound and Vibration, 2013, 332(4): 936-951 doi: 10.1016/j.jsv.2012.09.011
    [20]
    Gao XJ, True H, Li YH. Lateral dynamic features of a railway vehicle. Proceedings of the Institution of Mechanical Engineers, 2016, 230(3): 909-923 doi: 10.1177/0954409715572856
    [21]
    张波, 曾京, 董浩. 非线性轮对陀螺系统的稳定性及分岔研究. 振动测试与诊断, 2015, 35(5): 1-6 (Zhang Bo, Zeng Jing, Dong Hao. Stability and bifurcation of nonlinear gyroscopic wheelset system. Journal of Vibration,Measurement &Diagnosis, 2015, 35(5): 1-6 (in Chinese)
    [22]
    张波. 铁道车辆系统随机稳定性及随机分岔研究. [博士论文]. 成都: 西南交通大学, 2016

    (Zhang Bo. Study on stochastic stability and stochastic bifurcation for railway vehicle. [PhD Thesis]. Chengdu: Southwest Jiaotong University, 2016 (in Chinese))
    [23]
    Zeng XH, Han W, Jiang L, et al. The action of wheel set gyroscopic action on the hunting stability of high-speed trains. Vehicle System Dynamics, 2017, 55(6): 924-944 doi: 10.1080/00423114.2017.1293833
    [24]
    Zhang TT, Dai HY. Loss of stability of a railway wheel-set, subcritical or supercritica. Vehicle System Dynamics, 2017, 55(11): 1731-1747 doi: 10.1080/00423114.2017.1319963
    [25]
    张婷婷. 高速车辆系统非线性稳定性及Hopf分岔类型转迁机理研究. [博士论文]. 成都: 西南交通大学, 2019

    (Zhang Tingting. Research on the nonlinear stability and hopf bifurcation transformation mechanism of high-speed railway vehicles. [PhD Thesis]. Chengdu: Southwest Jiaotong University, 2019 (in Chinese))
    [26]
    Ge PH, Wei XK, Liu JZ, at al. Bifurcation of a modified railway wheelset model with nonlinear equivalent conicity and wheel–rail force. Nonlinear Dynamics, 2020, 102(1): 79-100 doi: 10.1007/s11071-020-05588-5
    [27]
    Kalker JJ. On the rolling contact of two elastic bodies in the presence of dry friction. [PhD Thesis]. Delft: University of Technology, 1967
    [28]
    田红亮. 一元三次方程根的解法. 湖北工程学院学报, 2019, 39(6): 97-105 (Tian Hongliang. Extracting roots of one variable cubic equation. Journal of Hubei Engineering University, 2019, 39(6): 97-105 (in Chinese) doi: 10.3969/j.issn.2095-4824.2019.06.018
    [29]
    Kuznetsov YA. Elements of Applied Bifurcation Theory. New York: Springer, 2004
    [30]
    谢建华, 乐源, 李登辉. 非线性动力学. 北京: 科学出版社, 2018

    (Xie Jianhua, Yue Yuan, Li Denghui. Nonlinear System Dynamics. Beijing: Chinese Science Press, 2018 (in Chinese))
    [31]
    郑继明, 朱伟, 刘勇等. 数值分析. 北京: 清华大学出版社, 2016

    (Zheng Jiming, Zhu Wei, Liu Yong, et al. Numerical Analysis. Beijing: Tsinghua University Press, 2016 (in Chinese))
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