轮对非线性随机动力学模型稳定性及分岔研究

doi:10.3901/JME.2023.10.210

机械工程学报 ›› 2023, Vol. 59 ›› Issue (10): 210-225.doi: 10.3901/JME.2023.10.210

扫码分享

轮对非线性随机动力学模型稳定性及分岔研究

王鹏^1,2, 杨绍普^1,2, 刘永强^1,3, 刘鹏飞¹, 赵义伟^1,2, 张兴^1,2

1. 石家庄铁道大学省部共建交通工程结构力学行为与系统安全国家重点实验室石家庄 050043;
2. 石家庄铁道大学交通运输学院石家庄 050043;
3. 石家庄铁道大学机械工程学院石家庄 050043

收稿日期:2022-10-12 修回日期:2023-03-01 出版日期:2023-05-20 发布日期:2023-07-19
通讯作者: 刘永强(通信作者),男,1983年出生,博士,教授,博士研究生导师。主要研究方向为车辆系统动力学与控制、车辆状态监测与故障诊断。E-mail:liuyq@stdu.edu.cn E-mail:liuyq@stdu.edu.cn
作者简介:王鹏,男,1989年出生,博士研究生。主要研究方向为车辆系统动力学与控制。E-mail:wangp@stdu.edu.cn
基金资助:
国家自然科学基金(11790282，12172235，12072208，52072249，U1934201)和石家庄铁道大学国家重点实验室开放基金(ZZ2021-13)资助项目。

Research on Stability and Bifurcation of Nonlinear Stochastic Dynamic Model of Wheelset

WANG Peng^1,2, YANG Shaopu^1,2, LIU Yongqiang^1,3, LIU Pengfei¹, ZHAO Yiwei^1,2, ZHANG Xing^1,2

1. State Key Laboratory of Mechanical Behavior and System Safety of Traffic Engineering Structures, Shijiazhuang Tiedao University, Shijiazhuang 050043;
2. School of Traffic and Transportation, Shijiazhuang Tiedao University, Shijiazhuang 050043;
3. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang 050043

Received:2022-10-12 Revised:2023-03-01 Online:2023-05-20 Published:2023-07-19

摘要/Abstract

摘要： 针对轮对系统的随机动力学问题,综合考虑等效锥度和悬挂刚度的随机因素影响,建立含有陀螺效应的非线性轮轨接触关系的轮对模型,研究轮对系统随机稳定性和随机Hopf分岔。利用随机平均法将轮对系统转化为一维扩散过程,通过判定奇异边界的性态,得到轮对系统随机失稳条件和失稳临界速度。理论推导求得平稳概率密度和联合概率密度函数,分析概率密度函数拓扑结构演化,确定轮对系统随机Hopf分岔类型。探究随机因素对失稳临界速度和Hopf分岔域的影响,仿真结果验证了理论分析的正确性。结果表明,扩散过程的边界性态决定了轮对系统的随机稳定性,左边界特征标值c_L=1是随机失稳的临界状态。考虑随机因素后,轮对系统的稳态概率密度函数随着分岔参数增加发生两次定性性态改变,分别对应轮对系统的随机D分岔和随机P分岔,且两种随机分岔的临界速度均随着随机参激强度的增大而减小。

关键词: 随机系统, 随机平均法, 奇异边界, 蛇行稳定性, 随机分岔

Abstract: Aiming at the stochastic dynamics of the wheelset system, considering the influence of the stochastic factors of the equivalent conicity and suspension stiffness, a wheelset model of nonlinear wheel-rail contact relationship with gyroscopic effect is established to investigate the stochastic stability and stochastic Hopf bifurcation of the wheelset system. The stochastic average method transforms the wheelset system into a one-dimensional diffusion process. By judging the behavior of the singular boundary, the stochastic instability conditions and critical speed of the wheelset system are obtained. The stationary probability density function and the joint probability density function are derived theoretically. The topological structure evolution of the probability density function is analyzed, and the type of stochastic Hopf bifurcation of the wheelset system is determined. The influence of stochastic factors on the critical speed of instability and the Hopf bifurcation region is explored. The simulation results verify the correctness of the theoretical analysis. The results reveal that the stochastic stability of the wheelset system is determined by the boundary behavior of the diffusion process, and the left boundary eigenvalue c_L=1 is the critical state of stochastic instability. After considering the stochastic factors, the steady-state probability density function of the wheelset system has two qualitative changes with the increase of the bifurcation parameters, which correspond to the stochastic D bifurcation and stochastic P bifurcation of the wheelset system respectively, and the critical speeds of the two stochastic bifurcations decrease with the increase of the random parameter intensity.

Key words: stochastic system, stochastic average method, singular boundary, hunting stability, stochastic bifurcation

中图分类号:

U271

王鹏, 杨绍普, 刘永强, 刘鹏飞, 赵义伟, 张兴. 轮对非线性随机动力学模型稳定性及分岔研究[J]. 机械工程学报, 2023, 59(10): 210-225.

WANG Peng, YANG Shaopu, LIU Yongqiang, LIU Pengfei, ZHAO Yiwei, ZHANG Xing. Research on Stability and Bifurcation of Nonlinear Stochastic Dynamic Model of Wheelset[J]. Journal of Mechanical Engineering, 2023, 59(10): 210-225.

参考文献

[1] LUO G W,SHI Y Q,ZHU X F,et al. Hunting patterns and bifurcation characteristics of a three-axle locomotive bogie system in the presence of the flange contact nonlinearity[J]. International Journal of Mechanical Sciences,2018,136:321-338.
[2] PLSSON B A,NIELSEN J C O. Wheelrail interaction and damage in switches and crossings[J]. Vehicle System Dynamics,2011,50(1):1-16.
[3] YAN Y,ZENG J. Hopf bifurcation analysis of railway bogie[J]. Nonlinear Dynamics,2018,92(1):107-117.
[4] TRUE H. Multiple attractors and critical parameters and how to find them numerically:The right,the wrong and the gambling way[J]. Vehicle System Dynamics,2013,51(3):443-459.
[5] PAPANGELO A,PUTIGNANO C,HOFFMANN N. Self-excited vibrations due to viscoelastic interactions[J]. Mechanical Systems and Signal Processing,2020,144:106894.
[6] WAGNER U V. Nonlinear dynamic behaviour of a railway wheelset[J]. Vehicle System Dynamics,2009,47 (5):627-640.
[7] AHMADIAN M,YANG S. Hopf bifurcation and hunting behavior in a rail wheelset with flange contact[J]. Nonlinear Dynamics,1998,15(1):15-30.
[8] TRUE H,ASMUND R. The dynamics of a railway freight wagon wheelset with dry friction damping[J]. Vehicle System Dynamics,2002,38(2):149-163.
[9] YABUNO H,OKAMOTO T,AOSHIMA N. Stabilization control for the hunting motion of a railway wheelset[J]. Vehicle System Dynamics,2001,35(Suppl.1):41-55.
[10] 孙建锋,池茂儒,吴兴文,等. 基于能量法的轮对蛇行运动稳定性[J]. 交通运输上程学报,2018,18 (2):82-89. SUN Jianfeng,CHI Maoru,WU Xingwen,et al. Hunting motion stability of wheelset based on energy method[J]. Journal of Traffic and Transportation Engineering,2018,18 (2):82-89.
[11] WU X,CHI M. Parameters study of Hopf bifurcation in railway vehicle system[J]. Journal of Computational and Nonlinear Dynamics,2015,10(3):031012.
[12] 史禾慕,曾晓辉,吴晗. 轮对非线性动力学系统蛇行运动的解析解[J]. 力学学报,2022,54(7):1807-1819. SHI Hemu,ZENG Xiaohui,WU Han. Analytical solution of the hunting motion of a wheelset nonlinear dynamical system[J]. Chinese Journal of Theoretical and Applied Mechanics,2022,54(7):1807-1819.
[13] WEI L,ZENG J,CHI M,et al. Carbody elastic vibrations of highspeed vehicles caused by bogie hunting instability[J]. Vehicle System Dynamics 2017,55 (9):1321-1342.
[14] QU S,WANG J,ZHANG D,et al. Failure analysis on bogie frame with fatigue cracks caused by hunting instability[J]. Engineering Failure Analysis,2021,128:105584.
[15] SUN J,MELI E,CAI W,et al. A signal analysis based hunting instability detection methodology for high-speed railway vehicles[J]. Vehicle System Dynamics,2021,59(10):1461-1483.
[16] GE P,WEI X,LIU J,et al. Bifurcation of a modified railway wheelset model with nonlinear equivalent conicity and wheel-rail force[J]. Nonlinear Dynamics,2020,102(1):79-100.
[17] CHENG L,WEI X,CAO H. Two-parameter bifurcation analysis of limit cycles of a simplified railway wheelset model[J]. Nonlinear Dynamics,2018,93(4):2415-2431.
[18] ZHANG T,DAI H. Bifurcation analysis of high-speed railway wheel-set[J]. Nonlinear Dynamics,2016,83(3):1511-1528.
[19] DONG H,ZENG J,WU L,et al. Analysis of the gyroscopic stability of the wheelset[J]. Shock and Vibration,2014,2014:1-7.
[20] KNOTHE K,BOHM F. History of stability of railway and road vehicles[J]. Vehicle System Dynamics,1999,31(5-6):283-323.
[21] NATH Y,JAYADEV K. Influence of yaw stiffness on the nonlinear dynamics of railway wheelset[J]. Communications in Nonlinear Science and Numerical Simulation,2005,10(2):179-190.
[22] JESUSSEK M,ELLERMANN K. Fault detection and isolation for a nonlinear railway vehicle suspension with a hybrid extended kalman filter[J]. Vehicle System Dynamics,2013,51(10):1489-1501.
[23] SUDA Y,SHIBANO K,MATSUMOTO A,et al. Dynamic characteristics of a single-axle truck for compatibility between stability and curving performance[J]. Vehicle System Dynamics,2002,37(Suppl.1):616-629.
[24] LUO R,SHI H,TENG W,et al. Prediction of wheel profile wear and vehicle dynamics evolution considering stochastic parameters for high-speed train[J]. Wear,2017,392:126-138.
[25] KAISER I,STRANO S,TERZO M,et al. Anti-yaw damping monitoring of railway secondary suspension through a nonlinear constrained approach integrated with a randomly variable wheel-rail interaction[J]. Mechanical Systems and Signal Processing,2021,146:107040.
[26] 刘伟渭,戴焕云,刘转华,等. 弹性约束轮对系统的随机Hopf分岔研究[J]. 铁道学报,2013,35(10):38-45. LIU Weiwei,DAI Huanyun,LIU Zhuanhua,et al. Research on stochastic Hopf bifurcation of elastic constraint wheelset system[J]. Journal of the China Railway Society,2013,35(10):38-45.
[27] 张波,朱海燕,曾京,等. 轮对系统随机动态分叉研究[J]. 铁道学报,2020,42(1):24-32. ZHANG Bo,ZHU Haiyan,ZENG Jeng,et al. Research on stochastic dynamical bifurcation in wheelset system[J]. Journal of the China Railway Society,2020,42(1):24-32.
[28] CLAUS H,SCHIEHLEN W. Dynamic stability and random vibrations of rigid and elastic wheelsets[J]. Nonlinear Dynamics,2004,36 (2):299-311.
[29] MEI T. GOODALL R. Wheelset control strategies for a two-axle railway vehicle[J]. Vehicle System Dynamics,2000,33:653-664.
[30] 武世江,张继业,隋皓,等. 轮对系统的Hopf分岔研究[J]. 力学学报,2021,53(9):2569-2581. WU Shijiang,ZHANG Jiye,SUI Hao,et al. Hopf bifurcation study of wheelset system[J]. Chinese Journal of Theoretical and Applied Mechanics,2021,53(9):2569-2581.
[31] QIAN J,CHEN L. Stochastic P-bifurcation analysis of a novel type of unilateral vibro-impact vibration system[J]. Chaos,Solitons & Fractals,2021,149:111112.

轮对非线性随机动力学模型稳定性及分岔研究

Research on Stability and Bifurcation of Nonlinear Stochastic Dynamic Model of Wheelset

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 3

编辑推荐

Metrics

本文评价

[1]	石怀龙, 郭金莹, 王勇. 变轨距高速列车的动力学[J]. 机械工程学报, 2020, 56(20): 98-105.
[2]	罗仁;曾京. 列车系统蛇行运动稳定性分析及其与单车模型的比较[J]. , 2008, 44(4): 184-188.
[3]	翟婉明;王开云;陈建政. 铁路货车横向非线性动态行为的理论与试验研究[J]. , 2008, 44(11): 138-144.