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

doi:10.3901/JME.2023.10.210

Abstract

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

CLC Number:

U271

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.

References

[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.