Nonlinear Dynamics Analysis of the Body Sway of Car-trailer Combinations

doi:10.3901/JME.2019.24.127

Abstract

Abstract: Considering the nonlinear characteristics of tires and shock absorbers, a 5-DOFs theoretical dynamics model describing the lateral, yaw and roll motions of car-trailer combinations is established. Based on the theory of nonlinear dynamics, the multi-equilibrium points characteristics and the time-domain responses near the equilibrium points of car-trailer combinations are analyzed. Combining with the understeer gradient and damping ratio, the generation mechanism of the system instability is investigated. The influences of the trailer system parameters and the tire-road friction coefficient on the system critical speed are considered as well. The simulation results reveal that due to the nonlinear coupling of shock absorbers and tire, the car-trailer combination has multiple equilibrium states, and the system instability under a specific initial state is determined by the closest equilibrium point. With the understeer gradient, the jackknife phenomenon caused by the sideslip of the rear axle of the towing car is a primary system instability when the towing car is oversteered. From the perspective of stability control, the system instability can be effectively avoided via a yaw rate control strategy applied in the towing car. In addition, the stability of car-trailer combinations can be improved by increasing the wheelbase of trailer and the distance between front axle of trailer and traction point.

Key words: car-trailer combinations, body sway, multi-equilibrium points bifurcation, understeer gradient, nonlinear dynamics

CLC Number:

U461

ZHANG Ning, LI Tian, MA Jian, YIN Guodong, ZHU Weigang, OUYANG Tiancheng. Nonlinear Dynamics Analysis of the Body Sway of Car-trailer Combinations[J]. Journal of Mechanical Engineering, 2019, 55(24): 127-136.

References

[1] 温品文. 中国汽车拖挂运输纪实[M]. 成都:四川大学出版社, 2008. WEN Pinwen. Car-trailer transport documentary in China[M]. Chengdu:Sichuan University Press, 2008.
[2] BENNETT S, NORMAN I A. Heavy duty truck systems[M]. New York:Delmar Cengage Learning, 2011.
[3] EDWARD F, KURTZ J, RONALD J A. Handling characteristics of car-trailer systems:a state-of-the-art survey[J]. Vehicle System Dynamics,1977,6(4):217-243.
[4] 张宁,殷国栋,陈南,等. 车辆动力学中的摆振问题研究现状综述[J]. 机械工程学报, 2017, 53(14):16-28. ZHANG Ning, YIN Guodong, CHEN Nan, et al. A state-of-the-art survey on shimmy problem in vehicle dynamics[J]. Journal of Mechanical Engineering, 2017, 53(14):16-28.
[5] 李军,方春杰,束海波. 紧急制动工况下车辆的PI稳定性控制[J]. 华侨大学学报, 2017(2):135-140. LI Jun, FANG Chunjie, SHU Haibo. PI stability control of vehicle under emergency braking conditions[J]. Journal of Huaqiao University, 2017(2):135-140.
[6] 杨炜,魏朗,刘晶郁. 商用车横向稳定性优化控制联合仿真分析[J]. 机械工程学报, 2017, 53(2):115-123. YANG Wei, WEI Lang, LIU Jingyu. Co-simulation analysis of commercial vehicle lateral stability optimization control[J]. Journal of Mechanical Engineering, 2017, 53(2):115-123.
[7] 赵树恩,李玉玲,于强. 基于底盘多子系统协调控制的车辆稳定性控制[J]. 交通运输工程学报, 2015, 15(4):77-85. ZHAO Shuen, LI Yuling, YU Qiang. Vehicle stability control based on chassis multiple subsystem coordinated control[J]. Journal of Traffic and Transportation Engineering, 2015, 15(4):77-85.
[8] MARCH C, SHIM T. Integrated control of suspension and front steering to enhance vehicle handling[J]. Part D:Journal of Automobile Engineering, 2007, 221(4):377-391.
[9] 宗长富,麦莉,李雅娟. 重型半挂车的动力学建模及侧倾稳定性分析[J]. 辽宁工业大学学报, 2008, 28(1):52-56. ZONG Changfu, MAI Li, LI Yajuan. Dynamic modeling and roll stability analysis of heavy tractor semi-trailers[J]. Journal of Liaoning University of Technology. 2008, 28(1):52-56.
[10] 李韶华,杨绍普,陈立群. 三向耦合非线性重型汽车建模及动力学分析[J]. 振动与冲击, 2014, 33(22):131-138. LI Shaohua, YANG Shaopu, CHEN Liqun. Modeling and dynamic analysis of a non-linear heavy vehicle with three-directional coupled motions[J]. Journal of Vibration and Shock, 2014, 33(22):131-138.
[11] HAC A, FULK D, CHEN H. Stability and control considerations of vehicle-trailer combination[J]. Sae International Journal of Passenger Cars Mechanical Systems, 2009, 1(1):925-937.
[12] 韦超毅,李贝,谢美芝. 半挂汽车列车操纵稳定性仿真研究[J]. 机械设计与制造, 2011, 10(3):129-131. WEI Yichao, LI Bei, XIE Meizhi. Simulation research on handling stability of tractor-semitrailer[J]. Machinery Design & Manufacture, 2011, 10(3):129-131.
[13] ZHANG N, SHAO Z J, XIAO H, et al. Stability investigation of car-trailer combinations depending on damper properties[C]//Proceedings of the 24th Symposium of the International Association for Vehicle System Dynamics, 2015:169-177.
[14] ZHANG N, ZHU W G, LIU T, et al. The influence of damping failure phenomenon on dynamic stability of cartrailer combinations[C]//25th International Symposium on Dynamics of Vehicles on Roads and Tracks, 2017:447-452.
[15] 关志伟,许洪国,刘宏飞,等. 基于闭环非线性系统的半挂汽车列车行驶稳定性分析[J]. 吉林大学学报, 2005, 35(6):587-591. GUAN Zhiwei, XU Hongguo, LIU Hongfei, et al. Analysis of tractor-semitrailer driving stability based on closed loop nonlinear system[J]. Journal of Jilin University of Technology, 2005, 35(6):587-591.
[16] 刘焕. 半挂汽车列车三自由度平面运动稳定性分析[D]. 长春:吉林大学, 2016. LIU Huan. Stability analysis of plane motion of threedegree-freedom of tractor-semitrailers[D]. Changchun:Jilin University, 2016.
[17] 张宁,琚安建,李鹏程,等. 悬架减震器非线性特性对汽车拖车组合系统稳定性的影响[J]. 东南大学学报, 2017, 47(2):247-253. ZHANG Ning, JU Anjian, LI Pengcheng, et al. Impact Study of nonlinear characteristics of suspension dampers on the stability of car-trailer combinations[J]. Journal of Southeast University, 2017, 47(2):247-253.
[18] 麦莉,宗长富,高越,等. 重型半挂车侧倾稳定性仿真与分析[J]. 吉林大学学报, 2008, 38(2):5-10. MAI Li, ZONG Changfu, GAO Yue, et al. Simulation and analysis of roll stability for heavy tractor semi-trailers[J]. Journal of Jilin University, 2008, 38(2):5-10.
[19] SHEN S W, WANG J, SHI P, et al. Nonlinear dynamics and stability analysis of vehicle plane motions[J]. Vehicle System Dynamics, 2007, 45(1):15-35.
[20] BAKKER E, PACEJKA H B, LIDNER L. A new tire model with an application in vehicle dynamics studies[J]. SAE Transactions, 1989(2):101-113.
[21] CHRISTOPHER B, MEHDI A, STEVE S. Efficient empirical modeling of a high-performance shock absorber for vehicle dynamics studies[J]. Vehicle System Dynamics, 2010, 48(4):481-505.
[22] RICHARD V K, WANG C G, QIAN L X, et al. A new shock absorber model with an application in vehicle dynamics studies[C]//SAE International Truck and Bus Meeting and Exhebition, 2003:3411-3420.
[23] ZHANG N, XIAO H, WINNER H. Nonlinearity-induced time-varying harmonic dynamic axle load and its impact on dynamic stability of car-trailer combinations[J]. Vehicle System Dynamics, 2016, 54:848-870.
[24] ZHANG N. Stability investigation of car-trailer combinations based on time-frequency analysis[D]. Darmstadt:Technische Universität Darmstadt, 2015.
[25] WU D H. A theoretical study of the yaw/roll motions of a multiple steering articulated vehicle[J]. Proc. IMechE. Part D:J Automobile Engineering, 2001, 215:1257-1265.
[26] GUCKENHIMER J, HOLMES P. Nonlinear oscillations, dynamical systems and bifurcations of vector fields[M]. New York:Springer-Verlag, 1983.
[27] 杨秀建, 李西涛. 半挂汽车列车操纵特性与横向稳定性的研究[J]. 汽车工程, 2012, 12(34):1107-1113. YANG Xiujian, LI Xitao. A study on the handling characteristics and lateral stability of tractor-semitrailer combination[J]. Automotive Engineering, 2012, 12(34):1107-1113.
[28] 林逸, 李胜. 非独立悬架汽车转向轮自激型摆振的分岔特性分析[J]. 机械工程学报, 2004(12):187-191. LIN Yi, LI Sheng. Study on the bifurcation character of steering wheel self-excited shimmy of motor vehicle with dependent suspension[J]. Chinese Journal of Mechanical Engineering, 2004(12):187-191.
[29] 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[J]. 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[J]. Acta Mechanica Sinica, 2000, 32(5):596-605.
[30] 杨秀建,李耀平,熊坚. 半挂汽车列车横向稳定性与失稳机理分析[J]. 汽车工程, 2011, 33(6):466-492 YANG Xiujian, LI Yaoping, XIONG Jian. Analysis on the lateral stability and instability mechanism of tractorsemitrailer combination[J]. Automotive Engineering, 2011, 33(6):466-492.