Longitudinal Dynamic Model of Tire Considering Hysteresis Characteristics

doi:10.3901/JME.2023.12.364

Abstract

Abstract: Tires are the only earthed part of the vehicle, which provide all the driving, steering, and braking force needed by the vehicle to move. The tire model is the basis for automobile dynamics, the further development of vehicle dynamics and control technology depends on accurate tire modeling technology. A simplified tire physical model considering the tire deformation hysteresis is proposed. Combined with the resistor-capacitor(RC) hysteresis operator, hysteresis characteristics of the tire in compression and rebound of the body, loading and unloading of braking force are analyzed, and the tire steady-state model HysTire and dynamic model Dyn-HysTire under longitudinal slip conditions are established respectively. To verify the accuracy of HysTire model and Dyn-HysTire model, the Pirelli tire test data of longitudinal slip condition are modeled. The modeling results show that the steady-state HysTire model and the Magic Formula(MF) have similar fitting precision, while the Mean Square Error(MSE) value of the dynamic Dyn-HysTire model which introduces the slip change rate decreases by about 30% comparing to MF, which significantly improves the tire simulation accuracy. In addition, Dyn-HysTire model also can express tire unsteady characteristics comparable to LuGre model and PAC2002 model. Finally, it is further verified in the 1/4 vehicle ABS simulation. The results show that compared with the MF, the Dyn-Hystire model with hysteresis characteristics can better reflect the real mechanical characteristics of tires, and the simulation accuracy of vehicle dynamics is improved.

Key words: semi-empirical tire model, hysteresis characteristics, longitudinal dynamics, steady state, dynamic state

CLC Number:

U461

DUAN Shunchang, XU Nan, SHI Qin, BAI Xianxu. Longitudinal Dynamic Model of Tire Considering Hysteresis Characteristics[J]. Journal of Mechanical Engineering, 2023, 59(12): 364-372.

References

[1] 何仁,李梦琪. 基于路面识别的复合制动与ABS集成控制策略[J]. 江苏大学学报(自然科学版),2020,41(1):20-26. HE Ren,LI Mengqi. Integrated control strategy of combined braking system and ABS based on road identification[J]. Journal of Jiangsu University(Natural Science Eidtion),2020,41(1):20-26.
[2] PENG H,CHEN X B. Active safety control of X-by-wire electric vehicles:A survey[J]. SAE Int. J. Veh. Dyn., Stab., and NVH,2022,6(2):115-133.
[3] 李顶根,张绿原,何保华. 基于滑移率的汽车电子机械制动系统的模糊控制[J]. 机械工程学报,2012,48(20):124-129. LI Dinggen,ZHANG Lüyuan,HE Baohua. Fuzzy control based on vehicle slip-ratio for electro-mechanical braking systems[J]. Journal of Mechanical Engineering,2012,48(20):124-129.
[4] 李韶华,周军魏,张志达. 轮胎三向动态特性试验及非线性建模[J]. 机械工程学报,2018,54(18):85-96. LI Shaohua,ZHOU Junwei,ZHANG Zhida. Experiment and nonlinear modeling on tire dynamic characteristics of three directional[J]. Journal of Mechanical Engineering,2018,54(18):85-96.
[5] GIM G,NIKRAVESH P E. A three dimensional tire model for steady-state simulations of vehicles[J]. SAE Transactions,1993:150-159.
[6] DUGOFF H,FANCHER P S,SEGEL L. An analysis of tire traction properties and their influence on vehicle dynamic performance[J]. SAE Transactions,1970:1219-1243.
[7] 彭晓燕,章兢,陈昌荣. 基于RBF神经网络的最佳滑移率在线计算方法[J]. 机械工程学报,2011,47(14):108-113. PENG Xiaoyan,ZHANG Jing,CHEN Changrong. Calculation of RBF neural network based optimal slip ratio[J]. Journal of Mechanical Engineering,2011,47(14):108-113.
[8] PACEJKE H B,BBAKER E. The magic formula tyre model[J]. Vehicle System Dynamics,1992,21(1):1-18.
[9] PACEJKE H B,BESSELINK I J M. Magic formula tyre model with transient properties[J]. Vehicle System Dynamics,1997,27(S1):234-249.
[10] GUO K H,LU D. UniTire:Unified tire model for vehicle dynamic simulation[J]. Vehicle System Dynamics,2007,45(S1):79-99.
[11] 郭孔辉,袁忠诚,卢荡. UniTire轮胎稳态模型的联合工况预测能力研究[J]. 汽车工程,2006,28(6):565-568. GUO Konghui,YUAN Zhongcheng,LU Dang. A study on the prediction capability of UniTire model for combined slips mode[J]. Automotive Engineering,2006,28(6):565-568.
[12] 郭孔辉. UniTire统一轮胎模型[J]. 机械工程学报,2016,52(12):90-99. GUO Konghui. UniTire:Unified tire model[J]. Journal of Mechanical Engineering,2016,52(12):90-99.
[13] 危银涛,沈筱亮. 轮胎稳态运动学与六分力预报I:理论与方法[J]. 机械工程学报,2012,48(15):65-74. WEI Yintao,SHEN Xiaoliang. Theory and method of tire rolling kinematics and prediction of tire forces and moments[J]. Journal of Mechanical Engineering,2012,48(15):65-74.
[14] XU N,YANG Y,GUO K. A discrete tire model for cornering properties considering rubber friction[J]. Automot. Innov.,2020,3:133-146.
[15] LU Y,ZHANG J,YANG S,et al. Study on improvement of LuGre dynamical model and its application in vehicle handling dynamics[J]. J Mech Sci Technol,2019,33:545-558.
[16] PACEJKE H B. (1934-2017):A life in tyre mechanics[J]. Vehicle System Dynamics,2021,59(8):1304-1311.
[17] KUIPER E,VAN OOSTEN J J M. The PAC2002 advanced handling tire model[J]. Vehicle System Dynamics,2007,45(S1):153-167.
[18] LI B,YANG X B,YANG J. In-plane flexible ring tire model parameter identification:Optimization algorithms[J]. SAE Int. J. Veh. Dyn.,Stab.,and NVH,2018,2(1):71-87.
[19] 吴杰,上官文斌,潘孝勇. 采用超弹性-黏弹性-弹塑性本构模型的橡胶隔振器动态特性计算方法[J]. 机械工程学报,2010,46(14):109-114. WU Jie,SHANGGUAN Wenbin,PAN Xiaoyong. Computational method for dynamic properties of rubber isolators using hyperelastic-viscoelastic-plastoelastic constitutive model[J]. Journal of Mechanical Engineering,2010,46(14):109-114.
[20] BOUC R. A mathematical model for hysteresis[J]. Acta Acustica united with Acustica,1971,24(1):16-25.
[21] WEN Y K. Method for random vibration of hysteretic systems[J]. Journal of the Engineering Mechanics Division,1976,102(2):249-263.
[22] STANWAY R. Smart fluids:current and future developments[J]. Materials Science and Technology,2004,20(8):931-939.
[23] CHEN P,BAI X X,QIAN L J,et al. An approach for hysteresis modeling based on shape function and memory mechanism[J]. IEEE/ASME Transactions on Mechatronics,2018,23(3):1270-1278.
[24] BAI X X,CAI F L,CHEN P. Resistor-capacitor (RC) operator-based hysteresis model for magnetorheological (MR) dampers[J]. Mechanical Systems and Signal Processing,2019,117:157-169.
[25] 赵又群. 一种非充气机械弹性安全车轮的研究进展[J]. 机械工程学报,2019,55(24):105-116. ZHAO Youqun. Research progress on kind of non-pneumatic mechanical elastic safety wheel[J]. Journal of Mechanical Engineering,2019,55(24):105-116.
[26] ROLLER M,BETSCH P,GALLERIN A,et al. An enhanced tire model for dynamic simulation based on geometrically exact shells[J]. Archive of Mechanical Engineering,2016,63(2):277-295.
[27] 胡国良,林豪,李刚. 采用磁流变阻尼器的三自由度半主动座椅悬架系统变论域模糊控制[J]. 机械科学与技术,2020,39(3):425-432. HU Guoliang,LIN Hao,LI Gang. Variable universe fuzzy control of 3-DOF semi-active seat suspension system using magnetorheological damper[J]. Mechanical Science and Technology for Aerospace Engineering,2020,39(3):425-432.
[28] DUAN S C,BAI X X,SHI Q,et al. Nonlinear dynamics analysis in pneumatic tire modeling[J]. Nonlinear Dynamics,2023,111:1095-1107.