特邀专栏:汽车先进动力系统的设计、优化与控制专栏(上)

车辆动力学中的摆振问题研究现状综述

  • 张宁 ,
  • 殷国栋 ,
  • 陈南 ,
  • 弥甜 ,
  • 李鹏程
展开
  • 东南大学机械工程学院 南京 211189

收稿日期: 2016-09-05

  修回日期: 2017-02-05

  网络出版日期: 2017-07-20

基金资助

国家自然科学基金(51605087,51375086)、江苏省自然科学基金青年基金(BK20160671)和中央高校基本科研业务费专项资金(2242017K40197)资助项目。

A State-of-the-Art Survey on Shimmy Problem in Vehicle Dynamics

  • ZHANG Ning ,
  • YIN Guodong ,
  • CHEN Nan ,
  • MI Tian ,
  • LI Pengcheng
Expand
  • School of Mechanical Engineering, Southeast University, Nanjing 211189

Received date: 2016-09-05

  Revised date: 2017-02-05

  Online published: 2017-07-20

摘要

针对汽车工程中存在的两类摆振问题,车轮摆振和车身摆振,分别描述它们的行为和产生机理,综述国内外对此两类摆振问题的研究的发展历程以及主要的研究成果。摆振现象本质上是较为复杂的非线性动力学行为,针对此问题的研究在理论和实践上都存在很多困难。无论是车轮摆振还是车身摆振,首先它们都是非线性系统自激振荡的表现,其次它们的产生都归因于轮胎接地力对系统做正功,向系统输入的能量恰好能够维持系统摆振行为的产生。同时,包含弹性轮胎的车轮子系统、转向子系统和悬架子系统是影响两种摆振行为的三大关键因素。鉴于摆振问题仍然是汽车动力学领域的研究难点之一以及新型汽车的快速发展,本文也指出了摆振研究目前仍存在的一些问题,并对此类问题的进一步工作进行展望。

本文引用格式

张宁 , 殷国栋 , 陈南 , 弥甜 , 李鹏程 . 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 . DOI: 10.3901/JME.2017.14.016

Abstract

Two types of shimmy problems in automotive engineering, wheel shimmy and vehicle body shimmy, as well as their behaviors and generation mechanism, are discussed in this paper. A review of their research history and significant achievements at home and abroad are presented as the main part of this paper. The shimmy phenomenon is essentially a very intricate nonlinear dynamics behavior, and many questions in theory and in practice still have to be answered. Both wheel shimmy and vehicle body shimmy are self-excited oscillations of nonlinear systems, and they can be attributed to the positive work generated by the forces at the contact patch between the tires and ground. The continuation of the shimmy behavior is just maintained by the input energy to the system. Meanwhile, the wheel subsystem with elastic tires, the steering subsystem and the suspension subsystem are the three key sources where influences on the shimmy behavior come from. Seeing that the shimmy problems are still challenges in vehicle dynamics and might change for the rapid developing new energy automobiles, the existing problems related to shimmy and their future research perspective are presented as well.

参考文献

[1] BECKER G,FROMM H,MARUHN H. Schwingungen in Automobil-lenkungen (‘Shimmy’)[M]. Berlin:M.Krayn,technischer Verlag gmbh, 1931. BECKER G,FROMM H,MARUHN H. Vibrations in Steering of Automobiles (‘Shimmy’)[M]. Berlin:M.Krayn, technischer Verlag gmbh, 1931.
[2] Von SCHLIPPE B,DIETRICH R. Das flattern eines bepneuten rades[R]. Bericht 140 der Lilienthal Gesellschaft,1941:NACA TM 1365. Von SCHLIPPE B,DIETRICH R. Shimmy of a pneumatic wheel[R]. Technical Report,English Translation 1941:NACA TM 1365.
[3] Von SCHLIPPE B,DIETRICH R. Zur mechanik des luftreifens[J]. Zentrale für wissenschaftliches Berichtwesen,1942,17(1):129-141. Von SCHLIPPE B,DIETRICH R. Mechanics of pneumatic tyres[J]. Zentrale für wissenschaftliches Berichtwesen,1942,17(1):129-141.
[4] Von SCHLIPPE B,DIETRICH R. Das flattern eines mit luftreifen versehenen rades[R]. Jahrbuch der deutsche Luftfahrtforschung,1943. Von SCHLIPPE B,DIETRICH R. Flutter of a wheel with pneumatic tire[R]. Jahrbuch der deutsche Luftfahrtfors-chung,1943.
[5] PACEJKA H B. The wheel shimmy phenomenon[D]. Delft:TU Delft,1966.
[6] BESSELINK I J M. Shimmy of aircraft main landing gears[D].Delft:TU Delft,2000.
[7] RAN S,BESSELINK I J M,NIJMEIJER H. Application of nonlinear tyre models to analyse shimmy[J]. Vehicle System Dynamics,2014,52(Suppl.1):387-404.
[8] RAN S,BESSELINK I J M,NIJMEIJER H. Energy analysis of the Von Schlippe tyre model with application to shimmy[J]. Vehicle System Dynamics,2015,53(12):1795-1810.
[9] RAN S,BESSELINK I J M,NIJMEIJER H. Energy balance and tyre motions during shimmy[C]//Proceedings of the 4th International Tyre Colloquium-Tyre Models for Vehicle Dynamics Analysis,Surrey,UK,2015,April 20-21,129-138.
[10] RAN S. Tyre models for shimmy analysis:From linear to nonlinear[D]. Eindhoven:TU Eindhoven,2016.
[11] SOMIESKI G. An eigenvalue method for calculation of stability and limit cycles in nonlinear systems[J]. Nonlinear Dynamics,2001,26(1):3-22.
[12] AYGLON V,JALILI N,HAQUE I. Nonlinear modeling and experimental validation of tire nonuniformity induced tangential steering wheel vibrations[C]//ASME 2006 International Mechanical Engineering Congress and Exposition,American Society of Mechanical Engineers,2006:553-561.
[13] STÉPÁN G. Delay,nonlinear oscillations and shimmying wheels[M]. Berlin:Springer,1999.
[14] TAKÁCS D,STÉPÁN G. Experiments on quasiperiodic wheel shimmy[J]. Journal of Computational and Nonlinear Dynamics,2009,4(3):983-990.
[15] TAKÁCS D,STÉPÁN G. Micro-shimmy of towed structures in experimentally uncharted unstable parameter domain[J]. Vehicle System Dynamics,2012,50(11):1613-1630.
[16] STÉPÁN G. Wheel shimmy and delayed tyre models[C/CD]//Proceedings of the 11th International Conference on Vibration Problems,Lisbon,Portugal,Sep. 9-12,2013.
[17] TAKÁCS D. Dynamics of towed wheels:Nonlinear theory and experiments[D]. Hungary:Budapest University of Technology and Economics,2010.
[18] TAKÁCS D,STÉPÁN G. Study on contact patch memory and travelling waves of tyres[C]//Proceedings of the 4th International Tyre Colloquium-Tyre Models for Vehicle Dynamics Analysis,Surrey,UK,2015:121-128.
[19] ZHURAVLEV V P,KLIMOV D M,PLOTNIKOV P K. A new model of shimmy[J]. Mechanics of Solids,2013,48(5):490-499.
[20] STUART J,CASSARA S,CHAN B,et al. Recent experimental and simulation efforts to mitigate wobble and shimmy in commercial line haul vehicles[J]. SAE International Journal of Commercial Vehicles,2014,7(2):366-380.
[21] DUTTA S,CHOI S B. Control of a shimmy vibration in vehicle steering system using a magneto-rheological damper[J]. Journal of Vibration and Control,2016,1(11):36-47.
[22] 管迪华,魏克严,胡师金,等. 汽车转向轮摆振的仿真计算研究[J]. 汽车工程,1982,4(1):33-38. GUAN Dihua,WEI Keyan,HU Shijin,et al. Research on the simulation of vehicle steering wheel shimmy[J]. Automotive Engineering,1982,4(1):33-38.
[23] 管迪华,何泽民,肖田元,等. 汽车转向轮振动的研究[J]. 汽车工程,1984(2):29-40. GUAN Dihua,HE Zemin,XIAO Tianyuan,et al. Study on vibration of automobile steering wheel[J]. Automotive Engineering,1984(2):29-40.
[24] 宋健. 导向轮轮胎和定位参数对汽车摆振影响的研究及整车横向动力学优化分析[D]. 北京:清华大学,1989. SONG Jian. Study on the effect of steering wheel tire and positioning parameters on vehicle shimmy and vehicle lateral dynamics optimization[D]. Beijing:Tsinghua University,1989.
[25] 钱珠声. 独立悬架汽车转向轮摆振的研究[D]. 北京:清华大学,1995. QIAN Zhusheng. Research on the steering wheel shimmy of independent suspension vehicle[D]. Beijing:Tsinghua University,1995.
[26] 郭孔辉. 轮胎动态侧偏特性对汽车摆振的影响[J]. 汽车技术,1995(4):1-6. GUO Konghui. Dynamic characteristics of wheel tire lateral distortion mechanics of motor vehicle[J]. Automobile Technology,1995(4):1-6.
[27] 詹文章. 汽车独立悬架多体系统动力学仿真及转向轮高速摆振研究[D]. 长春:吉林大学,2000. ZHAN Wenzhang. Study on multi-body system dynamics of the vehicle independent suspension simulation and the steering wheel shimmy at high speed[D]. Changchun:Jilin University,2000.
[28] 李胜. 分岔理论在汽车转向轮摆振机理及其控制策略研究中的应用[D]. 长春:吉林大学,2005. LI Sheng. Study on mechanism and control strategies of vehicle steering wheel shimmy with bifurcation theories[D]. Changchun:Jilin University,2005.
[29] 杨树凯,卢荡,张海涛,等. 前轮摆振机理分析[J]. 科学技术与工程,2015,15(32):221-223. YANG Shukai,LU Dang,ZHANG Haitao,et al. Mechanism analysis of the front wheel shimmy[J]. Science Technology and Engineering,2015,15(32):221-223.
[30] 熬策划,杨树凯,卢荡,等. 前轮摆振机理再分析[J]. 科学技术与工程,2016,16(4):246-248. AO Chehua,YANG Shukai,LU Dang,et al. The future mechanism analysis of the front wheel shimmy[J]. Science Technology and Engineering,2016,16(4):246-248.
[31] 张琪昌,李小涛,田瑞兰. 汽车转向轮摆振的稳定性及分岔行为分析[J]. 振动与冲击,2008,27(1):84-88. ZHANG Qichang,LI Xiaotao,TIAN Tuilan. Study on stability and bifurcation behavior of a car turning wheel shimmy[J]. Journal of Vibration and Shock,2008,27(1):84-88.
[32] 车华军,陈南,殷国栋. 基于遗传算法的一类越野车前轮摆振控制优化设计[J]. 中国机械工程,2006(24):2635-2638. CHE Huajun,CHEN Nan,YIN Guodong. Optimum design of wheel shimmy control for a kind of off-road vehicle based on genetic algorithm[J]. China Mechanical Engineering,2006(24):2635-2638.
[33] MI T,STÉPÁN G,TAKÁCS D,et al. A novel shimmy model of electric vehicle with independent suspensions[C/CD]//Proceedings of IUTAM Symposium on Nonlinear and Delayed Dynamics of Mechatronic Systems,October 17-21,Nanjing,China,2016.
[34] 肖闯,殷智宏. 单转向轮摆振非线性动力学研究[J]. 中国机械工程,2013,24(8):1131-1135. XIAO Chuang,YIN Zhihong. Research on nonlinear dynamics of caster wheel shimmy[J]. China Mechanical Engineering,2013,24(8):1131-1135.
[35] 卢剑伟,顾鴃,王其东. 运动副间隙对汽车摆振系统非线性动力学行为影响分析[J]. 机械工程学报,2008,44(8):169-173. LU Jianwei,GU Jue,WANG Qidong. Influence analysis of movement pair clearance on nonlinear dynamic behavior of vehicle shimmy system[J]. Chinese Journal of Mechanical Engineering,2008,44(8):169-173.
[36] 卢剑伟,陈昊,辛加运,等. 转向传动机构间隙对车辆摆振系统动力学行为的影响分析[J]. 振动与冲击,2013,32(16):171-175. LU Jianwei,CHEN Hao,XIN Jiayun,et al. Influence of steering linkage clearance on dynamic behavior of shimmy system[J]. Journal of Vibration and Shock,2013,32(16):171-175.
[37] 卢剑伟,辛加运,张士路. 考虑转向操纵机构万向节间隙的车辆摆振系统动力学行为分析[J]. 汽车工程,2014,36(7):853-856. LU Jianwei,XIN Jiayun,ZHANG Shilu. Dynamics behavior analysis on vehicle shimmy system considering the clearance in universal joint of steering handling mechanism[J]. Automotive Engineering,2014,36(7):853-856.
[38] LU J W,XU Y,HU C,et al. 5-DOF dynamic model of vehicle shimmy system with clearance at universal joint in steering handling mechanism[J]. Shock and Vibration,2013,20(5):951-961.
[39] LU J W,XIN J Y,VAKAKIS A F,et al. Influences of system parameters on dynamic behavior of the vehicle shimmy system with clearance in steering linkage[J]. Journal of Vibration and Control,2015,21(2):359-370.
[40] LU J W,JIANG J,LI J,et al. Analysis of dynamic mechanism and global response of vehicle shimmy system with multi-clearance joints[J]. Journal of Vibration and Control,2016,1(15):156-167.
[41] 胡辰,卢剑伟,许生. 动不平衡激励下光滑非线性车辆摆振系统建模分析[J]. 振动与冲击,2013,32(20):86-89. HU Chen,LU Jianwei,XU Sheng. Dynamic response of a vehicle smooth nonlinear shimmy system with excitation of dynamic unbalance[J]. Journal of Vibration and Shock,2013,32(20):86-89.
[42] 蒋艮生,魏道高. 前轮主销后倾角对汽车自激摆振影响研究[J]. 合肥工业大学学报,2012,35(1):9-12. JIANG Gensheng,WEI Daogao. Study of the effect of front wheel caster angle on self-excited shimmy of vehicle[J]. Journal of Hefei University of Technology,2012,35(1):9-12.
[43] 张志龙,潘宁,魏道高. 转向系参数对汽车自激摆振多极限环特性影响研究[J]. 农业装备与车辆工程,2014,52(10):1-6. ZHANG Zhilong,PAN Ning,WEI Daogao. Influence of steering parameters on self-excited shimmy with multi-limit cycle[J]. Agricultural Equipment and Vehicle Engineering,2014,52(10):1-6.
[44] WEI Daogao,XU Ke,JIANG Yibin,et al. Hopf bifurcation characteristics of dual-front axle self-excited shimmy system for heavy truck considering dry friction[J]. Shock and Vibration,2015,25(1):1-20.
[45] WEI Daogao,JIANG Tong,CHEN Changhe,et al. Hopf bifurcation character of an interactive vehicle-road shimmy system under bisectional road conditions[J]. Proceedings of the IMechE Part D:Journal of Automobile Engineering,2016,231(3):405-417.
[46] 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,2004,40(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,2004,40(12):187-191.
[47] 林逸,贺丽娟. 汽车前轮摆振非线性研究综述[J]. 农业机械学报,2007,38(11):174-177. LIN Yi,HE Lijuan. Overview of automobile front wheel shimmy in nonlinear field[J]. Transactions of the Chinese Society for Agricultural Machinery,2007,38(11):174-177.
[48] 王威,宋玉玲,李瑰贤. 独立悬架汽车转向系间隙与干摩擦对其Hopf分岔特性的影响[J]. 机械工程学报,2011,47(2):130-135. WANG Wei,SONG Yuling,LI Guixian. Influence of independent suspension automotive steering clearance and coulomb friction on Hopf bifurcation characteristic[J]. Journal of Mechanical Engineering,2011,47(2):130-135.
[49] 王威,宋玉玲,薛彦冰. 高速下轿车转向系非线性振动的分岔特性[J]. 机械工程学报,2012,48(9):103-110. WANG Wei,SONG Yuling,XUE Yanbing. Bifurcation characteristics on nonlinear vibration of its steering system when car running at a high speed[J]. Journal of Mechanical Engineering,2012,48(9):103-110.
[50] 王威,陈军,宋玉玲. 含双间隙模型轿车转向系非线性动力学特性研究[J]. 农业机械学报,2013,44(10):41-46. WANG Wei,CHEN Jun,SONG Yuling. Nonlinear dynamic characteristics of car's steering system with double clearance models[J]. Transactions of the Chinese Society for Agricultural Machinery,2013,44(10):41-46.
[51] 王威,陈军,宋玉玲. 轿车转向系与前悬架耦合动力学特性研究[J]. 农业机械学报,2013,44(12):17-21. WANG Wei,CHEN Jun,SONG Yuling. Coupled dynamic characteristics of car steering system and front suspension system[J]. Transactions of the Chinese Society for Agricultural Machinery,2013,44(12):17-21.
[52] 王威,宋玉玲,李瑰贤. 基于增量谐波平衡方法的汽车转向系非线性动力学特性研究[J]. 振动工程学报,2010,23(3):355-360. WANG Wei,SONG Yuling,LI Guixian. Nonlinear dynamics of automobile steering using incremental harmonic balance method[J]. Journal of Vibration Engineering,2010,23(3):355-360.
[53] 张立军. 前轮摆振对车辆稳定性的影响及后轮反馈控制[J]. 噪声与振动控制,2015,35(6):61-64. ZHANG Lijun. Influence of front wheels shimmy on vehicle stability and rear wheels feedback control[J]. Noise and Vibration Control,2015,35(6):61-64.
[54] 李欣业,贺丽娟,董正身,等. 解放CA10型载货汽车前轮摆振的数值仿真研究[J]. 汽车工程,2004,26(5):585-587. LI Xinye,HE Lijuan,DONG Zhengshen,et al. A numerical simulation on front wheel shimmy for CA10 truck[J]. Automotive Engineering,2004,26(5):585-587.
[55] 秦浩,董笑鹏. 汽车前轮低速摆振和高速摆振的分析[J]. 农业装备与车辆工程,2012,50(4):47-49. QIN Hao,DONG Xiaopeng. Analysis of front wheels shimmy of car at low and high velocity[J]. Agricultural Equipment and Vehicle Engineering,2012,50(4):47-49.
[56] ESHLEMAN R L. Particular handling safety problems of trucks and articulated vehicles[J]. Mathematical Analysis,1973,242(43):115-147.
[57] KURTZ E F,ANDERSON R J. Handling characteristics of car-trailer systems:A state-of-the-art survey[J]. Vehicle System Dynamics,1977,6:217-243.
[58] BEVAN B G,SMITH N P,ASHLEY C. Some factors influencing the stability of car/caravan combinations[C/CD]//Road Vehicle Handling,IMechE Conference Publications,1983.
[59] DENG W,KANG X. Parametric study on vehicle-trailer dynamics for stability control[R]. SAE Paper,2003-01-1321,2003.
[60] 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.
[61] ANDERSON R J,KURTZ E F. Handling characteristics simulations of car-trailer systems[R]. SAE Paper,800545,1980.
[62] FRATILA D,DARLING J. Simulation of coupled car and caravan handling behaviour[J]. Vehicle System Dynamics,1996,26(6):397-429.
[63] SHARP R S,FERNANDEZ M A A. Car-caravan snaking,Part 1:The influence of pintle pin friction[J]. Proceedings of the IMechE Part C:Journal of Mechanical Engineering Science,2002,216(7):707-722.
[64] WU D H. A theoretical study of the yaw/roll motions of a multiple steering articulated vehicle[J]. Proceedings of the IMechE Part D:Journal of Automobile Engineering,2001,215(12):1257-1265.
[65] FRATILA D. Lateral stability of passenger car/caravan combinations[D]. Bath:University of Bath,1994.
[66] STANDEN P. Towed vehicle aerodynamics[D]. Bath:University of Bath,1999.
[67] DARLING J,AKWE S O. An experimental investigation into car and caravan stability[R]. Bailey Caravans of Bristol,Department of Mechanical Engineering,University of Bath,UK,2002.
[68] DARLING J,TILLEY D,GAO B. An experimental investigation of car-trailer high-speed stability[J]. Proceedings of the IMechE Part D:Journal of Automobile Engineering,2009,223(4):471-484.
[69] SAGAN E. Fahreigenschaften von PKW-Wohnanhänger-zügen:Antrieb,Bremsen,Fahrstabilität und Schwingun-gen[D]. Braunschweig:TU Braunschweig,1983. SAGAN E. Driving characteristics of car-caravan combinations:Traction,braking,stability and vibrations[D]. Braunschweig:TU Braunschweig,1983.
[70] BEDÜK M D,ÇALIŞKAN K,HENZE R,et al. Effects of damper failure on vehicle stability[J]. Proceedings of the IMechE Part D:Journal of Automobile Engineering,2013,227(227):1024-1039.
[71] BEREGI S,TAKÁCS D,STÉPÁN G,et al. Stability analysis of the car-trailer system with a time-delayed tyre model[C/CD]//Proceedings of 24th International Symposium on Dynamics of Vehicles on Roads and Tracks,IAVSD,Graz,Austria,2015,August 17-21.
[72] BEREGI S,TAKÁCS D,STÉPÁN G. Tyre induced vibrations of the car-trailer system[J]. Journal of Sound and Vibration,2016,362:214-227.
[73] HE Y,ELMARAGHY H,ELMARAGHY W. A design analysis approach for improving the stability of dynamic systems with application to the design of car-trailer systems[J]. Journal of Vibration and Control,2005,11(12):1487-1509.
[74] ZHANG N,CLAUS S,WANG Y,et al. Analysis methods for time-variant harmonic vehicle dynamics Experiments[C]//Proceedings of the 14th International VDI Conference:Tyres-Chassis-Road,Hannover,Germany,October 22-23,2013,VDI Berichte 2211,273-286.
[75] ZHANG N,XIAO H,WINNER H. A parameter identification method based on time-frequency analysis for time-varying vehicle dynamics[J]. Proceedings of the IMechE Part D:Journal of Automobile Engineering,2016,230(1):3-17.
[76] ZHANG N,LI P C,YIN G D,et al. Application of Hilbert transform in vehicle dynamics analysis[C/CD]//Proceedings of IEEE International Conference on Vehicular Electronics and Safety,Beijing,China,2016,July 10-12.
[77] ZHANG N. Stability investigation of car-trailer combinations based on time-frequency analysis[D]. Darmstadt:TU Darmstadt,2015.
[78] ZHANG N,SHAO Z J,XIAO H,et al. Stability investigation of car-trailer combinations depending on damper properties[C/CD]//Proceedings of 24th International Symposium on Dynamics of Vehicles on Roads and Tracks,IAVSD,Graz,Austria,2015,August 17-21.
[79] GAO C. Modellierung und Simulation von Aerodynamik des Gespannsystems[D]. Darmstadt:TU Darmstadt,2013. GAO C. Modeling and simulation of aerodynamics of car-trailer combination system[D]. Darmstadt:TU Darmstadt,2013.
[80] LI H G. Modellierung und Validierung eines Gespannsystems[D]. Darmstadt:TU Darmstadt,2013. LI H G. Modeling and validation of a car-trailer combination system[D]. Darmstadt:TU Darmstadt,2013.
[81] WU Q P. Untersuchung der Radlastschwankungen vom Gespannsystem[D]. Darmstadt:TU Darmstadt,2013. WU Q P. Analysis of wheel load fluctuations of car-trailer combinations[D]. Darmstadt:TU Darmstadt,2013.
[82] ZHANG X L. Identifikation,Quantifizierung und Simulation des dynamischen Verhaltens von Dämpfern[D]. Darmstadt:TU Darmstadt,2013. ZHANG X L. Identification,quantification and simulation of damper dynamic behavior[D]. Darmstadt:TU Darmstadt,2013.
[83] SHAO Z J. Identifikation und Ermittlung der dynamischen Stabilität eines Gespanns in Abhängigkeit von Dämpfercharakteristiken durch die Änderung des Wankverhaltens des Systems[D]. Darmstadt:TU Darmstadt,2015. SHAO Z J. Identification and investigation of dynamic ctability of a car-trailer combination on the dependence of damper characteristics through the change of system roll behavior[D]. Darmstadt:TU Darmstadt,2015.
[84] KAGEYAMA I,NAGAI R. Stabilization of passenger car-caravan combination using four wheel steering control[J]. Vehicle System Dynamics,1995,24(4):313-327.
[85] FERNANDEZ M A A,SHARP R S. Caravan active braking system-effective stabilisation of snaking of combination vehicles[R]. SAE Technical Paper,2001-01-3188,2001.
[86] DENG W,LEE Y H,TIAN M. An integrated chassis control for vehicle-trailer stability and handling performance[R]. SAE Technical Paper,2004-01-2046,2004.
[87] 郭正康. 汽车列车制动力分配和制动稳定性分析(上、下)[J]. 汽车技术,1981(2-3):8-11. GUO Zhengkang. An analysis of braking force distribution and braking stability of automobile train[J]. Automobile Technology,1981(2-3):8-11.
[88] 郭正康. 现代汽车列车设计与使用[M]. 北京:北京理工大学出版社,2006. GUO Zhengkang. Design and application of modern train[M]. Beijing:Beijing Institute of Technology Press,2006.
[89] 黄朝胜,隗海林,吴振昕. 牵引车-半挂车列车动力学仿真研究[J]. 汽车工程,2005,27(6):744-750. HUANG Chaosheng,KUI Hailin,WU Zhenxin. A simulation study on the dynamics of tractor-semitrailer combination[J]. Automotive Engineering,2005,27(6):744-750.
[90] 韦超毅. 拖挂式房车列车操纵稳定性研究[D]. 镇江:江苏大学,2008. WEI Chaoyi. Study on handling stability of caravan[D]. Zhenjiang:Jiangsu University,2008.
[91] 陆永华. 拖挂式房车制动控制策略的研究[D]. 镇江:江苏大学,2005. LU Yonghua. Study on braking control strategy of caravan-trailer[D]. Zhenjiang:Jiangsu University,2005.
[92] 杨秀建,康南,李西涛. 半挂汽车列车横向失稳的非线性动力学机制[J]. 机械工程学报,2012,48(8):79-89. YANG Xiujian,KANG Nan,LI Xitao. Nonlinear dynamics and lateral stability of tractor-semitrailer vehicle[J]. Journal of Mechanical Engineering,2012,48(8):79-89.
[93] 刘宏飞. 半挂汽车列车横摆动力学仿真及控制策略研究[D]. 长春:吉林大学,2005. LIU Hongfei. Study on the simulation and control strategy for yaw motion dynamics of tractor-semitrailer[D]. Changchun:Jilin University,2005.
[94] 彭涛. 半挂汽车列车非线性稳定性控制研究[D]. 长春:吉林大学,2012. PENG Tao. A study on control of nonlinear stability for tractor-semitrailer[D]. Changchun:Jilin University,2012.
[95] 高红博. 半挂汽车列车转弯制动方向稳定性及控制策略研究[D]. 长春:吉林大学,2014. GAO Hongbo. Research on directional stability and control strategy of tractor-semitrailer steering and braking[D]. Changchun:Jilin University,2014.
[96] 贺丽娟,林逸. 汽车操纵稳定性与前轮摆振的非线性仿真分析[J]. 汽车工程,2007,29(5):389-392. HE Lijuan,LIN Yi. Nonlinear simulation on vehicle handling stability and front wheel shimmy[J]. Automotive Engineering,2007,29(5):389-392.
[97] 蔡世芳,高占章. 汽车的侧倾转向和垂直干涉[J]. 汽车工程,1983(2):19-27. CAI Shifang,GAO Zhanzhang. The roll-steer and bump interference of automobiles[J]. Automotive Engineering,1983(2):19-27.
[98] 王鹏. 悬架与转向系统干摩擦诱发汽车摆振系统多极限环特性研究[D]. 合肥:合肥工业大学,2014. WANG Peng. Research on multiple limit cycles in shimmy induced by dry friction of suspension and steering system[D]. Hefei:Hefei University of Technology,2014.
[99] 蒋亦斌. 双前桥转向重型汽车摆振系统Hopf分岔特性研究[D]. 合肥:合肥工业大学,2015. JIANG Yibin. Study on the Hopf bifurcation characteristics of dual-axle heavy-duty vehicles shimmy system[D]. Hefei:Hefei University of Technology,2015.
[100] 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(6):848-870.
[101] ZHANG N,YIN G D,MI T,et al. Analysis of dynamic stability of car-trailer combinations with nonlinear damper properties[C/CD]//Proceedings of IUTAM Symposium on Nonlinear and Delayed Dynamics of Mechatronic Systems,Nanjing,China,2016,October 17-21.
文章导航

/