摘要
本文针对悬架技术的几个关键问题，进行了系统化的深入分析和研究，提出了新的思路、方法和模型，并将理论计算、仿真分析与实物试验相结合，以试验结果数据为依据，验证了新方法的有效性以及新模型精度。本文主要研究内容包括以下几个方面：
(1)对考虑非线性的两自由度悬架模型进行了推导，给出了偏频和阻尼比的理论算法，针对已有阻尼比计算方法的缺陷，引入新的阻尼比计算方法，改进阻尼比辨识的方法，消除对数衰减法出现假峰的情况，利用面积法计算阻尼比，提高了阻尼比的辨识精度。
(2)对具有独立悬架系统的汽车而言，簧上质量无法用简单的质量叠加方法来计算。为此提出一种简化模型，避开轮胎非线性特性，利用试验得到的轮心及车身部分的加速度结果来辨识簧上、簧下质量，提高了质量参数估算的精准性，对悬架设计分析研究具有重要的意义。
(3)建立了新的橡胶衬套非线性光滑迟滞模型，结合试验数据，确定模型参数初始值，对衬套回复力进行求解；通过对模型参数进行灵敏度分析，忽略参数交互作用，确定主要参数对模型输出的影响，为有可能的模型修改提供参考依据。结合静刚度和动刚度测试试验结果，分析试验数据，提出考虑预载作用的修正模型，扩展了橡胶衬套非线性光滑迟滞模型的应用范围；采用遗传算法进行参数辨识，获取修正模型的精确参数，并将仿真结果与试验数据相对比，验证模型的正确性和精度。
(4)采用了一种新的试验方法，使用相对来说比较简单便宜的传感器，通过对加速度、位移、应变等比较容易获取的物理量进行测试，逆向求解轮心六分力。并在逆向求解得到轮心六分力后，还根据悬架多体系统动力学模型正向得到各连接点的受力，将仿真值与测量值进行对比，以验证逆向求解过程及结果的正确性。并在此基础上计算得到零部件的疲劳寿命，然后以悬架关键衬套刚度为设计变量进行优化分析，提高了悬架零部件的疲劳寿命。
本文以汽车悬架为研究对象，结合目前悬架研发过程中的实际情况，丰富了悬架研发的模型体系，该模型体系能够使悬架的研发流程更加具有合理性，使其研发过程更加规范化，从而提高悬架的研发品质与研发效率。本文所采用的创新方法对悬架研发过程具有极大的现实意义和促进作用。
Aiming to several key problems of suspension, the systematic analysis and researchare carried out. A new analysis method and model is proposed in this thesis, whichcombines the theory calculation and simulation analysis with physical experiment. Theexperiment data is used as the reference, which verifies the validation of new method andthe accuracy of new model. The research contents of this thesis are shown as following:
(1)Induce the two freedom degree suspension model considering the nonlinearcharacteristic, providing the theoretical calculation method of offset frequency anddamping ratio. To conquer the deficiency of current calculation method of damping ratio, anew damping ratio calculation method is derivate. In this method, the area method isemployed to calculate the damping ratio, which eliminates the false peak circumstance inthe logarithmic decrement method, so as to improve the estimation accuracy of dampingratio.
(2)The sprung mass of automotive with independent suspension may not be calculatedas the sum of each component mass. To avoid the nonlinear characteristic of tyre, asimplified model is proposed, in which the acceleration of wheel center and vehicle bodyobtained by experiment are used to estimate the sprung mass and unsprung mass. Thismethod provides higher accuracy of mass estimation, which has important influence ofsuspension analysis design and research.
(3)Build a new nonlinear smooth hysteresis model of rubber bushing, combining theexperiment dates to determine the initial value of parameters, solving the bushingrestoring force. The parameters sensitivity analysis of model is implemented, neglectingthe cross affection of parameters, determining the influence extent to model response ofmainly parameters, which provides reference to the possible model mending. Combiningthe test results of static stiffness and dynamic stiffness, a mended model considering thepreload effect is proposed, which extends the application range of nonlinear smoothhysteresis rubber bushing model. The genetic algorithm is utilized to estimate theparameters obtaining the exact value of parameters, and then compare the simulation results with experiment result verifying the validation and accuracy of model.
(4)A new experiment method is used, where the simple and cheap sensors areemployed, testing some more approachable physical quantities such as acceleration,displacement and strain and then back-calculating the six component forces of spindleload. After the six component forces of spindle load are obtained, the forces of joints arecalculated through the multi-body dynamics suspension model, which are compared withthe experiment data to test the validation of reverse solving process and results. Based onthese results, the fatigue lives of chassis components are calculated, and the optimizationchoosing the stiffness of key bushinges of suspension as design variables is implemented,which improves the fatigue lives of chassis components.
This thesis is focused on the automotive suspension. Combining some real situationsin suspension research and design, enrich the system of suspension research and design,which makes the process of suspension research and design more reasonable and morenormal, improving the quality and efficiency of suspension research and design. Thecreative method proposed in the thesis has large reality worth and promoting effect onsuspension research and design process.
引文
[1] Willumeit H P (德).车辆动力学：模拟及其方法.李宁，孙逢春.北京：北京理工大学出版社，1998
[2] Gillespie T D. Fundamentals of Vehicle Dynamics. Society of Automotive Engineers,Inc. Scientific&Technical Publishing Co.2000
[3] Reimpell J, Stoll H, Betzler W. The Automotive Chassis: Engineering Principles.2ndedition. AGET Limited. Oxford: Reed Educational and Professional PublishingLtd,2001
[4] Daniels J. Car Suspension at Work: Theory&Practice of Steering, Handling&Roadholding.2nd edition. Motor Racing Publications,1998
[5] http://www.carbibles.com/suspension_bible.html
[6] Tanaka M, Dulikravich G S. Inverse Problems in Engineering Mechanics. ISIP '98,Nagano, Japan,1998
[7] Serban R, Freeman J S. Parameter identification for multibody dynamics systems.Department of Mechanical Engineering, The University of Iowa,1996
[8] Chen S Y, Tsuei M S. Estimation of mass, stiffness and damping matrices fromfrequency response function. Journal of Vibration and Acoustics,1996,118:83~87
[9] Huang C S. Structural identifcation from ambient vibration measurement using themultivariate AR model. Journal of Sound and Vibration,241:337~359
[10]Huang C S, Lin H L. Modal identifcation of structures from ambient vibration, freevibration, and seismic response data via a subspace approach. EarthquakeEngineering and Structural Dynamics,2001,30:1857~1878
[11]Huang C S, Hung S L, Wen C M, et al. A neural network approach for structuralidentifcation and diagnosis of a building from seismic response data. EarthquakeEngineering and Structural Dynamics,2003,32:187~206
[12]Hung C F, Ko, W J, Peng Y T. Identifcation of modal parameters from measuredinput and output data using a vector backward auto-regressive with exogeneousmodel. Journal of Sound and Vibration,2004,276:1043~1063
[13]Chen C H. Structural idenftication from feld measurement data using a neuralnetwork. Smart Materials and Structures,2005,14:104~115
[14]Wang G S. Application of hybrid genetic algorithm to system identifcation. StructuralControl and Health Monitoring,2009,16(2):125~153
[15]Perry M J, Koh C G, Choo Y S. Modifed genetic algorithm strategy for structuralidentifcation. Computers and Structures,2006,84:529~540
[16]Guida D. Parameter identification of a two degrees of freedom mechanical system.INTERNATIONAL JOURNAL OF MECHANICS,2009,2(3):23~30
[17]Khanmirza E, Khaji N, Majd V J. Model updating of multistory shear buildings forsimultaneous identifcation of mass, stiffness and damping matrices using twodifferent soft-computing methods. Expert Systems with Applications,2011,38:5320~5329
[18]Huang F L, Wang X M, Chen Z Q, et al. A new approach to identification ofstructural damping ratios. Journal of Sound and Vibration,2006,12(303):144~153
[19]Koh C G, Hong B, Liaw C Y. Substructural and progressive structuralidentifcation methods. Engineering Structures,2003,25:1551~1563
[20]Xiao Jie. System identification for transit buses using a hybrid genetic algorithm.Pennsylvania: The Pennsylvania State University,2002
[21]Yang J N, Lei Y, Pan S W, et al. System identifcation of linear structures based onHilbert–Huang spectral analysis; Part1: Normal modes. Earthquake Engineeringand Structural Dynamics,2003,32:1443~1467
[22]Xu B, Wu Z, Chen G, et al. Direct identification of structural parameters fromdynamic responses with neural networks. Engineering Applications of ArtficialIntelligence,2004,17:931~943
[23]王玉勤.基于最小二乘递推算法的半主动悬架系统参数辨识[.井冈山大学学报(自然科学版),2011,32(5):82~86
[24]宋晓琳，基于免疫算法的悬架系统参数的辨识究.湖南大学学报(自然科学版),2007,34(5):29~33
[25]余志生,汽车理论(第五版).北京:机械工业出版社,2009
[26]顾信忠,张铁山.汽车减振器相对阻尼系数的确定.车辆与动力技术,2011,2:29~32
[27]薛定宇.控制系统计算机辅助设计:MATLAB语言与应用.北京：清华大学出版社,2006
[28]GB4783—84汽车悬挂系统的固有频率和阻尼比测定方法
[29]师汉民,谌刚,吴雅.机械振动系统:分析测试建模对策.武汉:华中理工大学出版社,1992
[30]刘惟信.汽车设计.北京:清华大学出版社,2001
[31]QC/T545-1999汽车筒式减振器台架试验方法
[32]GB/T4970-1996汽车平顺性随机输入行驶试验方法
[33]傅志方.振动模态分析与参数辨识.北京：机械工业出版社,1990
[34]宋晓琳,张乐栋,于德介等.基于免疫算法的悬架系统参数的辨识.湖南大学学报(自然科学版),2007,5(34):29~33
[35]孙靖民.机械优化设计(第四版).北京:机械工业出版社,2007
[36]Koppenaal J, Van Oosten J, Porsche I, et al. General Modeling of Nonlinear Isolatorsfor Vehicle Ride Studies. SAE International Journal of Materials&Manufacturing,2010,3(1):585~591
[37]Talukdar S, Mazumdar A, Mullasseril M, et al. Mathematical Modeling in VehicleRide Dynamics. SAE Paper2012-01-0056
[38]Berg M. A non-linear rubber spring model for rail vehicle dynamics analysis. Vehiclesystem dynamics,1998,30(3-4):197~212
[39]Sedlaczeka K, Dronkab S, Rauhc J. Advanced modular modelling of rubber bushingsfor vehicle simulations. Vehicle System Dynamics: International Journal ofVehicle Mechanics and Mobility,2011,49(5):741~759
[40]李鸿光,何旭,孟光. Bouc-Wen滞回系统动力学特性的仿真研究.系统仿真学报,2004,16(9):2009~2011
[41]Sj berg M M, Kari L. Non-linear behavior of a rubber isolator system using fractionalderivatives. Vehicle system dynamics,2002,37(3):217~236
[42]Spencer Jr B, Dyke S, Sain M, et al. Phenomenological model for magnetorheologicaldampers. Journal of engineering mechanics,1997,123(3):230~238
[43]Qu Y, Zhang L, Wu S, et al. Parameters Identification of Constitutive Models ofRubber Bushing. SAE Paper2011-01-0795
[44]Lu M, Tang Y, Wang E. Hydromount Parametric Study and Its Application inTroubleShooting. SAE Paper2010-01-0506
[45]Metered H, Bonello P, Oyadiji S. Nonparametric Identification Modeling ofMagnetorheological Damper Using Chebyshev Polynomials Fits. SAEInternational Journal of Passenger Cars-Mechanical Systems,2009,2(1):1125~1135
[46]Metered H. Application of Nonparametric Magnetorheological Damper Model inVehicle Semi-active Suspension System. SAE International Journal of PassengerCars-Mechanical Systems,2012,5(1):715~726
[47]Eugênio M, Barbosa R. Contribution for elastomeric bushing development for thelower control arm of a compact vehicle. SAE Paper2007-01-2533
[48]Zushi K, Sakai K, Sugawara H, et al. Development of Lead Free Copper Based Alloyfor Piston Pin Bushing Under Higher Load Engines. SAE Paper2006-01-1105
[49]杨译.基于Bouc-Wen模型和流体模型的减振器仿真及其整车实验仿真[硕士学位论文].长春：吉林大学,2011
[50]王唯,夏品奇,刘朝勇.基于Bouc-Wen方程的磁流变阻尼器实验建模.振动工程学报,2006,19(3):296~301
[51]乔雪冰.乘用车悬架系统液压衬套的建模与分析[硕士学位论文].长春：吉林大学,2012
[52]苏志勇.轴对称橡胶衬套高精度模型的建立及应用[硕士学位论文].长春：吉林大学,2007
[53]刘伟.客车悬架橡胶衬套对整车性能影响研究与多目标优化[博士学位论文].长春：吉林大学,2012
[54]杨顺根,白仲元.橡胶工业手册:橡胶机械(第三版).北京:化学工业出版社,1992
[55]郑明军.橡胶件的静动态特性及有限元分析[博士学位论文].北京:北方交通大学,2002
[56]赵振东,雷雨成,袁学明.悬架橡胶衬套变形响应的非线性有限元分析.上海汽车,2006,9:23~25
[57]Sj berg M. On dynamic properties of rubber isolators. KTH: Tidigare Institutioner,2002
[58]Scheiblegger C, Pfeffer P, Karrer H, et al. Modelling of elastomer and hydro mountsfor ride comfort and handling simulation. VDI-Berichte,2011,213(7):247~267
[59]Den Hartog J P. Mechanical vibrations. New York: Dover publications,1985
[60]Ulmer J. Strain dependence of dynamic mechanical properties of carbon black-filledrubber compounds. Rubber chemistry and technology,1996,69(1):15~47
[61]Wang B, Chen L Q. Asymptotic stability analysis with numerical confirmation of anaxially accelerating beam constituted by the standard linear solid model. Journalof Sound and Vibration,2009,328(4):456~466
[62]Li S, Patwardhan A G, Amirouche F M, et al. Limitations of the standard linear solidmodel of intervertebral discs subject to prolonged loading and low-frequencyvibration in axial compression. Journal of biomechanics,1995,28(7):779~790
[63]Shaw S. On the dynamic response of a system with dry friction. Journal of Sound andVibration,1986,108(2):305~325
[64]Wei S T, Pierre C. Effects of dry friction damping on the occurrence of localizedforced vibrations in nearly cyclic structures. Journal of Sound and Vibration,1989,129(3):397~416
[65]张义同.热粘弹性理论.天津:天津大学出版社,2002
[66]Olsson A K, Austrell P E. Finite element analysis of a rubber bushing considering rateand amplitude dependent effects. Constitutive models for rubber,2003,133~140
[67]Park Y, Wen Y, Ang A. Random vibration of hysteretic systems under bi‐directionalground motions. Earthquake engineering&structural dynamics,1986,14(4):543~557
[68]于增亮,张立军,余卓平.橡胶衬套力学特性半经验参数化模型.机械工程学报,2010,46(14):115~123
[69]Kwok N, Ha Q, Nguyen M, et al. Bouc–Wen model parameter identification for a MRfluid damper using computationally efficient GA. ISA transactions,2007,46(2):167~179
[70]王娜.面向汽车耐久性分析的底盘橡胶衬套建模研究[硕士学位论文].长春:吉林大学,2011
[71]李韶华,杨绍普.滞后非线性模型的研究进展.动力学与控制学报,2006,4(1):8~15
[72]Yang G, Spencer Jr B F, Jung H-J, et al. Dynamic modeling of large-scalemagnetorheological damper systems for civil engineering applications. Journalof engineering mechanics,2004,130(9):1107~1114
[73]Dzierzek S. Experiment-based modeling of cylindrical rubber bushings for thesimulation of wheel suspension dynamic behavior. SAE Paper2000-01-0095
[74]Bellizzi S, Bouc R. Identification of the hysteresis parameters of a nonlinear vehiclesuspension under random excitation. Nonlinear Stochastic Dynamic EngineeringSystems,1987,467~476
[75]Scheiblegger C, Lin J, Karrer H. New Nonlinear Bushing Model for Ride Comfortand Handling Simulation: Focussing on Linearization and the Implementationinto MBS Environment: proceedings of the Proceedings of the FISITA2012World Automotive Congress. Beijing,2012,325~331
[76]Johrendt J L. Optimizing road test simulation using neural network modelingtechniques. Canada: University of Windsor,2005
[77]Ma F, Zhang H, Bockstedte A, et al. On parameter analysis of the differential modelof hysteresis; proceedings of the IUTAM Symposium on Nonlinear StochasticDynamics: Illinois. Proceedings of the IUTAM Symposium Held in Monticello.USA,2003,26~30
[78]傅志方.振动模态分析与参数辨识.北京:机械工业出版社,1990
[79]施亮,何琳.磁流变阻尼器参数辨识方法研究.振动与冲击,2009,28(1):131~133
[80]王小平,曹立明.遗传算法:理论、应用及软件实现(第二版).西安:西安交通大学出版社,2002
[81]雷英杰,张善文,李续武. MATLAB遗传算法工具箱及应用.西安:西安电子科技大学出版社,2005
[82]李飞,郭孔辉,丁海涛等.汽车耐久性分析底盘载荷预测方法研究综述.科学技术与工程,2010,10(24):5960~5964
[83]李飞.轿车转向节耐久性寿命预测研究[博士学位论文].长春：吉林大学，2010
[84]Tebbe J C, Vivek C, Jason T, et al. Analytical. Chassis loads prediction usingmeasurements as input to an unconstrained multi-body dynamics model. SAEpaper2006-01-0992
[85]Joseph A S, Prasad K, Hyung J H, et al. Supplementation of measured vehicle roadloads to study vehicle configuration changes. SAE paper2005-01-1403
[86]Manfred B, Riccardo M, Michael K, et al. Load identification for CAE based fatiguelife prediction of a new bus type. SAE paper2007-01-4281
[87]邵建，董益亮，肖攀等.基于多体模型仿真的载荷谱虚拟迭代技术分析.重庆理工大学学报(自然科学版)，2010，24(12):84~87
[88]Rui Y, Saleem F, Zhou J. Road Load Simulation Using Effective Road Profile. SAEPaper971512
[89]Kao B, Perumalswami P, Dhir A, A Hybrid Road Loads Prediction Method with FullVehicle Dynamic Simulation. SAE Paper971513
[90]Manfred B, Thomas L, Markus O, et al. The hybrid road approach for durability loadsprediction. SAE paper2005-01-0628
[91]Cheng C, Sudhakar M. Truck frame motion prediction and correlation. SAE paper2006-01-1257
[92]Cheng C, Sudhakar M. Spindle-based engine mount load analysis-prediction andcorrelation. SAE paper2007-01-1203
[93]Sakai Y, Watanabe I, Nakamaru T. Road-load input contribution analysis forsuspension durability using a multi-axial road simulator. SAE paper2008-01-1482
[94]杜永昌.车辆道路模拟试验迭代算法研究.农业机械学报,2002,33(3):5~8
[95]蒋良潍，姚令侃，吴伟.边坡振动台模型实验动位移的加速度时程积分探讨.防灾减灾工程学报，2009，29(3):261~266
[96]Lee D C, Han C S. CAE driven durability model verification for the automotivestructure development. Finte Elements in Analysis and Design,2009,45(5):324~332
[97]FERRY W B, FRISE P R, ANDREWS G T, et al. Combining virtual simulation andphysical vehicle test data to optimize durability testing. Fatigue&Fracture ofEngineering Materials&Structures,2002,25(12):1127~1134
[98]Velosoa V, Magalh esa H S, Bicalhoa G I, et al. Failure investigation and stressanalysis of a longitudinal stringer of an automobile chassis. Engineering FailureAnalysis,2009,16(5):1696~1702
[99]Jayakumar P, Wang D, Cline S. Issues of Estimating Powertrain Mount Loads UsingMeasured Accelerations and Drive Torques for Durability Events. SAE Paper2005-01-0626
[100] Crescimanno M R, Cavallo P. On Duty Simulation of a Trimmed Body UnderDynamic Loads:Modal Superposition Approach to Evaluate Fatigue Life. SAEPaper1999-01-3150
[101] Meyer R A, Sharp M C. Optimizing Load Transducer Design usingComputer-Based Analytical Tools. SAE Paper2001-01-0787
[102] Kino H, Lwai M, Tamura M. A Study of Road Load Severity Prediction in Marketfor Power Spectrum Density. SAE Paper2003-01-2867
[103] Dannbauer H, Gattringer O, Steinbatz M. Integrating Virtual Test Methods andPhysical Testing to Assure Accuracy and to Reduce Effort and Time. SAE Paper2005-01-0484
[104] Xu P J, Wong D, LeBlanc P, et al. Road Test Simulation Technology in LightVehicle Development and Durability Evaluation. SAE Paper2005-01-0854
[105] Haq S, Temkin M, Black L, et al. Vehicle Road Simulation Testing,Correlationand Variability. SAE Paper2005-01-0856
[106] Zhang Y, Stawiarski T, Subramanian M, et al. Full Vehicle Finite Element Model4-Post Durability Analysis. SAE Paper2005-01-1402
[107] Yoshida T, Kishita Y, Shiratori M. Development of a Virtual Rough RoadSimulator for Motorcycle Frame Strength. SAE Paper2005-32-0086
[108] You S, Joo S G. Virtual Testing and Correlation with Spindle Coupled FullVehicle Testing System. SAE Paper2006-01-0993
[109]刘拥军，杨万安，姚列等. MTS329道路模拟试验机在整车道路模拟试验中的应用.上海汽车,2001,4:26~29
[110]于长清. MTS道路模拟机汽车可靠性试验当量系数的研究[硕士学位论文].长春:吉林大学，2006
[111]韩小平，马吉胜，邓辉咏等.道路模拟机的虚拟样机仿真平台.兵工自动化,2007,26(7):21~22
[112]江浩斌，戴云，于林涛.基于六通道道路模拟机的重型汽车路面激励再现试验.汽车技术，2008，9:46~49
[113]刘再生，霍福祥，杨立峰等.基于路谱输入的汽车台架耐久性试验方法研究.汽车技术，2010,9:47~50
[114]孙华锋.汽车台架耐久性试验与道路试验相关性探讨.工程与试验，2009，49(2):13~14
[115] Fernandes C, Duarte M. A semi-analytical approach for vehicle ride simulation.SAE Paper2008-36-0048
[116] Tebbe J, Mathers M, Multiple Load Input Sensitivity Analysis Technique forFinite Element-Based Durability Evaluation. SAE Paper951099
[117] Lee C. Input Force Reconstruction for Vehicle Durability. SAE Paper960568
[118] Cruz J M, Santo I L E, Oliveira A A. A Semi-Analytical Method to Generate LoadCases For CAE Durability Using Virtual Vehicle Prototypes. SAE Paper2003-01-3667
[119] Potukutchi R, Pal K, Agrawal H, et al. Practical Approach for Fast DurabilityAnalysis&Iterations. SAE Paper2006-01-0784
[120] Lin S H, Cheng C G, Liao C Y, et al. Experiments and CAE Analyses forSuspension under Durability Road Load Conditions. SAE Paper2006-01-1624
[121] Liu L G, Ran X F, Li L F. Hybrid Vehicle Road Loads Simulation and Correlation.SAE Paper2007-01-1202
[122] Huang L P, Agrawal H, Kurudiyara P. Dynamic Durability Analysis ofAutomotive Structures. SAE Paper980695
[123]蒋玮.车架疲劳强度的数值仿真与试验研究[硕士学位论文].上海:上海交通大学，2008
[124]江迎春，陈无畏.基于ANSYS的轿车转向节疲劳寿命分析.汽车科技，2008,3:32~36
[125]刘献栋，曾小芳，单颖春.基于试验场实测应变的车辆下摆臂疲劳寿命分析.农业机械学报，2009,40(5):34~38
[126]黄民峰，江迎春.基于有限元法的汽车构件疲劳寿命分析.机械研究与应用，2008,21(2):57~60
[127]朱茂桃，奚润，李伟.某轻型汽车后桥壳体疲劳寿命分析.汽车技术，2009,1:34~37
[128]王宏伟，骆红云，钟群鹏.汽车前轴的疲劳试验及其疲劳寿命的预测.金属热处理，2007,32(增刊)
[129]高晶，宋健，朱涛.随机载荷作用下汽车驱动桥壳疲劳寿命预估.机械强度，2008,30(6):982~987
[130]赵玮,温小霓.应用统计学教程.西安:西安电子科技大学出版社,2003
[131] Reddy C V R, Satheesh K M, Yang X, et al. Analysis of road load data to extractstatistical trends in spindle loads for vehicles with variants. SAE paper2005-01-0859
[132] Mahesh T, Yang X B, Gu Z Q, et al. Vehicle cradle durability design development.SAE paper2005-01-1003
[133] Lin S H, Cheng C G, Liao C Y, et al. Experiments and CAE analyses forsuspension under durability road load conditions. SAE paper2006-01-1624
[134] Yang X B, Men Y X, Minhael N, et al. Back-calculated splindle loads sensitivityto suspension component loads availability. SAE paper2008-01-1103
[135] Ilankamban R, Perumalswami P R, Page J. Back calculation-a method ofmeasuring component loads without load cells. MSC1996World Users'Conference Proceedings,1996
[136] Yang X B, Minhael N. Sensitivities of suspension bushings on vehicle impactharshness performances. SAE paper2005-01-0827
[137] Yang X B, Zhang D J, Minhael N, et al. Suspension tuning parameters affectingimpact harshness performance evaluation. SAE paper2006-01-0991
[138] Kim J H, Sin H C, Kang B J, et al. Characteristic study of bushing compliance inconsideration of stresses in a vehicle suspension system by the Taguchi method.Journal of Automobile Engeering,2006,220:1383~1399
[139] Dietz S, Netter H, Sachau D. Fatigue life prediction of a railway bogie underdynamic loads through simulation. Vehicle System Dynamics,1998,29:385~402
[140] Kang B J, Kim J W, Kim J H, et al. Improving the durability of automobilesuspension systems by optimizing the elastomeric bushing compliance. Journal ofAutomobile Engineering,2008,222:469~484
[141] Wood C. Integrated durability analysis of a vehicle through virtual simulation.Masters of Science Masters Thesis, Windsor University,2003
[142] Gobbi M, Mastinu G, Doniselli C. Optimising a car chassis. Vehicle SystemDynamics,1999,32:149~170
[143] Jorge A, Paulo V. Sensitivity of a vehicle ride to the suspension bushingcharacteristics. Journal of Mechanical Science and Technology,2009,23:1075~1082
[144]沈磊，张守元，郁强.轮心六分力作用下悬架疲劳载荷谱提取.汽车技术.2012,1:48~50
[145]霍福祥，刘再生，王长明等.虚拟迭代技术在油箱托挂件上的应用研究.汽车技术,2011,6:30~33
[146]徐灏.疲劳强度.北京:高等教育出版社,1988
[147]王国军,胡仁喜,陈欣等. nSOft疲劳分析理论与应用实例指导教程.北京:机械工业出版社,2007
[148] Su H. Automotive CAE Durability analysis using random vibration approach. In:MSC2nd Worldwide Automotive Conference. Dearborn, MI:2000
[149] Medepalli S, Rao R. Prediction of roadloads for fatigue design, a sensitivity study.International Journal of Vehicle Design,2000,23(1/2):161~175
[150] Riener H, Peiskammer D, Witteveen W. Modal durability analysis of a passengercars front supporting frame due to full vehicle simulation loads. In: Adams userconference. North America:2001
[151] Marcelo L E, Roberto S B. Contribution for Elastomeric Bushing Developmentfor the Lower Control Arm of a Compact Vehicle. SAE Paper2007-01-2533
[152] Chae C K. Identification of forces transmitted onto car body through rubberbushing system under driving conditions. SAE Paper1999-01-1841
[153] He Y P, McPhee J. A Review of Automated Design Synthesis Approaches forVirtual Development of Ground Vehicle Suspensions. SAE Paper2007-01-0856
[154] Chandrasekaran A K. Vehicle Design Optimization using Multibody DynamicSimulations and Large Design Space Search Methods. M.S.Thesis, Departmentof Mechanical Engineering, the Ohio State University
[155] Chakarvartula S, Haque I, Fadel G. A modified Monte-Carlo simulation approachto heavy vehicle design for good dynamic performance in multiple scenarios.International Journal of Heavy Vehicle Systems,2003,10(1-2):112~143
[156] Shinya W, Tomoyuki H, Mitsunori M. Neighborhood cultivation geneticalgorithm for multi-objective optimization problems. Proceedings of the4thAsia-Pacific Conference on Simulated Evolution And Learning(SEAL-2002),Singapore: Nanyang Technological University, School of Electrical&ElectronicEngineering,2002,198~202
[157] Loyera B, Jézéquela L. Robust design of a passive linear quarter car suspensionsystem using a multi-objective evolutionary algorithm and analytical robustnessindexes. Vehicle System Dynamics,2009,47(10):1253~1270
[158]陈无畏，李欣冉，陈晓新.车辆悬架中高频振动传递分析与橡胶衬套刚度优化.农业机械学报，2011,42(10)：25~29
[159]葛培明.改进的遗传算法及其在工程优化中的应用[博士论文].成都:西南交通大学，2003
[160]陈栋华，王云，周鋐等.基于实车试验数据的悬架零部件耐久性虚拟试验方法研究. LMS首届用户大会论文集，2006
[161]邢天伟.基于田口方法的整车平顺性仿真及优化[博士论文].长春：吉林大学图书馆，2008
[162]王文阁，刘祖斌，郑联珠.疲劳寿命曲线特性研究及在汽车部件疲劳试验优化中的应用.汽车技术,2005，11：19~21
[163]张林波，徐有忠，黄鹏程等.汽车悬架结构强度分析方法. MSC.Software中国用户论文集,2007
[164]苏小平.依维柯汽车多体动力学仿真分析、优化研究及工程实现[博士论文].南京：南京理工大学图书馆，2004
[165] Cho B Y. Spindle Load Application for NVH CAE Models by Using PrincipalVector Approach. SAE Paper2005-01-1505
[166] Park J, Gu P, Lee M R, et al. A New Experimental Methodology to EstimateTire/Wheel Blocked Force for Road NVH Application. SAE Paper2005-01-2260
[167] Ma Z, Shahihi B, Lee M J, et al. CAE Driven Body Durability and UpfrontStructure Development of the New Ford Edge. MSC Software Corporation's2007Americas VPD Conference. Detroit, Michigan USA. October2007
[168] Kim H S, Yim H J, Kim C B. Computational Durability Prediction of BodyStructures in Prototype Vehicles. International Journal of Automotive Technology,2002,4:129~135
[169] Yang X. Effects of bushings characteristics on suspension ball joint travels.Vehicle System Dynamics,2011,49(1):181~197
[170] Zoroufi M, Fatemi A. Experimental durability assessment and life prediction ofvehicle suspension components: a case study of steering knuckles. AutomobileEngineering,2006,220:1565~1579
[171] Kang B J. Sin H-C. Kim J H. Optimal Shape Design of the Front Wheel LowerControl Arm Considering Dynamic Effects. International Journal ofAutomotiveTechnology.2007,8(3):309~317
[172] Chandrasekaran A K. Vehicle Design Optimization using Multibody DynamicSimulations and Large Design Space Search Methods[M.S.Thesis]. Departmentof Mechanical Engineering, the Ohio State University
[173] Chakarvartula S, Haque I, Fadel G. A modified Monte-Carlo simulation approachto heavy vehicle design for good dynamic performance in multiple scenarios.International Journal of Heavy Vehicle Systems,2003,10(1-2):112~143