1.School of Automobile and Transportation, Xihua University, Chengdu 610039, China;
2.Key Laboratory of Automobile Measurement and Control & Safety, Xihua University, Chengdu 610039, China;
3.Provincial Engineering Resarch Center for New Energy Vehicle Intelligent Control and Simulation Test Technology of Sichuan, Xihua University, Chengdu 610039, China;
4.School of Automobile, Chang’an University, Xi’an 710064, China;
5.CRRC Zhuzhou Locomotive Co., Ltd., Zhuzhou 412001, China
Based on the generalized polynomial chaos (gPC) theory and automobile system dynamics, a vertical dynamics model of an electric vehicle considering electric motor vibration with uncertain parameters was established, and compared with the Monte Carlo method in which the correctness of the model was verified.Take a certain type electric vehicle as an example, under two kinds of parametric uncertainties (variation coefficient of 10%-30%) which result from the whole vehicle and the motor assembly respectively, the statistical indicators, such as the mean, variance, coefficient of variation, probability density and distribution, and overrun probability of the vehicle ride index and motor vibration were calculated, when the car runs over a pulse type pavement in the speed range of 10-60 km/h.Under different variation coefficient of the above two kinds of parameter uncertainties, the degree and rule of influence on respective vibration responses were analyzed.The results show that the degree and rule of influence of parametric uncertainty on their statistical indices can be obtained efficiently by the generalized polynomial chaos method, and the influences are significant.In the analyzed speed domain, the maximum values of each mean response are basically unchanged with the increase of the parameters’ uncertain degree, but the variances, variation coefficients and distribution ranges are all increasing, the changing rules of overrun probabilities have diversity.When the variation coefficient of uncertain parameters and vehicle speed are set to 30% and 60 km/h, respectively, the variation coefficients of the peaks of the vehicle body acceleration, suspension compression, tire load, motor acceleration and mount compression responses reach their maximums which are 34%, 47%, 42%, 15%, and 51%, respectively.Under different parametric variation coefficients and vehicle speeds, the largest probabilities of the above response peaks exceeding the given limits are 53%, 36%, 30%, 75%, and 68% respectively, and the biggest liftoff probability of the wheel is up to 64%.
田国英，张大伟，易兴利，邓鹏毅，孙树磊. 基于gPC理论的不确定参数电动汽车脉冲响应研究[J]. 振动与冲击, 2021, 40(16): 81-90.
TIAN Guoying，ZHANG Dawei，YI Xingli，DENG Pengyi，SUN Shulei. Impulse responses of an electric vehicle with uncertain parameters based on the generalized polynomial chaos theory#br#. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(16): 81-90.
［2］FARIS F W, BENLAHCENE Z, HASBULLAH F.Ride quality of passenger cars: an overview on the research trends［J］.International Journal of Vehicle Noise and Vibration, 2012,8(3): 185-199.
［3］TURKAY S, AKCAY H.A study of random vibration characteristics of the quarter-car model［J］.Journal of Sound and Vibration, 2005,282: 111-124.
［4］黄志刚, 毛恩荣, 梁新成, 等.微型轿车八自由度整车动力学仿真与试验［J］.农业机械学报, 2008,39(6): 29-33.
HUANG Zhigang, MAO Enrong, LIANG Xincheng, et al.Dynamic simulation and experiment of subminiature car based on eight DOF model［J］.Transactions of the Chinese Society of Agricultural Machinery, 2008,39(6): 29-33.
［5］李杰, 秦玉英, 赵旗.汽车随机振动的建模与仿真［J］.吉林大学学报, 2010,40(2): 316-319.
LI Jie, QIN Yuying, ZHAO Qi.Modelling and simulation of full-vehicle random vibration［J］.Journal of Jilin University, 2010,40(2): 316-319.
［6］AGOSTINACCHIO M, CIAMPA D, OLITA S.The vibrations induced by surface irregularities in road pavements: a Matlab approach［J］.European Transport Research Review, 2014,6(3): 267-275.
［7］戴军.基于四分之一车辆模型的具有随机结构参数车辆的随机动力分析［J］.振动与冲击, 2010,29(6): 211-215.
DAI Jun.Stochastic dynamic analysis of vehicles with random parameters based on a quarter-car model［J］.Journal of Vibration and Shock, 2010,29(6): 211-215.
［8］贾爱芹, 陈建军, 曹鸿钧.随机结构参数车辆在随机激励下的振动响应［J］.西南交通大学学报, 2014,49(3): 438-443.
JIA Aiqin, CHEN Jianjun, CAO Hongjun.Vibration response of vehicle with stochastic structural parameters under random excitation［J］.Journal of Southwest Jiaotong University, 2014,49(3): 438-443.
［9］GAO W, ZHANG N, JI J C, et al.Dynamic analysis of vehicles with uncertainty［J］.Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2008,222(5): 657-664.
［10］KEWLANI G, CRAWFORD J, IAGNEMMA K.A polynomial chaos approach to the analysis of vehicle dynamics under uncertainty［J］.Vehicle System Dynamics, 2012,50(5): 749-774.
［11］WIENER N.The homogeneous chaos［J］.American Journal of Mathematics, 1938,60(4): 897-936.
［13］XIU D B, KARNIADAKIS G E.The Wiener-Askey polynomial chaos for stochastic differential equations［J］.SIAM Journal on Scientific Computing, 2002,24(2): 619-644.
［14］XIU D B.Numerical methods for stochastic computations: a spectral method approach［M］.Princeton: Princeton University Press, 2010.
［15］SANDU A, SANDU C, AHMADIAN M.Modeling multibody systems with uncertainties, part I: theoretical and computational aspects［J］.Multibody System Dynamics, 2006,15(4): 369-391.
［16］SANDU A, SANDU C, AHMADIAN M.Modeling multibody systems with uncertainties, part II: numerical applications［J］.Multibody System Dynamics, 2006,15(3): 241-262.
［17］LI L, SANDU C.On the impact of cargo weight, vehicle parameters, and terrain characteristics on the prediction of traction for off-road vehicles［J］.Journal of Terramechanics, 2007,44(3): 221-238.
［18］LI L, SANDU C, LEE J, et al.Stochastic modeling of tire-snow interaction using a polynomial chaos approach［J］.Journal of Terramechanics, 2009,46(4): 165-188.
［19］LI L, SANDU C.Stochastic vehicle handling prediction using a polynomial chaos approach［J］.International Journal of Vehicle Design, 2013,63(4): 327-363.
［21］WU J L, LUO Z, ZHANG N, et al.A new uncertain analysis method and its application in vehicle dynamics［J］.Mechanical Systems and Signal Processing, 2015,51: 659-675.
［22］BRADFORD J, MONTOMOLI F, D’AMMARO A.Uncertainty quantification and race car aerodynamics［J］.Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2014,228(4): 403-411.
［23］DAMMAK K, KOUBAA S, HAMI A E, et al.Numerical modelling of vibro-acoustic problem in presence of uncertainty: application to a vehicle cabin［J］.Applied Acoustics, 2019,144: 113-123.
［24］AHLFELD R, CIAMPOLI F, PIETROPAOLI M, et al.Data-driven uncertainty quantification for formula 1: diffuser, wing tip and front wing variations［J］.Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 2019,233(6): 1495-1506.
