Research And Application Of Car Nonstationary Random Vibration Modeling And Solution Methods

With the development of science and the advancement of society,the research of vehicle property and the technology of vechicle develop rapidly,and are developing towards safety,comfort,energy saving and intelligence.The research on nonstationary random vibration of vehicle that conforms to the actual operation of vehicle meets the requirements of science and society for car better,and is an important component of the research on vehicle random vibration.Modeling and solution are the key problems in the study of nonstationary random vibration of car.The study of these two key problems need to combine the characteristics of the speed-changing car running on the road.The modeling of nonstaionary random vibration of vehicle refer to the modeling of vehicle and the modeling of road.Simultaneously,the solution of nonstationary random vibration of vehicle refer to the solutions of nonstationary random vibration response of vehicle and its statistical characerisitics.Aiming at the problems that covariance equivalent method lacks mathematical foundation support and derivation,the problems of covariance equivalent method are found by theoretical analysis.The correlation function equivalent method is built,and the stationary stochastic process model of road roughness and the nonstaionary stochastic process model on time domain of wheel road random excitation and its equivalent expression are derived.Aming at the influence problem of road random excitation on vertical vibration,coupling of vertical vibration and pitching motion,coupling of vertical vibration and rolling motion,three models of vehicle vibration are established.Aiming at the solution problem of car nonstaionary random vibration response and its statistical characteristics,the universal car vibration model on spatial domain and car vibration response characteristics on spatial domain are established,and two solution methods of car nonstaionary random vibration response and its statistical characteristics are put forward,which are solution method based on the spatial frequency Fourier transformation and solution method based on the spatial Pseudo Excitation Method(PEM).Setting three sets of car parameters,typical driving cycle and complex driving cycle for three car models,the simulation program of car nonstaionary random vibration response and its statistical characteristics by Matlab,and the car nonstationary random vibration response and its power spectral density(PSD)and root mean square(RMS)are solved and simulated,the results show that the solution results of two solution methods are agreed,and the two solution methods can be used to solve the statistical characteristics of car nonstationary vibration response,the statistical characteristics of car nonstationary vibration response varies with the speed of car,and has time-varying characteristics.The main contents of this paper are given as follows:(1)The stochastic process models of road roughness and wheel road random excitationAiming at the problems that covariance equivalent method lacks mathematical foundation support and derivation,two kinds of nonstaionary White Gaussian noise correlation function equivalent method is established based on mathematical basis,and approximate the exponential function in first order through Pade approximation.The stationary random progress model of road roughness is established in spatial domain,the nonstaionary random progress model of wheel road random excitation is established in time domain,and the equivalent expression of nonstaionary random progress model of wheel road random excitation based on the equivalent results of the two kinds nonstationary Gaussian white noise.(2)Single wheel,plane and spase models of car vibrationIn order to analyze the influence of nonstaionay road random excitation on vertical vibration,coupling of vertical vibration and pitching motion,coupling of vertical vibration and rolling motion,two degrees of freedom(DOF)single wheel model,six DOF plane model and twelve DOF spase model of car vibration are established,and the car vibration response and its expression are determined.(3)Solution method of car nonstaionary random vibration response and its statistical characteristicsAiming at the solution problem of car nonstationary random vibration response and it statistical characteristics,the road random excitation vector of wheel is expressed uniformly in time domain,the state equation of time-invariant car vibiration in time domain is derived,combine the state equation of car vibration in time domain and the road random excitation vector of wheel in time domain,and the state equation in time domain of car random vibration which is time-invariant when speed is constant and time varying when speed is changing is established.A solution method of statistical characteristics of car nonstationary random vibration response based on the spatial frequency Fourier transformation is put forward,and another solution method of statistical characteristics of car nonstationary random vibration response is presented based on extension of PEM and which is spatial domain PEM.The statistical characteristics expression of the three kind car vibration response is extablished by these two solution methods.(4)Simulation of car nonstationary random vibration response in time domianSetting three sets of car parameters,typical driving cycle and complex driving cycle for three car models,the simulation program of car nonstaionary random vibration response by Matlab,Oriented towards typical driving cycle,the nonstationary road random excitation of wheel and vibration response of three car models in time domain are solved,compared with the corresponding results of car stationary random vibration,and explains the difference between car nonstationary and stationary random vibration.Oriented towards complex driving cycle,the nonstationary road random excitation of wheel and vibration response of three car models are solved,and explains the complexity of car nonstationary random vibration.(5)Statistical characteristics simulation of car nonstationary random vibrationBased on Fourier transformation method and PEM method of statistical characteristics solution of car nonstationary random vibration response,the simulation program of statistical characteristics of car nonstaionary random vibration response is developed,statistical characteristics of car nonstaionary random vibration response in typical driving cycle and complex driving cycle are simulated by the Fourier transformation method and PEM method,the correctness and effectiveness of solution method of statistical characteristics of car nonstaionary random vibration response are verified by compare the results of the two methods.The innovations in this paper are described as follows:(1)Aiming at the problems that covariance equivalent method lacks mathematical foundation support and derivation,by means of Lagrange’s mean value theorem,Dirac function and complex Dirac function and its scaling properties,correlation function,correlation function of standard White Gaussian noise,two kinds of nonstationary White Gaussian noise,namely ‘frequnce modulation’ white noise and ‘amplitude modelation’ white noise,are obtained by transforming the standard white noise,it is proved in theory that the correlation function equivalent of the two kinds of nonstationary White Gaussian noise,it shows that the two kinds of nonstationary White Gaussian noise are correlation function equivalent and are not covariance equivalent,it should be called correlation function equivalent method instead of the covariance equivalent method,the stationary random progress model of road roughness and the nonstationary random progress model of wheel road random excitation in time domain are built,it is more perfect in theory,more clear in method and more convenient in application.(2)By mean of the method of tatistical characteristics of car nonstationary random vibration response based on the time frequency Fourier transformation,the solution method of tatistical characteristics of car nonstationary random vibration response based on the spatial frequency Fourier transformation is put forward,firstly,the spatial frequency relation of wheel road roughness,the spatial frequency response characteristics of car vibration and car vibration response is builts in theory,then the PSD and RMS of car nonstationary random vibration response are determined.The derivation of this method has systematicness and uniformity,but it is complicated,which need to establish the spatial frequency response characteristics of vehicle vibration and vibration response.(3)By mean of the solution method of statistical characterisitics of random vibration responde by random vibration PEM in time domain,the solution method of statistical characterisitics of nonstationary random vibration responde by PEM in spatial domain is put forward.Pseudo excitation,pseudo response and the fundamental formula of PSD are constructed in spatial domain,pseudo road rughness in spatial is established and spatial frequency response characteristics of car vibration is deduced by PEM fundamental formula in theory,then pseudo response and PSD and RMS of car nonstationary random vibration responde are obtained by algebraic operation.This method dose not need to deduce spatial frequency response characteristics of car vibration response,the spatial frequency response characteristics of car vibration can be obtaianed by the independent derivation of fundamental formula or direct use the spatial frequency response characteristics of car vibration by spatial frequency Fourier transformation.(4)In this paper,a car vibration twelve DOF space model considering the two front seats and three rear seats is built,is different from the seven DOF,eight DOF and eleven DOF space models which have zero seat,single seat and two front seat and two rear seat,and is more conform to the car reality.The car vibration model in special domain and the special frequency response characteristics of car vibration are universal,and can represent the car vibration model in special domain and the special frequency response characteristics of various kinds vehicle.The solution simulation program of car nonstaionary random vibration response in time domain and statistical characteristics is developed by Matlab can be used to analyze both car stationary random vibration and car nonstationary random vibration.On the study of car nonstationary random vibration,the cyclic driving state in research on vehicle economy is introduced,that can break through the limitation of ride comfort study at constant speed to make the ride comfort study at varying speed more in line with actual,and it is also advantageous to carry out the joint research of ride comfot and vehicle economy.