Modeling And Simulation In Time Domain For Random Road Excitation Based On Inverse Fourier Transform

There are two main models in road modeling, the frequency domain model and the time domain model. The frequency domain model has the characters of the briefness, clarity, and mature development. There are some limits to modeling in the time domain, but the frequency domain model does not achieve the superiorities property existing in the time domain model. To do research for automobile ride comfort, it is necessary to obtain the time domain model when the research aims at non-linearity dynamics or coupling dynamics in the road-automobile-people system.Though the international scholars have already founded various time domain models for simulating the random road excitation, there are the localizations in every model. Aiming at the problem of the random road excitation simulation based on inverse Fourier transform. The paper has researched deeply for improving the theory system. Firstly, the single wheel road time domain model was founded based on inverse Fourier transform by theory study; secondly, the four-wheel road time domain model conform to the characters of the actual road was founded, considering correlation character between left and right wheels; thirdly, the correctness and validity of the single wheel road time domain model was checked by 1/4 automobile two DOF vibration model; finally, automobile seven DOF vibration model was founded and realized the ride comfort simulation of the whole automobile in time domain using the four-wheel road time domain model.(1) The single wheel road time domain model based on inverse Fourier transform. The basic mathematics theory about the single wheel road time domain modeling based on inverse Fourier transform is summarized, and the method of time domain modeling is founded by transforming displacement power spectrum density of random road excitation. Through the rigorous deducing and analysis, the corresponding arithmetic is established.Based on the software of MATLAB, the random road excitation to the wheel at each time under different levels of road and different speed can be obtained through simulating time domain model. Transformed these data between time and frequency domain, the corresponding PSD curves can be obtained. The modeling method has proved correct, and the model has the characters of little account and accuracy through comparing these PSD curves and standard PSD curves.(2) The four-wheel correlation time domain model based on inverse Fourier transform.Considering the correlation of the four wheels input that the time is delayed between the front and rear wheel and the space is correlative between the left and right wheel. No any hypothesis, the brief and common expression of the spectrum matrix of road input to automobile is founded according to which usual expression based on some hypothesis is founded. Connecting with the character of the actual road, the time domain model of space four-wheel input coincident with the road coherent function is founded on the base on the single wheel time domain model. The basic thought and the process of deducing about founding four-wheel road time domain model have been expressed in this paper.The four-wheel road random excitation problem is settled using the simulation arithmetic of four-wheel time model under the condition of the given road coherent function. The result of simulation expressed that the random road excitation to the rear is some time delay to the front wheel which is equal to the quotient of wheelbase divided by the speed, and transform these data between time and frequency domain of the left and right random road excitation, and then calculate the coherent function and commutative power spectrum density function compared to the criterion values respectively. The four-wheel road time model has proved correct through the comparing results.(3) Ride comfort simulation and study to the 1/4 automobile two DOF vibration model.Based on the 1/4 automobile two DOF vibration model, frequency response characteristic of it, the perpendicular acceleration of bodywork (body), dynamic flexibility and relatively dynamic load of the wheel were summarized as well as the formula of the PSD of the response in frequency domain.The single wheel road time domain model was applied to the vibration differential equation which can be settled by the method of Newmark and each response was computed in time domain, the process of the PSD in time domain by the method of Welch is expressed. Two kinds of PSD curse were contrast in frequency domain and time domain. It validates the feasibility of the model by the satisfying compare results.(4) Ride comfort simulation and study to the automobile seven DOF vibration model.Aiming at the need of research, the automobile seven DOF vibration model was founded. Based on the space road time domain model, using the soft of MATLAB, the soft of ride comfort time domain simulation was excogitated; The paper researches and simulates the ride comfort of the CA141 in time domain under the condition of parameter of CA141 and the coherent function by testing. The result of the simulation suggests that the random road excitation method based on the inverse Fourier transform applied to the automobile vibration model makes the work forecast and evaluate the dynamics property of the automobile ride comfort more quickly.