Modeling the Road Roughness for Automotive Dynamics Simulation

It is meaningful to investigate the road roughness model and simulation approach for modern vehicle suspension design and development. Mathematical modeling of the road roughness was systematically carried out in this study, which includes modeling the Power Spectral Density (PSD) of road roughness in terms of spatial frequency, modeling the PSD of road roughness in terms of frequency, and modeling the road roughness function in the time domain. Simulations of road roughness and road classification were then performed using the established frequency and time domain models, finally the road models were incorporated into the dynamics simulation of a luxury car with air suspension. Simulation results show that the road model and simulation approach are convincing and accurate. The road theory and simulation approach obtained in this work could be useful and instructive for vehicle suspension development. Introduction Vehicle dynamics simulation plays an important role in modern vehicle design and development, especially in the process before any prototype is made. However, the simulation which is based on mature theory and data should be convincing and accurate enough to promote any decisions. In automotive suspension development, whether in the conventional suspension [1], or in the active [2, 3] suspension, or in modern air suspension [4-7], road input is crucial in vehicle vibration and suspension performance simulation, so it is meaningful to investigate the road roughness model and simulation approaches. In current automotive theories [8-10], although there are discussions about road roughness and its model, the theory and approach appear non-systematic or non-specific. In this study, mathematical modeling of the road roughness for vehicle system dynamics simulation was systematically carried out, which includes modeling the Power Spectral Density (PSD) of road roughness in terms of spatial frequency, modeling the PSD of road roughness in terms of frequency, and modeling the road roughness function in the time domain. Simulation of road roughness and road classification were then performed using the established frequency and time domain models, finally the road models were incorporated into the dynamics simulation of a luxury car with air suspension. Simulation results show that the road model and simulation approach are convincing and accurate. The road theory and simulation approach obtained in this work could be useful and instructive for vehicle suspension development. Mathematical Modeling Power Spectral Density of Road Roughness in Terms of Spatial Frequency In term of spatial frequency, the power spectral density of road roughness Gq(n) can be formulated by