engleski

Modeling and Analysis of Tire Dynamics with respect to Wheel Torque Variations

Development of high-performance ABS, TCS, and vehicle dynamics control systems requires precise tire dynamics models. There are two tire vibration modes when considering the longitudinal tire force response with respect to wheel torque variations. These modes correspond to torsional compliance of the tire sidewall and longitudinal compliance of the tire tread. The recently developed LuGre tire friction model is exploited in this study to model the tire dynamics and analyze the tire vibrations. For the purpose of vibration analysis, the LuGre model is linearized and represented by an equivalent spring-damper system. All parameters of the equivalent system are found to depend on slopes of the tire static curve. The overall tire dynamics model is of fourth order, and the values of vibration modes' natural frequencies and damping ratios can only be found numerically. In order to find an analytical solution for vibration mode parameters, four approximate methods are proposed and analyzed. The most accurate results are obtained by direct extraction of the high-frequency and low-frequency modes from the fourth-order characteristic polynomial of the overall model. The model is tested by plotting its frequency response, time response, and natural frequencies and damping ratios as functions of the tire force operating point and the wheel center speed. It is demonstrated that the proposed compact and fully physical model predicts comparable results as the more complex, semi-empirical, relaxation length-based model.

Modeling; tire; dynamics; friction; vibration analysis

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