Fractional Derivative Rigid Ring Tire Model with Berg Friction for Vehicle Dynamic Analysis

The tire is one of the key components that affect vehicle performance and ride quality. The rigid ring model has been widely used in the dynamic simulation of tire rolling uneven road surface, and calculate the tire stiffness and force of rim under quasi-static conditions. However, the traditional spring-damping between rim and belt is not accurate enough to describe the viscous damping force and hysteretic behavior of rubber. Therefore, it is necessary to propose a new rigid ring model, considering the viscoelasticity of tire side rubber and hysteretic behavior of rubber, to better adapt to the intermediate frequency response of tire. In this paper, the rigid ring model introduces the fractional derivative damping and friction force element to enhance the dynamic response of tire in higher frequency. Linear damping is replaced by a three-parameter fractional-order derivative damping model, and a Berg friction element was added between rim and belt. The influence of the parameters of the fractional derivative damping model and the Berg model on the dynamic force characteristics and hysteresis loop of the tire were compared and analyzed. To verify the model proposed in this paper, a quarter car model was established to analyze the influence of the model on the suspension response characteristics. Compared with the ordinary rigid ring, the model proposed has a better expression of the dynamic stiffness of tire and higher fitting accuracy under different frequencies. The effectiveness and accuracy of the fractional derivative rigid ring model with Berg are verified.