Transient lateral dynamic behavior of tire on μ-step road

In this paper, the transient response of tire to step change in road friction coefficient is studied. The brush model is used to analyze the tread deformation, and a mathematical model is established to describe the transient behavior of the tire. The transient response curves of lateral force, aligning torque, slip angle, yaw angle and lateral displacement are obtained. For large initial slip angle, the transient expressions of tire force and torque are established by analyzing the change of tread deformation, and a second-order ordinary differential equation is established to describe the transient characteristics of tire by combining with the equations of motion. In addition, the rigid ring model is used to investigate the influence of flexible sidewalls. For small initial slip angle, a set of partial differential-integral equations of tread deformation and lateral displacement is established, and a numerical method is provided to solve these equations. Furthermore, an estimation method is proposed to make the calculation more efficient. The relevant conclusions of this paper can provide theoretical reference for vehicle dynamics and control.