Analysis of transient longitudinal dynamic behavior of tire on μ-step road

In this paper, the variation of tire longitudinal force and vehicle motions is studied when vehicle passing through the boundary of two road surfaces with different friction coefficient. The critical longitudinal slip of total sliding on the front and back roads is obtained by theoretical analysis. Then the variation of longitudinal force in different range of longitudinal slip is analyzed and a mathematical model is established to describe the transient force characteristics of tire. The longitudinal force, the longitudinal slip, the forward speed, and the angular velocity of the wheel on mu,-step road are tested experimentally for different initial longitudinal slips, compared the tested results with those calculated by mathematical model. The results show that the initial longitudinal slip before passing through the road boundary is directly related to the change of longitudinal force and vehicle motions. The larger the initial longitudinal slip is, the more obvious the transient characteristics of the tire will be. For the vehicle driving from high-adhesion-road to low-adhesion-road. When the initial longitudinal slip is small, the longitudinal force decreases rapidly at first, and then quickly returns to the original value and remains constant on the low-adhesion-road. When the initial longitudinal slip exceeds the maximum recoverable longitudinal slip, the reduced longitudinal force cannot be recovered or can only be partially recovered on the low-adhesion-road. For the case of low-adhesion-road to high-adhesion-road, the longitudinal force will continue to increase as the tire passes through the boundary, and then gradually decrease to the original value when contact area passes through the boundary completely. In generally, the increased initial slip rate will not cause the longitudinal force irrecoverable. The relevant conclusions can provide theoretical references for vehicle dynamics and ABS control.