Relaxation Behavior

To predict the transient behavior of tire a linear relaxation model is used. In this model the tire contact patch is suspended with respect to the wheel rim plane by a longitudinal and lateral spring. The relative movement between contact patch and wheel rim plane models the carcass deflection.

The longitudinal deformation

and lateral deformation

For small values of u and v, the longitudinal and lateral forces will be

Where and are tire’s structural stiffness in longitudinal and lateral direction respectively. Using relaxation lengths in force calculation will result in following equations


The force calculation remains the same but and are used in place of and .

When the state value goes out of bounds; an artificial damping can be applied to the state values. It is required when a tire goes over large obstacles. Low_speed_threshold, damp_x, damp_y are three additional parameters in tire property file that can be used to tune artificial damping to avoid non-physical values of state.