Rubber friction and tire dynamics

We propose a simple rubber friction law, which can be used, e.g., in models of tire (and vehicle) dynamics. The friction law is tested by comparing numerical results to the full rubber friction theory (B.N.J. Persson, J. Phys.: Condensed Matter 18, 7789 (2006)). Good agreement is found between the two theories. We describe a two-dimensional (2D) tire model which combines the rubber friction model with a simple mass-spring description of the tire body. The tire model is very flexible and can be used to calculate accurate mu-slip (and the self-aligning torque) curves for braking and cornering or combined motion (e.g., braking during cornering). We present numerical results which illustrate the theory. Simulations of Anti-Blocking System (ABS) braking are performed using two simple control algorithms.