Analysis of frictional contact models for dynamic simulation

Simulation of dynamic systems possessing unilateral frictional contacts is important to many industrial applications. While rigid body models are often employed, it is well established that friction can cause problems with the existence and uniqueness of the forward dynamics problem. In these situations, we argue that compliant contact models, while increasing the length of the state vector, successfully resolve these ambiguities. The simplicity and efficiency of rigid body models, however, provide strong motivation for their use during those portions of a simulation when the compliant contact model indicates a unique and stable solution. We use singular perturbation theory in combination with linear complementarity theory to establish conditions for the validity of the rigid body model with rolling and sliding unilateral contacts for planar systems. The results are illustrated with a simple example