Friction vibration modeling with detachment and adhesion by Cellular Automata

Friction vibration in a dynamical system composed of a slider supported by a spring on a belt was modeled and simulated by Cellular Automata (CA). Friction vibration in mechanical systems has been studied for a long time and various models have been proposed to understand its physical phenomena, but dynamical behavior of an elastic body on friction surface has not been revealed yet. This may be caused by the complexity of friction between two surfaces, and CA can be used as a strong tool of modeling physical phenomena introducing local neighbor and transition rules based on observation of phenomena. It may not be easy to derive the governing equation of motion including the precise mechanism of friction. In this study, a modeling procedure of friction dynamics by CA was discussed. The new model was based on a two-dimensional spring-block model proposed by Olami, Feder and Christensen, but an additional layer of internal surface was introduced to consider the contact area of sliding surfaces. The self-excited vibration, including the stick-slip vibration and the damped free vibration could be simulated in the proposed CA model.