Friction model for planar two-dimensional motion

This paper describes a friction model that enables the simulation of mechanical motion with planar two-dimensional friction. Most existing friction models for control applications are applicable to one-dimensional motion only. The proposed model is derived by extending the conventional friction model, the Dahl model. This is achieved by replacing the scalar quantities in the Dahl model with vector quantities. The principal properties of the original model, that is, boundedness and rate independence, are preserved. In the proposed model, the maximum friction force is equal in all directions and the direction of the friction force coincides with the direction of motion, which a simple pair of one-dimensional models cannot obtain. A simulation application is presented for a typical example with planar two-dimensional friction.