Simulating two-dimensional stick-slip motion of a rigid body using a new friction model

This paper proposes a new method for simulating the two dimensional stick-slip response of a rigid body subjected to friction forces. The physical problem is complicated by the fact that the two-dimensional equations of motion are coupled and that the two separate directional responses are highly nonlinear, particularly at transition points, when the relative velocity between the rigid body and supporting surface is close to zero. The proposed model does not employ the commonly used imaginary spring concept, which is numerically convenient, but has no physical meaning. Rather, it extends Westermo and Udwadia's one-dimensional friction method to two dimensions. The proposed model explicitly solves the governing equation of motion by employing an interpolation technique and numerical integration to find exact transition points in the velocity response curve. Using simulation, the new model is compared to existing models for cases involving harmonic motions and is shown to overcome certain numerical problems associated with existing models.