Non-smooth numerical solution for Coulomb friction, rolling and spinning resistance of spheres applied to flexible multibody system dynamics

The general motion of a sphere in a mechanism in contact with a rigid planar surface under rolling, sliding and spinning friction is studied in the context of non-smooth contact dynamics. The equations of motion are solved by the non smooth generalized-a implicit time integration scheme, where the position and velocity level constraints are satisfied exactly without requiring to define any particular value for a penalty parameter. The geometrical properties of the spheres are described by a rigid-body formulation with translational and rotational degrees of freedom. The robustness and the performance of the proposed method-ology is demonstrated by different examples, including both flexible and/or rigid elements.

Automated summary

This paper studies the general motion of a sphere in contact with a rigid planar surface under rolling, sliding, and spinning friction in the context of non-smooth contact dynamics. The equations of motion are solved using a non-smooth generalized implicit time integration scheme, which ensures exact satisfaction of position and velocity level constraints without the need for defining a penalty parameter. The geometrical properties of the spheres are described using a rigid-body formulation with translational and rotational degrees of freedom. Various examples, including flexible and/or rigid elements, demonstrate the robustness and performance of the proposed methodology.