Frictional Impacts in Multibody Systems

TL;DR

This paper introduces a unified impact model for multibody systems with friction, ensuring energetic consistency and defining limits on friction and restitution coefficients to determine impact modes and stability.

Contribution

It presents a novel impact model that unifies slipping and sticking impacts with energetic consistency, and introduces the Critical CoF to determine impact modes and parameter bounds.

Findings

The model achieves energetic consistency in slip and stick states.

Critical CoF determines the minimum static friction to prevent impact violations.

Upper bounds on CoF and CoR depend on impact mode and are visualized in parameter space.

Abstract

A unifying slipping and sticking frictional impact model for multibody systems in contact with a frictional surface is presented. It is shown that the model can lead to energetic consistency in both slip state and stick state upon imposing specific constraints on the coefficient of friction (CoF) and the coefficient of restitution (CoR). A discriminator in the form of a quadratic function of the pre-impact velocity is introduced based on isotropic Coulomb constraint such that its sign determines whether the impact occurs in the sticking mode or in the slipping mode just prior to the contact. Solving the zero-crossings of such a function in terms of the CoF and the CoR variables leads to another discriminator called Critical CoF, which is the lowest static CoF required to prevent the subsequent impulse vector violating the isotropic friction cone constraint. Investigating conditions for the energetically consistent impact model reveals that the maximum values of either CoR or CoF should be limited depending on stick state or slip state. Furthermore, it is shown that these upper-bound limits in conjunction with the introduced Critical CoF variable can be used to specify the admissible set of CoR and CoF parameters, which can be represented by two distinct regions in the plan of CoF versus CoR.