Energetically consistent model of slipping and sticking frictional impacts in multibody systems

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 and stick states 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 an 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 for 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 the stick 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 plane of CoF versus CoR. Finally, a case study using the Kane’s example for impact in an MBS involving frictional impacts occurring in both slip and stick states are presented to support the analytical results.