Modeling and Analysis of Rigid Multibody Systems with Translational Clearance Joints Based on the Nonsmooth Dynamics Approach

The main purpose of this paper is to discuss a method for a dynamic modeling and analysis of multibody systems with translational clearance joints. The method is based on the nonsmooth dynamics approach, in which the interaction of the elements that constitute a translational clearance joint is modeled with multiple frictional unilateral constraints. In the following, the most fundamental issues of the nonsmooth dynamics theory are revised. The dynamics of rigid multibody systems are stated as an equality of measures, which are formulated at the velocity-impulse level. The equations of motion are complemented with constitutive laws for the normal and tangential directions. In this work, the unilateral constraints are described by a set-valued force law of the type of Signorini's condition, while the frictional contacts are characterized by a set-valued force law of the type of Coulomb's law for dry friction. The resulting contact-impact problem is formulated and solved as a linear complementarity problem, which is embedded in the Moreau's time-stepping method. Finally, the classical slider-crank mechanism is considered as a demonstrative application example and numerical results are presented. The obtained results show that the existence of clearance joints in the modeling of multibody systems influences their dynamics response.