Modeling and Analysis of Planar Rigid Multibody Systems with Translational Clearance Joints

Authors: Paolo Flores (University of Minho, Portugal), Remco Leine

Manufacturing tolerances, wear and material deformation lead to imperfect joints and, therefore, clearances. These clearances modify the dynamic response of the system, justify the deviations between the numerical predictions and the experimental measurements and eventually lead to important deviations between the projected behavior of the mechanisms and their real outcome. The presence of clearance in joints is a complex and important issue in the realistic modeling of multibody systems. This aspect gains paramount importance due to the demand for the proper design of the real joints in many industrial applications. Over the last few years, extensive work has been done to study the dynamic effect of the revolute joints with clearance in multibody systems. However, translational joints with clearance have received less attention.

The aim of this joint research project is to present and discuss a methodology for a dynamic modeling and analysis of rigid multibody systems with translational clearance joints. The methodology is based on the non-smooth 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 time-stepping method. Finally, the classical slider-crank mechanism is considered as a demonstrative application example and numerical results are presented. The results obtained show that the existence of clearance joints in the modeling of multibody systems influences their dynamics response.