A LCP method for the dynamics of planar multibody systems with impact and friction

This paper is presented to show the modeling and numerical method for the dynamics of the planar multi-rigid-body system with contact, impact and Coulomb's dry friction. The multibody system consists of the rigid bodies which are linked with ideal joints and driving motors, so the system constraint equations included two parts, scleronomic constraint equations and rheonomic constraint equations. Based on the theory of contact mechanics, the local deformations in contact bodies are taken into account and the normal forces of contact surfaces are expressed as nonlinear functions of relative penetration depth and its speed during impact between two bodies. The Coulomb dry friction model is used to describe the tangential frictional forces of contact surfaces. Using the concept of friction saturation and the relative acceleration of the contact point in the tangential direction, the complementarity conditions and formulations about the friction law are given. The problems of detecting stick-slip transitions of contact points and solving frictional forces in stick situation are formulated and solved as a linear complementarity problem (LCP) by the event-driven scheme. The dynamical equations of the system are obtained by Lagrange's equations of the first kind and Baumgarte stabilization method in order to reduce the constraint drift and solve the system motion, normal contact forces and tangential friction forces as well as ideal joint constraint forces and driven constraint forces in the system. Finally, the numerical example of a planar multi-rigid-body like flat beater is given to analyze its dynamical behavior and show the availability of the method in this paper.