A method for dynamic modeling and simulation of the translational joint with clearance and LuGre friction

The main purpose of this paper is to present a method for dynamic modeling and simulation of the translational joint with friction and clearance. The sizes of the clearances and the impacts between the slider and the guide in the translational joint can be neglected when the clearance sizes are very small. The geometric constraints of the translational joint are treated as bilateral constraints. The contact forces acting on the slider are reduced to the forces on the slider corners. The LuGre friction model is used to describe friction between slider and guide, because it can capture the variation of the friction force with slip velocity and the slider motion with stick-slip phenomenon. The problem of computing the normal forces on the slider is formulated and solved as a horizontal linear complementarity problem (HLCP), which is embedded in the event-driven method. Finally, a numerical example is considered and numerical results are presented to show the feasibility and the effectiveness of the method.