A NUMERICAL METHOD FOR DYNAMICS OF PLANAR MULTI- RIGID-BODY SYSTEM WITH FRICTIONAL TRANSLATIONAL JOINTS BASED ON LUGRE FRICTION MODEL

A numerical method for the dynamics of the planar multi-rigid-body system with frictional translational joints is presented in this paper. The multibody system consists of the several rigid bodies which are linked with ideal revolute joints and imperfect translational joints. The frictional forces on the slider in the imperfect translational joint are modeled by the LuGre friction law which can effectively describe stick-slip motion in the mechanical system. The sizes of the clearances and the impacts between the guide and the slider in the translational joints can be neglected when the clearance sizes are very small, so the geometric constraints of the translational joints are treated as bilateral constraints. In this work, firstly, the complementarity conditions and formulations about the normal forces on the slider in the translational joint are given. Secondly, the dynamical equations of the multibody system are obtained by the Lagrange's equations of the first kind and the Baumgarte stabilization method for the constrained multibody systems in order to reduce the constraint drift in the numerical simulation of the multibody systems. Thirdly, the problems of determining contact situations of the slider in the translational joint and solving normal forces on the slider in all contact situations are formulated and solved as a linear complementarity problem (LCP). Finally, two numerical examples of the planar multi-rigid-body system with a frictional translational joint are given to illustrate their dynamical behaviors such as stick-slip motion and several contact situations of the slider in the translational joint. The LuGre friction model and the Coulomb friction model are used in two numerical examples to compare the dynamical behaviors of two mechanical systems. The numerical results obtained by our method are compared with that obtained by other method. The numerical results of the examples show the availability of the method presented in this paper.