Modeling and simulation of a planar rigid multibody system with multiple revolute clearance joints based on variational inequality

Abstract

The main objective of this work is to provide a nonsmooth strategy for solving planar rigid multibody systems with multiple revolute clearance joints. In the present work, based on the variational inequality, the governing equations of the multibody system are obtained by the principle of Hamilton's variation, and the discrete form of the governing equations satisfies symplecticity. The impact reaction and the friction reaction are expressed by the Newton impact law and modified friction model. According to the complementary relationship of the impact reaction and relative velocity, the contact reaction together with the relative velocity are formulated as a standard linear complementary problem and solved by Lemke's method. Eventually, several examples with multiple revolute clearance joints are tested by the proposed method, correctness of the results obtained by the proposed method are compared with those of ADAMS. Meanwhile, the effects of different number of clearance joints, different values of impact coefficient and driving load on the dynamic behavior of multibody system are studied. The results show that the proposed method performs well for multibody system with multiple revolute clearance joints.