A differential approach for modeling revolute clearance joints in planar rigid multibody systems

A non-penetration approach of frictional contact analysis is presented for modeling revolute clearance joints of planar rigid multibody systems. In the revolute clearance joint, the motion modes of the journal are divided into three categories, namely, the free motion, collision, and permanent contact modes. The switch between different contact modes is identified by the state of the journal and bearing, including the gap and the normal relative velocity. When impact in the revolute clearance joint is detected, the collision process is simulated by the impulse-based differential approach, where Stronge’s improved model for restitution is employed to determine the relative velocity after impact. Instead of algebraic equations, the impact process is described by a set of ordinary differential equations (ODEs), which avoids solving complementarity problems. Moreover, in the permanent contact mode, the constraint-based approach and modified Coulomb’s friction law are adopted. The permanent contact mode maintains for most of the time and the governing ODEs are non-stiff. There is general agreement that the constraint-based approach is more efficient than the force-based method. A slider–crank mechanism with a revolute clearance joint is considered as a demonstrative application example where the comparison with the continuous contact force model is investigated.