Dynamics Analysis of Spatial Mechanisms with Dry Spherical Joints with Clearance Using Finite Particle Method

Abstract

The presence of clearance in a spherical joint makes the ball of the joint easy to collide with the socket, which causes additional dynamic effects on the motion of spatial mechanisms. The complexity of interaction between different clearance joints and that between a clearance joint and connected component requires an effective analysis method. In this paper, a practical method is proposed for evaluating the dynamic effects of spatial flexible mechanisms with multiple spherical clearance joints using finite particle method (FPM) combined with a clearance contact model. First, the equations of motion of the particles and internal force formulas of spatial beam elements in the discretized FPM model are derived, and the explicit generalized-[Formula: see text] method is adopted for time integration. Then, the contact state is detected based on the penetration depth, using the Lankanani–Nikravesh model to calculate the contact force and the Threlfall model to calculate the friction force during collision in the clearance joint. Specifically, a method considering the particle rotations is utilized to better evaluate the direction of the friction force. A spatial four-bar mechanism with spherical clearance joints is used to demonstrate the feasibilities of the proposed method. The effects of four parameters (i.e. clearance size, friction coefficient, multiple clearance joints, and bending stiffness) on the dynamic responses of the mechanism are fully investigated.