Dynamic Modeling for Spatial Revolute Joint with Clearances in Multibody Systems Based on HLCP

Abstract

This paper presents a modeling and simulation method for rigid multibody system (MBS) with clearance-affected spatial revolute joints (SRJ) under the assumption that the clearance is much less than the physical dimension of SRJ. The SRJ is treated as an assembly of a rigid journal undergoing no-impact fixed-point motion in a bearing. A simple formulation for solving non-smooth dynamics of MBS with spatial revolute joints with clearances (SRJC) is developed by employing the complementary condition of the normal contact force. The geometric constraints of the SRJ has been transformed into a set of orthogonal bilateral constraints. The contact state determined by the magnitude and orientation of normal constraint forces in cylindrical pairs is formulated as a horizontal linear complementarity problem (HLCP) which is solved by the first kind of Lagrange’s equation and the Baumgarte stabilization method. A precession gyro is considered as a demonstrative application and the numerical results show some dynamical behaviors of MBS containing SRJC. Particularly, the proposed method can be equally applied to non-smooth dynamics of MBS considering the friction and impact.