Modeling and analysis of sliding joints with clearances in flexible multibody systems

The modeling of the sliding joint with clearance between a flexible beam and a rigid hole is investigated in this paper. The flexible beam is discretized using the three-dimensional curved Euler–Bernoulli beam element of the Absolute Nodal Coordinate Formulation, while the motion of the rigid hole is described by the Cartesian coordinates. Moreover, the cross sections of both the flexible beam and the rigid hole are assumed to be circular. The existing joints with clearances are mainly rigid joints with small clearances, and the contact detection algorithm adopted can solve only one pair of potential contact points within one section. In order to model the contact problem in the sliding joint with clearance, a new contact detection method based on the intersection of the rigid hole’s cross section and the flexible beam is proposed, which yields a two-dimensional contact detection problem. Based on the common-normal concept, the ellipse–circle contact detection problem within the hole’s cross section can be solved. The potential contact point on the hole’s cross section will be determined, and the closest point projection on the beam’s neutral axis can be defined further. The proposed contact detection method can deal with the sliding joint with large clearance and the multiple-point contact problem within one section. In addition, the penalty method is adopted to model the frictionless contact between the flexible beam and the rigid hole. Finally, two numerical examples about sliding joints with clearances, one with an initially curved beam under gravity and the other with a straight beam under zero gravity, are presented to demonstrate the influence of the clearance of sliding joint on the dynamic performance of flexible multibody systems.