Modeling and Analysis of Spatial Flexible Mechanical Systems With a Spherical Clearance Joint Based on the LuGre Friction Model

Abstract

A computational methodology for modeling spatial flexible mechanical systems with stick-slip friction in a spherical clearance joint is presented. A modified three-dimensional (3D) absolute nodal coordinate formulation based shear deformable beam element with two nodes is proposed and employed to discretize the flexible components. To avoid locking problems, we employed an enhanced continuum mechanics approach to evaluate the beam element elastic forces. The strain components εyz, εyy, and εzz are approximated using linear interpolation to improve the computational efficiency while the loss of accuracy is acceptable. The contact and friction forces in a spherical clearance joint were evaluated by the hybrid contact and LuGre friction models, respectively. Three numerical examples are presented and discussed. A simple pendulum was utilized to prove the correctness of the modified beam element. A classical slider–crank mechanism was employed to validate the computational methodology. A spatial rigid–flexible slider–crank mechanism with a spherical clearance joint was used to investigate the effect of link flexibility and joint clearance on the dynamic behavior of mechanical systems. Using the LuGre friction model, we reproduced the Stribeck effect as it is expected in real world settings. The components with appropriate stiffness play the role of suspension for spatial mechanical systems with imperfect joints. The vibrations of the flexible components play an active role of intensifying the collision in kinematic joint with clearance.