Modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance

Abstract

A general methodology for dynamic modeling and analysis of planar multibody systems containing deep groove ball bearing with clearance is presented in this paper. The bearing joint has been modeled by introducing a nonlinear constraint force system, which takes into account the contact stiffness interaction between the rolling elements and the raceways. The evaluation of the contact forces is based on the Hertzian contact deformation theory that accounts for the geometrical and material properties of the contacting bodies. The proposed model has been applied in the dynamic simulations of a planar slider–crank mechanism with a deep groove ball bearing joint. By numerical calculation, the variations of the bearing eccentric trajectory, the contact force on each ball element, the equivalent joint constraint force and the crank moment are discussed. The results indicate that the effects of the bearing clearance and flexibility on the dynamic performance of high-speed mechanisms cannot be ignored. The present methodology can not only be used to analyze the overall dynamic behavior of multibody systems with the deep groove ball bearing, but also to obtain the dynamic load on each ball element in bearing. Furthermore, the simulations of the dynamic loads on ball elements can be used for the strength checking, fatigue life prediction and wear analysis of the deep groove ball bearing in multibody systems.