A Discrete Element Approach for Modeling Cage Flexibility in Ball Bearing Dynamics Simulations

A model for deep-groove and angular-contact ball bearings was developed to investigate the influence of a flexible cage on bearing dynamics. The cage model introduces flexibility by representing the cage as an ensemble of discrete elements that allow deformation of the fibers connecting the elements. A finite element model of the cage was developed to establish the relationships between the nominal cage properties and those used in the flexible discrete element model. In this investigation, the raceways and balls have six degrees of freedom. The discrete elements comprising the cage each have three degrees of freedom in a cage reference frame. The cage reference frame has five degrees of freedom, enabling three-dimensional motion of the cage ensemble. Newton's laws are used to determine the accelerations of the bearing components, and a fourth-order Runge-Kutta algorithm with constant step size is used to integrate their equations of motion. Comparing results from the dynamic bearing model with flexible and rigid cages reveals the effects of cage flexibility on bearing performance. The cage experiences nearly the same motion and angular velocity in the loading conditions investigated regardless of the cage type. However, a significant reduction in ball-cage pocket forces occurs as a result of modeling the cage as a flexible body. Inclusion of cage flexibility in the model also reduces the time required for the bearing to reach steady-state operation.