Ball Bearing Dynamic Analysis Using Computer Methods—Part I: Analysis

Abstract

An analytical ball bearing dynamics model was developed that rigorously models all of the significant kinematic, structural, and dynamic effects. The model can analyze bearings of any material combination for the races, balls and ball cage. This model analyzes the stresses and deflections of the loaded elements due to (1) preload, (2) external axial, radial and moment loads, (3) centrifugal and gyroscopic ball loads. A rigorous six-degree-of-freedom model of ball cage motions was developed to analyze ball and cage dynamics. The ball cage equations of motion were written in a rotating coordinate system, which greatly simplifies the equations, resulting in a highly efficient, but rigorous, model of bearing dynamics. A computer program was developed, incorporating the algorithms, to solve the multiple simultaneous quasi-static ball-to-race load equations using modified Newton-Raphson methods. The Lawrence Livermore Ode package (LSODA) is employed for numerical integration of the dynamic equations of motion. This method assures convergence, while controlling the accuracy of the calculations as a function of computer run time and automatically selects the appropriate integration method for stiff and non-stiff system of ODE. The program analyzes ball and cage motions in time domain, wear life, fatigue life, lubricant film effects, ball-to-cage forces, torque noise and many other bearing parameters.