An Investigation of Contact Angles in Angular Contact Ball Bearings Accounting for High Speed Effects and Preload

Angular contact ball bearings are the most commonly used types of bearings. Although simple in appearance, these bearings have a complicated and nonlinear behavior, and have significant effect on the dynamics of a rotating system. Accounting for high speed effects adds to the complexity of their behavior. The governing equations of the bearing amount to the solution of a set of nonlinear equations for each rolling element at each iteration, which represents a tedious and expensive solution. In this work, a simplified model for angular contact ball bearings under the action of arbitrary loading including high speed effects and preload is presented. The model considers five degrees of freedom for relative displacement of rings and a mean contact angle for inner and outer raceway contacts are introduced which renders the solution for all rolling elements to that for a single one. The use of the simplified model at high speeds is justified by presenting the analysis of a complete spindle-bearing system using the simplified model and comparing the results with those of the full model.