Minimum Energy Hypothesis in Quasi-Static Equilibrium Solutions for Angular Contact Ball Bearings

Abstract

The commonly used quasi-static model for angular contact bearings is enhanced by coupling contact mechanics and bearing kinematic analyses with traction or friction behavior in ball–race contacts. The points of pure rolling in the contacts, which constitute the primary inputs in the kinematic equations, are determined by minimizing the frictional dissipation based on a prescribed elastohydrodynamic traction model. Such an intricate coupling between contact mechanics, bearing kinematics, and lubricant behavior provides significant enhancement of simple quasi-static model for greatly improved prediction of traction behavior and heat generation in ball bearing contacts. The predictions are in close agreement with those obtained by much more sophisticated dynamic analysis based on integration of classical differential equations of motion of bearing elements. The enhanced quasi-static model can therefore be effectively used as a design tool for optimizing thermal dissipation in ball–race contacts in ball bearings. To facilitate immediate evaluation and implementation of the model to practical problems, a standalone software, containing the enhanced quasi-static model, is made freely available at www.PradeepKGuptaInc.com/AdoreQS.html.