Bearing Models for Advanced Ball Bearing Simulation

A comprehensive quasi-static and dynamic ball bearing model is described using many enhanced features, including novel calculations of the contact angle variations and ball–race sliding speeds in two directions, accounting for race curvature, pivoting effects and gyroscopic effects, appropriate lubricant rheology, and sliding forces (driving the balls against miscellaneous braking forces and moments such as, for example, the hydrodynamic rolling force). Ball–cage impact forces and cage-guiding ring forces are also considered, leading to a set of six dynamic differential equations to consider for each ball and three dynamic differential equations for the cage, where movement is assumed to be restricted to one plane. Quasi-static calculations can be undertaken by neglecting the cage and setting the accelerations of each degree of freedom of the ball to zero. New analytical or curve-fitted models are also provided using the mean values of sliding speed and viscosity to calculate sliding forces and moments, avoiding the use of contact slices with some useful relationships derived for calculating the rolling line locations, bearing torque, and dissipated bearing power. Several examples of calculated results are given and compared to available numerical or experimental results published in the literature. Finally, a new tool developed in-house is proposed for predicting many properties, particularly of interest at high speed, including the ball bearing torque, power loss, risk of smearing, and risk of cage failure.