A Model to Estimate Separator Forces during Ball Speed Variations

When the combined loads on ball bearings include forces in the radial or moment directions, the balls will not orbit the bearing at one common speed. This ball speed variation (BSV) might result in additional bearing friction forces if the variation in speed is large enough to allow the balls to spread out from their normal spacing by an amount that exceeds the cage pocket clearances. In this paper we present a model used to estimate the cage forces and friction torques caused by BSV and compare the model predictions with measured friction torque test data. The model first analyzes the forces on a single ball by determining the distance over which a ball must slip during a single orbit of the bearing center. The ball to race force is determined by equating the energy lost during this slip with the energy input through traction at the inner race interface. The component of the ball to cage force normal to the ball–pocket interface is then determined by balancing this force with the ball to race force. The cage to land force is similarly determined by balancing the collective forces at all the ball to race and ball to cage interfaces. Finally, the BSV drag torque is written as the sum of contributions from these three drag sources. In order to validate the model, test data were obtained using single 204 size bearings operating under applied thrust and radial loading. The bearing drag torque was found to depend on the degree of misalignment and cage pocket clearance, as predicted by the model.