Ball bearing friction assessment through power minimization

Two-point contact bearings are widely used in industry. In space applications, where the speed of the mechanisms is low, the main source of friction in the bearings is the one produced at the ball-raceway contact ellipses. This friction affects the motorization margin which is a key aspect of the operational envelope in space mechanisms. The traditional method to estimate this friction works by trying to find the force equilibrium for each ball. For that, an iterative sequence is arranged with six parameters defining the ball kinematics under the action of normal and friction forces assuming a constant friction coefficient. The force equilibrium model is reviewed analyzing the influence of the speed, and the implications of quasi-static assumption are assessed. For this last assumption, an energetic method is proposed established upon the minimization of the friction power generated within the contact patches. This model provides the same results as the force equilibrium model with a stronger convergence and a simple computational implementation. Finally, the two methods are compared obtaining better performances for the power minimization method. This work represents a first step in order to substitute force equilibrium methods with more stable energy based methods in bearing friction calculations.