In modern high-speed ball bearings the pressure areas, which result from elastic deformations at the ball-race contacts, are appreciably curved and interfacial slip can occur at most points within the pressure areas. These slippages give rise to friction forces acting on the ball which are held in equilibrium by reactions from the races and the inertia effects of the motion of the ball.
A method is derived for determining the motion of the ball and sliding friction in a high-speed, angular-contact ball bearing under thrust load in terms of the inertia effects on the ball and the frictional resistances resulting from interfacial slip at the contact areas. Possible elastic compliance at the interface, hysteresis, and dynamical perturbations of ball motion are neglected. The solution of eight, simultaneous equations involving double integrals for which closed-form solutions cannot be found is required. A solution for a particular case requires the services of a high-speed computer.
For the case where gyroscopic effects on the ball can be neglected, certain simplifications and assumptions can be made which enable the solution of a particular problem using conventional computation means.