Ball's motion, sliding friction, and internal load distribution in a high-speed ball bearing subjected to a combined radial, thrust, and moment load, applied to the inner ring's center of mass: Mathematical model

Abstract

A set of non-linear algebraic equations, which must to be solved using a numerical procedure, for ball's motion, sliding friction and internal loading distribution computation in a high-speed, single-row, angular-contact ball bearing, subjected to a known combined radial, thrust and moment load, which must be applied to the inner ring's centre of mass, is introduced. For each step of the procedure it is required the iterative solution of 9Z + 3 simultaneous non-linear equations—where Z is the number of the balls—to yield exact solution for contact angles, ball attitude angles, rolling radii, normal contact deformations and axial, radial, and angular deflections of the inner ring with respect the outer ring. While the focus of this work is obtaining the steady state forces and moments equilibrium conditions on the balls, under the selected loading, the numerical aspects of the procedure are treated in a companion paper. The numerical results derived from the described procedure shall be published later.