Ball Motion and Sliding Friction in a Four-Contact-Point Ball Bearing

An analysis of double arched ball bearing, which considers centrifugal forces and gyroscopic effects, is performed. Based on operating conditions of a five DOF inner ring and Coulomb friction model, the conventional bearing theory is extended from two to three or four-contact points. The commonly used control criterion of ball bearing by the inner or outer raceway is debatable and is known to fit with difficulty with experimental data. In addition, when more than two-contact points are involved, it becomes obsolete. The paper presents a mathematical model to describe the complex ball bearing internal kinematics under the effect of the external working conditions. Lubricant thickness is taken into account in geometrical equations and the nonlinear system of this quasistatic model is solved by a Newton-Raphson method. The model is first validated through comparisons with published data for conventional or single arched ball bearings. Results are also compared to those provided by the commercial software RBL4. The analysis of a double arched ball bearing is finally performed and the complex motion of the ball highlighted.