Quasi-static analysis of thrust-loaded angular contact ball bearings part I: theoretical formulation

Ball bearings play an important role in various rotating machineries, but the complicated kinematic and tribological features of ball bearings make many aspects of their operating behaviors still inconclusive. Most theoretical analyses of ball bearings up to date are based on either the hypothesis of race control or other empirical models to determine the ball motion of ball bearings, but none of these strategies can reveal and consequently employ the intrinsic coupling mechanism between the spin and the tangential traction of contacting bodies rolling upon one another. To remedy the deficiency of current analytical models for ball bearing analysis, the rolling contact theory is employed to establish an explicit link between motions and interactions within ball bearings. A differential slip model is established to precisely define the slip component due to the significant curvature of the common contact patches between the ball and inner/outer raceways. The creepage and the spin ratio are formulated to accurately define the relative rigid motion between the ball and the inner/outer raceway. Then a quasi-static analytical model is established that can accurately determine the motions of the balls and races of the ball bearing. It can also give a vivid description of the slip and traction distributions within the contact area. The analytical model can be effectively used to analyze the operational conditions and tribological features of solid-lubricated ball bearings. It can also be used optimize the construction of ball bearings for specific applications.