Hydrodynamic support and dynamic response for an inner-piloted bearing cage

Although many attempts have been made to model rolling-element bearings with inner-piloted cages, they all simplify the hydrodynamic cage-support mechanism. This can mean that some cage behaviour is inadequately explained, such as cage lap. This paper presents the development of a new three-dimensional analysis of the hydrodynamic support for an inner-piloted cage for a rolling-element bearing incorporating starved-film conditions. The solution of the generalized Reynolds equation along with a continuity equation leads to analytical expressions for the hydrodynamic forces. The equations of motion for the cage are then integrated numerically using the Newmark beta method to predict the cage response. The availability of analytical hydrodynamic force expressions means that the numerical integration process is computationally efficient. The influence of key parameters such as the level of lubrication and the angular velocity of the inner race are investigated.