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

Abstract

Although many attempts have been made to model rolling-element bearings with innerpiloted 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 rollingelement bearing incorporating starved-®lm 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 ef®cient. The in¯uence of key parameters such as the level of lubrication and the angular velocity of the inner race are investigated.

A Computational Fluid Dynamics Simulation of Oil–Air Flow Between the Cage and Inner Race of an Aero-engine Bearing

“…In describing the hydrodynamic influence, a Reynolds equation formulation is solved. In the formulations, the fluid (oil) is taken as single phase in the domain, for example between the cage and inner race and at the contact points [1,15].…”

“…Ashmore et al [1] made modelling progress by assuming that the cage-raceway can be considered to be a short journal bearing divided into sectors by the oil feeds providing hydrodynamic support for the cage. In the work presented in this paper, following Ashmore et al [1], the cage-race is assumed to be relatively unaffected by the bearing balls such that the flow can be studied in isolation but unlike their work, the 3D Navier-Stokes equations are solved with consideration for the oil-air interface.…”

“…In the work presented in this paper, following Ashmore et al [1], the cage-race is assumed to be relatively unaffected by the bearing balls such that the flow can be studied in isolation but unlike their work, the 3D Navier-Stokes equations are solved with consideration for the oil-air interface.…”

“…In the analysis of rolling element bearings there are essentially two approaches: quasi-static; and dynamic [1,[15][16][17]. In quasi-static analysis, for each of the bearing elements, the force and moment equilibrium equations acting are modelled such that they include the dynamic components such as the externally applied forces, centrifugal forces and gyroscopic moments.…”

“…Most of the analyses consider the contributions of fluid forces as small relative to the interaction of the bearing elements. One of the most sophisticated models for a cage-raceway analysis is based on the work of Ashmore et al [1], where the cage-raceway is considered to be a short journal bearing divided into sectors by the oil feeds. It is further assumed that the oil exits from the holes and forms a continuous block of oil that exits outwards on both sides of the cage-raceway.…”