Free Surface Thin Layer Flow on Bearing Raceways

In this paper, the effects of rotation on the distribution of a layer of oil on a bearing raceway are analyzed in relation to the geometry of the raceway. The research is motivated by the need to understand the behavior of grease lubricated bearings. Some specific aspects of grease lubrication can be understood by approximating the contact as a starved lubricated elastohydrodynamic lubrication contact. In such a contact, the shape and thickness of the inlet layer of oil, supplied to the contact on the running track, are of crucial importance to the film formation and contact performance. Small changes in the distribution of lubricant on the rolling track, as a result of reflow or redistribution, may have a large (local) effect on the film thickness inside the contact. Starting from the Navier–Stokes equations, the free surface thin layer flow equation for axisymmetric rotating surfaces is derived. For the case of bearing applications, it is shown that a simple quasilinear equation can be derived for the layer thickness, as a function of location and time, which can be solved analytically. Experiments have been carried out, measuring the changes of a layer of oil on rotating raceways in time in relation to the rotational speed and the raceway geometry. It is shown that the simplified model accurately predicts the thin layer flow, except in a region near the outflow boundary, where the effect of the boundary condition on the layer shape is crucial. This is further illustrated by results of numerical simulations.