The hydrodynamical theory of film lubrication

Abstract

The equations of film lubrication are derived from the general equations of hydrodynamics assuming only that the motion is steady, and that it takes place between two surfaces, in relative motion, which are both close together and nearly parallel. Consideration of the relative magnitude of the various term sunder typical conditions as measured in a bearing shows that they are of very unequal orders of magnitude, and that in particular the inertia term s in the momentum and the dilatation and conductivity term s in the energy equation can be neglected. I t is shown that film lubrication is possible if, and only if, either the distance between the surfaces decreases in the direction of motion (the geometric wedge), or the density of the fluid decreases in the same direction (the thermal wedge). These types of film are approximately equal when compared on a basis of equal film thickness and equal decrease. With the geometric wedge a much greater decrease, and therefore load-carrying capacity, is possible, but the thermal wedge from its simpler mechanical construction should be able to equalize matters by running with a thinner film. The equations of film lubrication are derived from the general equations of hydrodynamics assuming only that the motion is steady, and that it takes place between two surfaces, in relative motion, which are both close together and nearly parallel. Consideration of the relative magnitude of the various terms under typical conditions as measured in a bearing shows that they are of very unequal orders of magnitude, and that in particular the inertia terms in the momentum and the dilatation and conductivity terms in the energy equation can be neglected. It is shown that film lubrication is possible if, and only if, either the distance between the surfaces decreases in the direction of motion (the geometric wedge), or the density of the fluid decreases in the same direction (the thermal wedge). These types of film are approximately equal when compared on a basis of equal film thickness and equal decrease. With the geometric wedge a much greater decrease, and therefore load-carrying capacity, is possible, but the thermal wedge from its simpler mechanical construction should be able to equalize matters by running with a thinner film. The equations are reduced to non-dimensional form and the equation of state discussed. For the general case the integration is probably a major computing operation and, in view of the uncertainties in the exact form of the equation of state, not worth while. For the infinite bearing, on the other hand, integration is comparatively simple and has been carried out in the Mathematics Division, N.P.L., for a series of representative cases. The results show that viscosity variation has a profound effect on the performance of the thermal wedge, and that the additional wedging action provided by change of density is likely to be small unless the lubricating surfaces are close together. On the other hand, for surfaces close together and a small variation of viscosity the thermal wedge altogether outclasses the geometric.