A generalized Reynolds equation for fluid-film lubrication

Summary In the analysis of fluid-film bearings the basic equation employed is known as the Reynolds equation. This equation, which governs the generation of pressure in the lubricant film, is encountered in numerous forms each applicable to a particular set of circumstances only. The study of fluid-film lubrication suffers from this multiplicity of Reynolds-type equations, and the influence of different physical mechanisms associated with pressure generation is frequently masked by the difference in form of tho initial equations. In recent years a further mechanism of pressure generation associated with the variation of fluid properties across the film has been suggested, and this has resulted in new forms of the pressure equation. In this paper a generalized form of Reynolds equation is developed which permits tho variation of relevant quantities across, as well as along, tho lubricant film. This equation is derived from the fundamental equations of hydrodynamics with a minimum of restrictive assumptions, and it will be seen that it can bo reduced to any of the forms currently employed in the analysis of fluid-film bearings.