The Formulation of the Mixed Lubrication Problem as a Generalized Nonlinear Complementarity Problem

Abstract

The mixed-lubrication problem is formulated as a nonlinear generalized complementarity problem in which the pressure acting on the load-bearing surface is taken as the unknown, and the lubricant flow and the gap between the surfaces are taken as its complements. An iterative method was developed to find the solution, which satisfies the complementarity condition that at each point on the load-bearing surface, the pressure or at least one of its complements, is zero at all times. Moreover, the pressure and its complements satisfy non-negativity constraints. The solution intrinsically decomposes the load-bearing surface into three distinct subregions: solid-to-solid contact, hydrodynamically lubricated contact, and no contact (or cavitation). It is shown that the mixed-lubrication formulation degenerates into the special cases of hydrodynamic or solid-to-solid contacts under appropriate load and speed conditions. A journal bearing with elastic support is analyzed to illustrate the method of solution. The transition of the lubrication mode from pure hydrodynamic contact to mixed contact is demonstrated.