Homogenization of Reynolds Equation by Two-Scale Convergence

Abstract

To increase the hydrodynamic performance in different machine elements, ase.g. journal bearings and thrust bearings, during lubrication it is important to understandthe influence of surface roughness. In this connection one encounters homogenization ofthe incompressible Reynolds equation, where the roughness of the lubricated surface isassumed to be periodic. This problem has recently been studied in more engineering-oriented papers by using the formal method of multiple scale expansion. In this paper, werigorously prove both homogenization and corrector results by using two-scale convergence,which may be regarded as a justification of the formal multiple scale expansion methoddescribed above. Moreover, some numerical illustrations and results are presented.

Keywords

Homogenization / Two-scale convergence / Reynolds equation / Lubrication / 35B27 / 74Q99 / 76D08

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