A New Approach for Estimating the Friction in Thin Film Lubrication | Zendy

Dag Lukkassen | Zendy; Annette Meidell | Zendy; Peter Wall | Zendy

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A New Approach for Estimating the Friction in Thin Film Lubrication

Author(s) -

Dag Lukkassen,

Annette Meidell,

Peter Wall

Publication year - 2010

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2010/963983

Subject(s) - lubrication , computation , homogenization (climate) , lagrangian , surface roughness , reynolds equation , mathematics , surface finish , fluid bearing , mechanics , reynolds number , mathematical optimization , mathematical analysis , materials science , mechanical engineering , physics , engineering , algorithm , composite material , biodiversity , ecology , turbulence , biology

An important problem in the theory of lubrication is to model and analyze the effect of surface roughness on, for example, the friction and load carrying capacity. A direct numerical computation is often impossible since an extremely fine mesh is required to resolve the surface roughness. This suggests that one applies some averaging technique. The branch in mathematics which deals with this type of questions is known as homogenization. In this paper we present a completely new method for computing the friction. The main idea is that we study the variational problem corresponding to the Reynolds equation. We prove that the homogenized variational problem is closely related to the homogenized friction. Finally we use bounds on the homogenized Lagrangian to derive bounds for the friction. That these bounds can be used to efficiently compute the friction is demonstrated in a typical example

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