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Variational bounds applied to unstationary hydrodynamic lubrication
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.ORCID iD: 0000-0001-7029-1112
Department of Mathematics and Statistics, University of Cape Coast.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.ORCID iD: 0000-0001-8211-3671
2008 (English)In: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 46, no 9, p. 891-906Article in journal (Refereed) Published
Abstract [en]

This paper is devoted to the effects of surface roughness in hydrodynamic lubrication. The numerical analysis of such problems requires a very fine mesh to resolve the surface roughness, hence it is often necessary to do some type of averaging. Previously, homogenization (a rigorous form of averaging) has been successfully applied to Reynolds type differential equations. More recently, the idea of finding upper and lower bounds on the effective behavior, obtained by homogenization, was applied for the first time in tribology. In these pioneering works, it has been assumed that only one surface is rough. In this paper we develop these results to include the unstationary case where both surfaces may be rough. More precisely, we first use multiple-scale expansion to obtain a homogenization result for a class of variational problems including the variational formulation associated with the unstationary Reynolds equation. Thereafter, we derive lower and upper bounds corresponding to the homogenized (averaged) variational problem. The bounds reduce the numerical analysis, in that one only needs to solve two smooth problems, i.e. no local scale has to be considered. Finally, we present several examples, where it is shown that the bounds can be used to estimate the effects of surface roughness with very high accuracy.

Place, publisher, year, edition, pages
2008. Vol. 46, no 9, p. 891-906
National Category
Tribology (Interacting Surfaces including Friction, Lubrication and Wear) Mathematical Analysis
Research subject
Machine Elements; Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-8412DOI: 10.1016/j.ijengsci.2008.03.001ISI: 000258021900004Scopus ID: 2-s2.0-44749091068Local ID: 6ec4eff0-7349-11dd-a60f-000ea68e967bOAI: oai:DiVA.org:ltu-8412DiVA, id: diva2:981350
Note
Validerad; 2008; 20080826 (ysko)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2018-07-10Bibliographically approved

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Almqvist, AndreasEssel, Emmanuel KwameFabricius, JohnWall, Peter

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