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Almqvist, AndreasBurtseva, EvgeniyaWall, Peter
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Almqvist, AndreasBurtseva, EvgeniyaWall, Peter
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Machine ElementsMathematical Science
##### In the same journal

Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology
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Tribology (Interacting Surfaces including Friction, Lubrication and Wear)Mathematical Analysis
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On lower-dimensional models in lubrication, Part A: Common misinterpretations and incorrect usage of the Reynolds equationPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2021 (English)In: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 235, no 8, p. 1692-1702Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Sage Publications, 2021. Vol. 235, no 8, p. 1692-1702
##### Keywords [en]

Reynolds equation, elastohydrodynamic (or EHL), implicit constitutive relations, lower-dimensional models, piezo-viscous fluids
##### National Category

Tribology (Interacting Surfaces including Friction, Lubrication and Wear) Mathematical Analysis
##### Research subject

Applied Mathematics; Machine Elements
##### Identifiers

URN: urn:nbn:se:ltu:diva-81978DOI: 10.1177/1350650120973792ISI: 000666594700016Scopus ID: 2-s2.0-85097313267OAI: oai:DiVA.org:ltu-81978DiVA, id: diva2:1509668
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##### Funder

Swedish Research Council, 2019-04293
##### Note

Most of the problems in lubrication are studied within the context of Reynolds’ equation, which can be derived by writing the incompressible Navier-Stokes equation in a dimensionless form and neglecting terms which are small under the assumption that the lubricant film is very thin. Unfortunately, the Reynolds equation is often used even though the basic assumptions under which it is derived are not satisfied. One example is in the mathematical modelling of elastohydrodynamic lubrication (EHL). In the EHL regime, the pressure is so high that the viscosity changes by several orders of magnitude. This is taken into account by just replacing the constant viscosity in either the incompressible Navier-Stokes equation or the Reynolds equation by a viscosity-pressure relation. However, there are no available rigorous arguments which justify such an assumption. The main purpose of this two-part work is to investigate if such arguments exist or not. In Part A, we formulate a generalised form of the Navier-Stokes equation for piezo-viscous incompressible fluids. By dimensional analysis of this equation we, thereafter, show that it is not possible to obtain the Reynolds equation, where the constant viscosity is replaced with a viscosity-pressure relation, by just neglecting terms which are small under the assumption that the lubricant film is very thin. The reason is that the lone assumption that the fluid film is very thin is not enough to neglect the terms, in the generalised Navier-Stokes equation, which are related to the body forces and the inertia. However, we analysed the coefficients in front of these (remaining) terms and provided arguments for when they may be neglected. In Part B, we present an alternative method to derive a lower-dimensional model, which is based on asymptotic analysis of the generalised Navier-Stokes equation as the film thickness goes to zero.

Validerad;2021;Nivå 2;2021-07-05 (beamah)

Available from: 2020-12-14 Created: 2020-12-14 Last updated: 2021-07-09Bibliographically approved
doi
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