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research-article

# A comparison of the roughness regimes in hydrodynamic lubrication

[+] Author and Article Information
John Fabricius

Department of Engineering Sciences and Mathematics, Luleå University of Technology SE-971 87 Luleå, Sweden
john.fabricius@ltu.se

Afonso Fernando Tsandzana

Department of Engineering Sciences and Mathematics, Luleå University of Technology SE-971 87 Luleå, Sweden
afonso.tsandzana@ltu.se

Francesc Pérez-Ràfols

Department of Applied Physics and Mechanical Engineering Luleå University of Technology SE-971 87 Luleå, Sweden
francesc.perez.rafols@ltu.se

Peter Wall

Department of Engineering Sciences and Mathematics, Luleå University of Technology SE-971 87 Luleå, Sweden
peter.wall@ltu.se

1Corresponding author.

ASME doi:10.1115/1.4035868 History: Received March 15, 2016; Revised January 26, 2017

## Abstract

This work relates to previous studies concerning the asymptotic behavior of Stokes flow in a narrow gap between two surfaces in relative motion. It is assumed that one of the surfaces is rough, with small roughness wavelength $\mu$, so that the film thickness $h$ becomes rapidly oscillating. Depending on the limit of the ratio $h/\mu,$ denoted as $\lambda,$ three different lubrication regimes exist: Reynolds roughness ($\lambda=0$), Stokes roughness ($0<\lambda<\infty$) and high frequency roughness ($\lambda=\infty$). In each regime the pressure field is governed by a generalized Reynolds equation, whose coefficients (so called flow factors) depend on $\lambda.$ To investigate the accuracy and applicability of the limit regimes, we compute the Stokes flow factors for various roughness patterns by varying the parameter $\lambda.$ The results show that there are realistic surface textures for which the Reynolds roughness is not accurate and the Stokes roughness must be used instead.

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