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Homogenization‐based design of surface textures in hydrodynamic lubrication
Author(s) -
Waseem A.,
Temizer İ.,
Kato J.,
Terada K.
Publication year - 2016
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.5256
Subject(s) - homogenization (climate) , lubrication , microscale chemistry , discretization , isotropy , reynolds equation , anisotropy , materials science , mechanics , surface finish , geometry , mathematics , mathematical analysis , composite material , physics , reynolds number , optics , biodiversity , ecology , turbulence , mathematics education , biology
Summary An optimization framework is developed for surface texture design in hydrodynamic lubrication. The microscopic model of the lubrication interface is based on the Reynolds equation, and the macroscopic response is characterized through homogenization. The microscale setting assumes a unilateral periodic texture but implicitly accounts for the bilateral motion of the surfaces. The surface texture in a unit cell is described indirectly through the film thickness, which is allowed to vary between prescribed minimum and maximum values according to a morphology variable distribution that is obtained through the filtering of a design variable. The design and morphology variables are discretized using either element‐wise constant values or through first‐order elements. In addition to sharp textures, which are characterized by pillars and holes that induce sudden transitions between extreme film thickness values, the framework can also attain a variety of non‐standard smoothly varying surface textures with a macroscopically isotropic or anisotropic response. Copyright © 2016 John Wiley & Sons, Ltd.