Abstract:We study the behavior of the steady-state voltage potentials in a material composed by a bidimensional medium surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be ε-periodic, ε beeing the small thickness of the layer. We build approximate transmission conditions in order to replace the rough thin layer by these conditions on the boundary of the interior material. This paper extends previous works [8,7] of the third author, in which the layer had constant or weakly oscillating thickness.

Given a bearing of some specified macroscopic shape, what is the effect of texturing its surfaces uniformly? Experimental and numerical investigations on this question have recently been pursued, which we complement here with a mathematical analysis based on a seemingly novel combination of homogenization techniques and perturbation analysis. The flow is assumed governed by the Reynolds equation, with cavitation effects disregarded, and the texture length is assumed much smaller than the bearing’s length. The results, which hold true for small-amplitude periodic textures and in the limit of vanishing period, can be summarized as follows: (a) The texture that maximizes the load for a given minimum clearance is no texture at all (i.e., the untextured shape); and (b) the texture that minimizes the friction coefficient is again the untextured shape.

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