The Effect of Periodic Textures on the Static Characteristics of Thrust Bearings

Abstract

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.

Reiterated homogenization applied in hydrodynamic lubrication

“…In optimizing the performance in terms of film formation and induced frictional torque, it is clear that perfectly smooth surfaces are preferred, this was also previously confirmed, see e.g. [3]. However, disregarding the unrealistic perfectly smooth bearing, it is the artificially dimpled surface texture (33) that yields the thickest films and induces the smallest frictional torque.…”

“…[1][2][3][4][5][6][7]. In these works it was shown that the rapid oscillations (in the coefficients of the Reynolds type equation under consideration) induced by the surface roughness, could efficiently be averaged by the homogenization method employed.…”

“…[8,11]. The homogenization of Reynolds type equations involving only one local scale have been studied by multiple scale expansion in references [1], [3], [7], and [12].…”

“…To accomplish this aim the formal method of multiple scale expansion is employed to obtain a homogenized problem (8) for equation (1). For other problems connected to the incompressible Reynolds that have been studied by multiple scale expansion see [1,3,7].…”

Numerical Simulation of the Head/Disk Interface for Patterned Media

“…Buscaglia et al have done extensive theoretical analysis on the effect of surface textures for load carrying capacity (which is the integration of the pressure) in thrust bearings [19] and then extended the study in [20] to account for compressibility. In both these studies it was shown that the load carrying capacity is a function of the mean depth of surface textures only.…”