First Effects of Stokes Roughness on Hydrodynamic Lubrication

Abstract

Considering the actual roughness dimensions as well as the typical dimensions of a hydrodynamically lubricating film, the Stokes equations are used to analyze the roughness effects. The surface profile is modeled by an ergodic, stationary random process. It is revealed that the roughness effects can be determined by three parameters; viz., the rms roughness, the correlation length, and the correlation wavelength. The present results are significantly different from those in the literature, where the Reynolds equation is used for analysis.

Homogenization of the Stokes system in a thin film flow with rapidly varying thickness

“…The second way is associated to the « Stokes roughness », where the authors claim that the applicability of the Reynolds équation is not valid, especially when the roughness wavelength is small in front of the gap height The related studies retam the assumption of small roughness height, and use asymptotic expansions [15], [19] All the results have given nse to rnany controversies both at view of their numencal results than for the heunstic assumptions on which they are based [8], [21] , mtercompansons are very difficult due to the various assumptions introduced…”

Influence of location, number and shape of corrugations in slider bearings

“…A finite element numerical method is used for computation of the flow under non-isothermal conditions. Also, unlike many previous works where often approximations of a Reynolds type [3,4,5,6,9], or to a lesser extent, approximations of a Stokes type [7,8] have been used, no simplifying assumptions will be made in the present study.…”

“…Influence of surface corrugation on the performance of slider bearings has attracted the attention of many investigators [1,2,3,4,5,6,7,8,9]. However, in these works, invariably corrugation extends over the full length (in the direction of sliding motion) of the bearing gap.…”

On the Roughness Effect in Hydrodynamic Lubrication

“…However, hitherto unacknowledged sufficient conditions will be given for the equality (7) to hold approximately without the small variance assumption. Under these conditions the average equation (4) is approximately valid and may be simplified further.…”

“…Nevertheless, the present upper bound provides for a quantitative estimate of the roughness effect on the mean load deviation by avoiding the difficult task of solving for the mean pressure distribution. Also, the effects of Stokes roughness were studied in a recent paper [7] by using the first order perturbation of the Stokes equation, instead of the Reynolds equation, with respect to a small roughness parameter. This kind of problem known as a random-boundary problem, was discussed earlier by one of the authors [8].…”