AN APPROACH TO THE CALCULATION OF THE STOKES SURFACE ROUGHNESS EFFECT IN MULTISCALE HYDRODYNAMIC LUBRICATION WITH VERY LOW FILM THICKNESSES

A factor is introduced into the Poiseuille flow term in Zhang's multiscale flow equation to account for the Stokes surface roughness effect in multiscale hydrodynamic lubrication with very low film thicknesses. For the mean hydrodynamic film thickness far greater than the surface roughness or for the wavelength of the rough surface far greater than the mean hydrodynamic film thickness, this factor approaches unity and the lubrication equation becomes the Reynoldstype equation. Otherwise, the value of this factor is less than unity but positive, and the lubrication equation becomes the equivalent Reynolds-type equation. The interpretation is that the liquid lubricant vortex flow caused by the Stokes surface roughness reduces the magnitude of the Poiseuille flow rate of the lubricant through the lubricated contact. The modifying factor is regressed out as a function of the magnitude and the wavelength of the surface roughness. Its value is reduced (below unity) with the increase of the surface roughness or with the reduction of the wavelength of the rough surface. The results show that the carried load of the hydrodynamic lubricated thrust bearing with very low clearance calculated by this modified lubrication equation is greater than that calculated by considering the Reynolds surface roughness. It qualitatively agrees with the classic calculation results of the Stokes surface roughness effect in continuum lubrication. The study may form the framework of the efficient simulation of the Stokes surface roughness effect in multiscale hydrodynamic lubrication or mixed lubrication with low film thicknesses where both the effects of the adsorbed layer and the surface roughness are involved.