A wedge bearing with transverse sinusoidal roughness pattern is studied numerically in order to predict the effect of surface roughness on compressible fluid films. A variable grid implicit finite difference scheme is used to provide steady-state solutions of the Reynolds equation over a bearing number range of five orders of magnitude. At a fixed bearing geometry and orientation, the bearing load is found to increase to a maximum as the bearing number increases, then to decrease and asymptotically approach a limiting value as the bearing number increases further. This is quite unlike the behavior of an incompressible fluid bearing. Analysis indicates that the maximum load occurs at a condition where pressure diffusion and Couette effects of the fluid film are of an equal order of magnitude. The increased emphasis of the pressure diffusion physics is due to the short length scales of the rough surfaces which “trigger” the higher derivative diffusion terms in the Reynolds equation. The criterion required for validity of an infinite bearing number solution with a rough surface is found to be much more restrictive than that of a smooth surface bearing. Last, the type of rough surface film clearance averages used in incompressible lubrication are shown to be incorrect for analysis of very thin gas films. It would appear that one application of this information would be the design of an artificially roughened surface for the take-off and landing of magnetic head sliders so as to minimize contact and wear of the magnetic media.
Numerical study of surface roughness effects in the boundary layer of a blunted cone in a supersonic flow
