Hydrodynamic Lubrication of SelfAffine Fractal Surfaces

Hydrodynamic lubrication of an inclined slider bearing having self-affme fractal roughness is analyzed using the perturbation expansion of the Reynolds equation. Fractal characteristics are incorporated in the pertubation equations in terms of the power-law autocorrelation function defined by the fractal dimension and the correlation length. It is shown that the effect of transverse roughness in increasing the load capacity from that of smooth surfaces depends strongly on its fractal structure. The load capacity is larger for smaller correlation length, and the fractal dimension affects the load capacity in particular when the correlation length is larger than 1/100 of the bearing length. Contribution of surface asperities with different wavelengths to pressure generation is explained based on a flow simulation for sinusoidal roughness. The present results suggest that the effect of fractal structure of surfaces should be taken into account not only when the overall load capacity of a bearing is considered, but also when microscopic film formation on small asperities and their behavior are of interest.