The nature of Reynolds roughness for wide bearings with large bearing numbers and short wavelength stationary roughness is investigated. It is shown that the White and the To̸nder formulas both apply to the compressible Reynolds equation. However, they apply in different physical regimes—the limiting averaged pressure distribution depends upon the relative sizes of the bearing number and the roughness frequency. Asymptotic expansion methods and numerical calculations are used to find the pressure distributions for different relationships between the bearing number and the roughness frequency.

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