On the Effects of Roughness Orientation—A Mapping and Double Scale Analysis of Flow Factors

A comprehensive approach for computing the lubricant flow as functions of the roughness orientation is presented. By using a mapping function, a periodic, anisotropic surface is transformed into an isotropic one. The transformed isotropic roughness has only one characteristic wavelength, so that a double scale analysis based on this wavelength of roughness can be developed to calculate the flow factors introduced in the average Reynolds equation. In addition, the Bhushan number instead of the conventional Peklenik number is used to describe the surface property more clearly. The new analysis provides an accurate evaluation of the roughness effects with only a second order approximation. The agreement is excellent even for incipient surface contact. An explicit relationship between the nondiagonal flow factors, which are associated with the pumping flux, and the diagonal ones have been established. It has been found that the maximum pumping action takes place when the asperities are oriented at 45 degrees to the direction of pressure gradient or sliding motion. The pumping effect caused by the relative sliding is about 50 percent greater than the effect caused by the pressure gradient. Strictly speaking, the asperities oriented at 45 degrees to the sliding direction will give different flow factors for different Bhushan numbers. This differs from some prior studies for periodic or area-distributed random roughness. Marked difference in flow factors due to the difference of asperity orientation is also observed. It suggests that caution should be used when the average Reynolds equation is applied, such as in the case of axisymmetric punching where various asperity orientations exist.