A Modified Average Reynolds Equation for Rough Bearings With Anisotropic Slip

A lubrication theory that includes the coupled effects of surface roughness and anisotropic slips is proposed. The anisotropic-slip phenomena originate from the microscale roughness at the atomic scale (microtexture) and surface properties of the lubricating surfaces. The lubricant flow between rough surfaces (texture) is defined as the flow in nominal film thickness multiplied by the flow factors. A modified average Reynolds equation (modified ARE) as well as the related factors (pressure and shear flow factors, and shear stress factors) is then derived. The present model can be applied to squeeze film problems for anisotropic-slip conditions and to sliding lubrication problems with restrictions to symmetric anisotropic-slip conditions (the two lubricating surfaces have the same principal slip lengths, i.e., $b1x=b2x$ and $b1y=b2y$⁠). The performance of journal bearings is discussed by solving the modified ARE numerically. Different slenderness ratios 5, 1, and 0.2 are considered to discuss the coupled effects of anisotropic slip and surface roughness. The results show that the existence of boundary slip can dilute the effects of surface roughness. The boundary slip tends to “smoothen” the bearings, i.e., the derived flow factors with slip effects deviate lesser from the values at smooth cases (pressure flow factors $φxxp,φyyp=1$⁠; shear flow factors $φxxs=0$⁠; and shear stress factors $φf,φfp=1$ and $φfs=0$⁠) than no-slip one. The load ratio increases as the dimensionless slip length (⁠$B$⁠) decreases exception case is also discussed or the slenderness ratio (⁠$b/d$⁠) increases. By controlling the surface texture and properties, a bearing with desired performance can be designed.