Theoretical Analysis of the Influence of Asperity’s Dimensions Affected by a Scale Factor on the Mixed Lubrication between Parallel Surfaces

Mixed lubrication between a given pair of surfaces is directly related to the parameter ηu/p. Any change in microgeometry produces a shift in the transition between the boundary and lubricated regimes. Using an asperity based model including five families of asperities (2 for full fluid lubrication and 3 for local boundary lubrication), we simulate mixed lubricated behavior. Our theoretical results confirm the relation between the mixed regime and the ηu/p parameter. All homothetic changes in microgeometry affecting the vertical and horizontal directions by the same scaling factor Sc induce a shift in the transition. The most interesting result is that this shift is exactly the same if speed u is scaled by 1/Sc with the initial microgeometry. This particular behavior, which is in good agreement with experimental results proposed in the literature, comes from the fact that behavior at each asperity can be written using dimensionless parameters. Most of these parameters are independent to any scaling of the microgeometry and only one, the speed parameter, needs to be artificially scaled in order to remain unchanged by the modification of the microgeometry.