On the λ ratio range of mixed lubrication

Mixed lubrication is a mode of fluid lubrication in which both hydrodynamic lubricant film and rough surface asperity contact coexist. Mixed lubrication problems are usually associated with significant surface roughness effect. A common belief is that full-film lubrication occurs when the λ ratio, defined as average film thickness divided by composite root mean square roughness, is greater than 3.0, while boundary lubrication corresponds to λ < 0.5-1.0. Mixed lubrication, therefore, is roughly in the range 0.5-1.0 < λ < 3.0. However, these considerations were established long ago based on early stochastic analyses, which did not adequately consider rough surface asperity interaction and correlation, as well as reduction of asperity heights caused by surface deformation. Recent experimental studies and deterministic numerical simulations suggested that the λ ratio range of mixed lubrication needs to be re-visited. Actually, when the λ ratio is greater than 0.6-1.2, little or no asperity contact is found in either experimental results or numerical solutions. If λ is around 0.05-0.1, there may still be a considerable portion of load, e.g. greater than 10-15%, being supported by lubricant films. It appears that mixed lubrication spans a λ ratio range roughly from 0.01-0.05 up to 0.6-1.2, according to the numerical simulation results presented in this article. This estimated range is in a reasonably good agreement with experimental observations found in the literature.