Chapter 7: Mixed Lubrication at Micro-scale
Authors: Wang Wen-zhong , Hu Yuanzhong , Luo Jianbin 
Published: October 2009

TECHNOLOGY DEVELOPMENT DEMANDS MORE EFficient machines capable of operating in more critical conditions, e.g., under heavier loads and higher operating temperatures or using lower-viscosity oils, which result in thinner lubricant films. As a result, machine components operate in a regime of mixed lubrication where hydrodynamic lubrication and asperity contact act simultaneously, and lubrication performances are dominated by surface roughness. Great efforts were made over the past years to understand the role of surface roughness in mixed lubrication, and it is a first but substantial step in exploring the microscopic mechanisms of tribology. The classical theory of hydrodynamic lubrication and the Reynolds equation were published in 1886, but the complete solutions for the problems that combine the effects of lubrication and solid deformation, known as the elastohydrodynamic lubrication (EHL), were not available until the 1960s. Only after that were the attentions shifted to understanding the role of surface roughness, which led to the concept of mixed lubrication (ML) that emerged in the 1970s, also termed as the partial EHL at that time [1]. The idea is simply to consider that the hydrodynamic film, which separates two surfaces in relative motion, is penetrated by surface roughness when the film thickness becomes smaller than the asperity height. As a result, the lubrication domain is divided into two subregions, the hydrodynamic lubrication areas and the asperity contact areas, and the applied normal load is shared by hydrodynamic pressure and asperity contacts. Impressive progress has been achieved in studies of mixed lubrication, but due to the highly random and irregular nature of surface roughness and the consequent difficulties in measurements and numerical solutions, mixed lubrication remains a still poorly understood regime. The existence of asperity contacts in mixed lubrication causes great many local events and significant consequences. For example, the parameters describing lubrication and contact conditions, such as film thickness, pressure, subsurface stress, and surface temperature, fluctuate violently and frequently over time and space domain. It is expected that these local events would have significant effects on the service life of machine elements, but experimental measurements are difficult because of the highly random and time-dependent nature of the signals. Only a few successes were reported so far in experimental studies of mixed lubrication, mostly limited to the artificially manufactured surface roughness. Numerical simulations are thus considered to be a powerful means for exploring mixed lubrication, especially for extracting the local information of lubrication. Considerable efforts have been devoted during past 20–30 years to developing numerical models of mixed lubrication. This chapter is contributed to the description of approaches in modeling mixed lubrication, namely the statistic or average model and deterministic model, and the applications of the model to the studying mixed lubrication and the transition of the lubrication regime.