Deterministic mixed lubrication model

The word deterministic" means that the model employs a specific surface geometry or prescribed roughness data as an input of the numerical procedure for solving the governing equations. The method was originally adopted in micro-EHL to predict local film thickness and pressure distributions over individual asperities, and it can be used to solve the mixed lubrication problems when properly combined with the solutions of asperity contacts. 

Understanding the role of surface roughness in mixed lubrication is a first step toward the microscopic study of tribology. It has been an effort for more than 30 years, starting from statistic models, but it is the deterministic approach that provides a powerful means to explore the tribological events occurring at the micrometre scale. 

Most recently Jiang et al [12] published a deterministic EHL solution that handled hydrodynamic luhrication and asperity contacts (up to 12% of Hertzian contact area in presented cases) simultaneously. Shortly after that Zhu and Hu [13,14] presented a unified approach that is capable of simulating the entire transition fi-om the full-film, mixed, down to boundary lubrication. The contact load and area ratios could vary finm zero up to 100%, while the film thickness ratio, X, could be reduced from infinity down to zero. The numerical model has been proven to be robust under severe operating conditions (see [13-16]). Based on this model, a systematic study has been conducted by the present author for the effects of load and speed on the EHL film thickness in extended parameter ranges [17]. 

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