Statistic Approach of Mixed Lubrication

The statistic models consider surface roughness as a stochastic process, and concern the averaged or statistic behavior of lubrication and contact. For instance, the average flow model, proposed by Patir and Cheng [2], combined with the Greenwood and Williamsons statistic model of asperity contact [3] has been one of widely accepted models for mixed lubrication in early times. 

When the film thickness is of the order of roughness heights, the effects of roughness become significant which have to be taken into account in a profound model of mixed lubrication. The difficulty is that the stochastic nature of surface roughness results in randomly fluctuating solutions that the numerical techniques in the 1970s are unable to handle. As 

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The pressure flow factors describe how the surface roughness would affect the lubricant flow driven by the pressure gradient. It is defined as the ratio of pressure flow in an 

The shear flow factor represents additional flow transport introduced by the roughness in relative sliding. It is defined as the mean flow in an element bearing where the two surfaces are in relative sliding, but the mean pressure gradient would be zero. 

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