On Turbulent Lubrication

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Abstract
The paper concerns the hydrodynamic turbulent motion in the lubricant layer. Proceeding from the Reynolds equations and introducing the approximations currently used in lubrication problems, owing to the lubricant film thickness, the general motion equations for turbulent lubrication are written. Using the Prandtl mixing length hypothesis, exact and approximate solutions are obtained for the velocity distribution into the lubricant layer. The results are discussed by pointing out the pressure gradient and the Reynolds number influence on the velocity distributions, as well as the differences with respect to the laminar flow. In order to obtain simple formulae, the exact dependence of the rate of flow on the pressure gradient into a dimensionless form is replaced by a linear relation, the slope of which depends on the Reynolds number. This approximation allows the obtainment of the pressure differential equation under a simple form. The pressure equation is integrated in case of journal bearings, by assuming a constant or a variable viscosity of the lubricant. The results are compared to the experimental data obtained by M. I. Smith and D. D. Fuller and the good qualitative agreement is pointed out.

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