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.

A numerical method for solving the lubrication equations including an iterative procedure to account for the inertial effects is outlined, together with appropriate boundary conditions for film rupture. Data concerning the operating characteristics of full journal bearings are provided, function of length/diameter ratio, clearance ratio, Reynolds number, and eccentricity ratio. As compared to other existing numerical procedures, the present method has the main advantage that it can be easily implemented to any existing program for calculating the operating characteristics of a bearing in laminar and turbulent flow. Moreover, it was found that the first iteration gives sufficiently accurate results, so that convergence problems related to the iteration procedure (which may appear when the product between the Reynolds number and the clearance ratio is very large) does not alter its practical utility.

Proceeding from the results obtained previously [5] this paper analyzes theoretically the three-dimensional motion in the lubricant layer by using Prandtl’s mixing length theory. Formulas and diagram are presented for calculating journal and thrust bearings subjected to turbulent lubrication.

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