A Theory for Turbulent Fluid Films and Its Application to Bearings

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Abstract
In this paper a new turbulent lubrication analysis has been derived which takes into account certain well-established facts concerning turbulent shear flow. Consistent with lubrication-film theory, the nature of the local flow is taken to depend only on local film thickness, surface velocity, and pressure gradients. An eddy diffusivity treatment is used which incorporates the “law of wall” with the use of local (within the film) shear stress. Stress reversal phenomena are accommodated and isotropy of the turbulent exchange mechanism in the plane of the film is assured. Coefficients are developed for use in the generalized Reynolds (lubrication) equation, and computation procedures for the static and dynamic characteristics of turbulent, self-acting bearings have been prepared. The nonlinear effects due to the coupling of the shear induced flows and the flows due to the circumferential and axial pressure gradients are fully considered in this analysis. Thus, it is anticipated that it, unlike the previous linearized analysis, is directly applicable also to turbulent, externally pressurized, and hybrid bearings.

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