On Turbulent Lubrication

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.

Nanomanufacturing : nano-structured materials made layer-by-layer.

“…Many models exist for relaxing assumption 1 to study turbulent flows [Constantinescu (1959), Ng (1964), Elrod and Ng (1967), Hirs (1973)]. These models have been easily be incorporated into our formulation, but have been omitted here for simplicity of the presentation.…”

“…Many extensions of this basic theory exist, including elastohydrodynamic lubrication [Greenwood (1972), Taylor and O'Callaghan (1972), Oh and Huebner (1973), LaBouff and Booker (1985), Jones (1993) [Constantinescu (1959), Ng (1964), Elrod and Ng (1967), Hirs (1973)], and lubrication of non-Newtonian fluids [Ng and Saibel (1962), Swamy et al (1977), Johnson1993, Bhattacharjee and Das (1996), Hryniewicz et al (2001), Nair et al (2007), Mongkolwongrojn and Aiumpronsin (2010)], among others [Christensen (1971), Eringen and Okada (1995), Feng and Weinbaum (2000), Stone (2005), Jang and Khonsari (2005), Bujurke and Kudenatti (2007), Rojas et al (2010)]. Recent books by Hori [Hori (2006)] and Szeri [Szeri (2010)] thoroughly review the history and applications of lubrication theory and derive the governing equations.…”

Studies on tribology

“…These are big problems for bearings. On turbulence in bearings, since Wilcock's experimental work (1950) 49) and Constantinescu's theoretical contribution (1959), 50) many studies have been carried out, for example.…”

Feasibility Study of Air Bearing Rocket Sled Slippers

“…In the turbulent area, Equations similar to (16) for each combination of signs of S, •and Cx, are obtained as shown in Re erence (10).…”

“…After this operation is performed, the results may be plotted as shown in Figure 44, which has been taken from Reference (3) and is also presented in Reference (10).…”