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Generalized Reynolds equation and variational inequality in lubrication theory

Applied Mathematics and Mechanics, 1982
This paper has derived generalized Reynolds equation in lubrication theory in terms of tensor analysis and S-coordinate system, and has provided corresponding variational inequality. The curved effect of flow of lubricant fluid is considered, and the influence of intrinsic properties of surfaces of axis and axle sleeve on flow are counted.
Li, Kai-tai, Huang, Ai-xiang
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Generalized Reynolds Equation for Stochastic Lubrication and its Application

Journal of Mechanical Engineering Science, 1975
By using the theory of a stochastic process, a generalized form of Reynolds equation applicable to rough bearings is derived by assuming the fluxes to be represented by power series of a stochastic film-thickness function. In the case of a step slider bearing, it is shown that load capacity and friction force increase but that coefficient of friction
H. Christensen, J. B. Shukla, S. Kumar
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Reynolds equation and elastohydrodynamic lubrication in metal seals

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1976
Oil film profile and pressure distribution between a metal seal and a reciprocating hydraulic jack rod have been measured. A rapidly diverging oil film, which would normally be expected to cause rupture of the fluid and severe cavitation, was observed near the centre of the contact, but the corresponding pressure in this region was found to be high ...
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Lubrication with emulsion: first report, the extended Reynolds equation

Wear, 1997
A simplified model based on the continuum theory of mixtures is proposed to derive the extended Reynolds equation for lubrication with emulsion. This model has showed that there is a velocity difference between two phases of emulsion. The existence of the velocity difference is the reason why the oil concentration varies in lubrication film. Using this
Shengming Yan, Shigeaki Kuroda
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Modified Reynolds equations for thin film lubrication analysis with high viscosity surface layers on both solid surfaces and analysis of micro-tapered bearing

, 2020
This paper presents a modified Reynolds equation used for the analysis of thin film lubrication with high viscosity surface layers. The enhanced viscosity surface layers are considered on both sides of the bearing surfaces.
K. Ono
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Construction of an asymptotic Reynolds gas lubrication equation

Fluid Dynamics, 1992
We have derived an asymptotic equation free of limitations on both the macrogeometry of the bearing and on its periodic microgeometry, without having to make additional physical assumptions.
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Validity of the modified Reynolds equation for incompressible active lubrication

Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology, 2016
The modified Reynolds equation for active lubrication has been the cornerstone around which the theoretical investigations regarding actively lubricated bearings have evolved over the years. Introduced originally in 1994, it enables to calculate in a simplified manner the bearing pressure field as a function of servovalve controlled pressurized oil ...
Alejandro Cerda Varela, Ilmar F Santos
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A Generalized Reynolds Equation for Non-Newtonian Thermal Elastohydrodynamic Lubrication

Journal of Tribology, 1990
A new generalized Reynolds equation, which can incorporate most of the rheological laws found in the literature, is derived in this paper. A number of numerical solutions of the line contact thermal elastohydrodynamic lubrication problem has been obtained by using five rheological laws. The results show that, the influence of the non-Newtonian behavior
Yang Peiran, Wen Shizhu
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Nonlinear reynolds equation for lubrication of a rapidly rotating shaft

Applicable Analysis, 2000
Using the homogenization theory, we derive the nonlinear Reynolds equation governing the process of lubrication of a slipper bearing with rapidly rotating shaft. We prove that this nonlinear lubrication law is an approximation of the full Navier--Stokes equations in a thin cylinder with periodic roughness.
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A Reynolds-Eyring Equation for Elastohydrodynamic Lubrication in Line Contacts

Journal of Tribology, 1987
A new Reynolds equation, based on the Eyring theory of non-Newtonian flow, is derived for flow in one dimension. It is shown that this new equation reduces to the traditional Reynolds equation as the Eyring model approaches the Newtonian model in the limit. Numerical solutions are presented for a selected oil at two different temperatures.
T. F. Conry, S. Wang, C. Cusano
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