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RESEARCH PAPERS

Some Remarks on the Validity of Reynolds Equation in the Modeling of Lubricant Film Flows on the Surface Roughness Scale

[+] Author and Article Information
T. Almqvist, R. Larsson

Division of Machine Elements, Luleå University of Technology, SE-971 87 Luleå, Sweden

J. Tribol 126(4), 703-710 (Nov 09, 2004) (8 pages) doi:10.1115/1.1760554 History: Received July 01, 2003; Revised March 25, 2004; Online November 09, 2004
Copyright © 2004 by ASME
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References

Reynolds,  O., 1886, “On the Theory of Lubrication and Its Application to Mr. Beauchamps Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive Oil,” Philos. Trans. R. Soc. London, 177, pp. 157–234.
Khonsari, M. M., and Booser, E. R., 2001, Applied Tribology, John Wiley & Sons, New York.
Almqvist,  T., and Larsson,  R., 2001, “The Navier-Stokes Approach for Thermal EHL Line Contact Solutions,” Tribol. Int., 35, pp. 163–170.
Almqvist, T., and Larsson, R., 2001, “Comparison of Reynolds and Navier-Stokes Approaches for Solving Isothermal EHL Line Contacts,” Proceedings of the WTC Conference.
Schäfer, C. T., Giese, P., Rowe, W. B., and Woolley, N. H., 1999, “Elastohydrodynamically Lubricated Line Contact Based on the Navier-Stokes Equations,” Proceedings of the 26th Leeds-Lyon Symposium on Tribology, pp. 57–59.
Renardy,  M., 1986, “Some Remarks on the Navier-Stokes Equations With a Pressure-Dependent Viscosity,” Commun. Partial Differ. Equ., 11, pp. 779–793.
Bair,  S., Khonsari,  M., and Winer,  W. O., 1998, “High-Pressure Rheology of Lubricants and Limitations of the Reynolds Equation,” Tribol. Int., 31, pp. 573–586.
Odyck,  D. E. A., and Venner,  C. H., 2003, “Stokes Flow in Thin Films,” ASME J. Tribol., 125, pp. 121–134.
CFX 4.4 USER GUIDE, 1999, AEA Technology.
Conry,  T. F., Wang,  S., and Cusano,  C., 1987, “A Reynolds Equation for Elastohydrodynamic Lubrication in Line Contacts,” Transactions of the ASME, 109, pp. 648–658.
Johnson,  K. L., and Tevaarwerk,  J. L., 1977, “The Shear Behavior of Elasto hydrodynamic Oil Films,” Proc. R. Soc. London, Ser. A, 356, pp. 215–236.
Roelands, C. J. A., 1966, “Correlational Aspects of the Viscosity-Temperature-Pressure Relationships of Lubricating Oils,” Ph.D thesis, Druck, V. R. B., Groningen.
Dowson, D., and Higginson, G. R., 1966, Elasto-Hydrodynamic Lubrication: The Fundamentals of Roller or Gear Lubrication, Pergamon Press, Oxford.
Evans,  C. R., and Johnson,  K. L., 1986, “The Rheological Properties of Elastohydrodynamic Lubricants,” Proc. Inst. Mech. Eng., 200, pp. 303–312.

Figures

Grahic Jump Location
The denominator in the modified momentum equations for Newtonian (-) and Eyring (--) rheological models. The pressure is denoted beside the curves.
Grahic Jump Location
Pressure distribution for the two approaches when a Newtonian rheology is used. The CFD-solution denoted by (-) and the Reynolds solution by (* ), ω=2.5×10−3.
Grahic Jump Location
The CFD-solution (-) compared with the Reynolds equation solution (--) when the singularity influences the solution. The rheology is assumed to be Newtonian, ω=2.5×10−3.
Grahic Jump Location
The CFD and Reynolds equation solution for an Eyring rheological model, ω=2.5×10−3
Grahic Jump Location
The denominator in the modified momentum equations for a Newtonian (-) and an Eyring (--) rheological model. The Eyring stress τ0 is denoted beside the curves.
Grahic Jump Location
The ratio of the maximum deviation between the CFD and Reynolds equation and the maximum pressure. In the figure, three different ratios yr/h are shown versus ω.
Grahic Jump Location
The deviation in pressure between the CFD and Reynolds equation approaches versus ω. The ratio yr/h is held to a constant value yr/h=0.1.
Grahic Jump Location
The ratio of the maximum pressure difference across the fluid film and the maximum pressure along a trace in the middle of the film in the CFD-computations. In the figure, three different ratios yr/h are shown versus ω.

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