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TECHNICAL PAPERS

Towards a Reynolds Equation for Gas Lubricated Bearings When Contact Occurs

[+] Author and Article Information
M. Anaya-Dufresne

Read-Rite Corporation, Fremont, CA 94539

G. B. Sinclair

Mechanical Engineering Department, Louisiana State University, Baton Rouge, LA 70803

J. Tribol 124(2), 266-273 (Mar 07, 2001) (8 pages) doi:10.1115/1.1398548 History: Received January 25, 2000; Revised March 07, 2001
Copyright © 2002 by ASME
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References

Reynolds,  O., 1886, “On the Theory of Lubrication and its Application to Mr. Beauchamp Tower’s Experiments, Including an Experimental Determination of the Viscosity of Olive Oil,” Philos. Trans. R. Soc. London, 177, pp. 157–234.
Sommerfeld, A., 1904, “Zur hydrodynamischen Theorie der Schmiermittelreibung,” Zeitschrift für Mathematik und Physik, 50 , pp. 97–155.
Harrison,  W. J., 1913, “The Hydrodynamical Theory of Lubrication with Special Reference to Air as a Lubricant,” Trans. Cambridge Philos. Soc., 22, pp. 39–54.
Burgdorfer,  A., 1959, “The Influence of the Molecular Mean Free Path on the Performance of Hydrodynamic Gas Lubricated Bearings,” ASME J. Basic Eng., 81, pp. 94–100.
Hsia,  Y.-T., and Domoto,  G. A., 1983, “An Experimental Investigation of Molecular Rarefaction Effects in Gas Lubricated Bearings at Ultra-Low Clearances,” ASME J. Lubr. Technol., 105, pp. 120–130.
Fukui,  S., and Kaneko,  R., 1988, “Analysis of Ultra-Thin Gas Film Lubrication Based on Linearized Boltzmann Equation: First Report-Derivation of a Generalized Lubrication Equation Including Thermal Creep Flow,” ASME J. Tribol., 110, pp. 253–262.
Mitsuya,  Y., 1993, “Modified Reynolds Equation for Ultra-Thin Film Gas Lubrication Using 1.5-Order Slip-Flow Model and Considering Surface Accommodation Coefficient,” ASME J. Tribol., 115, pp. 289–294.
Ruiz,  O. J., and Bogy,  D. B., 1990, “A Numerical Simulation of the Head-Disk Assembly in Magnetic Hard Disk Files: Part 1—Component Models,” ASME J. Tribol., 112, pp. 593–602.
Anaya-Dufresne, M., and Sinclair, G. B., 1994, “Numerical Simulations of Reynolds Equation for Gas Lubricated Bearings When Local Contact Occurs,” Report SM94-1, Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA.
Anaya-Dufresne,  M., and Sinclair,  G. B., 1997, “On the Breakdown Under Contact Conditions of Reynolds Equation for Gas Lubricated Bearings,” ASME J. Tribol., 119, pp. 71–75.
Anaya-Dufresne,  M., and Sinclair,  G. B., 1995, “Some Exact Solutions of Reynolds Equation,” ASME J. Tribol., 117, pp. 560–562.
Huang,  W., and Bogy,  D. B., 1998, “An Investigation of a Slider Air Bearing with a Asperity Contact by a Three-Dimensional Direct Simulation Monte Carlo Method,” IEEE Trans. Magn., 34, pp. 1810–1812.
Vicenti, W. G., and Kruger, C. H., Jr., 1967, Introduction to Physical Gas Dynamics, John Wiley and Sons, Inc., New York.
Taylor, G. I., 1971, “On Scraping Viscous Fluid from a Plane Surface,” in The Scientific Papers of Sir Geoffrey Ingram Taylor, G. K. Batchelor, ed., IV , pp. 410–413, Cambridge University Press, London.
Ting,  T. C. T., 1984, “The Wedge Subjected to Tractions: A Paradox Re-Examined,” J. Elast., 14, pp. 235–247.
Milikan,  R. A., 1923, “Coefficients of Slip in Gases and the Law of Reflection of Molecules from the Surfaces of Solids and Liquids,” Phys. Rev., 21, pp. 217–238.
Kennard, E. H., 1938, Kinetic Theory of Gases, McGraw-Hill Book Co., New York.
Williams,  M. L., 1952, “Stress Singularities Resulting from Various Boundary Conditions in Angular Corners of Plates in Extension,” ASME J. Appl. Mech., 19, pp. 526–528.
Moffat,  H. K., 1964, “Viscous and Resistive Eddies Near a Sharp Corner,” J. Fluid Mech., 18, pp. 1–18.
Sinclair,  G. B., 1980, “On the Singular Eigenfunctions for Plane Harmonic Problems in Composite Regions,” ASME J. Appl. Mech., 47, pp. 87–92.
Anaya-Dufresne, M., 1996, “On the Development of a Reynolds Equation for Air Bearings with Contact,” Ph.D. dissertation, Carnegie Mellon University, Pittsburgh, PA.
Dempsey,  J. P., and Sinclair,  G. B., 1979, “On the Stress Singularities in the Plane Elasticity of the Composite Wedge,” J. Elast., 9, pp. 373–391.

Figures

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Schematic of a slider and magnetic disk
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Shear stress comparison between continuum and kinetic models for Couette flow
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Scraper and moving horizontal plate in contact
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Control volume used for momentum balance near the point of contact
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Stream function at y=x for: (a) Problem 1; (b) Problem 2.
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Pressure at y=0 for: (a) Problem 1; (b) Problem 2.

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