The various existing forms of Reynolds equation are known to yield pressure fields which are unbounded and nonphysical when contact occurs. With a view to developing a Reynolds equation that is suitable for contact, here we revisit Taylor’s plate scraping problem for incompressible flow. This problem has an infinite pressure where the scraper contacts the plate. By suitably modifying Maxwell’s slip condition, the scraping problem can be reformulated so as to lead to finite pressures. This is shown locally via asymptotics, and globally via convergence checks. The approach looks sufficiently promising to consider the further development needed for the compressible flow present in gas lubricated bearings.
Issue Section:
Technical Papers
1.
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
.2.
Sommerfeld, A., 1904, “Zur hydrodynamischen Theorie der Schmiermittelreibung,” Zeitschrift fu¨r Mathematik und Physik, 50, pp. 97–155.
3.
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
.4.
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
.5.
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
.6.
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
.7.
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
.8.
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
.9.
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.
10.
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
.11.
Anaya-Dufresne
, M.
, and Sinclair
, G. B.
, 1995
, “Some Exact Solutions of Reynolds Equation
,” ASME J. Tribol.
, 117
, pp. 560
–562
.12.
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
.13.
Vicenti, W. G., and Kruger, C. H., Jr., 1967, Introduction to Physical Gas Dynamics, John Wiley and Sons, Inc., New York.
14.
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.
15.
Ting
, T. C. T.
, 1984
, “The Wedge Subjected to Tractions: A Paradox Re-Examined
,” J. Elast.
, 14
, pp. 235
–247
.16.
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
.17.
Kennard, E. H., 1938, Kinetic Theory of Gases, McGraw-Hill Book Co., New York.
18.
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
.19.
Moffat
, H. K.
, 1964
, “Viscous and Resistive Eddies Near a Sharp Corner
,” J. Fluid Mech.
, 18
, pp. 1
–18
.20.
Sinclair
, G. B.
, 1980
, “On the Singular Eigenfunctions for Plane Harmonic Problems in Composite Regions
,” ASME J. Appl. Mech.
, 47
, pp. 87
–92
.21.
Anaya-Dufresne, M., 1996, “On the Development of a Reynolds Equation for Air Bearings with Contact,” Ph.D. dissertation, Carnegie Mellon University, Pittsburgh, PA.
22.
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
.Copyright © 2002
by ASME
You do not currently have access to this content.
