The technique of High-Resolution Modeling of Thin Films is combined with a two-scale analysis to formulate the Compressible Narrow Groove Analysis. The data bank of Fukui and Kaneko (1990) is emulated in the form of an empirical formula to treat the state of arbitrary rarefaction of the gas film. Due to its transcendental character, the compressible fine-scale solution is treated on the fly as a part of the global-scale computation. Derivations for the Compressible Narrow Groove Analysis are presented here. In a companion paper (Pan, 1998), the Compressible Narrow Groove Analysis is used to compute the pressure field of a spherical device operating in both the pressurizing and evacuating modes.
Issue Section:
Research Papers
1.
Bonneau
D.
Absi
J.
1994
, “Analysis of Aerodynamic Journal Bearings with Small Number of Herringbone Grooves by Finite Element Method
,” ASME JOURNAL OF TRIBOLOGY
, Vol. 116
, pp. 698
–704
.2.
Bonneau
D.
Huitric
J.
Tournerie
B.
1993
, “Finite Element Analysis of Grooved Gas Thrust Bearings and Grooved Gas Face Seals
,” ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol. 115
, pp. 348
–354
.3.
Denhard
W. G.
Pan
C. H. T.
1968
, “Application of Gas-Lubricated Bearings to Instruments
,” ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol. 90
, pp. 731
–740
.4.
Foster
D. J.
Carow
D.
Benson
D.
1969
, “An Approximate Theoretical Analysis of the Static and Dynamic Characteristics of the Herringbone Grooved, Gas Lubricated Journal Bearing, and Comparison with Experiment
,” ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol. 91
, pp. 25
–36
.5.
Fukui
S.
Kaneko
R.
1990
, “A Database for Interpolation of Poiseuille Flow Rates for High Knudsen Number Lubrication Problems
,” ASME JOURNAL OF TRIBOLOGY
, Vol. 112
, pp. 78
–83
.6.
Gupta
P. K.
Coleman
R. L.
Pan
C. H. T.
1974
, “Ambient Edge Correction for the Locally Incompressible Narrow-Groove Theory
,” ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol. 96
, pp. 284
–290
.7.
Harrison
W. J.
1913
, “The Hydrodynamic Theory of Lubrication with Special Reference to Air as a Lubricant
,” Trans. Cambridge Phil. Soc.
, XXii
, pp. 6
–54
.8.
ja¨ger, Diego Arturo, 1987, “An Unconditionally Stable, High Resolution Algorithm for Gas Lubrication Problems,” Dissertation in partial fulfillment of the requirements for the degree of Doctor of Engineering Science in the School of Engineering and Applied Science, Columbia University, New York, NY. UMI Order Number 8724042, Ann Arbor, MI.
9.
ja¨ger, Diego A., and Pan, Coda H. T., 1986, “Functional Analysis for the Numerical Treatment of the Theory of Gas Lubrication,” Mathematics Applied to Fluid Mechanics and Stability: Proceedings of a Conference Dedicated to Richard C. Diprima, SIAM, Philadelphia, PA.
10.
Murata
S.
Miyake
Y.
Kawabata
N.
1979
, “Exact Two-Dimensional Analysis of Circular Disk Spiral Groove Bearing
,” ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol. 101
, (Part 1) pp. 424
–430
, (Part 2) pp. 431–436.11.
Pan, C. H. T., 1998, “Compressible Narrow Groove Analysis—Part 2; Computation of the Pressure field in a Spherical Device Rotating in Either Direction,” ASME JOURNAL OF TRIBOLOGY, published in this issue pp. 765–771.
12.
Sedy
Josef
1980
, “Improved Performance of Film-Riding Gas Seals through Enhancement of Hydrodynamic Effects
,” ASLE Transactions
, Vol. 23
, pp. 35
–44
.13.
Vohr, J. H., and Pan, C. H. T., 1968, “Design Data of Gas-Lubricated Spin-Axis Bearings for Gyroscopes,” Technical Report MTI-68TR29, prepared for Office of Naval Research, US Department of the Navy under Contract N00014-67-C-0530 NR 062-370/2-21-27, Mechanical Technology Incorporated, Latham, NY.
14.
Whitley, S., and Williams, L. G., 1959, “The Gas-Lubricated Spiral Groove Thrust Bearing,” UKAEA-IG Report 28 RD/CA.
15.
Wildmann
M.
1968
, “On the Behavior of Grooved Plate Thrust Bearing with Compressible Lubricant
,” ASME JOURNAL OF LUBRICATION TECHNOLOGY
, Vol. 90
, pp. 226
–232
.
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