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TECHNICAL PAPERS

A Comparison of Homogenization and Averaging Techniques for the Treatment of Roughness in Slip-Flow-Modified Reynolds Equation

[+] Author and Article Information
M. Jai

UMR 5585, Insa de Lyon Bt 401, 20 Av. A. Einstein, 69621 Villeurbanne Cedex, France

B. Bou-Saı̈d

UMR 5514, Insa de Lyon Bt 113, 20 Av. A. Einstein, 69621 Villeurbanne Cedex, France

J. Tribol 124(2), 327-335 (Jul 06, 2001) (9 pages) doi:10.1115/1.1402131 History: Received February 02, 2001; Revised July 06, 2001
Copyright © 2002 by ASME
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References

Buscaglia,  G., and Jai,  M., 2000, “Sensitivity Analysis and Taylor Expansions in Numerical Homogenization Problems,” Numer. Math., 85, pp. 49–75.
Buscaglia, G., and Jai, M., 2001, “A New Numerical Scheme for Non-Uniform Homogenized Problems: Application to the Nonlinear Reynolds Compressible Equation,” Mathematical Problems in Engineering, in press.
Bushan, B., 1990, Tribology and Mechanics of Magnetic Storage Devices; Springer Verlag, New York.
Bushan,  B., and Tonder,  K., 1989, “Roughness-Induced Shear and Squeeze Film Effects in Magnetic Recording: Part. 1—Analysis,” ASME J. Tribol., 111, pp. 220–227.
Bushan,  B. and Tonder,  K., 1989, “Roughness-Induced Shear and Squeeze Film Effects in Magnetic Recording: Part 2—Applications,” ASME J. Tribol., 111, pp. 228–237.
Christensen, H., and Tonder, K. 1969, “Tribology of Rough Surfaces: Stochastic Models of Hydrodynamic Lubrication,” SINETF Report N 10/69-18; University of Trondhein, Norway.
Elrod,  H. G., 1979, “A General Theory for Laminar Lubrication With Reynolds Roughness,” ASME J. Lubr. Technol., 101, pp. 8–14.
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.
Jai, M., 1995, “Homogenization and Two-Scale Convergence of the Compressible Reynolds Lubrication Equation Modeling the Flying Characteristics of a Rough Magnetic Head Over a Rough Rigid-Disk Surface,” Math. Modell. Numer. Anal., pp. 199–233.
Jai, M., Bayada, G., Buscaglia, G., and Bou-said, B., 1999, “A New Approach for Characterizing the Roughness Effects in Compressible Fluid Contact,” Proc. 26th Leeds-Lyon Symp. on Trib, Thinning Films and Tribological Interfaces, D. Downson et al., eds., Elsevier, Amsterdam, pp. 125–136.
Mitsuya,  Y., and Fukui,  S., 1986, “Stokes Roughness Effects on Hydrodynamic Lubrication: Part. 1—Comparison Between Incompressible and Compressible Lubricating Films,” ASME J. Tribol., 108, pp. 151–158.
Mitsuya,  Y., and Koumura,  T., 1995, “Transient Response Solution Applying ADI Scheme to Boltzmann Flow-Modified Reynolds Equation Averaged With Respect to Surface Roughness,” ASME J. Tribol., 117, pp. 430–436.
Mitsuya,  Y., Ohkubo,  T., and Ota,  H., 1989, “Averaged Reynolds Equation Extended to Gas Lubricant Possessing Surface Roughness in the Slip Flow Regime: Approximate Method and Confirmation Experiments,” ASME J. Tribol., 111, pp. 495–503.
Patir,  N., and Cheng,  H. S., 1978, “An Average Flow Model for Determining Effects of Three-Dimensional Roughness on Partial Hydrodynamic Lubrication,” ASME J. Lubr. Technol., 100, pp. 12–17.
Patir,  N., and Cheng,  H. S., 1979, “Application of Average Flow Model to Lubrication Between Rough Sliding Surfaces,” ASME J. Lubr. Technol., 101, pp. 220–230.
Patir, N., and Cheng, H. S., 1979, “Effects of Surface Roughness Orientation in the Central Film Thickness in E.H.D Contact,” Proc. 5th Leeds Lyon Symp. on Trib., MEP, London, pp. 15–20.

Figures

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Taper flat slider configuration for magnetic disk use
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Slider having checkered pattern roughness
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Homogenized pressure contours
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Averaged pressure contours
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Exact pressure contours (N1=40,N2=4)
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The exact solutions, N1=20,N2=2, and N1=80,N2=8, the homogenized and the averaged solutions in the longitudinal centerline
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The exact solution, N1=40,N2=4 and N1=80,N2=8, the homogenized and the averaged solutions in the transversal centerline
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Normalized load versus gas bearing number
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Slider with anisotropic roughness
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Homogenized field pressure
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Homogenized pressure contours
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Averaged field pressure
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Averaged pressure contours
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Exact field pressure (N1=40,N2=4)
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Exact pressure contours (N1=40,N2=4)
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The exact solutions, N1=40,N2=4 and N1=80,N2=8, the homogenized and the averaged solutions in the longitudinal centerline
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The exact solution, N1=40,N2=4 and N1=80,N2=8, the homogenized and the averaged solutions in the transversal centerline
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Normalized load versus gas bearing number
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Normalized load versus gas bearing number for different values of parameter ax=ay
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Normalized drag force versus gas bearing number for different values of parameter ax=ay
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Slider having stochastic roughness
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Homogenized pressure contours
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Averaged pressure contours
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Exact pressure contours
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The exact solutions, N1=10,N2=1, the homogenized and the averaged solutions in the longitudinal centerline
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The exact solution, N1=10,N2=1, the homogenized and the averaged solutions in the transversal centerline

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