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TECHNICAL PAPERS

Homogenization of the Generalized Reynolds Equation for Ultra-Thin Gas Films and Its Resolution by FEM

[+] Author and Article Information
G. C. Buscaglia

Instituto Balseiro and Centro Atómico Bariloche, 8400, Bariloche, Argentina

M. Jai

CNRS-UMR 5585, INSA de LYON, Mathématiques Bat Leonard de Vinci, F-69621 Villeurbanne, France

J. Tribol 126(3), 547-552 (Jun 28, 2004) (6 pages) doi:10.1115/1.1739410 History: Received March 12, 2003; Revised November 07, 2003; Online June 28, 2004
Copyright © 2004 by ASME
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References

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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.
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, “New Numerical Scheme for Nonuniform Homogenized Problems: Application to the Nonlinear Reynolds Compressible Equation,” Mathematical Problems in Engineering, 7(4), pp. 355–377.
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Bensoussan, A., Lions, J. L., and Papanicolaou, G., 1978, Asymptotic Analysis for Periodic Structure, North-Holland.
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Figures

Grahic Jump Location
Accuracy of the Taylor expansion A11*(n) with respect to α1 with α2=2. The curve of the 4-th order expansion is not visible because it coincides (within resolution accuracy) with the exact solution.
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Accuracy of the Taylor expansion A12*(n) with respect to α1 with α2=2
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Scheme of the roughness/texture function
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The function H0, which is the smooth component of the normalized bearing thickness H
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Contour plots of the normalized pressure for different cases. The color scale on the right applies to all four plots: (a) 40×4 periods; (b) 80×8 periods; (c) Homogenized solution; and (d) smooth-case solution, with the nondimensional clearance increased by 0.5.
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Cross-sections of the pressure field to assess convergence to the homogenized solution when ε tends to zero: (a) midline parallel to the direction of movement (x2=0.05); and (b) midline transverse to the direction of movement (x1=0.5).

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