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TECHNICAL PAPERS

Multi-Constrained Optimization of Running Characteristics of Mechanisms Lubricated With Compressible Fluid

[+] Author and Article Information
M. Jai

CNRS-UMR 5585, INSA de LYON, Mathématiques Bat Leonard de Vinci, F-69621 Villeurbanne, Francee-mail: jai@insa-lyon.fr

G. Buscaglia

Instituto Balseiro and Centro Atómico Bariloche, 8400, Bariloche, Argentinae-mail: gustavo@cab.cnea.gov.ar

I. Iordanoff

CNRS-UMR 5514, INSA de LYON, Bat Jean D’Alembert, F-69621 Villeurbanne, Francee-mail: Ivan.Iordanoff@insa-lyon.fr

J. Tribol 126(1), 132-136 (Jan 13, 2004) (5 pages) doi:10.1115/1.1631011 History: Received April 09, 2002; Revised May 06, 2003; Online January 13, 2004
Copyright © 2004 by ASME
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References

Rayleigh,  L., 1918, “Notes on the Theory of Lubrication,” Philos. Mag., 35, pp. 1–12.
Maday,  C. J., 1970, “The Maximum Principle Approach to the Optimum One-Dimensional Journal Bearing,” ASME J. Lubr. Technol., 92, pp. 482–489.
Rodhe,  S. M., and McAllister,  G. T., 1976, “On the Optimization of Fluid Film Bearings,” Proc. R. Soc. London, Ser. A, 351, pp. 481–497.
Robert,  M. P., 1990, “Optimization of Self-Acting Gas Bearings for Maximum Static Siffness,” ASME J. Appl. Mech., 57, pp. 758–761.
Robert,  M. P., 1995, “New Class of Sliders Numerically Designed for Maximum Siffness,” ASME J. Tribol., 117, pp. 456–460.
Jai,  M., El Alaoui Talibi,  M., and Ciuperca,  I., 2002, “On the Optimal Control Coefficients in Elliptic Problems, Application to the Optimization of the Head Slider,” Appl. Math. Optim., accepted for publication.
Robert,  M. P., and Hendriks,  F., 1990, “Gap Optimization and Homogenization of an Externally Pressured Air Bearing,” STLE Tribol. Trans., 33(1), pp. 41–47.
Grau,  G., Iordanoff,  I., Bou Said,  B., and Berthier,  Y., 2003, “Profile Optimization of a Compliant Foil Journal Gas Bearing for Static and Dynamic Analysis,” submited in STLE Tribol. Trans.
Spellucci,  P., 1998, “A New Technique for Inconsistent QP Problems in the SQP Method,” Math. Methods Oper. Res., 47(3), pp. 355–400.
Evans, L. C., and Gariepy, R. F., 1992, Measure Theory and Fine Properties of Functions, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL.

Figures

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Unconstrained optimal profile H*. The graphics package interpolates as though H were bilinear, when in fact it is piecewise constant.
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Optimal profile for C=1.5
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Optimal profile for C=1.2
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Pressure distribution for the optimal design of Fig. 3(C=1.2)
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Adjoint state for the optimal design of Fig. 3(C=1.2)
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Optimal normalized load capacity versus gas bearing number. Also shown is the value of θ0 for each optimum, and the best attainable value when each pan has circular shape.
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Optimal gap profiles for different bearing numbers
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Pressure distributions corresponding to the profiles of Fig. 7
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Sketches of optimally shaped bearings for Λ=10 and Λ=300. The radius of the inner cylinder has been asigned the unrealistic value of 10 just for visualization purposes.
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Scheme of a classical three-pad bearing and its defining parameters
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Unconstrained optimal gap profile and pressure distribution for the journal bearing with Λ=100

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