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Research Papers: Hydrodynamic Lubrication

High-Speed Subsonic Compressible Lubrication

[+] Author and Article Information
Florence Dupuy, Benyebka Bou-Saïd

Laboratoire de Mécanique des Contacts
et des Structures,
Institut National des Sciences
Appliquées de Lyon,
Villeurbanne 69621, France

John Tichy

Laboratoire de Mécanique des Contacts
et des Structures,
Institut National des Sciences
Appliquées de Lyon,
Villeurbanne 69621, France
Department of Mechanical, Aerospace,
and Nuclear Engineering,
Rensselaer Polytechnic Institute,
Troy, NY 12180-3590
e-mail: tichyj@rpi.edu

1Corresponding author.

Contributed by the Tribology Division of ASME for publication in the JOURNAL OF TRIBOLOGY. Manuscript received January 27, 2015; final manuscript received February 19, 2015; published online May 6, 2015. Assoc. Editor: George K. Nikas.

J. Tribol 137(4), 041702 (Oct 01, 2015) (7 pages) Paper No: TRIB-15-1030; doi: 10.1115/1.4030207 History: Received January 27, 2015; Revised February 19, 2015; Online May 06, 2015

The present study extends the scope of compressible lubrication theory (CLT) by considering a more complete formulation of compressible flow in a thin film. A one-dimensional (1D) approximation is obtained, which is common in basic studies of compressible flow. A dimensionless formulation of the thin film compressible flow equations (continuity, momentum, energy, and perfect gas) is derived. There are three dimensionless governing parameters, the Mach number M, the compressibility or bearing number Λ, and a heat transfer number H (a sort of inverse Péclet number). The classical theory assumes isothermal conditions (a consequence of a large heat transfer number) and implicitly assumes low Mach number conditions. It turns out that neither of these conditions are met in high-speed applications such as foil bearings. Results are calculated by varying M and H in a parametric fashion. We find that the influence of Mach number is small (at least up to M = 0.5) but the influence of heat transfer is large: the classical predicted results are in error by a factor of four or so. The improved theory predicts much greater load than the traditional. This means that high-speed air bearing design based on CLT would function satisfactorily, as born out by their successful application; however, such bearings would be significantly over-designed.

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Figures

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Fig. 1

Schematic of contact 1D geometry

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Fig. 2

Temperature profile, Mach number M = 0.01, and heat transfer number H=100

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Fig. 3

Pressure profile: CLT versus present theory with M = 0.01, H = 100

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Fig. 4

Mean velocity profile: CLT versus present theory

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Fig. 5

Pressure profile variation with Mach number value, for heat transfer number H = 100

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Fig. 6

Pressure profile variation with heat transfer for Mach number M = 0.5

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Fig. 7

Temperature profile variation with heat transfer number, Mach number M = 0.1

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Fig. 8

Pressure profile variation with Mach number for heat transfer H = 0.1

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Fig. 9

Temperature profile variation with Mach number for heat transfer H = 0.1

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