Finite element analysis of gas bearings for oil-free turbomachinery
Keywords:
Gas bearings, rotordynamics, stability, finite element modelAbstract
Further advancements in high performance turbomachinery operating at extreme temperatures mandate the development of gas film bearing technology to procure compact units with improved efficiency in an oil-free environment. A novel finite element (FE) procedure to model thin film gas bearings follows. The FE model incorporates a novel class of high order shape functions ensuring computational efficiency and numerical stability even at (infinity) high speed bearing numbers. The method does not rely on cumbersome schemes for evaluation of advection flow terms in the Reynolds equation nor introduces artificial diffusion into the numerical solution. A computational FE program forwards predictions for the static performance and dynamic force coefficients of an externally pressurized gas bearing for ready application to an automotive turbocharger. The predictions show the strong effects of excitation frequency on the dynamic force coefficients and the onset of a hydrodynamic instability at moderately low rotor speeds. The analysis of predictions evidences the benefits and limits of rigid surface gas bearings for oil-free turbomachinery.
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References
[BAT 82] BATHE K.J., Finite Element Procedures in Engineering Analysis, Englewood Cliffs,
New Jersey, Prentice Hall, 1982.
[CAS 65] CASTELLI V., ELROD H.G., “Solution of the Stability Problem for 360 Deg Self-
Acting, Gas-Lubricated Bearings,” Journal of Basic Engineering, Series D, Vol. 87, No. 1,
, p. 199-212.
[CAS 67] CASTELLI V., VOHR J.H., “Performance Characteristics of Herringbone-Grooved
Journal Bearings Operating at High Eccentricity Ratios With Misalignment,” Paper No. 14,
Proceedings Gas Bearing Symposium, University of Southampton, Apr. 1967.
[CAS 68] CASTELLI V., PIRVICS J., “Review of Numerical Methods in Gas Bearing Film
Analysis”, ASME Journal of Lubrication Technology, 1968, p. 777-792.
[CHI 93] CHILDS D., Turbomachinery Rotordynamics, John Wiley & Sons, Inc., 1993.
[CZO 96] CZOLCZYNSKI K., “How to Obtain Stiffness and Damping Coefficients of
GasBbearings,” Wear, Vol. 201, No. 1-2, 1996, p. 265-275.
[ELR 60] ELROD H.G. Jr., MALANOSKI S.B., Theory and Design Data for Continuous-Film,
Self-Acting Journal Bearings of Finite Length, Report I-A 2049-13, Nov. 1960, The
Franklin Institute Laboratories for Research and Development.
[ELR 67] ELROD H.G. Jr., MCCABE J.T., CHU T.Y., “Determination of Gas-Bearing Stability
Response to a Step-Jump,” ASME Journal of Lubrication Technology, Vol. 89, No. 9, 1967,
p. 493-498.
[FAR 99] FARIA M.T.C., Finite Element Method of High Speed Grooved Gas Bearings, Ph.D.
Dissertation, Texas A&M University, June 1999.
[FAR 00] FARIA M.T.C., SAN ANDRES L., “On the Numerical Modeling of High-Speed
Hydrodynamic Gas Bearings,” ASME Journal of Tribology, Vol. 122, No. 1, 2000, p 124-
[FAR 01] FARIA M.T.C., “An Efficient Finite Element Procedure for Analysis of High-Speed
Spiral Groove Gas Face Seals,” ASME Journal of Tribology, Vol. 123, No. 1, 2001, p 205-
[FUL 69] FULLER D.D., “A Review of the State-of-the-Art for the Design of Self-Acting Gaslubricating
Bearings”, ASME Journal of Lubrication Technology, Vol. 91, No. 1, 1969, p 1-
[GRO 62] GROSS W.A., Gas Film Lubrication, New York, John Wiley & Sons, 1962.
[GUN 64] GUNTER E. J., HINKLE J. G., FULLER D. D., “The Effects of Speed, Load, and Film
Thickness on the Performance of Gas-Lubricated, Tilting-Pad Journal Bearings,” ASLE
Transactions, Vol. 7, 1964, p. 353-365.
[HAM 94] HAMROCK B.J., Fundamentals of Fluid Film Lubrication, New York, McGraw-Hill,
[HEI 77] HEINRICH J.C., HUYAKORN P.S., ZIENKIEWICZ O.C., MITCHELL A.R., “An Upwind
Finite Element Scheme for Two-dimensional Convective Transport Equation”,
International Journal for Numerical Methods in Engineering, Vol. 11, No.1, 1977, p 131-
[LUN 64] LUND J.W., “The Hydrostatic Gas Journal Bearing With Journal Rotation and
Vibration,” Journal of Basic Engineering, Trans. ASME, Series D, Vol. 86, No. 2., 1964, p.
-336.
[LUN 67] LUND J.W., “A Theoretical Analysis of Whirl Instability and Pneumatic Hammer for
a Rigid Rotor in Pressurized Gas Journal Bearings”, Journal of Lubrication Technology,
Transactions of the ASME, April 1967, p. 154-166.
[LUN 68] LUND J.W., “Calculation of Stiffness and Damping Properties of Gas Bearings”,
Journal of Lubrication Technology, 1968, p. 793-804.
[MAJ 88] MAJUMDER M.C., MAJUMDAR B.C., “Theoretical Analysis of Pneumatic Instability of
Externally Pressurized Porous Gas Journal Bearings Considering Velocity Slip”, ASME
Journal of Tribology, Vol. 110, No. 4, 1988, p. 730-733.