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A compressible flow model for the air-rotor–stator dynamics of a high-speed, squeeze-film thrust bearing

Published online by Cambridge University Press:  13 May 2010

J. E. GARRATT ,
K. A. CLIFFE ,
S. HIBBERD  and
H. POWER
J. E. GARRATT
Affiliation:
University Technology Centre in Gas Turbine Transmission Systems, Faculty of Engineering, University of Nottingham, Nottingham, NG7 2RD, UK
K. A. CLIFFE*
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK
S. HIBBERD
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK
H. POWER
Affiliation:
Fuels and Power Technology Research Division, Faculty of Engineering, University of Nottingham, Nottingham, NG7 2RD, UK
*
†Email address for correspondence: [email protected]
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Abstract

A compressible air-flow model is introduced for the thin film dynamics of a highly rotating squeeze-film thrust bearing. The lubrication approximation to the Navier–Stokes equations for compressible flow leads to a modified Reynolds equation incorporating additional rotation effects. To investigate the dynamics of the system, the axial position of the bearing stator is prescribed by a finite-amplitude periodic forcing. The dynamics of the squeeze-film are modelled in the uncoupled configuration where the axial position of the rotor is fixed. The coupled squeeze-film bearing dynamics are investigated when the axial position of the rotor is modelled as a spring-mass-damper system that responds to the film dynamics. Initially the uncoupled squeeze-film dynamics are considered at low operating speeds with the classical Reynolds equation for compressible flow. The limited value of the linearized small-amplitude results is identified. Analytical results indicate that finite-amplitude forcing needs to be considered to gain a complete understanding of the dynamics. Using a Fourier spectral collocation numerical scheme, the periodic bearing force is investigated as a nonlinear function of the frequency and amplitude of the stator forcing. High-speed bearing operation is modelled using the modified Reynolds equation. A steady-state analysis is used to identify the effect of rotation and the rotor support properties in the coupled air-flow–structure model. The unsteady coupled dynamics are computed numerically to determine how the rotor support structures and the periodic stator forcing influence the system dynamics. The potential for resonant rotor behaviour is identified through asymptotic and Fourier analysis of the rotor motion for small-amplitude, low-frequency oscillations in the stator position for key values of the rotor stiffness. Through the use of arclength continuation, the existence of resonant behaviour is identified numerically for a range of operating speeds and forcing frequencies. Changes in the minimum rotor–stator clearance are presented as a function of the rotor stiffness to demonstrate the appearance of resonance.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 655 , 25 July 2010 , pp. 446 - 471
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Agrawal, G. L., Patel, K. H. & Munson, J. H. 2007 (August 28) Hydrodynamic foil face seal. United States Patent 7,261,300 B2.Google Scholar
Belforte, G., Raparelli, T. & Viktorov, V. 1999 Theoretical investigation of fluid inertia effects and stability of self-acting gas journal bearings. J. Tribol. 121, 836–843.CrossRefGoogle Scholar
Blech, J. J. 1983 On isothermal squeeze-films. J. Lubr. Technol. 105, 615–620.CrossRefGoogle Scholar
Brunetière, N. & Tournerie, B. 2006 The effect of inertia on radial flows: application to hydrostatic seals. J. Tribol. 128, 566–574.CrossRefGoogle Scholar
Brunetière, N., Tournerie, B. & Frêne, J. 2002 Influence of fluid flow regime on performances of non-contacting liquid face seals. J. Tribol. 124, 515–523.CrossRefGoogle Scholar
Brunetière, N., Tournerie, B. & Frêne, J. 2003 a TEHD lubrication of mechanical face seals in stable tracking mode. Part 1. Numerical model and experiments. J. Tribol. 125, 608–616.Google Scholar
Brunetière, N., Tournerie, B. & Frêne, J. 2003 b TEHD lubrication of mechanical face seals in stable tracking mode. Part 2. Parametric study. J. Tribol. 125, 617–627.CrossRefGoogle Scholar
Cliffe, K. A., Spence, A. & Tavener, S. J. 2000 The numerical analysis of bifurcation problems with applications to fluid mechanics. Acta Numer. 9, 39–131.CrossRefGoogle Scholar
DellaCorte, C. & Valco, M. J. 2000 Load capacity estimation of foil air journal bearings for oil-free turbomachinery applications. Tribol. Trans. 43, 795–801.CrossRefGoogle Scholar
Dowson, D. 1961 Inertia effects in hydrostatic thrust bearings. J. Basic Engng 83, 227–234.CrossRefGoogle Scholar
Fourka, M., Tian, Y. & Bonis, M. 1996 Prediction of the stability of air thrust bearings by numerical, analytical and experimental methods. Wear 198, 1–6.CrossRefGoogle Scholar
Garratt, J. E., Cliffe, K. A., Hibberd, S. & Power, H. 2010 A numerical scheme for solving the periodically forced Reynolds equation. Intl J. Numer. Methods Fluids (submitted).Google Scholar
Gross, W. A. 1980 Fluid Film Lubrication. Wiley.Google Scholar
Hasegawa, E. & Izuchi, H. 1982 Inertia effects due to lubricant compressibility in a sliding externally pressurized gas bearing. Wear 80, 207–220.CrossRefGoogle Scholar
Heshmat, C. A., Xu, D. S. & Heshmat, H. 2000 Analysis of gas lubricated foil thrust bearings using coupled finite element and finite difference methods. J. Tribol. 122, 199–204.CrossRefGoogle Scholar
Keller, H. B. 1977 Numerical solution of bifurcation and nonlinear eigenvalue problems. In Applications of Bifurcation Theory (ed. Rabinowitz, P. H.), pp. 359–384. Academic Press.Google Scholar
Langlois, W. E. 1962 Isothermal squeeze-films. Q. Appl. Math. 20, 131–150.CrossRefGoogle Scholar
Malanoski, S. B. & Waldron, W. 1973 Experimental investigation of air bearings for gas turbine engines. ASLE Trans. 16 (4), 297–303.CrossRefGoogle Scholar
Minikes, A. & Bucher, I. 2003 Coupled dynamics of a squeeze-film levitated mass and a vibrating piezoelectric disk: numerical analysis and experimental study. J. Sound Vib. 263, 241–268.CrossRefGoogle Scholar
Munson, J. & Pecht, G. 1992 Development of film riding face seals for a gas turbine engine. Tribol. Trans. 35, 65–70.Google Scholar
Parkins, D. W. & Stanley, W. T. 1982 Characteristics of an oil squeeze-film. J. Lubr. Technol. 104, 497–502.CrossRefGoogle Scholar
Popper, B. & Reiner, M. 1956 The application of the centripetal effect in air to the design of a pump. Br. J. Appl. Phys. 7, 452–453.CrossRefGoogle Scholar
Salbu, E. O. J. 1964 Compressible squeeze-films and squeeze bearings. J. Basic Engng 86, 355–366.CrossRefGoogle Scholar
San Andrés, L. & Kim, T. H. 2009 Analysis of gas foil bearings integrating FE top foil models. Tribol. Intl 42, 111–120.CrossRefGoogle Scholar
Stolarski, T. A. & Chai, W. 2006 a Load-carrying capacity generation in squeeze-film action. Intl J. Mech. Sci. 48, 736–741.CrossRefGoogle Scholar
Stolarski, T. A. & Chai, W. 2006 b Self-levitating sliding air contact. Intl J. Mech. Sci. 48, 601–620.CrossRefGoogle Scholar
Stolarski, T. A. & Chai, W. 2008 Inertia effect in squeeze-film air contact. Tribol. Intl 41, 716–723.Google Scholar
Taylor, G. & Saffman, P. G. 1957 Effects of compressibility at low Reynolds number. J. Aeronaut. Sci. 24, 553–562.Google Scholar
Trefethen, L. N. 2000 Spectral Methods in Matlab. Wiley.CrossRefGoogle Scholar
Witelski, T. P. 1998 Dynamics of air bearing sliders. Phys. Fluids 10, 698–708.CrossRefGoogle Scholar