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Research Papers: Gas Turbines: Structures and Dynamics

Scaling Laws for Radial Clearance and Support Structure Stiffness of Radial Foil Bearings

[+] Author and Article Information
Srikanth Honavara Prasad

Mem. ASME
Department of Mechanical and Aerospace
Engineering,
The University of Texas at Arlington,
500 W. 1st Street,
Arlington, TX 76019
e-mail: srikanth.honavaraprasad@mavs.uta.edu

Daejong Kim

Department of Mechanical and Aerospace
Engineering,
The University of Texas at Arlington,
500 W. 1st Street,
Arlington, TX 76019
e-mail: daejongkim@uta.edu

1Corresponding author.

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 5, 2016; final manuscript received August 12, 2016; published online October 26, 2016. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(4), 042502 (Oct 26, 2016) (8 pages) Paper No: GTP-16-1308; doi: 10.1115/1.4034648 History: Received July 05, 2016; Revised August 12, 2016

Design and analysis of foil bearings involve consideration to various physical aspects such as fluid pressure, structural deformation, and heat generation due to viscous effects within the bearing. These complex physical interactions are mathematically governed by highly nonlinear partial differential equations. Therefore, foil bearing design involves detailed calculations of flow fields (velocities, pressures), support structure deflections (structural compliance), and heat transfer phenomena (viscous dissipation in the fluid, frictional heating, temperature profile, etc.). The computational effort in terms of time and hardware requirements make high level engineering analyses tedious which presents an opportunity for development of rule of thumb laws for design guidelines. Scaling laws for bearing clearance and support structure stiffness of radial foil bearings of various sizes are presented in this paper. The scaling laws are developed from first principles using the scale invariant Reynolds equation and support structure deflection equation. Power law relationships are established between the (1) radial clearance and bearing radius and (2) support structure stiffness and bearing radius. Simulation results of static and dynamic performance of various bearing sizes following the proposed scaling laws are presented.

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References

DellaCorte, C. , and Valco, M. J. , 2000, “ Load Capacity Estimation of Foil Air Journal Bearings for Oil-Free Turbomachinery Applications,” Tribol. Trans., 43(4), pp. 795–801. [CrossRef]
DellaCorte, C. , 2011, “ Stiffness and Damping Coefficient Estimation of Compliant Surface Gas Bearings for Oil-Free Turbomachinery,” Tribol. Trans., 54(4), pp. 674–684. [CrossRef]
Kim, D. , and Zimbru, G. , 2012, “ Start-Stop Characteristics and Thermal Behavior of a Large Hybrid Airfoil Bearing for Aero-Propulsion Applications,” ASME J. Eng. Gas Turbines Power, 134(3), p. 032502. [CrossRef]
Peng, Z. C. , and Khonsari, M. M. , 2004, “ On the Limiting Load-Carrying Capacity of Foil Bearings,” ASME J. Tribol., 126(4), pp. 817–818. [CrossRef]
Peng, Z. C. , and Khonsari, M. M. , 2004, “ Hydrodynamic Analysis of Compliant Foil Bearings With Compressible Air Flow,” ASME J. Tribol., 126(3), pp. 542–546. [CrossRef]
Radil, K. C. , Howard, S. A. , and Dykas, B. , 2002, “ The Role of Radial Clearance on the Performance of Foil Air Bearings,” Tribol. Trans., 45(4), pp. 485–490. [CrossRef]
Spakovszky, Z. S. , and Liu, L. X. , 2005, “ Scaling Laws for Ultra-Short Hydrostatic Gas Journal Bearings,” ASME J. Vib. Acoust., 127(3), pp. 254–261. [CrossRef]
Kim, D. , 2007, “ Parametric Studies on Static and Dynamic Performance of Air Foil Bearings With Different Top Foil Geometries and Bump Stiffness Distributions,” ASME J. Tribol., 129(2), pp. 354–364. [CrossRef]
Gunter, E. J. , and Trumpler, P. R. , 1969, “ The Influence of Internal Friction on the Stability of High Speed Rotors With Anisotropic Supports,” ASME J. Eng. Ind., 91(4), pp. 1105–1113. [CrossRef]
Childs, D. , 1993, Turbomachinery Rotordynamics: Phenomena, Modeling, and Analysis, Wiley, New York.
Timoshenko, S. P. , and Goodier, J. N. , 1970, Theory of Elasticity, McGraw-Hill, New York, pp. 80–83.
Wang, Y. P. , and Kim, D. , 2013, “ Experimental Identification of Force Coefficients of Large Hybrid Air Foil Bearings,” ASME Paper No. GT2013-95765.
Kim, D. , and Lee, D. , 2010, “ Design of Three-Pad Hybrid Air Foil Bearing and Experimental Investigation on Static Performance at Zero Running Speed,” ASME J. Eng. Gas Turbines Power, 132(12), p. 122504. [CrossRef]

Figures

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Fig. 1

Schematic description of three-pad bump foil bearing

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Fig. 2

Turbomachinery configuration of interest: (a) three-dimensional view and (b) sectional view

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Fig. 3

Eccentricity versus normalized speed

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Fig. 4

Pressure profiles for Nmin

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Fig. 5

Pressure profiles for Nmax

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Fig. 6

Film thickness at the bearing edge for Nmin

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Fig. 7

Film thickness at the bearing edge for Nmax

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Fig. 8

Nondimensional film thickness at bearing edge for Nmin

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Fig. 9

Nondimensional film thickness at bearing edge for Nmax

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Fig. 10

kxx versus normalized speed

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Fig. 11

kyy versus normalized speed

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Fig. 12

dxx versus normalized speed

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Fig. 13

dyy versus normalized speed

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Fig. 14

Stiffness components for 20 mm OD bearing

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Fig. 15

Stiffness components for 100 mm OD bearing

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Fig. 16

Stiffness components for 300 mm OD bearing

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Fig. 17

Damping components for 20 mm OD bearing

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Fig. 18

Damping components for 100 mm OD bearing

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Fig. 19

Damping components for 300 mm OD bearing

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