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Research Papers: Gas Turbines: Structures and Dynamics

# A Thermohydrodynamic Sparse Mesh Model of Bump-Type Foil Bearings

[+] Author and Article Information
Kai Feng

State Key Laboratory of Advanced Design
and Manufacturing for Vehicle Body,
Hunan University,
Changsha, Hunan,
P. R. C. 410082
e-mail: jkai.feng@gmail.com

Shigehiko Kaneko

Department of Mechanical Engineering,
The University of Tokyo,
7-3-1 Hongo, Bunkyo-ku,
Tokyo, Japan, 113-8656

Dellacorte and Valco [31] defined gas foil bearings into three generations.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Engineering for Gas Turbines and Power. Manuscript received February 14, 2012; final manuscript received August 7, 2012; published online January 8, 2013. Assoc. Editor: Patrick S. Keogh.

J. Eng. Gas Turbines Power 135(2), 022501 (Jan 08, 2013) (12 pages) Paper No: GTP-12-1036; doi: 10.1115/1.4007728 History: Received February 14, 2012; Revised August 07, 2012

## Abstract

A numerical model for 3D thermohydrodynamic analysis of bump-type foil bearings with a sparse mesh across the air film is described. The model accounts for heat convection into cooling air, thermal expansion of the bearing components, and material property variations due to temperature rise. Deflection of the compliant foil strip, described as a link-spring structure, is coupled to the solution of the generalized Reynolds equation and the energy equation to account for the effect of foil deformation on the film thickness. The variation in bump stiffness with the thermal growth of bumps is also considered in the model. The unique airflow in foil bearings created by the top foil detachment in the subambient region is analyzed for use in modifying the thermal boundary condition. The Lobatto point quadrature algorithm is used to represent the model on a sparse mesh and thereby reduce the computational effort. The calculated bearing temperatures are in remarkable agreement with both the published test data with the use of cooling air and that without the use of cooling air. The change of bearing radial clearance due to thermal growth of the bearing components was found to significantly affect the bearing load and to be a likely cause of the obvious drop in load capacity with a rise in ambient temperature.

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## References

WaltonJ. F., II, and Heshmat, H., 2002, “Application of Foil Bearing to Turbomachinery Including Vertical Operation,” ASME J. Eng. Gas Turbines Power, 124, pp. 1032–1041.
Agrawal, G. L., 1997, “Foil Air/Gas Bearing Technology—An Overview,” ASME Paper No. 97-GT-347.
O'Connor, L., 1993, “Fluid-Film Foil Bearings Control Engine Heat,” Mech. Eng., 115, pp. 72–75.
Hovard, S. A., 1999, “Preliminary Development of Characterization Methods for Compliant Air Bearings,” STLE Tribol. Trans., 42(4), pp. 789–794.
Mohawk Innovative Technology, Inc., 2004, “Foil Bearings and Compliant Seals Applications,”
Salehi, M., Heshmat, H., Walton, J. F., and Tomaszewski, M., 2007, “Operation of a Mesoscopic Gas Turbine Simulator at Speeds in Excess of 70,000 rpm on Foil Bearings,” ASME J. Eng. Gas Turbines Power, 129, pp. 170–176.
Dykas, B., and Howard, S. A., 2004, “Journal Design Consideration for Turbomachine Shafts Supported on Foil Air Bearings,” STLE Tribol. Trans., 47, pp. 508–516.
Salehi, M., and Heshmat, H., 2000, “On the Fluid Flow and Thermal Analysis of a Compliant Surface Foil Bearing and Seal,” STLE Tribol. Trans., 43(2), pp. 318–324.
Salehi, M., Swanson, E., and Heshmat, H., 2001, “Thermal Features of Compliant Foil Bearings—Theory and Experiments,” ASME J. Tribol., 123(3), pp. 566–571.
Peng, Z. C., and KhonsariM. M., 2006, “A Thermohydrodynamic Analysis of Foil Journal Bearings,” ASME J. Tribol., 128, pp. 534–541.
Feng, K., and Kaneko, S., 2009, “Thermohydrodynamic Study of Multiwound Foil Bearing Using Lobatto Point Quadrature,” ASME J. Tribol., 131, p. 021702.
Heshmat, H., Walowit, J. A., and Pinkus, O., 1983, “Analysis of Gas Lubricated Foil Journal Bearings,” ASME J. Lubr. Tech., 105, pp. 647–655.
Radil, K., and Zeszotek, M., 2004, “An Experimental Investigation Into the Temperature Profile of a Compliant Foil Air Bearing,” STLE Tribol. Trans., 47(4), pp. 470–479.
Sim, K., and Kim, D., 2008, “Thermohydrodynamic Analysis of Compliant Flexure Pivot Tilting Pad Gas Bearings,” ASME J. Eng. Gas Turbines Power, 130, p. 032502.
San Andres, L., and Kim, T. H., 2010, “Thermohydrodynamic Analysis of Bump Type Gas Foil Bearings: A Model Anchored to Test Data,” ASME J. Eng. Gas Turbines Power, 132(4), p. 042504.
Iordanoff, I., 1999, “Analysis of an Aerodynamic Compliant Foil Thrust Bearing: Method for a Rapid Design,” ASME J. Tribol., 121, pp. 816–822.
Lee, D., and Kim, D., 2010, “Thermohydrodynmic Analyses of Bump Air Foil Bearings With Detailed Thermal Model of Foil Structures and Rotor,” ASME J. Tribol., 132, p. 021704.
Kim, D., and Park, S., 2009, “Hydrostatic Air Foil Bearings: Analytical and Experimental Investigations.” Tribol. Int., 42(3), pp. 413–425.
Lee, D., Kim, D., and Sadashiva, R. P., 2011, “Transient Thermal Behavior of Preloaded Three-Pad Foil Bearings: Modeling and Experiments.” ASME J. Tribol., 133, p. 021703.
Kim, D., Ki, J., Kim, Y., and Ahn, K., 2012, “Extended Three-Dimensional Thermo-Hydrodynamic Model of Radial Foil Bearing: Case Studies on Thermal Behaviors and Dynamic Characteristics in Gas Turbine Simulator,” ASME J. Eng. Gas Turbines Power, 134, p. 052501.
Ruscitto, D., Mc Cormick, J., and Gray, S., 1978, “Hydrodynamic Air Lubricated Compliant Surface Bearing for an Automotive Gas Turbine Engine I-Journal Bearing Performance,” NASA CR-135368.
Kim, T. H., Breedlove, A. W., and San Andres, L., 2008, “Characterization of Foil Bearing Structure for Increasing Shaft Temperatures: Part I—Static Load Performance,” ASME Paper No. GT2008-50567.
Kim, T. H., Breedlove, A. W., and San Andres, L., 2008, “Characterization of Foil Bearing Structure for Increasing Shaft Temperatures: Part II—Dynamic Force Performance,” ASME Paper No. GT2008-50570.
Feng, K., and Kaneko, S., 2010, “Analytical Model of Bump-Type Foil Bearings Using A Link-Spring Structure and A Finite Element Shell Model,” ASME J. Tribol., 132, p. 021706.
Nittono, O., 2002, “Materials Science and Engineering An Introduction,” Baifukan Co., LTD, Tokyo, pp. 116–117 (in Japanese).
Moraru, L., and Keith, T. G., 2007, “Lobatto Point Quadrature for Thermal Lubrication Problems Involving Compressible Lubricants. EHL Applications.” ASME J. Tribol., 129(1), pp. 194–198.
Khonsari, M. M., Jang, J. Y., and Fillon, M., 1996, “On the Generalization of Thermohydrodynamic Analyses for Journal Bearings,” ASME J. Tribol., 118, pp. 571–579.
Holman, J. P., 2010, Heat Transfer, 10th ed., McGraw Hill, New York, pp. 231–240, 340–344.
LMNO Engineering, Research, and Software, Ltd., 2003, “Gas Viscosity Calculator,”
Engineering Toolbox, 2009, “The Engineering Toolbox,”
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.
Dellacorte, C., 1998, “A New Foil Air Bearing Test Rig for Use to 700 °C and 70,000 rpm,” STLE Tribol. Trans., 41(3), pp. 335–340.
Howard, S. A., DellaCrote, C., Valco, M. J., Prahl, J. M., and Heshmat, H., 2001, “Dynamic Stiffness and Damping Characteristics of a High Temperature Air Foil Journal Bearing,” STLE Tribol. Trans., 44(4), pp. 657–663.
Radil, K., Howard, S., and Dykas, B., 2002, “The Role of Radial Clearance on the Performance of Foil Air Bearing,” NASA Report No. NASA-2002-211705.
Seghir-Ouali, S., Saury, D., Harmand, S., Phillipart, O., and Laloy, D., 2006, “Convective Heat Transfer Inside a Rotating Cylinder With an Axial Air Flow,” Int. J. Therm. Sci., 45, pp. 1166–1178.

## Figures

Fig. 1

Structure of bump-type foil bearings

Fig. 2

Link-spring model of bump-type foil bearings

Fig. 3

Assembly of global stiffness matrix with bump stiffness

Fig. 4

Heat flows in a bump-type foil bearing with cooling air flowing through both hollow rotor and bump layer

Fig. 5

Heat transfer paths at the side of foils

Fig. 6

Fluid flow within bump-type foil bearings

Fig. 7

Comparison of calculated and measured maximum temperatures at different rotational speeds [13]

Fig. 9

Simulated temperature profile at middle cross-section of air film (y = L/2) with five grid points across film. Rotation: 30 krpm; bearing load: 398 N; cooling airflow: 1.3 m3/min, Hmin: 0.0182 mm.

Fig. 8

Simulated temperature profile at midlayer air (z = h/2). Rotation: 30 krpm; bearing load: 398 N; cooling airflow: 1.3 m3/min, Hmin: 0.0182 mm.

Fig. 10

Calculated temperature profile at middle cross-section of air film (y = L/2) with 20 grid points across film. Rotation: 30 krpm; bearing load: 398 N; cooling airflow: 1.3 m3/min, Hmin: 0.0182 mm.

Fig. 13

Bearing load as a function of ambient temperature at different thermal expansion coefficient of housing. 30 krpm, Hmin = 5.5 μm, αs = 12.3×10-6 K-1, αf = 12.1×10-6 K-1.

Fig. 12

Change in radial clearance as a function of thermal expansion coefficient of housing for different ambient temperatures. αs = 12.3×10-6 K-1.

Fig. 11

Minimum film thickness as a function of static load. Comparison of predictions from THD and isothermal models and tested data [21].

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