0
Applications

Foil Bearing Design Guidelines for Improved Stability

[+] Author and Article Information
J. Schiffmann

e-mail: jurg.schiffmann@epfl.ch

Z. S. Spakovszky

e-mail: zolti@mit.edu
Gas Turbine Laboratory
Massachusetts Institute of Technology
Cambridge, MA 02139

1Currently at Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.

Contributed by the Tribology Division of ASME for publication in the Journal of Tribology. Manuscript received February 10, 2012; final manuscript received September 8, 2012; published online December 20, 2012. Assoc. Editor: Luis San Andres.

J. Tribol 135(1), 011103 (Dec 20, 2012) (11 pages) Paper No: TRIB-12-1022; doi: 10.1115/1.4007759 History: Received February 10, 2012; Revised September 08, 2012

Experimental evidence in the literature suggests that foil bearing-supported rotors can suffer from subsynchronous vibration. While dry friction between top foil and bump foil is thought to provide structural damping, subsynchronous vibration is still an unresolved issue. The current paper aims to shed new light onto this matter and discusses the impact of various design variables on stable foil bearing-supported rotor operation. It is shown that, while a time domain integration of the equations of motion of the rotor coupled with the Reynolds equation for the fluid film is necessary to quantify the evolution of the rotor orbit, the underlying mechanism and the onset speed of instability can be predicted by coupling a reduced order foil bearing model with a rigid-body, linear, rotordynamic model. A sensitivity analysis suggests that structural damping has limited effect on stability. Further, it is shown that the location of the axial feed line of the top foil significantly influences the bearing load capacity and stability. The analysis indicates that the static fluid film pressure distribution governs rotordynamic stability. Therefore, selective shimming is introduced to tailor the unperturbed pressure distribution for improved stability. The required pattern is found via multiobjective optimization using the foil bearing-supported rotor model. A critical mass parameter is introduced as a measure for stability, and a criterion for whirl instability onset is proposed. It is shown that, with an optimally shimmed foil bearing, the critical mass parameter can be improved by more than two orders of magnitude. The optimum shim patterns are summarized for a variety of foil bearing geometries with different L/D ratios and different degrees of foil compliance in a first attempt to establish more general guidelines for stable foil bearing design. At low compressibility (Λ < 2), the optimum shim patterns vary little with bearing geometry; thus, a generalized shim pattern is proposed for low compressibility numbers.

FIGURES IN THIS ARTICLE
<>
© 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Agrawal, G. L., 1997, “Foil Air/Gas Bearing Technology—An Overview,” ASME Paper No. 1997-GT-347.
Moore, J. J., Lerche, A., Allison, T., Ransom, D. L., and Lubell, D., 2010, “Development of a High Speed Gas Bearing Test Rig to Measure Rotordynamic Force Coefficients,” ASME Paper No. GT2010-23217.
Lubell, D. R., Wade, J. L., Chauhan, N. S., and Nourse, J. G., 2008, “Identification and Correction of Rotor Instability in an Oil-Free Gas Turbine,” ASME Paper No. GT2008-50305.
Hou, Y., Zhu, Z. H., and Chen, C. Z., 2004, “Comparative Test on Two Kinds of New Compliant Foil Bearing for Small Cryogenic Turbo-Expander,” Cryogenics, 44, pp. 69–72. [CrossRef]
Heshmat, H., 1994, “Advancement in the Performance of Aerodynamic Foil Journal Bearings: High Speed and Load Capability,” ASME J. Tribol., 116, pp. 287–295. [CrossRef]
Lubell, D., Corte, C. D., and Stanford, M., 2006, “Test Evolution and Oil-Free Engine Experience of a High Temperature Foil Air Bearing Coating,” ASME Paper No. GT2006-90572.
Heshmat, H., 2000, “Operation of Foil Bearings Beyond the Bending Critical Mode,” ASME J. Tribol., 122, pp. 192–198. [CrossRef]
Walton, J. F., and Heshmat, H., 2002, “Application of Foil Bearings to Turbomachinery Including Vertical Operation,” ASME J. Eng. Gas Turbines Power, 124, pp. 1032–1041. [CrossRef]
Kim, T. H., Lee, J., Kim, C. H., and Lee, Y. B., 2010, “Rotordynamic Performance of an Oil-Free Turbocharger Supported on Gas Foil Bearings: Effects of an Assembly Radial Clearance,” ASME Paper No. GT2010-23243.
Heshmat, H., Saphiro, W., and Gray, S., 1982, “Development of Foil Journal Bearings for High Load Capacity and High Speed Whirl Stability,” ASME J. Lubr. Technol., 104(2), pp. 149–156. [CrossRef]
Lee, Y., Kim, T., Kim, C., Lee, N., and Choi, D., 2004, “Dynamic Characteristics of a Flexible Rotor System Supported by a Viscoelastic Foil Bearing,” Tribol. Int., 37, pp. 679–687. [CrossRef]
San Andrés, L., Chirathadam, T. A., and Kim, T. H., 2010, “Measurement of Structural Stiffness and Damping Coefficients in a Metal Mesh Foil Bearing,” ASME J. Eng. Gas Turbines Power, 132, p. 032503. [CrossRef]
San Andrés, L., and Chirathadam, T. A., 2010, “Identification of Rotordynamic Force Coefficients of a Metal Mesh Foil Bearing Using Impact Load Excitations,” ASME Paper No. GT2010-22440.
San Andrés, L., and Kim, T. H., 2008, “Forced Nonlinear Response of Gas Foil Bearing Supported Rotors,” Tribol. Int., 41, pp. 704–715. [CrossRef]
Rubio, D., and San Andrés, L., 2006, “Bump-Type Foil Bearing Structural Stiffness: Experiments and Predictions,” ASME J. Eng. Gas Turbines Power, 128, pp. 653–660. [CrossRef]
Kim, T. H., and San Andrés, L., 2006, “Limits for High-Speed Operation of Gas Foil Bearings,” ASME J. Tribol., 128, pp. 670–673. [CrossRef]
Kim, T. H., and San Andrés, L., 2008, “Heavily Loaded Gas Foil Bearings: A Model Anchored to Test Data,” ASME J. Eng. Gas Turbines Power, 130, p. 012504. [CrossRef]
Pan, C. H. T., 1964, “Spectral Analysis of Gas Bearing Systems for Stability Studies,” MTI Technical Report No. 64TR58.
Pan, C. H. T., and Kim, D., 2007, “Stability Characteristics of a Rigid Rotor Supported by a Gas-Lubricated Spiral-Groove Conical Bearing,” ASME J. Tribol., 129, pp. 375–383. [CrossRef]
Heshmat, H., Walowit, J. A., and Pinkus, O., 1983, “Analysis of Gas-Lubricated Foil Journal Bearings,” ASME J. Lubr. Technol., 105, pp. 647–655. [CrossRef]
Kim, T. H., and San Andrés, L., 2007, “Analysis of Advanced Gas Foil Bearings With Piecewise Linear Elastic Supports,” Tribol. Int., 40, pp. 1239–1245. [CrossRef]
San Andrés, L., and Kim, T. H., 2009, “Analysis of Gas Foil Bearings Integrating FE Top Foil Models,” Tribol. Int., 42, pp. 111–120. [CrossRef]
Carpino, M., and Talmage, G., 2003, “A Fully Coupled Finite Element Formulation for Elastically Supported Foil Journal Bearings,” STLE Tribol. Trans., 46, pp. 560–565. [CrossRef]
Carpino, M., and Talmage, G., 2006, “Prediction of Rotor Dynamic Coefficients in Gas Lubricated Foil Journal Bearings With Corrugated Sub-Foils,” STLE Tribol. Trans., 49, pp. 400–409. [CrossRef]
Ruscitto, D., Cormick, J. M., and Gray, S., 1978, “Hydrodynamic Air Lubricated Compliant Surface Bearing for an Automotive Gas Turbine Engine I—Journal Bearing Performance,” NASA Technical Report No. CR-135368.
Faria, M. T. C., and San Andrés, L., 2000, “On the Numerical Modeling of High-Speed Hydrodynamic Gas Bearings,” ASME J. Tribol., 122, pp. 124–130. [CrossRef]
Faria, M. T. C., 2001, “Some Performance Characteristics of High Speed Gas Lubricated Herringbone Groove Journal Bearings,” JSME Int. J., Ser. C, 44, pp. 775–781. [CrossRef]
Rubio, D., and San Andrés, L., 2007, “Structural Stiffness, Dry Friction Coefficient, and Equivalent Viscous Damping in a Bump-Type Foil Gas Bearing,” ASME J. Eng. Gas Turbines Power, 129, pp. 494–502. [CrossRef]
Kim, T. H., and San Andrés, L., 2009, “Effect of Side Feed Pressurization on the Dynamic Performance of Gas Foil Bearings: A Model Anchored to Test Data,” ASME J. Eng. Gas Turbines Power, 130, p. 012501. [CrossRef]
Schiffmann, J., and Favrat, D., 2010, “Integrated Design and Optimization of Gas Bearing Supported Rotors,” ASME J. Mech. Des., 132, p. 051007. [CrossRef]
Schiffmann, J., and Favrat, D., 2009, “Experimental Investigation of a Direct Driven Radial Compressor for Domestic Heat Pumps,” Int. J. Refrig., 32, pp. 1918–1928. [CrossRef]
Schiffmann, J., and Favrat, D., 2010, “The Effect of Real Gas on the Properties of Herringbone Grooved Journal Bearings,” Tribol. Int., 43, pp. 1602–1614. [CrossRef]
Lund, J. W., 1968, “Calculation of Stiffness and Damping Properties of Gas Bearings,” ASME J. Lubr. Technol., 90, pp. 783–803. [CrossRef]
Kim, T. H., and San Andrés, L., 2009, “Effects of a Mechanical Preload on the Dynamic Force Response of Gas Foil Bearings: Measurements and Model Predictions,” STLE Tribol. Trans., 52, pp. 569–580. [CrossRef]
San Andrés, L., Rubio, D., and Kim, T. H., 2007, “Rotordynamic Performance of a Rotor Supported on Bump Type Foil Gas Bearings: Experiments and Predictions,” ASME J. Eng. Gas Turbines Power, 129, pp. 850–857. [CrossRef]
Kim, D., Creary, A., Chang, S. S., and Kim, J. H., 2009, “Mesoscale Foil Gas Bearings for Palm-Sized Turbomachinery: Design, Manufacturing, and Modeling,” ASME J. Eng. Gas Turbines Power, 131, p. 042502. [CrossRef]
Sim, K., Lee, Y., Kim, T. H., and Lee, J., 2012, “Rotordynamic Performance of Shimmed Gas Foil Bearings for Oil-Free Turbochargers,” ASME J. Tribol., 134, p. 031102. [CrossRef]
Molyneaux, A., Leyland, G. B., and Favrat, D., 2010, “Environomic Multi-Objective Optimization of a District Heating Network Considering Centralized and Decentralized Heat Pumps,” Energy, 35, pp. 751–758. [CrossRef]
Ng, C. W., 1965, “Linearized Ph Stability Theory for Finite Length, Self-Acting Gas-Lubricated, Plain Journal Bearings,” J. Basic Eng., 87, pp. 559–567. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Bump foil gas bearing nomenclature

Grahic Jump Location
Fig. 2

Rotordynamic model for rigid body analysis

Grahic Jump Location
Fig. 3

Whirl speed map for cylindrical and conical modes for the reference rotor-bearing system (Table 1): onset of instability occurs at Λ = 0.43

Grahic Jump Location
Fig. 4

Critical mass for reference rotor-bearing system (Table 1): onset of instability occurs at Λ = 0.43

Grahic Jump Location
Fig. 5

Static eccentricity as a function of attitude angle and amplitude for reference journal bearing (Table 1) operating at Λ = 4

Grahic Jump Location
Fig. 6

Critical mass as a function of attitude angle and amplitude for reference bearing (Table 1) operating up to Λ = 4

Grahic Jump Location
Fig. 7

Critical mass as a function of compressibility, static load, and compliance for reference bearing (Table 1) with no structural damping

Grahic Jump Location
Fig. 8

Critical mass as a function of compressibility, static load, and structural damping for reference bearing (Table 1) at α = 0.67

Grahic Jump Location
Fig. 9

Pareto curves for reference bearing (Table 1) for different structural damping γ

Grahic Jump Location
Fig. 10

Improvement in threshold speed at instability onset for: original reference bearing (solid); optimum selective shim pattern (dotted); and three equal shim pattern (Kim and San Andrés [34], dashed)

Grahic Jump Location
Fig. 11

Pareto-optimum shim distribution as a function of logarithmic decrement Γ for γ = 0, α = 0.67

Grahic Jump Location
Fig. 12

Critical mass as a function of the highest operating compressibility number for optimized circumferential selective shim distributions

Grahic Jump Location
Fig. 13

Optimum selective shim patterns as a function of bearing compliance α, L/D ratio, and compressibility Λ

Grahic Jump Location
Fig. 14

Generalized selective shim pattern (Table 3) compared with individually optimized selective shim pattern

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In