Skip to main content

The Classical Linearization Technique’s Validity for Compliant Bearings

  • Conference paper
  • First Online:
Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM (IFToMM 2018)

Part of the book series: Mechanisms and Machine Science ((Mechan. Machine Science,volume 60))

Included in the following conference series:

  • 1416 Accesses

Abstract

The Gas Foil Bearing (GFB) is a promising and environmentally friendly technology allowing support of high-speed rotating machinery with low power loss and without oil or electronics. Unfortunately, GFBs provide limited damping, making an accurate prediction of the Onset Speed of Instability (OSI) critical. This has traditionally been assessed using linearised coefficients derived from the perturbed Reynolds Equation with compliance included implicitly. Recent work has, however, revealed significant discrepancies between OSIs predicted using these techniques and those observed from nonlinear analysis. In the present work, the perturbation method’s underlying assumption on the pressure field is investigated by including the hitherto neglected pressure–compliance dependency directly. This leads to an extended perturbation akin to that commonly applied to tilting pad bearings and is shown to predict OSIs with much better agreement to time integration results. The extended perturbation method is cumbersome, but serves to highlight the error introduced when applying the classical perturbation method—as developed for rigid bearings by J. W. Lund—to GFBs.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Baum, C., Hetzler, H., Seemann, W.: On the stability of balanced rigid rotors in air foil bearings. In: Proceedings of 11th Internationale Tagung Schwingungen in Rotierenden Maschinen (SIRM 2015), Magdeburg, Germany, pp. 23–25 (2015)

    Google Scholar 

  2. Bonello, P., Pham, H.M.: The efficient computation of the nonlinear dynamic response of a foil-air bearing rotor system. J. Sound Vib. 333(15), 3459–3478 (2014). https://doi.org/10.1016/j.jsv.2014.03.001

    Article  Google Scholar 

  3. Bonello, P., Pham, H.M.: Nonlinear dynamic analysis of high speed oil-free turbomachinery with focus on stability and self-excited vibration. J. Tribol. 136(4), 041705 (2014). https://doi.org/10.1115/1.4027859

    Article  Google Scholar 

  4. Feng, K., Kaneko, S.: Analytical model of bump-type foil bearings using a link-spring structure and a finite-element shell model. J. Tribol. 132(2), 021706 (2010). https://doi.org/10.1115/1.4001169

    Article  Google Scholar 

  5. Heshmat, H., Walowit, J.A., Pinkus, O.: Analysis of gas-lubricated foil journal bearings. J. Tribol. Technol. 105(4), 647–655 (1983). https://doi.org/10.1115/1.3254697

    Article  Google Scholar 

  6. Hoffmann, R., Pronobis, T., Liebich, R.: The impact of modified corrugated bump structures on the rotor dynamic performance of gas foil bearings. In: Turbo Expo, ASME, p. V07BT32A012 (2014). https://doi.org/10.1115/GT2014-25636

  7. Hoffmann, R., Pronobis, T., Liebich, R.: Non-linear stability analysis of a modified gas foil bearing structure. In: Proceedings of the 9th IFToMM International Conference on Rotor Dynamics, pp. 1259–1276 (2015). https://doi.org/10.1007/978-3-319-06590-8_103

  8. Kim, T.H., Andres, L.S.: Heavily loaded gas foil bearings: a model anchored to test data. J. Eng. Gas Turbine Power 130(1), 012504 (2008). https://doi.org/10.1115/1.2770494

    Article  Google Scholar 

  9. Kim, T.H., San Andrés, L.: Limits for high-speed operation of gas foil bearings. J. Tribol. 128(3), 670–673 (2006). https://doi.org/10.1115/1.2197851

    Article  Google Scholar 

  10. Kim, T.H., San Andrés, L.: Analysis of advanced gas foil bearings with piecewise linear elastic supports. Tribol. Int. 40(8), 1239–1245 (2007). https://doi.org/10.1016/j.triboint.2007.01.022

    Article  Google Scholar 

  11. Larsen, J.S., Santos, I.F.: Efficient solution of the non-linear reynolds equation for compressible fluid using the finite element method. J. Braz. Soc. Mech. Sci. Eng. 37(3), 945–957 (2014). https://doi.org/10.1007/s40430-014-0220-5

    Article  Google Scholar 

  12. Larsen, J.S., Santos, I.F.: On the nonlinear steady-state response of rigid rotors supported by air foil bearings—theory and experiments. J. Sound Vib. 346, 284–297 (2015). https://doi.org/10.1016/j.jsv.2015.02.017

    Article  Google Scholar 

  13. Larsen, J.S., Hansen, A.J., Santos, I.F.: Experimental and theoretical analysis of a rigid rotor supported by air foil bearings. Mech. Ind. 16(1), 106 (2015). https://doi.org/10.1051/meca/2014066

    Article  Google Scholar 

  14. Larsen, J.S., Santos, I.F., von Osmanski, S.: Stability of rigid rotors supported by air foil bearings: comparison of two fundamental approaches. J. Sound Vib. 381, 179–191 (2016). https://doi.org/10.1016/j.jsv.2016.06.022

    Article  Google Scholar 

  15. Le Lez, S., Arghir, M., Frene, J.: Nonlinear numerical prediction of gas foil bearing stability and unbalanced response. J. Eng. Gas Turbine Power 131(1), 012503 (2009). https://doi.org/10.1115/1.2967481

    Article  Google Scholar 

  16. Lee, Y.B., Kim, T.H., Kim, C.H., Lee, N.S., Choi, D.H.: Unbalance response of a super-critical rotor supported by foil bearings—comparison with test results. Tribol. Trans. 47(1), 54–60 (2004). https://doi.org/10.1080/05698190490279038

    Article  Google Scholar 

  17. Lund, J.W.: Calculation of stiffness and damping properties of gas bearings. J. Tribol. Technol. 90(4), 793–803 (1968). https://doi.org/10.1115/1.3601723

    Article  Google Scholar 

  18. von Osmanski, S., Larsen, J.S., Santos, I.F.: A fully coupled air foil bearing model considering friction - theory & experiment. J. Sound Vib. 400, 660–679 (2017). https://doi.org/10.1016/j.jsv.2017.04.008

    Article  Google Scholar 

  19. Peng, J.P., Carpino, M.: Calculation of stiffness and damping coefficients for elastically supported gas foil bearings. J. Tribol. 115(1), 20–27 (1993). https://doi.org/10.1115/1.2920982

    Article  Google Scholar 

  20. Pham, H.M., Bonello, P.: Efficient techniques for the computation of the nonlinear dynamics of a foil-air bearing rotor system. In: Turbo Expo, ASME, Texas, USA (2013) https://doi.org/10.1115/GT2013-94389

  21. Ruscitto, D., Mc Cormick, J., Gray, S.: Hydrodynamic air lubricated compliant surface bearing for an automotive gas turbine engine I – journal bearing performance. Technical report CR-135368, NASA, Cleveland, Ohio (1978)

    Google Scholar 

  22. San Andrés, L., Kim, T.H.: Improvements to the analysis of gas foil bearings: integration of top foil 1D and 2D structural models. In: Turbo Expo, ASME, Montreal, Canada, vol. 5, pp. 779–789 (2007). https://doi.org/10.1115/GT2007-27249

  23. San Andrés, L., Kim, T.H.: Analysis of gas foil bearings integrating FE top foil models. Tribol. Int. 42(1), 111–120 (2009). https://doi.org/10.1016/j.triboint.2008.05.003

    Article  Google Scholar 

  24. Vleugels, P., Waumans, T., Peirs, J., Al-Bender, F., Reynaerts, D.: High-speed bearings for micro gas turbines: stability analysis of foil bearings. J. Micromech. Microeng. 16(9), 282–289 (2006). https://doi.org/10.1088/0960-1317/16/9/S16

    Article  Google Scholar 

  25. Walowit, J.A., Anno, J.N.: Modern Developments in Lubrication Mechanics. Applied Science Publishers, London (1975)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ilmar F. Santos .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

von Osmanski, S., Larsen, J.S., Santos, I.F. (2019). The Classical Linearization Technique’s Validity for Compliant Bearings. In: Cavalca, K., Weber, H. (eds) Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM. IFToMM 2018. Mechanisms and Machine Science, vol 60. Springer, Cham. https://doi.org/10.1007/978-3-319-99262-4_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-99262-4_13

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-99261-7

  • Online ISBN: 978-3-319-99262-4

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics