Abstract
In this study, a new comprehensive fully coupled elastic-hydrodynamic model is developed for a multi-layer gas foil thrust bearing (GFTB). The interaction effects among the top foil, back board, middle foil, and bottom foil, as well as the Coulomb friction effect, are considered. The stiffness and static characteristics obtained by the experimental and theoretical approaches are in good agreement, which verifies the accuracy of the model. The contribution of each foil layer to the overall stiffness and the load-carrying mechanism are analyzed. Interaction effects of the load, preload, and rotational speed on the static performance are investigated comprehensively. Furthermore, start-stop tests are performed to achieve the lift-off speed, start-up torque, and shut-down torque under various operating conditions.
![](http://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2Fs40544-024-0889-0/MediaObjects/40544_2024_889_Fig1_HTML.jpg)
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- d c :
-
decay coefficient
- E :
-
elastic modulus
- F :
-
applied load (N)
- F d :
-
deformation gradient tensor
- F f :
-
vfriction force (N)
- F v :
-
volume force vector
- h :
-
gas film thickness (m)
- h 0 :
-
minimum gas film thickness (m)
- h b :
-
back board thickness (m)
- h d :
-
deformation of foil structure
- h g :
-
bottom foil thickness (m)
- h m :
-
middle foil thickness (m)
- h s :
-
height of the convex part of the middle foil (m)
- h t :
-
top foil thickness (m)
- N p :
-
number of top foils
- p :
-
gas film pressure (Pa)
- p a :
-
ambient gas pressure
- R 1 :
-
top foil inner diameter (m)
- R 2 :
-
top foil outer diameter (m)
- S :
-
Second Piola–Kirchhoff stress
- T :
-
friction torque (N · m)
- N :
-
normal load (N)
- W :
-
bearing capacity (N)
- (r,θ):
-
cylindrical coordinate
- Λ :
-
bearing number
- ω :
-
rotor angular speed (rad · s−1)
- η :
-
air viscosity
- δ h :
-
reference gas film thickness
- β :
-
the arc angle of the top foil
- ∇u :
-
displacement gradient
- (X, Y, Z):
-
material coordinate
- (x, y, z):
-
spatial coordinate
- ε :
-
the strain
- ν :
-
Poisson’s ratio
- μ s :
-
static friction coefficient
- μ k :
-
kinetic friction coefficient
- \(\dot \gamma \) :
-
slip rate
- μ :
-
friction coefficient
- FVM:
-
finite volume method
- FEM:
-
finite element method
- FDM:
-
finite difference method
- GFB:
-
gas foil bearing
- GFTB:
-
gas foil thrust bearing
References
Agrawal G L. Foil air/gas bearing technology—An overview. In: Proceedings of the ASME 1997 International Gas Turbine and Aeroengine Congress and Exhibition, Florida, USA, 1997: 1–11.
Heshmat H, Hermel P. Compliant foil bearings technology and their application to high speed turbomachinery. Tribology S 25: 559–575 (1993)
Howard S A. Misalignment in gas foil journal bearings: An experimental study. J Eng Gas Turb Power 131(2): 022501 (2009)
Samanta P, Murmu N C, Khonsari M M. The evolution of foil bearing technology. Tribol Int 135: 305–323 (2019)
Walowit J A, Anno J N, Hamrock B J. Modern developments in lubrication mechanics. J Lubr Technol 99(2): 304–305 (1977)
Heshmat H, Walowit J A, Pinkus O. Analysis of gas-lubricated foil journal bearings. J Lubr Technol 105(4): 647–655 (1983)
Peng Z C, Khonsari M M. Hydrodynamic analysis of compliant foil bearings with compressible air flow. J Tribol 126(3): 542–546 (2004)
Peng J P, Carpino M. Calculation of stiffness and damping coefficients for elastically supported gas foil bearings. J Tribol 115(1): 20–27 (1993)
Kim T H, San Andrés, L. Heavily loaded gas foil bearings: A model anchored to test data. J Eng Gas Turb Power 130(1): 012504 (2008)
Iordanoff I. Analysis of an aerodynamic compliant foil thrust bearing: Method for a rapid design. J Tribol 121(4): 816–822 (1999)
Ku C P R, Heshmat H. Compliant foil bearing structural stiffness analysis: Part I—Theoretical model including strip and variable bump foil geometry. J Tribol 114(2): 394–100 (1992)
Ku C P R, Heshmat H. Structural stiffness and coulomb damping in compliant foil journal bearings: Theoretical considerations. Tribol T 37(3): 525–533 (1994)
Rubio D, San Andrés L. Bump-type foil bearing structural stiffness: Experiments and predictions. J Eng Gas Turbines Power 128(3): 653–660 (2006)
Le Lez S, Arghir M, Frene J. A new bump-type foil bearing structure analytical model. In: Proceedings of the ASME Turbo Expo 2007: Power for Land, Sea, and Air Montreal, Canada, 2007: 747–757.
Carpino M, Medvetz L A, Peng J P. Effects of membrane stresses in the prediction of foil bearing performance©. Tribol T 37(1): 43–50 (2008)
San Andrés L, Kim T H. Analysis of gas foil bearings integrating FE top foil models. Tribol Int 42(1): 111–120 (2009)
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).
Paouris L I, Bompos D A, Nikolakopoulos P G. Simulation of static performance of air foil bearings using coupled finite element and computational fluid dynamics techniques. J Eng Gas Turb Power 136(2): 022503 (2014)
Balducchi F, Arghir M, Gauthier R, Renard E. Experimental analysis of the start-up torque of a mildly loaded foil thrust bearing. J Tribol 135(3): 031702 (2013).
Rudloff L, Arghir M, Bonneau O, Matta P. Experimental analyses of a first generation foil bearing: start-up torque and dynamic coefficients. J Eng Gas Turb Power 139(9): 092501 (2011).
Mahner, M., Bauer, M., Lehn, A., Schweizer, B. An experimental investigation on the influence of an assembly preload on the hysteresis, the drag torque, the lift-off speed and the thermal behavior of three-pad air foil journal bearings. Tribol Int, 137: 113–126 (2019).
Lee Y-B, Kim T Y, Kim C H, Kim T H. Thrust bump air foil bearings with variable axial load: Theoretical predictions and experiments. Tribol T 54(6): 902–910 (2011)
Park D J, Kim C H, Jang G H, Lee Y B. Theoretical considerations of static and dynamic characteristics of air foil thrust bearing with tilt and slip flow. Tribol Int 41(4): 282–295 (2008)
Kim T H, Park M, Lee T W. Design optimization of gas foil thrust bearings for maximum load Capacity. J Tribol 139(3): 031705 (2017)
Heshmat C A, Xu D S, Heshmat H. Analysis of gas lubricated foil thrust bearings using coupled finite element and finite difference methods. J Tribol 122(1): 199–204 (2000)
Li C L, Du J J, Yao Y X. Modeling of a multi-layer foil gas thrust bearing and its load carrying mechanism study. Tribol Int 114: 172–185 (2017)
Oden J T, Martins J A C. Models and computational methods for dynamic friction phenomena. Comput Meth Appl M 52(1–3): 527–634 (1985)
Zywica, G., Baginski, P., Bogulicz, M., Martowicz, A., Roemer, J., Kantor, S., Numerical identification of the dynamic characteristics of a nonlinear foil bearing structure: Effect of the excitation force amplitude and the assembly preload. J Sound Vib 520: 116663 (2022)
COMSOL LiveLink™ for MATLAB®User’s Guide, version 5.3a, 2017.
COMSOL® Multiphysics Programming Reference Manual, version 5.3a, 2017.
Kim D, Park S. Hydrostatic air foil bearings: Analytical and experimental investigation. Tribol Int 42(3): 413–425 (2009)
Acknowledgements
This work was supported by the National Natural Science Foundation of China (Nos. 52275204, 51905298, and 52075311) and the Shanghai Key Laboratory of Intelligent Manufacturing and Robotics.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
The authors have no competing interests to declare that are relevant to the content of this article. The author Yonggang MENG is the Associate Editor of this journal.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Hu, Y., Ding, P., Wu, F. et al. Theoretical and experimental research on static stiffness, performance, and lift-off characteristics of multi-layer gas foil thrust bearings. Friction (2024). https://doi.org/10.1007/s40544-024-0889-0
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/s40544-024-0889-0