Abstract

The compressible Reynolds equation (RE) is typically integrated within a fully coupled dynamical foil-air bearings (FABs)-rotor system via spatial Discretization transformation, e.g., finite difference (FD), finite element (FE). An alternative way of integrating the RE is through Galerkin reduction (GR). The motivation for using GR is the computational benefit coming from the drastic condensation of the problem due to the elimination of the two-dimensional grid used for the air film in FD or FE. This paper presents a novel application of arbitrary-order GR to both nonlinear and linearized analyses of rotor systems supported by single-pad FABs with variable radial clearance (preload). Simulations using FD gave a close correlation with those using GR for all preloads, with discrepancies increasing as the preload approaches the nominal clearance (c). The simulations show that the preload has to exceed a certain level in order to delay the onset of instability speed (OIS), and significant delay in OIS and suppression of subsynchronous vibration is possible when the preload is comparable to c. Experimental validation is provided.

References

1.
Berthe
,
D.
,
Dowson
,
D.
,
Godet
,
M.
and
Taylor
,
C. M.
eds.,
1987
,
Fluid Film Lubrication-Osborne Reynolds Centenary: Fluid Film Lubrication-Osborne Rey
, 11,
Elsevier
, North Holland, Amsterdam, The Netherlands.
2.
Bonello
,
P.
,
2019
, “
The Extraction of Campbell Diagrams From the Dynamical System Representation of a Foil-Air Bearing Rotor Model
,”
Mech. Syst. Signal Process.
,
129
, pp.
502
530
.10.1016/j.ymssp.2019.04.018
3.
Bonello
,
P.
, and
Pham
,
H. M.
,
2014
, “
The Efficient Computation of the Nonlinear Dynamic Response of a Foil–Air Bearing Rotor System
,”
J. Sound Vib.
,
333
(
15
), pp.
3459
3478
.10.1016/j.jsv.2014.03.001
4.
Pham
,
H.
, and
Bonello
,
P.
, “
Efficient Techniques for the Computation of the Nonlinear Dynamics of a Foil-Air Bearing Rotor System
,”
ASME
Paper No. GT2013-94389.10.1115/GT2013-94389
5.
Larsen
,
J. S.
, and
Santos
,
I. F.
,
2015
, “
On the Nonlinear Steady-State Response of Rigid Rotors Supported by Air Foil Bearings—Theory and Experiments
,”
J. Sound Vib.
,
346
, pp.
284
297
.10.1016/j.jsv.2015.02.017
6.
Carpino
,
M.
, and
Talmage
,
G.
,
2003
, “
A Fully Coupled Finite Element Formulation for Elastically Supported Foil Journal Bearings
,”
Tribol. Trans.
,
46
(
4
), pp.
560
565
.10.1080/10402000308982664
7.
Le Lez
,
S.
,
Arghir
,
M.
, and
Frêne
,
J.
,
2009
, “
Nonlinear Numerical Prediction of Gas Foil Bearing Stability and Unbalanced Response
,”
ASME J. Eng. Gas Turbines Power
,
131
(
1
), p.
012503
.10.1115/1.2967481
8.
Baum
,
C.
,
Hetzler
,
H.
,
Schröders
,
S.
,
Leister
,
T.
, and
Seemann
,
W.
,
2021
, “
A Computationally Efficient Nonlinear Foil Air Bearing Model for Fully Coupled, Transient Rotor Dynamic Investigations
,”
Tribol. Int.
,
153
(
2021
), p.
106434
.10.1016/j.triboint.2020.106434
9.
Ghalayini
,
I.
, and
Bonello
,
P.
,
2022
, “
Nonlinear and Linearised Analyses of a Generic Rotor on Single-Pad Foil-Air Bearings Using Galerkin Reduction With Different Applied Air Film Conditions
,”
J. Sound Vib.
,
525
(
2022
), p.
116774
.10.1016/j.jsv.2022.116774
10.
Lund
,
J. W.
,
1968
, “
Calculation of Stiffness and Damping Properties of Gas Bearings
,”
ASME J. Lubr. Technol.
, 90(4), pp.
793
803
.10.1115/1.3601723
11.
Peng
,
J. P.
, and
Carpino
,
M.
,
1993
, “
Calculation of Stiffness and Damping Coefficients for Elastically Supported Gas Foil Bearings
,”
ASME J. Tribol.
, 115(1), pp.
20
27
.10.1115/1.2920982
12.
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
.10.1115/1.2540065
13.
Von Osmanski
,
S.
,
Larsen
,
J. S.
, and
Santos
,
I. F.
,
2020
, “
Multi-Domain Stability and Modal Analysis Applied to Gas Foil Bearings: Three Approaches
,”
J. Sound Vib.
,
472
, p.
115174
.10.1016/j.jsv.2020.115174
14.
Pronobis
,
T.
, and
Liebich
,
R.
,
2019
, “
Comparison of Stability Limits Obtained by Time Integration and Perturbation Approach for Gas Foil Bearings
,”
J. Sound Vib.
,
458
, pp.
497
509
.10.1016/j.jsv.2019.06.034
15.
Kim
,
T. H.
, and
Andres
,
L. S.
,
2009
, “
Effects of a Mechanical Preload on the Dynamic Force Response of Gas Foil Bearings: Measurements and Model Predictions
,”
Tribol. Trans.
,
52
(
4
), pp.
569
580
.10.1080/10402000902825721
16.
Park
,
J.
,
Kim
,
D.
, and
Sim
,
K.
,
2021
, “
Rotordynamic Analysis of Piezoelectric Gas Foil Bearings With a Mechanical Preload Control Based on Structural Parameter Identifications
,”
Appl. Sci.
,
11
(
5
), p.
2330
.10.3390/app11052330
17.
Hu
,
H.
,
Feng
,
M.
, and
Ren
,
T.
,
2021
, “
Study on the Performance of Gas Foil Journal Bearings With Bump-Type Shim Foil
,”
Proc. Inst. Mech. Eng., Part J J. Eng. Tribol.
,
235
(
3
), pp.
509
523
.10.1177/1350650120969003
18.
Bonello
,
P.
,
2020
, “
The Effects of Air Film Pressure Constraints and Top Foil Detachment on the Static Equilibrium, Stability and Modal Characteristics of a Foil-Air Bearing Rotor Model
,”
J. Sound Vib.
,
485
, p.
115590
.10.1016/j.jsv.2020.115590
19.
Bonello
,
P.
, and
Hassan
,
M. B.
,
2018
, “
An Experimental and Theoretical Analysis of a Foil-Air Bearing Rotor System
,”
J. Sound Vib.
,
413
, pp.
395
420
.10.1016/j.jsv.2017.10.036
20.
Ghalayini
,
I.
,
2022
, “
Modal Matrix Data
,” Mendeley Data, V1.10.17632/v5mt7dzrs9.1
21.
Ghalayini
,
I.
, and
Bonello
,
P.
,
2020
, “
A Parametric Study Into the Effect of Variability in Clearance Shape and Bump Foil Stiffness Distribution in Foil-Air Bearings
,”
12th International Conference on Vibrations in Rotating Machinery, VIRM 12
,
CRC Press
, London, UK, Oct. 14–15,
p.
2020
.
22.
Ghalayini
,
I.
, and
Bonello
,
P.
,
2022
, “
Development of a Rotor Test Rig With a Novel Controllable Preload Foil-Air Bearing
,”
Precis. Eng.
,
76
, pp.
340
359
.10.1016/j.precisioneng.2022.04.002
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