Abstract
Gas bearings use pressurized gas as a lubricant to support and guide rotating machinery. These bearings have a number of advantages over traditional lubricated bearings, including higher efficiency in a variety of applications and reduced maintenance requirements. However, they are more complex to operate and exhibit nonlinear behaviors. This paper presents a parametric hyper reduced order model (h-ROM) of a gas bearings supported rotor enabling to speed up the computations up to a factor 100 while preserving satisfactory accuracy. A Galerkin projection setting is employed to reduce the dimension of the governing equations and the nonlinear terms are efficiently tackled with a sparse sampling technique. The performances of the h-ROM are compared to a high fidelity model both in terms of accuracy and computation time, demonstrating the potential for future anomaly detection applications.
Issue Section:
Research Papers
References
1.
Heng
,
A.
,
Zhang
,
S.
,
Tan
,
A. C.
, and
Mathew
,
J.
, 2009
, “
Rotating Machinery Prognostics: State of the Art, Challenges and Opportunities
,” Mech. Syst. Signal Process.
,
23
(3
), pp. 724
–739
.10.1016/j.ymssp.2008.06.0092.
Chinesta
,
F.
,
Cueto
,
E.
,
Abisset-Chavanne
,
E.
,
Duval
,
J. L.
, and
Khaldi
,
F. E.
, 2020
, “
Virtual, Digital and Hybrid Twins: A New Paradigm in Data-Based Engineering and Engineered Data
,” Arch. Comput. Methods Eng.
,
27
(1
), pp. 105
–134
.10.1007/s11831-018-9301-43.
Benner
,
P.
,
Gugercin
,
S.
, and
Willcox
,
K.
, 2015
, “
A Survey of Projection-Based Model Reduction Methods for Parametric Dynamical Systems
,” SIAM Rev.
,
57
(4
), pp. 483
–531
.10.1137/1309327154.
Sirovich
,
L.
, 1987
, “
Turbulence and the Dynamics of Coherent Structures, Parts I, II and III
,” Quart. Appl. Math.
,
45
(3
), pp. 561
–571
.10.1090/qam/9104625.
Rathinam
,
M.
, and
Petzold
,
L. R.
, 2003
, “
A New Look at Proper Orthogonal Decomposition
,” SIAM J. Numer. Anal.
,
41
(5
), pp. 1893
–1925
.10.1137/S00361429013890496.
Astrid
,
P.
,
Weiland
,
S.
,
Willcox
,
K.
, and
Backx
,
T.
, 2008
, “
Missing Point Estimation in Models Described by Proper Orthogonal Decomposition
,” IEEE Trans. Autom. Control
,
53
(10
), pp. 2237
–2251
.10.1109/TAC.2008.20061027.
Carlberg
,
K.
,
Farhat
,
C.
,
Cortial
,
J.
, and
Amsallem
,
D.
, 2013
, “
The GNAT Method for Nonlinear Model Reduction: Effective Implementation and Application to Computational Fluid Dynamics and Turbulent Flows
,” J. Comput. Phys.
,
242
, pp. 623
–647
.10.1016/j.jcp.2013.02.0288.
Chaturantabut
,
S.
, and
Sorensen
,
D. C.
, 2010
, “
Nonlinear Model Reduction Via Discrete Empirical Interpolation
,” SIAM J. Sci. Comput.
,
32
(5
), pp. 2737
–2764
.10.1137/0907664989.
Washabaugh
,
K.
,
Amsallem
,
D.
,
Zahr
,
M.
, and
Farhat
,
C.
, 2012
, “
Nonlinear Model Reduction for CFD Problems Using Local Reduced-Order Bases
,” 42nd AIAA Fluid Dynamics Conference and Exhibit
, New Orleans, LA, June 25–28, p. 2686
.10.2514/6.2012-268610.
Peherstorfer
,
B.
,
Butnaru
,
D.
,
Willcox
,
K.
, and
Bungartz
,
H.-J.
, 2014
, “
Localized Discrete Empirical Interpolation Method
,” SIAM J. Sci. Comput.
,
36
(1
), pp. A168
–A192
.10.1137/13092440811.
Amsallem
,
D.
,
Cortial
,
J.
,
Carlberg
,
K.
, and
Farhat
,
C.
, 2009
, “
A Method for Interpolating on Manifolds Structural Dynamics Reduced-Order Models
,” Int. J. Numer. Methods Eng.
,
80
(9
), pp. 1241
–1258
.10.1002/nme.268112.
Mosquera
,
R.
,
Hamdouni
,
A.
,
El Hamidi
,
A.
, and
Allery
,
C.
,Laboratoire LaSIE, Université de La Rochelle, Avenue M. Crépeau, 17042 La Rochelle, France
2019
, “
POD Basis Interpolation Via Inverse Distance Weighting on Grassmann Manifolds
,” Discrete Contin. Dyn. Syst.-S
,
12
(6
), pp. 1743
–1759
.10.3934/dcdss.201911513.
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.2014.03.00114.
Cherabi
,
B.
,
Hamrani
,
A.
,
Belaidi
,
I.
,
Khelladi
,
S.
, and
Bakir
,
F.
, 2016
, “
An Efficient Reduced-Order Method With PGD for Solving Journal Bearing Hydrodynamic Lubrication Problems
,” C. R. Méc.
,
344
(10
), pp. 689
–714
.10.1016/j.crme.2016.05.00615.
Iseli
,
E.
,
Guenat
,
E.
,
Tresch
,
R.
, and
Schiffmann
,
J.
, 2020
, “
Analysis of Spiral-Grooved Gas Journal Bearings by the Narrow-Groove Theory and the Finite Element Method at Large Eccentricities
,” ASME J. Tribol.
,
142
(4
), p. 041802.10.1115/1.404563616.
Liu
,
W.
,
Bättig
,
P.
,
Wagner
,
P. H.
, and
Schiffmann
,
J.
, 2021
, “
Nonlinear Study on a Rigid Rotor Supported by Herringbone Grooved Gas Bearings: Theory and Validation
,” Mech. Syst. Signal Process.
,
146
, p. 106983
.10.1016/j.ymssp.2020.10698317.
Vohr
,
J. H.
, and
Chow
,
C. Y.
, 1965
, “
Characteristics of Herringbone-Grooved, Gas-Lubricated Journal Bearings
,” ASME J. Basic Eng.
, 87(3), pp. 568
–576
.10.1115/1.365060718.
Bonneau
,
D.
, and
Absi
,
J.
, 1994
, “
Analysis of Aerodynamic Journal Bearings With Small Number of Herringbone Grooves by Finite Element Method
,” ASME J. Tribol.
,
116
(4
), pp. 698
–704
.10.1115/1.292732019.
Shampine
,
L. F.
, and
Reichelt
,
M. W.
, 1997
, “
The Matlab Ode Suite
,” SIAM J. Sci, Comput.
,
18
(1
), pp. 1
–22
.10.1137/S106482759427642420.
Zimmermann
,
R.
, 2020
, “
Hermite Interpolation and Data Processing Errors on Riemannian Matrix Manifolds
,” SIAM J. Sci. Comput.
,
42
(5
), pp. A2593
–A2619
.10.1137/19M1282878Copyright © 2024 by ASME
You do not currently have access to this content.
