Abstract

A new reduction method is proposed to investigate the behavior stability of rotor-bearing systems subject to a multifrequency rotational motion of their base. Combining the modal analysis and the construction of specific dynamic Ritz vectors, this method is able to deal with complex rotordynamics characteristics such as nonproportional damping, nonself-adjoint matrices, or time-varying parametric coefficients. This paper focuses first on assessing the accuracy and efficiency of the reduction method by computing time history and spectral responses of full and reduced models due to multifrequency base excitations. Its main potential is then highlighted in the parametric stability analysis through Floquet theory. The proposed numerical examples are composed with academic and industrial rotors, both modeled with one-dimensional Timoshenko beam finite element and supported by hydrodynamic journal bearings.

References

References
1.
Duchemin
,
M.
,
Berlioz
,
A.
, and
Ferraris
,
G.
,
2006
, “
Dynamic Behavior and Stability of a Rotor Under Base Excitation
,”
ASME J. Vib. Acoust.
,
128
(
5
), pp.
576
585
. 10.1115/1.2202159
2.
Dakel
,
M.
,
Baguet
,
S.
, and
Dufour
,
R.
,
2014
, “
Nonlinear Dynamics of a Support-Excited Flexible Rotor With Hydrodynamic Journal Bearings
,”
J. Sound Vib.
,
333
(
10
), pp.
2774
2799
. 10.1016/j.jsv.2013.12.021
3.
Dakel
,
M.
,
Baguet
,
S.
, and
Dufour
,
R.
,
2014
, “
Steady-State Dynamic Behavior of an On-Board Rotor Under Combined Base Motions
,”
J. Vib. Control
,
20
(
15
), pp.
2254
2287
. 10.1177/1077546313483791
4.
Han
,
Q.
, and
Chu
,
F.
,
2015
, “
Parametric Instability of Flexible Rotor-Bearing System Under Time-Periodic Base Angular Motions
,”
Appl. Math. Model.
,
39
(
15
), pp.
4511
4522
. 10.1016/j.apm.2014.10.064
5.
Tai
,
W.
, and
Shen
,
I.
,
2015
, “
Ground-Based Response of a Spinning, Cyclic Symmetric Rotor Assembled to a Flexible Stationary Housing Via Multiple Bearings
,”
ASME J. Vib. Acoust.
,
137
(
4
), p.
041011
. 10.1115/1.4029989
6.
Saimi
,
A.
, and
Hadjoui
,
A.
,
2016
, “
An Engineering Application of the hp Version of the Finite Elements Method to the Dynamics Analysis of a Symmetrical On-Board Rotor
,”
Eur. J. Comput. Mech.
,
25
(
5
), pp.
388
416
. 10.1080/17797179.2016.1245597
7.
Chen
,
L.
,
Wang
,
J.
,
Han
,
Q.
, and
Chu
,
F.
,
2017
, “
Nonlinear Dynamic Modeling of a Simple Flexible Rotor System Subjected to Time-Variable Base Motions
,”
J. Sound Vib.
,
404
, pp.
58
83
. 10.1016/j.jsv.2017.05.032
8.
Bouziani
,
R.
, and
Ouelaa
,
N.
,
2017
, “
Simulation of the Dynamic Behavior of a Rotor Subject to Base Motion Under Variable Rotational Speed
,”
Mech. Ind.
,
18
(
3
), p.
308
. 10.1051/meca/2016056
9.
Sousa
,
M.
,
Del Claro
,
V.
,
Cavalini
,
A.
, and
Steffen
,
V.
,
2017
, “
Numerical Investigation on the Dynamic Behavior of an Onboard Rotor System by Using the Fem Approach
,”
J. Braz. Soc. Mech. Sci. Eng.
,
39
(
7
), pp.
2447
2458
. 10.1007/s40430-016-0640-5
10.
Liu
,
Z.
,
Liu
,
Z.
,
Li
,
Y.
, and
Zhang
,
G.
,
2018
, “
Dynamics Response of an On-Board Rotor Supported on Modified Oil-Film Force Considering Base Motion
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
232
(
2
), pp.
245
259
. 10.1177/0954406216682052
11.
Sales
,
T. D. P.
,
Spuldaro
,
E.
,
Damy
,
L. F.
, and
Rade
,
D. A.
,
2018
, “
Dynamic Modeling of Flexible Rotors Mounted on an Elastic Base Undergoing Arbitrary Attitude Motion
,”
International Conference on Rotor Dynamics
,
Springer
,
New York
, pp.
562
576
.
12.
Yi
,
Y.
,
Qiu
,
Z.
, and
Han
,
Q.
,
2018
, “
The Effect of Time-Periodic Base Angular Motions Upon Dynamic Response of Asymmetric Rotor Systems
,”
Adv. Mech. Eng.
,
10
(
3
), p.
1687814018767172
. 10.1177/1687814018767172
13.
Soni
,
T.
,
Dutt
,
J. K.
, and
Das
,
A.
,
2019
, “
Parametric Stability Analysis of Active Magnetic Bearing-Supported Rotor System With a Novel Control Law Subject to Periodic Base Motion
,”
IEEE Trans. Indus. Electron
doi:10.1109/TIE.2019.2898604.
14.
AL-Shudeifat
,
M. A.
,
2015
, “
Stability Analysis and Backward Whirl Investigation of Cracked Rotors With Time-Varying Stiffness
,”
J. Sound Vib.
,
348
, pp.
365
380
. 10.1016/j.jsv.2015.03.007
15.
Nayfeh
,
A.
, and
Mook
,
D.
,
1995
,
Nonlinear Oscillations
,
Wiley
,
Hoboken, NJ
.
16.
Qu
,
Z.-Q.
,
2013
,
Model Order Reduction Techniques With Applications in Finite Element Analysis
,
Springer Science & Business Media
,
London
.
17.
Craig
,
R.
, and
Kurdila
,
A.
,
2006
,
Fundamentals of Structural Dynamics
,
Wiley
,
New York
.
18.
Wagner
,
M. B.
,
Younan
,
A.
,
Allaire
,
P.
, and
Cogill
,
R.
,
2010
, “
Model Reduction Methods for Rotor Dynamic Analysis: A Survey and Review
,”
Int. J. Rotating Mach.
doi:10.1155/2010/273716, pp.
1
17
(Article ID 273716).
19.
Lalanne
,
M.
, and
Ferraris
,
G.
,
1998
,
Rotordynamics Prediction in Engineering
,
2nd ed.
,
John Wiley and Sons
,
New York
.
20.
Nandi
,
A.
,
2004
, “
Reduction of Finite Element Equations for a Rotor Model on Non-Isotropic Spring Support in a Rotating Frame
,”
Finite Elements Anal. Des.
,
40
(
9–10
), pp.
935
952
. 10.1016/S0168-874X(03)00121-5
21.
Cunha-Filho
,
A.
,
Briend
,
Y.
,
De Lima
,
A.
, and
Donadon
,
M.
,
2018
, “
An Efficient Iterative Model Reduction Method for Aeroviscoelastic Panel Flutter Analysis in the Supersonic Regime
,”
Mech. Syst. Signal Proces.
,
104
, pp.
575
588
. 10.1016/j.ymssp.2017.11.018
22.
Kergourlay
,
G.
,
Balmes
,
E.
, and
Clouteau
,
D.
,
2001
, “
Model Reduction for Efficient FEM/BEM Coupling
,”
Proceedings of the International Seminar on Modal Analysis
, Vol.
3
,
KU Leuven
, pp.
1167
1174
.
23.
Bobillot
,
A.
, and
Balmes
,
É.
,
2002
Iterative Techniques for Eigenvalue Solutions of Damped Structures Coupled with Fluids
,”
43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
,
Denver, CO
,
Apr. 22–25
, p.
1391
.
24.
Chandraker
,
S.
, and
Roy
,
H.
,
2016
, “
Dynamic Study of Viscoelastic Rotor: Reduction of Higher Order Model Using Different Techniques
,”
Aerosp. Sci. Technol.
,
58
, pp.
306
317
. 10.1016/j.ast.2016.08.006
25.
Sanches
,
F. D.
, and
Pederiva
,
R.
,
2015
, “
Experimental Unbalance Identification by Means of Correlation Analysis and Model Order Reduction
,”
Proceedings of the 9th IFToMM International Conference on Rotor Dynamics
,
Springer
,
New York
, pp.
689
699
.
26.
Zuo
,
Y.
,
Wang
,
J.
,
Ma
,
W.
,
Zhai
,
X.
, and
Yao
,
X.
,
2014
, “
Method for Selecting Master Degrees of Freedom for Rotating Substructure
,”
ASME Turbo Expo 2014: Turbine Technical Conference and Exposition
,
American Society of Mechanical Engineers
,
Dusseldorf, Germany
, p.
V07AT31A013
.
27.
Rosyid
,
A.
,
ElMadany
,
M.
, and
Alata
,
M.
,
2015
, “
Optimal Control of Reduced-Order Finite Element Models of Rotor-Bearing-Support Systems
,”
J. Braz. Soc. Mech. Sci. Eng.
,
37
(
5
), pp.
1485
1497
. 10.1007/s40430-014-0292-2
28.
Rosyid
,
A.
,
Madany
,
M.
, and
Alata
,
M.
,
2013
, “
Reduction of Rotor-Bearing-Support Finite Element Modal Through Substructuring
,”
Int. Scholarly Scientific Res. Innovation
,
7
, pp.
1361
1368
.
29.
Zuo
,
Y.
, and
Wang
,
J.
,
2015
, “
A Component Mode Synthesis Method for 3-D Finite Element Models of Aero-Engines
,”
J. Mech. Sci. Technol.
,
29
(
12
), pp.
5157
5166
. 10.1007/s12206-015-1116-8
30.
Pechstein
,
A.
,
Reischl
,
D.
, and
Gerstmayr
,
J.
,
2011
, “
The Applicability of the Floating-Frame Based Component Mode Synthesis to High-Speed Rotors
,”
ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
Washington, DC, Aug. 28–31
, pp.
933
942
.
31.
Stringer
,
D. B.
,
Sheth
,
P. N.
, and
Allaire
,
P. E.
,
2011
, “
Modal Reduction of Geared Rotor Systems With General Damping and Gyroscopic Effects
,”
J. Vib. Control
,
17
(
7
), pp.
975
987
. 10.1177/1077546310372848
32.
Yang
,
Y.
,
Wang
,
X.
,
Wang
,
M.
,
Li
,
H.
, and
Dai
,
Y.
,
2017
, “
Dynamic Behaviors of Helical Geared Multishaft Rotor Systems by Modal Synthesis
,”
Proc. Inst. Mech. Eng., Part C: J. Mech. Eng. Sci.
,
231
(
8
), pp.
1410
1426
. 10.1177/0954406216681596
33.
Chahlaoui
,
Y.
, and
Van Dooren
,
P.
,
2005
, “Model Reduction of Time-Varying Systems,”
Dimension Reduction of Large-Scale Systems, Computational Science and Engineering
, Vol.
45
,
Springer
,
New York
, pp.
131
148
.
34.
Sandberg
,
H.
, and
Rantzer
,
A.
,
2002
, “
Balanced Model Reduction of Linear Time-Varying Systems
,”
IFAC Proc. Vol.
,
35
(
1
), pp.
255
260
. 10.3182/20020721-6-ES-1901.00204
35.
Billaud-Friess
,
M.
, and
Nouy
,
A.
,
2017
, “
Dynamical Model Reduction Method for Solving Parameter-Dependent Dynamical Systems
,”
SIAM J. Scientific Comput.
,
39
(
4
), pp.
A1766
A1792
. 10.1137/16M1071493
36.
Tamarozzi
,
T.
,
Heirman
,
G. H.
, and
Desmet
,
W.
,
2014
, “
An On-line Time Dependent Parametric Model Order Reduction Scheme With Focus on Dynamic Stress Recovery
,”
Comput. Methods Appl. Mech. Eng.
,
268
, pp.
336
358
. 10.1016/j.cma.2013.09.021
37.
Varona
,
M. C.
,
Geuss
,
M.
, and
Lohmann
,
B.
,
2015
, “
p (t) mor: Time-Varying Parametric Model Order Reduction and Applications for Moving Loads
,”
Proceedings of the 8th Vienna Conference on Mathematical Modelling (MATHMOD)
,
Vienna, Austria
,
Feb. 18–20
, Vol.
48
, pp.
677
678
.
38.
Baumann
,
M.
,
Hamann
,
D.
, and
Eberhard
,
P.
,
2017
, “Time-dependent parametric model order reduction for material removal simulations,”
Model Reduction of Parametrized Systems
,
Springer
,
New York
, pp.
491
504
.
39.
Frene
,
J.
,
Nicolas
,
D.
,
Degueurce
,
B.
,
Berthe
,
D.
, and
Godet
,
M.
,
1997
,
Hydrodynamic Lubrication: Bearings and Thrust Bearings
, Vol.
33
,
Elsevier
,
New York
.
40.
De Lima
,
A.
,
Da
,
Silva
, and
Bouhaddi
,
N.
,
2010
, “
Component Mode Synthesis Combining Robust Enriched Ritz Approach for Viscoelastically Damped Structures
,”
Eng. Struct.
,
32
(
5
), pp.
1479
1488
. 10.1016/j.engstruct.2010.01.028
41.
Sudret
,
B.
, and
Der Kiureghian
,
A.
,
2000
, “
Stochastic Finite Element Methods and Reliability: A State-of-the-art Report
,”
Department of Civil and Environmental Engineering, University of California
,
CA
.
You do not currently have access to this content.