Abstract

The mistuning problem of quasi-periodic structures has been the subject of numerous scientific investigations for more than 50 years. Researchers developed reduced-order models to reduce the computational costs of mistuning investigations including finite element models. One question which has also high practical relevance is the identification of mistuning based on modal properties. In this work, a new identification method based on the subset of nominal system modes method (SNM) is presented. Different to existing identification methods where usually the blade stiffness of each sector is scaled by a scalar value, N identification parameters are used to adapt the modal blade stiffness of each sector. The input data for the identification procedure consist solely of the mistuned natural frequencies of the investigated mode family as well as of the corresponding mistuned mode shapes in the form of one degree-of-freedom per sector. The reduction basis consists of the tuned mode shapes of the investigated mode family. Furthermore, the proposed identification method allows for the inclusion of centrifugal effects like stress stiffening and spin softening without additional computational effort. From this point of view, the presented method is also appropriate to handle centrifugal effects in reduced-order models using a minimum set of input data compared to existing methods. The power of the new identification method is demonstrated on the example of an axial compressor blisk. Finite element calculations including geometrical mistuning provide the database for the identification procedure. The correct functioning of the identification method including measurement noise is also validated to show the applicability to a case of application where real measurement data are available.

References

References
1.
Valero
,
N. A.
, and
Bendiksen
,
O. O.
,
1986
, “
Vibration Characteristics of Mistimed Shrouded Blade Assemblies
,”
ASME J. Eng. Gas Turbines Power
,
108
(
2
), pp.
293
299
.10.1115/1.3239902
2.
Lim
,
S.-H.
,
Bladh
,
R.
,
Castanier
,
M. P.
, and
Pierre
,
C.
,
2007
, “
Compact, Generalized Component Mode Mistuning Representation for Modeling Bladed Disk Vibration
,”
AIAA J.
,
45
(
9
), pp.
2285
2298
.10.2514/1.13172
3.
Judge
,
J. A.
,
Pierre
,
C.
, and
Ceccio
,
S. L.
,
2009
, “
Experimental Mistuning Identification in Bladed Disks Using a Component-Mode Based Reduced-Order Model
,”
AIAA J.
,
47
(
5
), pp.
1277
1287
.10.2514/1.41214
4.
Feiner
,
D. M.
, and
Griffin
,
J. H.
,
2004
, “
Mistuning Identification of Bladed Disks Using a Fundamental Mistuning Model—Part I: Theory
,”
ASME J. Turbomach.
,
126
(
1
), pp.
150
158
.10.1115/1.1643913
5.
Madden
,
A. C.
,
Castanier
,
M. P.
, and
Epureanu
,
B. I.
,
2008
, “
Reduced-Order Model Construction Procedure for Robust Mistuning Identification of Blisks
,”
AIAA J.
,
46
(
1
), pp.
890
2898
.10.2514/1.37314
6.
Hönisch
,
P.
,
Kühhorn
,
A.
, and
Beirow
,
B.
,
2011
, “
Experimental and Numerical Analyses of Radial Turbine Blisks With Regard to Mistuning
,”
ASME
Paper No. GT2011-45359.10.1115/GT2011-45359
7.
Yang
,
M.-T.
, and
Griffin
,
J. H.
,
2001
, “
A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes
,”
ASME J. Eng. Gas Turbines Power
,
123
(
4
), pp.
893
900
.10.1115/1.1385197
8.
Sternschüss
,
A.
, and
Balmès
,
E.
,
2006
, “
On the Reduction of Quasi-Cyclic Disk Models With Variable Rotation Speeds
,”
Proceedings of ISMA
, Leuven, Belgium, Sept. 18–20, pp.
3925
3939
.
9.
Waldherr
,
C. U.
, and
Vogt
,
D. M.
,
2018
, “
An Extension of the Classical Subset of Nominal Modes Method for the Model Order Reduction of Gyroscopic Systems
,”
ASME J. Eng. Gas Turbines Power
,
141
(
2
), p.
052501
.10.1115/1.4041117
10.
Lim
,
T. W.
, and
Kashangaki
,
T. A. I.
,
1994
, “
Structural Damage Detection of Space Truss Structures Using Best Achievable Eigenvectors
,”
AIAA J.
,
32
(
5
), pp.
1049
1057
.10.2514/3.12093
11.
Lim
,
T. W.
,
1995
, “
Structural Damage Detection Using Constrained Eigenstructure Assignment
,”
J. Guid., Control, Dyn.
,
18
(
3
), pp.
411
418
.10.2514/3.21403
12.
Laxalde
,
D.
,
Thouverez
,
F.
,
Sinou
,
J.-J.
,
Lombard
,
J.-P.
, and
Baumhauer
,
S.
,
2007
, “
Mistuning Identification and Model Updating of an Industrial Blisk
,”
Int. J. Rotating Mach.
,
2007
, p.
17289
.10.1155/2007/17289
13.
Craig
,
R. R.
, Jr.
, and
Bampton
,
M. C. C.
,
1968
, “
Coupling of Substructures for Dynamic Analyses
,”
AIAA J.
,
6
(
7
), pp.
1313
1319
.10.2514/3.4741
14.
Figaschewsky
,
F.
, and
Kühhorn
,
A.
,
2018
, “
An Inverse Approach to Identify Tuned Aerodynamic Damping, System Frequencies, and Mistuning—Part I: Theory Under Rotating Conditions
,”
Proceedings of the 15th International Symposium on Unsteady Aerodynamics
, Aeroacoustics and Aeroelasticity of Turbomachines (ISUAAAT15), Oxford, UK, Sept. 24–27.
15.
Yumer
,
M. E.
,
Cigeroglu
,
E.
, and
Özgüven
,
H. N.
,
2013
, “
Mistuning Identification of Integrally Bladed Disks With Cascaded Optimization and Neural Networks
,”
ASME J. Turbomach.
,
135
(
3
), p.
031008
.10.1115/1.4006667
16.
Weber
,
R.
, and
Kühhorn
,
A.
,
2018
, “
Mistuning Identification Approach With Focus on High-Speed Centrifugal Compressors
,”
ASME
Paper No. GT2018-75382.10.1115/GT2018-75382
17.
Kaszynski
,
A. A.
,
Beck
,
J. A.
, and
Brown
,
J. M.
,
2013
, “
Uncertainties of an Automated Optical 3D Geometry Measurement, Modeling, and Analysis Process for Mistuned Integrally Bladed Rotor Reverse Engineering
,”
ASME J. Eng. Gas Turbines Power
,
135
(
10
), p.
102504
.10.1115/1.4025000
18.
Maywald
,
T.
,
Backhaus
,
T.
,
Schrape
,
S.
, and
Kühhorn
,
A.
, “
Geometric Model Update of Blisks and Its Experimental Validation for a Wide Frequency Range
,”
ASME
Paper No. GT2017-63446.10.1115/GT2017-63446
19.
Nyssen
,
F.
, and
Golinval
,
J.-C.
,
2016
, “
Identification of Mistuning and Model Updating of an Academic Blisk Based on Geometry and Vibration Measurements
,”
Mech. Syst. Signal Process.
,
68
, pp.
252
264
.10.1016/j.ymssp.2015.08.006
20.
Mead
,
D. J.
,
1973
, “
A General Theory of Harmonic Wave Propagation in Linear Periodic Systems With Multiple Coupling
,”
J. Sound Vib.
,
27
(
2
), pp.
235
260
.10.1016/0022-460X(73)90064-3
21.
Thomas
,
D. L.
,
1979
, “
Dynamics of Rotationally Periodic Structures
,”
Int. J. Numer. Methods Eng.
,
14
(
1
), pp.
81
102
.10.1002/nme.1620140107
22.
Pichot
,
F.
,
Laxalde
,
D.
,
Sinou
,
J.-J.
,
Thouverez
,
F.
, and
Lombard
,
J.-P.
,
2006
, “
Mistuning Identification for Industrial Blisks Based on the Best Achievable Eigenvector
,”
Comput. Struct.
,
84
(
29–30
), pp.
2033
2049
.10.1016/j.compstruc.2006.08.022
23.
Mayorca
,
M. A.
,
2011
, “
Numerical Methods for Turbomachinery Aeromechanical Predictions
,” Doctoral dissertation,
Royal Institute of Technology
,
Stockholm, Sweden
.
24.
Ewins
,
D. J.
,
2000
,
Modal Testing: Theory, Practice and Application
, 2nd ed.,
Research Studies Press
,
Hertfordshire, England
.
25.
Kielb
,
R.
, and
Li
,
J.
,
2017
, “
Evaluation of Forced Response Methods on an Embedded Compressor Rotor Blade
,”
Proceedings of the First Global Power and Propulsion Forum
, Zurich, Switzerland, Jan. 16–18, GPPF-2017-183.
26.
Mayorca
,
M. A.
,
Vogt
,
D. M.
,
Màrtensson
,
H.
,
Andersson
,
C.
, and
Fransson
,
T. H.
,
2012
, “
Uncertainty of Forced Response Numerical Predictions of an Industrial Blisk-Comparison With Experiments
,”
ASME
Paper No. GT2012-69534.10.1115/GT2012-69534
27.
Myhre
,
M.
,
Moyroud
,
F.
, and
Fransson
,
T. H.
,
2003
, “
Numerical Investigation of the Sensitivity of Forced Response Characteristics of Bladed Disks to Mistuning
,”
ASME
Paper No. GT2003-38007.10.1115/GT2003-38007
28.
Klauke
,
T.
,
Kühorn
,
A.
,
Beirow
,
B.
, and
Golze
,
M.
,
2009
, “
Numerical Investigations of Localized Vibrations of Mistuned Blade Integrated Disks (Blisks)
,”
ASME J. Turbomach.
,
131
(
3
), p.
031002
.10.1115/1.2985074
29.
Kruse
,
M. J.
, and
Pierre
,
C.
,
1997
, “
An Experimental Investigation of Vibration Localization in Bladed Disks—Part I: Free Response
,”
ASME
Paper No. 97-GT-501.10.1115/97-GT-501
30.
Allemang
,
R. J.
, and
Brown
,
D. L.
,
1982
, “
A Correlation Coefficient for Modal Vector Analysis
,”
Proceedings of the First International Modal Analysis Conference and Exhibit
, Nov., pp.
110
116
.
31.
Bladh
,
R.
,
Pierre
,
C.
,
Castanier
,
M. P.
, and
Kruse
,
M. J.
,
2002
, “
Dynamic Response Predictions for a Mistuned Industrial Turbomachinery Rotor Using Reduced-Order Modeling
,”
ASME J. Eng. Gas Turbines Power
,
124
(
2
), pp.
311
324
.10.1115/1.1447236
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