Abstract

Bladed-disks in turbomachines experience high cycle fatigue failures due to high vibration amplitudes. Therefore, it is important to accurately predict their dynamic characteristics including the mechanical joints at blade-disk interfaces. Before the experimental identification of these joints, it is of paramount importance to accurately measure the interface degrees-of-freedom (DoF). However, they are largely inaccessible for the measurements. For this reason, expansion techniques can be used in order to update the single components. But the expansion can be affected adversely if the measurements are not properly correlated with the updated model. Therefore, a frequency domain expansion method called System Equivalent Model Mixing (SEMM) is used to expand a limited set of measurements to a larger set of numerical DoF. Different measured models—termed the overlay models—are taken from an impact testing campaign of a blade and a disk and coupled to the numerical model according to the SEMM. The expanded models—termed the hybrid models—are then correlated with the validation channels in a round-robin way by means of Frequency Response Assurance Criteria (FRAC). The global correlations depict whether or not a measurement and the respective expansion is properly correlated. By this approach, the least correlated channels can be eliminated from the measurements to have a better updated hybrid model. The method is tested on both the structures (the blade and the disk) and it is successfully shown that removing the uncorrelated channels does improve the quality of the hybrid models.

References

1.
Ewins
,
D. J.
,
2000
,
Modal Testing: Theory, Practice and Application, Research Studies Press Ltd. Baldock
,
Hertfordshire, UK
.
2.
Arras
,
M.
,
2016
, “
On the Use of Frequency Response Functions in the Finite Element Model Updating
,”
Ph.D. thesis
,
Sapienza University of Rome
,
Rome, Italy
. https://curve.carleton.ca/system/files/etd/e7368a29-ad7c-4bc7-83df-46f12a1e30cf/etd_pdf/5943ddbddb952e756e46a5a0dbc1664f/arras-ontheuseoffrequencyresponsefunctionsinthe.pdf
3.
Herman
,
A.
,
1979
, “
Mass Matrix Correction Using an Incomplete Set of Measured Modes
,”
AIAA J.
,
17
(
10
), pp.
1147
1148
.10.2514/3.61290
4.
Baruch
,
M.
,
1982
, “
Optimal Correction of Mass and Stiffness Matrices Using Measured Modes
,”
AIAA J.
,
20
(
11
), pp.
1623
1626
.10.2514/3.7995
5.
Dascotte
,
E.
,
1991
, “
Applications of Finite Element Model Tuning Using Experimental Modal Data
,”
Sound and Vibration
,
25
(
6
), pp.
22
26
.
6.
Chen
,
J. C.
, and
Garba
,
J. A.
,
1980
, “
Analytical Model Improvement Using Modal Test Results
,”
AIAA J.
,
18
(
6
), pp.
684
690
.10.2514/3.50805
7.
Cottin
,
N.
,
Felgenhauer
,
H. P.
, and
Natke
,
H. G.
,
1984
, “
On the Parameter Identification of Elastomechanical Systems Using Input and Output Residuals
,”
Ing.-Arch.
,
54
(
5
), pp.
378
387
.10.1007/BF00532820
8.
Sestieri
,
A.
, and
D'Ambrogio
,
W.
,
1988
, “
Why Be Modal: How to Avoid the Use of Modes in the Modification of Vibrating Systems
,”
Proceeding of the Sixth International Modal Analysis Conference
, Vol.
2
, Kissimmee, FL, Feb. 1–4, pp.
1100
1106
. https://www.researchgate.net/publication/230883078_Why_be_modal_ie_how_to_avoid_the_use_of_modes_in_the_modification_of_vibrating_systems
9.
O'Callahan
,
J.
,
1989
, “
System Equivalent Reduction Expansion Process (SEREP)
,” Proceedings of the
Seventh International Modal Analysis Conference, Las Vegas, NV, Jan. 30–Feb. 2, pp.
29
37
.
10.
Thibault
,
L.
,
Butland
,
A.
, and
Avitabile
,
P.
,
2012
,
Variability Improvement of Key Inaccurate Node Groups – VIKING
, R. Allemang, J. De Clerck, C. Niezrecki, and J. Blough, eds., Topics in Modal Analysis II, Volume 6. Conference Proceedings of the Society for Experimental Mechanics Series,
Springer
,
New York
, pp.
603
624
.
11.
Klaassen
,
S. W.
,
van der Seijs
,
M. V.
, and
de Klerk
,
D.
,
2018
, “
System Equivalent Model Mixing
,”
Mech. Syst. Signal Process.
,
105
, pp.
90
112
.10.1016/j.ymssp.2017.12.003
12.
De Klerk
,
D.
,
Rixen
,
D. J.
, and
De Jong
,
J.
,
2006
, “
The Frequency Based Substructuring (FBS) Method Reformulated According to the Dual Domain Decomposition Method
,”
24th International Modal Analysis Conference,
St. Louis, MO, Jan. 30–Feb. 2, pp.
2166
2179
.https://www.researchgate.net/publication/265790826_The_Frequency_Based_Substructuring_Method_reformulated_according_to_the_Dual_Domain_Decomposition_Method
13.
Heylen
,
W.
, and
Lammens
,
S.
,
1996
, “
FRAC: A Consistent Way of Comparing Frequency Response Functions
,”
International Conference on Identification in Engineering
, Swansea, UK, Mar. 27–29, pp.
48
57
.https://www.tib.eu/en/search/id/BLCP%3ACN016353984/FRAC-A-Consistent-Way-of-Comparing-Frequency-Response/
14.
Grafe
,
H.
,
1998
, “
Model Updating of Large Structural Dynamics Models Using Measured Response Functions
,”
Ph.D. thesis
,
Technology and Medicine University of London
,
London, UK
.https://www.imperial.ac.uk/media/imperial-college/research-centres-and-groups/dynamics/40375700.PDF
15.
Ewins
,
D. J.
,
2000
, “
Model Validation: Correlation for Updating
,”
Sadhana
, Vol.
25
, pp.
221
234
.10.1007/BF02703541
16.
Saeed
,
Z.
,
Firrone
,
C. M.
, and
Berruti
,
T. M.
,
2019
, “
Substructuring for Contact Parameters Identification in Bladed-Disks
,”
J. Phys.: Conf. Ser.
,
1264
(
1
), p.
012037
.10.1088/1742-6596/1264/1/012037
17.
Saeed
,
Z.
,
Klaassen
,
S. W. B.
,
Firrone
,
C. M.
,
Berruti
,
T. M.
, and
Rixen
,
D. J.
,
2019
, “
Joint Identification in Bladed-Disks Using SEMM and VPT
,”
Tribomechadynamics
,
M.
Brake
, ed., Houston, TX, pp.
1
4
. https://www.researchgate.net/publication/339302775_Joint_Identification_in_Bladed-disks_using_SEMM_and_VPT
18.
Saeed
,
Z.
,
Klaassen
,
S. W. B.
,
Firrone
,
C. M.
,
Berruti
,
T. M.
, and
Rixen
,
D. J.
,
2020
, “
Experimental Joint Identification Using System Equivalent Model Mixing in a Bladed Disk
,”
J. Vib. Acoust.
,
142
(
5
), p.
051001
.10.1115/1.4047361
19.
De Klerk
,
D.
,
Rixen
,
D. J.
, and
Voormeeren
,
S. N.
,
2008
, “
General Framework for Dynamic Substructuring: History, Review, and Classification of Techniques
,”
AIAA J.
,
46
(
5
), pp.
1169
1181
.10.2514/1.33274
20.
Klaassen
,
S. W.
,
2017
, “
Towards Hybrid Modular Design of Structural Dynamic Models
,”
Master's thesis
,
Delft University of Technology
,
Delft, The Netherlands
.http://resolver.tudelft.nl/uuid:c4c065cf-06d3-4ea2-a9c4-b58814058ee0
21.
Smith
,
S.
,
Bilbao-Ludena
,
J. C.
,
Catalfamo
,
S.
,
Brake
,
M. R.
,
Reuß
,
P.
, and
Schwingshackl
,
C. W.
,
2016
, “
The Effects of Boundary Conditions, Measurement Techniques, and Excitation Type on Measurements of the Properties of Mechanical Joints
,”
Nonlinear Dynamics, Conference Proceedings of the Society for Experimental Mechanics Series,
G.
Kerschen
, ed., Vol.
1
,
Springer
,
Cham, Switzerland
, pp.
415
431
.10.1007/978-3-319-15221-9_36
22.
Zanarini
,
A.
,
2019
, “
Full Field Optical Measurements in Experimental Modal Analysis and Model Updating
,”
J. Sound Vib.
,
442
, pp.
817
842
.10.1016/j.jsv.2018.09.048
23.
Hasheminejad
,
N.
,
Vuye
,
C.
,
Van den Bergh
,
W.
,
Dirckx
,
J.
, and
Vanlanduit
,
S.
,
2018
, “
A Comparative Study of Laser Doppler Vibrometers for Vibration Measurements on Pavement Materials
,”
Infrastructures
,
3
(
4
), p.
47
.10.3390/infrastructures3040047
24.
Stanbridge
,
A. B.
,
Khan
,
A. Z.
, and
Ewins
,
D. J.
,
2000
, “
Modal Testing Using Impact Excitation and a Scanning LDV
,”
Shock Vib.
,
7
(
2
), pp.
91
100
.10.1155/2000/527389
25.
Cakar
,
O.
, and
Sanliturk
,
K. Y.
,
2005
, “
Elimination of Transducer Mass Loading Effects From Frequency Response Functions
,”
Mech. Syst. Signal Process.
,
19
(
1
), pp.
87
104
.10.1016/S0888-3270(03)00086-4
26.
Bi
,
S.
,
Ren
,
J.
,
Wang
,
W.
, and
Zong
,
G.
,
2013
, “
Elimination of Transducer Mass Loading Effects in Shaker Modal Testing
,”
Mech. Syst. Signal Process.
,
38
(
2
), pp.
265
275
.10.1016/j.ymssp.2013.02.010
27.
Ren
,
J.
,
Wang
,
J.
,
Zhou
,
X.
, and
Ting
,
K. L.
,
2017
, “
Correction of Multiple Transducers Masses Effects From the Measured FRFs
,”
ASME
Paper No. DETC2017-67516.10.1115/DETC2017-67516
28.
Voormeeren
,
S. N.
, and
Rixen
,
D. J.
,
2012
, “
A Family of Substructure Decoupling Techniques Based on a Dual Assembly Approach
,”
Mech. Syst. Signal Process.
,
27
(
1
), pp.
379
396
.10.1016/j.ymssp.2011.07.028
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