Abstract
Blisks are subjected to frequent acceleration and deceleration, which leads to a transient forced response; however, there is limited understanding of this response. In this work, the mechanism on prediction of transient maximum amplitude is found. An analytical link is proposed between the transient maximum amplitude and a fundamental dimensionless parameter which combines the damping ratio, natural frequency, acceleration, and engine order of the system to reveal the mechanism of the transient maximum amplitude. Therefore, the transient maximum amplitudes of tuned and mistuned blisks are predicted analytically. First, a lumped parameter model is used to study the mechanism of the transient maximum amplitude for a tuned blisk, and an approximated analytical expression is derived between the fundamental parameter and the transient amplification factor of a 1DOF (degree-of-freedom) model. The relationship is also applicable to a reduced order, tuned finite element model (FEM). Second, the mechanism of the transient response for a mistuned blisk is studied in the decoupled modal space of the blisk, based on the 1DOF transient relationship. The transient maximum amplitude in a reduced order, mistuned FEM is predicted. Two lumped parameter models and a FEM are employed to validate the prediction.
Issue Section:
Research Papers
Topics:
Transients (Dynamics)
References
1.
Lewis
,
F. M.
, 1932
, “
Vibration During Acceleration Through a Critical Speed
,” ASME J. Appl. Mech.
,
54
, pp. 258
–261
.https://ci.nii.ac.jp/naid/10024045228/2.
Vyas
,
N.
, and
Rao
,
J.
, 1994
, “
Fatigue Life Estimation Procedure for a Turbine Blade Under Transient Loads
,” ASME J. Eng. Gas Turbines Power
,
116
(1
), pp. 198
–206
.10.1115/1.29067923.
Hartung
,
A.
, 2010
, “
A Numerical Approach for the Resonance Passage Computation
,” ASME
Paper No. GT2010-22051.10.1115/GT2010-220514.
Fricker
,
A.
, and
Potter
,
S.
, 1981
, “
Transient Forced Vibration of Rotationally Periodic Structures
,” Int. J. Numer. Meth. Eng.
,
17
(7
), pp. 957
–974
.10.1002/nme.16201707035.
Hackenberg
,
H.-P.
, and
Hartung
,
A.
, 2016
, “
An Approach for Estimating the Effect of Transient Sweep Through a Resonance
,” ASME J. Eng. Gas Turbines Power
,
138
(8
), p. 082502
.10.1115/1.40326646.
Castanier
,
M. P.
, and
Pierre
,
C.
, 2006
, “
Modeling and Analysis of Mistuned Bladed Disk Vibration: Current Status and Emerging Directions
,” J. Propul Power
,
22
(2
), pp. 384
–396
.10.2514/1.163457.
Whitehead
,
D. S.
, 1996
, “
The Maximum Factor by Which Forced Vibration of Blades Can Increase Due to Mistuning
,” ASME
Paper No. 96-GT-125.10.1115/96-GT-1258.
Petrov
,
E.
,
Sanliturk
,
K.
, and
Ewins
,
D.
, 2002
, “
A New Method for Dynamic Analysis of Mistuned Bladed Disks Based on the Exact Relationship Between Tuned and Mistuned Systems
,” ASME J. Eng. Gas Turbines Power
,
124
(3
), pp. 586
–597
.10.1115/1.14517539.
Bladh
,
R.
,
Pierre
,
C.
,
Castanier
,
M.
, and
Kruse
,
M.
, 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
.10.1115/1.144723610.
Petrov
,
E.
,
Di Mare
,
L.
,
Hennings
,
H.
, and
Elliott
,
R.
, 2010
, “
Forced Response of Mistuned Bladed Disks in Gas Flow: A Comparative Study of Predictions and Full-Scale Experimental Results
,” ASME J. Eng. Gas Turbines Power
,
132
(5
), p. 052504
.10.1115/1.320503111.
Whitehead
,
D.
, 1966
, “
Effect of Mistuning on the Vibration of Turbo-Machine Blades Induced by Wakes
,” Proc. Inst. Mech. Eng., Part C
,
8
(1
), pp. 15
–21
.10.1243/JMES_JOUR_1966_008_004_0212.
Kenyon
,
J. A.
,
Griffin
,
J. H.
, and
Feiner
,
D. M.
, 2003
, “
Maximum Bladed Disk Forced Response From Distortion of a Structural Mode
,” ASME J. Turbomach.
,
125
(2
), pp. 352
–363
.10.1115/1.154011813.
Bladh
,
R.
, 2001
, “
Efficient Predictions of the Vibratory Response of Mistuned Bladed Disks by Reduced Order Modeling
,” Ph.D. thesis
,
Department of Mechanical Engineering, University of Michigan
, Ann Arbor, MI.https://www.researchgate.net/publication/30514250_Efficient_predictions_of_the_vibratory_response_of_mistuned_bladed_disks_by_reduced_order_modeling14.
Chan
,
Y.-J.
, and
Ewins
,
D.
, 2011
, “
The Amplification of Vibration Response Levels of Mistuned Bladed Disks: Its Consequences and Its Distribution in Specific Situations
,” ASME J. Eng. Gas Turbines Power
,
133
(10
), p. 102502
.10.1115/1.400302115.
Martel
,
C.
, and
Corral
,
R.
, 2009
, “
Asymptotic Description of Maximum Mistuning Amplification of Bladed Disk Forced Response
,” ASME J. Eng. Gas Turbines Power
,
131
(2
), p. 022506
.10.1115/1.296886816.
Hemberger
,
D.
,
Filsinger
,
D.
, and
Bauer
,
H.-J.
, 2012
, “
Investigations on Maximum Amplitude Amplification Factor of Real Mistuned Bladed Structures
,” ASME
Paper No. GT2012-68084.10.1115/GT2012-6808417.
Ayers
,
J.
,
Feiner
,
D.
, and
Griffin
,
J.
, 2006
, “
A Reduced-Order Model for Transient Analysis of Bladed Disk Forced Response
,” ASME J. Turbomach.
,
128
(3
), pp. 466
–473
.10.1115/1.218567518.
Siewert
,
C.
, and
Stüer
,
H.
, 2017
, “
Transient Forced Response Analysis of Mistunedsteam Turbine Blades During Startup and Coastdown
,” ASME J. Eng. Gas Turbines Power
,
139
(1
), p. 012501
.10.1115/1.403415119.
Kaneko
,
Y.
, 2013
, “
Study on Transient Vibration of Mistuned Bladed Disk Passing Through Resonance
,” ASME
Paper No. GT2013-94052.10.1115/GT2013-9405220.
Bonhage
,
M.
,
Pohle
,
L.
,
Panning-von Scheidt
,
L.
, and
Wallaschek
,
J.
, 2015
, “
Transient Amplitude Amplification of Mistuned Blisks
,” ASME J. Eng. Gas Turbines Power
,
137
(11
), p. 112502
.10.1115/1.403027821.
Bonhage
,
M.
,
Adler
,
J. T.
,
Kolhoff
,
C.
,
Hentschel
,
O.
,
Schlesier
,
K.-D.
,
Panning-von Scheidt
,
L.
, and
Wallaschek
,
J.
, 2018
, “
Transient Amplitude Amplification of Mistuned Structures: An Experimental Validation
,” J. Sound Vib.
,
436
, pp. 236
–252
.10.1016/j.jsv.2018.07.03122.
Schlesier
,
K.-D.
,
Panning-von Scheidt
,
L.
, and
Wallaschek
,
J.
, 2018
, “
Investigations on Transient Amplitude Amplification by Applying Intentional Mistuning
,” ASME
Paper No. GT2018-75514.10.1115/GT2018-7551423.
Carassale
,
L.
,
Marrè-Brunenghi
,
M.
, and
Patrone
,
S.
, 2016
, “
Modal Identification of Dynamically Coupled Bladed Disks in Run-Up Tests
,” ASME
Paper No. GT2016-57251.10.1115/GT2016-5725124.
Markert
,
R.
, and
Seidler
,
M.
, 2001
, “
Analytically Based Estimation of the Maximum Amplitude During Passage Through Resonance
,” Int. J. Solids Struct.
,
38
(10–13
), pp. 1975
–1992
.10.1016/S0020-7683(00)00147-525.
Abramowitz
,
M.
, and
Stegun
,
I. A.
, 1965
, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables
, Vol.
55
,
Courier Corporation
, Chelmsford, MA, p. 308
.26.
Leul
,
F.
, 1994
, “
Zum Transienten Schwingungsverhalten Beim Resonanzdurchgang Linearer Systeme Mit Langsam Veranderlichen a Parametern
,” Bericht des Instituts fur Mechanik der Universitat-GH Kassl, Kassel, Germany, pp. 18
–29
.27.
Abrarov
,
S.
, and
Quine
,
B.
, 2016
, “
A New Application Methodology of the Fourier Transform for Rational Approximation of the Complex Error Function
,” J. Math. Res.
,
8
(1
), pp. 14
–23
.10.5539/jmr.v8n1p1428.
Mignolet
,
M. P.
,
Rivas-Guerra
,
A.
, and
Delor
,
J.
, 2001
, “
Identification of Mistuning Characteristics of Bladed Disks From Free Response Data—Part I
,” ASME J. Eng. Gas Turbines Power
,
123
(2
), pp. 395
–403
.10.1115/1.133894929.
Figaschewsky
,
F.
, and
Kühhorn
,
A.
, 2015
, “
Analysis of Mistuned Blade Vibrations Based on Normally Distributed Blade Individual Natural Frequencies
,” ASME
Paper No. GT2015-43121.10.1115/GT2015-4312130.
Feiner
,
D. M.
, and
Griffin
,
J.
, 2002
, “
A Fundamental Model of Mistuning for a Single Family of Modes
,” ASME J. Turbomach.
,
124
(4
), pp. 597
–605
.10.1115/1.1508384Copyright © 2020 by ASME
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