Abstract

Although the bladed disks of turbomachinery are nominally designed to be cyclically symmetric (tuned system), the vibration characteristics of individual blades on a disk vary slightly owing to manufacturing tolerances, deviations in material properties, wear during operation, etc. These small variations break the cyclic symmetry and split eigenvalue pairs. Actual bladed disks with small variations are called mistuned systems. The resonant stress on a mistuned bladed disk may become large and cause a blade failure due to high cycle fatigue. Especially for a bladed disk with a free-standing blade structure, it is essential to use a sufficiently large safety factor at the design stage, considering the mistuning effect. Traditionally, blade designers have adopted various countermeasures to reduce the resonant stress at the design stage. Besides the countermeasures adopted in blade design, for a variable speed engine, which cannot avoid resonance, it is thought that a practical optimization method for a mistuned system (bladed disk with a free-standing blade structure) is to sort the blades so that the resonant stress is minimized. In this study, a simultaneous method for optimizing the blade resonant stress and the amount of unbalance causing rotor vibration is proposed. In this method, first, the natural frequencies and weights of all blades on a disk are measured. Then, a mistuned system is assembled and the analysis model is generated. Next, the resonant stress and the amount of unbalance in the mistuned system are analyzed. To reduce the computation time, the reduced-order model known as fundamental mistuning model (FMM) is used to calculate the resonant stress in the mistuned system. The analyses of the resonant stress and the amount of unbalance are carried out repeatedly, sorting the blades on the disk, and the optimal solution is explored using Monte Carlo simulations (MCS) or discrete differential evolution (DDE). As an example, a mistuned bladed disk of an aero-engine was analyzed, and the validity of the proposed method was verified.

References

1.
Castanier
,
M. P.
, and
Pierre
,
C.
,
2006
, “
Modeling and Analysis of Mistuned Bladed Disk Vibrations: Status and Engineering Directions
,”
J. Propul. Power
,
22
(
2
), pp.
384
396
.10.2514/1.16345
2.
Petrov
,
E. P.
, and
Ewins
,
D. J.
,
2003
, “
Analysis of the Worst Mistuning Patterns in Bladed Disk Assemblies
,”
ASME J. Turbomach.
,
125
(
4
), pp.
623
631
.10.1115/1.1622710
3.
Srinivasan
,
A. V.
,
1997
, “
Flutter and Resonant Vibration Characteristics of Engine Blades
,”
ASME J. Eng. Gas Turbines Power
,
119
(
4
), pp.
742
775
.10.1115/1.2817053
4.
Gallus
,
H. E.
,
Grollius
,
H.
, and
Lambertz
,
J.
,
1982
, “
The Influence of Blade Number Ratio and Blade Row Spacing on Axial-Flow Compressor Stator Blade Dynamic Load and Stage Sound Pressure Level
,”
ASME J. Eng. Power
,
104
(
3
), pp.
633
641
.10.1115/1.3227326
5.
Hoyningen-Heune
,
M.
, and
Hermeler
,
J.
,
1999
, “
Time-Resolved Numerical Analysis of the 2-D Aerodynamics in the First Stage of an Industrial Gas Turbine for Different Vane-Blade Spacing
,”
ASME
Paper No. 99-GT-102
. 10.1115/1999-GT-102
6.
Hsu
,
S. T.
, and
Wo
,
A. M.
,
1998
, “
Reduction of Unsteady Blade Loading by Beneficial Use of Vortical and Potential Disturbance in an Axial Compressor With Rotor Clocking
,”
ASME J. Turbomach.
,
120
(
4
), pp.
705
713
.10.1115/1.2841781
7.
Benini
,
E.
, and
Toffolo
,
A.
,
2002
, “
Towards a Reduction of Compressor Blade Dynamic Loading by Means of Rotor-Stator Interaction Optimization
,”
ASME
Paper No. GT-2002-30396.10.1115/GT2002-30396
8.
Kaneko
,
Y.
,
Mori
,
K.
, and
Okui
,
H.
,
2004
, “
Study on the Effect of Asymmetric Vane Spacing on Vibratory Stress of Blade
,”
ASME
Paper No. GT2004-53023.10.1115/GT2004-53023
9.
Sun
,
T.
,
Hou
,
A.
,
Zhang
,
M.
,
Niu
,
Y.
,
Gao
,
J.
, and
Guo
,
H.
,
2015
, “
Analysis of the Reduction of Rotor Blade Vibration Using Asymmetry Vane Spacing
,”
ASME
Paper No. GT2015-42778
. 10.1115/GT2015-42778
10.
Cigeroglu
,
E.
,
An
,
H.
, and
Menq
,
C.-H.
,
2007
, “
Wedge Damper Modeling and Forced Response Prediction of Frictionally Constrained Blades
,”
ASME
Paper No. GT2007-27963.10.1115/GT2007-27963
11.
Petrov
,
E. P.
,
2011
, “
A High-Accuracy Model Reduction for Analysis of Nonlinear Vibrations in Structures With Contact Interfaces
,”
ASME J. Eng. Gas Turbines Power
,
133
(
10
), p.
102503
.10.1115/1.4002810
12.
Han
,
Y.
,
Murthy
,
R.
,
Mignolet
,
M. P.
, and
Lentz
,
J.
,
2014
, “
Optimization of Intentional Mistuning Patterns for the Mitigation of the Effects of Random Mistuning
,”
ASME J. Eng. Gas Turbines Power
,
136
(
6
), pp.
1
9
.10.1115/1.4026141
13.
Hohl
,
A.
, and
Wallaschek
,
J.
,
2016
, “
A Method to Reduce the Energy Localization in Mistuned Bladed Disks by Application—Specific Blade Pattern Arrangement
,”
ASME J. Eng. Gas Turbines Powers
,
138
(
9
), pp.
1
10
.10.1115/1.4032739
14.
Kaneko
,
Y.
,
Mori
,
K.
, and
Ooyama
,
H.
,
2018
, “
Practical Optimization of Mistuned Bladed Disk of Steam Turbine With Free-Standing Blade Structure for Forced and Self-Excited Vibration
,”
ASME
Paper No. GT2018-75056.10.1115/GT2018-75056
15.
Feiner
,
D. M.
, and
Griffin
,
J. H.
,
2002
, “
A Fundamental Model of Mistuning for a Single Family of Modes
,”
ASME, J. Turbomach.
,
124
(
4
), pp.
597
605
.10.1115/1.1508384
16.
Feiner
,
D. M.
, and
Griffin
,
J. H.
,
2003
, “
Mistuning Identification of Bladed Disks Using a Fundamental Mistuning Model-Part 1: Theory
,”
ASME
Paper No. GT2003-38952
. 10.1115/GT2003-38952
17.
Kaneko
,
Y.
,
Mori
,
K.
, and
Ooyama
,
H.
,
2015
, “
Resonant Response and Random Response Analysis of Mistuned Bladed Disk Consisting of Directionally Solidified Blade
,”
ASME
Paper No. GT2015-42875
.10.1115/GT2015-42875
18.
Kitayama
,
S.
,
Arakawa
,
M.
, and
Yamazaki
,
K.
,
2010
, “
Proposal of Discrete Differential Evolution
,”
Trans. Jpn. Soc. Mech. Eng., Ser. C
,
76
(
772
), pp.
2965
2970
(in Japanese).
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