The geometric mistuning problem is investigated for dual flow-path integrally bladed rotors (DFIBRs) by outlining two methods that explicitly account for blade geometry surface deviations. The methods result in reduced-order models (ROMs) that are a reduced form of a parent Craig–Bampton component mode synthesis (CB-CMS) model. This is accomplished by performing a secondary modal analysis on different degrees of freedom (DOF) of the parent model. The DFIBR is formulated in cyclic symmetry coordinates with a tuned disk and ring and blades with small geometric deviations. The first method performs an eigen-analysis on the constraint DOF that provides a truncated set of interface modes, while the second method includes the disk and ring fixed interface normal mode in the eigen-analysis to yield a truncated set of ancillary modes. Utilization of tuned modes have the benefit of being solved in cyclic symmetry coordinates and only need to be calculated once, which offers significant computational savings for subsequent mistuning studies. Each geometric mistuning method relies upon the use of geometrically mistuned blade modes in the component mode framework to provide an accurate ROM. Forced response results are compared to both the full finite element model (FEM) solutions and a traditional frequency-based approach outlined in a previous effort. It is shown that the models provide highly accurate results with a significant reduction in solution time compared to the full FEM and parent ROM.

References

References
1.
Beck
,
J. A.
,
Slater
,
J. C.
,
Brown
,
J. M.
,
Scott-Emuakpor
,
O. E.
, and
Cross
,
C. J.
,
2014
, “
Dynamic Response Characteristics of Dual Flow-Path Integrally Bladed Rotors
,”
52nd Aerospace Sciences Meeting
, National Harbor, MD, Jan. 13–17,
AIAA
Paper No. 2014-0098, pp.
1131
1146
.10.2514/6.2014-0098
2.
Castanier
,
M.
,
Ottarsson
,
G.
, and
Pierre
,
C.
,
1997
, “
A Reduced Order Modeling Technique for Mistuned Bladed Disks
,”
ASME J. Vib. Acoust.
,
119
(
3
), pp.
439
447
.10.1115/1.2889743
3.
Yang
,
M.-T.
, and
Griffin
,
J.
,
2001
, “
A Reduced-Order Model of Mistuning Using a Subset of Nominal System Modes
,”
ASME J. Gas Turbines Power
,
123
(
4
), pp.
893
900
.10.1115/1.1385197
4.
Yang
,
M.-T.
, and
Griffin
,
J. H.
,
1997
, “
A Reduced Order Approach for the Vibration of Mistuned Bladed Disk Assemblies
,”
ASME J. Gas Turbines Power
,
119
(
1
), pp.
161
167
.10.1115/1.2815542
5.
Feiner
,
D.
, and
Griffin
,
J.
,
2002
, “
A Fundamental Model of Mistuning for a Single Family of Modes
,”
ASME J. Turbomach.
,
124
(
4
), pp.
597
605
.10.1115/1.1508384
6.
Bladh
,
R.
,
Castanier
,
M. P.
, and
Pierre
,
C.
,
2001
, “
Component-Mode-Based Reduced Order Modeling Techniques for Mistuned Bladed Disks—Part 1: Theoretical models
,”
ASME J. Gas Turbines Power
,
123
(
1
), pp.
89
99
.10.1115/1.1338947
7.
Vargiu
,
P.
,
Firrone
,
C.
,
Zucca
,
S.
, and
Gola
,
M.
,
2011
, “
A Reduced Order Model Based on Sector Mistuning for the Dynamic Analysis of Mistuned Bladed Disks
,”
Int. J. Mech. Sci.
,
53
(
8
), pp.
639
646
.10.1016/j.ijmecsci.2011.05.010
8.
Lim
,
S.-H.
,
Bladh
,
R.
,
Castanier
,
M.
, 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
9.
Tran
,
D.-M.
,
2009
, “
Component Mode Synthesis Methods Using Partial Interface Modes: Application to Tuned and Mistuned Structures With Cyclic Symmetry
,”
Comput. Structures
,
87
(
17–18
), pp.
1141
1153
.10.1016/j.compstruc.2009.04.009
10.
Yang
,
M.-T.
, and
Griffin
,
J.
,
1997
, “
Normalized Modal Eigenvalue Approach for Resolving Modal Interaction
,”
ASME J. Gas Turbines Power
,
119
(
3
), pp.
647
650
.10.1115/1.2817033
11.
Beck
,
J. A.
,
Brown
,
J. M.
,
Slater
,
J. C.
, and
Cross
,
C. J.
,
2012
, “
Probabilistic Mistuning Assessment Using Nominal and Geometry Based Mistuning Methods
,”
ASME
Paper No. GT2012-68533.10.1115/GT2012-68533
12.
Lim
,
S.-H.
,
Castanier
,
M.
, and
Pierre
,
C.
,
2004
, “
Vibration Modeling of Bladed Disks Subject to Geometric Mistuning and Design Changes
,”
45th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
, Palm Springs, CA, April 19–22,
AIAA
Paper No. 2004-1686.10.2514/6.2004-1686
13.
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. Gas Turbines Power
,
124
(
3
), pp.
586
597
.10.1115/1.1451753
14.
Brown
,
J. M.
,
2009
, “
Reduced Order Modeling Methods for Turbomachinery Design
,” Ph.D. thesis, Wright State University, Dayton, OH.
15.
Sinha
,
A.
,
2009
, “
Reduced-Order Model of a Bladed Rotor With Geometric Mistuning
,”
ASME J. Turbomach.
,
131
(
3
), p.
031007
.10.1115/1.2987237
16.
Bhartiya
,
Y.
, and
Sinha
,
A.
,
2012
, “
Reduced Order Model of a Multistage Bladed Rotor With Geometric Mistuning Via Modal Analyses of Finite Element Sectors
,”
ASME J. Turbomach.
,
134
(
4
), p.
041001
.10.1115/1.4003224
17.
Ganine
,
V.
,
Legrand
,
M.
,
Michalska
,
H.
, and
Pierre
,
C.
,
2009
, “
A Sparse Preconditioned Iterative Method for Vibration Analysis of Geometrically Mistuned Bladed Disks
,”
Comput. Struct.
,
87
(
5–6
), pp.
342
354
.10.1016/j.compstruc.2008.12.011
18.
Mbaye
,
M.
,
Soize
,
C.
, and
Ousty
,
J.-P.
,
2010
, “
A Reduced-Order Model of Detuned Cyclic Dynamical Systems With Geometric Modifications Using a Basis of Cyclic Modes
,”
ASME J. Gas Turbines Power
,
132
(
11
), p.
112502
.10.1115/1.4000805
19.
Craig
,
R. R.
, and
Bampton
,
M. C. C.
,
1968
, “
Coupling of Substructures for Dynamic Analysis
,”
AIAA J.
,
6
(
7
), pp.
1313
1319
.10.2514/3.4741
20.
Beck
,
J. A.
,
Slater
,
J. C.
,
Brown
,
J. M.
, and
Cross
,
C. J.
,
2014
, “
Component Mode Reduced Order Models for Geometric Mistuning of Integrally Bladed Rotors
,”
AIAA J.
,
52
(
7
), pp.
1345
1356
.10.2514/1.J052420
21.
Fortescue
,
C. L.
,
1918
, “
Method of Symmetrical Co-Ordinates Applied to the Solution of Polyphase Networks
,”
Trans. Am. Inst. Electr. Eng.
,
XXXVII
(
2
), pp.
1027
1140
.10.1109/T-AIEE.1918.4765570
22.
Garzon
,
V. E.
, and
Darmofal
,
D. L.
,
2003
, “
Impact of Geometric Variability on Axial Compressor Performance
,”
ASME J. Turbomach.
,
125
(
4
), pp.
692
703
.10.1115/1.1622715
23.
Brown
,
J. M.
, and
Grandhi
,
R. V.
,
2008
, “
Reduced-Order Model Development for Airfoil Forced Response
,”
Int. J. Rotating Mach.
,
2008
, p. 387828.10.1155/2008/387828
24.
Sinha
,
A.
,
Hall
,
B.
,
Cassenti
,
B.
, and
Hilbert
,
G.
,
2008
, “
Vibratory Parameters of Blades From Coordinate Measurement Machine Data
,”
ASME J. Turbomach.
,
130
(
1
), p.
011013
.10.1115/1.2749293
You do not currently have access to this content.