Abstract

Numerical predictions of the forced vibration of a disk assembly including frictional effects between the shrouds are presented concerning engineering needs for the blade design process. Assuming a tuned disk assembly, numerical static, free, and then forced vibration analyses of a shrouded turbine blade measured in the spin pit are performed systematically. For the excitation forces of an air jet evaluated from the fairly linear behavior of the experimental blade resonance peaks, the reliability of the proposed approach is validated through the very close agreement of the computed and measured resonant peaks. These resonant peaks demonstrate either a fairly linear behavior or a nonlinear one like the jump effect of blade resonance amplitudes, or elastic impacts between the shrouds. Also, the damping performance for different contact configurations between the shrouds is numerically analyzed. These numerical results indicate that the shrouds generate higher frictional damping for small angles (030deg) between the circumferential direction and the normal vector to the contact surface.

References

1.
Jacquet-Richardet
,
G.
,
Moyround
,
F.
, and
Fransson
,
T. H.
, 1997, “
An Influence of Shroud Design on the Dynamic and Aeroelastic Behavior of Bladed Disk Assemblies
,” ASME Paper No. 97-GT-191.
2.
Bladh
,
R.
,
Castanier
,
M. P.
, and
Pierre
,
C.
, 1999, “
Reduced Order Modeling and Vibration Analysis of Mistuned Bladed Disk Assemblies With Shrouds
,”
Trans. ASME: J. Eng. Gas Turbines Power
0742-4795,
121
, pp.
515
522
.
3.
Petrov
,
E. P.
, and
Ewins
,
D. J.
, 2001, “
Analysis of the Worst Mistuning Patterns in Bladed Disk Assemblies
,” ASME Paper No. 2001-GT-0292.
4.
Feiner
,
D. M.
, and
Griffin
,
J. H.
, 2002, “
A Fundamental Model of Mistuning for a Single Family of Modes
,” ASME Paper No. GT-2002–30425.
5.
Filsinger
,
D.
,
Szwedowicz
,
J.
, and
Schäfer
,
O.
, 2002, “
Approach to Unidirectional Coupled CFD-FEM Analysis of Axial Turbocharger Turbine Blades
,“
ASME J. Turbomach.
0889-504X,
124
, pp.
125
131
.
6.
Wang
,
J. H.
, and
Yau
,
H. Y.
, 1990, “
Design of Shroud Interface-Angle to Minimize the Forced Vibration of Blades
,” ASME Paper No. 90-GT-247.
7.
Wang
,
J. H.
, and
Yau
,
H. Y.
, 1990, “
Design of Blade-Shroud to Minimize the Sensitivity of Response to Preload Mistuning
,”
Proceedings of the 3rd International Conference on Rotordynamics
, Sept. 9–12,
Lyon, France
.
8.
Wang
,
J. H.
, and
Shieh
,
W. L.
, 1991, “
The Influence of Variable Friction Coefficient on the Dynamic Behaviors of Blade with Friction Damper
,”
J. Sound Vib.
0022-460X,
149
, pp.
137
145
.
9.
Wang
,
J. H.
, and
Chen
,
W. K.
, 1993, “
Investigation of a Blade with a Friction Damper by HBM
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
115
, pp.
294
299
.
10.
Petrov
,
E. P.
, and
Ewins
,
D. J.
, 2002, “
Analysis of Nonlinear Multiharmonic Vibrations of Bladed Disks with Friction and Impacts Dampers
,” in
Proceedings of the 7th National Turbine Engine High Cycle Fatigue (HCF) Conference
, May 14–17, Palm Beach Gardens, Florida.
11.
Sanliturk
,
K. Y.
,
Ewins
,
D. J.
, and
Stanbridge
,
A. B.
, 2001, “
Under-platform Dampers for Turbine Blades: Theoretical Modelling, Analysis and Comparison with Experimental Data
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
123
, pp.
919
929
.
12.
Sextro
,
W.
, 2002,
Dynamical Contact Problems with Friction—Models, Methods, Experiments and Applications
,
Habilitationsschrift, Lecture Notes in Applied Mechanics
, Vol.
3
,
Springer-Verlag
,
Heidelberg
.
13.
Gaul
,
L.
, and
Nitsche
,
R.
, 2001, “The Role of Friction in Mechanical Joints,”
Appl. Mech. Rev.
0003-6900,
54
(
2
), pp.
93
106
.
14.
Popp
,
K.
, 1994, “
Nichtlineare Schwingungen Mechanischer Strukturen mit Füge—oder Kontakt-stellen (Non-linear Vibration of Mechanical Structures with Grooves of Contacts)
,”
Z. Angew. Math. Mech.
0044-2267,
74
, pp.
147
165
.
15.
Griffin
,
J. H.
, 1990, “
A Review of Friction Damping of Turbine Blade Vibration
,”
Int. J. Turbo Jet Engines
0334-0082,
7
, pp.
297
307
.
16.
Griffin
,
J. H.
, and
Labelle
,
R. F.
, 1996, “
A Rational Method for Optimizing Shrouded Damping
,” ASME Paper No. 96-GT-402.
17.
Yang
,
B.-D.
, and
Menq
,
C.-H.
, Oct. 1997, “
Modeling of Friction Contact and Its Application to the Design of Shroud Contact
,”
ASME J. Eng. Gas Turbines Power
0742-4795,
119
, pp.
958
963
.
18.
ABAQUS/Standard, 2001,
User’s Manual
,
Hibbitt, Karlsson & Sorensen, Inc.
, Pawtucket, Vol.
1–3
, Version 6.3.
19.
Thomas
,
D. L.
, 1974, “
Standing Waves in Rotationally Periodic Structures
,”
J. Sound Vib.
0022-460X,
37
, pp.
288
290
.
20.
Szwedowicz
,
J.
, 1999, “
Cyclic Finite Element Modeling of Shrouded Turbine Blades Including Frictional Contact
,” ASME Paper No. 99-GT-92.
21.
Sextro
,
W.
, 2000, “
The Calculation of the Forced Response of Shrouded Blades with Friction Contacts and Its Experimental Verification
,” ASME Paper No. 2000-GT-540.
22.
Szwedowicz
,
J.
,
Kissel
,
M.
,
Ravindra
,
B.
, and
Kellerer
,
R.
, 2001, “
Estimation of Contact Stiffness and its Role in the Design of a Friction Damper
,” ASME Paper No. 2001-GT-290, New Orleans.
23.
Treyde
,
T.
, 1995,
Modellierung des Kontaktes zwischen den Deckplatten von Turbinen-schaufeln
(
Contact Modeling between Shrouds of Turbine Blades
), Fortschr.-Ber. VDI-Reihe 11, No. 224,
VDI-Verlag
,
Düsseldorf
.
24.
Cattaneo
,
C.
, 1938, “
Sul Contatto di Due Corpi Elastici: Distribuzione Locale degli Sforzi (On Contact between Elastic Bodies: Local Stress Distribution)
,”
Rend. Accad. Naz. Lincei
0392-7881,
27
(
6
), pp.
342
348
;
Cattaneo
,
C.
, 1938,
Rend. Accad. Naz. Lincei
0392-7881
27
(
6
), pp.
434
436
;
Cattaneo
,
C.
, 1938,
Rend. Accad. Naz. Lincei
0392-7881
27
(
6
),
474
478
.
25.
Mindlin
,
R. D.
, 1949, “
Compliance of Elastic Bodies in Contact
,”
ASME J. Appl. Mech.
0021-8936,
16
, pp.
259
268
.
26.
Mindlin
,
R. D.
,
Mason
,
W. P.
,
Osmer
,
J. F.
, and
Deresiewicz
,
H.
, 1952, “
Effects of an Oscillating Tangential Force on the Contact Surfaces of Elastic Spheres
,” in
ASME: 1st US National Congress of Applied Mechanics
,
Chicago, IL
, 1951, ASME, New York, pp.
203
208
.
27.
Gudmundson
,
P.
, and
Wuethrich
,
C.
, 1986, “
Die Werkstoffdämpfung von Stählen bei hohen Dehnungsamplituden (Damping of Steels at High Strain Amplitudes)
,”
Z. Werkstofftech.
0049-8688,
17
, pp.
286
292
.
28.
Schmidt
,
R.
, 1962, “
Resonanzverhalten und Schwingungsschierheit der Schaufel von Turbomaschinen (Resonance Behaviour and Vibration Security of Blade from Turbomachinery)
,“
Maschinenbautechnik
,
11
(
12
), pp.
630
637
.
29.
Kielb
,
J. J.
, and
Abhari
,
R. S.
, 2003, “
Experimental Study of Aerodynamic and Structural Damping in a Full-Scale Rotating Turbine
,”
Trans. ASME: J. Eng. Gas Turbines Power
0742-4795,
125
, pp.
102
112
.
30.
Abbott
,
E. J.
, and
Firestone
,
F. A.
, 1933, “
Specifying Surface Quality
,”
Mech. Eng. (Am. Soc. Mech. Eng.)
0025-6501,
55
, pp.
569
575
.
31.
DIN
, 1990, “
Measurement of Surface Roughness Parameters Rk, Rpk, Rvk, Mr1, Mr2 for the Description of the Material Position in the Roughness
,” German Standard, DIN 4776.
You do not currently have access to this content.