The purpose of this paper is to propose an effective strategy for the design of turbine blades with underplatform dampers (UPDs). The strategy involves damper “pre-optimization,” already proposed by the authors, to exclude, before the blades-coupled nonlinear calculation, all those damper configurations leading to low damping performance. This paper continues this effort by applying pre-optimization to determine a damper configuration which will not jam, roll, or detach under any in-plane platform kinematics (i.e., blade bending modes). Once the candidate damper configuration has been found, the damper equilibrium equations are solved by using both the multiharmonic balance method (MHBM) and the direct-time integration (DTI) for the purpose of finding the correct number of Fourier terms to represent displacements and contact forces. It is shown that contrarily to non-preoptimized dampers, which may display an erratic behavior, one harmonic term together with the static term ensures accurate results. These findings are confirmed by a state-of-the-art code for the calculation of the nonlinear forced response of a damper coupled to two blades. Experimental forced response functions (FRF) of the test case with a nominal damper are available for comparison. The comparison of different damper configurations offers a “high-level” validation of the pre-optimization procedure and highlights the strong influence of the blades mode of vibration on the damper effectiveness. It is shown that the pre-optimized damper is not only the most effective but also the one that leads to a faster and more flexible calculation.

References

References
1.
Griffin
,
J. H.
,
1980
, “
Friction Damping of Resonant Stresses in Gas Turbine Engine Airfoils
,”
ASME J. Eng. Power
,
102
(
2
), pp.
329
333
.
2.
Srinvasan
,
A. V.
, and
Cutts
,
D. G.
,
1983
, “
Dry Friction Damping Mechanisms in Engine Blades
,”
ASME J. Eng. Power
,
105
(
2
), pp.
332
341
.
3.
Cameron
,
T. M.
,
Griffin
,
J. H.
,
Kielb
,
R. E.
, and
Hoosac
,
T. M.
,
1990
, “
An Integrated Approach for Friction Damper Design
,”
ASME J. Vib. Acoust.
,
112
(
2
), pp.
175
182
.
4.
Sanliturk
,
K. Y.
,
Ewins
,
D. J.
, and
Stanbridge
,
A. B.
,
2001
, “
Underplatform Dampers for Turbine Blades: Theoretical Modeling, Analysis, and Comparison With Experimental Data
,”
ASME J. Eng. Gas Turbines Power
,
123
(
4
), pp.
919
929
.
5.
Siewert
,
C.
,
Panning
,
L.
,
Wallaschek
,
J.
, and
Richter
,
C.
,
2010
, “
Multiharmonic Forced Response Analysis of a Turbine Blading Coupled by Nonlinear Contact Forces
,”
ASME J. Eng. Gas Turbines Power
,
132
(
8
), p.
082501
.
6.
Pennacchi
,
P.
,
Chatterton
,
S.
,
Bachschmid
,
N.
,
Pesatori
,
E.
, and
Turozzi
,
G.
,
2011
, “
A Model to Study the Reduction of Turbine Blade Vibration Using the Snubbing Mechanism
,”
Mech. Syst. Signal Process.
,
25
(
4
), pp.
1260
1275
.
7.
Berruti
,
T.
, and
Maschio
,
V.
,
2012
, “
Experimental Investigation on the Forced Response of a Dummy Counter-Rotating Turbine Stage With Friction Damping
,”
ASME J. Eng. Gas Turbines Power
,
134
(
12
), p.
122502
.
8.
Chen
,
J. J.
,
Yang
,
B. D.
, and
Menq
,
C. H.
,
2000
, “
Periodic Forced Response of Structures Having Three-Dimensional Frictional Constraints
,”
J. Sound Vib.
,
229
(
4
), pp.
775
792
.
9.
Berger
,
E.
,
2002
, “
Friction Modeling for Dynamic System Simulation
,”
ASME Appl. Mech. Rev.
,
55
(
6
), pp.
535
577
.
10.
Panning
,
L.
,
Sextro
,
W.
, and
Popp
,
K.
,
2003
, “
Spatial Dynamics of Tuned and Mistuned Bladed Disks With Cylindrical and Wedge-Shaped Friction Dampers
,”
Int. J. Rotating Mach.
,
9
(
3
), pp.
219
228
.
11.
Berruti
,
T.
,
Firrone
,
C. M.
,
Pizzolante
,
M.
, and
Gola
,
M. M.
,
2007
, “
Fatigue Damage Prevention on Turbine Blades: Study of Underplatform Damper Shape
,”
Key Eng. Mater.
,
347
, pp.
159
164
.
12.
Petrov
,
E. P.
, and
Ewins
,
D. J.
,
2007
, “
Advanced Modelling of Underplatform Friction Dampers for Analysis of Bladed Disk Vibration
,”
ASME J. Turbomach.
,
129
(
1
), pp.
143
150
.
13.
Petrov
,
E. P.
,
2008
, “
Explicit Finite Element Models of Friction Dampers in Forced Response Analysis of Bladed Discs
,”
ASME J. Eng. Gas Turbines Power
,
130
(
2
), p.
022502
.
14.
Cigeroglu
,
E.
,
An
,
N.
, and
Menq
,
C. H.
,
2008
, “
Forced Response Prediction of Constrained and Unconstrained Structures Coupled Through Frictional Contacts
,”
ASME J. Eng. Gas Turbines Power
,
131
(
2
), p.
022505
.
15.
Laxalde
,
D.
,
Thouverez
,
F.
, and
Lombard
,
J.-P.
,
2010
, “
Forced Response Analysis of Integrally Bladed Disks With Friction Ring Dampers
,”
ASME J. Vib. Acoust.
,
132
(
1
), p.
011013
.
16.
Firrone
,
C. M.
,
Zucca
,
S.
, and
Gola
,
M. M.
,
2011
, “
The Effect of Underplatform Dampers on the Forced Response of Bladed Disks by a Coupled Static/Dynamic Harmonic Balance Method
,”
Int. J. Non-Linear Mech.
,
46
(
2
), pp.
363
375
.
17.
Krack
,
M.
,
Salles
,
L.
, and
Thouverez
,
F.
,
2017
, “
Vibration Prediction of Bladed Disks Coupled by Friction Joints
,”
Arch. Comput. Methods Eng.
,
24
(
3
), pp.
589
636
.
18.
Pesaresi
,
L.
,
Salles
,
L.
,
Jones
,
A.
,
Green
,
J. S.
, and
Schwingshackl
,
C. W.
,
2017
, “
Modelling the Nonlinear Behaviour of an Underplatform Damper Test Rig for Turbine Applications
,”
Mech. Syst. Signal Process.
,
85
, pp.
662
679
.
19.
Gastaldi
,
C.
, and
Gola
,
M. M.
,
2016
, “
Pre-Optimization of Asymmetrical Underplatform Dampers
,”
ASME J. Eng. Gas Turbines Power
,
139
(
1
), p.
012504
.
20.
Lavella
,
M.
,
2016
, “
Contact Properties and Wear Behaviour of Nickel Based Superalloy René 80
,”
Metals
,
6
(
7
), p.
159
.
21.
Gastaldi
,
C.
, and
Gola
,
M. M.
,
2016
, “
On the Relevance of a Microslip Contact Model for Under-Platform Dampers
,”
Int. J. Mech. Sci.
,
115–116
, pp.
145
156
.
22.
Cardona
,
A.
,
Coune
,
T.
,
Lerusse
,
A.
, and
Geradin
,
M.
,
1994
, “
A Multiharmonic Method for Nonlinear Vibration Analysis
,”
Int. J. Numer. Methods Eng.
,
37
(
9
), pp.
1593
1608
.
23.
Zucca
,
S.
, and
Firrone
,
C. M.
,
2014
, “
Nonlinear Dynamics of Mechanical Systems With Friction Contacts: Coupled Static and Dynamic Multi-Harmonic Balance Method and Multiple Solution
,”
J. Sound Vib.
,
333
(
3
), pp.
916
926
.
24.
Gastaldi
,
C.
,
2017
, “
Vibration Control and Mitigation in Turbomachinery
,”
Ph.D. thesis
, Politecnico di Torino, Turin, Italy.
25.
Bessone
,
A.
, and
Toso
,
F.
,
2015
, “
Investigation on the Dynamic Response of Blades With Asymmetric Under Platform Dampers
,”
ASME
Paper No. GT2015-42597.
26.
Berruti
,
T.
,
2010
, “
A Test Rig for the Investigation of the Dynamic Response of a Bladed Disk With Underplatform Dampers
,”
Mech. Res. Commun.
,
37
(
6
), pp.
581
583
.
27.
Cameron
,
T.
, and
Griffin
,
I.
,
1989
, “
An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic System
,”
ASME J. Appl. Mech.
,
56
(
1
), pp.
149
154
.
28.
Botto, D.
,
Gastaldi, C.
,
Gola, M. M.
, and
Umer, M.
, 2017, “
An Experimental Investigation of the Dynamics of a Blade With Two Under-Platform Dampers
,”
ASME J. Eng. Gas Turbines Power
,
140
(3), p. 032504.
You do not currently have access to this content.