Among the major concerns for high aspect-ratio, turbine blades are forced and self-excited (flutter) vibrations, which can cause failure by high-cycle fatigue (HCF). The introduction of friction damping in turbine blades, such as by coupling of adjacent blades via under platform dampers, can lead to a significant reduction of resonance amplitudes at critical operational conditions. In this paper, the influence of basic geometric blade design parameters onto the damped system response will be investigated to link design parameters with functional parameters like damper normal load, frequently used in nonlinear dynamic analysis. The shape of a simplified turbine blade is parameterized along with the under platform damper configuration. The airfoil is explicitly included into the parameterization in order to account for changes in blade mode shapes. For evaluation of the damped system response, a reduced-order model for nonlinear friction damping is included into an automated three-dimensional (3D) finite element analysis (FEA) tool-chain. Based on a design of experiments approach, the design space will be sampled and surrogate models will be trained on the received dataset. Subsequently, the mean and interaction effects of the geometric design parameters onto the resonance amplitude and safety against HCF will be outlined. The HCF safety is found to be affected by strong secondary effects onto static and resonant vibratory stress levels. Applying an evolutionary optimization algorithm, it is shown that the optimum blade design with respect to minimum vibratory response can differ significantly from a blade designed toward maximum HCF safety.

References

References
1.
Petrov
,
E. P.
,
2003
, “
Method for Direct Parametric Analysis of Nonlinear Forced Response of Bladed Disks With Friction Contact Interfaces
,”
ASME J. Turbomach.
,
126
(
4
), pp. 654–662.
2.
Yang
,
B. D.
, and
Menq
,
C. H.
,
1996
, “
Modeling of Friction Contact and Its Application to the Design of Shroud Contact
,”
ASME
Paper No. 96-GT-472.
3.
Csaba
,
G.
,
1998
, “
Forced Response Analysis in Time and Frequency Domains of a Tuned Bladed Disk With Friction Dampers
,”
J. Sound Vib.
,
214
(
3
), pp.
395
412
.
4.
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
.
5.
Battiato, G.
,
Firrone, C.
,
Berruti, T.
, and
Epureanu, B.
, 2017, “
Reduced Order Modeling for Multi-Stage Bladed Disks With Friction Contacts at the Flange Joint
,”
ASME
Paper No. GT2017-64814.
6.
Cigeroglu
,
E.
, and
Özgüven
,
H. N.
,
2006
, “
Nonlinear Vibration Analysis of Bladed Disks With Dry Friction Dampers
,”
J. Sound Vib.
,
295
(
3–5
), pp. 1028–1043.
7.
Hohl
,
A.
,
Siewert
,
C.
,
Panning
,
L.
, and
Kayser
,
A.
,
2008
, “
Nonlinear Vibration Analysis of Gas Turbine Bladings With Shroud Coupling
,”
ASME
Paper No. GT2008-50787.
8.
Krack
,
M.
,
Salles
,
L.
, and
Thouverez
,
F.
,
2016
, “
Vibration Prediction of Bladed Disks Coupled by Friction Joints
,”
Arch. Comput. Methods Eng.
,
24
(
3
), pp. 589–636.
9.
Panning
,
L.
,
Sextro
,
W.
, and
Popp
,
K.
,
2004
, “
Optimization of the Contact Geometry Between Turbine Blades and Underplatform Dampers With Respect to Friction Damping
,”
ASME
Paper No. GT2002-30429.
10.
Giridhar
,
R. K.
,
Ramaiah
,
P.
,
Krishnaiah
,
G.
, and
Barad
,
S.
,
2012
, “
Gas Turbine Blade Damper Optimization Methodology
,”
Adv. Acoust. Vib.
,
2012
, p. 316761.
11.
Cigeroglu
,
E.
,
An
,
N.
, and
Menq
,
C. H.
,
2009
, “
Forced Response Prediction of Constrained and Unconstrained Structures Coupled Through Frictional Contacts
,”
ASME J. Eng. Gas Turbines Power
,
131
(2), p. 022505.
12.
Krack
,
M.
,
Panning
,
L.
,
Siewert
,
C.
, and
Wallaschek
,
J.
,
2012
, “
Robust Design of Friction Interfaces of Bladed Disks With Respect to Parameter Uncertainties
,”
ASME
Paper No. GT2012-68578.
13.
Afzal
,
M. M.
,
Arteaga
,
I.
,
Kari
,
L. L.
, and
Kharyton
,
V. V.
,
2016
, “
Investigation of Damping Potential of Strip Damper on a Real Turbine Blade
,”
ASME
Paper No. GT2016-57230.
14.
Gastaldi
,
C.
, and
Gola
,
M. M.
,
2015
, “
A Random Sampling Strategy for Tuning Contact Parameters of Underplatform Dampers
,”
ASME
Paper No. GT2015-42834.
15.
Gastaldi
,
C.
, and
Gola
,
M. M.
,
2016
, “
Pre-Optimization of Asymmetrical Underplatform Dampers
,”
ASME
Paper No. GT2016-57359.
16.
Szwedowicz
,
J.
,
Mahler
,
A.
,
Hulme
,
C. J.
, and
Slowik
,
S.
,
2005
, “
Nonlinear Dynamic Analyses of a Gas Turbine Blade for Attainment of Reliable Shroud Coupling
,”
ASME
Paper No. GT2005-69062.
17.
Panning
,
L.
,
Sextro
,
W.
, and
Popp
,
K.
,
2000
, “
Optimization of Interblade Friction Damper Design
,”
ASME
Paper No. 2000-GT-0541.
18.
Panning
,
L.
,
Sextro
,
W.
, and
Popp
,
K.
,
2003
, “
Spatial Dynamics of Tuned and Mistuned Bladed Disk Assemblies With Cylindrical and Wedge Shaped Friction Dampers
,”
Int. J. Rotating Mach.
,
9
(
3
), pp. 219–228.
19.
Siewert
,
C.
,
Panning
,
L.
,
Schmidt-Fellner
,
A.
, and
Kayser
,
A.
,
2006
, “
The Estimation of the Contact Stiffness for Directly and Indirectly Coupled Turbine Blading
,”
ASME
Paper No. GT2006-90473.
20.
Sextro
,
W.
,
2000
, “
The Calculation of the Forced Response of Shrouded Blades With Friction Contacts and Its Experimental Verification
,”
ASME
Paper No. 2000-GT-0540.
21.
Berruti
,
T.
,
Filippi
,
S.
,
Gola
,
M. M.
, and
Salvano
,
S.
,
2002
, “
Friction Damping of Interlocked Vane Segments: Validation of Friction Model and Dynamic Response
,”
ASME
Paper No. GT2002-30324.
22.
Asai
,
K.
, and
Gola
,
M. M.
,
2015
, “
Experimental Verification of Friction Behaviors Under Periodically-Varied Normal Force by Developing a Two-Directional Friction Test System
,”
ASME
Paper No. GT2015-42318.
23.
Gastaldi
,
C.
,
Grossi
,
E.
, and
Berruti
,
T.
,
2017
, “
On the Choice of Contact Parameters for the Forced Response Calculation of a Bladed Disk With Underplatform Dampers
,”
Global Power and Propulsion Forum (GPPF)
, Zurich, Switzerland, Jan. 16–18, Paper No. GPPF-2017-69.
24.
Cameron
,
T.
,
Griffin
,
J. H.
,
Kielb
,
R.
, and
Hoosac
,
T.
,
1990
, “
Integrated Approach for Friction Damper Design
,”
ASME J. Vib. Acoust.
,
112
(
2
), pp. 175–182.
25.
Tatzko
,
S.
,
Panning
,
L.
,
Schmidt-Fellner
,
A.
, and
Kayser
,
A.
,
2013
, “
Investigation of Alternate Mistuned Turbine Blades Non-Linear Coupled by Underplatform Dampers
,”
ASME
Paper No. GT2013-95681.
26.
Nichol
,
K. L.
,
2003
, “
Assessment of Current Turbine Engine High Cycle Fatigue Test Methods
,”
ASME J. Eng. Gas Turbines Power
,
125
(
3
), pp. 760–765.
27.
Siebertz
,
K.
,
Bebber
,
D.
, and
Hochkirchen
,
T.
,
2010
,
Statistische Versuchsplanung—Design of Experiments (Doe)
,
VDI Buch-Springer
,
Berlin
.
28.
Box
,
G.
, and
Behnken
,
D. W.
,
1960
, “
Some New Three Level Designs for the Study of Quantitative Variables
,”
Technometrics
,
2
(
4
), pp. 455–475.https://www.tandfonline.com/doi/abs/10.1080/00401706.1960.10489912
29.
Krige
,
D. G.
,
1951
, “
A Statistical Approach to Some Basic Mine Valuation Problems on the Witwatersrand
,”
J. Chem., Metall. Min. Soc. S. Afr.
,
52
(9), pp. 201–203.
30.
Ye
,
K. Q.
,
1993
, “
Orthogonal Column Latin Hypercubes and Their Application in Computer Experiments
,”
J. Am. Stat. Assoc.
,
93
(
444
), pp. 1430–1439.
31.
Petrov
,
E. P.
, and
Ewins
,
D. J.
,
2005
, “
Effects of Damping and Varying Contact Area at Blade-Disk Joints in Forced Response Analysis of Bladed Disk Assemblies
,”
ASME J. Turbomach.
,
128
(
2
), pp. 403–410.
32.
Deb
,
K.
,
Agrawal
,
S.
,
Pratap
,
A.
, and
Meyarivan
,
T.
,
2000
, “
A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II
,”
Parallel Problem Solving From Nature (PPSN VI)
, Springer, Berlin.
33.
Aulich
,
M.
, and
Siller
,
U.
,
2011
, “
High-Dimensional Constrained Multiobjective Optimization of a Fan Stage
,”
ASME
Paper No. GT2011-45618.
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