Abstract
This paper uses a recently derived reduction procedure to study the contact interactions of an industrial blade undergoing large displacements. The reduction technique consists in projecting the dynamical problem onto a reduction basis composed of Craig–Bampton modes and a selection of their modal derivatives. The internal nonlinear forces due to large displacements are evaluated with the stiffness evaluation procedure and contact is numerically handled using Lagrange multipliers. The numerical strategy is applied on an open industrial compressor blade model based on the NASA rotor 37 blade in order to promote the reproducibility of results. Two contact scenarios are investigated: one with direct contact between the blade and the casing and one with an abradable material deposited on the casing. The influence of geometric nonlinearities is assessed in both cases. In particular, contact interaction maps and abradable coating wear pattern maps are used to identify the main interactions that can be detrimental to the engine integrity.
Issue Section:
Research Papers
References
1.
Sakulkaew
,
S.
,
Tan
,
C. S.
,
Donahoo
,
E.
,
Cornelius
,
C.
, and
Montgomery
,
M.
, 2013
, “
Compressor Efficiency Variation With Rotor Tip Gap From Vanishing to Large Clearance
,” ASME J. Turbomach.
,
135
(3
), p. 031030. 10.1115/1.40075472.
Piollet
,
E.
,
Nyssen
,
F.
, and
Batailly
,
A.
, 2019
, “
Blade/Casing Rubbing Interactions in Aircraft Engines: Numerical Benchmark and Design Guidelines Based on NASA Rotor 37
,” J. Sound Vib.
,
460
, p. 114878
.10.1016/j.jsv.2019.1148783.
Nyssen
,
F.
,
Tableau
,
N.
,
Lavazec
,
D.
, and
Batailly
,
A.
, 2020
, “
Experimental and Numerical Characterization of a Ceramic Matrix Composite Shroud Segment Under Impact Loading
,” J. Sound Vib.
,
467
, p. 115040
.10.1016/j.jsv.2019.1150404.
Yi
,
M.
,
He
,
J.
,
Huang
,
B.
, and
Zhou
,
H.
, 1999
, “
Friction and Wear Behaviour and Abradability of Abradable Seal Coating
,” Wear
,
231
(1
), pp. 47
–53
.10.1016/S0043-1648(99)00093-95.
Ma
,
X.
, and
Matthews
,
A.
, 2007
, “
Investigation of Abradable Seal Coating Performance Using Scratch Testing
,” Surf. Coat. Technol.
,
202
(4–7
), pp. 1214
–1220
.10.1016/j.surfcoat.2007.07.0766.
Vakakis
,
A. F.
, 1992
, “
Dynamics of a Nonlinear Periodic Structure With Cyclic Symmetry
,” Acta Mech.
,
95
(1–4
), pp. 197
–226
.10.1007/BF011708137.
Grolet
,
A.
, and
Thouverez
,
F.
, 2011
, “
Vibration Analysis of a Nonlinear System With Cyclic Symmetry
,” ASME J. Eng. Gas Turbines Power
,
133
(2
), p. 022502
.10.1115/1.40019898.
Picou
,
A.
,
Capiez-Lernout
,
E.
,
Soize
,
C.
, and
Mbaye
,
M.
, 2019
, “
Mistuning Analysis of a Detuned Bladed-Disk With Geometrical Nonlinearities
,” ASME
Paper No. GT2019-90820.10.1115/GT2019-908209.
Balmaseda
,
M.
,
Jacquet-Richardet
,
G.
,
Placzek
,
A.
, and
Tran
,
D.-M.
, 2019
, “
Reduced Order Models for Nonlinear Dynamic Analysis With Application to a Fan Blade
,” ASME
Paper No. GT2019-90813.10.1115/GT2019-9081310.
Di Palma
,
N.
,
Martin
,
A.
,
Thouverez
,
F.
, and
Courtier
,
V.
, 2019
, “
Nonlinear Harmonic Analysis of a Blade Model Subjected to Large Geometrical Deflection and Internal Resonance
,” ASME
Paper No. GT2019-91213.10.1115/GT2019-9121311.
Kerschen
,
G.
,
Golinval
,
J.-C.
,
Vakakis
,
A. F.
, and
Bergman
,
L. A.
, 2005
, “
The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview
,” Nonlinear Dyn.
,
41
(1–3
), pp. 147
–169
.10.1007/s11071-005-2803-212.
Weeger
,
O.
,
Wever
,
U.
, and
Simeon
,
B.
, 2016
, “
On the Use of Modal Derivatives for Nonlinear Model Order Reduction
,” Int. J. Numer. Methods Eng.
,
108
(13
), pp. 1579
–1602
.10.1002/nme.526713.
Wu
,
L.
, and
Tiso
,
P.
, 2016
, “
Nonlinear Model Order Reduction for Flexible Multibody Dynamics: A Modal Derivatives Approach
,” Multibody Syst. Dyn.
,
36
(4
), pp. 405
–425
.10.1007/s11044-015-9476-514.
Longobardi
,
P.
, 2019
, “
Model Order Reduction for Nonlinear Vibrations of Geometrically Nonlinear Structures
,” Master thesis,
Politecnico di Torino
,
Italy
.15.
Joannin
,
C.
,
Chouvion
,
B.
,
Thouverez
,
F.
,
Ousty
,
J.-P.
, and
Mbaye
,
M.
, 2017
, “
A Nonlinear Component Mode Synthesis Method for the Computation of Steady-State Vibrations in Non-Conservative Systems
,” Mech. Syst. Signal Process.
,
83
, pp. 75
–92
.10.1016/j.ymssp.2016.05.04416.
Joannin
,
C.
,
Thouverez
,
F.
, and
Chouvion
,
B.
, 2018
, “
Reduced-Order Modelling Using Nonlinear Modes and Triple Nonlinear Modal Synthesis
,” Comput. Struct.
,
203
, pp. 18
–33
.10.1016/j.compstruc.2018.05.00517.
Capiez-Lernout
,
E.
,
Soize
,
C.
, and
Mignolet
,
M. P.
, 2012
, “
Computational Stochastic Statics of an Uncertain Curved Structure With Geometrical Nonlinearity in Three-Dimensional Elasticity
,” Comput. Mech.
,
49
(1
), pp. 87
–97
.10.1007/s00466-011-0629-y18.
Touzé
,
C.
,
Vidrascu
,
M.
, and
Chapelle
,
D.
, 2014
, “
Direct Finite Element Computation of Non-Linear Modal Coupling Coefficients for Reduced-Order Shell Models
,” Comput. Mech.
,
54
(2
), pp. 567
–580
.10.1007/s00466-014-1006-419.
Chaturantabut
,
S.
, and
Sorensen
,
D. C.
, 2009
, “
Discrete Empirical Interpolation for Nonlinear Model Reduction
,” Proceedings of the 48th IEEE Conference
, Shanghai, China, Dec. 15–18, pp. 4316
–4321
.https://www.caam.rice.edu/~sorensen/Talks/SIAM_CSE09/SIAM_CSE09T.pdf20.
McEwan
,
M. I.
,
Wright
,
J. R.
,
Cooper
,
J. E.
, and
Leung
,
A. Y.
, 2001
, “
A Combined Modal/Finite Element Analysis Technique for the Dynamic Response of a Non-Linear Beam to Harmonic Excitation
,” J. Sound Vib.
,
243
(4
), pp. 601
–624
.10.1006/jsvi.2000.343421.
Muravyov
,
A.
, and
Rizzi
,
S.
, 2003
, “
Determination of Nonlinear Stiffness With Application to Random Vibration of Geometrically Nonlinear Structures
,” Comput. Struct.
,
81
(15
), pp. 1513
–1523
.10.1016/S0045-7949(03)00145-722.
Sinha
,
S. K.
, 2013
, “
Rotordynamic Analysis of Asymmetric Turbofan Rotor Due to Fan Blade-Loss Event With Contact-Impact Rub Loads
,” J. Sound Vib.
,
332
(9
), pp. 2253
–2283
.10.1016/j.jsv.2012.11.03323.
Carpenter
,
N. J.
,
Taylor
,
R. L.
, and
Katona
,
M. G.
, 1991
, “
Lagrange Constraints for Transient Finite Element Surface Contact
,” Int. J. Numer. Methods Eng.
,
32
(1
), pp. 103
–128
.10.1002/nme.162032010724.
Ma
,
H.
,
Wang
,
D.
,
Tai
,
X.
, and
Wen
,
B.
, 2017
, “
Vibration Response Analysis of Blade-Disk Dovetail Structure Under Blade Tip Rubbing Condition
,” J. Vib. Control
,
23
(2
), pp. 252
–271
.10.1177/107754631557583525.
Williams
,
R. J.
, 2011
, “
Simulation of Blade Casing Interaction Phenomena in Gas Turbines Resulting From Heavy Tip Rubs Using an Implicit Time Marching Method
,” ASME
Paper No. GT2011-45495.10.1115/GT2011-4549526.
Delhez
,
E.
,
Nyssen
,
F.
,
Golinval
,
J.-C.
, and
Batailly
,
A.
, 2020
, “
Comparative Study of Blades Reduced Order Models With Geometrical Nonlinearities and Contact Interfaces
,” ASME
Paper No. GT2020-14882.10.1115/GT2020-1488227.
Batailly
,
A.
,
Legrand
,
M.
,
Cartraud
,
P.
, and
Pierre
,
C.
, 2010
, “
Assessment of Reduced Models for the Detection of Modal Interaction Through Rotor Stator Contacts
,” J. Sound Vib.
,
329
(26
), pp. 5546
–5562
.10.1016/j.jsv.2010.07.01828.
Legrand
,
M.
,
Batailly
,
A.
,
Magnain
,
B.
,
Cartraud
,
P.
, and
Pierre
,
C.
, 2012
, “
Full Three-Dimensional Investigation of Structural Contact Interactions in Turbomachines
,” J. Sound Vib.
,
331
(11
), pp. 2578
–2601
.10.1016/j.jsv.2012.01.01729.
Batailly
,
A.
,
Legrand
,
M.
,
Millecamps
,
A.
, and
Garcin
,
F.
, 2012
, “
Numerical-Experimental Comparison in the Simulation of Rotor/Stator Interaction Through Blade-Tip/Abradable Coating Contact
,” ASME J. Eng. Gas Turbines Power
,
134
(8
), p. 082504.10.1115/1.400644630.
Batailly
,
A.
,
Agrapart
,
Q.
,
Millecamps
,
A.
, and
Brunel
,
J.-F.
, 2016
, “
Experimental and Numerical Simulation of a Rotor/Stator Interaction Event Localized on a Single Blade Within an Industrial High-Pressure Compressor
,” J. Sound Vib.
,
375
, pp. 308
–331
.10.1016/j.jsv.2016.03.01631.
Craig
,
R. R.
, and
Bampton
,
M.
, 1968
, “
Coupling of Substructures for Dynamic Analyses
,” AIAA J.
,
6
(7
), pp. 1313
–1319
.10.2514/3.474132.
Tiso
,
P.
, 2011
, “
Optimal Second Order Reduction Basis Selection for Nonlinear Transient Analysis
,” Proceedings of the International Modal Analysis Conference (IMAC) XXIX
, Jacksonville, FL, Jan. 31–Feb. 3, pp. 27
–39
.10.1007/978-1-4419-9299-4_333.
Wu
,
L.
,
Tiso
,
P.
, and
van Keulen
,
F.
, 2016
, “
A Modal Derivatives Enhanced Craig-Bampton Method for Geometrically Nonlinear Structural Dynamics
,” Proceedings of the 27th International Conference on Noise and Vibration Engineering
, Leuven, Belgium, Sept. 19–21, pp. 3615
–3624
.https://research.tudelft.nl/en/publications/a-modal-derivatives-enhanced-craig-bampton-method-for-geometrical34.
Slaats
,
P.
,
de Jongh
,
J.
, and
Sauren
,
A.
, 1995
, “
Model Reduction Tools for Nonlinear Structural Dynamics
,” Comput. Struct.
,
54
(6
), pp. 1155
–1171
.10.1016/0045-7949(94)00389-K35.
Idelsohn
,
S. R.
, and
Cardona
,
A.
, 1985
, “
A Reduction Method for Nonlinear Structural Dynamic Analysis
,” Comput. Methods Appl. Mech. Eng.
,
49
(3
), pp. 253
–279
.10.1016/0045-7825(85)90125-236.
Tiso
,
P.
, 2011
, “
Effective Modal Derivatives Based Reduction Method for Geometrically Nonlinear Structures
,” ASME
Paper No. DETC2011-48315.10.1115/DETC2011-4831537.
Capiez-Lernout
,
E.
,
Soize
,
C.
, and
Mbaye
,
M.
, 2014
, “
Geometric Nonlinear Dynamic Analysis of Uncertain Structures With Cyclic Symmetry. Application to a Mistuned Industrial Bladed Disk
,” Proceedings of the 26th International Conference on Noise and Vibration Engineering
, Leuven, Belgium, Sept. 15–17, pp. 4481
–4494
.38.
Givois
,
A.
,
Grolet
,
A.
,
Thomas
,
O.
, and
Deü
,
J. F.
, 2019
, “
On the Frequency Response Computation of Geometrically Nonlinear Flat Structures Using Reduced-Order Finite Element Models
,” Nonlinear Dyn.
,
97
(2
), pp. 1747
–1781
.10.1007/s11071-019-05021-639.
Legrand
,
M.
,
Batailly
,
A.
, and
Pierre
,
C.
, 2012
, “
Numerical Investigation of Abradable Coating Removal in Aircraft Engines Through Plastic Constitutive Law
,” ASME J. Comput. Nonlinear Dyn.
,
7
(1
), pp. 1
–11
.10.1115/1.400495140.
Moore
,
R. D.
, and
Reid
,
L.
, 1980
, “
Performance of Single-Stage Axial-Flow Transonic Compressor With Rotor and Stator Aspect Ratios of 1.19 and 1.26, Respectively, and With Design Pressure Ratio of 2.05
,” NASA, Cleveland, OH, Report No. NASA TP 1659
.https://www.semanticscholar.org/paper/Performance-of-single-stage-axial-flow-transonic-of-Moore-Reid/7f13e7f3cbee9d72b2df49aa1d541ec5766f0b6141.
Reid
,
L.
, and
Moore
,
R. D.
, 1978
, “
Design and Overall Performance of Four Highly-Loaded, High Speed Inlet Stages for an Advanced High-Pressure Ratio Core Compressor
,” NASA, Cleveland, OH, Report No. NASA TP 1337
.42.
Denton
,
J. D.
, 1997
, “
Lessons From Rotor 37
,” J. Therm. Sci.
,
6
(1
), pp. 1
–13
.10.1007/s11630-997-0010-9Copyright © 2021 by ASME
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