Abstract

High-cycle fatigue failures of fan blade systems due to vibrational loads are of great concern in the design of aeroengines, where energy dissipation by the relative frictional motion in the dovetail joints provides the main damping to mitigate the vibrations. The performance of such a frictional damping can be enhanced by suitable coatings. However, the analysis and design of coated joint roots of gas turbine fan blades are computationally expensive due to strong contact friction nonlinearities and also complex physics involved in the dovetail. In this study, a data-driven surrogate model, known as the Nonlinear in Parameter AutoRegressive with eXegenous input (NP-ARX) model, is introduced to circumvent the difficulties in the analysis and design of fan systems. The NP-ARX model is a linear input–output model, where the model coefficients are nonlinear functions of the design parameters of interest, such that the Frequency Response Function (FRF) can be directly obtained and used in the system analysis and design. A simplified fan-bladed disc system is considered as the test case. The results show that using the data-driven surrogate model, an efficient and accurate design of aeroengine fan systems can be achieved. The approach is expected to be extended to solve the analysis and design problems of many other complex systems.

References

1.
Zhu
,
Y. P.
,
Luo
,
Z.
,
Zhao
,
X.
, and
Han
,
Q.
,
2015
, “
Determination Method of the Structure Size Interval of Dynamically Similar Models for Predicting Vibration Characteristics of the Coated Thin Plates
,”
Proc. Inst. Mech. Eng., C: J. Mech. Eng. Sci.
,
229
(
1
), pp.
59
68
.10.1177/0954406214532243
2.
Zhang
,
D.
,
Fu
,
J.
,
Zhang
,
Q.
, and
Hong
,
J.
,
2017
, “
An Effective Numerical Method for Calculating Nonlinear Dynamics of Structures With Dry Friction: Application to Predict the Vibration Response of Blades With Underplatform Dampers
,”
Nonlinear Dyn.
,
88
(
1
), pp.
223
237
.10.1007/s11071-016-3239-6
3.
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
.10.1007/s11831-016-9183-2
4.
He
,
B.
,
Ouyang
,
H.
,
Ren
,
X.
, and
He
,
S.
,
2017
, “
Dynamic Response of a Simplified Turbine Blade Model With Under-Platform Dry Friction Dampers Considering Normal Load Variation
,”
Appl. Sci.
,
7
(
3
), p.
228
10.3390/app7030228
5.
Sun
,
Y.
,
Yuan
,
J.
,
Pesaresi
,
L.
, and
Salles
,
L.
,
2018
, “
Nonlinear Vibrational Analysis for Integrally Bladed Disk Using Frictional Ring Damper
,”
J. Phys.: Conf. Ser.
,
1106
(
1
), p.
012026
.10.1088/1742-6596/1106/1/012026
6.
Fouvry
,
S.
, and
Paulin
,
C.
,
2014
, “
An Effective Friction Energy Density Approach to Predict Solid Lubricant Friction Endurance: Application to Fretting Wear
,”
Wear
,
319
(
1–2
), pp.
211
226
.10.1016/j.wear.2014.07.009
7.
Barman
,
K.
,
Shipway
,
P.
,
Voisey
,
K.
, and
Pattinson
,
G.
,
2018
, “
The Role of a Thermally Sprayed Cuniin Underlayer in the Durability of a Dry-Film Lubricant System in Fretting–a Phenomenological Model
,”
Tribol. Int.
,
123
, pp.
307
315
.10.1016/j.triboint.2018.03.018
8.
Yuan
,
J.
,
Scarpa
,
F.
,
Allegri
,
G.
,
Titurus
,
B.
,
Patsias
,
S.
, and
Rajasekaran
,
R.
,
2017
, “
Efficient Computational Techniques for Mistuning Analysis of Bladed Discs: A Review
,”
Mech. Syst. Signal Process.
,
87
, pp.
71
90
.10.1016/j.ymssp.2016.09.041
9.
Yuan
,
J.
,
El-Haddad
,
F.
,
Salles
,
L.
, and
Wong
,
C.
,
2019
, “
Numerical Assessment of Reduced Order Modeling Techniques for Dynamic Analysis of Jointed Structures With Contact Nonlinearities
,”
ASME J. Eng. Gas Turbines Power
,
141
(
3
), p.
031027
.10.1115/1.4041147
10.
Yuan
,
J.
,
Salles
,
L.
,
Wong
,
C.
, and
Patsias
,
S.
,
2020
, “
A Novel Penalty-Based Reduced Order Modelling Method for Dynamic Analysis of Joint Structures
,”
IUTAM Symposium on Model Order Reduction of Coupled Systems
, pp.
165
176
. Stuttgart, Germany, May 22–25
.
11.
Brunton
,
S. L.
,
Proctor
,
J. L.
, and
Kutz
,
J. N.
,
2016
, “
Discovering Governing Equations From Data by Sparse Identification of Nonlinear Dynamical Systems
,”
Proc. Natl. Acad. Sci.
,
113
(
15
), pp.
3932
3937
.10.1073/pnas.1517384113
12.
Kibangou
,
A. Y.
, and
Favier
,
G.
,
2006
, “
Wiener-Hammerstein Systems Modeling Using Diagonal Volterra Kernels Coefficients
,”
IEEE Signal Process. Lett.
,
13
(
6
), pp.
381
384
.10.1109/LSP.2006.871705
13.
Billings
,
S. A.
,
2013
,
Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains
,
John Wiley & Sons, Hoboken, NJ
.
14.
Zhu
,
Y. P.
, and
Lang
,
Z. Q.
,
2018
, “
Design of Nonlinear Systems in the Frequency Domain: An Output Frequency Response Function-Based Approach
,”
IEEE Trans. Control Syst. Technol.
,
26
(
4
), pp.
1358
1371
.10.1109/TCST.2017.2716379
15.
Zhu
,
Y. P.
, and
Lang
,
Z. Q.
,
2018
, “
The Effects of Linear and Nonlinear Characteristic Parameters on the Output Frequency Responses of Nonlinear Systems: The Associated Output Frequency Response Function
,”
Automatica
,
93
, pp.
422
427
.10.1016/j.automatica.2018.03.070
16.
Adetona
,
O.
,
Garcia
,
E.
, and
Keel
,
L. H.
,
2000
, “
A New Method for the Control of Discrete Nonlinear Dynamic Systems Using Neural Networks
,”
IEEE Trans. Neural Netw.
,
11
(
1
), pp.
102
112
.10.1109/72.822514
17.
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
.10.1016/j.ymssp.2016.09.007
18.
Liang
,
Y. Z.
,
Fang
,
K. T.
, and
Xu
,
Q. S.
,
2001
, “
Uniform Design and Its Applications in Chemistry and Chemical Engineering
,”
Chemometrics Intell. Lab. Syst.
,
58
(
1
), pp.
43
57
.10.1016/S0169-7439(01)00139-3
19.
Stein
,
M.
,
1987
, “
Large Sample Properties of Simulations Using Latin Hypercube Sampling
,”
Technometrics
,
29
(
2
), pp.
143
151
.10.1080/00401706.1987.10488205
20.
Wei
,
H. L.
,
Lang
,
Z. Q.
, and
Billings
,
S. A.
,
2008
, “
Constructing an Overall Dynamical Model for a System With Changing Design Parameter Properties
,”
Int. J. Modell. Identif. Control
,
5
(
2
), pp.
93
104
.10.1504/IJMIC.2008.022014
21.
Liu
,
H.
,
Zhu
,
Y. P.
,
Luo
,
Z.
, and
Han
,
Q.
,
2018
, “
PRESS-Based EFOR Algorithm for the Dynamic Parametrical Modeling of Nonlinear MDOF Systems
,”
Front. Mech. Eng.
,
13
(
3
), pp.
390
400
.10.1007/s11465-017-0459-5
22.
Jones
,
J. P.
, and
Billings
,
S. A.
,
1989
, “
Recursive Algorithm for Computing the Frequency Response of a Class of Non-Linear Difference Equation Models
,”
Int. J. Control
,
50
(
5
), pp.
1925
1940
.10.1080/00207178908953474
23.
Winker
,
P.
, and
Fang
,
K. T.
,
1997
, “
Application of Threshold-Accepting to the Evaluation of the Discrepancy of a Set of Points
,”
SIAM J. Numer. Anal.
,
34
(
5
), pp.
2028
2042
.10.1137/S0036142995286076
24.
Fang, K. T., “Uniform Design,” Hong Kong Baptist University, Kowloon Tong, Hong Kong.
25.
Fang
,
K. T.
,
Lin
,
D. K.
,
Winker
,
P.
, and
Zhang
,
Y.
,
2000
, “
Uniform Design: Theory and Application
,”
Technometrics
,
42
(
3
), pp.
237
248
.10.1080/00401706.2000.10486045
26.
Fang
,
K. T.
, and
Ma
,
C. X.
,
2001
, “
Wrap-Around L2-Discrepancy of Random Sampling, Latin Hypercube and Uniform Designs
,”
J. Complex.
,
17
(
4
), pp.
608
624
.10.1006/jcom.2001.0589
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