RESEARCH ARTICLE

Full-field dynamic strain reconstruction of an aero-engine blade from limited displacement responses

  • Chunyan AO 1,2 ,
  • Baijie QIAO , 1,2,3 ,
  • Kai ZHOU 1,2 ,
  • Lei CHEN 1,2 ,
  • Shunguo FU 3 ,
  • Xuefeng CHEN 1,2
Expand
  • 1. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China
  • 2. The State Key Laboratory for Manufacturing Systems Engineering, Xi’an 710061, China
  • 3. AECC Sichuan Gas Turbine Establishment, Chengdu 610500, China
qiao1224@xjtu.edu.cn

Received date: 17 Jan 2022

Accepted date: 22 Aug 2022

Copyright

2023 Higher Education Press

Abstract

Blade strain distribution and its change with time are crucial for reliability analysis and residual life evaluation in blade vibration tests. Traditional strain measurements are achieved by strain gauges (SGs) in a contact manner at discrete positions on the blades. This study proposes a method of full-field and real-time strain reconstruction of an aero-engine blade based on limited displacement responses. Limited optical measured displacement responses are utilized to reconstruct the full-field strain. The full-field strain distribution is in-time visualized. A displacement-to-strain transformation matrix is derived on the basis of the blade mode shapes in the modal coordinate. The proposed method is validated on an aero-engine blade in numerical and experimental cases. Three discrete vibrational displacement responses measured by laser triangulation sensors are used to reconstruct the full-field strain over the whole operating time. The reconstructed strain responses are compared with the results measured by SGs and numerical simulation. The high consistency between the reconstructed and measured results demonstrates the accurate strain reconstructed by the method. This paper provides a low-cost, real-time, and visualized measurement of blade full-field dynamic strain using displacement response, where the traditional SGs would fail.

Cite this article

Chunyan AO , Baijie QIAO , Kai ZHOU , Lei CHEN , Shunguo FU , Xuefeng CHEN . Full-field dynamic strain reconstruction of an aero-engine blade from limited displacement responses[J]. Frontiers of Mechanical Engineering, 2023 , 18(1) : 15 . DOI: 10.1007/s11465-022-0731-1

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 52075414) and the National Science and Technology Major Project, China (Grant No. 2017-V-0009).
1
Chen X F , Wang S B , Qiao B J , Chen Q . Basic research on machinery fault diagnostics: past, present, and future trends. Frontiers of Mechanical Engineering, 2018, 13(2): 264–291

DOI

2
Zhu Y P , Wang Y , Luo Z , Han Q K , Wang D Y . Similitude design for the vibration problems of plates and shells: a review. Frontiers of Mechanical Engineering, 2017, 12(2): 253–264

DOI

3
Ma H , Xie F T , Nai H Q , Wen B C . Vibration characteristics analysis of rotating shrouded blades with impacts. Journal of Sound and Vibration, 2016, 378: 92–108

DOI

4
Gao Y , Liu X Y , Xiang J W . FEM simulation-based generative adversarial networks to detect bearing faults. IEEE Transactions on Industrial Informatics, 2020, 16(7): 4961–4971

DOI

5
Yang F M , Yang Y M , Hu H F , Guan F J , Shen G J , Chen S Y , Bian Z F . Extraction of features due to breathing crack from vibration response of rotated blades considering tenon connection and shroud contact. Shock and Vibration, 2019, 2019: 8729620

DOI

6
Guo H T, Duan F J, Zhang J L. Blade resonance parameter identification based on tip-timing method without the once-per revolution sensor. Mechanical Systems and Signal Processing, 2016, 66–67: 625–639

DOI

7
Du Z H , Chen X F , Zhang H , Zi Y Y , Yan R Q . Multiple fault separation and detection by joint subspace learning for the health assessment of wind turbine gearboxes. Frontiers of Mechanical Engineering, 2017, 12(3): 333–347

DOI

8
Bouchain A , Picheral J , Lahalle E , Chardon G , Vercoutter A , Talon A . Blade vibration study by spectral analysis of tip-timing signals with OMP algorithm. Mechanical Systems and Signal Processing, 2019, 130: 108–121

DOI

9
Xu J H , Qiao B J , Liu M R , Yang Z B , Chen X F . Crack propagation monitoring of rotor blades using synchroextracting transform. Journal of Sound and Vibration, 2021, 509: 116253

DOI

10
Battiato G , Firrone C M , Berruti T M . Forced response of rotating bladed disks: blade tip-timing measurements. Mechanical Systems and Signal Processing, 2017, 85: 912–926

DOI

11
Poozesh P, Baqersad J, Niezrecki C, Avitabile P, Harvey E, Yarala R. Large-area photogrammetry based testing of wind turbine blades. Mechanical Systems and Signal Processing, 2017, 86(Part B): 98–115

DOI

12
Qiao B J , Ao C Y , Mao Z , Chen X F . Non-convex sparse regularization for impact force identification. Journal of Sound and Vibration, 2020, 477: 115311

DOI

13
Huh Y H , Kim J , Hong S G . Detection of local bonding failure damage by digital image correlation technique. Reliability Engineering & System Safety, 2019, 184: 21–26

DOI

14
Khadka A , Fick B , Afshar A , Tavakoli M , Baqersad J . Non-contact vibration monitoring of rotating wind turbines using a semi-autonomous UAV. Mechanical Systems and Signal Processing, 2020, 138: 106446

DOI

15
Retze U, Schüssler M. Dynamic Stress and Strain Measurement. Polytec Technical Papers, 2010

16
Sever I A , Maguire M . Correlation of full-field dynamic strain measurements with reverse engineered finite element model predictions. Experimental Techniques, 2021, 45(3): 377–387

DOI

17
Liu C H , Zang C P , Zhou B . Extension of continuous scanning laser Doppler vibrometry measurement for complex structures with curved surfaces. Chinese Journal of Aeronautics, 2020, 33(12): 3220–3227

DOI

18
Chen Y C , Escalera Mendoza A S , Griffith D T . Experimental and numerical study of high-order complex curvature mode shape and mode coupling on a three-bladed wind turbine assembly. Mechanical Systems and Signal Processing, 2021, 160: 107873

DOI

19
Vuye C , Vanlanduit S , Presezniak F , Steenackers G , Guillaume P . Optical measurement of the dynamic strain field of a fan blade using a 3D scanning vibrometer. Optics and Lasers in Engineering, 2011, 49(7): 988–997

DOI

20
Maguire M , Sever I . Full-field strain measurements on turbomachinery components using 3D SLDV technology. AIP Conference Proceedings, 2016, 1740(1): 080001

DOI

21
Luo W , Li J H , Ma X F , Wei W . A novel static deformation measurement and visualization method for wind turbine blades using home-made LiDAR and processing program. Optics and Lasers in Engineering, 2020, 134: 106206

DOI

22
Chen Y C , Joffre D , Avitabile P . Underwater dynamic response at limited points expanded to full-field strain response. Journal of Vibration and Acoustics, 2018, 140(5): 051016

DOI

23
Sarrafi A , Poozesh P , Niezrecki C , Mao Z . Mode extraction on wind turbine blades via phase-based video motion estimation. Proceeding SPIE 10171, Smart Materials and Nondestructive Evaluation for Energy Systems, 2017, 10171: 101710E

DOI

24
Baqersad J , Bharadwaj K . Strain expansion-reduction approach. Mechanical Systems and Signal Processing, 2018, 101: 156–167

DOI

25
Bharadwaj K , Sheidaei A , Afshar A , Baqersad J . Full-field strain prediction using mode shapes measured with digital image correlation. Measurement, 2019, 139: 326–333

DOI

26
Chen Z S , Sheng H , Xia Y M , Wang W M , He J . A comprehensive review on blade tip timing-based health monitoring: status and future. Mechanical Systems and Signal Processing, 2021, 149: 107330

DOI

27
Zhang X J , Wang Y R , Jiang X H , Gao S M . Blade vibration stress determination method based on blade tip timing simulator and finite element method. Journal of Engineering for Gas Turbines and Power, 2020, 142(3): 031001

DOI

28
Wang W M , Hu D F , Li Q H , Zhang X L . An improved non-contact dynamic stress measurement method for turbomachinery rotating blades based on fundamental mistuning model. Mechanical Systems and Signal Processing, 2020, 144: 106851

DOI

29
Mohamed M , Bonello P , Russhard P . A novel method for the determination of the change in blade tip timing probe sensing position due to steady movements. Mechanical Systems and Signal Processing, 2019, 126: 686–710

DOI

30
Wu S M , Zhao Z B , Yang Z B , Tian S H , Yang L H , Chen X F . Physical constraints fused equiangular tight frame method for blade tip timing sensor arrangement. Measurement, 2019, 145: 841–851

DOI

31
Bornassi S , Berruti T M , Firrone C M , Battiato G . Vibration parameters identification of turbomachinery rotor blades under transient condition using blade tip-timing measurements. Measurement, 2021, 183: 109861

DOI

32
Chakraborty A , Shishkin S , Birnkrant M J . Optimal control of build height utilizing optical profilometry in cold spray deposits. Proceeding SPIE 10168, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems, 2017, 10168: 101683H

DOI

33
Kochkin D Y , Zaitsev D V , Kabov O A . Thermocapillary rupture and contact line dynamics in the heated liquid layers. Interfacial Phenomena and Heat Transfer, 2020, 8(1): 1–9

DOI

34
Kranjc T , Slavič J , Boltežar M . A comparison of strain and classic experimental modal analysis. Journal of Vibration and Control, 2016, 22(2): 371–381

DOI

35
Rao S S , Atluri S N . The finite element method in engineering. Journal of Applied Mechanics, 1983, 50(4a): 914

DOI

36
HumarJ. Dynamics of Structures. 3rd ed. Boca Baton: CRC Press, 2012

37
Zhou Y D , Tao J Y . Theoretical and numerical investigation of stress mode shapes in multi-axial random fatigue. Mechanical Systems and Signal Processing, 2019, 127: 499–512

DOI

38
Chen H , Song H W . Analysis of strain modals and the relationship between the strain modals and displacement modals. Noise and Vibration Control, 2016, 36(4): 7–13

39
Ao C Y , Qiao B J , Chen L , Xu J H , Liu M R , Chen X F . Blade dynamic strain non-intrusive measurement using L1/2-norm regularization and transmissibility. Measurement, 2022, 190: 110677

DOI

40
Zhang X D. Matrix Analysis and Applications. Cambridge: Cambridge University Press, 2017

DOI

41
Kharyton V , Bladh R . Using tiptiming and strain gauge data for the estimation of consumed life in a compressor blisk subjected to stall-induced loading. In: Proceedings of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition. Volume 7B: Structures and Dynamics. Düsseldorf: ASME, 2014, V07BT33A028

DOI

42
Wu S M , Russhard P , Yan R Q , Tian S H , Wang S B , Zhao Z B , Chen X F . An Adaptive online blade health monitoring method: from raw data to parameters identification. IEEE Transactions on Instrumentation and Measurement, 2020, 69(5): 2581–2592

DOI

43
Duffy K P, Provenza A J, Bakhle M, Min J B, Abdul-Aziz A. Laser displacement measurements of fan blades in resonance and flutter during the boundary layer ingesting inlet and distortion-tolerant fan test. In: Proceedings of 2018 AIAA Aerospace Sciences Meeting. Kissimmee: AIAA, 2018

DOI

44
Aadnøy B, Looyeh R. Petroleum Rock Mechanics. Gulf Professional Publishing, 2011

DOI

45
Dowling N E. Mechanical Behavior of Materials: Engineering Methods for Deformation, Fracture, and Fatigue. 3rd ed. London: Pearson Prentice Hall Ltd., 2007

46
Wu Y , Liu G , Liu Z Q , Wang B . Formability and microstructure of Ti22Al24.5Nb0.5Mo rolled sheet within hot gas bulging tests at constant equivalent strain rate. Materials & Design, 2016, 108: 298–307

DOI

47
ANSYSI. Help System: Mechanical APDL Element Reference, 19.0. 2018

48
Kamaraj A V. Stress prediction in turbine blades under forced excitation. Thesis for the Master’s Degree. San Diego: San Diego State University, 2016

Outlines

/