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

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.

Graphical abstract

Keywords

aero-engine blade / displacement response / dynamic strain reconstruction / mode shape / strain gauge

References

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

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

[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

[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

[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

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

[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

[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

[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

[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

[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

[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

[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

[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

[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

[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

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

[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

[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 L_1/2-norm regularization and transmissibility. Measurement, 2022, 190: 110677

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

[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

[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

[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

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

[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

[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

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).

RIGHTS & PERMISSIONS

2023 Higher Education Press