Dynamic contact characteristics of a rotating twisted variable-section blade with breathing crack

Abstract

Crack failures frequently occur in aero-engine blades which can trigger a cascade of accidents. Previous studies have primarily focused on crack-induced nonlinear vibration, and the contact state of the crack surfaces during crack breathing is often neglected. However, it is important to consider the contact behavior of the crack surfaces as it is responsible for generating nonlinear vibrations. To further investigate the mechanism behind crack-induced nonlinear vibrations, a novel dynamic contact breathing crack model (DCBCM) for rotating blades is proposed based on the self-programmed incompatible hexahedral element (SNCHE). The breathing effect is simulated using spring elements. The proposed DCBCM is validated by the contact finite element model. Moreover, the effects of crack parameters (depth and location) and load parameters (aerodynamic amplitude and aerodynamic frequency) on the dynamic contact characteristics are investigated. Furthermore, a breathing crack quantification indicator (BCQI) is proposed to represent the nonlinear level of breathing crack. The results indicate that the crack may close from the sides of the blade toward the center of the crack front during crack breathing. Besides, the BCQI increases with the increase of crack depth, aerodynamic amplitude, and rotational speed; while decreases as the crack moves closer to the blade tip.

Keywords

breathing crack / dynamic contact characteristics / rotating blade / nonlinear dynamic / incompatible hexahedral element

References

[[1]] Fan Z-f, Li H-k, Dong J-n, et al.. Blade vibration difference-based identification of blade vibration parameters: A novel blade tip timing method. Journal of Sound and Vibration, 2021, 512: 116402, J]

[[2]] Mohamed M E, Bonello P, Russhard P. An experimentally validated modal model simulator for the assessment of different blade tip timing algorithms. Mechanical Systems and Signal Processing, 2020, 136: 106484, J]

[[3]] Ao C-y, Qiao B-j, Chen L, et al.. Blade dynamic strain non-intrusive measurement using L_1/2-norm regularization and transmissibility. Measurement, 2022, 190: 110677, J]

[[4]] Chen Y-g, Zhu Q-y, Zhai J-yu. Experimental investigation on fatigue of blade specimen subjected to resonance and effect of a damping hard coating treatment. Journal of Central South University, 2021, 28(2): 445-453, J]

[[5]] Wang W-w, Ni K-x, Ma H, et al.. Fatigue crack propagation simulation of airfoil section blade under aerodynamic and centrifugal loads. Engineering Fracture Mechanics, 2023, 293: 109702, J]

[[6]] Zhu Q-y, Zhao Y-l, Chen Y-g, et al.. Fatigue crack retardation by the application of hard damping coating to blades under resonance. Journal of Central South University, 2023, 30(4): 1095-1106, J]

[[7]] Xu J-h, Qiao B-j, Liu M-r, et al.. Crack propagation monitoring of rotor blades using synchroextracting transform. Journal of Sound and Vibration, 2021, 509: 116253, J]

[[8]] Zhang W, Gu X J, Zhang Y F. New modeling on vibrations and bifurcations of FGGP reinforced pretwisted composite rotating blade under axial aerodynamic force: Theoretical and numerical researches. Thin-Walled Structures, 2023, 184: 110523, J]

[[9]] Zhang Y F, Ma L, Zhang W, et al.. Nonlinear dynamic responses of functionally graded graphene platelet reinforced composite cantilever rotating warping plate. Applied Mathematical Modelling, 2023, 113: 44-70, J]

[[10]] Zhang Y F, Niu Y, Zhang W. Nonlinear and chaotic vibrations of rotating functionally graded GPL reinforced composite pre-twisted blade subjected to aerodynamic force. Thin-Walled Structures, 2022, 181: 110135, J]

[[11]] Gu X J, Zhang W, Zhang Y F. A novel dynamic model on nonlinear vibrations of functionally graded graphene platelet reinforced rotating pretwisted composite blade considering subsonic airflow excitation and blade-casing rubbing. Composite Structures, 2023, 315: 116936, J]

[[12]] Yang L-h, Mao Z, Chen X-f, et al.. Dynamic coupling vibration of rotating shaft-disc-blade system—Modeling, mechanism analysis and numerical study. Mechanism and Machine Theory, 2022, 167: 104542, J]

[[13]] Neves A C, Simões F M F, Pinto D, et al.. Vibrations of cracked beams: Discrete mass and stiffness models. Computers & Structures, 2016, 168: 68-77, J]

[[14]] Han H-s, Liu L, Cao D-qing. Analytical approach to coupled bending-torsional vibrations of cracked Timoshenko beam. International Journal of Mechanical Sciences, 2020, 166: 105235, J]

[[15]] Pan Z-z, Chen X-h, Zhang L-wen. Modeling large amplitude vibration of pretwisted hybrid composite blades containing CNTRC layers and matrix cracked FRC layers. Applied Mathematical Modelling, 2020, 83: 640-659, J]

[[16]] Zhang L-w, Pan Z-z, Chen X-hua. Vibration characteristics of matrix cracked pretwisted hybrid composite blades containing CNTRC layers. Journal of Sound and Vibration, 2020, 473: 115242, J]

[[17]] Guo H-l, Xu O-y, Yang T-z, et al.. On the dynamics of rotating cracked functionally graded blades reinforced with graphene nanoplatelets. Engineering Structures, 2021, 249: 113286, J]

[[18]] Li B, Chen X F, Ma J X, et al.. Detection of crack location and size in structures using wavelet finite element methods. Journal of Sound and Vibration, 2005, 285: 767-782, J]

[[19]] Hou C-c, Lu Yong. Identification of cracks in thick beams with a cracked beam element model. Journal of Sound and Vibration, 2016, 385: 104-124, J]

[[20]] Zhang K, Yan X-jun. Multi-cracks identification method for cantilever beam structure with variable cross-sections based on measured natural frequency changes. Journal of Sound and Vibration, 2017, 387: 353-365, J]

[[21]] Wu Z-y, Yan H, Zhao L-c, et al.. Influences of blade crack on the coupling characteristics in a bladed disk with elastic support. Aerospace Science and Technology, 2023, 133: 108135, J]

[[22]] Andreaus U, Baragatti P. Experimental damage detection of cracked beams by using nonlinear characteristics of forced response. Mechanical Systems and Signal Processing, 2012, 31: 382-404, J]

[[23]] Yang F-m, Yang Y-m, Hu H-f, et al.. Extraction of features due to breathing crack from vibration response of rotated blades considering tenon connection and shroud contact. Shock and Vibration, 2019, 2019: 1-20, J]

[[24]] Peng Z K, Lang Z Q, Billings S A. Crack detection using nonlinear output frequency response functions. Journal of Sound and Vibration, 2007, 301: 777-788, J]

[[25]] Wei C-x, Shang X-chun. Analysis on nonlinear vibration of breathing cracked beam. Journal of Sound and Vibration, 2019, 461: 114901, J]

[[26]] Gayen D, Chakraborty D, Tiwari R. Finite element analysis for a functionally graded rotating shaft with multiple breathing cracks. International Journal of Mechanical Sciences, 2017, 134: 411-423, J]

[[27]] Huang Y-h, Chen J-e, Ge W-m, et al.. Research on geometric features of phase diagram and crack identification of cantilever beam with breathing crack. Results in Physics, 2019, 15: 102561, J]

[[28]] Xu W, Su Z-q, Radzieński M, et al.. Nonlinear pseudo-force in a breathing crack to generate harmonics. Journal of Sound and Vibration, 2021, 492: 115734, J]

[[29]] Yang L-h, Mao Z, Wu X-f, et al.. Nonlinear dynamic behavior of rotating blade with breathing crack. Frontiers of Mechanical Engineering, 2021, 16: 196-220, J]

[[30]] Xie J-s, Zi Y-y, Zhang M-q, et al.. A novel vibration modeling method for a rotating blade with breathing cracks. Science China Technological Sciences, 2018, 62: 333-348, J]

[[31]] Yang L-h, Mao Z, Wu S-m, et al.. Steady-state coupling vibration analysis of shaft-disk-blade system with blade crack. Nonlinear Dynamics, 2021, 105: 61-98, J]

[[32]] Yang L-h, Ma M, Wu S-m, et al.. An improved analytical dynamic model for rotating blade crack: With application to crack detection indicator analysis. Journal of Low Frequency Noise, Vibration and Active Control, 2021, 40: 1935-1961, J]

[[33]] Yang L-h, Yang Z-s, Mao Z, et al.. Dynamic characteristic analysis of rotating blade with transverse crack—Part I: Modeling, modification, and validation. Journal of Vibration and Acoustics, 2021, 143(5): 051010, J]

[[34]] Yang L-h, Yang Z-s, Mao Z, et al.. Dynamic characteristic analysis of rotating blade with transverse crack—Part II: A comparison study of different crack models. Journal of Vibration and Acoustics, 2021, 1433(5): 051011, J]

[[35]] Andreaus U, Baragatti P. Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response. Journal of Sound and Vibration, 2011, 330: 721-742, J]

[[36]] Zhang W-s, Ma H, Zeng J, et al.. Vibration responses analysis of an elastic-support cantilever beam with crack and offset boundary. Mechanical Systems and Signal Processing, 2017, 95: 205-218, J]

[[37]] Ma H, Zeng J, Lang Z-q, et al.. Analysis of the dynamic characteristics of a slant-cracked cantilever beam. Mechanical Systems and Signal Processing, 2016, 75: 261-279, J]

[[38]] Zeng J, Ma H, Zhang W-s, et al.. Dynamic characteristic analysis of cracked cantilever beams under different crack types. Engineering Failure Analysis, 2017, 74: 80-94, J]

[[39]] Zeng J, Chen K-k, Ma H, et al.. Vibration response analysis of a cracked rotating compressor blade during run-up process. Mechanical Systems and Signal Processing, 2019, 118: 568-583, J]

[[40]] Liu C, Jiang D-xiang. Crack modeling of rotating blades with cracked hexahedral finite element method. Mechanical Systems and Signal Processing, 2014, 46: 406-423, J]

[[41]] Liu C, Jiang D-x, Chu F-lei. Influence of alternating loads on nonlinear vibration characteristics of cracked blade in rotor system. Journal of Sound and Vibration, 2015, 353: 205-219, J]

[[42]] Zhao C-g, Zeng J, Ma H, et al.. Dynamic analysis of cracked rotating blade using cracked beam element. Results in Physics, 2020, 19: 103306, J]

[[43]] Xiong Q, Guan H, Ma H, et al.. Dynamic characteristic analysis of rotating blade with breathing crack. Mechanical Systems and Signal Processing, 2023, 196: 110325, J]

[[44]] Zhang K, Yan X-jun. Multi-cracks identification method for cantilever beam structure with variable cross-sections based on measured natural frequency changes. Journal of Sound and Vibration, 2017, 387: 53-65, J]

[[45]] park H W, Lim T. Investigating a common premise in structural health monitoring: Are higher modal frequencies more sensitive to an incipient crack on a beam than lower ones?. Engineering Structures, 2018, 176: 385-395, J]

[[46]] Park H W, Lim T. A closed-form frequency equation of an arbitrarily supported beam with a transverse open crack considering axial - bending modal coupling. Journal of Sound and Vibration, 2020, 477: 115336, J]

[[47]] Yan D-l, Zheng Y, Wang W-y, et al.. Modeling and dynamic analyses of the bulb turbine blade with crack fault. Applied Mathematical Modelling, 2021, 89: 731-751, J]

[[48]] Wu Z-y, Yan H, Zhao L-c, et al.. Modal characteristics of a flexible dual-rotor coupling system with blade crack. Journal of Sound and Vibration, 2023, 567: 118061, J]

[[49]] Valverde M B, Muñoz A B, Rubio P, et al.. Influence of the rotation speed on the dynamic behaviour of a cracked rotating beam. Theoretical and Applied Fracture Mechanics, 2022, 117: 103209, J]

[[50]] Wu Z-y, Yan H, Zhao L-c, et al.. Axial-bending coupling vibration characteristics of a rotating blade with breathing crack. Mechanical Systems and Signal Processing, 2023, 182: 109547, J]

[[51]] Zhang X-d, Xiong Y-w, Huang X, et al.. Dynamic modeling of rotary blade crack with regard to three-dimensional tip clearance. Journal of Sound and Vibration, 2023, 544: 117414, J]

[[52]] Zare M. Free out-of-plane vibration of cracked curved beams on elastic foundation by estimating the stress intensity factor. Mechanics of Advanced Materials and Structures, 2019, 27: 1238-1245, J]

[[53]] Ji W-h, Sun W, Zhang Y, et al.. Parametric model order reduction and vibration analysis of pipeline system based on adaptive dynamic substructure method. Structures, 2023, 50: 689-706, J]

[[54]] Yan X-f, Gao J-n, Zhang Y, et al.. Modeling method of coating thickness random mistuning and its effect on the forced response of coated blisks. Aerospace Science and Technology, 2019, 92: 478-488, J]