Skip to main content
SpringerLink
Log in

Nonlinear dynamic behavior of rotating blade with breathing crack

  • Research Article
  • Published:
Frontiers of Mechanical Engineering Aims and scope Submit manuscript

Abstract

This study aims at investigating the nonlinear dynamic behavior of rotating blade with transverse crack. A novel nonlinear rotating cracked blade model (NRCBM), which contains the spinning softening, centrifugal stiffening, Coriolis force, and crack closing effects, is developed based on continuous beam theory and strain energy release rate method. The rotating blade is considered as a cantilever beam fixed on the rigid hub with high rotating speed, and the crack is deemed to be open and close continuously in a trigonometric function way with the blade vibration. It is verified by the comparison with a finite element-based contact crack model and bilinear model that the proposed NRCBM can well capture the dynamic characteristics of the rotating blade with breathing crack. The dynamic behavior of rotating cracked blade is then investigated with NRCBM, and the nonlinear damage indicator (NDI) is introduced to characterize the non-linearity caused by blade crack. The results show that NDI is a distinguishable indicator for the severity level estimation of the crack in rotating blade. It is found that severe crack (i.e., a closer crack position to blade root as well as larger crack depth) is expected to heavily reduce the stiffness of rotating blade and apparently result in a lower resonant frequency. Meanwhile, the super-harmonic resonances are verified to be distinguishable indicators for diagnosing the crack existence, and the third-order super-harmonic resonances can serve as an indicator for the presence of severe crack since it only distinctly appears when the crack is severe.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Abdelrhman A M, Leong M S, Saeed S A M, et al. A review of vibration monitoring as a diagnostic tool for turbine blade faults. Applied Mechanics and Materials, 2012, 229–231: 1459–1463

    Article  Google Scholar 

  2. Carter T J. Common failures in gas turbine blades. Engineering Failure Analysis, 2005, 12(2): 237–247

    Article  Google Scholar 

  3. Yang L, Chen X, Wang S. Mechanism of fast time-varying vibration for rotor-stator contact system: With application to fault diagnosis. Journal of Vibration and Acoustics, 2018, 140(1): 014501

    Article  Google Scholar 

  4. Gates D. Rolls-Royce spending millions of dollars to repair 787 engines. Available from The Seattle Times website on 2020-9-14

  5. Abdelrhman A M, Hee L M, Leong M, et al. Condition monitoring of blade in turbomachinery: A review. Advances in Mechanical Engineering, 2014, 6(1): 210717

    Article  Google Scholar 

  6. Gubran A. Vibration diagnosis of blades of rotating machines. Dissertation for the Doctoral Degree. Manchester: The University of Manchester, 2015

    Google Scholar 

  7. Rafiee M, Nitzsche F, Labrosse M. Dynamics, vibration and control of rotating composite beams and blades: A critical review. Thin-Walled Structures, 2017, 119: 795–819

    Article  Google Scholar 

  8. Yuan J, Scarpa F, Allegri G, et al. Efficient computational techniques for mistuning analysis of bladed discs: A review. Mechanical Systems and Signal Processing, 2017, 87: 71–90

    Article  Google Scholar 

  9. Ma H, Yin F, Guo Y, et al. A review on dynamic characteristics of blade-casing rubbing. Nonlinear Dynamics, 2016, 84: 437–472

    Article  Google Scholar 

  10. Wang L, Cao D, Huang W. Nonlinear coupled dynamics of flexible blade-rotor-bearing systems. Tribology International, 2010, 43(4): 759–778

    Article  Google Scholar 

  11. Ma H, Lu Y, Wu Z, et al. A new dynamic model of rotor-blade systems. Journal of Sound and Vibration, 2015, 357: 168–194

    Article  Google Scholar 

  12. She H, Li C, Tang Q, et al. The investigation of the coupled vibration in a flexible-disk blades system considering the influence of shaft bending vibration. Mechanical Systems and Signal Processing, 2018, 111: 545–569

    Article  Google Scholar 

  13. Ma H, Xie F, Nai H, et al. Vibration characteristics analysis of rotating shrouded blades with impacts. Journal of Sound and Vibration, 2016, 378: 92–108

    Article  Google Scholar 

  14. Sinha S K, Turner K E. Natural frequencies of a pre-twisted blade in a centrifugal force field. Journal of Sound and Vibration, 2011, 330(11): 2655–2681

    Article  Google Scholar 

  15. Oh Y, Yoo H H. Vibration analysis of a rotating pre-twisted blade considering the coupling effects of stretching, bending, and torsion. Journal of Sound and Vibration, 2018, 431: 20–39

    Article  Google Scholar 

  16. Batailly A, Meingast M, Legrand M. Unilateral contact induced blade/casing vibratory interactions in impellers: Analysis for rigid casings. Journal of Sound and Vibration, 2015, 337: 244–262

    Article  Google Scholar 

  17. Yuan J, Scarpa F, Titurus B, et al. Novel frame model for mistuning analysis of bladed disk systems. Journal of Vibration and Acoustics, 2017, 139(3): 031016

    Article  Google Scholar 

  18. Xie F, Ma H, Cui C, et al. Vibration response comparison of twisted shrouded blades using different impact models. Journal of Sound and Vibration, 2017, 397: 171–191

    Article  Google Scholar 

  19. Ma H, Lu Y, Wu Z, et al. Vibration response analysis of a rotational shaft-disk-blade system with blade-tip rubbing. International Journal of Mechanical Sciences, 2016, 107: 110–125

    Article  Google Scholar 

  20. Tang W, Epureanu B I. Nonlinear dynamics of mistuned bladed disks with ring dampers. International Journal of Non-linear Mechanics, 2017, 97: 30–40

    Article  Google Scholar 

  21. Yu P, Zhang D, Ma Y, et al. Dynamic modeling and vibration characteristics analysis of the aero-engine dual-rotor system with fan blade out. Mechanical Systems and Signal Processing, 2018, 106: 158–175

    Article  Google Scholar 

  22. Yang L, Chen X, Wang S. A novel amplitude-independent crack identification method for rotating shaft. Proceedings of the Institution of Mechanical Engineers. Part C, Journal of Mechanical Engineering Science, 2018, 232(22): 4098–4112

    Article  Google Scholar 

  23. Chasalevris A C, Papadopoulos C A. Identification of multiple cracks in beams under bending. Mechanical Systems and Signal Processing, 2006, 20(7): 1631–1673

    Article  Google Scholar 

  24. Zhang K, Yan X. 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

    Article  Google Scholar 

  25. Li B, Chen X, Ma J, et al. Detection of crack location and size in structures using wavelet finite element methods. Journal of Sound and Vibration, 2005, 285(4–5): 767–782

    Article  Google Scholar 

  26. Giannini O, Casini P, Vestroni F. Nonlinear harmonic identification of breathing cracks in beams. Computers & Structures, 2013, 129: 166–177

    Article  Google Scholar 

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

    Article  Google Scholar 

  28. Liu J, Shao Y, Zhu W. Free vibration analysis of a cantilever beam with a slant edge crack. Proceedings of the Institution of Mechanical Engineers. Part C, Journal of Mechanical Engineering Science, 2017, 231(5): 823–843

    Article  Google Scholar 

  29. Liu J, Zhu W D, Charalambides P G, et al. A dynamic model of a cantilever beam with a closed, embedded horizontal crack including local flexibilities at crack tips. Journal of Sound and Vibration, 2016, 382: 274–290

    Article  Google Scholar 

  30. Bovsunovsky A, Surace C. Non-linearities in the vibrations of elastic structures with a closing crack: A state of the art review. Mechanical Systems and Signal Processing, 2015, 62–63: 129–148

    Article  Google Scholar 

  31. Douka E, Hadjileontiadis L J. Time-frequency analysis of the free vibration response of a beam with a breathing crack. NDT & E International, 2005, 38(1): 3–10

    Article  Google Scholar 

  32. Rezaee M, Hassannejad R. Free vibration analysis of simply supported beam with breathing crack using perturbation method. Acta Mechanica Solida Sinica, 2010, 23(5): 459–470

    Article  Google Scholar 

  33. Vigneshwaran K, Behera R K. Vibration analysis of a simply supported beam with multiple breathing cracks. Procedia Engineering, 2014, 86: 835–842

    Article  Google Scholar 

  34. Andreaus U, Casini P, Vestroni F. Non-linear dynamics of a cracked cantilever beam under harmonic excitation. International Journal of Non-Linear Mechanics, 2007, 42(3): 566–575

    Article  Google Scholar 

  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(4): 721–742

    Article  Google Scholar 

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

    Article  Google Scholar 

  37. Zhang W, 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

    Article  Google Scholar 

  38. Liu C, Jiang D. Crack modeling of rotating blades with cracked hexahedral finite element method. Mechanical Systems and Signal Processing, 2014, 46(2): 406–423

    Article  Google Scholar 

  39. Kuang J W, Huang B W. Mode localization of a cracked blade-disks. In: Proceedings of the ASME 1998 International Gas Turbine and Aeroengine Congress and Exhibition. Volume 5: Manufacturing Materials and Metallurgy; Ceramics; Structures and Dynamics; Controls, Diagnostics and Instrumentation; Education. Stockholm: ASME, 1998, V005T014A013

    Google Scholar 

  40. Huang B W, Kuang J H. Variation in the stability of a rotating blade disk with a local crack defect. Journal of Sound and Vibration, 2006, 294(3): 486–502

    Article  Google Scholar 

  41. Panigrahi B, Pohit G. Effect of cracks on nonlinear flexural vibration of rotating Timoshenko functionally graded material beam having large amplitude motion. Proceedings of the Institution of Mechanical Engineers. Part C, Journal of Mechanical Engineering Science, 2018, 232(6): 930–940

    Article  Google Scholar 

  42. Kim S S, Kim J H. Rotating composite beam with a breathing crack. Composite Structures, 2003, 60(1): 83–90

    Article  Google Scholar 

  43. Xu H, Chen Z, Xiong Y, et al. Nonlinear dynamic behaviors of rotated blades with small breathing cracks based on vibration power flow analysis. Shock and Vibration, 2016, 2016(1): 1–11

    Google Scholar 

  44. Xu H, Chen Z, Yang Y, et al. Effects of crack on vibration characteristics of mistuned rotated blades. Shock and Vibration, 2017, 1785759

  45. Saito A. Nonlinear vibration analysis of cracked structures: Application to turbomachinery rotors with cracked blades. Dissertation for the Doctoral Degree. Michigan: The University of Michigan, 2009

    Google Scholar 

  46. Xie J, Zi Y, Zhang M, et al. A novel vibration modeling method for a rotating blade with breathing cracks. Science China. Technological Sciences, 2019, 62(2): 333–348

    Article  Google Scholar 

  47. Jousselin O. Development of blade tip timing techniques in turbo machinery. Dissertation for the Doctoral Degree. Manchester: The University of Manchester, 2013

    Google Scholar 

  48. Dimarogonas A D, Paipetis S A, Chondros T G. Analytical Methods in Rotor Dynamics. 2nd ed. Dordrecht: Springer, 2013

    Book  MATH  Google Scholar 

  49. Tata H, Paris P, Irwin G. The Stress Analysis of Crack Handbook. 3rd ed. New York: ASME Press, 2000

    Google Scholar 

  50. Chati M, Rand R, Mukherjee S. Modal analysis of a cracked beam. Journal of Sound and Vibration, 1997, 207(2): 249–270

    Article  MATH  Google Scholar 

  51. Saito A, Castanier M P, Pierre C. Estimation and veering analysis of nonlinear resonant frequencies of cracked plates. Journal of Sound and Vibration, 2009, 326(3–5): 725–739

    Article  Google Scholar 

  52. Zeng J, Chen 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(3): 568–583

    Article  Google Scholar 

Download references

Acknowledgements

This work was sponsored by the National Major Project of China (Grant No. 2017-V-0009) and the National Natural Science Foundation of China (Grant No. 51705397). The first author acknowledges the host and support from the Structural Dynamics and Acoustic Systems Laboratory at the University of Massachusetts Lowell, USA.

Author information

Authors and Affiliations

  1. The State Key Laboratory for Manufacturing Systems Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Laihao Yang, Shuming Wu, Xuefeng Chen & Ruqiang Yan

  2. School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an, 710049, China

    Laihao Yang, Shuming Wu, Xuefeng Chen & Ruqiang Yan

  3. The Structural Dynamics and Acoustic Systems Laboratory, University of Massachusetts Lowell, Lowell, MA, 01854, USA

    Zhu Mao

Authors
  1. Laihao Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhu Mao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shuming Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xuefeng Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ruqiang Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Laihao Yang.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, L., Mao, Z., Wu, S. et al. Nonlinear dynamic behavior of rotating blade with breathing crack. Front. Mech. Eng. 16, 196–220 (2021). https://doi.org/10.1007/s11465-020-0609-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11465-020-0609-z

Keywords

Search

Navigation