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Two-stage crack identification in an Euler-Bernoulli rotating beam using modal parameters and Genetic Algorithm

  • Belen Munoz-Abella (Department of Mechanical Engineering, University Carlos III of Madrid) ;
  • Lourdes Rubio (Department of Mechanical Engineering, University Carlos III of Madrid) ;
  • Patricia Rubio (Department of Mechanical Engineering, University Carlos III of Madrid)
  • Received : 2023.09.22
  • Accepted : 2023.11.10
  • Published : 2024.02.25
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Abstract

Rotating beams play a crucial role in representing complex mechanical components that are prevalent in vital sectors like energy and transportation industries. These components are susceptible to the initiation and propagation of cracks, posing a substantial risk to their structural integrity. This study presents a two-stage methodology for detecting the location and estimating the size of an open-edge transverse crack in a rotating Euler-Bernoulli beam with a uniform cross-section. Understanding the dynamic behavior of beams is vital for the effective design and evaluation of their operational performance. In this regard, modal parameters such as natural frequencies and eigenmodes are frequently employed to detect and identify damages in mechanical components. In this instance, the Frobenius method has been employed to determine the first two natural frequencies and corresponding eigenmodes associated with flapwise bending vibration. These calculations have been performed by solving the governing differential equation that describes the motion of the beam. Various parameters have been considered, such as rotational speed, beam slenderness, hub radius, and crack size and location. The effect of the crack has been replaced by a rotational spring whose stiffness represents the increase in local flexibility as a result of the damage presence. In the initial phase of the proposed methodology, a damage index utilizing the slope of the beam's eigenmode has been employed to estimate the location of the crack. After detecting the presence of damage, the size of the crack is determined using a Genetic Algorithm optimization technique. The ultimate goal of the proposed methodology is to enable the development of more suitable and reliable maintenance plans.

Keywords

Acknowledgement

This work was supported by the "Agencia Estatal de Investigacion" (AEI) of the Government of Spain through the project: PID2019-104799GB-I00/AEI/10.13039/501100011033.

References

  1. Ahmed, A.M. and Rifai, A.M. (2021), "Euler-Bernoulli and Timoshenko beam theories. Analytical and numerical comprehensive revision", Eur. J. Eng. Sci. Tech., 6(7), 20-32. https://doi.org/10.24018/ejeng.2021.6.7.2626 
  2. Aydin, K. (2013), "Influence of crack and slenderness ratio on the eigenfrequencies of Euler-Bernoulli and Timoshenko beams", Mech. Adv. Mater. Struct., 20, 339-352. https://doi.org/10.1080/15376494.2011.627635 
  3. Banerjee, J.R. (2000), "Free vibration of centrifugally stiffened uniform and tapered beams using the Dynamic stiffness method", J. Sound Vib., 233(5), 857-875. https://doi.org/10.1006/jsvi.1999.2855 
  4. Banerjee, A. and Pohit, G. (2014), "Crack detection in rotating cantilever beam by Continuous Wavelet Transform", Appl. Mech. Mater., 592-594, 2021-2025. https://doi.org/10.4028/www.scientific.net/AMM.592-594.2021 
  5. Banerjee, J.R., Su, H. and Jackson, D.R. (2006), "Free vibration of rotating tapered beams using the dynamic stiffness method", J. Sound Vib., 4-5, 1034-1054. https://doi.org/10.1016/j.jsv.2006.06.040 
  6. Bath, R.B. (1986), "Transverse vibrations of a rotating uniform cantilever beam with tip mass as predicted by using beam characteristic orthogonal polynomials in the Rayleigh-Ritz method", J. Sound Vib., 105(2), 199-210. https://doi.org/10.1016/0022-460X(86)90149-5 
  7. Bilotta, A, Morassi, A. and Turco, E. (2023), "Damage identification for steel-concrete composite beams through convolutional neural networks", J. Vib. Control, 30(3-4), 876-889. https://doi.org/10.1177/10775463231152926 
  8. Chen, L.W. and Chen, C.L. (1988), "Vibration and stability of cracked thick rotating blades", Comput. Struct., 28(1), 67-74. https://doi.org/10.1016/0045-7949(88)90093-4 
  9. Chen, H., Yong, H. and Zhou, Y. (2022), "Crack detection in bulk superconductor using genetic algorithm", Eng. Fract. Mech., 265, 108372. https://doi.org/10.1016/j.engfracmech.2022.108372 
  10. Cheng, Y., Yu, Z., Wu, X. and Yuan, Y. (2011), "Vibration analysis of a cracked rotating tapered beam using the p-version finite element method", Finite Elem. Anal. Des., 47, 825-834. https://doi.org/10.1016/j.finel.2011.02.013 
  11. Chondros, Y., Dimarogonas, A.D. and Yao, J. (1998), "A continuous cracked beam vibration theory", J. Sound Vib., 215(1), 17-34. https://doi.org/10.1006/jsvi.1998.1640 
  12. Fernandez-Saez, J., Morassi, A. and Rubio, L. (2017), "Crack identification in elastically restrained vibrating rods", Int. J. Non Linear Mech., 94, 257-267. https://doi.org/10.1016/j.ijnonlinmec.2017.03.018 
  13. Gairola, S., Rengaswamy, J. and Verma, R. (2023), "A study on XFEM simulation of tensile, fracture toughness, and fatigue crack growth behavior of Al 2024 alloy through fatigue crack growth rate models using genetic algorithm", Fatigue Fract. Eng. Mater. Struct., 46, 2121-2138. https://doi.org/10.1111/ffe.13987 
  14. Kim, H., Yoo, H.H. and Yung, J. (2013), "Dynamic model for free vibration and response analysis of rotating beams", J. Sound Vib., 332, 5917-5928. https://doi.org/10.1016/j.jsv.2013.06.004 
  15. Kindova-Petrova, D. (2022), "A new damage detection index based on beam mode shape slope", J. Theor. Appl. Mech., 52, 75-87. https://doi.org/10.55787/jtams.22.52.1.075 
  16. Krawczuk, M. (1993), "Natural vibration of cracked rotating beams", Acta Mech., 99, 35-48. https://doi.org/10.1007/BF01177233 
  17. Lee, J.W and Lee, J.Y. (2017), "In-plane bending vibration analysis of a rotating beam with multiple edge cracks by using the transfer matrix method", Meccanica, 52, 1143-1157. https://doi.org/10.1007/s11012-016-0449-4 
  18. Liu, C. and Yiang, D. (2014), "Crack modeling of rotating blades with cracked hexahedral finite element method", Mech. Syst. Signal. Process., 2, 406-423. https://doi.org/10.1016/j.ymssp.2014.01.007 
  19. Liu, C., Yiang, D. and Chu, F. (2015), "Influence of alternating loads on nonlinear vibration characteristics of cracked blade in rotor system", J. Sound Vib., 353, 205-219. https://doi.org/10.1016/j.jsv.2015.05.007 
  20. Maity, D. and Tripathy, R.R. (2005), "Damage assessment of structures from changes in natural frequencies using genetic algorithm", Struct. Eng. Mech., Int. J., 19(1), 21-42. https://doi.org/10.12989/sem.2005.19.1.021 
  21. Masoud, A.A. and Al-Said, S. (2009), "A new algorithm for crack localization in a rotating Timoshenko beam", J. Sound Vib., 15(10), 1541-1561. https://doi.org/10.1177/1077546308097272 
  22. Matlab (2023), MATLABTM, Optimization toolbox. User's guide. 
  23. Mohammed, A.A., Neilson, R.D., Deans, W.F. and MacConnell, P. (2014), "Crack detection in a rotating shaft using artificial neural networks and PSD characterisation", Meccanica, 49, 255-266. https://doi.org/10.1007/s11012-013-9790-z 
  24. Munoz-Abella, B., Rubio, L., Rubio, P. and Montero, L. (2018), "Elliptical crack identification in a nonrotating shaft", Shock Vib., vol. 2018, Article ID 4623035, 10 pages. https://doi.org/10.1155/2018/4623035 
  25. Munoz-Abella, B., Ruiz-Fuentes, A., Rubio, P., Montero, L. and Rubio, L. (2020), "Cracked rotor diagnosis by means of frequency spectrum and artificial neural networks", Smart Struct. Syst., Int. J., 25(4), 459-469. https://doi.org/10.12989/sss.2020.25.4.459 
  26. Munoz-Abella, B., Rubio, L. and Rubio, P. (2022a), "Closed-form solution for the natural frequencies of low-speed cracked Euler-Bernoulli rotating beams", Mathematics, 10(24), 4742. https://doi.org/10.3390/math10244742 
  27. Munoz-Abella, B., Rubio, L. and Rubio, P. (2022b), "Aplicacion de redes neuronales artificiales en la identificacion de fisuras en vigas rotatorias Euler-Bernoulli a bajas velocidades", XV Congreso Iberoamericano de Ingenieria Mecanica, Madrid, Spain, November. [In Spanish] 
  28. Munoz-Abella, B., Rubio, L. and Rubio, P. (2023), "Coefficients Cracked rotating beam", Zenodo repository. https://doi.org/10.5281/zenodo.8329047 
  29. Nayyar, A., Baneen, U., Naqvi, S.A.Z. and Ahsan, M. (2021), "Detection and localization of multiple small damages in beam", Adv. Mech. Eng., 13(1). https://doi.org/10.1177/1687814020987329 
  30. Ozdemir, O. and Kaya, M.O. (2006), "Flapwise bending vibration analysis of a rotating tapered cantilever Bernoulli-Euler beam by differential transform method", J. Sound Vib., 1-2, 413-420. https://doi.org/10.1016/j.jsv.2005.01.055 
  31. Ramezani, M. and Bahar, O. (2021), "Structural damage identification for elements and connections using an improved genetic algorithm", Smart Struct. Syst., Int. J.., 28(5), 643-660. https://doi.org/10.12989/sss.2021.28.5.643 
  32. Rubio, L. (2009), "An efficient method for crack identification in simply supported Euler-Bernoulli beams", J. Vib. Acoust., 131(5), 051001 (6 pages). https://doi.org/10.1115/1.3142876 
  33. Rubio, L., Fernandez-Saez, J. and Morassi, A. (2018), "A Identification of an open crack in a beam with variable profile by two resonant frequencies", J. Vib. Control., 24(5), 839-859. https://doi.org/10.1177/1077546316671483 
  34. Sekhar, A.S. (2004), "Crack identification in a rotor system: a model-based approach", J. Sound Vib., 270(4-5), 887-902. https://doi.org/10.1016/S0022-460X(03)00637-0 
  35. Suh, M.W., Yu, J.M. and Lee, J.H. (2000), "Crack identification using classical optimization technique", Key Eng. Mater., 183-187, 61-66. https://doi.org/10.4028/www.scientific.net/KEM.183-187.61 
  36. Talebi, S. and Ariaei, A. (2015), "Vibration analysis of a rotating Timoshenko beam with internal and external flexible connections", Arch. Appl. Mech., 85, 555-572. https://doi.org/10.1007/s00419-014-0930-2 
  37. Valverde-Marcos, B., Munoz-Abella, B., Rubio, P. and Rubio, L. (2022), "Influence of the rotation speed on the dynamic behaviour of a cracked rotating beam", Theor. Appl. Fract. Mech., 117, 103209. https://doi.org/10.1016/j.tafmec.2021.103209 
  38. Wauer, J. (1991), "Dynamics of cracked rotating blades", Appl. Mech. Rev., 44(11S), S273-S278. https://doi.org/10.1115/1.3121364 
  39. Yang, L.H., Yang, Z.S., Mao, Z., Wu, S.M., Chen, X.F. and Yan, R.Q., (2021a), "Dynamic characteristic analysis of rotating blade with transverse crack-Part I: modeling, modification, and validation", J. Vib. Acoust., 143(5), 051010 (15 pages). https://doi.org/10.1115/1.4049385 
  40. Yang, L.H., Yang, Z.S., Mao, Z., Wu, S.M., Chen, X.F. and Yan, R.Q., (2021b), "Dynamic characteristic analysis of rotating blade with transverse crack-Part II: A comparison study of different crack models", J. Vib. Acoust., 143(5), 051011 (13 pages). https://doi.org/10.1115/1.4049386 
  41. Yashar, A., Ferguson, N. and Ghandchi-Tehrani, M. (2018), "Simplified modelling and analysis of a rotating Euler-Bernoulli beam with a single cracked edge", J. Sound Vib., 420, 346-356. https://doi.org/10.1016/j.jsv.2017.12.041 
  42. Yazdanpanah, O., Seyedpoor, S.M. and Akbarzadeh-Bengar, H. (2015), "A new damage detection indicator for beams based on mode shape data", Struct. Eng. Mech., Int. J., 53(4), 725-744. https://doi.org/10.12989/sem.2015.53.4.725