Abstract
Flexible blades coupled to rotating systems are commonly used in industrial machines, such as compressors, exhausters, and turbines. These components are usually exposed to different operating conditions, including high speed, large centrifugal forces, high temperatures, and pressure. Considering the inevitable manufacturing flaws, cracks can emerge and grow particularly in blades of these systems. Thus, investigations on the dynamic behavior of cracked blades become mandatory to prevent failures. In this work, the development, solution, and instability analysis of a system composed of four flexible blades coupled to a flexible shaft are presented. The flexible blades are modeled as Euler-Bernoulli beams with tip masses attached at their ends. Their deformations are obtained by considering second order nonlinear terms to ensure that the centrifugal stiffness is correctly represented, thus characterizing a second order linearized model. The equations of motion are obtained by applying the so-called Newton-Euler-Jourdain method. The crack presence brings an additional flexibility to the blades, which is introduced in the model by using a torsional spring. The resulting blade stiffness is obtained through the beam elastic equation. The Newmark time integration method is associated with the Newton-Raphson iteration procedure to integrate the equations of motion. The system was evaluated for different situations, regarding the depth of the crack in the blades, as well as the operating condition of the rotor-blade system. Finally, the instability map and the vibration responses of the system is determined. The obtained results indicate the instability condition of the rotor-blade system for a certain combination of rotating speed, angular position of the blades, and crack depth.
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Xu, H., Chen, Z., Xiong, Y., Yang, Y., Tao, L.: Nonlinear dynamic behaviors of rotated blades with small breathing cracks based on vibration power flow analysis. J. Shock Vib. 2016 (2016)
Wu, M.C., Huang, S.C.: On the vibration of cracked rotating blade. J. Shock Vib. 5, 317–323 (1998)
Saavedra, P.N., Cuitiño, L.A.: Crack detection and vibration behavior of cracked beams. J. Comput. Struct. 79(2001), 1451–1459 (2001)
Legrand, M.: Modèles de prèdiction de l’interaction rotor/stator dans un moteur d’avion. Doctorat, thesis, L’École Centrale de Nantes et l’Université de Nantes, Nantes (2005)
Santos, I.F., Saracho, C.M., Smith, J.T., Eiland, J.: Contribution to experimental validation of linear and non-linear dynamics models for representing rotor-blade parametric coupled vibrations. J. Sound Vib. 271, 883–904 (2004)
Saracho, C.M.: Numerical and experimental analysis of flexible blade dynamic behavior. Campinas State University. Thesis (Doctorate), Campinas (2002)
Dimarogonas, A.D.: Vibration Engineering. St. Paul, West Publishers (1976)
Chondros, T.G.: Dynamic response of a cracked beam. University of Patras, Greece. M.Sc. thesis (1977)
Dimarogonas, A.D., Rizos, P.F., Aspragathos, N.: Identification of crack location and magnitude in a cantilever beam from the vibration modes. J. Sound Vib. 138, 331–338 (1990)
Dimarogonas, A.D., Paipetis, S.A.: Analytical Methods in Rotor Dynamics. Elsevier, London (1983)
Mayes, I.W., Davies, W.G.R.: Analysis of the response of a multi-rotor-bearing system containing a transversal crack in a rotor. J. Vib. Acoust. Stress Reliab. Des. 106, 139–146 (1984)
Simo, J.C., Vu-Quoc, L.: On the dynamics of flexible beams under large overall motion—the plane case. Part I and II. ASME J. Appl. Mech. 53, 849–863 (1986)
Kane, T.R., Ryan, R.R., Banerjee, A.K.: Dynamics of a cantilever beam attached to a moving base. J. Guid. Control Dyn. 10(2), 139–151 (1987)
Choi, Y.S., Gottfried, D.A., Fleeter, S.: Analysis of structural mistuning effects on bladed disc vibrations including aerodynamic damping. In: International Compressor Engineering Conference. Paper 1627 (2004)
Ogata, K.: Modern Control Engineering, 4th edn. Prentice Hall, Upper Saddle River (2002)
Acknowledgments
The authors are thankful to the Brazilian Research Agencies CAPES, CNPq (574001/2008-5/304546/2017-8) and FAPEMIG (TEC-APQ-022284-15/TEC-APQ-307609) for the financial support provided to this research effort. The authors are also thankful to the companies CERAN, BAESA, ENERCAN, and Foz do Chapecó for the financial support through the R&D project Robust Modeling for the Diagnosis of Defects in Generating Units (02476-3108/2016).
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Rende, B.R.F., da Silva, I.B., Morais, T.S., Cavalini, A.A., Steffen, V. (2019). Stability Analysis of a Cracked Blade Coupled with a Rigid Rotor. In: Cavalca, K., Weber, H. (eds) Proceedings of the 10th International Conference on Rotor Dynamics – IFToMM . IFToMM 2018. Mechanisms and Machine Science, vol 62. Springer, Cham. https://doi.org/10.1007/978-3-319-99270-9_13
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DOI: https://doi.org/10.1007/978-3-319-99270-9_13
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