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Dynamic modeling and stability analysis of a heavy-duty flywheel rotor-bearing system with two cracks. (English) Zbl 1537.74161

Summary: Cracks have a significant impact on the stability of rotating machinery. However, most studies focus on rotating machinery with only one crack. This paper discusses the influence of two cracks on the stability of a flywheel rotor-bearing system. In this study, the dynamic models of vertically placed flywheel rotor-bearing system with two open cracks and two breath cracks are established using the finite element method (FEM). Floquet theory is used to calculate the stability of the system and the influence of depth and positions of cracks are analyzed. The results show that breathing cracks cause more unstable regions than open cracks, and the range of rotating speeds over which the rotor is unstable increases with increasing crack depth. In addition, it is observed that when the crack locations are adjacent, the unstable region will become very large, covering most of the crack depth range and speed range, making the rotor extremely unstable. Besides, the bearing stiffness causes an offset in the unstable regions, whereas the damping influences the instability value of the rotor.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
70E50 Stability problems in rigid body dynamics
Full Text: DOI

References:

[1] Hou, J., Sun, J. and Hofmann, H., Control development and performance evaluation for battery/flywheel hybrid energy storage solutions to mitigate load fluctuations in all-electric ship propulsion systems, J. Appl. Energy212 (2018) 919-930.
[2] Olabi, A. G., Renewable energy and energy storage systems, J. Energy136 (2017) 1-6.
[3] Arani, A. A. K., Karami, H., Gharehpetian, G. B. and Hejazi, M. S. A., Review of flywheel energy storage systems structures and applications in power systems and microgrids, J. Renew. Sust. Energ. Rev.69 (2017) 9-18.
[4] Ren, Z. Y., Huang, T., Zhou, Y. W. and Zhang, S. W., Amplitude analysis of rigid flywheel rotor at critical speed, J. Mech. Des. Manuf.12 (2020) 5-8.
[5] Anifantis, N. K.et al., Coupled vibration response of a shaft with a breathing crack, J. Sound Vib.336 (2015) 191-206.
[6] Guo, C.et al., Crack detection for a Jeffcott rotor with a transverse crack: An experimental investigation, J. Mech. Syst. Signal Process.83 (2017) 260-271.
[7] Khorrami, H., Rakheja, S. and Sedaghati, R., Vibration behavior of a two-crack shaft in a rotor disc-bearing system, J. Mech. Mach. Theory.113 (2017) 67-84.
[8] Jin, Y.et al., Nonlinear dynamic analysis of a complex dual rotor-bearing system based on a novel model reduction method, J. Appl. Math. Modell.75 (2019) 553-571. · Zbl 1481.70011
[9] Papadopoulos, C. A. and Dimarogonas, A. D., Stability of cracked rotors in the coupled vibration mode, J. Vib. Acoust.110(3) (1988) 356-359.
[10] Sekhar, A. S. and Dey, J. K., Effects of cracks on rotor system instability, J. Mech. Mach. Theory.35(12) (2000) 1657-1674. · Zbl 1140.70381
[11] Azimi, M. and Moradi, S., Nonlinear dynamic and stability analysis of an edge cracked rotating flexible structure, Int. J. Struct. Stab. Dyn.21(7) (2021) 2150091. · Zbl 1535.74369
[12] Vervisch, B., Stockman, K. and Loccufier, M., Estimation of the damping matrix in rotating machinery for the calculation of the stability threshold speed, Int. J. Struct. Stab. Dyn.14(6) (2014) 1450012. · Zbl 1480.70028
[13] Xiao, S. F., Chen, H. Y. and Niu, H. P., Buckling and vibration of a long shaft rotor system with a stabilized bearing, Int. J. Struct. Stab. Dyn.17(4) (2016) 1750048. · Zbl 1535.74148
[14] Amirzadegan, S., Rokn-Abadi, M. and Firouz-Abadi, R. D., Optimization of nonlinear unbalanced flexible rotating shaft passing through critical speeds, Int. J. Struct. Stab. Dyn.22(1) (2022) 2250014.
[15] Sekhar, A. S., Vibration characteristics of a cracked rotor with two open cracks, J. Sound Vib.223(4) (1999) 497-512.
[16] Patel, T. H. and Darpe, A. K., Influence of crack breathing model on nonlinear dynamics of a cracked rotor, J. Sound Vib.311(3-5) (2008) 953-972.
[17] Peng, H.et al., Stability analysis of an open cracked rotor with the anisotropic rotational damping in rotating operation, J. Appl. Math. Modell.45 (2017) 405-421. · Zbl 1446.74043
[18] Varney, P. and Green, I., Comparing the Floquet stability of open and breathing fatigue cracks in an overhung rotordynamic system, J. Sound Vib.408 (2017) 314-330.
[19] Sinou, J. J., Effects of a crack on the stability of a non-linear rotor system, Int. J. Non-Linear Mech.42(7) (2007) 959-972.
[20] Chen, C., Dai, L. and Fu, Y., Nonlinear response and dynamic stability of a cracked rotor, J. Commun. Nonlinear Sci. Numer. Simul.12(6) (2007) 1023-1037. · Zbl 1146.74022
[21] Peng, H.et al., Stability analysis of the whirl motion of a breathing cracked rotor with asymmetric rotational damping, J. Nonlinear Dyn.90(3) (2017) 1545-1562.
[22] Gasch, R., Dynamic behaviour of the Laval rotor with a transverse crack, J. Mech. Syst. Signal Process.22(4) (2008) 790-804.
[23] Cheng, L.et al., The influence of crack breathing and imbalance orientation angle on the characteristics of the critical speed of a cracked rotor, J. Sound Vib.330(9) (2011) 2031-2048.
[24] He, Q.et al., The effects of unbalance orientation angle on the stability of the lateral torsion coupling vibration of an accelerated rotor with a transverse breathing crack, J. Mech. Syst. Signal Process.75 (2016) 330-344.
[25] Ricci, R. and Pennacchi, P., Discussion of the dynamic stability of a multi-degree-of-freedom rotor system affected by a transverse crack, J. Mech. Mach. Theory58 (2012) 82-100.
[26] Wang, S.et al., Parametric instability of anisotropic rotor-bearing systems with a transverse crack, J. Sound Vib.443 (2019) 253-269.
[27] Gayen, D., Chakraborty, D. and Tiwari, R., Stability behavior of two-crack functionally graded shaft in a rotor-disc system: Finite element approach, J. Mater. Today Proc.24 (2020) 432-441.
[28] Gayen, D., Tiwari, R. and Chakraborty, D., Finite element based stability analysis of a rotor-bearing system having a functionally graded shaft with transverse breathing cracks, Int. J. Mech. Sci.157-158 (2019) 403-414.
[29] Al-Shudeifat, M. A., Stability analysis and backward whirl investigation of cracked rotors with time-varying stiffness, J. Sound Vib.348 (2015) 365-380.
[30] Guo, C.et al., Stability analysis for transverse breathing cracks in rotor systems, J. Eur. J. Mech. A/Solids.42 (2013) 27-34. · Zbl 1406.70013
[31] Friswell, M. I.et al., Dynamics of Rotating Machines (Cambridge University Press, Cambridge, 2010). · Zbl 1206.70002
[32] Al-Shudeifat, M. A. and Butcher, E. A., New breathing functions for the transverse breathing crack of the cracked rotor system: Approach for critical and subcritical harmonic analysis, J. Sound Vib.330(3) (2011) 526-544.
[33] Sanz, S.et al., Evaluation of magnetic forces in permanent magnets, IEEE Trans. Appl. Supercond.20(3) (2010) 846-850.
[34] Vokoun, D.et al., Magnetic forces between arrays of cylindrical permanent magnets, J. Magn. Magn. Mater.323 (2011) 55-60.
[35] Bachovchin, K. D., Hoburg, J. F. and Post, R. F.. Magnetic fields and forces in permanent magnet levitated bearings, IEEE Trans. Magn. Mag.48(7) (2012) 2112-2120.
[36] Jin, Y.et al., Nonlinear dynamic analysis of a complex dual rotor-bearing system based on a novel model reduction method, J. Appl. Math. Modell.75 (2019) 553-571. · Zbl 1481.70011
[37] Fu, C.et al., Steady-state response analysis of cracked rotors with uncertain-but-bounded parameters using a polynomial surrogate method, J. Commun. Nonlinear Sci. Numer. Simul.68 (2019) 240-256. · Zbl 1456.74151
[38] Liu, L., Sun, S. and Han, J., Nonlinear traveling-wave vibration of a ring-stringer stiffened cylindrical shell, Int. J. Struct. Stab. Dyn.21(4) (2021) 2150059. · Zbl 1535.74254
[39] Wu, H., Zeng, X. H. and Gao, D. G., Periodic response and stability of a maglev system with delayed feedback control under aerodynamic lift, Int. J. Struct. Stab. Dyn.21(3) (2021) 2150040. · Zbl 1535.74386
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