Nonlinear Dynamics

, Volume 88, Issue 4, pp 2347–2357 | Cite as

Dynamics of a cracked rotor system with oil-film force in parameter space

  • Xiao-Bo Rao
  • Yan-Dong Chu
  • Ying-Xiang Chang
  • Jian-Gang Zhang
  • Ya-Ping Tian
Original Paper


An organization structure of global oscillation with respect to a cracked rotor system with oil-film force is investigated in this paper. We profit from GPU cluster parallel computing to present a number of high-quality phase diagrams, and exhibit global dynamic characteristics of the system. An interesting scenario, “eye” of chaos, is discovered in this cracked rotor system, emerging as the accumulation limit of forward and reverse period-doubling bifurcation cascades. In this system, it is a common phenomenon that the vibration response of the rotor presents three typical characteristics in parameter space with the rotation speed increasing. Moreover, these phase diagrams assist us to identify multi-attractor coexisting that makes the dynamics behavior of this system become more enrich and complex. These results we represent get us better to understand the nonlinear response of the cracked rotor system and are beneficial to control and diagnose the crack.


Cracked rotor system Oil-film force Dynamic characteristics Phase diagram Forward and reverse period-doubling bifurcation cascades 



This work is supported by the National Natural Science Foundation of China (Nos. 11161027, 11262009), the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20136204110001), and the Innovation and Entrepreneurship of Lanzhou city (No. 2015-RC-3).


  1. 1.
    Papadopoulos, C.A., Dimarogonas, A.D.: Coupling of bending and torsionalvibration of a cracked Timoshenko shaft. J. Arch. Appl. Mech. 57, 257–266 (1987)MATHGoogle Scholar
  2. 2.
    Papadopoulos, C.A., Dimarogonas, A.D.: Coupled longitudinal and bending vibrations of a rotating shaft with an open crack. J. Sound Vib. 117, 81–93 (1987)CrossRefGoogle Scholar
  3. 3.
    Gasch, R.: A survey of the dynamic behavior of a simple rotating shaft with a transverse crack. J. Sound Vib. 160, 313–332 (1993)CrossRefMATHGoogle Scholar
  4. 4.
    Sinou, J.-J., Lees, A.W.: A non-linear study of a cracked rotor. Eur. J. Mech. A-Solid 26, 152–170 (2007)CrossRefMATHGoogle Scholar
  5. 5.
    Zheng, J.B., zan, M., Guang, M.: Bifurcation and chaos of a nonlinear cracked rotor. Int. J. Bifurc. Chaos 8, 597–607 (1998)CrossRefMATHGoogle Scholar
  6. 6.
    Chen, C.P., Dai, L.M.: Bifurcation and chaotic response of a cracked rotor system with viscoelastic supports. Nonlinear Dyn. 50, 483–509 (2007)CrossRefMATHGoogle Scholar
  7. 7.
    Sinou, J.-J., Lees, A.W.: The influence of cracks in rotating shafts. J. Sound Vib. 285, 1015–1037 (2005)CrossRefGoogle Scholar
  8. 8.
    Sinou, J.-J.: Effects of a crack on the stability of a non-linear rotor system. Int. J. Nonlinear Mech. 42, 959–972 (2007)CrossRefGoogle Scholar
  9. 9.
    Sinou, J.-J.: Detection of cracks in rotor based on the 2x and 3x super-harmonic frequency components and the crackCunbalance interactions. Commun. Nonlinear Sci. Numer. Sim. 13(9), 2024–2040 (2008)CrossRefGoogle Scholar
  10. 10.
    AL-Shudeifat, M.A., Butcher, E.A., Stern, C.R.: General harmonic balance solution of a cracked rotor-bearing-disk system for harmonic and sub-harmonic analysis: analytical and experimental approach. Int. J. Eng. Sci. 48, 921–935 (2010)CrossRefGoogle Scholar
  11. 11.
    AL-Shudeifat, M.A.: On the finite element modeling of the asymmetric cracked rotor. J. Sound Vib. 332, 2795–2807 (2013)CrossRefGoogle Scholar
  12. 12.
    Al-Shudeifat, M.A., 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, 526–544 (2011)CrossRefGoogle Scholar
  13. 13.
    Han, Q.K., Chu, F.: Parametric instability of a rotor-bearing system with two breathing transverse cracks. Eur. J. Mech. A-Solid 36, 180–190 (2012)CrossRefGoogle Scholar
  14. 14.
    Sekhar, A., Mohanty, A., Prabhakar, S.: Vibrations of cracked rotor system: transverse crack versus slant crack. J. Sound Vib. 279, 1203–1217 (2005)CrossRefGoogle Scholar
  15. 15.
    Lin, Y.L., Chu, F.l: The dynamic behavior of a rotor system with a slant crack on the shaft. Mech. Syst. Signal Process. 24, 522–545 (2010)CrossRefGoogle Scholar
  16. 16.
    Gasch, R.: Dynamic behaviour of the Laval rotor with a transverse crack. Mech. Syst. Signal Process. 22, 790–804 (2008)CrossRefGoogle Scholar
  17. 17.
    Gasch, R.: A survey of the dynamic behaviour of a simple rotating shaft with a transverse crack. J. Sound Vib. 160, 313–332 (1993)CrossRefMATHGoogle Scholar
  18. 18.
    Mayes, I.W., Davies, W.G.R.: Analysis of the response of a multi-rotor-bearing system containing a transverse crack in a rotor. J. Vib. Acoust. Stress Reliab. Des. 106, 139–145 (1984)Google Scholar
  19. 19.
    Gao, J.M., Zhu, X.M.: Study on the model of the shaft crae openning and closing. Acta. Mech. Sinich-Prc. 9, 108–112 (1992)Google Scholar
  20. 20.
    Wen, B.C., Wang, Y.B.: Theoretical research, calaulation and experiments of cracked shaft dynamical respones. In: Proceedings of international conference on vibration in rotating machinery (1988)Google Scholar
  21. 21.
    Adiletta, G., Guido, A.R., Rossi, C.: Chaotic motions of a rotor in short juournal bearings. Nonlinear Dyn. 10, 251–269 (1996)CrossRefGoogle Scholar
  22. 22.
    Luo, Y.G., Ren, Z.H., Ma, H., Wen, B.C.: Stability of periodic motion on the rotor-bearing system with coupling faults of crack and rub-impact. J. Mech. Sci. Technol. 21, 860–864 (2007)CrossRefGoogle Scholar
  23. 23.
    Sack, A., Freire, J.G., Lindberg, E., Poschel, T., Gallas, J.A.C.: Discontinuous spirals of stable periodic oscillations. Sci. Rep-Uk. 27, 3350–3350 (2013)CrossRefGoogle Scholar
  24. 24.
    Gallas, J.A.C.: Periodic oscillations of the forced Brusselator. J. Mod. Phys. Lett. B 29, 1530018–1530027 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  • Xiao-Bo Rao
    • 1
  • Yan-Dong Chu
    • 2
  • Ying-Xiang Chang
    • 2
  • Jian-Gang Zhang
    • 2
  • Ya-Ping Tian
    • 1
  1. 1.School of Mechatronic EngineeringLanzhou Jiaotong UniversityLanzhouPeople’s Republic of China
  2. 2.Department of MathematicsLanzhou Jiaotong UniversityLanzhouPeople’s Republic of China

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