Nonlinear Dynamics

, Volume 86, Issue 2, pp 1057–1067 | Cite as

Nonlinear dynamics of an asymmetric rotor-bearing system with coupling faults of crack and rub-impact under oil-film forces

Original Paper


The parametric instability of a rotor-bearing system with coupling faults of crack and rub-impact under nonlinear oil-film force is studied in this paper. A model considering time-varying crack stiffness, rub-impact force and nonlinear oil-film force is put forward to analyze the complicated nonlinear behaviors of the rotor-bearing system. The numerical simulation focuses on the effects of crack depth and the stator stiffness on the onset of instability and nonlinear responses of the rotor-bearing system by using bifurcation diagrams, Poincaré maps, largest Lyapunov exponent and frequency spectrum. The multiple periodic, quasiperiodic and chaotic motions are observed in this study. The results indicate that crack depth and stator stiffness have influences on the vibration and instability of the rotor-bearing system with varied rotating speed. The motion of the system with coupling faults shows strong nonlinearity and instability in high speed region. Moreover, crack depth and stator stiffness interfere with the formation of oil whirl, thus, making the oil whirl appear later. There also exists interaction among coupling multiple faults. The research discloses the worthy energy exchange phenomenon of multi-fault system and is helpful for fault diagnosis and vibration control of real rotor-bearing systems.


Rotor-bearing system Nonlinear dynamics Crack Rub-impact Oil-film forces 



This work is supported by the National Natural Science Foundation of China (No. 51475164) and Natural Science Foundation of Hebei Province (E2013502226).


  1. 1.
    Dimarogonas, A.D.: Vibration of cracked structures: a state of art review. Eng. Fract. Mech. 55, 831–857 (1996)CrossRefGoogle Scholar
  2. 2.
    Gash, R.: A survey of the dynamic behavior of a simple rotating shaft with a transverse crack. J. Sound Vib. 160, 313–332 (1993)CrossRefGoogle Scholar
  3. 3.
    Jun, O.S., Eun, H.J., Earmme, Y.Y., Lee, C.W.: Modelling and vibration analysis of a simple rotor with breathing crack. J. Sound Vib. 155, 273–290 (1992)CrossRefMATHGoogle Scholar
  4. 4.
    Sekhar, A.S., Prabhu, B.S.: Transient analysis of a cracked rotor passing through critical speed. J. Sound Vib. 173, 415–421 (1994)CrossRefMATHGoogle Scholar
  5. 5.
    Sinou, J.J., Lees, A.W.: The influence of cracks in rotating shafts. J. Sound Vib. 285, 1015–1037 (2005)CrossRefGoogle Scholar
  6. 6.
    Chan, R.K., Lai, T.C.: Digital simulation of a rotating shaft with a transverse crack. Appl. Math. Model. 19, 411–420 (1995)CrossRefMATHGoogle Scholar
  7. 7.
    Darpe, A.K., Gupta, K., Chawla, A.: Dynamics of a two-cracked rotor. J. Sound Vib. 259, 649–675 (2003)Google Scholar
  8. 8.
    Darpe, A.K., Gupta, K., Chawla, A.: Dynamics of a bowed rotor with a transverse surface crack. J. Sound Vib. 296, 888–90 (2006)CrossRefGoogle Scholar
  9. 9.
    Guang, M.: The nonlinear influences of whirl speed on the stability and response of a cracked rotor. J. Mach. Vib. 6, 216–230 (1992)Google Scholar
  10. 10.
    Gounaris, G.D., Papadopoulos, C.A.: Crack identification in rotating shafts by coupled response measurements. Eng. Fract. Mech. 69, 339–352 (2002)CrossRefGoogle Scholar
  11. 11.
    Muszynska, A.: Rotor-to-stationary element rub-related vibration phenomena in rotating machinery literature survey. Shock Vib. Dig. 21, 3–11 (1989)CrossRefGoogle Scholar
  12. 12.
    Chu, F., Zhang, Z.: Bifurcation and chaos in rub-impact Jeffcott rotor system. J. Sound Vib. 210, 1–18 (1998)CrossRefGoogle Scholar
  13. 13.
    Goldman, P., Muszynska, A.: Chaotic behavior of rotor/stator systems with rubs. J. Eng. Gas Turbines Power 116, 692–701 (1994)CrossRefGoogle Scholar
  14. 14.
    Abu-Mahfouz, Issam, Banerjee, Amit: On the investigation of nonlinear dynamics of a rotor with rub-impact using numerical analysis and evolutionary algorithms. Procedia Comput. Sci. 20, 140–147 (2013)CrossRefGoogle Scholar
  15. 15.
    Liu, L., Cao, D.Q., Sun, S.P.: Dynamic characteristics of a disk-drum-shaft rotor system with rub-impact. Nonlinear Dyn. 80, 1017–1038 (2015)CrossRefGoogle Scholar
  16. 16.
    Lahriri, S., Santos, I.F.: Theoretical modelling, analysis and validation of the shaft motion and dynamic forces during rotor–stator contact. J. Sound Vib. 332, 6359–6376 (2013)CrossRefGoogle Scholar
  17. 17.
    Chang-Jian, C.-W., Chen, C.-K.: Couple stress fluid improve rub-impact rotor-bearing system—nonlinear dynamic analysis. Appl. Math. Model. 34, 1763–1778 (2010)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Shen, X.Y., Jia, J.H., Zhao, M.: Experimental and numerical analysis of nonlinear dynamics of rotor-bearing-seal system. Nonlinear Dyn. 53, 31–44 (1996)CrossRefMATHGoogle Scholar
  19. 19.
    Wan, F., Xu, Q., Li, S.: Vibration analysis of cracked rotor sliding bearing system with rotor–stator rubbing by harmonic wavelet transform. J. Sound Vib. 271, 507–518 (2004)CrossRefGoogle Scholar
  20. 20.
    Ren, Z., Zhou, S., Li, C., Wen, B.: Dynamic characteristics of multi-degrees of freedom system rotor-bearing system with coupling faults of rub-impact and crack. Chin. J. Mech. Eng. 27, 785–792 (2014)CrossRefGoogle Scholar
  21. 21.
    Adiletta, G., Guido, A.R., Rossi, C.: Chaotic motions of a rigid rotor in short journal bearings. Nonlinear Dyn. 10, 251–269 (1996)CrossRefGoogle Scholar
  22. 22.
    Aijun, Hu, Yan, Xiaoan, Xiang, Ling: Dynamic simulation and experimental study of an asymmetric double-disc rotor-bearing system with rub-impact and oil-film instability. Nonlinear Dyn. 84, 641–659 (2016)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringNorth China Electric Power UniversityBaodingChina

Personalised recommendations