Nonlinear Dynamics

, Volume 80, Issue 1–2, pp 1017–1038 | Cite as

Dynamic characteristics of a disk–drum–shaft rotor system with rub-impact

  • Lun Liu
  • Dengqing Cao
  • Shupeng Sun
Original Paper


The dynamic model of a disk–drum–shaft rotor system with rub-impact is established and its dynamic characteristics are analyzed. According to an elastic impact model and Coulomb’s friction law, two rub-impact force models are firstly developed which corresponding to the disk–stator contact and the drum–stator contact, respectively. Taking into account, the coupling of the whole rotor whirl and the local drum vibration, the dynamic model of a disk–drum–shaft rotor system with the disk–stator and the drum–stator rubbing is established by employing Sanders’ shell theory and Lagrange equation. The numeric results reveal that the continuous increase in rotating speed, disk mass eccentricity, and stator radial stiffness induces alternation of periodic-one motion of the disk without disk–stator contact, periodic-one motion with disk–stator full annular rubbing and the disk–stator partial rubbing region in which the quasi-periodic and periodic motions of the disk appear alternately. In addition, the motion of the drum is synchronous with that of the disk and has three situations, i.e., un-deformation, deformation with one circumferential wave, and periodic and quasi-periodic vibration with drum–stator rubbing. Due to the effects of the drum, the rotating speed corresponding to the start of the disk–stator full annular rubbing in the disk–drum–shaft rotor system is smaller than that in the disk–shaft rotor system, and there is only one disk–stator partial rubbing region which is near the critical speed of rotor system. What is more, compared with parameters of the disk, those of the drum can only affect the motion of the rotor system slightly.


Disk–drum–shaft rotor system  Rub-impact Drum vibration Rotor whirl  Dynamic characteristics 



This research has been supported by the Major State Basic Research Development Program of China. The authors are grateful to the reviewers for their helpful comments, and also to Yang Yang, Jing Li and Chuanzong Sun for the discussion on ANSYS finite element modeling.


  1. 1.
    Jacquet-Richardet, G., Torkhani, M., Cartraud, P., Thouverez, F., Nouri Baranger, T., Herran, M., Gibert, C., Baguet, S., Almeida, P., Peletan, L.: Rotor to stator contacts in turbomachines. Review and application. Mech. Syst. Signal Process. 40, 401–420 (2013)CrossRefGoogle Scholar
  2. 2.
    Sinha, S.K.: Dynamic characteristics of a flexible bladed-rotor with Coulomb damping due to tip-rub. J. Sound Vib. 273, 875–919 (2004)CrossRefGoogle Scholar
  3. 3.
    Sinha, S.K.: Rotordynamic analysis of asymmetric turbofan rotor due to fan blade-loss event with contact–impact rub loads. J. Sound Vib. 332, 2253–2283 (2013)CrossRefGoogle Scholar
  4. 4.
    Ma, H., Shi, C., Han, Q., Wen, B.: Fixed-point rubbing fault characteristic analysis of a rotor system based on contact theory. Mech. Syst. Signal Process. 38, 137–153 (2013)CrossRefGoogle Scholar
  5. 5.
    Hou, L., Chen, Y., Cao, Q.: Nonlinear vibration phenomenon of an aircraft rub-impact rotor system due to hovering flight. Commun. Nonlinear Sci. Numer. Simul. 19, 286–297 (2014)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Sun, Z., Xu, J., Zhou, T.: Analysis on complicated characteristics of a high-speed rotor system with rub-impact. Mech. Mach. Theory 37, 659–672 (2002)CrossRefzbMATHGoogle Scholar
  7. 7.
    Dai, X., Jin, Z., Zhang, X.: Dynamic behavior of the full rotor-stop rubbing: numerical simulation and experimental verification. J. Sound Vib. 251, 807–822 (2002)CrossRefGoogle Scholar
  8. 8.
    Yuan, Z., Chu, F., Hao, R.: Simulation of rotor’s axial rub-impact in full degrees of freedom. Mech. Mach. Theory 42, 763–775 (2007)CrossRefzbMATHGoogle Scholar
  9. 9.
    An, X., Zhou, J., Xiang, X., Li, C., Luo, Z.: Dynamic response of a rub-impact rotor system under axial thrust. Arch. Appl. Mech. 79, 1009–1018 (2009)CrossRefzbMATHGoogle Scholar
  10. 10.
    Zhang, L., Ma, Z., Song, B.: Dynamic characteristics of a rub-impact rotor-bearing system for hydraulic generating set under unbalanced magnetic pull. Arch. Appl. Mech. 83, 817–830 (2013)CrossRefzbMATHGoogle Scholar
  11. 11.
    Kim, Y.B., Noah, S.T.: Bifurcation analysis for a modified Jeffcott rotor with bearing clearances. Nonlinear Dyn. 1, 221–241 (1990)CrossRefGoogle Scholar
  12. 12.
    Chu, F., Zhang, Z.: Bifurcation and chaos in a rub-impact Jeffcott rotor system. J. Sound Vib. 210, 1–18 (1998)CrossRefGoogle Scholar
  13. 13.
    Wang, J., Zhou, J., Dong, D., Yan, B., Huang, C.: Nonlinear dynamic analysis of a rub-impact rotor supported by oil film bearings. Arch. Appl. Mech. 83, 413–430 (2013)CrossRefzbMATHGoogle Scholar
  14. 14.
    Chang-Jian, C.-W., Chen, C.-K.: Chaos of rub-impact rotor supported by bearings with nonlinear suspension. Tribol. Int. 42, 426–439 (2009)CrossRefGoogle Scholar
  15. 15.
    Chang-Jian, C.-W., Chen, C.-K.: Non-linear dynamic analysis of rub-impact rotor supported by turbulent journal bearings with non-linear suspension. Int. J. Mech. Sci. 50, 1090–1113 (2008)CrossRefzbMATHGoogle Scholar
  16. 16.
    Khanlo, H.M., Ghayour, M., Ziaei-Rad, S.: Chaotic vibration analysis of rotating, flexible, continuous shaft-disk system with a rub-impact between the disk and the stator. Commun. Nonlinear Sci. Numer. Simul. 16, 566–582 (2011)CrossRefGoogle Scholar
  17. 17.
    Shen, X., Jia, J., Zhao, M.: Nonlinear analysis of a rub-impact rotor-bearing system with initial permanent rotor bow. Arch. Appl. Mech. 78, 225–240 (2008)CrossRefzbMATHGoogle Scholar
  18. 18.
    Chang-Jian, C.-W., Chen, C.-K.: Chaos and bifurcation of a flexible rub-impact rotor supported by oil film bearings with nonlinear suspension. Mech. Mach. Theory 42, 312–333 (2007)CrossRefzbMATHGoogle Scholar
  19. 19.
    Behzad, M., Alvandi, M., Mba, D., Jamali, J.: A finite element-based algorithm for rubbing induced vibration prediction in rotors. J. Sound Vib. 332, 5523–5542 (2013)CrossRefGoogle Scholar
  20. 20.
    Ma, H., Li, H., Zhao, X., Niu, H., Wen, B.: Effects of eccentric phase difference between two discs on oil-film instability in a rotor-bearing system. Mech. Syst. Signal Process. 41, 526–545 (2013)CrossRefGoogle Scholar
  21. 21.
    Qin, W., Chen, G., Meng, G.: Nonlinear responses of a rub-impact overhung rotor. Chaos Solitons Fractals 19, 1161–1172 (2004)CrossRefzbMATHGoogle Scholar
  22. 22.
    Sun, S., Chu, S., Cao, D.: Vibration characteristics of thin rotating cylindrical shells with various boundary conditions. J. Sound Vib. 331, 4170–4186 (2012)CrossRefGoogle Scholar
  23. 23.
    Sun, S., Cao, D., Chu, S.: Free vibration analysis of thin rotating cylindrical shells using wave propagation approach. Arch. Appl. Mech. 83, 521–531 (2013)CrossRefzbMATHGoogle Scholar
  24. 24.
    Guo, D., Zheng, Z., Chu, F.: Vibration analysis of spinning cylindrical shells by finite element method. Int. J. Solids Struct. 39, 725–739 (2002)Google Scholar
  25. 25.
    Liu, L., Cao, D., Sun, S.: Vibration analysis for rotating ring-stiffened cylindrical shells with arbitrary boundary conditions. J. Vib. Acoust. 135, 061010 (2013)Google Scholar
  26. 26.
    Huang, S.C., Soedel, W.: On the forced vibration of simply supported rotating cylindrical shells. J. Acoust. Soc. Am. 84, 275–285 (1988)CrossRefGoogle Scholar
  27. 27.
    Li, F.M., Kishimoto, K., Huang, W.H.: The calculations of natural frequencies and forced vibration responses of conical shell using the Rayleigh–Ritz method. Mech. Res. Commun. 36, 595–602 (2009)CrossRefzbMATHGoogle Scholar
  28. 28.
    Sun, S., Cao, D., Chu, S.: Analysis of travelling wave vibration response for thin rotating cylindrical shell. J. Vib. Eng. 26, 459–466 (2013)Google Scholar
  29. 29.
    Pellicano, F., Avramov, K.V.: Linear and nonlinear dynamics of a circular cylindrical shell connected to a rigid disk. Commun. Nonlinear Sci. Numer. Simul. 12, 496–518 (2007)CrossRefzbMATHGoogle Scholar
  30. 30.
    Pellicano, F.: Dynamic instability of a circular cylindrical shell carrying a top mass under base excitation: experiments and theory. Int. J. Solids Struct. 48, 408–427 (2011)CrossRefzbMATHGoogle Scholar
  31. 31.
    Cao, D., Sun, S., Liu, L.: Effect of unbalanced rotor whirl on drum vibration. J. Vib. Shock 33, 69–75 (2014)Google Scholar
  32. 32.
    Huang, S.C., Hsu, B.S.: Vibration of spinning ring-stiffened thin cylindrical shells. AIAA J. 30, 2291–2298 (1992)CrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina
  2. 2.Hubei Aerospace Technology AcademeWuhanChina

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