Advertisement

Science China Technological Sciences

, Volume 54, Issue 8, pp 1977–1985 | Cite as

Bifurcation analysis on full annular rub of a nonlinear rotor system

  • HuaBiao Zhang
  • YuShu Chen
Article

Abstract

In this paper, analytical and numerical studies are carried out on the full annular rub motions of a nonlinear Jeffcott rotor. Transition sets of the synchronous full annular rub are given with the help of averaging method and constraint bifurcation theory to discuss the effects of system parameters on jump phenomena. Routh-Hurwitz criteria are employed to analyze the stability of synchronous full annular rub solution and determine the boundaries of static and Hopf bifurcations. Finally, the response and onset condition of reverse dry whip are investigated numerically, and at the same time, the influences of rotor parameters and rotation speed on the characteristics of the rotor response are investigated.

Keywords

nonlinear rotor dynamics synchronous full annular rub constraint bifurcation stability of motion reverse dry whip 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Chen Y S, Leung A Y T. Bifurcation and Chaos in Engineering. London: Springer, 1998MATHGoogle Scholar
  2. 2.
    Chu F L, Tang X Y, Tang Y. Stability of a rub-impact rotor system (in Chinese). J Tsinghua Univ (Sci Tech), 2000, 40: 119–123Google Scholar
  3. 3.
    Zhang S J, Zhou L B, Lu Q S. A map method for grazing bifurcation in linear vibro-impact system (in Chinese). Chin J Theor Appl Mech, 2000, 39: 132–136Google Scholar
  4. 4.
    Li Q H, Lu Q S. Single rub-impacting periodic motions of a rigid constrained rotor system. Commun Nonlinear Sci Num Simul, 2000, 4: 158–161CrossRefMathSciNetGoogle Scholar
  5. 5.
    Lu Q S, Li Q H, Twizell E H. The existence of periodic motions in rub-impact rotor systems. J Sound Vib, 2003, 264: 1127–1137CrossRefMathSciNetGoogle Scholar
  6. 6.
    Choi Y S. Investigation on the whirling motion of full annular rotor rub. J Sound Vib, 2002, 258: 191–198CrossRefGoogle Scholar
  7. 7.
    Yu J J, Goldman P, Bently D E. Rotor/seal experimental and analytical study on full annular rub. ASME J Eng Gas Turb Power, 2002, 124: 340–350CrossRefGoogle Scholar
  8. 8.
    Muszynska A. Rotordynamics. Florida: CRC Press, 2005MATHCrossRefGoogle Scholar
  9. 9.
    Zhang G F, Xu W N, Xu B, et al. Analytical study of nonlinear synchronous full annular rub motion of flexible rotor-stator system and its dynamic stability. Nonlinear Dyn, 2009, 57: 579–592MATHCrossRefGoogle Scholar
  10. 10.
    Xu B, Xu W N, Zhang W. Study of synchronous full annular rub of Jeffcott rotor and its dynamic stability (in Chinese). J Fudan Univ (Nat Sci), 2006, 45: 148–154MATHGoogle Scholar
  11. 11.
    Xu W N, Zhang W, Xu B. Analytical study of synchronous full annular rub motion of flexible stator and rotor system (in Chinese). J Vib Shock, 2007, 25: 1–9Google Scholar
  12. 12.
    Black H F. Interaction of a whirling rotor with a vibrating stator across a clearance annulus. J Mech Eng Sci, 1968, 10: 1–12CrossRefGoogle Scholar
  13. 13.
    Bartha A R. Dry friction backward whirl of rotors: theory, experiments, results, and recommendations. In: Proceedings of 7th International Symposium on Magnetic Bearings. ETH Zurich, 2000. 231–238Google Scholar
  14. 14.
    Crandall S. From whirl to whip in rotordynamics. In: Transactions of the IFToMM 3rd International Conference on Rotordynamics. Lyon, 1990. 19–26Google Scholar
  15. 15.
    Jiang J, Ulbrich H. Stability analysis of sliding whirling nonlinear Jeffcott rotor with cross-coupling stiffness coefficients. Nonlinear Dyn, 2001, 24(3): 269–283MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Jiang J, Ulbrich H. The physical reason and the analytical condition for the onset of reverse dry whip in rotor-to-stator contact systems. ASME J Vib Acoustics, 2005, 127: 594–603CrossRefGoogle Scholar
  17. 17.
    Jiang J, Shang Z Y, Hong L. Characteristics of dry friction backward whirl-A self-excited oscillation in rotor-to-stator contact systems. Sci China Tech Sci, 2010, 53(3): 674–683MATHCrossRefGoogle Scholar
  18. 18.
    Ma J M, Zhang W, Zheng T S. Analysis for rub-impact condition of Jeffcott rotor (in Chinese). Grinder Grinding, 2003, S1: 68–70Google Scholar
  19. 19.
    Ma J M, Zhang W, Zheng T S. Influence of rotor system parameters on critical rotation speed for rubbing (in Chinese). J Southwest Jiaotong Univ, 2003, 38: 537–539Google Scholar
  20. 20.
    Liu X D, Li Q H, Yang S P. The stability and Hopf bifurcation in the annular impact-rub of rotating machinery with imbalance (in Chinese). J Vib Eng, 1999, 12: 40–46Google Scholar
  21. 21.
    Groll G V, Ewins D J. The harmonic balance method with arc-length continuation in rotor/stator contact problems. J Sound Vib, 2001, 241: 223–233CrossRefGoogle Scholar
  22. 22.
    Wu Z Q, Chen Y S. Classification of bifurcations for nonlinear dynamical problems with constraints (in Chinese). Appl Math Mech, 2002, 23: 477–482Google Scholar
  23. 23.
    Wu Z Q, Chen Y S. New bifurcation patterns in elementary bifurcation problems with single-side constraint (in Chinese). Appl Math Mech, 2001, 22: 1135–1141Google Scholar

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.School of AstronauticsHarbin Institute of TechnologyHarbinChina

Personalised recommendations