Research on 1:2 subharmonic resonance and bifurcation of nonlinear rotor-seal system

doi:10.1007/s10483-012-1566-7

Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (4): 499-510.doi: https://doi.org/10.1007/s10483-012-1566-7

Research on 1:2 subharmonic resonance and bifurcation of nonlinear rotor-seal system

李忠刚, 陈予恕

School of Astronautics, Harbin Institute of Technology, P.O. Box 137, Harbin 150001, P. R. China

收稿日期:2011-09-30 修回日期:2012-02-24 出版日期:2012-04-15 发布日期:2012-04-15
通讯作者: Zhong-gang LI, Ph.D., E-mail: lizhonggang2001@163.com E-mail:lizhonggang2001@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (No. 10632040)

Research on 1:2 subharmonic resonance and bifurcation of nonlinear rotor-seal system

Zhong-gang LI, Yu-shu CHEN

School of Astronautics, Harbin Institute of Technology, P.O. Box 137,Harbin 150001, P. R. China

Received:2011-09-30 Revised:2012-02-24 Online:2012-04-15 Published:2012-04-15
Contact: Zhong-gang LI, Ph.D., E-mail: lizhonggang2001@163.com E-mail:lizhonggang2001@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (No. 10632040)

摘要/Abstract

摘要： The 1:2 subharmonic resonance of the labyrinth seals-rotor system is investigated, where the low-frequency vibration of steam turbines can be caused by the gas exciting force. The empirical parameters of gas exciting force of the Muszynska model are obtained by using the results of computational fluid dynamics (CFD). Based on the multiple scale method, the 1:2 subharmonic resonance response of the dynamic system is gained by truncating the system with three orders. The transition sets and the local bifurcations diagrams of the dynamics system are presented by employing the singular theory analysis. Meanwhile, the existence conditions of subharmonic resonance non-zero solutions of the dynamic system are obtained, which provides a new theoretical basis in recognizing and protecting the rotor from the subharmonic resonant failure in the turbine machinery.

Abstract: The 1:2 subharmonic resonance of the labyrinth seals-rotor system is investigated, where the low-frequency vibration of steam turbines can be caused by the gas exciting force. The empirical parameters of gas exciting force of the Muszynska model are obtained by using the results of computational fluid dynamics (CFD). Based on the multiple scale method, the 1:2 subharmonic resonance response of the dynamic system is gained by truncating the system with three orders. The transition sets and the local bifurcations diagrams of the dynamics system are presented by employing the singular theory analysis. Meanwhile, the existence conditions of subharmonic resonance non-zero solutions of the dynamic system are obtained, which provides a new theoretical basis in recognizing and protecting the rotor from the subharmonic resonant failure in the turbine machinery.

中图分类号:

O322
TH133

李忠刚;陈予恕. Research on 1:2 subharmonic resonance and bifurcation of nonlinear rotor-seal system[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(4): 499-510.

Zhong-gang LI;Yu-shu CHEN. Research on 1:2 subharmonic resonance and bifurcation of nonlinear rotor-seal system[J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(4): 499-510.

参考文献

[1] Dimarogonas, A. D. and Gomez-Mancilla, J. C. Flow-excited turbine rotor instability. International Journal of Rotating Machinery, 1(1), 37-51 (1994)
[2] Marquette, O. R., Childs, D. W., and Andres, L. S. Eccentricity effects on the rotordynamic coefficients of plain annular seals theory versus experiment. ASME Journal of Tribology, 119(3), 443-447 (1997)
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[4] Dietzed, F. J. and Nordmann, R. Calculating coefficients of seals by finite-difference techniques. ASME Journal of Tribology, 109(3), 388-394 (1987)
[5] Toshio, H., Guo, Z. L., and Gordon, K. R. Application of fluid dynamics analysis for rotating machinery-part : labyrinth seal analysis. Journal of Engineering for Gas Turbine and Power, 127(4), 820-826 (2005)
[6] Alford, J. S. Protecting turbomachinery from self-excited rotor whirl. ASME Journal of Engineering for Power, 87(4), 333-344 (1965)
[7] He, L. D. and Xia, S. B. Review on aerodynamic excitation and its elimination method in the rotor seal system (in Chinese). Journal of Vibration Engineering, 12(1), 64-72 (1999)
[8] Muszynska, A. Whirl and whip rotor-bearing stability problems. Journal of Sound and Vibration, 110(3), 443-462 (1986)
[9] Ding, Q., Cooper, J. E., and Leung, A. Y. T. Hopf bifurcation analysis of a rotor-seal system. Journal of Sound and Vibration, 252(5), 817-833 (2002)
[10] Liu, X. F. and Lu, S. Y. A study of methods used for three-dimensional CFD (computational fluid dynamics) numerical analysis of dynamic characteristics of rotors with labyrinth seals (in Chinese). Journal of Engineering for Thermal Energy and Power, 21(6), 635-639 (2006)
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Research on 1:2 subharmonic resonance and bifurcation of nonlinear rotor-seal system

Research on 1:2 subharmonic resonance and bifurcation of nonlinear rotor-seal system

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