Nonlinear vibration and dynamic stability analysis of a rotor-blade system

PDF(1567 KB)

Journal of Vibration and Shock ›› 2019, Vol. 38 ›› Issue (6) : 15-22.

LI Bingqiang1，MA Hui1,2，ZENG Jin1，GUO Xumin1，CUI Can1

Author information +

History +

Abstract

The vibration response and dynamic stability of a coupled rotor-blade system were investigated under main resonances. The equations of motion were derived by using the Hamilton principle, and then the Coleman and complex transformations were adopted to obtain the reduced-order system. The nonlinear vibration and stability of the system were studied by the multiple scales method. The influences of normal rubbing force, friction coefficient, damping, support stiffness, mass eccentricity of the rotor on the steady state response of rotor-blade system were investigated. The accuracy of the multiple scales perturbation solution was verified by the Runge-Kutta numerical integration method. The results show that greater rubbing force will increase the response amplitude and make the system instable. In addition, increasing the damping will enhance the stability of the system. Along with the increasing of mass eccentricity and support stiffness, the jump-down frequency, the resonant peak, as well as the frequency range in which the system has unstable response will increase. It needs larger damping to guarantee the stability of the system.

Key words

main resonances / rotor-blade system / stability / nonlinear vibration

Cite this article

EndNote

Ris (Procite)

Bibtex

Download Citations

LI Bingqiang1，MA Hui1,2，ZENG Jin1，GUO Xumin1，CUI Can1. Nonlinear vibration and dynamic stability analysis of a rotor-blade system[J]. Journal of Vibration and Shock, 2019, 38(6): 15-22

References

[1] Khadem S E, Shahgholi M, Hosseini S A A. Primary resonances of a nonlinear in-extensional rotating shaft [J]. Mechanism and Machine Theory, 2010,45(8): 1067-1081.
[2] Khadem S E, Shahgholi M, Hosseini S A A. Two-mode combination resonances of an in-extensional rotating shaft with large amplitude [J]. Nonlinear Dynamics, 2011,65 (3): 217–233.
[3] Shahgholi M, Khadem S E. Resonances of an in- extensional asymmetrical spinning shaft with speed fluctuations [J]. Meccanica, 2013,48(1): 103–120.
[4] Chiu Y Z, Chen D Z. The coupled vibration in a rotating multi-disk rotor system [J]. International Journal of Mechanical Science, 2011,53(1):1-10.
[5] Wang L, Cao D Q, Huang W. Nonlinear coupled dynamics of flexible blade-rotor-bearing systems [J]. Tribology International, 2010, 43(4):759-778.
[6] Sanches L, Michon G, Berlioz A，et al. Instability zones for isotropic and anisotropic multi-bladed rotor configurations [J]. Mechanism and Machine Theory, 2011,46 (8):1054-1065.
[7] Bab S, Khadem S E, Abbsi A, et al. Dynamic stability and nonlinear vibration analysis of a rotor system with flexble/rigid blades [J]. Mechanism and Machine Theory, 2016,105: 633-653.
[8] Parent M O, Thouverez F. Phenomenological model for stability analysis of bladed rotor-to-stator contacts [J]. International Symposium on Transport Phenomena and Dynamics of Rotating Machinery, 2016,10-15: 1-13.
[9] 高喆，秦卫阳，梁晓鹏，等. 碰摩转子-轴承系统的随机分叉与混沌特性研究[J].振动与冲击，2013,32(20):161-164.
GAO Zhe, QIN Wei-yang, Gao Qing, et al. Stochastic bifurcation and chaos analysis of a rub-impact rotor-bearing system [J]. Journal of Vibration and Shock, 2013,32(20):161-164.
[10] 陶海亮，潘波，高庆，等. 具有弹性静子的碰摩转子轴承系统非线性动力特性研究[J].振动与冲击，2013,32(15):197-202.
TAO Hai-liang, Pan Bo, Gao Qing, et al. Nonlinear dynamics of a rub-impact rotor supported by oil film bearings with an elastic stator [J]. Journal of Vibration and Shock,2013,32(15):197-202.
[11] 刘昕，张华彪，孙小磊，等. 叶轮转子碰摩的非线性动力学响应[J].振动与冲击，2016,35(20):172-177.
LIU Xin, ZHANG Hua-biao, SUN Xiao-lei, et al. Nonlinear dynamics on rubbing of a blade-rotor system [J]. Journal of Vibration and Shock, 2016, 35(20):172-177.
[12] Petrov E. Multiharmonic analysis of nonlinear whole engine dynamics with bladed disc-casing rubbing contacts [C]. ASME Turbo Expo 2012: Turbine Technical Conference and Exposition, American Society of Mechanical Engineer.
[13] Petrov E. Analysis of bifurcations in multiharmonic analysis of nonlinear forced vibrations of gas-turbine engine structures with friction and gaps [C]. ASME Turbo Expo 2015: Turbine Technical Conference and Exposition, American Society of Mechanical Engineers.
[14] Sinha S K. Non-linear dynamic response of a rotating radial Timoshenko beam with periodic pulse loading at the free-end [J]. International Journal of Nonlinear Mechanics, 2015, 40:113-149.
[15] Sinha S K. Combined torsional-bending-axial dynamics of a twisted rotating cantilever Timoshenko beam with contact–impact loads at the free end [J]. Journal of Applied Mechanics, 2007, 74: 505-522.
[16] Turner K, Adams M, Dunn M. Simulation of engine blade tip-rub induced vibration [C]. Proceedings of GT2005, Ren-Tahoe, Nevada, USA, 2005.
[17] Turner K, Dunn M, Padova C. Airfoil deflection characteristics during rub events [J]. Journal of Turbomachinery, 2012, 134: 112-121.
[18] Kou H J, Yuan H Q. Rub-induced non-linear vibrations of a rotating large deflection plate [J]. International Journal of Nonlinear Mechanics, 204, 58:283-294.
[19] Ma H, Wang D, Tai X Y, et al. Vibration response analysis of blade–disk dovetail structure under blade tip rubbing condition [J]. Journal of Sound and Vibration, 2017, 23:252-271.
[20] Ma H, Yin F L, Wu Z Y, et al. Nonlinear vibration response analysis of a rotor-blade system with blade-tip rubbing [J]. Nonlinear Dynamics, 2016,84: 1225-1258.
[21] 袁惠群.转子动力学分析方法[M].北京:冶金工业出版社，2017.
YUAN Hui-qun. Analysis method of rotor dynamics [M]. Beijing: Metallurgical Industry Press, 2017.