考虑弯扭耦合运动的旋转带冠叶片非线性气动弹性分析

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振动与冲击 ›› 2019, Vol. 38 ›› Issue (2) : 67-74.

论文

麻岳敏1,2，曹树谦1,2,3，郭虎伦1,2

作者信息 +

Nonlinear aeroelastic analysis of rotating shrouded blades under coupled bending and torsional vibration

MA Yuemin1,2，CAO Shuqian1,2,3，GUO Hulun1,2

Author information +

文章历史 +

摘要

本文针对旋转叶片的气动弹性问题，将带叶冠的叶片简化为末端加质量块的均质悬臂梁。悬臂梁受到离心力和气动力作用，发生弯曲和扭转耦合振动变形。利用Hamilton原理建立了叶片的偏微分运动方程。对方程无量纲化，运用Galerkin方法对其离散，得到两自由度的非线性常微分方程。通过数值求解叶片颤振速度和极限环响应，并用谐波平衡法求解极限环响应与数值解进行对比。最后，讨论了结构参数对颤振速度和极限环响应幅值的影响。

Abstract

In order to deal with the aerodynamic elasticity of rotating blades,a shrouded blade was simplified as a homogeneous cantilever beam with end mass.The cantilever beam was subjected to centrifugal force and aerodynamic force,and coupled bending and torsion vibration occured.The partial differential motion equation of the blade was established by using the Hamiltonian principle.After making the equation dimensionless,nonlinear ordinary differential equations with two degrees of freedom were obtained by using the Galerkin method.The flutter velocity and limit cycle oscillation response of the blade were solved by numerical method.The harmonic balance method was utilized to analyze the limit cycle oscillation responses,and the results were compared with the numerical solutions.The influences of structural parameters on the flutter velocity and limit cycle oscillation amplitudes were discussed.

导出引用

麻岳敏1,2，曹树谦1,2,3，郭虎伦1,2. 考虑弯扭耦合运动的旋转带冠叶片非线性气动弹性分析[J]. 振动与冲击, 2019, 38(2): 67-74

MA Yuemin1,2，CAO Shuqian1,2,3，GUO Hulun1,2. Nonlinear aeroelastic analysis of rotating shrouded blades under coupled bending and torsional vibration[J]. Journal of Vibration and Shock, 2019, 38(2): 67-74

参考文献

[1] Hodges D H, Dowell E H. Nonlinear equations of motion for the elastic bending and torsion of twisted nonuniform rotor blades. NASA TN D-7818[J]. 1974.
[2] Dowell E H, Tang D. Experimental and theoretical study on aeroelastic response of high-aspect-ratio wings[J]. Aiaa Journal, 2001, 39(39):1430-1441.
[3] Bercin A N, Tanaka M. Coupled flexural–torsional vibrations of timoshenko beams. Journal of Sound and Vibration, 1997, 207(207):47-59.
[4] Chandiramani N K, Librescu L, Shete C D. On the free-vibration of rotating composite beams using a higher-order shear formulation[J]. Aerospace Science and Technology, 2002, 6(8): 545-561.
[5] 张伟, 冯志青, 曹东兴. 航空发动机叶片非线性动力学分析[J]. 动力学与控制学报, 2012(3):213-221.
Zhang Wei, Feng Zhiqing, Cao Dongxing. Analysis on nonlinear dynamics of aero engine blade [J]. Journal of Dynamics and Control, 2012,10 (3): 213-221.
[6] 张伟, 冯志青, 郭翔鹰. 航空发动机压气机叶片的非线性振动问题[J]. 中国科学:物理学力学天文学, 2013(4):345-362.
Zhang W, Feng Z Q, Guo X Y. Analysis on nonlinear dynamics of the aero-engine compressor blade[J].Chinese Science:Physics, mechanics, astronomy, 2013 (4): 345-362.
[7] Eskandary K, Dardel M, Pashaei M H, et al. Nonlinear aeroelastic analysis of high-aspect-ratio wings in low subsonic flow[J]. Acta Astronautica, 2012, 70(1):6-22.
[8] Tavari H, Jalili M M, Movahhedy M R. Nonlinear analysis of chatter in turning process using dimensionless groups[J]. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2015, 37(4):1-12.
[9] Saxton C, Afagh F F. Modelling and dynamic stability of a hingeless active fibre composite blade[J]. Archive of Applied Mechanics, 2010, 80(8):843-868.
[10] 姜静, 韩广才. 考虑弯扭耦合旋转叶片的动力学分析[J]. 佳木斯大学学报(自然科学版), 2011, 29(4):560-563.
Jiang Jing, Han Guangcai. The dynamical analysis of a rotating blades considering the coupling vibration of bending and torsion [J]. Journal of Jiamusi University (Natural Science Edition), 2011, 29 (4): 560-563.

[11] Kashani M T T, Jayasinghe S, Hashemi S M. On the flexural-torsional vibration and stability of beams subjected to axial load and end moment[J]. Shock and Vibration,2014,(2014-10-13), 2014, 2014(9):594-601.
[12] 任勇生, 张明辉. 水平轴风力机叶片的弯扭耦合气弹稳定性研究[J]. 振动与冲击, 2010, 29(7):196-200.
Ren Yongsheng, Zhang Minghui. Study on the aeroelastic stability of blade of horizontal axis wind turbine blade [J]. Journal of Vibration and Shock, 2010, 29 (7): 196-200.
[13] Hansen M H. Aeroelastic instability problems for wind turbines[J]. Wind Energy, 2007, 10(6):551-577.
[14] 王丹, 陈予恕, 曹庆杰,等. 两自由度弯扭耦合涡轮机械叶片动力学分析[J]. 振动与冲击, 2014, 33(7):199-205.
Wang Dan, Chen Yushu, Cao Qingjie, et al. Dynamic analysis of a 2-DOF turbomachine blade with coupling of bending and torsion[J]. Journal of Vibration and Shock, 2014, 33(7):199-205.
[15] Hosseini M. Aerothermoelastic behavior of supersonic rotating thin-walled beams made of functionally graded materials[J]. Journal of Fluids & Structures, 2006, 23(8):1251-1264.
[16] Ladge S, Modarres-Sadeghi Y. Supercritical and subcritical dynamic flow-induced instabilities of a small-scale wind turbine blade placed in uniform flow[J]. Journal of Fluids & Structures, 2015, 54:936-946.
[17] Pourazarm P, Caracoglia L, Lackner M, et al. Stochastic analysis of flow-induced dynamic instabilities of wind turbine blades[J]. Journal of Wind Engineering and Industrial Aerodynamics, 2015, 137:37-45.
[18] 李剑钊, 闻雪友, 林志鸿,等. 汽轮机带冠叶片振动特性研究进展[J]. 汽轮机技术, 2005, 47(4):241-243.
Li Jianzhao, Wen Xueyou, Lin Zhihong, et al. The advancement of study on vibration characteristics of shrouded blades of steam turbine [J]. Turbine Technology, 2005, 47 (4): 241-243.
[19] 周传月, 邹经湘, 闻雪友,等. 燃气轮机带冠叶片耦合振动分析[J]. 哈尔滨工业大学学报, 2001, 33(1):129-133.
Zhou Chuanyue, Zou Jingxiang, Wen Xueyou, et al. Coupled vibrations of gas turbine shrouded blade [J]. Journal of Harbin Institute of Technology, 2001, 33 (1): 129-133.
[20] 汤凤, 胡柏安. 带冠涡轮叶片的振动特性分析[J]. 机械强度, 2007, 29(5):831-834.
Tang Feng, Hu Baian. Vibration characteristic analysis of shrouded turbine blades [J]. Journal of Mechanical Strength, 2007, 29 (5): 831-834.
[21] Ansari M, Esmailzadeh E, Jalili N. Exact frequency analysis of a rotating cantilever beam with tip mass subjected to torsional-bending vibrations[J]. Journal of Vibration and Acoustics, 2011, 133(4): 041003.
[22] 赵永辉, 黄锐. 高等气动弹性力学与控制[M]. 北京：科学出版社, 2015.
Zhao Yonghui, Huang Rui. Advanced aeroelasticity and control, [M]. Beijing: Science Press, 2015.
[23] Resor B R, Owens B C, Griffith D T. Aeroelastic instability of very large wind turbine blades[C]//European Wind Energy Conference Annual Event, Copenhagen, Denmark. 2012.
[24] 张成胜, 宋兆泓. 叶片三心与颤振特性分析[J]. 航空动力学报, 1986(2):121-124.
Zhang Chengsheng, Song Zhaohong. Effects of three centres of blade on fluttering [J]. Journal of Aerospace Power, 1986 (2): 121-124