航空发动机转子叶片振动方程及其频率计算
收稿日期: 2013-09-10
修回日期: 2013-10-21
网络出版日期: 2013-10-24
Vibration Equation and Frequency Computation of an Aero-engine Rotor Blade
Received date: 2013-09-10
Revised date: 2013-10-21
Online published: 2013-10-24
航空发动机工作过程中，转子叶片的工作环境较为恶劣，会无法避免地受到气动和机械等载荷的激励作用而引发强迫振动，特别是当载荷频率与叶片的动频相同时就会使叶片共振、应力增大甚至造成叶片破坏，故准确获得叶片在不同转速时的动频就显得尤为重要。根据叶片的受力分析，通过引入叶片的变形系数，建立了叶片的自由振动方程。然后利用Ritz-Galerkin方法得到了一种可以计算叶片静频和动频的数值方法，计算结果与实验测量结果比较接近。本文方法与现有相关方法相比，其特点在于所建立的叶片振动方程与实际情况更趋相符，计算简便、结果可靠，并具有一定的工程应用价值。
关键词： 航空发动机; 转子叶片; 振动方程; Ritz-Galerkin方法; 振动频率
李克安 , 林左鸣 , 杨胜群 , 李松华 , 万正苏 . 航空发动机转子叶片振动方程及其频率计算[J]. 航空学报, 2013 , 34(12) : 2733 -2739 . DOI: 10.7527/S1000-6893.2013.0437
During the running process of an aero-engine, the working conditions of the blade are extremely poor. Aerodynamics and mechanical force would inevitably excite the blade continuously and cause its forced vibration. Especially when the load frequency equals the dynamic frequency of the blade, resonance will occur, which can increase the stress evidently and even damage the blade. Therefore it is particularly important to learn about the natural frequency of the blade at different rotational speeds. Based on the force analysis of the blade, we establish its free vibration equation by introducing a deformation coefficient. And then we develop a numerical method to calculate the static and dynamic frequencies of the blade, with the help of Ritz-Galerkin method. Compared with traditional methods, the present method is more convenient and closer to the actual condition and its results match well with the experimental data, which supplies a reasonable method of engineering importance.
[1] Lin Z M, Li K A, Yang S Q. Experimental research on sound waves excitation to aero-engine compressor rotor blade. Journal of Dynamics and Control, 2010, 8(1): 12-18. (in Chinese) 林左鸣, 李克安, 杨胜群. 航空发动机压气机转子叶片声激振试验研究. 动力学与控制学报, 2010, 8(1): 12-18.
[2] Li K A, Lin Z M, Yang S Q. Transient response analysis of a rotor blade under acoustic excitation. Journal of Hunan University: Natural Sciences, 2010, 37(12): 41-44. (in Chinese) 李克安, 林左鸣, 杨胜群. 转子叶片声撞击瞬态响应分析. 湖南大学学报:自然科学版, 2010, 37(12): 41-44.
[3] Lin Z M, Li K A, Yang S Q. Investigation on micro-theory of sound wave excitation. Journal of Nanjing University of Aeronautics & Astronautics, 2010, 42(6): 676-679. (in Chinese) 林左鸣, 李克安, 杨胜群. 声波激振的微观机理探讨. 南京航空航天大学学报, 2010, 42(6): 676-679.
[4] Holehouse I. Sonic fatigue of aircraft structures due to fan noise. Journal of the Acoustical Society of America, 1970, 47(1): 115-123.
[5] Banmgarner M, Kameier F, Hourmouzia dis J. The high pressure compressor blade vibration of engine under non-normal working condition. Proceedings of the 12th International Conference on Aero-Engine, 1995.
[6] Liu Y X, Zhao W Q. Vibration analysis of aeroengine turbine blade-disc coupling system. Applied Mechanics and Materials, 2013, 327: 276-279.
[7] Wang L, Cao D Q, Huang W. Nonlinear coupled dynamics of flexible blade-rotor-bearing systems. Tribology International, 2010, 43(4): 759-778.
[8] Zhao W, Liu Y, Lu M, et al. FEA on vibration characteristics of an aero-engine turbine rotor. International Conference on Automatic Control and Artificial Intelligence (ACAI 2012), 2012: 1046-1048.
[9] Zhao W, Liu Y, Lu M, et al. Vibration analysis of a certain type of aero-engine turbine blade based on UG//Yang D H. Informatics in control, automation and robotics. Berlin: Springer Berlin Heidelberg, 2012: 377-382.
[10] Rao J S, Carnegie W. Solution of the equations of motion of coupled-bending bending torsion vibrations of turbine blades by the method of Ritz-Galerkin. International Journal of Mechanical Sciences, 1970, 12(10): 875-882.
[11] Kaya M O, Ozdemir O O. Flexural-torsional-coupled vibration analysis of axially loaded closed-section composite Timoshenko beam by using DTM. Journal of Sound and Vibration, 2007, 306(3): 495-506.
[12] Ozgumus O O, Kaya M O. Formulation for flutter and vibration analysis of a hingeless helicopter blade in hover: Part I. Aircraft Engineering and Aerospace Technology, 2007, 79(2): 177-183.
[13] Ozgumus O O, Kaya M O. Formulation for flutter and vibration analysis of a hingeless helicopter blade in hover: Part Ⅱ. Results of flutter stability and vibration analysis of a hingeless helicopter blade in hover. Aircraft Engineering and Aerospace Technology, 2007, 79(3): 231-237.
[14] Timoshenko S. Vibration problems in engineering. New York: D. van Nostrand Company, 1937.
[15] Li K A, Xiao H, Cui R F. Bifurcation control of nonlinear oscillator in primary and secondary resonance. Journal of Central South University of Technology, 2007, 14(6): 826-831.
/
| 〈 |
|
〉 |
CJA