Reduced Modelling for Turbine Rotor-Blade Coupled Bending Vibration Analysis
In a traditional turbine-generator set, rotor shaft designers and blade designers have their own models and design process which neglects the coupled effect. Since longer blade systems have recently been employed for advanced turbine sets to get higher output and efficiency, additional consideration...
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Published in | TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C Vol. 77; no. 775; pp. 742 - 754 |
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Main Authors | , , , , , , |
Format | Journal Article |
Language | Japanese |
Published |
The Japan Society of Mechanical Engineers
2011
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Abstract | In a traditional turbine-generator set, rotor shaft designers and blade designers have their own models and design process which neglects the coupled effect. Since longer blade systems have recently been employed for advanced turbine sets to get higher output and efficiency, additional consideration is required concerning rotor bending vibrations coupled with a one-nodal (k=1) blade system. Rotor-blade coupled bending conditions generally include two types so that the parallel and tilting modes of the shaft vibrations are respectively coupled with in-plane and out-of-plane modes of blade vibrations with a one-nodal diameter (k=1). In this paper, we propose a method to calculate the natural frequency of a shaft blade coupled system. According to our modeling technique, a certain blade mode is reduced to a single mass system, which is connected to the displacement and angle motions of the shaft. The former motion is modeled by the m-k system to be equivalent to the blade on the rotating coordinate. The latter motion is commonly modeled in discrete form using the beam FEM on an inertia coordinate. Eigenvalues of the hybrid system covering both coordinates provide the natural frequency of the coupled system. In order to solve the eigenfrequencies of the coupled system, we use a tracking solver based on sliding mode control. An eight-blade system attached to a cantilever bar is used for an example to calculate a coupled vibration with a one-nodal diameter between the blade and shaft. |
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AbstractList | In a traditional turbine-generator set, rotor shaft designers and blade designers have their own models and design process which neglects the coupled effect. Since longer blade systems have recently been employed for advanced turbine sets to get higher output and efficiency, additional consideration is required concerning rotor bending vibrations coupled with a one-nodal (k=1) blade system. Rotor-blade coupled bending conditions generally include two types so that the parallel and tilting modes of the shaft vibrations are respectively coupled with in-plane and out-of-plane modes of blade vibrations with a one-nodal diameter (k=1). In this paper, we propose a method to calculate the natural frequency of a shaft blade coupled system. According to our modeling technique, a certain blade mode is reduced to a single mass system, which is connected to the displacement and angle motions of the shaft. The former motion is modeled by the m-k system to be equivalent to the blade on the rotating coordinate. The latter motion is commonly modeled in discrete form using the beam FEM on an inertia coordinate. Eigenvalues of the hybrid system covering both coordinates provide the natural frequency of the coupled system. In order to solve the eigenfrequencies of the coupled system, we use a tracking solver based on sliding mode control. An eight-blade system attached to a cantilever bar is used for an example to calculate a coupled vibration with a one-nodal diameter between the blade and shaft. |
Author | KUDO, Takeshi OKABE, Akira FUJIWARA, Hiroyuki MATSUSHITA, Osami SAKURAI, Shigeo YODA, Hideo SHIOHATA, Koki |
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References | (4) Higuchi, M. and Tsuda, T., Telemetry test of blade shaft coupled torsional vibration at the Tsuruga No.2 Power Plant, American Power Conference, Vol. 51, (1989), pp. 1-6. (11) Santos, I.F., Saracho, C.M., Smith, J.T. and Eiland, J., Contribution to experimental validation of linear and non-linear dynamic models for representing rotor-blade parametric coupled vibrations, Journal of Sound & Vibration, Vol. 271, No. 3/5,(2004), pp. 883-904. (15) 日本機械学会編,機械工学便覧(2001),A3:52,53. (9) 岡部明,工藤健,依田秀夫,桜井茂雄,松下修巳,塩幡宏規,“モーダル定数の実機実測による翼軸連成振動解析法”,日本機械学会論文集C編,Vol.75,No.751(2009),pp. 54-61. (13) 藤原浩幸,松下修巳,伊藤誠,“ロータ-軸受系固有値問題のためのスライディングモード制御を用いた連続的捕捉解法”,日本機械学会論文集C編,Vol.71, No. 701(2005), pp.43-50. (8) Okabe, A., Kaneko, R., Matsushita, O., Namura, K., and Yoshida, T., Coupled vibration analysis: torsional vibration of turbine-generator coupled system, 12th ASME Conferene on Mechanical vibration and noise, Vol. 18, (1989), pp. 135- 140. (10) ISO,22266-1:2009(E), Mechanicalvibration-Torsional vibration of rotating machinery-, Part 1: Land-based steam and gas turbine generator sets in excess of 50MW. (2009). (2) Hammons, T. J., Stressing of large turbine- generators at shaft couplings and LP turbine final-stage blade roots following clearance of grid system faults and faulty synchronisation, Joint Conference on Power Generation, (1986) ,pp. 1-12. (12) 松下修巳,田中正人,神吉博,小林正生,回転機械の振動―実用的振動解析の基本―,コロナ社,(2009), pp.241 (5) Ziebarth, H. and Termuehlen, H., Evaluation method for the coupled system of shaft torsion and LP turbine blade deflection, American Power Conference, Vol. 51, (1989), pp. 1-7. (14) Matsushita, O. and Fujiwara, H., 1D and 2D Tracking Solvers for Solving Algebraic Equations Based upon Sliding Mode Control, Journal of Environment and Engineering, Vol. 3, No. 1,(2008), pp. 216-227. (1) La Rosa, J. A., Kung, D. G. C., and Rosard, D. D., Analysis of turbine blade vibration induced by electrical-mechanical interactions, Joint Conferece on Power Generation, (1980). (3) 真鍋和人, “伊方発電所1号機 発電機無負荷2相短絡による軸捩り振動計測について”,四国電力研究期報,Vol.40,(1982),pp.1-6. (6) 松下修巳,菅谷豊美,名村清,岡部明,金子了市,道村晴一,井田道秋,“等価縮小モデルを用いた連成振動の解析法”,日本機械学会論文集C編,Vol.54,No.499(1988),pp.587-595. (7) Matsushita, O., Namura, K., Yoshida, T., Kaneko, R., and Okabe, A., Torsional vibration analysis of turbine-generator-blade coupled system, American Power Conference, Vol. 51, (1989), pp. 81-86. |
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Title | Reduced Modelling for Turbine Rotor-Blade Coupled Bending Vibration Analysis |
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