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 (Saito et al. 1998, “Development of a 3000 rpm 43-in. last stage blade with high efficiency and reliability,” International Joint Power Generation Conference, pp. 89–96.) 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). This paper proposes a method to calculate the natural frequency of a shaft blade coupled system. According to this 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, a tracking solver method based on sliding mode control concept is used. 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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e-mail: akira.okabe.fn@hitachi-pt.com
e-mail: takeshi.kudo.fn@hitachi.com
e-mail: shiohata@mx.ibaraki.ac.jp
e-mail: myrot_osami@yahoo.co.jp
e-mail: hiroyuki@nda.ac.jphiroyuki@nda.ac.jp
e-mail: hideo.yoda.xq@hitachi.com
e-mail: shigeo.sakurai.jy@hitachi.com
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February 2012
Research Papers
Reduced Modeling for Turbine Rotor-Blade Coupled Bending Vibration Analysis
Akira Okabe,
Akira Okabe
Department of Mechanical Engineering,
e-mail: akira.okabe.fn@hitachi-pt.com
Ibaraki University
, 4-12-1 Naka-Narusawacho, Hitachi 316-8511, Japan
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Takeshi Kudo,
Takeshi Kudo
Department of Mechanical Engineering,
e-mail: takeshi.kudo.fn@hitachi.com
Ibaraki University
, 4-12-1 Naka-Narusawacho, Hitachi 316-8511, Japan
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Koki Shiohata,
Koki Shiohata
Department of Mechanical Engineering,
e-mail: shiohata@mx.ibaraki.ac.jp
Ibaraki University
, 4-12-1 Naka-Narusawacho, Hitachi 316-8511, Japan
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Osami Matsushita,
Osami Matsushita
Department of Mechanical Engineering,
e-mail: myrot_osami@yahoo.co.jp
National Defense Academy
, 1-10-20 Hashirimizu, Yokosuka 239-8686, Japan
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Hiroyuki Fujiwara,
Hiroyuki Fujiwara
Department of Mechanical Engineering,
e-mail: hiroyuki@nda.ac.jphiroyuki@nda.ac.jp
National Defense Academy
, 1-10-20 Hashirimizu, Yokosuka 239-8686, Japan
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Hideo Yoda,
Hideo Yoda
Hitachi Works, Hitachi, Ltd., 3-1-1 Saiwai-cho, Hitachi 317-8511,
e-mail: hideo.yoda.xq@hitachi.com
Japan
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Shigeo Sakurai
Shigeo Sakurai
Hitachi Works, Hitachi, Ltd., 3-1-1 Saiwai-cho, Hitachi 317-8511,
e-mail: shigeo.sakurai.jy@hitachi.com
Japan
Search for other works by this author on:
Akira Okabe
Department of Mechanical Engineering,
Ibaraki University
, 4-12-1 Naka-Narusawacho, Hitachi 316-8511, Japan
e-mail: akira.okabe.fn@hitachi-pt.com
Takeshi Kudo
Department of Mechanical Engineering,
Ibaraki University
, 4-12-1 Naka-Narusawacho, Hitachi 316-8511, Japan
e-mail: takeshi.kudo.fn@hitachi.com
Koki Shiohata
Department of Mechanical Engineering,
Ibaraki University
, 4-12-1 Naka-Narusawacho, Hitachi 316-8511, Japan
e-mail: shiohata@mx.ibaraki.ac.jp
Osami Matsushita
Department of Mechanical Engineering,
National Defense Academy
, 1-10-20 Hashirimizu, Yokosuka 239-8686, Japan
e-mail: myrot_osami@yahoo.co.jp
Hiroyuki Fujiwara
Department of Mechanical Engineering,
National Defense Academy
, 1-10-20 Hashirimizu, Yokosuka 239-8686, Japan
e-mail: hiroyuki@nda.ac.jphiroyuki@nda.ac.jp
Hideo Yoda
Hitachi Works, Hitachi, Ltd., 3-1-1 Saiwai-cho, Hitachi 317-8511,
Japan
e-mail: hideo.yoda.xq@hitachi.com
Shigeo Sakurai
Hitachi Works, Hitachi, Ltd., 3-1-1 Saiwai-cho, Hitachi 317-8511,
Japan
e-mail: shigeo.sakurai.jy@hitachi.com
J. Eng. Gas Turbines Power. Feb 2012, 134(2): 022502 (8 pages)
Published Online: December 7, 2011
Article history
Received:
April 12, 2011
Accepted:
April 13, 2011
Online:
December 7, 2011
Published:
December 7, 2011
Citation
Okabe, A., Kudo, T., Shiohata, K., Matsushita, O., Fujiwara, H., Yoda, H., and Sakurai, S. (December 7, 2011). "Reduced Modeling for Turbine Rotor-Blade Coupled Bending Vibration Analysis." ASME. J. Eng. Gas Turbines Power. February 2012; 134(2): 022502. https://doi.org/10.1115/1.4004145
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