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Research Papers: Gas Turbines: Structures and Dynamics

Reduced Modeling for Turbine Rotor-Blade Coupled Bending Vibration Analysis

[+] Author and Article Information
Akira Okabe

Department of Mechanical Engineering,  Ibaraki University, 4-12-1 Naka-Narusawacho, Hitachi 316-8511, Japanakira.okabe.fn@hitachi-pt.com

Takeshi Kudo

Department of Mechanical Engineering,  Ibaraki University, 4-12-1 Naka-Narusawacho, Hitachi 316-8511, Japantakeshi.kudo.fn@hitachi.com

Koki Shiohata

Department of Mechanical Engineering,  Ibaraki University, 4-12-1 Naka-Narusawacho, Hitachi 316-8511, Japanshiohata@mx.ibaraki.ac.jp

Osami Matsushita

Department of Mechanical Engineering,  National Defense Academy, 1-10-20 Hashirimizu, Yokosuka 239-8686, Japanmyrot_osami@yahoo.co.jp

Hiroyuki Fujiwara

Department of Mechanical Engineering,  National Defense Academy, 1-10-20 Hashirimizu, Yokosuka 239-8686, Japanhiroyuki@nda.ac.jp

Hideo Yoda

Hitachi Works, Hitachi, Ltd., 3-1-1 Saiwai-cho, Hitachi 317-8511, Japanhideo.yoda.xq@hitachi.com

Shigeo Sakurai

Hitachi Works, Hitachi, Ltd., 3-1-1 Saiwai-cho, Hitachi 317-8511, Japanshigeo.sakurai.jy@hitachi.com

J. Eng. Gas Turbines Power 134(2), 022502 (Dec 07, 2011) (8 pages) doi:10.1115/1.4004145 History: Received April 12, 2011; Accepted April 13, 2011; Published December 07, 2011; Online December 07, 2011

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 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.

FIGURES IN THIS ARTICLE
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Copyright © 2012 by American Society of Mechanical Engineers
Topics: Vibration , Blades , Equations
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References

Figures

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Figure 1

Coordinate system

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Figure 2

Transformation of coordinate systems

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Figure 3

Blade nodal eigenmodes (vector)

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Coordinate system and unit vector

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Coordinate system and unit vector

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One-nodal diameter modes (in-plane)

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Tilting modes of one-nodal diameter (out-of-plane)

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Blade setting angle

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Calculation procedure of one-nodal coupled system

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Coupling parameters

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Tracking solver for eigenvalue equation

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Calculation model

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Coupled bending natural frequency

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Figure 14

Example of blade model

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