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Research Papers

Nonlinear Vibration Analysis of the Wind Turbine Blade (Occurrence of the Superharmonic Resonance in the Out of Plane Vibration of the Elastic Blade)

[+] Author and Article Information
Tsuyoshi Inoue

Department of Mechanical Science and Engineering, School of Engineering,  Nagoya University, Nagoya, 464-8603, Japaninoue@nuem.nagoya-u.ac.jp

Yukio Ishida

Department of Mechanical Science and Engineering, School of Engineering,  Nagoya University, Nagoya, 464-8603, Japan

Takashi Kiyohara

Makita Corporation, 3-11-8, Sumiyoshi-cho, Anjo, Aichi, 446-8502, Japan

J. Vib. Acoust 134(3), 031009 (Apr 24, 2012) (13 pages) doi:10.1115/1.4005829 History: Received November 14, 2010; Revised October 26, 2011; Published April 23, 2012; Online April 24, 2012

The use of wind turbine generator has rapidly spread as a one of the foremost clean energy sources. Recently, as the size of the wind turbine generator has become larger, its maintenance has become more difficult. However, there are few studies on the vibration analysis and its suppression in the conventional researches. The wind turbine is a special type of rotating machinery which has a long heavy blade rotating in the vertical plane under the action of the gravitational force. The wind power acting on the wind turbine blade varies periodically because of the height-dependent characteristic of the wind. Therefore, the dynamical design and analysis of the wind turbine blade requires a more thorough study. This paper investigates the fundamental vibration characteristic of an elastic blade of the wind turbine. The nonlinear vibration analysis of the superharmonic resonance is performed, and its characteristics are explained. Furthermore, the effect of the interaction of both the gravitational force and the wind force on the superharmonic resonance is clarified.

Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Wind turbine model with the single elastic blade: (a) Sheared wind, (b) Theoretical model

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Figure 2

Coordinate systems: (a) Coordinate systems, (b) Displacement in the out of plane direction

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Figure 3

Free vibration of the wind turbine blade: (a) case with no static deflection and small free vibration amplitude, (b) case with considerable static deflection and small free vibration amplitude, (c) case with no static delfrection and considerable free vibration amplitude

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Figure 4

Natural frequency diagram: (a) Influence of the static deflection, (b) Influence of the amplitude of the free vibration

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Figure 5

Natural frequency diagram and resonance resonance (case with constant wind force of Qc  = 3.73 and periodic wind force of ΔQ = 1.24)

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Figure 6

Influence of the constant wind force component Qc and the periodic wind force component ΔQ on the resonance curve of the superharmonic resonance of the second order

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Figure 7

Influence of the constant wind force component Qc and the periodic wind force component ΔQ on the resonance curve of the superharmonic resonance of the third order

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Figure 8

Mechanism of the occurrence of superharmonic resonances

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Figure 9

Comparison of the numerically and theoretically obtained resonance curves for each vibration component (a) case with the constant wind force (Case of Qc  = 3.73 and ΔQ = 0.0), (b) case with both the constant wind force component and the periodic wind force component (Case of Qc  = 3.73 and ΔQ = 1.24)

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Figure 10

Resonance curves and back born curve

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Figure 11

Comparison of the backbone curve and characteristic curve

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Figure 12

Influence of parameters on the characteristic curve: (a) Influence of the length of blade l, (b) Influence of the width of blade b, (c) Influence of the thickness of blade h, (d) Influence of the constant wind Qc

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Figure 13

Experimental System (a) Experimental Setup, (b) Balancer for the rotating blade

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Figure 14

Resonance curve (experiment): case of no wind (Case (1) in Table 3)

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Figure 15

Resonance curve (experiment): case of a light wind (Case (2) in Table 3)

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Figure 16

Time history and spectrum in the case of the light wind shown in Fig. 1: (a) ω/(2π) = 1.360 Hz, (b) ω/(2π) = 1.480 Hz (c) ω/(2π) = 1.640 Hz

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Figure 17

Resonance curve (experiment): case of a moderate wind (Case (3) in Table 3)

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