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Ocean Renewable Energy

Floating Offshore Wind Turbine Dynamics: Large-Angle Motions in Euler-Space

[+] Author and Article Information
Bert Sweetman

Department of Maritime Systems Engineering, Texas A&M Universitysweetman@tamu.eduDepartment of Civil Engineering, Texas A&M Universitysweetman@tamu.edu

Lei Wang

Department of Maritime Systems Engineering, Texas A&M Universityraywong@tamu.eduDepartment of Civil Engineering, Texas A&M Universityraywong@tamu.edu

J. Offshore Mech. Arct. Eng. 134(3), 031903 (Feb 10, 2012) (8 pages) doi:10.1115/1.4004630 History: Received June 16, 2010; Accepted May 23, 2011; Published February 10, 2012; Online February 10, 2012

Floating structures have been proposed to support offshore wind turbines in deep water, where environmental forcing could subject the rotor to meaningful angular displacements in both precession and nutation, offering design challenges beyond conventional bottom-founded structures. This paper offers theoretical developments underlying an efficient methodology to compute the large-angle rigid body rotations of a floating wind turbine in the time domain. The tower and rotor-nacelle assembly (RNA) are considered as two rotational bodies in the space, for which two sets of Euler angles are defined and used to develop two systems of Euler dynamic equations of motion. Transformations between the various coordinate systems are derived in order to enable a solution for the motion of the tower, with gyroscopic, environmental, and restoring effects applied as external moments. An example is presented in which the methodology is implemented in matlab in order to simulate the time-histories of a floating tower with a RNA.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 1

Coordinate systems (X,Y,Z), (x,y,z), and (A,B,C) and Euler angles (θ1,θ2,η). Axis A shown slightly offset from z for clarity.

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Figure 2

Rotation of (A,B,C) in terms of φ, θ, and ψ

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Figure 3

Projection of Euler angular velocities

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Figure 4

Coordinate system for derivation of inertial and environmental forcing

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Figure 5

Case 1: Free vibration described by three Euler angles

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Figure 6

Case 1: Comparison of ωX

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Figure 7

Case 1: Comparisons of ωYand ωZ

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Figure 8

Precession angle of the RNA

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Figure 9

Gyro moments acting on the RNA

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