Equations of motion for a rotor blade, including gravity, pitch action and rotor speed variations

Kallesøe, Bjarne Skovmose

doi:10.1002/we.217

Cited by 54 publications

(40 citation statements)

References 7 publications

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“…In the earlier attempts to formulate the equation of the motion of a blade, the works of [20,21] developed an equation of motion for combined flapwise and chordwise bending and torsion of a twisted non-uniform rotor blade. More comprehensive models are developed subsequently to include pitch action, rotor speed variation, the effect of gravity [22], the coupling between blade and tower, and other phenomena.…”

Section: Structural Modelmentioning

confidence: 99%

“…For the present work, the formulation presented in [22] is adopted with constant rotor speed. Consider the following coordinates: In Figure 1, the Cartesian coordinate X, Y, Z is the inertial reference frame R, with Z-axis pointing downwind direction and the origin set at the center of the hub.…”

Section: Structural Modelmentioning

confidence: 99%

“…β is the pitch angle. The coordinate frame (x, y, z) is aligned with (x, y, z) p but rotating about the pitch axis x p , (see Figure 1); the transformation of these coordinates for the sake of brevity it is not discussed here, although thorough information is available in [22].…”

Section: Structural Modelmentioning

confidence: 99%

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Comparative Study on Uni- and Bi-Directional Fluid Structure Coupling of Wind Turbine Blades

Ageze

2017

Energies

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Abstract:The current trends of wind turbine blade designs are geared towards a longer and slender blade with high flexibility, exhibiting complex aeroelastic loadings and instability issues, including flutter; in this regard, fluid-structure interaction (FSI) plays a significant role. The present article will conduct a comparative study between uni-directional and bi-directional fluid-structural coupling models for a horizontal axis wind turbine. A full-scale, geometric copy of the NREL 5MW blade with simplified material distribution is considered for simulation. Analytical formulations of the governing relations with appropriate approximation are highlighted, including turbulence model, i.e., Shear Stress Transport (SST) k-ω. These analytical relations are implemented using Multiphysics package ANSYS employing Fluent module (Computational Fluid Dynamics (CFD)-based solver) for the fluid domain and Transient Structural module (Finite Element Analysis-based solver) for the structural domain. ANSYS system coupling module also is configured to model the two fluid-structure coupling methods. The rated operational condition of the blade for a full cycle rotation is considered as a comparison domain. In the bi-directional coupling model, the structural deformation alters the angle of attack from the designed values, and by extension the flow pattern along the blade span; furthermore, the tip deflection keeps fluctuating whilst it tends to stabilize in the uni-directional coupling model.

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Section: Structural Modelmentioning

confidence: 99%

Section: Structural Modelmentioning

confidence: 99%

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Comparative Study on Uni- and Bi-Directional Fluid Structure Coupling of Wind Turbine Blades

Ageze

2017

Energies

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“…Wendell [1] developed the partial differential equations of motion for a rotating wind turbine blade. Additional efforts have been made by to include gravity and pitch action by Kallosóe [2] . Caruntu [3] has developed nonlinear equations that model the flexural potential in non-uniform beam that can be extended to large flexible blades of wind turbines.…”

Section: Introductionmentioning

confidence: 99%

In-Plane Nonlinear Dynamics of Wind Turbine Blades

Ramakrishnan

Feeny

2011

Volume 1: 23rd Biennial Conference on Mechanical Vibration and Noise, Parts a and B

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“…A new aeroelastic blade model for wind turbine blades with pitch actuation [6] includes the bending-torsion coupling for largely bend blades and the inertia coupling from the rotational motion in the pitch bearing. A test case with the blade of the RWT shows that a step in the pitch angle induces both torsional and bending motion of the blade.…”

Section: Introductionmentioning

confidence: 99%

Servo-Elastic Dynamics of a Hydraulic Actuator Pitching a Blade with Large Deflections

Hansen¹,

Kallesøe²

2007

J. Phys.: Conf. Ser.

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Abstract. This paper deals with the servo-elastic dynamics of a hydraulic pitch actuator acting on a largely bend wind turbine blade. The compressibility of the oil and flexibility of the hoses introduce a dynamic mode in the pitch bearing degree of freedom. This mode may obtain negative damping if the proportional gain on the actuator position error is defined too large relative to the viscous forces in the hydraulic system and the total rotational inertia of the pitch bearing degree of freedom. A simple expression for the stability limit of this proportional gain is derived for tuning the gain based on the Ziegler-Nichols method. Computed transfer functions from reference to actual pitch angles indicate that the actuator can be approximated as a low-pass filter with some appropriate limitations on pitching speed and acceleration. The structural blade model includes the geometrical coupling of edgewise bending and torsion for large flapwise deflections. This coupling is shown to introduce edgewise bending response for pitch reference oscillations around the natural frequency of the edgewise bending mode, in which frequency range the transfer function from reference to actual pitch angle cannot be modeled as a simple low-pass filter. The pitch bearing is assumed to be frictionless as a first approximation. IntroductionThis paper deals with the modeling and analysis of the servo-elastic dynamics of a hydraulic pitch actuator acting on the blade of the 5 MW Reference Wind Turbine (RWT) by NREL [1]. This work has two objectives: A dynamic characterization of hydraulic pitch actuators and an identification of bending-torsion coupling effects for largely bend blades with pitch actuation.The authors have not found any previous work on detailed modeling and analysis of hydraulic pitch actuators acting on wind turbine blades. Caselitz et al. [2] have presented a numericalexperimental analysis of a pitch controller using electrical pitch actuators, where the dynamics of these electrical actuators are included in the analysis as hardware-in-the-loop.Nonlinear effects of large flapwise blade deflections on the power production and loads of MWsized wind turbines have been studied from nonlinear aeroelastic simulations [3,4]. These studies showed two main effects: A reduction in power production by up to 5 % due to reduced effective rotor area when the blade bend downwind and inward under the loading, and an increased pitch torque by up to 50 % at the blade root due to the increased distance from the pitch axis to the point of action of the inplane forces on the blade. The reduced power production is compensated by the controller through the blade pitch angle settings [3], which causes the blade loads and tower thrust loads to increase above rated wind speeds. The effect of the increased pitch torque on the pitch actuator and its control has not been considered.

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Equations of motion for a rotor blade, including gravity, pitch action and rotor speed variations

Cited by 54 publications

References 7 publications

Comparative Study on Uni- and Bi-Directional Fluid Structure Coupling of Wind Turbine Blades

Comparative Study on Uni- and Bi-Directional Fluid Structure Coupling of Wind Turbine Blades

In-Plane Nonlinear Dynamics of Wind Turbine Blades

Servo-Elastic Dynamics of a Hydraulic Actuator Pitching a Blade with Large Deflections

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