Nonlinear Multibody Dynamics of Wind Turbines

Kristian Holm-Jørgensen

    Research output: PhD thesis

    2164 Downloads (Pure)

    Abstract

    The continuing development of wind turbines aim at higher effect production and reducing the purchase and maintenance costs for the customers. This demands that the components in the wind turbine are optimized closer to the limit than previously. In order to determine the design loads it is necessary with a numericalmodel, which represents the reality as good as possible. For this purpose a flexible multibody formulation is suitable because large nonlinear geometric deformations of e.g. the blades can be accounted for while still having the possibility of modelling the remaining components individually and next couple them by use of joints. This gives a high level of modelling flexibility, where parts of the structure with relative ease can be interchanged to analyze other possibilities in a design process, or if a higher detail level is wanted for some components. In a multibody formulation each substructure e.g. a part of the blade is modelled by use of Bernoulli-Euler beam elements with St. Venant torsion. For each substructure a belonging moving frame is present, where to the displacements of the substructure must be relative small, in order for the linear displacement assumption to be fulfilled inside the moving frame. By modelling e.g. the blades by use of several substructures it is possible to account for large nonlinear geometric deformations.

    The multibody formulation focused on in this project is based on the Local Observer Frame formulation, where the parameters that determine the motion of the frames do not enter the state vector, like in the more standard Floating Frame of Reference formulation. Hereby, the otherwise mixed set of referential and elastic coordinates are avoided and thereby the highly nonlinear equations of motion. However, this demands that the parameters to define the motion  of the moving frames are regularly updated so the relative motion of the substructure from the belonging moving frame is reduced. The update algorithm of these parameters is based on the motion of the belonging beam element substructure. Based on a number of static analyses for a wind turbine blade with large nonlinear displacements it has shown most favorable to use the end points in the substructure for updating the moving frames.

    For speeding up dynamical simulations for use in e.g. active control or parameter studies, system reduction of substructures in the multibody formulation is investigated. I the first method a Ritz basis is used, which contains rigid body modes and a number of elastic eigenmodes compatible to the kinematical boundary conditions. By use of very few elastic eigenmodes to model a blade it has shown convenient to use a quasi-static term for the truncated elastic eigenmodes. The second method is based on a Component Mode Synthesis method with constraint modes and fixed interface normal modes. Hereby, the coupling degrees of freedom between adjacent substructures are preserved for use in setting op the kinematical constraints which secure compatibility at the assembling point. This method is more general and can also be used to model the blade in e.g. two substructures or to model other components in the wind turbine.

    To determine the structural properties of a blade for use in beam element models, a FEmodel is implemented which besides the more common beam element parameters also can determine e.g. torsional stiffness and the position of the shear center. The method makes use of three node triangular elements where the different material layers in the blade profile are taken into consideration. The results are compared to a similar tool which makes use of straight elements of uniform thickness to discretize the cross section, where a mean value of the material layers over the thickness direction is used. Good correspondence is demonstrated between the used discretization methods.

    Original languageEnglish
    Place of PublicationAalborg
    Publisher
    Publication statusPublished - 2009

    Bibliographical note

    PDF for print: 152 pp.

    Keywords

    • Wind Turbines
    • Wind Turbine Blades
    • Dynamics
    • Moving Frame
    • Multibody Dynamics
    • System Reduction
    • Quasi-Static Reduction
    • Nonlinear Vibrations
    • Bernoulli-Euler Beams
    • Co-Rotating Finite Elements
    • Truncated Modal Expansion

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