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Research Papers

Integration of Nonlinear Models of Flexible Body Deformation in Multibody System Dynamics

[+] Author and Article Information
Martin Schulze

e-mail: Martin.Schulze@simpack.de

Bernhard Burgermeister

SIMPACK AG,
Friedrichshafener Straße 1,
Gilching 82205, Germany

Andrey Tuganov

7-4270 Rue Saint-Dominique,
Montreal, QC H2W 2B1, Canada
e-mail: Andrey.Tuganov@gmail.com

Holger Lang

Chair of Applied Dynamics,
University of Erlangen-Nuremberg,
Konrad-Zuse-Str. 3/5,
Erlangen 91052, Germany
e-mail: Holger.Lang@ltd.uni-erlangen.de

Joachim Linn

Fraunhofer Institut für Techno-und
Wirtschaftsmathematik (ITWM),
Fraunhofer-Platz 1,
Kaiserslautern 67663, Germany
e-mail: Joachim.Linn@itwm.fraunhofer.de

Martin Arnold

Institute of Mathematics,
Martin Luther University Halle-Wittenberg,
Halle (Saale) 06099, Germany
e-mail: Martin.Arnold@mathematik.uni-halle.de

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 5, 2012; final manuscript received April 26, 2013; published online October 14, 2013. Assoc. Editor: Hiroyuki Sugiyama.

J. Comput. Nonlinear Dynam 9(1), 011012 (Oct 14, 2013) (10 pages) Paper No: CND-12-1191; doi: 10.1115/1.4025279 History: Received November 05, 2012; Revised April 26, 2013

Current challenges in industrial multibody system simulation are often beyond the classical range of application of existing industrial simulation tools. The present paper describes an extension of a recursive order-n multibody system (MBS) formulation to nonlinear models of flexible deformation that are of particular interest in the dynamical simulation of wind turbines. The floating frame of reference representation of flexible bodies is generalized to nonlinear structural models by a straightforward transformation of the equations of motion (EoM). The approach is discussed in detail for the integration of a recently developed discrete Cosserat rod model representing beamlike flexible structures into a general purpose MBS software package. For an efficient static and dynamic simulation, the solvers of the MBS software are adapted to the resulting class of MBS models that are characterized by a large number of degrees of freedom, stiffness, and high frequency components. As a practical example, the run-up of a simplified three-bladed wind turbine is studied where the dynamic deformations of the three blades are calculated by the Cosserat rod model.

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Figures

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Fig. 1

Interaction of SIMPACK and the Cosserat rod model

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Fig. 2

Difference approximation of a band structured Jacobian matrix with the minimum number of rhs evaluations, N = 6

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Fig. 3

Time evolution of a swinging rubber beam

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Fig. 4

Wind turbine rotor blade being deformed by a constant wind field

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Fig. 5

Static deformation of the NREL 5 MW wind turbine rotor blade in the constant force distribution of a wind field: Comparison of the Abaqus B31, the Cosserat rod, and the segmented SIMBEAM models

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Fig. 6

Comparison of the first and the 12th eigenmodes of the NREL 5 MW wind turbine rotor blade obtained with the Abaqus B31 and with the Cosserat rod models, respectively (normalized units)

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Fig. 7

Simplified model of a three-bladed wind turbine

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Fig. 8

Steady state of the simplified wind turbine. The left diagram shows the blade deformation perpendicular to the movement plane, the right diagram the main shaft velocity for one rotation.

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