Research Papers

Aspects of Symbolic Formulations in Flexible Multibody Systems

[+] Author and Article Information
Markus Burkhardt

Institute of Engineering and Computational Mechanics,
University of Stuttgart,
Stuttgart 70569, Germany
e-mail: markus.burkhardt@itm.uni-stuttgart.de

Robert Seifried

Institute of Vehicle Technology,
Dynamical Systems Group,
Department Mechanical Engineering,
University of Siegen,
Siegen 57068, Germany
e-mail: robert.seifried@uni-siegen.de

Peter Eberhard

Institute of Engineering and Computational Mechanics,
University of Stuttgart,
Stuttgart 70569, Germany
e-mail: peter.eberhard@itm.uni-stuttgart.de

Contributed by the Design Engineering Division of ASME for publication in the Journal of Computational and Nonlinear Dynamics. Manuscript received May 31, 2013; final manuscript received October 28, 2013; published online July 11, 2014. Assoc. Editor: Javier Cuadrado.

J. Comput. Nonlinear Dynam 9(4), 041013 (Jul 11, 2014) (8 pages) Paper No: CND-13-1114; doi: 10.1115/1.4025897 History: Received May 31, 2013; Revised October 28, 2013; Accepted October 31, 2013

The symbolic modeling of flexible multibody systems is a challenging task. This is especially the case for complex-shaped elastic bodies, which are described by a numerical model, e.g., an FEM model. The kinematic and dynamic properties of the flexible body are in this case numerical and the elastic deformations are described with a certain number of local shape functions, which results in a large amount of data that have to be handled. Both attributes do not suggest the usage of symbolic tools to model a flexible multibody system. Nevertheless, there are several symbolic multibody codes that can treat flexible multibody systems in a very efficient way. In this paper, we present some of the modifications of the symbolic research code Neweul-M2 which are needed to support flexible bodies. On the basis of these modifications, the mentioned restrictions due to the numerical flexible bodies can be eliminated. Furthermore, it is possible to re-establish the symbolic character of the created equations of motion even in the presence of these solely numerical flexible bodies.

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Fig. 1

Available implementations in Neweul-M2

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Fig. 2

Kinematic relationships for non-nodal-fixed frame types

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Fig. 3

Software management

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Fig. 4

Comparison of the x-components of the position vectors of the weights

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Fig. 5

Flexible components of the V-twin engine

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Fig. 6

Multibody system of a V-twin engine

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Fig. 7

Comparison of the time required for symbolic calculations, file export, and a simulation using different levels of abbreviations (abb) for the NewtonEuler (NE) and the RecursiveMinimal (RM) formulations

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Fig. 8

Comparison of the different formulations with respect to the rotational speed of the crank drive and a dominant elastic coordinate



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