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Research Papers

Reduction of Physical and Constraint Degrees-of-Freedom of Redundant Formulated Multibody Systems

[+] Author and Article Information
Daniel Stadlmayr

Faculty of Engineering and
Environmental Sciences,
University of Applied Sciences Upper Austria,
Stelzhamerstrasse 23,
Wels 4600, Austria;
Institute of Mechanics and Mechatronics,
Vienna University of Technology,
Getreidemarkt 9/325,
Wien 1060, Austria
e-mail: daniel.stadlmayr@fh-wels.at

Wolfgang Witteveen

Faculty of Engineering and
Environmental Sciences,
University of Applied Sciences Upper Austria,
Stelzhamerstrasse 23,
Wels 4600, Austria
e-mail: wolfgang.witteveen@fh-wels.at

Wolfgang Steiner

Faculty of Engineering and
Environmental Sciences,
University of Applied Sciences Upper Austria,
Stelzhamerstrasse 23,
Wels 4600, Austria;
Institute of Mechanics and Mechatronics,
Vienna University of Technology,
Getreidemarkt 9/325,
Wien 1060, Austria
e-mail: wolfgang.steiner@fh-wels.at

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 27, 2015; final manuscript received September 1, 2015; published online October 23, 2015. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 11(3), 031010 (Oct 23, 2015) Paper No: CND-15-1079; doi: 10.1115/1.4031553 History: Received March 27, 2015; Revised September 01, 2015

Commercial multibody system simulation (MBS) tools commonly use a redundant coordinate formulation as part of their modeling strategy. Such multibody systems subject to holonomic constraints result in second-order d-index three differential algebraic equation (DAE) systems. Due to the redundant formulation and a priori estimation of possible flexible body coordinates, the model size increases rapidly with the number of bodies. Typically, a considerable number of constraint equations (and physical degrees-of-freedom (DOF)) are not necessary for the structure's motion but are necessary for its stability like out-of-plane constraints (and DOFs) in case of pure in-plane motion. We suggest a combination of both, physical DOF and constraint DOF reduction, based on proper orthogonal decomposition (POD) using DOF-type sensitive velocity snapshot matrices. After a brief introduction to the redundant multibody system, a modified flat Galerkin projection and its application to index-reduced systems in combination with POD are presented. The POD basis is then used as an identification tool pointing out reducible constraint equations. The methods are applied to one academic and one high-dimensional practical example. Finally, it can be reported that for the numerical examples provided in this work, more than 90% of the physical DOFs and up to 60% of the constraint equations can be omitted. Detailed results of the numerical examples and a critical discussion conclude the paper.

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References

Figures

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Cart double-pendulum

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Rigid V8 crank-drive

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Fig. 4

Cart double-pendulum—combined snapshots

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Fig. 5

Cart double-pendulum—DOF-type sensitive snapshots

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Fig. 6

Flex pendulum—relative CoM error

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Fig. 7

V8—DOF-type sensitive snapshots

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Fig. 8

V8—relative CoM error of second piston

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