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Influence of model reduction techniques on the impact force calculation of two flexible bodies
Author(s) -
Eberhard Peter,
Fehr Jörg,
Mathuni Stefan
Publication year - 2009
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200910030
Subject(s) - reduction (mathematics) , finite element method , gramian matrix , computer science , multibody system , krylov subspace , subspace topology , armature (electrical engineering) , model order reduction , control theory (sociology) , algorithm , engineering , mathematics , mechanical engineering , structural engineering , eigenvalues and eigenvectors , artificial intelligence , iterative method , projection (relational algebra) , physics , geometry , control (management) , quantum mechanics , magnet
One important issue for the simulation of flexible multibody systems is the reduction of the flexible body's degrees of freedom. For the reduction process finite element data and user inputs are necessary. The model reduction program for elastic multibody systems MOREMBS, which is developed at the ITM, has an easy‐to‐use interface and the data can be gained from the programs ABAQUS or ANSYS. In this work, the simulation of a fuel injection process is investigated with MOREMBS. We focus on the interaction between valve and armature. These two bodies impact in every injection circle. The impacting bodies are modeled as flexible and the contact force is calculated by a penalty approach. One essential part of this work is the investigation of the influence of different model reduction techniques on the impact force calculation of the flexible multibody system. The main reduction techniques modal reduction, Krylov‐subspace based and Gramian matrix based techniques are compared. The results achieved with modal reduction, the state of the art reduction method, are not acceptable here. Krylov‐subspace based techniques are especially well‐suited for large sparse systems but are not error controlled. However, by choosing appropriate moment‐matching properties the impact force calculation is nearly as good as with a full finite element model. The Gramian matrix based reduction techniques can be fully automated and are error controlled but require high computational effort. Hence, appropriate approximation schemes have to be used for them. With Gramian matrix based methods we can even further reduce the size of the subsystems compared to Krylov‐subspace based methods and still have an impact force calculation nearly as good as with finite element results, but we gain a simulation speedup by the factor 4000. In addition, a parameter study of the parameters involved in the model reduction process is presented. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)