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Thermo-energetic Design of Machine Tools pp 85–93Cite as

Model Order Reduction for Thermo-Elastic Assembly Group Models

Part of the Lecture Notes in Production Engineering book series (LNPE)

Abstract

We present two model order reduction approaches based on different modelling strategies for a thermo-elastic assembly group model. Here, we consider the machine stand example given in Chap. 7. The focus is on capturing the structural variability. Therefore, we compare a switched linear systems (SLS) approach based on reduced order models determined by the Balanced Truncation (BT) method and a parametric model order reduction (PMOR) scheme based on an interpolatory projection method via the iterative rational Krylov algorithm (IRKA). In order to avoid the high dimensional coupled thermo-elastic system, additionally a Schur complement representation is applied to exploit the special structure of the one-sided coupling property of the system. The results show that both methods generate relative errors in the range of one per thousand.

Keywords

  • Iterative Rational Krylov Algorithm (IRKA)
  • Parametric Model Order Reduction (PMOR)
  • Switched Linear Systems (SLS)
  • Balanced Truncation (BT)
  • Tool Slide

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Fig. 8.1
Fig. 8.2

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Authors and Affiliations

  1. Mathematics in Industry and Technology, Department of Mathematics, University of Technology, Chemnitz, Germany

    Norman Lang, Jens Saak & Peter Benner

Authors
  1. Norman Lang
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  2. Jens Saak
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  3. Peter Benner
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Corresponding author

Correspondence to Norman Lang .

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Editors and Affiliations

  1. Institut für Werkzeugmaschinen und Steuerungstechnik, TU Dresden, Dresden, Germany

    Knut Großmann

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Lang, N., Saak, J., Benner, P. (2015). Model Order Reduction for Thermo-Elastic Assembly Group Models. In: Großmann, K. (eds) Thermo-energetic Design of Machine Tools. Lecture Notes in Production Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-12625-8_8

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  • DOI: https://doi.org/10.1007/978-3-319-12625-8_8

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