Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Computation of thermo-elastic deformations on machine tools a study of numerical methods

  • Computer Aided Engineering
  • Published:
Production Engineering Aims and scope Submit manuscript

Abstract

Modern machine tools are highly optimized with respect to their design and the production processes they are capable to. Now for further advances, especially a detailed knowledge about the thermo-elastic behavior is needed, because the nowadays still existing deficits are mainly related to this. That is why, endeavors in improvement, like the optimization of the design, the evaluation of new materials and the regulation of the production process, particularly rely on accurate computed thermal deformations. One possible approach to increase their quality is to also include the relevant structural variabilities of the machine tools as well as the resulting interactions between the coupled parts within the calculations. In this article, three different numerical methods are presented, which include structural motions in thermo-elastic analyses. Thereby, several conflicting criteria, like real-time capability, memory saving issues and accuracy are fulfilled each time in a different manner. Those methods are afterwards compared with respect to their runtime and accuracy. Finally, the paper concludes with a classification of the usability of the methods in real-time control and optimization tasks.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

Notes

  1. Collaborative Research Center/Transregio 96—“Thermo-Energetic Design of Machine Tools,” http://transregio96.de.

  2. AMDiS - Adaptive Multi-Dimensional Simulations, www.amdis-fem.org/.

References

  1. Antoulas AC (2005) Approximation of large-scale dynamical systems. SIAM Publications, Philadelphia

    Book  MATH  Google Scholar 

  2. Baur U, Beattie CA, Benner P, Gugercin S (2011) Interpolatory projection methods for parameterized model reduction. SIAM J Sci Comput 33(5):2489–2518

    Article  MathSciNet  MATH  Google Scholar 

  3. Calvo M, Chartier P, Murua A, Sanz-Serna J (2011) Numerical stroboscopic averaging for odes and daes. Appl Numer Math 61(10):1077–1095. doi:10.1016/j.apnum.2011.06.007

    Article  MathSciNet  MATH  Google Scholar 

  4. Weinan E, Engquist B (2003) The heterognous multiscale methods. Commun Math Sci 1(1):87–132

    Article  MathSciNet  MATH  Google Scholar 

  5. Freitas F, Rommes J, Martins N (2008) Gramian-based reduction method applied to large sparse power system descriptor models. IEEE Trans Power Syst 23(3):1258–1270

    Article  Google Scholar 

  6. Großmann K, Städel C, Galant A, Mühl A (2012) Werkzeugmaschinen-Berechnung von Temperaturfeldern an Werkzeugmaschinen. Zeitschrift fur Wirtschaftlichen Fabrikbetrieb 107(6):452–456

    Google Scholar 

  7. Gerisch A, Naumann A, Wensch J (2015) Defect corrected averaging for highly oscillatory problems. Appl Math Comput 261(0):90–103

    MathSciNet  Google Scholar 

  8. Gugercin S, Antoulas AC, Beattie C (2008) \({\cal H}_2\) model reduction for large-scale dynamical systems. SIAM J Matrix Anal Appl 30(2):609–638

    Article  MathSciNet  MATH  Google Scholar 

  9. Haasdonk B, Ohlberger M (2009) Efficient reduced models for parametrized dynamical systems by offline/online decomposition. In: Proceedings of MATHMOD 2009, 6th Vienna international conference on mathematical modelling

  10. Hüeber S, Wohlmuth B (2009) Thermo-mechanical contact problems on non-matching meshes. Comput Methods Appl Mech Eng 198:1338–1350

    Article  MATH  Google Scholar 

  11. Jungnickel G (2010) Simulation des thermischen Verhaltens von Werkzeugmaschinen/Modellierung und Parametrierung. Inst. für Werkzeugmaschinen und Steuerungstechnik, Lehrstuhl für Werkzeugmaschinen, Inst. für Werkzeugmaschinen und Steuerungstechnik, Lehrstuhl für Werkzeugmaschinen, Dresden

  12. Lang N, Saak J, Benner P (2014) Model order reduction for systems with moving loads. at-Automatisierungstechnik 62(7):512–522

    Article  Google Scholar 

  13. Nestmann S (2006) Mittel und Methoden zur Verbesserung des thermischen Verhaltens von Werkzeugmaschinen. In: Reinhart G, Zäh M (eds) IWB Seminarberichte, vol 83. Herbert Utz Verlag

  14. Partzsch M, Beitelschmidt M (2015) Simulation of pose- and process-dependent machine tool models. In: Großmann K (ed) Thermo-energetic design of machine tools, chap. 6, pp 61–68. Springer International Publishing, Switzerland. doi:10.1007/978-3-319-12625-8_6

  15. Saad Y, Schultz MH (1986) Gmres: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J Sci Stat Comput 7(3):856–869

    Article  MathSciNet  MATH  Google Scholar 

  16. Strehmel K, Weiner R, Podhaisky H (2012) Numerik gewöhnlicher Differentialgleichungen/nichtsteife, steife und differential-algebraische Gleichungen, 2., überarb. und erw. aufl. edn. Springer Spektrum, Springer Spektrum

  17. Verwer J, Spee E, Blom J, Hundsdorfer W (1999) A second-order Rosenbrock method applied to photochemical dispersion problems. SIAM J Sci Comput 20(4):1456–1480. doi:10.1137/S1064827597326651

    Article  MathSciNet  MATH  Google Scholar 

  18. Witkowski T, Ling S, Praetorius S, Voigt A (2015) Software concepts and numerical algorithms for a scalable adaptive parallel finite element method. Advances in computational mathematics, pp 1–33. doi:10.1007/s10444-015-9405-4

Download references

Acknowledgments

The authors thank the German Research Foundation for funding this work within the CRC/TR 96 and ZIH for the provided computing resources. We further thank Alexander Galant for providing the example used here.

Author information

Authors and Affiliations

  1. Institute for Solid Mechanics, Technische Universität Dresden, Dresden, Germany

    Marian Partzsch & Michael Beitelschmidt

  2. Faculty of Mathematics, Technische Universität Chemnitz, Chemnitz, Germany

    Norman Lang & Peter Benner

  3. Max Planck Institute for Dynamics of Complex Technical Systems, Magdeburg, Germany

    Peter Benner

  4. Institute for Scientific Computing, Technische Universität Dresden, Dresden, Germany

    Andreas Naumann, Axel Voigt & Jörg Wensch

Authors
  1. Andreas Naumann
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Norman Lang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marian Partzsch
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Michael Beitelschmidt
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Peter Benner
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Axel Voigt
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Jörg Wensch
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andreas Naumann.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Naumann, A., Lang, N., Partzsch, M. et al. Computation of thermo-elastic deformations on machine tools a study of numerical methods. Prod. Eng. Res. Devel. 10, 253–263 (2016). https://doi.org/10.1007/s11740-016-0674-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11740-016-0674-7

Keywords

Search

Navigation