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Multi-frequency Induction Hardening: A Challenge for Industrial Mathematics

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The Impact of Applications on Mathematics

Part of the book series: Mathematics for Industry ((MFI,volume 1))

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Abstract

Multi-frequency induction hardening is a rather new technology to produce contour-hardened gears by applying ac current of two different frequencies to the inductor coil. The approach results in a number of additional control parameters as compared to the standard induction heating approach. Accordingly, there is a strong demand in industry for mathematical modelling and simulation of this process. This paper reports on the results of a collaborative project between partners from academia and industry. We describe a mathematical model of multi-frequency induction hardening and remark on its qualitative mathematical analysis, we derive a numerical approximation strategy, compare the results with experiments and conclude with a further validation in collaboration with one of our industrial partners.

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References

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Acknowledgments

The work of E. Rocca was supported by the FP7-IDEAS-ERC-StG Grant #256872 (EntroPhase). D. Hömberg and T. Petzold were partially supported by the Federal Ministry of Education and Research through the priority program “Mathematics for innovations in industry and services”.

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Authors and Affiliations

  1. Weierstrass Institute, Mohrenstr. 39, 10117, Berlin, Germany

    Dietmar Hömberg, Thomas Petzold & Elisabetta Rocca

  2. Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133, Milan, Italy

    Elisabetta Rocca

Authors
  1. Dietmar Hömberg
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  2. Thomas Petzold
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  3. Elisabetta Rocca
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Corresponding author

Correspondence to Dietmar Hömberg .

Editor information

Editors and Affiliations

  1. Institute for Mathematics and Industry, Kyushu University, Fukuoka, Japan

    Masato Wakayama

  2. CSIRO (Commonwealth Scientific and Industrial Research Organisation), Canberra, Aust Capital Terr, Australia

    Robert S. Anderssen

  3. School of Mathematical Sciences, Fudan University, Shanghai, China

    Jin Cheng

  4. Kyushu University, Fukuoka, Japan

    Yasuhide Fukumoto

  5. Institute of Natural and Mathematical Sciences, Massey University, Palmerston North, Auckland, New Zealand

    Robert McKibbin

  6. Institute of Mathematics, Free University of Berlin, Berlin, Germany

    Konrad Polthier

  7. Kyushu University, Fukuoka, Japan

    Tsuyoshi Takagi

  8. Department of Mathematics, National University of Singapore, Singapore, Singapur, Singapore

    Kim-Chuan Toh

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Hömberg, D., Petzold, T., Rocca, E. (2014). Multi-frequency Induction Hardening: A Challenge for Industrial Mathematics. In: Wakayama, M., et al. The Impact of Applications on Mathematics. Mathematics for Industry, vol 1. Springer, Tokyo. https://doi.org/10.1007/978-4-431-54907-9_19

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  • DOI: https://doi.org/10.1007/978-4-431-54907-9_19

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  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-54906-2

  • Online ISBN: 978-4-431-54907-9

  • eBook Packages: EngineeringEngineering (R0)

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