Multi-frequency Induction Hardening: A Challenge for Industrial Mathematics

  • Dietmar Hömberg
  • Thomas Petzold
  • Elisabetta Rocca
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 1)

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.

Keywords

Induction hardening Joule heating Maxwell’s equations Finite element simulation 

Notes

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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Copyright information

© Springer Japan 2014

Authors and Affiliations

  • Dietmar Hömberg
    • 1
  • Thomas Petzold
    • 1
  • Elisabetta Rocca
    • 1
    • 2
  1. 1.Weierstrass InstituteBerlinGermany
  2. 2.Dipartimento di MatematicaUniversità di MilanoMilanItaly

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