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)


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.


Induction hardening Joule heating Maxwell’s equations Finite element simulation 



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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