Multi-frequency Induction Hardening: A Challenge for Industrial Mathematics
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.
KeywordsInduction 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”.