A semi-analytical coupled simulation approach for induction heating

Maialen Areitioaurtena, Unai Segurajauregi, Ville Akujärvi, Martin Fisk, Iker Urresti, Eneko Ukar

Research output: Contribution to journalArticlepeer-review


The numerical simulation of the induction heating process can be computationally expensive, especially if ferromagnetic materials are studied. There are several analytical models that describe the electromagnetic phenomena. However, these are very limited by the geometry of the coil and the workpiece. Thus, the usual method for computing more complex systems is to use the finite element method to solve the set of equations in the multiphysical system, but this easily becomes very time consuming. This paper deals with the problem of solving a coupled electromagnetic - thermal problem with higher computational efficiency. For this purpose, a semi-analytical modeling strategy is proposed, that is based on an initial finite element computation, followed by the use of analytical electromagnetic equations to solve the coupled electromagnetic-thermal problem. The usage of the simplified model is restricted to simple geometrical features such as flat or curved surfaces with great curvature to skin depth ratio. Numerical and experimental validation of the model show an average error between 0.9% and 4.1% in the prediction of the temperature evolution, reaching a greater accuracy than other analyzed commercial softwares. A 3D case of a double-row large size ball bearing is also presented, fully validating the proposed approach in terms of computational time and accuracy for complex industrial cases.

Original languageEnglish
Article number14
JournalAdvanced Modeling and Simulation in Engineering Sciences
Issue number1
Publication statusPublished - 2021

Subject classification (UKÄ)

  • Other Materials Engineering
  • Computational Mathematics

Free keywords

  • 42CrMo4
  • Analytical solution
  • Bearing
  • Finite element method
  • Process simulation
  • Rapid computation


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