FEM-BEM Coupling for the Modelling of Induction Heating Processes Including Moving Parts

Every electrical conductive medium placed in a time varying magnetic field is the seat of eddy currents that dissipate power through Joule effect. The induction hardening process takes advantage of this effect. The power concentrates in the surface of the piece (skin effect), the thickness of which depends on the electromagnetic properties and the frequency of the currents. The numerical simulation of such a process is of major interest to control and estimate the thickness of the treated layer, the superficial hardness, the residual stresses (often compressive in the surface) or the residual distortions. In this paper we focus on the interactions between electromagnetism and heat transfer for the simulation of the heating stage. The method used to couple both phenomena is detailed. A magnetic vector potential formulation is used for the electromagnetic analysis and an approach coupling finite elements with boundary elements is presented. Such a method is especially useful when moving parts are involved as it is generally the case for induction hardening processes. The air is represented by a boundary element that enables to consider independent meshes for all the conductive media within the device (piece and coils). Moreover, meshes are now the same for the electromagnetic and thermal analyses. This considerably facilitates the analysis that is performed step by step, each step corresponding to a position of the moving media. At each step, the matrices associated with the boundary element are calculated and the magneto-dynamic and thermal analyses are performed. Finally, an application is presented.