Modelling, Analysis and Simulation of Multifrequency Induction Hardening

For nearly all workpieces made of steel a surface heat treatment to raise the hardness and the wear resistance is indispensable.
A classic method for the heat treatment is induction hardening, where the heating is done by electromagnetic fields. Due to the induced eddy currents and the skin effect, the necessary heat to produce the high temperature phase austenite is generated directly in the workpiece. During the subsequent quenching, martensite forms in the boundary layer, which is characterized by its high hardness. The recently developed concept of multifrequency induction hardening uses two superimposed alternating currents with different frequencies to generate a hardening profile following the contour. This method is well suited to harden complex shaped workpieces such as gears, where the coupling distance to the inductor varies.
The determination of optimal process parameters requires a lot of experience and validation by time-consuming and costly experiments. Therefore, there is a huge demand for numerical simulations of multifrequency induction hardening.

The present work describes the modelling and the simulation of inductive heating of workpieces made of steel using the multifrequency concept. The model consists of a coupled system of partial and ordinary differential equations to determine the temperature distribution in the workpiece, the electromagnetic fields as the source of the Joule heat and the distribution of the high temperature phase austenite, which provides information about the resulting hardening pattern. Nonlinearities resulting from temperature dependent material parameters and a magnetic permeability that depends on the magnetic field itself are of great importance for the performance of the simulation.
The coupled PDE-system is solved by the finite element method, whereby the electromagnetic subproblem is discretized by curl-conforming edge elements. Since due to the skin effect, the boundary layer of the workpiece must be resolved very accurately, the grid is generated adaptively using residual based error estimators.