For product optimization regarding weight reduction, material properties have
to be adapted efficiently. To achieve this, new compositions of materials can be created
or the manufacturing process can be changed in a way that heterogeneous distributions
of material properties are enabled. An example for such an improved process chain is
the production of thermo-mechanically graded structures like shafts. The manufacturing
method mainly consists of three stages. The first one is characterized by a local temperature
increase of the workpiece due to inductive heating. In the second phase the workpiece
is deformed and simultaneously cooled throughout the contact with the forming die. In
the last step, however, a high pressured air stream is applied, leading to a partial cooling
of the workpiece.
The inductive heating step is controlled by an alternating current inducing a high frequency
magnetic field, which causes a temperature increase due to the resulting eddy
currents. To analyse this process, the coupling between the electric and the magnetic
field is described by the fully coupled Maxwell equations. Moreover the heat conduction
equation is considered to describe thermal effects. To solve this multifield the
equations are in the first step decoupled using an additional time differentiation. In the
second step an axisymmetric case is considered, motivated by the fact that the inductive
heating process of a cylindrical shaft is analysed. Afterwards the resulting equations are
spatially discretized by the Galerkin finite element method. The temporal discretization
is carried out via the Newmark method so that afterwards the electrical source
distribution can be achieved. As a consequence the temperature evolution is determined
in a postprocessing step.
