Thixoforming : Semi-solid Metal Processing

374j 10 Thixoforging and Rheoforging of Steel and Aluminium Alloys
Figure 10.5 The induction furnace [26].
An optimized coil geometry is used to increase the energy entry at the edges. Thus,
the losses at the edges are compensated and a homogeneous temperature distribution
is produced. The coil consists of two separate parts positioned above each other,
which are independently adjustable in height. The distance between these two parts
can be changed and thus the energy entry to the face and the bottom surface can be
influenced [20].
The eddy currents cause a power distribution in the billet, the so-called volume
power density. The volume power density can be determined through Maxwell
equations. Due to the optimal geometry of the coil, the variation of the magnetic field
strength height (z-direction) can be neglected. Therefore, only deviations in the radial
direction have to be considered. This assumption and the cylindrical form of the billet
yield the following Maxwell equations in cylindrical coordinates:
and
0 ¼ q2 ^H z 1 q^H z
þ
qr2 r qr
^E j ðrÞ ¼ 1 q^H z
k qr
kmjw^H z
ð10:1Þ
where ^H z is the magnetic field strength, ^ E j the electric field, w the circular frequency
of the resonant circuit, k the electric conductivity and m the magnetic permeability.