Thixoforming : Semi-solid Metal Processing

380j 10 Thixoforging and Rheoforging of Steel and Aluminium Alloys
where ber() and bei() are Kelvin functions. To ensure that the needed power is induced
into the billet, the coil current has to be controlled. We can convert Equation 10.13 to
achieve the coil current peak value:
^I ðtÞ ¼ Sp LSp
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
kd
ber
PðtÞ pffiffiffi NSp 2pRB
2
ffiffi
pffiffi 2RB
þ bei2 d
pffiffi 2RB
ber ber0 pffiffi 2RB
þ bei bei 0
v
u
t
pffiffi 2RB
d
p
2RB
d
pffiffi 2RB
d
d
d
ð10:14Þ
The converter is controlled with a simple proportional–integral–derivative (PID)
controller to ensure that the actual current match the desired coil current trajectory
and thus the needed power is induced into the billet.
Control with a Pyrometer
In the following, we will discuss another approach to heating steel into the semi-solid
state. For a more detailed description of the control scheme, see [39]. Because direct
measurement of the temperature via thermocouples is not feasible in a production
environment, a radiation pyrometer was used as a contactless measurement device.
The accuracy of the pyrometer depends heavily on the exact knowledge of the radiation
coefficient, which can vary from billet to billet due to different surface properties and
which is subject to change during the heating process. These uncertainties prohibit
the implementation of a closed-loop control scheme since the exact temperature
cannot be measured with the required accuracy. In order to be independent of
the measurement errors, the proposed control scheme relies only on the slope of
the temperature. By detecting the distinct change of slope that occurs when the solidus
temperature is crossed, the beginning of the melting process can be determined. The
energy fed into the billet from this point onward determines the resulting liquid
fraction. By feeding the same amount of energy to each billet, it is guaranteed that the
billets reach the desired liquid fraction despite the uncertain absolute value of the
temperature and small variations of the alloy composition.
During the heating of X210CrW12, there are two distinct changes in the slope of
the heating curve, one at about 800 C where the billet loses its magnetic properties
and therefore the efficiency falls considerably. The second appears around 1230 C
and this is the beginning of melting of the alloy. By detecting the slope change and
controlling the energy fed to the billet after this point, the liquid fraction can be
controlled. After the required melting energy has been induced into the billet, the
billet temperature needs to be homogenized since the core temperature lags behind
the surface temperature. This is achieved by reducing the converter power to a level,
which ensures that the surface temperature remains nearly constant and only the
radiation losses are compensated.
The proposed heating control scheme consists of four steps [39]:
1. heating of the billet with constant converter power until the crossing of the solidus
temperature;
2. automatic detection of the entry into the melting region by evaluation of the
temperature slope;