Thixoforming : Semi-solid Metal Processing

394j 10 Thixoforging and Rheoforging of Steel and Aluminium Alloys
explained in Section 10.3.1. When the billet has reached the desired temperature, the
PC sends a signal to the robot controller. The robot can now engage the heated billet
and transport it into the forming press. The forging process will be started as soon as
the billet has been placed in the cavity and the robot has left the area of the forging
press. After the forming process, the finished part can be removed from the forming
press by the unloading unit.
10.3.6.6 Control of the Forming Process
The requirements for handling material in the semi-solid state are very demanding.
On the one hand, the forming process has to be done as fast as possible. On the other
hand, the flow of the material must not stall because this would lead to imperfections
in the work piece. Therefore, the velocity of the piston has to be limited. Commonly,
the velocity is constant during the forming process and the flow velocity of the
material is limited by the minimum width of the cavity. Hence the forming process is
not time optimal. If we could follow an optimal trajectory from form filling
simulations, we would obtain a time-optimal process without imperfections in the
parts. Therefore, feed-forward control for the trajectories is needed. For these
reasons, the flatness-based approach is used (see Section 10.3.1). However, the
velocity of the piston is not a flat output for the system of a differential cylinder [43]. To
calculate the servo valve voltage from a given velocity trajectory of the piston, one has
to measure the pressures in the two chambers of the differential cylinder. Therefore,
offline computing of the servo valve voltage is not possible.
In order to achieve a system of the differential cylinder, which has the velocity as a
flat output, the compressibility of the hydraulic fluid is neglected. This leads to a
simplified system without the pressure dynamics. With the simplified system, we
achieve the following equation to calculate the servo valve voltage:
uðtÞ ¼ 1
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
A
KVBV
3
s
K ð1þa3Þ AKpV m_vðtÞ FR FL
T V _vðtÞþvðtÞ 1 þ T (
"
V
2
m€vðtÞþ _ FR þ _ FL #)
AKpV m_vðtÞ FR FL
ð10:15Þ
The voltage u(t) depends on the velocity v(t) of the piston, the friction force FR and the
load FL. Inafirst approximation, the load is considered to be proportional to the
velocity. Also, the friction force is a function of the velocity. Therefore, we can
conclude that the piston velocity is a flat output of the simplified model and we can
calculate the servo valve voltage from a smooth velocity trajectory. For more details,
see [44].
We have to consider that the feed-forward control does not contain the pressure
dynamics. Therefore, a controller is needed to make sure that the piston follows the
desired velocity trajectory. A simple PID controller is sufficient.
The experiments were carried out with a differential cylinder where the behaviour
of the thixotropic material was simulated by a damper. Figure 10.21 shows the desired