Civil Engineering Reference
In-Depth Information
Fig. 11.10
Model
verification for the classical
case [
1
,
2
]. The model
and experimental profiles
are shown for the case of
classical bending for the two
different die widths
120
38.1
mm Die width /
91.5
° Die angle
model
100
experiment
80
60
model
experiment
50.8
mm Die width /
109
° Die angle
40
20
0
0
2
4
6
8
10
12
14
Position [mm]
11.1.8 Validation of the Model via Experiments
The analytical model developed earlier was solved by following the solution scheme
from Fig.
11.5
, and the bending force needed to reach a desired stroke or bending
angle was determined. The model was initially solved for the classical bending case
and its predictions were compared with experimental results for two different die
widths (Fig.
11.10
). A friction coefficient of 0.25 was used, as recommended by pre-
vious research [
5
]. The predictions agree well for the two cases. The differences can
be attributed to the simplifications and assumptions of the model.
Next, the model for EAB was solved and compared with experimental results
for two current densities, 20 and 30 A/mm
2
. The variation of the strength,
C
, with
the temperature was determined by using the data from Fig.
5.6
[
7
], and this was
integrated into the model. The next step is to determine the EEC. Average EEC
values are taken from experimental results of previous research specific to the
same material, die speed, and current density [
8
]. The coefficients were approxi-
mated as
ξ
=
0.18 for
C
d
=
20 A/mm
2
, and
ξ
=
0.35 for
C
d
=
30 A/mm
2
. For
compression tests, the overall EEC profile with respect to time can be used, which
is more accurate than an approximated EEC value. However, in tension, the elec-
tricity is only applied for several seconds and an EEC profile as a function time
was not able to be determined for this case. These values were included in the
numerical solution. Figures
11.11
and
11.12
compare the model prediction with
Fig. 11.11
Model
verification for EAB at
CD
=
20 A/mm
2
[
1
,
2
]. The
piece-wise model for the
38.1 mm die width and a
current density of 20 A/mm
2
120
100
80
60
model
experiment
40
20
C
d
=
20
Amps/mm
2
0
0
2
4
6
8
10
12
14
Position [mm]
