Civil Engineering Reference
In-Depth Information
function of the punch force
F
p
, bending angle,
α
, and friction coefficient,
μ
[Eq. (
11.6
)].
F
p
N
=
.
(11.6)
cos
2
+
µ
sin
2
2
The equilibrium of moments about point
A
leads to Eq. (
11.7
).
M
µ
t
2
+
a
.
N
=
(11.7)
The length of the arm,
a
, is determined geometrically using Eq. (
11.8
).
a
=
w
d
−
2
(
r
p
+
t
b
)
sin
2
(11.8)
2 cos
2
After substituting Eq. (
11.8
) into Eq. (
11.7
), the resultant equation is combined
with Eq. (
11.6
), and the punch force is resolved as follows in Eq. (
11.9
).
4 cos
2
cos
2
+ µ
sin
2
F
p
=
·
M
.
(11.9)
µ
t
b
cos
2
+
w
d
−
2
(
r
p
+
t
b
)
sin
2
Then, Eq. (
11.4
) is substituted into Eq. (
11.9
). Thus, the bending force needed to
deform the material to the bending angle
α
and to overcome the friction at die/
workpiece interfaces can be obtained from Eq. (
11.10
).
wt
b
cos
2
cos
2
+ µ
sin
2
n
1
+
t
b
r
p
F
p
=
K
·
·
ln
.
(11.10)
µ
t
b
cos
2
+
w
d
−
2
(
r
p
+
t
b
)
sin
2
Total power for plastic bending is derived mechanically as Eq. (
11.11
):
J
m
=
F
p
u
(11.11)
where
u
is the velocity of the die/punch.
11.1.4 Analytical Modeling of EAB
Previous research indicated that the application of electricity through a deforming
workpiece results in reduced required flow stress to reach the same deformation as
in the classical process. When analyzing an EAF process, two aspects have to be
considered: (i) the applied electrical energy, and (ii) the electroplastic effect on the
material behavior and on the energy efficiency of the process.
For EAB, the electricity was applied in pulses, since constantly applied elec-
tricity would lead to negative effects because the cross section of the specimen is
