Sheet Metal Forming

1.2 Forces and Stresses 
The cutting forces do not act linearly along 
the cutting edge. Instead, the vertical force, 
F
V
, 
and horizontal force, 
F
H
, act in a small area near 
the cutting edge, as shown in Fig. 1.3 (Ref 1.2). 
The distribution of those compressive forces 
is nonuniform. The distance, 
l
, between the 
forces 
F
V
and 
F
V
′
causes a bending moment that 
either bends or tilts the workpiece. This moment 
must be compensated for by a counterbending 
moment that is created by bending stresses and 
horizontal normal stresses between the work-
piece and tool. Figure 1.3 also shows the result-
ing frictional forces, 
µ⋅
F
H
and 
µ⋅
F
V
. These fric-
tional forces increase the total blanking force. 
When the punch and die surfaces are flat and the 
motion of the punch is at right angles to the die, 
the force required in a blanking process can be 
determined using the following formula:
F = LtS
s
(Eq 1.1)
The compressive stress in the punch can be cal-
culated using the following formula:
S
p
= F/A
p
(Eq 1.2)
where 
F
is the force required for blanking, 
L
is 
the total length (perimeter) of the cut, 
t
is the 
sheet material thickness, 
S
s
is the shear strength 
of the material, and
 A
p
is the cross-sectional 
area of the punch.
Stripping force is the force needed to free the 
blank from the die or the strip from the punch 
when they stick or jam because of springback 
and friction. Stripping force can be calculated 
using: 
L
st
 = kA
s
 
(Eq 1.3)
where 
L
st
is the stripping force (in pounds), 
k
is 
a stripping constant (in pounds per square inch), 
and 
A
s
is the area of the cut surface (in square 
inches) (stock thickness, 
t
, multiplied by length 
or perimeter of cut, 
l 
). Approximate values for 
the constant 
k
(as determined by experiment for 
low-carbon steel) are (Ref 1.2): 
•
1500 for sheet metal thinner than 1.57 mm 
(0.060 in.) when the cut is near an edge or 
near a preceding cut
•
2100 for other cuts in sheet thinner than
1.57 mm 
•
3000 for sheet more than 1.57 mm thick
The blanking process can be investigated by 
monitoring the changes in the blanking force 
during the cutting process. The force varies with 
punch displacement, punch entry time, or crank 
angle. Because part quality is evaluated in terms 
of regions formed along the part edge, it is pre-
ferred to present the load versus punch displace-
ment. In addition, the cutting work can be cal-
culated by integrating the force over the stroke. 
The theoretical load-stroke curve in a blanking 
process can be described schematically as seen 
in Fig. 1.4: 
•
Step 1:
The sheet metal deforms elastically. 
•
Step 2:
The limit of elastic deformation is 
reached, and the material starts to deform 
plastically. The material flows along the cut
-
ting edges in the direction of the punch pen-
etration and into the gap between punch and 
die (comparable to deep drawing). The ma-
terial flow causes strain hardening, which