Blanking and Punching
43
Material thickness
4.5.2 Shaving a Blanked Workpiece
Thin layers of material can be removed from blanked surfaces by a process similar to punching. In Fig. 4.18 is illustrated the shaving process for improving the accuracy of a blanked workpiece. If the workpiece,
after shaving needs to have a diameter the punch diameter for blanking operation is:
M A T E R I A L Copper, aluminum, and
Medium-carbon steel High-carbon and alloy steel
d,
=
The die diameter for the blanking operation is:
=
d,
+
+
where:
=
diameter of final workpiece,
=
clearance between die and punch,
=
amount of material for shaving.
4.18
4.19
Scrap Workpiece
Die
Fig. 4.18
Shaving a blanked workpiece
The value of an amount can be found from Table 4.6; it depends on the kind and thickness
of
material.
5.1
Introduction
5.2
Mechanics of bending
5.3
Moment of bending
5.4
Bending forces
5.5
Bending radius
5.6
Bend allowance
5.7
Springback
5.8
Clearance
BENDING
5.1 INTRODUCTION
One of the most common processes for sheet-metal forming is bending, which is used not only to form pieces such as
L, U, or V- profiles, but also to improve the stiffness of a piece by increasing its moment of
inertia. Bending consists of uniformly straining flat sheets or strips of metal around a linear axis, but it also may be used to bend tubes, drawn profiles, bars, and wire.
The bending process has the greatest number of applications in the automotive and aircraft industries and for the production of other sheet-metal products. Typical examples of sheet-metal bends are illustrat-
ed in Fig. 5.1.
Fig. 5.1
Typical examples of sheet-metal bend parts.
5.2 MECHANICS OF BENDING
The terminology used in the bending process is explained visually in Fig. 5.2. The bend radius is meas-
ured on the inner surface of the bend piece. The bend angle is the angle of the bent piece. The bend
45
46
Bending Length of bend
Bend allowance
I ;
‘
Bendangle
,
Bendradius
Fig. 5.2
Schematic
illustration of
terminology
used in
the
bending process. allowance is the arc of the neutral bend line. The length of the bend is the width of the sheet. In bending,
the outer fibers of the material are placed in tension and the inner fibers are placed in compression. Theoretically, the strain on the outer and inner fibers is equal in absolute magnitude and is given by the
following equation:
e,
= =
+
1
where:
=
bend radius
T
=
material thickness. Experimental research indicates that this formula is more precise for the deformation of the inner fibers of
the material than for the deformation of the outer fibers The deformation in the outer fibers is notably
greater, which
is
why the neutral fibers move to the inner side
of
the bent piece. The width
of
the piece on the outer side
is
smaller and on the inner side is larger than the original width. As RT decreases, the bend radius becomes smaller, the tensile strain at the outer fibers increases, and the material eventually cracks.
5.3
MOMENT OF BENDING
Suppose we have a long, thin, straight beam having a cross-section
x
and length L, bent into a curve by moments
M.
The beam and moments lie in the vertical plane nxz, as shown in Fig. 5.3 At a distance
x
from the left end, the deflection of the beam is given by distance z. Fig. shows, enlarged, two slices
A-B and A’-B’ of different lengths dx, cut from the beam at location x. The planes cutting A-B and A ’-B’ are taken perpendicular to the longitudinal
axis
of the original straight beam. It is customary to assume that these cross-sections will remain planar and perpendicular to
the longitudinal elements of the beam after moments are applied Bernoulli hypothesis. Laboratory
experiments have in general verified this assumption. After bending, some of the fibers have been extend- ed B-B’, some have been compressed A-A’, and at one location, called the neutral surface, no change
in length has taken place n- n.
The loading of Fig. 5.3 is called pure bending. No shear or tangential stress will exist on the end sur-
faces A-B and A’-B’, and the only stress will be acting normally on the surface. An equation can be
Bending
47
Fig.5.3
Schematic illustration of bending beam: a bending beam; b neutral line; c bending stress in elastic-plastic zone.
derived to give the value of this bending stress at any desired distance from the neutral surface. Let 0 be
the center of curvature for slice of the deformation beam,
the small angle included between the cut- ting planes, and
the radius of curvature. Consider a horizontal element located a distance z below the neutral surface. Draw a line n-D parallel to
The angle is equal to the angle D-n-C’ and the fol-
lowing proportional relationship results:
Since the total deformation of the element 2d9 divided by the original length is the unit deformation or
strain, equation 5.2 indicates that the elongation of the element will vary directly with the distance from a neutral surface.
For a more detailed definition of the stress-to-strain relationship in the bending process, the concept of a reduction in the radius of the neutral curvature R,, is useful. This value is the ratio to the bend radius
of
the neutral surface-to-material thickness:
where:
=
reduction radius of the neutral curvature surface. 5.3
Considering the kind and magnitude of stresses that exist during beam bending, as well as the reduction radius
bending problems can be analyzed in two ways:
48
Bending
a Bending in the centrally located inner zone, on both sides of the neutral zone, is a domain of elas- b Bending in the outlying zones on both the inside and outside of the bend, is a domain of pure
Bending as a domain of elastic-plastic deformation Fig. can be considered as a linear stress problem.
tic-plastic deformation, but plastic deformation.
The true stresses in the bent beam are in the intervals:
The reduction radius of the neutral surface is in the intervals:
5 200
The following events may occur during the bending process: a The core of the beam to a certain level
T 2 with both sides of the neutral surface may be elastically deformed, but
that level to
=
T 2 the fibers may be plastically deformed Fig. Assume that:
Let it be assumed that the material of the beam follows Hooke’s law see Fig. 2.6. Since the strains at the yield point
are very small, the difference between the true and the engineering yield stresses is negli- gible
for
metals, and that
is:
k,
=
=
This phenomenon is bending in the elastic-plastic domain, because the core of the beam is elastically deformed, and the fibers nearer the outer and inner sides are plastically deformed.
b The magnitude of the stresses is directly proportional to the fibers’ distance from the neutral sur-
face, but the maximum stresses in the inner A-A’ and outer B-B‘ fibers are less than the yield stresses. Fig.
shows that stresses in the outer and inner fibers are as follows:
This phenomenon is bending in the elastic domain of the material. c The stresses may be constant in all cross-sections of the beam and equal to the yield stress Fig.
Providing that the material is ideally plastic and does not harden,
=
=
this kind of bending is in the linear-plastic domain. A pure plastic bending of the beam will appear
Bending
49
In that case, true stresses are in intervals:
k
For all cases of bending, Bernoulli’s hypothesis concerning the cutting of the planes is in effect.
5.3.1 Moment of Bending in Elastic-Plastic Domain
The engineering moment of bending in the elastic-plastic domain can be expressed as the sum of the moments
of bending in the elastic and plastic zones for the same axis, and is given by the general formula,
zo
1
The first segment of this equation is the moment of resistance in the elastic deformation zone with regard to the y-axis:
W
2
The second segment of the equation is the moment of static at the plastic deformation zone with regard to the y-axis:
S
=
2
Therefore, the bending moment in the elastic-plastic domain in the final form is:
M
=
+
where:
=
yield strength,
=
moment of resistance, and
=
moment of static. For a rectangular cross-section of a beam, the bending moment in the elastic-plastic domain is given
by the formula:
The value of can be calculated by
law:
50
Bending
Therefore,
When the above expression is substituted for in equation
equation is changes to:
Respecting equation the bending moment may be expressed as the reduction radius
of a curve Rr:
However, with bending in the elastic-plastic domain 5 200 the influence of part of the equation
is very slight, and the engineering calculation can be disregarded. Setting aside this part of the equation, we may assume, as a matter of fact, that the entire cross-section of the beam experiences
linear-plastic deformation Fig.
so
that the moment of the bending beam is loaded by stresses in the linear-plastic domain:
4
=
The Moment of Bending in the Purely Plastic Domain
The moment of bending in the purely plastic domain for a rectangular cross-section is given by the formula:
4
where:
=
hardening coefficient of material, k
=
true strain of material,
=
width of beam length of bending, and
T
=
material thickness. This expression can be simplified to:
4
Bending
51
where: n
=
correction coefficient hardening of the material n to 1
=
ultimate tensile strength of the material,
=
width of beam length of bending, and T
=
material thickness.
5.4 BENDING FORCES
Bending forces can be estimated, if the outer moments of bending and the moments of the inner forces are equal, by assuming that the process is one of a simple bending beam. Thus, the bending force is a function
of the strength of the material, the length and thickness of the piece, and the die opening.
5.4.1 Force for U-die
The bending force for a U-die Fig. can be generally expressed by the formula:
2M
F
where:
=
+
+
T see Fig. 5.4. If the bending is in a die with an ejector Fig.
the bending force needs to increase by about 30 per-
cent
so
that the total bending force for a U-die is:
Punch Workpiece
Fig.5.4
Bending a U-profile a
without
ejector;
b with
ejector.
If the bottom of the piece needs to be additionally planished Fig. the force required for bending and
planishing is given by the equation:
52
Material thickness
3 to 10
Bending
F
=
M A T E R I A L Aluminum
Brass
Low carbon
steel
Steel 29.4 to
39.2 58.8 to 78.4
78.4 to 98.0 98.0
to 117.6 49.0 to 58.8
59.8 to 78.4 98.0 to 117.6
117.6
to
147.1 0.1
to 0.25 to
where:
p
=
specific pressure Table and
A
=
area of the bottom.
\Ejector
Fig. 5.5
Planished bottom.
5.4.2 Forces for a Wiping Die
The bending force for a wiping die Fig. is two times less than for a U-die, and it is given by the
formula:
M
where:
=
+
+ T ,
and
=
Material holder
\
Die Workpiece
Fig. 5.6
Bending in a wiping die.
Bending
53
5.4.3 Forces for V-die
Bending V-profiles may be considered as air bending free bending see or as coin bending Fig.
5.8. What exactly do these terms mean? In the beginning phase of bending, the distance between the holds is
and the force is applied in the middle, between the holds. The profile of a die for air bending V-profiles can have a right angle as shown in Fig.
or an acute angle, as shown in Fig
In this initial phase, the edges of the die with which the workpiece is in con- tact are rounded at radius
R,. The radius of the punch will always be smaller than the bending radius.
The force for air bending a V-profile is given by the formula:
where:
=
die opening, and
=
bend angle.
Punch
5.9
IF
Fig. 5.7
Air bending a right-angle die profile; b acute-angle die profile.
The coin bend process of the V-profile has four characteristic phases Fig. 5.8: Phase
I
is free bending: the distance between the bend points of the die is unchanged and it is equal to
In Phase the ends of the workpiece are touching the side surfaces of the die, the bend points of the die are
changed, and the bend radius is bigger than the punch radius. In Phase the ends of the workpiece
are touching the punch. Between Phase and Phase
the workpiece is actually being bent in the opposite direction from Phase I and
negative springback. When the workpiece is touching the die and the punch on all surfaces, the bend radius and the punch radius are equal, phase IV is terminat-
ed, and bending the workpiece is completed.
It is usually necessary to flatten the bottom bend area between the tip of the punch and the die sur- face in order to avoid springback. At the moment of completing phase
it is advisable to increase the
54
Bending
Fig. 5.8
V-profile
bending
phases.
force for a final reinforcement of the bend and completion of the bottoming operation. The force neces- sary for this final reinforcement is given by the formula:
where:
p
=
specific pressure Table
=
contact length width of the workpiece, and
=
length of the straight end of the workpiece. The relationship between the bend forces and the punch travels is shown in Fig.5.9
V
Punch travel
5.9
Typical load-punch travel curve
for coin
bending
process.
Air bending interval-OG, has three parts: The first part is elastic deformation OE. In the second, the force is mostly constant
EF, and in the third, the force decreases because of material slip FG. After that, the force again increases to a definitive point. The workpiece is bent
GH. If the workpiece needs to be bottomed, the force very quickly increases
HM.
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