INTRODUCTION MECHANICS OF BENDING
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.
Bending
55
5.4.4
Curling
Two examples of curling are shown in Fig. 5.10 and Fig. 5.1 1. Curling gives stiffness to the workpiece by
increasing the moment of inertia at the ends, and providing smooth rounded edges.
In the first example in Fig. 5.10, the edge of the sheet metal is bent into the cavity of
a punch.
Material holder
Fig. 5.10
process.
In the second example in Fig. 5.1 the circular edge of the initial deep-drawn workpiece is curled by a tool that incorporates a cavity punch.
D
Die Workpiece
Workpiece holder Fig. 5.1
Circular edge curling.
The curling force is given by the equation:
+
5.10 where:
M
=
moment of bending,
=
inside curling radius, and
T
=
material thickness.
56
Bending
Example. Define the curling force for the workpiece shown in fig. 5.1 1. Assume:
Diameter
=
400 mm, Material thickness
1.2 mm, Inner radius
=
1.2 mm, The ultimate tensile strength
=
Solution:
M
+
M
-
4 4
=
39903.055 143651
3
+
0.5
x1.2 Known bend and curl forces often are not
so important for the process because very often, the maxi- mum force of the press machine
is greater than the bending or curling force. However, knowing the mag- nitude of these forces is necessary for a definition of the blank-holder forces. Because of the phenomenon
of material fatigue of the blank springs, these forces need to be 30 to 50 percent greater than the bending or the curling forces.
5.4.5
Three-Roll Forming
For bending differently shaped cylinders plain round, corrugated round, flattened, elliptical, etc. or trun- cated cones
of
sheet metal, the three-roll forming process
is
used. Depending upon such variables as the composition of the work metal, machine capability, or part size, the shape may be formed in a single pass
or a series of passes. Fig. 5.12 illustrates the basic setup for three-roll forming on pyramid-type machines. The two lower rolls on pyramid-type machines are driven, and the adjustable top roll serves as an idler and
is rotated by friction with the workpiece.
Workpiece
1-11
D Driven rolls
Fig. 5.12
Three-
roll
bending.
Bending
57
In most set-ups, short curved sections of circular work are performed on the ends of the metal piece in a press brake or on a hydraulic press. Otherwise, the workpieces would have ends that, instead of
being curved, would be straight. In the process described above, the radius of the bend allowance is much greater than the material thickness of the workpiece; under these conditions, the bending is entirely in the
elastic-plastic domain.
To achieve permanent deformation in the outer and inner fibers of the material, the following rela- tionship must apply:
D E
T
5.1 1
Otherwise, the workpiece, instead of being curved, will be straight after unloading. The bending force on the upper roll is given by the formula:
5.12
where:
=
outer diameter of the workpiece,
=
length of bend, T
=
material thickness,
=
yield stress, E
=
modulus of elasticity, and
=
bend angle. The bend angle can be calculated from the geometric ratio in Fig.
5.12 and is given by the formula:
=
D + d where:
=
distance between lower rolls, and d
=
lower rolls diameter.
5.5
BEND RADIUS
One of the most important factors that influence the quality of a bent workpiece is the bend radius
Ri
see Fig.
which must be within defined limits. The bend radius is the inside radius of a bent workpiece.
Minimum Bend Radius
The minimum bend radius is usually determined by how much outer surface fracture is acceptable. However, many other factors may limit the bend radius. For instance, wrinkling of the inner bend surface
may be of concern if it occurs before initiation of fracture on the outer surface. In developing a descrip- tion of the minimum bend radius, it is necessary to have some knowledge of the amount of strain imposed
58
Bending and the material ductility. We have a good definition of strain, but the term “ductility” is vague, and it is
necessary to have a quantitative measurement of the amount of deformation that the material can undergo
before fracture. As with most mechanical properties, fracture strain can be obtained from tensile testing. There may be no need to run a bending test if tensile test data are available, which they usually are.
The strain of certain fibers at distance z from the neutral surface is defined by formula 5.2.
- The greatest tensile strain appears in the outer fibers:
R
=
+
T see Fig. 5.3. When
=
+
ten- sile strain can be calculated by the following formula 5.13
e =
+
I
5.13 If the strain at which the cracks in the outer fibers appear
is defined as and the minimum bend radius,
which causes these strains, as
then: 5.14
It is apparent from equation 5.13 that as the decreases, the bend radius becomes smaller, the
tensile strain on the outer fibers increases, and the material may crack after a certain strain is reached. The minimum radius to which a workpiece can be bent safely is normally expressed in terms of the material
thickness and is given by the following formula:
The coefficient for a variety of materials has been determined experimentally, and some typical results are given in Table 5.2.
Table 5.2 Values of the coefficient
Bending
59
The bendability of a metal may be increased by techniques such as applying compressive forces in the plane of the sheet during bending to minimize tensile stress in the outer fibers of the bend area, or
increasing tensile reduction of area by heating. If the length of the bend increases, the state of stress at the outer fibers changes from uniaxial stress to biaxial stress, which reduces the ductility of the material.
Therefore, as the length increases, the minimum bend radius increases. Bendability decreases with rough edges because rough edges form points of stress concentration. Anisotropy of the sheet metal is also an
important factor in bendability.
If
the bending operation takes place parallel to the direction of rolling, sep- arations will occur and cracking will develop as shown in Fig. 5.13.
Grain direction Crack
Fig. 5.13
Cracking results when the direction of bending is parallel to the original rolling
direction of the sheet.
If bending takes place at right angles to the rolling direction of the sheet metal, there should be no cracks, as shown in Fig.
5.14. In bending such a sheet or strip, caution should be used in cutting the blank from the rolled sheet in the proper direction, although thimay not always be possible in practice.
Fig. 5.14
Bending at an angle to the original rolling direction of the sheet will tend to avoid
cracking. Grain direction
T 2