CUTTING OPERATIONS

The sheet cutting is carried out by a shearing action between two sharp cutting edges.
The shearing action is described in the four steps outlined in figure 20.1.
where the upper cutting edge (the punch) moves down exceeding the
lower stationary cutting edge (the die). When the punch starts to push the
work, a plastic deformation occurs on the surfaces of the sheet; as this happens
it moves downward, penetration occurs, in which it compresses the sheet and cuts the
metal. This penetration zone is generally one third of the thickness of the
sheet. As the punch continues its journey within the work, the fracture begins.
in this between the two cutting edges. If the space between the punch and the die is
Correct, the two fracture lines meet and the result is a clean separation.
of work in two pieces.

Engineering analysis of metal sheet cutting

The important parameters in metal sheet cutting are the space between the
punch and die, the thickness of the material, the type of metal and its strength, and the length
of the cut. The following examines some related aspects.
Space: In an operation, the space is the distance between the punch and the die.
as shown in figure 1. The typical spaces in conventional pressing fluctuate
between 4 and 8% of the thickness of the metal sheet.

FIGURE 1

The correct space depends on the type of sheet and its thickness. The recommended one is
you can calculate using the following formula:

= ×

where
c= space, mm (in);
Ac = space tolerance; and
t = thickness of the material, mm (in).

Tolerance is determined according to the type of material. Materials are classified

for convenience in three groups given in Table 1, with an associated tolerance value
to each group.

The calculated values of the space can be applied to conventional punching and to
drilling operations for determining punch sizes and the
adequate die cuts. It is clear that the opening of the die must always be larger
that the size of the punch. The addition of the value of the space to the size of the die or its
the size of the punch is determined by whether the piece being cut is a disc or
pieces, as illustrated in figure 2, for a circular piece.
 FIGURE 2

Due to the shape of the sheared edge, the exterior dimension of the piece being cut from the
the sheet will be larger than the size of the hole; therefore, the size of the punch and of
The die for a round shape or piece of diameter Db is determined as follows:

Diameter of the cutting die forms = Db - 2c

Die cut shape diameter = Db

The sizes of the die and the punch for a round hole with a diameter Dhse
determine as follows:

Punch diameter for hole cutting = Dh

Die diameter for hole cutting = Dh + 2c

Shear forces
It is important to estimate the cutting force because it determines the size (tonnage) of the
Necessary press. The cutting force in sheet work can be determined by:
= × ×

where

S = shear resistance of the sheet, MPa (lb/in2);

t = thickness of the material, mm (in) and
L = length of the cutting edge, mm (in).

In punching, perforating, shaving, and similar operations, the length of the

perimeter of the shape or hole that is cut. In the determination of it, it can be annulled.
lesser effect of space.

If the shear strength is unknown, the cutting force can be estimated by the
use of the tension resistance, as follows:

F = 0.7 × TS × t × L
where
TS = ultimate tensile strength, MPa (lb/in²).

In the previous equations to estimate the shear force, it is assumed that the shear
The whole thing is done at the same time along the cutting edge. In this case the
shear force will be a maximum.

Example:

A disk of 150 mm diameter is cut from a strip of steel that is 3.2 mm thick, rolled in
medium hard cold, with a shear strength of 310 MPa. Determine: a) the
appropriate diameters of the punch and die and b) the punching force.

Solution:
a) The tolerance for cold-rolled steel of medium hardness is Ac = 0.075.
Consequently, the space is:

c = 0.075(3.2 mm) = 0.24 mm

The disc will have a diameter of 150 mm and the size of the die determines the size of the
form; therefore,

Die diameter of the die opening = 150.00 mm

Punch diameter = 150–2(0.24) = 149.52 mm

b) To determine the punching force, it is assumed that the entire perimeter of the
The shape is cut in a single operation. The length of the cutting edge is:

= ×
L = π × 150 mm = 471.2 mm

and the force is:

= × ×
F = 310 MPa × 3.2 mm × 471.2 mm = 467469 N ≅ 53 Tons

PROBLEMS

A cutting operation of shapes is carried out on a cold-rolled steel of 2.0.

mm in thickness (medium hardened). The piece is circular with a diameter of 75.0 mm.
Determine:
a) the appropriate sizes of the punch and die for this operation.
b) the cutting force required, if the steel has a shear strength of 325 MPa and
a tensile strength of 450 MPa.
2.- A compound die will be used to cut the shape and punch a washer.
alloy aluminum sheet 3.50 mm thick. The outer diameter of the washer is
of 50 mm and the inner diameter is 15.0 mm. Determine:

Part I
a) the sizes of the punch and the die for the punching operation
b) the sizes of the punch and the die for the perforating operation.

Part II
Determine the minimum tonnage of the press to perform the punching and the operation of
perforated, if the aluminum sheet has a tensile strength of 310 MPa, a
resistance coefficient of 350 MPa.
a) Suppose that punching and perforating occur simultaneously.
b) Suppose that the drilling is done in stages, so the drilling takes place
first than the punching.

3.- A die is designed for cutting shapes to cut the outline of the piece that is
shown in the figure. The material is 4 mm thick and is made of stainless steel.
hardened). Determine:
a) the dimensions of the punch for cutting shapes and the opening of the die.
b) Determine the tonnage requirements if stainless steel has a resistance to
cut of 600 MPa.
BENDING OPERATIONS (2nd partial)

In the metal sheet work, bending is defined as the deformation of the metal.
around a straight axis, as shown in figure 4. During the operation of
bent, the metal inside the neutral plane is compressed, while the metal outside
the neutral plane is stretched. These deformation conditions can be seen in the figure
The metal deforms plastically, so the bend takes on a permanent shape.
remove the stresses that caused it. Bending produces little or no change in the
thickness of the metal sheet.

FIGURE 4

V-bending and edge bending

Bending operations are carried out using various tools.

types of punches and dies. The two most common bending methods and their
associated tools are V-bending, executed with a V-die; and bending
of edges, executed with a sliding die. These methods are illustrated in figure 5.

FIGURE 5. Two common bending methods: a) V-bending and b) edge bending;

Before
holding force.

In V-bending, the metal sheet is bent between a punch and a die in shape.
of V. The included angles, which range from very obtuse to very acute,
they can be made with V-shaped dies. V-bending is generally used for
low production operations and is frequently carried out in a curtain press; the
corresponding V dies are relatively simple and low cost.
Edge doubling involves a cantilever load on the metal sheet. It is used a
pressure plate that applies a clamping force Fh to support the base of the piece
against the die, while the punch forces the workpiece to bend over the edge
from a die. In a layout illustrated in figure 5b), the bending is limited to angles
of 90º or smaller. More complicated sliding dies can be designed for angles
over 90º. Due to the pressure plate, the sliding dies are more
more complicated and costlier than V dies and are generally used for jobs
high production.

Analysis of bending engineering

Some important terms of bending are identified in figure 5. The metal, whose
thickness is equal to t, it bends through an angle, called bending angle α. The
The result is a metal sheet with an included angle α', such that α + α' = 180º. The radius
The fold is usually indicated on the inner part of the piece, instead of on top.
the neutral axis, and it is determined by the radius of the tool that is used to execute the
operation. The bending is done over the width of the workpiece.

Bending tolerance: If the bending radius is small relative to the thickness of the
material, the metal tends to stretch during bending. It is important to be able to estimate the
magnitude of the stretching that occurs, so that the length of the final piece can be
match the specified dimension. The problem is to determine the length of the axis
neutral before bending, to take into account the stretching of the final bent section.
This length is called bend tolerance and can be estimated as follows:

= 2π × ( + × )
360

where
Abbending tolerance, mm (in)
α = bending angle in degrees;
bending radius, mm (in);
t = thickness of the material, mm (in); and y
Kbait is a factor for estimating the stretch.

The following design values are recommended for K.basiR< 2t,Kba= 0.33; and if R ≥
2t,Kba= 0.50. These values of Kbait is predicted that stretching occurs only if the
the bending radius is smaller in relation to the thickness of the sheet.

Bending force
The force required to perform the bending depends on the shape of the punch and the
die, as well as the resistance, thickness, and width of the metal sheet that is being bent.
The maximum bending force can be estimated using the following equation:
 × × × 2
=

where
bending force, N (lb);
TS = tensile strength of the sheet metal, MPa (lb/in2);
w = width of the piece in the bending axis direction, mm (in);
t = thickness of the material or the piece, mm (in); and
D = die of the open die in mm (in).

This equation is based on the bending of a simple beam, andKbfit is a constant that
consider the differences found in a real bending process. Its value depends
of the type of bending; for V, K bendingbf= 1.33, and for edge bending, K0.33.

EXAMPLE
A piece of metal sheet is folded as shown in the figure. The metal has a
205 (103) MPa
450 MPa
bent, if a V die is used with a die opening dimension of 25 mm.

Solución:a) La pieza inicial = 44.5 mm de ancho. Su longitud = 38 +Ab+ 25 (mm).

As shown, for an included angle α`= 120º, the bending angle α= 60º. The
Kba value = 0.33 since R/t = 4.75/3.2 = 1.48 (less than 2.0).

= 2π × ( + × )
360

60
= 2π × ( 4.75 mm + 0.33 × 3.2 mm6.8
) mm
360

The length of the piece is then 38 + 6.08 + 25 = 69.08 mm.

b) Using Kbf= 1.33.

× × × 2
=
 1.33 × 450 MPa × 44.5 mm × (3.2 mm)2
= = 10909 N
25 mm

PROBLEMS

1.- A bending operation is performed on a cold-rolled steel of 5.00 mm

thick. The drawings of the piece are shown in the figure. Determine:

a) The size of the required shape. R. 129.34 mm

b) The bending force required, if the bending will be done in a V-die, with
a die opening of 40 mm. The material has a tensile strength of 600
MPa and a shear strength of 430 MPa. R. 17460 N

A sheet of 3.0 mm thick and 20.0 mm long is bent at an angle

included at 60º and a bend radius of 7.5 mm in a V-die. The metal has a
tensile strength of 340 MPa. Calculate the force required to bend the part if the
The die opening is 15 mm. R. 5426 N

3.- An L-shaped profile is bent in a V-bending operation in a press.

curtain made from a flat shape of 4.0 inches by 1.5 inches with a thickness of 5/32 inches.
The 90º fold will be made at half the length of 4 inches.

a) Determine the dimensions of the two equal sides that will result after the
bent, if the bending radius is 3/16 inch. For convenience, these sides should
measure at the beginning of the bend radius. R. 1.8122 inches

b) Also determine the length of the neutral axis of the piece after bending.
R.4.0417 inch

BIBLIOGRAPHY

Groover, Mickell. Fundamentals of Modern Manufacturing. 2007