Sheet Metal Bending Mechanics and Spring Back Elimination Methods

Unit-4
Sheet metal operations
Part 2
Dr. L.K. Bhagi
Associate Professor
School of Mechanical Engineering
Lovely Professional University

Sheet Metal Working »Sheet Metal Bending » Mechanics
Of Sheet Metal Bending
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Bend allowance
The bend allowance describes
the length of the neutral axis
between the bend lines, or in
other words, the arc length of
the bend. Therefore, the bend
allowance added to the flange
lengths is equal to the total
flat length.

Sheet Metal Working »Sheet Metal Bending »
Numerical Problem 05
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A sheet-metal blank is to be bent as shown in Figure. The metal
has a modulus of elasticity = 205 (103) MPa, yield strength =
275 MPa, and tensile strength = 450 MPa.
Determine
(a) the starting blank size and (b) the bending force if a V-die is
used with a die opening dimension = 25 mm.

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(a)
The starting blank = 44.5 mm wide.
Its length= 38 + Ab+ 25(mm).
For the included angle αʹ =120°, the bend angle α = 60°.
The value of Kba in = 0.33 since R/t = 4.75/3.2 = 1.48 (less than
2.0).

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(b) The Maximum Bending Force
TS = tensile strength of the sheet metal,MPa
w = width of part in the direction of the bend axis, mm
t = stock thickness, mm
D = die opening
Kbf is a constant that accounts for differences encountered in an
actual bending process. Its value depends on type of bending: for
V-bending, Kbf = 1.33; and for edge bending, Kbf = 0.33.
( )
D
wtTSK
F
bf
2
=

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A bending operation is to be performed on 5.00-mm thick cold-
rolled steel. The part drawing is given in Figure. Determine the
blank size required.

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From drawing, αʹ = 40°, R = 4.75 mm
α = 180° - 40° = 140°.
For K
( )tKRBA ba+







=
360
2
330,271
5
58
.So Kess thanratio is li.e..
.
t
R
===

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α = 180° - 40° = 140°.
BA = 24.82 mm
So, Dimensions of starting blank:
w = 35 mm, L = 58 + 24.82 + 46.5 = 129.32 mm
( )533058
360
140
2 +






= ..BA

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Solve previous Problem except that the bend radius R = 11.35
mm.

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α = 180° - 40° = 140°.
For K
( )tKRBA ba+







=
360
2
500,22702
5
3511
.So Kore thanratio is mi.e..
.
t
R
===

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α = 180° - 40° = 140°.
BA = 34.21 mm
So, Dimensions of starting blank:
w = 35 mm, L = 58 + 34.21 + 46.5 = 138.71 mm
( )5503511
360
140
2 +






= ..BA

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An L-shaped part is to be bent in a V-bending operation on a
press brake from a flat blank 4.0 inch by 1.5 inch that is 5/32
inch thick. The bend of 90° is to be made in the middle of the 4-
inch length.
(a) Determine the dimensions of the two equal sides that will
result after the bend, if the bend radius = 3/16 inch. For
convenience, these sides should be measured to the
beginning of the bend radius.
(b) Also, determine the length of the part’s neutral axis after the
bend.

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Of Sheet Metal Bending » Spring Back

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• In bending, after plastic deformation there is an elastic recovery
this recovery is called spring back.
• Reason for spring-back: When bending pressure is removed,
elastic energy remains in bent part, causing it to recover
partially toward its original shape

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This elastic recovery i.e. Spring Back, defined as the increase in
included angle of the bent part relative to the included angle of the
forming tool after the tool is removed and is expressed:

Spring back can be calculated approximately
As Ri/Rf is increasing the spring back is also increased.
Spring Back depends on
Ri/Rf = 1 means Spring back =0
Yield strength (Y)
Modulus of elasticity (E)
Thickness of the sheet (T)
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134
3
+





−





=
ET
YR
ET
YR
R
R ii
f
i

As Ri/Rf is increasing the spring back is also increased.
Yield strength (Y)
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134
3
+





−





=
ET
YR
ET
YR
R
R ii
f
i

As Ri/Rf is increasing the spring back is
also increased.
Yield strength (Y)
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134
3
+





−





=
ET
YR
ET
YR
R
R ii
f
i

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Methods Of Eliminating Spring back

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Methods Of Eliminating Spring back
• Smaller Y/E
• Larger thickness
• Over-bending
• Stretch forming
• “coining” or bottoming the punch

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Techniques have been developed, in manufacturing industry, that
can eliminate the effects of spring back. One common technique
is OVERBENDING. The amount of spring back is calculated
and the sheet metal is over bent to a smaller bend angle than
needed.

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Another method for eliminating springback is by plastically
deforming the material in the bend region. Localized
compressive forces between the punch and die in that area will
plastically deform the elastic core, preventing springback. This
can be done by applying additional force through the tip of the
punch after completion of bending. A technique known as
bottoming, or bottoming the punch.

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Stretch forming is a metal bending technique that eliminates
most of the spring back in a bend. Subjecting the work to tensile
stress while bending will force the elastic region to be plastically
deformed. Stretch forming can not be performed for some
complex bends and for very sharp angles. The amount of
tension must be controlled to avoid cracking of the sheet metal.
Stretch forming is a process often used in the aircraft building
industry.

Stretch forming is a metal forming process in which a piece of sheet
metal is stretched and bent simultaneously over a die in order
to form large bent parts.
Sheet Metal Working »Sheet Metal Bending»
Stretch Forming
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The sheet is held by jaws at both
the ends and then stretched by
punch/die, such that the sheet is
stressed above yield strength.
Stretch Forming
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When the tension is released, the metal has been plastically
deformed.
The combined effect of stretching and bending results in
relatively less spring back in the part.
Stretch Forming
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Forming process are particular
manufacturing process which make
use of suitable stresses (like
compression, tension, shear or
combined stresses) which cause
plastic deformation of the materials
to produce required shapes.
Drawing is a sheet-metal-forming operation used to make cup-
shaped, box-shaped, or other complex-curved and concave parts.
Sheet Metal Forming» DRAWING
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It is performed by placing a piece of sheet metal over a die cavity
and then pushing the metal into the opening with a punch, as in
Figure.
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Cooking Pots
Common parts made by drawing include
Beverage Cans
Automobile Body Panels.
Car Body Panel Press 2000Ton for Automotive
Industry
Ammunition Shells
Sinks
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Shallow Drawing (h<D/2)
when the height of cup formed is
less than half its diameter.
Deep drawing (h>D/2)
When the height of cup formed is
greater that half of its diameter.
In case of deep drawing the chances of excessive wrinkle
formation at the edges of blank increases. So, to prevent this, a
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Sheet Metal Forming» DRAWING » Mechanics of
Drawing
Bending at die
and punch
radius
Straightening
the bent sheet,
stretching
Fh: Blank holding force
F: Punch force Wall thinning maximum at bottom
corner of cup (max: 25%)
Wall thickness
variation: yes
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Drawing
(i) As the punch pushes the sheet, it is subjected to a bending
operation.
Bending of sheet occurs over the punch corner and die corner.
The outside perimeter of the blank moves slightly inwards toward
the cup center.
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Drawing
(ii) In this stage, the sheet region that was bent over the die corner will be
straightened in the clearance region at this stage, so that it will become
cup wall region.
In order to compensate the presence of sheet in cup wall, more metal will
be pulled from the sheet edge, i.e. more metal moves into the die
opening.
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Drawing
(iv) Other than friction, compression occurs at the edge of the sheet.
Since the perimeter is reduced, the sheet is squeezed into the die
opening.
Because volume remains constant, with reduction in perimeter,
thickening occurs at the edge.
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Drawing
In thin sheets, this is reflected in the form of wrinkling.
This also occurs in case of low blank holding force (BHF).
If BHF is very small, wrinkling occurs. If it is high, it prevents the sheet from
flowing properly toward the die hole, resulting in stretching and tearing of
sheet.
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Drawing
(v) The final cup part will have some thinning in side wall.
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Drawing
Drawing of a cup shaped part
is the basic drawing operation,
with dimensions and
parameters as pictured in
Figure.
A blank of diameter Db is drawn
into a die cavity by means of a
punch with diameter Dp. The
punch and die must have corner
radii, given by Rp and Rd.
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Drawing
If the punch and die were to have sharp corners (Rp and Rd = 0), a hole-
punching operation would be accomplished rather than a drawing operation.
The sides of the punch and die are separated by a clearance c. This clearance in
drawing is about 10% greater than the stock thickness
c = (1.1)×t
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Drawing
Measures of Drawing
2
4 bD

2
4
pD

hDp
hDDD ppb +

=
 22
44
hRRR ppb += 222
hRRR ppb 22
+=
Corner radius on the punch is very very small
so, we can neglect
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Drawing
Measures of Drawing
R
RRb = 22
RRb = 2
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Drawing
Measures of Drawing
d1
d2
( )2
1
2
21
2
1
2
444
ddhddDb −

++

=
 d1
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Drawing
Measures of Drawing
Drawing Ratio
Drawing ratio help to determine the maximum amount of deep drawing
possible. Higher the drawing ratio, the more extreme the amount of
deep drawing.
Due to the geometry, forces, metal flow and material properties of the
work, there is a limit to the amount of deep drawing that can be
performed on a sheet metal blank in a single operation.
cupp
b
R
DorD
D
D =
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Drawing
Measures of Drawing
Reduction
Another way to express drawing ratio is the reduction (r). Reduction
can be calculated by
Reduction should be 0.5 (50%) or under. Often expressed as the percent
reduction.
( )
b
pb
D
DD
r
−
=
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Drawing
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Drawing
= 200 mm
d1
First Draw r =0.5 (50%)






−=
bD
d
. 1
150






−=
200
150 1d
.
mmd 1001 =200>d>100 Require one draw
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Drawing
= 200 mm
d2
Second Draw r = 0.3 (30%)






−=
1
2
130
d
d
.






−=
100
130 2d
.
mmd 702 =
100>d>70 Require two draws
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Sheet Metal Forming» DRAWING » Mechanics
of Drawing
= 200 mm
d3
Third Draw r = 0.2 (20%)






−=
2
3
120
d
d
.






−=
70
120 3d
.
mmd 562 =
70>d>56 Require three draws
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Sheet Metal Forming» DRAWING » Numerical
Problem 11
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Problem 11
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Problem 12
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Question: What are some of the simple measures used to
assess the feasibility of a proposed cup drawing operation?
Answer. Measures of drawing feasibility include:
(1) Drawing ratio, DR = Db/Dp; (DR ≤ 2)
(2) Reduction, ; (r ≤ 0.5) and
(3) Thickness-to-Diameter ratio, t/Db;
where t = stock thickness, Db = blank diameter. (t/Db≥ 1%)
( )
b
pb
D
DD
r
−
=

Problem 13
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Problem 13
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Problem 13
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of Drawing
Drawing force required by punch
During the drawing operation, the movement of the blank into the die cavity induces
compressive circumferential (hoop) stresses in the flange, which tend to cause the
flange to wrinkle during drawing.
Wrinkling can be reduced or eliminated if a
blank holder is loaded by a certain force. In
order to improve performance, the magnitude
of this force can be controlled as a function of
punch travel.
This phenomenon can be demonstrated
simply by trying to force a circular piece of
paper into a round cavity, such as a drinking
glass.
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of Drawing
Drawing force required by punch
The drawing force required to perform a given operation can be estimated
roughly by the formula
It can be seen that the force increases with
increasing blank diameter, thickness,
strength, and the drawing ratio (Db/Dp).
The wall of the cup is subjected principally
to a longitudinal (vertical) tensile stress
due to the punch force.
Elongation under this stress causes the cup
wall to become thinner and, if excessive,
can cause tearing of the cup.
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of Drawing
Blank holding force
The holding force is an important factor in a drawing operation.
As a rough approximation, the holding pressure can be set at a
value = 0.015 of the yield strength of the sheet metal. This value
is then multiplied by that portion of the starting area of the blank
that is to be held by the blank holder. In equation form,
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Problem 14
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Determine (a) drawing force and (b) holding force, given that the
tensile strength of the sheet metal (low-carbon steel) = 300 MPa and
yield strength = 175 MPa. The die corner radius = 6 mm.

Problem 14
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(a) Maximum drawing force is given by Eq. :
( ) 







−= 70.
D
D
TStDF
p
b
p ( )( )( ) 





−= 70
75
138
3004275 ..F
N396193.F =

Problem 14
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(b) Blank holding force given by Eq. :
( ) 22
2220150 dpbh Rt.DDY.F ++−=
( ) ( ) ( ) 22
624222751381750150 ++−= ...Fh
N82486.Fh =

Problem 15
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A cup is to be drawn in a deep drawing operation. The height of the cup
is 75 mm and its inside diameter = 100 mm. The sheet metal thickness =
2 mm. If the blank diameter = 225 mm, determine: (a) drawing ratio, (b)
reduction, and (c) thickness-to-diameter ratio. (d) Does the operation
seem feasible?

Problem 16
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A cup is to be drawn in a deep drawing operation. The height of the cup
is 75 mm and its inside diameter = 100 mm. The sheet metal thickness =
2 mm. If the blank diameter = 175 mm, determine: (a) drawing ratio,
(b) reduction, and (c) thickness-to-diameter ratio. (d) Does the operation
seem feasible?
Hint:
Check (1) Drawing ratio, (2) Reduction, and (3) Thickness-to-Diameter
ratio and then
Also Check actual cup height possible with a 175 mm diameter blank.

Problem 17
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A cup drawing operation is performed in which the inside diameter = 80
mm and the height = 50 mm. The stock thickness = 3.0 mm, and the
starting blank diameter = 150 mm. Punch and die radii = 4 mm. Tensile
strength = 400 MPa and a yield strength = 180 MPa for this sheet metal.
Determine: (a) drawing ratio, (b) reduction, (c) drawing force, and (d)
blank holder force.
1.875
0.46
354.418 N.
114.942 N

In many cases, the shape change involved in making that part will
be severe (drawing ratio is very high). In such cases, complete
forming of the part requires more than one deep drawing step.
Redrawing refers to any further drawing steps that is required to
complete the drawing operation.
Sheet Metal Forming» Redrawing
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Guidelines for successful redrawing:
(Refer Numerical Problem 11)
First draw:
Maximum reduction of the starting blank - 40% to 50%
In case Second draw: 30% reduction in 2nd draw
In case Third draw : 20% reduction in 3rd draw
Sheet Metal Forming» Redrawing
( )0.5 1
b
b
D
DD
r
−
== RangeD1Check
( )0.3
1
21
D
DD
r
−
== RangeD2Check
( )0.2
2
32
D
DD
r
−
== RangeD3Check
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In reverse redrawing, the intermediate part is flipped over before
being placed on the die for the next operation. This will cause the
sheet metal to now be drawn in the opposite direction as the first
draw.
Sheet Metal Forming» Reverse
Drawing
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Sheet Metal Forming» Drawing without blank
holder
The main function of Blank Holder is to reduce wrinkling.
The tendency of wrinkling decreases with increase in thickness to
blank diameter ratio (t/Db).
For a large t/Db ratio, drawing without blank holder is possible.
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Sheet Metal Forming» Defects in Deep
Drawing
Wrinkling:
This is like ups and downs or waviness that is
developed on the flange. If the flange is drawn into
the die hole, it will be retained in cup wall region.
Wrinkling Tearing Earing Scratches
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Drawing
Tearing:
It is a crack in the cup, near the base, happening due
to high tensile stresses causing thinning and failure
of the metal at this place. This can also occur due to
sharp die corner.
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Drawing
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Earing:
The height of the walls of drawn cups have peaks and
valleys called as earing.

Drawing
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Surface scratches:
Usage of rough punch, dies and poor lubrication
cause scratches in a drawn cup.

Sheet Metal Forming» Dies
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Made up of die/tool steel and used to cut or
shape material.
1. Simple die
2. Compound die
3. Combination die
4. Progressive die
5. Transfer die

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Simple dies or single
action dies perform
single operation for
each stroke of the press
slide.
The operation may be
one of the cutting or
forming operations.

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Several operations on
the same strip may be
performed in one stroke
with a compound die in
one station.
These operations are usually limited to relatively simple shearing
because they are somewhat slow and the dies are more expensive
than those for individual shearing operations.

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Schematic illustrations: (a) before and (b) after blanking a common washer in a
compound die. Note the separate movements of the die (for blanking) and the
punch (for punching the hole in the washer).
Compound Die
a b

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In this die also , more than one
operation may be performed at
one station.
It is different from compound
die in that in this die, a cutting
operation is combined with a
bending or drawing operation,
due to that it is called
combination die.

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Progressive Die
Parts requiring multiple operations, such as
punching, blanking and notching are made at high
production rates in progressive dies.
The sheet metal is fed through a coil strip and a
different operation is performed at the same station
with each stroke of a series of punches.

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At each station, an
operation is
performed on a work
piece during a stroke
of the press.

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In a transfer die setup, the sheet metal
undergoes different operations at different
stations, which are arranged along a straight
line or a circular path.
After each operation, the part is transfer to
the next operation for additional operations.
Transfer Die

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Sheet Metal Forming» Spinning
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Forming deeper axi-symmetric parts from a blank
against a rotating mandrel is known as spinning.
Rigid rollers are used as the spinning tool.
The shaping of the circular blank over a rotating
mandrel is done using rigid roller tool.

Sheet Metal Forming» Spinning
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In conventional spinning, the blank is bent around the
rotating mandrel using a roller.
Spun parts may have diameter as large as 6 m.
Utensils are made by conventional spinning, as this process
is cheaper.

Sheet Metal Forming» Difference between
Deep Drawing and Wire Drawing in
metal forming
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In Deep drawing operation the sheet piece which will be
formed in the production operation, has been set into die and
apply pressure with a blank holder vertically. Then the sheet
between blank holder and die is transformed into cup under
plastic deformation, by applying a vertical pressure by a punch
which moves vertically to the workpiece.
( ) 







−= 70.
D
D
TStDF
p
b
p
Maximum drawing force

Sheet Metal Forming» Difference between
Deep Drawing and Wire Drawing in
metal forming
20-10-2019 99
(Dr. L K Bhagi)
Wire or Bar drawing is a bulk deformation process used to
reduce the diameter of a cylindrical workpart.
In this process the cross section of a round rod or wire is
typically reduced or changed by pulling it through a die Die
angle has great influence on the drawing force and the quality of
the drawn product

Sheet Metal Bending Mechanics and Spring Back Elimination Methods

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