Tsch?tsch H., Koth A. Metal Forming Practise: Processes - Machines - Tools
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14 Deep drawing
14.1 Definition
Deep drawing is the forming of smooth (sheet) blanks into hollow parts. It is a process which
involves forming by tensile and compressive forces. The deformation takes place using:
a deep drawing ring, drawing punch and blank
holder (Figure 14.1)
In the process, the punch draws the material
through the gap formed by the punch and the draw-
ing ring, forming it into a cup.
Figure 14.1 Tooling and workpiece layout during the
deep drawing process. 1 drawing punch, 2
blank holder, 3 drawing ring, 4 container, 5
base plate, 6 ejector
14.2 Application of the process (Figures 14.2 and 14.3)
The process is used to produce hollow parts of all shapes where the wall thickness is the same
as that of the bottom.
Figure 14.2 Deep drawn parts for the household Figure 14.3 Deep drawn oil pan.
a) blank, b) finished part
142 14 Deep drawing
14.3 Forming process and stress distribution
14.3.1 The individual phases of the drawing process
a) Place the round blank on the drawing ring, in the centre (Figure 14.1).
b) Blank holder presses blank firmly onto drawing ring.
c) Drawing punch draws blank over radius of die, through opening of drawing ring, This
reduces the external diameter of the blank until it has been completely formed into a cup.
d) If a flange of sheet metal remains on the drawn part, the deep drawing must be limited.
14.3.2 Formation of characteristic triangles
If a hollow part is formed back into a circular sheet, then it can be seen that
a) the bottom of the cup with its radius r
C
remains unchanged;
b) the walls of the hollow part are formed from a series of rectangles with a width of w and a
length of (r
a
– r
C
);
c) triangular areas í “characteristic triangles” remain between the rectangles (Figure 14.4).
Figure 14.4 Folded-up rectangles form the walls of the drawn part. Characteristic triangles between
the rectangles.
14.3.3 Consequences of the characteristic triangles
a) Excess material does not go to waste, but without a blank holder it would lead to wrinkling.
b) The blank holder therefore prevents wrinkling.
c) As the material can not escape, the sheet is compressed between the blank holder and the
drawing ring, then stretched again between the drawing ring and the punch, which length-
ens the drawn part.
d) The blank holder force must also be applied, as well as the actual drawing force; for this
reason the drawing force is raised.
e) At first, the drawing force is carried by the material cross-section of the drawn part, near the
bottom, then í as the drawing process progresses í by the cylindrical part near the bottom.
14.4 Starting stock 143
f) This results in a weakening of the material cross-section near the bottom.
14.3.4 Stress distribution (Figure 14.5)
Tangential compression
V
t
occurs as the
material is forced into smaller and smaller
diameters.
Radial tensile stress
V
r
occurs due to the
tensile force when the blank is drawn into the
space between the punch and the die.
Compressive stress
V
p
occurs due to the
blank holder force í the material is subjected
to pressure.
Bending stress
V
b
occurs when the blank is
bent over the radius of the die.
Figure 14.5 State of stress of the blank dur-
ing deep drawing
14.4 Starting stock
The starting stock is a disk of sheet metal. The size and shape of the blank are important for
material consumption (correct sizing reduces waste during trimming), for the design of the
deep drawing tooling and the cost-effectiveness of the process.
When determining the size of the blank, it is assumed that the material thickness remains con-
stant throughout drawing.
14.4.1 Determining the blank size for cylindrical parts with small radii (r < 10 mm)
Cup without flange (Figure 14.6)
22
ʌʌ
ʌ
44
Dd
dh
2
4Dd dh
D in mm diameter of the blank
d in mm
h in mm
½
¾
¿
see Figure 14.6
Figure 14.6 Cup with small bottom radius (r < 10
mm)
144 14 Deep drawing
Cup with flange (Figure 14.7)
2
2
1
22
1
21
ʌ
ʌʌ
ʌ ()
44 4
d
D
dh d d
2
222
1
121
ʌʌ
(4 )
44
D
ddhdd
2
1
2
4Dd dh
Figure 14.7 Cup with flange
14.4.2 Determining the blank size for axisymmetric (rotationally symmetric)
parts with large radii (r > 10 mm)
Bottom radii of > 10 mm must be given particular consideration when determining the blank
size. This takes place using Guldin’s (Pappus’s) theorem: “The surface of a body of revolution
generated by rotating a curve around its axis is equal to the product of the generating curve and
the distance travelled by its geometric centroid at distance r
s
from the axis of rotation.”
c
2 ʌSr l
S in mm
2
surface of revolution
r
c
in mm radius of the centroid
l in mm length of the rotating
curve
D in mm diameter of the blank
Figure 14.8 Surface of revolution
This surface must correspond to the area of
the blank (Figure 14.9)
2
c
ʌ
2 ʌ
4
D
rl
2
c
ʌʌ
42
44
D
rl
c8Drl
Figure 14.9 Size of the centroid radius in a body
of revolution
14.4 Starting stock 145
For bodies of any type, which have more than one limiting line and therefore more than one
centroid radius, the following applies (Figure 14.10)
c
8()Drl
¦
Example:
1.
1
2
2
dr
l
c1
2
4
dr
r
2.
2
2 ʌʌ
42
rr
l
c2
2
0.64
2
dr
rr
3.
3
lhr#
c3
2
d
r
Figure 14.10 Determining the centroid radii and lengths of the segmented parts of a body of revolution
with large radii (r > 10 mm), a) centroid of a quarter-circle
1c1 2c2 3c3
22
8( )
22 2
80.64()
242 2 2
(2)4[1.57(2)2 ( )]
Dlrlrlr
drdrr dr d
rhr
Ddr rdrrdhr
S
ªº
§·§·§ ·
«»
¨¸¨¸¨ ¸
©¹©¹© ¹
¬¼
146 14 Deep drawing
Table 14.1 Formulae for calculating the blank diameter of various receptacle shapes
2
4ddh
2
1
2
4ddh
2
11 2 2
3
4( )ddhdh
2
112
1
42( )ddhfdd
2
11 2 2 2 3
2
4( ) 2 ( )ddhdhfdd
2
21.4dd
22
12
dd
2
12
1
1.4 ( )dfdd
2
1.4 2ddh
14.4 Starting stock 147
Table 14.1 (continued)
22
1
12
4dd dh
2
112
1
1.4 2 ( )ddhfdd
22
4dh
22
2
4dh
22
12
21
4( )dhdh
22
2
1
4( )dhdh
22
12
1
42( )dh fdd
1
22
12 1 2
11
2
4[ ( )]dhdh dd
2
12
1
2( )dsdd
148 14 Deep drawing
14.4.3 Determining the blank size for rectangular drawn parts
The blank size for rectangular drawn parts is determined by breaking down the hollow part
into elements of equal area:
Figure 14.11 Breakdown of a rectangular hollow part a), into elements of equal area b)
1. Sketch the bottom of the cup without the radius. A rectangle with sides a and b is produced
(Figure 14.11).
2. Move the side walls including the radius r
b
around (lay out the radius) and add them on the
corresponding sides of the rectangle a - b.
3. The cross this produces has lengthened the basic a – b rectangle by H
a
on side a and by H
b
on side b.
4. In the re-entrant angles of the cross, a quarter circle is drawn with the radius R
1
.
5. The sharp, angular spaces in between are balanced out by drawing arcs or other curves so
that the area of the basic body remains the same.
The compensation radii R
a
and R
b
are set at about a/4 or b/4 (Figure 14.12). If a = b then
the blank is a circle.
6. With simple shapes, the evening-out can also be done using a straight line (this produces an
octagon). However, this method is less precise.
14.4 Starting stock 149
Figure 14.12 Evening out the design of the blank using arcs or straight lines
14.4.3.1 Calculating the design values R
1
, H
a
, H
b
when h, a, b, r are provided
Case 1: corner radius = bottom radius
r
e
=r
b
= r
Design radius R:
2
1.42Rrhr
Correction value x:
2
0.074 0.982
2
R
x
r
§·
¨¸
©¹
Corrected design radius R
1
:
1
RxR
Developed length H
a
:
2
2
a
1.57 0.785 ( 1)
R
Hrh x
a
Developed length H
b
:
2
2
b
1.57 0.785 ( 1)
R
Hrh x
b
a = L – 2 r
e
b = B – 2 r
e
h = H – r
b
r
e
= r
b
Figure 14.13 Rectangular hollow part with
different bottom and corner radii
Case 2: corner radius different to bottom radius
150 14 Deep drawing
eb
rrz
Design radius R:
2
ee b
1.012 2 ( 0.506 )Rrrhr
Correction value x:
2
e
0.074 0.982
2
R
x
r
§·
¨¸
©¹
Corrected design radius R
1
:
R
1
= x · R
Developed length H
a
:
2
2
abe
0.57 0.785 ( 1)
R
Hrhr x
a
Developed length H
b
:
2
2
bbe
0.57 0.785 ( 1)
R
Hrhr x
b
14.4.4 Determining blank design for oval and various curved, cylindrical drawn
parts
Here, the blank is generally taken to be cylindrical, as long as the relationship of the semi-axes
of the ellipse is
1.3
a
b
d
.
14.5 Permissible deformation
In deep drawing, the limits for the permissible deformation are set by the draw ratio. The draw
ratio is used to
a) determine how many drawing operations are necessary to produce a drawn part;
b) judge the drawability of deep drawing steels;
c) determine the correction value n = f (draw ratio) to calculate the drawing force.
A difference is made between:
14.5.1 Lowest draw ratio m
p
unch diameter
b
lank diameter
d
m
D