Tsch?tsch H., Koth A. Metal Forming Practise: Processes - Machines

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14.5 Permissible deformation 151

The smallest permissible draw ratio m is the limit for the ratio of the punch diameter to the

blank diameter. The actual draw ratio m

actual

may be equal to or larger than, but not lower than

perm

actual

t m

perm

14.5.2 Highest draw ratio

is the reciprocal value of m.

lank diameter

unch diameter

14.5.2.1 Largest permissible draw ratio at the first draw

0perm

Table 14.2 Mean values for

perm

, e.g. for WUSt 1403, USt 1303, Ms 63, Al 99.5

d/s

30 50 100 150 200 250 300 350 400 450 500 600

0 perm

2.1 2.05 2.0 1.95 1.9 1.85 1.8 1.75 1.7 1.65 1.60 1.5

The actual draw ratio

actual

may be the same as or lower than, but not higher than the permis-

sible draw ratio

0 perm

The permissible draw ratio

for the first draw can also be calculated mathematically: for mate-

rials with good drawability, e.g. St 1403, Ms 63

0perm

2.15

1000 s





For materials which draw less well, e.g. St 1203

0perm

1.1

2.0

1000 s







d in mm punch diameter

s in mm sheet thickness

14.5.2.2 Permissible draw ratio on further draws (second, third draw)

For deep drawing steels such as St 1203 and St 1303 the average permissible draw ratio is

around

= 1.2 to 1.3

152 14 Deep drawing

At the second draw, the higher value must be assumed, and at the third draw the lower.

e.g. on the 2

draw,

on the 3

draw,

= 1.3

= 1.2

without intermediate annealing

If intermediate annealing takes place after the first draw, then the values are higher by about 20

%. Then,

= 1.6

can be assumed for the second draw.

14.6 Deep drawing steps

14.6.1 Deep drawing steps for cylindrical parts

draw



The required number of draws for cylindrical cups can be roughly calculated with Hubert’s

approximation formula (Figure 14.14).

hDd





n — required number of

draws

in mm cup height after the n

draw

in mm cup diameter after

the n

draw

in mm diameter of the blank

Figure 14.14 Cylindrical cup

14.6 Deep drawing steps 153

For 1.3

the deep drawing steps are the same as with round parts, starting out from a circu-

lar blank.

lank diameter

small diam. of ellipse

Figure 14.15 Drawn part with elliptical base

The smaller diameter of the ellipse is the decisive factor for the draw ratio.

For

1.3

the deep drawing steps are the same as with rectangular drawn parts.

14.6.3 Deep drawing steps for rectangular parts

This depends upon the design radius

(see section 14.4.3.1) and the mate-

rial constant q.

For St 12 to St 14 deep drawing steel:

0.3q |

draw r

= 1.2 · q · R

draw r

= 0.6 · r

draw (fin. part) r

= 0.6 · r

If further draws are necessary, then

the following generally applies:

draw r

= 0.6 · r

n – 1

Figure 14.16 Deep drawing steps with a rectangular

drawn part

In other words, just as when determining the blank size, the cup base is assumed to be a basic

rectangle and the permissible corner radii are determined.

The number of draws required is that which will produce the final corner radius.

14.6.2 Deep drawing steps for oval parts and parts with an elliptical base

154 14 Deep drawing

Example:

Determine the steps for a rectangular drawn part.

Sheet thickness s = 1mm

= r

= 10 mm

q = 0.34

= 46.8 mm

draw: r

= 1.2 q · R

= 1.2 · 0.34 · 46.8 mm = 19 mm

draw: r

= 0.6 · r

= 0.6 · 19 mm= 11.4 mm

draw: r

= 0.6 · r

= 0.6 · 11.4 mm = 6.84 mm

draw: r

= 6.84 mm < 10 mm (< than the radius of the finished part),

so the finished part can be produced with three draws.

14.7 Calculating the drawing force

14.7.1 Drawing force for cylindrical parts at the first draw

dr m m

CsRnd sRn    

in N drawing force

C in mm circumference of the drawing punch

d in mm punch diameter

s in mm sheet thickness

in N/mm

tensile strength

n correction value

The correction value n takes into account the ratio of drawing tension to tensile strength. It

depends mainly upon the actual draw ratio, which comes from the dimensions of the drawn

part.

Table 14.3 Correction value n = f (

actual

)

0.2 0.3 0.5 0.7 0.9 1.1 1.3

actual

1.1 1.2 1.4 1.6 1.8 2.0 2.2

Table 14.4 Maximum tensile strengths R

of some deep drawing steels

Material St 1303 St 1404

CuZn28

(Ms 72)

Al 99.5

(F10)

max

in N/mm

400 380

300

D. drawing quality

100

medium hard

14.8 Blank holder force 155

14.7.2 Drawing force for cylindrical parts at the second draw

sec 1 m

dsRn 

punch diameter at the second draw.

14.7.3 Drawing force for rectangular parts

dr e m

4( )

2 ʌ

rRsn



§·

  

¨¸

©¹

in mm corner radius (see Figure 14.11)

a in mm length of the cup without bottom radius r

(Figure 14.11)

b in mm width of the cup without bottom radius r

14.8 Blank holder force

14.8.1 Blank holder pressure

actual

(1)

200 400

ªº



«»



¬¼

p in N/mm

blank holder pressure

d in mm punch diameter

D in mm diameter of the blank

s in mm sheet thickness

in N/mm

tensile strength

actual

– actual draw ratio (first draw).

14.8.2 Blank holder area

BH e

()ADd 

22dd w r  (see Figure 14.17)

in mm

blank holder area

in mm effective diameter of the blank holder

w in mm drawing clearance

in mm die edge curvature radius.

156 14 Deep drawing

Figure 14.17 Layout of drawing punch, blank holder and drawing ring

14.8.3 Blank holder force

BH BH

FpA 

in N blank holder force.

14.9 Drawing work

14.9.1 With double-action presses:

WFxh 

A double-action press basically has two rams (Fig-

ure 14.18). The outer ram is used for the blank

holder and the inner ram for the actual drawing

operation. Both rams can be controlled separately.

Normal deep drawing requires this kind of double-

action press; in other words: a drawing press is

always double-action.

Figure 14.18 The principle of the deep drawing process

with a double-action press;

a) drawing ram,

b) blank holder,

c) drawing ring,

d) ejector.

14.9 Drawing work 157

14.9.2 With single-action presses:

dr BH

()WFxF h  

W in Nmm drawing work

in N drawing force

in N blank holder force

h in mm cup height = drawing depth

x – process factor

(x = 0.63).

A single-action press has only one ram and an

ejector. This ejector can be used to operate the

blank holder, if the drawing die is rotated by 180°.

Then, the drawing ring is fixed onto the ram and

the drawing punch (the pommel) is fixed to the

lower platen. The blank holder is operated by the

ejector using thrust pins. As the blank holder force

needs to be variable, this kind of machine can only

be used for deep drawing if the ejector force is

adjustable. A device of this kind, when installed

specially for deep drawing, is known as a die

cushion.

In this kind of assembly, as the ram has to over-

come not only the drawing force F

, but also the

blank holder force F

, the two forces add up

when calculating mechanical work.

Figure 14.19 The principle of the deep

drawing process with a single-action press,

a) drawing punch (pommel),

b) blank holder,

c) drawing ring,

Diagram of work (force-displacement diagram):

The work diagram shows the force-displacement

path during deep drawing. The force-displacement

curve is nearly an inverted parabola. The area

under the parabola is the drawing work. To deter-

mine the drawing work mathematically from the

force and the drawing depth, the mean resultant

force F

is used, imagined as constant across the

entire path. The area of the rectangle formed by

and s must be the same as the area under the

parabola. The F

max

ratio is considered the

process factor as it characterises the force path of

the particular manufacturing process.

0,63x

mmax

Fx 

max

Figure 14.20

Force-displacement path

during deep drawing

158 14 Deep drawing

14.10 Drawing tooling (Figure 14.17)

14.10.1 Drawing clearance w

The drawing clearance, w, is half the difference between the diameter of the drawing ring

and the diameter of the punch.

w in mm drawing clearance

D in mm diameter of the blank

d in mm punch diameter

s in mm sheet thickness

For more precise calculations, the following applies (according to Oehler):

wsk s 

Table 14.5 Material factor k to determine the drawing clearance w

Material Steel

High-temperature

alloys

Aluminium

Other nonferrous

metals

k in mm

0.07 0.2 0.02 0.04

14.10.2 Punch radius r

for cylindrical parts

(4... 5)rs 

This depends upon the part being drawn.

14.10 Drawing tooling (Figure 14.17) 159

14.10.3 Die edge curvature r

For cylindrical parts:

Too small radii subject the sheet to additional strain. Too large radii lead to the formation of

wrinkles at the end of the draw, as then the blank holder is no longer effective.

0.035

50 mm ( )

rDds 

in mm die edge curvature radius

D in mm diameter of the blank

d in mm diameter of the finished part = punch diameter

s in mm sheet thickness

So r

depends upon:

the sheet thickness s

the blank diameter D

the diameter of the finished part d (= punch diameter).

With low drawing depths, a smaller r

must be selected as otherwise, the area where the blank

holder presses is too small.

The parts of the drawing rings which come into contact with the sheet must be kept smoothly

ground and polished to reduce frictional forces.

For rectangular parts:

a) for rectangle side a: (see Figure 14.11)

aae

0.035

50 mm 2( )

rHrs 

b) for rectangle side b:

bbe

0.035

50 mm 2( )

rHrs 

c) radii in the corners of the rectangular die:

1.5 .rr|

160 14 Deep drawing

14.10.4 Structural design of drawing tooling

The structural design of drawing tooling is determined by two factors:

1. The type of deep drawing

Here, a difference is made between tooling for the first draw and for further draws (second,

third, fourth).

The main elements of deep drawing tool-

ing are shown in Figure 14.21 for the first

draw and Figure 14.22 for further draws

(second, third, etc.).

Figure 14.21 Deep drawing tooling for the

first draw:

1 drawing punch,

2 blank holder ram,

3 blank holder,

4 drawing ring,

5 ejector,

6 base plate

2. The press which is available (sin

le or

double-action presses).

If a deep drawing operation is carried out

on a single-action press, then the drawing

ring must be fixed onto the ram and the

lank holder must be operated from the die

cushion.

Figure 14.22 Deep drawing tooling for the second

draw:

1 drawing ram, 2 blank holder ram, 3 blank holder,

4 drawing punch, 5 drawing ring, 6 base plate, 7

centring ring, 8 ejector.

Tsch?tsch H., Koth A. Metal Forming Practise: Processes - Machines - Tools

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