3 Fundamentals of press design

Deep drawing and stretch drawing
β tot
Initial −∅ D
=
Final −∅ d
The maximum draw ratio depends on the properties of the blank material
used. As a rough estimate, the first drawing can be calculated as
having a maximum ratio of � = 2. To achieve � > 2 several drawings are
required and it must be noted that �, because of work hardening, can
only achieve a level of 1.3 in the next drawing step. If the part is
annealed before the next drawing operation, a � of 1.7 can be assumed.
With several drawing steps, the total draw ratio becomes a product of
the individual draw ratios:
β = β ⋅β ⋅…⋅β
tot 1 2 n
Example:
From a 1 mm thick blank of sheet metal material number 1.0338 (St 14) a hollow
cylindrical part with a diameter of 45 mm and a can body height of 90 mm
is to be drawn. First, the initial diameter of the circular blank D is calculated as
per Formula 1 from Table 4.2.1:
2 2
D= d + 4⋅d⋅ h = 45 + 4⋅45⋅ 90 = 18, 225 = 135 mm
Thus, the total draw ratio � tot is established:
β tot
D 135
= = = 3
d 45
Because � tot is greater than the remaining limiting draw ratio of 2, several drawing
operations are needed whereby � 1 may have a maximum value of 2, and all
following � values are less than 1.3.
β = β ⋅β ⋅…⋅ β = 3
tot 1 2
n
3= β ⋅β ⋅…⋅ β < 2⋅1313 . ⋅ .
1 2
n
The required draw ratio can be attained with three operations. In order to have
a robust and reproducable production sequence, the maximum permitted draw
ratios should not be fully utilised. In the event that � tot = 1.95 · 1.25 · 1.25 = 3
is selected. This calls for punch diameters of:
Metal Forming Handbook / Schuler (c) Springer-Verlag Berlin Heidelberg 1998
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