Principle of the process
Metal
forming
Structure
Process modeling
Drawing
Defects
Design For Manufacturing (DFM)
Process variation
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Bulk Drawing: Engineering Analysis
1. Introduction
In the bulk deformation processes, drawing is an
operation in which the cross section of a bar, rod, or
wire is reduced by pulling it through a die opening, as
shown in Figure 1.
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Extrusion
Drawing
Has pushing force
Has pulling force
Figure 1 here
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Bulk Drawing: Engineering Analysis
2. Objectives of the Analysis
Rolling process
Drawing process
Torque (force)
Pulling force
Power
Power
Velocity (productivity)
Pulling velocity
Max draft
Max draft
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3. Mechanics Phenomenon
There is a tensile stress due to pulling force, but
compression still plays a significant role since the
metal is squeezed down as it passes through the
die opening.
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4. Parameters
r=(A0-Af)/A0
r: area reduction
Contact length
A0: initial area of work
Die angle
Af: final area
Friction between work
and die
d=D0-Df, draft
Drawing stress
Force
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5. Drawing stress, drawing force, power
Accounts for inhomogeneous deformation
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5. Drawing stress, drawing force, power
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Allowable power
6. Limit of Drawing
Yield stress
Maximum power < Allowable power of a drive system
Maximum stress < Yield stress
If not, material goes into
plastic region & no “drawing”
occurs, just “elongation”
- If done, as Reduction , draw stress also
Entire reduction not done in a single pass (done in steps)
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6. Finding Max draw stress & Max reduction (1 pass)
Assumption: no friction, no strain hardening (n=0),
no redundant work (perfectly plastic)
Max. draw stress = Yield Strength
d  Y
Also,
Yf  Y
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because (n=0)
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d  Y
A0
A0
1
 d  Y f ln
 Y ln
 Y ln
Y
Af
Af
1 r
A0
e
Af
1
e
1 r
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e 1
 rmax
e
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Example
Wire stock of initial diameter = 0.125 in. is drawn
through two dies each providing a 0.20 area reduction.
The staring metal has a strength coefficient = 40,000
lb/in.2 and a strain hardening exponent =0.15. Each die
has an entrance angle of 12o, and the coefficient of
friction at the work-die interface is estimated to be 0.10.
The motors driving the capstans at the die exists can
each deliver 1.50 hp at 90% efficiency. Determine the
maximum possible speed of the wire as it exits the
second die.
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From this calculation, the velocity of the second die is the
limiting velocity. That is to say, the velocity of the whole
system should take 3.47 ft /s. As a result,
1. the first operation would have to be operated at well
below its maximum possible speed; or
2. the second draw die could be powered by a higher
horsepower motor; or
3. the reductions to achieve the two stages would be
reallocated to achieve a higher reduction in the first
drawing operation.
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