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Handout 8 c 1
Drawing
Principle of the process
Structure
Process modeling
Defects
Design For Manufacturing (DFM)
Process variation
Metal forming
Handout 8 c 2
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.
Handout 8 c 3
Figure 1 here
Has pulling forceHas pushing force
Extrusion Drawing
Handout 8 c 4
Rolling process
Torque (force)
Power
Velocity (productivity)
Max draft
Drawing process
Pulling force
Power
Pulling velocity
Max draft
Bulk Drawing: Engineering Analysis
2. Objectives of the Analysis
Handout 8 c 5
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.
Handout 8 c 6
4. Parameters
r: area reduction
A0: initial area of work
Af: final area
d=D0-Df, draft
Drawing stress
Contact length
Die angle
Friction between work and die
Force
r=(A0-Af)/A0
Handout 8 c 7
5. Drawing stress, drawing force, power
Accounts for inhomogeneous deformation
Handout 8 c 8
5. Drawing stress, drawing force, power
Handout 8 c 9
6. Limit of Drawing Allowable power
Yield stress
Maximum power < Allowable power of a drive system
Maximum stress < Yield stressIf not, material goes into plastic region & no “drawing” occurs, just “elongation”
Entire reduction not done in a single pass (done in steps)
- If done, as Reduction , draw stress also
Handout 8 c 10
Assumption: no friction, no strain hardening (n=0), no redundant work (perfectly plastic)
6. Finding Max draw stress & Max reduction (1 pass)
Yd Max. draw stress = Yield Strength
Also,
YY f because (n=0)
Handout 8 c 11
eAA
f
0 er
11
max1 ree
Yr
YAA
YAA
Yff
fd
1
1lnlnln 00
Yd
Handout 8 c 12
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.
Handout 8 c 13
Handout 8 c 14
Handout 8 c 15
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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