1. Principle of the process Design For Manufacturing (DFM)
Structure
Process modeling
Defects
Design For Manufacturing (DFM)
Process variation
Metal forming
Drawing
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2. Bulk Drawing: Process modeling
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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3. Extrusion Drawing Has pushing force Has pulling force Figure 1 here
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4. 2. Objectives of the Modeling
Rolling process
Drawing process
Torque (force)
Power
Velocity (productivity)
Max draft
Pulling force
Power
Pulling velocity
Max draft
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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.
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6. Friction between work and die
4. Parameters
r=(A0-Af)/A0
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
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7. 5. Drawing stress, drawing force, power
r=(A0-Af)/A0
Accounts for inhomogeneous deformation
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8. 5. Drawing stress, drawing force, power
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9. 6. Limit of Drawing Allowable power Yield stress
Maximum power < Allowable power of a drive system
Maximum stress < Yield stress
Otherwise, material enters a plastic region at the exit, and no “drawing” but “elongation” occurs
Remark:
Reduction or reduction rate (r) increases  Power increases and stress at the exit increases.
If one pass does not achieve a desired reduction, try several passes.
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10. 6. Finding Max draw stress & Max reduction (1 pass)
Assumption: no friction, no strain hardening (n=0), no redundant work (perfectly plastic), no power capacity limit
Critical point: Max. draw stress = Yield Strength
Also,
because (n=0)
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11. Handout 8 c

12. Example
Wire stock of initial diameter = in is drawn through two dies, each providing a 0.20 area reduction rate (r). The starting metal has a strength coefficient = 40,000 lb/in2 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 The motors driving the capstans at the die exits 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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13. At the exit of the first die
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14. At the exit of the second die
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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,
the first operation would have to be operated at well below its maximum possible speed; or
the second draw die could be powered by a higher horsepower motor; or
the reductions to achieve the two stages would be reallocated to achieve a higher reduction in the first drawing operation.
Line balancing
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