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.

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Figure 1 here

Has pulling forceHas pushing force

Extrusion Drawing

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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

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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: 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

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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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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

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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)

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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.

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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.