1. Principle of the process Structure Process modeling Defects Design For Manufacturing (DFM) Process variation Metal forming Drawing Handout 8 c

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. Handout 8 c

3. Extrusion Drawing Has pushing force Has pulling force Figure 1 here Handout 8 c

4. 2. Objectives of the Modeling Rolling process Drawing process Torque (force) Power Velocity (productivity) Max draft Pulling force Power Pulling velocity Max draft Handout 8 c

5. 3. Mechanics Phenomenon There is a tensile stress at the right side of the exit due to pulling force, but compression plays a major role since the metal is squeezed to pass through the die opening. Handout 8 c

6. r=(A0-Af)/A0 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 Handout 8 c

7. Accounts for inhomogeneous deformation 5. Drawing stress, drawing force, power r=(A0-Af)/A0 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 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. Handout 8 c

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) Handout 8 c

11. 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 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 0.10. 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. Handout 8 c

13. At the exit of the first die Handout 8 c

14. At the exit of the second die 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, • 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 Handout 8 c