1. Chapter 5 Power Estimation in Extrusion and Wire-rod Drawing
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Chapter 5: Extrusion and rod drawing - IE252

2. 5.1 Extrusion 5.1.1 Extrusion Technology
Description:. Extrusion process is characterized as a solid material, one-dimensional forming process with compressive state of stresses. In extrusion, a work-piece (billet) of cylindrical shape is placed in closed container. The closed container has an orifice (extrusion die) and extrusion punch, that forces the material toward the extrusion die orifice.
Extrusion Process Techniques: Two distinguished techniques are commonly used in extrusion, namely; Forward and backward extrusions.
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Direct (Forward) extrusion process
Chapter 5: Extrusion and rod drawing - IE252
Indirect (Backward) extrusion process

3. 5.1 Extrusion 5.1.1 Extrusion Technology
Extrusion Process Techniques :
In direct extrusion, punch-displacement is equal to the extruded product displacement both in magnitude and direction.
The punch has an opposite displacement direction, compared to the extruded product displacement in case of indirect process.
Hollow ram or punch is used in case of indirect extrusion, while solid ram is used in case of direct extrusion.
Load capacity is larger in case of direct extrusion when compared with indirect extrusion process.
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Direct (Forward) extrusion process
Chapter 5: Extrusion and rod drawing - IE252
Indirect (Backward) extrusion process

4. Typical hot extrusion products
5.1.1 Extrusion Technology
Applications :
Hot and cold extrusion processes are common.
Hot extrusion is commonly used to produce wide range of regular and irregular cross-sections, e.g. window frame cross-sections, door frame cross-sections, electric motor frames, angles, I section, H section ..etc.
Wire products can be used as raw material for electric cable and wire industries, through wire drawing process.
Fig below shows regular and irregular sections that can be produced using hot extrusion process.
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(a)
Typical hot extrusion products
Fig. 5.2 (a) regular and irregular section (b) wire..
Chapter 5: Extrusion and rod drawing - IE252

5. 5.1 Extrusion 5.1.1 Extrusion Technology Materials:
Ferrous and non-ferrous metals are commonly extruded in hot extrusion which provide sufficient ductility during the deformation at elevated temperature.
For example, aluminum is heated between C. At these temperatures the flow stress of the aluminum alloys is very low and by applying pressure by means of an ram to one end of the billet the metal flows through the steel die, located at the other end of the container to produce a section, the cross sectional shape of which is defined by the shape of the die.
Extrusion machines :
Special horizontal hydraulic presses are used for hot extrusion while general vertical mechanical and hydraulic presses are commonly used for cold extrusion.
Billets are commonly of round cross-sections having diameters range between 50 and 500 mm and length from 2-4 times the diameter size.
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Chapter 5: Extrusion and rod drawing - IE252

6. Some of extruded products for different industries
5.1 Extrusion
5.1.1 Extrusion Technology
Surface finish and tolerances:
Hot extrusion provides good surface finish especially with non-ferrous materials.
While cold extrusion provides closed tolerances (between %).
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Chapter 5: Extrusion and rod drawing - IE252
Some of extruded products for different industries
Extrusion dies

7. 5.1 Extrusion 5.1.2 Extrusion Processes
The extrusion process is classified based on the type of cross-section into two categories:
Rod extrusion.
Tube extrusion (closed hollows of regular or irregular cross-sections).
Both extrusion processes are carried out either as direct or indirect techniques.
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Chapter 5: Extrusion and rod drawing - IE252
Direct Rod Extrusion
Indirect Rod Extrusion

8. 5.1 Extrusion 5.1.2 Extrusion Processes
The extrusion process is classified based on the type of cross-section into two categories:
Rod extrusion.
Tube extrusion (closed hollows of regular or irregular cross-sections).
Both extrusion processes are carried out either as direct or indirect techniques.
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Chapter 5: Extrusion and rod drawing - IE252
Direct Tube Extrusion
Indirect Tube Extrusion

9. 5.1 Extrusion 5.1.2 Extrusion Processes
The extrusion process is classified based on the type of cross-section into two categories:
Rod extrusion.
Tube extrusion (closed hollows of regular or irregular cross-sections).
Both extrusion processes are carried out either as direct or indirect techniques.
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Chapter 5: Extrusion and rod drawing - IE252
Can Extrusion

10. 5.1 Extrusion 5.1.2 Extrusion Processes
Effective stress and strain for extrusion
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The principle stresses along direction 2 and 3 are equal, due to billet axi- symmetric. Hence, the effective stress is obtained as follows;
Chapter 5: Extrusion and rod drawing - IE252
Eq. 5.1a
Then
Eq. 5.1

11. The principle strains are : Using Volume constancy:
5.1 Extrusion
5.1.2 Extrusion Processes
Effective stress and strain for extrusion
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The principle strains are :
Using Volume constancy:
Chapter 5: Extrusion and rod drawing - IE252
Then effective strain :
Eq. 5.2

12. 5.1 Extrusion 5.1.2 Extrusion Processes Definition of Extrusion Ratio
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R= (Ao/Af)
Extrusion ratio (R); The extrusion ratio is defined as the ratio between the initial billet area to its final cross-sectional area or R= (Ao/Af). The effective strain expressed based on the extrusion ratio s given as:
Chapter 5: Extrusion and rod drawing - IE252
Eq. 5.3
Extrusion ratios between 40:1 for ferrous metals and between to 400:1 for aluminum alloys are acceptable

13. Extrusion pressure area Extrusion force-displacement
5.1.3 Load and power estimation:
The external pressure is obtained by equating the external work of the extrusion force to the internal work of the deformation (Wext=Wint):
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Eq. 5.4a
Chapter 5: Extrusion and rod drawing - IE252
Eq. 5.4b
Extrusion force
Extrusion pressure
Extrusion pressure area
Extrusion force-displacement
Extruded section area

14. 5.1.3 Load and power estimation:
5.1 Extrusion
5.1.3 Load and power estimation:
The external pressure is obtained by equating the external work of the extrusion force to the internal work of the deformation (Wext=Wint):
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Eq. 5.4a
Chapter 5: Extrusion and rod drawing - IE252
Extruded section area
Eq. 5.4b
From Eq5.4a and 5.4b
Eq. 5.4c

15. 5.1.3 Load and power estimation:
5.1 Extrusion
5.1.3 Load and power estimation:
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Eq. 5.4a
Extruded section area
Eq. 5.4b
Chapter 5: Extrusion and rod drawing - IE252
Eq. 5.4c
Amending Eq.5.4c for friction effect and redundant deformation by 50%, then
Eq. 5.4

16. 5.1 Extrusion
5.1.3 Load and power estimation for different cross-sections and extrusion processes:
(a) Direct round rod extrusion
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Sec A-A A
Chapter 5: Extrusion and rod drawing - IE252
Where
Extruded section area

17. 5.1 Extrusion
5.1.3 Load and power estimation for different cross-sections and extrusion processes:
(b) Indirect round rod extrusion
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Sec A-A A
Chapter 5: Extrusion and rod drawing - IE252
Where
Extruded section area

18. 5.1 Extrusion
5.1.3 Load and power estimation for different cross-sections and extrusion processes:
(c) Direct tube extrusion
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Sec A-A A
Chapter 5: Extrusion and rod drawing - IE252
Dp Mandrel diameter
Extruded section area

19. 5.1.3 Load and power estimation for different cross-sections and
5.1 Extrusion
5.1.3 Load and power estimation
for different cross-sections and
extrusion processes:
(d) Indirect tube extrusion
Extruded section area
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Sec A-A
Mandrel A
Chapter 5: Extrusion and rod drawing - IE252
Dp Mandrel diameter , Ad Mandrel area

20. 5.1.3 Load and power estimation for different cross-sections and
5.1 Extrusion
5.1.3 Load and power estimation
for different cross-sections and
extrusion processes:
(e) Can extrusion
Extruded section area
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Where
Internal Can Diameter.
Chapter 5: Extrusion and rod drawing - IE252
External Can Diameter.

21. 5.1.3 Load and power estimation for different cross-sections and
5.1 Extrusion
5.1.3 Load and power estimation
for different cross-sections and
extrusion processes:
(f) In general extrusion process
Extruded section area
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The principle variables that affect the extrusion force are:
Type of extrusion process (direct or indirect).
Extrusion ratio
Work-piece or billet temperature.
The speed of deformation.
Friction and lubrication used to decrease friction condition.
Chapter 5: Extrusion and rod drawing - IE252

22. Example 5.1
Calculate the extrusion force direct extrusion of a circular tube having 40mm outer diameter and 20 mm mandrel diameter. If the billet has a diameter of 100 mm and length of 200 mm, calculate the tube length? Given material follows; .
Solution
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Extrusion ratio:
Chapter 5: Extrusion and rod drawing - IE252
Extrusion force :
The tube length obtained using volume constancy;
As exercise, calculate the extrusion pressure for same problem using in-direct tube extrusion and comment on the results

23. 5.2.1 Wire and rod drawing technology 5.2 Wire and Rod Drawing
Description:
Wire and rod drawing is an operation in which a round bar (or tube or wire) is reduced in its cross-section area by pulling it through a converging die.
Wire and rod drawing process along with the strain and stresses developed in the deformation zone (conversion die).
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Chapter 5: Extrusion and rod drawing - IE252

24. 5.2.1 Wire and rod drawing technology 5.2 Wire and Rod Drawing
Applications:
Wire and rod drawing processes are finishing operations. For example, rod drawing used for small pistons, shafts, spindle, and as raw material for screw and bolts manufacturing .
Wire products are used in various industries like wire & wire products, heating wires, copper wires for electric and coil industries, spring manufacture, wire baskets, electric cables,…etc.
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Drawn shaft
Chapter 5: Extrusion and rod drawing - IE252
High power cable

25. 5.2.1 Wire and rod drawing technology 5.2 Wire and Rod Drawing
Applications:
Wire and rod drawing processes are carried out in multiple passes when high reduction of area is required.
For example, it is possible to draw wires down to mm diameter using 10 or more drawing dies depending on the initial wire diameter.
Usually heat treatment process is involved between the drawing passes.
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Chapter 5: Extrusion and rod drawing - IE252

26. 5.2.1 Wire and rod drawing technology 5.2 Wire and Rod Drawing
Applications:
Rod drawing is also applied for decreasing the cross-sectional area of circular pipes to obtain tie and accurate dimensions, and better surface finish.
Pipe drawing is usually applied for different materials e.g. stainless steel, copper, aluminum, ..etc.
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Chapter 5: Extrusion and rod drawing - IE252

27. 5.2.1 Wire and rod drawing technology 5.2 Wire and Rod Drawing
Die
Rod
Drawing Practices:
Die angle varies between 6º to 15º.
The reduction in cross-section area per pass ranges between 10% to 45%.
Smaller cross-sectional areas requires smaller area reduction per pass.
Higher reduction of area (>45%) may result in breakdown of lubrication and deterioration of surface finish of drawn product.
Light reduction of area is usually applied in the final pass for sizing (dimension accuracy) and improving surface finish.
Drawing speed varies between 0.15 m/s (for heavy sections), to 50 m/s for very fine wires.
Die materials include: tool steel (hot and cold worked), carbide insert, and diamond for longer tool live.
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Chapter 5: Extrusion and rod drawing - IE252

28. 5.2.1 Wire and rod drawing technology 5.2 Wire and Rod Drawing
Extrusion and drawing processes:
The extrusion of 0.5 mm is quite difficult and requires more power than when drawn as wire in drawing processes.
Tube drawing:
Like extrusion process, mandrel is used to draw tubes. Two types of mandrels are used namely; cylindrical and tapered mandrels
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Mandrel
Fig. 5.3 Cylindrical and taper mandrel of tube drawing.
Chapter 5: Extrusion and rod drawing - IE252

29. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Effective stress and strain for wire drawing: As in the extrusion process, the principle stresses along direction 2 and 3 are equal, due to wire axi-symmetric. Hence, the effective stress is obtained as follows;
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Then
Chapter 5: Extrusion and rod drawing - IE252

30. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Effective stress and strain for wire drawing: As in the extrusion process, the principle stresses along direction 2 and 3 are equal, due to wire axi-symmetric. Hence, the effective stress is obtained as follows;
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The principle strains are :
using the volume constancy
Chapter 5: Extrusion and rod drawing - IE252
Hence, the effective strain
where

31. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Definition: Reduction of area:
The reduction of area in wire drawing “r” is defined as follows
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Chapter 5: Extrusion and rod drawing - IE252

32. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Similar to the extrusion process, the external pressure is obtained by equating external work of the drawing force to the internal work of deformation (Wext=Wint), where
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Eq 5.8
where
Chapter 5: Extrusion and rod drawing - IE252
Eq 5.9
Where
drawing force
final drawn cross-section area
drawing pressure
drawing force-displacement
mean yield stress

33. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Similar to the extrusion process, the external pressure is obtained by equating external work of the drawing force to the internal work of deformation (Wext=Wint), where
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Eq 5.8
where
Chapter 5: Extrusion and rod drawing - IE252
Eq 5.9
From Eq 5.8 and 5.9 OR
Eq 5.10

34. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
For friction and redundant deformation effect, a deformation efficiency term“η” is used.
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Eq 5.10
Eq.5.11
Chapter 5: Extrusion and rod drawing - IE252
e.g. if η=80, the 1/ η =1.25 , hence
Eq.5.12

35. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Maximum reduction of area:
Maximum reduction of area in one pass is limited by the tensile or ultimate strength (instability condition) for heavy cold work, i.e. when the drawing pressure reaches the ultimate tensile load ( ) as ideal case.
From Eq 5.10
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Eq 5.10
Then
Chapter 5: Extrusion and rod drawing - IE252
Eq 5.13
For
The value of
Assume n=0
This applied for Ideal case

36. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Maximum reduction of area: (for Ideal case)
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For
The value of
Assume n=0 pp
=σ0ε ε σ
σ=K ε n
Chapter 5: Extrusion and rod drawing - IE252

37. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Maximum reduction of area: (for Ideal case)
The maximum reduction of area is a function of strain hardening exponent n , for example;
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The final drawn area is calculated as follows
Chapter 5: Extrusion and rod drawing - IE252
Conclusion:
Hence, the maximum reduction of area “rm” increases with the increase of strain hardening exponent ”n”.

38. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Maximum reduction of area: (for Ideal case)
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Conclusion:
Hence, the maximum reduction of area “rm” increases with the increase of strain hardening exponent ”n”.
Therefore, for maximum reduction of area per pass
Chapter 5: Extrusion and rod drawing - IE252
where Af* maximum reduction of area per drawing pass.

39. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Maximum reduction of area: (for Ideal case, 2nd method)
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For maximum reduction of area
Effective strain at instability
Therefore, for maximum reduction of area per pass:
Chapter 5: Extrusion and rod drawing - IE252
Eq. 5.15
For n=0 : (Ideal plastic flow)

40. 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Maximum reduction of area: (for Ideal case, 2nd method)
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Eq. 5.15
Effective strain at instability
For n=0 : (Ideal plastic flow)
Eq. 5.16
For
(strain hardening material)
Chapter 5: Extrusion and rod drawing - IE252
Eq. 5.17
Using deformation efficiency (η):
Eq. 5.18

41. Solution: 5.2.2 Wire and rod load estimation 5.2 Wire and Rod Drawing
Example 5.2
A round rod of annealed stainless steel 302 is being drawn from Do=10 mm to Df=8 mm at speed of 0.5 m/s. Assuming the friction and redundant work together 40%. Calculate the drawing power,
given the material follows the relationship:
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Die
Rod
Solution:
then
Chapter 5: Extrusion and rod drawing - IE252

42. 5.2 Wire and Rod Drawing Solution: Example 5.3
Find the maximum possible reduction in thickness of a tube having an outer diameter of 60 mm and initial thickness of 10 mm , drawn to 50 mm outer diameter in simple pipe drawing process.
The material follows the relation of :
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Solution:
Given Do=60 mm, to=10 mm, Df=50 mm.
rm=? , Af =? at rm , Pd*=?
Then
Chapter 5: Extrusion and rod drawing - IE252

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Chapter 5: Extrusion and rod drawing - IE252

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Chapter 5: Extrusion and rod drawing - IE252

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Chapter 5: Extrusion and rod drawing - IE252