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F. O. Neves et al

/ Vol. XXVII, No. 4, October-December 2005 ABCM

426

F. O. Neves

Federal University of Sao Joao del Rei

Praça Frei Orlando 170, Centro

36360-000 São João del-Rei, MG. Brazil

fred@ufsj.edu.br

S. T. Button

C. Caminaga

and F. C. Gentile

State University of Campinas

School of Mechanical Engineering

Department of Materials Engineering

C. P. 6122

13083-970 Campinas, SP. Brazil

sergio1@fem.unicamp.br

celioc@fem.unicamp.br

and gentile@fem.unicamp.br

Numerical and Experimental Analysis

of Tube Drawing With Fixed Plug

Numerical simulation of manufacturing processes has become in the last years an

important tool to improve these processes reducing lead times and try out, and providing

products free of defects and with controlled mechanical properties. Finite Element Method

(FEM) is one of the most important methods to simulate metal forming. In tube drawing

with fixed plug both the outer diameter and the inner diameter of the tube are properly

defined if correct process conditions are chosen for the die angle, drawing speed,

lubrication and area reduction per pass. These conditions have great influence on drawing

loads and residual stresses present in the product. In this work, the cold drawing of tubes

with fixed plug was simulated by FEM with the commercial software MSC.Superform to

find the best geometry of die and plug to reduce the drawing force. The numerical analysis

supplied results for the reactions of the die and plug and the stresses in the tube, the

drawing force and the final dimensions of the product. Those results are compared with

results obtained from analytic models, and used tooling design. Experimental tests with a

laboratory drawing bench were carried out with three different lubricants and two

different lubrication conditions.

Keywords: Cold tube drawing, finite element analysis, die design, upper bound solution

Introduction

Superior quality products with precise dimensions, good surface

finish and specified mechanical properties can be obtained with

drawing processes. However, the design of optimized cold drawing

by means of classical trials and errors procedures, based

substantially on designers’ experience, has become increasingly

heavy in terms of time and cost.

1

In recent years, rapid development of computer techniques and

the application of the theory of plasticity made possible to apply a

more complex approach to problems of metals formability and

plasticity. Numerical simulation is a very usefull tool to predict

mechanical properties of the products and to optimize the tools

design (Bethenoux et al., 1996). Pospiech (1997) presented a

description of a mathematical model for the process of tube drawing

with fixed mandrels. Karnezis and Farrugia (1966) had made an

extensive study on tube drawing using finite element modelling. In

addition, other studies have been done to relate reduction drawn

force and process costs to process parameters and tool design (Jallon

e Hergesheimer, 1993; Joun e Hwang, 1993; Chin e Steif, 1995;

Dixit e Dixit, 1995; El-Domiat e Kassab, 1998). Lubrication is also

an object of study, in order to obtain a perfect liquid film in the

tool/part interface (Martinez, 1998; Button, 2001).

In this study, we present a tool device specially designed to

reduce drawn force, formed by two dies assembled within a

recipient wich can be sealed, generating a pressurized lubrication

during the process. Die and plug geometry are obtained from the

numerical simulation. Experimental tests with this tooling in a

laboratory drawing bench were performed, using three different

lubricants and pressurized and unpressurized lubrication. The

experimental results were compared to numerical results and the

performance of the process was analyzed with a statistical model.

Paper accepted August, 2005. Technical Editor: Anselmo Eduardo Diniz.

Nomenclature

R

i

= external inlet radius of the tube

R

ii

= internal inlet radius of the tube

R

f

= external outlet radius of the tube

R

f

= internal outlet radius of the tube

L = bearing length

Wh = Homogeneous work

Wr = redundant work

Wa = fricition work

Greek Symbols

α = die semi-angle

α

p

= plug semi-angle

d

p

= nib diameter

β = semi-angle of the internal cone of the tube after drawing

without plug

ε = true strain

µ

1

= Coulomb friction between tube and die

µ

2

= Coulomb friction between plug and tube

σ = stress

σ

tref

=drawing stress

σ

0

= average yield stress

τ

1

= Velocity surface descontinuity on inner die

τ

2

= Velocity surface descontinuity on outter die

τ

3

= Contact surface in the work zone at die/workpiece interface

τ

4

= C ontact surface in the die bearing/workpiece interface

τ

5

= Contact surface in the plug bearing/workpiece interface

τ

6

= contact surface in the work at zone plug/workpiece interface

Plug Geometry

Plug geometry is shown in Fig. 1. The region A is a cylindrical

portion to position the plug inside the die. Its diameter is slightly

smaller than the tube inner diameter. The plug semi-angle (α

p

) in the

work zone B is smaller than die semi-angle (α). It is defined to be 2

degrees or more smaller than die semi-angle (Avitzur, 1983 and

Pawelsky, O. and Armstroff, O., 1968).

Numerical and Experimental Analysis of Tube Drawing With Fixed Plug

J. of the Braz. Soc. of Mech. Sci. & Eng. Copyright

2005 by ABCM October-December 2005, Vol. XXVII, No. 4 /

427

Figure 1. Plug geometry.

Region C, called ‘nib’, is cylindrical and controls the inner

diameter of the tube. In the present study the wall thickness of the

tube was reduced by 0.1 mm. The length of the nib was fixed in 2

mm for all tests.

Finite Element Model

Tube drawing process was simulated with the software

MSC.Superform 2002 using a 3D finite element model as shown in

Fig. 2. Tubes with dimension 10 x 1.5 mm (outer diameter x

thickness) were drawn to three diferent area reduction, using four

die angles for each reduction, as shown on Tab. 1. In all simulations,

the wall thickness was reduced from 1.5 mm to 1.4 mm.

A quarter piece of tube 100 mm long was modeled using 3200

bricks elements with 8 nodes to define the mesh. This length was

tested in order to obtain the steady-state condition. The die geometry

consisted of a 30º half entry angle, a 15º half exit angle and a

bearing length of 0.4 times the outlet dameter.

Friction between die and tube and between tube and plug was

estimated as 0.05, assumed to be Coulomb friction. Die and plug

were modeled with an elastic material, assumed to be tugsten

carbide (Young modulus of 700 GPa).

Figure 2. FE meshes of tube, die and plug used in the numerical

simulation.

Table 1. Area reductions and die angles used in the numerical simulation.

Simulation #

Area

reduction (%)

Die semi-angle

(degrees)

Outlet

diameter (mm)

1 34.4 7.0 7.94

2 34.4 8.8 7.94

3 34.4 10.0 7.94

4 34.4 14.0 7.94

5 26.5 7.0 8.40

6 26.5 8.8 8.40

7 26.5 10.0 8.40

8 26.5 14.0 8.40

9 20.0 7.0 8.76

10 20.0 8.8 8.76

11 20.0 10.0 8.76

12 20.0 14.0 8.76

An elasto-plastic model was used for the material of the tube.

Tensile tests of stainless A304 steel tubes were carried out to obtain

the stress-strain curve (σ x ε) to be used in the simulation. This

stress-strain curve was approached by Holloman’s equation as

shown in Eq. (1).

σ = 1137 ε

0,52

[MPa] (1)

Young modulus of 210 GPa and a Poisson ratio of 0.3 were

defined to the tube material, which was assumed to be isotropic and

insensitive to strain rate. During experimental drawing it was

noticed that the temperature at the tube was not higher than 100 ºC,

thus allowing the tube material to be modelled independent on the

temperature.

Analytical Model

An upper bound solution (UBS) of tube drawing with fixed plug

was developed in this work. This solution was adapted from that

obtained by Avitzur (1983) for tube sinking. This analytical model

considered an isotropic strain-hardening material for the tube,

Coulomb frictions, a cylindrical stress state, and the Tresca´s flow

rule. The process geometry is represented in Fig. 3. Equation (2) is

the analytical expression obtained with this solution for the tube

drawing tension with fixed plug.

Figure 3. Tube drawing with fixed plug.

σ

tref

= σ

0

Wh + Wr + Wa

2µ

1

L

R

f

(2)

Wh = 2f(α) ln

R

i

R

f

(3)

Wr =

2

3

α

sen

2

(α)

- cotg (α) -

β

sen

2

(β)

+ cotg (β) (4)

DIE

PLUG

TUBE

F. O. Neves et al

/ Vol. XXVII, No. 4, October-December 2005 ABCM

428

Wa = B(1 – ln

R

i

R

f

) ln

R

i

R

f

+ 2µ

1

L

R

f

;1 + 2µ

1

L

R

f

(5)

B = 2{µ

1

cotg (α)+µ

2

cotg (β)} (6)

f(γ) =

1

sen

2

(α)

cos(β) 1-

11

12

sen

2

(β) - cos(α) 1-

11

12

sen

2

(α) +

+

1-

11

12

sen

2

(β)

11

12

cos(α) + 1-

11

12

sen

2

(α)

(7)

Experimental Tests

A304 stainless steel tubes were drawn in a laboratory drawing

bench. Tubes with 10 x 1.5 mm (outer diameter x thickness) were

reduced to 7.94 x 1.4 mm, which represents a drawing pass with

34.4% of area reduction. Two dies were used, both of tungsten

carbide with die semi-angle α of 7º and bearing length of 3 mm.

One die has an exit diameter of 9.8 mm and the other an exit

diameter of 7.94 mm.

The tube initial length was 500 mm. First, it was cold swaged to

reduce one of its ends and to allow it to pass through the dies. Figure

4 shows an illustration of the die support. The tooling was

assembled with three chambers. The first chamber receives a die,

called second reduction die, wich promotes the most significant tube

reduction. It also receives the load cell, to measure the drawing

force. A second chamber receives another die, called first reduction

die, which will promote a very low reduction. This chamber length

is greater than the die body lenght. A third chamber is designed to

receive the lubricant. After the tube was located inside the die, the

die support was filled with oil and closed to be pressurized. Then the

tube was forced to pass through the dies. Therefore the first

reduction die is pulled, increasing the pressured within the

chambers, and forcing the lubricant to pass with the tube through the

second reduction die, being the first reduction from 10 to 9.8 mm

and the second, from 9.8 to 7.94 mm.

Tubes were drawn at speeds of 1 m/min, 2 m/min and 5 m/min.

Three lubricants were used: a commercial mineral oil (22 cSt at 100

ºC), a semi-synthetic oil (190 cSt at 100 ºC), and a mineral oil

formulated with extreme pressure additives and MoS

2

grease,

indicated to cold forming processes (69,3 cSt at 100 ºC).

The plug was made with AISI D6 tool steel, quenched and

tempered to 52 HC. Plug semi-angle was 5.4º with a nib length of 2

mm. Tube cavity was filled with the same oil used in the die

support. Finally the plug was positioned at the work zone and

fastened with a stick to the drawing bench structure.

Figure 4. Schematic representation of the die support, dies and tube.

In Figure 4:

1 – tube

2 – first reduction die

3 – die support

4 – second reduction die

5 – load cell

6 – pressure chamber

7 – fixed plug

Experimental Design

To evaluate the drawing force, a random factorial analysis

(Montgomery & Runger, 1994) was designed with the following

variables:

- Lubricants: commercial mineral oil, semi-synthetic oil, and

mineral oil with extreme pressure additives;

- Drawing speed: 1 m/min; 2 m/min and 5 m/min;

- Lubrication: Pressurized and not-pressurized.

FEM Analysis

Figure 5 shows the drawn stress (longitudinal stress) obtained

from numerical simulation with the Finite Element Method

previously discussed. It is seen that the best die semi-angle is found

between 7 to 10º for all area reductions simulated (20, 25 and

34,4%).

0

100

200

300

400

500

600

700

800

900

5 7 8,8 10,5 14

Die semi angle (degrees)

Drawn Stress (MPa)

34.4% 26.5% 20%

Figure 5. Drawn stress x die semi-angle, predicted with FEM analysis.

Figure 6 shows the variation of equivalent stress for a point

located at the outer surface of the tube, since the die entry until a

point located 40 mm far from there, during the a drawing pass with

34.4% of area reduction for each die semi-angle simulated. Note

that the average equivalent stress is very unstable until beyond 10

mm and thereafter the process becomes stable.

100

250

400

550

700

850

0 5 10 15 20 25 30 35 40

Point position (mm)

Equivalent Stress (MPa) .

7º 8.8º 10º 14º

Figure 6. Variation of equivalent stress of a point passing through the die.

Numerical and Experimental Analysis of Tube Drawing With Fixed Plug

J. of the Braz. Soc. of Mech. Sci. & Eng. Copyright

2005 by ABCM October-December 2005, Vol. XXVII, No. 4 /

429

In Fig. 7 it is shown the equivalent stress distribuition along the

tube with 34.4% of area reduction, die semi-angle of 7º and friction

coefficent of 0.05 to plug-tube and die-tube interface. It can be

noticed that there is a great variation of equivalent stress along the

die length. Just after the die exit the equivalent stress reaches an

uniform value. The inner and outer tube diameters at die exit did not

show any significant variation in all simulations.

Figure 7. Equivalent stress distribution along the tube.

Analytical Results

Figure 8 shows the drawing stress variation with die semi-angle

for the three area reductions studied where was assumed a Coulomb

friction of 0.05 in all interfaces.

It can be seem that the results quite agree with drawn stress

obtained from FE analisys. The best die semi-angles again were

found between 7º and 10º, as FEM analisys had predicted.

0

200

400

600

800

1000

1200

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Die semiangle (degrees)

Drawn Stress (MPa)

34,4% 26,5% 20%

Figure 8. Drawing stress variation with die semi-angle and area reduction,

obtained with the upper bound method.

Figure 9 shows the drawing stress for some values of friction

coefficient adopted on die-tube interface and plug-tube interface. In

curve 1 friction coefficient between die and plug was 0.05 and

between tube and plug was 0.0, which represents a tube drawing

without a plug. The friction coefficients used in curve 2 were 0.05

and 0.05, respectively. For curve 3, it was adopted 0.1 and 0.05, for

curve 4, 0.1 and 0.1 and, finally, for curve 5, 0.05 and 0.1.

As it was expected, drawn stress increases with increasing

friction on die-tube interface, as well as increasing friction on plug-

tube interface. However, it can be noticed that drawn stress

increases more significantly with an increasing friction on plug-tube

interface than on die-tube interface.

0

500

1000

1500

2000

2500

1 3 5 7 9 11

Die semi-angle (degrees)

Drawn Stress (MPa) .

Curve 1

Curve 2

Curve 3

Curve 4

Curve 5

Figure 9. Drawn stress calculated with upper bound method varying the

die semi-angle and the friction coefficient on die-tube and plug-tube

interfaces.

Experimental Results

Figure 10 shows the three observations for drawing force using

as lubricant the mineral oil SAE 20W50 and drawing speed of 1

m/min. Figures 11 and 12 shows the drawing force using the same

lubricant for speeds of 2 and 5 m/min, respectively.

0

5000

10000

15000

20000

25000

0 3 6 9 12 15 18 21 24 27 30 33

Time (s)

Drawn Force (N) .

Figure 10. Measured Drawing Force x time – Lubricant: SAE 20W50 – v =

1 m/min.

0

2000

4000

6000

8000

10000

12000

14000

0 2 4 6 8 10 12 14 16 18

Time (s)

Drawn Force (N) .

Figure 11. Measured Drawing Force x time – Lubricant: SAE 20W50 – v =

2 m/min.

F. O. Neves et al

/ Vol. XXVII, No. 4, October-December 2005 ABCM

430

0

2000

4000

6000

8000

10000

12000

14000

0 1 2 3 4 5 6 7 8 9 10

Time (s)

Drawn Force (N)

Figure 12. Measured Drawing Force x time – Lubricant: SAE 20W50 – v = 5

m/min.

It can be seen that during the tests drawing force increases

quickly and reaches a steady state. At the end of drawing process,

occurs an instantaneous increase of drawing force that can be related

to the moment in which the whole tube had passed through the

second reduction die, opened the system and the pressure dropped

down. The mean drawing force in the pressurized tests is verified

from the point where this force reaches a steady state until the point

where pressure drops. In not-pressurized tests the mean load is

observed from this point till the end of the process.

Figures 13 to 15 show experimental results for the drawing force

in tests with the lubricant Renoform MZA 20 and drawing speeds of

1, 2 and 3 m/min, respectively. Here, the transition from pressurized

to not-pressurized lubrication can be seen more accuratelly than

with the lubricant previously discussed. The effect is greather with

the two highest drawing speeds. As in the previous analysis,

drawing force increases when the process begins and keeps a steady

state till the moment the whole tube passes through the second

reduction die.

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

0 5 10 15 20 25 30 35 40

Time (s)

Drawn Force (N) .

Figure 13. Measured Drawing Force x time – Lubricant: Renoform MZA

20 – v = 1 m/min.

0

5000

10000

15000

20000

0 2 4 6 8 10 12 14 16 18 20

Time (s)

Drawn Force (N) .

Figure 14. Measured Drawing Force x time – Lubricant: Renoform MZA

20 – v = 2 m/min.

0

2000

4000

6000

8000

10000

12000

14000

16000

0 1 2 3 4 5 6 7 8

Time (s)

Drawn Force (N)

Figure 15. Measured Drawing Force x time – Lubricant: Renoform MZA 20

– v = 5 m/min.

Drawing force of tests using as lubricant Extrudoil MOS 319 is

shown on Fig. 16 to 18, also with drawing speeds of 1, 2 and 5

m/min. The same caracteristics on drawn force behavior pointed in

the previous case can be observed here. Note that behavior can be

clearly observed also for drawing speed of 1 m/min. It isn’t so clear

with the other lubricants used in this work.

0

2000

4000

6000

8000

10000

12000

14000

0 5 10 15 20 25 30 35

Time (s)

Drawn Force (N) .

Figure 16. Measured Drawing Force x time – Lubricant: Extrudoil MOS

319 – v = 1 m/min.

0

2000

4000

6000

8000

10000

12000

0 2 4 6 8 10 12 14 16

Time (s)

Drawn Force (N) .

Figure 17. Measured Drawing Force x time – Lubricant: Extrudoil MOS

319 – v = 2 m/min.

0

2000

4000

6000

8000

10000

12000

0 1 2 3 4 5 6 7

Time (s)

Drawn Force (N) .

Figure 18. Measured Drawing Force x time – Lubricant: Extrudoil MOS

319 – v = 5 m/min.

Numerical and Experimental Analysis of Tube Drawing With Fixed Plug

J. of the Braz. Soc. of Mech. Sci. & Eng. Copyright

2005 by ABCM October-December 2005, Vol. XXVII, No. 4 /

431

Table 1 shows experimental results of mean drawing force and

the relative increase of this force in pressurized and not-pressurized

lubrication conditions. The results indicate that it is possible to

achieve a reduction on drawing force around 10% if the pressurized

lubrication is established with lubricants mineral oil SAE 20W50 or

Renform MZA 20. The reduction on drawing force is more

significant with the lubricant Extrudoil MOS 319, more than 16%

for any drawing speed tested. Statistical analysis showed that

Extrudoil MOS 319, in fact, presents the highest performance to

reduces drawing forces. The best drawing conditions are represented

by this lubricant, with the highest drawing speed and the pressurized

lubrication.

Table 2. Experimental results of the average drawing force.

LUBRICATION SAE 20W40

1 m/min 2 m/min 5 m/min

PRESSURIZED 450,0 273,8 328,3

UNPRESSURIZED 498.7 308,2 358,8

Relative increasing (%)

10,8 12,6 9,3

RENOFORM MZA 20

1 m/min 2 m/min 5 m/min

PRESSURIZED 448,3 374,1 323,0

UNPRESSURIZED 445,0 435,2 358,7

Relative increasing (%)

-0,7 14 11

EXTRUDOIL 319 MOS

1 m/min 2 m/min 5 m/min

PRESSURIZED 266,3 229,3 228,2

UNPRESSURIZED 310,7 272,7 285,1

Relative increasing (%)

16,7 18,9 24,9

Conclusions

a. The tool device designed in this work showed to be able to

promote pressurized lubrication during tube drawing with

fixed plug and, therefore, to reduce drawing forces.

b. The analytical model developed in this work presented

drawing stress results in good agreement to those calculated

with the finite element method.

c. Lubricant Extrudoil 319 MOS is the most efficient to reduce

drawing force in tests with pressurized lubrication;

d. Drawing speeds of 2 and 5 m/min are the best to promote

pressurized lubrication and to reduce drawing forces.

Acknowledgement

Authors would like to thank FAPESP – Fundação de Amparo a

Pesquisa do Estado de São Paulo for the financial support,

MSC.Software Corporation for the software MSC.Superform 2002

and Fuchs do Brasil, that kindly gave us the lubricants Renoform

MZA-20 and Extrudoil MOS 319.

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