Numerical and experimental analysis of tube drawing with fixed plug

Abstract

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.

Full text

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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