Question:
Can Lube Evaluation for the wire
drawing process be conducted by instrumenting the production equipment
itself?
Answer:
Instrumenting drawing equipment on the production line
is a possibility. Another possibility is to dedicate a specially
designed, highly instrumented, laboratory unit for Lube Evaluation. There
are pros and cons for each approach that must be evaluated.
One reason for the commitment of a lab unit for the task of lube
evaluation is to avoid disruption of the production line for
testing, because the operators might become irritated and you lose their
cooperation. Another reason is that you do not want to flush all the
lubricant out of a big machine in order to run a test. It becomes too
expensive. More information is provided in the publication ref188.
A segment of our seminar
on Wire Drawing (May 1998) will cover the subject of Lube
Evaluation.
Question:
What keeps a floating plug in
position, and where can I learn about the mechanics of tube drawing with
floating plugs?
Answer:
The plug maintains its equilibrium position because the
resultant axial force acting on the plug is zero. This axial force is
composed of:
- friction drag in the direction of the flow of the tube,
- the axial component of the pressure force acting between
the plug and the tube,
- the lubricant pressure acting on the plug, and
- the liquid drag transferred from the tube to the plug through
the shear in the lubricant between them. (See Figure 1.)
If the plug temporarily wavers out of position, the balance of
these forces is disturbed and a non-zero resultant axial force
develops to push the plug back to its equilibrium position of zero
axial force.
Here we will describe the "built-in" mechanism that is
incorporated into the design of the system to automatically establish
and maintain the position of the plug. The mechanism senses the
position of the plug and corrects it instantaneously, without external
sensors and controls, as follows:
Since the angle of the cone of the plug is smaller
than that of the die, the plug is forced to contact the inside of the
tube midway between the large and small diameter on the inside of the
converging tube. If the plug is pushed too far into the exit, the point
of contact approaches the entrance, increasing the area of contact
between the plug and the tube, and the subsequent increased force
exerted by the tube on the plug will drive the plug back to the entry.
The opposite will occur if the plug is pushed too far away from the
exit, i.e., the contact point will move towards the exit, the force
exerted by the tube on the plug will drop and the plug will restore its
equilibrium in the middle. The change in the position of the plug is
sensed by changed forces which instantaneously and directly drive the
plug in the right direction to restore the plug into its equilibrium
position.
FIGURE
<1> [ 48k]
The point of equilibrium is established through the proper choice of
the parameters, such as:
- the lubricant, which might be a fluid squirted into the
back of the plug, or solid lubricant coating on the inside of
the tube, contributing to the friction value,
- the plug and die angles, and
- the diameter and length of the Nib.
The relations between the position of the plug
and the independent process parameters are discussed in Chapter 9 of the
"Handbook
of Metalforming Processes".
Question:
What is the formula for the
determination of the diameter of the Nib and that of the body of a
floating plug in tube drawing?
Answer:
The design rules for the drawing of tubes over a mandrel
or a plug are strongly dictated by the factors controlling the behavior
of the tube during the process of tube sinking without a plug under
otherwise identical conditions. This behavior during tube sinking can be
studied experimentally, or modelled analytically. Such an analytical
model, and the software available for it, are described in our numerous
papers and textbooks, as listed in the reference list, and in our
seminar on tube
making.
The diameter of the Nib is determined by the expected
inner diameter of the tube when the tube is produced by the process of
tube sinking without a mandrel or plug. In order for the Nib to control
the inner surface its diameter should be slightly larger than the
expected diameter from tube sinking under otherwise identical
conditions. The diameter of the Nib should not exceed that size by too
much, or the tube will tear by thinning. The role of the plug is to
control the precision of the size, the surface finish of the inside of
the tube and to prevent the "orange pill" and flaking
phenomena. The wall thickness during tube sinking even without a plug
can be controlled by the other parameters, such as die angle.
The length of the Nib can be determined by the need to establish a zero
axial force on the plug. The angle of the conical surface of the plug is
slightly smaller than that of the die.
The chatter phenomena and
the bamboo marks are directly related to the oscillations of the plug.
The expected wall thickness of the tube varies with speed, and the
dragging force on the plug changes accordingly. The plug jumps in and
out at a periodic rhythm leaving rings called "bamboo
marks".
The parameters that control the process of tube
drawing with floating plugs are:
- the diameter and lenght of the body of the plug,
- the viscosity of the lubricant,
- the geometry of the enclosed entrapped lube between the
plug and the tube,and
- the drawing speed.
You can learn of these factors in the seminar on tube
sinking.
The phenomena of skidding, (bamboo marks or
stick-slip) and its relation to the above parameters is also treated in
the seminar on tube
making. During this seminar we also present the software for the
treatment of the process of tube sinking, and the guidelines
(experimental and numerical) of the plug design.
Question:
What is hydrodynamic lubrication?
Can hydrodynamic lubrication occur between the tube and the plug during
tube drawing?
Answer:
When a very thin film of fluid separates the workpiece
from the tool and there is practically no metal to metal contact between
them, then hydrodynamic lubrication prevails. Such a phenomena can be
established when the pressure at the entry zone between the plug and the
tube is high. (see eddy flow
in the entrapped lubricant). Eddy flow occurs because any liquid that
contacts the surface of a solid (metal) will adhere to that
surface at the first molecular depth, as elaborated in the next
paragraph.
When a liquid is in contact with a solid (metal) the
liquid adheres to the surface of the solid and the first layer of liquid
clings to the surface and moves with it. Thus, in our description the
liquid that touches the tube moves with the tube at the speed of the
drawn tube. Because the plug is stationary, the liquid that touches it
becomes stationary itself. The profile of the speed of the liquid in the
gap between the tube and the plug is undergoing a reversal as the point
of contact between the plug and the tube is reached. A pressure is
generated by the reversal of the direction of the flow of the lubricant.
When the pressure is high enough the point of contact gets closer to the
exit of the tube and the lubricant will create a gap between the plug
and the tube and escape through this gap.
The factors that
promote higher pressure and therefore hydrodynamic lubrication are:
- high drawing speed and therefore high lubricant velocity,
- high lubricant viscosity,
- smaller die and plug angles,
- smaller gap between the larger plug body diameter the tube,
- longer plug body, and
- the diameter and length of the Nib.
The effect of the reservoir of lubricant piling at the entry side of
the plug is somewhat complex. On the one hand this reservoir supplies
the liquid that enters the gap and produces the eddy flow and pressure
of the entrapped lubricant in the wedge, which affect the hydrodynamic
phenomena. On the other hand this liquid mass at the back of the plug
produces a seal between the plug and the tube on their contact conical
surface. Too much liquid may not only prevent liquid from escaping but
under critical conditions (of small diameter plug body) may push the
plug to escape. (A phenomena called "swallowing".)
The relations between the position of the plug and the independent
process parameters are discussed in Chapter 9 of the "Handbook
of Metalforming Processes".
The nature of the
contribution of the diameter and length of the body of the plug, in
combination with the viscosity of the lubricant, and the geometry of the
enclosed entrapped lube between the plug and the tube will be introduced
in the upcoming seminar on tube
making. The phenomena of skidding, (bamboo marks or stick-slip) and
its relations to the parameters above and to speed, is also treated in
the seminar on tube
making.
Question:
How useful is it to assist the
tube drawing process with the application of ultrasonic
vibrations?
Answer:
The application of ultrasonic vibration was attempted 30
to 40 years ago with great enthusiasm. It was applied as a panacea,
without discrimination, to any situation. In most of the cases it was
found ineffective and a nuisance. These failures caused to the
disapproval of the process, even when it could have been helpful.
To understand the possibilities one should be aware of a few
facts.
- Ultrasonic equipment is limited in the energy it can
deliver. It might only reach up to 10% of the power that the
motor of the bull block delivers at a steady state drawing speed.
- Although at steady state speeds the power supplied by the
ultrasonic equipment may be negligible, at start up lower
speed this power may accede the power supplied by the bull block.
- At start-up the friction is higher than at steady state speeds.
- If the tube breaks at start-up, or stick-slip occurs at
start-up, and no other solution is found, it makes sense to
explore the use of ultrasonic vibrations. The introduction of
ultrasonic vibrations will reduce the friction at start-up,
and therefore will reduce the drawing force, the vibrations,
and tearing at start-up.
Question:
When is it useful to replace a
single die with a double or triple die pass for tube sinking (or wire
drawing) in a single draw?
Answer:
The assumption is made in this evaluation that the
drawing is performed by a single set of tongs. In the first alternative
the entire reduction is performed through a single die. The second
alternative is that the same total reduction is performed through two or
three dies arranged in tandem (one after the other). Each die causes a
smaller reduction, while the pulling is applied at the exit from the die
box. Note that as an alternative to the employment of multi-dies, one
can always consider replacing a single die with more stations with
several dies and a pull at the exit from each die, at higher production
costs.
SUMMARY
We will use analytical
simulation models to determine the optimal die angle and the drawing
stress for wire and for tube drawing through a single die and through
tandem dies. By comparing the drawing stress we will determine whether
or not the use of multiple dies in tandem actually reduces the load.
For tube sinking we will also observe the effect of these choices on the
final wall thickness. We will provide the procedures for the
determination, but first we will present the summary and
conclusions.
Wire
Drawing The relative drawing stress
(sxf/so) and the values of the optimal semi-cone
angle of the die (aopt), as functions of the
independent input parameters as they are determined by Eq. (3.1) of the
"Handbook
of Metalforming Processes" are presented in Table
1. Friction factor (m), percent reduction in area
(r%), and size ratio
(Ro/Rf) are the input parameters
and they are also displayed in Table 1.
In general the drawing stress increases when
multiple dies replace a single die. See details by clicking here to Appendix. 1.
FIGURE<2>
[ 108k]
TubeSinking
The relative drawing stress
(sxf/so) and the wall thickening
ratio of the emerging tube
(tf/to) as functions of the input
parameters of the process (as determined by Eq. (9.3) of the "Handbook
of Metalforming Processes") are presented in Table 2.
In general, during tube sinking, as in wire
drawing, the drawing stress increases when multiple dies replace a
single die.
However, the range of control over the emerging wall
thickness can be expanded by selecting a multi-die arrangement. During
tube sinking the wall thickness of the emerging tube is a function of:
Reduction Ratio (Ro/Rof), Die
Angle (a), Initial Wall
Thickness (to/Ro) and Friction
(m). The emerging wall thickness as a function of
reduction is described next. Starting with
Ro/Rof=1 and increasing this
ratio, tf/to will initially
increase monotonously, reach a peak and then commence to decrease with
further increases in Ro/Rof . See
section (9.4.3.3) of the "Handbook
of Metalforming Processes".
The emerging wall thickness may decrease or increase
slightly depending on the choice of the parameters listed above. Common
knowledge suggests that, in the range of reasonably high reductions, if
a reduction through a single die is too high, the emerging wall
thickness gets thinner. By replacing the single large reduction with a
pair of dies with a smaller reduction in each die, a final thicker wall
can be produced. Such a measure penalizes the economy and introduces an
extra processing step. With the introduction of multi-dies in a single
die box, this extra step is circumvented.
If the required wall thickness is higher than
that which can be made in a pass through a single die, then a slightly
heavier wall thickness can result in the use of multi-dies, but the wall
will never be as thick as the one you can get by sinking through two
stations. See details by clicking here
to Appendix. 2.
FIGURE<3 >[ 126k]
APPENDIX 1 WIRE DRAWING
TABLE 1. SINGLE DIE VS.
MULTI DIES WIRE DRAWING
(Total Percent Reduction in Area, r% = 35%)
| | A |
B | C |
D | E |
F | G |
| 1 |
Dies | Friction
factor
m
| r%
per
Die
|
Ro/Rf | Die Semi
Cone
Angle in
degrees
| Partial
Drawing
Stress
| Total
Drawing
Stress
|
| 2 | 1 Die |
0.05 | 35.000 | 1.240 |
7.277 | 0.626 | 0.626 |
| 3 | | |
| | | |
|
| 4 | 1st of 2 | 0.05 |
19.354 | 1.114 | 5.146 | 0.353 |
0.353 |
| 5 | 2nd of 2 | 0.05 |
19.354 | 1.114 | 5.146 | 0.353 |
0.706 |
| 6 | 2nd of 2 | 0.03 |
19.354 | 1.114 | 3.986 | 0.322 |
0.675 |
| 7 | | |
| | | |
|
| 8 | 1st of 3 | 0.05 |
13.360 | 1.074 | 4.200 | 0.256 |
0.256 |
| 9 | 2nd of 3 | 0.05 |
13.360 | 1.074 | 4.200 | 0.256 |
0.512 |
| 10 | 3rd of 3 | 0.05 |
13.360 | 1.074 | 4.200 | 0.256 |
0.768 |
| 11 | | |
| | | |
|
| 12 | 1 Die | 0.20 |
35.000 | 1.240 | 14.550 | 0.820 |
0.820 |
| 13 | | |
| | | |
|
| 14 | 1st of 2 | 0.20 |
19.354 | 1.114 | 10.310 | 0.491 |
0.491 |
| 15 | 2nd of 2 | 0.03 |
19.354 | 1.114 | 3.990 | 0.322 |
0.813 |
| 16 | | |
| | | |
|
| 17 | | |
| | | |
|
| 18 | 1st of 3 | 0.20 |
13.360 | 1.074 | 8.385 | 0.256 |
0.369 |
| 19 | 2nd of 3 | 0.03 |
13.360 | 1.074 | 3.247 | 0.231 |
0.487 |
| 20 | 3rd of 3 | 0.03 |
13.360 | 1.074 | 3.247 | 0.231 |
0.718 |
| 21 | | |
| | | |
|
The columns in Table 1 represent the parameters as follows:
- Column A
- Displays the number of dies in the die box, i.e., 1, 2 or 3.
-
- Column B
- Displays the value of the friction factor (m).
-
- Column C
- Displays the percent reduction in area affected (r%).
-
- Column D
- Displays the ratio between the incoming and exiting
(Ro/Rf) wire size for each die.
Note that for multiple die use we intentionally distributed the load
between the dies evenly.
-
- Column E
- Displays the choice
of the die angle for each die. To make a fair comparison between single
and multiple die draws we will choose the optimal die angle for each
die. The optimal die angle is that angle which minimizes the drawing
force for each die (as treated in Section 3.6.2 of Ref. 3 of Books
in the reference list).
-
- Column F
- The partial
stress, displays the component of the relative drawing stress required
to overcome the resistance occurring through the respective die. The
relative drawing stress is the ratio of the drawing stress to the
strength of the wire (sxf/so).
-
- Column G
- The total relative drawing stress, displays the relative drawing
stress at the exit from the last die. The drawing stress experienced
at the exit from a previous die becomes an Intermediate tension existing
between two subsequent dies. Thus the stress load to pull the wire
through the subsequent die is the sum of the partial stress load to draw
through the die plus the back tensile stress imposed by the pull through
the previous die. See the "Handbook
of Metalforming Processes".
The calculations are presented in the next section. As
clearly demonstrated, the optimal die angle monotonously decreases with
decrease in reduction and in friction.
In lines 2-10 of Table 1
we compare statistics of drawing with a total reduction of 35% and
friction value of m = 0.05, for a single die (line 2)
against multiple dies (lines 4, 5, and 8-10). In this output, for a
constant low friction value, we observe that a single die requires lower
drawing stress. Even if the friction for the second die (line 6) is
lower (m= 0.03), a single die is favored. However,
lines 12 to 20, demonstrate that if drawing through a single die results
in excessively high friction, and if intermediate lubrication
dramatically improves the lubricity, then multiple dies show significant
improvement over a single die draw.
Part of the original question was:
When is
it useful to replace a single die with a double or triple die pass for
wire drawing?
If there are no serious lubrication problems that can't
be handled otherwise, and if the lubricant is not wiped off the surface
of the wire before the wire reaches the exit from the die, then the
drawing force with a single die is lower than for a multi-die
arrangement. However, one justification for the use of multi-dies, may
be the more effective application of the lubricant through the portal
between subsequent dies. At that intermediate point the tension in the
wire (causing lower pressure between the wire and the die), and the
higher speed of the wire, both promote better lubrication. If we assume
in the two die arrangement that the friction through the single die and
through the first die of a double die arrangement is m=
0.2, and through the second die of a double die arrangement is
m= 0.03, then the use of double die makes more sense.
The calculations for triple die will lead to the same observation.
It is very rare that a multi-die arrangement is required
to improve the lubrication. Better lubricants and lubrication systems
can provide lower friction with a single die. (Please see the question on Hydrodynamic lubrication)
The calculations for the relative drawing stress can be
performed when the friction values (m) are determined
experimentally. The procedure for the measurement of friction is
described in Chapter 3 of the "Handbook
of Metalforming Processes", and in the following
pages of this web site.
During our numerous visits to wire
making facilities we did not find many applications of multi-die
arrangements. When we found it, it was not always clear to the present
staff why the multi-dies where originally installed. Even when benefits
were demonstrated, it was not always explained convincingly. I am sure
that a few readers of this present appraisal can shed much more light on
the concept. If you are willing, I ask that you forward to me at <avitzur@metalforming-inc.com>
any information on the subject. I cannot open a conversation box, but
if you will indicate your preference I will consider providing your
comments with acknowledgement.
Treatment of the Analytical Simulation for Wire
Drawing
SINGLE DIE
As a typical example we will consider a 35% total reduction in area,
(r% = 35%),
with assumed friction value of
m = 0.05
The ratio of the initial (Ro) to final
(Rf) size of the rod,
(Ro/Rf) is:
Ro/Rf =
1/SQRT[1-(r%/100)]
For 35% reduction in area
Ro/Rf = 1.24
We will select the die angle by calculating the appropriate optimal
die angle, which minimizes the drawing force for the prevailing reduction and
friction values.
Optimal Die Angle (aopt)
(see Section 3.6.2 of Ref. 3 of Books
in the reference list)
The optimal die angle in degrees can be approximated directly by
the equation:
aopt =
(180/3.1416)*SQRT[(3/2)*m*ln(Ro/Rf)]
For 35% reduction in area and friction value of:
m = 0.05
aopt = 7.277
degrees
Relative Drawing Stress
(sxf/so)
(The ratio of the drawing stress (sxf) to the flow strength (so) of the rod)
The relative drawing stress for flow through conical converging dies
is calculated by Eq. (3.1) of the "Handbook
of Metalforming Processes".
The Relative Drawing Stress becomes
sxf/so = 0.626
The procedures and equations to determine the die angle and the
drawing stress as functions of reduction, friction, flow strength of the
wire, etc. are provided in Chapter 3 of the "Handbook
of Metalforming Processes", in many of the papers listed in the
reference
list, and presented in Seminars,
and a user-friendly software package called "
Flowthru".
MULTI DIES IN
TANDEM
For the same total reduction as above (r% = 35%), 2
or 3 dies in tandem are placed to affect this total reduction in smaller
reductions per die. If identical reductions are made in each of the
individual dies, and the exit sizes from the first and second die
are R1 and R2
respectively, then:
For two dies: Ro/R1 =
R1/Rf =
(Ro/Rf)1/2 = 1.11355
Percent Reduction in Area is r% =
100[1-(Rf/Ro)2] = 19.3544
The optimal die angle for both dies is:
aopt =
(180/3.1416)*SQRT[(3/2)*m*ln(Ro/R1)] = 5.146 degrees
The relative drawing stress for drawing through the first die, as
calculated by Eq.(3.1) of the Handbook is: sxf/so = 0.353
The relative drawing stress for drawing through the second die, as
calculated by Eq.(3.1) of the Handbook is: sxf/so = 0.706
Please note that the drawing stress from the second die is due to the
back tension exerted by the need to draw through the first die plus the
resistance to the draw through the second die.
For Three dies:
Ro/R1 =
R1/R2 = R2/Rf =
(Ro/Rf)(1/3) = 1.074333
Percent Reduction in Area is: r% = 100[1-
(Rf/Ro)2] = 13.36
The optimal die angle for all three dies is:
aopt =
(180/3.1416)*SQRT[(3/2)*m*ln(Ro/R1)] = 4.2 degrees
The relative drawing stress for drawing through the
first die, as calculated by Eq.(3.1) of the Handbook is: sxf/so = 0.256
The relative drawing stress for drawing through the second die, as
calculated by Eq.(3.1) of the Handbook is: sxf/sxf = 0.512, and through the
third die is: sxf/so = 0.768.
Please note that the smaller the reduction per die, with the same
friction value (m) , the smaller is the optimal die
angle. Nevertheless, the larger the number of dies in tandem, the higher
is the total drawing stress (and force) applied at the tongs.
APPENDIX 2. TUBE SINKING
TABLE 2. SINGLE DIE VS.
MULTIPLE DIES TUBE SINKING
(In Table 2 the Friction Factor is m = 0.05)
| |
A |
B |
C |
D |
E |
F |
G |
H |
I |
J |
| 1 | Dies |
Rof/Ro | Die
Semi
Cone
Angle
|
to/Ro |
Ri/Ro |
tf/Rof |
Rif/Rof | Partial
tf/to
|
Total
tf/to
|
Total
Drawing
Stress
|
| 2 | |
| | |
| | |
| | |
| 3 | 1 Die |
0.800 | 8.50 | 0.100 | 0.900 |
0.12407 | 0.87594 | 0.99252 | 0.99252 |
0.82351 |
| 4 | | |
| | | |
| | | |
| 5 |
1st of 2 | 0.894 | 8.50 | 0.100 |
0.900 | 0.11347 | 0.88653 | 1.01490 |
1.01490 | 0.46888 |
| 6 | 2nd of 2 | 0.894 |
3.50 | 0.113 | 0.887 | 0.12413 |
0.87587 | 0.97850 | 0.99308 | 1.11315 |
| 7 |
| | | |
| | | |
| |
| 8 | 1 Die | 0.800 |
8.25 | 0.200 | 0.800 | 0.25312 |
0.74687 | 1.01250 | 1.01250 | 0.61641 |
| 9 |
| | | |
| | | |
| |
| 10 | 1st of 2 |
0.894 | 8.00 | 0.200 | 0.800 |
0.22810 | 0.77190 | 1.02010 | 1.02010 |
0.37546 |
| 11 |
2nd of 2 | 0.894 | 3.30 | 0.228 |
0.772 | 0.25403 | 0.74597 | 0.99610 |
1.01612 | 0.80747 |
| 12 | |
| | | |
| | | |
|
| 13 | 1 Die | 0.800 |
6.00 | 0.200 | 0.800 | 0.25274 |
0.74726 | 1.01096 | 1.01096 | 0.66252 |
| 14 |
| 0.800 | 8.00 | 0.200 |
0.800 | 0.25311 | 0.74689 | 1.01245 |
1.01245 | 0.61898 |
| 15 |
| 0.800 | 10.00 | 0.200 |
0.800 | 0.25288 | 0.74712 | 1.01152 |
1.01152 | 0.60957 |
| 16 |
| 0.800 | 8.25 | 0.200 |
0.800 | 0.25312 | 0.74687 | 1.01250 |
1.01250 | 0.61641 |
| 17 | |
| | | |
| | | |
|
In Table 2 the optimal die angle, the relative exit wall
thickness and the drawing stress for tube sinking through a single die
and through tandem dies are determined for typical examples. By
comparing the options we can study the effect of these choices and get
better control of the exit wall thickness.
The columns in Table 2 represent the parameters as follows:
- Column A
- Displays the number of dies in the die box,i.e., 1, 2,
or 3.
-
- Column B
- Displays the ratio of the emerging to
incoming outer radius of the tube as a measure of the severity of the
reduction.
-
- Column C
- Displays the semicone angle of the die.
-
- Column D
- Displays the relative thickness of the incoming(mother tube).
-
- Column E
- Displays the inner to outer size ratio of the incoming tube.
-
- Column F
- Displays the relative thickness of the emerging tube.
-
- Column G
- Displays the inner to outer size ratio of the emerging tube.
-
- Column H
- Displays the emerging to incoming wall
thickness ratio as calculated from Eq. (9.3) for the individual die.
-
- Column I
- Displays the ratio of the emerging wall
thickness for the specific die to the original incoming wall thickness
of the mother tube.
-
- Column J
- Displays the calculated
relative drawing stress at the exit from the specific die, i.e.,first,
second or subsequent die.
All the data in Table 2 assumes a
friction value of m = 0.05.
Line 3 treats data for a typical single die drawing
where the output is: (tf/to),
and total relative drawing stress (sxf/so). The choice of the
8.5o semicone angle of the die maximizes the emerging wall
thickness for this specific pass.
Lines 5 & 6 treat data for a typical two die pass
through a single die box. Here we distribute evenly the load between the
two dies, so that we obtain the same total reduction as in line 3. Note
that for the second die the optimal die angle is much smaller. The
emerging wall thickness for two dies
(tf/to = 0.99308) is slightly
larger than for a single die
(tf/to = 0.99252). However, we
pay the penalty of higher drawing stress.
In the next three lines(8,10 & 11) we display data for a
thicker tube with similar results, i.e., two dies provide thicker
relative emerging wall thickness and higher drawing stress.
The last group of lines demonstrate how to determine the
optimal die angle. To make a fair comparison between single and
multiple-die draws we choose the optimal die angle for each die. The
optimal die angle here is that angle which maximizes the thickness of
the emerging tube as treated by Eq. 9.3 of Ref. 3 of Books
listed in the reference.
The relative drawing stress (column J) is the ratio of
the drawing stress to the flow strength of the tube (sxf/so). When back tension
prevails at the entrance to the die, then column J, accounts for it.
The drawing stress experienced at the exit from a previous die becomes
an intermediate tension existing between the previous and the subsequent
dies. Thus the stress load to pull the wire through the subsequent die
is the sum of the partial stress load to draw through the die plus the
back tensile stress imposed by the drag through the previous die.
Part of the original question was:
When is it useful
to replace a single die with a double or triple die pass for tube
sinking?
A partial answer is that two dies provide an
added control of the emerging wall thickness
If there are no serious lubrication problems that cannot
be handled otherwise, and if the lubricant is not wiped off the surface
of the tube before the tube reaches the exit from the die, then the
drawing force with a single die is lower than for the multi-dies
arrangement. However, one justification for the use of multi-dies, may
be the more effective application of the lubricant through the portal
between subsequent dies. At that intermediate point the tension in the
tube (causing lower pressure between the tube and the die) and the
higher speed of the tube both promote better lubrication.
The calculations for the relative drawing stress can be performed when the
friction values (m) are determined experimentally. The
procedure for the measurement of friction during wire drawing is
described in Chapter 3 of the "Handbook
of Metalforming Processes", and in the following
pages of this web site. However the values of friction
(m) as determined expermentally for wire drawing may be
unreliable when applied for tube. Experimental determination of the
friction value for tube sinking is much more complex.
During our many visits to tube making facilities we found only
sparse applications of multi-dies arrangements. But the practice is
more popular than in the wire industry. It was not always clear to
the prsent staff why the multi-dies where originally installed. Even
when benefits were demonstrated it was not always explained
convincingly. I am sure that a few readers of this present appraisal
can shed much more light on the concept. If you are willing, I ask
that you forward to me at <avitzur@metalforming-inc.com>
any information on the subject. I cannot open a conversation box, but
if you will indicate your preference I will consider providing your
comments with acknowledgement.(Please see FIGURE<3>
and Table 2.)
Treatment of the Analytical Simulation for Tube
Sinking
We will use the simulation model for tube sinking, as
presented by Eq. (9.3) of the "Handbook
of Metalforming Processes", in many of the papers listed in the
reference
list, and presented in Seminars,
and a user-friendly software package called "TubeSink"
.
Equation (9.3) provides the relative drawing stress (sxf/so ) as a function of the
following input parameters:
- (Ro/Rof) the ratio of
incoming to exit tube outer radius (Diameter/2).
- (a) the semi-cone angle of the die.
- (m) the friction factor.
- (sxb/so) the relative back tension.
- (to/Ro) the
incoming relative wall thickness of the tube.
Thus, symbolically:
sxf/so =
f(Ro/Rof, a , m, sxb/so,
to/Ro,and
tf/to)
The relative wall thickness at the exit
(tf/to) is a unique parameter. We
treat it temporarily as an input (independent) parameter,and then
subject it to the process of optimization, after which it becomes a
dependent parameter. Through an optimization procedure this expression
is utilized in the determination of the following dependent parameters:
sxf/so
,tf/to and aopt , as functions of
Ro/Rof,
to/Ro, a, m, and sxb/so.
The maximum possible
reduction is determined by setting a limit on the permissible drawing
stress (sxf/so). The treatment of this
complex procedure is available by a software package called
"TubeSink ", as presented in our Seminars.
Question:
What is the concept of wet wire
drawing?
Answer:
To be completed at a later date.
Question:
How important is the wire (or
tube) alignments on either side of the die during wire (or tube)
drawing?
Answer:
To be completed at a later date.
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