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Extrusion
Introduction
An extruder is a common machine in industry, not only used in extrusion operations, but
also used in molding operations, such as injection molding and blow molding. In plastic
industry, the screw extruder is the most common.
Figure 1. The extruder.
What Happens in an Extruder?
The screw in the extruder will rotate and develop sufficient pressure to force material to
go through die and produce products with different geometries.
Components of an Extruder
There are five main components of an extruder: screw, extruder drive, barrel, feed hopper,
die. The helical structured extruder screw is the heart of an extruder, which includes
transport, heating, melting and mixing functions for plastic. An extruder drive, an
electrical motor, supplies power to rotate the screw. The stability and quality of products
is highly dependent of the design of the screw. The extruder barrel is outside the screw
providing heating and cooling capabilities. There is a feed throat connect feed hopper and
barrel. The feed hopper is designed to hold the plastic pellets, and allows plastic pellets
flow into the barrel steadily. The die is placed at the end of the extruder, and can
determine the shape of the product. Different types of dies are: tubing die, flat film dies,
feeding zone melting, mixing & pumping zone
mixing & pumping zone
air
tube die
blown film dies, etc. In this lab, we are using an annular structured tubing die. Note that
the size and shape of the extruded products will not be exactly the same as the size and
shape of the die, because of several reasons: draw down, cooling, swelling and relaxation.
Figure 2. The cross section of the die for tubes.
Extrusion Lines
For a complete extrusion process, in addition to extruder, upstream and downstream
equipment is needed to produce useful products. The main equipment of an extrusion line
is resin handling, drying system, extruder, post-shaping or calibrating device, cooling
device, take-up device, and cutter or saw. The extrusion line in this lab includes extruder,
take-off roller and cooling water trough, which are shown in Figure 3.
Figure 3. The extrusion line in this lab, including extruder, take-off roller and cooling
water trough.
Extruder
Air
Cooling water trough
Take-off roller
Objectives for Extrusion
1. Determine the material volumetric feeding rates based on different screw rotating
speed (ω).
2. Find the tube dimensions based on different screw rotating speeds (ω), different take-
off speeds (vt) and different pressure differences (pi).
3. Compare the experiment data with theoretical prediction.
Proposed Goals
1. Run the equipment and determine the volumetric feeding rates based on different
screw rotating speeds. Plot the volumetric feeding rate versus screw rotating speed.
Refer “Investigation of the Thickness (θ) of Tube with Different Screw Rotating
Speeds (ω)” in Experimental Procedures.
2. Plot the tube thickness versus screw rotating speed (ω), take-off speed (vt) and
pressure difference (pi).
Refer “Investigation of the Thickness (θ) of Tube with Different Screw Rotating
Speeds (ω)”, “Investigation of the Thickness (θ) of Tube with Different Take-Off
Speeds (vt)” and “Investigation of the Thickness (θ) of Tube with Different Pressure
Differences (pi)” in Experimental Procedures, respectively.
Figure 4. Scheme of control variables in this experiment, where ω is the screw rotating
speed, vt is the take-off speed of the roller and pi is the internal air pressure.
Motor Screw Motor
Output material
Take-off speed
(vt)
Die
Internal air pressure
(pi) Hopper
Screw rotating speed
(ω)
Theory
Theoretical Background
In this lab, we are going to use an annular structured tubing die to produce tubes in
different dimensions. When a polymer melt is extruded through an annular die and
stretched under tension to a desired diameter, a hollow tube can be made. Although the
overall process that involves die swell followed by draw down (or stretching) is rather
complicated as indicated in Figure 5, analytic understanding of the process can be made
under some simplifying assumptions.
Figure 5. The diagram for analyzing polymer flow through the die.
z=0
u = (u, w)
z=L
die exit
die swell zone
r
z
r = Ro(z)
r = Ri(z)
draw down region
F, wL
In Figure 5., r and z are the radial and axial direction, respectively. Ro(z) and Ri(z) are the
outer and inner radius at different z position, respectively. The polymer flowing velocity
is defined as u, which including r-direction velocity u and z-direction velocity w.
When a polymer melt flows out of the die exit, “die swell” occurs in that the polymer
melt expands in the radial direction (i.e., swells) due to residual stress in the melt. Die
swell is a very complicated phenomenon because it depends on the strain history (i.e.,
memory effect) in the die as well as the rheological properties (both viscous and
viscoelastic) of the melt. Thus, prediction of it is very difficult. The die swell, however, is
restricted to a very short region near the die exit and an analytic progress can be made by
simply neglecting the die swell region and focusing on the draw-down region.
The simplifying assumptions for the current analysis are
a) Isothermal and axisymmetric flow
b) Length of the draw-down region (L) is much longer than the radius of the exit hole of
the die
c) Viscous force is dominant and the viscoelastic force, inertia, gravity and surface
tension are negligible.
d) Newtonian fluid
Although polymer melts are non-Newtonian and the viscoelasticity effects are often
important, the current flow of interest is weakly extensional and slow. Furthermore, the
shear strain is also very weak throughout the entire draw-down region for this free
surface problem. Thus, the Newtonian assumption is not too restrictive. Considering that
the viscosity of polymer melts are quite high, assumption (c) is also not very restrictive.
As the draw-down region is typically exposed to the air, the temperature may decrease as
it flows down due to the cooling by air. However, the temperature variation may not be
very large unless air is blown against the polymer melt for forced convective cooling.
We consider the cylindrical coordinates while determining the variables in the extruder
process. Figure 6. is the figure of a standard cylindrical system.
Figure 6. Standard cylindrical coordinate
Governing Equations
Under the assumptions ((a)~(d)), the governing equations, continuity equation and the r-
and z-directional momentum equation, for the flow in the draw-down region are as
follows:
1
r
¶
¶rru( ) +
¶w
¶z= 0 (1)
2
21
z
uru
rrrr
p
(2)
2
21
z
w
r
wr
rrz
p
(3)
As indicated in Figure 5, u and w are the r- and z-directional component of the velocity
vector u. Ro(z) and Ri(z) are the position of the outer and the inner surface of the tube
that should be also determined as the solution along with u, w and p for this free surface
problem.
The boundary conditions at the two free surfaces are follows,
At r = Ro(z),
0
w
z
Ru
o (4)
012
2
r
w
z
u
z
R
z
w
r
u
z
R oo
(5)
z
w
z
R
r
w
z
u
z
R
r
u
z
R
poo
o
2
2
1
2
(6)
At r = Ri(z),
0
w
z
Ru
i (7)
012
2
r
w
z
u
z
R
z
w
r
u
z
R ii
(8)
z
w
z
R
r
w
z
u
z
R
r
u
z
R
ppii
i
i
2
2
1
2
(9)
Here (4) and (7) are the kinematic conditions, (5) and (8) the tangential stress balances,
and (6) and (9) are the normal stress balances at the outer and the inner surfaces of the
tube. In (9), pi is the pressure inside the tube (i.e., internal pressure) that can be
controlled. That is, the inner (hence the outer) radius can be controlled by varying the
internal pressure when other conditions are fixed.
At z = 0,
oooii wwrRrR ,, (10)
At z = L,
Lww (11)
Here wo is the average velocity in the axial direction that is determined once the output
flow rate and the die geometry (i.e., ri and ro) are specified. the axial velocity at z = L
(i.e., position the fiber is quenched or solidified instantaneously). wL is also known as the
take-up velocity (vt) that is controlled by the take-up device.
With boundary conditions occur at r = Ro(z), r = Ri(z), z = 0 and z = L, the inner and
outer surface profile can be determined as follows.
2/1
2
22
)(
))(1(exp
)(/)1()(
i
i
iii
rzw
zwp
zwrrzR
(12)
2/12
2
)(
)1()()(
zw
rzRzR
iio
(13)
zzw exp)(
(14)
o
L
w
wln
(15)
where ri and ro are known as the die geometry factors (i.e., inner and outer diameters of
exit of the die), wo is output rate at die exit and wL is the take-off velocity.
Sample Calculations
Figure 7 through 9 provide the theoretical predictions given by the equations (12) through
(15) for the following conditions:
the outer radius of the die, ro : 2.788 mm (7/32” diameter)
the inner radius of the die, ri : 1.588 mm (1/8” diameter)
draw span, L : 50 cm
viscosity, : 1000 Pa-s
density, : 0.92 g/cm3
mass flow rate, m : 50 g/min
take-up speed, w(L) : 40 cm/s
internal pressure, pi : 0 ~60 Pa
Figure 7. Dimensionless axial velocity
(a) (b)
(c) (d)
Figure 8. Variation of inner and outer radius of the tube at various internal pressure
0.0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
0.0 0.2 0.4 0.6 0.8 1.0
W(z)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
z
pi = 0 Pa
Ro(z)
Ri(z)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
z
pi = 20 Pa
Ro(z)
Ri(z)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
z
pi = 40 Pa
Ro(z)
Ri(z)
0.0
0.2
0.4
0.6
0.8
1.0
0.0 0.2 0.4 0.6 0.8 1.0
z
pi = 60 Pa
Ro(z)
Ri(z)
Figure 9. Variation of inner to outer radius ratio for various internal pressure
Operating Procedures
General Operations
Start Up
Figure 10. The control panel of the extrusion system.
0.5
0.6
0.7
0.0 0.2 0.4 0.6 0.8 1.0
Ri(z)/Ro(z)
pi = 0 Pa
pi = 60 Pa(increasing pi)
Die
15 rpm
325 ℉
Zone 3 Zone 2 Zone 1
Off On Off Auto On Off Auto On Off Auto On
Stop Start
Motor
Thermal meter
for each zone
Ammeter for
each zone
Screw rotating speed
Present temp. of die Motor speed
controller
SD S3 S2 S1
TD T3 T2 T1
1. Switch the main power from “OFF” to “ON”.
2. Turn the heating switches of Zone 1 (S1), Zone 2 (S2) and Zone 3 (S3) to “Auto.” Turn
the heating switch of Die (SD) to “On.”
3. Adjust the temperature of each zone to the desired temperature. (Goal temperature
depends on the material we are using. For DYNH-1, the goal temperature T1=250°F
T2=280°F, T3=280°F and TD=280°F)
WARNING: EVERY PART OF THE EQUIPMENT IS EXTREMLY HOT. DON’T
TOUCH IT.
4. Wait until green light is displayed on every thermal meter, and check that the “present
temperature of die” is the same as the goal temperature.
5. Wait for another 15 minutes to make sure the temperature of die indeed reaches the
goal temperature.
WARNING: EXTREMELY HOT POLYMER MAY SHOOT OUT AND
SERIOUSLY HURT PEOPLE IF YOU FORGET TO WAIT ANOTHER 15
MINUTES BEFORE STARTING.
6. The equipment is ready to start.
7. Place a water bath under die to cool down the output material.
8. Make sure there are enough DYNH-1 beads in hopper.
9. Press green “Start” button on the control panel.
WARNING: NEVER STAND IN FRONT OF DIE SECTION AFTER START.
10. Slowly adjust the motor speed to make the screw rotate at a certain speed. (Stand
behind the motor, you can see the screw rotation direction is counter-clockwise.)
11. Open the air valve.
12. Introduce air into the die to provide a certain internal pressure (pi).
13. Open the feed gate of hopper to introduce DYNH-1 beads into barrel.
Shut Down
1. Close the feed gate of hopper.
2. Let the screw run until barrel is empty, which means there is no more material going
out.
3. Slowly adjust the motor speed to zero.
4. Press red “Stop” button on the control panel.
5. Turn off the switches of Zone 1 (S1), Zone 2 (S2) and Zone 3 (S3) and Die (SD) to
“Off.”
6. Switch the main power to “OFF.”
7. Place the warning board near die section.
WARNING: EVERY PART OF THE EQUIPMENT IS STILL EXTREMLY HOT.
DON’T TOUCH IT.
Experimental Procedures
In this experiment, different dimensions of tube will be obtained by changing three
variables: screw rotation speed (ω), take-off speed (vt) and internal pressure (pi).
Do (Ro) and m can be measured. Based on the conservation of mass shown as follows, Di
(Ri) can be calculated.
mvDD
tio
22
4 (16)
where Do is the outer diameter of tube, which can be measured; ρ is the density of the
material used in this experiment, which is DYNH-1, and m is the mass feeding rate,
which is related to the screw rotation speed.
NOTE: You can time and collect tube. Then, Weigh the rod and get the mass feeding
rate. Furthermore, divide the mass feeding rate by density of DYNH-1, and volumetric
feeding rate can be obtained.
Then, the thickness of the tube can be easily obtained.
θ = 𝑅𝑜 − 𝑅𝑖 (17)
These are the experimental dimensions of tube. By comparing experimental data with
theoretical prediction, you can find out how the model works.
Investigation of the Thickness of Tube with Different Screw Rotating Speeds
1. Develop a table as follows:
Table 1. Table for the dimensions of the tube with different screw rotating speeds,
different take-off speeds and different pressure differences.
ω
(rpm)
vt
(m/s)
pi
(psi)
m
(kg/min)
V
(m3/min)
wo
(m/s)
Ro
(mm)
Ri
(mm)
θ
(mm)
SECTION 1
Run 1 ω ○1 vt ○1 pi ○1
Run 2 ω ○2 vt ○1 pi ○1
Run 3 ω ○3 vt ○1 pi ○1
Run 4 ω ○4 vt ○1 pi ○1
Run 5 ω ○5 vt ○1 pi ○1
SECTION 2
Run 1 ω ○3 vt ○1 pi ○1
Run 2 ω ○3 vt ○2 pi ○1
Run 3 ω ○3 vt ○3 pi ○1
Run 4 ω ○3 vt ○4 pi ○1
Run 5 ω ○3 vt ○5 pi ○1
SECTION 3
Run 1 ω ○3 vt ○3 pi ○1
Run 2 ω ○3 vt ○3 pi ○2
Run 3 ω ○3 vt ○3 pi ○3
Run 4 ω ○3 vt ○3 pi ○4
Run 5 ω ○3 vt ○3 pi ○5
2. Fix the take-off speed, and slowly adjust motor speed to make the screw rotate at a
certain speed (rpm).
3. Record the pressure gauge of the die section.
4. Start to time and collect the tube.
5. Weigh the tube and get the mass feeding rate. Then, divide the mass feeding rate by
density of DYNH-1, and volumetric feeding rate can be obtained.
6. Calculate the output speed by dividing the volumetric feeding rate with cross area at
the exit of die.
7. Measure the outer diameter (Do) of the obtained tube to obtain outer radius (Ro).
8. Calculate the inner diameter (Di) from Eq. (16) to obtain inner radius (Ri).
9. Calculate the thickness (θ) from Eq. (17)
10. Repeat several different screw rotating speeds to finish section 1 in Table 1. (Choose
at least 5 different screw rotating speeds.)
11. Plot tube outer and inner radius versus screw rotating speed and versus theoretical
prediction.
(Note: the diagrams may or may not be linear.)
Investigation of the Thickness of Tube with Different Take-Off Speeds
1. Fix the screw rotating speed and internal pressure (pi), and adjust the take-off speed
(vt) to a certain value.
2. Record the pressure gauge of the die section.
3. Refer to the previous section to get the volumetric feeding rate at a specific screw
rotating speed (rpm).
4. Measure the outer diameter (Do) of the obtained tube to obtain outer radius (Ro).
5. Calculate the inner diameter (Di) to obtain inner radius (Ri) and thickness (θ) from
Eq. (16) and Eq. (17), respectively.
6. Repeat with several different take-off speeds to finish section 2 in Table 1. (Choose at
least 5 different take-off speeds.)
7. Plot tube outer and inner radius versus take-off speed and versus theoretical
prediction.
(Note: the diagrams may or may not be linear.)
Investigation of the Thickness of Tube with Different Pressure Differences
1. Fix the screw rotating speed and take-off speed, and adjust the internal pressure (pi) to
a certain value.
2. Record the pressure gauge of the die section.
3. Refer to the previous section to get the volumetric feeding rate at a specific screw
rotating speed (rpm).
4. Measure the outer diameter (Do) of the obtained tube to obtain outer radius (Ro).
5. Calculate the inner diameter (Di) to obtain inner radius (Ri) and thickness (θ) from
Eq. (16) and Eq. (17), respectively.
6. Repeat with several different internal pressures to finish section 3 in Table 1. (Choose
at least 5 different internal pressures.)
7. Plot tube outer and inner radius versus internal pressure and versus theoretical
prediction.
(Note: the diagrams may or may not be linear.)
Notations
u Velocity factor (m/s)
u r-directional component of the velocity vector u (m/s)
w z-directional component of the velocity vector u (m/s)
μ Viscosity of fluid (Pas)
wo Output speed at die exit (m/s)
wL Take-off speed (m/s)
ro Outer radius at die exit (mm)
ri Inner radius at die exit (mm)
Ro Outer radius of tube (mm)
Ri Inner radius of tube (mm)
pi Internal pressure (pa)
ω Screw rotating speed (rpm)
vt Take-off speed (m/s)
m Mass feeding rate of DYNH-1 (kg/min)
V Volumetric feeding rate of DYNH-1 (m3/min)
ρ Density of DYNH-1 (kg/m3)
Do Outer diameter of tube (mm)
Di Inner diameter of tube (mm)
θ Thickness of tube (mm)
Reference
Dr. Chang-Won Park, Extrusion of Hollow Tubes
Mark, H. F. (ed.), Encyclopedia of Polymer Science and Technology, Edition 3rd
., John
Wiley & Sons (2004) (Vol. 2)
Stanley Middleman, Fundamentals of Polymer Processing, McGraw Hill (1977)
