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Master's Theses
Student Research
1988
Evaluation of a computer simulation of the radiant
heat curing process for primary URD electrical
cable
Grover L. Stell
Follow this and additional works at: http://scholarship.richmond.edu/masters-theses
Part of the Business Administration, Management, and Operations Commons
Recommended Citation
Stell, Grover L., "Evaluation of a computer simulation of the radiant heat curing process for primary URD electrical cable" (1988).
Master's Theses. Paper 1047.
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3 3082 01027 9056
EVALUATION OF A COMPUTER SIMULATION OF
THE RADIANT HEAT CURING PROCESS FOR
PRIMARY ORD ELECTRICAL CABLE
An independent research project
submitted in partial fulfillment of
the requirements for the MBA degree
by
Grover L. Stell, Jr.
Executive MBA, Class Of 1988
University of Richmond
March 11, 1988
TABLE OF CONTENTS
.................................... 1
PRIMARY URD CABLE ..................... .......... 2
MODELLING THE PRODUCTION PROCESS ...... ......... 15
RESULTS ........ .. . ............................. 27
CONCLUSIONS .................................... 36
REFERENCES ... ... . .... ............. ............. 39
INTRODUCTION
Stell, 1988
INTRODUCTION
It
is
the
intent
of
this
paper
to
compare
predictions of an in-house developed computer model,
radiant heat curing process for plastic insulated
cable,
with
facility
data
and
gathered
from
actual
manufacturing plant.
product
trial~
both from
production
First,
in
temperatures
during
a
pilot
full
scale
background explanations of the
and chemical basis of the computer
discussed in some detail.
Then
the
model
are
The model predictions of
processing
are then
product
compared
to
results obtained during trials at the pilot facility.
degree
of
compared
cure data from actual plant
to
Finally,
accuracy
for
the
values generated by
conclusions
are
drawn
production
the
concerning
the
that
should
be
predictions is desired.
-1-
examined
if
the
Next,
runs . is
computer
of the model predictions and suggestions
areas
the
electrical
and the manufacturing process are given.
thermodynamic
of
in
a
the
model.
overall
are
improvement
made
in
Stell, 1988
PRIMARY URD CABLE
To get their product to the customer most companies -use
a
delivery
channel consisting of
manufacturers,
wholesalers,
various
retailers and
combinations
the
like.
of
The
delivery system for electricity utilizes electrical cables as
the
connection
customer.
between the manufacturing
Just
distribution
as
there
channels
for
are
the
many
more
utility
types
of
standard
and
marketing
goods
and
services depending on which system best fits the need,
are many different types of electrical cables,
such
things
customers
as how much power must be
are,
the
there
depending
delivered,
who
where they live, and how reliable the
on
the
power
must be.
In
this
paper
we
are
concerned
primarily
with
a
particular class of plastic insulated cables known as primary
Underground Residential Distribution (URD) cable [2].
cables
are
typically
buried in the ground
to
These
provide
intermediate link in the electricity distribution chain.
general,
cable
the
is
amount of power that can be
proportional
current ratings.
cross-sectional
insulation,
the
to the product of
conveyed
its
an
In
by
the
voltage
and
The larger the electrical conductivity and
area
of the conductor and the
more power can be delivered by
-2-
thicker
the
the
cable.
Stell, 1988
Of course,
there is the usual trade off that more capability
means more cost.
system
can
be
For illustration purposes,
compared
to a
water
supply
generator is analogous to a pumping station.
like pipes,
more
flow
higher pressures.
can
electrical
system • . The
The cables are
the voltage like water pressure, and the current
like water flow.
carry
an
Pipes with larger cross sectional areas can
and pipes with thicker
Similarly,
wall·s
can
handle
cables with larger conductors
carry more current and cables with
thicker
insulations
can handle higher voltages.
The components of a typical primary URD cable are
in Figure 1.
Working from the inside out,
shown
The first object
NEUTRAL
WIRES
CONDUCTOR
SHIELD
INSULATION
SHIELD
INSULATION
CONDUCTOR
FIGURE 1: TYPICAL PRIMARY URD CABLE
-3-
Stell, 1988
is the metallic conductor.
This is the supply pipe
which the current going to the end user flows.
aluminum
cost,
It is usually
for this application due to the combination of
light
conductivity,
size.
through
weight,
and
moderately
high
electrical
approximately 62% of that of copper
of
cross-sectional area unit of measure is a circular
abbreviated "cmil".
is
A cylindrical conductor whose
one mil (0.001 inches) has an area of one
thousand
circular mils (26 kcmil) to
conductor sizes less than 250 kcmil,
(AWG)
up.
mil,
diameter
circular
Typical sizes for primary URD cable range from
26
equal
Conductors are designated by cross-sectional area and
number of individual wires twisted together to ·make them
The
low
mil.
approximately
1000
kcmil.
For
the American Wire Gauge
is usually used to describe the conductor
size
[19].
Table 1 below shows the common AWG sizes used for primary URD
cable and the corresponding kcmil sizes (19]:
.
Table 1: Common primary URD conductor sizes
AWG
kcmil
#2
#1
#1/0
#2/0
#3/0
#4/0
41.74
66.36
105.6
133.1
167.8
211.6
Conductors may be made up of from one to 61 wires.
larger
the number of wires, the more flexible
-4-
the
The
finished
Stell, 1988
product
used
will be.
for
The more flexible strandings are
the larger size conductors in order to
usually
make
them
called
the
easier to handle during installation.
The
layer
conductor
shield.
conducting
smooth
uniformly
the
conductor
is an extruded
called
of
of
semi-conducting
over which the
distributed
is
layer
It serves two purposes [5].
surf ace
performance
to
It
plastic
polyethylene.
a
closest
[5].
partially
cross linked
First it provides
electrical
stresses
It is vital to the
the cable that this layer
be
long
very
electrical
- service.
close
stress
and
thus
failure
bonding to the insulating plastic layer to avoid
internal
than
in
Second, the conductor shield provides a surface for
between the two plastic layers [5].
the
premature
term
smooth.
Discontinuities on the surface can be sources of higher
normal
are
These
gaps can lead to
electrical discharge which eventually
integrity
of
the
insulation
layer
gaps
can
and
destroy
create
an
electrical short circuit [5].
Just
over
insulation
very
the
layer.
conductor
shield
essential
out"
that
homogeneous.
before
this
Even
the
extruded
This allows the conductor to be held
high electrical potentials.
"leaking
is
it
gets
layer
very
be
It keeps the
to
the
customer.
microscopically
small imperfections
-5-
power
from
It
clean
can
at
lead
is
and
to
Stell, 1988
distorted electrical stresses and subsequent early failure of
a cable.
Just as pipe walls must be thicker to
higher water pressures,
higher voltages.
for
accommodate
insulation must be thicker to
allow
Typical thicknesses range from 0.175 inches
15000 volt applications to 0.345 inches for 35000
[4].
able
Another must for the insulation material is that it be
to withstand the heat generated by the conductor as
carries current.
generates
The
volts
insulation
proportional to the square of
of
primary
which
is
up
to 90
temperatures
catalyst
The electrical resistance of the conductor
heat
majority
it
URD
capable
c.
cables
of
in
the
use
operating
current.
today
at
This is achieved by
have
conductor
blending
with the thermoplastic polyethylene such that
a
when
the material is subjected to heat during cable manufacturing,
the
insulation
crosslinking,
material
imparts
is
cured.
improved
properties to the insulation [5].
This
physical
curing,
and
called
electrical
This curing process is the
subject of the model which is under investigation herein.
The
last plastic layer is the insulation shield.
the conductor shield,
it
it also has two purposes [SJ.
Like
First,
provides a smooth surface to which the insulation can
mated
to
avoid gaps and subsequent
discharges [5].
neutral
Secondly,
detrimental
be
electrical
in conjunction with the metallic
wires it confines the high energy electrical
-6-
fields
Stell, 1988
within
the insulation and provides safety from shock
hazard
[5].
The
concentric neutral wires shown in Figure 1
thought
of as the return pipe in the water
system
They are typically made of copper due to its high
conductivity
corrosion
and
the
fact that
it
can
generally
analogy.
electrical
has
better
resistance than aluminum in the presence of
and minerals in the ground.
The neutral wires
be
water
both help the
insulation shield provide containment for the electric fields
and provide the return path for the electrical current to get
back to the generating source.
Figure 2 shows the typical stages in the processing of a
primary
URD
crosslinked
manufacturers
material,
dies
cable with an aluminum conductor
polyethylene
insulation.
Generally
produce smaller size wires by drawing
in
extruded
cable
would start with the electrical rod as
with successively smaller holes,
together
and
the stranding operation to
and then
form
it
a
raw
through
twist
the
them
finished
metallic conductor.
The
continuous extrusion/curing/cooling
operation
the plastic materials is diagrammed in more detail in
3.
The conductor shield, insulation and insulation
are
each applied to the conductor in an
extrusion
Figure
shield,
process.
Figure 4 shows a cutaway side view of a typical extruder
-7-
for
for
Stell, 1988
the
application
polyethylene,
of
a
single
in pellet form,
layer
is fed
of
plastic.
The
onto a rotating screw
where it is pushed through the heated barrel and melted.
The
pumping and mixing action of the screw acts to homogenize the
molten plastic and move it to the front of the extruder where
it enters the crosshead,
so called because in it the
plastic
angle turn
makes
BAUXITE DRE - - - -
'
,NA
ALUMINUM
a
right
-1
I
I
I
I
I
PLASTIC
+
ALLfING
CASTING
'
RDl.t'NG
COILING
I
-----·
I
I
I
I
I
I
I
I
I
the
EXTRUSION
-----,
'+
.
cur'
I
I
PLASTIC LAYERS
I
I
I
-----·
+
NEUTRAL VIRES - - - - -1
FINISHED CABLE
I
TESTING
-----·
FIGURE 2.
to
STRANDING
COOLING
B..ECTRICAL ROD
parallel
-----..
ALUMINUM
. CONDUCTOR
-----·
CRAVING
METALLIC ALUMINUM
-----
from
melted
'
I
-----·
MANUFACTURING STEPS
FOR PRIMARY URD CABLE
-8-
Stell, 1988
extrusion screw to parallel to the incoming conductor.
the
melted plastic wraps around the conductor
hollow
tube
Typically
3.
over it as they exit
crosshead
forms· a
together.
the layout of the extruders is as shown in
The
conductor
shield
followed
generally
by
insulation
and
SEMI-CONDUCTING
PLASTIC PELLETS
<INPUT>
a
is
applied
few feet
of
first,
air
by
Figure
itself,
cooling.
insulation shields are then applied
by
The
two
INSULATING
PLASTIC PELLETS
<INPUT>
CONDUCTDR
SHIELD
EXTRUDER
HlSULA TIOff
EXTRUDER
HEATING/CURING TUBE
ALUMINUM
CONDUCTOR
<INPUT>
the
and
Here
CONDUCTOR PLUS
SHIELDS ANO
INSULATION
<OUTPUT>
CONDUCTOR
WITH
JNSULATJON
SHIELD
SHIELD
COOLING TUSE
EXTRUDER
SEHI-CONOUCTJNG
PLASTJC PELLETS
<JNPUT>
FIGURE 3.
EXTRUSION, RADIANT HEAT CURING,
COOLING PROCESS FOR URD CABLE
-9-
Stell, 1988
separate extruders feeding them through one common crosshead.
Immediately as the metallic conductor and plastic layers
emerge
from the insulation-insulation shield crosshead
enter the curing tube.
As they travel through it,
heated in a pressurized nitrogen atmosphere to a
sufficient
primarily
to
initiate the curing
serves
process.
two purposes. First
it
they are
temperature
The
nitrogen
prevents
gaseous
,.--- CONDUCTOR
PLASTIC
PELLETS
CROSSHEAD
HEATED
BARREL
SCREW
MOTOR/
GEAR BOX
MOLTEN
PLASTIC
FIGURE 4.
PLASTIC EXTRUDER
-10-
they
Stell, 1988
by-products
of
the
curing process
from
creating voids within the insulation.
inert
bubbling
up
and
Second, it provides·an
atmosphere so unwanted chemical reactions do not
place during the curing.
In the radiant heat/cure
the
heat is provided by passing electrical
the
walls
nitrogen.
of
the
stainless
steel
process,
current
pipes
take
through
enclosing
the
A typical system will have one to ten individually
controllable heating zones to accommodate the varying heating
requirements
for different conductor size and plastic
layer
thickness combinations.
As
the
product
leaves
the
heated
pipe,
it
passes
directly into a water filled cooling pipe where it is kept at
the same pressure as in the heating pipe.
Before the
can
plastic
exit
the
sufficiently
pressurized
cooled
system,
the
must
be
due
to
Once cooling
is
to prevent voids from forming
gaseous by products of the curing process.
cable
complete, the product exits the curing/cooling system through
a
water
seal
and
is
wound
up
onto
reels
for
further
we see that next
the
neutral
processing.
Returning
wires
are
to
Figure 2,
twisted around the partially
completed
product.
Finally, electrical and mechanical testing takes place before
shipment
to
the
customer
to
requirements are being met.
-11-
assure
that
specification
Stell, 1988
There
use
the
are currently two manufacturing facilities
computer model discussed herein to
radiant
heat
curing
process lines.
which
simulate
Each
plant
their
has
one
production line similar in layout to that shown in Figure
The
lines
primary
There
represent approximately two thirds of
URD
plant.
are ten heated zones on each line with a total
curing
of
cooling
manufacturing capacity
approximately
portion
at
total
each
length
cable
the
3.
two hundred feet
of the individual lines
per
is
line.
The
roughly
three
hundred feet long.
In addition to the two production facilities making
of the model,
there is one research and development location
with a scaled down radiant cure line for testing of
and processes.
totalling
use
products
This pilot line has three heated curing zones
around
twenty feet and a
cooling
section
about
fifty feet long.
Two
dictate
industry
the
properties
cable.
their
requirements
for
publish
mechanical
standards
and
which
electrical
of crosslinked polyethylene used in
The first of these,
Association,
publish
associations
primary
the Insulated Cable
URD
Engineer's
consists of a group of cable manufacturers that
standards
that may be referenced
own purchase specifications [12].
by
utilities
The second
the Association of Edison Illuminating Companies,
-12-
in
group,
is a group
Stell, 1988
of cable users,
which
In
primarily utilities,
that publish standards
any utility may reference or adopt as their
addition
especially
to
these
industry
own
standards,
the larger ones, write their
own
[4).
utilities,
specifications
for physical and electrical properties and cable performance.
One
minimum
requirement
degree
of
of many of these specifications
cure as measured
by
either
a
is
solvent
extraction
test or a hot creep test [12).
In the
extraction
test
polyethylene
weighed,
a
sample
of
the
cured
solvent
boiled away, the less cured the material is.
The more plastic
ICEA limits the
maximum plastic boiled away to thirty percent of the
[12).
plastic
is
boiled in a solvent, and weighed again to determine
the amount of plastic dissolved away [12).
weight
a
In the hot creep test a sample of
initial
the
is heated in an oven while being held under
cured
tension
[12).
The amount of elongation and permanent stretch cannot
exceed
175
degree
of cure is a function of the time and temperature
percent and 10 percent,
respectively.
As
the
to
which the cable was subjected during curing these tests limit
the maximum speed at which the cable can be processed [11).
Another
limit
on the maximum processing speed
length of time required to cool the cable.
to
prevent the formation of voids,
cable
the
As stated before,
the hottest part of
insulation must be cooled sufficiently before
-13-
is
the
exiting
Stell, 1988
the pressurized system.
for
this
A generally accepted industry value
maximum temperature at exit from
the
pressurized
cooling system is approximately 200 degrees Fahrenheit.
The
hottest area normally occurs in the innermost layer since the
cooling water cools the cable from the outside to the inside.
Indirectly,
two
limitation
on
specification requirements
maximum
exit temperature.
call
for
this
First
AEIC
has
requirements for maximum size and number of voids allowed
the
insulation
limitations
cable
[4].
both
AEIC
and
ICEA
have
on the amount of partial discharge allowed in
[4,12].
generated
Second,
in
Partial
discharge
is
electrical
within voids in the cable insulation when
is applied to it.
a
noise
voltage
It is used as an indicator of the presence
of voids.
In the case of the radiant heat curing process, there is
also a limitation on the minimum speed at which a primary URD
cable
can
be
processed.
This is due to
the
high
cable
surface temperatures which can be encountered as a result
the
750 to 850 degree Fahrenheit curing
The
polyethylenes
show
If
temperatures.
used for the insulation shield
deterioration at approximately 575 degrees
the
long,
pipe
cable is allowed to remain in the
of
curing
begin
to
Fahrenheit.
pipe
too
the surface can heat beyond this temperature and cause
damage to the insulation shield material.
-14-
Stell, 1988
Outside of the curing/cooling process limitations, there
exist others that control how a primary URD cable
line
can
maximum
linear
be
operated.
output
production
Among these are
the
minimum
volumes of the extruders,
and
the
speeds at which the other machines in the
and
maximum
production
line can be operated.
MODELLING THE PRODUCTION PROCESS
The algorithm used to model the radiant curing and water
cooling
portions
of
the primary
URD
cable
manufacturing
process is based on work reported by Boysen in 1970 [6].
describes
a
method
curing/cooling process,
In Boysen's model,
of
sections
thickness
for
computer
a
similar
only using steam as the heat source.
the curing tube is divided into a
along its length,
is
modelling
He
and
the
plastic
divided into a number of annular
number
extrusion
rings.
For
instance, if the pipe were one hundred feet long, it might be
divided
The
into one hundred one foot increments for the
length
model.
of the increment selected is influenced
opposing factors.
First,
by
it must be small enough to
large temperature changes in any of the plastic rings as
cable moves from one section of the heating tube to
Too
large
a
temperature
change
-15-
would
two
avoid
the
another.
invalidate
the
Stell, 1988
assumption
Boysen makes that the temperature throughout
incremental element of plastic is constant [6].
This in turn
would severely affect the accuracy of the model.
The second
factor to be considered in choosing an appropriate
length is calculation time.
more
of
them
there
increment
The smaller the increment,
must be,
and
calculations that must be made.
limits
the
subsequently
the
At some point the
on the time that can be spent doing the
the
more
practical
calculations
will force a lower bound on the increment size.
The
temperatures
of each of the annular rings
inside of the cable, in Boysen•s algorithm,
at every section of the heating pipe.
on
the
are recalculated
The new temperature is
based on the temperature of the ring as it exits the previous
heating section,
the amount of heat being conducted into
and out of it by the ring inside and outside of it,
own
internal
section.
function
energy
over the
time
The time spent in each section,
of
the
speed at which
through the process.
steam,
change
the
and
its
in
the
spent
of course,
cable
is
it
is
a
travelling
The outer ring, the one exposed to the
is assumed to always have a surface temperature equal
to that of the steam, due to the condensation of the steam on
the surface of the cable.
The remainder of the heat transfer
occurs similarly to the other rings.
-16-
The metallic conductor
Stell, 1988
receives its heat from the inner plastic ring.
The equations
for the heat flow from Boysen are summarized below [6]:
Equation 1) Heat Conduction from ring to ring
Q= KA
h.T/
~
L
Equation 2) Change in internal energy of material
from heating section to heating ·section
AQ/ 6.T
Cp = (l/M)
where:
Q= heat flow from ring to ring
aT= temperature difference
A L=
distance in direction of
A T
A= area normal to direction of plastic flow
K= thermal conductivity of plastic
M= mass of plastic
~
Q= heat flow difference
cp = specific heat capacity of plastic
As
Boysen
explains,
if
the
temperatures
of
the
cable
components as they exit the extrusion operation and enter the
curing
along
and cooling phases are known,
the
above
with the concept of energy balance between
and sections,
equations,
the
rings
can be used to calculate a new temperature for
-17-
Stell, 1988
each ring in each heating section [6].
The equation for the
new temperature of a given ring is shown below [6]:
Equation 3) Tn= To + (Q -Q )t/M/Cp
2 1
where:
Tn= new temperature of ring
T0 = old temperature of ring
Q2= heat flow into/out of outer edge of ring
o1= heat
flow into/out of inner edge of ring
t= length of time for ring to travel through
heating increment
M= mass of plastic flowing through heating
increment
Cp= specific heat capacity of plastic
Once
the
calculated
that
has
figured.
cable
temperature
of
all
for a given heat section,
taken
the
rings
the degree
place as a result of the
heating
has
of
been
curing
is
The crosslinkable polyethylenes typically used for
applications cure by means of the decomposition
peroxide catalyst in a first order rate reaction [11].
first
then
order
temperature,
constant [9].
rate
reaction the time required,
at
a
to reduce the amount of catalyst by half
Figure 5 shows a typical "half-life" time
-18-
of
a
In a
given
is
a
Stell, 1988
Half-life Time, min
1
0.5
0.3
0.1
0.05
0.03
0.01
0.005
0.003
0.001 .___
__,___._..___._-.L._._~_.___.___....__~_.___._---1"--'--.......__.___.---J
J50
JOO
400
500
450
Temperature, Deg F
FIGURE 5.
versus
With
temperature curve for a
the
temperature
calculated,
5.
HALF LIFE TIME VS TEMPERATURE FOR
TYPICAL CROSSUNKING PROCESS
of
crosslinkable
each
ring
having
already
been
the half-life time can be determined from Figure
The number of half-lives is then readily
dividing
polyethylene.
the
time
the
plastic
ring
has
calculated
been
at
once the number of half-lives
temperature
of interest.
known,
the
amount of peroxide decomposed
period
of interest can then be determined by
relationship:
-19-
during
the
the
by
the
is
time
following
Stell, 1988
Eqµation 4:
where:
P= fraction of peroxide decomposed in
N half lives
N= number of half-lives
Figure 6 is a graphical representation of this
relationship.
Once the amount of peroxide decomposed is known,
of
crosslinking
is also known since they
are
the
degree
proportional
[11].
Peroxide Decomposed, % of Remaining
100
90
80
70
60
50
40
30
20
10
2
4
J
5
6
7
Number of Half Lives
FIGURE 6:
PEROXIDE DECOMPOSED VS NUMBER HALF LIVES
FOR FIRST ORDER RATE REACTION
-20-
Stell, 1988
An
additional calculation related to degree of cure
performed
by
the
model.
As was mentioned
in
section on industry and customer specification
the
is
above
requirements,
the solvent extraction test requires a thirty percent maximum
level for dissolved plastic.
extractibles"
estimate
The model includes a
calculation which is an empirical
the amount of plastic that can be
"percent
attempt
dissolved
to
after
all processing has taken place.
In
Boysen•s
model
the
temperature
and
peroxide
calculations for the cooling zone are essentially the same as
those
for
the
heating
zone, except
the
heat
flows
are
reversed since the outer medium is now cooler than the cable.
The
model
under
study here
generally
utilizes
the
same
assumptions and thermodynamic equations for heat transfer
as
explained by Boysen, once the heat has reached the surface of
the
cable.
refinements.
There are a few
The
minor
differences,
thermal conductivities
for
primarily
the
materials are allowed to vary with temperature.
In addition,
in an attempt to empirically account for differences
actual
an
various
between
and predicted values of heat transfer and cure
rate,
artificial thermal resistance between the inner layer
plastic
and
the metallic conductor was added to
during it initial development.
-21-
the
of
model
Stell, 1988
The
primary
difference in calculations occurs
in
the
Recall that
the
method
used to get the heat to the cable.
Boysen
model assumes that since the steam condenses
and
temperature
steam (6].
is
on
directly
the
surface
of
the
cable,
rapidly
that
of the surface of the cable is the same
as
the
the
In the case of the radiant cure process, the heat
transferred
from the heated pipe to
primarily by radiation.
the
cable
surface
Itaka et al have described
typical
radiant heat transfer equations as follows (13]:
Equation 5) Wr=
4
4
S (T 2 -T1 ) A1
----------------------1/E1 + A /A (l/E - 1)
1
2
2
where:
Wr= heat transferred by radiation
S= Stefan Boltzman constant
Tl= absolute temperature of cable surface
T2= absolute temperature of pipe
surface area per unit length of cable
A=
1
area per unit length of pipe
A=
2 surface
El= emissivity of cable
E2= emissivity of pipe
An
additional mode of heat transfer to the cable is
convection.
Again,
by
Itaki et al have described typical heat
-22-
Stell, 1988
transfer equations for this situation [13].
The form is
as
follows:
Equation 6) W =
c
where:
W0 = heat transferred by convection
K0 = constant, 14.9 for nitrogen gas
P= gas pressure
d 1= cable diameter
d 2= pipe diameter
T1= absolute cable surface temperature
T2= absolute pipe temperature
a= constant, 2.2
Another
the
Boysen
model is the use of from one to ten insulated heating
pipes,
each
of
settings,
between
model
variation
which
can
that our model has from
have its
own
and the use of a short,
the
allows
length
temperature
variable non-heated
last heating zone and the
the
and
lengths to be input
cooling
zone.
The
by
user.
The
the
customarily used lengths are based on actual physical
of
the pipes less some allowance for non-insulated
of
the pipe where internal temperatures may be
lower than in the insulated sections.
-23-
zone
length
sections
considerably
Stell, 1988
Why is it important to know how well a computer
models
the
radiant
electrical
cable?
applications
Boysen
model
for
The
the
identifies
of
curing process for
a
answer
model and
lies
their
three categories of
curing
process
[6].
the
in
program
production
the
potential
possible
benefits.
applications
One
of
of
these
for
is
a
the
prediction of optimum operating conditions for the production
line [6].
Processing problems, product quality problems and
productivity
case.
considerations are the primary issues
Processing
problems
would
include
limitations
imposed
loss
heating zone or the reduction in
of
a
in
this
temporary
due to equipment failures such
output
as
the
of
an
extruder to which the curing/cooling process must be matched.
The
model could be used to determine the
cooling
and
temporary
line speed conditions necessary
to
curing,
match
the
limits.
Product quality problems for which the model could be
useful investigation tool would be where the cable failed
meet
specification requirements and would require
or reprocessing.
overheated
cables
surfaces
and
cables with internal voids as evidenced by partial
measurements
at
the
final
electrical
production.
The model could be used to examine
-24-
testing
to
scrapping
Examples of scrap generating problems
with scorched
a
are
undercooled
discharge
stage
the
of
actual
Stell, 1988
processing
conditions
used such as cure
cooling water temperature,
tube
temperature,
etc., as determined by production
records, to determine if any variation in standard procedures
that
might
problem.
model
be present were sufficient to
caused
the
For product quality problems like undercuring,
the
could
not
only be used
to
have
determine
the
possible
reasons for the problem but also the conditions· necessary for
potential
scrap reducing remedies like recuring
by
passing
the cable through the curing/cooling process again.
As
Bartnikas points out,
due to the amount of
capital
typically required to build this type of production line,
is
economically
essential
that
a
company
productivity by maximizing production speeds [5].
can
maximize
The model
be used to assist in developing target production
used
to
establish
subsequent
industrial
engineering
standard costs of production,
it
rates
standards
even for
and
products
which have never actually been produced.
A second application of cure calculation models cited by
Boysen is the prediction of cure performance of new materials
without
the
need for expensive plant trials [6].
This
is
particularly valuable when production capacity is limited and
profit
making
production
experiments on new products.
with
must be
forgone
to
accommodate
In the case of an organization
pilot facilities where material characteristics can
-25-
be
Stell, 1988
determined on small scale prototype equipment,
the model can
then be used to predict full scale production performance ·of
the candidate materials.
The
final
Boysen
is
the
Here
we
are
with the design of new production facilities or
the
prediction
dealing
of
application
optimum
referred to by
process design
(6].
By being able to
upgrade of current facilities.
reasonably
accurately predict production speeds for various combinations
of curing and cooling lengths and temperatures,
of
these
parts
of the production process
matched to the extruder outputs.
the
outputs
be
closely
can
This helps to minimize
capital
investment necessary to achieve
rates.
It
entire
cable
also may help to maximize
desired
production
productivity
production facility since
the
the
for
an
curing/cooling
process is typically the bottleneck operation.
The ability to predict production speeds through the use
of the model has other potential applications in addition
to
those mentioned by Boysen.
be
made
of
production costs.
For instance,
Once the costs
estimates can
are
predicted,
business problems like how many of which products are best to
make, what is the potential return on the capital investment,
and what are the best ways in which to schedule production of
orders, may be examined.
-26-
Stell, 1988
RESULTS
Since
is
to
the first step in calculating the degree of
calculate
logical
that
temperatures
if
the
appropriate
there
were
a
temperatures,
way
to
it
actually
cure
seems
measure
inside the cable as it is being produced,
this
would be the place to start examining the capabilities of the
model.
Mitchell [14-16] and Robbins [17] report methods for
measuring
the
temperature of the cable surface and
of
interface between the conductor shield and insulation
the
during
experimental runs on a pilot radiant heat, dry cure extrusion
line.
The surface temperature is measured with an
infrared
pyrometer through quartz glass inspection ports at the end of
each
of
the
three
heating
zones
on
the
line.
This
measurement method is subject to considerable variability and
error
since it depends on calibration of the system
quality
of
the
optics being used and
the
to
the
emissivity
and
surface condition of the material being measured [7].
The
temperature
is
accomplished by placing a thermocouple on the surface of
the
conductor
where
the
applied.
measurement
of
the
internal
shield just before the cable enters the
insulation
and
insulation
shield
A thermocouple measures temperature by
crosshead
layers
are
generating
an electrical signal proportional to the temperature at which
-27-
Stell, 1988
it is being held (8].
display
The signal generated must be sent to a
device which converts it to a readable
temperature.
In trials described here, the thermocouple is attached to the
readout device through a sufficient length of lead wire
that
the
wire can be fed into the crosshead
travels through the pilot production line.
as
the
such
cable
In this way
the
temperature at the interface between the conductor shield and
insulation
can
Measurement
be
read at any
errors
point
for the type of
along
the
thermocouples
process.
used
in
these studies are generally believed to be plus or minus four
degrees Fahrenheit [3].
All
of
the
trials reported by
Mitchell
[14-16]
Robbins [17] were done on #1/0 AWG solid aluminum
and
conductors
with 0.260 inches of crosslinked insulation. These trials are
listed
in
represent
Tables
2
through 9
as
Tl
AWG
insulation
and
Trial
T9 was on a #2 AWG
compare
the
temperature
data
conductor
collected
7
predictions of the computer model.
the
such
inches
wire
as
of
aluminum
Tables 2 through
shield/insulation
during
They
Trial TS was on a
19 strand aluminum conductor with .175
conductor with 0.175 inches of insulation.
6
T7.
minor variations in processing variables
line speed and cooling water temperature.
#1/0
through
trials
interface
with
the
Tables 2 through 4,
show
the errors in the calculated values through the three heating
-28-
Stell, 1988
zones are relatively small, less than ten percent.
Tables 5
and
6 show the errors start increasing in the
neutral
zone
and
then
thirty
seven
become
quite
significant,
up
to
percent, after the cooling zone.
TABLE 2:
TABLE 3:
Conductor Shield / Insulation Interface Temperature
Data from Thermocouple Trials - End of Heat Zone 1
Trial
Meas.
Cale.
Error
Tl
T2
T3
T4
T5
T6
T7
TS
T9
264
256
263
251
249
251
250
270
258
270
265
266
270
270
269
269
274
267
2.3%
3.5%
1.1%
7.6%
8.4%
7.2%
7.6%
1.5%
3.5%
Conductor Shield / Insulation Interface Temperature
Data from Thermocouple Trials - End of Heat Zone 2
Trial
Meas.
Cale.
Tl
T2
T3
T4
TS
T6
T7
TS
T9
314
306
312
291
290
304
303
334
313
317
314
317
304
304
313
313
329
313
-29-
Error
1.0%
2.6%
1.6%
4.5%
4.8%
3.0%
3.3%
-1.5%
0.0%
Stell, 1988
TABLE 4:
TABLE 5:
Conductor Shield / Insulation Interface Temperature
Data from Thermocouple Trials - End of Heat Zone 3
Trial
Meas.
Cale.
Tl
T2
T3
T4
TS
T6
T7
TS
T9
349
340
343
336
33S
360
359
386
363
357
355
358
346
346
36S
368
379
360
Error
2.3%
4.4%
4.4%
3.0%
3.3%
2.2%
2.5%
-l.S%
-0.8%
Conductor Shield / Insulation Interface Temperature
Data from Thermocouple Trials - End of Neutral Zone
Trial
Meas.
Cale.
Error
Tl
T2
T3
T4
TS
T6
T7
TS
T9
34S
340
340
351
351
384
38S
386
378
363
361
364
384
3S4
417
417
409
395
4.3%
6.2%
7.1%
9.4%
9.4%
8.6%
7.S%
6.0%
4.5%
-30-
Stell, 1988
TABLE 6:
Conductor Shield / Insulation Interface Temperature
Data from Thermocouple Trials - End of Cooling Zone
Trial
Meas.
Cale.
Error
Tl
T2
T3
T4
TS
T6
T7
TS
T9
133
140
142
158
158
205
210
192
146
147
144
145
167
141
172
181
121
124
10.5%
2.9%
2.1%
5.7%
-10.8%
-16.1%
-13.8%
-37.0%
-15.1%
Tables 7 through 9 compare the surface temperature
collected
the
during the trials with the calculated values
from
There is considerable variation in errors
with
model.
values
data
ranging up to approximately twenty-two
must be remembered,
percent.
though, that this particular measurement
itself is subject to substantial errors.
TABLE 7:
It
Cable Surface Temperature Data from Thermocouple
Trials - End of Heat Zone 1
Trial
Meas.
Cale.
Tl
T2
T6
T7
425
435
510
510
400
397
427
428
-31-
Error
-5.9%
-8.7%
-16.3%
-16.1%
Stell, 1988
TABLE 8:
Cable Surface Temperature Data from Thermocouple
Trials - End of Heat Zone 2
Trial
Meas.
Cale.
Tl
T2
T6
T7
435
440
548
463
461
502
502
TABLE 9:
548
Error
6.4%
4.8%
-8.4%
-8.4%
Cable Surface Temperature Data from Thermocouple
Trials - End of Heat Zone 3
Trial
Meas.
Cale.
Tl
T2
T4
TS
T6
T7
320
330
473
473
540
540
390
389
489
489
556
556
Error
21.9%
17.9%
3.4%
3.4%
3.0%
3.0%
To test the ability of the model to predict cure results
on products made on full scale factory production
the
products
shown in Table 10 were selected
for
equipment,
testing.
They represent as wide a range of products as could be chosen
given
the
production schedules in effect
frame of this research.
-32-
during
the
time
Stell, 1988
TABLE 10:
Sample
1
2
3
4
5
6
7
8
9
10
Two
samples.
Product Descriptions for Cure Test Samples
Description
#4/0 AWG 19 wire aluminum, .175" insulation
500 kcmil 37 wire aluminum, .175" insulation
750 kcmil 61 wire aluminum, .175 11 insulation
#4/0 AWG 19 wire aluminum, .220 11 insulation
#1/0 AWG 19 wire aluminum, .260 11 insulation
#1/0 AWG solid aluminum, .260 11 insulation
#4/0 AWG 19 wire aluminum, .260 11 · insulation
500 kcmil 37 wire aluminum, .260 11 insulation
#1/0 AWG solid aluminum, .345 11 insulation
750 kcmil 61 wire aluminum, .345 11 insulation
sets
of cure related tests were performed
on
The first was the normal solvent extraction
the
test,
on a specimen taken from the inner twenty-five percent of the
insulation
thickness,
specifications
tests
the
required
by
industry
as described previously.
customer
The results of
and the model predictions are shown in Table
table
shows,
there is considerable
predicted and actual.
in
the
As
between
In most cases the model predicts more
#3, the model predicts substantially less cure.
shown
11.
variation
cure than actually exists, but in some cases,
has
and
a series of
round-robin
such as Sample
As Adams [l]
solvent
extraction
tests, the variation in actual test results is typically four
percent.
This accounts for only a small part of
discrepancies seen here.
-33-
the
large
Stell, 1988
TABLE 11:
The
samples
% Extractables, Inner 25% of Insulation
Plant samples, Plant Measurements
second
were
Meas.
Cale.
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
17.4
20.2
21.1
16.7
16.6
18.0
18.6
16.8
17.6
18.3
13.5
11.3
36.0
16.6
19.2
18.6
12.5
11.3
11.3
12.4
set of cure tests performed
done
Chromatography)
these,
Sample
using
HPLC
-22.4%
-44.1%
70.6%
-0.6%
15.7%
3.3%
-32.8%
-32.7%
-35.8%
-32.2%
on
the
Performance
samples of the uncured plastic are collected
uncured
cable
Liquid
analysis as described by Hercules (10].
cables are being manufactured.
the
(High
Error
the
HPLC analysis is performed on
samples to determine the concentration
Then HPLC analysis is
peroxide catalyst present.
as
In
of
the
performed
on the· cured samples, also to determine the level of peroxide
present.
The percent of original peroxide remaining in
the
cured samples is then calculated.
The
model
results of the HPLC measurements and
predictions
Insulation
insulation
ring
are
one
thickness.
shown
is the
in
Tables
innermost
The
-34-
measured
12
the
through
one-eighth
values
computer
of
shown
14.
the
are
Stell, 1988
questionable
since they don't show the expected decrease
cure
as the sample position gets nearer to the inside.
very
small sample quantities available for each
likely contributed to the experimental error.
which
that
may
ring
the time the ring samples were cut from them.
The
quite
Another factor
have affected the results is the length
elapsed between the time the cables were
in
of
produced
· Robbins
time
and
(18]
suggests that the concentrations of the peroxide catalyst may
tend
His
to equalize across the insulation wall as time
best
samples
estimate
of a time frame is
a
few
passes.
weeks.
in this study typically were not cut up for four
The
to
eight weeks after production.
TABLE 12:
Percent Remaining Peroxide, Insulation Ring 1
Plant Samples, Lab HPLC Measurements
Sample
Meas.
1
7
1
3
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
2
1
4
5
0
0
-35-
Cale.
0
0
77
19
28
24
5
0
0
0
Error
-100%
-100%
7600%
533%
1300%
2300%
25%
-100%
0%
0%
Stell, 1988
TABLE 13:
Percent Remaining Peroxide, Insulation Ring 2
Plant Samples, Lab HPLC Measurements
Sample
Meas.
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
TABLE 14:
Cale.
1
7
4
0
57
10
16
15
2
0
0
0
1
4
2
2
2
2
0
0
Error
471%
-100%
5082%
186%
662%
838%
25%
-100%
0%
0%
Percent Remaining Peroxide, Insulation Ring 3
Plant Samples, Lab HPLC Measurements
sample
Meas.
#1
#2
#3
#4
#5
#6
#7
#8
#9
#10
Cale.
l
l
Error
67%
l
0
28
4
3
3900%
-14%
2
2
2
0
0
5
7
0
0
0
0
-100%
-100%
0%
0%
338%
CONCLUSIONS
Comparisons
to
reasonably
accurate
temperature
measurements performed during experimental trials on a
line
show
the
model to
have
-36-
conductor
pilot
shield/insulation
Stell, 1988
interface
temperature calculation errors ranging from
percent to +10.5 percent.
temperatures
-16.9
to
however,
+
21.9
percent.
The
measurements
to
The solvent extraction data from
production records show the model to be · substantially
more deficient in percent extractibles,
with probable errors
ranging from -44.1 percent to +15.7 percent.
HPLC
from
may contain considerable error due
their inherent inaccuracy.
plant
surface
during the trials indicate errors ranging
percent
themselves,
Measurement of the cable
-37.0
analysis
were
inconclusive
due
probability of high experimental error.
therefore,
to draw conclusions directly,
presented herein,
The results of
to
a
substantial
It is not possible,
based on the
about the ability of the model to
percent remaining peroxide.
It is probable,
data
predict
however,
that
since the percent remaining peroxide calculation is dependent
on the temperature calculations, the errors will be about the
same at best.
As
a
consequence
of
the
results
reported
above,
substantial caution should be exercised in the application of
the
model.
comparisons
It is probably most useful for making
relative
of the results of small changes in operating pa-
rameters.
There are numerous potential sources of the large errors
exhibited
by the model.
Basically it is a
-37-
combination
of
Stell, 1988
theoretical thermodynamic equations and empirical
attempting to provide a "best fit"
model.
parameters
Either of
these
two areas contain possible problem sources.
A possible theoretical problem might be
for
heat
exchange
surface.
The
between the curing pipe
equations
used
radiation and natural convection.
mode
of
include
the
equations
and
heat
the
exchange
Natural convection is
heat transfer when there is little or
no
the
cable such as in the gas spacer cable
Itaki,
et
al [13].
the
surface
described
In the case of a radiant
by
relative
movement between the gas pressurizing medium and the
of
cable
heat
by
curing
production line, however, the cable may be moving through the
line at speeds in excess of one hundred feet per minute.
It
may be necessary to include a heat transfer component for the
forced convection mode of heat transfer such as is
done
for bare electrical conductors installed
typically
outdoors
and
exposed to the wind [2].
Another
transfer
possible
point.
problem
is
the
function used between the conductor shield and
aluminum conductor.
creates
theoretical
an
heat
the
The model has built in an equation which
artificial resistance to heat transfer
at
this
This was originally done in an attempt to account for
differences
between measured and calculated temperatures
-38-
in
Stell, 1988
early development work on the model.
Perhaps another method
of accounting for the differences might yield better results.
For
instance,
increase
in
the
model
contains
no
provision
strand shield material volume
that
for
exists
the
on
stranded conductors versus solid conductors due to the strand
interstices.
in
Accounting for this material volume difference
conjunction with other potential sources of
improve the accuracy of the model,
error
might
particularly for stranded
conductors.
Empirical parameters which might be sources of error are
the
variables
and constants in the equations
which
either
cannot be directly measured or derived from accepted physical
constants.
Such error sources would include items like pipe
and
cable emissivities,
and the effective heated length
the
heating pipes which are not insulated over their
length.
-39-
of
entire
Stell, 1988
REFERENCES
[l]
[2]
Adams, James.
"Round Robin Decalin Extraction Tests."
Richmond, VA:
Reynolds Metals Company, 1986
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