Note: Descriptions are shown in the official language in which they were submitted.
CA 02268673 1999-04-08
PREVENTING PENCIL PIPE DEFECTS IN STEEL
Field of the Invention:
The invention is directed to the field of the continuous
casting of molten steel.
Background of the Invention:
Steel is conti.nuousl.y cast by del.iveri.nd it in molten
form from a tundish through the bore of refractory nozzle
components and into a continuous casting mold. The typical
refractory components are an upper tundish nozzle disposed
beneath a tundish, refractory plates to control flow, and a
submerged entry nozzle that extends into molten steel in the
mold. Aluminum oxide inclusions in the steel tend to deposit
on the refractory walls of the components over time. Such
buildup will choke off the bore and terminate casting unless
prevented. The conventional way to prevent such nozzle
clogging is to deliver argon gas to the bore, through a porous
refractory material of the upper tundish nozzle and an upper
slide plate. The argon gas bubbles exiting the refractory
pores are intended to prevent aluminum oxide particles from
contacting and adhering to the refractory walls and to prevent
nozzle clogging.
In the case of continuous casting machines having curved
portions, some of the injected argon gas bubbles become
trapped at the inner radius of solidifying strands of steel.
This is a particular problem for ultra low carbon (ULC) or
extra low carbon (ELC) steel. During subsequent high
temperature annealing of the coiled steel, the trapped argon
bubbles may expand and "blister" the surface of coils of the
steel, rendering the formed steel unsuitable for exposed
automotive applications. This argon-based, raised surface
coil defect is known as a "pencil pipe" defect or a "blister."
In an attempt to eliminate this defect, one approach has been
CA 02268673 1999-04-08
to cast pencil-pipe sensitive steel at very low cast speeds or
steel throughputs. This can be a very significant production
disadvantage to steel producers. Pencil pipe defects and
clogging of the nozzle components thus continue to be serious
problems for steel producers.
Summary of the Invention:
In general form, the present invention can direct
nitrogen-containing gas along substantially an entire
passageway formed by a nozzle assembly to avoid pencil pipe
defects upon high temperature annealing of resulting coils of
the steel. Any portions of the passageway which are not
subjected to the nitrogen-containing gas such as the entry
nozzle, can include insert sleeves formed of a lime-zirconia
material. The passageway extends between a tundisr and a mold
of a continuous casting apparatus. The invention is
particularly applicable to the use of ultra low carbon and
extra low carbon steel, which are susceptible to pencil pipe
defects in view of their reduced strength. The invention is
also applicable to the use of continuous casters having curved
portions, in which the inner strand of steel is susceptible to
pencil pipe defects. The present invention avoids the
conventional use of argon, which has been the cause of pencil
pipe defects. By using the nitrogen-containing gas under
predetermined flow conditions that prevent excess nitrogen
pick-up in the steel and yet inhibit clogging, the present
invention offers a valuable solution to the pencil pipe
problem that has been faced by continuous casting steel
producers.
One embodiment of the present invention is directed to a
method of eliminating pencil pipe defects in steel, comprising
the step of flowing molten steel through a passageway formed
by: an upper tundish nozzle disposed beneath a tundish; nozzle
plates for controlling flow of the molten steel; and an entry
nozzle disposed between the nozzle plates and a mold, in
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particular, the entry nozzle being submerged in molten steel
of the mold. A nitrogen-containing gas is directed under
predetermined gas flow conditions to portions of the
passageway formed by the upper tundish nozzle, the nozzle
plates and the entry nozzle. The gas flow conditions are
effective to eliminate pencil pipe defects in the steel.
In particular, the upper tundish nozzle, the nozzle
plates and the submerged entry nozzle comprise a porous
refractory material through which the nitrogen-containing gas
is passed. The molten steel is passed through the passageway
and into the mold which forms a part of a continuous casting
apparatus, and especially, into arcuate mold portions of the
continuous casting apparatus. The gas flow conditions are
effective to prevent excessive nitrogen accumulation in the
steel.
Either a two or a three nozzle plate assembly is
preferably employed. The two-plate nozzle assembly includes a
stationary upper plate and a lower, movable throttle plate.
An intermediate nozzle is disposed between the throttle plate
and the entry nozzle. The gas is passed to portions of the
passageway formed by the upper plate. The three-plate
assembly includes a stationary upper plate, a movable middle
throttle plate, and a stationary lower plate. The submerged
entry nozzle includes an upper surface that is in contact with
the lower plate. The gas is passed to portions of the
passageway formed by the upper plate and the lower plate.
As to preferable processing parameters, the nitrogen-
containing gas is directed at flow rates through the upper
tundish nozzle, the upper nozzle plate, and the submerged
entry nozzle in ranges of from about 8 to about 12
liters/minute (1/min), from about 2 to about 6 1/min and from
about 2 to about 6 1/min, respectively. The nitrogen-
containing gas is directed at back pressures through the upper
tundish nozzle, the upper nozzle plate, and the submerged
entry nozzle in ranges of from about 10 to about 15 pounds per
square inch (psi), from about 12 to about 20 psi and from
about 1.5 to about 5.0 psi, respectively. If a third lower
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plate is used in the nozzle plate assembly (i.e., the three-
plate assembly), the nitrogen-containing gas is directed
through it at a flow rate ranging from about l0 to about 14
1/min at a back pressure ranging from about 3 to about 6 psi.
Another preferred embodiment of the invention is directed
to a method of eliminating pencil pipe defects in steel,
comprising the step of flowing molten steel through the
passageway formed by: the upper tundish nozzle disposed
beneath the tundish; the nozzle plates; and the submerged
entry nozzle disposed between the nozzle plates and the mold.
The nitrogen-containing gas is directed under predetermined
gas flow conditions to portions of the passageway formed by
the upper nozzle and the nozzle plates and into the
passageway. The molten steel is exposed to the gas which is
directed under the predetermined gas flow conditions to a
portion of the passageway formed by the submerged entry
nozzle. Instead of or in addition to exposing the molten
steel adjacent the submerged entry nozzle to the nitrogen-
containing gas, the molten steel may be exposed to a "slippery
bore" reactive surface formed of a Ca0-Zr02 composition, the
reactive surface forming a portion of the submerged entry
nozzle. The nitrogen-containing gas may be directed through a
porous refractory sleeve of the submerged entry nozzle (formed
of the slippery bore insert material or a different porous
refractory) and into the passageway. The gas flow conditions
are effective to eliminate pencil pipe defects in the steel.
The present invention offers numerous advantages over
conventional continuous casting production. The inventive
method employs nitrogen gas, which is relatively inexpensive.
More importantly, the invention eliminates the occurrence of
pencil pipe defects. When using the inventive method, steel
sheet such as in exposed automotive applications, in
particular formed by ELC or ULC steel cast using a continuous
caster with curved mold portions, will no longer suffer from
pencil pipe defects. Steel sheet made by hot rolling slabs of
solidified steel processed according to the present invention,
can now be widely used in these and other exposed
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applications. Therefore, the present method offers a
significant cost advantage to steel producers by fully
utilizing the steel that is produced, and provides automotive
manufacturers with a product of superior quality. All of
these advantages are achieved at a molten steel throughput at
the continuous caster that is the same as or faster than in
conventional practices.
Many additional features, advantages and a fuller
understanding of the invention will be had from the
accompanying drawings and the detailed description that
foflows.
Brief Description of the Drawings:
Figure 1 is a vertical cross-sectional view of one
embodiment of a nozzle assembly used in the method of the
present invention;
Figure 2 is a vertical cross-sectional view of another,
more preferred embodiment of a nozzle assembly used in the
method of the present invention; and
Figure 3 is a vertical cross-sectional view of an entry
nozzle employing a refractory portion, which may be used in
the method of the present invention.
Detailed Description of Preferred Embodiments:
Referring now to the drawings, Fig. 1 refers to a nozzle
assembly used in the method of the present invention
designated generally at 10. Molten steel M flows from a
distribution vessel or tundish 12 through a passageway P
formed by an upper tundish nozzle ("UTN") 14, a movable gate
plate assembly 16 and a lower or submerged entry nozzle
("SEN") 18, and into a portion of a mold 20 of a continuous
caster. A nitrogen-containing gas depicted as "Nz" in the
drawings is directed to portions of the passageway formed by
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each of the UTN 14 and the gate plate assembly 1.6 under
predetermined gas flow conditions. Nitrogen-containing gas
can also be directed to the SEN 18, under predetermined gas
flow conditions, although injection of the nitrogen-containing
gas at the SEN is optional if slippery bore inserts are
employed in the SEN.
Annular spaces or slits 22, 24 are preferably formed in
each of the UTN 14 and SEN 18 by known techniques. The sizes
of the annular slits are not drawn to scale, but may be
enlarged somewhat for clarity of description. A wax ring or
paper may be used during manufacturing of the refractory
component, in the location of the annular space. Upon firing
of the refractory the wax ring or paper burns off, leaving the
annular space. The only communication of the annular spaces
with the exterior of the components are passageways 26, 28
drilled through the refractory from the exterior surface of
the UTN and from the exterior surface of the SEN. t~ ~.he
annular spaces 22, 24, respectively. Gas supply conduits 30,
32 are coupled to these passageways 26, 28, respectively. The
nitrogen-containing gas is fed from a gas source through
appropriate valves, through the gas supply conduits 30, 32,
through the passageways 26, 28, into the annular spaces 22, 24
of the UTN and SEN, and through the refractory into the
passageway P. Flowing the gas through the pores of the
refractory causes the gas to be released as bubbles into the
molten metal.
The following describes variations that are contemplated
by the present invention although not specifically shown in
the drawings or described. Other variations of flowing the
gas to the passageway may be possible, such as using a
plurality of small transverse passageways through the
refractory and to the passageway P (not shown), but are not
preferred. Throughout this description it will be apparent
that each of the nozzle components has a central bore that
forms a portion of the passageway P which extends from the
tundish to the mold. In all the drawings molten steel is not
shown in the nozzle assembly for improving the clarity of the
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drawings. Throughout the drawings the gas supply conduits are
shown schematically, and it will be appreciated that the gas
supply conduits are suitably coupled to the gas passageways in
a manner known to those skilled in the art. For example, the
gas passageways may be drilled or formed from wax upon firing,
and a steel fitting may be fixed with mortar in the
passageway. A corresponding fitting of the conduit may be
threaded to the fitting in the passageway.
The slide gate plate assembly 16 may employ two plates as
shown in Figure 1. The upper plate 34 of the gate plate
assembly includes an upper protrusion 36 that is received by a
recess 38 in a lower portion of the UTN for fixing the upper
plate in place. The upper plate 34 has a recess 40 that
receives a porous sleeve 42 which partially forms the
passageway P. In communication with the porous sleeve is a
gas passageway 44 that is coupled to a gas supply conduit 46.
The lower plate is a throttle plate 48 with an annular opening
that forms a portion of the passageway P. The upper plate and
the throttle plate each include a centrally located opening
for forming a portion of the passageway. The throttle plate
48 slides between the upper plate 34 and a flat upper surface
50 of an intermediate nozzle 52 that is secured to the SEN 18.
Movement of the throttle plate blocks or permits the flow of
molten metal through the passageway P.
For supporting the nozzle assembly, a mounting plate 54
is mounted to the tundish shell. Fastened to the mounting
plate is a cassette 56. Both the mounting plate and the
cassette are formed of metal. The cassette is engaged below a
flange 58 formed on the intermediate nozzle, to support the
nozzle assembly in place.
The SEN includes exit ports 60 at its lower end. The
annular slit 24 extends in "dog-ear" fashion between the
outlet ports of the SEN without communicating with the ports.
Figure 2 refers to a preferred nozzle assembly used in
the method of the present invention designated generally at
80, where like reference numerals designate like parts through
the views. Molten steel M flows from a tundish 12 through a
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passageway P formed by an upper tundish nozzle ("UTN") 14, a
movable gate plate assembly 17 and a lower or submerged entry
nozzle ("SEN") 18, and into a portion of a mold 20 of a
continuous caster. A nitrogen-containing gas, which is
depicted as "NZ" in the figure, is directed to portions of the
passageway formed by each of the UTN 14 and the gate plate
assembly 17 under predetermined gas flow conditions.
Nitrogen-containing gas is also directed to the SEN 18, under
predetermined gas flow conditions, but use of the nitrogen-
containing gas at the SEN is optional if slippery bore inserts
are employed in the SEN.
The annular spaces 22, 24 are preferably formed in each
of the UTN 14 and SEN 18 by known techniques, for example,
using the wax ring/paper manufacturing procedure. The only
communication of the annular spaces with the exterior of the
components are the passageways 26, 28 drilled through the
refractory from the exterior surface of the UTN and from the
exterior surface of the SEN to the annular spaces 22, 24,
respectively. The gas supply conduits 30, 32 are coupled to
these passageways 26, 28, respectively. The gas is fed from a
gas source through appropriate valves, through the gas supply
conduits 30, 32, and the passageways 26, 28, into the annular
spaces 22, 24 of the UTN and SEN, and through the refractory
into the passageway P. Flowing the gas through the pores of
the refractory causes the gas to be released as bubbles into
the molten metal. Other variations of flowing the gas to the
passageway may be possible such as using a plurality of small
transverse passageways through the refractory and to the
passageway P (not shown), but are not preferred.
The sliding gate assembly 17 is a three-plate system
which employs an additional stationary lower plate 82 compared
to the gate assembly 16 shown in Fig. 1. This assembly 17
employs the similar porous upper plate 34 as in the two-plate
assembly. The assembly 17 also employs a similar throttle
plate 48 as in the two-plate assembly. The lower plate 82
includes an annular groove 84 at a lower portion thereof in
communication with a flat upper surface of the SEN. A gas
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passageway 88 is drilled into the refractory into
communication with the annular groove. A gas supply conduit
90 is coupled to the gas passageway 88. Each of the upper
plate, the throttle plate and the lower plate includes a
centrally located opening that partially forms the passageway
P. The throttle plate 48 slides between the upper plate 34
and the lower plate 82. Movement of the throttle plate blocks
or permits the flow of molten steel in the passageway P.
During the casting operation using the three-plate gate
assembly shown in Fig. 2, graphite powder is entrained, using
appropriate valves, into the nitrogen-containing gas stream to
the annul-ar groove 84. When nitrogen gas is used instead of
argon and when no graphite injection is used, a vacuum is
created which aspirates air into the .joint between the upper
surface 86 of the SEN and the lower surface 92 of the lower
plate 82 of the gate assembly. The air enters the passageway
and forms alumina in the molten steel, leading to clogging of
the passageway. Graphite is injected to prevent clogging due
to aspiration. The graphite seals this joint and prevents the
air from entering the passageway, thereby avoiding clogging.
This graphite injection process has been developed by Vesuvius
Refractories.
For supporting the nozzle assembly, the mounting plate 54
is mounted to the tundish shell. Fastened to the mounting
plate is the cassette 56. The cassette engages the lower
surface 92 of the lower gate plate 82 to support the nozzle
assembly 80 in place.
In the preferred embodiment shown in Figure 2, the
vertical slit 24 formed in the SEN preferably extends to a
greater height than in the SEN shown in Figure 1. All but an
upper end portion of the SEN contains the slit. This feature
is preferably combined with the use of the three-plate gate
assembly to reduce clogging of the passageway P.
The UTN, the slide gate plate and the SEN of all
embodiments are formed of refractory components that are
designed to have a sufficiently small pore size to ensure high
back pressure. The UTN is formed of porous alumina or
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magnesium oxide. The upper plate of the two-plate assembly
and the upper plate of the three-plate gate assembly, are
formed of one of porous alumina, zirconia or magnesia. In the
three-plate gate assembly a zirconia insert (not shown)
extends at least on the sliding surfaces of the lower plate
and the throttle plate. The SEN body is formed of alumina and
graphite.
Nozzle components suitable for use in the present
invention may be formed of various compositions, and with
individual portions or inserts of each component formed of
different compositions, other than what is specifically shown
and described herein. For example, the SEN shown in Figure 1
may have a refractory body of one composition and a porous
portion located radially inward of the slit forming a portion
of the bore, located in a position such as the position of the
sleeve shown in Figure 3. The SEN and the intermediate
nozzle, depending upon whether a two or three plate n,te
apparatus is used, may be formed with portions having
different compositions than the body, which exhibit properties
such as are suitable for the wear encountered by the throttle
plate.
In particular, the UTN was supplied by TYK Refractory
Co., Model No. DAS-7. The three-plate gate assembly was
supplied by Vesuvius Refractories and employs their upper
plate with a porous mix, and throttle and lower plates. The
two-plate gate system may be supplied by Kurosaki Co.; this
assembly may employ a porous upper plate, and a lower plate
and intermediate nozzle, supplied by North American
Refractories Co. The SEN was supplied by Shinagawa
Refractories Co., Model No. SBX-G32H6 (body mix) and SBX-61801
(inner bore porous mix).
Referring to Fig. 3, a slippery bore inserts) (generally
shown at 94) may be used in the main passageway and between
the ports of the SEN. The slippery bore inserts are comprised
of a lime-zirconia (e. g., Ca0-ZrOz) material. If the slippery
bore inserts are used, the SEN preferably does not employ gas
injection. When no slippery bore inserts are used as in Figs.
CA 02268673 1999-04-08
1 and 2, the SEN is slitted and employs gas injection. The
slippery bore inserts shown in Figure 3 may be used in the
assembly 10 of Fig. 1 and in the assembly 80 of Fig. 2 without
gas injection.
The slippery bore inserts may also be formed to be
sufficiently porous so that the nitrogen-containing gas can be
passed through them. In this case, a gas passageway 96 is
drilled through the SEN into communication with the slippery
bore inserts 94. Coupled to the passageway is a gas conduit
98. Other porous refractory inserts may also be employed in
place of the slippery bore inserts 94, and are located in a
position similar to that of the inserts shown in Figure 3,
while employing gas injection.
The predetermined gas flow conditions are broadly defined
herein as flow rates and/or back pressures which are effective
to prevent excessive nitrogen pick-up in the steel according
to conventional tolerable levels of nitrogen, to inhibit
clogging of the nozzle components, and to prevent pencil pipe
defects in coils of the resulting steel. Since nitrogen
dissolves quickly in the molten steel, low gas flow rates
minimize undesirable nitrogen pickup in the steel. Moreover,
since the nitrogen dissolves in the steel, there are no
bubbles which expand during annealing.
The nitrogen-containing gas may contain a gas or gases
other than nitrogen but is preferably substantially all
nitrogen gas, even more preferably, 100% nitrogen gas. To
prevent pencil pipe defects and inhibit clogging, the gas is
directed to each of the UTN, the slide gate plate assembly and
the SEN (unless a slippery bore insert is used in which case
the gas injection is optional). Injecting the nitrogen-
containing gas to portions of the passageway formed by only
one or two of the components, if a slippery bore insert is not
used, is not sufficient to inhibit clogging. Argon gas is
preferably not utilized in the present invention since even
when present in small amounts it may lead to pencil pipe
defects.
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While not wanting to be bound by theory, the lime-
zirconia slippery bore inserts are believed to prevent the
formation and accumulation of alumina on surfaces that form
the bore of the SEN. The material of the slippery bore
inserts is believed to be reactive. It is believed that the
solid alumina which deposits in the SEN bore and ports reacts
with the lime content of the inserts to form liquid calcium
aluminate inclusions in the molten steel. The calcium
aluminate inclusions are believed to flow with the steel into
the casting mold and are not injurious to the final steel
sheet product. The nitrogen bubbles at the UTN and the gate
plate assembly (and nitrogen gas bubbles at the SEN when gas
injection is used at the SEN) are believed to provide a
scrubbing action on the surfaces of the bore to prevent
deposition and accumulation of alumina. Some of the nitrogen
bubbles may help to liberate the liquid calcium aluminate from
the SEN and expose new lime units to react with the solid
alumina particles.
In the case of using the slitted SEN without a slippery
bore, the flow rates of nitrogen gas at the upper tundish
nozzle, the upper slide gate plate and the submerged entry
nozzle are, for example, in the range of: from about 8 to
about 12 liters/minute (1/min), from about 2 to about 6 1/min
and from about 2 to about 6 1/min, respectively. Back
pressures to the tundish nozzle, the upper gate plate and the
SEN are, for example, in the range of: from about 10 to about
15 psi, from about 12 to about 20 psi and from about 1.5 to
about 5.0 psi, respectively. Graphite injection at the lower
plate is preferably used to prevent clogging due to
aspiration. At the lower plate groove of the gate assembly,
the nitrogen-containing gas flows at a rate in the range of,
for example, from about 10 to about 14 1/min, with about 10
1/min being preferred. The back pressure to the annular
opening at the lower plate is, for example, in the range of
from about 3 to about 6 psi, with about 4 psi being preferred.
Back pressure is measured continuously at the passageway while
nitrogen injection occurs. The continuous caster is operated
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at throughputs up to about 4.5 tons of molten steel per
minute. It is believed that under the foregoing conditions
the resulting coils of steel will not exhibit any noticeable
pencil pipe defects after annealing.
In the case of using a non-slitted SEN employing the
slippery bore inserts, the flow rates of nitrogen gas at the
upper tundish nozzle and the upper slide gate plate are, for
example, in the range of: from about 8 to about 12 1/min and
from about 2 to about 8 1/min, respectively. Back pressures
to the tundish nozzle and the upper gate plate are: about 10
to about 15 psi and about 12 to about 20 psi, respectively.
Graphite injection at the lower plate is used to prevent
clogging due to aspiration. At the lower plate of the gate
assembly, the nitrogen-containing gas flows at a rate in the
range of, for example, from about l0.to about 14 1/min, with
about 10 1/min being preferred. The back pressure to the
annular opening at the lower plate is, for example, in the
range of from about 3 to about 6 psi, with about 4 psi being
preferred. It is believed that under the foregoing conditions
the resulting coils of steel will not exhibit any noticeable
pencil pipe defects after annealing.
In the method of the present invention, since nitrogen
rather than argon gas is used, instances of clogging of the
SEN may increase due to the rapid dissolving of nitrogen into
the steel and thus the lesser effectiveness of nitrogen in
reducing clogging. Therefore, the SEN's may be changed more
frequently. The SEN's are preferably changed using a
commercially available SEN carriage replacement system.
Preferred aspects of the invention will now be described
by reference to the following non-limiting examples.
EXAMPLE 1
The slitted SEN was used without slippery bore inserts in
a curved continuous caster casting ELC or ULC steel. The flow
rates of nitrogen gas at the UTN, the upper slide gate plate,
the lower slide gate plate and the SEN were: about 10 1/min,
about 4 1/min, about 10 1/min and about 4 1/min, respectively.
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Back pressures to the UTN, the upper slide gate plate, the
lower slide gate plate and the SEN were: about 12 psi, about
16 psi, about 4 psi and under 5 psi, respectively. The SEN
had a lifetime of about 120-250 minutes (275-650 tons), due to
alumina clogging of the SEN. Graphite injection at the lower
plate was used to prevent clogging due to aspiration. The
continuous caster was operated at throughputs up to about 4.5
tons of molten steel per minute. The resulting coiled steel
did not exhibit any noticeable pencil pipe defects after
annealing.
EXAMPLE 2
A SEN supplied by TYK Refractories Co., was used without
gas injection, employing Ca0-Zr02 slippery bore inserts in the
bore and around the ports designated,by the trade name PASC in
a curved continuous caster casting ELC or ULC steel. The flow
rates of nitrogen gas at the tundish nozzle, the up~:_1 slide
gate plate and the lower slide gate plate were: about 10
1/min, about 5 1/min and about 10 1/min, respectively. Back
pressures to the tundish nozzle, the upper gate plate and the
lower gate plate were: about 12 psi, about 16 psi and about 4
psi, respectively. Graphite injection at the lower plate was
used to prevent clogging due to aspiration. The SEN had a
lifetime of about 120-250 minutes (275-650 tons), due to
alumina clogging of the SEN. The continuous caster was
operated at throughputs up to about 4.5 tons of molten steel
per minute. The resulting coiled steel did not exhibit any
noticeable pencil pipe defects after annealing.
COMPARATIVE EXAMPLE
A regular SEN was used without gas injection and without
slippery bore inserts in a curved continuous caster casting
ELC or ULC steel. The flow rate of nitrogen gas at the UTN
was 12 1/min and the flow rate of argon at the upper gate
plate was 6-8 1/min. Back pressures to the UTN and the upper
gate plate were: 12 psi and 16 psi, respectively. The SEN had
a lifetime of about 200-350 minutes. The continuous caster
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was operated at throughputs of under 3 tons of molten steel
per minute. Although the SEN's used in this process had a
greater life due to less clogging, coils of the resulting
steel sheet exhibited pencil pipe defects after annealing,
which significantly reduced the value of the steel.
Many modifications and variations of the invention will
be apparent to those of ordinary skill in the art in light of
the foregoing disclosure. Therefore, it is to be understood
that, within the scope of the appended claims, the invention
can be practiced otherwise than has been specifically shown
and described.
