Note: Descriptions are shown in the official language in which they were submitted.
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13-781
CAST STEEL CUT-LENGTH OPTIMIZATION
FIELD OF ~HE I~V~N110N
The present invention relates generally to the field
of cut length optimization.
BACRGROUND OF THE INVENTION
Continuous casting of steel is a known process for
producing elongated steel blooms and billets. For one
process, a ladle of molten steel is treated to produce a
desired grade of steel as necessary to fulfill a
customer's order, for example. A ladle of steel is also
referred to as a heat. The molten steel is cast into
blooms by pouring the molten steel through a mold and
cooling the steel as the steel exits the mold to form a
continuous solid strand. The steel strand travels
vertically beneath the mold and bends along an arcuate
path defined by guide rollers into a horizontal travel
path. As the strand travels horizontally, the strand is
cut to form a number of elongated steel blooms.
The steel blooms may be reheated, rolled, and cut to
form elongated steel billets having a relatively smaller
cross-sectional area as compared to the blooms. The
billets can then be further processed in a roll mill to
produce steel bars or directly shipped to the customer
for customer fabrication of the steel endproduct.
In ordering steel, each customer may require billets
having a specified cross-sectional area, length, steel
grade, and/or weight for example. As each heat is
poured, then, a suitable number of blooms of suitable
size are cut from the cast steel strand for processing
into the billets required by the customer. Any remaining
cast steel length from the cast strand for the heat,
however, is typically scrapped.
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~UMMARY AND OBJECTS OF THE INVEN~ION
One object of the present invention is to provide
for an optimization method and apparatus for cutting a
strand of material into separate pieces.
Another object of the present invention is to
minimize the amount of scrap material in cutting a strand
of material into separate pieces.
Another object of the present invention is to
minimize the amount of scrap steel in cutting a steel
strand into blooms and billets.
A method for cutting a strand of material is
disclosed. A cut length for at least one piece to be cut
from the strand of material is determined and is based on
a predetermined submultiple length, and the strand of
material is cut to produce the at least one piece having
the determined cut length. The cut length for one
embodiment is reduced by at least one predetermined
submultiple length if the cut length is greater than a
predetermined maximum length.
A next-to-last length for a next-to-last piece to be
cut from the strand of material and a last length for a
last piece to be cut from the strand of material are
determined. The next-to-last length for the next-to-last
piece to be cut from the strand of material is assigned,
and the last length for the last piece to be cut from the
strand of material is determined based on the assigned
next-to-last length. The cut length may be assigned as
the next-to-last length for the next-to-last piece.
The next-to-last length and the last length are
adjusted by adding at least one predetermined submultiple
length from the next-to-last length to the last length.
The next-to-last length and the last length may be
adjusted such that the next-to-last length and the last
length are each greater than a predetermined minimum
length. The strand of material is cut to produce the
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next-to-last piece having the next-to-last length and to
produce the last piece having the last length.
Another method for cutting a strand of material is
disclosed. A cut length for at least one piece to be cut
from the strand of material is determined such that the
cu~ length is wilhin a predetermined range of cut lengths
and such that each of the at least one piece may be cut
into a number of subpieces each having a predetermined
subpiece length within a predetermined range of subpiece
lengths. The cut length for one embodiment is reduced by
at least one predetermined submultiple length if the cut
length is greater than a predetermined maximum length,
and the at least one predetermined submultiple length is
based on the predetermined subpiece length. The strand
of material is cut to produce the at least one piece
having the determined cut length.
A next-to-last length for a next-to-last piece to be
cut from the strand of material and a last length for a
last piece to be cut from the strand of material are
determined. The next-to-last length is determined such
that the next-to-last length is within the predetermined
range of cut lengths and such that the next-to-last piece
may be cut into a number of subpieces each having a first
subpiece length within the predetermined range of
subpiece lengths. The first subpiece length for one
embodiment is the predetermined subpiece length.
The last length is determined such that the last
length is within the predetermined range of cut lengths
and such that the last piece may be cut into a number of
subpieces each having a second subpiece length within the
predetermined range of subpiece lengths.
The next-to-last length and the last length are
determined to minimize a length of scrap material
remaining from the strand. The next-to-last length and
the last length may be adjusted by adding at least one
predetermined submultiple len~th from the next-to-last
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length to the last length such that the next-to-last
length and the last length are each greater than a
predetermined minimum length, wherein the at least one
predetermined submultiple length is based on the first
subpiece length. The strand of material is cut to
produce the next-to-last piece having the next-to-last
length and to produce the last piece having the last
length.
The material may comprise steel and may be produced
with a continuous steel caster. Each of the at least one
piece of steel is a bloom having a length based on a
billet length. Bach bloom may be cut into at least one
billet have the billet length. The steel strand may be
cut with a traveling torch cut-off station.
The next-to-last length and the last length may be
determined in response to one of at least one strand
field event prompting a determination of an alternative
cut length for the last piece. The at least one strand
field event may comprise an absence of steel in a mold
and a stopping of the strand.
Other objects, features, and advantages of the
present invention will be apparent from the accompanying
drawings and from the detailed description that follows
below.
BRIEF DE8CRIPTION OF THE DRAWINGS
The present invention is illustrated by way of
example and not limitation in the figures of the
accompanying drawings, in which like references indicate
similar elements and in which:
Figure 1 illustrates a continuous steel caster;
Figure 2 illustrates software organization for
controlling the cutting of steel strands into blooms;
Figure 3 illustrates a flow diagram for Level 3
bloom yield optimization;
Figure 4 illustrates a flow diagram for Level 2
bloom caster optimization;
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Figure 5 illustrates a top view of four strands that
are to be cut length optimized to produce blooms having
alternative cut lengths; and
Figure 6 illustrates a flow diagram for determining
alternative bloom cut lengths.
DETAILED DESCRIPTION
Figure 1 illustrates a continuous steel caster 100
for producing steel blooms and billets for customer
orders. Scrap steel is first heated to a molten state
using an electric arc furnace to produce molten steel for
transfer in a ladle 112 by a ladle transfer car. The
molten steel may then be refined at a ladle refiner
station and degassed in a vacuum degasser as appropriate
to cast a desired grade of steel. The molten steel in
ladle 112 is also referred to as a heat.
As illustrated in Figure 1, ladle 112 is moved to a
casting position on a casting floor 110 for pouring the
molten steel into a tundish 114 at a controlled rate
through a spout from the underside of ladle 112. The
release of molten steel through this spout is controlled
by a gate. Tundish 114 serves as a manifold for routing
the molten steel into a mold 116 through a nozzle at the
underside of tundish 114. The release of molten steel
through this nozzle is also controlled by a gate.
Mold 116 includes a water jacket that cools the
molten steel as the molten steel flows through mold 116.
Inside mold 116, the molten steel begins to form an outer
skin or shell as the molten steel starts to solidify into
a steel strand 120. The cross-sectional dimensions of
steel strand 120 are defined by the exit opening of mold
116 and may be of any suitable size.
Steel strand 120 falls past mold 116 along an
arcuate path defined by guide rollers 124, a curved
cooling chamber 126, and guide rollers 128. Cooling
chamber 126 includes nozzles that spray water onto the
outer surface of steel strand 120 for further
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solidification of steel strand 120. Guide rollers 128
guide steel strand 120 into a horizontal path where
withdrawal rollers 130 straighten steel strand 120.
Steel strand 120 may also be subjected to soft reduction
by withdrawal rollers 130 so as to resize steel strand
120 with a suitable cross-section. As one example, steel
strand 120 may be rolled to a cross-section of
approximately 10 inches by approximately 13 inches.
Steel strand 120 is then fed into a surface
quenching station 134 to treat the outer surface of steel
strand 120 prior to cutting steel strand 120 into
elongated blooms by traveling torch cut-off station 136.
A torch cut-off control system or digital data processing
system 140 is programmed with suitable software to
interface with cut-off station 136 for controlling the
cutting of steel strand 120. Data processing system 140
determines the cut length for each bloom and controls
cut-off station 136 in cutting steel strand 120.
The cut blooms are each discharged into a reheat
furnace and subsequently rolled and cut into elongated
billets each having a relatively smaller cross-sectional
area as compared to the blooms. The billets may then be
further processed in a roll mill to produce steel bars or
directly shipped to the customer for customer fabrication
of the steel endproduct.
As all the molten steel from ladle 112 is poured
into tundish 114, another ladle may be positioned to pour
more molten steel into tundish 114 so as to cast more of
steel strand 120. In this manner, the same or different
grades of steel may be continuously cast by caster 100
into one steel strand 120. Although steel strand 120 may
have regions of mixed steel as a result of this heat
sequencing process, such regions may be later cut from
steel strand 120 or from the resulting blooms or billets.
For convenience, caster 100 is illustrated in Figure
1 as casting one steel strand 120. Caster 100, however,
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may be configured to cast a plurality of steel strands
similarly as steel strand 120. ~s one example, caster
100 may include a tundish 114 having four nozzles
controlled by four gates for simultaneously pouring
molten steel from ladle 112 into four separate molds to
cast four parallel steel strands. Each of these strands
may be directed and processed similarly as steel strand
120 to produce blooms and billets.
Bloom Casting for Customer Orders
For each customer order, a cross-sectional area,
range of lengths, steel grade, and produced weight for
steel billets are specified. A measured amount of molten
steel is treated for each order to cast a heat of steel
having the specified grade. As each heat of molten steel
is cast by caster 100 into one or more steel strands, a
suitable number of blooms of suitable length are cut from
the cast strand or strands by cut-off station 136 for
later processing into billets for the order.
Data processing system 140 determines an optimized
bloom cutting schedule for each heat to be cast such that
the resulting blooms may be rolled and cut into a
suitable number of billets having a suitable cross-
sectional area, length, and weight to satisfy the order.
As data processing system 140 determines the cut length
for each bloom, data processing system 140 attempts to
maximize the bloom cut length to produce a maximum number
of billets from each bloom while maximizing the billet
length for each customer order. The bloom cut length may
be restricted, however, by other considerations
including, for example, mechanical limitations of the
reheat furnace used to reheat blooms for processing into
billets.
Data processing system 140 also determines the
cutting schedule to cast as much available molten steel
as possible for each heat. Available molten steel
excludes ladle losses and tundish skulls. Data
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processing system 140 attempts to minimize the amount of
scrap steel that results in casting each heat or strand.
Scrap steel length may result, for example, from uncut
steel remaining at the end of a heat or heat sequence
after blooms have been cut for the heat or heat sequence.
The casting of a heat or heat sequence may end because of
a number of conditions.
For one condition, the flow of molten steel into
caster 100 is stopped to stop the casting of a steel
strand or strands by caster 100. For another condition,
molten steel of one grade is poured into tundish 114
followed by molten steel of another grade. This
condition creates mixed steel in tundish 114, resulting
in the casting of a steel strand or strands having a
region of mixed steel. This region may or may not be cut
from the strand or strands. The mixing of steel in
tundish 114 may be avoided with a flying tundish change
by temporarily stopping the current casting of each
strand and exchanging tundish 114 with another tundish to
cast a different grade of steel. To separate the
different steel grades for each strand, a steel
transition piece may be dropped in each mold during the
tundish exchange.
Scrap steel may also result, for example, from
cutting blooms around a defective region in the strand or
strands. As one example, the temporary stopping of the
casting operation may cause steel in the mold or molds to
become defective as a result of overcooling during the
dwell time of the stop. Scrap steel length may remain in
avoiding the defective region to cut a bloom or blooms of
suitable length from each strand.
Data Processinq System Orqanization
As illustrated in Figure 2, data processing system
140 executes software organized in levels 210, 220, and
230 for determining an optimized bloom cutting schedule
and for controlling the cutting of blooms from each
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strand by cut-off station 136. Levels 210, 220, and 230
are also referred to as Level 3, Level 2, and Level 1,
respectively. Data processing system 140 may include any
suitable hardware architecture, including any suitable
programmable logic controllers for example, for e~ecuting
software in controlling cut-off station 136.
At Level 3, data processing system 140 executes a
production program 212 that maintains a database of
information for tracking steel production and for
controlling the cutting of blooms. Production program
212 generates a heat table 214 for maintaining
information about and tracking each heat of steel to be
cast. Each heat is iden~ified in heat table 214 by an
identifier heat_id. Heat table 214 may be used to store
pertinent information for each heat, such as steel grade
and test codes for example.
Production program 212 also generates a separate
rolling order table 216 for each heat to maintain
information about and track each customer order to be
cast from each heat. The location of rolling order table
216 for each heat may be identified in heat table 214.
Rolling order table 216 identifies each rolling order for
a heat by an identifier ID. Rolling order table 216 may
be used to store pertinent information for each rolling
order, such as a specified minimum billet length, a
specified maximum billet length, and a specified produced
weight for example.
For each rolling order identified in rolling order
table 216, production program 212 determines suitable
bloom and billet production information for an optimized
bloom yield independent of the amount of available steel
and independent of the occurrence of any strand field
events. This production information is stored in rolling
order table 216 and includes, for example, cold bloom cut
lengths and the number of blooms to be cut for each
rolling order.
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At Level 2, data processing system 140 e~ecutes
software including a cut optimization model 226 for
determining, among other things, programmed bloom cut
lengths and alternative bloom cut lengths based on the
bloom and billet production information stored in rolling
order table 216 at Level 3, the amount of available
steel, and the occurrence of strand field events as the
steel is cast. Cut optimization model 226 may also
assign each programmed and alternative bloom cut length
to a specific one of a plurality of strands being cast by
caster 100. The Level 2 software also includes a
metallurgical database having casting program tables 222
and cut optimization model parameters 224. Casting
program tables 222 store various information, including:
(1) a tail crop length (Lcrop);
(2) steel bloom density;
(3) soft-reduction settings ( P~trand); and
(4) bloom temperature settings (T).
Cut optimization model parameters 224 store a cut
optimization model configuration for use by cut
optimization model 226.
At Level 1, data processing system 140 executes a
strand cutting program 232 to control cut-off station 136
in cutting blooms from each strand based on the cut
lengths determined at Level 2. Data processing system
140 also executes strand field events software 234 at
Level 1 to report to cut optimization model 226 at Level
2 various strand field events as they occur, including:
(1) uncut material length left on each strand;
(2) emerging bloom length for each strand;
(3) length of the last bloom cut for each strand;
(4) ladle gate open (yes/no flag);
(5) presence or absence of steel in mold
(yes/no flag);
(6) temporary strand stop or restart (yes/no flag);
and
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(7) quality separation point (yes/no flag).
Level 3 Bloom Yield Optimization
As customers order steel to be cast, a rolling order
is defined at Level 3 in accordance with each customer's
steel requirements. The rolling order specifies:
(1) a desired cross-sectional dimension for cold
billets;
(2) a minimum length (lmin) for the cold billets;
(3) a maximum length (lmax) for the cold billets;
lo and
(4) a produced weight (Wro) required to fill the
customer's order.
Production program 212 stores this information in rolling
order table 216 for the heat having the desired grade of
steel to be cast.
Production program 212 executes an algorithm, as
illustrated in Figure 3 in flow diagram form, to
determine a solution for cutting from a steel strand or
strands a suitable number of nominal blooms and a last
bloom with each cut bloom having a suitable length so as
to produce an integer number of billets having a nominal
billet length, accounting for crops, and such that the
produced weight Wro for the customer's order is obtained.
Production program 212 determines the solution for each
rolling order when the rolling order is first defined and
after any updates for the rolling order. The solution
includes the following:
(1) an integer number of nominal blooms (Nn);
(2) a nominal bloom length (Ln);
(3) a last bloom length (Ll);
(4) an integer number of billets per nominal bloom
(nn);
(5) an integer number of billets for the last bloom
(nl);
(6) a nominal billet length (l); and
(7) a bloom submultiple length (Lbsm).
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For the solution, the billet length 1 is greater than or
equal to the minimum billet length lmin, as defined in
the rolling order, and less than or equal to the maximum
billet length lmax, as defined in the rolling order.
Also, the nominal bloom length Ln and the last bloom
length Ll are each greater than or equal to a minimum
bloom length (Lmin) and less than or equal to a maximum
bloom length (Lmax). The maximum bloom length Lmax is
defined in the metallurgical database at Level 2 and is
determined by the maximum permissible length for a bloom
to be discharged into and heated in the reheat furnace
for billet production. The minimum bloom length Lmin is
also defined in the metallurgical database at Level 2.
Production program 212 determines a solution for each
rolling order independent of the amount of steel
available and independent of the occurrence of any strand
field events.
For step 302 of Figure 3, the nominal bloom length
Ln is initialized to the m~; mum bloom length Lmax while
the billet length l is initialized to the maximum billet
length lmax. Also, a smallest potential steel scrap
length Ldiff is initialized to the minimum bloom length
Lmin.
For steps 304-314, the nominal billet number nn is
determined for an as large as possible nominal bloom
length Ln in accordance with the following equation:
Ln= (nn*l+lcrop) (1)
where:
lcrop = a billet crop length; and
p = a billet rolling mill (BRM) reduction
factor.
The billet crop length lcrop is size dependent and may be
equal to, for example, twice the length for a head crop
as defined in casting program tables 222 at Level 2. The
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billet rolling mill reduction factor p is size dependent
and may be determined by the bloom cross-section divided
by the specified billet cross-section a$ calculated at
Level 3 or as defined in casting program tables 222 at
Level 2.
For step 304, the nominal billet number nn is
determined in accordance with equation (1) above based on
the nominal bloom length Ln and the billet length l as
initialized for step 302, and the calculated nominal
billet number nn is rounded up to the nearest integer for
step 306. The billet length l is then determined for
step 308 in accordance with equation (1) above based on
the initialized nominal bloom length Ln and the rounded
nominal billet number nn.
If the calculated billet length l is less than the
minimum billet length lmin as determined for step 310,
the nominal billet number nn and the billet length l are
recalculated. For step 312, the billet length l is reset
to the maximum billet length lmax while the nominal bloom
length Ln is reduced by delta_L. So long as the nominal
bloom length Ln remains greater than or equal to the
minimum bloom length Lmin as determined for step 314, the
nominal billet number nn and the billet length l are
recalculated for steps 304-312 until the billet length l
as calculated for step 308 is greater than or equal to
the minimum billet length lmin as determined for step
310. If the nominal bloom length Ln is reduced to a
value below the minimum bloom length Lmin as determined
for step 314, control proceeds to step 338 to determine
suitable default values as a final solution for the
present rolling order.
When a suitable nominal billet number nn and a
suitable billet length l are determined for steps 304-
314, the nominal bloom number Nn, the last bloom billet
number nl, and the last bloom length Ll are determined
~ 22nlll0n ~3
for steps 316-324 in accordance with the following
equations:
Nn*nn*1*Wlnorm=Wro (2)
(Nn*nn+nl) *l*Wlrlorm2Wro (3)
Ll = (n~ l crop)
where:
Wlnorm = cold billet weight per unit length.
The cold billet weight per unit length Wlnorm is size
dependent and may be defined in casting program tables
10222 or calculated from billet dimensions and density.
For step 316, the nominal bloom number Nn is
determined in accordance with equation (2) above based on
the calculated nominal billet number nn and the
calculated billet length l, and the calculated nominal
bloom number Nn is truncated to the nearest integer for
step 318. The last bloom billet number nl is then
determined for step 320 in accordance with equation (3)
above based on the calculated nominal billet number nn,
the calculated billet length l, and the truncated nominal
bloom number Nn, and the calculated last bloom billet
number nl is rounded up to the nearest integer for step
322. Based on the calculated last bloom billet number nl
and the calculated billet length l, the last bloom length
Ll is determined for step 324 in accordance with equation
(4) above. If the last bloom length Ll is determined for
step 326 to be greater than or equal to the minimum bloom
length Lmin, a suitable solution based on the current
calculated values has been determined for the present
rolling order and control proceeds to step 334.
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If the last bloom length Ll is determined for step
326 to be less than the minimum bloom length Lmin, then
another potential solution is calculated based on a
shorter nominal bloom length Ln until a suitable last
bloom length Ll is found as determined for step 326.
For step 328, the difference of the last bloom
length Ll from the minimum bloom length Lmin is
determined and compared with the smallest potential steel
scrap length Ldiff. As the scrap length Ldiff is
initialized to the minimum bloom length Lmin for step
302, this difference is less than the scrap length Ldiff
the first time the comparison for step 328 is performed
for the present rolling order. The scrap length Ldiff is
set to the difference of the last bloom length Ll from
the minimum bloom length Lmin for step 330 and represents
the smallest potential steel loss in the event a suitable
last bloom length Ll greater than or equal to the minimum
bloom length Lmin is not found. The current calculated
values are saved for step 332 as a possible final
solution for the present rolling order.
To calculate another potential solution for the
present rolling order, control proceeds to step 312 where
the nominal bloom length Ln is reduced by delta_L. Steps
304-332 are repeated so long as the nominal bloom length
Ln remains greater than or equal to the minimum bloom
length Lmin as determined for step 314 and until a
suitable solution has been found as determined for step
326.
If the last bloom length Ll for the new potential
solution is less than the minimum bloom length Lmin as
determined for step 326, the difference of this last
bloom length Ll from the minimum bloom length Lmin is
determined and compared with the smallest scrap length
Ldiff for step 328. If this difference is less than the
smallest scrap length Ldiff, this difference becomes the
new smallest scrap length Ldiff for step 330. The new
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potential solution is saved for step 332 as a poten~ial
final solution for the present rolling order that would
minimize the amount of steel scrap as compared to the
just prior saved solution. Control then proceeds to step
312 in an attempt to calculate for the present rolling
order a solution that has a last bloom length Ll greater
than or equal to the minimum bloom length Lmin as
determined for step 326 or that would reduce the amount
of steel scrap as compared to the just saved solution.
If the difference of the last bloom length Ll for
the new potential solution from the minimum bloom length
Lmin is greater than or equal to the smallest scrap
length Ldiff for step 328, then the new potential
solution would not minimize the amount of steel scrap as
compared to the just prior saved solution. Control then
proceeds to step 312 in an attempt to calculate for the
present rolling order a solution that has a last bloom
length Ll greater than or equal to the minimum bloom
length Lmin as determined for step 326 or that would
reduce the amount of steel scrap as compared to the just
prior saved solution for step 328.
If a suitable solution having a last bloom length Ll
greater than or equal to the minimum bloom length Lmin is
determined for step 326, control proceeds to step 334 and
the calculated values for this determined solution are
used for the present rolling order. For step 336, the
bloom submultiple length Lbsm is calculated in accordance
with the following equation.
Lbsm= 1 ( 5 )
If, however, the nominal bloom length Ln is reduced to a
value less than the minimum bloom length Lmin as
determined for step 314, control proceeds to step 338.
If the nominal bloom length Ln was reduced to a
value less than the minimum bloom length Lmin as
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determined for step 314 prior to the determination of a
first potential solution for the present rolling order as
determined for step 338, default values are used for the
present rolling order. For step 340, the nominal bloom
length Ln and the billet length l are set to nominal
lengths Lnom and lnom, respectively. The nominal billet
number nn is then determined for step 342 in accordance
with equation (1) above and truncated to the nearest
integer for step 344. The nominal bloom number Nn is
then determined for step 346 in accordance with equation
(2) above and truncated to the nearest integer for step
348. The last bloom billet number nl is then determined
for step 350 in accordance with equation (3) above and
rounded up to the nearest integer for step 352. For step
354, the last bloom length Ll is determined for step 354
in accordance with equation (4) above. The submultiple
bloom length Lbsm is then determined for step 336 in
accordance with equation (5) above.
If at least a first potential solution has been
determined for step 338, then for step 356 the just prior
saved solution is used for the present rolling order
while for step 358 the last bloom length Ll is set equal
to the minimum bloom length Lmin for the present rolling
order. This solution is determined to minimize the
amount of remaining scrap steel for the last bloom for
the present rolling order. The submultiple bloom length
Lbsm is then determined for step 336 in accordance with
equation (5) above.
Production program 212 stores in rolling order table
216 the final solution determined for each rolling order
for use by cut optimization model 226 at Level 2.
Level 2 Bloom Caster Optimization
Cut optimization model 226 at Level 2 determines the
bloom cut lengths (L) at which each bloom is to be cut
from a steel strand by cut-off station 136 based on
information from rolling order table 216 at Level 3,
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information from the metallurgical database at Level 2,
the amount of available steel, and the occurrence of
strand field events reported from strand events 234 at
Level 1 as the steel is cast. Figure 4 illustrates in
flow diagram form one algorithm for cut optimization
model 226.
For step 402 of Figure 4, cut optimization model 226
begins determining programmed bloom cut lengths L upon
the occurrence of one of a number of field events that
prompt for the determination of programmed bloom cut
lengths L. Such field events include the opening of the
ladle gate and the occurrence of a strand restart. The
ladle gate open event indicates molten steel from ladle
112 has been released into tundish 114 to start casting a
steel strand or strands. The strand restart event
indicates strand casting has been restarted after a
temporary strand stop.
For step 404 of Figure 4, a next cold bloom length
(Lcut) is popped from rolling order table 216. The cold
bloom length Lcut corresponds to the nominal bloom length
Ln or the last bloom length Ll for each rolling order of
rolling order table 216. Cut optimization model 226
treats rolling order table 216 as a first-in, first-out
(FIF0) stack so as to help charge blooms into the billet
production reheat furnace in the same order in which they
were cut. In this manner, the blooms for a given rolling
order may be grouped together in the reheat furnace to
facilitate billet production for the rolling order.
For step 406 of Figure 4, the popped cold bloom
length Lcut is assigned to the steel strand having the
largest emerging bloom length as reported by strand
events 234 at Level 1. For one example, rolling order
table 216 may include the following information.
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Rolling Order Nominal Bloom Nominal Bloom Last Bloom
ID Number (Nn) Length (Ln) Length (Ll)
0 0 10000
2 1 11000 10000
3 4 12000 11000
Strand events 234 may include the following information.
Data from Level 1 Strand 1 Strand 2 Strand 3 Strand 4
Emerqinq Lenqth 4500 5500 8000 9000
For this example, cut optimization model 226 may pop from
rolling order table 216 the 10000 cold bloom length for
rolling order ID 1 as the next cold bloom length for step
404. Cut optimization model 226 may then for step 406 -
assign this bloom to strand 4 because strand 4 at this
time has the longest emerging bloom length of the
strands. That is, strand 4 has the longest length of
unassigned, uncut steel that has passed cut-off station
136.
For a next step 404, cut optimization model 226 may
pop from rolling order table 216 the 11000 cold bloom
length for rolling order ID 2 as the next cold bloom
length. Cut optimization model 226 may then for a next
step 406 assign this bloom to strand 3 which at that time
would have the longest emerging bloom length of the
strands.
For subsequent steps 404 and 406, the assignment of
popped cold bloom lengths to strands may be as follows.
Strand 1 2 3 4
Next Bloom Length 12000 10000 11000 10000
Second-Next Bloom 11000 12000 12000 12000
Length
19
~ ~ o ~ ~ o ~ ~
For step 408 of Figure 4, the programmed bloom cut
length L for each popped cold bloom length Lcut may be
determined in accordance with the following equation.
Ktemp*T*LCuti~testi j+ 1 * ~ k (6)
P s~Iand
If Li j > Lmax, then the cold bloom length Lcuti is
reduced by one bloom submultiple length Lbsmi in
accordance with the following equation.
Lcuti=Lcuti- i (7)
Li j is then calculated again in accordance with equation
(6). Cut optimization model 226 determines the
programmed bloom cut length Li j in accordance with
equations (6) and (7) until Li j < Lmax.
For equations (6) and (7):
i = rolling order (R0) identifier;
j = bloom identifier;
k = billet identifier;
Li j = programmed cut length for identified
bloom;
Ktemp = experimental coefficient;
T = bloom temperature;
Lcuti = cold bloom length for identified R0;
~testi j = test length for identified bloom;
Pi = billet rolling mill (BRM) reduction
factor for identified R0;
testsi j = integer number of BRM tests on the
billets for identified bloom;
~i ' k = length of the BRM test cut for
",
identified billet;
CLL = length lost by cut;
~, ~ 2 0 ~
Pstrand = soft-reduction on strand;
Lmax = maximum bloom length;
li = cold billet length for identified R0;
and
Lbsmi = bloom submultiple length for
identified R0.
The values for Lcuti, Pi~ tests~ i j k~ li, and
Lbsmi may be defined in rolling order table 216. The
values for Ktemp, ~testi j, CLL, and Lmax may be defined
in the metallurgical database at Level 2. The values for
T and P8trand may be defined in casting program tables 222
of the metallurgical database at Level 2.
For step 410 of Figure 4, cut optimization model 226
sends the programmed bloom cut length Li j as determined
for step 408 to strand cutting program 232 at Level 1 so
that a bloom having this programmed bloom cut length Li
may be cut from the assigned strand.
Cut optimization model 226 continues to determine
programmed bloom cut lengths Li j for step 404 through
step 410 until the occurrence of one of a number of field
events that prompt for the determination of alternative
bloom cut lengths L, as determined for step 402. Such
field events include the absence of steel in the mold or
molds and the temporary stopping of a strand or strands.
Steel may be absent from the mold or molds due to a
programmed stopping of a corresponding strand or due to a
strand break out. Also, a strand or strands may be
temporarily stopped to perform a flying tundish change,
for example.
When such a field event has occurred, each strand
may be stopped, if necessary, for step 414 of Figure 4 so
that cut optimization model 226 may determine alternative
bloom cut lengths L to minimize the amount of scrap steel
that may result in cutting blooms from each strand. For
step 416 of Figure 4, cut optimization model 226
determines the alternative cut lengths L for a last bloom
-
-
2 ~ 0 ~3
and a next-to-last bloom that are to be cut from each
strand at the end of a heat or heat sequence or just
prior to a defective region of the strand.
Figure 5 illustrates a top view of four strands 510,
520, 530, and 540 that are to be cut length optimized to
cast blooms having alternative cut lengths as determined
for step 416 of Figure 4. caster loo moves each strand
510, 520, 530, and 540 along the direction indicated by
arrow 502. Each strand 510, 520, 530, and 540 of Figure
5 includes a crop portion 512, 522, 532, and 542,
respectively. Each crop portion 512, 5Z2, 532, and 542
may represent a defective region of the strand or may
represent a tail crop or transition piece for the end of
a heat or heat sequence. Strands 510, 520, 530, and 540
also include bloom portions 514-515, 524-525, 534-535,
and 544-545 that may be cut from strands 510, 520, 530,
and 540 as illustrated in Figure 5. Each strand 510,
520, 530, and 540 further includes a remaining portion
516, 526, 536, and 546, respectively.
The cut lengths for bloom portions 514-515, 524-525,
534-535, and 544-545 are programmed bloom cut lengths as
determined for step 408 of Figure 4. The length of each
remaining portion 516, 526, 536, and 546 is less than
that needed for blooms having programmed cut lengths. In
determining alternative cut lengths, each remaining
portion 516, 526, 536, and 546 corresponds to the last
bloom for each strand 510, 520, 530, and 540,
respectively, and each bloom portion 515, 525, 535, and
545 corresponds to the next-to-last bloom for each
strand.
For step 416 of Figure 4, the length of the last
bloom for each strand is first compared with the minimum
bloom length Lmin. If the last bloom length is greater
than or equal to the minimum bloom length Lmin, then the
lengths for the last bloom and the next-to-last bloom are
sent to Level 1 for step 410 without modification.
-
~ O ~ 1 ~ n ~
.
Otherwise, the next-to-last bloom length is reduced by a
bloom submultiple length or lengths to lengthen the last
bloom until the last bloom length is greater than or
equal to the minimum bloom length Lmin.
The alternative cut length for the last bloom may be
determined for each strand in accordance with the
following equation.
Ktemp*T*r* Pi +~testi,j+ Pi* k~l 8i,j,k ~)
strand
The alternative cut length for the next-to-last
bloom may be determined for each strand in accordance
with the following equation.
Ktemp*~*s* p +~\ test~ + p * k~ i,j-l,k ~9 )
Pf~trand
For equations (8) and (9):
i = rolling order (RO) identifier;
j = bloom identifier;
k = billet identifier;
Li j = alternative cut length for last
bloom;
Li,j-1 alternative cut length for next-to
last bloom;
Xtemp = experimental coefficient;
T = bloom temperature;
r = integer number of billets for last
bloom;
s = integer number of billets for next-
to-last bloom;
lai = cold billet length for last bloom of
identified RO;
. ~ -
~ 10 ~ ~
.
li = cold billet length for next-to-last
bloom of identified RO;
PL = billet rolling mill (BRM) reduction
factor for identified R0;
atesti j = test length for identified bloom;
testsi j = integer number of BRM tests on the
billets for identified bloom;
Si,j,k = length of the BRM test cut for
identified billet;
CLL = length lost by cut; and
P~trand = soft-reduction on strand.
For equations (8) and (9), the number of billets r
for the last bloom, the number of billets s for the next-
to-last bloom, and the billet length lai for the last
bloom are determined such that the following five
criteria are met:
(a) s is as large as possible;
(b) lmini < lai < lmaxi;
(c) Lmin < Li j < Lmax;
(d) Lmin < Li j-1 < Lmax; and
(e) Llost is minimized in accordance with the
following equation:
Llost=Lres-Li j-Li j l-Lcrop ( 10)
.
where:
- lmini = minimum cold billet length for
identified R0;
lmaxi = maximum cold billet length for
identified RO;
Lmin = minimum bloom length;
Lmax = maximum bloom length;
Llost = lost length of scrap material;
Lres = length of remaining portion of strand
for last two blooms and crop; and
Lcrop = length for aim tail crop, transition
24
',~ 2~01~n~ ~
.
piece, or defective region.
The values for li, Pi~ teStsi~ ,k~ lmini~ and
lmaxi may be defined in rolling order table 216. The
values for Ktemp, ~testi j, CLL, Lmin, and Lmax may be
defined in the metallurgical database at Level 2. The
values for T, P8trandl and Lcrop may be defined in casting
program tables 222 of the metallurgical database at Level
2. The value for Lres may be defined from the uncut
material length left on each strand from strand events
234 at Level 1.
If cut optimization model 226 determines no solution
for equations (8) and (9) meets the five criteria (a)
through (e) above, the original programmed cut length for
the next-to-last bloom is sent to Level 1 for step 410
while no alternative cut length is sent for the last
bloom as the last bloom is to become part of the crop for
scrap.
Figure 6 illustrates in flow diagram form one
algorithm for determining alternative bloom cut lengths L
for each strand for step 416 of Figure 4. For step 602
of Figure 6, the initial next-to-last bloom length
LneXtla8t and last bloom length Llaat are determined. The
initial next-to-last bloom length Lnextlagt is the
programmed cut length for the next-to-last bloom as
determined for step 408 of Figure 4. The initial last
bloom length Ll~ a~ .is determined in accordance with the
_ _
following equation.
Llast=Lres-Lnoxtlagt-Lcrop (11)
If this initial last bloom length Lla9t is greater
than or equal to the minimum bloom length Lmin as
determined for step 604, then the billet number r, the
billet length la, and the bloom length Lla9t are
determined for step 606. The billet number r and the
billet length la may be determined to maximize the last
0 ~10 0 ~
bloom length Lla8t in accordance with equation (8) above
so as to minimize the lost length of scrap material Llost
in accordance with equation (10) above.
For one example, one of two solutions may be
selected for step 606. For one solution, the billet
length la may be set to the maximum billet length lmax to
determine the bille~ number r in accordance with equation
(8) above, using the initial last bloom length L1a~t as
determined for step 602. This billet number r may be
rounded up to the nearest integer and the billet length
la may be shortened such that Lla8t remains its initial
value in accordance with equation (8) above.
For the second solution for this example, the billet
length la may be set to the minimum billet length lmin to
determine the billet number r in accordance with equation
(8) above, using the initial last bloom length Llagt as
determined for step 602. This billet number r may be
truncated to the nearest integer and the billet length la
may be lengthened such that Lla~t remains its initial
value in accordance with equation (8) above.
of the above two solutions, the solution that would
yield the longest billet length la greater than or equal
to the minimum billet length lmin and less than or equal
to the maximum billet length lmax is selected for step
606.
If neither solution would yield such a billet length
la, then a suitable billet number r and a suitable billet
length la are determined so as to maximize the last bloom
length Lla8t for the last bloom to be cut from the strand.
For one embodiment, the billet number r may be truncated
to the nearest integer for each of the above two
solutions, and the solution resulting in the greater
yield may then be used.
If the last bloom length Llagt as determined for step
606 is greater than or equal to the minimum bloom length
Lmin as determined for step 608, then for step 610 the
26
n ~
.
next-to-last bloom length LneXtla~t as determined for step
602 and the last bloom length Lla~t as determined for step
606 are to be sent to Level 1 for step 410 of Figure 4.
If the initial last bloom length LlaSt is less than
the minimum bloom length Lmin as determined for step 604
or if alternative bloom lengths are to be determined for
step 612, then the next-to-last bloom length LneXtlast is
reduced by a bloom submultiple length or lengths in an
attempt to lengthen the last bloom to a suitable length
LlaSt that is greater than or equal to the minimum bloom
length Lmin. For step 614, the next-to-last bloom length
LneXtla~t is reset to the ~;mum bloom length Lmax. The
number of billets s for the next-to-last bloom is then
determined for step 616 in accordance with equation (9)
above based on the reset bloom length LneXtlast and
truncated to the nearest integer for step 618. Based on
this truncated billet number s, the next-to-last bloom
length LneXtlast is determined for step 620 in accordance
with equation (9) above.
If this next-to-last bloom length Lnextlast is less
than the minimum bloom length Lmin as determined for step
622, then for step 624 the initial next-to-last bloom
length LneXtlast as determined for step 602 is to be sent
to Level 1 for step 410 of Figure 4 while no cut length
is sent for the last bloom as the last bloom is to become
part of the crop for scrap. If the next-to-last bloom
length LneXtla~t is greater than or equal to the minimum
bloom length Lmin as determined for step 622, then the
last bloom length ~la~t iS determined for step 626 in
accordànce with equation (11) above based on the next-to-
last bloom length ~nextla8t as determined for step 620.
If the last bloom length Llaat is greater than or
equal to the minimum bloom length Lmin as determined for
step 628, then the billet number r, the billet length la,
and the last bloom length Lla~t are determined for step
~J 2 2 ~
.
606. Step 606 through step 612 are performed similarly
as described above.
If the last bloom length L1aSt is less than the
minimum bloom length Lmin as determined for step 628 or
if alternative bloom lengths are being determined for
step 612, then the billet number s is reduced by one for
step 630 to reduce the next-to-last bloom length LneXtlast
by one bloom submultiple in an attempt to lengthen the
last bloom to a suitable length. Steps 620 through 630
and steps 606 through 612 are repeated until a suitable
last bloom length LlaSt as determined for step 606 is
greater than or equal to the minimum bloom length Lmin as
determined for step 608 or until the next-to-last bloom
length LneXtlast has been reduced below the minimum bloom
length Lmin as determined for step 622.
Reassiqnment of Bloom Cut Lenqths
Cut optimization model 226 may also reorder the
assignment of bloom cut lengths to strands in response to -
a field event from strand events 234 that one or more
strands have been stopped as another strand or strands
continue to be cast. If the emerging bloom length for a :~
strand or strands becomes greater than that for a stopped
strand or strands, cut optimization model 226 may
reassign cut lengths for strand cutting program 232 based
on the current emerging bloom lengths for the strands.
As with the example above, strand events 234 may
include the following information.
Data from Level 1 Strand 1 Strand 2 Strand 3 Strand 4
Emerqinq Lenqth 4500 5500 8000 9000
Cut optimization model 226 may assign popped cold bloom
lengths to strands as follows.
28
-; ~ 2 2 ~ 0
.
Strand 1 2 3 4
Next Bloom Length 12000 10000 11000 10000
Second-Next Bloom 11000 12000 12000 12000
Length
s
For this example, if strand 4 is stopped and the emerging
bloom length for strand 3 becomes greater than that for ~ --
strand 4, cut optimization model 226 may reorder the
assignment of bloom cut lengths as follows.
Strand 1 2 3 4
Next Bloom Length 12000 10000 10000 11000
Second-Next Bloom 11000 12000 12000 12000
Length
The bloom length previously assigned to strand 4 iS now
assigned to strand 3 as the emerging bloom length for =
strand 3 became greater than that for strand 4.
If strand 4 is restarted with steel in the mold as
reported by strand events 234, cut optimization model 226
' 20 may determine alternative bloom cut lengths for strand 4
to account for the defective region in the restarted
strand that resulted from the overcooling of steel in the
mold. If strand 4 is restarted without steel in the mold
as reported by strand events 234, cut optimization model
226 may determine alternative bloom cut lengths for
strand 4 to account for the tail crop length at the end
of the restarted strand.
Cut optimization model 226 may continue to reassign
cut lengths for strand cutting program 232 as the
emerging bloom lengths for each strand change. Cut
optimization model 226 may also continue to determine
suitable programmed bloom cut lengths and alternative
bloom cut lengths as necessary to account for defective
regions, transition pieces, and tail crops of the
3 5 s trands.
29
~ 0 ~3
.
Level 1 Strand Cutting Program
Strand cutting program 232 at Level 1, as
illustrated in Figure 2, stores for each strand being
cast by caster 100 the bloom cut lengths L sent from cut
optimization model 226 at Level 2. Based on these bloom
cut lengths L, strand cutting program 232 controls cut-
off station 136 to cut the blooms from each strand.
Data processing system 140 may be configured to
execute software at Level 1 to display on a monitor or
monitors the bloom cut lengths L sent to strand cutting
program 232 for viewing by an operator as cut-off station
136 cuts blooms from the strand or strands. Data
processing system 140 may also execute software at Level
to provide for interactive modification of cut lengths
as desired by the operator so that the operator may also
control the cutting of blooms by cut-off station 136.
Billet and Bar Production
After being cut from the strand or strands by cut-
off station 136, each bloom may be discharged into the
reheat furnace and subsequently rolled and cut into
billets. For each rolling order, the billets are rolled
to a cross-sectional size in accordance with the billet
rolling mill reduction factor p for the rolling order.
The billets are also cut to lengths in accordance with
the billet length l for the rolling order as determined
at Level 3 or with the billet length la as determined by
cut optimization model 226 at Level 2 for a last bloom.
Once cut, the billets may then be further processed in a
roll mill to produce steel bars or directly shipped to
the customer for customer fabrication of the steel
endproduct.
In the foregoing description, the invention has been
described with reference to specific exemplary
embodiments thereof. It will, however, be evident that
various modifications and changes may be made thereto
without departing from the broader spirit or scope of the
011~ ~ ~
.
present invention as defined in the appended claims. The
specification and drawings are, accordingly, to be
regarded in an illustrative rather than a restrictive
sense.
What is claimed is:
