CA2201100A1

CA2201100A1 - Cast steel cut length optimization

Info

Publication number: CA2201100A1
Application number: CA002201100A
Authority: CA
Inventors: James M. Kellams; Johan I. Harsta; Andrea Pilastro; Francesco Fabris
Original assignee: Republic Engineered Steels Inc
Current assignee: Individual
Priority date: 1996-08-02
Filing date: 1996-08-02
Publication date: 1998-02-03
Also published as: WO1998006052A1

Abstract

A continuous steel caster (100) uses cut length optimization to minimize the amount of scrap steel in cutting a steel strand (120; 510; 520; 530; 540) into blooms with a traveling torch cut-off station (136). The steel strand is cut to produce at least one bloom (514;
524; 534; 544) having a determined cut length. The length for a next-to-last bloom (515; 525; 535; 545) is determined (416; 602-630) such that the next-to-last length is within a predetermined range of cut lengths and such that the next-to-last bloom may be cut into a number of billets each having a billet length within a predetermined range of billet lengths. The length for a last bloom (516; 526; 536; 546) is also determined (416;
602-630) such that the last length is within a predetermined range of cut lengths and such that the last bloom may be cut into a number of billets each having a billet length within the predetermined range of billet lengths. The next-to-last length and the last length are determined to minimize the amount of scrap steel remaining from the strand and may be adjusted by adding at least one predetermined submultiple length from the next-to-last length to the last length such that the next-to-last length and the last length are each greater than a predetermined minimum length. The steel strand is cut to produce the next-to-last bloom having the next-to-last length and to produce the last bloom having the last length.

Description

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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 ,~ 22~110~ ~
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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 ~ 220110~ ~3 --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.

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 ~J ~ 2 0 ~ 1 0 0 ~
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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, ~) 220~100 ~

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 ~, 2 2 0 ~ ~ O ~ ~

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 ~ 2~0~00 ~
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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.

.- 22~1~00 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 ~ 2~ O O ~

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 ~ ~ 2 ~

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 ~ ~ 2 ~ 0 1 1 0 0 ~3 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, ~J 2 ~ n 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) 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 ~ ~ 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;

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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 ',~ 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 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.

-; ~ 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.

~ 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:

Claims

1. A method for cutting a strand of material, comprising the steps of:
(a) determining a cut length for at least one piece to be cut from the strand of material, wherein the determined cut length is based on a predetermined submultiple length;
(b) cutting the strand of material to produce the at least one piece having the determined cut length;
(c) determining 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, wherein the determining step (c) comprises the steps of:
(i) assigning the next-to-last length for the next-to-last piece to be cut from the strand of material, (ii) determining the last length for the last piece to be cut from the strand of material based on the assigned next-to-last length, and (iii) adjusting the next-to-last length and the last length by adding at least one predetermined submultiple length from the next-to-last length to the last length; and (d) cutting the strand of material to produce the next-to-last piece having the next-to-last length and to produce the last piece having the last length.

2. The method of claim 1, wherein the determining step (a) comprises the step of reducing the cut length by at least one predetermined submultiple length if the cut length is greater than a predetermined maximum length.

3. The method of claim 1, wherein the assigning step (c)(i) comprises the step of assigning the cut length as the next-to-last length for the next-to-last piece.

4. The method of claim 1, wherein the adjusting step (c)(iii) comprises the step of adjusting the next-to-last length and the last length such that the next-to-last length and the last length are each greater than a predetermined minimum length.

5. The method of claim 1, wherein the material comprises steel, wherein each of the at least one piece of material is a bloom, and wherein the predetermined submultiple length is based on a predetermined billet length.

6. The method of claim 5, comprising the step of cutting each bloom into at least one billet have the predetermined billet length.

7. The method of claim 1, wherein the determining step (c) comprises the step of determining the next-to-last length and the last length in response to one of at least one strand field event prompting a determination of an alternative cut length for the last piece.

8. The method of claim 7, wherein the material comprises steel and wherein the at least one strand field event comprises an absence of steel in a mold and a stopping of the strand.

9. The method of claim 1, comprising the step of producing the strand with a continuous steel caster.

10. The method of claim 9, wherein the cutting steps (b) and (d) each comprise the step of cutting the strand with a traveling torch cut-off station.

11. A bloom cut from a strand of material comprising steel in accordance with the method of claim 5.

12. A billet cut from a bloom comprising steel in accordance with the method of claim 6.

13. A method for cutting a strand of material, comprising the steps of:
(a) determining a cut length for at least one piece to be cut from the strand of material such that the cut length is within 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;
(b) cutting the strand of material to produce the at least one piece having the determined cut length;
(c) determining 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, wherein the determining step (c) comprises the steps of:
(i) determining the next-to-last length 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, (ii) determining the last length 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, and (iii) determining the next-to-last length and the last length to minimize a length of scrap material remaining from the strand; and (d) cutting the strand of material to produce the next-to-last piece having the next-to-last length and to produce the last piece having the last length.

14. The method of claim 13, wherein the determining step (a) comprises the step of reducing the cut length by at least one predetermined submultiple length if the cut length is greater than a predetermined maximum length, wherein the at least one predetermined submultiple length is based on the predetermined subpiece length.

15. The method of claim 13, wherein the determining step (c) comprises the step of adjusting the next-to-last length and the last length by adding at least one predetermined submultiple length from the next-to-last 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.

16. The method of claim 13, wherein the first subpiece length is the predetermined subpiece length.

17. The method of claim 13, wherein the material comprises steel, wherein each of the at least one piece of material is a bloom, and wherein each subpiece is a billet.

18. The method of claim 17, comprising the step of cutting each bloom into at least one billet have the predetermined subpiece length.

19. The method of claim 13, wherein the determining step (c) comprises the step of determining the next-to-last length and the last length in response to one of at least one strand field event prompting a determination of an alternative cut length for the last piece.

20. The method of claim 19, wherein the material comprises steel and wherein the at least one strand field event comprises an absence of steel in a mold and a stopping of the strand.

21. The method of claim 13, comprising the step of producing the strand with a continuous steel caster.

22. The method of claim 21, wherein the cutting steps (b) and (d) each comprise the step of cutting the strand with a traveling torch cut-off station.

23. A bloom cut from a strand of material comprising steel in accordance with the method of claim 17.

24. A billet cut from a bloom comprising steel in accordance with the method of claim 18.