Abstract:
Maximum yield in the production of a slab from a bottle-cap mold ingot is obtained by a method of selecting the ingot mold size.

Description:
BACKGROUND OF THE INVENTION 
     This invention relates to a method of producing steel slabs. More particularly, it relates to such a method in which the slabs are rolled from a bottle-cap mold ingot. 
     Slabs of steel are ordered on the basis of metallurgical grade, maximum weight, and specified width. According to the metallurgical grade, the steel is poured either into a bottle-cap ingot mold, which is characterized by a fixed volume, or into either an open-top or a hot-top ingot mold, which has a variable volume. 
     In the past, bottle-cap ingots were somewhat arbitrarily assigned a maximum providing yield of 96% when rolled into slabs of various widths. This percentage was based upon the maximum yield from the highest yielding ingot size. Thus, to determine the proper size ingot mold for a particular slab, a data base was first searched to obtain the smallest bottle-cap ingot mold in stock that would product as ingot: (1) having one cross-sectional dimension larger than the sum of said specified width plus the width increment reserved for edge work, and (2) a full mold ingot weight greater than the ordered maximum slab weight. 
     The ordered maximum slab weight was then divided by the maximum providing yield to obtain the required ingot weight. If this weight was about the same as the full mold ingot weight of the ingot mold selected from the data base, this mold was used. If not, the next larger ingot mold was selected. 
     It has been found that the yield from a bottle-cap ingot varies as much as 8%, depending upon the size of the ingot and the width of the slab. Thus, if ingot sizes other than the highest yielding ingot size were used, the resultant slab was sometimes lighter than the desired weight. 
     It is an object of the present invention to provide a method of producing a slab of steel from a bottle-cap ingot in which the actual weight of the slab is about equal to the ordered maximum weight of the slab. 
     SUMMARY OF THE INVENTION 
     I have discovered that the foregoing object can be obtained by searching a data base, in the same manner as in the prior art, to obtain the smallest bottle-cap ingot mold size in stock that will produce an ingot: (1) having one cross-sectional dimension larger than the sum of the desired slab width plus the width increment reserved for edge work, and (2) a full mold ingot weight greater than the maximum slab weight. 
     Next, the average providing yield for the width to be rolled from an ingot produced in said smallest ingot mold is obtained from an equation representing the average providing ingot yields for various width slabs rolled from this ingot size. The minimum required ingot weight for this slab is then determined by: (1) determining the estimated maximum providing yield for said width by adding to said average providing yield a number representing the difference between the average providing yield and the maximum providing yield for a bottle-cap ingot produced in said smallest ingot mold, and (2) dividing said maximum slab weight by said maximum providing yield. 
     The next step in the process comprises comparing the minimum required ingot weight with the full mold ingot weight. If the minimum required ingot weight and the full mold ingot weight are substantially the same, this smallest ingot size is selected. If the minimum required ingot weight and the full mold ingot weight are not the same, the steps beginning with obtaining the average yield are repeated for successively larger ingot sizes until the minimum required ingot weight and the full mold ingot weight are substantially the same. 
     The selected ingot mold is then filled with molten steel of the ordered metallurgical grade, and the ingot mold is capped. The steel is allowed to solidify into an ingot, and the ingot is then rolled into a slab of the specified width. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     FIGS. 1 and 2 are curves showing the yield as a function of slab width for first and second ingot sizes, respectively. 
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENT 
     As a specific example of the invention, assume that an order for a bottle-cap steel grade is received specifying a maximum slab weight of 21,700 lbs (9,843 Kg) and a slab width of 45 in (114 cm). 
     Bottle-cap ingots must be reduced by a minimum of 4 in (10.2 cm) to provide the slab with the desired edge characteristics. This reduction, referred to in the art as &#34;edge work&#34;, must then be added to the specified slab width to obtain the dimension used to determine the minimum ingot size to be poured. 
     Table 1 is a data base showing various parameters for bottle-cap ingot molds. Column 1 lists the mold number, and column 2 list the cross-sectional dimensions of each mold. Column 3 lists the full mold ingot weight. Columns 4, 5 and 6 are the coefficients of a parabola, representing average yield, resulting from a regression analysis of empirical data. This equation is: 
     
         yield = C.sub.1 + C.sub.2 w + C.sub.3 W.sup.2 
    
     where w is the width of the slab and the C&#39;s are constants. 
     The last column in Table 1 shows the maximum difference between the maximum and average providing yields. 
     
                                           TABLE 1__________________________________________________________________________MOLD MOLD  INGOT           COEFFICIENTS        MAXNO.  SIZE  WT.  1      2     3      DIF__________________________________________________________________________01   23×35      13,180           00.52019700                  00.02778040                        00.00055968-                               .05002   25×37      15,760           00.73629300                  00.01276480                        00.00024028-                               .05003   25×44      18,170           00.47185200                  00.02435500                        00.00036706-                               .05504   28×49      22,420           00.29789800                  00.03132840                        00.00040780-                               .06005   26×56      23,530           00.11830600                  00.03282920                        00.00035677-                               .05006   33×55      27,270            00.13878000-                  00.04423130                        00.00047334-                               .05007   30×66      32,310            01.88245000-                  00.09589520                        00.00083928-                               .050__________________________________________________________________________ 
    
     As shown in Table 1, ingot mold #4 is the smallest ingot mold having one cross-sectional dimension larger than the sum of slab width plus edge work. The weight of an ingot poured in this mold is disclosed in the table in FIG. 1 as 22,420 lbs (10,170 Kg). 
     FIG. 1 is a curve showing average ingot yield as a function of slab width for steel of a certain grade poured in a 28 × 49 in (71.1 × 124.5 cm) mold. As above stated, this curve is a parabola resulting from a regression analysis of empirical data. As can be seen, the yield for a 45 in (114 cm) wide slab is about 88%. To obtain a more accurate figure for yield, Table 2 is consulted. This table lists the coordinates of the curve, viz., average yield as a function of slab width for an ingot poured in mold #4. The yields were calculated from the above equation. The &#34;R-SQUARED&#34; number in the table is the Coefficient of Determination. This coefficient is a value that varis from 0 to 1 and is defined as the proportion of the total variance in the dependent variable that is explained by the independent variable. In other words, &#34;R-SQUARED&#34; is the percentage of the data that is explained by the equation. 
     
                                           TABLE 2__________________________________________________________________________Ingot Size = 28 × 49               Maximum Width = 45Minimum Width = 35  Width/Yield__________________________________________________________________________ 35.0    35.5  36.0     36.5        37.0           37.5              38.0                 38.5                     39.0                       39.5                          40.0                             40.5.8948   .8961 .8972    .8981       .8988          .8992             .8995                .8996                    .8994                      .8991                         .8986                            .8978 41.0    41.5  42.0     42.5        43.0           43.5              44.0                 44.5                     45.0.8968   .8957 .8943    .8928       .8910          .8890             .8868                .8845                    .8819__________________________________________________________________________C.sub.1 = .297898E + 00C.sub.2 = .313284E - 01C.sub.3 = -.407801E - 03R-SQUARED = .645580__________________________________________________________________________ 
    
     For this width, the yield is 0.8819. 
     Returning again to Table 1, it is seen that the maximum difference between the average and the maximum providing yield is 0.060 for this ingot size. Thus, the maximum possible yield for this ingot, when rolled into the desired slab width, is 0.8819 + 0.060, or 0.9419. 
     To obtain the required ingot weight, the desired slab weight is divided by the maximum providing yield. ##EQU1## Inasmuch as this required ingot weight is substantially greater than the weight of the ingot poured in mold #4, it is clear that this mold is too small and that mold #5 must be considered. As shown in FIG. 1, the weight of an ingot poured in mold #5 is 23.530 lb (10,673 Kg). 
     FIG. 2 is a curve showing average providing yield as a function of slab width for an ingot poured in a 26 × 56 in (66.0 × 142 cm) mold. As shown in Table 3 the average yield for a 45.0 l in (114 cm) wide slab is 0.8732. From Table 1, the maximum difference between the average and the maximum yield for this ingot size is 0.050. Thus, the maximum possible yield for this ingot, when rolled into the desired slab width, is 0.8732 × 0.050, or 0.9232. 
     The desired slab weight is divided by the maximum providing yield to obtain the required ingot weight. ##EQU2## 
     Since this ingot weight is in close agreement with the weight of an ingot poured in mold #5, viz., 23,530 lb (10,673 Kg), mold #5 is the correct mold to use for this slab order. 
     
                                           TABLE 3__________________________________________________________________________Ingot Size = 26 × 56               Maximum Width = 52Minimum Width = 39  Width/Yield__________________________________________________________________________ 39.0    39.5  40.0     40.5        41.0           41.5              42.0                 42.5                    43.0                       43.5                          44.0                             44.5.8560   .8584 .8606    .8627       .8646          .8663             .8678                8691                   .8703                      .8713                         .8721                            .8727 45.0    45.5  46.0     46.5        47.0           47.5              48.0                 48.5                    49.0                       49.5                          50.0                             50.5.8732   .8734 .8735    .8734       .8732          .8727             .8721                .8713                   .8703                      .8692                         .8678                            .8663 51.0    51.5  52.0.8646   .8628 .8607__________________________________________________________________________A.sub.1 = .118306E + 00A.sub.2 = .328292E - 01A.sub.3 = -.356773E - 03R-SQUARED = .590485__________________________________________________________________________ 
    
     Molten steel of the ordered metallurgical grade is then poured into mold #5 until it is full, and the ingot mold is capped. The steel is allowed to solidify into an ingot, and the ingot is then rolled into a slab of the specified width.