How to determine the slab length and the slab charging position in a walking beam furnace

Abstract

The method for determining the slab length and the charging position of the slab in a walking beam type heating furnace involves determining the slab length and the charging position of the slab per heating furnace so as to minimize the first evaluation function under the first constraint condition, and determining the charging position of the slab per heating furnace so as to minimize the second evaluation function under the second constraint condition, and using the leading end overhang amount, which is the distance between the slab's tip coordinate in the heating furnace and the second skid coordinate counting from the tip to the tail end, and the tail end overhang amount, which is the distance between the slab's tail end coordinate in the heating furnace and the second skid coordinate counting from the tail end in the leading direction, as the overhang amount.

Description

[Technical field]

[0001] The present disclosure relates to a plurality of walking beam type heating furnaces installed in a hot rolling mill or a plate mill for manufacturing steel plates, and to a method for determining the length of a slab to be charged into such a heating furnace and the charging position of the slab. [Background technology]

[0002] In hot rolling plants, slabs received from continuous casting etc. are heated in walking beam heating furnaces to the specified extraction temperature (approximately 1050 to 1200°C), and then go through the processes of rough rolling, finish rolling, runout table cooling, and coiling to produce hot rolled coils.

[0003] In a walking beam furnace, the slab is elevated on a moving skid while it is heated to a high temperature. During such lifting, the slab may sag from the support points to its leading and trailing ends due to creep deformation, and when the slab is lowered from the movable skid, this portion may come into contact with the fixed skid part on the outside, causing scuff marks. Alternatively, if there is a movable skid at the outermost part, when the slab is lowered and the movable skid is retreating, a sagging portion will be generated as a cantilever due to the fixed skid, and this sagging portion may come into contact with the movable skid that has returned to its fixed position, causing scuff marks.

[0004] Such creep deformation occurring at high temperatures is unlikely to occur in general steel that becomes austenite phase at high temperatures, but tends to occur easily in grain-oriented electrical steel sheets that become ferrite phase at high temperatures. As described in Patent Document 1, the amount of deformation due to creep deformation increases under conditions such as a long distance from the support point to the slab end (amount of overhang), a thin slab, or a high temperature, which also makes scab defects more likely to occur. Generally, the thickness and width of the slab and the heating conditions in the heating furnace are designed for each standard and have little room for change, but the slab length may be adjustable to some extent. Therefore, it is possible to use the slab length as a means for adjusting the overhang amount.

[0005] In addition, the multiple heating furnaces in a hot strip mill do not always have the same skid arrangement. Therefore, even if the slab length is the same, the overhang amount often differs depending on the heating furnace. Furthermore, if there is a skid shift structure, the overhang amount changes even within the same heating furnace. Therefore, a slab length with a small overhang amount in one heating furnace may be long in another heating furnace, making the design of the slab length difficult.

[0006] In response to this, Patent Document 1 discloses a method for avoiding contact scratches that occur due to creep deformation when a discharge fork is inserted into a heating furnace. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] Japanese Patent Application Publication No. 6-346132 Summary of the Invention [Problem to be solved by the invention]

[0008] However, Patent Document 1 does not disclose a method for designing the slab length and charging position to suppress the occurrence of scab defects that occur in the above-mentioned skid section.

[0009] The present disclosure has been made in consideration of the above circumstances, and aims to provide a design method for minimizing the occurrence probability of scab defects occurring at the skid section for the slab length and charging position of a slab to be charged into a walking beam heating furnace. In particular, the present disclosure aims to provide a design method for minimizing the occurrence probability of scab defects when there are multiple walking beam heating furnaces. [Means for solving the problem]

[0010] (1) A method for determining a slab length and a slab charging position in a walking beam heating furnace according to an embodiment of the present disclosure includes: When determining the length of a slab to be charged into two or more walking beam heating furnaces and the charging position of the slab using a mixed integer programming method, a constraint equation that specifies the amount of overhang and a previously obtained model that specifies the relationship between the amount of overhang and the probability of scab defects occurring in the skid section are used to set a first constraint condition using a constraint equation that specifies the probability of scab defects occurring corresponding to the amount of overhang, an equality constraint on the slab length of each heating furnace, and a constraint equation that specifies upper and lower limits of the slab length, and a first evaluation using a constraint equation that specifies the maximum value of the probability of scab defects occurring. a function is used to determine the length of a slab and the charging position of the slab in each heating furnace so as to minimize the first evaluation function under the first constraint condition, and the slab length determined by the above minimization is added to a constraint equation that defines upper and lower limits of the slab length as a second constraint condition, and further, a second evaluation function using a constraint equation that defines a sum of the maximum values ​​of the scab defect occurrence probabilities is used to determine the charging position of the slab in each heating furnace so as to minimize the second evaluation function under the second constraint condition, thereby determining the slab length and the charging position in a walking beam type heating furnace, The overhang amounts used are the leading end overhang amount, which is the distance between the leading end coordinate of the slab in the heating furnace and the second skid coordinate counting from the leading end toward the tail end, and the tail end overhang amount, which is the distance between the tail end coordinate of the slab in the heating furnace and the second skid coordinate counting from the tail end toward the leading end.

[0011] (2) As an embodiment of the present disclosure, in (1), When the walking beam type heating furnace is equipped with a shift function, the following overhang amounts are used: pre-shift leading end overhang amount, which is the distance between the leading end coordinate of the slab in the heating furnace and the second pre-shift skid coordinate counting from the leading end to the tail end; pre-shift tail end overhang amount, which is the distance between the tail end coordinate of the slab in the heating furnace and the second pre-shift skid coordinate counting from the tail end to the leading end; post-shift leading end overhang amount, which is the distance between the leading end coordinate of the slab in the heating furnace and the second post-shift skid coordinate counting from the leading end to the tail end; and post-shift tail end overhang amount, which is the distance between the tail end coordinate of the slab in the heating furnace and the second post-shift skid coordinate counting from the tail end to the leading end.

[0012] (3) As an embodiment of the present disclosure, in (1) or (2), The constraint equation that defines the probability of scab occurrence is selected according to the maximum attainable temperature of the slab that is determined in advance. Effect of the Invention

[0013] According to the present disclosure, when there are multiple walking beam heating furnaces, the probability of scab defects occurring in the skid section is reduced and yield is improved. [Brief description of the drawings]

[0014] [Figure 1] FIG. 1 is a diagram showing an implementation flow of an embodiment of the present disclosure. [Diagram 2] FIG. 2 is a diagram showing the relationship between the tip coordinate and the overhang amount. [Diagram 3] FIG. 3 shows a model of the overhang amount dependence of the probability of scab defects. [Figure 4] FIG. 4 shows a probability model for scab defects. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0015] An embodiment of the present disclosure will be described based on the implementation flow shown in Fig. 1. Here, the present embodiment is a method used for a walking beam type heating furnace (hereinafter, also simply referred to as a "heating furnace") that heats slabs for steel plates received from continuous casting or the like. The following description will be given of a case where multiple heating furnaces are installed in the same factory and the heating furnaces perform one shift during heating. However, when using a heating furnace that does not have a shift, the following description regarding the post-shift period need not be adopted. In addition, this embodiment is a method that uses mixed integer programming when determining the length of the slab and the charging position of the slab, and the specific procedure will be described below.

[0016] First, the first constraint condition creating unit (101) shown in Fig. 1 creates equality and inequality constraints. The equality and inequality constraints stipulate the pre-shift top overhang amount, pre-shift tail overhang amount, post-shift top overhang amount, post-shift tail overhang amount, slab length, and scab defect occurrence probability for each heating furnace. As a specific procedure, the inequality constraint that specifies the pre-shift tip overhang amount for a certain furnace is explained. As a preparation, for the case where the furnace has N skids, constants including the skid coordinates listed in Table 1 below are read in.

[0017] [Table 1]

[0018] Next, the decision variables listed in Table 2 below are prepared.

[0019] [Table 2]

[0020] x listed in Table 2 LE But the skid coordinate w i and the index of the continuous variable t i Using and, it is expressed by the equality constraint of the following (1a).

[0021]

number

[0022] Such (1a) is a continuous variable t with at most adjacent indices i is positive, and the sum is 1, so the coordinates are calculated as internal division points of the skid coordinates. Therefore, at this time, the binary variable z i (i=1,2,…,N+1) and a continuous variable t i The inequalities that (i=1, . . . , N+2) must satisfy are the following equations (1b) to (1e).

[0023]

number

[0024] Next, the skid coordinate w i from tip coordinate x LE Distance to L i is expressed by the following equality constraint (1f).

[0025]

number

[0026] Here, the decision variable L i ´, L i If is greater than 0, then L i Take L i The inequality is constructed so that if is less than or equal to 0, then it is 0. i A binary variable δ that takes a value depending on whether i Through L i An inequality is created that chooses between zero and zero. That is, L i A binary variable δ that takes the value 1 if is greater than 0 and takes the value 0 if is less than or equal to 0 i The inequality that must be satisfied is the following equation (1g).

[0027]

number

[0028] Therefore, L i Decision variable L that takes the greater value of i ´ is L i and δ i Using this, we obtain the following equation (1h).

[0029]

number

[0030] Next, as shown in Figure 2, the tip coordinate x LE But w i And w i+1 When the overhang is between i-1 ´ becomes. L i-1 ´ is the distance between the tip coordinate of the slab in the heating furnace and the second skid coordinate counting from the tip to the tail end. i If is 1, then L i-1 ´,z i If is 0, variable D becomes 0 i The inequality that must be satisfied is constructed as shown in (1i) below. Then, the overhang amount O LE1 can be expressed by the equality constraint in equation (1j). The above are the equalities and inequalities for the amount of overhang at the tip before shifting. Here, if the tip overhang amount is defined as the distance between the tip coordinate of the slab in the heating furnace and the first skid coordinate counting from the tip to the tail end, no effect can be obtained, as shown in the examples described later. On the other hand, there is no need to consider defining such tip overhang amount as the distance between the tip coordinate of the slab in the heating furnace and the third (or higher) skid coordinate counting from the tip to the tail end. This is because, as a physical phenomenon, creep deformation progresses in a cantilever state due to the second skid.

[0031]

number

[0032] Next, in the same way, we construct the equalities and inequalities that the amount of overhang at the tail end before the shift must satisfy. The tail end coordinate at this time is x TE Then, the slab length L slab is the tip coordinate x LE and is expressed by the following equation (2).

[0033]

number

[0034] This slab length L slab Upper and lower limit constraints are specified for L U slab , the lower limit is L L slab Then, the slab length L slab This results in the following inequality (3).

[0035]

number

[0036] Next, the equalities and inequalities that the post-shift head and tail end overhang amount must satisfy are constructed in the same manner as above. Here, the tip coordinate x LE and the tail coordinate x TE Since it does not change after the shift, the tip coordinate x LE and the tail coordinate x TE can be used as is.

[0037] Next, the inequality constraints that govern the probability of scab defects are explained. The relationship between the amount of overhang and the probability of scab defects is modeled in advance, as shown in Fig. 3. The model is constructed, for example, as a broken line model that pairs the amount of overhang with the corresponding probability of scab defects, as shown in Table 3.

[0038] [Table 3]

[0039] Next, when the head and tail end overhang amounts before and after the shift of the heating furnace unit (heating furnace number j) are given as shown in Table 4 below, an inequality is constructed that defines the probability of scab defects occurring. LE1,j A method for calculating the probability of scab defect occurrence corresponding to the above is explained.

[0040]

number

[0041] [Table 4]

[0042] [Table 5]

[0043] O LE1,j If,is expressed as the equality constraint in (4a), then,this is a continuous variable s i,j is positive, and the sum is 1, so the coordinates are calculated as internal division points of the skid coordinates. At this time, the binary variable d i,j (i=1,2,…,n-1) and continuous variable s i,j The inequalities that (i=1, ..., n) must satisfy are the following expressions (4b) to (4e), and the probability of scab defects occurring is the following expression (4f).

[0044]

number

[0045] Next, the first evaluation function creation unit (102) shown in FIG. 1 creates an evaluation function consisting of the maximum value of the probability of scab defect occurrence at the front and rear ends before the shift and the front and rear ends after the shift of all the heating furnaces. This is the maximum value of the probability of scab defect occurrence P LE1,j , P TE1,j, P LE2,j , P TE2,j At this point, it is the maximum value among all heating furnaces (subscript j).

[0046] The first optimum condition search unit (103) shown in FIG. 1 searches for a slab length (L) that minimizes the evaluation function created by the first evaluation function creation unit (102) under the constraint conditions created by the first constraint condition creation unit (102). * slab ) and the slab charging position for each heating furnace.

[0047] In the second constraint condition creating section (104) shown in FIG. 1, in addition to the constraint conditions in the first constraint condition creating section (101), the slab length (L * slab ) is added as a constraint.

[0048]

number

[0049] The second evaluation function creation unit (105) shown in FIG. 1 sets, as an evaluation function, a constraint equation that specifies the sum of the maximum values ​​of the probability of scab defect occurrence at the front and rear ends before the shift and at the front and rear ends after the shift for each heating furnace unit.

[0050] The second optimum condition search unit (106) shown in FIG. 1 determines the slab charging position for each heating furnace that minimizes the evaluation function created by the second evaluation function creation unit (105) under the constraint conditions created by the second constraint condition creation unit (104).

[0051] By going through the above procedure, it is possible to determine the slab length and the charging position for each heating furnace unit that minimizes the probability of scab defects occurring. EXAMPLES

[0052] The contents of the present disclosure were applied to a hot rolling plant having three heating furnaces, the first heating furnace, the second heating furnace, and the third heating furnace, each of which had a function of shifting once. The skid arrangement of each heating furnace in this embodiment was as shown in Table 6 (before the shift) and Table 7 (after the shift) below. In addition, the probability of scab occurrence is higher for the same overhang amount than before the shift because the slab becomes hotter after the shift. For this reason, the model of the probability of scab occurrence is different before and after the shift, as shown in the broken line model in FIG. 4 described above. The constraint on the slab length to be searched was set to a range of 10,000 to 12,000 mm, taking into account actual operation.

[0053] [Table 6]

[0054] [Table 7]

[0055] The amount of front end overhang was set as the distance between the front end coordinate of the slab in the heating furnace and the second skid coordinate counting from the front end to the tail end. Furthermore, the amount of tail end overhang was set as the distance between the tail end coordinate of the slab in the heating furnace and the second skid coordinate counting from the tail end to the front end, and the first optimum condition search section was executed. As a result, the slab length was determined to be 11020 mm, as shown in Table 8, and the maximum probability of scab defects occurring between the heating furnaces (maximum probability of scab defects occurring at the front and tail ends, before and after a shift) was 58.2% for the third heating furnace. Next, the second optimum condition search part was executed with the constraint of the slab length (11020 mm) obtained above added, and the maximum probability of scab defect occurrence (maximum probability of scab defect occurrence at the head and tail ends, before and after the shift) shown in Table 9 was obtained. For the first and third heating furnaces, the head and tail end coordinates representing the slab charging position did not change, but for the second heating furnace, the maximum probability of scab defect occurrence decreased from 57.0% to 46.2%, and the slab charging position was optimized. Here, the slab charging position (tip coordinate) was 5800 mm in the first heating furnace, 5320 mm in the second heating furnace, and 5120 mm in the third heating furnace.

[0056] [Table 8]

[0057] [Table 9]

[0058] For comparison, Table 10 shows the calculation results for the conventional condition of a slab length of 10,000 mm, and a charging position (tip coordinate) of 5,980 mm in the first heating furnace, 4,140 mm in the second heating furnace, and 3,980 mm in the third heating furnace. The tip overhang amount was determined as the distance between the tip coordinate of the slab in the heating furnace and the second skid coordinate counting from the tip to the tail end. Furthermore, the tail end overhang amount was determined as the distance between the tail end coordinate of the slab in the heating furnace and the second skid coordinate counting from the tail end to the tip. The maximum probability of scab defects in the table was 67.8% in the third heating furnace. Since this example is higher than the inventive example according to this embodiment, it can be seen that the occurrence of scab defects can be expected to be reduced by following this embodiment.

[0059] [Table 10]

[0060] The amount of front end overhang is defined as the distance between the coordinate of the front end of the slab in the heating furnace and the coordinate of the first skid, counting from the front end toward the tail end. The amount of tail end overhang is defined as the distance between the coordinate of the tail end of the slab in the heating furnace and the coordinate of the first skid, counting from the tail end toward the front end. In this case, Table 11 shows the results of calculating the probability of slab formation due to the second skid contact at the front and tail ends when the slab length and charging position that minimize the sum of the amounts of front and tail end overhang are calculated. In this case, the slab length was 10940 mm, and the maximum probability of scab defects in the table was 64.2% in the third heating furnace. This example is also higher than the invention example according to this embodiment, so it can be seen that a reduction in scab defects can be expected by following this embodiment.

[0061]

Table 11

Claims

1. In determining the lengths of slabs to be charged into two or more walking beam heating furnaces and the charging locations of the slabs using a mixed integer programming method, A constraint equation that defines an amount of overhang; A constraint equation that defines the probability of occurrence of scab defects corresponding to the amount of overhang from a previously obtained model that defines the relationship between the amount of overhang and the probability of occurrence of scab defects in the skid portion; Equality constraints on the slab length of each furnace; A constraint equation that specifies the upper and lower limits of the slab length. The first constraint is set as Furthermore, a first evaluation function using a constraint equation that specifies the maximum value of the scab defect occurrence probability Using A length of a slab and a charging position of the slab in a heating furnace unit are obtained so as to minimize the first evaluation function under the first constraint condition, and The slab length obtained by the above minimization is added to the constraint equation defining the upper and lower limits of the slab length as a second constraint condition, Further, a second evaluation function using a constraint equation that specifies the sum of the maximum values ​​of the scab defect occurrence probabilities Using A method for determining a slab charging position in each heating furnace so as to minimize the second evaluation function under the second constraint condition, and determining a slab length and a charging position in a walking beam heating furnace, comprising: The overhang amount is The distance between the tip coordinate of the slab in the heating furnace and the second skid coordinate counting from the tip to the tail end, and The tail end overhang is the distance between the tail end coordinate of the slab in the heating furnace and the second skid coordinate counting from the tail end toward the tip end. A method for determining the slab length and the slab charging position in a walking beam furnace using

2. The walking beam heating furnace has a shift function, The overhang amount is The amount of tip overhang before the shift is the distance between the tip coordinate of the slab in the heating furnace and the second skid coordinate before the shift, counting from the tip to the tail end. The amount of overhang at the tail end before the shift is the distance between the tail end coordinate of the slab in the heating furnace and the second skid coordinate before the shift, counting from the tail end toward the tip end. The amount of tip overhang after the shift, which is the distance between the tip coordinate of the slab in the heating furnace and the second skid coordinate after the shift, counting from the tip to the tail end, and The amount of tail end overhang after a shift is the distance between the tail end coordinate of the slab in the heating furnace and the second skid coordinate after a shift, counting from the tail end toward the tip end.

2. The method for determining the slab length and the slab charging position in a walking beam heating furnace according to claim 1, wherein

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