JP2002283022A - Method for changing width of cast slab during continuous casting, system for changing width of cast slab, unit for making positional pattern table of short sides in mold and computer program and recording medium - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for changing the width of a cast slab, a system for changing the width of the cast slab, a unit for making a positional pattern table of short sides in a mold, a computer program and a recording medium with which the mold width for changing the cast slab width during continuous casting, is controlled at high accuracy and high speed, and the improvement of yield and the restraint of cost-up can be realized. SOLUTION: The positional pattern table generating unit 1 generates the positional pattern table expressing a relation between positions of the upper end and the lower end of the short sides 41, 41 in the mold 4 and a time, with a polygonal line continuously connected with straight lines. Then, upper end servo-amplifiers 31, 31 and lower end servo-amplifiers 32, 32 control the positions of the upper end and the lower end of the short sides 41, 41 to target positions outputted from the positional pattern table generating unit 1 based on the positional pattern table to change the mold width and the cast slab width.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

The present invention relates to a method for changing the width of a slab by changing the width of a mold during continuous casting, a system for changing the width of a slab using the method, and a method for changing the width of a mold. Pattern table generating apparatus for generating a position pattern table that defines the position of the short side when the short side of the mold moves, a computer program for realizing a computer as the position pattern table generating apparatus, and the computer program The present invention relates to a computer-readable recording medium having recorded thereon.

[0002]

2. Description of the Related Art In a continuous casting operation, a molten metal, that is, a molten metal is poured into a mold having an opening at the top and bottom, brought into contact with a water-cooled inner wall of the mold and cooled, and the outside thereof is covered with a solidified shell. This is performed in a procedure of obtaining a product slab, which is further cooled while extracting the slab below the mold and solidified to the inside.

Conventionally, in order to produce slabs having various widths in continuous casting, a mold having a mold width changeable has been used. From the viewpoint of productivity, it is inefficient to stop the operation when changing the mold width, so a method of changing the mold width during continuous casting to change the slab width has been proposed.

FIG. 10 is a perspective view showing a continuous casting mold capable of changing the mold width. The mold 4 is formed in a rectangular shape in plan view, and the long sides 42, 42 of the mold 4 are fixed, and the short sides 41, 41 of the mold 4 move in the horizontal direction to change the mold width. FIG. 11 is a vertical sectional view of the mold 4. During continuous casting with a constant mold width, the short sides 41, 41 are supported with a slight inclination, and the cross section of the mold 4 has a wide upper end and a narrower lower end. Called state. In this state, the molten metal is poured from above and the slab is drawn downward. The difference between the upper end width and the lower end width of the mold 4 is determined from the shrinkage ratio of the solidified slab, and at the same time, the inclination of the short sides 41, 41.

[0005] When narrowing the mold width during continuous casting,
The upper and lower ends of the short sides 41, 41 are individually controlled, and the short sides 41, 4 are adjusted while adjusting the inclination of the short sides 41, 41.
Move 1 The inclination of the short sides 41, 41 during the movement of the short sides 41, 41, in addition to the shrinkage ratio of the slab,
It is determined from the casting speed and the speed of the short sides 41,41. In the conventional method of changing the width of the mold, the steps of accelerating the upper end and the lower end to a predetermined speed while adjusting the inclination of the short sides 41, 41, and the step of accelerating the upper end at a predetermined speed while keeping the inclination of the short sides 41, 41 constant. And the step of moving the lower end, and the step of decelerating the upper end and the lower end while adjusting the inclination of the short sides 41, 41 to stop.
The width of the mold is changed by controlling the inclination and the amount of movement of the short sides 41, 41. In the step in which the inclination of the short sides 41, 41 is constant, the inclination of the short sides 41, 41 has an inverted tapered shape in which the upper end width of the mold 4 is narrow and the lower end width is wide.

FIG. 12 is a graph showing changes in the positions and speeds of the upper and lower ends of the short sides 41 when the width of the mold is reduced using the conventional technique. FIG.
In (a), the position of the upper end and the lower end of the short side is shown on the vertical axis, with the direction in which the mold width increases, the upper end position is shown by a thin line, and the lower end position is shown by a thick line. Similarly, FIG.
The moving speed of the upper end and the lower end is shown by a thin line and a thick line. In the first acceleration step, the upper end accelerates at a higher speed than the lower end, overtaking the position of the lower end, and the short sides 41, 4
In the next step, the upper end and the lower end move at the same speed, and in the last step of deceleration, the lower end overtakes the upper end and the inclination of the short sides 41, 41 becomes tapered. Return. In the prior art, a change pattern of the position or speed of the upper end and the lower end as shown in FIG. 12 is obtained from conditions such as the amount of change in the mold width and the shrinkage ratio of the solidified slab. The movement of the lower end was controlled to change the width of the mold.

[0007]

When the short side of the mold is moved during continuous casting, it is important to control the inclination of the short side, and the upper and lower ends of the short side are accurately positioned and moved every moment. I need to be able to do it. Therefore, many of the conventional techniques control the width of the mold by controlling the speed to control the instantaneous positions of the upper end and the lower end. For this reason, in order to control the positions of the upper end and the lower end of the short side with high precision, it is necessary to control the speed of the motor that moves the upper end and the lower end. Since it is necessary to control the switching of the current flowing through the computer, a computer that performs control at a period of 0.05 to 5 ms is required. When speed control is not directly performed by the computer, a dedicated speed control is used. A control device is required, and there is a problem that the control device becomes expensive and the cost increases. In addition, when the change in the inclination of the short side is reduced and the change of the mold width is repeated a plurality of times, an increase in cost can be suppressed by using an inexpensive controller, but the slab width cannot be changed at high speed. There is a problem that the slab having an intermediate stage width increases and the yield decreases.

The present invention has been made in view of such circumstances, and an object of the present invention is to provide a target function representing the relationship between the position of the upper end and the lower end of the short side of the mold and time.
High-precision positioning of the top and bottom of the short side by approximating with a polygonal line that connects multiple straight lines and controlling the top and bottom of the short side according to the relationship between the position and the time approximated by the polygonal line A slab width changing method capable of controlling at a high speed to achieve an improvement in yield and suppression of cost increase, a system for changing a slab width using the slab width changing method, and a change in a mold width. A position pattern table generation device that generates a position pattern table that defines a target position of the short side when the short side of the mold moves, a computer program for realizing a computer as the position pattern table generation device, and It is another object of the present invention to provide a computer-readable recording medium storing the computer program.

[0009]

According to a first aspect of the present invention, there is provided a method for changing the width of a slab during continuous casting, wherein the long side of the mold is fixed and the inclination of the short side of the mold is adjusted during continuous casting. When the short side is moved and the slab width is changed by changing the width of the mold, a target function that expresses a parameter relationship when the short side is moved is obtained, and the short function is determined based on the obtained target function. In the method of controlling the movement of the side and changing the slab width, a target function expressing the relationship between the position of the upper end and the lower end of the short side and time is obtained, and the obtained target function is defined by a plurality of straight lines. The method is characterized in that the positions of the upper end and the lower end are controlled based on a target function approximated by a polygonal line connected continuously and a polygonal line.

[0010] A slab width changing system according to a second aspect of the present invention comprises a mold used for continuous casting, means for fixing a long side of the mold, and a method for changing the width of the mold by moving a short side of the mold. A slab width changing system comprising: generating means for generating a target function expressing the relationship of the parameters; and control means for controlling the movement of the short side to change the width of the slab based on the generated target function. The generating means includes means for generating a target function expressing the relationship between the position of the upper end and the lower end of the short side and time, and approximating the generated target function by a polygonal line connecting a plurality of straight lines continuously. Means, and discretely extract the values of the position and time of the upper end and the lower end from the target function approximated by a polygonal line,
Means for generating a position pattern table showing the relationship between the position of the upper end and the lower end and time, and means for outputting the generated position pattern table to the control means, wherein the control means Means for controlling the positions of the upper end portion and the lower end portion based on the position pattern table.

According to a third aspect of the present invention, there is provided an apparatus for generating a position pattern table of a short side of a mold, wherein the relationship between the position of the upper end and the lower end of the short side and the time when the short side of the mold used for continuous casting moves. An apparatus for generating a position pattern table of a short side of a mold for generating a tabulated position pattern table, wherein the upper end and the lower end are moved to realize a movement amount required for the upper end and the lower end. Means for determining the relationship between the speed and time to be performed, means for determining the change in the position of the upper end and the lower end as a function of time from the determined relationship between the speed and time, and a plurality of the determined functions. Means for approximating the straight line with a polygonal line connected continuously, and the values of the position and time of the upper end and the lower end from the function approximated by the polygonal line are discretely extracted in association with each other, and the upper end and the upper Bottom position and time Characterized in that it comprises relevant means for generating a position pattern table that in the table of and means for outputting the generated position pattern table to an external apparatus.

[0012] A computer program according to a fourth aspect of the present invention is a computer readable storage medium storing a position pattern table showing a relationship between the position of the upper end and the lower end of the short side and the time when the short side of the mold used for continuous casting moves. A computer program to be generated by a computer, wherein the computer realizes a movement amount required for the upper end portion and the lower end portion,
A procedure for determining the relationship between the speed and time at which the upper end and the lower end move, and the computer, based on the determined relationship between the speed and the time, changes in the positions of the upper end and the lower end with respect to time. A procedure for causing the computer to approximate the determined function by a polygonal line in which a plurality of straight lines are continuously connected; and a computer for determining the position and time of the upper end and the lower end from the function approximated by the polygonal line. And extracting the discrete values in association with each other to generate a position pattern table in which the relationship between the positions of the upper end portion and the lower end portion and the time is generated.

According to a fifth aspect of the present invention, there is provided a recording medium readable by a computer, wherein the relationship between the position of the upper end and the lower end of the short side and the time when the short side of the mold used for continuous casting moves. A computer-readable recording medium having recorded thereon a computer program for causing a computer to generate a tabulated position pattern table, and realizes the amount of movement required for the upper end and the lower end by the computer. A procedure for determining the relationship between the speed and time at which the upper end and the lower end move, and causing a computer to change the positions of the upper end and the lower end from the determined relationship between the speed and the time. And a procedure for causing the computer to approximate the obtained function with a polygonal line that connects a plurality of straight lines continuously. From the function approximated by a polygonal line, the values of the position and time of the upper end and the lower end were discretely extracted in association with each other, and the relationship between the position of the upper end and the lower end and the time was tabulated. A computer program including a procedure for generating a position pattern table is recorded.

In the present invention, the target function representing the relationship between the position of the upper end and the lower end of the short side of the mold and time is approximated by a polygonal line connecting a plurality of straight lines, and the position and time approximated by the polygonal line By generating a position pattern table that discretely extracts the relationship with the position pattern table and controlling the positions of the upper and lower ends of the short sides according to the position pattern table, the width of the mold can be controlled with high precision using an inexpensive controller. can do. Further, the width of the mold can be changed at a high speed, and the yield of the product slab is improved.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The present invention will be specifically described below with reference to the drawings showing the embodiments. FIG. 1 is a block diagram showing the configuration of the slab width changing system of the present invention. In the figure, reference numeral 1 denotes a position pattern according to the present invention for generating a position pattern table in which the relationship between the positions of the upper and lower ends of the short sides 41 and 41 of the mold 4 from the center of the mold and the time is measured. Upper position servo amplifiers 31 and 31 and lower end servos for inputting the generated position pattern table and controlling the positions of the upper and lower ends of the short sides 41 and 41 of the mold 4 are input to the position pattern table generating device 1. Amplifiers 32, 3
2 are connected.

The upper servo amplifier 31 includes a servo motor M1 whose rotation is controlled by the upper servo amplifier 31,
It is connected to a position detector P1 which detects the rotational position of the servomotor M1 and inputs it to the upper end servo amplifier 31. The servomotor M1 is connected to a transmission G1 for shifting the rotation of the rotation shaft of the servomotor M1, and an upper end moving shaft 33 driven by the servomotor M1 via the transmission G1. The upper end moving shaft 33 is connected to the upper end of the short side 41 of the mold 4 and moves in the longitudinal direction by receiving the rotation of the servomotor M1 by a transmission mechanism such as a ball screw.
The upper end of the short side 41 is moved. Similarly, a servomotor M2 and a position detector P2 are connected to the lower end servo amplifier 32, and a transmission G2 and a lower end moving shaft 34 are connected to the servomotor M2, and are driven by the servomotor M2. The lower end of the short side 41 is moved by the lower end moving shaft 34.

The position pattern table generating device 1 is configured using a computer, and includes a CPU 11, a RAM 12,
An external storage device 13 such as a D-ROM drive and an internal storage device 14 such as a hard disk are provided, and a computer program 20 according to the present invention is stored in a storage medium 2 such as a CD-ROM according to the present invention. Then, the computer program 20 is read and stored in the internal storage device 14, the computer program 20 is loaded into the RAM 12, and the CPU 11 executes processing necessary for the position pattern table generation device 1 based on the computer program 20. The position pattern table generating device 1 includes an output unit 15 connected to upper servo amplifiers 31 and 31 and lower servo amplifiers 32 and 32, and an input unit 16 connected to a production management device of a continuous casting machine (not shown). Equipped,
Information such as the change amount of the slab width or the casting speed is input to the input unit 16.
, And the respective position pattern tables for controlling the upper and lower ends of the short sides 41, 41 are output from the output unit 15 to the upper and lower servo amplifiers 31, 31 and 32, 3 respectively.
2 is output. With the above configuration, the slab width changing system of the present invention is configured.

FIG. 2 is a flowchart showing a processing procedure of the slab width changing system of the present invention. The position pattern table generation device 1 obtains the slab width change amount, the casting speed, or 1500 ° C. immediately after the slab solidifies from the production management device of the continuous casting machine.
Input of parameters necessary for generating a position pattern table, such as strength at a temperature of about (hereinafter, referred to as high-temperature strength of a slab), is received (S1). Next, based on the received parameters, the position pattern table generation device 1 generates a position pattern table that expresses the relationship between the position of the upper end and the lower end to be moved to realize the change of the slab width and time in a table. (S2), the generated upper end and lower end position pattern tables are stored in the upper end servo amplifiers 31 and 31 and the lower end servo amplifier 3
2 and 32 (S3). Upper end servo amplifier 31,
31 receives an upper end position pattern table (S4), the lower end servo amplifiers 32 and 32 receive a lower end position pattern table (S5), and the upper end servo amplifier 31 and the lower end servo amplifier 32 synchronize with the servo motor M1. And the control of the servo motor M2 is started.
The servo motor M is adjusted so that the upper end position input from the position detector P1 matches the received upper end position pattern table.
1 is controlled to control the upper end position (S6), and the lower end servo amplifier 32 adjusts the position of the lower end input from the position detector P2 to the received lower end position pattern table by the servo motor M2. Is controlled to control the position of the lower end (S7), and the width of the mold 4 is changed to change the slab width.

FIG. 3 is a flowchart showing a processing procedure for generating a position pattern table in step S2. First, the position pattern table generation device 1 generates a speed pattern that is a relationship between the speed at the lower end and time (S21), and then generates a speed pattern at the upper end (S22). FIG. 4 is a graph showing an example of the lower end speed pattern and the upper end speed pattern when the slab width is reduced. The lower end speed pattern is indicated by a thick line, and the upper end speed pattern is indicated by a thin line. The speed pattern at the lower end is composed of an acceleration section, a section moving at a predetermined speed V, and a deceleration section. The pattern of acceleration and deceleration is determined from the high-temperature strength of the slab.If the high-temperature strength of the slab is large, the acceleration rate and deceleration rate are increased.If the high-temperature strength of the slab is small, the acceleration rate and deceleration rate are reduced. I do. The length of the section moving at the predetermined speed V is determined by the change amount of the slab width. The speed pattern at the upper end is determined based on the speed pattern at the lower end, the shrinkage ratio of the solidified slab, and the casting speed in order to optimize the inclination of the short side 41 as in the related art.

Next, the position pattern table generating device 1 integrates the generated upper and lower speed patterns with respect to time,
A function of the position of the upper end and the lower end and time is generated (S2
3). FIG. 5 is a graph showing an example of a function of the positions of the upper and lower ends and time when the slab width is reduced, where the lower end position is indicated by a thick line and the upper end position is indicated by a thin line. Regarding the relationship between the positions of the upper end and the lower end and time, a section moving at a predetermined speed V is represented by a straight line, and an acceleration and deceleration section is represented by a curve. Next, the position pattern table generation device 1 approximates the function of the position of the upper end and the lower end and the time by a polygonal line in which a plurality of straight lines are continuously connected (S24). FIG. 6 is a graph showing an example of a function between the positions of the upper and lower ends approximated by a polygonal line and time, in which the lower end position is indicated by a bold line and the upper end position is indicated by a thin line. In the example shown in FIG. 6, the section of acceleration is divided into three small sections, and the section of deceleration is divided into four small sections. In each of the small sections, the relationship between the position of the upper end and the lower end and the time is approximated by a straight line, The change in the curved position in the acceleration and deceleration sections is approximated by a polygonal line.

Next, the position pattern table generating device 1 regenerates the upper and lower speed patterns from the function of the upper and lower positions and time approximated by a polygonal line (S).
25). FIG. 7 is a graph showing an example of the upper and lower speed patterns generated again, in which the lower speed pattern is indicated by a thick line and the upper end speed pattern is indicated by a thin line. In order to realize the function of the position and time approximated by a polygonal line as shown in FIG. 6, the speed pattern changes stepwise.

Next, the position pattern table generating device 1 integrates the stepped speed patterns at the upper end and the lower end to generate a polygonal position pattern again (S26). Since the final movement of the lower end corresponds to half of the slab width change,
The length of the section in which the upper end and the lower end move at a predetermined speed is adjusted, and the final movement amount of the lower end is adjusted according to the input change amount of the slab width to correct the position pattern (S2).
7). Next, the corrected position pattern is discretized in accordance with the control cycle of the position pattern table generation device 1, and is converted into a position pattern table in which the relationship between the position of the upper end and the lower end and time is shown in a table (S28). The control cycle for discretizing the position pattern is the short side 41 corresponding to the difference between the upper and lower positions.
Although it depends on the accuracy required for the inclination, the position control accuracy is sufficient at 10 ms or more, and can be made longer than the control cycle of 0.05 to 5 ms when speed control is performed. The control cycle is preferably 20 ms or more, and more preferably 50 ms or more, in consideration of reducing the load on the position pattern table generation device 1. If the control cycle is too long, the accuracy of the position control is reduced. Therefore, depending on the conditions required when changing the slab width, about 200 ms is the upper limit of the control cycle. By performing the above processing, the position pattern table generation device 1
Terminates the process of generating the position pattern table in step S2.

According to the above procedure, the width of the mold is changed and the width of the slab is changed. Since the upper end servo amplifiers 31, 31 and the lower end servo amplifiers 32, 32 control the positions of the upper end and the lower end based on the position pattern table of the upper end and the lower end, the positions of the upper end and the lower end can be controlled with high precision. Thus, the slab width can be changed with high accuracy. Further, by using a servo amplifier capable of realizing calculation of a continuous amount for position control with an inexpensive circuit configuration, the control cycle can be lengthened and the position pattern table generation device 1 can be realized at low speed. The position pattern table generation device 1, which is a position control device for controlling the width change, can be configured at low cost. Also, to change the mold width at once,
The slab width can be changed at high speed, and the slab yield is improved.

Next, an embodiment in which the slab width is changed by using the present invention will be described. FIG. 8 is a graph showing changes in the upper end width and the lower end width of the mold 4 when the width of the mold 4 is reduced in the related art. FIG. 9 is a graph showing changes in the upper end width and the lower end width of the mold 4 when the width of the mold 4 is reduced using the present invention. 8 and 9
In the figure, the lower end width of the mold 4 is indicated by a thick line, and the upper end width is indicated by a thin line. In both cases, when the casting speed is 5 (m / min), the width of the lower end is changed from 1000 mm to 950 mm,
The control cycle of the position control device in the related art for performing the speed control is 0.1 ms, and the control cycle of the position pattern table generation device 1 in the present invention is 100 ms.

In the present invention, the upper end width and the lower end width are controlled in a polygonal line in the acceleration / deceleration section, and the control cycle of the position control is made much longer than the control cycle of the conventional speed control. It can be seen that the mold width was changed with the same change width as before, despite the fact that the mold width was changed at the same speed as that described above.

In the present embodiment, the form in which the position pattern table generating apparatus is realized by a computer and a computer program has been described. However, the present invention is not limited to this.
The position pattern table generation device may be realized by using dedicated hardware. The parameters required to generate the position pattern table, such as the slab width change amount, the casting speed or the high-temperature strength of the slab, indicate the form that is input from the production management device of the continuous casting machine to the position pattern table generation device. However, the present invention is not limited to this, and the parameters may be input by an operator's operation from an input device such as a keyboard.

[0027]

According to the present invention, in order to change the width of the mold during continuous casting to change the width of the slab, the target function representing the relationship between the position of the upper and lower ends of the short sides of the mold and time is set. ,
A position pattern table is created by approximating the relationship between the position approximated by the broken line and the time discretely by approximating a plurality of straight lines with a continuous connected polygonal line, and determining the position of the upper end and the lower end of the short side with the position pattern table. Is performed to change the width of the mold to change the slab width. Since the width of the mold is controlled by performing the position control, the width of the mold can be controlled with high precision. In addition, in the case where the position control is performed as compared with the case where the speed control is performed, since the control can be performed in a long cycle, the present invention has excellent effects such as the controller can be configured at low cost.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration of a slab width changing system of the present invention.

FIG. 2 is a flowchart showing a processing procedure of the slab width changing system of the present invention.

FIG. 3 is a flowchart illustrating a processing procedure for generating a position pattern table in step S2.

FIG. 4 is a graph showing an example of speed patterns at the lower end and the upper end when the slab width is reduced.

FIG. 5 is a graph showing an example of a function of the position of the upper end and the lower end and time when the slab width is reduced.

FIG. 6 is a graph showing an example of a function of the position of the upper end and the lower end approximated by a polygonal line and time.

FIG. 7 is a graph showing an example of upper and lower speed patterns generated again.

FIG. 8 is a graph showing changes in the upper end width and the lower end width of the mold when the width of the mold is reduced according to the related art.

FIG. 9 is a graph showing changes in the upper end width and the lower end width of the mold when the width of the mold is reduced using the present invention.

FIG. 10 is a perspective view showing a continuous casting mold capable of changing the mold width.

FIG. 11 is a vertical sectional view of a mold.

FIG. 12 is a graph showing changes in the position and speed of the upper and lower ends of the short side when the width of the mold is reduced using the conventional technique.

[Explanation of symbols]

 DESCRIPTION OF SYMBOLS 1 Position pattern table generation apparatus 2 Recording medium 20 Computer program 31 Upper servo amplifier 32 Lower servo amplifier 4 Mold 41 Short side 42 Long side M1 Servo motor M2 Servo motor

 ────────────────────────────────────────────────── ─── Continued on the front page (72) Inventor Kazutoshi Kanda 4-33, Kitahama, Chuo-ku, Osaka-shi, Osaka F-term in Sumitomo Metal Industries, Ltd. 4E004 AE02 MA03 MA04 MA04 NB01

Claims (5)

[Claims] 1. During continuous casting, the long side of the mold is fixed, the short side is moved while adjusting the inclination of the short side of the mold, and the width of the slab is changed by changing the width of the mold. On the occasion,
In the method of obtaining a target function expressing the relationship between parameters when moving the short side, controlling the movement of the short side based on the obtained target function, and changing the slab width, the upper end of the short side And a target function expressing the relationship between the position and time of the lower end portion is obtained, the obtained target function is approximated by a polygonal line in which a plurality of straight lines are continuously connected, and the upper end portion and the upper end portion are determined based on the target function approximated by a polygonal line. A method for changing the width of a slab during continuous casting, wherein the position of the lower end is controlled. 2. A mold used for continuous casting, means for fixing a long side of the mold, and a target function expressing a relationship between parameters for changing a width of the mold by moving a short side of the mold. In a slab width changing system comprising: a generating unit that generates, and a control unit that controls the movement of the short side to change the width of the slab based on the generated target function. Means for generating a target function expressing the relationship between the position of the upper end and the lower end and time, means for approximating the generated target function by a polygonal line in which a plurality of straight lines are continuously connected, and a target function approximated by a polygonal line And discretely extract the values of the position and time of the upper end and the lower end from each other, and generate a position pattern table showing the relationship between the position of the upper end and the lower end and the time. Means and generated position pattern Means for outputting a position table to the control means, wherein the control means includes means for controlling the positions of the upper end and the lower end based on the input position pattern table. Medium slab width changing system. 3. A position of a short side of a mold for generating a position pattern table showing a relationship between a position of an upper end and a lower end of the short side and a time when a short side of the mold used for continuous casting moves. A pattern table generating apparatus, comprising: a unit that determines a relationship between a speed and a time at which the upper end and the lower end move, in order to realize a movement amount required for the upper end and the lower end. From the relationship between the speed and the time, a means for obtaining a change in the position of the upper end and the lower end as a function of time, and means for approximating the obtained function with a polygonal line in which a plurality of straight lines are continuously connected, The positions of the upper end and the lower end and the value of the time are discretely extracted from the function approximated by the polygonal line in association with each other, and the position of the relationship between the position of the upper end and the lower end and the time is tabulated. Means for generating a pattern table; Position pattern table generator of the mold short side, characterized in that it comprises a means for outputting the generated position pattern table to an external apparatus. 4. A computer program for causing a computer to generate a position pattern table showing a relationship between a position of an upper end portion and a lower end portion of a short side of a mold used for continuous casting and a time when the short side moves. A procedure for causing a computer to determine a relationship between a speed and a time at which the upper end and the lower end move in order to realize a movement amount required for the upper end and the lower end; and From the relationship between the determined speed and time,
A procedure for determining the change in the position of the upper end and the lower end as a function with respect to time; a procedure for causing the computer to approximate the determined function with a polygonal line in which a plurality of straight lines are connected in series; From the function, the values of the position and time of the upper end and the lower end are discretely extracted in association with each other, and a position pattern table showing a relationship between the position of the upper end and the lower end and time is displayed. Generating a computer program. 5. A computer program for causing a computer to generate a position pattern table showing a relationship between a position of an upper end portion and a lower end portion of a short side of a mold used for continuous casting and a time when the short side moves. A computer-readable recording medium on which is recorded a speed at which the upper end and the lower end move to realize a required movement amount of the upper end and the lower end. And the procedure for determining the relationship between time and the computer, from the relationship between the determined speed and time,
A procedure for determining the change in the position of the upper end and the lower end as a function with respect to time; a procedure for causing the computer to approximate the determined function with a polygonal line in which a plurality of straight lines are connected in series; From the function, the values of the position and time of the upper end and the lower end are discretely extracted in association with each other, and a position pattern table showing a relationship between the position of the upper end and the lower end and time is displayed. A computer-readable recording medium having recorded thereon a computer program including a procedure for generating the computer program.