METHOD FOR CONTROLLING ROLLING OF METAL SHEET, ROLLING CONTROL DEVICE, AND METHOD FOR MANUFACTURING ROLLED METAL SHEET

Abstract

To accurately predict a metal plate shape after rolling, and freely control the metal plate shape.SOLUTION: A rolling control method for a metal plate includes: a first step of performing buckling analysis using an elastic strain difference existing in the metal plate even after buckling based on a plastic elongation strain difference imparted to the metal plate in rolling under a predetermined rolling condition, and calculating a buckling inherent strain difference as a determination reference of buckling generation of the metal plate; a second step of adding a difference between the plastic elongation strain difference and the buckling inherent strain difference, and the plastic elongation strain difference when the plastic elongation strain difference exceeds the buckling inherent strain difference, and calculating a true elongation strain difference; and a third step of rolling the metal plate without changing a predetermined rolling condition when the plastic elongation strain difference does not exceed the buckling inherent strain difference, and rolling the metal plate under the rolling condition set based on the true elongation strain difference when the plastic elongation strain difference exceeds the buckling inherent strain difference.SELECTED DRAWING: Figure 11

Description

[Technical field]

[0001] The present invention relates to a rolling control method for controlling the shape of a metal sheet after rolling, a rolling control device for executing the rolling control method, and a method for manufacturing a rolled metal sheet. [Background technology]

[0002] Various methods have been proposed as techniques for predicting the shape of a metal plate, such as a thin plate or a thick plate, after rolling.

[0003] Patent Document 1 discloses a technique for improving prediction accuracy in the extrapolation region where no performance data exists, and for correcting errors in a rolling model. Specifically, a performance database that stores the manufacturing conditions of products manufactured in the past in association with the information on the results of the manufacturing is used to calculate the similarity between each sample in the performance database and a required point (a prediction target point), and a prediction formula for the vicinity of the required point is created by weighted regression using the similarity as a weight. This prediction formula improves prediction accuracy in the extrapolation region.

[0004] Patent Document 2 discloses a technology for predicting the shape of a metal plate by separating the elongation strain (stress) distributed in the width direction of the metal plate during rolling into elongation strain that is geometrically transformed into a wave shape upon buckling and elongation strain that remains inherent in the metal plate even after buckling.

[0005] Patent Document 3 discloses a technology for predicting the shape of a metal sheet by determining, in addition to the shape feature quantities of the metal sheet measured at the delivery side of the rolling mill, the elongation strain inherent in the metal sheet at the time of measurement, and measuring the true shape feature quantities given by the rolling mill by superimposing the determined elongation strain on the shape feature quantities. Note that, in this technology, the plate threading direction, plate width direction position, and height direction displacement are measured at the delivery side of the rolling mill as geometric values, and the profile, steepness, and elongation strain difference are determined as shape feature quantities.

[0006] Patent Document 4 discloses a rolling control method for a metal plate having the following first to third steps. In the first step, a provisional elongation-strain difference distribution of the metal plate during rolling is obtained under conditions in which the out-of-plane deformation of the metal plate is constrained, and a buckling critical strain difference distribution is obtained based on this provisional elongation-strain difference distribution, the thickness and width of the metal plate, and the tension acting on the metal plate at the exit side of the rolling mill. In the second step, when the provisional elongation-strain difference distribution exceeds the buckling critical strain difference distribution, a difference between the provisional elongation-strain difference distribution and the buckling critical strain difference distribution is obtained by adding this difference to the provisional elongation-strain difference distribution. In the third step, rolling conditions are set based on the true elongation-strain difference distribution, and the shape of the metal plate is controlled by rolling the metal plate. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] JP 2008-112288 A [Patent Document 2] JP 2005-153011 A [Patent Document 3] JP 2012-218010 A [Patent Document 4] Patent No. 6172401 Summary of the Invention [Problem to be solved by the invention]

[0008] However, the method disclosed in Patent Document 1 does not take into account nonlinear phenomena such as the buckling phenomenon of the metal plate, and the nonlinear phenomenon cannot be reflected in the prediction formula. If the nonlinear phenomenon is not taken into account, an error will occur in the model, and the shape of the metal plate after rolling cannot be accurately predicted.

[0009] Moreover, the methods disclosed in each of Patent Documents 2 to 4 predict the shape of a metal plate taking into account the buckling phenomenon of the metal plate, and the prediction accuracy is improved compared to when the buckling phenomenon is not considered. In particular, the invention in Patent Document 4 is an advanced version of the inventions in Patent Documents 2 and 3, and quantitatively grasps the correlation between the rolling load difference distribution and the elongation strain difference distribution in the plate width direction of the metal plate, which changes due to buckling, to obtain the true elongation strain difference distribution of the metal plate and predict the shape of the metal plate. However, as a result of intensive research by the inventors, it was found that there is room for improvement in the prediction accuracy, as described below.

[0010] In the method disclosed in Patent Document 4, after the buckling judgment of the metal plate is performed, if the metal plate does not buckle (the provisional elongation strain difference distribution does not exceed the buckling critical strain difference distribution), the metal plate is rolled without changing the predetermined rolling conditions. On the other hand, if the metal plate buckles (the provisional elongation strain difference distribution exceeds the buckling critical strain difference distribution), the metal plate is rolled under the rolling conditions set based on the true elongation strain difference distribution. Therefore, it is essential to improve the prediction accuracy of the shape of the metal plate.

[0011] The present invention has been made in view of the above-mentioned points, and has an object to accurately predict the shape of a metal sheet after rolling and to freely control the shape of the metal sheet. [Means for solving the problem]

[0012] In order to achieve the above-mentioned object, the present inventors have predicted the shape of a metal sheet after rolling and investigated a method for controlling the shape of the metal sheet based on the predicted shape of the metal sheet, and as a result, have come to the following findings.

[0013] In the method disclosed in Patent Document 4, the true elongation strain difference distribution of the metal plate is obtained by quantitatively grasping the correlation between the rolling load difference distribution and the elongation strain difference distribution that change due to the above-mentioned buckling, and the shape of the metal plate is predicted. That is, when the elongation strain difference that is converted into a wave shape and causes out-of-plane deformation among the elongation strain differences distributed in the sheet width direction of the metal plate is actually converted into a wave shape by the buckling of the metal plate, the load distribution corresponding to the elongation strain difference is further converted into an elongation strain difference and is contained in the metal plate. Then, the true elongation strain difference distribution of the metal plate increases by the amount of this increased elongation strain difference. In this way, the shape of the metal plate is controlled by predicting the true elongation strain difference distribution of the metal plate.

[0014] The present invention is a further development of the invention of Patent Document 4. As a result of intensive research by the present inventors, it was found that in the invention of Patent Document 4, an error occurs in the shape profile because it is assumed that the shape profile calculated by the buckling eigenanalysis remains the same even after buckling. Then, the inventors came up with the idea that the shape of the metal plate can be appropriately predicted by performing a recalculation (eigenvalue analysis calculation using a theoretical buckling model) with the elastic strain difference reallocated due to the occurrence of the shape profile generated after buckling, rather than calculating with the plastic elongation strain difference of the evaluation target in the buckling eigenvalue analysis. That is, it was previously thought that the shape profile after buckling disclosed was determined by the plastic elongation strain difference used in the initial calculation, but as a result of intensive research by the present inventors, it was found that the shape profile is determined by the elastic strain difference that is reallocated to the metal plate after the buckling shape occurs, that is, the elastic strain difference that exists in the plate even after buckling. Then, by predicting the true elongation strain difference from the determined shape profile, the shape of the metal plate can be controlled with higher accuracy. The present invention is based on the above findings, and the gist of the present invention is as follows.

[0015] According to the present invention, there is provided a method for predicting and controlling the shape of a metal plate, the method comprising the steps of: determining a true elongation strain difference by buckling analysis using an elastic strain difference that remains in the metal plate even after buckling when predicting a wave shape profile after buckling based on a plastic elongation strain difference imparted to the metal plate; and rolling the metal plate under rolling conditions set based on the true elongation strain difference.

[0016] In the rolling control method for a metal plate, the step of calculating the true elongation strain difference and the step of rolling the metal plate include a step of calculating a critical tension in the plate width direction at which the metal plate buckles, based on a plastic elongation strain difference, which is the difference in the plate width direction of strain elongating in the rolling direction of the metal plate during rolling under predetermined rolling conditions, the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate at the exit side of a rolling mill, which is calculated under conditions in which out-of-plane deformation of the metal plate is constrained by using a top-bottom symmetrical model that allows the displacement of the plate thickness center of the metal plate to be in-plane displacement of a reference plane that passes through the midpoint of a line connecting the rotation centers of the top and bottom rolls and is parallel to the plate surface of the metal plate, and does not allow the displacement to be out-of-plane of the reference plane. The rolling method may include a first step of determining a buckling inherent strain difference, which is a strain difference; a second step of calculating a new buckling inherent strain difference using an elastic strain difference that is reallocated by buckling wave generation and remains in the metal plate even after buckling when the plastic elongation strain difference exceeds the buckling inherent strain difference, and determining a true elongation strain difference by adding the difference between the plastic elongation strain difference and the new buckling inherent strain difference to the plastic elongation strain difference; and a third step of rolling the metal plate without changing the specified rolling conditions when the plastic elongation strain difference does not exceed the buckling inherent strain difference, and rolling the metal plate under rolling conditions set based on the true elongation strain difference when the plastic elongation strain difference exceeds the buckling inherent strain difference.

[0017] The method for controlling rolling of a metal sheet may further include a step of determining the plastic elongation strain difference.

[0018] In the second step of the metal plate rolling control method, a converted tension is obtained by converting the difference between the plastic elongation strain difference and the buckling inherent strain difference into a tension acting on the metal plate at the exit side of the rolling mill, and the true elongation strain difference is obtained by adding the elongation strain difference corresponding to the converted tension to the plastic elongation strain difference.

[0019] In the second step of the method for controlling rolling of a metal plate, a rolling load difference in the plate width direction of the metal plate corresponding to the converted tension may be second-order differentiated in the plate width direction to obtain an elongation strain difference corresponding to the converted tension.

[0020] In the rolling control method for a metal plate, the step of determining the true elongation strain difference and the step of rolling the metal plate include a first step of determining a rolling load difference, which is a difference in rolling load in the width direction of the metal plate during rolling under predetermined rolling conditions, and a plastic elongation strain difference, which is a difference in the width direction of strains elongating in the rolling direction of the metal plate during rolling, under a condition in which out-of-plane deformation of the metal plate is constrained by using a top-bottom symmetrical model that allows a displacement of the thickness center of the metal plate to be in-plane displacement of a reference plane that passes through the midpoint of a line connecting the rotation centers of the top and bottom rolls and is parallel to the plate surface of the metal plate, and does not allow a displacement out-of-plane of the reference plane; and a second step of determining a buckling inherent strain difference, which is a critical strain difference in the width direction at which the metal plate buckles, based on the plastic elongation strain difference, the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate at the exit side of a rolling mill. When the plastic elongation strain difference exceeds the buckling inherent strain difference, a new buckling inherent strain difference is calculated using the elastic strain difference that is reallocated by the generation of buckling waves and remains in the metal plate even after buckling, and a buckling inherent load difference that is a rolling load difference corresponding to the new buckling inherent strain difference is calculated from the correlation between the rolling load difference and the plastic elongation strain difference, and the difference between the rolling load difference and the buckling inherent load difference is calculated, and there is no change in the crown ratio of the metal plate between the exit side and the entry side of the rolling mill. and a fourth step of rolling the metal plate without changing the specified rolling conditions if the plastic elongation-strain difference does not exceed the buckling inherent strain difference, and rolling the metal plate under rolling conditions set based on the true elongation-strain difference if the plastic elongation-strain difference exceeds the buckling inherent strain difference.

[0021] In the rolling control method for a metal plate, the step of calculating the true elongation strain difference and the step of rolling the metal plate are performed under a condition in which the displacement of the center of thickness of the metal plate is permitted to be a displacement in the plane of a reference plane that passes through the midpoint of a line connecting the rotation centers of the upper and lower rolls and is parallel to the plate surface of the metal plate, and the displacement out of the plane of the reference plane is not permitted, thereby restraining the out-of-plane deformation of the metal plate. The step of calculating the true elongation strain difference and the step of rolling the metal plate are performed under a condition in which the out-of-plane deformation of the metal plate is restrained by using a top-bottom symmetrical model that does not allow the displacement out of the plane of the reference plane. A first step of determining a plastic elongation and strain difference, which is a difference in the width direction of the metal plate between the rolling load difference and the strain elongating in the rolling direction of the metal plate during rolling; a second step of determining a buckling inherent strain difference, which is a critical strain difference in the width direction at which the metal plate buckles, based on the plastic elongation and strain difference, the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate at the exit side of the rolling mill; and a second step of determining a buckling inherent strain difference, which is a critical strain difference in the width direction at which the metal plate buckles, based on the plastic elongation and strain difference, the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate at the exit side of the rolling mill. A third step of calculating a new buckling inherent strain difference using an elastic strain difference inherent in the metal plate, calculating a buckling shape transformation load difference corresponding to a buckling shape transformation elongation strain difference, which is the difference between the plastic elongation strain difference and the new buckling inherent strain difference, from the correlation between the rolling load difference and the plastic elongation strain difference, and deriving a new rolling load difference by superimposing the buckling shape transformation load difference on the rolling load difference, assuming that the metal plate has a crown ratio change, and calculating the new rolling load difference. a fourth step of adding the plastic elongation and strain difference to obtain a true elongation and strain difference and determining convergence of the true elongation and strain difference; and a fifth step of rolling the metal plate without changing the specified rolling conditions if the plastic elongation and strain difference does not exceed the buckling inherent strain difference obtained in the second step, and rolling the metal plate under rolling conditions set based on the true elongation and strain difference if the plastic elongation and strain difference exceeds the buckling inherent strain difference obtained in the second step.

[0022] In the method for controlling rolling of a metal plate, the new plastic elongation strain difference obtained in the third step may be assumed to be the plastic elongation strain difference obtained in the first step, and the new buckling inherent strain difference obtained in the third step may be assumed to be the buckling inherent strain difference obtained in the second step.

[0023] In the method for controlling rolling of a metal sheet, the metal sheet may be subjected to out-of-plane deformation at an entry side of the rolling mill.

[0024] The metal plate rolling control method may further include a step of measuring the shape of the metal plate after rolling using a shape meter installed on the outlet side of the rolling mill, and a step of correcting the plastic elongation strain difference based on the difference between an actual elongation strain difference converted into an out-of-plane deformation obtained from the measured shape of the metal plate and a predicted elongation strain difference converted into an out-of-plane deformation.

[0025] According to another aspect of the present invention, a plastic elongation strain difference, which is the difference in the width direction of the strain that elongates in the rolling direction of the metal plate during rolling under predetermined rolling conditions, is obtained under conditions in which the out-of-plane deformation of the metal plate is restrained by using a top-bottom symmetrical model that allows the displacement of the thickness center of the metal plate to be in the plane of a reference plane that passes through the midpoint of a line connecting the rotation centers of the top and bottom rolls and is parallel to the plate surface of the metal plate, and does not allow the displacement to be out-of-plane of the reference plane; a buckling inherent strain, which is the critical strain difference in the width direction at which the metal plate buckles, is obtained based on the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate at the delivery side of the rolling mill; a calculation unit that calculates a true elongation-strain difference by adding the difference between the plastic elongation-strain difference and the new buckling inherent strain difference to the plastic elongation-strain difference when the plastic elongation-strain difference exceeds the buckling inherent strain difference, and a control unit that rolls the metal plate without changing the predetermined rolling conditions when the plastic elongation-strain difference does not exceed the buckling inherent strain difference, and rolls the metal plate under rolling conditions set based on the true elongation-strain difference when the plastic elongation-strain difference exceeds the buckling inherent strain difference.

[0026] According to another aspect of the present invention, a first step of calculating a buckling inherent strain difference, which is a critical strain difference in the width direction at which the metal plate buckles, based on a plastic elongation strain difference, which is a difference in the width direction of the strain that elongates in the rolling direction of the metal plate during rolling under predetermined rolling conditions, the thickness of the metal plate, the width of the metal plate, and a tension acting on the metal plate at the delivery side of a rolling mill, the first step of calculating a buckling inherent strain difference, which is a critical strain difference in the width direction at which the metal plate buckles, based on a plastic elongation strain difference, which is a difference in the width direction of the strain that elongates in the rolling direction of the metal plate during rolling under predetermined rolling conditions, the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate at the delivery side of a rolling mill, the first step of calculating a buckling inherent strain difference, which is a critical strain difference in the width direction at which the metal plate buckles, based on a top-bottom symmetrical model that allows a displacement of the thickness center of the metal plate to be in the plane of a reference plane that passes through the midpoint of a line connecting the rotation centers of the top and bottom rolls and is parallel to the plate surface of the metal plate, and does not allow a displacement out of the plane of the reference plane, and the first step of calculating a buckling inherent strain difference, which is a critical strain difference in the width direction at which the metal plate buckles, based on a top-bottom symmetrical model that allows a displacement of the thickness center of the metal plate to be in the plane of a reference plane that passes through the midpoint of a line connecting the rotation centers of the top and bottom rolls and is parallel to the plate surface of the metal plate, and does not allow a displacement out of the plane of the reference plane; a second step of calculating a new buckling inherent strain difference using an elastic strain difference that is reallocated by buckling wave generation and remains in the metal plate even after buckling when the plastic elongation-strain difference exceeds the buckling inherent strain difference, and calculating a true elongation-strain difference by adding the difference between the plastic elongation-strain difference and the new buckling inherent strain difference to the plastic elongation-strain difference; and a third step of rolling the metal plate without changing the specified rolling conditions when the plastic elongation-strain difference does not exceed the buckling inherent strain difference, and rolling the metal plate under rolling conditions set based on the true elongation-strain difference when the plastic elongation-strain difference exceeds the buckling inherent strain difference. Effect of the Invention

[0027] According to the present invention, the elastic strain difference reallocated by the shape deformation after buckling is calculated, and the elastic strain difference is used for recalculation (eigenvalue analysis calculation using a theoretical buckling model), so that the shape of the metal sheet (true elongation strain difference) can be predicted with high accuracy. As a result, the rolling conditions are set based on the true elongation strain difference, and the metal sheet is rolled under the rolling conditions, so that the shape of the metal sheet after rolling can be freely controlled. [Brief description of the drawings]

[0028] [Figure 1] FIG. 1 is a diagram illustrating a target wave shape. [Diagram 2]FIG. 1 is a diagram showing the plastic elongation strain difference Δεpl(y) and the rolling load difference ΔP(y) of a metal plate when the metal plate is rolled under conditions in which the out-of-plane deformation of the metal plate is restrained. [Diagram 3] FIG. 13 is a diagram showing the buckling inherent strain difference Δεcr(y) and the buckling shape transformation elongation strain difference Δεts(y) that constitute the plastic elongation strain difference Δεpl(y), and the buckling inherent load difference ΔPcr(y) and the buckling shape transformation load difference ΔPts(y) that constitute the rolling load difference ΔP(y) when a metal plate is rolled under conditions in which the out-of-plane deformation of the metal plate is constrained. [Figure 4] FIG. 13 is a diagram showing the state after the buckling shape transformation elongation strain difference Δεts(y) and the buckling shape transformation load difference ΔPts(y) disappear when the metal plate is allowed to undergo out-of-plane deformation. [Diagram 5] FIG. 13 is a diagram showing how metal flows into a load-reduced region in the roll bite, increasing the difference in elongation strain in the metal sheet. [Figure 6] 2 to 5, and are explanatory diagrams showing a schematic plan view of the relationship between the elongation strain difference of a metal plate and the rolling load in a conventional metal plate rolling control method, in which (a) shows the plastic elongation strain difference Δεpl(y), (b) shows the buckling inherent strain difference Δεcr(y) and the buckling shape transformation elongation strain difference Δεts(y), and (c) shows the true elongation strain difference Δε'pl(y). [Figure 7] 1 is a flowchart showing a conventional rolling control method. [Figure 8] FIG. 1 is an explanatory diagram showing the results of shape prediction of a metal sheet when a conventional rolling control method (shape prediction method) and FEM are used. [Figure 9] FIG. 1 is an explanatory diagram showing the shape of a metal sheet when a conventional rolling control method (shape prediction method) and FEM are used. [Figure 10] 2 to 5, and are explanatory diagrams showing a schematic plan view of the relationship between the elongation strain difference of a metal plate and the rolling load in the rolling control method of the metal plate of the present embodiment, in which (a) shows the plastic elongation strain difference Δεpl(y), (b) shows the buckling inherent strain difference Δεcr(y) and the buckling shape transformation elongation strain difference Δεts(y), and (c) shows the true elongation strain difference Δε'pl(y). [Figure 11] 1 is a flowchart showing a rolling control method according to a first embodiment. [Figure 12] FIG. 1 is an explanatory diagram illustrating a rolling control method according to a first embodiment. [Figure 13] FIG. 3 is an explanatory diagram showing a result of predicting the shape of a metal sheet when the rolling control method according to the first embodiment is used. [Figure 14] FIG. 3 is an explanatory diagram showing a result of predicting the shape of a metal sheet when the rolling control method according to the first embodiment is used. [Figure 15] 5 is a flowchart showing a rolling control method according to a second embodiment. [Figure 16] 10 is a flowchart showing a rolling control method according to a third embodiment. [Figure 17] FIG. 1 is a diagram showing a schematic diagram of a rolling line equipped with a rolling mill, a rolling control device, and a shape meter. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0029] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In this specification and the drawings, elements having substantially the same functional configurations are denoted by the same reference numerals, and duplicated description will be omitted.

[0030] <Symmetrical wave shape> First, the target wave shape will be explained using Figure 1. The X axis is the longitudinal direction in which periodic waves occur, the Y axis is the plate width direction, and the Z axis is the plate thickness or wave height direction, and the wave shown in Figure 1 shows a typical ear wave. Note that periodic buckling waves (X direction in the figure) of waves represented by medium waves and quarter waves occurring at an intermediate position between ear waves and medium waves are also targeted. The definition of steepness or flatness used as the size of the wave is expressed as a percentage by dividing the wave piece amplitude height H of the width direction edge part of the metal plate by the wave pitch P (period P) and multiplying it by 100. In addition, this wave shape is called a width direction position-wise shape profile (wave shape profile) cut out at the position indicated by the wave piece amplitude height H in the YZ cross section, and the shape profile obtained in the buckling analysis described later is a normalized profile of 0 to 1 without a height dimension.

[0031] <The principle of difference in elongation strain in metal sheets> Next, the principle of the occurrence of strain difference (hereinafter referred to as "elongation strain difference") in the longitudinal direction (rolling direction) of a metal plate when the rolled metal plate buckles (when out-of-plane deformation occurs in the metal plate) will be described with reference to Figs. 2 to 6. Fig. 6 corresponds to Figs. 2 to 5, and is an explanatory diagram that shows a schematic plan view of the relationship between the elongation strain difference in a metal plate and the rolling load. As will be described later, Fig. 6 is a diagram showing the relationship between the elongation strain difference and the rolling load in a conventional method for controlling the rolling of a metal plate.

[0032] As shown in Fig. 2, a metal sheet H is rolled using a rolling mill 10 equipped with a pair of rolls. The X-axis in Fig. 2 indicates the longitudinal direction of the metal sheet H, and the metal sheet H is transported and rolled from the negative side of the X-axis to the positive side. The Y-axis in Fig. 2 indicates the width direction of the metal sheet H. In Fig. 2, half of the metal sheet H in the width direction, i.e., the center H in the width direction of the metal sheet H, is c From Edge H e Up to is shown in the figure.

[0033] Figure 2 shows the difference in plastic elongation strain Δε in the width direction of metal sheet H in the roll bite when metal sheet H is rolled under conditions in which the out-of-plane deformation of metal sheet H is restrained (i.e., conditions in which the out-of-plane deformation of metal sheet H is not permitted). pl (y) and the rolling load difference ΔP(y) in the sheet width direction acting in the vertical direction (Z-axis direction) of the metal sheet H. pl (y) is the strain in the longitudinal direction of the metal plate during rolling when the rolled metal plate H buckles (when out-of-plane deformation occurs in the metal plate). e The difference in the rolling load ΔP(y) is the difference in the rolling load ΔP(y) at the position y in the sheet width direction based on the elongation strain of the edge H in the sheet width direction of the metal sheet H. e The difference in the rolling load at the position y in the width direction of the plate is based on the rolling load at the position y in the width direction of the plate. The difference in the plastic elongation strain Δε pl(y) and the rolling load difference ΔP(y) correspond 1:1 in the sheet width direction. In Fig. 2, the out-of-plane deformation of the metal sheet H is restrained, so compressive stress is generated in the longitudinal direction immediately after the roll bite exit (bold arrow in Fig. 2). The plastic elongation strain difference Δε pl The relationship between (y) and the rolling load difference ΔP(y) is shown diagrammatically in FIG. 6(a).

[0034] Plastic elongation strain difference Δε pl (y) is the difference in elongation strain Δε that exists in the metal plate H even after buckling, as shown in Fig. 3. cr (y) (hereinafter, "buckling inherent strain difference Δε cr (y)" and the difference in elongation strain Δε ts (y) (hereinafter, "buckling shape transformation elongation strain difference Δε ts (y)". Of these, the buckling inherent strain difference Δε cr (y) is the limit of the strain difference beyond which the metal plate H buckles. In other words, the buckling inherent strain difference Δε cr (y) is the critical strain difference in the sheet width direction at which the metal sheet H buckles. Similarly, the rolling load difference ΔP(y) is the buckling inherent strain difference Δε cr (y) is the rolling load difference ΔP that corresponds 1:1 to the plate width direction cr (y)(hereinafter referred to as “buckling specific load difference ΔP cr (y) and the buckling shape transformation elongation strain difference Δε ts (y) is the rolling load difference ΔP that corresponds 1:1 to the plate width direction ts (y)(hereinafter referred to as “buckling shape conversion load difference ΔP ts The buckling inherent strain difference Δε cr (y), Buckling shape transformation elongation strain difference Δε ts (y), buckling specific load difference ΔP cr (y), Buckling shape transformation load difference ΔP ts (y) is shown diagrammatically in FIG. 6(b).

[0035] Next, if the metal plate H is allowed to deform out of plane, the buckling shape transformation elongation strain difference Δεts (y) is converted to out-of-plane deformation and disappears. In addition, the compressive stress indicated by the thick arrow in Fig. 2 decreases, and the apparent longitudinal tension acting on the metal plate H increases (thick arrow in Fig. 4). Then, the rolling load corresponding to this tension, that is, the buckling shape transformation elongation strain difference Δε ts Buckling shape transformation load difference ΔP corresponding to (y) ts (y) disappears. Buckling shape transformation load difference ΔP ts When (y) disappears, the load decreases toward the center H of the metal plate H as shown in FIG. c From Edge H e Metal flows in the width direction toward the edge H of metal sheet H (thick arrow in Fig. 5). As a result, according to the principle of constant volume, the edge H of metal sheet H is expanded in accordance with the amount of metal flowing in the width direction. e In other words, the buckling shape transformation load difference ΔP ts The difference in elongation strain corresponding to the disappearance of (y) occurs (thin arrow in Fig. 5). Therefore, as shown in Fig. 6(c), the buckling shape transformation load difference ΔP ts The difference in elongation strain Δε increases with the disappearance of (y) n (y) (hereinafter, "buckling strain difference Δε n (y) is the difference in plastic elongation strain Δε pl (y), the true difference in elongation strain in metal plate H, Δε' pl (y) is obtained. Buckling strain difference Δε n (y) is the difference in elongation strain caused by the buckling of the metal plate H. If the out-of-plane deformation of the metal plate H is restrained, buckling does not occur, and the difference in strain is not observed. Note that the difference in elongation strain caused by the buckling shape transformation, Δε ts (y) and buckling strain difference Δε n (y) is the buckling shape transformation load difference ΔP ts (y) is the elongation strain difference corresponding to (y), and although these have the same distribution, for convenience, different terms are used.

[0036] As described above, when the out-of-plane deformation of the metal sheet H is restrained in the rolling load difference and the elongation strain difference in the sheet width direction of the metal sheet H that change due to buckling, the rolling load difference ΔP(y) and the plastic elongation strain difference Δε shown in Fig. 6(a) pl (y), and the rolling load difference ΔP shown in Fig. 6(b) cr (y), ΔP ts (y) and the difference in elongation strain Δε cr (y), Δε ts (y), whereas when out-of-plane deformation of the metal plate H is allowed, the rolling load difference ΔP cr (y) and the difference in elongation strain Δε cr (y), Δε ts (y), Δε n (y) and the true elongation strain difference Δε' shown in Fig. 6(c). pl (y) is the difference in plastic elongation strain Δε obtained under the condition of constraining the out-of-plane deformation shown in Fig. 6(a) and (b). pl (y) than the buckling strain difference Δε n It increases by (y), and the following equation (1) is derived. Δε' pl (y)=Δε pl (y)+Δε n (y) (1)

[0037] <Conventional rolling control method> As described above, the present invention is a further development of the invention according to Patent Document 4. Therefore, before describing the rolling control method according to this embodiment, a conventional rolling control method disclosed in Patent Document 4 will be described. Fig. 7 is a flowchart showing a conventional shape prediction method.

[0038] (Step X1) In step X1, the plastic elongation strain difference Δε of the metal plate to be evaluated at any position y in the plate width direction (y direction) divided into N parts at a predetermined width is calculated. pl Set (y).

[0039] (Step X2) In step X2, an eigenvalue analysis calculation is performed using a theoretical buckling model. The theoretical buckling model is a model that performs buckling analysis using a wave-shaped buckling equation created based on a model formulated with a triangular residual stress distribution, for example, as shown in the Journal of the Japan Society for Technology of Plasticity, Plasticity and Processing, Vol. 28, No. 312 (1987-1), pp. 58-66. In the theoretical buckling model, the plastic elongation strain difference Δε pl (y) Buckling inherent strain difference Δε based on the thickness, width, and tension acting on the metal plate cr Calculate (y).

[0040] (Step X3) In step X3, it is determined whether or not buckling occurs. pl (y) and the difference in buckling inherent strain Δε cr (y) and Δε pl (y) is Δε cr If it is equal to or less than (y), it is determined that the metal plate is not buckled and is flat, and the process proceeds to step X4. pl (y) is Δε cr If it is larger than (y), it is determined that the metal plate will buckle, and the process proceeds to step X5.

[0041] (Step X4) In step X4, it is determined that the metal plate does not buckle and is flat. In this case, the shape of the metal plate is controlled by rolling the metal plate without changing the rolling conditions.

[0042] (Step X5) In step X5, it is determined that the metal plate buckles. In this case, the plastic elongation strain difference Δε pl (y) and the difference in buckling inherent strain Δε cr (y) is calculated, and this difference is the buckling promoting strain difference Δε shown in Figure 6(c) above. n (y). Then, according to the above formula (1), the buckling promoting strain difference Δε n (y) is the plastic elongation strain difference Δε pl (y) plus the true elongation strain difference Δε' pl We predict (y).

[0043] (Step X6) In step X6, the true elongation strain difference Δε ' predicted in step X5 is pl Based on (y), the rolling conditions are set and the shape of the metal sheet after rolling is controlled. Specifically, for example, the true elongation strain difference Δε' pl (y) is the buckling inherent strain difference Δε cr Set the rolling conditions so that the rolling temperature is less than (y). Then, the metal plate after rolling will not buckle and will be flat.

[0044] <Verification of conventional rolling control methods> In the conventional method, the buckling inherent strain difference Δε cr (y) and the true elongation strain difference Δε' pl The rolling of the metal plate is controlled by predicting (y). Here, the inventors have conducted extensive research and found that the shape profile predicted by the conventional buckling eigenanalysis has an error from the actual shape profile. Specifically, the conventionally predicted shape was compared with the analysis result by the finite element method (FEM) for verification.

[0045] Figures 8 and 9 are explanatory diagrams showing the shapes of metal sheets when using the conventional method and FEM under the same metal sheet conditions and the same plastic elongation strain difference. Note that Figure 8 shows the plate thickness direction displacement in the longitudinal direction displacement of the plate width center part, i.e., the wave height direction displacement, and Figure 9 shows an enlarged view of the wave height profile of cross section A in Figure 8.

[0046] Referring to Fig. 8, the wave pitch after buckling is almost the same when comparing the conventional method with FEM. On the other hand, referring to Fig. 9, the wave height displacement in the width direction center part is almost the same when comparing the conventional method with FEM, but the wave height displacement in the range surrounded by the dotted line in Fig. 9 is different, which shows that an error occurs in the shape profile.

[0047] The inventors conducted extensive research and found that the cause of the error in the shape profile is that in the conventional method, the shape profile calculated in the buckling eigenanalysis in step X2 is assumed to remain the same even after buckling. The inventors then came up with the idea that the shape of the metal plate can be appropriately predicted by recalculating (eigenvalue analysis calculation using a theoretical buckling model) using the elastic strain difference that exists in the metal plate as residual stress even after buckling, which is redistributed to the metal plate due to the generation of buckling waves after buckling, rather than calculating using the plastic elongation strain difference of the evaluation target in the buckling eigenvalue analysis. Specifically, the buckling eigenstrain difference Δε calculated by the conventional method shown in FIG. 6 is cr (y) and the buckling specific load difference ΔP cr When the method of the present invention is used for (y), the buckling inherent strain difference Δε cr (y) and the buckling specific load difference ΔP cr The shape of (y) is obtained. In the following, based on the above findings, the rolling control method for a metal sheet according to this embodiment will be described.

[0048] <Rolling control method according to the first embodiment> A method for controlling rolling of a metal sheet according to the first embodiment will be described. FIG. 11 is a flowchart showing the rolling control method according to the first embodiment. FIG. 12 is an explanatory diagram showing a schematic diagram of a method for predicting the shape of a metal sheet in the rolling control method according to the first embodiment. In the first embodiment, steps A12 to A20 described below are repeated to perform convergence calculation. In the first embodiment, steps A11 to A13 correspond to the first step of the present invention, steps A14 to A21 correspond to the second step of the present invention, and steps A22 and A23 correspond to the third step of the present invention.

[0049] (Step A11) In step A11, as shown in FIG. 12(a), the plastic elongation strain difference Δε of the metal plate to be evaluated at an arbitrary sheet width direction position y divided into N parts by a predetermined width in the sheet width direction (y-axis direction) is calculated. pl (y) Set the plastic elongation strain difference Δε pl(y) can be calculated by using a known method, such as the finite element method (FEM), the slab method, a physical model, or a regression equation of experiments or calculations. More specifically, the plastic elongation strain difference Δε is calculated under the condition that the out-of-plane deformation of the metal sheet is restrained by using a top-bottom symmetrical model that allows the displacement of the thickness center of the metal sheet to be in-plane displacement of a reference plane that is a plane that passes through the midpoint of a line connecting the rotation centers of the top and bottom rolls and is parallel to the sheet surface of the metal sheet, but does not allow the displacement to be out-of-plane of the reference plane. pl (y) can be calculated. Note that N represents the number of nodes equally divided in the width direction. Hereafter, N will be the number of nodes.

[0050] Models predicting the rolled shape in step A11 have been worked on for some time. The sheet crown prediction formula required for actual operation is obtained for each rolling mill by statistical methods based on the results of calculations using numerical analysis methods. For example, as shown in the Journal of the Japan Society for Technology of Plasticity, Plasticity and Processing, Vol. 25, No. 286 (1984-11), pp. 1034-1041, there is a method that uses a general-purpose sheet crown prediction formula for the delivery side of a rolling mill, which is derived by separating the sheet crown into factors that depend only on the elastic deformation conditions of the rolling mill and factors that depend on the plastic deformation conditions of the rolled material. Using these, it is possible to obtain the sheet crown at the entry side and the sheet crown at the exit side of the rolling mill. Then, by multiplying the shape change coefficient ξ obtained by a separate experiment by the crown ratio change (Ch / h-CH / H), the plastic elongation strain difference Δε pl (y) can be obtained. That is, the plastic elongation strain difference Δε pl (y) can be expressed by the following equation (2). Δε pl (y)=ξ×(Ch(y) / h(y)-CH(y) / H(y)) ···(2) Here, CH is the crown on the entry side of the rolling mill, H is the thickness on the entry side of the rolling mill, Ch is the crown on the exit side of the rolling mill, and h is the thickness on the exit side of the rolling mill. Based on the above formula (2), the plastic elongation strain difference Δε pl (y) can be found.

[0051] (Step A12) In step A12, in the first iterative calculation, the plastic elongation strain difference Δε pl Normalized elongation strain difference Δε normalized to a value between 0 (zero) and 1, with (y) being the maximum value 1 normal In the second and subsequent calculations of the repeated calculations, the normalized elongation strain difference Δε normal (y) is the normalized elongation strain difference in the next and subsequent steps.

[0052] (Step A13) In step A13, an eigenvalue analysis calculation is performed using a theoretical buckling model. The theoretical buckling model is a model that performs buckling analysis using a wave-shaped buckling equation created based on a model formulated with a triangular residual stress distribution, for example, as shown in the Journal of the Japan Society for Technology of Plasticity, Plasticity and Processing, Vol. 28, No. 312 (1987-1), pp. 58-66. In the theoretical buckling model, the normalized elongation-strain difference Δε normal (y), the thickness t of the metal plate, the width B of the metal plate, and the tension Ut acting on the metal plate are input, and the plastic elongation strain difference Δε pl The buckling inherent strain difference Δε, which is similar to (y) cr (y) (criterion for buckling), wave pitch P generated by buckling, and height profile (shape profile) W(y) normalized from 0 to 1 in the cross-section in the width direction at the time of buckling are output. Note that in the second and subsequent calculations of the iterative calculation, the buckling inherent strain difference Δε cr (y) is the elongation strain error Δε er (y), the difference in plastic elongation and strain Δε pl It is not similar to (y).

[0053] Here, the longitudinal stress acting on a metal plate is essentially a residual stress component that is 0 (zero) when integrated across the plate width and a tension (unit tension) component overlap. However, in the buckling model, the tension component is given separately, so here, it is assumed that it is 0 when integrated across the plate width, that is, the residual stress component is the integral across the plate width, or the average across the plate width, and is 0. The residual stress σ is calculated using the following formula (3): res Distribution of (y) and plastic elongation strain difference Δεpl The distribution of (y) is converted. Δε pl (y)=-(σ res (y) / E-Max(σ res (y)) / E) ···(3)

[0054] (Step A14) In step A14, it is determined whether it is the first calculation of the repeated calculations or the second or subsequent calculations. If it is the first calculation, the process proceeds to step A15, which will be described later, and if it is the second or subsequent calculations, the process proceeds to step A16, which will be described later. In step A15, it is determined whether buckling has occurred, but in the case of the second or subsequent calculations, since it has been determined that the metal plate will buckle, step A15 can be omitted.

[0055] (Step A15) In step A15, the occurrence of buckling is judged. Specifically, the plastic elongation strain difference Δε pl (y) and the difference in buckling inherent strain Δε cr (y) and Δε pl (y) is Δε cr If it is greater than (y), it is determined that the metal plate buckles, and the process proceeds to step A16. cr (y) is the plastic elongation strain difference Δε pl Since Δε(y) has a similar relationship to Δε(y), it may be judged at any position in the strip width direction y, but here the maximum values ​​are compared. pl (y) is Δε cr If it is equal to or less than (y), it is determined that the metal plate is not buckled and is flat, and the process proceeds to step A22.

[0056] (Step A22) In step A22, it is determined that the metal plate does not buckle and is flat. In this case, the shape of the metal plate is controlled by rolling the metal plate without changing the rolling conditions.

[0057] (Step A16) In step A16, it is determined that the metal plate will buckle, and the shape of the metal plate is predicted using a shape prediction model. First, as shown in FIG. 12(b), the plastic elongation strain difference Δε pl The component that converts (y) into the shape deformation after buckling (buckling shape transformation elongation strain difference Δε ts (y)) and the component that remains in the metal plate after buckling (buckling inherent strain difference Δε cr Then, the plastic elongation strain difference Δε pl (y) to buckling inherent strain difference Δε cr (y) is subtracted, and the buckling shape transformation elongation strain difference Δε ts Calculate (y). Δε ts (y)=Δε pl (y)-Δε cr (y) (4)

[0058] Next, the buckling shape transformation elongation strain difference Δε calculated from the above formula (4) ts Assuming that the wave pitch P calculated in step A13 does not change with respect to (y), the wave height width distribution h(x,y) = H × W(y) × Sin(2πx / P) obtained by multiplying the standardized height profile W(y) by the wave piece amplitude height H is predicted as the shape of the metal plate after buckling. Here, the steepness λ(y) of the waveform after buckling is expressed by the wave piece amplitude height H, the standardized height profile W(y), and the wave pitch P for each position y in the plate width direction, i.e., the geometric shape elongation strain difference Δε that appears in the shape due to out-of-plane deformation gs Using (y), it is expressed by the following formula (5). However, in general, when expressing the magnitude of the wave in rolling operations, it is often expressed as (5') with a double amplitude of the maximum amplitude H of the half amplitude wave. In addition, this formula (5) is expressed as the geometric shape elongation strain difference Δε gs Rearranging with respect to (y) gives equation (6). λ(y)=2×H×W(y) / P=(2 / π)√Δε gs (y) (5) λ=2×H / P (5') Δε gs (P, H, W(y))=(π / 2×W(y)×2×H / P) 2 (6)

[0059] Since the value of the normalized height profile W(y) is a profile normalized from 0 to 1, if we assume the maximum amplitude H of the single amplitude wave, the geometrical shape elongation strain difference Δε gs (P, H, W(y)) can be calculated. The buckling shape transformation elongation strain difference Δε ts (y) is approximately the same as the elongation strain difference Δε er (y) (hereinafter, "elongation strain error Δε er (y) is expressed by the following formula (7). Δε er (y)=Δε gs (P, H, W(y))-Δε ts (y) (7)

[0060] (Step A17) In step A17, the residual stress redistributed after the buckling wave is generated, i.e., the elastic strain difference Δε el * Specifically, as shown in FIG. 12(d), the elastic buckling inherent strain difference (Δε el_cr (y)) and the elastic elongation strain error (Δε er (y)) is added together to obtain the elastic strain difference Δε that is redistributed by the buckling wave generation and remains in the metal plate even after buckling. el * In this way, in step A17, the elastic strain difference Δε el * (y) is calculated. Δε el_cr (y)=-(Δε cr (y)-(ΣΔε cr (y)) / N) ···(8') Δε el * (y)=-{Δε pl (y)-Δε gs (P, H, W(y))}=Δε el_cr (y)+Δε er (y) (8)

[0061] (Step A18) In step A18, the normalized elongation strain difference Δε is calculated based on the residual stress distribution of the redistributed metal plate after buckling. normal * Specifically, in a convergence calculation in which steps A12 to A20 are repeated as described below, the elastic strain difference Δε inherent in the reallocated metal plate is calculated by the following formula (9). el * (y), the corresponding normalized elongation strain difference Δε with a value between 0 and 1 normal * (y) is determined. FIG. 12(e) shows the normalized elongation strain difference Δε normal * An example of (y) is shown below. Δε normal * (y)=-(Δε el * (y)-Max(ε el * (y))) / (Max(ε el * (y))-Min(ε el * (y))) ···(9)

[0062] (Step A19) In step A19, whether or not a solution has been found in the convergence calculation is determined by the normalized elongation strain difference Δε after buckling and reallocation. normal * (y) value and normalized elongation strain difference Δε before reallocation normal First, the error Δerror(y) of the standardized elongation-strain difference before and after reallocation is calculated for each widthwise position y by the following formula (10). That is, the error Δerror(y) is calculated based on the standardized elongation-strain difference Δε normal Next, as shown in the following formula (11), the square error for each position y in the strip width direction is integrated to obtain Δerror * Calculate the error Δerror * and a predetermined threshold value. Then, the error Δerror * If is greater than a predetermined threshold, the reallocated normalized elongation strain difference Δεnormal * It is determined that (y) has not converged, and the process proceeds to step A20 to perform recalculation (eigenvalue analysis calculation using a theoretical buckling model). * If is less than a predetermined threshold, the normalized elongation strain difference Δε normal * It is determined that (y) has converged, and the process proceeds to step A21. Δerror(y)=Δε normal * (y)-Δε normal (y) (10) Δerror * = {Σ(Δerror(y)) 2}>Threshold (11)

[0063] (Step A20) In step A20, the normalized elongation strain difference Δε used in the recalculation is calculated by returning to step A12. normal (y) is Δε normal * Specifically, the error Δerror(y) is multiplied by the relaxation coefficient α using the following formula (12), and the normalized elongation strain difference Δε after reallocation is calculated. normal Add to (y) to obtain the normalized elongation strain difference Δε for recalculation. normal (y) is reset. Here, when recalculating, if all the errors Δerror(y) are superimposed without multiplying the relaxation coefficient α, the calculation result will vibrate and the normalized elongation strain difference Δε normal (y) is difficult to converge. Therefore, in this embodiment, the normalized elongation-strain difference Δε is multiplied by the relaxation coefficient α. normal This makes it easier for (y) to converge. Note that the relaxation coefficient α is arbitrary, but after extensive investigation, the present inventors have confirmed that a value of 0.1 to 0.4 is appropriate. Δε normal (y)=Δε normal (y)+α×Δerror(y)=Δε normal (y) + α × {Δε normal * (y)-Δε normal (y)} ···(12)

[0064] Next, return to step A12, and calculate the normalized elongation strain difference Δε corrected in step A20. normal Steps A12 to A20 are then repeated, and the standardized elongation strain difference Δε normal * The convergence calculation is continued until it is determined that (y) has converged.

[0065] (Step A21) In step A19, the normalized elongation strain difference Δε normal * If it is determined that (y) has converged, the process proceeds to step A21. In step A21, the true elongation strain difference Δε′ shown in FIG. pl Specifically, the elastic strain difference Δε redistributed to the metal plate after buckling is calculated using the following formula (13): el * The new buckling inherent strain difference Δε calculated in (y) cr (y) and plastic elongation strain difference Δε pl From (y), the true elongation strain difference Δε' pl (y) is calculated. In addition, the true elongation strain difference Δε' is calculated by expanding the formula (13). pl (y) is the difference in plastic elongation strain Δε pl (y) and the difference in elongation strain at the time of buckling shape transformation Δε ts It can also be calculated from (y). Δε' pl (y)=Δε pl (y)+(Δε pl (y)-Δε cr (y))=Δε pl (y)+Δε ts (y) ···(13)

[0066] (Step A23) In step A23, the true elongation strain difference Δε′ calculated in step A21 is pl Based on (y), the rolling conditions are set and the shape of the metal sheet after rolling is controlled. Specifically, for example, the true elongation strain difference Δε' pl (y) is the buckling inherent strain difference Δε crThe rolling conditions are set so that the true elongation strain difference Δε' is equal to or less than (y). If this is done, the metal plate after rolling will not buckle and will be flat. Examples of the rolling conditions include the rolling load and the moment of the roll bender that controls the deflection of the rolls. The rolling conditions can be set arbitrarily, and the true elongation strain difference Δε' can be calculated through this algorithm as necessary. pl (y) can be determined to control the shape of the metal sheet after rolling.

[0067] According to the first embodiment, the plastic elongation strain difference Δε pl (y) and the buckling inherent strain difference Δε cr (y) or buckling shape transformation elongation strain difference Δε ts (y) and the true difference in elongation strain of the metal plate, Δε' pl (y) is calculated. By calculating the difference in elongation-strain in this manner, it is possible to improve the prediction accuracy of the difference in elongation-strain compared to the conventional method. Therefore, the true difference in elongation-strain Δε′ pl By setting the rolling conditions based on (y), the shape of the metal sheet after rolling can be freely controlled.

[0068] As described above, the conventional method assumes that the shape profile is maintained even after buckling. However, in reality, the effect of the shape profile changing due to the residual stress distribution redistributed after buckling is not taken into consideration, resulting in an error in the shape profile as shown in Fig. 9.

[0069] In this regard, the present inventors have found that the shape profile changes due to the shape deformation after buckling. According to the rolling control method according to the first embodiment described above, the elastic strain difference Δε el * (y) is calculated, and the elastic strain difference Δε el * Since the calculation is performed using (y), the shape of the metal sheet can be predicted appropriately. As a result, it becomes possible to more appropriately control the shape of the metal sheet after rolling.

[0070] In order to verify the effect of the first embodiment (the effect of improving the accuracy of shape prediction), the inventors compared the shape prediction results (converged solutions) obtained by the first embodiment with the shape prediction results obtained by a conventional method and the analysis results by FEM. The verification results are shown in Fig. 13 and Fig. 14. Fig. 13 shows the width-direction distribution of the elastic strain difference present in the metal plate after buckling, and Fig. 14 shows the width-direction distribution of the normalized profile.

[0071] 13 and 14, the shape prediction result of the conventional method is slightly different from the analysis result by FEM, whereas the shape prediction result of the first embodiment is almost the same as the analysis result by FEM. Therefore, it was found that the shape of the metal plate can be appropriately predicted according to the first embodiment.

[0072] In the first embodiment, the true elongation strain difference Δε′ is calculated based on the fluctuation in tension on the delivery side of the rolling mill caused by buckling. pl (y) may be calculated. Specifically, the buckling shape transformation elongation strain difference Δε ts (y) is converted into tension acting on the metal plate. The change in rolling load difference in the plate width direction caused by the fluctuation in tension on the exit side of the rolling mill, ΔP ts (y) is calculated, and then ΔP is calculated as shown in the following formula (14). ts The difference in elongation strain Δε is calculated by differentiating (y) twice with respect to the plate width direction x. ts Then, as shown in the following formula (8), the elongation strain difference Δε ts '(y) is the plastic elongation strain difference Δε set in step A11 pl The difference in elongation strain Δε' is added to (y) pl It is calculated as (y). Δε ts '(y)=d 2 ΔP ts (y) / dx 2 (14) Δε' pl (y)=Δε pl (y)+Δε ts '(y)...(15)

[0073] Thus, the buckling shape transformation elongation strain difference Δε ts (y) is converted into tension to obtain the converted tension, and the elongation strain difference Δε corresponding to this converted tension is calculated. ts Since we are looking for '(y), the calculated difference in elongation strain Δε ts '(y) is close to the actual phenomenon. Moreover, the difference in elongation strain Δε ts When calculating '(y), the change in rolling load difference ΔP ts Since (y) is differentiated twice, it is closer to the actual phenomenon. Therefore, the true difference in elongation strain of the metal plate, Δε' pl (y) can be predicted with even greater accuracy.

[0074] In the first embodiment, the plastic elongation strain difference Δε pl (y) is set, but the plastic elongation strain difference Δε pl If (y) is known, or if it is possible to use what has already been obtained, step A11 can be omitted. In this case, in step A13, the known plastic elongation strain difference Δε pl Using (y), the buckling inherent strain difference Δε cr Find (y).

[0075] <Rolling control method according to the second embodiment> A method for controlling rolling of a metal sheet according to the second embodiment will be described. Fig. 15 is a flow chart showing the method for controlling rolling according to the second embodiment. In the second embodiment, step B11 corresponds to the first step of the present invention, steps B12 and B13 correspond to the second step of the present invention, steps B14 to B21 correspond to the third step of the present invention, and steps B22 and B23 correspond to the fourth step of the present invention.

[0076] (Step B11) In step B11, the rolling load difference ΔP(y) acting on the metal plate and the plastic elongation strain difference Δε of the metal plate are calculated at an arbitrary width y in the width direction of the plate, which is divided into N parts by a predetermined width in the width direction. pl (y). The rolling load difference ΔP(y) and the plastic elongation strain difference Δε plAs in step A11 above, (y) can be calculated using a known method, such as the finite element method (FEM), the slab method, a physical model, or a regression equation based on experiments or calculations.

[0077] (Steps B12 to B20) In steps B12 to B20, convergent calculations are performed to predict the shape of the metal plate. These steps B12 to B20 are similar to the above steps A12 to A20, and detailed explanations thereof will be omitted here.

[0078] (Step B22) Step B22 is a case where it is determined in step B15 whether or not buckling has occurred that the metal sheet is not buckled and is flat. In this case, the shape of the metal sheet is controlled by rolling the metal sheet without changing the rolling conditions.

[0079] (Step B21) Step B21 is a step of determining whether or not buckling has occurred in the metal plate as a result of determining whether or not buckling has occurred in the metal plate in step B15, and determining whether or not the normalized elongation strain difference Δε normal * In step B21, the true elongation strain difference Δε′ is calculated. pl Calculate (y).

[0080] Here, in the above step B11, the rolling load difference ΔP(y) and the plastic elongation strain difference Δε pl (y) are set, and the rolling load difference ΔP(y) and the plastic elongation strain difference Δε pl (y) is derived. In step B21, based on this correlation, the buckling inherent strain difference Δε cr Buckling specific load difference ΔP corresponding to (y) cr (y) is calculated. Then, the rolling load difference ΔP(y) set in step B11 and the buckling specific load difference ΔP cr (y) is the difference between the buckling shape transformation load and ΔP ts (y)(ΔP ts (y) = ΔP(y) - ΔP crFurthermore, assuming that there is no change in the crown ratio of the metal plate at the exit side and the entry side of the rolling mill, the buckling shape transformation load difference ΔP is calculated using a known method, such as the finite element method (FEM), the slab method, a physical model, or a regression equation of experiments or calculations. ts (y) to buckling shape transformation elongation strain difference Δε ts (y) is calculated. Note that the buckling shape transformation load difference ΔP ts (y) to buckling shape transformation elongation strain difference Δε ts When calculating (y), the rolling load difference ΔP(y) and the plastic elongation strain difference Δε pl The correlation with (y) may be used. Then, the buckling shape transformation elongation strain difference Δε ts (y) is the plastic elongation strain difference Δε set in step B11 pl The difference in elongation strain Δε' is added to (y) pl It is calculated as (y). Δε' pl (y)=Δε pl (y)+Δε ts (y) ···(16)

[0081] (Step B23) In step B23, the true elongation strain difference Δε′ calculated in step B21 is pl Based on (y), the rolling conditions are set and the metal plate is rolled to control the shape of the metal plate. This step B23 is similar to the above-mentioned step A23.

[0082] The second embodiment is a modified example of the first embodiment. In the first and second embodiments, the plastic elongation strain difference Δε pl The method of calculating the difference in elongation and strain by the amount increased from (y) is different. In step A21 of the first embodiment, the difference in plastic elongation and strain Δε pl (y) and the difference in buckling inherent strain Δε cr In contrast, in step B21 of the second embodiment, the increase in the elongation strain difference is calculated from the difference between the rolling load difference ΔP(y) and the buckling inherent load difference ΔP crThe increase in the difference in elongation strain is calculated from the difference in (y). Therefore, in the second embodiment, the same effects as in the first embodiment can be obtained. That is, the true difference in elongation strain Δε′ of the metal plate pl (y) can be predicted more accurately than ever before. pl By setting the rolling conditions based on (y), the shape of the metal sheet after rolling can be freely controlled.

[0083] <Rolling control method according to the third embodiment> A rolling control method for a metal sheet according to the third embodiment will be described. Fig. 16 is a flowchart showing the rolling control method according to the third embodiment. As described later in this embodiment, i indicates the number of repeated calculations of steps C12 to C26 (hereinafter referred to as "first repeated calculations"), and j indicates the number of repeated calculations of steps C13 to C22 (hereinafter referred to as "second repeated calculations"). In the third embodiment, steps C11 and C12 correspond to the first step of the present invention, steps C13 and C14 correspond to the second step of the present invention, steps C15 to C24 correspond to the third step of the present invention, steps C25 and C26 correspond to the fourth step of the present invention, and steps C27 and C28 correspond to the fifth step of the present invention.

[0084] (Step C11) Start the first iteration (i=1) of the first iteration.

[0085] (Step C12) In step C12, the rolling load difference ΔP(i, y) acting on the metal plate and the plastic elongation strain difference Δε of the metal plate are calculated at any position y in the width direction of the plate divided into N by a predetermined width in the width direction. pl Set (i, y). This step C12 is similar to the above step B11.

[0086] (Steps C13 to C21) In steps C13 to C21, a convergent calculation (second iterative calculation) is performed to predict the shape of the metal sheet. These steps C13 to C21 are similar to the above steps B12 to B20, and detailed explanations are omitted here. In the above second embodiment, each parameter is a distribution of the sheet width direction position y and is marked with (y), but in this third embodiment, each parameter is a distribution of the sheet width direction position y, and is the i-th iteration of the first iterative calculation and is marked with (i, y).

[0087] (Step C22) In step C20, the normalized elongation strain difference Δε normal * If it is determined that (y) has not converged, the normalized elongation strain difference Δε for recalculation is calculated in step C21. normal After resetting (y), the process returns to step C13, where the number j of the second iterative calculations is incremented by one (j=j+1) in step C22.

[0088] (Step C27) Step C27 is a step in which it is determined in step C16 whether or not buckling has occurred that the metal sheet is not buckled and is flat. In this case, the shape of the metal sheet is controlled by rolling the metal sheet without changing the rolling conditions.

[0089] (Step C23) Step C23 is a step in which, as a result of judging whether or not buckling has occurred in step C16, it is determined that the metal plate has buckled, and the normalized elongation strain difference Δε normal * This is the case where it is determined that (y) has converged. In step C23, the number of times i of the first iterative calculation is incremented by one (i=i+1). Note that, in FIG. 16, the first iterative calculation (j=1) is illustrated as an example, but this number varies depending on the actual number of times.

[0090] (Step C24) In step C24, a new rolling load difference ΔP′(i, y) is calculated. Here, in step C12, the rolling load difference ΔP(i, y) and the plastic elongation strain difference Δε pl (i, y) are set, and the rolling load difference ΔP(i, y) and the plastic elongation strain difference Δε pl The correlation between (i, y) is derived. In step C24, the buckling inherent strain difference Δε calculated in step C14 is calculated based on this correlation. cr Buckling specific load difference ΔP corresponding to (i-1, y) cr (i-1, y) is calculated. Then, the rolling load difference ΔP(i-1, y) set in step C12 and the buckling inherent load difference ΔP calculated in step C24 are calculated. cr The difference between (i-1, , y) and the buckling shape transformation load difference ΔP ts (i-1, y)(ΔP ts (i-1,y)=ΔP(i-1,y)-ΔP cr Then, the buckling shape transformation load difference ΔP(i-1, y) is calculated for the rolling load difference ΔP(i-1, y) of the previous first iterative calculation by the following formula (17). ts (i-1, y) is added to calculate a new rolling load difference ΔP'(i, y). ΔP'(i,y)=ΔP(i-1,y)+ΔP ts (i-1, y) (17)

[0091] In the third embodiment, it is assumed that the crown ratio of the metal sheet changes between the exit side and the entry side of the rolling mill. In other words, it is assumed that when the rolling load acting on the metal sheet varies, the deflection of the rolls of the rolling mill varies due to the variation of the rolling load, and the elongation strain of the metal sheet varies. Then, in step C24, a new rolling load difference ΔP'(i, y) is calculated.

[0092] (Step C25) In step C25, the true elongation strain difference Δε' pl Calculate (i, y). Specifically, the buckling shape transformation load difference ΔP obtained in step C24 is calculated using a known method, such as the finite element method (FEM), the slab method, a physical model, or a regression equation of experiments or calculations. ts(i-1, y) to buckling shape transformation elongation strain difference Δε ts (i-1, y) is calculated. Note that the buckling shape transformation load difference ΔP ts (i-1, y) to buckling shape transformation elongation strain difference Δε ts When calculating (i-1, y), the rolling load difference ΔP(i, y) and the plastic elongation strain difference Δε pl The correlation with (i, y) may be used. Then, the new plastic elongation strain difference Δε pl (i-1, y) is the buckling shape transformation elongation strain difference Δε ts (i-1, y) is added to the true elongation strain difference Δε' pl It is calculated as (i, y). Δε' pl (i, y) = Δε pl (i-1, y)+Δε ts (i-1, y) (18)

[0093] (Step C26) In step C26, it is determined whether a solution has been found in the convergence calculation (first iterative calculation). First, the true elongation strain difference Δε′ is calculated for each position y in the sheet width direction by the following formula (19). pl (i, y) and the difference in plastic elongation strain from the previous time, Δε pl Calculate the error Δer(y) of (i-1, y). That is, the error Δer(y) is the plastic elongation strain difference Δε pl Next, as shown in the following formula (20), the square error for each position y in the strip width direction is integrated to obtain Δer * Calculate the error Δer * and a predetermined threshold value. Then, the error Δer * is greater than a predetermined threshold, the true elongation strain difference Δε' pl It is determined that (i, y) has not converged, and the process returns to step C12 to perform recalculation. At this time, as shown in the following formulas (21) and (22), the new rolling load difference ΔP'(i, y) is set as the rolling load difference ΔP(i, y), and the true elongation strain difference Δε' pl (i, y) is the difference in elongation strain Δε pl (i, y). On the other hand, the error Δer *If is less than a predetermined threshold, the true elongation strain difference Δε' pl It is determined that (i, y) has converged, and the process proceeds to step C28. Δer(y)=Δε' pl (i, y)-Δε pl (i-1, y) (19) Δer * = {Σ(Δer(y)) 2}>Threshold (20) ΔP(i, y)=ΔP'(i, y) ···(21) Δε pl (i, y)=Δε' pl (i, y) (22)

[0094] (Step C28) In step C28, the true elongation strain difference Δε ′ calculated in step C25 is pl Based on (i, y), the rolling conditions are set and the metal plate is rolled to control the shape of the metal plate. This step C28 is similar to the above-mentioned step B23. In addition, it may be assumed that the new plastic elongation strain difference obtained in the third step is the plastic elongation strain difference obtained in the first step, and that the new buckling inherent strain difference obtained in the third step is the buckling inherent strain difference obtained in the second step.

[0095] According to the third embodiment, it is assumed that the crown ratio of the metal sheet changes between the exit side and the entry side of the rolling mill, and the calculation is repeated. Therefore, the true elongation strain difference Δε' pl (i, y)) can be predicted with greater accuracy.

[0096] <Other embodiments> The above-mentioned first, second and third embodiments are each implemented in a rolling line 1 shown in Fig. 17. The rolling line 1 has the above-mentioned rolling mill 10 and a rolling control device 20 that controls the rolling mill 10. The rolling control device 20 has a calculation unit 21 and a control unit 22.

[0097] The calculation unit 21 first accepts input of provisional rolling conditions set in the rolling control device 20. Next, the calculation unit 21 performs calculations in steps A11 to A21 of the first embodiment, steps B11 to B21 of the second embodiment, and steps C11 to C26 of the third embodiment based on the rolling conditions that have been accepted as input. Then, in step A22 of the first embodiment, step B22 of the second embodiment, and step C27 of the third embodiment, if it is determined that the rolling conditions are not changed, the calculation unit 21 notifies the control unit 22 that it is not necessary to change the provisional rolling conditions described above. On the other hand, in step A21 of the first embodiment, step B21 of the second embodiment, and step C25 of the third embodiment, the true elongation strain difference Δε' is calculated based on the rolling conditions that have been accepted as input. pl Once (y) is calculated, the true elongation strain difference Δε' pl The calculation unit 21 notifies the control unit 22 of (y).

[0098] The control unit 22 calculates the true elongation strain difference Δε′ notified by the calculation unit 21. pl The control unit 22 sets the rolling conditions based on, for example, the true elongation strain difference Δε′ pl (y) is the buckling inherent strain difference Δε cr (y) The rolling conditions are derived so that the following is satisfied. Note that the calculation unit 21 may derive new rolling conditions.

[0099] Then, when the control unit 22 receives a notification from the calculation unit 21 that it is not necessary to change the rolling conditions, the control unit 22 outputs the original rolling conditions to the rolling mill 10 and controls the rolling mill 10, thereby controlling the shape of the metal sheet H after rolling. On the other hand, when new rolling conditions are derived as described above, the control unit 22 outputs the new rolling conditions to the rolling mill 10 and controls the rolling mill 10, thereby controlling the shape of the metal sheet H after rolling.

[0100] Furthermore, the control unit 22 judges whether or not to end the rolling. When the control unit 22 judges not to end the rolling, the process returns to input of the rolling conditions, and performs step A11 in the first embodiment, step B11 in the second embodiment, step C11 in the third embodiment, and subsequent steps. On the other hand, when the control unit 22 judges to end the rolling, it ends this routine.

[0101] Furthermore, in the rolling line 1, a shape meter 30 may be installed at the exit side of the rolling mill 10. The shape meter 30 measures the shape of the metal sheet H after rolling. As the shape of the metal sheet H, the longitudinal position and the widthwise position of the metal sheet H, and the height displacement at those positions are measured. The measurement results of the shape meter 30 are output to the rolling control device 20. In the rolling control device 20, a calculation unit 21 calculates the buckling shape transformation elongation strain difference Δε based on the measurement results of the shape meter 30. ts (y) is corrected, and the true elongation strain difference Δε' pl (y) is corrected. This true elongation strain difference Δε' pl The correction of (y) follows the method described in Patent Document 3 (JP Patent Publication 2012-218010 A). That is, first, based on the measurement results of the shape meter 30, the actual buckling shape transformation elongation strain difference Δε ts (y) is calculated. The buckling shape transformation elongation strain difference Δε ts (y) and the buckling shape transformation elongation strain difference Δε predicted in the above embodiment ts (y), and the difference (error) E between them is taken as the model error. Based on this difference E, the plastic elongation strain difference Δε pl (y) (rolling load difference ΔP(y)) is learned and corrected. Specifically, the plastic elongation strain difference Δε pl (y) (rolling load difference ΔP(y)) is added to the difference E, and the subsequent processes are performed to obtain the true elongation strain difference Δε' pl Then, the control unit 22 calculates the true elongation strain difference Δε′ in the calculation unit 21. plBased on the correction result of (y), the rolling conditions are corrected so that the shape of the metal sheet H becomes the target shape. In this way, based on the measurement result of the shape meter 30, the rolling conditions are feedback-controlled.

[0102] The present invention can also be applied to the case where the metal sheet H is out-of-plane deformed at the entry side of the rolling mill 10. The inventors have found that when the metal sheet H is out-of-plane deformed at the entry side of the rolling mill in this way, the difference in elongation strain in the metal sheet H after rolling is larger than when the metal sheet H is not out-of-plane deformed at the entry side of the rolling mill. In other words, the conventional method further deteriorates the shape prediction accuracy of the metal sheet. In contrast, in the present invention, the difference in elongation strain corresponding to the out-of-plane deformation at the entry side of the rolling mill is calculated as the buckling shape transformation elongation strain difference Δε ts (y), the true difference in elongation strain in metal plate H, Δε' pl Therefore, even if the metal sheet H is deformed out of plane at the entry side of the rolling mill, the shape of the metal sheet H can be appropriately controlled.

[0103] Although the embodiment of the present invention has been described above, the present invention is not limited to such examples. It is clear that a person skilled in the art can come up with various modified or altered examples within the scope of the technical ideas described in the claims, and it is understood that these also naturally belong to the technical scope of the present invention. [Industrial Applicability]

[0104] INDUSTRIAL APPLICABILITY The present invention is useful for predicting the shape of a metal plate, such as a thin plate or a thick plate, after rolling, and controlling the shape of the metal plate based on the prediction result. [Explanation of symbols]

[0105] 1. Rolling Line 10. Rolling Mill 20 Rolling control device 21 Arithmetic section 22 Control section 30 Shape meter H Metal plate

Claims

1. A method for predicting and controlling the shape of a metal plate, comprising: a first step of calculating a plastic elongation strain difference, which is the difference in the width direction of the strain that elongates in the rolling direction of the metal plate during rolling under specified rolling conditions, based on the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate at the exit side of the rolling mill, and a buckling inherent strain difference, which is the critical strain difference in the width direction at which the metal plate buckles, obtained under conditions in which out-of-plane deformation of the metal plate is constrained by using a top-bottom symmetrical model that allows the displacement of the center of thickness of the metal plate to be in the plane of a reference plane that passes through the midpoint of a line connecting the rotation centers of the top and bottom rolls and is parallel to the plate surface of the metal plate, and does not allow the displacement to be out-of-plane of the reference plane; If the plastic elongation strain difference exceeds the buckling inherent strain difference, a new buckling inherent strain difference is calculated using the elastic strain difference that is reallocated by the buckling wave generation and remains in the metal plate even after buckling, and a second step of calculating a true elongation strain difference by adding the difference between the plastic elongation strain difference and the new buckling inherent strain difference to the plastic elongation strain difference; a third step of rolling the metal plate without changing the predetermined rolling conditions if the plastic elongation strain difference does not exceed the buckling inherent strain difference, and rolling the metal plate under rolling conditions set based on the true elongation strain difference if the plastic elongation strain difference exceeds the buckling inherent strain difference.

2. The method for controlling rolling of a metal plate according to claim 1 , further comprising a step of determining the plastic elongation strain difference.

3. 3. The method for controlling rolling of a metal plate according to claim 1, wherein in the second step, a converted tension is obtained by converting a difference between the plastic elongation strain difference and the buckling inherent strain difference into a tension acting on the metal plate at the delivery side of the rolling mill, and the true elongation strain difference is obtained by adding the elongation strain difference corresponding to the converted tension to the plastic elongation strain difference.

4. 4. The rolling control method for a metal plate according to claim 3, characterized in that in the second step, a rolling load difference in the plate width direction of the metal plate corresponding to the converted tension is second-order differentiated in the plate width direction to obtain an elongation strain difference corresponding to the converted tension.

5. A method for predicting and controlling the shape of a metal plate, comprising: A first step of calculating a rolling load difference, which is the difference in rolling load in the width direction of the metal plate during rolling under predetermined rolling conditions, and a plastic elongation strain difference, which is the difference in strain elongating in the rolling direction of the metal plate during rolling, in the width direction of the metal plate during rolling, under a condition that out-of-plane deformation of the metal plate is constrained by using an up-down symmetrical model that allows the displacement of the thickness center of the metal plate to be in the plane of a reference plane that passes through the midpoint of a line connecting the rotation centers of the upper and lower rolls and is parallel to the plate surface of the metal plate, and does not allow the displacement to be out-of-plane of the reference plane; A second step of determining a buckling inherent strain difference, which is a critical strain difference in the plate width direction at which the metal plate buckles, based on the plastic elongation strain difference, the plate thickness of the metal plate, the plate width of the metal plate, and a tension acting on the metal plate at the delivery side of a rolling mill; a third step of calculating a new buckling inherent strain difference using the elastic strain difference that is reallocated by the generation of buckling waves and remains in the metal plate even after buckling, calculating a buckling inherent load difference that is the rolling load difference corresponding to the new buckling inherent strain difference from the correlation between the rolling load difference and the plastic elongation strain difference, and calculating the difference between the rolling load difference and the buckling inherent load difference, and adding the buckling shape transformation elongation strain difference and the plastic elongation strain difference to calculate a true elongation strain difference, assuming that there is no change in the crown ratio of the metal plate between the exit side and the entry side of the rolling mill; a fourth step of rolling the metal plate without changing the predetermined rolling conditions if the plastic elongation strain difference does not exceed the buckling inherent strain difference, and rolling the metal plate under rolling conditions set based on the true elongation strain difference if the plastic elongation strain difference exceeds the buckling inherent strain difference.

6. A method for predicting and controlling the shape of a metal plate, comprising: A first step of calculating a rolling load difference, which is the difference in rolling load in the width direction of the metal plate during rolling under predetermined rolling conditions, and a plastic elongation strain difference, which is the difference in strain elongating in the rolling direction of the metal plate during rolling, in the width direction of the metal plate during rolling, under a condition that out-of-plane deformation of the metal plate is constrained by using an up-down symmetrical model that allows the displacement of the thickness center of the metal plate to be in the plane of a reference plane that passes through the midpoint of a line connecting the rotation centers of the upper and lower rolls and is parallel to the plate surface of the metal plate, and does not allow the displacement to be out-of-plane of the reference plane; A second step of determining a buckling inherent strain difference, which is a critical strain difference in the plate width direction at which the metal plate buckles, based on the plastic elongation strain difference, the plate thickness of the metal plate, the plate width of the metal plate, and a tension acting on the metal plate at the delivery side of a rolling mill; When the plastic elongation strain difference exceeds the buckling inherent strain difference, a new buckling inherent strain difference is calculated using the elastic strain difference that is reallocated by the buckling wave generation and is still present in the metal plate after buckling, and a buckling shape transformation load difference corresponding to the buckling shape transformation elongation strain difference, which is the difference between the plastic elongation strain difference and the new buckling inherent strain difference, is calculated from the correlation between the rolling load difference and the plastic elongation strain difference, and the buckling shape transformation load difference is superimposed on the rolling load difference to derive a new rolling load difference, and a third step of calculating the new rolling load difference on the assumption that the metal plate has a crown ratio change; A fourth step of calculating a true elongation-strain difference by adding the buckling shape transformation elongation-strain difference and a new plastic elongation-strain difference, and determining whether the true elongation-strain difference has converged; a fifth step of rolling the metal plate without changing the specified rolling conditions if the plastic elongation strain difference does not exceed the buckling inherent strain difference obtained in the second step, and rolling the metal plate under rolling conditions set based on the true elongation strain difference if the plastic elongation strain difference exceeds the buckling inherent strain difference obtained in the second step.

7. The rolling control method for a metal plate according to claim 6, characterized in that the new plastic elongation strain difference obtained in the third step is assumed to be the plastic elongation strain difference obtained in the first step, and the new buckling inherent strain difference obtained in the third step is assumed to be the buckling inherent strain difference obtained in the second step.

8. The method for controlling rolling of a metal sheet according to any one of claims 1 to 7, characterized in that the metal sheet is subjected to out-of-plane deformation at the entry side of the rolling mill.

9. Measuring the shape of the metal sheet after rolling using a shape meter installed on the delivery side of the rolling mill; The rolling control method for a metal plate according to any one of claims 1 to 8, further comprising a step of correcting the plastic elongation strain difference based on a difference between an actual elongation strain difference converted into an out-of-plane deformation obtained from the measured shape of the metal plate and a predicted elongation strain difference converted into an out-of-plane deformation.

10. A plastic elongation strain difference, which is the difference in the strain extending in the rolling direction of the metal plate during rolling under specified rolling conditions in the sheet width direction, is obtained under conditions in which the out-of-plane deformation of the metal plate is constrained by using a top-bottom symmetrical model that allows the displacement of the thickness center of the metal plate to be in-plane displacement of a reference plane that is a plane that passes through the midpoint of a line connecting the rotation centers of the top and bottom rolls and is parallel to the sheet surface of the metal plate, and does not allow the displacement to be out-of-plane of the reference plane, the thickness of the metal plate ... a calculation unit that calculates a buckling inherent strain difference, which is a critical strain difference in the plate width direction at which the metal plate buckles, based on a plate width and a tension acting on the metal plate at the delivery side of a rolling mill, and when the plastic elongation strain difference exceeds the buckling inherent strain difference, calculates a new buckling inherent strain difference using an elastic strain difference that is reallocated after buckling, and calculates a true elongation strain difference by adding the difference between the plastic elongation strain difference and the new buckling inherent strain difference to the plastic elongation strain difference; a control unit that rolls the metal plate without changing the specified rolling conditions when the plastic elongation strain difference does not exceed the buckling inherent strain difference, and that rolls the metal plate under rolling conditions set based on the true elongation strain difference when the plastic elongation strain difference exceeds the buckling inherent strain difference.

11. a first step of calculating a plastic elongation strain difference, which is the difference in the width direction of the strain that elongates in the rolling direction of the metal plate during rolling under specified rolling conditions, based on the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate at the exit side of the rolling mill, and a buckling inherent strain difference, which is the critical strain difference in the width direction at which the metal plate buckles, obtained under conditions in which out-of-plane deformation of the metal plate is constrained by using a top-bottom symmetrical model that allows the displacement of the center of thickness of the metal plate to be in the plane of a reference plane that passes through the midpoint of a line connecting the rotation centers of the top and bottom rolls and is parallel to the plate surface of the metal plate, and does not allow the displacement to be out-of-plane of the reference plane; If the plastic elongation strain difference exceeds the buckling inherent strain difference, a new buckling inherent strain difference is calculated using the elastic strain difference that is reallocated by the buckling wave generation and remains in the metal plate even after buckling, and a second step of calculating a true elongation strain difference by adding the difference between the plastic elongation strain difference and the new buckling inherent strain difference to the plastic elongation strain difference; a third step of rolling the metal plate without changing the specified rolling conditions if the plastic elongation strain difference does not exceed the buckling inherent strain difference, and rolling the metal plate under rolling conditions set based on the true elongation strain difference if the plastic elongation strain difference exceeds the buckling inherent strain difference.

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