JP2022175007A - Rolling control method for metal plate, rolling control device and method for manufacturing rolled metal plate - Google Patents

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 The present invention relates to a rolling control method for controlling the shape of a rolled metal plate, a rolling control device for executing the rolling control method, and a method for manufacturing a rolled metal plate.

Conventionally, various methods have been proposed as techniques for predicting the shape of a rolled metal plate such as a thin plate or a thick plate.

Patent Literature 1 discloses a technique for improving prediction accuracy in an extrapolation region where actual data does not exist and correcting errors in a rolling model. Specifically, by using a performance database in which the manufacturing conditions of products manufactured in the past and the result information of the manufacturing are associated and stored, each sample in the performance database and the similarity of the required point (prediction target point) A prediction formula near the requested point is created by weighted regression using this similarity as a weight. This prediction formula improves the prediction accuracy of the extrapolation region.

In Patent Document 2, the elongation strain (stress) distributed in the plate width direction of the metal plate during rolling is geometrically converted into a wave shape during buckling, and the elongation strain inherent in the metal plate even after buckling A technique is disclosed for predicting the shape of a metal plate by separating it from the elongation strain to be applied.

In Patent Document 3, in addition to the shape feature amount of the metal plate measured at the delivery side of the rolling mill, the elongation strain inherent in the metal plate at the time of measurement is obtained, and this is superimposed on the above shape feature amount and output from the rolling mill. A technique for predicting the shape of a metal plate is disclosed by measuring as a given true shape feature amount. Here, as geometric values, the position and height direction displacement in the strip threading direction and strip width direction were measured at the delivery side of the rolling mill, and profile, steepness, and elongation strain difference were obtained as shape feature quantities. there is

Patent Document 4 discloses a metal plate rolling control method having the following first to third steps. In the first step, the provisional elongation-strain difference distribution of the metal plate during rolling is obtained under conditions that constrain the out-of-plane deformation of the metal plate, and this provisional elongation-strain difference distribution, the thickness of the metal plate and the plate A buckling critical strain difference distribution is determined based on the width and the tension acting on the metal plate on the delivery side of the rolling mill. In the second step, when the provisional elongation strain difference distribution exceeds the buckling critical strain difference distribution, the difference between the provisional elongation strain difference distribution and the buckling critical strain difference distribution is obtained, and this difference is provisionally The true elongation strain difference distribution is obtained by adding it to the elongation strain difference distribution. In the third step, the shape of the metal sheet is controlled by setting the rolling conditions based on the true elongation strain difference distribution and rolling the metal sheet.

Japanese Patent Application Laid-Open No. 2008-112288 JP 2005-153011 A JP 2012-218010 A Japanese Patent No. 6172401

However, the method disclosed in Patent Document 1 does not consider a nonlinear phenomenon 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, the model will have an error, so the shape of the rolled metal sheet cannot be accurately predicted.

Further, the methods disclosed in each of Patent Documents 2 to 4 are for predicting the shape of the metal plate in consideration of the buckling phenomenon of the metal plate. Prediction accuracy has been improved. In particular, the invention according to Patent Document 4 is a development of the inventions according to Patent Documents 2 and 3, and quantifies the correlation between the rolling load difference distribution and the elongation strain difference distribution in the plate width direction of the metal plate that changes due to buckling. By grasping the true elongation strain difference distribution of the metal plate, the shape of the metal plate is predicted. However, as a result of the inventor's earnest study, it was found that there is room for improvement in improving the prediction accuracy, as will be described later.

And in the method disclosed in Patent Document 4, after performing the buckling determination of the metal plate, if it does not buckle (when the provisional elongation strain difference distribution described above does not exceed the buckling critical strain difference distribution) , rolling the metal sheet without changing the predetermined rolling conditions. On the other hand, when buckling occurs (when 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 accuracy of predicting the shape of the metal plate.

The present invention has been made in view of the above points, and an object of the present invention is to accurately predict the shape of a rolled metal plate and freely control the shape of the metal plate.

In order to achieve the above object, the present inventor predicted the shape of the metal plate after rolling, and based on the predicted shape of the metal plate, studied a method for controlling the shape of the metal plate. I came to obtain the knowledge of

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

The present invention is a further development of the invention disclosed in Patent Document 4. As a result of intensive study by the present inventor, in the invention according to Patent Document 4, it is assumed that the shape profile calculated by the buckling eigenanalysis maintains the shape profile even after buckling, so an error occurs in the shape profile. I found out. In the buckling eigenvalue analysis, instead of calculating with the plastic elongation strain difference to be evaluated, recalculation is performed with the elastic strain difference redistributed by the generation of the shape profile that occurred after buckling (eigenvalue using the theoretical buckling model Analytical calculation), we thought that the shape of the metal plate could be predicted appropriately. That is, conventionally, it was thought that the disclosed post-buckling shape profile was determined by the difference in plastic elongation strain used in the initial calculation, but as a result of intensive studies by the present inventors, a buckling shape occurred. We have found that the shape profile is determined by the elastic strain difference that is redistributed in the metal plate after buckling. 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.

According to the present invention, there is provided a method for predicting and controlling the shape of a metal plate, in which when predicting a post-buckling corrugated profile based on a plastic elongation strain difference imparted to the metal plate, A step of obtaining a true elongation strain difference by buckling analysis using an elastic strain difference inherent in the metal plate, and a step of rolling the metal plate under rolling conditions set based on the true elongation strain difference. A rolling control method for a metal plate is provided, comprising:

In the metal plate rolling control method, the step of obtaining the true elongation strain difference and the step of rolling the metal plate are performed so that the displacement of the thickness center of the metal plate is within the line connecting the rotation centers of the upper and lower rolls. A vertically symmetrical model that allows displacement in the plane of a reference plane that passes through a point and is parallel to the plane of the metal plate, but does not allow displacement out of the plane of the reference plane. Plastic elongation strain difference, which is the difference in the width direction of the strain that extends in the rolling direction of the metal plate during rolling under predetermined rolling conditions, which is obtained under conditions that constrain the out-of-plane deformation of the metal plate by using , the critical strain in the plate width direction leading to buckling of the metal plate based on the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate on the delivery side of the rolling mill A first step of obtaining a buckling inherent strain difference that is a difference, and when the plastic elongation strain difference exceeds the buckling inherent strain difference, it is redistributed by the generation of buckling waves and is inherent in the metal plate even after buckling Calculate a new inherent buckling strain difference using the elastic strain difference, add the difference between the plastic elongation strain difference and the new inherent buckling strain difference, and the plastic elongation strain difference to obtain the true elongation strain difference and when the plastic elongation strain difference does not exceed the buckling inherent strain difference, the metal plate is rolled without changing the predetermined rolling conditions, and the plastic elongation strain difference is and a third step of rolling the metal sheet under rolling conditions set based on the true elongation strain difference when the buckling inherent strain difference is exceeded.

The metal plate rolling control method may further include the step of obtaining the plastic elongation strain difference.

In the metal sheet rolling control method, in the second step, the difference between the plastic elongation strain difference and the buckling inherent strain difference is converted into tension acting on the metal sheet on the delivery side of the rolling mill. may be obtained, and the true elongation strain difference may be obtained by adding the elongation strain difference corresponding to the converted tension and the plastic elongation strain difference.

In the method for controlling rolling of a metal plate, in the second step, the rolling load difference in the plate width direction of the metal plate corresponding to the conversion tension is second-order differentiated in the plate width direction as the conversion tension. It may be obtained as the corresponding elongation strain difference.

In the metal plate rolling control method, the step of obtaining the true elongation strain difference and the step of rolling the metal plate are performed so that the displacement of the thickness center of the metal plate is within the line connecting the rotation centers of the upper and lower rolls. A vertically symmetrical model that allows displacement in the plane of a reference plane that passes through a point and is parallel to the plane of the metal plate, but does not allow displacement out of the plane of the reference plane. Under the condition that the out-of-plane deformation of the metal plate is constrained by using, the rolling load difference, which is the difference in the rolling load in the width direction of the metal plate during rolling under predetermined rolling conditions, and the metal during rolling A first step of obtaining a plastic elongation strain difference that is the difference in the width direction of the strain extending in the rolling direction of the plate, the plastic elongation strain difference, the thickness of the metal plate, the width of the metal plate, and the rolling mill A second step of obtaining 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 tension acting on the metal plate on the exit side of the plastic elongation When the strain difference exceeds the buckling inherent strain difference, a new buckling inherent strain difference is calculated using the elastic strain difference that is redistributed by the buckling wave generation and is inherent in the metal plate even after buckling, and From the correlation between the rolling load difference and the plastic elongation strain difference, the buckling specific load difference, which is the rolling load difference corresponding to the new buckling specific strain difference, is obtained, and the rolling load difference and the buckling specific load difference are calculated. , and assuming that there is no change in the crown ratio of the metal plate between the delivery side and the entry side of the rolling mill, add the buckling shape transformation elongation strain difference and the plastic elongation strain difference to obtain the true elongation strain A third step of obtaining a difference, and when the plastic elongation strain difference does not exceed the buckling inherent strain difference, the metal plate is rolled without changing the predetermined rolling conditions, and the plastic elongation strain difference is exceeds the inherent buckling strain difference, a fourth step of rolling the metal sheet under rolling conditions set based on the true elongation strain difference.

In the metal plate rolling control method, the step of obtaining the true elongation strain difference and the step of rolling the metal plate are performed so that the displacement of the thickness center of the metal plate is within the line connecting the rotation centers of the upper and lower rolls. A vertically symmetrical model that allows displacement in the plane of a reference plane that passes through a point and is parallel to the plane of the metal plate, but does not allow displacement out of the plane of the reference plane. Under the condition that the out-of-plane deformation of the metal plate is constrained by using, the rolling load difference, which is the difference in the rolling load in the width direction of the metal plate during rolling under predetermined rolling conditions, and the metal during rolling A first step of obtaining a plastic elongation strain difference that is the difference in the width direction of the strain extending in the rolling direction of the plate, the plastic elongation strain difference, the thickness of the metal plate, the width of the metal plate, and the rolling mill A second step of obtaining 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 tension acting on the metal plate on the exit side of the plastic elongation When the strain difference exceeds the buckling inherent strain difference, a new buckling inherent strain difference is calculated using the elastic strain difference that is redistributed by the buckling wave generation and is inherent in the metal plate even after buckling, and From the correlation between the rolling load difference and the plastic elongation strain difference, a buckling shape conversion load difference corresponding to the buckling shape conversion elongation strain difference, which is the difference between the plastic elongation strain difference and the new buckling inherent strain difference, is obtained. Then, the buckling shape transformation load difference is superimposed on the rolling load difference to derive a new rolling load difference, and assuming that the metal plate has a crown ratio change, the new rolling load difference is obtained. A fourth step of determining the true elongation strain difference by adding the buckling shape conversion elongation strain difference and the new plastic elongation strain difference, and determining the convergence of the true elongation strain difference; If the difference does not exceed the inherent buckling strain difference obtained in the second step, the metal sheet is rolled without changing the predetermined rolling conditions, and the plastic elongation strain difference is the second step and a fifth step of rolling the metal plate under rolling conditions set based on the true elongation strain difference when the inherent buckling strain difference obtained in is exceeded. .

In the metal plate rolling control method, assuming that the new plastic elongation strain difference obtained in the third step is the plastic elongation strain difference obtained in the first step, the It may be assumed that the new inherent buckling strain difference is the inherent buckling strain difference determined in the second step.

In the metal sheet rolling control method, the metal sheet may be out-of-plane deformed on the entry side of the rolling mill.

The method for controlling rolling of the metal plate includes the steps of measuring the shape of the metal plate after rolling using a shape meter installed on the delivery side of the rolling mill, and measuring the shape of the metal plate after rolling; modifying the plastic elongation strain difference based on the difference between the actual elongation strain difference converted to deformation and the predicted elongation strain difference converted to out-of-plane deformation.

According to the present invention from another aspect, the displacement of the thickness center of the metal plate is on the reference plane which is a plane parallel to the plate surface of the metal plate passing through the midpoint of the line connecting the rotation centers of the upper and lower rolls. It is obtained under conditions that constrain the out-of-plane deformation of the metal plate by using a vertically symmetrical model that allows in-plane displacement and does not allow out-of-plane displacement of the reference plane, The plastic elongation strain difference, which is the difference in the width direction of the strain that extends 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 rolling mill Based on the tension acting on the metal plate on the exit side, the buckling inherent strain difference, which is the critical strain difference in the plate width direction at which the metal plate buckles, is obtained. When the flexion intrinsic strain difference is exceeded, a new buckling intrinsic strain difference is calculated using the elastic strain difference redistributed after buckling, and the difference between the plastic elongation strain difference and the new buckling intrinsic strain difference and the plastic elongation strain difference, and a calculation unit that obtains the true elongation strain difference by adding the Without rolling the metal plate, and when the plastic elongation strain difference exceeds the inherent buckling strain difference, the metal plate is rolled under the rolling conditions set based on the true elongation strain difference. A control unit for performing rolling is provided for a metal sheet.

According to the present invention from another aspect, the displacement of the thickness center of the metal plate is on the reference plane which is a plane parallel to the plate surface of the metal plate passing through the midpoint of the line connecting the rotation centers of the upper and lower rolls. It is obtained under conditions that constrain the out-of-plane deformation of the metal plate by using a vertically symmetrical model that allows in-plane displacement and does not allow out-of-plane displacement of the reference plane, The plastic elongation strain difference, which is the difference in the width direction of the strain that extends 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 rolling mill A first step of obtaining 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 tension acting on the metal plate on the delivery side, and the plastic elongation strain If the difference exceeds the inherent buckling strain difference, a new inherent buckling strain difference is calculated using the elastic strain difference that is redistributed by the generation of buckling waves and is inherent in the metal plate even after buckling. A second step of obtaining a true elongation strain difference by adding the difference between the elongation strain difference and the new inherent buckling strain difference and the plastic elongation strain difference; If it does not exceed, the metal plate is rolled without changing the predetermined rolling conditions, and when the plastic elongation strain difference exceeds the inherent buckling strain difference, the true elongation strain difference and a third step of rolling the metal plate under rolling conditions set based on.

According to the present invention, the elastic strain difference redistributed by the shape deformation after buckling is calculated, and recalculation (eigenvalue analysis calculation using the theoretical buckling model) is performed using the elastic strain difference. , the shape of the metal plate (true elongation strain difference) can be predicted with high accuracy. As a result, it is possible to freely control the shape of the metal sheet after rolling by setting the rolling conditions based on this true elongation strain difference and rolling the metal sheet under the rolling conditions.

It is a figure explaining the wave shape used as object. FIG. 4 is a diagram showing a plastic elongation strain difference Δε _pl (y) and a rolling load difference ΔP(y) of a metal plate when the metal plate is rolled under conditions that constrain the out-of-plane deformation of the metal plate. Buckling intrinsic strain difference Δε _cr (y) and buckling shape transformation elongation strain difference Δε that constitute the plastic elongation strain difference Δε _pl (y) when the metal plate is rolled under conditions that constrain the out-of-plane deformation of the metal plate FIG. 10 is a diagram showing _ts (y), and a buckling specific load difference ΔP _cr (y) and a buckling shape transformation load difference ΔP _ts (y) that constitute the rolling load difference ΔP(y). FIG. 8 is a diagram showing a state after the buckling shape transformation elongation strain difference Δε _ts (y) and the buckling shape transformation load difference ΔP _ts (y) disappear when out-of-plane deformation of the metal plate is permitted. FIG. 5 is a diagram showing how metal flows into a load-lowering region in a roll bite and an increase in elongation-strain difference in a metal plate. Corresponding to FIGS. 2 to 5 above, FIG. The elongation strain difference Δε _pl (y) is shown, (b) is the buckling intrinsic strain difference Δε _cr (y) and the buckling shape transformation elongation strain difference Δε _ts (y), and (c) is the true elongation strain difference. Δε′ _pl (y) is shown. It is a flowchart which shows the conventional rolling control method. It is explanatory drawing which shows the shape prediction result of the metal plate at the time of using the conventional rolling control method (shape prediction method) and FEM. It is explanatory drawing which shows the shape of the metal plate at the time of using the conventional rolling control method (shape prediction method) and FEM. FIG. 5 is an explanatory view schematically showing the relationship between the elongation strain difference of the metal plate and the rolling load in the metal plate rolling control method of the present embodiment in a plan view, corresponding to FIGS. 2 to 5; is the plastic elongation strain difference Δε _pl (y), (b) is the buckling intrinsic strain difference Δε _cr (y) and the buckling shape transformation elongation strain difference Δε _ts (y), and (c) is the true elongation The strain difference Δε' _pl (y) is shown. 4 is a flow chart showing a rolling control method according to the first embodiment; BRIEF DESCRIPTION OF THE DRAWINGS It is explanatory drawing which shows typically the rolling control method concerning 1st Embodiment. FIG. 4 is an explanatory diagram showing a shape prediction result of a metal plate when using the rolling control method according to the first embodiment; FIG. 4 is an explanatory diagram showing a shape prediction result of a metal plate when using the rolling control method according to the first embodiment; 8 is a flow chart showing a rolling control method according to the second embodiment; 9 is a flow chart showing a rolling control method according to a third embodiment; 1 is a diagram schematically showing a rolling line equipped with a rolling mill, a rolling control device, and a shape meter; FIG.

BEST MODE FOR CARRYING OUT THE INVENTION Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the present specification and drawings, elements having substantially the same functional configuration are given the same reference numerals to omit redundant description.

<Symmetric wave shape>
First, the target waveform will be described with reference to FIG. The X axis is the longitudinal direction in which periodic waves are generated, the Y axis is the plate width direction, and the Z axis is the plate thickness or wave height direction, and the waves shown in FIG. 1 show typical ear waves. Periodic buckling (in the figure, X direction) waves of waves typified by medium waves and quarter waves occurring at an intermediate position between ear waves and medium waves are also targets. The definition of the steepness or flatness used as the magnitude of the wave is divided by the wave pitch P (period P) of the wave piece amplitude height H at the edge portion in the width direction of the metal plate, multiplied by 100, and expressed in percent. . In addition, this wave shape is called a shape profile (wave shape profile) for each width direction position cut out in the YZ cross section at the position indicated by the wave piece amplitude height H, and the shape profile obtained in the buckling analysis described later is It is a 0-1 scaled profile with no height dimension.

<Principle of occurrence of difference in elongation strain of metal plate>
Next, when the rolled metal plate buckles (when out-of-plane deformation occurs in the metal plate), the strain difference extending in the longitudinal direction (rolling direction) of the metal plate (hereinafter referred to as “elongation strain difference”). The principle of the generation of is described with reference to FIGS. 2 to 6. FIG. FIG. 6 corresponds to FIGS. 2 to 5 and is an explanatory view schematically showing the relationship between the elongation strain difference and the rolling load in the metal plate in plan view. As will be described later, FIG. 6 is a diagram showing the relationship between the difference in elongation strain and the rolling load in a conventional method for controlling rolling of a metal plate.

A metal sheet H is rolled using a rolling mill 10 having a pair of rolls as shown in FIG. The X-axis of FIG. 2 indicates the longitudinal direction of the metal plate H, and the metal plate H is conveyed and rolled from the negative direction side to the positive direction side of the X-axis. The Y-axis in FIG. 2 indicates the plate width direction of the metal plate H. As shown in FIG. In FIG. 2, half of the metal plate H in the plate width direction, that is, from the center _Hc to the edge _He in the plate width direction of the metal plate H is illustrated.

FIG. 2 shows the width of the metal plate H in the roll bite when the metal plate H is rolled under conditions that constrain the out-of-plane deformation of the metal plate H (that is, conditions that do not allow out-of-plane deformation of the metal plate H). The plastic elongation strain difference Δε _pl (y) in the direction and the rolling load difference ΔP(y) in the plate width direction acting in the vertical direction (Z-axis direction) of the metal plate H are illustrated. The plastic elongation strain difference Δε _pl (y) is the width direction of elongation 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). It is the difference at the sheet width direction position y with reference to the elongation strain of the edge _He . In the following description, the definitions of elongation strain and elongation strain difference are the same. Further, the rolling load difference ΔP(y) is the rolling load difference at the sheet width direction position y with the rolling load of the edge _He of the metal sheet H in the sheet width direction as a reference. Also, the plastic elongation strain difference Δε _pl (y) and the rolling load difference ΔP(y) correspond to 1:1 in the strip width direction. In FIG. 2, since the out-of-plane deformation of the metal plate H is restrained, a compressive stress is generated in the longitudinal direction immediately after the delivery side of the roll bite (bold arrow in FIG. 2). The relationship between the plastic elongation strain difference Δε _pl (y) and the rolling load difference ΔP(y) shown in FIG. 2 is schematically shown in FIG. 6(a).

The plastic elongation strain difference Δε _pl (y) _is the elongation strain difference Δε _cr (y) inherent in the metal plate H after buckling as shown in FIG. ) and the elongation strain difference Δε _ts (y) that is converted into wave-shaped out-of-plane deformation after buckling (hereinafter referred to as “buckling shape conversion elongation strain difference Δε _ts (y)”). be. Of these, the buckling inherent strain difference Δε _cr (y) is the limit strain difference at which the metal plate H buckles when the strain difference increases further. In other words, the inherent buckling strain difference Δε _cr (y) is the critical strain difference in the plate width direction at which the metal plate H causes buckling. Similarly, the rolling load difference ΔP ₍ y) is the rolling load difference ΔP _cr (y) (hereinafter referred to as “the buckling specific load difference ΔP _{cr (y)”) and the rolling load difference ΔP ts (} y) (hereinafter referred to as “buckling shape conversion (referred to as the load difference ΔP _ts (y)”). In addition, the specific buckling strain difference Δε _cr (y), the buckling shape conversion elongation strain difference Δε _ts (y), the buckling specific load difference ΔP _cr (y), and the buckling shape conversion load difference ΔP _ts shown in FIG. (y) is schematically shown in FIG. 6(b).

Next, if the out-of-plane deformation of the metal plate H is allowed, the buckling shape conversion elongation strain difference Δε _ts (y) is converted into out-of-plane deformation and disappears as shown in FIG. Moreover, the compressive stress indicated by the thick arrow in FIG. 2 decreases, and the apparent longitudinal tension acting on the metal plate H increases (the thick arrow in FIG. 4). Then, the rolling load corresponding to this tension, that is, the buckling shape transformation load difference ΔP _ts (y) corresponding to the buckling shape transformation elongation strain difference Δε _ts (y) disappears. When the buckling shape conversion load difference ΔP _ts (y) disappears, the metal flows in the width direction of the metal plate H toward the load lowering region, that is, from the center _Hc of the metal plate H toward the edge _He as shown in FIG. (thick arrow in FIG. 5). As a result, due to the principle of constant volume, the elongation strain at the edge _He of the metal plate H increases according to the amount of metal flowing in the width direction of the plate. That is, the elongation strain difference increases corresponding to the disappearance of the buckling shape transformation load difference ΔP _ts (y) (thin arrow in FIG. 5). Therefore, as shown in FIG. 6(c), the elongation strain difference _{Δε n (} y) (hereinafter referred to as the “buckling assisting strain difference Δε _n (y)”) is added to the plastic elongation strain difference Δε _pl (y) when the out-of-plane deformation of the metal plate H shown in FIG. Δε′ _pl (y) is obtained. The buckling-promoting strain difference Δε _n (y) is the elongation strain difference caused by the buckling of the metal plate H, and when the out-of-plane deformation of the metal plate H is constrained, buckling does not occur, so it is not observed. strain difference. Both the buckling shape transformation elongation strain difference Δε _ts (y) and the buckling enhancement strain difference Δε _n (y) are elongation strain differences corresponding to the buckling shape transformation load difference ΔP _ts (y), and these are Although the distribution is the same, different terms are used for convenience.

As described above, when the out-of-plane deformation of the metal plate H is restrained in the rolling load difference and the elongation strain difference in the plate width direction of the metal plate H that change due to buckling, the rolling load difference shown in FIG. There is a correlation between ΔP (y) and the plastic elongation strain difference Δε _pl (y), and furthermore, the rolling load differences ΔP _cr (y) and ΔP _ts (y) shown in FIG. 6(b) and the elongation strain difference Δε _cr ( y), there is a correlation with Δε _ts (y), whereas when the out-of-plane deformation of the metal plate H is allowed, the rolling load difference ΔP _cr (y) and the elongation strain difference Δε There is a correlation with _cr (y), Δε _ts (y) and Δε _n (y). Then, the true elongation strain difference Δε' _pl (y) shown in FIG. Δε _pl (y) is increased by the buckling-enhancing strain difference Δε _n (y), and the following equation (1) is derived.
Δε′ _pl (y)=Δε _pl (y)+Δε _n (y) (1)

<Conventional rolling control method>
As described above, the present invention is a further development of the invention disclosed in Patent Document 4. Therefore, prior to explaining the rolling control method according to the present embodiment, the conventional rolling control method disclosed in Patent Document 4 will be explained. FIG. 7 is a flow chart showing a conventional shape prediction method.

(Step X1)
In step X1, the plastic elongation strain difference Δε _pl (y) of the metal sheet to be evaluated at an arbitrary position y in the sheet width direction divided by a predetermined width in the sheet width direction (y direction) is set.

(Step X2)
At step X2, eigenvalue analysis calculation is performed using the theoretical buckling model. The theoretical buckling model is based on a model formulated with a triangular residual stress distribution shown in, for example, Journal of Japan Society for Technology of Plasticity, Plasticity and Processing, Vol. 28, No. 312 (1987-1), p. 58-66. It is a model that performs buckling analysis using the wave-shaped buckling equation created by Then, in the theoretical buckling model, the specific buckling strain difference Δε _cr (y) is calculated based on the plastic elongation strain difference Δε _pl (y), the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate. calculate.

(Step X3)
At step X3, it is determined whether or not buckling occurs. Compare the plastic elongation strain difference Δε _pl (y) and the buckling intrinsic strain difference Δε _cr (y), and if Δε _pl (y) is Δε _cr (y) or less, it is considered that the metal plate is flat without buckling. Make a decision and proceed to step X4. On the other hand, if Δε _pl (y) is greater than Δε _cr (y), it is determined that the metal plate buckles, and the process proceeds to step X5.

(Step X4)
At step X4, it is determined that the metal plate is not buckled and the metal plate is flat. In such a case, the shape of the metal sheet is controlled by rolling the metal sheet without changing the rolling conditions.

(Step X5)
At step X5, it is determined that the metal plate buckles. In this case, the difference between the plastic elongation strain difference Δε _pl (y) and the buckling inherent strain difference Δε _cr (y) is obtained, and this difference is the buckling promoting strain difference Δε _n (y) shown in FIG. becomes. Then, according to the above formula (1), the buckling assisted strain difference Δε _n (y) is added to the plastic elongation strain difference Δε _pl (y) to predict the true elongation strain difference Δε' _pl (y).

(Step X6)
At step X6, based on the true elongation strain difference Δε′ _pl (y) predicted at step X5, the rolling conditions are set to control the shape of the metal sheet after rolling. Specifically, for example, the rolling conditions are set such that the true elongation strain difference Δε′ _pl (y) is equal to or less than the buckling inherent strain difference Δε _cr (y). As a result, the rolled metal plate does not buckle and becomes flat.

<Verification of conventional rolling control method>
In the conventional method, the buckling inherent strain difference Δε _cr (y) is calculated by performing the buckling inherent analysis as described above, and further, the true elongation strain difference Δε' _pl (y) is predicted, and the metal plate It controls rolling. Here, as a result of intensive studies, the inventors of the present invention have found that the shape profile predicted by the conventional buckling peculiar analysis has an error from the actual shape profile. Specifically, the conventionally predicted shape was verified by comparing with the analysis result by the finite element method (FEM).

8 and 9 are explanatory diagrams showing the shape of the metal plate when using the conventional method and FEM under the same metal plate conditions and the same plastic elongation strain difference. 8 shows the displacement in the thickness direction in the longitudinal direction displacement of the width center portion, ie, the displacement in the wave height direction, and FIG. 9 is an enlarged view of the wave height profile of section A in FIG.

Referring to FIG. 8, comparing the conventional method and FEM, the wave pitch after buckling is almost the same. On the other hand, referring to FIG. 9, when comparing the conventional method and FEM, the wave height displacement in the center portion in the width direction is almost the same, but the wave height displacement in the range surrounded by the dotted line in FIG. It turned out to be an error.

The inventors of the present invention conducted extensive studies and found that the cause of this error in the shape profile is that, in the conventional method, the shape profile calculated by the buckling peculiar analysis in step X2 maintains the shape profile as it is even after buckling. I found that there is a point. In the buckling eigenvalue analysis, instead of calculating the plastic elongation strain difference of the evaluation target, the residual stress redistributed in the metal plate due to the buckling wave generated after buckling is inherent in the metal plate after buckling. By recalculating (eigenvalue analysis calculation using a theoretical buckling model) with the elastic strain difference, we thought that the shape of the metal plate could be predicted appropriately. Specifically, using the method of the present invention for the inherent buckling strain difference Δε _cr (y) and the inherent buckling load difference ΔP _cr (y) calculated by the conventional method shown in FIG. As shown in 10, different shapes of the specific buckling strain difference Δε _cr (y) and the specific buckling load difference ΔP _cr (y) are obtained. In the following description, the metal sheet rolling control method according to the present embodiment will be described based on the above findings.

<Rolling control method according to the first embodiment>
A metal plate rolling control method according to the first embodiment will be described. FIG. 11 is a flow chart showing a rolling control method according to the first embodiment. FIG. 12 is an explanatory diagram schematically showing a method of predicting the shape of a metal plate in the rolling control method according to the first embodiment. In the first embodiment, steps A12 to A20, which will be described later, are repeated to perform convergence calculation. Further, 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. corresponds to

(Step A11)
In step A11, as shown in FIG. 12A, the plastic elongation strain difference of the metal plate to be evaluated at an arbitrary plate width direction position y divided by N with a predetermined width in the plate width direction (y-axis direction) Set Δε _pl (y). The plastic elongation strain difference Δε _pl (y) can be calculated using known methods such as the finite element method (FEM), the slab method, physical models, and regression equations for experiments and calculations. More specifically, the displacement of the thickness center of the metal plate is the in-plane displacement of a reference plane that passes through the midpoint of the line connecting the rotation centers of the upper and lower rolls and is parallel to the plate surface of the metal plate. The plastic elongation strain difference Δε _pl (y) is Desired. Note that N represents the number of nodes obtained by equally dividing the width direction. Hereinafter, N is the number of nodes.

A model for predicting the rolling shape in step A11 has been worked on for some time. A strip crown prediction formula required for actual operation is obtained by statistical methods for each individual rolling mill based on calculation results by numerical analysis methods. For example, as shown in Journal of Japan Society for Technology of Plasticity, Plasticity and Processing, Vol. 25, No. 286 (1984-11), p. There is a method using a general-purpose strip crown prediction formula on the delivery side of the rolling mill, which is derived separately from factors that depend on plastic deformation conditions.
By using these, it is possible to determine the strip crown on the entry side of the rolling mill and the strip crown on the delivery side. Then, the plastic elongation strain difference Δε _pl (y) can be obtained by multiplying the shape change coefficient ξ obtained by a separate experiment by the crown ratio change (Ch/h−CH/H). 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 plate thickness on the entry side of the rolling mill, Ch is the crown on the delivery side of the rolling mill, and h is the plate thickness on the delivery side of the rolling mill. Then, the plastic elongation strain difference Δε _pl (y) can be obtained based on the above formula (2).

(Step A12)
In step A12, in the first calculation of the repeated calculation, the normalized elongation strain difference Δε _pl (y) is _normalized to a value from 0 (zero) to 1, with the plastic elongation strain difference Δε pl (y) being the maximum value of 1 ( y). In the second and subsequent repeated calculations, the normalized elongation strain difference Δε _normal (y) corrected in step A20 described later is used as the normalized elongation strain difference in subsequent steps.

(Step A13)
In step A13, eigenvalue analysis calculation is performed using the theoretical buckling model. The theoretical buckling model is based on a model formulated with a triangular residual stress distribution shown in, for example, Journal of Japan Society for Technology of Plasticity, Plasticity and Processing, Vol. 28, No. 312 (1987-1), p. 58-66. It is a model that performs buckling analysis using the wave-shaped buckling equation created by Then, in the theoretical buckling model, if the normalized elongation strain difference Δε _normal (y), the metal plate thickness t, the metal plate width B, and the tension Ut acting on the metal plate are input, the plastic elongation strain difference Δε The _buckling inherent strain difference Δε _cr (y) (criteria for buckling occurrence), which has a similar shape to pl (y), the wave pitch P generated by buckling, and the cross section in the width direction at the time of buckling, from 0 to 1 A scaled height profile (shape profile) W(y) is output. In addition, in the case of the second and subsequent iterative calculations, the inherent buckling strain difference Δε _cr (y) is corrected by the elongation strain error Δε _er (y) in step A17 described later, so the plastic elongation strain difference Δε _pl It is not similar to (y).

Here, originally, the longitudinal stress acting on the metal plate overlaps the residual stress component and the tension (unit tension) component that become 0 (zero) when integrated in the plate width direction. However, since the tension component is given separately in the buckling model, it is assumed that the integral in the width direction is 0, that is, the residual stress component is 0 when integrated in the width direction or averaged in the width direction. The distribution of the residual stress σ _res (y) and the distribution of the plastic elongation strain difference Δε _pl (y) are converted by the equation (3).
Δε _pl (y)=−(σ _res (y)/E−Max(σ _res (y))/E) (3)

(Step A14)
At step A14, it is determined whether it is the first calculation of the repeated calculations or the second and subsequent calculations. Then, in the case of the first calculation, the process proceeds to step A15, which will be described later, and in the case of the second and subsequent calculations, the process proceeds to step A16, which will be described later. In step A15, it is determined whether or not buckling occurs, but in the case of the second and subsequent calculations, it is determined that the metal plate will buckle, so step A15 can be omitted.

(Step A15)
At step A15, it is determined whether or not buckling occurs. Specifically, the plastic elongation strain difference Δε _pl (y) and the buckling intrinsic strain difference Δε _cr (y) are compared. Then, if Δε _pl (y) is greater than Δε _cr (y), it is determined that the metal plate buckles, and the process proceeds to step A16. By the way, as in the conventional method, the inherent buckling strain difference Δε _cr (y) has a similar relationship with the plastic elongation strain difference Δε _pl (y), so it may be determined anywhere in the sheet width direction position y, but here each is compared with the maximum value of On the other hand, if Δε _pl (y) is equal to or less than Δε _cr (y), it is determined that the metal plate is flat without buckling, and the process proceeds to step A22.

(Step A22)
At step A22, it is determined that the metal plate is not buckled and the metal plate is flat. In such a case, the shape of the metal sheet is controlled by rolling the metal sheet without changing the rolling conditions.

(Step A16)
At 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), a component that converts the plastic elongation strain difference Δε _pl (y) into shape deformation after buckling (buckling shape conversion elongation strain difference Δε _ts (y)) and a seat It is separated from the component (the buckling intrinsic strain difference Δε _cr (y)) remaining in the metal plate even after bending. Then, the buckling _shape conversion elongation strain difference Δε _ts (y) is calculated by subtracting the buckling intrinsic strain difference Δε _cr (y) from the plastic elongation strain difference Δε pl (y) using the following equation (4).
Δε _ts (y)=Δε _pl (y)−Δε _cr (y) (4)

Next, assuming that the wave pitch P calculated in step A13 does not change with respect to the buckling shape conversion elongation strain difference Δε _ts (y) calculated by the above equation (4), the normalized height profile W Wave height width distribution h(x, y)=H×W(y)×Sin(2πx/P) obtained by multiplying (y) by wave leaf amplitude height H is predicted as the shape of the metal plate after buckling. Here, the steepness λ (y) of the wave shape after buckling is represented by the wave leaf amplitude height H, the normalized height profile W (y), and the wave pitch P for each position y in the sheet width direction. Using the geometrical elongation strain difference Δε _gs (y) appearing in the shape due to out-of-plane deformation, it is represented by the following formula (5). However, in general, when expressing the magnitude of the wave in rolling operations, it is often expressed as (5') as double amplitude of the maximum amplitude H of the single amplitude wave. Further, if this formula (5) is rearranged by the geometric shape elongation strain difference Δε _gs (y), the formula (6) is obtained.
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)

Since the value of the normalized height profile W(y) is a profile normalized from 0 to 1, if the maximum amplitude H of the single amplitude wave is assumed, the geometric shape elongation strain difference Δε _gs (P, H, W(y)) can be calculated. Therefore, considering that it is almost the same as the buckling shape _conversion elongation strain difference Δε _ts (y), as shown in FIG. error Δε _er (y)”) is expressed by the following equation (7).
Δε _er (y)=Δε _gs (P, H, W (y))−Δε _ts (y) (7)

(Step A17)
In step A17, the residual stress redistributed after the occurrence of the buckling wave, that is, the elastic strain difference Δε _el ^* (y) inherent in the metal plate is calculated. 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 )) are added together to calculate the elastic strain difference Δε _el ^* (y) redistributed by the buckling wave generation and inherent in the metal plate even after buckling. Thus, in step A17, the elastic strain difference Δε _el ^* (y) redistributed by shape deformation after buckling 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)

(Step A18)
In step A18, the normalized elongation strain difference Δε _normal ^* (y) is determined again based on the redistributed residual stress distribution of the metal plate after buckling. Specifically, in the convergence calculation in which steps A12 to A20 are repeated as described later, the elastic strain difference Δε _el ^* (y) inherent in the redistributed metal plate is used according to the following equation (9). Determine the normalized elongation strain difference Δε _normal ^* (y) with a value between 0 and 1 corresponding to . FIG. 12(e) shows an example of this normalized elongation strain difference Δε _normal ^* (y).
Δε _normal ^* (y) = - (Δε _el ^* (y) - Max(ε _el ^* (y)))/(Max(ε _el ^* (y)) - Min(ε _el ^* (y))) .・(9)

(Step A19)
In step A19, it is determined whether _or not a _solution has been ^found in the convergence calculation. are equal to each other. First, the error Δerror(y) of the standardized elongation strain difference before and after redistribution is calculated for each strip width direction position y by the following equation (10). That is, the error Δerror(y) is the amount of change in the normalized elongation strain difference Δε _normal (y). Next, as shown in the following formula (11), Δerror ^* is calculated by accumulating squared errors for each position y in the width direction of the sheet, and this error Δerror ^* is compared with a predetermined threshold. Then, if the error Δerror ^* is larger than a predetermined threshold, it is determined that the redistributed normalized elongation strain difference Δε _normal ^* (y) has not converged, and recalculation (eigenvalue using the theoretical buckling model analysis calculation), the process proceeds to step A20. On the other hand, if the error Δerror ^* is equal to or less than the predetermined threshold value, it is determined that the normalized elongation strain difference Δε _normal ^* (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)

(Step A20)
In step A20, the process returns to step A12 to correct the normalized elongation strain difference Δε _normal (y) used in the recalculation using Δε _normal ^* (y) and Δerror(y). Specifically, by the following formula (12), the error Δerror (y) multiplied by the relaxation coefficient α is added to the normalized elongation strain difference Δε _normal (y) after redistribution, and the recalculation Reset the normalized elongation strain difference Δε _normal (y). Here, in performing recalculation, if all the errors Δerror(y) are superimposed without applying the relaxation coefficient α, the calculation result oscillates and the normalized elongation strain difference Δε _normal (y) is difficult to converge. Therefore, in the present embodiment, the normalized elongation strain difference Δε _normal (y) is facilitated to converge by applying the relaxation coefficient α. Although the relaxation coefficient α is arbitrary, the present inventor has confirmed that 0.1 to 0.4 is appropriate as a result of extensive studies.
Δε _normal (y)=Δε _normal (y)+α×Δerror(y)=Δε _normal (y)+α×{Δε _normal ^* (y)−Δε _normal (y)} (12)

Next, returning to step A12, steps A13 to A20 are performed using the normalized elongation strain difference Δε _normal (y) corrected in step A20. Then, steps A12 to A20 are repeated, and convergence calculation is performed until it is determined in step A19 that the normalized elongation strain difference Δε _normal ^* (y) has converged.

(Step A21)
If it is determined in step A19 that the normalized elongation strain difference Δε _normal ^* (y) has converged, the process proceeds to step A21. At step A21, the true elongation strain difference Δε' _pl (y) shown in FIG. 6 is calculated. Specifically, the new buckling intrinsic strain difference Δε _cr (y) calculated from the elastic strain difference Δε _el ^* (y) redistributed to the metal plate after buckling and the plastic elongation A true elongation strain difference Δε′ _pl (y) is calculated from the strain difference Δε _pl (y). Further, by expanding this formula (13), the true elongation strain difference Δε' _pl (y) can also be calculated from the plastic elongation strain difference Δε _pl (y) and the buckling shape transformation elongation strain difference Δε _ts (y). .
Δε′ _pl (y)=Δε _pl (y)+(Δε _pl (y)−Δε _cr (y))=Δε _pl (y)+Δε _ts (y) (13)

(Step A23)
In step A23, based on the true elongation strain difference Δε' _pl (y) calculated in step A21, the rolling conditions are set to control the shape of the metal sheet after rolling. Specifically, for example, the rolling conditions are set such that the true elongation strain difference Δε′ _pl (y) is equal to or less than the buckling inherent strain difference Δε _cr (y). As a result, the rolled metal plate does not buckle and becomes flat. Rolling conditions include the rolling load, the moment of the roll bender that controls the deflection of the rolls, and the like. The rolling conditions can be set arbitrarily, and if necessary, the true elongation strain difference Δε' _pl (y) can be determined through this algorithm to control the shape of the metal sheet after rolling.

According to the first embodiment, from the plastic elongation strain difference Δε _pl (y) and the buckling intrinsic strain difference Δε _cr (y) or the buckling shape transformation elongation strain difference Δε _ts (y), the metal plate Determine the true elongation strain difference Δε' _pl (y). By obtaining the elongation-strain difference in this way, the prediction accuracy of the elongation-strain difference can be made higher than before. Therefore, by setting the rolling conditions based on the true elongation strain difference Δε' _pl (y), the shape of the rolled metal sheet can be freely controlled.

As mentioned above, the conventional method assumed that the shape profile would be maintained even after buckling. Therefore, an error in the shape profile as shown in FIG. 9 occurred.

In this regard, the inventors have found that the shape profile changes due to shape deformation after buckling. Then, according to the rolling control method according to the first embodiment described above, the elastic strain difference Δε _el ^* (y) redistributed by the shape deformation after buckling is calculated, and the elastic strain difference Δε _el ^* ( Since recalculation is performed using y), the shape of the metal plate can be predicted appropriately. As a result, it becomes possible to more appropriately control the shape of the rolled metal plate.

In order to verify the effect of the first embodiment (the effect of increasing the accuracy of shape prediction), the present inventors used a conventional method for the shape prediction result (convergent solution) obtained by the first embodiment. The shape prediction result thus obtained was compared with the analysis result by FEM. The verification results are shown in FIGS. 13 and 14. FIG. FIG. 13 shows the widthwise distribution of the elastic strain difference inherent in the metal plate after buckling, and FIG. 14 shows the widthwise distribution of the normalized profile.

Referring to FIGS. 13 and 14, the conventional shape prediction results are slightly different from the FEM analysis results, whereas the shape prediction results of the first embodiment substantially match the FEM analysis results. Therefore, according to 1st Embodiment, it turned out that the shape of a metal plate can be predicted appropriately.

In the first embodiment, the true elongation strain difference Δε' _pl (y) may be obtained based on the variation in tension on the delivery side of the rolling mill due to buckling. Specifically, the buckling shape conversion elongation strain difference Δε _ts (y) obtained in step A16 is converted into tension acting on the metal plate. The change ΔP _ts (y) in the rolling load difference in the strip width direction caused by the variation of the tension on the delivery side of the rolling mill is obtained, and ΔP _ts (y) is 2 in the strip width direction x as shown in the following equation (14). An elongation strain difference Δε _ts '(y) is obtained by differential differentiation. Then, as shown in the following formula (8), the addition of the elongation strain difference Δε _ts '(y) obtained by the formula (15) to the plastic elongation strain difference Δε _pl (y) set in step A11 is Elongation strain difference Δε' _pl (y).
Δε _ts ′(y)=d ² ΔP _ts (y)/dx ² (14)
Δε′ _pl (y)=Δε _pl (y)+Δε _ts′ (y) (15)

In this way, the converted tension obtained by converting the buckling shape conversion elongation strain difference Δε _ts (y) into tension is obtained, and the elongation strain difference Δε _ts '(y) corresponding to this converted tension is obtained. The obtained elongation strain difference Δε _ts '(y) becomes close to the actual phenomenon. Moreover, when obtaining the elongation strain difference Δε _ts '(y), since the change ΔP _ts (y) in the rolling load difference is differentiated second order, the phenomenon becomes even closer to the actual phenomenon. Therefore, it is possible to predict the true elongation strain difference Δε′ _pl (y) of the metal plate with higher accuracy.

In the first embodiment, the plastic elongation strain difference Δε _pl (y) is set in step A11, but if the plastic elongation strain difference Δε _pl (y) is known, or the already obtained If it can be used, step A11 can be omitted. In this case, in step A13, the inherent buckling strain difference Δε _cr (y) is obtained using the known plastic elongation strain difference Δε _pl (y).

<Rolling control method according to the second embodiment>
A metal plate rolling control method according to the second embodiment will be described. FIG. 15 is a flow chart showing a rolling control method 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, and steps B14 to B21 correspond to the third step of the present invention. Steps B22 and B23 correspond to the fourth step of the present invention.

(Step B11)
In step B11, the rolling load difference ΔP (y) acting on the metal plate and the plastic elongation strain difference of the metal plate to be evaluated at an arbitrary plate width direction position y divided by a predetermined width in the plate width direction Set Δε _pl (y). These rolling load difference ΔP(y) and plastic elongation strain difference Δε _pl (y) can be obtained by known methods such as finite element method (FEM), slab method, physical model, regression of experiments and calculations, as in step A11 above. It can be calculated using the formula:

(Steps B12 to B20)
Steps B12 to B20 perform convergence calculations to predict the shape of the metal plate. These steps B12 to B20 are the same as steps A12 to A20 described above, and detailed description thereof will be omitted here.

(Step B22)
At step B22, as a result of determining whether or not buckling occurs in step B15, it is determined that the metal plate is not buckling and that the metal plate is flat. In such a case, the shape of the metal sheet is controlled by rolling the metal sheet without changing the rolling conditions.

(Step B21)
Step B21 is when it is determined in step B15 that the metal plate has buckled and that the normalized elongation strain difference Δε _normal ^* (y) has converged as a result of determining whether or not buckling has occurred in step B15. At step B21, the true elongation strain difference Δε' _pl (y) is calculated.

Here, in 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) A correlation is derived. In this step B21, based on this correlation, the specific buckling load difference ΔP _cr (y) corresponding to the specific buckling strain difference Δε _cr (y) calculated in step B13 is obtained. Then, the buckling shape conversion load difference ΔP _ts ( _y ) ( ΔP _ts (y)=ΔP(y)−ΔP _cr (y)) is calculated. Furthermore, assuming that there is no change in the crown ratio of the metal plate between the delivery side and the entry side of the rolling mill, using a known method such as the finite element method (FEM), the slab method, a physical model, and the regression equation of experiments and calculations buckling shape conversion elongation strain difference Δε _ts (y) from the buckling shape conversion load difference ΔP _ts (y). When obtaining the buckling shape conversion elongation strain difference Δε _ts (y) from the buckling shape conversion load difference ΔP ts (y), the rolling load difference _ΔP (y) obtained in step B11 and the plastic elongation strain difference Δε _pl A correlation with (y) may be used. Then, according to the following formula (16), _{the true} elongation strain difference Δε' _pl (y).
Δε′ _pl (y)=Δε _pl (y)+Δε _ts (y) (16)

(Step B23)
In step B23, based on the true elongation strain difference Δε' _pl (y) calculated in step B21, rolling conditions are set and the metal plate is rolled to control the shape of the metal plate. This step B23 is the same as the above step A23.

The second embodiment is a modification of the first embodiment. 1st Embodiment and 2nd Embodiment differ in the method of calculating the elongation-strain difference of the part which increases from plastic elongation-strain difference ( _DELTA )epsilon(y). In step A21 of the first embodiment, the increment of the elongation strain difference is obtained from the difference between the plastic elongation strain difference Δε _pl (y) and the buckling intrinsic strain difference Δε _cr (y), whereas in the second embodiment In step B21, an increase in elongation strain difference is obtained from the difference between the rolling load difference ΔP(y) and the buckling specific load difference ΔP _cr (y). Therefore, in the second embodiment, the same effects as in the first embodiment can be enjoyed. That is, it is possible to accurately predict the true elongation strain difference Δε' _pl (y) of the metal plate with higher accuracy than before. Furthermore, by setting the rolling conditions based on the true elongation strain difference Δε' _pl (y), the shape of the rolled metal sheet can be freely controlled.

<Rolling control method according to the third embodiment>
A metal plate rolling control method according to the third embodiment will be described. FIG. 16 is a flow chart showing a rolling control method according to the third embodiment. In this embodiment, as will be described later, i indicates the number of iterative calculations of steps C12 to C26 (hereinafter referred to as "first iterative calculation"), and j indicates the number of iterative calculations of steps C13 to C22 (hereinafter referred to as (referred to as "second iterative calculation"). In the third embodiment, steps C11 and C12 correspond to the first step of the invention, steps C13 and C14 correspond to the second step of the invention, and steps C15 to C24 correspond to the third step of the 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.

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

(Step C12)
In step C12, the rolling load difference ΔP (i, y) acting on the metal plate to be evaluated at an arbitrary plate width direction position y divided by a predetermined width in the plate width direction and the plastic elongation of the metal plate Set the strain difference Δε _pl (i, y). This step C12 is the same as the above step B11.

(Steps C13 to C21)
Steps C13 to C21 perform convergence calculation (second repeated calculation) to predict the shape of the metal plate. These steps C13 to C21 are the same as the above steps B12 to B20, and detailed description thereof will be omitted here. In the second embodiment, each parameter is the distribution of the strip width direction position y, and (y) is attached, but in the third embodiment, each parameter has the strip width direction position y is the i-th iteration of the first iteration, labeled (i, y).

(Step C22)
If it is determined that the normalized elongation strain difference Δε _normal ^* (y) has not converged in step C20, after resetting the normalized elongation strain difference Δε _normal (y) for recalculation in step C21, step Return to C13. At this time, in step C22, the number of times j of the second iterative calculation is increased by one (j=j+1).

(Step C27)
At step C27, as a result of determining whether or not buckling has occurred at step C16, it is determined that the metal plate is not buckling and that the metal plate is flat. In such a case, the shape of the metal sheet is controlled by rolling the metal sheet without changing the rolling conditions.

(Step C23)
Step C23 is when it is determined in step C16 that the metal plate has buckled and that the normalized elongation strain difference Δε _normal ^* (y) has converged as a result of determining whether or not buckling has occurred in step C16. At step C23, the number i of the first iterative calculations is incremented by one (i=i+1). Although FIG. 16 exemplifies the first iteration (j=1) of the second iterative calculation, this number of times varies according to the actual number of times.

(Step C24)
At 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 these rolling load difference ΔP (i, y) and the plastic elongation strain difference Δε A correlation of _pl (i,y) is derived. In this step C24, based on this correlation, the specific buckling load difference ΔP _cr (i−1, y) corresponding to the specific buckling strain difference Δε _cr (i−1, y) calculated in step C14 is obtained. Then, the buckling shape, which is the difference between the rolling load difference ΔP (i−1, y) set in step C12 and the buckling specific load difference ΔP _cr (i−1, y) obtained in step C24, A converted load difference ΔP _ts (i−1, y) (ΔP _ts (i−1, y)=ΔP(i−1, y)−ΔP _cr (i−1, y)) is calculated. Then, the buckling shape conversion load difference ΔP _ts (i−1, y) is calculated with respect to the rolling load difference ΔP (i−1, y) one time before the first repeated calculation by the following formula (17). In addition, a new rolling load difference ΔP'(i, y) is calculated.
ΔP′(i, y)=ΔP(i−1, y)+ΔP _ts (i−1, y) (17)

In the third embodiment, it is assumed that there is a change in the crown ratio of the metal plate between the delivery side and the entry side of the rolling mill. That is, it is assumed that when the rolling load acting on the metal sheet fluctuates, the deflection of the rolls of the rolling mill fluctuates due to the fluctuation of the rolling load, and the elongation strain of the metal sheet fluctuates. Then, in step C24, a new rolling load difference ΔP'(i, y) is calculated.

(Step C25)
In step C25, the true elongation strain difference Δε' _pl (i, y) is calculated.
Specifically, the buckling shape transformation load difference ΔP _ts (i−1 , y), the buckling shape transformation elongation strain difference Δε _ts (i−1, y) is obtained. When calculating the buckling shape conversion elongation strain difference Δε _ts (i−1, y) from the buckling shape conversion load difference ΔP _ts (i−1, y), the rolling load difference ΔP (i , y) and the plastic elongation strain difference Δε _pl (i, y) may be used. Then, according to the following equation (18), the sum of the new plastic elongation strain difference Δε _pl (i−1, y) and the buckling shape transformation elongation strain difference Δε _ts (i−1, y) is the true elongation It is obtained as the strain difference Δε' _pl (i, y).
Δε′ _pl (i, y)=Δε _pl (i−1, y)+Δε _ts (i−1, y) (18)

(Step C26)
At step C26, it is determined whether or not a solution has been found in the convergence calculation (first iterative calculation). First, the error between the true elongation strain difference Δε′ _pl (i, y) and the previous plastic elongation strain difference Δε _pl (i−1, y) for each plate width direction position y by the following formula (19) Calculate Δer(y). That is, the error Δer(y) is the amount of change in the plastic elongation strain difference Δε _pl (y). Next, as shown in the following equation (20), Δer ^* is calculated by accumulating squared errors for each position y in the width direction of the sheet, and this error Δer ^* is compared with a predetermined threshold value. Then, if the error Δer ^* is larger than the predetermined threshold, it is determined that the true elongation strain difference Δε' _pl (i, y) has not converged, and the process returns to step C12 for recalculation. At this time, as shown in the following formulas (21) and (22), the new rolling load difference ΔP' (i, y) is the rolling load difference ΔP (i, y), and the true elongation strain difference Δε' _pl ( i, y) is defined as the elongation strain difference Δε _pl (i, y). On the other hand, if the error Δer ^* is equal to or less than the predetermined threshold, it is determined that the true elongation strain difference Δε′ _pl (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)

(Step C28)
In step C28, the rolling conditions are set based on the true elongation strain difference Δε′ _pl (i, y) calculated in step C25, and the metal plate is rolled to control the shape of the metal plate. . This step C28 is the same as step B23.
Assuming that the new plastic elongation strain difference obtained in the third step is the plastic elongation strain difference obtained in the first step, the new buckling intrinsic strain difference obtained in the third step is obtained in the second step. may be assumed to be the buckling intrinsic strain difference

According to the third embodiment, it is assumed that there is a change in the crown ratio of the metal plate between the delivery side and the entry side of the rolling mill, and calculation is repeated. Therefore, the true elongation strain difference Δε' _pl (i, y)) can be predicted with higher accuracy.

<Other embodiments>
The first, second and third embodiments described above are executed in the rolling line 1 shown in FIG. 17, respectively. The rolling line 1 has the above-described rolling mill 10 and a rolling control device 20 that controls the rolling mill 10 . The rolling control device 20 has a calculation section 21 and a control section 22 .

The calculation unit 21 first receives an input of provisional rolling conditions set in the rolling control device 20 . Subsequently, the calculation unit 21 performs steps A11 to A21 of the first embodiment, steps B11 to B21 of the second embodiment, and step C11 of the third embodiment based on the rolling conditions whose inputs are accepted. Perform the calculations in ∼C26. Then, in step A22 of the first embodiment, step B22 of the second embodiment, and step C27 of the third embodiment, if the rolling conditions are not changed, the temporary rolling conditions are changed. The calculation unit 21 notifies the control unit 22 that it is unnecessary. On the other hand, in step A21 of the first embodiment, step B21 of the second embodiment, and step C25 of the third embodiment, when the true elongation strain difference Δε' _pl (y) is calculated, the true The calculation unit 21 notifies the control unit 22 of the elongation strain difference Δε′ _pl (y).

The control unit 22 sets the rolling conditions based on the true elongation strain difference Δε′ _pl (y) notified from the calculation unit 21 . The control unit 22 derives the rolling conditions so that the true elongation strain difference Δε′ _pl (y) becomes equal to or less than the buckling inherent strain difference Δε _cr (y), for example. Note that the computation unit 21 may derive new rolling conditions.

Then, when the control unit 22 receives the notification that the rolling conditions do not need to be changed from the calculation unit 21, the initial rolling conditions are output to the rolling mill 10 to control the rolling mill 10. Control the shape of the metal plate H after rolling. On the other hand, when the new rolling conditions are derived as described above, the control unit 22 outputs the new rolling conditions to the rolling mill 10 to control the rolling mill 10, so that the rolled metal plate Controls the shape of H.

Furthermore, the control unit 22 determines whether or not to end rolling. When the control unit 22 determines not to end the rolling, the process returns to the input of the rolling conditions, and step A11 of the first embodiment, step B11 of the second embodiment, and step C11 of the third embodiment are performed. Do the following. On the other hand, when the control unit 22 determines to end the rolling, it ends this routine.

Further, the rolling line 1 may be provided with a shape meter 30 on the delivery side of the rolling mill 10 . The shape meter 30 measures the shape of the metal plate H after rolling. As for the shape of the metal plate H, the position in the longitudinal direction and the width direction of the metal plate H, and the height displacement at that position are measured. A measurement result of the shape meter 30 is output to the rolling control device 20 . In the rolling control device 20, the calculation unit 21 corrects the buckling shape conversion elongation strain difference Δε _ts (y) based on the measurement result of the shape meter 30, and accordingly the true elongation strain difference Δε' _pl (y). is corrected. Correction of this true elongation strain difference Δε' _pl (y) follows the method described in Patent Document 3 (Japanese Patent Application Laid-Open No. 2012-218010). That is, first, based on the measurement result of the shape meter 30, the actual buckling shape conversion elongation strain difference Δε _ts (y) is obtained. This actual buckling shape conversion elongation strain difference Δε _ts (y) is compared with the buckling shape conversion elongation strain difference Δε _ts (y) predicted in the above embodiment, and the difference (error) E of these is calculated from the model. Using this difference E as an error, the plastic elongation strain difference Δε _pl (y) (rolling load difference ΔP(y)) obtained in steps A11, B11, and C12 is learned and corrected. Specifically, after adding the difference E to the plastic elongation strain difference Δε _pl (y) (rolling load difference ΔP (y)) obtained in steps A11, B11, and C12, the following processes are performed. Determine the true elongation strain difference Δε' _pl (y). Then, based on the correction result of the true elongation strain difference Δε′ _pl (y) in the calculation unit 21 , the control unit 22 corrects the rolling conditions so that the shape of the metal plate H becomes the target shape. Thus, the rolling conditions are feedback-controlled based on the measurement results of the shape meter 30 .

The present invention can also be applied when the metal plate H is deformed out of plane on the entry side of the rolling mill 10 . According to the inventor's investigation, when the metal plate H is deformed out of the plane at the entrance side of the rolling mill, the rolling rate is higher than when the metal plate H is not deformed out of the plane at the entrance side of the rolling mill. It was found that the difference in elongation strain in the metal plate H after that was increased. In other words, according to the conventional method, the shape prediction accuracy of the metal plate is further deteriorated. On the other hand, in the present invention, the difference in elongation strain corresponding to the out-of-plane deformation at the entry side of the rolling mill can be included in the difference in buckling shape conversion elongation strain Δε _ts (y), so the metal plate H It has no effect on predicting the true elongation strain difference Δε′ _pl (y) at . Therefore, even if the metal plate H is deformed out of plane at the entry side of the rolling mill, the shape of the metal plate H can be appropriately controlled.

Although the embodiments of the present invention have been described above, the present invention is not limited to such examples. It is obvious that a person skilled in the art can conceive various modifications or modifications within the scope of the technical idea described in the claims, and these are also within the technical scope of the present invention. be understood to belong to

INDUSTRIAL APPLICABILITY The present invention is useful when 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.

REFERENCE SIGNS LIST 1 rolling line 10 rolling mill 20 rolling control device 21 calculation unit 22 control unit 30 shape meter H metal plate

Claims (12)

A method for predicting and controlling the shape of a metal plate,
When predicting the corrugated profile after buckling based on the plastic elongation strain difference applied to the metal plate, the true elongation strain difference was obtained by buckling analysis using the elastic strain difference inherent in the metal plate even after buckling. and
and a step of rolling the metal plate under rolling conditions set based on the true elongation strain difference. The step of obtaining the true elongation strain difference and the step of rolling the metal plate are
Displacement of the thickness center of the metal plate is allowed to be displacement in the plane of the reference plane which is a plane parallel to the plate surface of the metal plate passing through the midpoint of the line connecting the rotation centers of the upper and lower rolls. However, by using a vertically symmetrical model that does not allow out-of-plane displacement of the reference plane, the out-of-plane deformation of the metal plate is restrained, which is obtained under predetermined rolling conditions. The plastic elongation strain difference, which is the difference in the width direction of the strain extending in the rolling direction of the metal plate, the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate on the delivery side of the rolling mill. A first step of obtaining a buckling intrinsic strain difference, which is a critical strain difference in the plate width direction at which the metal plate buckles, based on
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 redistributed by the buckling wave generation and is inherent in the metal plate even after buckling. A second step of adding the difference between the plastic elongation strain difference and the new buckling inherent strain difference and the plastic elongation strain difference to obtain the true elongation strain difference;
When the plastic elongation strain difference does not exceed the buckling inherent strain difference, the metal sheet is rolled without changing the predetermined rolling conditions, and the plastic elongation strain difference exceeds the buckling inherent strain difference. and a third step of rolling the metal plate under rolling conditions set based on the true elongation strain difference when exceeding the metal plate according to claim 1. Rolling control method. 3. The metal sheet rolling control method according to claim 2, further comprising the step of obtaining said plastic elongation strain difference. In the second step, a converted tension is obtained by converting the difference between the plastic elongation strain difference and the inherent buckling strain difference into the tension acting on the metal plate on the delivery side of the rolling mill, and the converted tension corresponds to the converted tension. 4. A metal sheet rolling control method according to claim 2, wherein the true elongation strain difference is obtained by adding the elongation strain difference and the plastic elongation strain difference. In the second step, the 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 the elongation strain difference corresponding to the converted tension. The rolling control method for a metal plate according to claim 4, characterized in that. The step of obtaining the true elongation strain difference and the step of rolling the metal plate are
Displacement of the thickness center of the metal plate is allowed to be displacement in the plane of the reference plane which is a plane parallel to the plate surface of the metal plate passing through the midpoint of the line connecting the rotation centers of the upper and lower rolls. Then, under conditions that constrain the out-of-plane deformation of the metal plate by using a vertically symmetrical model that does not allow displacement out of the plane of the reference plane, the metal during rolling under predetermined rolling conditions A first step of obtaining a rolling load difference that is a difference in rolling load in the width direction of the plate and a plastic elongation strain difference that is a difference in the width direction of the strain that extends in the rolling direction of the metal plate during rolling;
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 on the delivery side of the rolling mill, the plate width direction in which the metal plate buckles a second step of determining the intrinsic buckling strain difference, which is the critical strain difference at
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 redistributed by the buckling wave generation and is inherent in the metal plate even after buckling. Then, from the correlation between the rolling load difference and the plastic elongation strain difference, a buckling specific load difference that is a rolling load difference corresponding to the new buckling specific strain difference is obtained, and the rolling load difference and the buckling Find the difference in the specific load difference, and assuming that there is no change in the crown ratio of the metal plate between the delivery side and the entry side of the rolling mill, add the buckling shape transformation elongation strain difference and the plastic elongation strain difference to obtain the true A third step of obtaining the elongation strain difference of
When the plastic elongation strain difference does not exceed the buckling inherent strain difference, the metal sheet is rolled without changing the predetermined rolling conditions, and the plastic elongation strain difference exceeds the buckling inherent strain difference. and a fourth step of rolling the metal plate under rolling conditions set based on the true elongation strain difference when it exceeds the metal plate according to claim 1. Rolling control method. The step of obtaining the true elongation strain difference and the step of rolling the metal plate are
Displacement of the thickness center of the metal plate is allowed to be displacement in the plane of the reference plane which is a plane parallel to the plate surface of the metal plate passing through the midpoint of the line connecting the rotation centers of the upper and lower rolls. Then, under conditions that constrain the out-of-plane deformation of the metal plate by using a vertically symmetrical model that does not allow displacement out of the plane of the reference plane, the metal during rolling under predetermined rolling conditions A first step of obtaining a rolling load difference that is a difference in rolling load in the width direction of the plate and a plastic elongation strain difference that is a difference in the width direction of the strain that extends in the rolling direction of the metal plate during rolling;
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 on the delivery side of the rolling mill, the plate width direction in which the metal plate buckles a second step of determining the intrinsic buckling strain difference, which is the critical strain difference at
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 redistributed by the buckling wave generation and is inherent in the metal plate even after buckling. Then, from the correlation between the rolling load difference and the plastic elongation strain difference, the buckling shape conversion load corresponding to the buckling shape conversion elongation strain difference, which is the difference between the plastic elongation strain difference and the new buckling inherent strain difference The difference is obtained, the buckling shape conversion load difference is superimposed on the rolling load difference to derive a new rolling load difference, and assuming that the metal plate has a crown ratio change, the new rolling load difference a third step of determining
A fourth step of determining the true elongation strain difference by adding the buckling shape conversion elongation strain difference and the new plastic elongation strain difference, and determining the convergence of the true elongation strain difference;
When the plastic elongation strain difference does not exceed the inherent buckling strain difference obtained in the second step, the metal plate is rolled without changing the predetermined rolling conditions, and the plastic elongation strain difference is A fifth step of rolling the metal plate under rolling conditions set based on the true elongation strain difference when the inherent buckling strain difference obtained in the second step is exceeded. The metal plate rolling control method according to claim 1, characterized in that: Assuming that the new plastic elongation strain difference obtained in the third step is the plastic elongation strain difference obtained in the first step, the new inherent buckling strain difference obtained in the third step is the 8. The metal sheet rolling control method according to claim 7, wherein the buckling inherent strain difference obtained in the second step is assumed. 9. The metal sheet rolling control method according to claim 2, wherein the metal sheet is out-of-plane deformed on the entry side of the rolling mill. a step of measuring the shape of the rolled metal plate using a shape meter installed on the delivery side of the rolling mill;
The plastic elongation strain difference is corrected based on the difference between the actual elongation strain difference converted to out-of-plane deformation obtained from the measured shape of the metal plate and the predicted elongation strain difference converted to out-of-plane deformation. The metal plate rolling control method according to any one of claims 2 to 9, further comprising: Displacement of the thickness center of the metal plate is allowed to be displacement in the plane of the reference plane which is a plane parallel to the plate surface of the metal plate passing through the midpoint of the line connecting the rotation centers of the upper and lower rolls. However, by using a vertically symmetrical model that does not allow out-of-plane displacement of the reference plane, the out-of-plane deformation of the metal plate is restrained, which is obtained under predetermined rolling conditions. The plastic elongation strain difference, which is the difference in the width direction of the strain extending in the rolling direction of the metal plate, the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate on the delivery side of the rolling mill. Based on, the buckling inherent strain difference, which is the critical strain difference in the plate width direction that causes the metal plate to buckle, is obtained, and when the plastic elongation strain difference exceeds the buckling inherent strain difference, A new inherent buckling strain difference is calculated using the elastic strain difference redistributed after bending, and the difference between the plastic elongation strain difference and the new inherent buckling strain difference and the plastic elongation strain difference are calculated. In addition, a calculation unit for obtaining a true elongation strain difference,
When the plastic elongation strain difference does not exceed the buckling inherent strain difference, the metal sheet is rolled without changing the predetermined rolling conditions, and the plastic elongation strain difference exceeds the buckling inherent strain difference. and a control unit for rolling the metal plate under the rolling conditions set based on the true elongation strain difference when exceeding the true elongation strain difference. Displacement of the thickness center of the metal plate is allowed to be displacement in the plane of the reference plane which is a plane parallel to the plate surface of the metal plate passing through the midpoint of the line connecting the rotation centers of the upper and lower rolls. However, by using a vertically symmetrical model that does not allow out-of-plane displacement of the reference plane, the out-of-plane deformation of the metal plate is restrained, which is obtained under predetermined rolling conditions. The plastic elongation strain difference, which is the difference in the width direction of the strain extending in the rolling direction of the metal plate, the thickness of the metal plate, the width of the metal plate, and the tension acting on the metal plate on the delivery side of the rolling mill. A first step of obtaining a buckling intrinsic strain difference, which is a critical strain difference in the plate width direction at which the metal plate buckles, based on
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 redistributed by the buckling wave generation and is inherent in the metal plate even after buckling. A second step of adding the difference between the plastic elongation strain difference and the new buckling inherent strain difference and the plastic elongation strain difference to obtain the true elongation strain difference;
When the plastic elongation strain difference does not exceed the buckling inherent strain difference, the metal sheet is rolled without changing the predetermined rolling conditions, and the plastic elongation strain difference exceeds the buckling inherent strain difference. and a third step of rolling the metal plate under the rolling conditions set based on the true elongation strain difference when exceeding the true elongation strain difference.

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