METHOD FOR PREDICTION OF METAL PLATE SHAPE AND METAL PLATE MANUFACTURING METHOD

Abstract

To accurately predict a metal plate shape.SOLUTION: A method for predicting a metal plate shape determines a waveform profile by buckling analysis using an elastic strain difference existing inside the metal plate even after buckling, when the waveform after buckling is predicted based on a plastic elongation strain difference imparted to the metal plate.SELECTED DRAWING: Figure 5

Description

[Technical field]

[0001] The present invention relates to a method for predicting the shape of a metal sheet after rolling, and a method for manufacturing a metal sheet using said method. [Background technology]

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

[0003] Patent Document 1 discloses a method for evaluating flatness by multiplying the crown ratio change of a rolled material, which is a thick plate, by a shape change coefficient, and reducing the thermal strain difference caused by the temperature difference applied to the steel plate during rolling. In the flatness evaluation formula used in this case, the crown ratio change defined at a fixed point of the steel plate is multiplied by the shape change coefficient, and converted into a steepness (hereinafter flatness) equivalent to residual stress, which is taken as the flatness.

[0004] Patent Document 2 discloses a shape prediction method based on the residual stress of a steel plate. In this method, first, the plate surface temperature distribution of the steel plate is measured, and the residual stress distribution in the plate longitudinal direction after air cooling is calculated based on the measured temperature distribution, and the residual stress distribution is then approximated to a rectangle. Next, the residual stress at the buckling critical point is calculated using a predetermined simplified prediction formula from the rectangularly approximated residual stress distribution. Then, the residual stress at the calculated buckling critical point is compared with the rectangularly approximated residual stress to determine whether or not there is a shape defect.

[0005] Non-Patent Document 1 discloses a buckling model formulated with a triangular residual stress distribution.

[0006] Patent Document 3 discloses a method for predicting the shape of a metal plate, which includes the following steps: (a) determining the widthwise distribution of buckling stress using the widthwise distribution of longitudinal residual stress of the metal plate, (b) separating the stress components into those to be transformed into a wave shape and those that remain in the metal plate after buckling when it is determined that buckling will occur, and (c) predicting the wave shape after buckling using the stress components to be transformed into a wave shape. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] Japanese Patent Application Publication No. 6-15321 [Patent Document 2] Japanese Patent Application Publication No. 8-187505 [Patent Document 3] Patent No. 4262142 [Non-patent literature]

[0008] [Non-Patent Document 1] Journal of the Japan Society for Technology of Plasticity: Plasticity and Processing, Vol. 28, No. 312 (1987-1) p58-66 Summary of the Invention [Problem to be solved by the invention]

[0009] However, the method disclosed in Patent Document 1 does not take into consideration the shape dead zone that should exist. In other words, there is no concept of buckling, and all the inherent residual stress is converted into a wave shape. The shape dead zone refers to a stress region in which out-of-plane deformation due to buckling does not occur up to the buckling limit even if residual stress exists in the metal plate.

[0010] In addition, in the method disclosed in Patent Document 2, although the buckling phenomenon of metal plates is taken into consideration, the residual stress distribution is approximated by a rectangle as a simple formula for predicting buckling, and the buckling judgment is performed, so the model does not accurately reflect the stress distribution. The same is true in the case of approximating the residual stress distribution by a triangle, as disclosed in Non-Patent Document 1.

[0011] In this regard, the method disclosed in Patent Document 3, which is a shape prediction method based on residual stress inherent in a metal plate, enables buckling judgment and shape prediction at the time of buckling by inputting residual stress distribution distributed in the width direction, and therefore improves the accuracy of wave-shaped buckling judgment compared to the methods disclosed in Patent Documents 1 and 2 and Non-Patent Document 1. However, as a result of extensive investigations by the inventors, it was found that there is room for improvement in prediction accuracy, as will be described later.

[0012] If the shape after buckling cannot be accurately predicted, it is impossible to determine whether or not to send the metal sheet to the straightening line. In other words, if the prediction is not accurate, even if the shape is good, there is a possibility that the sheet will be sent to the finishing process, which will lead to increased costs. Therefore, it is essential to improve the prediction accuracy of the shape of the metal sheet.

[0013] The present invention has been made in consideration of the above-mentioned points, and has an object to provide a method for predicting the shape of a metal plate which is highly accurate in predicting the shape of the metal plate and which can accurately perform the separation of the metal plate required for the refinement process in advance, and a method for manufacturing a metal plate using this method. [Means for solving the problem]

[0014] In order to achieve the above object, the present inventors have investigated a method for predicting the shape of a metal plate, and as a result, have come to the following findings.

[0015] As disclosed in Patent Document 3, it is known that the residual stress (elongation strain) of a metal plate is separated into a component that converts to a wave shape and a component that remains in the metal plate even after buckling. In the invention of Patent Document 3, the component that converts to a wave shape is used to predict the shape of the metal plate after buckling.

[0016] The present invention is a further development of the invention of Patent Document 3. As a result of intensive research by the present inventors, it was found that in the invention of Patent Document 3, an error occurs in the shape profile because it is assumed that the shape profile calculated by the buckling eigenanalysis remains the same even after buckling. Then, it was conceived that the shape of the metal plate can be appropriately predicted by recalculating (eigenvalue analysis calculation using a theoretical buckling model) with the elastic strain difference reallocated due to the occurrence of the shape profile generated after buckling, rather than calculating with the plastic elongation strain difference of the evaluation target in the buckling eigenvalue analysis. That is, it was previously thought that the shape profile after buckling disclosed was determined by the plastic elongation strain difference used in the initial calculation, but as a result of intensive research by the present inventors, it was found that the shape profile is determined by the elastic strain difference that is reallocated to the metal plate after the buckling shape occurs, that is, that exists in the plate even after buckling. The present invention is based on the above findings, and the gist of the present invention is as follows.

[0017] The present invention is a method for predicting the shape of a metal plate, and is characterized in that when predicting the waveform after buckling based on the difference in plastic elongation strain imparted to the metal plate, the waveform profile is determined by buckling analysis using the difference in elastic strain that remains in the metal plate even after buckling.

[0018] In carrying out the method for predicting the shape of a metal plate, the following three algorithms can be given as specific examples.

[0019] The first metal plate shape prediction method (algorithm) is: When a rolled metal plate buckles, this is the difference in the width direction of the longitudinal strain of the metal plate during rolling.A first step of setting a plastic elongation and strain difference; a second step of converting the plastic elongation and strain difference into a standardized elongation and strain difference in the first calculation of the iterative calculation, and using the standardized elongation and strain difference calculated in the tenth step below in the second and subsequent calculations of the iterative calculation; a third step of performing a buckling analysis based on the standardized elongation and strain difference, and calculating a buckling inherent strain difference, a wave pitch, and a standardized shape profile of the metal plate, which are criteria for determining whether the metal plate will buckle; a fourth step of judging whether the calculation is the first or subsequent calculation of the iterative calculation in the fourth step; a fifth step of comparing the plastic elongation and strain difference with the buckling inherent strain difference to judge whether buckling has occurred or not, when the calculation is judged in the fourth step to be the second or subsequent calculation of the iterative calculation, or when the calculation is judged in the fifth step to be the second or subsequent calculation of the iterative calculation, the plastic elongation and strain difference is compared with the buckling inherent strain difference and the plastic elongation and strain difference is compared with the buckling inherent strain difference and the buckling inherent strain difference. a buckling shape transformation elongation strain difference, which is a difference between the geometric shape elongation strain difference appearing in the shape of the metal plate after out-of-plane deformation and the buckling shape transformation elongation strain difference, and an elongation strain error, which is a difference between the geometric shape elongation strain difference appearing in the shape of the metal plate after out-of-plane deformation and the buckling shape transformation elongation strain difference, is calculated to determine a wave height at which an integrated value of the square of the elongation strain error is a minimum value, and a wave shape profile is determined; a seventh step is a sum of the elastic buckling inherent strain difference and the elongation strain error to calculate an elastic strain difference inherent in the metal plate after buckling; a ninth step of calculating an error between the standardized elongation-strain difference set in the second step and the standardized elongation-strain difference calculated in the eighth step, and comparing the square of the error with a predetermined threshold; and a tenth step of correcting the standardized elongation-strain difference set in the second step by a value obtained by multiplying the error by a relaxation coefficient, if the square of the error in the ninth step is greater than the predetermined threshold, until the square of the error in the ninth step becomes equal to or less than the predetermined threshold.The method is characterized in that the second step to the tenth step are repeatedly performed.

[0020] The second metal plate shape prediction method (algorithm) is: When a rolled metal plate buckles, this is the difference in the width direction of the longitudinal strain of the metal plate during rolling. The first step is to set the difference in plastic elongation and strain, and the number of iterations is M timesa second step of setting the standardized elongation-strain difference in the first calculation of the iterative calculation, converting the plastic elongation-strain difference into a standardized elongation-strain difference, and using the standardized elongation-strain difference corrected in the tenth step below in the second and subsequent calculations of the iterative calculation; a fourth step of performing a buckling analysis based on the standardized elongation-strain difference, and calculating a buckling inherent strain difference, a wave pitch, and a standardized shape profile of the metal plate, which are criteria for determining whether buckling of the metal plate occurs; and a fourth step of determining whether the calculation is the first calculation of the iterative calculation or the second or subsequent calculations. a fifth step, a sixth step of comparing the plastic elongation strain difference with the buckling inherent strain difference to determine whether or not buckling has occurred if it is determined in the fifth step that this is the first calculation of the repeated calculations, and a sixth step of dividing the plastic elongation strain difference into the buckling inherent strain difference and a buckling shape transformation elongation strain difference, which is a difference between the plastic elongation strain difference and the buckling inherent strain difference and is a component that transforms the shape of the metal plate, and dividing the buckling shape transformation elongation strain difference into M-1 divisions. a seventh step of calculating an M-1 division buckling shape transformation elongation strain difference and replacing the buckling inherent strain difference of the first iteration of the iterative calculation with an initial buckling inherent strain difference; and if it is determined in the fifth step that the iterative calculation is the second or subsequent iterative calculation, or if it is determined in the sixth step that the plastic elongation strain difference is greater than the buckling inherent strain difference and buckling will occur, correcting the buckling shape transformation elongation strain difference using the M-1 division buckling shape transformation elongation strain difference and the initial buckling inherent strain difference to obtain a geometric shape elongation strain difference appearing in the shape of the metal plate after the out-of-plane deformation. an eighth step of calculating an elongation-strain error, which is the difference between the corrected buckling shape transformation elongation-strain difference, and determining a wave height at which an integrated value of the square of the elongation-strain error is a minimum value to determine a wave shape profile; a ninth step of calculating an elastic strain difference inherent in the metal plate after buckling by replacing the buckling inherent strain difference with an elastic strain distribution and adding the elongation-strain error; and a tenth step of calculating a standardized elongation-strain difference corresponding to the elastic strain difference using the elastic strain difference calculated in the ninth step,The method is characterized in that the number of repeated calculations set in the second step is performed.

[0021] The third metal plate shape prediction method (algorithm) is: When a rolled metal plate buckles, this is the difference in the width direction of the longitudinal strain of the metal plate during rolling. The first step is to set the difference in plastic elongation and strain, and the number of iterations is M timesA second step of setting the plastic elongation and strain difference; a third step of dividing the plastic elongation and strain difference by M and calculating the plastic elongation and strain difference according to the number of repeated calculations; in the first calculation of the repeated calculations or in the seventh step below, if the plastic elongation and strain difference is equal to or less than the buckling inherent strain difference, the plastic elongation and strain difference is converted into a standardized standardized elongation and strain difference, and in the second or subsequent calculations of the repeated calculations and in the seventh step below, if it is determined that buckling occurs, the standardized elongation and strain difference calculated in the eleventh step below is used; A fifth step is a step of performing a buckling analysis based on the strain difference, and calculating a buckling inherent strain difference, a wave pitch, and a standardized shape profile of the metal plate, which are criteria for determining whether buckling occurs in the metal plate; a sixth step is a seventh step before the repeat calculation, in which it is determined whether buckling has occurred; if it is determined in the sixth step that buckling has not occurred, the seventh step is a step of comparing the plastic elongation strain difference with the buckling inherent strain difference to determine whether buckling has occurred; and if it is determined in the seventh step that the plastic elongation strain difference is equal to or less than the buckling inherent strain difference and therefore buckling has not occurred, an eighth step of checking the number of iterative calculations, and returning to the second step if the number is not the final time; and if it is determined in the sixth step that buckling has occurred, or if it is determined in the seventh step that the plastic elongation and strain difference is greater than the buckling inherent strain difference and buckling will occur, separating the plastic elongation and strain difference into the buckling inherent strain difference and a buckling shape transformation elongation and strain difference which is a component that transforms the shape of the metal plate and is a difference between the plastic elongation and strain difference and the buckling inherent strain difference, and calculating a geometric shape elongation and strain difference that appears in the shape of the metal plate after the out-of-plane deformation and a geometric shape ... The method includes a ninth step of calculating an elongation-strain error, which is a difference between the buckling shape transformation elongation-strain difference, and determining a wave height at which an integrated value of the square of the elongation-strain error is a minimum value to determine a wave shape profile; a tenth step of calculating an elastic strain difference inherent in the metal plate after buckling by replacing the buckling inherent strain difference with an elastic strain distribution and adding the elongation-strain error; and an eleventh step of calculating a normalized elongation-strain difference corresponding to the elastic strain difference using the elastic strain difference calculated in the tenth step,The method is characterized in that the number of repeated calculations set in the second step is performed.

[0022] In the method for predicting the shape of a metal plate, It is calculated by converting The width-direction distribution of the longitudinal residual stress of the metal plate may be a thermal stress distribution based on the width-direction temperature distribution before and after cooling.

[0023] In the method for predicting the shape of a metal plate, It is calculated by converting The width-direction distribution of the longitudinal residual stress of the metal plate may be the distribution of residual stress imparted at least during rolling or straightening.

[0024] In the method for predicting a shape of a metal plate, the shape of the metal plate before cooling or the shape of the metal plate after cooling is measured, Geometrical shape elongation strain difference appearing in the shape of metal sheets after out-of-plane deformation may be superimposed on the plastic elongation strain difference.

[0025] According to another aspect of the present invention, a determination is made as to whether or not shape correction should be performed in a finishing process by using the metal plate shape prediction method, The width direction distribution of the longitudinal residual stress of the metal plate is determined as a thermal stress distribution based on the width direction temperature distribution before and after cooling, and based on the shape of the metal plate predicted by the shape prediction method, the metal plate is To avoid buckling The above It is characterized by the production of flat plates by controlling the temperature distribution in the width direction.

[0026] In the method for manufacturing a metal plate, whether or not to perform shape correction in the refinement step may be judged based on the predicted steepness. Effect of the Invention

[0027] According to the present invention, the elastic strain difference redistributed by the shape deformation after buckling is calculated, and the elastic strain difference is used to perform recalculation (eigenvalue analysis calculation using a theoretical buckling model), so that the shape of the metal plate can be predicted with high accuracy. As a result, the separation of the metal plate required for the finishing process can be performed with high accuracy. In addition, by using the result of the shape prediction of the metal plate, it is also possible to manufacture the metal plate flat. [Brief description of the drawings]

[0028] [Figure 1] FIG. 1 is a diagram illustrating a target wave shape. [Diagram 2] 1 is a flowchart illustrating a conventional shape prediction method. [Diagram 3] FIG. 1 is an explanatory diagram showing the results of shape prediction of a metal plate when a conventional shape prediction method and FEM are used. [Figure 4] FIG. 1 is an explanatory diagram showing the shape of a metal plate when a conventional shape prediction method and FEM are used. [Diagram 5] 3 is a flowchart showing a feature prediction method according to the first embodiment. [Figure 6] FIG. 2 is an explanatory diagram illustrating a shape prediction method according to the first embodiment. [Figure 7] FIG. 2 is an explanatory diagram showing a shape prediction result of a metal plate when the shape prediction method according to the first embodiment is used. [Figure 8] FIG. 2 is an explanatory diagram showing a shape prediction result of a metal plate when the shape prediction method according to the first embodiment is used. [Figure 9] 13 is a flowchart showing a feature prediction method according to a second embodiment. [Figure 10] FIG. 11 is an explanatory diagram showing a shape prediction result of a metal plate when the shape prediction method according to the second embodiment is used. [Figure 11] FIG. 11 is an explanatory diagram showing a shape prediction result of a metal plate when the shape prediction method according to the second embodiment is used. [Figure 12] 13 is a flowchart showing a feature prediction method according to a third embodiment. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

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

[0030] First, the target wave shape will be explained using Figure 1. The X axis is the longitudinal direction in which periodic waves occur, the Y axis is the plate width direction, and the Z axis is the plate thickness or wave height direction, and the wave shown in Figure 1 shows a typical ear wave. Note that periodic buckling waves (X direction in the figure) of waves represented by medium waves and quarter waves occurring at an intermediate position between ear waves and medium waves are also targeted. The definition of steepness or flatness used as the size of the wave is expressed as a percentage by dividing the wave piece amplitude height H of the width direction edge part of the metal plate by the wave pitch P (period P) and multiplying it by 100. In addition, this wave shape is called a width direction position-wise shape profile (wave shape profile) cut out at the position indicated by the wave piece amplitude height H in the YZ cross section, and the shape profile obtained in the buckling analysis described later is a normalized profile of 0 to 1 without a height dimension. In this embodiment, the standardized profile is multiplied by the wave piece amplitude height H to predict a waveform profile distribution h(x, y)=H×W(y)×Sin(2πx / P).

[0031] <Conventional shape prediction method> As described above, the present invention is a further development of the invention disclosed in Patent Document 3. Therefore, before describing the feature prediction method according to this embodiment, a description will be given of the conventional feature prediction method disclosed in Patent Document 3. Fig. 2 is a flowchart showing the conventional feature prediction method.

[0032] (Step X1) In step X1, the plastic elongation strain difference Δε of the metal plate to be evaluated at any position y divided into N parts with a predetermined width in the plate width direction (y direction) is calculated. pl (y) Set the plastic elongation strain difference Δε pl (y) is the difference in the width direction of the strain (hereinafter referred to as "elongation strain") that elongates the metal plate in the longitudinal direction during rolling when the rolled metal plate buckles (when out-of-plane deformation occurs in the steel plate). In the following explanation, the definitions of elongation strain and elongation strain difference are the same.

[0033] (Step X2) In step X2, the plastic elongation strain difference Δε plThe difference in elongation strain Δε normalized to a value between 0 (zero) and 1, with (y) being the maximum value 1 normal Convert to (y).

[0034] (Step X3) In step X3, an eigenvalue analysis calculation is performed using a theoretical buckling model. This theoretical buckling model is the model disclosed in Patent Document 3. That is, the theoretical buckling model is a model for performing a buckling analysis using a wave-shaped buckling equation created based on a model formulated with a triangular residual stress distribution shown in Non-Patent Document 1. In the theoretical buckling model, the normalized elongation strain difference Δε normal (y), the thickness t of the metal plate, the width B of the metal plate, and the tension Ut acting on the metal plate are input, and the plastic elongation strain difference Δε pl The buckling inherent strain difference Δε, which is similar to (y) cr The output includes wave pitch P (y) (criterion for buckling), and height profile W(y) normalized from 0 to 1 in the width direction cross section at the time of buckling. Note that in the model disclosed in Patent Document 3, residual stress distribution is input to obtain the buckling stress distribution, but here elongation strain is used instead of stress.

[0035] Here, the longitudinal stress acting on a metal plate is essentially a residual stress component that is 0 (zero) when integrated in the plate width direction and a tension (unit tension) component overlap. However, in the buckling model, the tension component is given separately, so here, it is assumed that it is 0 when integrated in the plate width direction, that is, the residual stress component is the integral value in the plate width direction or the average in the plate width direction is 0, and the residual stress σ is calculated using the following formula (1). res Distribution of (y) and plastic elongation strain difference Δε pl The distribution of (y) is converted. Δε pl (y)=-(σ res (y) / E-Max(σ res (y)) / E) ···(1)

[0036] (Step X4) In step X4, it is determined whether or not buckling occurs. pl(y) and the difference in buckling inherent strain Δε cr (y) and Δε pl (y) is Δε cr If it is greater than (y), it is determined that the metal plate buckles, and the process proceeds to step X5. cr (y) is the plastic elongation strain difference Δε pl Since Δε(y) has a similar relationship, it may be judged at any position in the width direction y, but here, the maximum values ​​of each are compared. pl (y) is Δε cr If it is equal to or less than (y), it is determined that the metal plate is not buckled and is flat, and the process proceeds to step X6.

[0037] (Step X5) In step X5, the shape of the metal sheet is predicted using a shape prediction model. In the shape prediction model, the plastic elongation strain difference Δε pl The component that converts (y) into the shape deformation after buckling (buckling shape transformation elongation strain difference Δε ts (y)) and the component that remains in the metal plate after buckling (buckling inherent strain difference Δε cr (y)) and the buckling shape transformation elongation strain difference Δε ts Assuming that the wave pitch P calculated in step X3 based on (y) does not change, the wave height distribution h(x,y)=H×W(y)×Sin(2πx / P) obtained by multiplying the standardized height profile W(y) by the wave piece amplitude height H is determined so that the error with the geometric elongation strain difference distribution is small, thereby predicting the shape of the metal sheet. This shape prediction model is similar to the model disclosed in Patent Document 3. However, while the model disclosed in Patent Document 3 predicts the shape using stress, here elongation strain difference is used instead of stress.

[0038] As described above, the shape of the metal plate (wave piece amplitude height H) is output in step X5, or the fact that the metal plate is flat is output in step X6, and then the shape prediction is terminated.

[0039] <Verification of conventional shape prediction methods> In the conventional method, the shape (wave height width distribution h(y)) of the metal sheet is predicted as described above. The present inventors verified the shape predicted by this conventional shape prediction method by comparing it with the analysis result by the finite element method (FEM).

[0040] Figures 3 and 4 are explanatory diagrams showing the shape of a metal sheet when a conventional shape prediction method and FEM are used under the same metal sheet conditions and the same plastic elongation strain difference. Note that Figure 3 shows the plate thickness direction displacement in the longitudinal direction displacement of the plate width center part, i.e., the wave height direction displacement, and Figure 4 shows an enlarged wave height profile of cross section A in Figure 3.

[0041] Referring to Fig. 3, the wave pitch after buckling is almost the same when comparing the conventional shape prediction method with FEM. On the other hand, referring to Fig. 4, the wave height displacement in the width direction center part is almost the same when comparing the conventional shape prediction method with FEM, but the wave height displacement in the range surrounded by the dotted line in Fig. 4 is different, which shows that an error occurs in the shape profile.

[0042] The present inventors have conducted extensive research and found that the cause of the error in the shape profile is that the conventional shape prediction method assumes that the shape profile calculated in the buckling eigenanalysis in step X3 remains the same even after buckling. The inventors have come up with the idea that the shape of the metal plate can be appropriately predicted by recalculating (eigenvalue analysis calculation using a theoretical buckling model) the elastic strain difference that exists in the metal plate as residual stress even after buckling, which is redistributed to the metal plate due to the generation of the buckling wave after buckling, instead of calculating using the plastic elongation strain difference of the evaluation target in the buckling eigenvalue analysis. In the following description, the shape prediction method of the metal plate according to the present embodiment will be described based on the above findings.

[0043] <Shape prediction method according to the first embodiment> A shape prediction method for a metal plate according to a first embodiment will be described. Fig. 5 is a flowchart showing the shape prediction method according to the first embodiment. Fig. 6 is an explanatory diagram showing a schematic view of the shape prediction method according to the first embodiment. In the first embodiment, steps A2 to A10 described below are repeated to perform convergence calculations.

[0044] (Step A1) In step A1, as shown in FIG. 6(a), the plastic elongation strain difference Δε pl Set (y). This step A1 is the same as the above step X1.

[0045] (Step A2) In step A2, in the first iteration of the iterative calculation, the plastic elongation strain difference Δε pl (y) is the normalized elongation strain difference Δε from 0 to 1 normal (y). In the second and subsequent calculations of the repeated calculations, the normalized elongation strain difference Δε normal (y) is the normalized elongation strain difference in the next or subsequent steps. This step A2 is the same as the above step X2 if there is no repeated calculation.

[0046] (Step A3) In step A3, an eigenvalue analysis calculation is performed using a theoretical buckling model. This step A3 is the same as the above step X3, and the normalized elongation strain difference Δε normal (y), the thickness t of the metal plate, the width B of the metal plate, and the tension Ut acting on the metal plate are input, and the plastic elongation strain difference Δε pl The buckling inherent strain difference Δε, which is similar to (y) cr (y) (criterion for buckling), wave pitch P, and normalized height profile (shape profile) W(y) from 0 to 1 in the cross section in the width direction at the time of buckling are output. Note that in the case of the second or subsequent calculation of the iterative calculation, the buckling inherent strain difference Δε cr (y) is the elongation strain error Δε er (y), the difference in plastic elongation and strain Δε plIt is not similar to (y).

[0047] (Step A4) In step A4, it is determined whether it is the first calculation of the repeated calculations or the second or subsequent calculations. If it is the first calculation, the process proceeds to step A5, which will be described later, and if it is the second or subsequent calculations, the process proceeds to step A6, which will be described later. In step A5, it is determined whether buckling has occurred, but in the case of the second or subsequent calculations, since it has been determined that the metal plate will buckle, step A5 can be omitted.

[0048] (Step A5) In step A5, it is determined whether or not buckling occurs. This step A5 is the same as step X4 described above, and the plastic elongation strain difference Δε pl (y) and the difference in buckling inherent strain Δε cr (y) and Δε pl (y) is Δε cr If it is greater than (y), it is determined that the metal plate buckles, and the process proceeds to step A6. cr (y) is the plastic elongation strain difference Δε pl Since Δε(y) has a similar relationship, it may be judged at any position in the width direction y, but here, the maximum values ​​of each are compared. pl (y) is Δε cr If it is equal to or less than (y), it is determined that the metal plate is not buckled and is flat, and the process proceeds to step A11.

[0049] (Step A11) In step A11, as in step X6, it is output that the metal plate is flat, and the shape prediction ends. In addition, when the metal plate is flat, the plastic elongation strain difference Δε pl (y) is the elastic strain difference Δε el (y) remains in the metal plate, that is, the elastic strain difference Δε that exists in the metal plate without buckling is expressed by the following formula (2): el (y) is calculated. Furthermore, the elastic strain difference Δε calculated by the following formula (3) is el Multiplying (y) by Young's modulus E gives the residual stress σres (y) is also calculated. N represents the number of nodes equally divided in the width direction. Hereafter, N will be the number of nodes. Δε el (y)=-(Δε pl (y)-(ΣΔε pl (y)) / N) ···(2) σ res (y) = E × Δε el (y) (3)

[0050] As mentioned above, the longitudinal stress acting on a metal plate is essentially a combination of residual stress components and tension (unit tension) components, which are zero when integrated in the plate width direction. However, in the buckling model, the tension components are given separately, so here, assuming that they are zero when integrated in the plate width direction, that is, the residual stress components are zero when integrated in the plate width direction or averaged in the plate width direction, the residual stress distribution and the plastic elongation strain difference Δε are calculated using the above formula (1). pl The distribution of (y) is converted.

[0051] (Step A6) In step A6, the shape of the metal sheet is predicted using a shape prediction model. This step A6 is similar to the above-mentioned step X5. First, as shown in FIG. 6(b), the plastic elongation strain difference Δε pl The component that converts (y) into the shape deformation after buckling (buckling shape transformation elongation strain difference Δε ts (y)) and the component that remains in the metal plate after buckling (buckling inherent strain difference Δε cr Then, the plastic elongation strain difference Δε pl (y) to buckling inherent strain difference Δε cr (y) is subtracted, and the buckling shape transformation elongation strain difference Δε ts Calculate (y). Δε ts (y)=Δε pl (y)-Δε cr (y) (4)

[0052] Next, the buckling shape transformation elongation strain difference Δε calculated from the above formula (4) tsAssuming that the wave pitch P calculated in step A3 does not change with respect to (y), the wave height width distribution h(x,y) = H × W(y) × Sin(2πx / P) obtained by multiplying the standardized height profile W(y) by the wave piece amplitude height H is predicted as the shape of the metal plate after buckling. Here, the steepness λ(y) of the waveform after buckling is expressed by the wave piece amplitude height H, the standardized height profile W(y), and the wave pitch P for each width direction position y, that is, the geometric shape elongation strain difference Δε that appears in the shape due to out-of-plane deformation gs Using (y), it is expressed by the following formula (5). However, in general, when expressing the magnitude of the wave in rolling operations, it is often expressed as (5') with a double amplitude of the maximum amplitude H of the half amplitude wave. In addition, this formula (5) is expressed as the geometric shape elongation strain difference Δε gs Rearranging with respect to (y) gives equation (6). λ(y)=2×H×W(y) / P=(2 / π)√Δε gs (y) (5) λ=2×H / P (5') Δε gs (P, H, W(y))=(π / 2×W(y)×2×H / P) 2 (6)

[0053] Since the value of the normalized height profile W(y) is a profile normalized from 0 to 1, if we assume the maximum amplitude H of the single amplitude wave, the geometrical shape elongation strain difference Δε gs (P, H, W(y)) can be calculated. The buckling shape transformation elongation strain difference Δε ts (y) is approximately the same as the elongation strain difference Δε er (y) (hereinafter, "elongation strain error Δε er (y) is expressed by the following formula (7). Then, for example, by using the least squares method, the elongation strain error Δε er By determining the wave amplitude H of the wave with the minimum integral of the square of (y), the shape of the metal plate after buckling is predicted as h(x,y) = H × W(y) × Sin(2πx / P). Δε er (y)=Δε gs (P, H, W(y))-Δε ts(y) (7) Min[Σ(Δε er (y) 2 ] ···(8)

[0054] (Step A7) In step A7, the residual stress redistributed after the buckling wave is generated, i.e., the elastic strain difference Δε el * Specifically, as shown in FIG. 6(d), the elastic buckling inherent strain difference (Δε el_cr (y)) and the elastic elongation strain error (Δε er (y)) is added together to obtain the elastic strain difference Δε inherent in the metal plate that is redistributed due to the initiation of the buckling wave. el * In this way, in step A7, the elastic strain difference Δε el * (y) is calculated. The elastic strain difference Δε el * Multiplying (y) by Young's modulus E gives the residual stress σ inherent in the redistributed metal plate. res * It becomes possible to calculate (y). Δε el_cr (y)=-(Δε cr (y)-(ΣΔε cr (y)) / N) ···(9') Δε el * (y)=-{Δε pl (y)-Δε gs (P, H, W(y))}=Δε el_cr (y)+Δε er (y) (9) σ res * (y) = E × Δε el * (y) (10)

[0055] (Step A8) In step A8, the normalized elongation strain difference Δε is calculated based on the residual stress distribution of the redistributed metal plate after buckling. normal* Specifically, in a convergence calculation in which steps A2 to A10 are repeated as described below, the elastic strain difference Δε inherent in the reallocated metal plate is calculated by the following formula (11). el * (y), the corresponding normalized elongation strain difference Δε with a value between 0 and 1 normal * (y) is determined. Figure 6(e) shows the normalized elongation strain difference Δε normal * An example of (y) is shown below. Δε normal * (y)=-(Δε el * (y)-Max(ε el * (y))) / (Max(ε el * (y))-Min(ε el * (y))) ···(11)

[0056] (Step A9) In step A9, whether or not a solution has been found in the convergence calculation is determined by the normalized elongation strain difference Δε after buckling and reallocation. normal * (y) value and normalized elongation strain difference Δε before reallocation normal First, the error Δerror(y) of the standardized elongation-strain difference before and after reallocation is calculated for each width direction position y by the following formula (12). That is, the error Δerror(y) is calculated based on the standardized elongation-strain difference Δε normal Next, as shown in the following formula (13), the square error for each width direction position y is integrated to obtain Δerror * Calculate the error Δerror * and a predetermined threshold value. Then, the error Δerror * If is greater than a predetermined threshold, the reallocated normalized elongation strain difference Δε normal * (y) is judged not to have converged, and the procedure proceeds to step A10 to perform recalculation (eigenvalue analysis calculation using the theoretical buckling model).* If is less than a predetermined threshold, the normalized elongation strain difference Δε normal * It is determined that (y) has converged, and the process proceeds to step A12. Δerror(y)=Δε normal * (y)-Δε normal (y) ···(12) Δerror * = {Σ(Δerror(y)) 2}>Threshold (13)

[0057] (Step A10) In step A10, return to step A2 to calculate the standardized elongation strain difference Δε normal (y) is Δε normal * Specifically, the error Δerror(y) is multiplied by the relaxation coefficient α using the following formula (14), and the normalized elongation strain difference Δε after reallocation is calculated. normal Add to (y) to obtain the normalized elongation strain difference Δε for recalculation. normal (y) is reset. Here, when recalculating, if all the errors Δerror(y) are superimposed without multiplying the relaxation coefficient α, the calculation result will vibrate and the normalized elongation strain difference Δε normal (y) is difficult to converge. Therefore, in this embodiment, the normalized elongation-strain difference Δε is multiplied by the relaxation coefficient α. normal This makes it easier for (y) to converge. Note that the relaxation coefficient α is arbitrary, but after extensive investigation, the present inventors have confirmed that a value of 0.1 to 0.4 is appropriate. Δε normal (y)=Δε normal (y)+α×Δerror(y)=Δε normal (y) + α × {Δε normal * (y)-Δε normal (y)} ···(14)

[0058] Next, returning to step A2, the normalized elongation strain difference Δε corrected in step A10 is normalSteps A2 to A10 are then repeated, and the standardized elongation strain difference Δε normal * The convergence calculation is continued until it is determined that (y) has converged.

[0059] (Step A12) In step A9, the normalized elongation strain difference Δε normal * If it is determined that (y) has converged, the process proceeds to step A12, where shape prediction ends. Then, the wave pitch P and wave height h(x, y)=H×W(y)×Sin(2πx / P) at this time are predicted as the shape of the metal plate.

[0060] In addition, the normalized elongation strain difference Δε normal * When (y) converges, the elastic strain difference Δε that exists in the plate even after buckling is calculated by the above equations (9) and (10). el * (y) remains in the metal plate, and multiplied by Young's modulus E, the residual stress σ res is also calculated.

[0061] As described above, the conventional shape prediction method assumes that the shape profile is maintained even after buckling. However, in reality, the effect of the shape profile changing due to the residual stress distribution redistributed after buckling is not taken into consideration, resulting in an error in the shape profile as shown in Fig. 4.

[0062] In this regard, the inventors have found that the shape profile changes due to the shape deformation after buckling. According to the shape prediction method according to the first embodiment, the elastic strain difference Δε redistributed due to the shape deformation after buckling is el * (y) is calculated, and the elastic strain difference Δε el * Since the calculation is performed using (y), the shape of the metal plate can be appropriately predicted.

[0063] In order to verify the effect of the first embodiment, the inventors compared the shape prediction results (converged solutions) obtained by the first embodiment with the shape prediction results obtained by a conventional shape prediction method and the analysis results by FEM. The verification results are shown in Fig. 7 and Fig. 8. Fig. 7 shows the width-direction distribution of the elastic strain difference present in the metal plate after buckling, and Fig. 8 shows the width-direction distribution of the normalized profile.

[0064] 7 and 8, the shape prediction result of the conventional method is slightly different from the analysis result by FEM, whereas the shape prediction result of the first embodiment is almost the same as the analysis result by FEM. Therefore, it was found that the shape of the metal plate can be appropriately predicted according to the first embodiment.

[0065] <Shape prediction method according to the second embodiment> A feature prediction method according to the second embodiment will be described below with reference to a flowchart shown in FIG 9.

[0066] The shape prediction method of the second embodiment has a technical feature in that recalculation is performed using the elastic strain difference reallocated due to the generation of a shape profile generated after buckling, which is common to the shape prediction method of the first embodiment. However, whereas the first embodiment performs convergent calculations, the second embodiment repeats steps B2 to B10 described below to perform sequential calculations.

[0067] (Step B1) In step B1, the plastic elongation strain difference Δε of the metal plate to be evaluated is calculated. pl (y) is set. This step B1 is similar to the above step A1.

[0068] (Step B2) In step B2, the number of repeated calculations (sequential calculations) is set, and it is determined which calculation is currently being performed. In this embodiment, the number of repeated calculations is M. In addition, in the following description, the calculation currently being performed is represented as the i-th calculation.

[0069] (Step B3) In step B3, in the first iteration (i=1), the plastic elongation strain difference Δε pl (y) is the normalized elongation strain difference Δε from 0 to 1 normal In the second and subsequent calculations (i=2 and after) of the repeated calculation, the normalized elongation strain difference Δε normal * (y) is Δε normal This should be read as (y) and used as the normalized elongation strain difference in the next and subsequent steps.

[0070] (Step B4) In step B4, an eigenvalue analysis is performed using the theoretical buckling model to obtain the buckling eigenstrain difference Δε cr (y), wave pitch P, and the normalized height profile (shape profile) W(y) of 0-1 are calculated. This step B4 is similar to the above step A3, and the normalized elongation strain difference Δε normal (y), the thickness t of the metal plate, the width B of the metal plate, and the tension Ut acting on the metal plate are input, and the plastic elongation strain difference Δε pl The buckling inherent strain difference Δε, which is similar to (y) cr (y) (criterion for buckling occurrence), wave pitch P, and normalized height profile (shape profile) W(y) from 0 to 1 in the width direction cross section at the time of buckling are output.

[0071] (Step B5) In step B5, it is determined whether it is the first calculation (i=1) of the repeated calculations, or the second or subsequent calculations (i=2 or subsequent). If it is the first calculation, the process proceeds to step B6, which will be described later, and if it is the second or subsequent calculations, the process proceeds to step B8, which will be described later. In step B6, it is determined whether buckling has occurred, but in the case of the second or subsequent calculations, since it has been determined that the metal plate will buckle, steps B6 and B7 can be omitted.

[0072] (Step B6) In step B6, it is determined whether or not buckling occurs. This step B6 is similar to the above step A5, and the plastic elongation strain difference Δε pl (y) and the difference in buckling inherent strain Δε cr (y) and Δε pl (y) is Δε cr If it is greater than (y), it is determined that the metal plate buckles, and the process proceeds to step B7. pl (y) is Δε cr If it is equal to or less than (y), it is determined that the metal plate is not buckled and is flat, and the process proceeds to step B12.

[0073] (Step B12) In step B12, it is output that the metal plate is flat, and the shape prediction ends. Note that, according to the above equations (2) and (3), the elastic strain difference Δε el (y) and residual stress σ res (y) is also calculated. This step B12 is similar to the above step A11.

[0074] (Step B7) In step B7, the shape of the metal sheet for each iteration of the repeated calculation (sequential calculation) is predicted using the shape prediction model. Specifically, first, the plastic elongation strain difference Δε pl The component that converts (y) into the shape deformation after buckling (buckling shape transformation elongation strain difference Δε ts (y)) and the component that remains in the metal plate after buckling (buckling inherent strain difference Δε cr (y)) and the buckling shape transformation elongation strain difference Δε ts (y) is divided into M-1 parts, and the difference in elongation strain at the M-1 part buckling shape transformation Δε ts Then, as shown in the following formula (16), the first buckling inherent strain difference Δε cr (y) is the initial buckling inherent strain difference Δε cr 'Read as (y). Δε ts '(y)=(Δε pl (y)-Δε cr (y)) / (M-1) (15) Δε cr '(y)=Δε cr (y) ···(16)

[0075] (Step B8) In step B8, the shape of the metal plate in each iteration of the repeated calculation (sequential calculation) is predicted using a shape prediction model. Specifically, first, the buckling shape transformation elongation strain difference Δε ts (y) is calculated. That is, in this calculation, the M-1 division buckling shape transformation elongation strain difference Δε ts '(y) and the initial buckling inherent strain difference Δε cr Using '(y), the buckling shape transformation elongation strain difference Δε ts Correct (y). Δε ts (y)=(Δε ts '(y)×(i-1)+Δε cr '(y))-Δε cr (y) ···(17)

[0076] The subsequent shape prediction of the metal plate is the same as in step A6. That is, the buckling shape transformation elongation strain difference Δε ts Using (y), the geometric shape elongation strain difference Δε gs (y) and elongation strain error Δε er (y) is calculated, and the elongation strain error Δε er By determining the maximum amplitude H of the single amplitude wave where the integrated value of the square of (y) is the minimum, the shape of the metal plate after buckling is predicted as h(x,y) = H × W(y) × Sin(2πx / P).

[0077] (Step B9) In step B9, the elastic strain difference Δε inherent in the metal plate is calculated using the above equations (9) and (10). el * (y) and residual stress σ res * (y) is calculated. This step B9 is the same as step A7 above.

[0078] (Step B10) In step B10, the normalized elongation strain difference Δε is calculated based on the residual stress distribution of the redistributed metal plate after buckling. normal * (y) is determined again. Specifically, the elastic strain difference Δε inherent in the reallocated metal plate is calculated by the above formula (11). el * (y), the corresponding normalized elongation strain difference Δε with a value between 0 and 1 normal * (y) is determined. This step B10 is the same as the above step A8. Then, the normalized elongation strain difference Δε normal * (y) is the normalized elongation strain difference to be used in recalculation in step B2.

[0079] Next, the process returns to step B2, and the second and subsequent iterative calculations are performed. In the second and subsequent iterative calculations, the normalized elongation strain difference Δε calculated in the previous step B10 is normal * (y) is Δε normal This is used as (y) and the following steps B4 to B10 are carried out.

[0080] (Step B11) The above steps B2 to B10 are repeated M times, and the shape prediction is completed. The wave amplitude height H at this time is predicted as the shape of the metal sheet. normal * When (y) converges, the elastic strain difference Δε that exists in the plate even after buckling is calculated by the above equations (9) and (10). el * (y) remains in the metal plate, and multiplied by Young's modulus E, the residual stress σ res is also calculated.

[0081] The second embodiment described above can also achieve the same effects as the first embodiment. That is, the elastic strain difference Δε el * (y) is calculated, and the elastic strain difference Δε el *Since the calculation is performed using (y), the shape of the metal plate can be appropriately predicted.

[0082] In order to verify the effect of the second embodiment, the inventors compared the shape prediction results of the second embodiment with the shape prediction results of the first embodiment, the shape prediction results of the conventional shape prediction method, and the analysis results by FEM. The verification results are shown in Fig. 10 and Fig. 11. Fig. 10 shows the width-direction distribution of the elastic strain difference existing in the metal plate after buckling, and Fig. 11 shows the width-direction distribution of the normalized profile.

[0083] 10 and 11, the shape prediction results of the conventional method are slightly different from the analysis results by FEM, whereas the shape prediction results of the first and second embodiments are almost the same as the analysis results by FEM. Therefore, it was found that the shape of the metal plate can be appropriately predicted according to the second embodiment.

[0084] <Shape prediction method according to the third embodiment> A feature prediction method according to the third embodiment will be described below with reference to a flowchart of FIG 12.

[0085] In the second embodiment described above, the buckling shape transformation elongation strain difference Δε ts (y) was divided into M-1 parts and sequential calculation was performed. In the third embodiment, the plastic elongation strain difference Δε pl Divide (y) into M parts and perform sequential calculations.

[0086] (Steps C1 to C2) In step C1, the plastic elongation strain difference Δε of the metal plate to be evaluated is calculated. pl In step C1, the number of iterative calculations (sequential calculations) (M times) is set, and it is determined which calculation (i-th calculation) is currently being performed. Note that steps C1 to C2 are similar to steps B1 to B2 described above, respectively.

[0087] (Step C3) In step C3, the plastic elongation strain difference Δε of the metal plate to be evaluated set in step C1 is pl (y) is divided into M parts, and the plastic elongation and strain difference when performing the sequential calculation is defined. Specifically, the M-partition plastic elongation and strain difference Δε is calculated using the following formula (18): pl '(y) is calculated, and the plastic elongation strain difference Δε in the i-th iteration of the repeated calculation is calculated using the following formula (19). pl Define (calculate) (y). Δε pl '(y)=Δε pl (y) / M (18) Δε pl (y)=Δε pl '(y)×i (19)

[0088] (Step C4) In step C4, in the first iteration (i=1), the plastic elongation strain difference Δε pl (y) is the normalized elongation strain difference Δε from 0 to 1 normal In the second and subsequent iterative calculations (i=2 and subsequent), if it is determined that buckling does not occur in the buckling determination in step C7 (the buckling determination one iterative calculation before), the plastic elongation strain difference Δε pl (y) is the normalized elongation strain difference Δε normal On the other hand, if it is determined in the buckling determination in step C7 that buckling occurs, the normalized elongation strain difference Δε normal * (y) is Δε normal This should be read as (y) and used as the normalized elongation strain difference in the next and subsequent steps.

[0089] (Step C5) In step C5, an eigenvalue analysis is performed using the theoretical buckling model to obtain the buckling eigenstrain difference Δε cr (y), wave pitch P, and the normalized height profile (shape profile) W(y) of 0-1 are calculated. This step C5 is similar to step B4 above, and the normalized elongation strain difference Δε normal(y), the thickness t of the metal plate, the width B of the metal plate, and the tension Ut acting on the metal plate are input, and the plastic elongation strain difference Δε pl The buckling inherent strain difference Δε, which is similar to (y) cr (y) (criterion for buckling occurrence), wave pitch P, and normalized height profile (shape profile) W(y) from 0 to 1 in the width direction cross section at the time of buckling are output.

[0090] (Step C6) In step C6, the next step to proceed to is determined based on the result of the buckling determination in step C7 described later (the buckling determination one iteration before the iterative calculation). If it is determined in the buckling determination in step C7 that buckling will not occur, the process proceeds to step C7 described later, and if it is determined that buckling will occur, the process proceeds to step C9 described later. Once it is determined that buckling will occur, the buckling determination in step C7 can be omitted.

[0091] (Step C7) In step C7, it is determined whether or not buckling occurs. This step C7 is similar to the above step B6, and the plastic elongation strain difference Δε pl (y) and the difference in buckling inherent strain Δε cr (y) and Δε pl (y) is Δε cr If it is greater than (y), it is determined that the metal plate buckles, and the process proceeds to step C9. pl (y) is Δε cr If it is equal to or less than (y), it is determined that the metal plate is not buckled and is flat, and the process proceeds to step B8.

[0092] (Step C8) In step C8, it is determined whether the calculation is the final iteration (i=M) or the calculation before that (i=M-1 or earlier). If the calculation is before the final iteration, the process returns to step C2 and performs the subsequent steps C3 and after. This is to confirm whether the metal plate will buckle in the end, although it was determined in the sequential calculations that it would not buckle. On the other hand, if it is the final Mth calculation, it is determined that the metal plate will not buckle and is flat, and the process proceeds to step C13.

[0093] (Step C13) In step C13, it is finally output that the metal plate is flat, and the shape prediction ends. Note that, according to the above equations (2) and (3), the elastic strain difference Δε el (y) and residual stress σ res (y) is also calculated. This step C13 is similar to the above step B12.

[0094] (Step C9) In step C9, the shape of the metal sheet is predicted using the shape prediction model. This step C9 is similar to the above step A6, and the buckling shape transformation elongation strain difference Δε is calculated by the above formula (4). ts (y) was calculated, and the geometric shape elongation strain difference Δε was calculated using the above formulas (6) and (7). gs (y) and elongation strain error Δε er (y) is calculated, and the elongation strain error Δε er By determining the maximum amplitude H of the single amplitude wave where the integrated value of the square of (y) is the minimum, the shape of the metal plate after buckling is predicted as h(x,y) = H × W(y) × Sin(2πx / P).

[0095] (Step C10) In step C10, the elastic strain difference Δε inherent in the metal plate is calculated by the above equations (9) and (10). el * (y) and residual stress σ res * (y) is calculated. This step C10 is similar to the above step B9.

[0096] (Step C11) In step C11, the normalized elongation strain difference Δε is calculated based on the residual stress distribution of the redistributed metal plate after buckling. normal * (y) is determined again, and the corrected standardized elongation strain difference Δε is calculated using the above formula (11). normal * (y) is determined. This step C11 is similar to the above step B10.

[0097] Next, the process returns to step C2 and repeats the calculation. In this repeated calculation, the normalized elongation strain difference Δε calculated in the previous step C11 is normal * Using (y), the following steps B4 to B11 are carried out.

[0098] (Step C12) The above steps C2 to C11 are repeated M times, and the shape prediction is completed. The wave amplitude height H at this time is predicted as the shape of the metal sheet. normal * When (y) converges, the elastic strain difference Δε that exists in the plate even after buckling is calculated by the above equations (9) and (10). el * (y) remains in the metal plate, and multiplied by Young's modulus E, the residual stress σ res is also calculated.

[0099] The third embodiment described above can also achieve the same effects as the first and second embodiments. That is, the elastic strain difference Δε el * (y) is calculated, and the elastic strain difference Δε el * Since the calculation is performed using (y), the shape of the metal plate can be appropriately predicted.

[0100] <Other embodiments> In the above steps A6, B7, and C9, the plastic elongation strain difference Δε pl(y) and the buckling inherent strain difference Δε that remains in the metal plate even after buckling cr For (y), the buckling inherent strain difference Δε cr When considering the residual stress of the metal plate corresponding to (y) from the results of an FEM analysis that takes into account the transformation during cooling, it was confirmed that the longitudinal residual stress distribution across the width of the metal plate can be taken as thermal stress based on the width-wise temperature distribution before and after cooling. Therefore, the residual stress is determined based on the temperature distribution before and after cooling. In such a case, it is possible to predict the residual stress distribution and the shape after cooling simply by measuring the temperature.

[0101] In addition, the above-mentioned buckling inherent strain difference Δε cr The residual stress of the metal plate corresponding to (y) may be defined by adding at least the residual stress distribution imparted during rolling or straightening to the measured longitudinal residual stress distribution of the metal plate. In such a case, the residual stress distribution and cold shape of a metal plate without controlled cooling after rolling or straightening can be predicted.

[0102] In addition, the plastic elongation strain difference Δε set in steps A1, B1, and C1 pl For (y), the shape of the metal sheet before or after cooling may be measured, and the difference in elongation strain obtained when the shape is assumed to be flat may be superimposed. In this case, by superimposing the strain due to the rolling shape and the thermal strain before or after cooling, it becomes possible to predict the residual stress and shape with higher accuracy, and the accuracy of the judgment of the possibility of shape correction is improved.

[0103] By using the method for predicting the shape of a metal plate according to the above-described first, second or third embodiment, it becomes possible to manufacture a flat metal plate.

[0104] Specifically, the shape of the metal plate is predicted by the above embodiment, and based on the prediction result, it is determined whether or not to perform shape correction in the finishing process. In this case, since highly accurate shape prediction is possible, a flat plate can be manufactured by controlling the width direction temperature distribution before and after cooling so as not to buckle.

[0105] Here, the decision as to whether or not to perform shape correction in the finishing process may be based on the presence or absence of buckling as well as on the flatness level according to the needs of the user, for example, 2% or less, 1% or less, 0.5% or less, etc. In such cases, it is more practical to set judgment criteria according to the needs of the user rather than judging only on the presence or absence of buckling.

[0106] Therefore, the predicted steepness may be used to determine whether or not to perform shape correction in the above-mentioned refinement process. In this case, the determination is made based on a predetermined steepness, rather than on the presence or absence of buckling, which makes it possible to rank the flatness of the metal plate and determine whether or not to apply a correction process according to the rank and customer needs. This allows for a more practical judgment, and the correction process can be optimized.

[0107] Although the embodiment of the present invention has been described above, the present invention is not limited to such examples. It is clear that a person skilled in the art can come up with various modified or altered examples within the scope of the technical ideas described in the claims, and it is understood that these also naturally belong to the technical scope of the present invention. EXAMPLES

[0108] Taking the manufacturing process of a thick plate as an example, the flatness of the metal plate (shape prediction) was predicted, and an experiment was conducted to determine whether the plate could be passed through the finishing process. In the manufacturing process of a thick steel plate as a metal plate, the thick steel plate passes through a finishing rolling mill, a hot leveler, is water-cooled to a predetermined temperature in an accelerated cooling facility, and is air-cooled on a cooling bed. At this time, the thermal strain and thermal stress distribution were obtained using a thermometer on the exit side of the rolling mill and before accelerated cooling, and shape prediction was performed using a model of a comparative example (Patent Document 3, Patent No. 4262142) and this model (model of the first embodiment), and the plate shape measured in a cold state was compared. In addition, the steel plate used was a steel type that is difficult to predict the shape of when it is strongly cooled in an accelerated cooling facility.

[0109] As a result, the rate of false detection, in which the shape was judged to be good even though it was poor and required a fine-tuning strip, was 1% (2 coils out of 200 coils) in the comparative example, while it was 0% (2 coils out of 200 coils) in the embodiment of the present application. [Industrial Applicability]

[0110] The present invention is useful in predicting and controlling the shape of a metal sheet after rolling.

Claims

1. A method for predicting the shape of a metal plate, comprising: A first step of setting a plastic elongation strain difference, which is a difference in the width direction of the strain that elongates in the longitudinal direction of the metal plate during rolling when the rolled metal plate buckles; In the first calculation of the repeated calculation, the plastic elongation and strain difference is converted into a standardized elongation and strain difference, and in the second and subsequent calculations of the repeated calculation, the standardized elongation and strain difference calculated in the tenth step below is used; A third step of performing a buckling analysis based on the normalized elongation strain difference to calculate a buckling inherent strain difference, which is a criterion for determining whether or not the metal plate will buckle, a wave pitch, and a normalized shape profile of the metal plate; a fourth step of determining whether the calculation is the first calculation of the repeated calculations or the second or subsequent calculations; A fifth step of comparing the plastic elongation strain difference with the buckling inherent strain difference to determine whether or not buckling has occurred when it is determined in the fourth step that this is the first calculation of the repeated calculations; a sixth step of separating the plastic elongation-strain difference into the buckling inherent strain difference and a buckling shape transformation elongation-strain difference, which is a difference between the plastic elongation-strain difference and the buckling inherent strain difference and is a component that is transformed into the shape of the metal plate, calculating an elongation-strain error, which is a difference between a geometric shape elongation-strain difference that appears in the shape of the metal plate after out-of-plane deformation and the buckling shape transformation elongation-strain difference, and determining a wave height at which an integrated value of the square of the elongation-strain error is a minimum value to determine a wave shape profile; A seventh step of calculating an elastic strain difference inherent in the metal plate after buckling by adding the elastic buckling inherent strain difference and the elongation strain error; An eighth step of calculating a normalized elongation strain difference corresponding to the elastic strain difference calculated in the seventh step by using the elastic strain difference calculated in the seventh step; A ninth step of calculating an error between the standardized elongation-strain difference set in the second step and the standardized elongation-strain difference calculated in the eighth step, and comparing the square of the error with a predetermined threshold value; and a tenth step of correcting the standardized elongation strain difference set in the second step by a value obtained by multiplying the error by a relaxation coefficient when the square of the error is greater than a predetermined threshold value in the ninth step, A method for predicting a shape of a metal plate, comprising repeating steps 2 to 10 until the square of the error in step 9 becomes equal to or smaller than a predetermined threshold value.

2. A method for predicting the shape of a metal plate, comprising: A first step of setting a plastic elongation strain difference, which is a difference in the width direction of the strain that elongates in the longitudinal direction of the metal plate during rolling when the rolled metal plate buckles; A second step of setting the number of iterations to M; A third step of converting the plastic elongation-strain difference into a standardized elongation-strain difference in the first calculation of the iterative calculation, and using the standardized elongation-strain difference corrected in the tenth step below in the second and subsequent calculations of the iterative calculation; A fourth step of performing a buckling analysis based on the normalized elongation strain difference to calculate a buckling inherent strain difference, which is a criterion for determining whether or not the metal plate will buckle, a wave pitch, and a normalized shape profile of the metal plate; A fifth step of determining whether the calculation is the first calculation of the repeated calculations or the second or subsequent calculations; A sixth step of comparing the plastic elongation strain difference with the buckling inherent strain difference to determine whether or not buckling has occurred when it is determined in the fifth step that this is the first calculation of the repeated calculations; a seventh step of dividing the plastic elongation strain difference into the buckling inherent strain difference and a buckling shape transformation elongation strain difference, which is a difference between the plastic elongation strain difference and the buckling inherent strain difference and is a component for transforming the shape of the metal plate, dividing the buckling shape transformation elongation strain difference into M-1, calculating M-1 divided buckling shape transformation elongation strain differences, and replacing the buckling inherent strain difference in the first iteration of the iterative calculation with an initial buckling inherent strain difference; If it is determined in the fifth step that the calculation is the second or subsequent iteration of the repeated calculation, or if it is determined in the sixth step that the plastic elongation strain difference is greater than the buckling inherent strain difference and buckling will occur, an eighth step of correcting the buckling shape transformation elongation strain difference using the M-1 division buckling shape transformation elongation strain difference and the initial buckling inherent strain difference, calculating an elongation strain error, which is the difference between the geometric shape elongation strain difference appearing in the shape of the metal plate after the out-of-plane deformation and the corrected buckling shape transformation elongation strain difference, and determining a wave height at which the integrated value of the square of the elongation strain error is the minimum value to determine a wave shape profile; A ninth step of calculating an elastic strain difference inherent in the metal plate after buckling by replacing the buckling inherent strain difference with an elastic strain distribution and adding the elongation strain error; A tenth step of calculating a standardized elongation strain difference corresponding to the elastic strain difference calculated in the ninth step, A method for predicting a shape of a metal plate, comprising: repeating the second step to the tenth step a number of times set in the second step.

3. A method for predicting the shape of a metal plate, comprising: A first step of setting a plastic elongation strain difference, which is a difference in the width direction of the strain that elongates in the longitudinal direction of the metal plate during rolling when the rolled metal plate buckles; A second step of setting the number of iterations to M; A third step of dividing the plastic elongation and strain difference into M parts and calculating a plastic elongation and strain difference according to the number of repeated calculations; In the first calculation of the repeated calculation or in the seventh step below, if the plastic elongation-strain difference is equal to or less than the buckling inherent strain difference, the plastic elongation-strain difference is converted into a standardized standardized elongation-strain difference, and in the second or subsequent calculation of the repeated calculation and in the seventh step below, if it is determined that buckling occurs, the standardized elongation-strain difference calculated in the eleventh step below is used in the fourth step; A fifth step of performing a buckling analysis based on the normalized elongation strain difference, and calculating a buckling inherent strain difference, which is a criterion for determining whether or not the metal plate will buckle, a wave pitch, and a normalized shape profile of the metal plate; A sixth step of determining whether or not buckling has occurred in the seventh step immediately before the iterative calculation; A seventh step of comparing the plastic elongation strain difference with the buckling inherent strain difference to determine whether or not buckling has occurred when it is determined in the sixth step that buckling has not occurred; In the seventh step, if it is determined that the difference in plastic elongation strain is equal to or less than the difference in inherent buckling strain and buckling does not occur, the number of times of the repeated calculation is confirmed, and if the number is not the final time, the eighth step returns to the second step; a ninth step of separating the plastic elongation-strain difference into the buckling inherent strain difference and a buckling shape transformation elongation-strain difference, which is a difference between the plastic elongation-strain difference and the buckling inherent strain difference and is a component that is transformed into the shape of the metal plate, calculating an elongation-strain error, which is the difference between the geometric shape elongation-strain difference that appears in the shape of the metal plate after out-of-plane deformation and the buckling shape transformation elongation-strain difference, and determining a wave height at which an integrated value of the square of the elongation-strain error is a minimum value to determine a wave shape profile; A tenth step of calculating an elastic strain difference inherent in the metal plate after buckling by replacing the buckling inherent strain difference with an elastic strain distribution and adding the elongation strain error; An eleventh step of calculating a standardized elongation strain difference corresponding to the elastic strain difference calculated in the tenth step, A method for predicting a shape of a metal plate, comprising: repeating the second step to the eleventh step a number of times set in the second step.

4. The method for predicting a shape of a metal plate according to any one of claims 1 to 3, characterized in that the width direction distribution of the longitudinal residual stress of the metal plate, calculated by converting the buckling inherent strain difference, is set to a thermal stress distribution based on the width direction temperature distributions before and after cooling.

5. The method for predicting a shape of a metal plate according to any one of claims 1 to 3, characterized in that a width direction distribution of a longitudinal residual stress of the metal plate, calculated by converting the buckling inherent strain difference, is set to a residual stress distribution imparted at least during rolling or straightening.

6. The shape prediction method for a metal plate according to any one of claims 1 to 3, characterized in that the shape of the metal plate before cooling or the shape of the metal plate after cooling is measured, and the geometric shape elongation strain difference is superimposed on the plastic elongation strain difference.

7. A method for manufacturing a metal plate, comprising: determining whether or not to perform shape correction in a finishing process by using the metal plate shape prediction method according to any one of claims 1 to 6; setting a width direction distribution of longitudinal residual stress in the metal plate as a thermal stress distribution based on width direction temperature distributions before and after cooling; and controlling the width direction temperature distribution so that the metal plate does not buckle, based on the shape of the metal plate predicted by the shape prediction method, thereby manufacturing a flat plate.

8. 8. The method for manufacturing a metal plate according to claim 7, wherein the judgment as to whether or not to perform shape correction in the finishing step is made based on the predicted steepness.

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