JP2022175003A - Method for predicting metal plate shape and method for manufacturing metal plate - Google Patents

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 The present invention relates to a method for predicting the shape of a metal plate after rolling, and a method for manufacturing a metal plate using the method.

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 Document 1 describes a method for evaluating the flatness by multiplying the shape change coefficient with respect to the change in the crown ratio of the material to be rolled, which is a thick plate, and reducing the thermal strain difference due to the temperature difference applied to the steel plate during rolling. is disclosed. In the flatness evaluation formula used at this time, the change in crown ratio defined at a fixed point of the steel sheet is multiplied by the shape change coefficient and replaced with steepness (hereafter, flatness) equivalent to residual stress to obtain flatness.

Patent Literature 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, the residual stress distribution in the longitudinal direction of the plate after air cooling is calculated based on this, and the residual stress distribution is approximated by a rectangle. Next, the residual stress at the buckling critical point is calculated using a predetermined simple prediction formula from the rectangular residual stress distribution. Then, the residual stress at the calculated buckling critical point is compared with the rectangular residual stress to determine the presence or absence of a shape defect.

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

Patent Document 3 discloses a metal plate shape prediction method having the following steps. That is, this method includes (a) the step of determining the width direction distribution of buckling stress using the width direction distribution of the longitudinal residual stress of the metal plate, and (b) when it is determined that buckling will occur, the waveform transformation and (c) predicting the wave shape after buckling using the stress component for wave shape transformation.

JP-A-6-15321 JP-A-8-187505 Japanese Patent No. 4262142

Journal of Japan Society for Technology of Plasticity: Plasticity and Processing, Vol. 28, No. 312 (1987-1), p58-66

However, the method disclosed in Patent Literature 1 does not take into consideration the shape dead zone that should originally exist. In other words, there is no concept of buckling, and all 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.

Further, in the method disclosed in Patent Document 2, although the buckling phenomenon of the metal plate is considered, buckling determination is performed by approximating the residual stress distribution by a rectangle as a simple buckling prediction formula. It is not a model that accurately reflects the The same applies to the case of approximating the residual stress distribution to a triangle as disclosed in Non-Patent Document 1.

In this regard, in the method disclosed in Patent Document 3, as a shape prediction method based on the residual stress inherent in the metal plate, it is possible to determine buckling and predict the shape at the time of buckling by inputting the residual stress distribution distributed in the width direction. Therefore, compared to the methods disclosed in Patent Documents 1 and 2 and Non-Patent Document 1, the accuracy of wave-shaped buckling determination is improved. However, as a result of the inventor's intensive studies, it was found that there is room for improvement in improving the prediction accuracy, as will be described later.

If the shape after buckling cannot be predicted correctly, it cannot be determined whether or not to turn the metal plate to the correction line. That is, if the prediction is not accurate, there is a possibility that even a good-shaped strip will be passed through the finishing process, resulting in an increase in cost. 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 provides a method for predicting the shape of a metal plate with high accuracy in predicting the shape of the metal plate, and capable of accurately separating the metal plate necessary for the refining process in advance, and It aims at providing the manufacturing method of a metal plate using this method.

In order to achieve the above object, the present inventors have studied a method for predicting the shape of a metal plate, and as a result, have obtained the following findings.

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 transforms into a wave shape and a component that remains in the metal plate even after buckling. Then, in the invention according to Patent Document 3, the shape of the metal plate after buckling is predicted using the component to be converted into the wave shape.

The present invention is a further development of the invention disclosed in Patent Document 3. As a result of intensive studies by the present inventor, in the invention according to Patent Document 3, 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. It has been found that the shape profile is determined by the elastic strain difference inherent in the metal plate after it has been redistributed, that is, even after buckling. The present invention is based on the above findings, and the gist of the present invention is as follows.

The present invention is a method for predicting the shape of a metal plate, and when predicting the wave shape after buckling based on the plastic elongation strain difference imparted to the metal plate, It is characterized by determining the corrugated profile by buckling analysis using elastic strain difference.

Note that the following three algorithms are listed as specific algorithms for executing the method for predicting the shape of the metal plate.

The first metal plate shape prediction method (algorithm) is the first step of setting the plastic elongation strain difference, and in the first calculation of the repeated calculation, the plastic elongation strain difference is normalized. Converted to the difference in elongation strain, in the second and subsequent calculations of the repeated calculation, the second step using the normalized elongation strain difference calculated in the tenth step below, and the buckling based on the normalized elongation strain difference A third step of performing an analysis and calculating a buckling inherent strain difference, a wave pitch, and a standardized shape profile of the metal plate, which serve as criteria for determining the occurrence of buckling in the metal plate; or a fourth step for determining whether it is the second or later calculation, and when it is determined that the fourth step is the first calculation of the repeated calculation, the plastic elongation strain difference A fifth step of determining whether or not buckling has occurred by comparing the buckling inherent strain difference with the If it is determined in the fifth step that the plastic elongation strain difference is greater than the buckling inherent strain difference and buckling occurs, the plastic elongation strain difference is determined as buckling shape conversion elongation strain difference, which is the difference in the buckling intrinsic strain difference and is the component that converts to the shape of the metal plate, and the geometric shape elongation strain that appears in the shape of the metal plate after out-of-plane deformation The elongation strain error, which is the difference between the difference and the buckling shape conversion elongation strain difference, is calculated, and the wave height at which the integrated value of the square of the elongation strain error is the minimum value is obtained to determine the wave shape profile. 6 step, a seventh step of calculating the elastic strain difference inherent in the metal plate after buckling by adding the elastic buckling inherent strain difference and the elongation strain error, and the calculated in the seventh step Using the elastic strain difference, the eighth step of calculating the normalized elongation strain difference corresponding to the elastic strain difference, the normalized elongation strain difference set in the second step, and the eighth step calculated A ninth step of calculating the error from the standardized elongation strain difference and comparing the square of the error with a predetermined threshold, and if the square of the error is greater than the predetermined threshold in the ninth step, the second and a tenth step of correcting the normalized elongation strain difference set in the step with a value obtained by multiplying the error by a relaxation coefficient, and the square of the error in the ninth step is less than or equal to a predetermined threshold. until the second step It is characterized by repeatedly performing the tenth step from the top.

The second metal plate shape prediction method (algorithm) includes the first step of setting the plastic elongation strain difference, the second step of setting the number of repeated calculations, and the first calculation of the repeated calculations, A third step that converts the plastic elongation strain difference into a standardized elongation strain difference, and uses the standardized elongation strain difference corrected in the following tenth step in the second and subsequent calculations of the repeated calculation; , buckling analysis is performed based on the normalized elongation strain difference, and the buckling inherent strain difference, the wave pitch, and the normalized shape profile of the metal plate, which are the criteria for determining the occurrence of buckling in the metal plate, are calculated. a fourth step of determining whether it is the first calculation of the repeated calculation or the second or subsequent calculation; and in the fifth step, in the first calculation of the repeated calculation If it is determined that there is, a sixth step for determining whether or not buckling occurs by comparing the plastic elongation strain difference and the buckling inherent strain difference, and in the sixth step, the plastic elongation strain difference is the above When it is determined that buckling occurs larger than the inherent buckling strain difference, the plastic elongation strain difference is the inherent buckling strain difference and the difference between the plastic elongation strain difference and the inherent buckling strain difference, which is the metal The buckling shape conversion elongation strain difference, which is a component that converts to the shape of the plate, is separated into M-1 division of the buckling shape conversion elongation strain difference, and the M-1 divided buckling shape conversion elongation strain difference is and a seventh step of replacing the first buckling inherent strain difference of the repeated calculation with the initial buckling inherent strain difference, and the fifth step determined to be the second and subsequent calculations of the repeated calculation. case, or when it is determined in the sixth step that buckling occurs when the plastic elongation strain difference is greater than the buckling inherent strain difference, the M-1 split buckling shape transformation elongation strain difference and the initial buckling inherent strain difference Using the strain difference, the buckling shape transformation elongation strain difference is corrected, the geometric shape extension strain difference that appears in the shape of the metal plate after out-of-plane deformation, and the corrected buckling shape transformation elongation strain difference An eighth step of calculating the elongation strain error, which is the difference between the elongation strain errors, determining the wave height at which the integrated value of the squares of the elongation strain errors is the minimum value, and determining the wave shape profile; A ninth step of calculating the elastic strain difference inherent in the metal plate after buckling by replacing the strain distribution and adding the elongation strain error, and using the elastic strain difference calculated in the ninth step, elastic strain and a tenth step of calculating a normalized elongation strain difference corresponding to the difference, and performing the number of repetition calculations set in the second step from the second step to the tenth step. there is

A third metal plate shape prediction method (algorithm) includes a first step of setting the plastic elongation strain difference, a second step of setting the number of repetition calculations, and dividing the plastic elongation strain difference into M, In the third step of calculating the plastic elongation strain difference according to the number of iterative calculations, and in the first calculation of the iterative calculation, or in the seventh step below, when the plastic elongation strain difference is less than the buckling intrinsic strain difference In, the plastic elongation strain difference is converted into a normalized normalized elongation strain difference, and if it is determined that buckling occurs after the second time of the repeated calculation and in the seventh step below, A fourth step using the normalized elongation strain difference calculated in 11 steps, and a buckling intrinsic strain difference that serves as a criterion for the occurrence of buckling in the metal plate by performing buckling analysis based on the normalized elongation strain difference. , a fifth step of calculating the wave pitch and the normalized shape profile of the metal plate, and a sixth step of determining whether or not buckling has occurred in the following seventh step, which is one time before the iterative calculation. And, when it is determined that there is no buckling in the sixth step, the seventh step of comparing the plastic elongation strain difference and the buckling intrinsic strain difference to determine whether or not buckling occurs; If it is determined in the step that the plastic elongation strain difference is equal to or less than the buckling intrinsic strain difference and buckling does not occur, the number of times of the iterative calculation is confirmed, and if the number is not the final time, the process returns to the second step. If it is determined that buckling occurs in the eighth step and the sixth step, or if it is determined in the seventh step that the plastic elongation strain difference is greater than the inherent buckling strain difference and buckling occurs, The plastic elongation strain difference is the inherent buckling strain difference, and the difference between the plastic elongation strain difference and the buckling inherent strain difference is the difference between the plastic elongation strain difference and the buckling shape conversion elongation strain difference, which is a component that converts the shape of the metal plate. Separated into 2 A ninth step of determining the wave height at which the integrated value of the power is the minimum value to determine the wave shape profile, replacing the inherent buckling strain difference with the elastic strain distribution and adding the elongation strain error, Using the tenth step of calculating the elastic strain difference inherent in the metal plate and the elastic strain difference calculated in the tenth step, the normalized elongation strain difference corresponding to the elastic strain difference is calculated. and an eleventh step of calculating the number of iterations set in the second step.

In the metal plate shape prediction method, the widthwise distribution of the longitudinal residual stress of the metal plate corresponding to the inherent buckling strain difference may be the thermal stress distribution based on the widthwise temperature distribution before and after cooling.

In the method for predicting the shape of a metal plate, the widthwise distribution of residual stress in the longitudinal direction of the metal plate corresponding to the inherent buckling strain difference may be used as the residual stress distribution imparted at least during rolling or straightening.

In the metal plate shape prediction method, the shape of the metal plate before cooling or the shape of the metal plate after cooling is measured, and the elongation strain difference obtained when it is assumed that the shape has become flat is the plastic elongation strain difference. may be superimposed on

According to another aspect of the present invention, the metal plate shape prediction method is used to determine whether or not shape correction is to be performed in the refining process, and the temperature distribution in the width direction before and after cooling is determined so as not to cause buckling. It is characterized by manufacturing a flat plate by controlling.

In the method for manufacturing a metal plate, the predicted steepness may be used to determine whether or not shape correction is to be performed in the refining process.

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 can be predicted with high accuracy. As a result, the separation of the metal plates necessary for the finishing process can be carried out with high precision. Moreover, by using the shape prediction result of this metal plate, it is also possible to manufacture a flat metal plate.

It is a figure explaining the wave shape used as object. 1 is a flow chart showing a conventional shape prediction method; It is explanatory drawing which shows the shape prediction result of the metal plate at the time of using the conventional shape prediction method and FEM. It is explanatory drawing which shows the shape of the metal plate at the time of using the conventional shape prediction method and FEM. 4 is a flow chart showing a shape prediction method according to the first embodiment; It is an explanatory view showing typically a shape prediction method concerning a 1st embodiment. FIG. 4 is an explanatory diagram showing a shape prediction result of a metal plate when using the shape prediction method according to the first embodiment; FIG. 4 is an explanatory diagram showing a shape prediction result of a metal plate when using the shape prediction method according to the first embodiment; 8 is a flow chart showing a shape prediction method according to the second embodiment; It is explanatory drawing which shows the shape prediction result of a metal plate at the time of using the shape prediction method concerning 2nd Embodiment. It is explanatory drawing which shows the shape prediction result of a metal plate at the time of using the shape prediction method concerning 2nd Embodiment. 9 is a flow chart showing a shape prediction method according to the third embodiment;

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.

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. Then, in this embodiment, a waveform profile distribution h(x, y)=H×W(y)×Sin(2πx/P) obtained by multiplying the standardized profile by the wave leaf amplitude height H is predicted.

<Conventional shape prediction method>
As described above, the present invention is a further development of the invention disclosed in Patent Document 3. Therefore, prior to describing the shape prediction method according to the present embodiment, the conventional shape prediction method disclosed in Patent Document 3 will be described. FIG. 2 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 plate to be evaluated at arbitrary positions y divided by a predetermined width in the plate width direction (y direction) is set. The plastic elongation strain difference Δε _pl (y) is the strain that extends in the longitudinal direction of the metal plate during rolling (hereinafter, “elongation strain” ) is the difference in the width direction. In the following description, the definitions of elongation strain and elongation strain difference are the same.

(Step X2)
At step X2, the plastic elongation strain difference Δε _pl (y) is converted into an elongation strain difference Δε _normal (y) normalized to a value from 0 (zero) to 1 with a maximum value of 1.

(Step X3)
At step X3, eigenvalue analysis calculation is performed using the 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 executing buckling analysis using a wavy buckling equation created based on a model formulated with a triangular residual stress distribution shown in Non-Patent Document 1. . 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 W(y) is output. In the model disclosed in Patent Document 3, the residual stress distribution is input to obtain the buckling stress distribution.

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 (1).
Δε _pl (y)=−(σ _res (y)/E−Max(σ _res (y))/E) (1)

(Step X4)
At step X4, it is determined whether or not buckling occurs. The plastic elongation strain difference Δε _pl (y) and the buckling inherent strain difference Δε _cr (y) are compared, and if Δε _pl (y) is larger than Δε _cr (y), it is determined that the metal plate buckles, and step Proceed to X5. Incidentally, the inherent buckling strain difference Δε _cr (y) has a similar relationship with the plastic elongation strain difference Δε _pl (y), so it can be judged at any position y in the width direction, but here the maximum values of each are used for comparison. ing. 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 X6.

(Step X5)
At step X5, the shape of the metal plate is predicted using the shape prediction model. In the shape prediction model, the 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 the component that remains in the metal plate even after buckling After separating into a component (buckling intrinsic strain difference Δε _cr (y)), it is assumed that the wave pitch P calculated in step X3 based on the buckling shape conversion elongation strain difference Δε _ts (y) does not change. , the geometric elongation strain The shape of the metal plate is predicted by determining the wave leaf amplitude height H so that the error with the difference distribution becomes small. This shape prediction model is similar to the model disclosed in Patent Document 3. However, in the model disclosed in Patent Document 3, stress is used to predict the shape, but here, instead of stress, an elongation strain difference is used.

As described above, the shape of the metal plate (corrugation amplitude height H) is output at step X5, or the fact that the metal plate is flat is output at step X6, and the shape prediction ends.

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

3 and 4 are explanatory diagrams showing the shape of the metal plate when using the conventional shape prediction method and FEM under the same metal plate conditions and the same plastic elongation strain difference. FIG. 3 shows the displacement in the thickness direction in the longitudinal displacement of the width center portion, ie, the displacement in the wave height direction, and FIG. 4 is an enlarged view of the wave height profile of section A in FIG.

Referring to FIG. 3, comparing the conventional shape prediction method and FEM, the wave pitch after buckling is almost the same. On the other hand, referring to FIG. 4, comparing the conventional shape prediction method and FEM, the wave height displacement in the width direction center part is almost the same, but the wave height displacement in the range surrounded by the dotted line in FIG. 4 is different. It was found that there was an error in the shape profile.

The inventors of the present invention conducted extensive studies and found that the cause of this error in the shape profile was that, in the conventional shape prediction method, the shape profile calculated by the buckling peculiar analysis in step X3 maintains the shape profile even after buckling. I found out what I was assuming. 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. In the following description, a metal plate shape prediction method according to the present embodiment will be described based on the above knowledge.

<Shape Prediction Method According to First Embodiment>
A metal plate shape prediction method according to the first embodiment will be described. FIG. 5 is a flow chart showing a shape prediction method according to the first embodiment. FIG. 6 is an explanatory diagram schematically showing the shape prediction method according to the first embodiment. In the first embodiment, steps A2 to A10, which will be described later, are repeated to perform convergence calculation.

(Step A1)
In step A1, as shown in FIG. 6A, the plastic elongation strain difference Δε _pl (y) of the metal plate to be evaluated is set. This step A1 is the same as the above step X1.

(Step A2)
In step A2, the plastic elongation strain difference Δε _pl (y) is converted into a normalized elongation strain difference Δε _normal (y) of 0 to 1 in the first iterative calculation. In the second and subsequent repeated calculations, the normalized elongation strain difference Δε _normal (y) corrected in step A10 described later is used as the normalized elongation strain difference in the subsequent steps. This step A2 is the same as step X2 when there is no repeated calculation.

(Step A3)
In step A3, eigenvalue analysis calculation is performed using the theoretical buckling model. This step A3 is the same as step _X3 above. Buckling inherent strain difference Δε _cr (y) (criteria for occurrence of buckling), which has a similar shape to the elongation strain difference Δε _pl (y), wave pitch P, cross section in the width direction at the time of buckling is based on 0 to 1 A 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 A7 described later, so the plastic elongation strain difference Δε _pl It is not similar to (y).

(Step A4)
At step A4, 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 A5, which will be described later, and in the case of the second and subsequent calculations, the process proceeds to step A6, which will be described later. In step A5, it is determined whether or not buckling occurs. However, in the case of the second and subsequent calculations, since it is determined that the metal plate will buckle, step A5 can be omitted.

(Step A5)
At step A5, it is determined whether or not buckling occurs. This step A5 is the same as the above step X4, and compares the plastic elongation strain difference Δε _pl (y) and the buckling intrinsic strain difference Δε _cr (y). Then, if Δε _pl (y) is greater than Δε _cr (y), it is determined that the metal plate is buckled, and the process proceeds to step A6. 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 at any position y in the width direction, but here, each The maximum value is used for comparison. 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 A11.

(Step A11)
At step A11, similarly to step X6, it is output that the metal plate is flat, and the shape prediction ends. When the metal plate is flat, the plastic elongation strain difference Δε _pl (y) remains in the metal plate as the elastic strain difference Δε _el (y). An elastic strain difference Δε _el (y) is calculated. Furthermore, by the following equation (3), the residual stress σ _res (y) inherent in the metal plate is also calculated by multiplying the elastic strain difference Δε _el (y) calculated by this equation (3) by the Young's modulus E. N represents the number of nodes equally divided in the width direction. Hereinafter, N is the number of nodes.
Δε _el (y)=−(Δε _pl (y)−(ΣΔε _pl (y))/N) (2)
_σres (y)=E× _Δεel (y) (3)

As described above, originally, the longitudinal stress acting on the metal plate overlaps the residual stress component and the tension (unit tension) component that become 0 when integrated in the plate width direction. However, since the tension component is given separately in the buckling model, it is assumed that integration in the strip width direction is 0, that is, the residual stress component is 0 when integrated in the strip width direction or averaged in the strip width direction. The residual stress distribution and the distribution of the plastic elongation strain difference Δε _pl (y) are converted by the equation (1).

(Step A6)
At step A6, the shape of the metal plate is predicted using the shape prediction model. This step A6 is the same as the above step _X5 . First, as shown in FIG. 6(b), the component (buckling shape conversion elongation strain difference Δε _ts (y)) and a component remaining in the metal plate after buckling (specific buckling strain difference Δε _cr (y)). 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 A3 does not change with respect to the buckling shape conversion elongation strain difference Δε _ts (y) calculated from 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 standardized height profile W(y), and the wave pitch P for each width direction position y. It is represented by the following formula (5) using the geometric shape elongation strain difference Δε _gs (y) that appears in the shape due to external deformation. 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), the elongation strain difference Δε _er (y) (hereinafter referred to as “elongation strain error Δε _er (y)”) is expressed by the following equation (7). Then, for example, using the method of least squares, the sum of the squares of the elongation strain error Δε _er (y) represented by the following formula (8) is the minimum value, and the half amplitude H of the half amplitude wave is determined. h(x, y)=H×W(y)×Sin(2πx/P) is predicted as the shape of the metal plate after buckling.
Δε _er (y)=Δε _gs (P, H, W (y))−Δε _ts (y) (7)
Min[Σ(Δε _er (y)) ² ] (8)

(Step A7)
At step A7, 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. 6(d), the elastic buckling inherent strain difference (Δε _{el_cr} (y)) and the elastic elongation strain error (Δε _er (y )) to calculate the elastic strain difference Δε _el ^* (y) inherent in the metal plate that is redistributed by buckling wave generation. Thus, in step A7, the elastic strain difference Δε _el ^* (y) redistributed by shape deformation after buckling is calculated. In addition, it is possible to calculate the residual stress σ _res ^* (y) inherent in the redistributed metal plate by multiplying the elastic strain difference Δε _el ^* (y) by the Young's modulus E according to the following formula (10). Become.
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)
_σres ^* (y)=E× _Δεel ^* (y) (10)

(Step A8)
In step A8, 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 that repeats steps A2 to A10 as described later, the elastic strain difference Δε _el ^* (y) inherent in the redistributed metal plate is used according to the following equation (11) to Determine the normalized elongation strain difference Δε _normal ^* (y) with a value between 0 and 1 corresponding to . FIG. 6(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))) .・(11)

(Step A9)
In _{step A9} , 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 the redistribution is calculated for each width direction position y by the following formula (12). 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 equation (13), Δerror ^* is calculated by accumulating the square error for each position y in the width direction, 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 A10. On the other hand, if the error Δerror ^* is equal to or less than the predetermined threshold, it is determined that the normalized elongation strain difference Δε _normal ^* (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)

(Step A10)
In step A10, the process returns to step A2 to correct the normalized elongation strain difference Δε _normal (y) used in the recalculation using Δε _normal ^* (y) and Δerror(y). Specifically, according to the following formula (14), 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)} (14)

Next, returning to step A2, the following steps A3 to A10 are performed using the normalized elongation strain difference Δε _normal (y) corrected in step A10. Then, steps A2 to A10 are repeated, and convergence calculation is performed until it is determined in step A9 that the standardized elongation strain difference Δε _normal ^* (y) has converged.

(Step A12)
When it is determined in step A9 that the normalized elongation strain difference Δε _normal ^* (y) has converged, the process proceeds to step A12 and shape prediction ends. Then, 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.

Note that when the normalized elongation strain difference Δε _normal ^* (y) converges in this way, the elastic strain difference Δε _el ^* (y) inherent in the plate even after buckling can be calculated from the above-described equations (9) and (10) as Residual stress σ _res that remains in the metal plate and is inherent in the metal plate is also calculated by multiplying the Young's modulus E.

Here, as described above, in the conventional shape prediction method, it was assumed that the shape profile would be maintained even after buckling. Since the influence was not taken into consideration, an error in the shape profile as shown in FIG. 4 occurred.

In this regard, the inventors have found that the shape profile changes due to shape deformation after buckling. Then, according to the shape prediction 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.

In order to verify the effect of the first embodiment, the present inventors used the shape prediction result (convergent solution) obtained by the first embodiment with the shape prediction result obtained by the conventional shape prediction method, It was compared with the analysis result by FEM. The verification results are shown in FIGS. 7 and 8. FIG. FIG. 7 shows the widthwise distribution of the elastic strain difference inherent in the metal plate after buckling, and FIG. 8 shows the widthwise distribution of the normalized profile.

Referring to FIGS. 7 and 8, while the conventional shape prediction results are slightly different from the FEM analysis results, 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.

<Shape Prediction Method According to Second Embodiment>
A shape prediction method according to the second embodiment will be described. FIG. 9 is a flow chart showing a shape prediction method according to the second embodiment.

In the shape prediction method of the second embodiment, the technical feature of performing recalculation with the elastic strain difference redistributed by the generation of the shape profile generated after buckling is the same as the shape prediction method of the first embodiment. common. However, while the first embodiment performs convergence calculation, the second embodiment repeats steps B2 to B10 described later to perform sequential calculation.

(Step B1)
In step B1, the plastic elongation strain difference Δε _pl (y) of the metal plate to be evaluated is set. This step B1 is the same as the above step A1.

(Step B2)
In step B2, the number of repetition calculations (sequential calculations) is set, and it is determined what number of calculations are currently being performed. In this embodiment, the number of iterative calculations is M times. Also, in the following description, the calculation currently being performed is referred to as the i-th calculation.

(Step B3)
In step B3, in the first iterative calculation (i=1), the plastic elongation strain difference Δε _pl (y) is converted into a normalized 0 to 1 normalized elongation strain difference Δε _normal (y). In the calculation after the second iteration (i = 2 or later), the normalized elongation strain difference Δε _normal ^* (y) corrected in step B10 described later is replaced with Δε _normal (y) and used in the following steps. It is the standardized elongation strain difference.

(Step B4)
In step B4, an eigenvalue analysis calculation is performed using the theoretical buckling model, and the buckling intrinsic strain difference Δε _cr (y), the wave pitch P, and the normalized height profile (shape profile) W (y) of 0-1 are calculated. calculate. This step _B4 is the same as step A3 above. Buckling inherent strain difference Δε _cr (y) (criteria for occurrence of buckling), which has a similar shape to the elongation strain difference Δε _pl (y), wave pitch P, cross section in the width direction at the time of buckling is based on 0 to 1 A height profile (shape profile) W(y) is output.

(Step B5)
At step B5, it is determined whether the calculation is the first (i=1) of the repeated calculations or the second or later (i=2 or later) calculations. Then, in the case of the first calculation, the process proceeds to step B6, which will be described later, and in the case of the second and subsequent calculations, the process proceeds to step B8, which will be described later. In step B6, it is determined whether or not buckling occurs. In the case of the second and subsequent calculations, it is determined that the metal plate will buckle, so steps B6 and B7 can be omitted.

(Step B6)
At step B6, it is determined whether or not buckling occurs. This step B6 is the same as the above step A5, and compares the plastic elongation strain difference Δε _pl (y) and the buckling intrinsic strain difference Δε _cr (y). Then, if Δε _pl (y) is larger than Δε _cr (y), it is determined that the metal plate is buckled, and the process proceeds to step B7. 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 B12.

(Step B12)
At step B12, it is output that the metal plate is flat, and the shape prediction ends. The elastic strain difference Δε _el (y) and the residual stress σ _res (y) inherent in the metal plate are also calculated from the above equations (2) and (3). This step B12 is the same as the above step A11.

(Step B7)
In step B7, the shape of the metal plate for each iterative calculation (sequential calculation) is predicted using a shape prediction model. Specifically, first, according to the above formula (4), the component (buckling shape conversion elongation strain difference Δε _ts (y)) that converts the plastic elongation strain difference Δε _pl (y) into the shape deformation after buckling, After buckling, the strain is separated from the component remaining in the metal plate (specific buckling strain difference Δε _cr (y)). Furthermore, using the following formula (15), the buckling shape conversion elongation strain difference Δε _ts (y) is divided by M−1 to calculate the M−1 divided buckling shape conversion elongation strain difference Δε _ts '(y). do. Then, as shown in the following equation (16), the first buckling specific strain difference Δε _cr (y) is read as the initial buckling specific strain difference Δε _cr ′(y).
Δε _ts ′(y)=(Δε _pl (y)−Δε _cr (y))/(M−1) (15)
Δε _cr ′(y)=Δε _cr (y) (16)

(Step B8)
In step B8, the shape of the metal plate in each iterative calculation (sequential calculation) is predicted using a shape prediction model. Specifically, first, the buckling shape conversion elongation strain difference Δε _ts (y) is calculated by the following formula (17). That is, in this calculation, using the M−1 split buckling shape conversion elongation strain difference Δε _ts '(y) and the initial buckling intrinsic strain difference Δε _cr '(y) calculated in step B7, the buckling shape conversion The elongation strain difference Δε _ts (y) is corrected.
Δε _ts (y)=(Δε _ts '(y)×(i−1)+Δε _cr '(y))−Δε _cr (y) (17)

The subsequent shape prediction of the metal plate is the same as step A6. That is, using the buckling shape transformation elongation strain difference Δε _ts (y) calculated by the above equation (17), the geometric shape elongation strain difference Δε _gs (y) and the elongation are obtained by the above equations (6) and (7). By calculating the strain error Δε _er (y) and determining the maximum amplitude H of the single amplitude wave where the integrated value of the square of the elongation strain error Δε _er (y) shown in the above formula (8) is the minimum value Predict h(x, y)=H×W(y)×Sin(2πx/P) as the shape of the metal plate after buckling.

(Step B9)
In step B9, the elastic strain difference Δε _el ^* (y) and the residual stress σ _res ^* (y) inherent in the metal plate are calculated from the above equations (9) and (10). This step B9 is the same as the above step A7.

(Step B10)
In step B10, 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, according to the above equation (11), using the elastic strain difference Δε _el ^* (y) inherent in the redistributed metal plate, the normalized elongation strain difference having a value of 0 to 1 corresponding to this Determine Δε _normal ^* (y). This step B10 is the same as the above step A8. Then, this normalized elongation strain difference Δε _normal ^* (y) returns to step B2 and becomes the normalized elongation strain difference used for recalculation.

Next, the process returns to step B2 to perform the second and subsequent iterative calculations. In the second and subsequent iterative calculations, the normalized elongation strain difference Δε _normal ^* (y) calculated in step B10 one time before is replaced with Δε _normal (y), and the subsequent steps B4 to B10 are performed. .

(Step B11)
The above steps B2 to B10 are repeated M times, and the shape prediction ends. Then, the wave amplitude height H at this time is predicted as the shape of the metal plate. Note that when the normalized elongation strain difference Δε _normal ^* (y) converges in this way, the elastic strain difference Δε _el ^* (y) inherent in the plate even after buckling can be calculated from the above-described equations (9) and (10) as Residual stress σ _res that remains in the metal plate and is inherent in the metal plate is also calculated by multiplying the Young's modulus E.

The above-described second embodiment can also enjoy the same effects as the first embodiment. That is, the elastic strain difference Δε _el ^* (y) redistributed due to the shape deformation after buckling is calculated, and recalculation is performed using the elastic strain difference Δε _el ^* (y). Shapes can be reasonably predicted.

In order to verify the effect of the second embodiment, the present inventors investigated the shape prediction result of the second embodiment, the shape prediction result of the first embodiment, and the conventional shape. The shape prediction result obtained by the prediction method was compared with the analysis result by FEM. The verification results are shown in FIGS. 10 and 11. FIG. FIG. 10 shows the widthwise distribution of the elastic strain difference inherent in the metal plate after buckling, and FIG. 11 shows the widthwise distribution of the normalized profile.

Referring to FIGS. 10 and 11, the conventional shape prediction results are slightly different from the FEM analysis results, whereas the shape prediction results of the first and second embodiments are different from the FEM analysis results. They are almost identical. Therefore, according to the second embodiment, it was found that the shape of the metal plate can be predicted appropriately.

<Shape Prediction Method According to Third Embodiment>
A shape prediction method according to the third embodiment will be described. FIG. 12 is a flow chart showing a shape prediction method according to the third embodiment.

In the second embodiment described above, the buckling shape conversion elongation strain difference Δε _ts (y) was sequentially calculated by dividing it by M−1 in step B7, but in the third embodiment, it was set in step C1 Perform sequential calculation by dividing the plastic elongation strain difference Δε _pl (y) into M

(Steps C1-C2)
In step C1, the plastic elongation strain difference Δε _pl (y) of the metal plate to be evaluated is set, and in step C2, the number of repeated calculations (sequential calculations) is set (M times), and the calculation currently being performed is It is determined what time (i-th time) the calculation is. These steps C1-C2 are the same as steps B1-B2, respectively.

(Step C3)
In step C3, the plastic elongation strain difference Δε _pl (y) of the metal plate to be evaluated, which is set in step C1, is divided by M to define the plastic elongation strain difference for sequential calculation. Specifically, the M-divided plastic elongation strain difference Δε _pl '(y) is calculated by the following formula (18), and the following formula (19) is used to calculate the plastic elongation strain difference Δε _pl (y) at the i-th iteration calculation. Define (calculate)
Δε _pl ′(y)=Δε _pl (y)/M (18)
Δε _pl (y)=Δε _pl ′(y)×i (19)

(Step C4)
In step C4, in the first iterative calculation (i=1), the plastic elongation strain difference Δε _pl (y) is converted into a normalized 0 to 1 normalized elongation strain difference Δε _normal (y). When it is determined that buckling does not occur in the buckling presence/absence determination in step C7 described later (buckling presence/absence determination before the repetitive calculation) in the second and subsequent iterative calculations (i=2 and subsequent). , transforming the plastic elongation strain difference Δε _pl (y) into a normalized elongation strain difference Δε _normal (y). On the other hand, in the buckling presence/absence determination in step C7, if it is determined that buckling occurs, the normalized elongation strain difference Δε _normal ^* (y) corrected in step C11 described later is read as Δε _normal (y), and the following This is the standardized elongation strain difference in the subsequent steps.

(Step C5)
In step C5, eigenvalue analysis calculation is performed using the theoretical buckling model, and the buckling intrinsic strain difference Δε _cr (y), the wave pitch P, and the normalized height profile (shape profile) W (y) of 0-1 are calculated. calculate. This step _C5 is the same as step B4 above. Buckling inherent strain difference Δε _cr (y) (criteria for occurrence of buckling), which has a similar shape to the elongation strain difference Δε _pl (y), wave pitch P, cross section in the width direction at the time of buckling is based on 0 to 1 A height profile (shape profile) W(y) is output.

(Step C6)
In step C6, the next step is determined based on the result of the buckling presence/absence determination in step C7 described later (buckling presence/absence determination one time before repeated calculation). If it is determined that buckling does not occur in step C7, the process proceeds to step C7, and if it is determined that buckling occurs, the process proceeds to step C9. Once it is determined that buckling occurs, the buckling presence/absence determination in step C7 can be omitted.

(Step C7)
At step C7, it is determined whether or not buckling occurs. This step C7 is the same as the above step B6, and compares the plastic elongation strain difference Δε _pl (y) and the buckling intrinsic strain difference Δε _cr (y). Then, if Δε _pl (y) is greater than Δε _cr (y), it is determined that the metal plate is buckled, and the process proceeds to step C9. 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 B8.

(Step C8)
At step C8, it is determined whether the calculation is the final iteration (i=M) or the previous calculation (before i=M−1). Then, if the number of iterative calculations is before the final one, the process returns to step C2, and subsequent steps C3 and subsequent steps are performed. This is to confirm whether or not the metal plate will finally buckle, although it was determined in the sequential calculation that the metal plate would not buckle. On the other hand, if it is the final M-th calculation, it is finally determined that the metal plate is flat without buckling, and the process proceeds to step C13.

(Step C13)
At step C13, it is finally output that the metal plate is flat, and the shape prediction ends. The elastic strain difference Δε _el (y) and the residual stress σ _res (y) inherent in the metal plate are also calculated from the above equations (2) and (3). This step C13 is the same as step B12.

(Step C9)
At step C9, the shape of the metal plate is predicted using the shape prediction model. This step C9 is the same as the above step A6, the buckling shape conversion elongation strain difference Δε _ts (y) is calculated by the above formula (4), and the geometric shape elongation strain is calculated by the above formulas (6) and (7). Calculate the difference Δε _gs (y) and the elongation strain error Δε _er (y), and the sum of the squares of the elongation strain error Δε _er (y) shown in the above formula (8) is the minimum value of the single amplitude wave By determining the maximum amplitude H, h(x, y)=H×W(y)×Sin(2πx/P) is predicted as the shape of the metal plate after buckling.

(Step C10)
In step C10, the elastic strain difference Δε _el ^* (y) and the residual stress σ _res ^* (y) inherent in the metal plate are calculated from the above equations (9) and (10). This step C10 is the same as the above step B9.

(Step C11)
In step C11, the normalized elongation strain difference Δε _normal ^* (y) is determined again based on the redistributed residual stress distribution of the metal plate after buckling, and the corrected normalized Determine the elongation strain difference Δε _normal ^* (y). This step C11 is the same as step B10.

Next, the process returns to step C2 and repeats the calculation. In such repeated calculation, subsequent steps B4 to B11 are performed using the normalized elongation strain difference Δε _normal ^* (y) calculated in step C11 one time before.

(Step C12)
The above steps C2 to C11 are repeated M times, and the shape prediction ends. Then, the wave amplitude height H at this time is predicted as the shape of the metal plate. Note that when the normalized elongation strain difference Δε _normal ^* (y) converges in this way, the elastic strain difference Δε _el ^* (y) inherent in the plate even after buckling can be calculated from the above-described equations (9) and (10) as Residual stress σ _res that remains in the metal plate and is inherent in the metal plate is also calculated by multiplying the Young's modulus E.

The third embodiment described above can also enjoy the same effects as those of the first and second embodiments. That is, the elastic strain difference Δε _el ^* (y) redistributed due to the shape deformation after buckling is calculated, and recalculation is performed using the elastic strain difference Δε _el ^* (y). Shapes can be reasonably predicted.

<Other embodiments>
Regarding the inherent buckling strain difference Δε _cr (y) that is separated from the plastic elongation strain difference Δε _pl (y) in steps A6, B7, and C9 above and remains in the metal plate even after buckling, The residual stress of the metal plate corresponding to the strain difference Δε _cr (y) is considered in the FEM analysis results considering the transformation during cooling, and the residual stress distribution in the longitudinal direction across the width of the metal plate is It was confirmed that the thermal stress based on the temperature distribution in the width direction would suffice. 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 at the time of cooling only by measuring the temperature.

In addition, the residual stress of the metal plate corresponding to the above-described inherent buckling strain difference Δε _cr (y) is added to the width direction distribution of the measured longitudinal direction residual stress of the metal plate, at least the residual stress given during rolling or straightening. It may be defined by summing the distributions. In such a case, the residual stress distribution and cold shape after rolling or straightening of the metal sheet without controlled cooling can be predicted.

In addition, the shape of the metal plate before cooling or the shape of the metal plate after cooling is measured with respect to the plastic elongation strain difference Δε _pl (y) set in steps A1, B1, and C1, and the shape becomes flat. The elongation strain differences obtained for the hypothetical cases may be superimposed. In such a 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 the shape with higher accuracy, and the accuracy of determining whether the shape can be corrected is improved.

A flat metal plate can be manufactured by using the metal plate shape prediction method according to the first embodiment, the second embodiment, or the third embodiment.

Specifically, the shape of the metal plate is predicted according to the above-described embodiment, and whether or not to perform shape correction in the refining process is determined based on the prediction result. In such a case, the shape can be predicted with high accuracy, so that a flat plate can be manufactured by controlling the temperature distribution in the width direction before and after cooling so as not to cause buckling.

Here, in addition to the presence or absence of buckling, the determination of whether or not to perform shape correction in the finishing process depends on the flatness according to the user's needs, such as 2% or less, 1% or less, or 0.5% or less. etc. may be used as a standard. In such a case, it is more practical to provide judgment criteria according to the user's needs, instead of judging only by the presence or absence of buckling.

Therefore, the predicted steepness may be used to determine whether or not to perform shape correction in the above-described refinement process. In this case, it is not determined by the presence or absence of buckling, but by a predetermined steepness, so it is possible to rank the flatness of the metal plate, and it is possible to determine the application of the straightening process according to the rank and the customer's needs. It becomes possible. Therefore, it becomes possible to make a judgment within a more practical range, and it is possible to optimize the correction process.

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

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

As a result, the erroneous detection rate of determining that the shape is good even though the shape is bad and requires a fine threading plate was 1% (2 coils out of 200 coils) in the comparative example, whereas it was 0 in the example of the present application. % (2 coils out of 200 coils).

INDUSTRIAL APPLICABILITY The present invention is useful in predicting and controlling the shape of a rolled metal plate.

Claims (9)

This is a method for predicting the shape of a metal plate. When predicting the wave shape after buckling based on the plastic elongation strain difference given to the metal plate, the elastic strain difference inherent in the metal plate even after buckling is used. A method for predicting the shape of a metal plate, characterized in that the corrugation profile is determined by the buckling analysis used. A first step of setting the plastic elongation strain difference;
In the first calculation of the repeated calculation, the plastic elongation strain difference is converted to a normalized normalized elongation strain difference, and in the second and subsequent calculations of the repeated calculation, the standard calculated in the tenth step below a second step using the strain difference;
A buckling analysis is performed based on the normalized elongation strain difference, and a buckling inherent strain difference, a wave pitch, and a normalized shape profile of the metal plate, which are criteria for determining the occurrence of buckling in the metal plate, are calculated. a third step;
A fourth step of determining whether it is the first calculation of the repeated calculation or the calculation after the second time;
If it is determined that the fourth step is the first calculation of the repeated calculation, the fifth step of determining whether or not buckling occurs by comparing the plastic elongation strain difference and the buckling intrinsic strain difference When,
If it is determined in the fourth step that the calculation is the second or later iterative calculation, or in the fifth step it is determined that the plastic elongation strain difference is greater than the buckling intrinsic strain difference and that buckling occurs In the case, the plastic elongation strain difference is the buckling inherent strain difference and the buckling shape conversion elongation strain, which is the difference between the plastic elongation strain difference and the buckling inherent strain difference and is a component that converts the shape of the metal plate. The 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 conversion elongation strain difference, is calculated, and the elongation strain is calculated. a sixth step of determining the waveform profile by obtaining the wave height at which the integrated value of the square of the error is the minimum value;
a seventh step of adding the elastic buckling inherent strain difference and the elongation strain error to calculate the elastic strain difference inherent in the metal plate after buckling;
An eighth step of calculating a normalized elongation strain difference corresponding to the elastic strain difference using the elastic strain difference calculated in the seventh step;
Calculate the error between the standardized elongation strain difference set in the second step and the standardized elongation strain difference calculated in the eighth step, and compare the square of the error with a predetermined threshold A ninth step When,
A tenth step of correcting the normalized 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 larger than a predetermined threshold in the ninth step; has
2. The metal plate shape prediction method according to claim 1, wherein the second step to the tenth step are repeated until the square of the error in the ninth step becomes equal to or less than a predetermined threshold value. A first step of setting the plastic elongation strain difference;
a second step of setting the number of iterations;
In the first calculation of the repeated calculation, the plastic elongation strain difference is converted to a normalized normalized elongation strain difference, and in the second and subsequent calculations of the repeated calculation, the standard corrected in the tenth step below a third step using the change elongation strain difference;
A buckling analysis is performed based on the normalized elongation strain difference, and a buckling inherent strain difference, a wave pitch, and a normalized shape profile of the metal plate, which are criteria for determining the occurrence of buckling in the metal plate, are calculated. a fourth step;
A fifth step of determining whether it is the first calculation of the repeated calculation or the calculation after the second time;
If it is determined that the fifth step is the first calculation of the repeated calculation, the sixth step of determining whether or not buckling occurs by comparing the plastic elongation strain difference and the buckling intrinsic strain difference When,
When it is determined in the sixth step that the plastic elongation strain difference is greater than the buckling inherent strain difference and that buckling occurs, the plastic elongation strain difference is defined as the buckling inherent strain difference and the plastic elongation strain difference. The buckling shape transformation elongation strain difference, which is the difference in the buckling intrinsic strain difference and is the component that converts to the shape of the metal plate, is separated into M−1 division of the buckling shape transformation elongation strain difference, A seventh step of calculating the M-1 split buckling shape conversion elongation strain difference and replacing the first buckling inherent strain difference of the repeated calculation with the initial buckling inherent strain difference;
If it is determined in the fifth step that the calculation is the second or later calculation of the repeated calculation, or in the sixth step it is determined that the plastic elongation strain difference is greater than the buckling intrinsic strain difference and that buckling occurs In the case, the M-1 split buckling shape conversion elongation strain difference and the initial buckling intrinsic strain difference are used to correct the buckling shape conversion elongation strain difference, and the geometry that appears in the shape of the metal plate after out-of-plane deformation Calculate the elongation strain error, which is the difference between the mechanical shape elongation strain difference and the corrected buckling shape conversion elongation strain difference, and obtain the wave height at which the integrated value of the square of the elongation strain error is the minimum value. an eighth step of determining a wave shape profile by
a ninth step of replacing the inherent buckling strain difference with an elastic strain distribution and adding the elongation strain errors to calculate the elastic strain difference inherent in the metal plate after buckling;
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,
2. The metal plate shape prediction method according to claim 1, wherein said second step to said tenth step are repeated the number of times set in said second step. A first step of setting the plastic elongation strain difference;
a second step of setting the number of iterations;
A third step of dividing the plastic elongation strain difference by M and calculating the plastic elongation strain difference according to the number of repeated calculations;
In the first calculation of the repeated calculation, or when the plastic elongation strain difference is less than the buckling intrinsic strain difference in the seventh step below, the plastic elongation strain difference is normalized to the normalized elongation strain difference If it is determined that buckling occurs in the second and subsequent repeated calculations and in the seventh step below, a fourth step using the standardized elongation strain difference calculated in the eleventh step below;
A buckling analysis is performed based on the normalized elongation strain difference, and a buckling inherent strain difference, a wave pitch, and a normalized shape profile of the metal plate, which are criteria for determining the occurrence of buckling in the metal plate, are calculated. a fifth step;
A sixth step of determining whether or not buckling has occurred in the following seventh step, which is one time before the repeated calculation;
a seventh step for determining whether or not buckling occurs by comparing the plastic elongation strain difference and the buckling intrinsic strain difference when it is determined that there is no buckling in the sixth step;
If it is determined in the seventh step that the plastic elongation strain difference is equal to or less than the buckling intrinsic strain difference and buckling does not occur, the number of iterations is checked, and if the number is not the final time, the second an eighth step returning to a step;
If it is determined that there is buckling in the sixth step, or if it is determined in the seventh step that the plastic elongation strain difference is greater than the inherent buckling strain difference and buckling occurs, the plastic elongation strain difference is , the buckling intrinsic strain difference, and the buckling shape transformation elongation strain difference, which is the difference between the plastic elongation strain difference and the buckling intrinsic strain difference and is the component that converts to the shape of the metal plate, and the surface Calculate the elongation strain error, which is the difference between the geometric shape elongation strain difference that appears in the shape of the metal plate after external deformation and the buckling shape conversion elongation strain difference, and the integrated value of the square of the elongation strain error a ninth step of determining the wave shape profile by obtaining the minimum wave height;
a tenth step of replacing the inherent buckling strain difference with an elastic strain distribution and adding the elongation strain errors to calculate the elastic strain difference inherent in the metal plate after buckling;
and an eleventh step of calculating a standardized elongation strain difference corresponding to the elastic strain difference using the elastic strain difference calculated in the tenth step,
2. The metal plate shape prediction method according to claim 1, wherein said second step to said eleventh step are repeated the number of times set in said second step. Claims 2 to 3, wherein the widthwise distribution of the residual stress in the longitudinal direction of the metal plate corresponding to the inherent buckling strain difference is a thermal stress distribution based on the temperature distribution in the widthwise direction before and after cooling. 5. The metal plate shape prediction method according to any one of 4. 5. The distribution of residual stress in the longitudinal direction corresponding to the inherent buckling strain difference in the width direction of the metal plate is defined as the residual stress distribution imparted at least during rolling or straightening. The method for predicting the shape of the metal plate according to item 1. The shape of the metal plate before cooling or the shape of the metal plate after cooling is measured, and the elongation strain difference obtained when it is assumed that the shape is flattened is superimposed on the plastic elongation strain difference, The metal plate shape prediction method according to any one of claims 2 to 4. Determine whether or not to perform shape correction in the refinement process by the metal plate shape prediction method according to any one of claims 1 to 7, and the width before and after cooling so as not to buckle A method for producing a metal plate, characterized in that a flat plate is produced by controlling a directional temperature distribution. 9. The method of manufacturing a metal plate according to claim 8, wherein a predicted steepness is used to determine whether or not shape correction is to be performed in the finishing step.

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