JP7570118B2 - Calculation method for heating plan used in bending metal plate by line heating - Google Patents

Description

The present invention relates to a method for calculating a heating plan to be used in bending a metal plate by line heating.

Ships have complex curved shapes in the bow, bulbous bow, stern, etc. To create these curved shapes, multiple steel plates are bent and then joined by welding. Line heating is widely used as a bending technique in the shipbuilding industry.
Linear heating utilizes the thermal deformation that occurs when the surface of a steel plate is heated with a gas burner, and is a technology that has been used for a long time in many shipyards in Japan. When bending a steel plate using linear heating, the steel plate is locally heated with the flame of a gas burner and the heated area is rapidly cooled by pouring water on the steel plate, which causes plastic deformation in the steel plate. This plastic deformation can be controlled by adjusting the heat input to the steel plate by changing the moving speed of the gas burner that heats the plate, the mixture ratio of the combustion gas and the inflowing oxygen, the distance between the burner and the steel plate, etc. In addition, bending using linear heating is a processing technology that brings the steel plate closer to the desired curved shape by arranging multiple heating wires in appropriate positions.
However, the deformation that occurs during line heating is complex, involving a mixture of vertical and horizontal shrinkage and vertical and horizontal bending, and is extremely difficult to predict because it depends on the amount of heat input, the moving speed of the gas burner, the heating position, etc., so bending by line heating is one of the technologies that is considered difficult to automate.
A method for calculating a heating plan used to realize automation of bending processing by line heating has been proposed (see, for example, Patent Document 1).

JP 2013-66902 A

In the conventional heating plan calculation method, the heating plan is calculated based on the target inherent strain calculated from the target shape, so complex correction is required in areas where heating lines are densely packed.
The present invention has been made in consideration of the above circumstances, and provides a calculation method capable of calculating a heating plan including a plurality of heating lines that is optimal for bringing a metal plate closer to a target shape.

The present invention is a method for calculating a heating plan used in bending a metal plate by line heating, comprising a first step of performing a finite element method structural analysis under a first heating condition including at least one first heating wire set at a first position of an analysis model of the metal plate, and repeating a first trial in which the analysis result is compared with a target shape by changing the position of the first heating wire; a second step of selecting, as a first selected heating wire, at least one first heating wire set in a first trial in which the analysis result of the repeated first trials is closest to the target shape; and a second step of selecting the first selected heating wire and at least one second heating wire set at a second position of the analysis model. a third step of performing a finite element method structural analysis under second heating conditions including a first heating condition and a second trial of comparing the analysis result with a target shape by changing the position of the second heating wire, and a fourth step of selecting, as a second selected heating wire, at least one second heating wire set in a second trial in which the analysis result approaches the target shape among the repeated second trials, wherein the heating plan includes first and second selected heating wires, and in the first or third step, the analysis result and the target shape are divided into a plurality of blocks, and the analysis result and the target shape are compared for each block.

According to the calculation method of the present invention, the heating wire that approaches the target shape is repeatedly selected from the heating wires set at various positions, so that it is possible to calculate a heating plan including a plurality of heating wires that is optimal for making the metal plate approach the target shape. In addition, by heating the metal plate based on the calculated heating plan, it is possible to deform the metal plate into a shape that is close to the target shape.
In the calculation method of the present invention, in the first or third step, the analysis result and the target shape are divided into a plurality of blocks, and the analysis result and the target shape are compared for each block, so that it is possible to appropriately evaluate a complex shape. Therefore, it is possible to create a heating plan for a complex target shape. In addition, it is possible to create a heating plan with fewer selected heating lines.

1 is a flowchart of a calculation method according to an embodiment of the present invention. 4A to 4C are diagrams illustrating a calculation method according to one embodiment of the present invention. FIG. 11 is an explanatory diagram of a method for setting a heating line included in a calculation method according to an embodiment of the present invention. FIG. 11 is an explanatory diagram of a method for selecting elements on a heating line included in a calculation method according to an embodiment of the present invention. 10 is an explanatory diagram of a comparison between an analysis result included in a calculation method according to an embodiment of the present invention and a target shape. 10 is an explanatory diagram of a comparison between an analysis result included in a calculation method according to an embodiment of the present invention and a target shape. (a) to (e) are heating methods calculated in the simulation. 4(a) to 4(d) are the results of structural analysis based on the calculated heating plan. (a) is the target shape (bowl-shaped) used in the simulation, and (b) is the analysis result of the structural analysis based on the calculated heating plan. 10 is a graph comparing the target shape and the analysis results along the dashed line A-A' shown in FIGS. 9(a) and 9(b). 10 is a graph comparing the target shape and the analysis results along the dashed dotted line B-B' shown in FIGS. 9(a) and 9(b). (a) is the target shape (saddle shape) used in the simulation, and (b) is the analysis result of the structural analysis based on the calculated heating plan. This is a heating method calculated in a simulation. 13 is a graph comparing the target shape and the analysis results along the dashed line A-A' shown in FIGS. 12(a) and 12(b). 13 is a graph comparing the target shape and the analysis results along the dashed line B-B' shown in FIGS. 12(a) and 12(b). (a) is the target shape (twisted type) used in the simulation, and (b) is the analysis result of the structure analysis based on the calculated heating plan. This is a heating method calculated in a simulation. 17 is a graph comparing the target shape and the analysis results along the dashed line A-A' shown in FIGS. 16(a) and 16(b). 17 is a graph comparing the target shape and the analysis results along the dashed line B-B' shown in FIGS. 16(a) and 16(b). 1 is a graph showing a change in error between an analysis result and a target shape with an increase in the number of selected heating wires in the process of creating a heating plan. FIG. 11 is an explanatory diagram of a method for calculating an evaluation value by comparing an analysis result with a target shape for each block. FIG. This is a heating method (selected heating wires: 200 wires) created through structural analysis. The results of structural analysis using the created heating plan (created shape) and the difference between the structural analysis results and the target shape. 13 is a graph showing a change in error (sum of squared error of Z displacement) between the analysis result and the target shape with an increase in the number of selected heating lines in the heating plan creation process. (a) shows the result of structural analysis (created shape) using a heating plan (selected heating wires: 60 wires) created by evaluating the analysis results without dividing the wire and performing structural analysis, and (b) shows the error between the result of this structural analysis and the target shape. (a) shows the result of structural analysis (created shape) using a heating plan (selected heating wires: 60 wires) created by dividing the analysis result and target shape into 100 parts, evaluating the analysis result, and performing structural analysis, and (b) shows the error between the result of this structural analysis and the target shape. 13 is a graph showing a change in error (sum of squared error of Z displacement) between the analysis result and the target shape with an increase in the number of selected heating lines in the heating plan creation process. 13 is a graph showing a change in error (sum of squared error of Z displacement) between the analysis result and the target shape with an increase in the number of selected heating lines in the heating plan creation process.

The present invention is a method for calculating a heating plan used in bending a metal plate by line heating, comprising a first step of performing a finite element method structural analysis under first heating conditions including at least one first heating wire set at a first position of an analytical model of the metal plate, and repeating a first trial in which the analysis result is compared with a target shape by changing the position of the first heating wire; a second step of selecting, as a first selected heating wire, at least one first heating wire set in a first trial in which the analysis result of the first trial is closer to the target shape; a third step of performing a finite element method structural analysis under second heating conditions including the first selected heating wire and at least one second heating wire set at a second position of the analytical model, and repeating a second trial in which the analysis result is compared with a target shape by changing the position of the second heating wire; and a fourth step of selecting, as a second selected heating wire, at least one second heating wire set in a second trial in which the analysis result of the second trial is closer to the target shape. In the first or third step, the analysis result and the target shape are divided into a plurality of blocks, and the analysis result and the target shape are compared for each block.

The heating plan includes first and second selected heating lines, and the analysis model is a finite element model having a plurality of elements and a plurality of nodes. In the first step, the analysis result is compared with the target shape using one of the curvature and the displacement at the nodes, and in the third step, the analysis result is compared with the target shape using the other of the curvature and the displacement at the nodes. By changing the way of comparison in this way, it is possible to improve both the calculation speed and accuracy.

In the calculation method of the present invention, if the target shape has either positive curvature or negative curvature, it is preferable that in the first and third steps, the analysis result is compared with the target shape using the curvature at the node, and if the target shape has both positive curvature and negative curvature, it is preferable that in the first and third steps, the analysis result is compared with the target shape using the displacement at the node. This makes it possible to create an excellent heating plan that can steadily bring the analysis result closer to the target shape.

The metal plate has a front surface and a back surface. Under the first heating condition, it is preferable that the first heating line is set on either the front surface or the back surface, and under the second heating condition, it is preferable that the second heating line is set on either the front surface or the back surface. In addition, the fourth step is preferably a step of selecting at least one second heating line set in the second trial in which the analysis result of the repeated second trials is close to the target shape, and selecting, as the second selected heating line, the second heating line set on the same surface as the surface on which the first selected heating line is set, from the selected second heating lines. This makes it possible to suppress frequent switching of the heating surface on which the selected heating line is set, and improves the efficiency of bending processing using the heating plan.

The fourth step is preferably a step of selecting at least one second heating wire set in the second trial in which the analysis result is close to the target shape among the repeated second trials, and selecting the second heating wire with the smallest bending amount among the selected second heating wires as the second selected heating wire. This makes it possible to prevent the bending amount from becoming too large, and to reduce the number of selected heating wires included in the heating plan.

The present invention will be described in more detail below with reference to several embodiments. The configurations shown in the drawings and the following description are examples, and the scope of the present invention is not limited to those shown in the drawings and the following description.

Fig. 1 is a flow chart of the calculation method of this embodiment, Fig. 2(a) to (c) are explanatory diagrams of the calculation method, Fig. 3 is an explanatory diagram of a method of setting a heating line, and Fig. 4 is an explanatory diagram of a method of selecting elements on a heating line.
The calculation method of this embodiment is a calculation method for a heating plan 6 used in bending a metal plate by line heating. The calculation method of this embodiment also includes a first step of performing a finite element method structural analysis under a first heating condition including at least one first heating wire 4 set at a first position of the analysis model 2 of the metal plate, and repeating a first trial in which the analysis result 3 is compared with the target shape 10 by changing the position of the first heating wire 4; a second step of selecting, as a first selected heating wire 5, at least one first heating wire 4 set in the first trial in which the analysis result 3 is closer to the target shape 10 among the repeated first trials; a third step of performing a finite element method structural analysis under a second heating condition including the first selected heating wire 5 and at least one second heating wire 4 set at a second position of the analysis model 2, and repeating a second trial in which the analysis result 3 is compared with the target shape 10 by changing the position of the second heating wire 4; and a fourth step of selecting, as a second selected heating wire 5, at least one second heating wire 4 set in the second trial in which the analysis result 3 is closer to the target shape 10 among the repeated second trials.
The analysis model 2 is a finite element model having a plurality of elements 8 and a plurality of nodes 9. In a first step, the analysis result 3 is compared with the target shape 10 using one of the curvature and the displacement amount at the nodes 9, and in a third step, the analysis result 3 is compared with the target shape 10 using the other of the curvature and the displacement amount at the nodes 9.
In addition, the heating scheme 6 includes a first selected heating line 5 and a second selected heating line 5 .

In the second or fourth step, the heating wire 4 whose analysis result 3 is closest to the target shape 10 may be selected, or the heating wire 4 whose analysis result 3 is second or third closest to the target shape 10 may be selected.
The program of this embodiment is created to cause a computer to execute the calculation method of this embodiment.

The calculation method of the present embodiment is a method of calculating a heating plan used in bending a metal plate by line heating, utilizing finite element method structural analysis (FEM structural analysis).
The heating method is a plan for heating and bending a metal plate.
In the calculation method of this embodiment, an analytical model 2 of a metal plate is used. The length, width, thickness, etc. of the metal plate are set in the analytical model 2. The analytical model 2 of the metal plate has a front surface and a back surface. The analytical model 2 is divided into a plurality of elements (meshes) 8. The elements 8 may be, for example, a rectangular or triangular shell, or may be a solid such as a cube, a rectangular parallelepiped, a triangular pyramid, or a triangular prism. Each vertex of the element 8 becomes a node 9. For example, in the analytical model 2 shown in FIG. 2(a), the analytical model 2 is divided into 20×20 (400) elements 8, and the elements 8 are quadrangular shells. In this case, the analytical model 2 is in a lattice shape, and each intersection becomes a node 9.
The calculation method of this embodiment uses a model of a target shape 10. The target shape 10 is a target shape for bending a metal plate. The model of the target shape 10 is created by moving the nodes 9 so that the shape of the analytical model 2 of the metal plate becomes the target shape 10.

In the calculation method of the present embodiment, for example, a program created based on the flowchart shown in Fig. 1 is executed by a computer to calculate the heating plan 6. Here, the calculation method will be described with reference to the flowchart shown in Fig. 1.
First, the model of the target shape 10 and the analytical model 2 are read into a computer.
Next, the heating wire 4 is set at a first position on the analytical model 2. The first position can be set randomly at any position on the analytical model 2. The first position may be a position included on the front side of the analytical model 2 of the metal plate, or a position included on the back side of the analytical model 2. The heating wire 4 may be a straight line or a curved line. Furthermore, a plurality of heating wires 4 may be set. For example, five heating wires 4 can be set.
For example, when the heating line 4 is a straight line, as shown in Fig. 3, any two nodes 9 ( _x1 , _y1 ) and ( _x2 , _y2 ) of the analysis model 2 can be randomly selected, and the heating line 4 can be set as a straight line connecting these two nodes 9. In this case, the set heating line 4 can be expressed by the formula: y = {( _y2 - _y1 )/( _x2 - _x1 )}x + _{ ( _x2 y1 - _{x1 y2} )/( _x2 - _x1 )}.
For example, the heating wire 4a shown in Fig. 2(a) can be set. When five heating wires 4 are set, the heating wires 4a to 4e can be set. In Figs. 2(a) to 2(c), no distinction is made between the heating wires 4 or selected heating wires 5 set on the front surface of the metal plate and the heating wires 4 or selected heating wires 5 set on the back surface of the metal plate, but among the heating wires 4a to 4v and the selected heating wires 5, some are set on the front surface of the metal plate, and some are set on the back surface of the metal plate.

Next, select elements 8 on the set heating line 4. If at least one of the sides of element 8 intersects with heating line 4, the element 8 can be considered to be on heating line 4. For example, in analysis model 2 shown in Figure 4, elements (1), (2), and (3) are on heating line 4, but element (4) is not on heating line 4. If multiple heating lines 4 are set, select elements 8 on multiple heating lines 4.

Next, a finite element method structural analysis is performed on the analytical model 2. In the finite element method structural analysis, a distortion is imparted to the selected elements 8 under the heating conditions set for linear heating of the heating wire 4 to obtain an analytical result 3 (analysis model deformed by structural analysis). The heating conditions can include the amount of heat input in addition to the position of the heating wire 4. When the first heating wire 4 is set on the front surface of the analytical model 2 of the metal plate, the metal plate is heated from the front surface side in the analysis. When the first heating wire 4 is set on the back surface of the analytical model 2 of the metal plate, the metal plate is heated from the back surface side in the analysis.
The finite element method structural analysis may be FEM thermal elastic-plastic analysis or elastic analysis using the inherent strain method. In the structural analysis, linear heating using a gas burner may be assumed, linear heating using a laser (laser forming, etc.) may be assumed, or linear heating using induction heating may be assumed. In addition, in the structural analysis, the material property values (Young's modulus, Poisson's ratio, density, etc.) of the metal plate to be bent are used.
In FEM thermo-elastic-plastic analysis, the inherent strain of four components (longitudinal shrinkage, transverse shrinkage, angular distortion, and longitudinal bending) of the selected element 8 is calculated for the heating conditions (set heating wire 4 position (including heating surface) and heat input (J/mm)). In FEM thermo-elastic-plastic analysis, the thermal and deformation history is reproduced sequentially and deformation analysis is performed, so transient conditions can be analyzed.

In elastic analysis using the inherent strain method, it is considered that the deformation of the metal plate (analysis model 2) caused by linear heating occurs due to inherent deformation. If this inherent deformation is known, the deformation of the metal plate (analysis model 2) caused by linear heating can be predicted by applying the inherent deformation as a forced strain along the heating line 4 in elastic analysis. Therefore, in elastic analysis using the inherent strain method, structural analysis is performed using inherent strain calculated or measured in advance. For example, inherent strain calculated using FEM thermal elastic-plastic analysis, or inherent strain obtained by measuring a metal plate that has actually been deformed by linear heating, can be used in elastic analysis using the inherent strain method. In addition, elastic analysis using the inherent strain method can be performed using an equation that expresses the relationship between the heat input amount calculated or measured in advance and the inherent strain.
In addition, since the inherent strain method is an elastic analysis, it has the characteristic that the calculation time is significantly shorter than that of a thermal elastic-plastic analysis.

Next, the analysis result 3 is compared with the target shape 10, and an error between the analysis result 3 and the target shape 10 is evaluated. Then, the evaluation value and the set position of the heating wire 4 are stored in a storage unit.
For the entire analysis model, the analysis result 3 and the target shape 10 can be compared to calculate an evaluation value.
In addition, the analysis result 3 and the target shape 10 can be divided into a plurality of blocks, and the analysis result 3 and the target shape 10 can be compared for each block to calculate an evaluation value. For example, the analysis model 2 can be divided into 4 equal parts, 9 equal parts, 16 equal parts, 25 equal parts, 36 equal parts, 49 equal parts, 64 equal parts, 81 equal parts, or 100 equal parts into blocks.
Moreover, it is possible to calculate an evaluation value by comparing both the analysis result 3 of the entire analysis model with the target shape 10 and the analysis result of each block with the target shape.
The evaluation index may be, for example, the out-of-plane displacement (displacement) or curvature of the node 9 .
5 is an explanatory diagram of a comparison between the analysis result 3 and the target shape 10 when the analysis result 3 is compared with the target shape 10 as a whole analysis model and the evaluation index is the out-of-plane displacement amount 13 of the node 9. For example, as shown in FIG. 5, the out-of-plane displacement amount d (error) from the node 9 of the analysis result 3 to the corresponding node 12 of the target shape 10 is calculated. In this way, when the evaluation index is the displacement amount d of the node 9, it is possible to calculate a heating plan that can bring the metal plate closer to the target shape relatively quickly. Furthermore, an evaluation value can be calculated in this comparison.
When comparing the analysis result 3 with the target shape 10 for the entire analytical model, the evaluation value can be the sum (Σd ² ) of the squares of the displacement amounts d of all the nodes 12 included in the analytical model.

FIG. 6 is an explanatory diagram of a comparison between the analysis result 3 and the target shape 10 in a case where the analysis result 3 and the target shape 10 are divided into a plurality of blocks and the analysis result 3 and the target shape 10 are compared for each block. Although the analysis model is three-dimensional, FIG. 6 shows it in two dimensions for the sake of explanation. For example, the analysis result 3 and the target shape 10 are divided into four blocks A to D. Then, the least squares line (regression line) of the node 9 of the analysis result 3 included in the block A is calculated (in a three-dimensional analysis model, a least squares plane is calculated). The node 9 included in the block A is rotated so that this least squares line is parallel to the x-axis (in a three-dimensional analysis model, the node 9 is rotated so that the least squares plane is parallel to the x-axis and y-axis. In other words, the node 9 is rotated so that the normal vector of the least squares plane faces (0, 0, 1)). In addition, the least squares line (least squares plane) is set to z=0. After the rotation, the z-axis coordinates of each node are _z6 to _z10 .

Also, the least squares line (regression line) of the nodes 12 of the target shape 10 included in the block A is calculated (in a three-dimensional analysis model, a least squares plane is calculated). The nodes 12 included in the block A are rotated so that this least squares line is parallel to the x-axis (in a three-dimensional analysis model, the nodes 12 are rotated so that the least squares plane is parallel to the x-axis and y-axis). Also, the least squares line (least squares plane) is set to z=0. After the rotation, the z-axis coordinates of each node become _z1 to _z5 . By rotating the analysis result 3 or the target shape 10 in this way, the orientation of the analysis result 3 and the orientation of the target shape 10 become the same, and the local error between the analysis result 3 and the target shape 10 can be appropriately evaluated.
Then, the differences (displacement amounts) _d1 to _d5 in the z-axis coordinates of node 9 of analysis result 3 and the corresponding node 12 of the target shape are calculated. Specifically, _d1 = _z1 - _z6 , _d2 = _z2 - _z7 , _d3 = _z3 - _z8 , _d4 = _z4 - _z9 , _d5 = _z5 - _z10 . The displacement amounts _d1 to _d5 of the nodes included in block A are then squared and added together ( _d12 + ^d22 + _d32 + _d42 + ^d52 ₎ ^. This obtained value becomes the evaluation ^value (sum of _squared errors) for block ^A.

The evaluation value (sum of squared errors) is calculated for each of blocks B, C, and D in the same manner as for block A. Then, the evaluation value of the analysis result can be calculated by adding up the evaluation values of all blocks A to D included in the analysis model.

When calculating an evaluation value by comparing both the analysis result 3 of the entire analysis model with the target shape 10 and the analysis result 3 for each block with the target shape 10, the evaluation value can be calculated using, for example, the formula: Evaluation value = (overall sum of squared errors) ^α × Σ (sum of squared errors in each block) ^β . α and β are weighting parameters. α and β can be determined based on empirical rules or past data. The overall sum of squared errors contributes to maintaining the overall shape, and the sum of squared errors in each block contributes to creating a local shape.

When the evaluation index is the curvature of node 9, the error (curvature error r) between the curvature of node 9 in analysis result 3 and the curvature of node 12 of target shape 10 corresponding to node 9 is calculated. In this way, when the evaluation index is the curvature, it is possible to calculate a heating plan that can accurately approximate the metal plate to the target shape. Furthermore, in this comparison, an evaluation value can be calculated.
When comparing the analysis result 3 with the target shape 10 for the entire analysis model, the evaluation value can be the sum (Σr ² ) of the squared curvature errors r of all the nodes 9 included in the analysis model.

When the evaluation index is the curvature of node 9, the analysis result 3 and target shape 10 are divided into multiple blocks, and the analysis result 3 and target shape 10 are compared for each block, the evaluation value (sum of squared errors) of each block is calculated by squaring and adding up the curvature errors r of all nodes contained in the block, and the evaluation value of the analysis result can be calculated by adding up the evaluation values of all blocks.

When the evaluation indexes are both the displacement amount and the curvature of the node 9, the displacement amount d and the curvature error r are calculated for each node 9. Furthermore, an evaluation value can be calculated from this comparison.
When comparing the analysis result 3 with the target shape 10 for the entire analysis model, the evaluation value can be the product of the sum of the squares of the displacement amounts d of all the nodes 12 included in the analysis model ( ^Σd2 ) and the sum of the squares of the curvature errors r of all the nodes 12 included in the analysis model ( ^Σr2 ). For example, the evaluation value can be calculated using the formula: Evaluation value = ( ^Σd2 ) ^α × ( ^Σr2 ) ^β . α and β are weighting parameters. α and β can be determined based on empirical rules or past data. For example, when α is 1, β can be set to 5 or more and 10 or less.

When the analysis result 3 and the target shape 10 are divided into a plurality of blocks and the analysis result 3 and the target shape 10 are compared for each block with both the displacement amount and the curvature of the node 9 as the evaluation indexes, the evaluation value of each block can be the product of the sum ( ^Σd2 ) of the squared displacement amounts d of all the nodes 12 (after rotation) included in the block and the sum ( ^Σr2 ) of the squared curvature errors r of all the nodes 12 included in the block. For example, the evaluation value can be calculated using the formula: Evaluation value = ( ^Σd2 ) ^α × ( ^Σr2 ) ^β . Then, the evaluation value of the analysis result can be calculated by adding up the evaluation values of all the blocks.
Whether to use the displacement amount, the curvature, or both the displacement amount and the curvature as the evaluation index can be determined in consideration of the target shape, processing efficiency, and the like.
The flow from setting the heating wire 4 to saving the evaluation value and the set position of the heating wire 4 is called a first trial.

After the first trial is completed, the second trial is performed. The second trial is basically the same as the first trial, but the heating wire 4 in the second trial is set at a position different from the setting position of the heating wire 4 in the first trial. This position can be set randomly at any position on the analysis model 2. This position may be a position included on the front side of the analysis model 2 of the metal plate, or a position included on the back side of the analysis model 2. In the second trial, the heating wire 4 may be a straight line or a curved line. Furthermore, multiple heating wires 4 may be set. For example, the heating wire 4b shown in FIG. 2(a) is set. Furthermore, when five heating wires 4 are set, for example, heating wires 4f to 4j can be set. Then, the elements 8 on the set heating wire 4 are selected, and a finite element method structural analysis is performed to obtain an analysis result 3. The obtained analysis result 3 is compared with the target shape 10, and an evaluation value is calculated. Furthermore, the calculated evaluation value and the set position of the heating wire 4 are stored in the storage unit.
Such trials are repeated X times. For example, as shown in FIG. 2A, the positions of the heating wires 4 can be set as heating wires 4c to 4k, and trials can be performed at each position. Also, a plurality of heating wires 4 can be set in each trial. For example, when five heating wires are set, five heating wires 4 are set in each trial and a trial is performed. The number of trials can be, for example, 100 to 1500.
In the second to Xth trials, the index for evaluating the error between the analysis result 3 and the target shape 10 may be the displacement amount, the curvature, or both the displacement amount and the curvature, but the same index as in the first trial is used. The evaluation value is also calculated in the same way as in the first trial.
The analysis result 3 in each trial has a shape corresponding to a heating wire 4 in a different position, and is therefore different from one another, and the error (evaluation value) between the analysis result 3 and the target shape 10 differs for each trial.

Next, the heating wire 4 in the trial in which the error (evaluation value) between the analysis result 3 and the target shape 10 is the smallest among the trials is selected as the selected heating wire 5. The heating wire 4 in the trial in which the error (evaluation value) between the analysis result 3 and the target shape 10 is the second, third, fourth, or fifth smallest among the trials may be selected as the selected heating wire 5. The heating wire 4 in which the trial is selected as the selected heating wire 5 can be determined in consideration of the target shape 10, the magnitude of the bending amount, and the like. In addition, when multiple heating wires 4 are set in a trial, multiple heating wires 4 are selected as the selected heating wire 5. For example, the heating wire 4d can be selected from the heating wires 4a to 4k shown in FIG. 2(a). In addition, when five heating wires 4 are set in each trial, for example, the heating wires 4f to 4j can be selected.
The process from the first trial to the selection of the selected heating wire 5 is referred to as the first heating wire selection flow.

After the first heating wire selection flow is completed, the second heating wire selection flow is performed. The second heating wire selection flow is basically the same as the first heating wire selection flow, but when randomly setting the heating wire 4 at an arbitrary position of the analysis model 2, both the selected heating wire 5 selected in the first heating wire selection flow and the heating wire 4 randomly set in each trial of the second heating wire selection flow are set, and the element 8 on the selected heating wire 5 and the element 8 on the set heating wire 4 are selected. Then, by performing a structural analysis under these heating conditions, an analysis result 3 reflecting both the selected heating wire 5 and the set heating wire 4 can be obtained. In the second heating wire selection flow, multiple heating wires 4 may be set in each trial. In addition, the number of heating wires 4 set in each trial of the first heating wire selection flow and the number of heating wires 4 set in each trial of the second heating wire selection flow may be different. For example, the selected heating wire 5 and the heating wire 4l shown in FIG. 2(b) can be set. In addition, in the case where five heating wires 4 are set in each trial, for example, the selected heating wires (heating wires 4f to 4j) and the heating wires 4l to 4p selected in the first heating wire selection flow can be set.
In the second heating wire selection flow, trials are repeated up to X times, and the heating wire 4 in the trial in which the error (evaluation value) between the analysis result 3 and the target shape 10 is the smallest among the trials is selected as the selected heating wire 5. The heating wire 4 in the trial in which the error (evaluation value) between the analysis result 3 and the target shape 10 is the second or third smallest among the trials may be selected as the selected heating wire 5. Furthermore, when multiple heating wires 4 are set in a trial, multiple heating wires 4 are selected as the selected heating wire 5. For example, the heating wire 4s can be selected from the heating wires 4l to 4v shown in FIG. 2B. Furthermore, when five heating wires 4 are set in each trial, for example, the heating wires 4l to 4p can be selected.

The 3rd, 4th, ..., nth heating wire selection flows are performed in order. Each heating wire selection flow (referred to as the Ath heating wire selection flow) is basically the same as the first heating wire selection flow, but when randomly setting at least one heating wire 4 at an arbitrary position of the analysis model 2, at least one heating wire 4 to be set randomly in each trial of the Ath heating wire selection flow and all selected heating wires 5 selected in the (A-1)th or earlier heating wire selection flows are set. Also, multiple heating wires 4 can be set in each trial of the Ath heating wire selection flow to perform trials. For example, when setting five heating wires 4, trials are performed by setting five heating wires 4 to be set randomly in each trial and all selected heating wires 5 selected in the (A-1)th or earlier heating wire selection flows.
For example, in the third heating wire selection flow, the selected heating wire 5 (4d) selected in the first heating wire selection flow, the selected heating wire 5 (4s) selected in the second heating wire selection flow, and at least one heating wire 4 randomly set in each trial of the third heating wire selection flow are set. That is, the number of selected heating wires 5 to be set increases as the number of heating wire selection flows increases.

Then, the elements 8 on all the selected heating lines 5 and the elements 8 on the set heating lines 4 are selected, and a structural analysis is performed under these heating conditions, whereby an analysis result 3 reflecting all the selected heating lines 5 and the set heating lines 4 can be obtained.
In the Ath heating wire selection flow, trials are repeated up to X times, and the heating wire 4 in the trial in which the error (evaluation value) between the analysis result 3 and the target shape 10 is the smallest among the trials is selected as the selected heating wire 5. The heating wire 4 in the trial in which the error (evaluation value) between the analysis result 3 and the target shape 10 is the second or third smallest among the trials may be selected as the selected heating wire 5. Furthermore, when multiple heating wires 4 are set in the trial, multiple heating wires 4 are selected as the selected heating wires 5.
When it is determined that the error (evaluation value) between the analysis result 3 under the heating conditions including the selected heating wire 5 selected in the n-th heating wire selection flow and the target shape 10 is small, the repetition of the heating wire selection flow is terminated, and the heating plan 6 including the selected heating wire 5 selected in the 1st to nth heating wire selection flows is completed. The heating plan 6 includes a plurality of selected heating wires 5, for example, as shown in FIG. 2(c).
In addition, an upper limit can be set for the number of times of the heating wire selection flow. This upper limit can be set to a number that exceeds the number of selected heating wires 5 that are considered to be necessary to reach the first target shape 10. This makes it possible to prevent the heating plan from including too many selected heating wires 5, and to prevent the heating plan from having high processing costs.

In this embodiment, among the heating wire selection flows performed multiple times, in some of the heating wire selection flows, the displacement amount is used as an index for evaluating the error between the analysis result 3 and the target shape 10 (the evaluation value is calculated using the displacement amount), and in other heating wire selection flows, the curvature can be used as an index for evaluating the error between the analysis result 3 and the target shape 10 (the evaluation value is calculated using the curvature). That is, when moving from the Ath heating wire selection flow to the (A+1)th heating wire selection flow, the index for evaluating the error between the analysis result 3 and the target shape 10 is switched from the displacement amount to the curvature or from the curvature to the displacement amount. For example, in the heating wire selection flow until the analysis result 3 approaches the target shape to a certain extent, the displacement amount is used as an index for evaluating the error between the analysis result 3 and the target shape 10, and in the subsequent heating wire selection flow, the curvature can be used as an index for evaluating the error between the analysis result 3 and the target shape 10. In heating with the selected heating wire 5 selected in the heating wire selection flow using the displacement amount, the processing speed can be increased, and in heating with the selected heating wire 5 selected in the heating wire selection flow using the curvature, the processing accuracy can be increased. Therefore, it is possible to achieve both high processing efficiency and high processing accuracy.
Further, the calculation may be carried out while selecting whether to use the displacement amount, the curvature amount, or both the displacement amount and the curvature amount as the error evaluation index for each heating line selection flow according to the analysis result.

The metal plate can be deformed into a shape close to the target shape by linearly heating and bending the metal plate based on the obtained heating scheme 6. The bending of the metal plate can be performed by an operator or automatically by a machine. When bending the metal plate by a machine, multiple selected heating wires 5 can be heated simultaneously.
The heating scheme 6 may include an order of the selected heating wires 5 corresponding to the order of the heating wire selection flow. When the metal plate is subjected to linear heating and bending according to the heating scheme 6, the selected heating wires 5 can be heated according to this order. This makes it possible to deform the metal plate into a shape closer to the target shape.

A processing method for processing a metal plate based on the obtained heating plan 6 can include the steps of linearly heating the metal plate under heating conditions including the selected heating wire 5 selected in the Ath (A=1 to n) heating wire selection flow, and bending the metal plate, measuring the three-dimensional shape of the metal plate that has been bent, comparing the measured three-dimensional shape of the metal plate with analysis result 3 of the finite element method structural analysis performed under heating conditions including the selected heating wire 5 in the Ath heating wire selection flow, and heating the metal plate so that the three-dimensional shape of the metal plate approaches the analysis result 3 based on the comparison result.
The step of measuring the three-dimensional shape of the metal plate can be performed using a three-dimensional measuring device. The three-dimensional measuring device can be a contact type or a non-contact type such as a scanning laser probe type or an optical type. This makes it possible to deform the metal plate into a shape closer to the target shape.

A processing device that automatically processes a metal plate based on heating plan 6 can include, for example, a heating unit that heats the metal plate and a control unit that controls the processing device. The control unit is configured to be able to read heating plan 6 and to control the heating unit to heat the metal plate according to heating plan 6.

Second embodiment In the second embodiment, an index for evaluating the error between the analysis result 3 and the target shape 10 is determined based on the target shape 10. Specifically, when the target shape 10 has either a positive curvature or a negative curvature (for example, when the target shape 10 is bowl-shaped), the curvature at the node 9 is used as the index for evaluating the error between the analysis result 3 and the target shape 10. This allows the analysis result 3 to steadily approach the target shape 10 from the first heating line selection flow to the nth heating line selection flow, and an excellent heating plan can be created.
On the other hand, when the target shape 10 has both positive and negative curvatures (for example, when the target shape 10 is a saddle shape, a twisted shape, etc.), the displacement amount at the node 9 is used as an index for evaluating the error between the analysis result 3 and the target shape 10. This allows the analysis result 3 to steadily approach the target shape 10 from the first heating wire selection flow to the nth heating wire selection flow, and an excellent heating plan can be created.
Other configurations are similar to those of the first embodiment. Furthermore, the description of the first embodiment also applies to the second embodiment unless there is a contradiction.

In the third embodiment , a heating plan is created while preferentially selecting the heating wire 4 set on the same heating surface (either the front or back surface of the metal sheet) as the selected heating wire 5 selected in the immediately preceding heating wire selection flow is set on. This makes it possible to prevent the heating surface on which the selected heating wire 5 is set from being frequently changed, and improves the efficiency of bending using the heating plan.

Specifically, among the multiple trials performed in the Ath heating line selection flow, multiple trials are selected that have small errors (evaluation values) between the analysis result 3 and the target shape 10. For example, when 500 trials are performed, 10 trials are selected that have small errors (evaluation values) between the analysis result 3 and the target shape 10. The number of trials to be selected can be, for example, 2 or more and 10 or less.
Next, among the selected multiple trials, among the trials in which the heating wire 4 is set on the same heating surface as the selected heating wire 5 selected in the (A-1)th heating wire selection flow, the heating wire 4 of the trial with the smallest error (evaluation value) between the analysis result 3 and the target shape 10 is selected as the selected heating wire 5. This makes it possible to continue the selected heating wire 5 set on the same heating surface.
For example, in FIG. 2( b ), when the selected heating wire 5 (4d) selected in the immediately preceding heating wire selection flow is set on the front surface of the metal plate, and the error (evaluation value) between the analysis result 3 and the target shape 10 is small in the trial in which the heating wire 4s is set on the front surface of the metal plate, the trial in which the heating wire 4q is set on the rear surface of the metal plate, and the trial in which the heating wire 4v is set on the rear surface of the metal plate, the heating wire 4s set on the same heating surface as the selected heating wire 5 (4d) is selected as the selected heating wire 5 even if the error (evaluation value) between the analysis result 3 and the target shape 10 in the trial in which the heating wire 4q is set and the trial in which the heating wire 4v is set is smaller than the error (evaluation value) between the analysis result 3 and the target shape 10 in the trial in which the heating wire 4s is set.

If the selected multiple trials do not include a trial in which the heating wire 4 is set on the same heating surface as the heating surface on which the selected heating wire 5 selected in the (A-1)th heating wire selection flow is set, the heating wire 4 of the trial in which the error (evaluation value) between the analysis result 3 and the target shape 10 is the smallest among the selected multiple trials is selected as the selected heating wire 5. In this case, the heating surfaces are swapped.
Other configurations are similar to those of the first or second embodiment. Furthermore, the description of the first or second embodiment also applies to the third embodiment unless there is a contradiction.

Fourth embodiment In the fourth embodiment, in the heating wire selection flow, a heating wire 4 with a small amount of bending is preferentially selected as a selected heating wire 5. This makes it possible to prevent the amount of bending from becoming too large, and to reduce the number of selected heating wires 5 included in the heating plan. If the amount of bending is too large, it becomes necessary to set a selected heating wire 5 to correct the excessively bent portion, and the number of selected heating wires 5 included in the heating plan tends to increase.
Specifically, among the multiple trials performed in the Ath heating line selection flow, multiple trials are selected that have small errors (evaluation values) between the analysis result 3 and the target shape 10. For example, when 500 trials are performed, 10 trials are selected that have small errors (evaluation values) between the analysis result 3 and the target shape 10. The number of trials to be selected can be, for example, 2 or more and 10 or less.
Next, the heating wire 4 set in the trial with the smallest amount of bending from among the selected multiple trials is selected as the selected heating wire 5.

For example, in FIG. 2A , when the error (evaluation value) between the analysis result 3 and the target shape 10 is small in the trial in which the heating wire 4a is set, the trial in which the heating wire 4d is set, and the trial in which the heating wire 4j is set, if the bending amount in the trial in which the heating wire 4d is set is smaller than those in the trial in which the heating wire 4a is set and the trial in which the heating wire 4j is set, then the heating wire 4d is selected as the selected heating wire 5 even if the error (evaluation value) between the analysis result 3 and the target shape 10 in the trial in which the heating wire 4a is set and the trial in which the heating wire 4j is set is smaller than the error (evaluation value) between the analysis result 3 and the target shape 10 in the trial in which the heating wire 4d is set.
In addition, among the selected multiple trials, trials with excessively large bending amounts can be excluded from the candidates for the selected heating wire 5.
Other configurations are the same as those of the first, second or third embodiment. Furthermore, the description of the first, second or third embodiment also applies to the fourth embodiment unless there is a contradiction.

Fifth embodiment In this embodiment, from the first heating wire selection flow to the Ath heating wire selection flow, the displacement is used as an index for evaluating the error between the analysis result 3 and the target shape 10 (the displacement is used to calculate an evaluation value), and in the (A+1)th and subsequent heating wire selection flows, both the curvature and the displacement are used as indexes for evaluating the error between the analysis result 3 and the target shape 10. The timing for switching the index from the displacement to both the displacement and the curvature can be, for example, when the difference between the evaluation value of the selected heating wire selected in the (A-1)th heating wire selection flow and the evaluation value of the selected heating wire selected in the Ath heating wire selection flow falls below a predetermined value.
By switching the indicators in this way, a heating plan with a smaller number of heating wires can be created.
Other configurations are the same as those of the first, second, third or fourth embodiment. Furthermore, the description of the first, second, third or fourth embodiment also applies to the fifth embodiment unless there is a contradiction.

Simulation: A heating plan (target shape: bowl-shaped, saddle-shaped, twisted-shaped) was calculated using the calculation method of the present invention (structural analysis: elastic analysis using the inherent strain method), and a simulation was performed to perform elastic analysis (structural analysis) using the calculated heating plan.
The inherent strain to be applied to the elements for the deformation analysis using the inherent strain method was obtained from the deformation results of a FEM thermo-elastic-plastic analysis performed on the analysis model.
In the structural analysis using the inherent strain method, a plate-shaped analytical model with a plate length of 500 mm and a plate width of 500 mm was used, and the analytical model was divided into rectangular shell elements so that the number of nodes and elements was 2,601 and 2,500, respectively. The material of the metal plate was assumed to be SM490A (rolled steel for welded structures), and the plate thickness was assumed to be 16 mm. The material constants of SM490A are shown in Table 1. In the simulation, three types of target shapes (bowl type, saddle type, and twist type) were set. The number of trials required to determine the position of one selected heating wire was 500.

In the FEM thermal elastic-plastic analysis to obtain the inherent strain, the analytical model had a plate length of 500 mm, plate width of 500 mm, plate thickness of 16 mm, and the number of nodes and elements was 61,711 and 50,000. The welding conditions were current 150 A, voltage 20 V, welding speed 2.286 mm/sec, and welding efficiency 0.8. The resulting inherent strains (longitudinal shrinkage, transverse shrinkage, longitudinal curvature, transverse curvature) are shown in Table 2.

Target shape: bowl-shaped. Figures 7(a) to 7(e) are heating plans calculated with the number of selected heating wires set to 10, 20, 30, 40, and 55, respectively, and Figures 8(a) to 8(d) are analysis results when structural analysis was performed using the inherent strain method based on the heating plans calculated with the number of selected heating wires set to 10, 20, 30, and 40, respectively. Figure 9(a) is the target shape used in the structural analysis, and Figure 9(b) is the analysis result when structural analysis was performed using the inherent strain method based on the heating plan calculated with the number of selected heating wires set to 55. Figure 10 is the out-of-plane displacement distribution comparing the target shape and the analysis result at the dashed line A-A' in Figures 9(a) and 9(b), and Figure 11 is the out-of-plane displacement distribution comparing the target shape and the analysis result at the dashed line B-B' in Figures 9(a) and 9(b).

In the simulation in which the target shape was a bowl shape, the curvature at the node was used as an index to evaluate the error between the target shape and the analysis result. The number of selected heating wires was set to 10, 20, 30, 40, and 55.
In this simulation, the heating plans shown in Figures 7(a) to 7(e) could be calculated. In addition, when a structural analysis was performed using the inherent strain method based on the calculated heating plans, the analysis results shown in Figures 8(a) to 8(d) and 9(b) could be obtained. Note that the solid lines in Figure 7 represent the selective heating lines on the front surface of the metal plate, and the dotted lines represent the selective heating lines on the back surface of the metal plate.

As can be seen from Figures 8(a) to (d), the bowl-shaped tendency was captured when there were 10 selected heating wires, and when there were 20 selected heating wires, a shape that almost matched the target shape was formed. After that, it was confirmed that the number of selected heating wires that fine-tuned the shape or had little effect on the shape increased. Also, looking at the heating positions shown in Figure 7, it was found that many of the selected heating wires were placed in the diagonal direction of the base material. This is thought to be the result of the selection of the positions of the selected heating wires that evenly bend the entire base material using both angular distortion and vertical bending in order to form a bowl-shaped shape with a concave center.
It was also confirmed that the analysis results shown in Figures 9(a), 9(b), 10, and 11 capture the tendency of the target shape well. Therefore, it was found that by heating a metal plate based on the heating plan calculated by the calculation method of the present invention, the metal plate can be bent into a shape close to the target shape.

Target shape: saddle type Figure 12(a) shows the target shape used in the structural analysis, and Figure 12(b) shows the analysis results when structural analysis was performed by the inherent strain method based on a heating plan calculated with 40 selected heating wires. Figure 13 shows the heating plan calculated with 40 selected heating wires. Figure 14 shows the out-of-plane displacement distribution comparing the target shape and the analysis result along the dashed line A-A' in Figures 12(a) and (b), and Figure 15 shows the out-of-plane displacement distribution comparing the target shape and the analysis result along the dashed line B-B' in Figures 12(a) and (b).

In the simulation in which the target shape was a saddle shape, the out-of-plane displacement at the node was used as an index to evaluate the error between the target shape and the analysis result. The number of selected heating wires was set to 40.
In this simulation, it was possible to calculate the heating plan shown in Fig. 13. Furthermore, when a structural analysis was performed using the inherent strain method based on the calculated heating plan, the analysis result shown in Fig. 12(b) was obtained.
It was confirmed that the analysis results shown in FIG. 12, FIG. 14, FIG. 15 and FIG. 12(b) satisfactorily captured the tendency of the target shape.

Target shape: twisted type Figure 16(a) shows the target shape used in the structural analysis, and Figure 16(b) shows the analysis results when structural analysis was performed by the inherent strain method based on a heating plan calculated with 16 selected heating wires. Figure 17 shows the heating plan calculated with 16 selected heating wires. Figure 18 shows the out-of-plane displacement distribution obtained by comparing the target shape with the analysis results along the dashed line A-A' in Figures 16(a) and 16(b), and Figure 19 shows the out-of-plane displacement distribution obtained by comparing the target shape with the analysis results along the dashed line B-B' in Figures 16(a) and 16(b).

In the simulation in which the target shape was twisted, the out-of-plane displacement at the nodes was used as an index to evaluate the error between the target shape and the analysis result. The number of selected heating wires was set to 16.
In this simulation, it was possible to calculate the heating plan shown in Fig. 17. Furthermore, when a structural analysis was performed using the inherent strain method based on the calculated heating plan, the analysis result shown in Fig. 16(b) was obtained.
It was confirmed that the analysis results shown in Figs. 16, 18, and 19 and Fig. 16(b) adequately capture the tendency of the target shape.

Target shape: Bowl shape (evaluation of evaluation index)
A heating plan was created by performing structural analysis with the target shape being a bowl shape (FIG. 9(a)) and using the displacement, curvature, or both the displacement and curvature as indices for evaluating the error between the analysis result and the target shape. FIG. 20 is a graph showing the change in error between the analysis result and the target shape with an increase in the number of selected heating wires in the heating plan creation process. The Z displacement squared error sum on the vertical axis of FIG. 20 is the sum of the squares of the displacements in the z direction (out-of-plane direction, the direction perpendicular to the front and back surfaces of the initial metal plate) at the nodes.
The evaluation value of the analysis result was calculated using the formula: Evaluation value = ( ^Σd2 ) ^α × ( ^Σr2 ) ^β . ^Σd2 is the value obtained by squaring and adding up the displacement amounts d of all nodes included in the analysis model, and ^Σr2 is the value obtained by squaring and adding up the curvature errors r of all nodes included in the analysis model. α and β are weighting parameters. When β = 0, evaluation was performed based on the displacement amount alone, and when α = 0, evaluation was performed based on the curvature error alone. When α ≥ 1 and β ≥ 1, evaluation was performed based on both the displacement amount and the curvature error, and the weight of the curvature error was changed by changing β.
When the analysis results were evaluated based only on the curvature error (α = 0), the sum of squared errors of the Z displacement was over 100, even when the number of selected heating wires reached 50. When the analysis results were evaluated based only on the amount of displacement (β = 0), the sum of squared errors of the Z displacement decreased significantly until the number of selected heating wires increased to 5, but thereafter the sum of squared errors of the Z displacement decreased gradually. Moreover, even when the number of selected heating wires reached 50, the sum of squared errors of the Z displacement was over 10.
When the analysis results were evaluated using both the displacement amount and the curvature error (α≧1, β≧1), the sum of squared errors of Z displacement was smaller than when evaluated using only the curvature error or when evaluated using only the displacement amount. In particular, in the analysis where β=6 or β=8, the sum of squared errors of Z displacement was 1 or less.

Target shape: Complex shape (evaluation of number of divisions)
A structural analysis was performed with a complex shape as shown in Fig. 21 and Fig. 22 as the target shape, and a heating plan was created. In this target shape, convex parts 16 and concave parts 17 are arranged alternately. In this structural analysis, the amount of displacement is used as an index for evaluating the error between the analysis result and the target shape. In this structural analysis, the analysis result and the target shape are divided into 4, 16, or 64 parts, and the analysis result and the target shape are compared for each block to calculate an evaluation value. In addition, when comparing the analysis result and the target shape for each block, the analysis result and the target shape are rotated so that the orientation of the analysis result and the orientation of the target shape are the same. A structural analysis without division was also performed.
Specifically, when evaluating the analysis results, the evaluation value was calculated using the formula: Evaluation value = (total sum of squared errors) ^α × Σ (sum of squared errors in each block) ^β , and the selected heating line in the trial with the smallest evaluation value was selected. The sum of squared errors is the sum of the squares of the displacements in the z direction (out-of-plane direction, the direction perpendicular to the front and back surfaces of the initial metal plate) at the nodes. In addition, the "total sum of squared errors" in the formula is a value that contributes to maintaining the overall shape, and the "sum of squared errors in each block" in the formula is a value that contributes to creating a local shape. In addition, α is the weight of the overall error, and β is the weight of the local error.

Fig. 23 shows a heating plan (selected heating wires: 200 wires) created by structural analysis. Fig. 24 shows the results of structural analysis using the created heating plan (created shape) and the difference between the structural analysis result and the target shape. Fig. 25 is a graph showing the change in error (sum of squared error of Z displacement) between the analysis result and the target shape with an increase in the number of selected heating wires in the heating plan creation process. In these analyses, α=1 and β=12.
As shown in the graph of Fig. 25, in the structural analysis in which the evaluation value was calculated without division (no division), even when the number of selected heating wires was 200, the sum of squares of the Z displacement error was over 200, but as the number of divisions increased, the sum of squares of the Z displacement error became smaller, and in the structural analysis calculated by dividing into 64, when the number of selected heating wires became 200, the sum of squares of the Z displacement error became small to about 10. Also, as shown in Fig. 24, the difference became clearly smaller as the number of divisions increased.

Target shape: Bowl shape (evaluation of number of divisions)
A structural analysis was performed with the target shape being a bowl shape (Figure 9(a)) and the displacement as an index for evaluating the error between the analysis result and the target shape to create a heating plan. In this structural analysis, the analysis result and target shape were divided into 4, 16, 64, or 100 parts, and the analysis result and target shape were compared for each block to calculate an evaluation value. The evaluation value was calculated using the formula: evaluation value = Σ (sum of squared error for each block). A structural analysis without division was also performed, with the evaluation value being the sum of squared error for the entire block.
FIG. 26(a) shows the result (created shape) of a structural analysis using a heating plan (selected heating wires: 60 wires) created by evaluating the analysis results without dividing the structure, and FIG. 26(b) shows the error between the result of this structural analysis and the target shape.
FIG. 27(a) shows the result of structural analysis (created shape) using a heating plan (selected heating wires: 60 wires) created by dividing the analysis result and target shape into 100 parts, evaluating the analysis result, and performing structural analysis, and FIG. 27(b) shows the error between the result of this structural analysis and the target shape.
FIG. 28 is a graph showing the change in error (sum of squared error of Z displacement) between the analysis result and the target shape with an increase in the number of selected heating wires in the heating plan creation process.

In a structural analysis in which the analysis results were evaluated without division, as shown in Figure 28, the sum of the Z displacement errors was approximately 30 even when the number of selected heating wires was 60, and when the heating plan obtained from this structural analysis was used, an irregular bowl shape was formed as shown in Figure 26. Also, as shown in Figure 28, the sum of the Z displacement errors became smaller as the number of divisions increased, and in a structural analysis in which the analysis results and the target shape were divided into 100 and the analysis results were evaluated, the sum of the Z displacement errors was reduced to approximately 3 when the number of selected heating wires was 60. Also, as shown in Figure 27, when the heating plan obtained from this structural analysis was used, a neat bowl shape could be formed. From these results, it was clear that the greater the number of divisions, the better the heating plan that could be obtained.

Target shape: Bowl shape (weight parameter evaluation)
A structural analysis was performed to create a heating plan, with the target shape being a bowl shape (Figure 9 (a)) and the amount of displacement being used as an index for evaluating the error between the analysis result and the target shape. In this structural analysis, the analysis result and target shape were divided into 64 parts, and the analysis result and target shape were compared for each block to calculate an evaluation value. The evaluation value was calculated using the formula: Evaluation value = (total sum of squared error) ^α ×Σ (sum of squared error in each block) ^β , where α is the weight of the overall error and β is the weight of the local error. α was set to 0 or 1, and β was set to 0, 1, 2, 4, 8, 16, or 32.
Fig. 29 is a graph showing the change in error (sum of square error of Z displacement) between the analysis result and the target shape with an increase in the number of selected heating wires in the heating plan creation process. α and β are also shown in Fig. 29. From these results, it was found that an excellent heating plan can be obtained by setting β to about 8.

2: Analysis model 3: Analysis results 4, 4a to 4v: Heating lines 5: Selected heating lines 6: Heating method 8: Elements 9: Nodes 10: Target shape 11: Elements of target shape 12: Nodes of target shape 13: Displacement between analysis results and target shape 16: Convex parts 17: Concave parts 19: Least squares line (regression line)

Claims (8)

A method for calculating a heating plan used in bending a metal plate by line heating, comprising:
a first step of performing a finite element method structural analysis under a first heating condition including at least one first heating wire set at a first position of an analysis model of the metal plate, and repeating a first trial of comparing the analysis result with a target shape by changing the position of the first heating wire;
a second step of selecting, as a first selected heating line, at least one first heating line set in a first trial in which an analysis result of the first trial is close to a target shape among the repeated first trials;
a third step of performing a finite element method structural analysis under second heating conditions including a first selected heating line and at least one second heating line set at a second position of the analysis model, and repeating a second trial of comparing the analysis result with a target shape by changing the position of the second heating line;
and a fourth step of selecting, as a second selected heating line, at least one second heating wire set in a second trial in which an analysis result of the repeated second trials approaches a target shape,
the analytical model is a finite element model having a plurality of elements and a plurality of nodes;
The heating scheme includes a first and a second selected heating line;
A calculation method characterized in that in the first or third step, the analysis result and the target shape are divided into a plurality of blocks, and for each block, the least squares plane of the nodes is matched to compare the analysis result with the target shape. The method according to claim 1 , wherein in the first or third step, the analysis result is compared with the target shape using both the displacement and the curvature at the nodes. In a first step, the analysis result is compared to the target shape using displacements at the nodes;
The method of claim 1 , wherein in a third step, the analysis result is compared with the target shape using both the curvature and the displacement at the nodes. In a first step, the analysis result is compared to the target shape using one of the curvature and the displacement at the node;
The method according to claim 1 , wherein in a third step, the analysis result is compared with the target shape using the other of the curvature and the displacement at the node. If the target shape is a shape having either positive curvature or negative curvature, in a first and third step, the analysis result is compared with the target shape using the curvature at the node;
2. The calculation method according to claim 1, wherein, in the first and third steps, when the target shape is a shape having both positive and negative curvature, the analysis result is compared with the target shape using the displacement amount at the node. 6. The calculation method according to claim 1, wherein in the first or third step, both a comparison of the analysis result for each block with the target shape and a comparison of the analysis result for the entire analytical model with the target shape are performed. The metal plate has a front surface and a back surface,
In the first heating condition, the first heating line is set on either the front surface or the back surface,
In the second heating condition, the second heating line is set on either the front surface or the back surface,
The calculation method according to any one of claims 1 to 6, wherein a fourth step is a step of selecting at least one second heating line set in a second trial in which an analysis result of the repeated second trials approaches a target shape, and selecting, from the selected second heating lines, a second heating line set on the same surface as a surface on which the first selected heating line is set, as the second selected heating line. The calculation method according to any one of claims 1 to 7, wherein a fourth step is a step of selecting at least one second heating wire set in a second trial in which an analysis result of the repeated second trial approaches a target shape, and selecting a second heating wire having a small amount of bending from the selected plurality of second heating wires as a second selected heating wire.