Calculation method of heating scheme used in bending processing of metal plate using linear heating

Abstract

The calculation method of the present application is characterized by comprising: a first step of performing structural analysis under a first heating condition including a first heating line, and repeatedly performing a first trial of comparing an analysis result with a target shape; a second step of selecting a first heating line set in a first trial in which the analysis result is close to the target shape in the repeatedly performed first trials as a first selected heating line; a third step of performing structural analysis under a second heating condition including the first selected heating line and a second heating line, and repeatedly performing a second trial of comparing an analysis result with a target shape; and a fourth step of selecting a second heating line set in a second trial in which the analysis result is close to the target shape in the repeatedly performed second trials as a second selected heating line; 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.

Description

Technical Field

[0001] This invention relates to a method for calculating a heating scheme used in the bending process of a metal sheet utilizing linear heating. Background Technology

[0002] Ships often have complex curved shapes at the bow, bulbous bow, and stern. To create these shapes, multiple steel plates are bent and then welded together. Wire heating is widely used in shipbuilding as a bending technique.

[0003] Linear heating refers to the heating process that utilizes the thermal deformation generated when heating the surface of a steel plate using a gas burner. This technique has been used in many shipyards in China since ancient times. When bending steel plates using linear heating, if the steel plate is locally heated by the flame of the gas burner while simultaneously being rapidly cooled by adding water, plastic deformation occurs within 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 heated gas burner, the mixing ratio of the combustion gas and the incoming oxygen, and the distance between the burner and the steel plate. Furthermore, bending using linear heating is a processing technique that uses multiple heating lines positioned appropriately to bring the steel plate close to the desired curved surface shape.

[0004] However, the deformation produced by linear heating is a complex deformation that is a mixture of longitudinal and transverse contraction and longitudinal and transverse bending. It also depends on the input heat and the moving speed and heating position of the gas burner, making it very difficult to predict. Therefore, bending processing based on linear heating is one of the technologies that is difficult to automate.

[0005] To automate bending processes based on linear heating, a method for calculating the heating scheme is proposed (for example, see Patent Document 1).

[0006] Existing technical documents

[0007] Patent documents

[0008] Patent Document 1: Japanese Patent Publication No. 2013-66902 Summary of the Invention

[0009] In existing methods for calculating heating schemes, since the heating scheme is calculated based on the inherent strain of the target based on the target shape, complex corrections are required in areas with dense heating lines.

[0010] The present invention was made in view of the following situation, and provides a calculation method capable of calculating a heating scheme including multiple heating lines for bringing a metal plate close to a target shape.

[0011] This invention provides a calculation method for a heating scheme used in the bending process of a metal plate using linear heating. The method comprises: a first step of performing finite element method structural analysis under first heating conditions including at least one first heating line set at a first position in an analysis model of the metal plate, and repeatedly performing a first trial by changing the position of the first heating line and comparing the analysis result with a target shape; a second step of selecting at least one first heating line set in a first trial where the analysis result in the repeatedly performed first trial is close to the target shape as a first selected heating line; a third step of performing finite element method structural analysis under second heating conditions including the first selected heating line and at least one second heating line set at a second position in the analysis model, and repeatedly performing a second trial by changing the position of the second heating line and comparing the analysis result with the target shape; and a fourth step of selecting at least one second heating line set in a second trial where the analysis result in the repeatedly performed second trial is close to the target shape as a second selected heating line; the heating scheme includes the first selected heating line and the second selected heating line, and in the first or third step, the analysis result and the target shape are divided into multiple blocks, and the analysis result is compared with the target shape for each block.

[0012] By employing the calculation method of this invention, since heating wires that closely approximate the target shape are repeatedly selected from heating wires positioned at various locations, it is possible to calculate a heating scheme that includes the most suitable multiple heating wires to bring the metal plate close to the target shape. Furthermore, by heating the metal plate using the calculated heating scheme, the metal plate can be deformed into a shape close to the target shape.

[0013] In the calculation method of this invention, in the first or third step, the analysis result and the target shape are divided into multiple blocks, and the analysis result and the target shape are compared for each block, thereby enabling appropriate evaluation of complex shapes. Therefore, heating schemes for complex target shapes can be fabricated. Furthermore, heating schemes requiring fewer heating wires can be fabricated. Attached Figure Description

[0014] Figure 1 This is a flowchart of a calculation method according to one embodiment of the present invention.

[0015] Figure 2 (a) to (c) are explanatory diagrams of a calculation method according to one embodiment of the present invention.

[0016] Figure 3 This is an explanatory diagram of a method for setting a heating wire included in a calculation method according to an embodiment of the present invention.

[0017] Figure 4This is an explanatory diagram of a method for selecting units on a heating line, included in a calculation method according to an embodiment of the present invention.

[0018] Figure 5 This is an illustrative diagram comparing the target shape with the analysis results included in the calculation method of one embodiment of the present invention.

[0019] Figure 6 This is an illustrative diagram comparing the target shape with the analysis results included in the calculation method of one embodiment of the present invention.

[0020] Figure 7 (a) to (e) are the heating schemes calculated in the simulation.

[0021] Figure 8 (a) to (d) are the results of structural analysis based on the calculation of the heating scheme.

[0022] Figure 9 (a) is the target shape (bowl shape) used for simulation, and (b) is the analysis result of the structural analysis based on the calculated heating scheme.

[0023] Figure 10 It is a comparison Figure 9 (a) and (b) are charts showing the target shape at the dashed line A-A' and the analysis results.

[0024] Figure 11 It is a comparison Figure 9 (a) and (b) are graphs showing the target shape at the single-dotted line B-B' and the analysis results.

[0025] Figure 12 (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 scheme.

[0026] Figure 13 The heating scheme is calculated in the simulation.

[0027] Figure 14 It is a comparison Figure 12 (a) and (b) are charts showing the target shape at the dashed line A-A' and the analysis results.

[0028] Figure 15 It is a comparison Figure 12 (a) and (b) are graphs showing the target shape at the dashed line B-B' and the analysis results.

[0029] Figure 16 (a) is the target shape (twisted type) used in the simulation, and (b) is the analysis result of the structural analysis based on the calculated heating scheme.

[0030] Figure 17The heating scheme is calculated in the simulation.

[0031] Figure 18 It is a comparison Figure 16 (a) and (b) are charts showing the target shape at the dashed line A-A' and the analysis results.

[0032] Figure 19 It is a comparison Figure 16 (a) and (b) are graphs showing the target shape at the dashed line B-B' and the analysis results.

[0033] Figure 20 This is a graph showing the changes in the analysis results and the error of the target shape as the number of heating wires selected increases during the fabrication of the heating scheme.

[0034] Figure 21 It is a 3D representation of the target shape.

[0035] Figure 22 This is an illustration of a method for calculating evaluation values ​​by comparing the analysis results of each block with the target shape.

[0036] Figure 23 The heating scheme was developed through structural analysis (selection of 200 heating wires).

[0037] Figure 24 It is the result of structural analysis using the heating scheme (the fabricated shape) and the difference between the structural analysis result and the target shape.

[0038] Figure 25 This is a graph showing the changes in the analysis results and the error (sum of squared errors of Z displacement) of the target shape as the number of heating wires selected increases during the fabrication of the heating scheme.

[0039] Figure 26 (a) shows the structural analysis results (formed shape) of a heating scheme (selected heating lines: 60) created using structural analysis without segmentation and evaluating the analysis results. (b) shows the error between the structural analysis results and the target shape.

[0040] Figure 27 (a) shows the results of structural analysis (shape making) using a heating scheme (selecting heating lines: 60) made by performing structural analysis by dividing the analysis results and the target shape by 100 and evaluating the analysis results. (b) shows the error between the results of structural analysis and the target shape.

[0041] Figure 28 This is a graph showing the changes in the analysis results and the error (sum of squared errors of Z displacement) of the target shape as the number of heating wires selected increases during the fabrication of the heating scheme.

[0042] Figure 29 This is a graph showing the changes in the analysis results and the error (sum of squared errors of Z displacement) of the target shape as the number of heating wires selected increases during the fabrication of the heating scheme. Detailed Implementation

[0043] This invention relates to a calculation method for a heating scheme used in the bending process of a metal sheet using linear heating. The method comprises: a first step, performing finite element method structural analysis under first heating conditions including at least one first heating line set at a first position in an analysis model of the metal sheet, and repeatedly performing a first trial by changing the position of the first heating line and comparing the analysis result with a target shape; a second step, selecting at least one first heating line set in the first trial where the analysis result in the repeatedly performed first trial is close to the target shape as a first selected heating line; a third step, performing finite element method structural analysis under second heating conditions including the first selected heating line and at least one second heating line set at a second position in the analysis model, and repeatedly performing a second trial by changing the position of the second heating line and comparing the analysis result with the target shape; and a fourth step, selecting at least one second heating line set in the second trial where the analysis result in the repeatedly performed second trial is close to the target shape as a second selected heating line. In the first or third step, the analysis result and the target shape are divided into multiple blocks, and the analysis result and the target shape are compared for each block.

[0044] The heating scheme includes a first selected heating line and a second selected heating line, and the analysis model is a finite element model with multiple elements and multiple nodes. Furthermore, in the first step, the analysis result is compared with the target shape using either the curvature or displacement at the nodes; in the third step, the analysis result is compared with the target shape using the other of the curvature and displacement at the nodes. By changing the comparison method in this way, both the calculation speed and accuracy can be improved.

[0045] In the calculation method of the present invention, preferably, if the target shape has either positive or negative curvature, then in the first and third steps, the analysis result is compared with the target shape using the curvature at the node. Preferably, if the target shape has both positive and negative curvature, then in the first and third steps, the analysis result is compared with the target shape using the displacement at the node. Thus, an excellent heating scheme can be created that makes the analysis result closer to the target shape.

[0046] The metal plate has a front and a back. Under the first heating condition, it is preferable to set the first heating line on either the front or the back surface; under the second heating condition, it is preferable to set the second heating line on either the front or the back surface. Furthermore, a preferred fourth step is to select at least one second heating line set in a plurality of second trials in which the analysis results in repeated second trials are close to the target shape, and to select the second heating line among the selected plurality of second heating lines that is set on the same surface as the surface on which the first selected heating line is set as the second selected heating line. This suppresses frequent changes in the heating surface on which the selected heating line is set, and improves the efficiency of bending processing using the heating scheme.

[0047] Preferably, the fourth step involves selecting at least one second heating line from multiple second trials in which the analysis results are close to the target shape, and then selecting the second heating line with the smallest bending amount from among the selected second heating lines as the second selected heating line. This suppresses excessive bending and reduces the number of selected heating lines in the heating scheme.

[0048] The present invention will now be described in more detail with reference to several embodiments. The structures shown in the accompanying drawings and the following description are merely exemplary, and the scope of the invention is not limited to the structures shown in the accompanying drawings and the following description.

[0049] First Implementation Method

[0050] Figure 1 This is a flowchart of the calculation method in this embodiment. Figure 2 (a) to (c) are diagrams illustrating the calculation method. Figure 3 This is an explanatory diagram showing how to set up the heating wire. Additionally, Figure 4 This is an explanatory diagram of the method for selecting units on the heating line.

[0051] The calculation method of this embodiment is the calculation method of heating scheme 6 used in the bending process of a metal plate using linear heating. Furthermore, the calculation method of this embodiment includes: a first step, performing finite element method structural analysis under a first heating condition including at least one first heating line 4 set at a first position of the analysis model 2 of the metal plate, and repeatedly performing a first trial by changing the position of the first heating line 4 and comparing the analysis result 3 with the target shape 10; a second step, selecting at least one first heating line 4 set in the first trial where the analysis result 3 in the repeated first trial is close to the target shape 10 as a first selected heating line 5; a third step, performing finite element method structural analysis under a second heating condition including the first selected heating line 5 and at least one second heating line 4 set at a second position of the analysis model 2, and repeatedly performing a second trial by changing the position of the second heating line 4 and comparing the analysis result 3 with the target shape 10; and a fourth step, selecting at least one second heating line 4 set in the second trial where the analysis result 3 in the repeated second trial is close to the target shape 10 as a second selected heating line 5.

[0052] Analysis model 2 is a finite element model with multiple elements 8 and multiple nodes 9. In the first step, the analysis result 3 is compared with the target shape 10 using one of the curvature and displacement at node 9. In the third step, the analysis result 3 is compared with the target shape 10 using the other of the curvature and displacement at node 9.

[0053] In addition, heating scheme 6 includes a first selective heating line 5 and a second selective heating line 5.

[0054] In the second or fourth step, you can select the heating line 4 that is closest to the target shape 10 in analysis result 3, or you can select the second or third heating line 4 that is closest to the target shape 10 in analysis result 3.

[0055] Furthermore, the program of this embodiment is created in such a way that a computer executes the calculation method of this embodiment.

[0056] The calculation method of this embodiment is to calculate the heating scheme used in the bending process of a metal sheet using linear heating by means of finite element method (FEM structural analysis).

[0057] The heating scheme is a plan for heating metal sheets for bending processes.

[0058] In the calculation method of this embodiment, an analysis model 2 of a metal plate is used. The length, width, and thickness of the metal plate are set in the analysis model 2. Furthermore, the analysis model 2 of the metal plate has a surface and a back surface. Additionally, the analysis model 2 is divided into multiple elements (mesh) 8. Elements 8 can be, for example, quadrilateral or triangular shells, or solids such as cubes, cuboids, triangular pyramids, or triangular prisms. Furthermore, each vertex of element 8 becomes a node 9. For example, in... Figure 2 In the analysis model 2 shown in (a), the analysis model 2 is divided into 20×20 (400) units 8, and each unit 8 is a quadrilateral shell. At this time, the analysis model 2 is lattice-shaped, and each intersection is a node 9.

[0059] In the calculation method of this embodiment, a model of target shape 10 is used. Target shape 10 is the shape that is the target for the bending process of the metal sheet. The model of target shape 10 is created by moving node 9 so that the shape of the analysis model 2 of the metal sheet becomes target shape 10.

[0060] In the calculation method of this embodiment, for example, it is possible to make a computer perform calculations based on... Figure 1 The flowchart shown illustrates the program that calculates heating scheme 6. Here, according to... Figure 1 The flowchart shown is used for illustration.

[0061] First, the computer reads the model of the target shape 10 and the analysis model 2.

[0062] Then, a heating line 4 is set at a first position in the analysis model 2. This first position can be randomly set at any location on the analysis model 2. The first position can be a location encompassed by the surface of the metal plate in the analysis model 2, or it can be a location encompassed by the back surface of the analysis model 2. The heating line 4 can be a straight line or a curve. Alternatively, multiple heating lines 4 can be set. For example, five heating lines 4 can be set.

[0063] For example, when heating line 4 is a straight line, such as Figure 3 As shown, 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 the two nodes 9. In this case, the set heating line 4 can be represented by the formula: y = {(y2-y1) / (x2-x1)}x + {(x2y1-x1y2) / (x2-x1)}.

[0064] For example, it can be set Figure 2 Heating wire 4a is shown in (a). Alternatively, when five heating wires 4 are set, heating wires 4a to 4e can be set. Figure 2In (a) to (c), although there is no difference between the heating wire 4 or selective heating wire 5 set on the surface of the metal plate and the heating wire 4 or selective heating wire 5 set on the back of the metal plate, some of the heating wires 4a to 4v and the selective heating wire 5 are set on the surface of the metal plate and some are set on the back of the metal plate.

[0065] Then, select the unit 8 on the designated heating line 4. If at least one side of unit 8 intersects the heating line 4, then unit 8 can be considered to be on the heating line 4. For example, in... Figure 4 In the analysis model 2 shown, units (1), (2), and (3) are on heating line 4, but unit (4) is not on heating line 4. When multiple heating lines 4 are set, units 8 on multiple heating lines 4 are selected.

[0066] Then, finite element method structural analysis is performed using analysis model 2. In the finite element method structural analysis, under the heating condition of linear heating by the set heating line 4, strain is applied to the selected element 8 to obtain analysis result 3 (analysis model deformed through structural analysis). The heating condition can include the input heat in addition to the position of the heating line 4. If the first heating line 4 is set on the surface of the analysis model 2 of the metal plate, the metal plate is heated from the surface side during the analysis. If the first heating line 4 is set on the back side of the analysis model 2 of the metal plate, the metal plate is heated from the back side during the analysis.

[0067] Finite element structural analysis can be either FEM thermo-elastic-plastic analysis or elastic analysis using the inherent strain method. In structural analysis, one can envision linear heating using a gas burner, linear heating using a laser (laser forming, etc.), or linear heating using induction heating. Furthermore, the material properties (Young's modulus, Poisson's ratio, density, etc.) of the metal sheet to be bent are used in the structural analysis.

[0068] In FEM thermo-elastic-plastic analysis, the inherent strain of the four components (i.e., longitudinal shrinkage, transverse shrinkage, angular deformation, and longitudinal bending) of the selected element 8 is calculated relative to the heating conditions (the location of the set heating line 4 (including the heating surface) and the heat input (J / mm)). In FEM thermo-elastic-plastic analysis, the thermal and deformation processes are reproduced sequentially for deformation analysis, thus enabling the analysis of transitional conditions.

[0069] In elastic analysis using the inherent strain method, the deformation of the metal plate (analysis model 2) caused by linear heating is considered to be 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 inherent deformation as a forced strain along the heating line 4 in the elastic analysis. Therefore, in elastic analysis using the inherent strain method, the structural analysis is performed using pre-calculated or measured inherent strain. For example, the inherent strain calculated using FEM thermo-elastic-plastic analysis, or the inherent strain obtained by measuring the actual linear heating deformation of the metal plate, can be used in the elastic analysis using the inherent strain method. Furthermore, elastic analysis using the inherent strain method can be performed using pre-calculated or measured formulas representing the relationship between input heat and inherent strain.

[0070] In addition, the inherent strain method is an elastic analysis, so as a characteristic, the calculation time is much shorter than that of thermo-elastic-plastic analysis.

[0071] Then, the analysis result 3 is compared with the target shape 10, and the error between the analysis result 3 and the target shape 10 is evaluated. Then, the evaluation value and the set position of the heating line 4 are saved in the storage unit.

[0072] As a whole, the evaluation value can be calculated by comparing the analysis result 3 with the target shape 10.

[0073] Furthermore, the analysis result 3 and the target shape 10 are divided into multiple blocks, and an evaluation value can be calculated by comparing the analysis result 3 with the target shape 10 for each block. For example, the analysis model 2 can be divided into blocks by dividing it into 4, 9, 16, 25, 36, 49, 64, 81, or 100 equal parts.

[0074] In addition, the evaluation value can be calculated by comparing the analysis result 3 as a whole of the analysis model with the target shape 10, and by comparing the analysis result of each block with the target shape.

[0075] As an evaluation metric, it could be the out-of-plane displacement (displacement amount) or curvature of node 9.

[0076] Figure 5 This is an explanatory diagram comparing analysis result 3 with target shape 10, using the out-of-plane displacement 13 of node 9 as an evaluation index, as part of the overall comparative analysis model. For example, as... Figure 5As shown, the out-of-plane displacement d (error) from node 9 of analysis result 3 to node 12 of the corresponding target shape 10 is calculated. Thus, when the evaluation index is the displacement d of node 9, a heating scheme that allows the metal plate to approach the target shape relatively quickly can be calculated. Furthermore, an evaluation value can be calculated in this comparison.

[0077] When comparing the analysis result 3 with the target shape 10 as a whole analysis model, the sum of the squared displacements d of all nodes 12 included in the analysis model (∑d) can be obtained. 2 To obtain an evaluation value.

[0078] Figure 6 This is an illustrative diagram illustrating the comparison between analysis result 3 and target shape 10 when analysis result 3 and target shape 10 are divided into multiple blocks and the comparison is performed on each block. The analysis model is three-dimensional, but... Figure 6 For illustration, a two-dimensional representation is used. For example, analysis result 3 and target shape 10 are divided into four blocks A to D. Then, the least squares line (regression line) of node 9 of analysis result 3 contained in block A is calculated (the least squares plane is calculated in the three-dimensional analysis model). Node 9 included in block A is rotated such that the least squares line is parallel to the x-axis (in the three-dimensional analysis model, node 9 is rotated such that the least squares plane is parallel to both the x-axis and y-axis, i.e., node 9 is rotated such that the normal vector of the least squares plane points to (0, 1)). Furthermore, the least squares line (least squares plane) is set to z = 0. After rotation, the z-axis coordinates of each node are z6 to z7. 10 .

[0079] Additionally, the least squares line (regression line) of node 12 of the target shape 10 included in block A is calculated (in the 3D analysis model, the least squares plane is calculated). Node 12 included in block A is rotated such that the least squares line is parallel to the x-axis (in the 3D analysis model, node 12 is rotated such that the least squares plane is parallel to both the x-axis and y-axis). Furthermore, the least squares line (least squares plane) is set to z = 0. After rotation, the z-axis coordinates of each node are z1 to z5. By rotating the analysis result 3 or the target shape 10 in this way, the direction of the analysis result 3 becomes the same as the direction of the target shape 10, thereby allowing for appropriate evaluation of the local error between the analysis result 3 and the target shape 10.

[0080] Then, calculate the difference (displacement) d1 to d5 between the z-axis coordinates of node 9 in analysis result 3 and its corresponding target shape node 12. Specifically, d1 = z1 - z6, d2 = z2 - z7, d3 = z3 - z8, d4 = z4 - z9, d5 = z5 - z 10Then, the displacements d1 to d5 of the nodes included in block A are squared and summed (d1... 2 +d2 2 +d3 2 +d4 2 +d5 2 The obtained value is used as the evaluation value (sum of squared errors) for block A.

[0081] Similar to block A, calculate the evaluation values ​​(sum of squared errors) for blocks B, C, and D respectively. Then, the evaluation value of the analysis result can be calculated by summing the evaluation values ​​of all blocks A to D included in the analysis model.

[0082] When calculating the evaluation value by comparing the analysis result 3 as a whole of the analysis model with the target shape 10, and by comparing the analysis result 3 of each block with the target shape 10, for example, the formula can be used: Evaluation value = (sum of squared errors of the whole). α ×∑(sum of squared errors in each block) β To calculate the evaluation value, α and β are weighting parameters. α and β can be determined based on rules of thumb or past data. The overall sum of squared errors helps maintain the overall shape, while the sum of squared errors in each block helps create the local shape.

[0083] If the evaluation metric is the curvature of node 9, then the error (curvature error r) between the curvature of node 9 in analysis result 3 and the curvature of node 12 of the target shape 10 corresponding to node 9 is calculated. Thus, when the evaluation metric is curvature, a heating scheme that can make the metal plate closely approximate the target shape can be calculated. Furthermore, in this comparison, an evaluation value can be calculated.

[0084] When comparing the overall analysis result 3 with the target shape 10 as part of the analysis model, the evaluation value ∑r can be obtained by summing the squares of the curvature errors r of all nodes 9 included in the analysis model. 2 .

[0085] When the evaluation index is the curvature of node 9, the analysis result 3 and the target shape 10 are divided into multiple blocks, and the analysis result 3 is compared with the target shape 10 for each block. The evaluation value (sum of squared errors) of each block can be calculated by squaring the curvature error r of all nodes included in the block and adding them together. The evaluation value of the analysis result can be calculated by adding the evaluation values ​​of all blocks together.

[0086] If the displacement and curvature of node 9 are used as evaluation indicators, then the displacement d and curvature error r of each node 9 can be calculated. Furthermore, in this comparison, an evaluation value can be calculated.

[0087] When comparing the overall analysis result 3 with the target shape 10 as an analysis model, the evaluation value can be obtained by squaring and summing the displacements d of all nodes 12 included in the analysis model (∑d). 2 The value obtained by squaring and summing the curvature errors r of all nodes 12 included in the analysis model (∑r) 2 The product of ) . For example, the evaluation value can be expressed using the formula: Evaluation value = (∑d 2 ) α ×(∑r 2 ) β To calculate this, we need to consider the weighting parameters α and β. α and β can be determined based on rules of thumb or historical data. For example, when α is 1, β can be greater than 5 and less than 10.

[0088] If we take the displacement and curvature of node 9 as the evaluation indicators, divide the analysis result 3 and the target shape 10 into multiple blocks, and compare the analysis result 3 and the target shape 10 for each block, then the evaluation value of each block can be the sum of the squares of the displacements d of all nodes 12 (after rotation) included in the block (∑d 2 The sum of the squares of the curvature errors r of all nodes 12 included in the block (∑r) 2 The product of ) . For example, the evaluation value can be expressed using the formula: Evaluation value = (∑d 2 ) α ×(∑r 2 ) β Then, the evaluation value of the analysis result can be calculated by summing the evaluation values ​​of all blocks.

[0089] Factors such as target shape and processing efficiency can be considered to determine whether to use displacement, curvature, or both as evaluation metrics.

[0090] The process from setting the heating line 4 to saving the evaluation value and the set position of the heating line 4 is called the first trial.

[0091] After the first trial runs, a second trial runs are conducted. The second trial runs follow essentially the same procedure as the first, but the heating line 4 is set at a different location than in the first trial. This location can be randomly set at any position on the analysis model 2. Furthermore, this location can be within the surface of the metal plate analysis model 2 or within the back surface of the analysis model 2. In the second trial, the heating line 4 can be a straight line or a curve. Additionally, multiple heating lines 4 can be set. For example, setting... Figure 2(a) shows the heating line 4b. Alternatively, if five heating lines 4 are set, for example, heating lines 4f to 4j can be set. Then, the elements 8 on the set heating lines 4 are selected, and finite element method structural analysis is performed to obtain analysis result 3. The obtained analysis result 3 is compared with the target shape 10 to calculate an evaluation value. Furthermore, the calculated evaluation value and the positions of the set heating lines 4 are saved in the storage unit.

[0092] Repeat this trial X times. For example, ... Figure 2 As shown in (a), the positions of heating wire 4 can be designated as heating wires 4c to 4k, and trials can be conducted at each position. Furthermore, multiple heating wires 4 can be set up for each trial. For example, if 5 heating wires are set up, 5 heating wires 4 can be set up for each trial. The number of trials can be set to, for example, more than 100 and less than 1500.

[0093] In the second to the Xth trials, displacement, curvature, or both displacement and curvature can be used as indicators to evaluate the error between analysis result 3 and target shape 10, but the same indicators as in the first trial are used. Furthermore, the evaluation values ​​are calculated in the same way as in the first trial.

[0094] The analysis result 3 in each trial becomes the shape corresponding to the heating line 4 at different positions, and becomes a different shape. The error (evaluation value) between the analysis result 3 and the target shape 10 is different in each trial.

[0095] Then, the heating line 4 in the trial with the smallest error (evaluation value) between analysis result 3 and target shape 10 is selected as the heating line 5. Alternatively, the heating line 4 in the trial with the second, third, fourth, or fifth smallest error (evaluation value) between analysis result 3 and target shape 10 can be selected as the heating line 5. The choice of which heating line 4 to use as the heating line 5 can be determined by considering factors such as the target shape 10 and the magnitude of the bending amount. Furthermore, if multiple heating lines 4 are set in the trial, multiple heating lines 4 are selected as the heating line 5. For example, it can be obtained from... Figure 2 (a) Heating wire 4d can be selected from heating wires 4a to 4k shown. Alternatively, if five heating wires 4 are set in each trial, heating wires 4f to 4j can be selected, for example.

[0096] The process from the first trial to the selection of heating line 5 is called the first heating line selection process.

[0097] After the first heating wire selection process ends, the second heating wire selection process begins. The second heating wire selection process is essentially the same as the first; however, when a heating wire 4 is randomly set at any position in the analysis model 2, both the selected heating wire 5 from the first heating wire selection process and the randomly set heating wire 4 in each trial of the second heating wire selection process are used to select the unit 8 on the heating wire 5 and the unit 8 on the set heating wire 4. By performing structural analysis under these heating conditions, analysis results 3 reflecting both the selected heating wire 5 and the set heating wire 4 can be obtained. Multiple heating wires 4 can also be set in each trial of the second heating wire selection process. Furthermore, the number of heating wires 4 set in each trial of the first heating wire selection process and the number of heating wires 4 set in each trial of the second heating wire selection process can be different. For example, it is possible to set... Figure 2 (b) shows the selection of heating line 5 and heating line 4l. In addition, if 5 heating lines 4 are set in each trial, for example, the selected heating lines (heating lines 4f to 4j) and heating lines 4l to 4p selected in the first heating line selection process can be set.

[0098] In the second heating wire selection process, trials are repeated up to X times. The heating wire 4 from the trial with the smallest error (evaluation value) between analysis result 3 and target shape 10 is selected as the chosen heating wire 5. Alternatively, the heating wire 4 from the trial with the second or third smallest error (evaluation value) between analysis result 3 and target shape 10 can be selected as the chosen heating wire 5. Furthermore, if multiple heating wires 4 are set during the trials, multiple heating wires 4 are selected as the chosen heating wire 5. For example, it can be from... Figure 2 (b) Heating wire 4s is selected from heating wires 4l to 4v shown. Alternatively, when setting 5 heating wires 4 in each trial, heating wires 4l to 4p can be selected, for example.

[0099] The heating wire selection process is performed sequentially for the 3rd, 4th, ..., nth time. Each heating wire selection process (referred to as the Ath heating wire selection process) is basically the same as the first heating wire selection process, but when at least one heating wire 4 is randomly set at any position in analysis model 2, the process includes at least one heating wire 4 randomly set in each trial of the Ath heating wire selection process, as well as all the selected heating wires 5 selected in the heating wire selection processes before (A-1). Furthermore, multiple heating wires 4 can be set for each trial of the Ath heating wire selection process. For example, when setting 5 heating wires 4, the process includes setting 5 heating wires 4 randomly set in each trial, as well as all the selected heating wires 5 selected in the heating wire selection processes before (A-1).

[0100] For example, in the third heating wire selection process, at least one heating wire 4 is set, including the selected heating wire 5 (4d) in the first heating wire selection process, the selected heating wire 5 (4s) in the second heating wire selection process, and randomly set in each trial of the third heating wire selection process. That is, as the number of heating wire selection processes increases, the number of selected heating wires 5 increases.

[0101] Furthermore, all units 8 on the selected heating line 5 and the set heating line 4 are selected, and structural analysis is performed under the heating conditions, thereby obtaining analysis results 3 that reflect all selected heating lines 5 and the set heating line 4.

[0102] In the Ath heating line selection process, the trial is repeated X times. The heating line 4 in the trial with the smallest error (evaluation value) between analysis result 3 and target shape 10 is selected as the heating line 5. Alternatively, the heating line 4 in the trial with the second or third smallest error (evaluation value) between analysis result 3 and target shape 10 can be selected as the heating line 5. Furthermore, if multiple heating lines 4 are set in the trial, multiple heating lines 4 are selected as the heating line 5.

[0103] If the analysis result 3 under the heating conditions of the selected heating line 5 in the nth heating line selection process is determined to have a small error (evaluation value) compared with the target shape 10, then the repetition of the heating line selection process is terminated, and the heating scheme 6, which includes the selected heating line 5 in the 1st to nth heating line selection processes, is completed. Heating scheme 6 is, for example, as follows: Figure 2 As shown in (c), it includes multiple selectable heating lines 5.

[0104] Furthermore, an upper limit can be set on the number of times the heating wire selection process is performed. This upper limit can be set to exceed the number of selected heating wires 5 required to achieve the first target shape 10. This prevents the heating scheme from including too many selected heating wires 5, thus preventing a heating scheme that results in high processing costs.

[0105] In this embodiment, in a portion of the multiple heating wire selection processes, displacement can be used as an indicator of the error between the analysis result 3 and the target shape 10 (the evaluation value is calculated using displacement), while in other heating wire selection processes, curvature can be used as an indicator of the error between the analysis result 3 and the target shape 10 (the evaluation value is calculated using curvature). That is, when transitioning from the Ath heating wire selection process to the (A+1)th heating wire selection process, the indicator of the error between the analysis result 3 and the target shape 10 is switched from displacement to curvature or vice versa. For example, in the heating wire selection process up to the point where the analysis result 3 is close to the target shape, displacement can be used as an indicator of the error between the analysis result 3 and the target shape 10, while in subsequent heating wire selection processes, curvature can be used as an indicator of the error between the analysis result 3 and the target shape 10. By using heating wire selection process that selects heating wire 5 based on displacement, the processing speed can be accelerated; by using heating wire selection process that selects heating wire 5 based on curvature, the processing accuracy can be improved. Therefore, both processing efficiency and processing accuracy can be balanced.

[0106] Alternatively, based on the analysis results, in each heating line selection process, one can choose whether to use displacement, curvature, or both displacement and curvature as error evaluation indicators, and perform calculations simultaneously.

[0107] By linearly heating and bending the metal sheet based on the obtained heating scheme 6, the metal sheet can be deformed into a shape close to the target shape. The bending of the metal sheet can be performed by an operator or automatically by a machine. When bending the metal sheet mechanically, multiple selective heating lines 5 can also be heated simultaneously.

[0108] Heating scheme 6 may include a sequence for selecting heating wires 5 that corresponds to the order of the heating wire selection process. When bending a metal sheet by linear heating based on heating scheme 6, the heating wires 5 can be selected and heated in this sequence. This allows the metal sheet to be deformed into a shape closer to the target shape.

[0109] The processing method for processing a metal plate according to the obtained heating scheme 6 may include the following steps: linearly heating the metal plate under heating conditions including the selected heating line 5 in the Ath (A=1 to n) heating line selection process to perform bending processing on the metal plate; measuring the three-dimensional shape of the bent metal plate; comparing the measured three-dimensional shape of the metal plate with the analysis result 3 of the finite element method structural analysis performed in the Ath heating line selection process under heating conditions including the selected heating line 5; and heating the metal plate based on the comparison result so that the three-dimensional shape of the metal plate is close to the analysis result 3.

[0110] The process of measuring the three-dimensional shape of a metal sheet can be performed using a 3D measuring instrument. This instrument can be contact-type, scanning laser probe-type, or optical non-contact type. This allows the metal sheet to be deformed into a shape closer to the target shape.

[0111] An automatic processing apparatus for metal sheets based on heating scheme 6 may include, for example, a heating unit for heating the metal sheet and a control unit for controlling the processing apparatus. The control unit is configured to read heating scheme 6 and control the heating unit to heat the metal sheet according to heating scheme 6.

[0112] Second Implementation Method

[0113] 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 is a shape with either positive or negative curvature (for example, when the target shape 10 is bowl-shaped), the curvature at node 9 is used as an index for evaluating the error between the analysis result 3 and the target shape 10. Thus, from the first heating wire selection process to the nth heating wire selection process, the analysis result 3 can reliably approximate the target shape 10, and an excellent heating scheme can be produced.

[0114] On the other hand, when the target shape 10 has both positive and negative curvature (for example, when the target shape 10 is saddle-shaped, twisted, etc.), the displacement at node 9 is used as an indicator to evaluate the error between the analysis result 3 and the target shape 10. Thus, from the first heating wire selection process to the nth heating wire selection process, the analysis result 3 can reliably approach the target shape 10, and an excellent heating scheme can be produced.

[0115] The other components are the same as in the first embodiment. Furthermore, the descriptions of the first embodiment, as long as they are not contradictory, also apply to the second embodiment.

[0116] Third Implementation Method

[0117] In the third embodiment, a heating line 4 is preferentially selected on the same heating surface (either the surface or the back of the metal plate) as the heating surface selected in the previous heating line selection process, and a heating scheme is simultaneously created. This suppresses frequent changes in the heating surface of the selected heating line 5, improving the efficiency of bending processes using the heating scheme.

[0118] Specifically, in the multiple trials conducted during the Ath heating line selection process, the trials with the smallest error (evaluation value) between analysis result 3 and target shape 10 are selected. For example, in the case of 500 trials, the 10 trials with the smallest error (evaluation value) between analysis result 3 and target shape 10 are selected. Furthermore, the number of trials selected can be set to, for example, 2 or more and 10 or less.

[0119] Next, in the selected trials, the heating line 4 with the smallest error (evaluation value) between the analysis result 3 and the target shape 10 is selected as the heating line 5, where the heating line 4 is set on the same heating surface as the heating line 5 selected in the (A-1)th heating line selection process. Thus, the selection of heating lines 5 set on the same heating surface can continue.

[0120] For example, in Figure 2 In (b), the selected heating line 5 (4d) in the previous heating line selection process is set on the surface of the metal plate. If the error (evaluation value) between the analysis results 3 of the trials of setting heating line 4s on the surface of the metal plate, setting heating line 4q on the back of the metal plate, and setting heating line 4v on the back of the metal plate and the target shape 10 is small, even if the error (evaluation value) between the analysis results 3 of the trials of setting heating line 4q and setting heating line 4v and the target shape 10 is smaller than the error (evaluation value) between the analysis results 3 of the trials of setting heating line 4s and the target shape 10, the heating line 4s set on the same heating surface as the selected heating line 5 (4d) is selected as the selected heating line 5.

[0121] In the selected trials, if no trials with heating line 4 are included on the same heating surface as the selected heating line 5 in the (A-1)th heating line selection process, the heating line 4 of the trial with the smallest error (evaluation value) between analysis result 3 and target shape 10 in the selected trials is selected as the selected heating line 5. In this case, the heating surface is replaced.

[0122] The other components are the same as in the first or second embodiment. Furthermore, the descriptions of the first or second embodiment, provided they are not contradictory, also apply to the third embodiment.

[0123] Fourth Implementation Method

[0124] In the fourth embodiment, during the heating wire selection process, heating wire 4 with a small bending amount is preferentially selected as the selected heating wire 5. This prevents the bending amount from becoming excessive and reduces the number of selected heating wires 5 included in the heating scheme. If the bending amount is too large, selected heating wires 5 need to be set to correct the excessive bending, which tends to increase the number of selected heating wires 5 included in the heating scheme.

[0125] Specifically, in the multiple trials conducted during the Ath heating line selection process, the trials with the smallest error (evaluation value) between analysis result 3 and target shape 10 are selected. For example, in the case of 500 trials, the 10 trials with the smallest error (evaluation value) between analysis result 3 and target shape 10 are selected. Furthermore, the number of trials selected can be set to, for example, 2 or more and 10 or less.

[0126] Next, among the selected trials, heating wire 4, which was set in the trial with the smallest bending amount, was chosen as the selected heating wire 5.

[0127] For example, in Figure 2 In (a), if the error (evaluation value) between the analysis results 3 of the trials with heating wire 4a, heating wire 4d, and heating wire 4j and the target shape 10 is small, and if the bending amount of the trial with heating wire 4d is smaller than that of the trials with heating wire 4a and heating wire 4j, then even if the error (evaluation value) between the analysis results 3 of the trials with heating wire 4a and heating wire 4j and the target shape 10 is smaller than that of the trial with heating wire 4d, heating wire 4d is selected as the selected heating wire 5.

[0128] Alternatively, trials with excessive bending during multiple trials can be excluded from the pool of candidates for heating wire 5.

[0129] The other components are the same as in the first, second, or third embodiments. Furthermore, the descriptions of the first, second, or third embodiments also apply to the fourth embodiment, provided they are not contradictory.

[0130] Fifth Implementation Method

[0131] In this embodiment, from the first heating wire selection process to the Ath heating wire selection process, the displacement is used as an indicator of the error between the evaluation analysis result 3 and the target shape 10 (the evaluation value is calculated using the displacement). In the (A+1)th and subsequent heating wire selection processes, both curvature and displacement are used as indicators of the error between the evaluation analysis result 3 and the target shape 10. The moment when the indicator is switched to both displacement and curvature based on the displacement can be, for example, set when the difference between the evaluation value of the selected heating wire in the (A-1)th heating wire selection process and the evaluation value of the selected heating wire in the Ath heating wire selection process is less than a predetermined value.

[0132] By switching the indicators in this way, a heating scheme with fewer heating lines can be created.

[0133] The other components are the same as in the first, second, third, or fourth embodiments. Furthermore, the descriptions of the first, second, third, or fourth embodiments also apply to the fifth embodiment, provided they are not contradictory.

[0134] simulation

[0135] The heating scheme (target shape: bowl-shaped, saddle-shaped, torsion-shaped) is calculated using the calculation method of the present invention (structural analysis: elastic analysis using the inherent strain method), and the calculated heating scheme is used to implement the simulation of elastic analysis (structural analysis) using the inherent strain method.

[0136] The inherent strain assigned to the element for deformation analysis using the inherent strain method is obtained by performing FEM thermo-elastic-plastic analysis on the analysis model and based on its deformation results.

[0137] In the structural analysis using the inherent strain method, a plate-shaped analysis model with a length and width of 500 mm was used. The model was divided into quadrilateral shell elements to achieve 2,601 nodes and 2,500 elements. The metal plate material was assumed to be SM490A (rolled steel for welded structures), and the plate thickness was assumed to be 16 mm. The material constants for SM490A are shown in Table 1. Three target shapes (bowl-shaped, saddle-shaped, and torsion-shaped) were selected for the simulation. The number of trials required to determine the location of a single selected heating wire was set to 500.

[0138] [Table 1]

[0139] Young's modulus: 212000MPa Poisson's ratio: 0.3 <![CDATA[Density: 7.81×10 -3 g / cm 3 >

[0140] In the FEM thermo-elastic-plastic analysis used to obtain the inherent strain, the analysis model was set with a plate length of 500 mm, a plate width of 500 mm, a plate thickness of 16 mm, and a number of nodes and elements of 61,711 and 50,000, respectively. The welding conditions were a current of 150 A, a voltage of 20 V, a welding speed of 2.286 mm / sec, and a welding efficiency of 0.8. The resulting inherent strains (longitudinal shrinkage, transverse shrinkage, longitudinal curvature, and transverse curvature) are shown in Table 2.

[0141] [Table 2]

[0142] <![CDATA[Longitudinal contraction ε x : -1.135476×10 -2 > <![CDATA[Longitudinal curvature ρ x : -4.790146×10 -4 > <![CDATA[Transverse contraction ε y .: -8.340290×10 -3 > <![CDATA[Transverse curvature ρ y : -3.917135×10 -6 >

[0143] Target shape: Bowl

[0144] Figure 7 (a) to (e) are heating schemes calculated with the number of heating wires selected set to 10, 20, 30, 40, and 55 respectively. Figure 8 (a) to (d) are the results of structural analysis using the inherent strain method based on heating schemes calculated with the number of heating wires set to 10, 20, 30 and 40 respectively. Figure 9 (a) is the target shape used in structural analysis. Figure 9 (b) is the analysis result of the structural analysis using the inherent strain method based on the heating scheme calculated with the number of heating wires set to 55. Figure 10 It is a comparison Figure 9 The target shape at the dashed line A-A' in (a) and (b) corresponds to the out-of-plane displacement distribution in the analysis results. Figure 11 It is a comparison Figure 9 The target shape at the dotted line B-B' in (a) and (b) corresponds to the out-of-plane displacement distribution of the analysis results.

[0145] In simulations where the target shape is set to a bowl shape, the curvature at the nodes is used as an indicator to evaluate the error between the target shape and the analysis results. Additionally, the number of heating wires is selected as 10, 20, 30, 40, and 55.

[0146] In this simulation, it is possible to calculate Figure 7 The heating schemes shown in (a) to (e) are further illustrated. Furthermore, structural analysis using the inherent strain method based on the calculated heating schemes yields… Figure 8 (a)~(d) Figure 9 The analysis results are shown in (b). Furthermore, Figure 7 The solid lines represent the selective heating lines on the surface of the metal plate, and the dashed lines represent the selective heating lines on the back of the metal plate.

[0147] from Figure 8From (a) to (d), it can be seen that selecting 10 heating wires tends to capture the bowl shape, while selecting 20 heating wires can shape a shape that is roughly consistent with the target shape. After this, it can be confirmed whether the shape can be fine-tuned or whether adding heating wires has almost no effect on the shape. Furthermore, if one focuses on... Figure 7 As shown in the heating positions, there are a number of selective heating lines arranged along the diagonal direction of the base material. This can be considered as the result of selecting the heating line positions to use both angular deformation and longitudinal bending to uniformly bend the base material as a whole in order to form a bowl-shaped depression in the center.

[0148] in addition, Figure 9 (a)(b) Figure 10 , Figure 11 It can be confirmed Figure 9 (b) shows an analysis result that captures the tendency of the target shape well. Therefore, it can be seen that by heating the metal plate based on the heating scheme calculated by the calculation method of the present invention, the metal plate can be bent into a shape close to the target shape.

[0149] Target shape: saddle-shaped

[0150] Figure 12 (a) is the target shape used for structural analysis. Figure 12 (b) is the analysis result of the structural analysis using the inherent strain method based on the heating scheme calculated with the number of heating wires set to 40. Figure 13 This is a heating scheme calculated with the number of heating wires selected set to 40. Figure 14 It is a comparison Figure 12 The target shape at the dashed line A-A' in (a) and (b) corresponds to the out-of-plane displacement distribution in the analysis results. Figure 15 It is a comparison Figure 12 The target shape at the dotted line B-B' in (a) and (b) corresponds to the out-of-plane displacement distribution of the analysis results.

[0151] In simulations where the target shape is set to a saddle shape, the out-of-plane displacement at the nodes is used as an indicator to evaluate the error between the target shape and the analysis results. Additionally, 40 heating lines are selected.

[0152] In this simulation, it is possible to calculate Figure 13 The heating scheme is shown. Furthermore, based on the calculated heating scheme, structural analysis using the inherent strain method can yield... Figure 12 The analysis results are shown in (b).

[0153] from Figure 12 , Figure 14 , Figure 15 It can be confirmed Figure 12The analysis results shown in (b) capture the tendency of the target shape well.

[0154] Target shape: Twisted

[0155] Figure 16 (a) is the target shape used for structural analysis. Figure 16 (b) is the analysis result of the structural analysis using the inherent strain method based on the heating scheme calculated with the number of heating wires set to 16. Figure 17 This is a heating scheme calculated with the number of heating wires selected set to 16. Figure 18 It is a comparison Figure 16 The target shape at the dashed line A-A' in (a) and (b) corresponds to the out-of-plane displacement distribution in the analysis results. Figure 19 It is a comparison Figure 16 The target shape at the dotted line B-B' in (a) and (b) corresponds to the out-of-plane displacement distribution of the analysis results.

[0156] In simulations where the target shape is distorted, the out-of-plane displacement at the nodes is used as an indicator to evaluate the error between the target shape and the analysis results. Additionally, 16 heating lines are selected.

[0157] In this simulation, it is possible to calculate Figure 17 The heating scheme is shown. Furthermore, based on the calculated heating scheme, structural analysis using the inherent strain method can yield... Figure 16 The analysis results are shown in (b).

[0158] from Figure 16 , Figure 18 , Figure 19 It can be confirmed Figure 16 The analysis results shown in (b) capture the tendency of the target shape well.

[0159] Target shape: Bowl shape (evaluation of evaluation indicators)

[0160] Set the target shape to a bowl shape. Figure 9 (a) The error between the evaluation analysis results and the target shape is set as the index of displacement, curvature, or both displacement and curvature. Structural analysis is carried out and a heating scheme is made. Figure 20 It is a graph showing the changes in the analysis results and the error of the target shape as the number of heating wires selected increases during the heating scheme production process. Figure 20 The sum of squared errors of the Z displacement along the vertical axis is the sum of the squared displacements in the z direction (out-of-plane direction, orthogonal to the surface and back of the initial metal plate) at the node.

[0161] The evaluation value of the analysis results is expressed using the formula: Evaluation value = (∑d 2 )α ×(∑r 2 ) β The calculated value. ∑d 2 ∑r is the value obtained by squaring and summing the displacements d of all nodes in the analysis model. 2 This value is obtained by squaring and summing the curvature errors *r* of all nodes included in the analysis model. α and β are weighting parameters. When β = 0, only displacement is used for evaluation; when α = 0, only curvature error is used for evaluation. When α ≥ 1 and β ≥ 1, both displacement and curvature error are used for evaluation, and the weight of curvature error is changed by varying β.

[0162] When evaluating the analysis results using only curvature error (α = 0), even with 50 heating lines selected, the sum of squared errors in Z-displacement exceeds 100. When evaluating the analysis results using only displacement (β = 0), the sum of squared errors in Z-displacement decreases significantly before the number of heating lines increases to 5, but then decreases slowly. Furthermore, even with 50 heating lines selected, the sum of squared errors in Z-displacement remains above 10.

[0163] When the analysis results are evaluated using both displacement and curvature error (α≥1, β≥1), the sum of squared errors of the Z displacement decreases compared to the cases evaluated using only curvature error and those evaluated using only displacement. Particularly in analyses with β=6 or β=8, the sum of squared errors of the Z displacement is less than 1.

[0164] Target shape: Complex shape (evaluation of segmentation number)

[0165] Will Figure 21 , Figure 22 The complex shape shown is used as the target shape for structural analysis, and a heating scheme is developed. In this target shape, protrusions 16 and concave parts 17 are alternately arranged. In this structural analysis, displacement is used as an indicator to evaluate the error between the analysis results and the target shape. Furthermore, in the structural analysis, the analysis results and the target shape are divided into 4, 16, or 64 segments, and the analysis results are compared with the target shape for each segment to calculate an evaluation value. Additionally, when comparing the analysis results with the target shape for each segment, the segments are rotated in a manner that aligns the direction of the analysis results with the direction of the target shape, and then compared. Structural analysis without segmentation is also performed.

[0166] Specifically, when evaluating the analysis results, the formula is used: Evaluation value = (Sum of squared errors of the whole) α ×∑(sum of squared errors in each block) βCalculate the evaluation value and select the heating line from the trial with the smaller evaluation value. The sum of squared errors is the sum of the squares of the displacements in the z-direction (out-of-plane direction, orthogonal to the front and back faces of the initial metal plate) at the node. Additionally, the "overall sum of squared errors" in the formula is a value that helps maintain the overall shape, while the "sum of squared errors in each block" is a value that helps create the local shape. Furthermore, α is the weight of the overall error, and β is the weight of the local error.

[0167] Figure 23 The heating scheme was developed through structural analysis (selection of heating wires: 200). Figure 24 The results of structural analysis using the fabricated heating scheme (fabricated shape) are shown, along with the differences between the structural analysis results and the target shape. Additionally, Figure 25 This is a graph showing how the analysis results change with the error (sum of squared errors of Z displacement) of the target shape as the number of heating wires selected increases during the fabrication of the heating scheme. In these analyses, α = 1, β = 12.

[0168] like Figure 25 As shown in the chart, in structural analysis where evaluation values ​​are calculated without segmentation (no segmentation), even with 200 heating lines, the sum of squared Z-displacement errors exceeds 200. However, as the number of segments increases, the sum of squared Z-displacement errors decreases. In structural analysis with 64 segments, if 200 heating lines are selected, the sum of squared Z-displacement errors decreases to approximately 10. Furthermore, as... Figure 24 As shown, the difference decreases significantly with the increase of the number of segments.

[0169] Target shape: Bowl-shaped (evaluation of the number of segments)

[0170] Set the target shape to a bowl shape. Figure 9 (a) A heating scheme was developed for structural analysis using the error between the evaluation results and the target shape as the displacement. In this structural analysis, the analysis results and the target shape were divided into 4, 16, 64, or 100 segments, and the evaluation value was calculated by comparing the analysis results with the target shape for each segment. The evaluation value was calculated using the formula: Evaluation value = ∑(sum of squared errors in each segment). Additionally, a structural analysis was also performed where the evaluation value was considered as the sum of squared errors for the entire structure without segmentation.

[0171] Figure 26 (a) Shows the results of structural analysis (formed shape) using a heating scheme (selected heating lines: 60) that was used to evaluate the analysis results without segmentation. Figure 26 (b) shows the result of the structural analysis and the error between the target shape and the result.

[0172] Figure 27(a) Shows the results of structural analysis (shape creation) using a heating scheme (selecting heating lines: 60) created by dividing the analysis results and target shape by 100 and evaluating the analysis results. Figure 27 (b) shows the result of the structural analysis and the error between the target shape and the result.

[0173] Figure 28 This is a graph showing how the analysis results change with the error (sum of squared errors of Z displacement) of the target shape as the number of heating wires selected increases during the fabrication of the heating scheme.

[0174] like Figure 28 As shown, in structural analysis where the results are evaluated without segmentation, even if 60 heating lines are selected, the Z-displacement error is approximately 30. If the heating scheme obtained from this structural analysis is used, the result will be as follows: Figure 26 The twisted bowl shape shown. Additionally, as... Figure 28 As shown, the sum of Z-displacement errors decreases with increasing segmentation number. In structural analysis where the analysis results and target shape are evaluated by segmenting the analysis results and target shape by 100, selecting 60 heating lines reduces the sum of Z-displacement errors to approximately 3. Additionally, as... Figure 27 As shown, the heating scheme obtained through this structural analysis can form an aesthetically pleasing bowl shape. These results indicate that a higher number of divisions leads to a better heating scheme.

[0175] Target shape: Bowl shape (evaluation of weighted parameters)

[0176] Set the target shape to a bowl shape. Figure 9 (a) Using the error between the evaluation analysis results and the target shape as the displacement index for structural analysis, a heating scheme was developed. In this structural analysis, the analysis results and the target shape were divided into 64 sections, and the evaluation value was calculated by comparing the analysis results with the target shape for each section. The evaluation value was calculated using the formula: Evaluation value = (Sum of squared errors of the whole). α ×∑(sum of squared errors in each block) β Calculate. α is the weight of the overall error, and β is the weight of the local error. α can be 0 or 1, and β can be 0, 1, 2, 4, 8, 16, or 32.

[0177] Figure 29 This is a graph showing how the error (sum of squared Z-displacement errors) between the analysis results and the target shape changes as the number of heating wires selected increases during the fabrication of the heating scheme. Additionally, Figure 29 The values ​​of α and β are shown in the figure. These results indicate that an excellent heating scheme can be obtained if β is set to around 8.

[0178] Explanation of reference numerals in the attached figures

[0179] 2: Analysis Model 3: Analysis Results 4, 4a~4v: Heating Line 5: Selecting Heating Line 6: Heating Scheme 8: Element 9: Node 10: Target Shape 11: Element of Target Shape 12: Node of Target Shape 13: Displacement of Analysis Results and Target Shape 16: Convex Part 17: Concave Part 19: Least Squares Line (Regression Line)

Claims

1. A calculation method for a heating scheme used in the bending process of a metal sheet using linear heating, characterized in that, This calculation method has the following characteristics: The first step involves performing a finite element method structural analysis under a first heating condition, including at least one first heating line set at a first position of the analysis model of the metal plate, and repeatedly performing a first trial by changing the position of the first heating line and comparing the analysis results with the target shape. The second step is to select at least one first heating line set in the first trial in which the analysis results of the repeated first trial are close to the target shape as the first selected heating line. The third step involves performing finite element structural analysis under second heating conditions, including a first selected heating line and at least one second heating line set at a second position in the analysis model, and repeatedly performing a second trial by changing the position of the second heating line to compare the analysis results with the target shape. as well as The fourth step is to select at least one second heating line from the second trial in which the analysis results are close to the target shape in the repeated second trial as the second selected heating line; The analysis model is a finite element model with multiple elements and multiple nodes; The heating scheme includes a first selective heating wire and a second selective heating wire; In the first or third step, the analysis result and the target shape are divided into multiple blocks. For each block, the least squares plane of the node is made consistent, and the analysis result is compared with the target shape.

2. The calculation method according to claim 1, wherein, In the first or third step, the analysis results are compared with the target shape using both the displacement and curvature at the node.

3. The calculation method according to claim 1, wherein, In the first step, the analysis results are compared with the target shape using the displacement at the node. In the third step, the analysis results are compared with the target shape using both the curvature and displacement at the node.

4. The calculation method according to claim 1, wherein, In the first step, the analysis result is compared with the target shape using either the curvature or the displacement at the node. In the third step, the analysis result is compared with the target shape using either the curvature or the displacement at the node.

5. The calculation method according to claim 1, wherein, If the target shape has either positive or negative curvature, then in the first and third steps, the analysis results are compared with the target shape using the curvature at the nodes. If the target shape has both positive and negative curvature, then in the first and third steps, the analysis results are compared with the target shape using the displacement at the node.

6. The calculation method according to any one of claims 1-5, wherein, In the first or third step, both the analysis results of each block are compared with the target shape, and the analysis results of the entire analysis model are compared with the target shape.

7. The calculation method according to any one of claims 1-5, wherein, The metal plate has a front surface and a back surface. Under the first heating condition, the first heating wire is set on either the surface or the back surface. Under the second heating condition, the second heating wire is set on either the surface or the back surface. The fourth step is to select at least one second heating line set in a second trial in which the analysis results of the repeated second trials are close to the target shape, and to select the second heating line among the selected second heating lines that is set on the same surface as the surface where the first selected heating line is set as the second selected heating line.

8. The calculation method according to any one of claims 1-5, wherein, The fourth step is to select at least one second heating line from the multiple second trials in which the analysis results are close to the target shape, and to select the second heating line with the smallest bending amount from the multiple selected second heating lines as the second selected heating line.

Images