Analysis method, program and analyzer of spring back characteristic of press molded article

Abstract

To provide an analysis method for predicting presence / absence of occurrence of a non-linear spring back of a press molded article before manufacturing the press molded article.SOLUTION: An analysis method of spring back characteristic of a press molded article performs a reference finite element model creation step of creating a reference finite element model including material characteristic including a Young's modulus, and data of a shape, plate thickness and stress of a press molded article before spring back deformation, a stress change finite element model creation step of creating a stress change finite element model whose magnitude of the stress in all or a part of a region of the reference finite element model is changed on the basis of a stress coefficient, a spring back simulation step by a finite element method, a spring back deformation evaluation value calculation step of determining a spring back deformation evaluation value from the shape before the spring back deformation of each of the models and the shape after the spring back deformation, and a spring back non-linearity evaluation step of determining a relation between the stress coefficient and the spring back deformation evaluation value, and thereby analyzes spring back characteristic of a press molded article.SELECTED DRAWING: Figure 12

Description

Technical Field

[0001] The present invention relates to a method, program, and analysis apparatus for analyzing springback characteristics of press-formed products of metal plates.

Background Art

[0002] In the production of press-formed products of metal plates such as steel plates and aluminum plates, when the metal plate is press-formed, the metal plate undergoes plastic deformation and internal stress (hereinafter referred to as "residual stress") is generated in the member after press-forming. When the press-formed product is removed from the press die, springback deformation occurs in which the member is deformed by the residual stress. As a result, the shape of the press-formed product after springback deformation is different from the die shape. Therefore, in order to ensure the shape accuracy of the press-formed product and make it the predetermined component design shape (hereinafter referred to as the "correct dimension shape"), generally, the die shape is preliminarily set to a shape that takes into account springback deformation.

[0003] Die anticipation means modifying the die (hereinafter referred to as "anticipated modification") to a shape in which the die surface shape is deformed in the direction opposite to the springback deformation from the correct dimension shape (hereinafter referred to as the "anticipated shape"). It is a technique for ensuring shape accuracy by performing press-forming with a die having an anticipated shape so that the shape of the press-formed product after springback deformation becomes the predetermined component design shape. When performing this die anticipation, if the amount of die anticipation modification (hereinafter referred to as the "anticipated amount" or "die anticipation amount") is excessively large or excessively small with respect to the appropriate modification amount, the formed product will not have the correct dimension shape. Therefore, in order to ensure shape accuracy, it is necessary to optimize the die anticipation amount with respect to springback deformation.

[0004] In general mold manufacturing, in order to ensure the dimensional accuracy of press-formed products, first, a press-forming trial is carried out using a mold with a correct dimension shape without prior mold estimation. The deviation amount of the shape of the trial press-formed product from the correct dimension shape is measured, and based on this deviation amount (hereinafter referred to as "differential displacement") or an amount obtained by correcting the differential displacement based on experience as the estimated amount, the mold shape is corrected. Next, a press-forming trial is carried out again using the estimated and corrected mold. If the shape accuracy of the trial press-formed product still cannot be ensured, the mold is estimated and corrected again based on the differential displacement of the shape of the trial press-formed product pressed by the estimated and corrected mold from the correct dimension shape. The mold is manufactured by repeating such mold estimation and correction based on the trial press and the shape of the trial press-formed product until the shape accuracy of the press-formed product can be ensured.

[0005] Here, as a prior art document, in Patent Document 1, a forming simulation using an elastic-plastic finite element method with a plate material model and a mold model is carried out to obtain the springback shape of the plate material model, and the deformation stress that causes the deformation amount of the shape difference between the springback shape and the product model shape is obtained by the forming simulation, and a method for creating press mold correction shape data for correcting the mold model using the deformation stress is disclosed.

[0006] In Patent Document 2, the shape of forming at the bottom dead center of press forming and the residual stress are calculated by the finite element method, and further, based on these, the shape after springback is calculated by the finite element method. The residual stress at the bottom dead center of press forming is decomposed into a moment component, an in-plane stress component, and an out-of-plane stress component. The moment component is multiplied by a coefficient α with α = 0, the in-plane stress component is multiplied by a coefficient β with -1 ≦ β < 0, and the out-of-plane stress component is multiplied by a coefficient γ with -1 ≦ γ < 0. A corrected residual stress obtained by adding up the moment component, the in-plane stress component, and the out-of-plane stress component each multiplied by the coefficient is calculated. The shape after springback is calculated by the finite element method from the shape of forming at the bottom dead center of press forming and the corrected residual stress, and a mold shape simulation system in which the calculated shape after springback is used as the expected shape of the twist correction mold for the press forming mold is disclosed.

[0007] In Patent Document 3, the surface of a metal panel after press forming is divided into a plurality of regions, and in each region, a stamper is pressed against the surface of the metal panel to measure the relationship between displacement and load. It is assumed that buckling occurs when the rigidity defined by (load increment / displacement increment) first becomes 1 / 8 or less (including 0) of the initial rigidity, and an evaluation method for obtaining the buckling occurrence distribution of the metal panel is disclosed. Buckling refers to a jump buckling that occurs when a part of a press-formed product is constrained by an arbitrary constraint method and another arbitrary part is partially loaded and pushed in with a stamper or the like. At the initial stage of pushing in, the increase in the pushing-in load with respect to the pushing-in amount is large and the rigidity is high, but as the pushing-in amount increases, the increase in the pushing-in load with respect to the pushing-in amount becomes small and the rigidity decreases.

[0008] In Patent Document 4, springback analysis is performed based on the data of the residual stress distribution and strain distribution before the release of a press-formed product to calculate the data of the shape of the press-formed product after release. Further, the residual stress distribution in a certain region including a part of the press-formed product before release is changed to 0, and based on this changed data, springback analysis is performed to calculate the data of the shape of the press-formed product after release. It is calculated how a certain defined quantity related to springback changes before and after changing the residual stress distribution in the certain region, and a press forming analysis method for calculating the contribution of the certain region and one or more regions other than the certain region to springback is disclosed.

Prior Art Documents

Patent Documents

[0009]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Summary of the Invention

Problems to be Solved by the Invention

[0010] The form of springback deformation becomes different forms of deformation such as wall warping, mouth opening, camber, and torsion depending on the form of the residual stress after press forming. In many cases, there are multiple forms of deformation even in one part. In the normal springback deformation form, since the shape of the press-formed product changes approximately proportionally to the mold allowance, it is easy to estimate the optimal mold allowance in the repetition of trial presses and mold allowance corrections. However, among the forms of springback deformation, there is also a form of springback deformation (hereinafter referred to as "non-linear springback") in which the amount of change in the shape of the press-formed product does not proportionally change with respect to the mold allowance. Press-formed products containing non-linear springback are difficult to deal with by mold allowance, and the number of repetitions of trial presses and mold allowance corrections becomes very large, resulting in a long lead time for mold production and an increase in costs, which is a problem.

[0011] Therefore, for non-linear springback, instead of ensuring shape accuracy by correcting the mold allowance, it is effective to take measures to reduce the residual stress that causes springback deformation itself by means such as press working methods and pre-processing of metal sheets, thereby reducing the springback deformation itself. For this purpose, it is necessary to predict the occurrence of non-linear springback in advance and manufacture a mold incorporating a method for reducing the resulting residual stress. However, it is difficult to predict non-linear springback in advance, and usually, non-linear springback is found in the press forming trial with the manufactured mold and the mold allowance correction. From such a point, in order to adopt a method for reducing the residual stress that causes non-linear springback, it is necessary to remanufacture the mold again, so the lead time and cost still increase significantly.

[0012] As described above, in order to reduce the number of repetitions of trial presses and mold allowance corrections and reduce the lead time and cost of mold production, it has been an issue to predict the presence or absence of non-linear springback before mold production.

[0013] However, the method for creating the corrected die shape data disclosed in Patent Document 1 is based on the shape difference between the springback shape and the product model shape, and assumes that the shape of the press-formed product changes approximately in proportion to the die allowance. Therefore, it is possible to obtain an optimal die allowance shape for a normal springback deformation mode in which the shape of the press-formed product changes approximately in proportion to the die allowance. However, it is difficult to obtain an optimal die allowance shape for the occurrence site of non-linear springback, and it is also impossible to predict the presence or absence of non-linear springback before die manufacturing.

[0014] The method for calculating the expected shape of the twist correction die disclosed in Patent Document 2 also assumes that the shape of the press-formed product changes approximately in proportion to the die allowance. Therefore, it is difficult to obtain an optimal expected die shape for the occurrence site of non-linear springback, and it is also impossible to predict the presence or absence of non-linear springback before die manufacturing.

[0015] Regarding the evaluation method for obtaining the occurrence distribution of buckling of a metal panel disclosed in Patent Document 3, the location where non-linear springback occurs is often the location where jumping buckling called buckling occurs because the relationship between the external load and the deformation is not linear. Therefore, a method for predicting the location where non-linear springback occurs by investigating the buckling location using the evaluation method of Patent Document 3 is also conceivable. However, in order to investigate the buckling location by the evaluation method of Patent Document 3 and predict the location where non-linear springback occurs, it is necessary to measure the rigidity of the actual press-formed product by a test. Therefore, it is impossible to predict the presence or absence of non-linear springback before die manufacturing.

[0016] In the press analysis method of Patent Document 4, it is possible to predict how the residual stress in a certain region among the residual stresses before demolding of the press-formed part affects the springback. However, it is impossible to predict the presence or absence of non-linear springback before die manufacturing.

[0017] The present invention has been made in view of the above circumstances, and an object thereof is to provide an analysis method, a program, and an analysis apparatus for predicting the presence or absence of occurrence of non-linear springback of a press-formed product before manufacturing a press die.

Means for Solving the Problems

[0018] The inventors investigated and studied various press forming and springback deformations after press forming by using numerical simulation of press forming by the finite element method using a computer (hereinafter referred to as "forming simulation"), numerical simulation of springback deformation after press forming (hereinafter referred to as "springback simulation"), and performing press forming prototypes, and obtained the following findings.

[0019] When a general springback deformation occurs in a press-formed product, the amount of deformation is approximately proportional to the expected amount of the press die, that is, it changes linearly. For example, when a part having a U-shaped cross section shown in a general FIG. 1 is press-formed with a die having a normal size shape, a springback deformation occurs in which the vertical wall portion opens outward like the cross-sectional shapes of the forming bottom dead center (solid line) and after springback deformation (dotted line) of the A-A cross section shown in FIG. 2. On the other hand, when press forming is performed with a die having an expected shape (dashed-dotted line) modified by expecting the vertical wall portion of the press die to deform in the direction of closing the opening opposite to the springback deformation as shown in FIG. 3, the shape after springback deformation changes in the direction of closing the opening according to the expected amount, so the shape of the press-formed product approaches the normal size shape more than when press forming is performed with a die having a normal size shape.

[0020] FIG. 4 shows the relationship between the expected amount h1 of the mold at point B and the distance (differential displacement) with respect to the nominal shape when a steel plate with a thickness of 1.0 mm and a tensile strength of 980 MPa is pressed using a mold with a nominal shape and a mold with an expected shape to form a U-shaped cross-section part (length 180 mm, cross-section height 45 mm, width 52 mm) shown in FIG. 1, and after pressing, the molded product is taken out from each mold and springback deformed. Note that point B is the end of cross-section A-A shown in FIG. 1. The expected amount h1 in FIG. 4 is the expected amount in the inner direction of the U-shape with respect to the nominal shape, and the result when the expected amount h1 is 0 mm is the result when press forming is performed using a mold without expected correction, that is, a mold with a nominal shape. Also, the sign of the differential displacement in FIG. 4 is represented by plus when the shape after springback deformation is displaced in the outer direction of the U-shape with respect to the nominal shape, and is represented by minus when it is displaced in the inner direction.

[0021] As shown in FIG. 4, the differential displacement at point B changes linearly with respect to the expected amount of the mold. When the differential displacement changes linearly in this way, by adjusting the expected amount of the mold while comparing the shape after springback deformation of the press-molded product with the nominal shape, the required shape accuracy of the press-molded product can be ensured. Springback deformation is a deformation caused by residual stress generated in the member during press forming, and when the level of the residual stress is changed, the springback deformation amount also changes accordingly. In particular, when the springback deformation amount changes approximately linearly with respect to the expected amount of the mold, the springback deformation amount also changes approximately linearly with respect to the change amount of the level of the residual stress.

[0022] In this case, in the springback simulation based on the part shape and residual stress at the bottom dead center of press forming, when an arbitrary coefficient (hereinafter referred to as the "stress coefficient" and represented by the variable symbol k) is multiplied by the stress of the finite element method model to numerically change the magnitude of the stress, the springback amount of the springback simulation result also changes approximately linearly with the change amount of the stress coefficient k.

[0023] For example, in a springback simulation assuming that a steel sheet with a thickness of 1.0 mm and a tensile strength of 980 MPa is press-formed using a mold with the part shape (true dimension shape) to form a U-shaped cross-section part shown in FIG. 1, FIG. 5 shows the change in the springback amount at point B when the stress value is changed by multiplying the residual stress of the finite element method model by the stress coefficient k. As shown in FIG. 5, the relationship between the stress coefficient k and the springback deformation amount at point B in the simulation results is approximately linear. Note that the sign of the springback deformation amount in FIG. 5 is positive for the deformation amount in the outer direction (mouth opening direction) of the U-shape and negative for the deformation amount in the inner direction (mouth closing direction).

[0024] By the way, when a rectangular tube drawing shape (bathtub shape) as shown in FIG. 6 is drawn and formed, depending on the forming conditions, springback deformation occurs in which the bottom surface portion bends and undergoes out-of-plane deformation as shown in FIGS. 7 and 8. Note that FIG. 7 is a contour diagram showing the springback amount in the z direction in the figure, and FIG. 8 is a diagram showing the cross-sectional shape at the bottom dead center of forming (shown by a solid line) and after springback deformation (shown by a dotted line) in the C-C cross-section of FIG. 6.

[0025] For the purpose of suppressing the bending of the part bottom surface portion as shown in FIG. 8, for example, as shown in FIG. 9, even if mold anticipation (shown by a dashed-dotted line) is performed in the direction opposite to the bending of the bottom surface portion of the press mold, in a press-formed product with a bathtub shape, usually such mold anticipation does not cause a large change in the bending of the bottom surface portion. That is, this bending deformation is a deformation due to non-linear springback in which the relationship between the mold anticipation amount and the change amount of the shape of the press-formed product after springback deformation is not linear.

[0026] Figure 10 shows the difference displacement between the expected amount h2 of the mold at point D and the distance (differential displacement) with respect to the nominal shape when a steel sheet with a thickness of 1.0 mm and a tensile strength of 980 MPa is pressed with a nominal shape mold and an expected shape mold to form a bathtub-shaped part (length 457 mm, width 257 mm, height 40 mm) shown in Figure 6, and the formed product is taken out from each mold after pressing to deform the springback. Note that point D is the center of the bottom surface of the part shown in Figure 6, that is, the position of the center of the bottom surface in the C-C cross section. The expected amount h2 in Figure 10 is the expected amount in the negative z direction. The result when the expected amount h2 is 0 mm is the result when press forming is performed with a mold without expected correction, that is, a nominal shape mold. Also, the differential displacement in Figure 10 indicates the springback deformation amount in the positive z direction with respect to the nominal shape.

[0027] As shown in Figure 10, even when the expected amount h2 changes, the differential displacement does not change much, and it is difficult to make the shape after springback approach the nominal shape by increasing the expected amount. Therefore, it is difficult to ensure the required shape accuracy by adjusting the expected amount. The reason why it is difficult to adjust the expected amount in a bathtub-shaped part is that the deflection deformation of the bottom surface of the part is caused by the compressive stress generated as residual stress.

[0028] When the bathtub-shaped part is taken out from the mold after press forming, the compressive stress is released at the bottom surface of the part and the cross-sectional line length extends. However, since the periphery of the bottom surface is constrained by the vertical wall, it cannot extend in the in-plane direction. As a result, out-of-plane deformation occurs and deflection occurs at the bottom surface. Furthermore, when the mold is expected with the deflection deformation of the bottom surface in mind, the cross-sectional line length of the bottom surface part at the bottom dead center of the press mold is longer than the nominal shape without mold expectation, and since the expected amount is a small amount, compressive stress almost at the same level as when no mold expectation is made is generated at the bottom surface. Therefore, the cross-sectional line length of the bottom surface after springback deformation extends further than the bottom surface shape of the expected mold that is longer than the nominal shape, so it becomes longer than the nominal shape and deflection occurs.

[0029] The amount of deformation of such non-linear springback does not change in proportion to the residual stress even when the level of the residual stress is changed. Therefore, in springback simulation, even if the residual stress of the finite element method model for performing the simulation is numerically changed by multiplying an arbitrary stress coefficient k to the residual stress, the amount of springback deformation of the simulation result does not change linearly with respect to the stress coefficient k.

[0030] FIG. 11 is a diagram showing a change in the amount of springback at the position of point D when the stress value is changed by multiplying the residual stress of the finite element method model by the stress coefficient k in a springback simulation assuming press forming a steel sheet with a thickness of 1.0 mm and a tensile strength of 980 MPa using a mold of a part shape (nominal shape) in order to form the bathtub shape shown in FIG. 6. In FIG. 11, the amount of springback deformation on the plus side in the z direction with respect to the nominal shape is represented by a positive numerical value, and the amount of springback deformation on the minus side in the z direction is represented by a negative numerical value.

[0031] As shown in FIG. 11, when the stress coefficient k is changed in the springback simulation of the bathtub shape, the amount of springback does not change linearly with respect to the stress coefficient k, and has a non-linear relationship.

[0032] According to the results of FIGS. 5 and 11 described above, if the linearity of the amount of springback deformation with respect to the stress coefficient k in the springback simulation is evaluated, it is possible to evaluate whether the springback deformation of the press-formed product is non-linear springback with low linearity with respect to the mold allowance amount, and it is possible to predict the presence or absence of non-linear springback before mold manufacturing.

[0033] The present invention has been made based on the above findings, and one aspect of the present invention for solving the above-described problems is a method for analyzing springback characteristics of a press-formed product of a metal plate, including: a reference finite element model creation step of creating a reference finite element model including material properties including the Young's modulus of the metal plate and data of the shape, plate thickness, and stress before springback deformation of the press-formed product to be analyzed; a stress change finite element model creation step of creating two or more stress change finite element models in which the magnitude of the stress in all or a part of the regions of the reference finite element model is changed based on a stress coefficient, with one or different stress coefficients; a springback simulation step of performing a deformation analysis by the finite element method for each of two or more of the created reference finite element model and the stress change finite element models to obtain the shape after springback deformation; a springback deformation evaluation value calculation step of obtaining a springback deformation evaluation value related to springback deformation from the shape before springback deformation and the shape after springback deformation of each model for which the shape after springback deformation has been obtained; and a springback non-linearity evaluation step of obtaining the relationship between the stress coefficient and the springback deformation evaluation value from the stress coefficient and the springback deformation evaluation value of each model for which the shape after springback deformation has been obtained, and is characterized by including these steps.

Advantages of the Invention

[0034] According to the present invention, it is possible to predict the presence or absence of occurrence of non-linear springback of a press-formed product before manufacturing a press die.

Brief Description of the Drawings

[0035]

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Mode for Carrying Out the Invention

[0036] Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the present specification and drawings, elements having substantially the same functional configuration are denoted by the same reference numerals, and redundant description is omitted.

[0037] 〔Method for analyzing springback characteristics〕 <First Embodiment> FIG. 12 is a flowchart for explaining a method for analyzing springback characteristics according to the first embodiment. The outline of the analysis method according to this embodiment is as follows.

[0038] First, in a reference finite element model creation step S11, a finite element method model (hereinafter referred to as "reference finite element model") serving as a reference for performing springback simulation is created. This reference finite element model includes material properties including the Young's modulus of the metal plate that is the material of the press-formed product to be analyzed, the shape of the press-formed product before springback deformation, the plate thickness, and data on stress (residual stress). Note that the "shape of the press-formed product before springback deformation" can be rephrased as the shape of the metal plate before being released from the press die or the shape of the metal plate at the bottom dead center of the press die.

[0039] Next, in a stress change finite element model creation step S12, a finite element method model (hereinafter referred to as "stress change finite element model") in which the magnitude of the residual stress in the reference finite element model is changed based on a stress coefficient k is created.

[0040] Next, in a springback simulation step S13, springback simulation is performed on both the above-mentioned reference finite element model and the above-mentioned stress change finite element model or only the stress change finite element model to obtain the shape after springback deformation.

[0041] Next, in the springback deformation evaluation value calculation step S14, a springback deformation evaluation value SI for performing an analysis of springback deformation from the shape after each springback deformation is calculated, and the relationship between the stress coefficient k and the springback deformation evaluation value SI is obtained.

[0042] Then, in the springback non-linearity evaluation step S15, based on the relationship between the stress coefficient k and the springback deformation evaluation value SI, the non-linearity is evaluated, and it is determined whether the springback deformation occurring in the target press-formed product is non-linear springback.

[0043] Hereinafter, the details of each step will be described.

[0044] (Reference finite element model creation step S11) In the reference finite element model creation step S11, a reference finite element model for performing a springback simulation, which is a deformation analysis due to the release of residual stress, is created from the data of the shape, plate thickness, and residual stress generated in the member at the bottom dead center of the press during the press forming of the metal plate that is the material of the press-formed product. The shape, plate thickness, and residual stress generated in the member at the bottom dead center of the press may be obtained, for example, by performing a forming simulation that is an elastoplastic deformation analysis using the finite element method, but it is not necessarily required to be obtained by the forming simulation. For example, when analyzing the influence on non-linear springback when the shape, plate thickness, stress, etc. of the press-formed product change, the analyst may arbitrarily set the shape, plate thickness, and stress of the press-formed product based on certain assumptions.

[0045] (Stress change finite element model creation step S12) In the stress change finite element model creation step S12, the shape and thickness of the press-formed product are set to the same conditions as the reference finite element model, and a stress change finite element model is created by multiplying the residual stress in all or part of the regions of the reference finite element model by a stress coefficient k to change the residual stress. In principle, in order to evaluate the non-linearity of the springback amount with respect to the stress coefficient k, three or more sets of the relationship between the stress coefficient k and the springback amount are required. In order to obtain three or more sets of this relationship, for example, three or more stress change finite element models with different stress coefficients k are created.

[0046] However, when the residual stress is 0, that is, when the stress coefficient k for changing the residual stress of the finite element model is 0, the springback amount is also 0. Therefore, even without performing a springback simulation by the finite element method, one set of the relationship between the stress coefficient k and the springback amount can be obtained. Thus, if at least two springback simulations by the finite element method are performed, three sets of the relationship between the stress coefficient k and the springback amount can be obtained. Also, the reference finite element model can be regarded as a stress change finite element model under the condition of stress coefficient k = 1. If the reference finite element model is used as one set of models for obtaining the relationship between the stress coefficient k and the springback amount, only one stress change finite element model needs to be created at least. Of course, three stress change finite element models with stress coefficients k other than 0 and 1 can also be created.

[0047] Note that the number of sets of the relationship between the stress coefficient k and the springback amount for evaluating non-linearity is not limited to three sets. The larger the number of sets, the more accurately the non-linearity of springback can be evaluated, and thus the prediction accuracy of whether the springback occurring in the press-formed product is non-linear springback is improved.

[0048] (Springback Simulation Step S13) In the springback simulation step S13, a springback simulation using the finite element method with a computer is performed on the reference finite element model created in the reference finite element model creation step S11 and the stress change finite element model created in the stress change finite element model creation step S12. Through this springback simulation, the shapes after springback deformation of the reference finite element model and the stress change finite element model are obtained respectively.

[0049] Note that the springback simulation of the reference finite element model and the stress change finite element model is a deformation analysis by releasing the residual stress. However, if this is performed as an elastoplastic deformation analysis similar to the press forming simulation, the non-linearity of the stress-strain characteristics of the material may affect the shape after springback deformation. Therefore, in order to obtain the shape after springback deformation excluding the influence of the non-linearity of the stress-strain characteristics of the material, it is desirable to perform the springback simulation by elastic deformation analysis in which plastic deformation does not occur.

[0050] (Springback Deformation Evaluation Value Calculation Step S14) In the springback deformation evaluation value calculation step, by comparing the shapes after springback deformation of the reference finite element model and the stress change finite element model obtained in the springback simulation step S13 with the shape before springback deformation, a springback deformation evaluation value SI, which is an index indicating the change in shape due to springback, is calculated. Note that the springback deformation evaluation value SI is not an index limited to a specific value, and any index indicating the change in shape due to springback may be used. Hereinafter, an example of the springback deformation evaluation value SI will be described.

[0051] The springback deformation evaluation value SI is, for example, the displacement amount from before springback deformation to after springback deformation at an arbitrary node of the reference finite element model or the stress change finite element model, or a function value using these as variables. When using such a springback deformation evaluation value SI, it is possible to evaluate the non-linearity of the springback deformation at each node site.

[0052] On the other hand, when the surface accuracy of a flat surface such as a seating surface of an automotive press part or the like is important, the springback deformation amount in the in-plane direction of the material is not a problem, and the springback deformation amount in the out-of-plane direction becomes important. When the springback deformation in a specific direction is important in this way, it is preferable to use, as the springback deformation evaluation value SI, the amount of any directional component of the displacement from before springback deformation to after springback deformation at an arbitrary node of the stress change finite element model or a function value having any directional component of the displacement as a variable. Thereby, it is possible to evaluate the non-linearity of the springback deformation in the said direction.

[0053] In addition, the springback deformation evaluation value SI can be not only for an arbitrary node of the finite element model but also for the deformation state of the whole part such as the opening, twist, and warp of the press-formed product. For example, if the springback deformation evaluation value SI is set to the amount of change in the distance between any two parts or nodes or a function value having the distance between these nodes as a variable, it is possible to evaluate the non-linearity related to the opening deformation. Also, for example, if the springback deformation evaluation value SI is set to the amount of angular change of another part with respect to any one part or a function value having this amount of angular change as a variable, it is possible to evaluate the non-linearity related to the twist deformation. Also, for example, if the springback deformation evaluation value SI is set to the amount of change in the curvature of any part or a function value having this amount of change in the curvature as a variable, it is possible to evaluate the non-linearity related to the warp deformation.

[0054] (Springback non-linearity evaluation step S15) In the springback non-linearity evaluation step S15, the non-linearity of the springback deformation evaluation value SI with respect to the stress coefficient k is evaluated from three or more sets of the stress coefficient k and the springback deformation evaluation value SI.

[0055] Here, a set of a stress coefficient k and a springback deformation evaluation value SI is set as follows, for example. As an example, when creating a stress change finite element model, the stress coefficient k multiplied by the residual stress of the reference finite element model and the springback deformation evaluation value SI calculated from the shape after springback simulation of the stress change finite element model can be set as a set of the stress coefficient k and the springback deformation evaluation value SI. Also, for example, since the reference finite element model can be regarded as a stress change finite element model when the stress coefficient k is 1, 1 (i.e., stress coefficient k = 1) and the springback deformation evaluation value SI calculated from the shape after springback simulation of the reference finite element model can be set as a set of the stress coefficient k and the springback deformation evaluation value SI. Also, for example, in creating a stress change finite element model, when changing the residual stress by multiplying the stress coefficient k in all regions of the reference finite element model, when the stress coefficient k is 0, the residual stress of the stress change finite element model becomes 0 and no springback deformation occurs. Therefore, a set of 0 (i.e., stress coefficient k = 0) and the springback deformation evaluation value SI when the springback deformation amount is 0 can be set as one of the sets of the stress coefficient k and the springback deformation evaluation value SI for evaluating non-linearity.

[0056] Here, the evaluation of the non-linearity of the stress coefficient k and the springback deformation evaluation value SI is performed as follows, for example. As an example, a graph is created by plotting the set of the stress coefficient k and the springback deformation evaluation value SI with the stress coefficient k and the springback deformation evaluation value SI as variables, and is displayed or printed for the analyst. The analyst determines based on, for example, the linearity of the graph, whether it monotonically increases or decreases. Specifically, when the linearity of the stress coefficient k and the springback deformation evaluation value SI is strong and the springback deformation evaluation value SI monotonically increases or decreases with respect to the change in the stress coefficient k, it can be determined that a springback occurs that is easy to correct the shape accuracy according to the mold prediction. On the other hand, when the springback deformation evaluation value SI does not monotonically increase or decrease with respect to the change in the stress coefficient k and the springback deformation evaluation value SI changes non-linearly, it can be determined that a non-linear springback occurs that is difficult to correct the shape accuracy according to the mold prediction.

[0057] Also, as another example of the non-linearity evaluation method, in the graph of the stress coefficient k and the springback deformation evaluation value SI, not only the set of the stress coefficient k and the springback deformation evaluation value SI is plotted, but also an approximation formula of the springback deformation evaluation value SI with respect to the stress coefficient k is obtained from the set of the stress coefficient k and the springback deformation evaluation value SI, and the approximation formula may be displayed on the graph. The presence or absence of non-linear springback may be determined by, for example, the analyst checking the linearity of the approximation formula.

[0058] As described above, the method for analyzing the springback characteristics according to the first embodiment has been described. According to this analysis method, it is possible to determine the presence or absence of non-linear springback occurring in the press-formed product to be analyzed by simulation using the finite element method. That is, it is possible to predict the presence or absence of non-linear springback of the press-formed product before mold production.

[0059] <Second Embodiment> FIG. 13 is a flowchart for explaining a method for analyzing springback characteristics according to the second embodiment. In this embodiment, the springback characteristics are analyzed as follows.

[0060] (Step S21 for creating a reference finite element model) First, in step S21 for creating a reference finite element model, a reference finite element model is created that includes material properties including the Young's modulus of the metal plate that is the material of the press-formed product to be analyzed, the shape of the press-formed product before springback deformation, the plate thickness, and data of stress (residual stress).

[0061] (Step S22 for creating a stress change finite element model) Next, in step S22 for creating a stress change finite element model, a stress change finite element model is created in which the stress value is changed by multiplying the residual stress in the reference finite element model by a stress coefficient k.

[0062] (Step S23 for springback simulation) Next, in step S23 for springback simulation, springback simulation is performed for both the reference finite element model and the stress change finite element model or only the stress change finite element model to obtain the shape after springback deformation.

[0063] (Step S24 for calculating springback deformation evaluation value) Next, in step S24 for calculating springback deformation evaluation value, a springback deformation evaluation value SI for analyzing springback deformation is calculated from each shape after springback deformation, and the relationship between the stress coefficient k and the springback deformation evaluation value SI is obtained.

[0064] The above-mentioned reference finite element model creation step S21, stress change finite element model creation step S22, springback simulation step S23, and springback deformation evaluation value calculation step S24 are the same steps as the reference finite element model creation step S11, stress change finite element model creation step S12, springback simulation step S13, and springback deformation evaluation value calculation step S14 in the first embodiment. In the analysis method according to the second embodiment, a non-linear index calculation step S25 is performed after the springback deformation evaluation value calculation step S24. The details of the non-linear index calculation step S25 will be described below.

[0065] (Non-linear index calculation step S25) In the non-linear index calculation step S25, a non-linear index NLI, which is an index of the non-linearity of the change in the springback amount, is calculated from a plurality of sets of the stress coefficient k and the springback deformation evaluation value SI.

[0066] Here, for example, a set of the stress coefficient k and the springback deformation evaluation value SI is set as follows. As an example, when creating a stress change finite element model, the stress coefficient k multiplied by the residual stress of the reference finite element model and the springback deformation evaluation value SI calculated from the shape after springback obtained by the springback simulation of the stress change finite element model can be set as a set of the stress coefficient k and the springback deformation evaluation value SI. Also, for example, since the reference finite element model can be regarded as a stress change finite element model when the stress coefficient k is 1, 1 (i.e., stress coefficient k = 1) and the springback deformation evaluation value SI calculated from the shape after springback obtained by the springback simulation of the reference finite element model can be set as a set of the stress coefficient k and the springback deformation evaluation value SI. Also, for example, when creating a stress change finite element model, if the residual stress is changed by multiplying the stress coefficient k in all regions of the reference finite element model, when the stress coefficient k is 0, the residual stress of the stress change finite element model becomes 0 and no springback deformation occurs. Therefore, a set of 0 (i.e., stress coefficient k = 0) and the springback deformation evaluation value SI when the springback deformation amount is 0 can be set as one of the sets of the stress coefficient k and the springback deformation evaluation value SI for evaluating non-linearity. Here, for example, when the springback deformation evaluation value SI is set as the displacement amount and the displacement direction component amount at each node, the change amount of the distance between any two parts or nodes, the angle change amount of another part with respect to any part, or the curvature change amount of any part, etc. of the shape after springback with respect to the shape before springback, or a function value obtained by non-dimensionalizing them, the springback deformation evaluation value SI when there is no springback deformation is 0. That is, when the stress coefficient k is 0, the springback deformation evaluation value SI is also 0.

[0067] The non-linearity index NLI is not limited to specific function values or indices, and any index that indicates the non-linearity between the stress coefficient k and the springback deformation evaluation value SI may be used.

[0068] Here, when the stress coefficient k is 1, the springback deformation evaluation value SI is defined as Sa, and when the stress coefficient k is -1, the springback deformation evaluation value SI is defined as Sb. Also, as described above, when the stress coefficient k is 0, SI is 0. Considering this case, the relationship between the stress coefficient k and the springback deformation evaluation value SI is shown in the graphs of FIGS. 14(a) to (f). Here, Sa in FIGS. 14(a) to (e) is the same value, and this is denoted as S. Also, Sa in FIG. 14(f) is -S, which is -1 times Sa in FIGS. 14(a) to (e).

[0069] In FIG. 14(a), the graph of the stress coefficient k and the springback deformation evaluation value SI is linear, showing an example where the stress coefficient k and the springback deformation evaluation value SI have a linear relationship. On the other hand, FIGS. 14(b) to (e) show examples where the stress coefficient k and the springback deformation evaluation value SI have a non-linear relationship, and Sb in FIGS. 14(b) to (e) is -0.5S, 0.0S, 0.5S, and 1.0S, respectively. In FIGS. 14(b) to (e), the non-linearity increases in the order of FIGS. 14(b), 14(c), 14(d), and 14(e), and the non-linearity in FIG. 14(e) is the strongest. Also, in FIG. 14(f), the springback deformation evaluation value SI on the graph is the value obtained by inverting the graph of FIG. 14(e) vertically, but the non-linearity is the same strength as in the case of FIG. 14(e).

[0070] (Nonlinear Index NLI - Example 1) When the non-linear index NLI is defined as Sa + Sb, the non-linear index NLI represents the difference between the change amount of the springback deformation evaluation value SI from k = 0 to k = 1 and the change amount of the springback deformation evaluation value SI from k = -1 to k = 0. In this case, the non-linear indices NLI in FIGS. 14(a) to (e) are 0.0S, 0.5S, 1.0S, 1.5S, and 2.0S, respectively, in order. When the non-linear index NLI is defined as Sa + Sb, a linear relationship exists when the non-linear index NLI is 0, and the non-linearity becomes stronger as the non-linear index NLI becomes larger or smaller than 0.

[0071] In Fig. 14(f), the non-linear index NLI is -2.0S. The absolute value is the same as that in Fig. 14(e), but the sign is opposite. Considering that the non-linearity of Fig. 14(f) is the same as that of Fig. 14(e), when the non-linear index NLI is set to Sa + Sb, the strength of the non-linearity is indicated by the absolute value, and the plus-minus sign has no influence. Therefore, the absolute value of Sa + Sb, i.e., abs(Sa + Sb), is also a valid evaluation value of non-linearity, and this can be adopted as the non-linear index NLI. Note that abs is the absolute value function.

[0072] When the non-linear index NLI is set to Sa + Sb or abs(Sa + Sb), if the absolute value of the springback deformation evaluation value SI is large, the non-linearity will be evaluated higher. Therefore, if these are divided by a representative value of the springback deformation evaluation value SI, for example, max{abs(Sa), abs(Sb)} or {abs(Sa) + abs(Sb)} / 2, to make it dimensionless, a non-linear index NLI that is not affected by the absolute value of the springback deformation evaluation value SI will be obtained. Note that abs is the absolute value function and max is the maximum value function. Also, the representative value of the springback deformation evaluation value SI is not limited to the examples described here, and any representative index indicating the magnitude of the springback deformation evaluation value SI is acceptable.

[0073] From the above, the non-linear index NLI may be defined by any of the following formulas, for example. NLI = (Sa + Sb) ···(1) NLI = (Sa + Sb) / max{abs(Sa), abs(Sb)} ···(2) NLI = (Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2] ···(3) NLI = abs(Sa + Sb) ···(4) NLI = abs(Sa + Sb) / max{abs(Sa), abs(Sb)} ···(5) NLI = abs(Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2] ···(6)

[0074] (Non-linear index NLI - Example 2) To evaluate non-linearity, the change in the slope of the graph may be evaluated. For example, in the case of the graph in Fig. 14(a), the slope is constant regardless of the stress coefficient k and it is judged that the non-linearity is weak. However, in Figs. 14(b) to (f), since the slope of the graph changes depending on the stress coefficient k, it is judged that the non-linearity is strong. Therefore, for example, if the non-linearity index NLI is set to Sa / Sb or Sb / Sa, the non-linearity index NLI is the ratio of the average slope from k = 0 to k = 1 and the average slope from k = -1 to k = 0.

[0075] However, when the absolute value of Sa or Sb is close to 0, using it as the denominator will result in an overestimation of non-linearity. Therefore, in order to define the non-linearity index NLI as, for example, the smaller value of the absolute values of Sa / Sb and Sb / Sa, NLI = sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} may be defined as the non-linearity index NLI. Here, sign is the sign function. The non-linearity indices NLI for Figs. 14(a) to (f) in this case are -1.0, -0.5, 0.0, 0.5, 1.0, 1.0 in order. And in the case of linearity, NLI = -1, and as the non-linearity becomes stronger, the value becomes larger, so it is an effective index for evaluating non-linearity.

[0076] On the other hand, when the non-linearity index NLI is set to sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)}, since the non-linearity index NLI in the case of showing a linear relationship is NLI = -1, it becomes difficult to handle mathematically. Therefore, sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1, which is obtained by adding 1 to the above non-linearity index NLI, may be defined as the non-linearity index NLI. The non-linearity indices NLI for Figs. 14(a) to (f) in this case are 0, 0.5, 1.0, 1.5, 2.0, 2.0 in order. And in the case of linearity, NLI = 0, and it becomes an index where the value becomes larger as the non-linearity becomes stronger. Therefore, if the non-linearity index NLI is defined as sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1, it can be an index that is easy to handle mathematically and easy to understand.

[0077] Also, for example, raise sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1 to the power of n (n: real number), and NLI = [sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n Then, the weight for non-linearity can be adjusted. For example, when performing analysis centered only on large non-linearity, by setting n to a value greater than 1, when the value of sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1 is large, the non-linearity index NLI obtained by raising that value to the power of n will also be relatively larger, making it easier to analyze large non-linear parts. On the other hand, when detailed analysis of small non-linearity is also desired, if n is set to a value less than 1, when sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1 is small, the non-linearity index NLI obtained by raising it to the power of n will be relatively larger, making it easier to analyze small non-linear parts.

[0078] For the above reasons, the non-linearity index NLI may be defined as [sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n However, when performing non-linearity evaluation on mass-produced press parts such as automotive press parts, it is desirable that 0.2 ≤ n ≤ 5.0. When 0.2 ≤ n, analysis becomes easier by avoiding the situation where the difference between non-linearity and linearity becomes excessively small. Also, when n ≤ 5.0, analysis becomes easier by avoiding the situation where the area where non-linearity is undervalued increases excessively.

[0079] Note that the non-linearity index NLI is [sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1] nWhen defined in this way, unlike the case where the non-linear index NLI is defined as Sa + Sb described above, the magnitude of the springback deformation evaluation value SI is not considered. However, the difficulty of mold prediction correction is affected not only by non-linearity but also by the magnitude of the springback deformation evaluation value SI. Therefore, [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n For [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1], multiply by the representative value of the magnitude of the springback deformation evaluation value SI, which is max{abs(Sa),abs(Sb)} or {abs(Sa)+abs(Sb)} / 2, n ×max{abs(Sa),abs(Sb)} or [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×[{abs(Sa)+abs(Sb)} / 2] may be defined as the non-linear index NLI. Such a non-linear index NLI is a non-linear index that takes into account the magnitude of the springback deformation evaluation value SI. Note that the representative value of the springback deformation evaluation value SI is not limited to the examples described here, and any representative index indicating the magnitude of the springback deformation evaluation value SI may be used.

[0080] From the above, the non-linear index NLI may be defined by any of the following formulas, for example. NLI = sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)} ···(7) NLI = [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ···(8) NLI = [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×max{abs(Sa), abs(Sb)} ···(9) NLI = [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×[{abs(Sa)+abs(Sb)} / 2] ···(10)

[0081] (Nonlinear Index NLI - Example 3) The examples of the non - linear evaluation values described so far are expressed as equations calculated based on the springback deformation evaluation values Sa and Sb when the stress coefficient k is - 1.0 and 1.0. However, the stress coefficient k does not necessarily have to be - 1.0 and 1.0. For example, as shown in FIGS. 15(a) and 15(b), when one of the stress coefficients k is an arbitrary value ka, the other stress coefficient k is taken as a value kb(=-ka) which is - 1 times ka. Even if the springback deformation evaluation value SI when the stress coefficient k is ka is defined as Sa and the springback deformation evaluation value SI when the stress coefficient k is kb is defined as Sb, the concept of the non - linear index NLI described above still holds. Note that FIG. 15(a) is an example of a case with strong linearity, and FIG. 15(b) is an example of a case with strong non - linearity.

[0082] Therefore, the above equations (1) to (10) may be used as the non - linear index NLI when the springback deformation evaluation values SI when the stress coefficient k is an arbitrary value ka other than 0.0 and kb which is - 1 times ka are taken as Sa and Sb respectively.

[0083] (Nonlinear Index NLI - Example 4) Furthermore, the springback deformation evaluation values Sa and Sb which are SI when the stress coefficients k are ka and kb may be obtained by the springback simulation of the stress - change finite - element model. However, they may also be obtained by estimating the relationship between the stress coefficient k and the springback deformation evaluation value SI from the springback deformation evaluation values SI when using a plurality of different stress coefficients k other than ka and kb.

[0084] FIG. 16 is a diagram for explaining an example of obtaining the relationship between the stress coefficient k and the springback deformation evaluation value SI as an approximation formula of the springback deformation evaluation value SI with respect to the stress coefficient k, and obtaining the springback deformation evaluation values Sa and Sb when the stress coefficients k are ka and kb. In FIG. 16(a), from the springback deformation evaluation values SI for the seven stress coefficients k indicated by white circles in the graph, an approximation formula of the springback deformation evaluation value SI with respect to the stress coefficient k indicated by the thick broken line in the graph is derived, and further, from the approximation formula, the springback deformation evaluation values Sa and Sb when the stress coefficients k indicated by black squares in the graph are ka and kb are obtained. Further, FIG. 16(b) is a diagram showing the springback deformation evaluation values Sa and Sb when the stress coefficients k are ka = 1.0 and kb = -1.0 using the above approximation formula.

[0085] As described above, an approximation formula of the springback deformation evaluation value SI with respect to the stress coefficient k may be derived, and by estimating the relationship between the stress coefficient k and the springback deformation evaluation value SI, Sa and Sb used in the above formulas (1) to (10) may be obtained, and the non-linear index NLI may be defined.

[0086] (Non-linear index NLI - Example 5) Furthermore, non-linearity can also be evaluated from an approximation formula showing the relationship of the springback deformation evaluation value SI with respect to the stress coefficient k. For example, when the springback deformation evaluation values SI for a plurality of stress coefficients k are obtained and an approximation formula of the springback deformation evaluation value SI with respect to the stress coefficient k is obtained as a quadratic polynomial from the results, if the value of the quadratic coefficient of the obtained polynomial is 0 or the absolute value of the coefficient is a small value, the non-linearity is weak, and if the absolute value of the coefficient is large, the non-linearity is strong. Therefore, the quadratic coefficient of the quadratic polynomial approximation formula of the springback deformation evaluation value SI with respect to the stress coefficient k or the function value with the quadratic coefficient as a variable is an effective index from the viewpoint of evaluating non-linearity. That is, the quadratic coefficient of the quadratic polynomial approximation formula of the springback deformation evaluation value SI with respect to the stress coefficient k or the function value with the quadratic coefficient as a variable may be defined as the non-linear index NLI.

[0087] By calculating the non - linear index NLI defined as above in the non - linear index calculation step S25, the non - linearity of the springback deformation can be evaluated. When the non - linearity is weak, the springback occurring in the press - formed product can be predicted to be a springback whose shape accuracy can be easily corrected according to the mold prediction. When the non - linearity is strong, it can be predicted that the springback occurring in the press - formed product is a non - linear springback.

[0088] That is, also in the method for analyzing springback characteristics according to the present embodiment, it is possible to predict the presence or absence of non - linear springback of the press - formed product before mold production. In the analysis method for calculating the non - linear index NLI, not only can the springback characteristics be judged simply by dividing the calculated non - linear index NLI into cases where the non - linearity is weak and cases where the non - linearity is strong, but the value of the non - linear index NLI may also be used as a value for evaluating the difficulty of correcting the shape accuracy according to the mold prediction.

[0089] <Third Embodiment> FIG. 17 is a flowchart for explaining the method for analyzing springback characteristics according to the third embodiment. The analysis method according to the present embodiment is a method for analyzing the springback characteristics of the entire press - formed product or a partial region with respect to the springback deformation evaluation value for an arbitrary node of the reference finite element model. In the present embodiment, the springback characteristics are analyzed as follows.

[0090] (Reference Finite Element Model Creation Step S31) First, in the reference finite element model creation step S31, a reference finite element model is created that includes the material properties including the Young's modulus of the metal plate that is the material of the press - formed product to be analyzed, the shape of the press - formed product before springback deformation, the plate thickness, and the data of the stress (residual stress).

[0091] (Stress Change Finite Element Model Creation Step S32) Next, in the stress change finite element model creation step S32, a stress change finite element model is created by multiplying the residual stress in the reference finite element model by a stress coefficient k to change the stress value.

[0092] (Springback simulation step S33) Next, in the springback simulation step S33, a springback simulation is performed for both the reference finite element model and the stress change finite element model or only the stress change finite element model to obtain the shape after springback deformation.

[0093] The above reference finite element model creation step 31, stress change finite element model creation step 32, and springback simulation step S33 are the same steps as the reference finite element model creation step S21, stress change finite element model creation step S22, and springback simulation step S23 in the second embodiment.

[0094] (Springback deformation evaluation value calculation step S34) Next, in the springback deformation evaluation value calculation step S34, in order to analyze the springback deformation from each shape after springback deformation, a springback deformation evaluation value SI for an arbitrary node is calculated to obtain the relationship between the stress coefficient k and the springback deformation evaluation value.

[0095] In the above-described second embodiment, the springback deformation evaluation value SI calculated in the springback deformation evaluation value calculation step S24 may be a value related to an arbitrary node (for example, the displacement amount from before springback deformation to after springback deformation at an individual node, the component amount in an arbitrary direction of the displacement, or a function value using these variables), or may be a value that is not a value related to an arbitrary node (for example, the warp of the press-formed product, the twist, or a value related to the deformation state of the whole part such as the opening, or a function value thereof). However, in the springback deformation evaluation value calculation step S34 in the third embodiment, the calculated springback deformation evaluation value SI is limited to a value related to an arbitrary node, and in this regard, it is different from the springback deformation evaluation value calculation step S24 in the second embodiment.

[0096] In other words, the springback deformation evaluation value calculation step S34 in the third embodiment is the same as the springback deformation evaluation value calculation step S24 in the second embodiment, except that the calculated springback deformation evaluation value SI is limited to a value related to an arbitrary node.

[0097] (Nonlinear index calculation step S35) Next, in the nonlinear index calculation step S35, a nonlinear index NLI, which is an index of the nonlinearity of the springback deformation evaluation value SI with respect to the stress coefficient k, is calculated. In the nonlinear index calculation step S35, the nonlinear index NLI for an arbitrary node is obtained. However, the nonlinear index NLI is obtained not only for one node but also for each of all the nodes or a plurality of nodes in a partial region of the reference finite element model. Note that a specific example of the nonlinear index NLI is the same as the example described in the nonlinear index calculation step S25 in the second embodiment.

[0098] (Nonlinear index analysis step S36) Next, in the non-linear index analysis step S36, a contour diagram is created in which the non-linear index NLI is displayed as color contours or contour lines on the three-dimensional shape of the finite element model, and is displayed or printed for the analyst, for example. Also, for example, for the nodes designated by the analyst, a graph plotting a set of the stress coefficient k and the springback deformation evaluation value SI may be created and displayed or printed for the analyst. Further, for example, an approximate expression for the springback deformation evaluation value SI with respect to the stress coefficient k is obtained, and a graph is created in which the approximate expression is displayed on the plot of the set of the stress coefficient k and the springback deformation evaluation value SI, and may be displayed or printed for the analyst.

[0099] From the contour diagram of the non-linear index NLI, the analyst can visually grasp the state of the springback non-linearity of the whole or a partial region of the part. Further, for the noteworthy nodes at the sites where the non-linear index NLI is large on the contour diagram, the details of the non-linearity can be grasped from the graph showing the relationship between the springback deformation evaluation value SI with respect to the stress coefficient k.

[0100] Therefore, also in the method for analyzing the springback characteristics according to the present embodiment, the site where non-linear springback of the press-formed product occurs can be confirmed from the contour diagram of the non-linear index NLI. That is, the presence or absence of non-linear springback can be predicted before die manufacturing.

[0101] <Fourth Embodiment> FIG. 18 is a flowchart for explaining the method for analyzing the springback characteristics according to the fourth embodiment. The analysis method according to the fourth embodiment is a method of obtaining the non-linear index for an arbitrary node for each of a plurality of reference finite element models having different fixed points (constraint points), and obtaining the intrinsic non-linear index from the plurality of non-linear indices for the node.

[0102] When obtaining the springback deformation evaluation value SI through springback simulations of the reference finite element model and the stress change finite element model, the springback deformation amount becomes 0 at the fixed points of the reference finite element model and the stress change finite element model. Therefore, when the springback deformation evaluation value SI relates to the springback displacement of an arbitrary node, the springback deformation evaluation value SI at the node that is the fixed point becomes 0, and the non-linearity index NLI also becomes a value evaluated as having weak non-linearity. Therefore, in the vicinity of the fixed points of the reference finite element model and the stress change finite element model, the evaluation accuracy of the springback non-linearity may be low.

[0103] In the fourth embodiment, in view of the above circumstances, in order to more appropriately evaluate the springback non-linearity in the vicinity of the fixed points of the reference finite element model and the stress change finite element model, the springback characteristics are analyzed as follows. Note that since the analysis method according to the fourth embodiment is a method including the analysis method according to the third embodiment, the differences will be described below in comparison with the third embodiment.

[0104] (Reference Finite Element Model Creation Step S41) First, in the reference finite element model creation step S41, a plurality of reference finite element models are created, including the material properties of the metal plate that is the material of the press-formed product to be analyzed, such as Young's modulus, the shape of the press-formed product before springback deformation, the plate thickness, and the data of stress (residual stress). The plurality of reference finite element models to be created are all the same for conditions other than the fixed points, and the nodes that are the fixed points are different models.

[0105] Then, for each of the plurality of reference finite element models with different fixed points, the following stress change finite element model creation step S42, springback simulation step S43, springback deformation evaluation value calculation step S44, and non-linearity index calculation step S45 are performed.

[0106] (Stress Change Finite Element Model Creation Step S42) In the stress change finite element model creation step S42, a stress change finite element model is created by multiplying the residual stress in the reference finite element model by a stress coefficient k to change the stress value. The stress change finite element model creation step S42 in the fourth embodiment is the same as the stress change finite element model creation step S32 in the third embodiment.

[0107] (Springback simulation step S43) Next, in the springback simulation step S43, springback simulations are performed on both the reference finite element model and the stress change finite element model or only on the stress change finite element model to obtain the shape after springback deformation. The springback simulation step S43 in the fourth embodiment is the same as the springback simulation step S33 in the third embodiment.

[0108] (Springback deformation evaluation value calculation step S44) Next, in the springback deformation evaluation value calculation step S44, similar to the springback deformation evaluation value calculation step S34 in the third embodiment, a springback deformation evaluation value SI for an arbitrary node is calculated to obtain the relationship between the stress coefficient k and the springback deformation evaluation value SI. In the springback deformation evaluation value calculation step S34 in the third embodiment, the calculated springback deformation evaluation value SI is taken as a value related to an arbitrary node, and values that are not related to an arbitrary node are not adopted as the springback deformation evaluation value SI. However, in the springback deformation evaluation value calculation step S44 in the fourth embodiment, this point is the same, and the springback deformation evaluation value SI is taken as a value related to an arbitrary node. Also, the springback deformation evaluation value SI may be calculated for only one node, or may be calculated for all nodes or a plurality of nodes in a partial region of the reference finite element model.

[0109] (Nonlinear index calculation step S45) Next, in the non-linear index calculation step S45, a non-linear index NLI, which is an index of the non-linearity of the springback deformation evaluation value SI with respect to the stress coefficient k, is calculated. The non-linear index NLI may be calculated for only one node, or may be calculated for all nodes of the reference finite element model or a plurality of nodes in a partial region. Also, for example, a plurality of non-linear indices NLI may be calculated for one node, or a plurality of non-linear indices NLI may be calculated for each of all nodes or a plurality of nodes in a partial region.

[0110] (Eigen non-linear index calculation step S46) Next, in the eigen non-linear index calculation step S46, an eigen non-linear index ENLI is obtained from a plurality of non-linear indices NLI related to an arbitrary node obtained in the non-linear index calculation step S45. The calculation of the eigen non-linear index ENLI may be performed for only one node, or may be performed for all nodes of the reference finite element model or a plurality of nodes in a partial region.

[0111] As described above, when the springback deformation evaluation value SI relates to the displacement of the springback of an arbitrary node, at the node that is the fixed point of the reference finite element model, the springback deformation evaluation value SI becomes 0, and the non-linearity of the springback cannot be evaluated. On the other hand, if the springback deformation evaluation value SI is obtained for a plurality of reference finite element models with different fixed points, since the node that is the fixed point of a certain reference finite element model does not become the fixed point in other reference finite element models, it becomes possible to evaluate the non-linearity of the springback at that fixed point.

[0112] The eigen non-linear index ENLI may be, for example, the average value of a plurality of non-linear indices NLI, or the maximum value of a plurality of non-linear indices NLI, or alternatively, the average value of non-linear indices NLI having a value of a certain value or more excluding non-linear indices NLI with small values. Note that the calculation method of the eigen non-linear index ENLI is not limited to a specific method, and any method that can eliminate or reduce the influence on the non-linear index NLI of the fixed point may be used.

[0113] (Intrinsic Nonlinear Index Analysis Step S47) Next, in the intrinsic nonlinear index analysis step S47, for example, a contour diagram in which the intrinsic nonlinear index ENLI is displayed as color contours or contour lines on the three-dimensional shape of the finite element method model is created and displayed or printed for the analyst. The analyst can visually grasp the state of the springback nonlinearity of the entire part or a partial region from the contour diagram of the intrinsic nonlinear index ENLI.

[0114] Therefore, also in the springback characteristic analysis method according to the present embodiment, the site where the nonlinear springback of the press-formed product occurs can be confirmed from the contour diagram of the intrinsic nonlinear index ENLI. That is, the presence or absence of nonlinear springback can be predicted before die manufacturing.

[0115] The analysis method of the springback characteristics of the press-formed product of the metal plate according to the embodiment has been described above.

[0116] Note that a program that operates on a computer that controls the analysis apparatus so that the analysis apparatus executes the analysis method described above is created, and the program can be installed in, for example, a personal computer or the like. Further, the above program may be stored in a computer-readable recording medium. The recording medium is, for example, a magnetic disk, an optical disk, a magneto-optical disk, a flash memory, or the like. Further, the above program may be distributed via a network, for example, without using a recording medium.

[0117] 〔Springback Characteristic Analysis Apparatus〕 Next, a springback characteristic analysis apparatus for a press-formed product of a metal plate will be described. The analysis apparatus is an apparatus capable of executing the analysis method exemplified in the above-described embodiment. Hereinafter, an example of the functional configuration and an example of the hardware configuration of the analysis apparatus will be described in order.

[0118] FIG. 19 is a block diagram showing an example of the functional configuration of the analyzer. As shown in FIG. 19, the analyzer 10 includes a reference finite element model creation unit 11, a stress change finite element model creation unit 12, a springback simulation unit 13, and a springback deformation evaluation value calculation unit 14. Each of the units 11 to 14 is realized by, for example, a CPU, a ROM, a RAM, etc.

[0119] The reference finite element model creation unit 11 creates a reference finite element model described, for example, in the above-mentioned reference finite element model creation step. The stress change finite element model creation unit 12 creates a stress change finite element model described, for example, in the above-mentioned stress change finite element model creation step. The springback simulation unit 13 performs a spring simulation described, for example, in the above-mentioned reference finite element model creation step. The springback deformation evaluation value calculation unit 14 calculates a springback deformation evaluation value SI described, for example, in the above-mentioned springback deformation evaluation value calculation step.

[0120] Further, the analyzer 10 includes, as necessary, a springback non-linearity evaluation unit 15, a non-linear index calculation unit 16, a non-linear index analysis unit 17, a specific non-linear index calculation unit 18, and a specific non-linear index analysis unit 19. Each of the units 15 to 19 is realized by, for example, a CPU, a ROM, a RAM, etc.

[0121] The springback non-linearity evaluation unit 15 creates, for example, a graph showing the relationship between the stress coefficient k and the springback deformation evaluation value SI in order to evaluate the non-linearity of the springback described in the above-mentioned springback non-linearity evaluation step. The non-linear index calculation unit 16 calculates a non-linear index NLI described, for example, in the above-mentioned non-linear index calculation step. The non-linear index analysis unit 17 creates a contour diagram based on the non-linear index NLI described, for example, in the above-mentioned non-linear index analysis step. The specific non-linear index calculation unit 18 calculates a specific non-linear index ENLI described, for example, in the above-mentioned specific non-linear index calculation step. The specific non-linear index analysis unit 19 creates a contour diagram based on the specific non-linear index ENLI described, for example, in the above-mentioned specific non-linear index analysis step.

[0122] Next, an example of the hardware configuration of the analyzer 10 will be described with reference to FIG. 20. As shown in FIG. 20, the analyzer 10 mainly includes a CPU 901, a ROM 903, and a RAM 905. The analyzer 10 also includes a bus 907, an input device 909, an output device 911, a storage device 913, a drive 915, a connection port 917, and a communication device 919.

[0123] The CPU 901 functions as a central processing unit and a control unit, and controls all or part of the operations within the analyzer 10 according to various programs recorded in the ROM 903, the RAM 905, the storage device 913, or the removable recording medium 921. The ROM 903 stores programs, arithmetic parameters, etc. used by the CPU 901. The RAM 905 stores programs used by the CPU 901 and parameters that change as appropriate during program execution, etc. temporarily. These are interconnected by a bus 907 constituted by an internal bus such as a CPU bus.

[0124] The bus 907 is connected to an external bus such as a PCI (Peripheral Component Interconnect / Interface) bus via a bridge.

[0125] The input device 909 is, for example, an operation means operated by a user such as a mouse, a keyboard, a touch panel, buttons, switches, and levers. The input device 909 may be, for example, a remote control means (so-called remote control) using infrared rays or other radio waves, or an external connection device 923 such as a PDA corresponding to the operation of the analyzer 10. Further, the input device 909 is composed of, for example, an input control circuit that generates an input signal based on information input by the user using the above operation means and outputs it to the CPU 901. The user of the analyzer 10 can input various data to the analyzer 10 or instruct a processing operation by operating this input device 909.

[0126] The output device 911 is composed of a device capable of visually or auditorily notifying the user of the acquired information. Such devices include display devices such as CRT display devices, liquid crystal display devices, plasma display devices, EL display devices, and lamps, audio output devices such as speakers and headphones, printer devices, mobile phones, facsimiles, and the like. The output device 911 outputs, for example, the results obtained by various processes performed by the analysis device 10. Specifically, the display device displays the results obtained by various processes performed by the analysis device 10 in text or image. On the other hand, the audio output device converts an audio signal composed of reproduced audio data, acoustic data, etc. into an analog signal and outputs it.

[0127] The storage device 913 is a data storage device configured as an example of the storage unit of the analysis device 10. The storage device 913 is composed of, for example, a magnetic storage device such as an HDD (Hard Disk Drive), a semiconductor storage device, an optical storage device, or a magneto-optical storage device. This storage device 913 stores programs executed by the CPU 901, various data, and various data acquired from the outside.

[0128] Drive 915 is a reader / writer for recording media and is built into or externally attached to the analyzer 10. Drive 915 reads the information recorded on a removable recording medium 921 such as a mounted magnetic disk, optical disk, magneto-optical disk, or semiconductor memory, and outputs it to the RAM 905. Further, Drive 915 can also write records to the removable recording medium 921 such as a mounted magnetic disk, optical disk, magneto-optical disk, or semiconductor memory. The removable recording medium 921 is, for example, a CD medium, DVD medium, Blu-ray (registered trademark) medium, etc. Further, the removable recording medium 921 may be a CompactFlash (registered trademark) (CF), flash memory, or an SD memory card (Secure Digital memory card), etc. Further, the removable recording medium 921 may be, for example, an IC card (Integrated Circuit card) or an electronic device equipped with a non-contact type IC chip.

[0129] The connection port 917 is a port for directly connecting a device to the analyzer 10. Examples of the connection port 917 include a USB (Universal Serial Bus) port, IEEE1394 port, SCSI (Small Computer System Interface) port, RS-232C port, HDMI (registered trademark) (High-Definition Multimedia Interface) port, etc. By connecting an external connection device 923 to this connection port 917, the analyzer 10 can directly acquire various data from the external connection device 923 or provide various data to the external connection device 923.

[0130] The communication device 919 is a communication interface composed of, for example, a communication device for connecting to a communication network 925. The communication device 919 is, for example, a communication card for wired or wireless LAN (Local Area Network), Bluetooth (registered trademark), or WUSB (Wireless USB). Further, the communication device 919 may be a router for optical communication, a router for ADSL (Asymmetric Digital Subscriber Line), or a modem for various types of communication. This communication device 919 can transmit and receive signals, etc. in accordance with a predetermined protocol such as TCP / IP, for example, between the Internet and other communication devices. Also, the communication network 925 connected to the communication device 919 is composed of a network connected by wire or wirelessly, etc., and may be, for example, the Internet, an in-home LAN, an in-company LAN, infrared communication, radio wave communication, or satellite communication.

[0131] As described above, an example of the hardware configuration capable of realizing the functions of the analysis device 10 according to the embodiment of the present invention has been shown. Each of the above-described components may be configured using general-purpose members, or may be configured by hardware specialized for the functions of each component. Therefore, it is possible to appropriately change the hardware configuration to be used according to the technical level at the time of implementing this embodiment.

[0132] As described above, the embodiments of the present invention have been illustrated, but the present invention is not limited to such examples. It is obvious that those skilled in the art can conceive of various modification examples or correction examples within the scope of the technical idea described in the claims, and it is naturally understood that those also belong to the technical scope of the present invention.

[0133] For example, the constituent elements of the above embodiment can be arbitrarily combined. From such an arbitrary combination, the actions and effects of each constituent element related to the combination can be naturally obtained, and other actions and other effects obvious to those skilled in the art from the description of this specification can also be obtained.

Example

[0134] Hereinafter, embodiments of the present invention will be described.

[0135] <Examples 1 to 36> Examples 1 to 36 are cases where springback characteristics were analyzed assuming that foam molding was performed using a steel sheet with a tensile strength of 980 MPa and a plate thickness of 1.0 mm to produce a press-molded product having the shapes shown in FIGS. 21(a) and 21(b) (length 653 mm, width 332 mm, height 23 mm).

[0136] First, a press molding simulation was performed to obtain the shape, plate thickness, and residual stress at the bottom dead center of the press molding, and a reference finite element model was created based on them. The Young's modulus of the material was set to 206 GPa.

[0137] The fixed points of the reference finite element models of Examples 1 to 36 are points P1, P2, and P3 shown in FIG. 22(a). The restraint conditions are six-degree-of-freedom restraints. Based on the coordinate system shown in the figure, point P1 restrains displacements in the x, y, and z directions, point P2 restrains displacements in the x and z directions, and point P3 restrains displacement in the z direction. In the following description, the set of fixed points with these restraint conditions is referred to as fixed point 1, and the reference finite element model with fixed point 1 set is referred to as reference finite element model 1.

[0138] FIG. 22(b) is a contour diagram showing the displacement amount (springback displacement amount) of each element of the shape after springback deformation with respect to the shape before springback deformation in the springback simulation of the reference finite element model. In the coordinate system shown in the figure (the coordinate systems shown in FIGS. 22(a) and 22(b) are the same, and the z direction is perpendicular to the paper surface in FIG. 22(b)), the plus side in the z direction is defined as the surface side of the press-molded product, and the minus side in the z direction is defined as the back side of the press-molded product. When the position after springback deformation with respect to the position before springback deformation is on the surface side of the press-molded product, the springback displacement amount is expressed as a positive value, and when it is on the back side of the press-molded product, the value of the springback displacement amount is expressed as a negative value.

[0139] Regarding the creation of the stress change finite element models in Examples 1 to 36, for Examples 1 to 28 and Examples 30 to 36, a stress change finite element model was created by multiplying the stress values of all elements of the reference finite element model by a stress coefficient to change the stress values. In Example 29, a stress change finite element model was created by multiplying the stress values of some elements of the reference finite element model by a stress coefficient to change the stress values.

[0140] Hereinafter, the details of Examples 1 to 36 will be described.

[0141] (Example 1) In Example 1, a reference finite element model 1 with the fixed point of the reference finite element model set as fixed point 1 was created, and a plurality of stress change finite element models with stress coefficients k being -1.0, -0.8, -0.6, -0.4, -0.2, 0.2, 0.4, 0.6, and 0.8 were created. Next, springback simulations were performed on the created reference finite element model 1 and each stress change finite element model to obtain the shapes after springback deformation of each. Note that the springback simulation was an elastic deformation analysis.

[0142] Next, the displacement amount at the nodes of the reference finite element model 1 and each stress change finite element model was taken as the springback deformation evaluation value SI, and from the shapes after springback deformation of each model, the springback deformation evaluation values SI at three nodes, namely node NP1, node NP2, and node NP3 shown in FIG. 23, were obtained. From the results and the data that the springback deformation evaluation value SI is also 0 when the stress coefficient k is 0, an approximate formula by a quadratic function was obtained for the relationship between the stress coefficient k and the springback deformation evaluation value SI. Further, on a graph with the stress coefficient k on the horizontal axis and the springback deformation evaluation value SI on the vertical axis, the springback deformation evaluation value SI for each stress coefficient k was plotted and the approximate formula was shown. Note that for the reference finite element model 1, the stress coefficient k was assumed to be 1.

[0143] Figures 24(a), (b), and (c) are graphs showing the relationship between the stress coefficient k and the springback deformation evaluation value SI at nodes NP1, NP2, and NP3. The white circles in the figures are the plotted points, and the dotted lines are the approximate expressions. Note that since the springback deformation evaluation value SI on the vertical axis is a displacement amount, the unit is mm.

[0144] Since the approximate expression in Fig. 24(a) is approximately linear and the relationship between the springback deformation evaluation value SI and the stress coefficient k is approximately linear, it can be determined that the springback deformation at node NP1 has weak non-linearity. Since the approximate expression in Fig. 24(c) is not linear but greatly curved, the relationship between the springback deformation evaluation value SI and the stress coefficient k is non-linear, and it can be determined that the springback deformation at NP3 has strong non-linearity. Since the approximate expression in Fig. 24(b) is at a level between that of Fig. 24(a) and Fig. 24(c), it can be determined that the springback deformation at node NP2 has stronger non-linearity than node NP1 but weaker non-linearity than node NP3.

[0145] (Example 2) In Example 2, a reference finite element model 1 with the fixed point of the reference finite element model as fixed point 1 was created, and a plurality of stress change finite element models with the stress coefficient k being -1.0, -0.8, -0.6, -0.4, -0.2, 0.2, 0.4, 0.6, 0.8 were created. Next, springback simulations were performed on the created reference finite element model 1 and the plurality of stress change finite element models to obtain the shapes after springback deformation. Note that the springback simulation was an elastic deformation analysis.

[0146] Next, from the shapes after springback deformation of each model, the springback deformation evaluation values SI at three nodes, namely node NP1, node NP2, and node NP3 shown in Fig. 23, were obtained. In Example 2, the function value with the z-direction component amount of the displacement of each node NP1 - NP3 as a variable was used as the springback deformation evaluation value SI, and the springback deformation evaluation value SI was the value of the following formula. SI = g / max{abs(x1), abs(x2)} Here, g is the z-direction component of the displacement of each of the nodes NP1 to NP3, x1 is the z-direction component of the displacement of each of the nodes NP1 to NP3 when the stress coefficient k is 1, and x2 is the z-direction component of the displacement of each of the nodes NP1 to NP3 when the stress coefficient k is -1. Also, max represents the maximum value function, and abs represents the absolute value function.

[0147] Next, from the data of the plurality of springback deformation evaluation values SI obtained by the above formula at each of the nodes NP1 to NP3 of the reference finite element model 1 and each stress conversion finite element model, and the data where the springback deformation evaluation value SI is also 0 when the stress coefficient k is 0, an approximate formula by a quadratic function was obtained for the relationship between the stress coefficient k and the springback deformation evaluation value SI. Further, on a graph with the stress coefficient k on the horizontal axis and the springback deformation evaluation value SI on the vertical axis, the springback deformation evaluation value SI for each stress coefficient k was plotted and the approximate formula was shown. Note that the reference finite element model 1 assumed that the stress coefficient k was 1.

[0148] Figures 25(a), (b), and (c) are graphs showing the relationship between the stress coefficient k and the springback deformation evaluation value SI at the node NP1, the node NP2, and the node NP3. The white circles in the figures are the plotted points, and the dotted lines are the approximate formulas. Note that the springback deformation evaluation value SI on the vertical axis is a dimensionless value because the z-direction component of the displacement amount is divided by the larger value of the absolute value of the springback deformation evaluation value SI when the stress coefficient k is -1 and the springback deformation evaluation value SI when the stress coefficient k is 1.

[0149] In view of the linearity of the approximate formula, similar to Example 1, it can be determined that at the node NP1 shown in Fig. 25(a), the non-linearity of the springback deformation is weak, at the node NP3 shown in Fig. 25(c), the non-linearity of the springback deformation is strong, and at the node NP2 shown in Fig. 25(b), the non-linearity of the springback deformation is at an intermediate level between them.

[0150] (Examples 3 to 14) In Examples 3 to 14, a reference finite element model 1 with the fixed point of the reference finite element model as Fixed Point 1 was created, and a stress change finite element model with a stress coefficient k of -1.0 was created. Next, springback simulations were performed on the created reference finite element model 1 and stress change finite element model, and the shapes after springback deformation were obtained for each. Note that the springback simulation was an elastic deformation analysis.

[0151] Next, the z-direction component amount of the displacement at the nodes of the reference finite element model 1 and stress change finite element model was taken as the springback deformation evaluation value SI, and from the shapes after springback deformation of each model, the z-direction component amounts at three nodes, namely Node NP1, Node NP2, and Node NP3 shown in FIG. 23, were obtained. Further, from the springback deformation evaluation values SI of the reference finite element model 1 and stress change finite element model at each of the nodes NP1 to NP3, a non-linear index NLI was obtained. Note that in Examples 3 to 14, the springback deformation evaluation value SI when the stress coefficient k is 1 was taken as Sa, and the springback deformation evaluation value SI of the stress change finite element model when the stress coefficient k is -1 was taken as Sb, and the non-linear index NLI was taken as the calculated value of any one of Expressions 1 to 12 shown in Table 1 below.

[0152]

Table 1

[0153] Expressions 1 to 10 are the same as Expressions 1 to 10 described in the second embodiment. Expression 11 is a function value with abs(Sa + Sb) / max{abs(Sa), abs(Sb)} of Expression 5 as a variable, and Expression 12 is n a function value with [sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1] of Expression 8 as a variable, and they are exponential functions of Expression 5 and Expression 8, respectively.

[0154] The equations used in each embodiment and the non-linear index NLI for each calculated node are shown in Table 2 below. Note that the unit of the non-linear index NLI in Equation 1, Equation 4, Equation 9, and Equation 10 is the unit of length, and the non-linear index NLI in other equations is a dimensionless value. Also, although the variable n is included in Equation 8, Equation 9, Equation 10, and Equation 12, n = 0.8 in Example 10, n = 1.0 in Example 11, n = 2.0 in Example 12, and n = 0.8 in Example 14.

[0155]

Table 2

[0156] The non-linear index NLI of Equations 1 to 6 used in Examples 3 to 8 indicates that it is linear when the value is 0, and the non-linearity becomes stronger as the value deviates from 0. According to the values of the non-linear index NLI of Examples 3 to 8 shown in Table 2, it can be judged that in any of the examples, the non-linearity of node NP3 is the strongest, the non-linearity of node NP2 is the second strongest, and the non-linearity of node NP1 is the weakest.

[0157] The non-linear index NLI of Equation 7 used in Example 9 indicates that it is linear when the value is -1, and the non-linearity becomes stronger as the value increases. According to the value of the non-linear index NLI of Example 9 shown in Table 2, it can be judged that the non-linearity of node NP3 is the strongest, the non-linearity of node NP2 is the second strongest, and the non-linearity of node NP1 is the weakest.

[0158] The non-linear index NLI of Equations 8 to 10 used in Examples 10 to 12 indicates that it is linear when the value is 0, and the non-linearity becomes stronger as the value increases. According to the values of the non-linear index NLI of Examples 10 to 12 shown in Table 2, it can be judged that in any of the examples, the non-linearity of node NP3 is the strongest, the non-linearity of node NP2 is the second strongest, and the non-linearity of node NP1 is the weakest.

[0159] The non - linear indices NLI of formulas 11 - 12 used in Examples 13 - 14 indicate that when the value is 1, it is linear, and the larger the value, the stronger the non - linearity. According to the values of the non - linear index NLI of Examples 13 - 14 shown in Table 2, it can be determined that the non - linearity of node NP3 is the strongest, the non - linearity of node NP2 is the second strongest, and the non - linearity of node NP1 is the weakest.

[0160] As described above, in Examples 3 - 14 using calculation formulas for different non - linear indices NLI, in all cases, it can be determined that the non - linearity of node NP3 is the strongest, the non - linearity of node NP2 is the second strongest, and the non - linearity of node NP1 is the weakest, and equivalent evaluations are possible. Also, the calculation method of the non - linear index NLI is not limited to a specific calculation method such as the formulas shown in Table 1, and the non - linear index NLI only needs to be an index that can evaluate non - linearity.

[0161] (Examples 15 - 26) In Examples 15 - 26, a reference finite element model 1 with the fixed point of the reference finite element model as fixed point 1 was created, and two stress - change finite element models with stress coefficients k of - 0.8 and 0.8 were created. Next, spring - back simulations were performed on the two created stress - change finite element models to obtain the shapes after spring - back deformation. The spring - back simulation was regarded as elastic deformation analysis.

[0162] Next, the z - direction component amount of the displacement at the nodes of each stress - change finite element model was used as the spring - back deformation evaluation value SI, and from the shapes after spring - back deformation of each model, the z - direction component amounts at the three nodes of node NP1, node NP2, and node NP3 shown in FIG. 23 were obtained. Furthermore, the non - linear index NLI was obtained from the spring - back deformation evaluation values SI of the stress - change finite element models at each of nodes NP1 - NP3. In Examples 3 - 14, when the stress coefficient k is 0.8, the spring - back deformation evaluation value SI was designated as Sa, and when the stress coefficient k is - 0.8, the spring - back deformation evaluation value SI of the stress - change finite element model was designated as Sb, and the non - linear index NLI was taken as the calculated value of any of the formulas 1 - 12 shown in Table 1 above.

[0163] The equations used in each example and the calculated non-linear index NLI for each node are shown in Table 3 below. Note that the unit of the non-linear index NLI in Equations 1, 4, 9, and 10 is the unit of length, and the non-linear index NLI in the other equations is a dimensionless value. Also, although variables n are included in Equations 8, 9, 10, and 12, n = 0.8 in Example 22, n = 1.0 in Example 23, n = 2.0 in Example 24, and n = 0.8 in Example 26.

[0164]

Table 3

[0165] According to the values of the non-linear index NLI shown in Table 3, in any of Examples 15 to 26, it can be determined that the non-linearity of node NP3 is the strongest, the non-linearity of node NP2 is the next strongest, and the non-linearity of node NP1 is the weakest, and the same evaluation results as those of the aforementioned Examples 1 to 14 were obtained.

[0166] (Example 27) In Example 27, a reference finite element model 1 with the fixed point of the reference finite element model as fixed point 1 was created, and four stress change finite element models were created when the stress coefficient k was -0.8, -0.2, 0.4, and 0.6. Next, springback simulations were performed on the four created stress change finite element models to obtain the shapes after springback deformation. Note that the springback simulation was an elastic deformation analysis.

[0167] Next, the displacement at the nodes of each stress change finite element model was taken as the springback deformation evaluation value SI. From the shapes of each model after springback deformation, the springback deformation evaluation values SI at three nodes, namely node NP1, node NP2, and node NP3 shown in Fig. 23, were obtained. Further, from the stress coefficient k and the springback deformation evaluation value SI of the stress change finite element model at each of the nodes NP1 to NP3, an approximate formula for the springback deformation evaluation value SI with respect to the stress coefficient k was obtained, and the springback deformation evaluation values SI when the stress coefficient k was -0.5 and 0.5 were estimated from the approximate formula. Note that the approximate formula at node NP1 was approximated by a linear function, the approximate formula at node NP2 was approximated by a quadratic function, and the approximate formula at node NP3 was approximated by a cubic function.

[0168] Figs. 26(a), (b), and (c) are graphs showing the relationship between the stress coefficient k and the springback deformation evaluation value SI at nodes NP1, NP2, and NP3. The white circles in the figures indicate the springback deformation evaluation values SI when the stress coefficient k is -0.8, -0.2, 0.4, and 0.6. The dotted lines indicate the approximate formulas, and the black squares indicate the springback deformation evaluation values SI when the stress coefficient k estimated from the approximate formula is -0.5 and 0.5.

[0169] Furthermore, the non-linear index NLI was obtained from the springback deformation evaluation values SI when the stress coefficient k estimated from the approximate formula was -0.5 and 0.5. Note that the springback deformation evaluation value SI when the stress coefficient k is 0.5 was designated as Sa, and the springback deformation evaluation value SI of the stress change finite element model when the stress coefficient k is -0.5 was designated as Sb. The non-linear index NLI was taken as the calculated value of Equation 11 shown in Table 1 above. The calculated non-linear index NLI is shown in Table 4.

[0170]

Table 4

[0171] According to the values of the non-linear index NLI shown in Table 4, also in Example 27, it can be determined that the non-linearity of node NP3 is the strongest, the non-linearity of node NP2 is the second strongest, and the non-linearity of node NP1 is the weakest, and the same evaluation results as those of the aforementioned Examples 1 to 26 were obtained.

[0172] (Example 28) In Example 28, a reference finite element model 1 with the fixed point of the reference finite element model as fixed point 1 was created, and three stress change finite element models were created when the stress coefficient k was -0.8, -0.2, and 0.6. Next, springback simulations were performed for each stress change finite element model, and the shapes after springback deformation were obtained. Note that the springback simulation was an elastic deformation analysis.

[0173] Next, the amount of the z-direction component of the displacement at the nodes of each stress change finite element model was used as the springback deformation evaluation value SI, and from the shapes after springback deformation of each model, the amounts of the z-direction components at the three nodes of node NP1, node NP2, and node NP3 shown in FIG. 23 were obtained. Further, from the stress coefficient k and the springback deformation evaluation value SI of the stress change finite element model at each of the nodes NP1 to NP3, an approximate expression of the quadratic function of the springback deformation evaluation value SI with respect to the stress coefficient k was obtained, and the quadratic coefficient of the approximate expression was defined as Sc, and the non-linear index NLI was obtained from Sc. Note that the relationship between the stress coefficient k and the springback deformation evaluation value SI is linear when the coefficient Sc is 0, the non-linearity increases as the absolute value of the coefficient Sc increases, and the sign of the coefficient Sc does not affect the non-linearity. Therefore, the non-linear index NLI was defined as abs(Sc), which is the function value of the quadratic coefficient Sc of the approximate expression. abs is the absolute value function.

[0174] Figs. 27(a), (b), and (c) are graphs showing the relationship between the stress coefficient k and the springback deformation evaluation value SI at nodes NP1, NP2, and NP3. The white circles in the figures indicate the springback deformation evaluation values SI when the stress coefficient k is -0.8, -0.2, and 0.6, and the dotted lines indicate the approximate formulas. Table 5 below shows the values of the second-order coefficient Sc and the non-linearity index NLI of the approximate formulas at nodes NP1, NP2, and NP3.

[0175]

Table 5

[0176] According to the values of the non-linearity index NLI shown in Table 5, also in Example 28, it can be judged that the non-linearity of node NP3 is the strongest, the non-linearity of node NP2 is the next strongest, and the non-linearity of node NP1 is the weakest, and the same evaluation results as those of the aforementioned Examples 1 to 27 were obtained.

[0177] (Example 29) In Example 29, a reference finite element model 1 with the fixed point of the reference finite element model as fixed point 1 was created, and a plurality of stress change finite element models with the stress coefficient k being -1.0, -0.8, -0.6, -0.4, -0.2, 0.0, 0.2, 0.4, 0.6, and 0.8 were created. When creating the stress change finite element models, the elements for changing the stress with respect to the reference finite element model were only the elements within the region SCR indicated by the dotted line in Fig. 28, and the condition was set such that the stress was not changed for the elements outside the region SCR. Next, springback simulations were performed on the created reference finite element model 1 and each stress change finite element model, and the shapes after springback deformation were obtained. The springback simulation was an elastic deformation analysis.

[0178] Next, at node NP4 shown in FIG. 28, the springback deformation evaluation value SI for each stress coefficient k was obtained, and further, an approximate expression by a quadratic function was obtained for the relationship between the stress coefficient k and the springback deformation evaluation value SI. The springback deformation evaluation value SI was taken as the z-direction component amount of the displacement after springback deformation with respect to before the springback deformation at node NP4. Note that the springback deformation evaluation value SI when the stress coefficient k is 1 was taken as the springback deformation evaluation value SI of the reference finite element model 1.

[0179] FIG. 29 plots the springback deformation evaluation value SI for each stress coefficient k at node NP4 on a graph with the stress coefficient k on the horizontal axis and the springback deformation evaluation value SI on the vertical axis, and further shows the approximate expression by a dotted line. The springback deformation evaluation value SI on the vertical axis is a displacement amount, and the unit is mm.

[0180] Although the approximate expression in FIG. 29 is somewhat curved, it is approximately close to a straight line and is monotonically increasing, so it is judged that the non-linearity is not very strong. Thus, regarding the non-linearity of the partial springback deformation of the press-formed product, it is also possible to analyze using the stress change finite element model created by changing the stress in a part of the region of the reference finite element model.

[0181] In Examples 1 to 28, in the stress change finite element model, the stress coefficient k is multiplied by the stress of all elements to change it, and the springback deformation evaluation value SI is set to be a function of the displacement amount after springback deformation, the z-direction component amount of the displacement, or the z-direction component amount of the displacement with respect to before springback deformation, that is, it becomes 0 when there is no springback deformation. Therefore, when the stress coefficient k is 0, the stress of all elements becomes 0 and no springback deformation occurs, so the springback deformation evaluation value SI also becomes 0. On the other hand, when creating a stress change finite element model by multiplying the stress coefficient k by the stress of the elements in a part of the region of the reference finite element model, the springback deformation evaluation value SI is set to be 0 when there is no springback deformation. Even if the stress coefficient k is 0, there is stress in the part where the stress is not changed and springback deformation occurs, so the springback deformation evaluation value SI does not necessarily become 0. In Example 29, even when the stress coefficient k is 0, stress remains in the region other than the region SCR shown by the dotted line in Fig. 28 and springback deformation occurs. Therefore, even when the springback deformation evaluation value SI is the z-direction component amount of the displacement after springback deformation with respect to before springback deformation, the springback deformation evaluation value SI does not become 0.

[0182] (Example 30) In Example 30, a reference finite element model 1 with the fixed point of the reference finite element model as the fixed point 1 was created, and a stress change finite element model with the stress coefficient k set to -1.0 was created. Next, springback simulations were performed on the created reference finite element model 1 and stress change finite element model, and the shapes after springback deformation of each were obtained. Note that the springback simulation was an elastic deformation analysis.

[0183] Next, the displacement amounts at the nodes of the reference finite element model 1 and the stress change finite element model were used as the springback deformation evaluation value SI, and at all the nodes of each model, the springback deformation evaluation value SI was obtained from the shape after springback deformation. Also, taking the springback deformation evaluation value SI at each node of the reference finite element model 1 as Sa and the springback deformation evaluation value SI at each node of the stress change finite element model as Sb, the non-linear index NLI for all the nodes was obtained by the following Equation 1. NLI = Sa + Sb ···(1)

[0184] Next, a figure was created in which the non-linear index NLI of all the nodes was displayed in contour on the three-dimensional shape of the reference finite element model 1. The created figure is shown in FIG. 30. In this contour diagram, the part where the non-linear index NLI is close to 0 mm has weak non-linearity, and the part where the non-linear index NLI is away from 0 mm, that is, the absolute value of the non-linear index NLI is large, has strong non-linearity and can be judged as the location where non-linear springback occurs. Thus, by displaying the non-linear index NLI in contour on the three-dimensional shape of the part, the details of the non-linearity of the springback can be visually grasped, and the analysis can be facilitated.

[0185] (Example 31) In Example 31, a reference finite element model 1 with the fixed point of the reference finite element model as the fixed point 1 was created, and a stress change finite element model with a stress coefficient k of -1.0 was created. Next, springback simulations were performed on the created reference finite element model 1 and stress change finite element model, and the shapes after springback deformation of each were obtained. Note that the springback simulation was an elastic deformation analysis.

[0186] Next, the displacement amounts at the nodes of the reference finite element model 1 and the stress change finite element model were used as the springback deformation evaluation value SI, and at all the nodes of each model, the springback deformation evaluation value SI was obtained from the shape after springback deformation. Also, taking the springback deformation evaluation value SI at each node of the reference finite element model 1 as Sa and the springback deformation evaluation value SI at each node of the stress change finite element model as Sb, the non-linear index NLI of all the nodes was obtained by the following formula (2). NLI = (Sa + Sb) / max{abs(Sa), abs(Sb)} ···(2)

[0187] Next, a figure was created in which the non-linear index NLI of all the nodes was displayed in contour on the three-dimensional shape of the reference finite element model 1. The created figure is shown in FIG. 31. In this contour diagram, since the non-linear index NLI divides Sa + Sb by the larger value of the absolute value of Sa and the absolute value of Sb, the influence of the magnitude of the springback deformation amount is removed, and compared with FIG. 30 which is the contour diagram of Example 30, the non-linearity of the part with smaller springback deformation is clearer.

[0188] (Examples 32 to 33) In Examples 32 to 33, a reference finite element model 1 with the fixed point of the reference finite element model as the fixed point 1 was created, and a stress change finite element model with the stress coefficient k = -1.0 was created. Next, springback simulations were performed on the created reference finite element model 1 and stress change finite element model, and the shapes after springback deformation of each were obtained. Note that the springback simulation was an elastic deformation analysis.

[0189] Next, the displacement amounts at the nodes of the reference finite element model 1 and the stress change finite element model were used as the springback deformation evaluation value SI, and at all the nodes of each model, the springback deformation evaluation value SI was obtained from the shape after springback deformation. Also, taking the springback deformation evaluation value SI at each node of the reference finite element model 1 as Sa and the springback deformation evaluation value SI at each node of the stress change finite element model as Sb, the non-linear index NLI of all the nodes was obtained by the following formula (9). NLI = [sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n × max{abs(Sa), abs(Sb)} ···(9)

[0190] In Equation (9), n was set to 1.0 in Example 32 and 2.0 in Example 33. When calculating the non-linear index NLI using Equation (9), if the non-linear index NLI is 0 mm, it indicates that there is no non-linearity and it is linear. The larger the non-linear index NLI, the stronger the non-linearity.

[0191] Next, a contour diagram showing the non-linear index NLI of all nodes on the three-dimensional shape of the reference finite element model 1 was created. The contour diagram created in Example 32 is shown in FIG. 32, and the contour diagram created in Example 33 is shown in FIG. 33. In Example 33, since n in the calculation formula (Equation (9)) of the non-linear index NLI is a larger value than in Example 32, in the contour diagram of Example 33 shown in FIG. 33, the parts with stronger non-linearity are emphasized compared to the contour diagram of Example 32 shown in FIG. 32, making it easier to grasp the main parts with strong non-linearity.

[0192] (Example 34) In Example 34, a reference finite element model 1 with the fixed point of the reference finite element model set as fixed point 1 was created, and a stress change finite element model with a stress coefficient k of -1.0 was created. Next, a springback simulation was performed on the created reference finite element model 1 and stress change finite element model to obtain the shape after springback deformation for each. The springback simulation was regarded as an elastic deformation analysis.

[0193] Next, the z-direction component amount at the nodes of the reference finite element model 1 and the stress change finite element model was defined as the springback deformation evaluation value SI, and at all the nodes of each model, the springback deformation evaluation value SI was obtained from the shape after springback deformation. Also, taking the springback deformation evaluation value SI at each node of the reference finite element model 1 as Sa and the springback deformation evaluation value SI at each node of the stress change finite element model as Sb, the non-linearity index NLI for all the nodes was obtained by the following Equation 1. NLI = Sa + Sb ···(1)

[0194] Next, a figure was created in which the non-linearity index NLI of all the nodes was displayed in contour on the three-dimensional shape of the reference finite element model 1. The created figure is shown in FIG. 34. When calculating the non-linearity index NLI using Equation 1, the portion where the non-linearity index NLI is close to 0 mm has weak non-linearity, and the portion where the non-linearity index NLI is away from 0 mm, that is, the portion where the absolute value of the non-linearity index NLI is large, has strong non-linearity. Therefore, the locations where non-linear springback occurs can be grasped from the contour diagram.

[0195] (Example 35) In Example 35, a reference finite element model 1 with the fixed point of the reference finite element model as fixed point 1 was created, and a stress change finite element model with a stress coefficient k of -1.0 was created. Next, springback simulations were performed on the created reference finite element model 1 and stress change finite element model, and the shapes after springback deformation of each were obtained. Note that the springback simulation was an elastic deformation analysis.

[0196] Next, the z-direction component amount at the nodes of the reference finite element model 1 and the stress change finite element model was defined as the springback deformation evaluation value SI, and at all the nodes of each model, the springback deformation evaluation value SI was obtained from the shape after springback deformation. Also, taking the springback deformation evaluation value SI at each node of the reference finite element model 1 as Sa and the springback deformation evaluation value SI at each node of the stress change finite element model as Sb, the non-linearity index NLI for all the nodes was obtained by the following Equation 4. NLI = abs(Sa + Sb) ···(4)

[0197] Next, a figure showing the contour display of the non - linear index NLI of all nodes on the three - dimensional shape of the reference finite element model 1 was created. The created figure is shown in FIG. 35. The non - linear index NLI of Example 35 is the absolute value of the non - linear index NLI of Example 34. Since the non - linear index NLI is not affected by the sign, in the contour diagram of FIG. 35, it is easier to grasp the non - linear state than in FIG. 34.

[0198] (Example 36) In Example 36, a reference finite element model 1 with the fixed point of the reference finite element model set as fixed point 1 was created, and a plurality of stress - change finite element models with stress coefficients k of - 1.0, - 0.8, - 0.6, - 0.4, - 0.2, 0.2, 0.4, 0.6, 0.8 were created. Next, spring - back simulations were performed on the created reference finite element model 1 and each stress - change finite element model to obtain the shape after each spring - back deformation. Note that the spring - back simulation was an elastic deformation analysis.

[0199] Next, the amount of change due to spring - back deformation of the angle formed by the straight line L1 represented by the dotted line connecting node NP5 and node NP6 shown in FIG. 36 and the straight line L2 represented by the dotted line connecting node NP7 and node NP8 was defined as the spring - back deformation evaluation value SI, and the relationship between each stress coefficient k and the spring - back deformation evaluation value SI was obtained. Note that the spring - back deformation evaluation value SI obtained from the reference finite element model was set as the spring - back deformation evaluation value SI when the stress coefficient k is 1.0. Furthermore, including the data where the spring - back deformation evaluation value SI is also 0 when the stress coefficient k is 0, an approximate formula by a quadratic function for the relationship between the stress coefficient k and the spring - back deformation evaluation value SI was obtained, and a graph was created.

[0200] FIG. 37 is a graph showing the relationship between the springback deformation evaluation value SI on the vertical axis and the stress coefficient k on the horizontal axis, indicating the relationship of the springback deformation evaluation value SI for each stress coefficient k. The white circles in the figure are the plots of the springback deformation evaluation value SI for each stress coefficient k, and the dotted line is an approximate formula. Since the approximate formula shown in FIG. 37 has low linearity, it can be seen that the springback deformation regarding the angular change between the straight line L1 and the straight line L2 has strong non-linearity.

[0201] Next, Examples 37 to 40 will be described below. <Example 37> In Example 37, five reference finite element models 2 to 6 were created, which were the same as the reference finite element model 1 used in Examples 1 to 36 as the reference finite element model, except for the fixed points. In the reference finite element model 2, the points P21, P22, and P23 shown in FIG. 38(a) were set as fixed points. The constraint conditions were 6-degree-of-freedom constraints by each of the points P21 to P23. Point P21 constrained the displacements in the x, y, and z directions, point P22 constrained the displacements in the x and z directions, and point P23 constrained the displacement in the z direction. In the reference finite element model 3, the points P31, P32, and P33 shown in FIG. 38(b) were set as fixed points. The constraint conditions were 6-degree-of-freedom constraints by each of the points P31 to P33. Point P31 constrained the displacements in the x, y, and z directions, point P32 constrained the displacements in the x and z directions, and P33 constrained the displacement in the z direction. In the reference finite element model 4, the points P41, P42, and P43 shown in FIG. 38(c) were set as fixed points. The constraint conditions were 6-degree-of-freedom constraints by each of the points P41 to P43. Point P41 constrained the displacements in the x, y, and z directions, point P42 constrained the displacements in the x and z directions, and P43 constrained the displacement in the z direction. In the reference finite element model 5, the points P51, P52, and P53 shown in FIG. 38(d) were set as fixed points. The constraint conditions were 6-degree-of-freedom constraints by each of the points P51 to P53. Point P51 constrained the displacements in the x, y, and z directions, point P52 constrained the displacements in the y and z directions, and P53 constrained the displacement in the z direction. In the reference finite element model 6, points P61, P62, and P63 shown in Fig. 38(e) were set as fixed points. The constraint conditions were six-degree-of-freedom constraints by each of the points P61 to P63. Point P61 constrained displacements in the x, y, and z directions, point P62 constrained displacements in the x and z directions, and P63 constrained displacement in the z direction. Note that the coordinate systems and displacement directions of the reference finite element models 2 to 6 are the same as those shown in Fig. 21.

[0202] Next, at all the nodes of each of the reference finite element models 2 to 6, the non-linear index NLI was obtained by the following method. First, a stress change finite element model with a stress coefficient k of -1.0 was created for the reference finite element model 2, and by performing a springback simulation, the springback deformation evaluation value SI of the reference finite element model 2 and the stress change finite element model was obtained. Then, from the obtained springback deformation evaluation value SI, the non-linear index NLI was obtained for all the nodes. The operation of obtaining the non-linear index NLI at all the nodes of the reference finite element model 2 in this way was performed for each of the other reference finite element models 3 to 6. Note that the springback simulation was an elastic deformation analysis. Also, when creating the stress change finite element model, the stress was changed by multiplying the stress value of all the elements of the reference finite element model by the stress coefficient.

[0203] Next, taking the z-direction component amount of the displacement at the node as the springback deformation evaluation value SI, and using Sa for the springback deformation evaluation value SI at each node of each of the reference finite element models 2 to 6, and Sb for the springback deformation evaluation value SI at each node of each stress change finite element model, the non-linear index NLI of all the nodes was obtained by the following formula (1). NLI = Sa + Sb ···(1)

[0204] Next, the average value of the non-linear index NLI of each of the reference finite element models 2 to 6 for an individual node was defined as the inherent non-linear index ENLI for that node, and the operation of obtaining this inherent non-linear index ENLI was performed for all the nodes.

[0205] Next, a figure was created that shows a contour display of the eigen non-linear index ENLI of all nodes on the three-dimensional shape of the reference finite element model. The created figure is shown in Fig. 39. The part where the eigen non-linear index ENLI is close to 0 mm has weak non-linearity, and the part where the eigen non-linear index ENLI is away from 0 mm, that is, the part with a large absolute value of the eigen non-linear index ENLI, has strong non-linearity and is judged to be the location where non-linear springback occurs. Thus, based on the distribution of the eigen non-linear index ENLI obtained from multiple reference finite element models, compared with the distribution of the non-linear index NLI obtained from a single reference finite element model, the influence of the fixed point can be excluded and a more accurate distribution of non-linearity can be grasped.

[0206] <Example 38> Example 38 is a case where the springback characteristics were analyzed assuming the production of a press-formed product (length 180 mm, cross-sectional height 45 mm, width 52 mm) shown in Fig. 40 using a steel sheet with a tensile strength of 1180 MPa and a thickness of 1.2 mm.

[0207] First, a press-forming simulation was performed to obtain the shape, plate thickness, and residual stress at the bottom dead center of the press-forming, and based on these, a reference finite element model was created. The Young's modulus of the material was set to 206 GPa.

[0208] Next, a plurality of stress change finite element models with stress coefficients k of -0.8, -0.6, -0.4, -0.2, 0.2, 0.4, 0.6, and 0.8 were created, and springback simulations were performed for the created reference finite element model and each stress change finite element model to obtain the shape after springback deformation. The springback simulation was an elastic deformation analysis. Also, when creating the stress change finite element model, the stress was changed by multiplying the stress value of all elements of the reference finite element model by the stress coefficient.

[0209] Next, the change in the length of the line segment L3 connecting the points P71 and P72 at the end of the component shown in FIG. 40 was defined as the springback deformation evaluation value SI, and the springback deformation evaluation value SI for each stress coefficient was determined. Further, from the springback deformation evaluation value SI for each stress coefficient, an approximate formula by a quadratic function was obtained for the relationship between the stress coefficient k and the springback deformation evaluation value SI, and a graph was created with the stress coefficient k on the horizontal axis and the springback deformation evaluation value SI on the vertical axis. FIG. 41 shows this graph, where the springback deformation evaluation value SI for each stress coefficient k is plotted as white circles, and the approximate formula is shown as a dotted line.

[0210] The change in the length of the line segment L3 serves as an index indicating the U-shaped opening deformation of the component. However, the approximate formula in FIG. 41 has high linearity, and the springback deformation evaluation value SI changes approximately linearly with respect to the stress coefficient, with weak non-linearity. It can be judged that the springback deformation that can occur in press forming is not non-linear springback.

[0211] <Example 39> Example 39 is a case where springback characteristics were analyzed assuming that foam forming was performed using an "aluminum plate" with a tensile strength of 275 MPa and a plate thickness of 1.0 mm, and a press-formed product (length 653 mm, width 332 mm, height 23 mm) having the shapes shown in FIGS. 21(a) and 21(b) was manufactured in the same manner as in Example 1.

[0212] First, a press forming simulation was performed to obtain the shape, plate thickness, and residual stress at the bottom dead center of the press forming, and a reference finite element model was created based on these. The Young's modulus of the material was set to 70 GPa. Also, the fixed points of the reference finite element model of Example 39 are the points P1, P2, and P3 shown in FIG. 22(a), similar to Example 1. The restraint conditions are six-degree-of-freedom restraints. Based on the coordinate system shown in the figure, point P1 restrains the displacements in the x, y, and z directions, point P2 restrains the displacements in the x and z directions, and point P3 restrains the displacement in the z direction.

[0213] Next, a stress change finite element model with a stress coefficient k of -1.0 was created. When creating the stress change finite element model, the stress was changed by multiplying the stress values of all elements of the reference finite element model by the stress coefficient.

[0214] Next, springback simulations were performed on the created reference finite element model and the stress change finite element model to obtain the shapes after springback deformation for each. The springback simulation was performed as an elastic deformation analysis.

[0215] Next, the z-direction component amount at the nodes of the reference finite element model and the stress change finite element model was defined as the springback deformation evaluation value SI, and the springback deformation evaluation value SI was obtained from the shape after springback deformation at all nodes of each model. Also, the springback deformation evaluation value SI at each node of the reference finite element model was designated as Sa, and the springback deformation evaluation value SI at each node of the stress change finite element model was designated as Sb, and the nonlinear index NLI for all nodes was obtained by the following Equation (1). NLI = Sa + Sb ···(1)

[0216] Next, a figure was created in which the nonlinear index NLI of all nodes was displayed in contour on the three-dimensional shape of the reference finite element model. The created figure is shown in FIG. 42. When calculating the nonlinear index NLI using Equation (1), the part where the nonlinear index NLI is close to 0 mm has weak nonlinearity, and the part where the nonlinear index NLI is away from 0 mm, that is, the part with a large absolute value of the nonlinear index NLI, has strong nonlinearity. Therefore, the location where nonlinear springback occurs can be grasped from the contour diagram.

[0217] Thus, the analysis target of the springback characteristic analysis method disclosed in this specification is not limited to press-formed products made of steel, and may be press-formed products made of non-ferrous metal materials such as aluminum plates that undergo plastic deformation and springback deformation.

[0218] <Example 40> Example 40 is a case where springback characteristics were analyzed assuming that foam forming was performed using a steel sheet with a tensile strength of 603 MPa and a thickness of 1.0 mm, and a press-formed product having the shapes shown in FIGS. 21(a) and 21(b) (length 653 mm, width 332 mm, height 23 mm) was manufactured in the same manner as in Example 1.

[0219] First, a press forming simulation was performed to obtain the shape, plate thickness, and residual stress at the bottom dead center of the press forming, and a reference finite element model was created based on them. The Young's modulus of the material was set to 206 GPa. Also, the fixed points of the reference finite element model in Example 39 were the points P1, P2, and P3 shown in FIG. 22(a), similar to Example 1. The restraint condition was a six-degree-of-freedom restraint. Based on the coordinate system shown in the figure, point P1 restrained the displacements in the x, y, and z directions, point P2 restrained the displacements in the x and z directions, and point P3 restrained the displacement in the z direction.

[0220] Next, a stress change finite element model with a stress coefficient k of -1.0 was created. When creating the stress change finite element model, the stress of all elements in the reference finite element model was changed by multiplying the stress value of each element by the stress coefficient.

[0221] Next, a springback simulation was performed on the created reference finite element model and stress change finite element model to obtain the shape after springback deformation for each. The springback simulation was set as "elastoplastic deformation analysis".

[0222] Next, the z-direction component amount at the nodes of the reference finite element model and the stress change finite element model was defined as the springback deformation evaluation value SI, and the springback deformation evaluation value SI was obtained from the shape after springback deformation at all nodes of each model. Also, letting the springback deformation evaluation value SI at each node of the reference finite element model be Sa and the springback deformation evaluation value SI at each node of the stress change finite element model be Sb, the non-linear index NLI of all nodes was obtained by the following equation (1). NLI = Sa + Sb ···(1)

[0223] Next, a figure was created in which the non-linear index NLI of all nodes was displayed as a contour on the three-dimensional shape of the reference finite element model. The created figure is shown in FIG. 43. When performing a springback simulation by "elastoplastic" deformation analysis as in Example 40, compared with the case of performing a springback simulation by "elastic" deformation analysis as in Examples 1 to 39, the calculation time of the springback simulation increases, but the non-linearity of the springback can be evaluated in consideration of the non-linearity of the stress-strain characteristics of the material.

[0224] The embodiments of the present invention have been described above.

[0225] Note that the effects described in this specification are merely illustrative or exemplary and not limiting. That is, the technology according to the present disclosure may exhibit other effects apparent to those skilled in the art from the description of this specification, together with or instead of the above effects.

[0226] Note that the following configuration examples also belong to the technical scope of the present disclosure. (1) A method for analyzing the springback characteristics of a press-formed product of a metal plate, comprising: a reference finite element model creation step of creating a reference finite element model including material properties including the Young's modulus of the metal plate and data on the shape, plate thickness, and stress before springback deformation of the press-formed product to be analyzed; a stress change finite element model creation step of creating two or more stress change finite element models in which the magnitude of the stress in all or part of the regions of the reference finite element model is changed based on a stress coefficient with one or different stress coefficients; a springback simulation step of performing a deformation analysis by the finite element method for each of two or more of the created reference finite element model and the stress change finite element model to obtain the shape after springback deformation; A springback deformation evaluation value calculation step of obtaining a springback deformation evaluation value related to springback deformation from the shape before springback deformation and the shape after springback deformation of each model for which the shape after springback deformation has been obtained, A springback non-linearity evaluation step of obtaining the relationship between the stress coefficient and the springback deformation evaluation value from the stress coefficient and the springback deformation evaluation value of each model for which the shape after springback deformation has been obtained, and an analysis method characterized by comprising the same. (2) An analysis method for springback characteristics of a press-formed product of a metal plate, A reference finite element model creation step of creating a reference finite element model including material characteristics including the Young's modulus of the metal plate and data on the shape, plate thickness, and stress before springback deformation of the press-formed product to be analyzed, A stress change finite element model creation step of creating two or more stress change finite element models in which the magnitude of the stress in all or part of the regions of the reference finite element model is changed based on a stress coefficient with one or different stress coefficients, A springback simulation step of performing a deformation analysis by the finite element method for each of two or more of the created reference finite element model and the stress change finite element model to obtain the shape after springback deformation, A springback deformation evaluation value calculation step of obtaining a springback deformation evaluation value related to springback deformation from the shape before springback deformation and the shape after springback deformation of each model for which the shape after springback deformation has been obtained, A non-linear index calculation step of obtaining a non-linear index related to the non-linearity of the springback deformation evaluation value with respect to the stress coefficient from the stress coefficient and the springback deformation evaluation value of each model for which the shape after springback deformation has been obtained, and an analysis method characterized by comprising the same. (3) In the reference finite element model creation step, a plurality of the reference finite element models with different fixed points are created, In the non-linear index calculation step, the non-linear index is calculated for each of the created plurality of reference finite element models, The analysis method according to (2), further comprising an eigen non-linear index calculation step of obtaining an eigen non-linear index from each of the calculated non-linear indices. (4) The eigen non-linear index is the average value or the maximum value of the plurality of non-linear indices calculated in the non-linear index calculation step, or the average value of the non-linear indices that are equal to or greater than a certain value among the plurality of non-linear indices. The analysis method according to (3). (5) The analysis method according to any one of (1) to (4), wherein in the reference finite element model creation step, the reference finite element model is created by a forming simulation using the finite element method. (6) The analysis method according to any one of (1) to (5), wherein in the stress change finite element model creation step, the stress change finite element model is created by multiplying the stress value of all elements or elements in a partial region of the reference finite element model by the stress coefficient to change the stress value. (7) The springback deformation evaluation value is Of the nodes of the reference finite element model or the stress change finite element model, The displacement amount from before the springback deformation to after the springback deformation, or A function value with the displacement amount as a variable, or The directional component amount of the displacement from before the springback deformation to after the springback deformation, or A function value with the directional component amount as a variable. The analysis method according to any one of (1) to (6). (8) When the springback deformation evaluation value at the node of the stress change finite element model when the stress coefficient is a value ka other than 0.0 is defined as the springback deformation evaluation value Sa, When the springback deformation evaluation value at the node of the stress change finite element model when the stress coefficient is a value kb obtained by multiplying the value ka by -1.0 is defined as the springback deformation evaluation value Sb, The non-linear index is a value calculated by any of the following formulas, or a function value using any of the following formulas as variables, and is characterized by the analysis method according to any of (2) to (7). Sa + Sb, (Sa + Sb) / max{abs(Sa), abs(Sb)}, (Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], abs(Sa + Sb), abs(Sa + Sb) / max{abs(Sa), abs(Sb)}, abs(Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}, [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n , [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n ×max{abs(Sa), abs(Sb)}, [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n ×[{abs(Sa) + abs(Sb)} / 2] However, n is a real number, sign is the sign function, abs is the absolute value function, max is the maximum value function, min is the minimum value function, and when the stress coefficient is 1.0, the stress change finite element model is the reference finite element model. (9) In the step of creating the stress change finite element model, create the stress change finite element model for a plurality of the stress coefficients, In the step of calculating the springback deformation evaluation value, obtain one or more sets of the stress coefficient and the springback deformation evaluation value at the node by obtaining the springback deformation evaluation value for each stress coefficient at the node of the stress change finite element model, which is procedure (A), Using the springback deformation evaluation value for the node of the reference finite element model as the springback deformation evaluation value when the stress coefficient is 1.0, a set of the stress coefficient and the springback deformation evaluation value for the node is obtained in procedure (B); By using the springback deformation evaluation value for the node when the stress coefficient is 0 as the springback deformation evaluation value for the node when the springback deformation amount is 0, all or some of the procedures in procedure (C) for obtaining a set of the stress coefficient and the springback deformation evaluation value for the node are performed to obtain sets of the stress coefficient and the springback deformation evaluation value for the node for three or more different stress coefficients; An approximation formula for the springback deformation evaluation value with respect to the stress coefficient of the node is obtained from the sets of the three or more stress coefficients and the springback deformation evaluation values thus obtained; From the approximation formula, the springback deformation evaluation value Sa of the node when the stress coefficient is a value ka other than 0 and the springback deformation evaluation value Sb of the node when the stress coefficient is a value kb obtained by multiplying the value ka by -1 are obtained; The non-linear index is a value calculated by any of the following formulas, or a function value having any of the following formulas as variables, and is characterized by the analysis method according to any of (2) to (7). Sa + Sb, (Sa + Sb) / max{abs(Sa), abs(Sb)}, (Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], abs(Sa + Sb), abs(Sa + Sb) / max{abs(Sa), abs(Sb)}, abs(Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}, [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n , [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×max{abs(Sa),abs(Sb)}, [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×[{abs(Sa)+abs(Sb)} / 2] However, n is a real number, sign is the sign function, abs is the absolute value function, max is the maximum value function, and min is the minimum value function. (10) In the stress change finite element model creation step, create the stress change finite element model for a plurality of the stress coefficients, In the springback deformation evaluation value calculation step, Procedure (A) for obtaining one or more sets of the stress coefficient and the springback deformation evaluation value at the node of the stress change finite element model by obtaining the springback deformation evaluation value for each stress coefficient at the node of the stress change finite element model, Procedure (B) for obtaining one set of the stress coefficient and the springback deformation evaluation value for the node by using the springback deformation evaluation value for the node of the reference finite element model as the springback deformation evaluation value when the stress coefficient is 1.0, By performing all or part of the procedures among procedures (A), (B), and (C) for obtaining one set of the stress coefficient and the springback deformation evaluation value for the node by setting the springback deformation evaluation value for the node when the stress coefficient is 0 as the springback deformation evaluation value when the springback deformation amount is 0, obtain sets of the stress coefficient and the springback deformation evaluation value for the node for three or more different stress coefficients, Obtain an approximation formula of a quadratic function of the springback deformation evaluation value with respect to the stress coefficient of the node from the obtained sets of three or more stress coefficients and springback deformation evaluation values, The analysis method according to any one of (2) to (7), characterized in that when the quadratic coefficient of the approximation formula is the coefficient Sc, the non-linear index is the coefficient Sc or a function of the coefficient Sc. (11) In the non-linear index calculation step, the non-linear index at all or a plurality of nodes of the reference finite element model is obtained, The analysis method according to (2), further comprising a non-linear index analysis step of performing a contour display of the non-linear index of each node on the reference finite element model. (12) In the inherent non-linear index calculation step, the inherent non-linear index at all or a plurality of nodes of the reference finite element model is obtained, The analysis method according to (3) or (4), further comprising an inherent non-linear index analysis step of performing a contour display of the inherent non-linear index of each node on the reference finite element model. (13) The springback deformation evaluation value is The change amount of the distance between any two parts or nodes of the shape after springback deformation with respect to the shape before springback deformation, or The change amount of the angle of another part with respect to any part, or The change amount of the curvature of any part, or A function value using these change amounts as variables, and is characterized by the analysis method according to any one of (1) to (6). The analysis method according to any one of (1) to (6), characterized in that the relationship between the stress coefficient and the springback deformation evaluation value is displayed as a graph. (14) The analysis method according to any one of (1) to (13), characterized in that the relationship between the stress coefficient and the springback deformation evaluation value is displayed as a graph. (15) In the springback simulation step, the springback simulation is performed by elastic deformation analysis using the finite element method, and is characterized by the analysis method according to any one of (1) to (14). (16) A program that operates on a computer that controls an analyzer so that the analyzer executes the analysis method for the springback characteristics of a press-formed product of a metal plate according to any one of (1) to (15). (17) An analyzer for the springback characteristics of a press-formed product of a metal plate, A reference finite element model creation unit that creates a reference finite element model including material properties including the Young's modulus of the metal plate, the shape, plate thickness, and stress data of the press-formed product before springback deformation to be analyzed; A stress change finite element model creation unit that creates two or more stress change finite element models in which the magnitude of the stress in all or part of the regions of the reference finite element model is changed based on a stress coefficient, with one or different stress coefficients; A springback simulation unit that performs deformation analysis by the finite element method for each of two or more of the created reference finite element model and the stress change finite element models to obtain the shape after springback deformation; A springback deformation evaluation value calculation unit that obtains a springback deformation evaluation value related to springback deformation from the shape before springback deformation and the shape after springback deformation of each model for which the shape after springback deformation has been obtained; An analysis apparatus comprising: a springback non-linearity evaluation unit that obtains the relationship between the stress coefficient and the springback deformation evaluation value from the stress coefficient and the springback deformation evaluation value of each model for which the shape after springback deformation has been obtained. (18) An analysis apparatus for springback characteristics of a press-formed product of a metal plate, A reference finite element model creation unit that creates a reference finite element model including material properties including the Young's modulus of the metal plate, the shape, plate thickness, and stress data of the press-formed product before springback deformation to be analyzed; A stress change finite element model creation unit that creates two or more stress change finite element models in which the magnitude of the stress in all or part of the regions of the reference finite element model is changed based on a stress coefficient, with one or different stress coefficients; A springback simulation unit that performs deformation analysis by the finite element method for each of two or more of the created reference finite element model and the stress change finite element models to obtain the shape after springback deformation; A springback deformation evaluation value calculation unit that obtains a springback deformation evaluation value related to springback deformation from the shape before springback deformation and the shape after springback deformation of each model for which the shape after springback deformation has been obtained, An analysis apparatus comprising: a non-linear index calculation unit that obtains a non-linear index related to the non-linearity of the springback deformation evaluation value with respect to the stress coefficient from the stress coefficient of each model for which the shape after springback deformation has been obtained and the springback deformation evaluation value. (19) In the reference finite element model creation unit, a plurality of the reference finite element models with different fixed points are created, In the non-linear index calculation unit, the non-linear index is calculated for each of the created plurality of reference finite element models, The analysis apparatus according to (18), further comprising: a specific non-linear index calculation unit that obtains a specific non-linear index from the calculated non-linear indices. (20) The specific non-linear index is an average value or a maximum value of the plurality of non-linear indices calculated by the non-linear index calculation unit, or an average value of the non-linear indices that are equal to or greater than a certain value among the plurality of non-linear indices. The analysis apparatus according to (19). (21) The analysis apparatus according to any one of (17) to (20), wherein the reference finite element model creation unit creates the reference finite element model by performing a forming simulation using the finite element method. (22) In the stress change finite element model creation unit, the stress change finite element model is created by multiplying the stress value of all elements or elements in a partial region of the reference finite element model by the stress coefficient to change the stress value. The analysis apparatus according to any one of (17) to (21). (23) The springback deformation evaluation value is the displacement amount of a node of the reference finite element model or the stress change finite element model from before springback deformation to after springback deformation, or a function value using the displacement amount as a variable, or ​ The directional component amount of the displacement from before the springback deformation to after the springback deformation, or a function value with the directional component amount as a variable, and the analyzer according to any one of (17) to (22). (24) When the stress coefficient is a value ka other than 0.0, the springback deformation evaluation value at the node of the stress change finite element model is defined as the springback deformation evaluation value Sa, When the stress coefficient is a value kb obtained by multiplying the value ka by -1.0, and the springback deformation evaluation value at the node of the stress change finite element model is defined as the springback deformation evaluation value Sb, The non-linear index is a value calculated by any of the following formulas, or a function value with any of the following formulas as a variable, and the analyzer according to any one of (18) to (23). Sa + Sb, (Sa + Sb) / max{abs(Sa), abs(Sb)}, (Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], abs(Sa + Sb), abs(Sa + Sb) / max{abs(Sa), abs(Sb)}, abs(Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}, [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n , [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n ×max{abs(Sa), abs(Sb)}, [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n ×[{abs(Sa) + abs(Sb)} / 2] However, n is a real number, sign is the sign function, abs is the absolute value function, max is the maximum value function, and min is the minimum value function. When the stress coefficient is 1.0, the stress change finite element model is the reference finite element model. (25) In the stress change finite element model creation unit, the stress change finite element models for a plurality of the stress coefficients are created. In the springback deformation evaluation value calculation unit, Procedure (A) for obtaining one or more sets of the stress coefficient and the springback deformation evaluation value at the node of the stress change finite element model for each stress coefficient, and obtaining the springback deformation evaluation value at the node; Procedure (B) for obtaining one set of the stress coefficient and the springback deformation evaluation value for the node, where the springback deformation evaluation value for the node of the reference finite element model is used as the springback deformation evaluation value when the stress coefficient is 1.0; Procedure (C) for obtaining one set of the stress coefficient and the springback deformation evaluation value for the node by setting the springback deformation evaluation value for the node when the stress coefficient is 0 as the springback deformation evaluation value when the springback deformation amount is 0. By performing all or part of the procedures, sets of the stress coefficient and the springback deformation evaluation value for the node for three or more different stress coefficients are obtained. An approximate formula for the springback deformation evaluation value with respect to the stress coefficient of the node is obtained from the obtained sets of three or more stress coefficients and springback deformation evaluation values. From the approximate formula, the springback deformation evaluation value Sa of the node when the stress coefficient is a value ka other than 0 and the springback deformation evaluation value Sb of the node when the stress coefficient is a value kb obtained by multiplying the value ka by -1 are obtained. The non-linear index is a value calculated by any of the following formulas, or a function value having any of the following formulas as variables. The analyzer according to any one of (18) to (23). Sa + Sb, (Sa + Sb) / max{abs(Sa), abs(Sb)}, (Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], abs(Sa + Sb), abs(Sa + Sb) / max{abs(Sa), abs(Sb)}, abs(Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)}, [sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n , [sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n × max{abs(Sa), abs(Sb)}, [sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} + 1] n × [{abs(Sa) + abs(Sb)} / 2] However, n is a real number, sign is the sign function, abs is the absolute value function, max is the maximum value function, and min is the minimum value function. (26) In the stress change finite element model creation unit, create the stress change finite element model for a plurality of the stress coefficients, In the springback deformation evaluation value calculation unit, A procedure (A) for obtaining one or more sets of the stress coefficient and the springback deformation evaluation value at the node of the stress change finite element model by obtaining the springback deformation evaluation value for each stress coefficient at the node of the stress change finite element model, A procedure (B) for obtaining one set of the stress coefficient and the springback deformation evaluation value for the node by using the springback deformation evaluation value for the node of the reference finite element model as the springback deformation evaluation value when the stress coefficient is 1.0, By setting the springback deformation evaluation value for the node when the stress coefficient is 0 to the springback deformation evaluation value for the node when the springback deformation amount is 0, a set of the stress coefficient and the springback deformation evaluation value for the node is obtained. By performing all or some of the procedures in procedure (C), sets of the stress coefficient and the springback deformation evaluation value for the node with respect to three or more different stress coefficients are obtained. From the obtained sets of three or more stress coefficients and springback deformation evaluation values, an approximate quadratic function of the springback deformation evaluation value with respect to the stress coefficient of the node is obtained. The analyzer according to any one of (18) to (23), characterized in that when the quadratic coefficient of the approximate formula is coefficient Sc, the non-linear index is coefficient Sc or a function of coefficient Sc. (27) In the non-linear index calculation unit, the non-linear index at all or some of the plurality of nodes of the reference finite element model is obtained. The analyzer according to (18), characterized by having a non-linear index analysis unit that contour-displays the non-linear index of each node on the reference finite element model. (28) In the intrinsic non-linear index calculation unit, the intrinsic non-linear index at all or some of the plurality of nodes of the reference finite element model is obtained. The analyzer according to (19) or (20), characterized by having an intrinsic non-linear index analysis unit that contour-displays the intrinsic non-linear index of each node on the reference finite element model. (29) The springback deformation evaluation value is The amount of change in the distance between any two parts or nodes of the shape after springback deformation with respect to the shape before springback deformation, or The amount of change in the angle of another part with respect to any part, or The amount of change in the curvature of any part, or A function value with these amounts of change as variables. The analyzer according to any one of (17) to (22), characterized by this. ​The analyzer according to any one of (17) to (29), characterized in that the relationship between the stress coefficient and the springback deformation evaluation value is displayed as a graph. The analyzer according to any one of (17) to (30), characterized in that in the springback simulation unit, the springback simulation is performed by elastic deformation analysis using the finite element method.

Industrial Applicability

[0227] The present invention can be applied to the analysis of the springback characteristics of press-formed products of metal plates.

Explanation of Signs

[0228] 10 Analyzer Straight lines L1 to L2 Line segment L3 Nodes NP1 to NP8 Region SCR Fixed points P1 to P3 Fixed points P21 to P23 Fixed points P31 to P33 Fixed points P41 to P43 Fixed points P51 to P53 Fixed points P61 to P63 End points of line segment P71 to P72

Claims

1. A method for analyzing springback characteristics of a press-formed product of a metal plate, comprising: a reference finite element model creation step of creating a reference finite element model including material properties including the Young's modulus of the metal plate and data of the shape, plate thickness, and stress before springback deformation of the press-formed product to be analyzed; a stress change finite element model creation step of creating two or more stress change finite element models in which the magnitude of the stress in all or part of the regions of the reference finite element model is changed based on a stress coefficient, with one or different stress coefficients; a springback simulation step of performing a deformation analysis by the finite element method for each of two or more of the created reference finite element model and the stress change finite element models to obtain the shape after springback deformation; a springback deformation evaluation value calculation step of obtaining a springback deformation evaluation value related to springback deformation from the shape before springback deformation and the shape after springback deformation of each model for which the shape after springback deformation has been obtained; a springback non-linearity evaluation step of obtaining the relationship between the stress coefficient and the springback deformation evaluation value from the stress coefficient and the springback deformation evaluation value of each model for which the shape after springback deformation has been obtained. The analysis method is characterized by comprising the above steps.

2. A method for analyzing springback characteristics of a press-formed product of a metal plate, comprising: a reference finite element model creation step of creating a reference finite element model including material properties including the Young's modulus of the metal plate and data of the shape, plate thickness, and stress before springback deformation of the press-formed product to be analyzed; a stress change finite element model creation step of creating two or more stress change finite element models in which the magnitude of the stress in all or part of the regions of the reference finite element model is changed based on a stress coefficient, with one or different stress coefficients; a springback simulation step of performing a deformation analysis by the finite element method for each of two or more of the created reference finite element model and the stress change finite element models to obtain the shape after springback deformation; A springback deformation evaluation value calculation step of obtaining a springback deformation evaluation value related to springback deformation from the shape before springback deformation and the shape after springback deformation of each model for which the shape after springback deformation has been obtained; A non-linear index calculation step of obtaining a non-linear index related to the non-linearity of the springback deformation evaluation value with respect to the stress coefficient from the stress coefficient and the springback deformation evaluation value of each model for which the shape after springback deformation has been obtained, characterized by comprising: an analysis method.

3. In the reference finite element model creation step, a plurality of the reference finite element models with different fixed points are created; In the non-linear index calculation step, the non-linear index is calculated for each of the created plurality of reference finite element models; The analysis method according to claim 2, characterized by comprising an inherent non-linear index calculation step of obtaining an inherent non-linear index from the calculated non-linear indices.

4. The analysis method according to claim 3, characterized in that the inherent non-linear index is an average value or a maximum value of the plurality of non-linear indices calculated in the non-linear index calculation step, or an average value of the non-linear indices greater than or equal to a certain value among the plurality of non-linear indices.

5. The analysis method according to any one of claims 1 to 4, characterized in that in the reference finite element model creation step, the reference finite element model is created by a forming simulation using the finite element method.

6. The analysis method according to any one of claims 1 to 4, characterized in that in the stress change finite element model creation step, the stress change finite element model is created by multiplying the stress value of all elements or elements in a partial region of the reference finite element model by the stress coefficient to change the stress value.

7. The springback deformation evaluation value is: Of the nodes of the reference finite element model or the stress change finite element model, The displacement amount from before springback deformation to after springback deformation, or, A function value having the displacement amount as a variable, or, The direction component amount of the displacement from before springback deformation to after springback deformation, or, A function value having the direction component amount as a variable, and is characterized by the analysis method according to any one of claims 1 to 4.

8. When the stress coefficient is a value ka other than 0.0, the springback deformation evaluation value at the node of the stress change finite element model is defined as the springback deformation evaluation value Sa. When the stress coefficient is a value kb which is the value ka multiplied by -1.0, and the springback deformation evaluation value at the node of the stress change finite element model is defined as the springback deformation evaluation value Sb. The non-linear index is a value calculated by any of the following formulas, or a function value with any of the following formulas as variables, characterized by the analysis method according to any one of claims 2 to 4. Sa + Sb, (Sa + Sb) / max{abs(Sa), abs(Sb)}, (Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], abs(Sa + Sb), abs(Sa + Sb) / max{abs(Sa), abs(Sb)}, abs(Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)}, [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n 、 [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×max{abs(Sa),abs(Sb)}、 [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×[{abs(Sa)+abs(Sb)} / 2] However, n is a real number, sign is the sign function, abs is the absolute value function, max is the maximum value function, min is the minimum value function, and when the stress coefficient is 1.0, the stress change finite element model is the reference finite element model.

9. In the step of creating the stress change finite element model, stress change finite element models for a plurality of the stress coefficients are created. In the step of calculating the springback deformation evaluation value. A procedure (A) for obtaining one or more sets of the stress coefficient and the springback deformation evaluation value at the node by obtaining the springback deformation evaluation value for each stress coefficient at the node of the stress change finite element model. A procedure (B) for obtaining one set of the stress coefficient and the springback deformation evaluation value for the node, where the springback deformation evaluation value for the node of the reference finite element model is used as the springback deformation evaluation value when the stress coefficient is 1.

0. By setting the springback deformation evaluation value for the node when the stress coefficient is 0 to the springback deformation evaluation value for the node when the springback deformation amount is 0, a set of the stress coefficient and the springback deformation evaluation value for the node is obtained. By performing all or part of the procedures in procedure (C), sets of the stress coefficient and the springback deformation evaluation value for the node for three or more different stress coefficients are obtained. From the obtained sets of three or more stress coefficients and springback deformation evaluation values, an approximation formula for the springback deformation evaluation value with respect to the stress coefficient of the node is obtained. From the approximation formula, the springback deformation evaluation value Sa of the node when the stress coefficient is a non-zero value ka and the springback deformation evaluation value Sb of the node when the stress coefficient is a value kb obtained by multiplying the value ka by -1 are obtained. The non-linear index is a value calculated by any of the following formulas, or a function value having any of the following formulas as variables, according to the analysis method according to any one of claims 2 to 4. Sa + Sb (Sa + Sb) / max{abs(Sa), abs(Sb)} (Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2] abs(Sa + Sb) abs(Sa + Sb) / max{abs(Sa), abs(Sb)} abs(Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2] sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n 、 [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×max{abs(Sa),abs(Sb)}, [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×[{abs(Sa)+abs(Sb)} / 2] However, n is a real number, sign is a sign function, abs is an absolute value function, max is a maximum value function, and min is a minimum value function.

10. In the step of creating the stress change finite element model, stress change finite element models for a plurality of the stress coefficients are created. In the step of calculating the springback deformation evaluation value Procedure (A) for obtaining one or more sets of the stress coefficient and the springback deformation evaluation value at the node by obtaining the springback deformation evaluation value for each stress coefficient at the node of the stress change finite element model, and Procedure (B) for obtaining a set of the stress coefficient and the springback deformation evaluation value for the node by setting the springback deformation evaluation value for the node of the reference finite element model as the springback deformation evaluation value when the stress coefficient is 1.

0. By setting the springback deformation evaluation value for the node when the stress coefficient is 0 to the springback deformation evaluation value for the node when the springback deformation amount is 0, a set of the stress coefficient and the springback deformation evaluation value for the node is obtained. By performing all or some of the procedures in procedure (C), sets of the stress coefficient and the springback deformation evaluation value for the node for three or more different stress coefficients are obtained, From the obtained sets of three or more stress coefficients and springback deformation evaluation values, an approximate expression of a quadratic function of the springback deformation evaluation value with respect to the stress coefficient of the node is obtained, The analysis method according to any one of claims 2 to 4, wherein when the quadratic coefficient of the approximate expression is defined as coefficient Sc, the non-linear index is coefficient Sc or a function of coefficient Sc.

11. In the non-linear index calculation step, the non-linear index at all or some of the plurality of nodes of the reference finite element model is obtained, The analysis method according to claim 2, further comprising a non-linear index analysis step of performing a contour display of the non-linear index of each node on the reference finite element model.

12. In the intrinsic non-linear index calculation step, the intrinsic non-linear index at all or some of the plurality of nodes of the reference finite element model is obtained, The analysis method according to claim 3 or 4, further comprising an intrinsic non-linear index analysis step of performing a contour display of the intrinsic non-linear index of each node on the reference finite element model.

13. The springback deformation evaluation value is the change amount of the distance between any two parts or nodes of the shape after springback deformation with respect to the shape before springback deformation, or the change amount of the angle of another part with respect to any part, or the change amount of the curvature of any part, or a function value using these change amounts as variables, and is characterized by the analysis method according to any one of claims 1 to 4.

14. The analysis method according to any one of claims 1 to 4, characterized in that the relationship between the stress coefficient and the springback deformation evaluation value is displayed as a graph.

15. ​ The analysis method according to any one of claims 1 to 4, wherein in the springback simulation step, the springback simulation is performed by elastic deformation analysis using the finite element method.

16. A program that operates on a computer that controls an analyzer so that the analyzer executes an analysis method for springback characteristics of a press-formed product of a metal plate according to any one of claims 1 to 4.

17. An analyzer for springback characteristics of a press-formed product of a metal plate, a reference finite element model creation unit that creates a reference finite element model including material characteristics including the Young's modulus of the metal plate and data on the shape, plate thickness, and stress before springback deformation of the press-formed product to be analyzed; a stress change finite element model creation unit that creates two or more stress change finite element models in which the magnitude of the stress in all or part of the regions of the reference finite element model is changed based on a stress coefficient, with one or different stress coefficients; a springback simulation unit that performs deformation analysis by the finite element method for each of two or more of the created reference finite element model and the stress change finite element models to obtain the shape after springback deformation; a springback deformation evaluation value calculation unit that obtains a springback deformation evaluation value related to springback deformation from the shape before springback deformation and the shape after springback deformation of each model for which the shape after springback deformation has been obtained; An analyzer, comprising: a springback non-linearity evaluation unit that obtains the relationship between the stress coefficient and the springback deformation evaluation value from the stress coefficient and the springback deformation evaluation value of each model for which the shape after springback deformation has been obtained.

18. An analyzer for springback characteristics of a press-formed product of a metal plate, a reference finite element model creation unit that creates a reference finite element model including material characteristics including the Young's modulus of the metal plate and data on the shape, plate thickness, and stress before springback deformation of the press-formed product to be analyzed; a stress change finite element model creation unit that creates two or more stress change finite element models in which the magnitude of the stress in all or part of the regions of the reference finite element model is changed based on a stress coefficient, with one or different stress coefficients; Of the created reference finite element model and the stress change finite element model, for each of two or more models, perform a deformation analysis by the finite element method to obtain the shape after springback deformation, a springback simulation unit; From the shape before springback deformation and the shape after springback deformation of each model for which the shape after springback deformation has been obtained, obtain a springback deformation evaluation value related to springback deformation, a springback deformation evaluation value calculation unit; From the stress coefficient and the springback deformation evaluation value of each model for which the shape after springback deformation has been obtained, obtain a non-linear index related to the non-linearity of the springback deformation evaluation value with respect to the stress coefficient, a non-linear index calculation unit, an analysis apparatus characterized by comprising the same.

19. In the reference finite element model creation unit, create a plurality of the reference finite element models with different fixed points; In the non-linear index calculation unit, calculate the non-linear index for each of the created plurality of reference finite element models; An analysis apparatus according to claim 18, characterized by having a unique non-linear index calculation unit that obtains a unique non-linear index from the calculated non-linear indices.

20. The unique non-linear index is the average value or the maximum value of the plurality of non-linear indices calculated by the non-linear index calculation unit, or the average value of the non-linear indices that are a certain value or more among the plurality of non-linear indices, an analysis apparatus according to claim 19.

21. The analysis apparatus according to any one of claims 17 to 20, characterized in that in the reference finite element model creation unit, the reference finite element model is created by a forming simulation by the finite element method.

22. The analysis apparatus according to any one of claims 17 to 20, characterized in that in the stress change finite element model creation unit, the stress change finite element model is created by multiplying the stress value of all elements or elements in a partial region of the reference finite element model by the stress coefficient to change the stress value.

23. The springback deformation evaluation value is Of the nodes of the reference finite element model or the stress change finite element model, The displacement amount from before springback deformation to after springback deformation, or A function value with the displacement amount as a variable, or The directional component amount of the displacement from before the springback deformation to after the springback deformation, or a function value having the directional component amount as a variable, wherein the analyzer according to any one of claims 17 to 20 is characterized in that

24. When the stress coefficient is a value ka other than 0.0, the springback deformation evaluation value at the node of the stress change finite element model is defined as the springback deformation evaluation value Sa, When the stress coefficient is a value kb obtained by multiplying the value ka by -1.0, the springback deformation evaluation value at the node of the stress change finite element model is defined as the springback deformation evaluation value Sb, The non-linear index is a value calculated by any of the following formulas, or a function value having any of the following formulas as a variable, wherein the analyzer according to any one of claims 18 to 20 is characterized in that Sa + Sb, (Sa + Sb) / max{abs(Sa), abs(Sb)}, (Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], abs(Sa + Sb), abs(Sa + Sb) / max{abs(Sa), abs(Sb)}, abs(Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2], sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)}, [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n 、 [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×max{abs(Sa),abs(Sb)}、 [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×[{abs(Sa)+abs(Sb)} / 2] However, n is a real number, sign is a sign function, abs is an absolute value function, max is a maximum value function, min is a minimum value function, and the stress change finite element model when the stress coefficient is 1.0 is the reference finite element model.

25. In the stress change finite element model creation unit, stress change finite element models for a plurality of the stress coefficients are created, In the springback deformation evaluation value calculation unit, a procedure (A) for obtaining one or more sets of the stress coefficient and the springback deformation evaluation value at the node by obtaining the springback deformation evaluation value for each stress coefficient at the node of the stress change finite element model; a procedure (B) for obtaining one set of the stress coefficient and the springback deformation evaluation value for the node by using the springback deformation evaluation value for the node of the reference finite element model as the springback deformation evaluation value when the stress coefficient is 1.0; By setting the springback deformation evaluation value for the node when the stress coefficient is 0 to the springback deformation evaluation value for the node when the springback deformation amount is 0, a set of the stress coefficient and the springback deformation evaluation value for the node is obtained. By performing all or some of the procedures in procedure (C), sets of the stress coefficient and the springback deformation evaluation value for the node for three or more different stress coefficients are obtained. An approximate expression for the springback deformation evaluation value with respect to the stress coefficient of the node is obtained from the obtained sets of three or more stress coefficients and springback deformation evaluation values. From the approximate expression, the springback deformation evaluation value Sa of the node when the stress coefficient is a value ka other than 0 and the springback deformation evaluation value Sb of the node when the stress coefficient is a value kb obtained by multiplying the value ka by -1 are obtained. The analyzer according to any one of claims 18 to 20, wherein the non-linear index is a value calculated by any of the following expressions or a function value having any of the following expressions as variables. Sa + Sb (Sa + Sb) / max{abs(Sa), abs(Sb)} (Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2] abs(Sa + Sb) abs(Sa + Sb) / max{abs(Sa), abs(Sb)} abs(Sa + Sb) / [{abs(Sa) + abs(Sb)} / 2] sign(Sa / Sb) × min{abs(Sa / Sb), abs(Sb / Sa)} [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n 、 [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×max{abs(Sa),abs(Sb)}、 [sign(Sa / Sb)×min{abs(Sa / Sb), abs(Sb / Sa)}+1] n ×[{abs(Sa)+abs(Sb)} / 2] However, n is a real number, sign is a sign function, abs is an absolute value function, max is a maximum value function, and min is a minimum value function.

26. In the stress change finite element model creation unit, stress change finite element models for a plurality of the stress coefficients are created. In the springback deformation evaluation value calculation unit Procedure (A) for obtaining one or more sets of the stress coefficient and the springback deformation evaluation value at the node by obtaining the springback deformation evaluation value for each stress coefficient at the node of the stress change finite element model, Procedure (B) for obtaining a set of the stress coefficient and the springback deformation evaluation value for the node by setting the springback deformation evaluation value for the node of the reference finite element model to the springback deformation evaluation value when the stress coefficient is 1.

0. By using, as the springback deformation evaluation value for the node when the stress coefficient is 0, the springback deformation evaluation value for the node when the springback deformation amount is 0, a set of the stress coefficient and the springback deformation evaluation value for the node is obtained. By performing all or some of the procedures in procedure (C), sets of the stress coefficient and the springback deformation evaluation value for the node with respect to three or more different stress coefficients are obtained, From the obtained sets of three or more stress coefficients and springback deformation evaluation values, an approximate formula of a quadratic function of the springback deformation evaluation value with respect to the stress coefficient of the node is obtained, The analyzer according to any one of claims 18 to 20, wherein when the quadratic coefficient of the approximate formula is defined as coefficient Sc, the non-linear index is coefficient Sc or a function of coefficient Sc.

27. In the non-linear index calculation unit, the non-linear index at all or some of a plurality of nodes of the reference finite element model is obtained, The analyzer according to claim 18, further comprising a non-linear index analysis unit that contour-displays the non-linear index of each node on the reference finite element model.

28. In the inherent non-linear index calculation unit, the inherent non-linear index at all or some of a plurality of nodes of the reference finite element model is obtained, The analyzer according to claim 19 or 20, further comprising an inherent non-linear index analysis unit that contour-displays the inherent non-linear index of each node on the reference finite element model.

29. The springback deformation evaluation value is the amount of change in the distance between any two parts or nodes of the shape after springback deformation with respect to the shape before springback deformation, or the amount of change in the angle of another part with respect to any part, or the amount of change in the curvature of any part, or a function value using these amounts of change as variables, and is characterized by the analyzer according to any one of claims 17 to 20.

30. The analyzer according to any one of claims 17 to 20, characterized in that the relationship between the stress coefficient and the springback deformation evaluation value is displayed as a graph.

31. ​ The analyzer according to any one of claims 17 to 20, wherein in the springback simulation unit, springback simulation is performed by elastic deformation analysis using the finite element method.

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