JP5839323B2 - Automatic die size search system for metal plates - Google Patents

Description

  The present invention relates to press molding that uses a relative motion of two or more tools (metal molds) to apply a pressure or force to a metal plate (blank) to cause plastic deformation and finish it into a desired dimensional shape. The die includes a die, a punch, and a holder. In the drawing process, the blank is plastically deformed by pressing the punch while holding the blank against the die with the holder. The present invention provides a system for assisting in automatically determining the dimensions of a mold by utilizing a press molding numerical simulation. In particular, the present invention provides a system for assisting in determining a die size for press molding having a complicated shape and multi-step press molding that exceeds a limit drawing ratio that can be molded in one process.

  Many technical proposals have been made in this field, and the following documents can be cited as background art of the present invention.

  In Patent Document 1, for the purpose of shortening the lead time of new product development using press-formed products, the objective function is examined as the maximum thickness of the metal plate after forming in order to obtain the optimum bead shape and trim line. ing.

  In Patent Document 2, an evaluation variable (objective function) is calculated based on the equivalent stress and equivalent strain of a metal plate obtained by press forming simulation, and the wrinkle generation state of the plate material during and after forming is predicted. The way to do it is presented.

  Patent Document 3 discloses a press molding simulation analysis method for analyzing the spring back of a thick plate with high accuracy and reducing the man-hours and working time for mold design and correction for the purpose of formability and productivity. Presenting. In particular, we provide press forming simulation that can analyze the press forming of thick plates for automobile steel plates with high accuracy.

  In Non-Patent Document 1, the design of experiments using an orthogonal table is applied, and the amount of spring back of a metal plate is examined by a spring back experiment based on a spring back evaluation method by tensile bending and its simulation. The amount of spring back of the metal plate is optimized in consideration of such variations in press forming conditions.

  Non-Patent Document 2 examines the influence of the material properties of the metal plate on the plate shape in deep drawing, clarifies the method for determining the optimal metal plate shape using slip line field theory, etc. The optimum metal plate shape in the die deep drawing press forming is calculated.

  As described above, in any of the above conventional techniques, the objective function and the optimization method are focused on single-step forming, but it is difficult to directly apply these research results to multi-step design press forming. Also, these prior arts are not intended to automatically determine the dimensions of the mold.

  Regarding process design of multi-process press molding, there are Non-Patent Documents 3 to 5 as conventional techniques.

Non-Patent Document 3 aims to equalize the thickness of the metal plate in press forming in order to optimize the metal plate forming problem in the two-step press forming. The optimization is merely advanced by analysis focusing on the mold shape of the first stage of the pressing process. In this conventional technology, a method combining the optimization method of the finite element method, the sweeping simplex method, the simulated annealing method, and the lattice search method / simplex composite method is studied. It shows that it has search performance.

  Non-Patent Document 4 discloses a technique for automatically correcting a defect predicted by a press molding simulation at the time of mold design. However, in order to shorten the mold production period, a mold design with little mold correction is required.

  Non-Patent Document 5 proposes a method for designing a cylindrical redrawing die based on plastic mechanics, but does not take into account the occurrence of wrinkles or warpage, which is a product molding defect.

  In addition, the design formula of Romanowski shown in Non-Patent Document 6 is widely used to determine the dimensions of simple-shaped multi-step press molding dies such as cylindrical drawing and rectangular drawing. It cannot be applied to press-formed products.

  When press molding a complicated shape, molding defects due to breakage, warpage, and wrinkles become a problem. For this, a method in which press molding is performed in multiple steps is used, but time is required for process design and mold correction. However, the process design method for multi-step molding as shown in the above prior art does not consider molding defects such as dimensional accuracy, wrinkles and warpage, and the mold depends on the experience of the mold designer. Mold correction work is inevitable. Further, many of these conventional techniques are limited to methods for finding optimum conditions in individual processes, and it cannot be said that a system capable of automatically determining mold dimensions in multi-step press molding has been established.

  Non-Patent Document 7 is a study investigating the influence of lubrication on the punch side and die side on the formability of cylindrical deep drawing. However, no study has clarified the effect of the friction coefficient between the blank and the mold on the formability of cylindrical deep drawing.

JP 2006-167766 A JP-A-11-319971 JP 2004-42098 A

Hiroyuki Sugai, Ikuo Tanabe, Junnosuke Mizutani, Shingo Sugii, Atsushi Katayama, Prediction of optimum machining conditions for press forming combining computer simulation and quality engineering, Transactions of the Japan Society of Mechanical Engineers (C), 72, 721 (2006-9) , pp. 360-367. Hideo Iseki, Tadao Murota, Toshihiro Sato, Determination Method of Deep Drawing Blank Shape by Finite Element Method (2nd Report, Influence of Plastic Anisotropy on Optimum Blank Shape), Transactions of the Japan Society of Mechanical Engineers (C), 54, 505 (63-9), pp. 2257-2264. Eiji Nakamachi, Tadashi Honda, Hidetoshi Nakayasu, Yasuo Katayama, Yasunori Nakamura, Optimal Design of Molds for Forming Metal Sheets by Finite Element Method / Discrete Optimization Method-Application to Multipurpose Multistage Process Design Variable Problems-Plasticity Machining, 39, 446 (1998-3), pp. 247-251. Takeshi Moriya, Susumu Takahashi, Toshihiko Kuwahara: Development of automatic optimization of molding conditions for automotive panel drawing process, plasticity and processing, 49, 574 (2008), 1081. Hideo Iseki, Tadao Murota, Kazunori Kato: Calculation method of redrawing ratio by numerical simulation of cylindrical redrawing, Transactions of the Japan Society of Mechanical Engineers, C, 52, 480 (1986), 2257. Edited by Japan Society for Technology of Plasticity: Handbook of Plasticity Processing, Corona (2006), 485. Kenzo Kato and Yasuhiko Uchida: Effect of lubricant on drawability, plasticity and processing, 7, 70 (1966), 576.

  Press molding, in which a metal plate is plastically deformed and finished into a predetermined shape using relative movement of a mold, is used for mass production of parts such as automobiles and mobile phone bodies that are produced in large quantities. However, diversification of consumer needs has shortened the product life cycle, so it is necessary to produce a mold that satisfies customer needs in a short period of time. In order to shorten the mold design and production period, press molding numerical simulation and CAD / CAM are actively introduced, but the shape and dimensions of the mold depend on the experience and intuition of the designer. The current situation is that there are still many parts to be reduced, and the reduction of man-hours required for mold correction to improve molding defects is a problem to be solved.

  The present invention has been made to solve the above-mentioned problems, and automatically searches for a die size for multi-step additional drawing, which automatically searches for a die size using a numerical simulation of press molding and a genetic algorithm. System.

The invention according to claim 1 of the present invention comprises a metal plate body and two or more molds facing the metal plate body, and a plurality of metal plate bodies are utilized by utilizing the relative movement of the mold and the metal plate body. In the multi-step press forming system that undergoes plastic deformation through the above process, analysis means for analyzing the thickness and shape of the metal plate body during or after forming, and the design variables that determine the shape of the mold are repeatedly changed. Means for performing the analysis, means for adjusting the shape of the metal plate used for the analysis according to the thickness and shape of the metal plate during or after forming determined by the analyzing means, and the analysis A means for finding the number of press forming processes satisfying the constraint conditions and the mold dimensions in each process from the results, and maximizing the objective function from a plurality of combinations of the number of processes satisfying the constraint conditions and the mold dimensions in each process Number of processes and gold in each process A die size automatic search system of the metal plate body characterized by having a means for finding a dimension.

According to a second aspect of the present invention, in the automatic metal mold size searching system for the metal plate according to the first aspect, the coefficient of friction between the metal plate and the die is converted into a multi-step press forming simulation result. An automatic metal mold size search system for a metal plate , comprising means for applying an analysis of variance of an experimental design method and employing a friction coefficient obtained from the means as one of design variables .

  The invention according to claim 3 of the present invention is the metal plate automatic die size search system according to claim 1 or 2, wherein the limiting plate thickness in each step is set as the constraint condition.

  The invention according to claim 4 of the present invention is characterized in that the limit plate thickness in each process is gradually reduced to the forming limit plate thickness as the process progresses. This is an automatic die size search system for metal plates.

In the invention according to claim 5 of the present invention, the forming limit plate thickness is a point at which the plate thickness starts to rapidly decrease from the relationship between the plate thickness and the true strain obtained by the numerical simulation of the tensile test of the metal plate body. The metal plate automatic mold size searching system according to claim 4, wherein

  The invention according to claim 6 of the present invention is the metal plate automatic die size search system according to any one of claims 1 to 5, wherein the aperture height is an objective function. .

The invention according to claim 7 of the present invention is composed of a metal plate body and two or more molds facing the metal plate body, and a plurality of metal plate bodies are utilized by utilizing the relative movement of the mold and the metal plate body. In the multi-step cylindrical deep drawing processing system that undergoes plastic deformation through the above steps, the analysis means for analyzing the thickness and shape of the metal plate during and after forming, and the design variables that determine the shape of the mold are changed. Means for repeatedly executing the analysis, means for adjusting the shape of the metal plate used in the analysis according to the thickness and shape of the metal plate during or after forming determined by the analyzing means, From the results of analysis, the number of steps of multi-step cylindrical deep drawing that satisfies the constraint conditions and means for finding the mold dimensions in each process, and the combination of the number of processes that satisfy the constraint conditions and the mold dimensions in each process Number of steps to maximize objective function and each A die size automatic search system of the metal plate body characterized by having a means for finding the mold dimensions in extent.

According to an eighth aspect of the present invention, in the automatic metal mold size searching system for the metal plate according to the seventh aspect, the friction coefficient between the metal plate and the die is further calculated by a multi-step cylindrical deep drawing simulation. A metal plate automatic die size search system comprising means for obtaining a result of applying an analysis of variance of an experimental design to a result and employing a friction coefficient obtained from the means as one of design variables .

  The invention according to claim 9 of the present invention is the metal plate automatic die size search system according to claim 7 or 8, wherein the limiting plate thickness in each step is set as the constraint condition.

  The invention according to claim 10 of the present invention is characterized in that the limit plate thickness in each process is gradually reduced to the forming limit plate thickness as the process progresses. This is an automatic die size search system for metal plates.

According to the eleventh aspect of the present invention, the forming limit plate thickness is a point at which the plate thickness starts to decrease rapidly from the relationship between the plate thickness obtained by the numerical simulation of the tensile test of the metal plate and the true strain. The metal plate size automatic search system for a metal plate according to claim 10 .

  The invention according to claim 12 of the present invention is the metal plate automatic die size search system according to any one of claims 7 to 11, wherein the aperture height is an objective function. .

  The invention according to claim 13 of the present invention is characterized in that the die diameter is determined so that the product of the drawing height and the die diameter is constant. This is an automatic mold dimension search system.

  A fourteenth aspect of the present invention is a program executed by a computer to implement the mold dimension automatic search system according to any one of the first to thirteenth aspects.

  A fifteenth aspect of the present invention is a recording medium in which the program according to the fourteenth aspect is recorded so as to be readable by a computer.

  According to the present invention, it is possible to automatically determine the dimensions of a mold used for press-molding a mass-produced product having a complicated shape, so that it is possible to manufacture a mold that satisfies customer needs in a short time. In addition, since there is no part that depends on the intuition and experience of the designer in the shape and dimensions of the mold, it is possible to reduce the man-hours required for correcting the mold in order to improve press molding defects.

It is a figure which shows the flowchart of the metal mold | die automatic search system of this invention. It is a figure which shows the dimension of the cylinder with a flange used in order to apply a metal mold | die automatic search system to multi-process cylinder deep drawing. It is a figure which shows the model comprised from a punch, die | dye, a holder (plate restraint), and a blank used by press molding numerical simulation. It is a figure which shows the relationship between the true stress of a cold rolled steel plate (SPCC), and a true strain. It is a figure explaining the design variable set in order to determine the multi-process cylindrical deep drawing metal mold | die, and its dimension. It is a figure which shows the process of converging the drawing height of the molded article in FIG. 2 using the metal mold | die automatic search system of FIG. 1 shown in Example 1. FIG. It is a figure which shows the tension test model used for the numerical simulation. It is a figure which shows the relationship between the tensile force F obtained by numerical simulation, and the true distortion | strain (epsilon) calculated | required from the forced displacement. FIG. 8 is a diagram showing the relationship between the thickness t ₀ and the true strain ε at the origin O in FIG. It is a figure which shows the plate | board thickness distribution of the tension test model corresponding to the A point and B point in FIG. It is a figure which shows the mode of the restrictions condition of the plate | board thickness in each process. It is the figure which showed the shape error of the flange part on the basis of the blank position before shaping | molding. It is a figure which shows the state of the plate | board thickness of the molded article obtained at each process. It is a figure which shows the forming limit diagram (FLD) with respect to the method using the automatic mold size design system of a present Example, and the design formula of Romanowski. It is a figure which shows the deformation | transformation state and board thickness of the element in the 5th process of the metal mold | die automatic search system of a present Example. It is a figure which shows the deformation | transformation state and board thickness of the element in the 2nd process by the design formula of Romanowski. It was used to study a diagram illustrating the dimensions of the initial thickness t ₀ = 0.5 mm cold rolled steel plate (SPCC) manufactured flanged cylinder. It is a figure which shows the design variable of the metal mold | die comprised from a punch, die | dye, a holder, and a blank used by press molding numerical simulation. It is a figure for demonstrating the main effects of the factor in Table 7, A (micro | micron | mu) _1, and B (micro | micron | mu) ₂ . It is a figure for demonstrating the effect of the factor in Table 7, A ((micro | micron | mu) ₁ ) * B ((mu) ₂ ). It is a figure which shows the influence which the result shown in FIG. 19 has on a moldability.

  The automatic die size search system for multi-step drawing of the present invention searches for an optimum die size by applying a press molding numerical simulation and a genetic algorithm. Embodiments of an automatic mold dimension search system according to the present invention will be described below with reference to FIGS. 1 to 21 and Tables 1 to 7. However, although Examples 2 and 3 are described for cylindrical deep drawing, the present invention is not limited to this cylindrical deep drawing, and rectangular tube deep drawing and complex-shaped press molding are performed. It is a system that can also be applied to.

  The mold dimension automatic search system of the present embodiment will be described with reference to FIG.

  FIG. 1 shows a flowchart of a mold size automatic search system of the present invention. It consists of a definition unit, a simulation unit, a determination unit, and a search / update unit. The definition part defines the mold dimensions to be searched, sets initial values thereof, and defines objective functions and constraints. The objective function is a criterion for finally selecting one combination of mold dimensions in the combination of allowable mold dimension values. In this embodiment, the objective function is the aperture height. Further, the constraint conditions are conditions such as a range of values taken by the mold dimensions, shape / dimension errors during the process and after molding. The simulation unit creates a finite element model based on the die dimension value sampled by the update / search unit, and performs a press molding numerical simulation thereof.

  In this embodiment, the press molding simulation is assumed to be a simulation by a dynamic explicit finite element method, but is not limited to the simulation by this method. Based on the result of numerical simulation of press molding, the determination unit extracts the blank thickness during or after molding, calculates the objective function from the extracted thickness, and determines the quality of the mold based on the objective function value. . The search / update unit samples the die dimension value that satisfies the constraint conditions using a genetic algorithm.

  Using such an automatic mold dimension search system, the dimensions of the multi-process drawing mold are determined as follows. First, the process shown in the flowchart of FIG. 1 is performed with the final dimension of the molded product as the initial value of the mold dimension. When the dimensions, plate thickness, and wrinkles of the molded product satisfy the constraint conditions, the process ends at the first step. If not, the mold size is updated by a genetic algorithm, and the first step is completed by finding a range satisfying a condition in which the mold size with the maximum drawing height as the objective function is a constraint condition. In the second step, the molded product obtained in the first step is used as a blank, and the final size of the molded product is used as the mold size to perform redrawing. If the constraint condition is satisfied, the process ends in the second step. If it is not satisfied, the die size that maximizes the drawing height is found as in the first step, and the process proceeds to the next step. As described above, the number of steps necessary to reach the final size of the molded product and the die size of each step are derived.

  An embodiment in which the mold size automatic search system of the present invention described in Embodiment 1 is applied to a multi-step cylindrical deep drawing will be described. In addition, the effectiveness of the automatic mold dimension search using the mold dimension automatic search system of the present embodiment will be examined by comparing with the numerical simulation result using the mold of the dimension required by the Romanowski design formula.

FIG. 2 shows the dimensions of a flanged cylinder used to apply the automatic mold size search system to a multi-step cylindrical deep drawing. In this example, the test was performed on a cold-rolled steel plate (SPCC) having an initial plate thickness (t ₀ = 0.5 mm) and having a small effect of springback on the molded product. Since this product has a large drawing ratio, it cannot be formed by single-step press molding, and it is necessary to implement process design and process optimization for multi-stage press molding.

FIG. 3 shows a model composed of a punch, a die, a holder, and a blank used in the press molding numerical simulation. In this example, since the press-formed product is a flanged cylinder, the numerical simulation was performed with a 1/4 model. The punch, die, and holder were all rigid bodies. The element corresponding to the die was completely fixed, and the punching speed was 120 mm / s. Further, the holder force in the first step was controlled to the holder surface pressure p _H = 2.5 MPa obtained by the equation (1).

p _H = σ _y / 100 (1)
Here, σ _y is the yield stress of the blank. In order to adjust the wrinkle of the flange after the second step, a pressure of 2.5 MPa was applied after the punch lowered and the flange contacted the die. The blank was an isotropic four-node square shell element, and the work hardening characteristic was applied with the n-th power hardening law given by equation (2).

σ = Kε ⁿ (2)
Here, σ is the true stress after yielding, K is the plasticity coefficient, ε is the true strain, and n is the work hardening index. Note that the strain rate dependency of the blank was not considered.

  Table 1 shows the material property values used in the press molding numerical simulation. The blank was made of SPCC having a thickness of 0.5 mm, and the values of K and n in Table 1 were obtained by carrying out a tensile test of JIS Z 2201. It calculated | required by the least squares method using the tension test result shown with the broken line in FIG. The solid line in FIG. 4 shows the diagram of equation (2) using these values.

When the die size for multi-step cylindrical deep drawing is determined by Romanowski's design formula, the friction coefficient between members is not considered, but the friction coefficient between members affects the formability of cylindrical deep drawing. Therefore, the friction coefficient shown in Table 2 was used for the press molding numerical simulation. The friction coefficient between the die and the blank and between the holder and the blank was set to 0.1 with reference to the value at 25 ° C. of the press oil for ordinary steel plates. However, the friction coefficient between the punch and the blank was set to 0.2 in consideration of the solution convergence state in the numerical simulation.

FIG. 5 is a diagram for explaining a multi-step cylindrical deep drawing die and design variables set to determine the dimensions thereof. Here, c is the clearance between the punch and the die, it is d _d die diameter, r _p is the punch shoulder radius, r _d is the die shoulder radius. Note that c in the final step was set to 0.5 mm, which is equal to the initial plate thickness.

FIG. 6 shows a process of converging the drawing height of the molded product in FIG. 2 using the mold size automatic search system of FIG. 1 shown in the first embodiment. Here, one of the constraint conditions given by the multi-step cylindrical deep drawing of the present embodiment will be described. In deep drawing, a deep shape with a narrow opening is pressed. Therefore, the objective function in each process is the drawing height h shown in FIG. 5, and the combination of design variables related to the die and punch that maximizes h within the drawing height 19.5 mm in FIG. It was. In order to prevent only the drawing height in the middle of the process from reaching the final dimension of 19.5 mm shown in FIG. 2, the expression (3) is applied between the drawing height h and the die diameter d _d. The inverse relationship shown is given.
hd _d = (diaphragm height 19.5 mm) x (cylinder diameter 16.0 mm) = 312 mm ² (3)
FIG. 6 shows a process of applying the automatic mold size search system of FIG. 1 to converge to the aperture height in FIG. 2 according to the relational expression (3).

  In this example, a numerical simulation of a tensile test was performed, and a constraint condition for the plate thickness at the time of molding was obtained from the plate thickness change.

FIG. 7 shows a tensile test model used for the numerical simulation. The shape was based on JIS Z2201 13A test piece, and forced displacement was applied at 8 mm / s in the x direction. FIG. 8 shows the relationship between the tensile force F obtained by the numerical simulation and the true strain ε obtained from the forced displacement. F reached its maximum at ε = 0.26 corresponding to the n value, and decreased rapidly as ε increased with 0.3 <ε <0.4. FIG. 9 shows the relationship between the plate thickness t ₀ and the true strain ε at the origin O in FIG. t ₀ gradually decreased as ε increased when ε ≦ 0.26, but was the same as F when 0.3 <ε <0.4. FIG. 10 shows the thickness distribution of the tensile test model corresponding to points A and B in FIG. In FIG. 10 (a) where ε = 0.31, the reduction of the plate thickness is limited to the vicinity of the origin in FIG. On the other hand, in FIG. 10B with ε = 0.34, constriction is recognized over the entire central plate width. From the above, and a 0.4 mm of the initial wall thickness 0.5 mm and forming limit thickness t _a.

  By the way, when the reduction | decrease in plate | board thickness is too large at one process, possibility that it will fracture | rupture at a post process will become high. Therefore, the plate thickness constraint in each process is represented by equation (4), and the state is shown in FIG.

t ≧ t _a + (0.1 / 2 ⁱ ) (t _a = 0.4 mm) (4)
Here, i is a process number.

Next, when the drawing height h and the die diameter d _d in FIG. 5 reach the final dimension in FIG. 5 during the process, the punch shoulder radius r _p must also be 0.3 mm of the final dimension. There is a geometric relationship between d _d and r _p d _d = d _b + 2r _p + 2c. Here, d _b is a bottom flat portion diameter, c in FIG. 2 is a clearance shown in Figure 5. Therefore, from d _b = 14.4 mm and c = 0.5 mm of the final process, r _p of each process is given by the equation (5).

r _p = (1/2) d _d -7.7 (5)
In this example, the allowable range of the shape error of the flange portion due to wrinkles and the dimensional error of the cylindrical side surface was within 0.25 mm, which is 50% of the initial plate thickness = 0.5 mm, regardless of the process. The shape error of the flange portion was judged from the difference between the maximum value and the minimum value of the z-direction coordinate values of the 30 flange portion outer edge upper nodes shown in FIG. 12 with reference to the blank position before molding. Similarly, the dimensional error of the cylindrical side straight portion was obtained from the x-direction coordinate values of 25 nodes in FIG. 12 with the die cylindrical straight portion shown in FIG. 5 as a reference. In this example, the influence of the springback after unloading on the shape error and dimensional error was not considered. In addition, as shown in FIG. 5, in the case of the mold used in this research, the cylindrical bottom surface is formed only by the punch inside the cylinder and is not affected by external force, so the shape of the cylindrical bottom surface cannot be corrected. Therefore, the dimensional error at the bottom of the cylinder was not a problem.

  Table 3 shows the mold dimensions in each process obtained by the mold dimension automatic search system of the present embodiment.

Table 4 shows the mold dimensions determined using the Romanowski design formula.

In order to achieve the dimensions of the flanged cylinder in FIG. 2, there were four steps in the Romanowski design formula, whereas in the automatic mold size search system of this embodiment, there were five steps. However, as will be described later, when the die and punch dimensions obtained by the Romanowski design formula are used and numerical simulation of press forming is performed with the friction coefficient shown in Table 2, the plate thickness is greatly reduced locally in the second step. have done. On the other hand, in the automatic mold size search system of the present embodiment, there is no such a situation because the plate thickness has the constraint condition of the formula (4). This suggests that the automatic mold size search system of this embodiment is superior to the Romanowski design formula that cannot give constraints on the plate thickness and the dimensional accuracy of the press-formed product.

FIG. 13 shows the thickness of the molded product obtained in each step. In the mold shape according to Romanowski's design formula, the minimum thickness in the second process was much less than the forming limit t _a = 0.4 mm. However, using the automatic mold dimension search system of this example requires 5 processes. However, the flanged cylinder of the dimensions shown in FIG. 2 is applied to the relational expression between the drawing height h and the die diameter d _d in Expression (3), the constraint condition in Expression (4) with respect to the plate thickness t, and the shape accuracy. It was achieved within the tolerance of dimensional accuracy.

FIG. 14 shows a forming limit diagram (FLD) for the method using the automatic mold size design system of this embodiment and the design formula of Romanowski. As in this example, it is said that FLD cannot be used for fracture prediction in multi-step cylindrical deep drawing where the strain path changes greatly, but here, FLD is shown for reference. In FIG. 14, ε ₁ is the maximum principal strain and ε ₂ is the minimum principal strain. In any case, there are many points exceeding the FLC after the second step. However, according to the automatic mold size search system of the present embodiment, it is possible to mold to the dimensions in FIG. 2 within the allowable range of dimensional accuracy and shape accuracy.

  FIG. 15 shows the deformation state and plate thickness of the element in the fifth step of the automatic mold size search system of this embodiment, and FIG. 16 shows them in the second step according to the Romanowski design formula. In the design formula of Romanowski, the elements for the second process punch shoulder were greatly extended and fractured. On the other hand, in the mold dimensions obtained by the automatic mold dimension search system of the present embodiment, although a plate thickness reduction portion was seen at the die shoulder, the plate thickness was 0.415 mm and there was no problem.

  As described above, in this embodiment, an automatic mold dimension search system that automatically searches for a mold dimension in each step necessary to obtain a cylindrical deep-drawn container having a given dimension by numerical simulation, Its usefulness was studied with a cold rolled steel plate (SPCC) flanged cylinder. As a result, by giving the following conditions (i) to (c) for the drawing height and the plate thickness, there is no local decrease in the plate thickness without evaluating the formability due to strain, and the predetermined dimensions. We were able to find processes and mold dimensions that could be molded with high accuracy and shape accuracy. The condition is a. The relationship between the drawing height and the die diameter is proportional. The point at which the plate thickness starts to decrease rapidly from the relationship between the plate thickness and the true strain obtained by numerical simulation of the tensile test is defined as the forming limit plate thickness. The limit plate thickness of each process is to decrease stepwise from the initial plate thickness to the forming limit plate thickness as the process progresses.

  Conventionally, the number of processes and mold dimensions for multi-step cylindrical deep drawing are based on Romanowski's design formula considering geometric constraints. According to the design formula, the die size of the drawing ratio (= punch diameter / blank diameter) for each process is shown for the relative thickness (= initial thickness / blank diameter) of a given cylindrical container. The coefficient of friction and the material properties of the blank are not considered, and the success or failure of container molding cannot be predicted.

  In the present embodiment, a means for obtaining a coefficient of friction between a metal plate and a mold by applying a variance analysis of an experimental design method to a multi-step press forming simulation result is shown for multi-step cylindrical deep drawing.

FIG. 17 shows the dimensions of a cold-rolled steel plate (SPCC) flanged cylinder with an initial plate thickness t ₀ = 0.5 mm used for the study. The initial blank diameter was 49 mm. The dynamic explicit FEM software ANSYS LS-DYNA was used for the press forming numerical simulation. The blank was an isotropic four-node square shell element. For numerical simulations, a Cowper-Symonds power law rate-dependent model was used, with K = 0.59 GPa, n = 0.26, strain rate parameter C = 40.4 s ⁻¹ , P = 5. SPCC springback was small and was not considered.

  FIG. 18 shows the design variables of a die composed of a punch, a die, a holder, and a blank used in the press molding numerical simulation. Table 5 shows the mold dimensions obtained with the Romanowski design formula. Based on the relationship between the plate thickness and the true strain obtained by the numerical simulation of the tensile test of SPCC specimens (plate thickness 0.5 mm), the point at which the plate thickness starts to decrease rapidly is the forming limit plate thickness (= 0.4 mm). It was used to determine whether or not it was formed.

Effect of friction coefficient on the moldability of the cylindrical deep drawing was investigated by analysis of variance using the orthogonal table L ₂₇ for the first step in Table 5.

Table 6 shows the coefficient of friction and the level at four locations in FIG. 18 selected as the four factors. The friction coefficient between the blank and the mold is about 0.1. Here, in order to clarify the influence of the friction coefficient on the formability, a wide range of 0.1 to 0.5 is used.

The drawing height h and the minimum plate thickness t _min at the end of the first step were selected as representatives of the shape dimensions and the constraint conditions, respectively, and an analysis of variance was performed using the ratio of these as an index. Table 7 shows the results. When the plate thickness locally decreased and t _min <0.4 mm, t _min = 0.4 mm and h at that time were used.

Judging from the dispersion ratio F ₀ in Table 7, the factors affecting the moldability are factor B, factor A, and interaction A × B in descending order. FIG. 19 shows the main effects of A (μ ₁ ) and B (μ ₂ ). The main effect of μ ₁ was higher as μ ₁ increases. The main effect of μ ₂ was the opposite, and the level effect on the main effect was significant. FIG. 20 shows the effect of A (μ ₁ ) × B (μ ₂ ). The effect did not vary much with the μ ₁ level, and became smaller as the μ ₂ level increased. From this, μ ₁ and μ ₂ are independent factors.

FIG. 21 shows the influence of the results shown in FIG. 19 on the moldability. The factors C and D, which were less effective in analysis of variance, were set to the first level, that is, μ ₃ = μ ₄ = 0.1. In FIG. 21 , (a) is the case where the main effects of μ ₁ and μ ₂ are the maximum, (b) is the intermediate case, and (c) is the minimum case. The flanged cylinder in FIG. 17 was formed in the four steps shown in Table 5 only in the case of (a), and in the cases of (b) and (c), the plate thickness was obtained in the second step or the first step. However, the forming limit plate thickness was locally less than 0.4 mm. From the above, it can be said that by performing analysis of variance using h / t _min as an index, it is possible to find a friction coefficient between a blank and a die that is effective for cylindrical deep drawing.

  If a computer environment capable of executing press working simulation in a short time is prepared, the automatic mold size searching system of the present invention can be applied to rectangular tube drawing and complex shaped part forming.

Claims (15)

A multi-step press forming system comprising a metal plate and two or more molds facing the metal plate, and plastically deforming the metal plate through a plurality of processes using relative movement of the mold and the metal plate The analysis means for analyzing the thickness and shape of the metal plate body during or after forming, the means for repeatedly executing the analysis by changing the design variable defining the shape of the mold, and the analysis means Means for adjusting the shape of the metal mold used for the analysis according to the thickness and shape of the metal plate body during or after forming determined in step 3, and the number of press forming steps satisfying the constraints from the results of the analysis And means for finding out the mold dimensions in each process, means for finding out the number of processes that satisfy the constraints and the number of processes that maximizes the objective function from a plurality of combinations of the mold dimensions in each process, and the mold dimensions in each process Having Mold dimensions automatic search system of the metal plate body characterized. 2. The metal plate size automatic search system according to claim 1, further comprising means for obtaining a coefficient of friction between the metal plate and the die by applying a variance analysis of an experimental design method to a multi-step press forming simulation result. And adopting a friction coefficient obtained by the means as one of the design variables .   3. The metal plate size automatic search system for metal plate according to claim 1 or 2, wherein a limit plate thickness in each step is set as the constraint condition.   4. The automatic metal mold size searching system for a metal plate according to claim 1, wherein the limit plate thickness in each process is gradually reduced to the forming limit plate thickness as the process progresses. 5. The metal according to claim 4, wherein the forming limit plate thickness is a point at which the plate thickness starts to decrease rapidly from the relationship between the plate thickness obtained by numerical simulation of the tensile test of the metal plate and the true strain. Automatic die size search system for plate.   6. The automatic die size search system for a metal plate according to claim 1, wherein the aperture height is an objective function. A multi-stage cylindrical deep drawing that is composed of a metal plate and two or more molds facing the metal plate, and plastically deforms the metal plate through a plurality of processes using the relative movement of the mold and the metal plate. In the processing system, analysis means for analyzing the thickness and shape of the metal plate body during or after forming, means for repeatedly executing the analysis by changing design variables that determine the shape of the mold, and Means for adjusting the shape of the metal mold used for the analysis according to the thickness and shape of the metal plate body during or after forming determined by the analyzing means, and a multi-step cylinder satisfying the constraints from the results of the analysis Means for finding the number of steps of deep drawing and the die size in each step, the number of steps satisfying the constraint conditions, the number of steps to maximize the objective function from a plurality of combinations of the die size in each step, and in each step Means for finding mold dimensions Mold dimensions automatic search system of the metal plate body characterized by having a. The metal plate automatic die size search system according to claim 7, wherein the coefficient of friction between the metal plate and the die is applied to the multi-step cylindrical deep drawing simulation result by applying an analysis of variance of the experimental design method. An automatic die size search system for a metal plate comprising a means for obtaining and adopting a friction coefficient obtained from the means as one of design variables .   9. The metal plate size automatic search system according to claim 7 or 8, wherein a limit plate thickness in each step is set as the constraint condition.   10. The automatic metal mold size search system for a metal plate according to claim 7, wherein the limit plate thickness in each process is gradually reduced to the forming limit plate thickness as the process progresses. 11. The metal according to claim 10, wherein the forming limit plate thickness is a point at which the plate thickness starts to decrease rapidly from a relationship between a plate thickness obtained by a numerical simulation of a tensile test of a metal plate and a true strain. Automatic die size search system for plate.   12. The automatic die size search system for a metal plate according to claim 7, wherein the aperture height is an objective function.   The die size automatic search system for a metal plate according to any one of claims 7 to 12, wherein the die diameter is determined so that a product of the drawing height and the die diameter is constant.   A program executed by a computer to implement the mold size automatic search system according to any one of claims 1 to 13. The recording medium which recorded the program of Claim 14 so that reading by a computer was possible.