Ear shape prediction method, apparatus, and program

Abstract

The present invention provides an ear shape prediction method, an ear shape prediction device, and an ear shape prediction program that can predict ear shape more accurately. [Solution] An ear shape prediction method according to one aspect of the present invention is a method for predicting the ear shape that occurs in cylindrical drawing of an aluminum plate or aluminum alloy plate, wherein the ear shape is predicted by determining the shape of each of the multiple regions obtained by dividing the aluminum plate or aluminum alloy plate in the circumferential direction in the cylindrical drawing, based on the Rankford value of the aluminum plate or aluminum alloy plate in that region, the work hardening index, and the coefficient of friction between the aluminum plate or aluminum alloy plate and the die used in the cylindrical drawing, after the cylindrical drawing.

Description

[Technical Field]

[0001] The present invention relates to a method, apparatus, and program for predicting the shape of the edges that occur during cylindrical drawing of aluminum sheets or aluminum alloy sheets. [Background technology]

[0002] It is known that when a metal sheet is formed into a cylindrical shape using the deep drawing process, a wavy, uneven surface in the height direction occurs on the edge of the cylinder in the deep-drawn product. This raised portion (peak portion) is generally called an "ear." This ear is an unnecessary part of the deep-drawn product and is usually removed by trimming. Since this removed material is wasted, it is desirable for the ear to be small. Also, if the ear is large, the recess will also be large, and if the product is processed using trimming with predetermined processing dimensions, the recess may remain, potentially causing processing defects such as wrinkles or cracks in subsequent processing steps (for example, opening drawing or opening widening). For this reason, it is desirable to be able to predict the shape of the ear, as disclosed in Non-Patent Document 1, for example. [Prior art documents] [Non-patent literature]

[0003] [Non-Patent Document 1] Hideaki Fukumasu et al., "Material Modeling and Drawing Formation Simulation of 3000 Series Aluminum Alloy Sheets Using Biaxial Stress Testing," Japan Institute of Light Metals, Proceedings of the 137th Autumn Meeting (2019), pp. 125-126. [Overview of the project] [Problems that the invention aims to solve]

[0004] Incidentally, the ear shape prediction method disclosed in Non-Patent Document 1 is a method for determining ear shape by numerical simulation using the finite element method (FEM) or the like, which takes into account the in-plane anisotropy of the Rankford value (r value). However, the ear shape prediction method disclosed in Non-Patent Document 1 only takes into account the in-plane anisotropy of the Rankford value, and there is room for improvement in order to predict ear shape more accurately.

[0005] This invention was made in view of the above circumstances, and its purpose is to provide an ear shape prediction method, an ear shape prediction device, and an ear shape prediction program that can predict ear shape more accurately. [Means for solving the problem]

[0006] As a result of various studies, the inventors have found that the above objective can be achieved by the present invention as follows. That is, an ear shape prediction method according to one aspect of the present invention is a method for predicting the ear shape that occurs in cylindrical drawing of an aluminum plate or aluminum alloy plate, wherein the ear shape is predicted by determining the shape of each of the multiple regions obtained by dividing the aluminum plate or aluminum alloy plate in the circumferential direction in the cylindrical drawing, based on the Rankford value of the aluminum plate or aluminum alloy plate in that region, the work hardening index, and the coefficient of friction between the aluminum plate or aluminum alloy plate and the die used in the cylindrical drawing.

[0007] This method of predicting ear shape divides the circumference into multiple regions and determines the shape of each region after cylindrical drawing based on the Rankford value (r value), work hardening index (n value), and friction coefficient. Therefore, it can predict the ear shape more accurately than when only the Rankford value is considered.

[0008] In another embodiment, in the ear shape prediction method described above, the Rankford value has in-plane anisotropy, the work hardening index has in-plane anisotropy, and the friction coefficient has in-plane anisotropy.

[0009] This ear shape prediction method can predict ear shape by taking into account the anisotropy of each value.

[0010] In another embodiment, in the ear shape prediction method described above, the ear shape is determined using Goto's fourth-order yield function.

[0011] This method of predicting ear shape can be easily used by employing Goto's fourth-order yield function to determine the ear shape.

[0012] An ear shape prediction device according to another aspect of the present invention is a device for predicting the ear shape generated in cylindrical drawing of an aluminum plate or aluminum alloy plate, comprising: a storage unit that stores, in association with each of a plurality of regions obtained by dividing the aluminum plate or aluminum alloy plate in the circumferential direction in the cylindrical drawing, the Lankford value of the aluminum plate or aluminum alloy plate in that region, the work hardening index, and the coefficient of friction between the aluminum plate or aluminum alloy plate and the die used in the cylindrical drawing, in that region; and a shape prediction processing unit that predicts the ear shape by determining the shape of the region after cylindrical drawing based on the Lankford value of the aluminum plate or aluminum alloy plate in that region, the work hardening index, and the coefficient of friction between the aluminum plate or aluminum alloy plate and the die used in the cylindrical drawing, which are stored in the storage unit in association with that region.

[0013] Another aspect of the present invention is a program that is executed by a computer and predicts the shape of an aluminum plate or aluminum alloy plate that occurs in cylindrical drawing of an aluminum plate or aluminum alloy plate, and predicts the shape of the region after cylindrical drawing based on the Rankford value of the aluminum plate or aluminum alloy plate in each of a plurality of regions divided in the circumferential direction in the cylindrical drawing, and the coefficient of friction between the aluminum plate or aluminum alloy plate and the die used in the cylindrical drawing.

[0014] Such ear shape prediction devices and programs divide the circumference into multiple regions and determine the shape of each region after cylindrical drawing based on the Rankford value, work hardening index, and friction coefficient. This allows for more accurate prediction of the ear shape compared to considering only the Rankford value. [Effects of the Invention]

[0015] The ear shape prediction method, ear shape prediction device, and ear shape prediction program according to the present invention can predict ear shape more accurately. [Brief explanation of the drawing]

[0016] [Figure 1] This is a block diagram showing the configuration of the ear shape prediction device in the embodiment. [Figure 2] This figure shows the data table stored in the ear shape prediction device. [Figure 3] This is a diagram illustrating the cylindrical drawing process. [Figure 4] This is a diagram illustrating the division of regions in an aluminum plate or similar material. [Figure 5] This is a diagram illustrating the balance of forces within a single element. [Figure 6] This is a flowchart showing the operation of the ear shape prediction device. [Figure 7] This graph shows the ear shapes of the examples and comparative examples. [Figure 8] This figure illustrates the tensile tests in the above-mentioned embodiments and comparative examples. [Figure 9] This figure illustrates the testing method for frictional force (coefficient of friction) in the above-mentioned examples and comparative examples. [Modes for carrying out the invention]

[0017] Hereinafter, one or more embodiments of the present invention will be described with reference to the drawings. However, the scope of the invention is not limited to the disclosed embodiments. In each figure, components denoted by the same reference numerals are identified as identical components, and their descriptions will be omitted where appropriate. In this specification, general reference numerals are used without subscripts, while individual components are indicated by subscripts.

[0018] The ear shape prediction device in this embodiment is a device that predicts the ear shape that occurs in cylindrical drawing of an aluminum plate or aluminum alloy plate. This ear shape prediction device comprises a storage unit and a shape prediction processing unit. The storage unit stores, for each of a plurality of regions into which the aluminum plate or aluminum alloy plate is divided in the circumferential direction in the cylindrical drawing, the Lankford value of the aluminum plate or aluminum alloy plate in that region, the work hardening index, and the coefficient of friction between the aluminum plate or aluminum alloy plate and the die used in the cylindrical drawing, in association with that region. The shape prediction processing unit predicts the ear shape by determining the shape of the region after cylindrical drawing, based on the Lankford value of the aluminum plate or aluminum alloy plate in that region, the work hardening index, and the coefficient of friction between the aluminum plate or aluminum alloy plate and the die used in the cylindrical drawing, which are stored in the storage unit in association with that region. The following describes in more detail such an ear shape prediction device, as well as the ear shape prediction method and ear shape prediction program implemented therein.

[0019] Figure 1 is a block diagram showing the configuration of the ear shape prediction device in an embodiment. Figure 2 is a diagram showing the data table stored in the ear shape prediction device. Figure 3 is a diagram illustrating cylindrical drawing. Figure 3A shows the initial state (before cylindrical drawing), and Figure 3B shows the state during cylindrical drawing. Figure 4 is a diagram illustrating region division in an aluminum plate, etc. Figure 4A is a diagram illustrating each region in an aluminum plate, etc., and Figure 4B is a diagram illustrating a reference line that defines the angle in the circumferential direction. Figure 5 is a diagram illustrating the balance of forces in a single element.

[0020] The ear shape prediction device 1000 in this embodiment is a device that predicts the ear shape that occurs in cylindrical drawing of an aluminum plate or aluminum alloy plate, and comprises, for example, a control processing unit 1, an input unit 2, an output unit 3, an interface unit (IF unit) 4, and a storage unit 5, as shown in Figure 1. The aluminum plate or aluminum alloy plate that is the target of cylindrical drawing (blank; i.e., the prediction target) will be appropriately abbreviated as "aluminum plate, etc."

[0021] The input unit 2 is connected to the control processing unit 1 and is a device that inputs various data necessary for operating the ear shape prediction device 1000, such as various commands including a command to instruct the start of prediction, the name of the aluminum plate, and the values ​​of each data. For example, it may be a keyboard, a mouse, or multiple input switches assigned to predetermined functions. The output unit 3 is connected to the control processing unit 1 and is a device that outputs commands, data, and prediction results input from the input unit 2 according to the control of the control processing unit 1. For example, it may be a display device such as a CRT display, LCD (liquid crystal display device), or organic EL display, or a printing device such as a printer.

[0022] The input unit 2 and output unit 3 may be configured as touch panels. In this configuration, the input unit 2 is a position input device that detects and inputs the operating position, such as a resistive or capacitive touch panel, and the output unit 3 is a display device. In this touch panel, a position input device is provided on the display surface of the display device, and one or more candidate input contents that can be input to the display device are displayed. When the user touches the display position that displays the input content they wish to input, the position input device detects that position, and the display content displayed at the detected position is input to the ear shape prediction device 1000 as the user's operation input. With such a touch panel, the user can easily understand the input operation intuitively, thus providing an ear shape prediction device 1000 that is easy for the user to use.

[0023] The IF unit 4 is connected to the control processing unit 1 and is a circuit that inputs and outputs data to and from external devices, for example, according to the control of the control processing unit 1. Examples include an RS-232C serial communication interface circuit, an interface circuit using the Bluetooth® standard, and an interface circuit using the USB standard. Alternatively, the IF unit 4 may be a communication interface circuit that sends and receives communication signals to and from external devices, such as a data communication card or a communication interface circuit conforming to the IEEE 802.11 standard.

[0024] The memory unit 5 is connected to the control processing unit 1 and is a circuit that stores various predetermined programs and various predetermined data in accordance with the control of the control processing unit 1.

[0025] The various predetermined programs mentioned above include, for example, a control processing program, which includes, for example, a control program and a shape prediction processing program. The control program controls each of the parts 2 to 5 of the ear shape prediction device 1000 according to the function of each part. The shape prediction processing program predicts the ear shape by determining the shape of each region after cylindrical drawing, based on the Rankford value of the aluminum plate, the work hardening index, and the coefficient of friction between the aluminum plate and the die used in cylindrical drawing, for each of the multiple regions of the aluminum plate.

[0026] The various predetermined data mentioned above include, for example, the name of an aluminum plate, the Rankford value (r value), the work hardening index (n value), and the coefficient of friction (μ value) in each region, various calculation results during the calculation process, and prediction results, as well as other data necessary for executing each of these programs. Such a storage unit 5 includes, for example, a non-volatile memory element such as ROM (Read Only Memory) or a rewritable non-volatile memory element such as EEPROM (Electrically Erasable Programmable Read Only Memory). The storage unit 5 also includes RAM (Random Access Memory), which serves as the working memory of the control processing unit 1, storing data generated during the execution of the predetermined programs. Furthermore, the storage unit 5 may be configured to include a hard disk drive or solid-state drive (SSD) with a relatively large storage capacity.

[0027] The Rankford value (r value), work hardening index (n value), and friction coefficient (μ value) for each of the aforementioned regions are associated with each region and stored in the storage unit 5, and in this embodiment, they are stored in the storage unit 5 in table format. The data table DT for registering the Rankford value (r value), work hardening index (n value), and friction coefficient (μ value) for each of the aforementioned regions includes, for example, as shown in Figure 2, a region name field 51 for registering the name of the region assigned to the region (region name), a Rankford value field 52 for registering the Rankford value for the region of the region name registered in the region name field 51, a work hardening index field 53 for registering the work hardening index for the region of the region name registered in the region name field 51, and a friction coefficient field 54 for registering the friction coefficient for the region of the region name registered in the region name field 51, and has a record for each region.

[0028] The Rankford value (r-value) is the ratio of the logarithmic width strain to the logarithmic thickness strain when a uniform tensile strain is applied to the parallel section of a tensile test specimen. The work hardening index (n-value) is expressed using Hollomon's equation for the true stress-true strain curve: σ = Kε nThis is the value of n when organized using the metric system, and can also be determined from the slope when the true stress-true strain curve is plotted on a log-log graph. The coefficient of friction (μ value) is the coefficient of friction between the aluminum plate, etc., and the die used in cylindrical drawing. The region name is an identifier (ID) used to identify and distinguish the region, and can be appropriately represented by, for example, a serial number.

[0029] The Lankford value, work hardening index, and friction coefficient for each of these regions are input, for example, from the input unit 2 and stored in the storage unit 5. Alternatively, for example, the Lankford value, work hardening index, and friction coefficient for each of the regions are stored (recorded) on a storage medium such as a USB memory or SD card (registered trademark), or on a recording medium such as a CD-R (Compact Disc Recordable) or DVD-R (Digital Versatile Disc Recordable), input to the ear shape prediction device 1000 via the IF unit 4, and stored in the storage unit 5. Alternatively, for example, the Lankford value, work hardening index, and friction coefficient for each of the regions are downloaded from a management server that manages them, for example, via the IF unit 4 to the ear shape prediction device 1000, and stored in the storage unit 5.

[0030] The control processing unit 1 is a circuit for predicting the shape of the ears (ear shape) produced by cylindrical drawing, by controlling each part 2 to 5 of the ear shape prediction device 1000 according to the function of each part. The control processing unit 1 is configured, for example, with a CPU (Central Processing Unit) and its peripheral circuits. When the control processing program is executed, the control unit 11 and the shape prediction processing unit 12 are functionally configured in the control processing unit 1.

[0031] The control unit 11 controls each of the parts 2 to 5 of the ear shape prediction device 1000 according to the function of each part, and is in charge of the overall control of the ear shape prediction device 1000.

[0032] The shape prediction processing unit 12 predicts the edge shape by determining the shape of each of the multiple regions in the aluminum plate, etc., after cylindrical drawing, based on the Rankford value, work hardening index, and friction coefficient between the aluminum plate, etc., and the die used in cylindrical drawing, which are stored in the storage unit 5 in association with the region. The calculation method for the edge shape will be explained in more detail below.

[0033] Cylindrical drawing (cylindrical deep drawing) is performed using a die consisting of an annular (cylindrical) die DI, an annular (cylindrical) blank holder BH, and a cylindrical punch PN, as shown in Figure 3. The die DI and the blank holder BH each have a cylindrical opening of the same diameter and are concentric, and the punch PN has a diameter (punch diameter) that is slightly smaller than the diameter of the openings (die hole diameter) in the die DI and the blank holder BH. In the example shown in Figure 3, the edges of both the die DI and the punch PN are rounded. An aluminum plate or the like WK is sandwiched between the die DI and the blank holder BH, and the blank holder BH presses against the die DI. In this state (Figure 3A), the punch PN is pressed into the opening of the die DI with a press machine (not shown), causing the aluminum plate or the like WK to be drawn (Figure 3B) and cylindrically formed. In Figure 3, the die DI, blank holder BH, punch PN, and aluminum plate WK are shown in a cross-section that is half the diameter from the center line.

[0034] The aluminum plate WK can be any shape, such as a rectangle, but to reduce losses in cylindrical drawing, a disc shape is usually used, as shown in Figure 4. In cylindrical drawing, the punch PN is pressed concentrically against this disc-shaped aluminum plate WK, so in predicting the edge shape, the remaining annular (ring-shaped) portion of the disc-shaped aluminum plate WK, excluding the punch PN, is the target of the calculation. Since the edge shape produced in cylindrical drawing often appears periodically in the circumferential direction, here it is divided into multiple regions in the circumferential direction in cylindrical drawing, and roughly 1 / 4 of the entire circumference is the target of the calculation. In the case shown in Figure 4A, five first to fifth regions AR1 to AR5, divided into central angles of 22.5 degrees each, are the target of the calculation. The aluminum plate WK is created by cutting a disc shape from a rolled plate, for example, as shown in Figure 4B. In the annular portion of the calculation target, if the line segment along the rolling direction of the rolled plate is taken as the reference line of 0 degrees in the circumferential direction, and the clockwise direction (or counterclockwise direction) is taken as the positive direction (positive direction, + direction), then the first region AR1 is the region from -11.25 degrees from the first center line and the region from +11.25 degrees from the first center line, with the reference line being the center line (first center line). In other words, the first region AR1 is a region with a central angle of 22.5 degrees, symmetrical with respect to the first center line. The second region AR2 is the region from -11.25 degrees from the second center line and the region from +11.25 degrees from the second center line, assuming that the center line (second center line) is a line segment along the radial direction at +22.5 degrees from the reference line. The third region AR3 is the region from -11.25 degrees from the third center line and the region from +11.25 degrees from the third center line, assuming that the center line (third center line) is a line segment along the radial direction at +45 degrees from the reference line. The fourth region AR4 is the region from -11.25 degrees from the fourth center line and the region from +11.25 degrees from the fourth center line, assuming that the center line (fourth center line) is a line segment along the radial direction at +67.5 degrees from the reference line. The fifth region AR5 is defined as the region from -11.25 degrees from the fifth center line and the region from +11.25 degrees from the fifth center line, assuming that the center line (fifth center line) is a line segment along the radial direction at +90 degrees from the reference line.These first to fifth regions AR1 to AR5 are of the same shape and the same size as each other, and when referring to any one of the first to fifth regions AR1 to AR5, it shall be referred to as "region AR".

[0035] In predicting the ear shape in the region AR, the region AR is divided into a plurality of elements PE in the radial direction. m is an identifier for specifying and identifying the element PE, and for m, for example, integers from 0 to (total number of elements - 1) are used. In one example, the radius R b of the aluminum plate or the like WK b is 70 [mm] (R (m) = 70), and it is divided into 22 elements PE (21) at intervals of 1 [mm] in the radial direction, and m = 0, 1, 2, ···, 21. The radius of the element PE s is 49 [mm]. In the aluminum plate or the like WK, the minute element PE1 (= PE (1) ) located at the radius R m shown in FIG. 3A before cylindrical drawing forming moves to the position of the radius a (the start position of the R chamfer of the chamfered die DI, a is the inner radius of the region AR) shown in FIG. 3B by cylindrical drawing forming, and the radial elongation at that time is calculated. Here, before cylindrical drawing forming, the radial length of each element PE (0) is defined as dR (in the above example, dR = 1 [mm]), and its thickness is defined as t0 (= t m ), and after cylindrical drawing forming, the radial length of each element PE R(m) is defined as dR (1 + dε (m) ), and its thickness is defined as t d ). The radius of the R chamfer of the die DI is defined as ρ d , and the outer radius of the cylindrical drawing portion of the aluminum plate or the like WK after cylindrical drawing forming is defined as R d , then a = R d + ρ p . The radius of the R chamfer of the punch PN is defined as ρ

[0036] R0 is the radius of the outermost circumference of the WK when the aluminum plate or the like WK is cylindrical drawing formed, and R f is the radius after the element PE m is radially constricted.

[0037] To predict ear shape, the following equations are prepared:

[0038] First, the element PE during deep drawing. (m) The forces shown in Figure 5 act on it. Here, σ R(m) σ is the radial stress (radial stress), θ(m) σ is the circumferential stress (circumferential stress), μR(m) σ is the radial friction stress (radial friction stress), μθ(m) Fμ is the circumferential friction stress (frictional friction stress), and R(m) F is the radial friction force (radial friction force), μθ(m) is the frictional force in the circumferential direction (circumferential frictional force). The radial strain increment is dε. R(m) And element PE (m) If R and φ are the inner radius and central angle, respectively, then the following equation 1 holds from the equilibrium of forces shown in Figure 5.

[0039]

number

[0040] On the other hand, assuming that the pressing force BHF (symbol: P) via the blank holder BH acts uniformly across the entire area AR on the lower surface, this lower surface pressing force P L The following equation 2-1 is obtained, and assuming that the pressing force BHF via the blank holder BH acts only on the third to fifth regions AR3 to AR5 on the upper surface due to the effect of thickness changes (the fourth and fifth regions AR4 and AR5 are thicker), this upper surface pressing force P U For the first and second regions AR1 and AR2, the equation is given by equation 2-2, and for the third through fifth regions, the equation is given by equation 2-3.

[0041]

number

[0042] Radial friction coefficient μ R(m)Radial friction force F μR(m) In the first and second regions AR1 and AR2, equation 3 is obtained from equations 2-1 and 2-2, and in the third to fifth regions AR3 to AR5, equation 4 is obtained from equations 2-1 and 2-3. Here, p = P((π(R0 2 -a 2 ))

[0043]

number

[0044]

number

[0045] Circumferential friction coefficient μ θ(m) Circumferential frictional force F μθ(m) In the first and second regions AR1 and AR2, equation 5 is obtained from equations 2-1 and 2-2, and in the third to fifth regions AR3 to AR5, equation 6 is obtained from equations 2-1 and 2-3. Here, p = P((π(R0 2 -a 2 )), and sin(φ / 2) ≈ φ / 2.

[0046]

number

[0047]

number

[0048] Based on equations 1, 3, and 5, the equation of equilibrium of radial forces in the first and second regions AR1 and AR2 is given by equation 7-1, and based on equations 1, 4, and 6, the equation of equilibrium of radial forces in the third to fifth regions AR3 to AR5 is given by equation 7-2.

[0049]

number

[0050] On the other hand, radial strain increment dε R(m) , and circumferential strain increment dε θ(m) Using the so-called Goto's fourth-order yield function, which is shown in Equation 9 below, we obtain Equations 8-1 and 8-2 respectively. Here, σ 0.2R(m) σ is the yield stress when uniaxially tensile in the direction of angle α from the rolling direction, 0.2θ(m) σ is the yield stress when uniaxially tensile in the direction of angle α+90 from the rolling direction, b is the yield stress in equibiaxial tension, and r (α) This is the Rankford value obtained when uniaxial tension is applied in the direction of angle α from the rolling direction, and r (α+90) This is the Lankford value obtained when uniaxial tension is applied in the direction of angle α+90 from the rolling direction. Note that when using Goto's fourth-order yield function in this prediction method, the shear stress is assumed to be zero.

[0051]

number

[0052]

number

[0053] Furthermore, the Hollomon formula used to determine the work hardening index is specifically the following equation 10. Here, σ eq(m) This is the equivalent stress in Goto's fourth-order yield function, and K (α) This is the Hollomon equation mentioned above: σ = Kε n K (plasticity coefficient) is the coefficient of plasticity in the given shape, R1 is the radius of element PE before cylindrical drawing, and R2 is the radius of element PE after cylindrical drawing.

[0054]

number

[0055] With these equations prepared, the shape prediction processing unit 12 predicts the ear shape as follows.

[0056] First, in any one of the first to fifth regions AR1 to AR5, the shape prediction processing unit 12 determines the element PE (m) In this case, R=R m ~R 21 Within the range, the circumferential strain ε is given by Equation 10. θ(m) The equivalent stress σ is calculated using equation 10. eq(m) The work hardening index n is calculated (equivalent stress calculation process). (α) and the plasticity coefficient K (α) The initial thickness t0 is given in advance. Here, in the first (1st) equivalent stress calculation process, the initial thickness t0 is used, and in the second equivalent stress calculation process, as described later, the initial thickness t0 is the thickness t obtained in the thickness calculation process described later. m It can be replaced with this.

[0057] Next, the shape prediction processing unit 12 calculates f(α)-σ from equation 9. eq(m) 4 By solving =0, the circumferential stress σ θ(m) This calculates (circumferential stress calculation process). Note that R=R0 is σ R(m) = 0

[0058] Next, the shape prediction processing unit 12 solves equation 7 for force equilibrium using, for example, the fourth-order Runge-Kutta method, thereby determining the radial stress σ R(m) This calculates (radial stress calculation process).

[0059] Next, the shape prediction processing unit 12 uses the yield function as the plastic potential and calculates the radial strain increment dε R(m) We then determine the increment in strain in the thickness direction dε from the constant volume rule before and after cylindrical drawing. t(m) Find the thickness t (m) The thickness is calculated (thickness calculation process).

[0060] Next, the shape prediction processing unit 12 determines that the initial thickness t0 is the thickness t obtained in the thickness calculation process. mReplaced with, the equivalent stress calculation process, the circumferential stress calculation process, the radial stress calculation process and the thickness calculation process are executed sequentially, and the radial strain increment dε R(m) Retrieve (update) (update process).

[0061] The shape prediction processing unit 12 sequentially executes the equivalent stress calculation process, the circumferential stress calculation process, the radial stress calculation process, the thickness calculation process, and the update process for each element PE from m=1 to m=21. (1) ~PE (21) Radial strain dε R(m) We seek.

[0062] Next, the shape prediction processing unit 12 analyzes each of the obtained elements PE (1) ~PE (21) Radial strain dε R(m) The sum of these, and the radial extension △R (α) Find (=(Σdε R(m) )dR), the side wall height H of the cylindrical drawn portion of the aluminum plate, etc. WK after cylindrical drawing. (α) Find (H (α) =(t0+ρ p )+((R b -a)+△R (α) ))

[0063] The shape prediction processing unit 12 performs each of the above processes for each of the first to fifth regions AR1 to AR5, and determines the height H of each side wall in each of the first to fifth regions AR1 to AR5. (α) We seek.

[0064] The control unit 11 processes the ear shape (each side wall height H) predicted by the shape prediction processing unit 12. (α) The output unit 3 outputs the ear shape (each side wall height H) to the output unit 3. (α) ) is output externally.

[0065] The control processing unit 1, input unit 2, output unit 3, IF unit 4, and storage unit 5 in such an ear shape prediction device 1000 can be configured by a computer such as a desktop or notebook computer.

[0066] Next, the operation of this embodiment will be described. Figure 6 is a flowchart showing the operation of the ear shape prediction device.

[0067] When the power is turned on, the ear shape prediction device 1000 with this configuration performs the initialization of each necessary part and starts operating. The control processing unit 1 is functionally configured with a control unit 11 and a shape prediction processing unit 12 through the execution of its control processing program.

[0068] In Figure 6, the user inputs data necessary for predicting the ear shape, such as the Rankford value, work hardening index, and friction coefficient in each region, into the ear shape prediction device 1000, which is stored in the storage unit 5 (S1). When the user is instructed to start the prediction, the ear shape prediction device 1000 uses the shape prediction processing unit 12 of the control processing unit 1 to set m to 1 (m←1) (S2).

[0069] Next, the ear shape prediction device 1000 sequentially executes the equivalent stress calculation process, the circumferential stress calculation process, the radial stress calculation process, and the thickness calculation process using the shape prediction processing unit 12, and calculates the radial strain increment dε R(m) The result is calculated and stored in memory unit 5 (S3).

[0070] Next, the ear shape prediction device 1000 sequentially executes the equivalent stress calculation process, the circumferential stress calculation process, the radial stress calculation process, the thickness calculation process, and the update process using the shape prediction processing unit 12, and the element PE (m) Radial strain increment dε R(m) The result is calculated and stored in memory unit 5 (S4).

[0071] Next, the ear shape prediction device 1000 uses the shape prediction processing unit 12 to determine whether m is (total number of elements - 1) or not (S5). If the result of this determination is that m is not (total number of elements - 1) (No), the ear shape prediction device 1000 uses the shape prediction processing unit 12 to increment m by 1 (m ← m + 1) (S6) and returns to process S3. On the other hand, if the result of the above determination is that m is (total number of elements - 1) (Yes), the ear shape prediction device 1000 then executes process S7.

[0072] In this process S7, the ear shape prediction device 1000 determines the radial elongation ΔR by the shape prediction processing unit 12. (α) Determine the height H of the side wall. (α) The result is calculated and stored in memory unit 5.

[0073] Next, the ear shape prediction device 1000 determines whether the calculation for all regions AR1 to AR5 has been completed by the shape prediction processing unit 12 (S8). If the result of this determination is that the calculation for all regions AR1 to AR5 has not been completed (No), the radial elongation ΔR is calculated for the uncalculated region AR. (α) Determine the height H of the side wall. (α) To determine this, the ear shape prediction device 1000 returns to process S2. On the other hand, if the result of the above determination is that calculations for all regions AR1 to AR5 have been completed (Yes), the ear shape prediction device 1000 then executes process S9.

[0074] In this process S9, the ear shape prediction device 1000 outputs each calculation result to the output unit 3 via the control unit 11 of the control processing unit 1, and the output unit 3 outputs each calculation result to an external device, thereby terminating this process. The control unit 11 may also output each calculation result to an external device via the IF unit 7 if necessary.

[0075] Next, examples and comparative examples will be described. Figure 7 is a graph showing the ear shapes of the examples and comparative examples. Figure 7A shows the case of material A having a first anisotropic coefficient of friction in the circumferential direction, Figure 7B shows the case of material A having a second anisotropic coefficient of friction in the circumferential direction, and Figure 7C shows the case of material B having a third anisotropic coefficient of friction in the circumferential direction. In Figures 7A to 7C, each horizontal axis represents the angle in the circumferential direction, and each vertical axis represents the normalized sidewall height. The value is normalized by dividing it by its circumferential average value, and the normalized value is obtained. Figure 8 is a diagram for explaining the tensile test in the examples and comparative examples. Figure 9 is a diagram for explaining the test method for frictional force (coefficient of friction) in the examples and comparative examples.

[0076] The aluminum plates WK used in the examples and comparative examples were formed from either material A or material B, which have the components shown in Table 1. Material A and material B are alloys mainly composed of aluminum, containing 0.35 [mass%] silicon (Si), 0.43 [mass%] iron (Fe), 0.21 [mass%] copper (Cu), 0.8 [mass%] manganese (Mn), and 1.2 [mass%] magnesium (Mg), and were formed as rolled plates through direct chill casting, homogenization treatment, hot rolling, and cold rolling processes. The thickness of material A was 0.30 [mmt]. Material B was further formed by etching by immersing it in a 10 [%] sodium hydroxide (NaOH) aqueous solution heated to 60 [°C] for 45 [seconds]. The thickness of material B was 0.29 [mmt].

[0077] [Table 1]

[0078] As shown in Figure 8, JIS No. 5 test specimens were prepared from material A at angles of 0°, 22.5°, 45°, 67.5°, and 90°, corresponding to the first to fifth regions AR1 to AR5, respectively. Tensile tests were conducted at a tensile speed of 5 mm / min in accordance with JIS Z 2241 (2011). As mentioned above, the angle reference was a line segment (reference line) along the rolling direction, and the angle was the clockwise angle from this reference line. The Rankford value (r value) was determined for each test specimen in accordance with JIS Z 2254 by graphing the relationship between the true strain in the longitudinal direction and the true strain in the width direction of the specimen, and calculating the slope of the linear regression within the range of nominal strain from 1% to 3%. The work hardening index (n-value) and plasticity coefficient (K-value) were determined for each of the aforementioned test specimens in accordance with the provisions of JIS Z 2253. The relationship between true stress and true strain was graphed, and the slope and intercept (logarithm of the F-value) were obtained from the linear regression within the range of nominal strain from 1% to 3%. The results are shown in Table 2. Note that these r-values, n-values, and K-values ​​were considered identical for both material A and material B, and were measured only for material A.

[0079] [Table 2]

[0080] The r, n, and K values ​​for the specimen at an angle of 0 degrees (first specimen) were 0.50, 0.047, and 363, respectively. The r, n, and K values ​​for the specimen at an angle of 22.5 degrees (second specimen) were 0.51, 0.041, and 356, respectively. The r, n, and K values ​​for the specimen at an angle of 45 degrees (third specimen) were 0.98, 0.051, and 374, respectively. The r, n, and K values ​​for the specimen at an angle of 67.5 degrees (fourth specimen) were 1.02, 0.060, and 392, respectively. The r, n, and F values ​​for the specimen at an angle of 90 degrees (fifth specimen) were 1.20, 0.060, and 394, respectively.

[0081] On the other hand, the in-plane anisotropy of the coefficient of friction was imparted by applying oil between the test piece SP (strip-shaped with a width of 25 [mm] and a length of 200 [mm]) and each of the first and second clamping members PR1 and PR2, which were formed with cemented carbide (aiming for an arithmetic mean roughness of the surface of 0.1 [μm]) at the contact portions, pressing with a pressing force P (contact surface pressure of 1.5 [MPa]), and pulling out at a test speed of 8.3 [mm / s] in the case of a sliding test. The coefficient of friction can be changed by changing the amount of oil applied. An ester-based synthetic oil (kinematic viscosity at room temperature of 182 [mm 2 / s]) was used for the oil. The sliding test was carried out at three levels of the amount of oil applied for each of the A material and the B material, and from the graph of the relationship between the amount of oil applied and the coefficient of friction, the relationship between the amount of oil applied and the coefficient of friction was approximated by a function, and the coefficient of friction at the amount of oil applied in cylindrical drawing was estimated. The results of the amount of oil applied and the coefficient of friction are shown in Table 3.

[0082]

Table 3

[0083] The A material having a first anisotropic coefficient of friction in the circumferential direction had an oil application amount of 400 [mg / m 2 , and the respective coefficients of friction at angles of 0 [degrees], 22.5 [degrees], 45 [degrees], 67.5 [degrees], and 90 [degrees] were 0.23, 0.17, 0.16, 0.14, and 0.14. This A material having a first anisotropic coefficient of friction in the circumferential direction was taken as Example 1. The A material having a second anisotropic coefficient of friction in the circumferential direction had an oil application amount of 2400 [mg / m 2 , and the respective coefficients of friction at angles of 0 [degrees], 22.5 [degrees], 45 [degrees], 67.5 [degrees], and 90 [degrees] were 0.13, 0.10, 0.09, 0.09, and 0.08. This A material having a second anisotropic coefficient of friction in the circumferential direction was taken as Example 2. The B material having a third anisotropic coefficient of friction in the circumferential direction had an oil application amount of 3400 [mg / m 2and the coefficients of friction at angles of 0°, 22.5°, 45°, 67.5° and 90° were 0.08, 0.07, 0.07, 0.06 and 0.07, respectively. Material B having a third anisotropic coefficient of friction in the circumferential direction was used as Example 3.

[0084] On the other hand, in Comparative Example 1, for Material A having a first anisotropic coefficient of friction in the circumferential direction, the coefficient of friction was set to 0 (no friction), and the side wall height H (α) was determined.

[0085] In Comparative Example 2, for Material A having a first anisotropic coefficient of friction in the circumferential direction, the coefficient of friction was made uniform within the plane of the plate (no in-plane anisotropy), and further, assuming that the pressing force BHF through the blank holder BH acts uniformly on the entire area AR on the lower and upper surfaces, the side wall height H (α) was determined.

[0086] In Comparative Example 3, for Material A having a first anisotropic coefficient of friction in the circumferential direction, the coefficient of friction was made uniform within the plane of the plate (no in-plane anisotropy), and further, assuming that the pressing force BHF through the blank holder BH has anisotropy as described above, the side wall height H (α) was determined.

[0087] In Comparative Example 4, for Material A having a first anisotropic coefficient of friction in the circumferential direction, the coefficient of friction was assumed to have in-plane anisotropy, and further, assuming that the pressing force BHF through the blank holder BH acts uniformly on the entire area AR on the lower and upper surfaces, the side wall height H (α) was determined.

[0088] In Comparative Example 5, for Material A having a second anisotropic coefficient of friction in the circumferential direction, the coefficient of friction was set to 0 (no friction), and the side wall height H (α) was determined.

[0089] Comparative Example 6 involves material A having a second anisotropic coefficient of friction in the circumferential direction, but with the coefficient of friction being uniform within the plate surface (no in-plane anisotropy), and furthermore, assuming that the pressing force BHF via the blank holder BH acts uniformly across the entire area AR on the lower and upper surfaces, the side wall height H (α) This is what was sought.

[0090] Comparative Example 7 involves material A having a second anisotropic coefficient of friction in the circumferential direction, but with the coefficient of friction being uniform within the plate surface (no in-plane anisotropy), and furthermore, the side wall height H being assumed to have anisotropy in the same way as described above for material A having a second anisotropic coefficient of friction in the circumferential direction. (α) This is what was sought.

[0091] Comparative Example 8 is a material A having a second anisotropic coefficient of friction in the circumferential direction, but with the coefficient of friction being anisotropic in the plane, and further, the side wall height H is assumed to be uniformly applied across the entire area AR on the lower and upper surfaces, with respect to material A having a second anisotropic coefficient of friction in the circumferential direction. (α) This is what was sought.

[0092] Comparative Example 9 is a comparison of material B, which has a third anisotropic coefficient of friction in the circumferential direction, with the coefficient of friction set to 0 (no friction), and the side wall height H (α) This is what was sought.

[0093] Comparative Example 10 is a material B having a third anisotropic coefficient of friction in the circumferential direction, but with respect to the material B having a uniform coefficient of friction within the plate surface (no in-plane anisotropy), and furthermore, the side wall height H is assumed to be uniform in that the pressing force BHF via the blank holder BH acts uniformly across the entire area AR on the lower and upper surfaces. (α) This is what was sought.

[0094] Comparative Example 11 is a material B with a third anisotropic coefficient of friction in the circumferential direction, but with a uniform coefficient of friction within the plate surface (no in-plane anisotropy), and furthermore, the pressing force BHF via the blank holder BH is anisotropic as described above, and the side wall height H (α) This is what was sought.

[0095] Comparative Example 12 involves material B having a first anisotropic coefficient of friction in the circumferential direction, while the coefficient of friction is anisotropic in the plane, and furthermore, the side wall height H is assumed to be uniformly applied to the entire surface of region AR on the lower and upper surfaces by the pressing force BHF via the blank holder BH. (α) This is what was sought.

[0096] In the cylindrical drawing process, a blank WK with a radius of 70 mm was held between a blank holder BH and a die DI with a chamfer radius of 3.175 mm, and drawn by a punch PN with a radius of 45 mm and a chamfer radius of 3.175 mm. The aforementioned ester-based synthetic oil was used as the lubricant, and the wrinkle-holding force was 13.6 kN (initial surface pressure of 1.5 MPa). The contact portions of each die were formed from cemented carbide (aiming for an arithmetic mean surface roughness of 0.1 μm). The die diameter for material A was 90.770 mm, and the die diameter for material B was 90.740 mm.

[0097] The results of Examples 1 to 3 and Comparative Examples 1 to 12 are shown in Figure 7 and Table 4, respectively.

[0098] [Table 4]

[0099] In Figure 7A, ◇ indicates the calculation result for Example 1, ◆ indicates the measured value for material A having the first anisotropic friction coefficient in the circumferential direction, ○ indicates the calculation result for Comparative Example 1, ● indicates the calculation result for Comparative Example 2, △ indicates the calculation result for Comparative Example 3, and ▲ indicates the calculation result for Comparative Example 4.

[0100] In Figure 7B, ◇ indicates the calculation result for Example 2, ◆ indicates the measured value for material A having a second anisotropic friction coefficient in the circumferential direction, ○ indicates the calculation result for Comparative Example 5, ● indicates the calculation result for Comparative Example 6, △ indicates the calculation result for Comparative Example 7, and ▲ indicates the calculation result for Comparative Example 8.

[0101] In Figure 7C, ◇ indicates the calculation result for Example 3, ◆ indicates the measured value for material B having a third anisotropic friction coefficient in the circumferential direction, ○ indicates the calculation result for Comparative Example 9, ● indicates the calculation result for Comparative Example 10, △ indicates the calculation result for Comparative Example 11, and ▲ indicates the calculation result for Comparative Example 12.

[0102] The RMSE (Root Mean Square Error) in Table 4 is calculated as √((1 / 5) × (((Calculated side wall height at angle 0 degrees) - (Measured side wall height at angle 0 degrees)) 2 +((Calculated side wall height at an angle of 22.5 degrees)-(Measured side wall height at an angle of 22.5 degrees)) 2 +((Calculated side wall height at an angle of 45 degrees)-(Measured side wall height at an angle of 45 degrees)) 2 +((Calculated side wall height at an angle of 67.5 degrees)-(Measured side wall height at an angle of 67.5 degrees)) 2 +((Calculated side wall height at a 90-degree angle)-(Measured side wall height at a 90-degree angle)) 2 This was obtained by ). A smaller RMSE indicates higher accuracy in predicting ear shape.

[0103] As can be seen from Figure 7 and Table 4, Example 1 approximates the measured value better than Comparative Examples 1 to 4, has a smaller RMSE, and is therefore better than Comparative Examples 1 to 4. Example 2 approximates the measured value better than Comparative Examples 5 to 8, has a smaller RMSE, and is therefore better than Comparative Examples 5 to 8. Example 3 approximates the measured value better than Comparative Examples 9 to 12, has a smaller RMSE, and is therefore better than Comparative Examples 9 to 12.

[0104] As described above, the ear shape prediction device 1000 and the ear shape prediction method and ear shape prediction program implemented therein in the embodiment divide the material into multiple regions AR in the circumferential direction and determine the shape of the region after cylindrical drawing based on the Rankford value (r value), work hardening index (n value), and friction coefficient (μ value) for each region AR. Therefore, compared to the case where only the Rankford value is considered, the ear shape can be predicted more accurately.

[0105] The ear shape prediction device 1000, ear shape prediction method, and ear shape prediction program described above can predict ear shape while taking into account the anisotropy of each value.

[0106] The above-described ear shape prediction device 1000, ear shape prediction method, and ear shape prediction program can easily determine the coefficient of friction by using Goto's fourth-order yield function.

[0107] To illustrate the present invention, the embodiments have been adequately and fully described above with reference to the drawings. However, those skilled in the art should recognize that it is easy to modify and / or improve upon the embodiments described above. Therefore, unless such modifications or improvements implemented by those skilled in the art fall outside the scope of the claims, such modifications or improvements shall be considered to be included within the scope of the claims. [Explanation of Symbols]

[0108] 1000 Ear Shape Prediction Device 1 Control Processing Unit 2 Input section 3. Output section 4. Interface section (IF section) 5 Storage section 11 Control Unit 12 Shape prediction processing unit

Claims

1. A method for predicting the shape of the edges that occur in cylindrical drawing of an aluminum plate or an aluminum alloy plate, The shape of the tab is predicted by determining the shape of each of the multiple regions obtained by dividing the aluminum plate or aluminum alloy plate in the circumferential direction during the cylindrical drawing process, based on the Rankford value of the aluminum plate or aluminum alloy plate in that region, the work hardening index, and the coefficient of friction between the aluminum plate or aluminum alloy plate and the die used in the cylindrical drawing process. Method for predicting ear shape.

2. The aforementioned Rankford value has in-plane anisotropy, The work hardening index has in-plane anisotropy, The coefficient of friction has in-plane anisotropy. The method for predicting ear shape according to claim 1.

3. The aforementioned ear shape can be determined using Goto's fourth-order yield function. The method for predicting ear shape according to claim 1 or claim 2.

4. An ear shape prediction device for predicting the ear shape that occurs in cylindrical drawing of an aluminum plate or aluminum alloy plate, A storage unit that stores, for each of the multiple regions obtained by dividing the aluminum plate or aluminum alloy plate circumferentially in the cylindrical drawing process, the Rankford value of the aluminum plate or aluminum alloy plate in that region, the work hardening index, and the coefficient of friction between the aluminum plate or aluminum alloy plate and the die used in the cylindrical drawing process, in association with that region. The system includes a shape prediction processing unit that predicts the edge shape by determining the shape of each of the aforementioned multiple regions after cylindrical drawing, based on the Rankford value of the aluminum plate or aluminum alloy plate in the region, the work hardening index, and the coefficient of friction between the aluminum plate or aluminum alloy plate and the die used in the cylindrical drawing, which are stored in the memory unit in association with the region. Ear shape prediction device.

5. A computer-based ear shape prediction program that predicts the ear shape that occurs in cylindrical drawing of an aluminum sheet or aluminum alloy sheet, The shape of the tab is predicted by determining the shape of each of the multiple regions obtained by dividing the aluminum plate or aluminum alloy plate in the circumferential direction during the cylindrical drawing process, based on the Rankford value of the aluminum plate or aluminum alloy plate in that region, the work hardening index, and the coefficient of friction between the aluminum plate or aluminum alloy plate and the die used in the cylindrical drawing process. Ear shape prediction program.

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