Simulation method and simulation system

Abstract

In simulations of powder compression molding, we aim to achieve high fidelity to real-world phenomena while simultaneously reducing calculation time and improving calculation accuracy. [Solution] The simulation method for the compression molding process of powder or granules includes a simulation step in which the powder or granules are arranged in a predetermined analytical space as multiple particles in a discrete element method (DEM) model that uses a spring to represent the repulsive and attractive forces acting as interactions between two particles when they come into contact, a dashpot to represent energy dissipation, and a slider to represent slip, and the multiple particles are compressed. In the simulation step, the spring constant of the spring, the damping coefficient of the dashpot, and the friction coefficient of the slider are changed according to the displacement of the particles due to compression, the stress the particles experience due to compression, or the energy state of the particles.

Description

Technical Field

[0001] The present invention relates to a simulation method for a compression molding process of forming a ceramic compact and a simulation system.

Background Art

[0002] When simulating powder compression molding by computer, generally, the finite element method (FEM: Finite Element Method) that can understand the deformation behavior in detail is used. However, since FEM treats an object as a continuum, it cannot capture the movement of each individual particle.

[0003] On the other hand, there is the discrete element method (DEM: Discrete Element Method), which is a type of particle method. DEM treats each individual particle of the powder as a calculation target and represents the interaction between particles by a spring model, a dashpot model, etc., so it can capture the movement of each individual particle of the powder. A non-patent document 1 discloses such a DEM method.

Prior Art Documents

Non-Patent Documents

[0004]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] Here, in the simulation of powder compression molding, although DEM has high reproducibility of actual phenomena, there are problems of calculation accuracy such as long calculation time and different simulation results depending on the interaction model.

[0006] This invention was made in consideration of the above-mentioned problems, and aims to improve calculation accuracy while shortening calculation time, while achieving high reproducibility of actual phenomena in simulations of powder compression molding. [Means for solving the problem]

[0007] To solve the above-mentioned problems, one aspect of the present invention provides a simulation method for a compression molding process of powder or granules, comprising: arranging the powder or granules as a plurality of particles in a predetermined analysis space using the Discrete Element Method (DEM), which employs a model in which repulsive and attractive forces acting as interactions between particles when two particles come into contact are represented by springs, energy dissipation is represented by dashpots, and slip is represented by sliders; and performing a simulation step of compressing the plurality of particles, characterized in that the spring constant of the spring, the damping coefficient of the dashpot, and the friction coefficient of the slider are changed according to the displacement of the particles due to the compression, the stress the particles experience due to the compression, or the energy state of the particles. [Effects of the Invention]

[0008] According to the present invention, for example, in the simulation of powder compression molding, it is possible to improve calculation accuracy while shortening the calculation time, while achieving a high degree of reproducibility of the actual phenomenon. [Brief explanation of the drawing]

[0009] [Figure 1] A diagram showing the configuration of the simulation system according to the embodiment. [Figure 2] A schematic diagram showing the compression molding process for forming a ceramic molded body, which is simulated in the embodiment of this diagram. [Figure 3] A diagram showing an interparticle model according to an embodiment. [Figure 4] A schematic diagram illustrating a uniaxial compression test. [Figure 5]A diagram showing load-displacement data related to the disintegration behavior of particles obtained in a uniaxial compression test. [Figure 6] A diagram showing the execution conditions of the simulation according to the embodiment. [Figure 7] A flowchart showing the simulation execution process according to the embodiment. [Figure 8] A diagram showing the execution result (load-displacement data) of the simulation according to the embodiment. [Figure 9A] A diagram showing load-displacement data for each particle size obtained in a uniaxial compression test. [Figure 9B] A diagram showing fracture strength-strain data for each particle size obtained in a uniaxial compression test. [Figure 10] A diagram showing longitudinal strain and lateral strain in a granular assembly. [Figure 11] A diagram showing a cubic cell of a particle. [Figure 12] A diagram showing an overview of the initial arrangement, rearrangement process, and consolidation process included in the compression molding process targeted by the simulation according to the embodiment. [Figure 13] A diagram schematically showing an adhesion model.

Mode for Carrying Out the Invention

[0010] Hereinafter, an embodiment of the present invention will be described with reference to the drawings.

[0011] In the following description, when describing without distinguishing between elements of the same kind, common reference numerals among the reference numerals are used, and when distinguishing between elements of the same kind, reference numerals may be used.

[0012] (Configuration of the Simulation System 1 According to the Embodiment) FIG. 1 is a diagram showing the configuration of a simulation system 1 according to an embodiment. The simulation system 1 is configured using a computer and includes a processor 11, a memory 12, a storage 13, and an input / output unit 14.

[0013] Processor 11 reads various programs and various data including the simulation program according to the embodiment from storage 13 and loads them into memory 12. Then, processor 11 executes the various programs loaded in memory 12.

[0014] Processor 11 is a CPU (Central Processing Unit), ASIC (Application Specific Integrated Circuit), FPGA (Field Programmable Gate Array), GPU (Graphics Processing Unit), etc.

[0015] Memory 12 is a semiconductor storage device or the like that provides a temporary working area for the execution of programs for processor 11. Storage 13 is a semiconductor storage device or the like that permanently stores various programs and various data including the simulation program according to the embodiment. Input / output unit 14 receives the operations and information input by the user to simulation system 1, or outputs the information provided by simulation system 1 to the user.

[0016] (Compression molding process simulated in the simulation according to the embodiment) FIG. 2 is a diagram schematically showing the compression molding process for forming a ceramic molded body simulated in the simulation according to the embodiment. The compression molding process simulated by the simulation according to the embodiment fills the granules 42, which are the raw material of the ceramics, into the analysis space 100sp inside the cylinder 100 with a diameter of Φ to a height H to form a granule group 100a. Then, a load F1 is applied in the direction of height H from the upper punch 100b of the granule group 100a to compress and form a molded body. In this embodiment, the raw material of the ceramics is granules, but it may also be powder.

[0017] Here, "ceramics" refers to a general term for inorganic materials composed of polycrystalline materials, but may also include metals and organic compounds. "Ceramics" may be composed of single crystals or amorphous materials such as glass. In this embodiment, "ceramics" may be polycrystalline, single crystal, amorphous, or a mixture thereof.

[0018] (Interparticle model M1 according to the embodiment) Figure 3 shows the interparticle model M1 according to this embodiment.

[0019] In this embodiment, the simulation of the compression molding process for forming a ceramic molded body is performed using the discrete element method (DEM), which is a type of particle method.

[0020] DEM uses an interparticle model. In the interparticle model, instead of ignoring particle deformation, it calculates a repulsive force proportional to the overlapping distance of particles.

[0021] In the interparticle model M1 according to this embodiment, the granules 42 that serve as the raw material for ceramics are represented by spherical DEM particles 31. The repulsive and attractive forces acting as interactions between two DEM particles 31a and 31b when they come into contact are represented by a spring 32, energy dissipation is represented by a dashpot 33, and sliding is represented by a slider 34.

[0022] In Figure 3, the normal direction of DEM particle 31a is defined as the X-axis, and the tangential direction of DEM particle 31a is defined as the Y-axis. In Figure 3, the repulsive and attractive forces in the X-axis direction acting as an interaction between two DEM particles 31a and 31b when they come into contact are represented by spring 32a, and the repulsive and attractive forces in the Y-axis direction are represented by 32b. Furthermore, the energy dissipation in the X-axis direction acting as an interaction between two DEM particles 31a and 31b when they come into contact is represented by dashpot 33a, and the energy dissipation in the Y-axis direction is represented by dashpot 33b. Additionally, the slip in the Y-axis direction acting as an interaction between two DEM particles 31a and 31b when they come into contact is represented by slider 34b.

[0023] Then, if we denote the displacement of the particle as u, the spring constants of springs 32a and 32b as k, the damping coefficients of dashpots 33a and 33b as η, and the friction coefficient of slider 34b as μ, then the equations of motion shown in equations (1-1) and (1-2) hold for the X-axis and Y-axis directions, respectively.

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[0024] The simulation of the compression molding process for forming the ceramic molded body according to this embodiment is performed based on the equations of motion, equations (1-1) and (1-2).

[0025] The model shown in Figure 3 is as described in the well-known reference 1 below. Publicly known reference 1: Mikio Yamai, Yoichi Nakata, Fundamentals and application examples of the Discrete Element Method, Journal of the Japan Society for Precision Engineering, 2018, Vol. 84, No. 7, pp. 615-619.

[0026] (Uniaxial compression test) Figure 4 is a schematic diagram illustrating a uniaxial compression test.

[0027] In order to perform a simulation of the compression molding process for forming the ceramic molded body according to this embodiment, it is necessary to understand the characteristics of each individual granule 42 that serve as the raw material for the ceramics (hereinafter referred to as "granule characteristics"). In this embodiment, the spring constants k of springs 32a and 32b are estimated based on load-displacement data obtained from the collapse behavior of granules 42 by a uniaxial compression test. The damping coefficients η of dashpots 33a and 33b, and the friction coefficient μ of slider 34b are also estimated in the same way as the spring constants k.

[0028] As shown in Figure 4, in the uniaxial compression test, a load F0 is applied to granules 42 placed on a flat plate 41 via a pressure plate 43 to compress them and cause the granules 42 to collapse. In the uniaxial compression test, as a measurement result during the collapse process of the granules 42, load-displacement data showing the relationship between the load used to compress the granules 42 and the displacement of the granules 42 was obtained, as shown in Figure 5. The uniaxial compression test is also called a single-particle compression test because it compresses one granule 42 at a time.

[0029] (Load-displacement data related to the collapse behavior of granules 42 obtained in a uniaxial compression test) Figure 5 shows the load-displacement data related to the collapse behavior of granules 42 obtained in a uniaxial compression test. Note that Figure 5 shows a schematic representation of the load-displacement data obtained in the uniaxial compression test.

[0030] In Figure 5, line 50 shows a comparative example of the load-displacement relationship estimated by a conventional DEM in a uniaxial compression test. The load-displacement data obtained in the uniaxial compression test includes three linear sections: line 51, line 52, and line 53.

[0031] In this embodiment, the collapse behavior of the granules 42 is divided into three modes: (1) granular state, (2) during collapse, and (3) primary particle state. (1) Granular state is a mode in which the load-displacement relationship represented by the straight line 51 holds true. (2) During collapse is a mode in which the load-displacement relationship represented by the straight line 52 holds true. (3) Primary particle state is a mode in which the load-displacement relationship represented by the straight line 53 holds true.

[0032] "(1) Granular state" refers to the initial stage in the uniaxial compression test when a load is applied to the granules 42, in which the granules 42 are elastically deformed. "(2) Collapse" refers to the state in the uniaxial compression test when the granules 42 are plastically deformed, and it represents the intermediate state of collapse from "(1) Granular state" to primary particles. "(3) Primary particle state" refers to the state in the uniaxial compression test when the granules 42 have completed collapse after "(2) Collapse" and have become primary particles. However, "(3) Primary particle state" also includes a state in which primary particles and secondary particles with remaining aggregates are mixed. In this case, the load-displacement data obtained in the uniaxial compression test will be nonlinear in the straight line 53 in Figure 5.

[0033] Note that line 54 is the "(4) Collapse (Return)" mode, which is set so that the solution does not oscillate during unloading in "(2) Collapse".

[0034] In this embodiment, the spring constants k of springs 32a and 32b, which differ for each mode, "(1) granular state", "(2) during collapse", and "(3) primary particle state", are determined based on load-displacement data related to the collapse behavior of granules 42 obtained from a uniaxial compression test. For example, the spring constant k is estimated by the load / displacement. By determining the spring constant k based on the load-displacement data obtained from the uniaxial compression test, the actual behavior of the granules 42 can be incorporated into the interparticle model M1. Similarly, by determining the damping coefficient η for each mode based on a fall experiment or ultrasonic attenuation rate measurement, and determining the friction coefficient μ based on a shear test or angle of repose measurement, the actual behavior of the granules 42 can be incorporated into the interparticle model M1.

[0035] In this embodiment, the spring constant k of springs 32a and 32b is set to a different constant for each mode: (1) granular state, (2) during collapse, and (3) primary particle state, depending on the displacement of the granules 42, the stress on the granules 42 due to compression, or the temperature and energy state of the granules 42. The displacement of the granules 42 includes the distance between the granules 42, the distance between the granules 42 and the inner wall of the analytical space 100sp, the amount of overlap between two granules 42, etc.

[0036] However, the spring constant k is not limited to this, and may also be given as a function of each mode, with variables such as the displacement of the granules 42, the stress on the granules 42 due to compression, and the temperature and energy state of the granules 42, based on the collapse behavior of the granules 42 in a uniaxial compression test.

[0037] (Execution conditions for the simulation according to the embodiment) Figure 6 shows the execution conditions for the simulation according to the embodiment. The execution conditions for the simulation according to the embodiment, including the spring constant k determined as described above, are as shown in Figure 6.

[0038] "Granule size" is the diameter of the granules 42 used in the simulation, and is "c1" [μm]. "Number of granules" is the number of granules 42 used in the simulation, and is "c2" [pieces]. "Coarse-graining ratio" is the coarse-graining ratio of the granules 42 used in the simulation, and is "c3" [times]. "Simulation time" is the execution time of the simulation, and is "c4" [h]. "Density" is the density of the granules 42 used in the simulation, and is "c5" [kg / m3]. "Young's modulus" is the Young's modulus of the granules 42 used in the simulation, and is "c6" [N / m2].

[0039] The “(1)-(2) overlap amount” is the ratio of the length of the overlapping portion of each granule 42 to the particle size of each granule 42 when the mode switches from “(1) granular state” to “(2) decaying” for the two granules 42 used in the simulation, and is expressed as “c7” [%]. In other words, the ratio of the overlapping portion lengths of the two granules 42, “c7” [μm], is used as a threshold. When it is less than “c7” [μm], it is in the “(1) granular state,” and when it is less than or equal to “c7” [μm], the mode switches to “(2) decaying.”

[0040] The “(2)-(3) overlap amount” is the ratio of the length of the overlapping portion to the particle size of each granule 42 when the mode switches from “(2) decaying” to “(3) primary particle state” for the two granules 42 used in the simulation, and is “c8” [μm]. In other words, the ratio of the length of the overlapping portion of the two granules 42, “c8” [μm], is used as a threshold. When it is less than “c8” [μm], it is in the “(2) decaying” state, and when it is less than or equal to “c8” [μm], the mode switches to “(3) primary particle state”.

[0041] "(1) Granule spring constant" is the spring constant k = "c9" [N / m] of springs 32a and 32b when the mode is "(1) granule state". "(2) Collapse spring constant" is the spring constant k = "c10" [N / m] of springs 32a and 32b when the mode is "(2) collapse state". "(3) Primary particle spring constant" is the spring constant k = "c11" [N / m] of springs 32a and 32b when the mode is "(3) primary particle state". "(4) Collapse spring constant (return)" is the spring constant k = "c12" [N / m] of springs 32a and 32b when the mode is "(4) collapsing (return)". The value of the spring constant k depends on the material of the particles, but as an example, c10 is about 1 / 10 of c9, and c11 and c12 are about 1.8 to 2 times c9.

[0042] The "coefficient of friction (particle-particle)" is the coefficient of friction between the granules 42 used in the simulation, and is "c13". The "coefficient of friction (particle-wall)" is the coefficient of friction between the granules 42 used in the simulation and the inner wall of the cylinder 100 that forms the analysis space, and is "c14". The "coefficient of restitution" is the coefficient of restitution of the granules 42 used in the simulation, and is "c15". The "coefficient of rotational resistance" is the coefficient of rotational resistance of the granules 42 used in the simulation, and is "c16".

[0043] The thresholds for switching between the modes "(1) granular state," "(2) decaying," and "(3) primary particle state," namely "(1)-(2) overlap amount" and "(2)-(3) overlap amount," are the overlap amount of the granules 42 (maximum value, total amount, etc.). Furthermore, the thresholds for switching between each mode are not limited to the aforementioned "(1)-(2) overlap amount" and "(2)-(3) overlap amount," but may also be the stress (maximum value, total amount, etc.) experienced by the granules 42.

[0044] (Simulation execution process according to the embodiment) Figure 7 is a flowchart showing the simulation execution process according to the embodiment.

[0045] First, in step S11, the processor 11 (Figure 1) reads and sets the simulation execution conditions (Figure 6). The simulation execution conditions include the initial values ​​of the granule displacements.

[0046] Next, in step S12, the processor 11 places the granules 42 into the analysis space 100sp. Next, in step S13, the processor 11 sets a spring constant k corresponding to the current displacement of the granules 42. In step S13, the processor 11 calculates the ratio R of the displacement of the upper punch 100b in the height H direction to the height H in the analysis space 100sp as the current displacement of the granules.

[0047] The processor 11 sets the "(1) granule spring constant" "c9" to the spring constant k of springs 32a and 32b if the ratio R is less than "c7" of "(1)-(2) overlap amount". The processor 11 also sets the "(2) collapse spring constant" "c10" to the spring constant k of springs 32a and 32b if the ratio R is greater than or equal to "c7" of "(1)-(2) overlap amount" and less than "c8" of "(2)-(3) overlap amount". The processor 11 also sets the "(3) primary particle spring constant" "c11" to the spring constant k of springs 32a and 32b if the ratio R is greater than or equal to "c8" of "(2)-(3) overlap amount".

[0048] Next, in step S14, the processor 11 calculates all the forces acting on the granules 42 placed in the analysis space 100sp, including the repulsive and attractive forces between the DEM particles 31a and 31b, which are represented by springs 32a and 32b based on the spring constant k set in step S13.

[0049] Next, in step S15, the processor 11 determines whether it has calculated all the forces acting on all the granules 42 placed in the analysis space 100sp. If the processor 11 has calculated all the forces acting on all the granules 42 (step S15 YES), it proceeds to step S16. On the other hand, if the processor 11 has not calculated all the forces acting on all the granules 42 (step S15 NO), it returns to step S14.

[0050] In step S16, the processor 11 solves the equations of motion in equations (1-1) and (1-2) to perform the simulation and calculates the displacement (position) of the granules after one step of the simulation. Next, in step S17, the processor 11 determines whether the simulation termination conditions (execution time, number of executions, etc.) have been met. If the termination conditions are met (step S17 YES), the processor 11 moves to step S18; otherwise, it returns to step S13.

[0051] In step S18, the processor 11 outputs the results of the simulation.

[0052] (Simulation results according to the embodiment (load-displacement data)) Figure 8 shows the results of a simulation according to the embodiment (load-displacement data). As shown in Figure 8, in the conventional DEM method, the spring constants k of springs 32a and 32b were always kept constant, so the load-displacement data obtained from the simulation is a linear function, as shown by the straight line 80. The straight line 80 deviates significantly from the curve 83, which shows the measured values ​​of the upper punch 100b, and the curve 84, which shows the measured values ​​of the bottom surface 100c, as shown in Figure 8.

[0053] On the other hand, in the simulation results using the DEM method of this embodiment, the spring constant k of springs 32a and 32b was made different during each of the three modes: (1) granular state, (2) decay, and (3) primary particle state. Therefore, the curve 81 showing the simulated value of the upper punch 100b in Figure 8 is a curve that approximates the measured value of the upper punch 100b by the curve 83, which shows the actual value of the upper punch 100b, compared with the straight line 80. Similarly, the curve 82 showing the simulated value of the bottom surface 100c in Figure 8 is a curve that approximates the measured value of the bottom surface 100c by the curve 84, which shows the actual value of the bottom surface 100c, compared with the straight line 80.

[0054] (Effects of the embodiment) In the above-described embodiment, a DEM model is used in the simulation method for the compression molding process of powder or granules, in which the repulsive and attractive forces acting as interactions between two particles when they come into contact are represented by springs, energy dissipation by dashpots, and slip by sliders. The simulation process involves arranging the powder or granules as multiple particles in a predetermined analysis space in the DEM model and compressing the multiple particles. The spring constant of the spring, the damping coefficient of the dashpot, and the friction coefficient of the slider are changed according to the displacement of the particles due to compression, the stress the particles experience due to compression, or the energy state of the particles.

[0055] Therefore, according to the embodiment, based on the characteristic test of the raw material particles, the overall behavior (deformation, internal stress state, density distribution, etc.) during powder compression can be evaluated with high precision. In addition, the local state of each particle (degree of disintegration, force and energy received during compression) can also be evaluated simultaneously, and the high precision and productivity improvement of the compression molding process can be achieved.

[0056] (Modified Example of Embodiment) (Modified Example 1: Correction of Load-Displacement Data According to Granule Size) FIG. 9A is a diagram showing load-displacement data for each granule size obtained in a uniaxial compression test. FIG. 9B is a diagram showing fracture strength-strain data for each granule size obtained in a uniaxial compression test. FIG. 9B shows data with the influence of the granule size excluded by converting the load of the load-displacement data for each granule size of granule 42 in FIG. 9A to the fracture strength and the displacement to the strain, respectively.

[0057] The granule sizes corresponding to the curves 91a, 91b in FIGS. 9A and 9B are r1, the granule sizes corresponding to the curves 92a, 92b are r2, the granule sizes corresponding to the curves 93a, 93b are r3, and the granule sizes corresponding to the curves 94a, 94b are r4. The magnitude relationship of r1 < r2 < r3 < r4 holds.

[0058] From FIG. 9B, the fracture strength-strain data obtained in the uniaxial compression test has substantially the same curve shape regardless of the granule size. Therefore, the load-displacement data for calculating the spring constant k is corrected so that the spring constant increases as the granule size increases, and the spring constant k is given based on the corrected load-displacement data.

[0059] By this correction according to the granule size, the influence of the granule size of granule 42 in the uniaxial compression test on the spring constant k can be excluded.

[0060] (Modified Example 2: Correction of Load-Displacement Data Considering Poisson's Effect) In conventional DEM methods, longitudinal strain is considered in granular aggregates, but transverse strain is not. In contrast, in this embodiment, the accuracy of the interparticle model is improved by considering the transverse strain (Poisson effect) that occurs in granular aggregates.

[0061] (Longitudinal and transverse strains in granular aggregates) Figure 10 shows the longitudinal and transverse strains in a granular aggregate. Consider the case where a load F1 is applied to two granules 42a and 42b contained in a granular aggregate filled in an analysis space 100sp, via an upper punch 100b.

[0062] As a result, longitudinal strains ε1 and ε2 are generated in granules 42a and 42b in the positive and negative directions of the Y-axis, respectively. Additionally, transverse strains ε1' and ε2' are generated between granules 42a and 42b in the X-axis direction. These transverse strains are taken into account by multiplying the spring constant k by a correction coefficient α. The method for calculating the correction coefficient is explained below.

[0063] First, load-displacement data (σ-u curve) is created as a result of the uniaxial compression test. Next, the created σ-u curve is converted into a consolidation curve (σ-ρ curve). ρ is the relative density of granules 42a and 42b. A semi-logarithmic graph of this σ-ρ curve is created. From the semi-logarithmic graph of the σ-ρ curve, the relative density ρ at the start of the consolidation process is obtained. min and load σ(ρ min ), relative density ρ at the end max and load σ(ρ max ) obtain.

[0064] Using these results, we can obtain the load normalization curve ({σ(ρ)-σ(ρ)}, which is the normalized curve of the σ-ρ curve of the uniaxial compression test results. min )} / {σ(ρ max )-σ(ρ min We obtain the )}-ρ curve.

[0065] From the load normalization curve described above, the parameters (n, a, m) of the yield condition equation for the island-to-large roof, represented by equation (2), are determined.

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[0066] (Regarding the method for calculating relative density ρ) Here, the calculation of the relative density ρ in equation (2-3) requires the volumetric strain of the granules. However, unlike FEM, which has volumetric strain information, DEM is used in this embodiment and does not have volumetric strain information, so it is necessary to calculate the volumetric strain separately. Therefore, in this embodiment, the volumetric strain is calculated for each granule from the amount of overlap between adjacent granules. The calculation of volumetric strain and relative density ρ in this embodiment will be explained below.

[0067] Before explaining the calculation of volumetric strain and relative density ρ, we define the cubic cell di of granule pi. Figure 11 shows the cubic cell di of granule pi. The granule pi is a cube that circumscribes each granule pi (i=1~N (N is a predetermined natural number)) that is packed in the analysis space sp. In this embodiment, volumetric strain and relative density ρ are calculated for each cubic cell di.

[0068] Figure 12 is a diagram showing an overview of the initial placement, rearrangement, and consolidation processes included in the compression molding process covered by the simulation according to the embodiment. As shown in Figure 12, the compression molding process covered by the simulation according to the embodiment includes (a) the initial placement stage, in which each granule pi is compressed in the direction of the arrow in the figure, and (b) the rearrangement process and (c) the consolidation process, starting from when the container d (analysis space sp) is filled with granules pi.

[0069] (b) During the rearrangement process, each granule pi is compressed in the direction of the arrow, but because there are gaps between the granules pi, the rearrangement only changes the position of each granule pi within the container d. (b) After the rearrangement process is complete, (c) during the consolidation process, each granule pi packed in the container d is compressed into close contact with each other. (c) After the consolidation process is complete, the collapse behavior of the granules pi in the uniaxial compression test shown in Figure 5 is observed.

[0070] (b) In the rearrangement process, only the granules pi are rearranged, so there is no need to consider the Poisson effect. On the other hand, (c) in the consolidation process, the granules pi overlap each other, so it is necessary to consider the Poisson effect. The method for calculating the relative density ρ1i of the cubic cell di in the (c) consolidation process is described below.

[0071] The relative density ρ0i of cubic cells di during (a) initial arrangement and (b) rearrangement is calculated using equation (3), where V0p is the total volume of granules inside container d and V0d is the initial volume of container d. In equation (3), ρp is the relative density of granules pi.

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[0072] On the other hand, (c) the volume strain ε1p,i of each cubic cell di during the consolidation process is determined based on equation (4). In equation (4), Di is the particle size of the granule pi, Si is the sum of the volume overlap sni,j between the granule pi and the surrounding granules pj based on equation (4-2) over all granules pj, and β is a correction coefficient. Here, when calculating Si based on equation (4-2), the granules overlap in a complex manner, so not all overlap amounts sni,j can be considered. β is a positive correction coefficient that guarantees consistency between the overlap amounts sni,j that cannot be fully considered in the calculation of Si based on equation (4-2) and the volume of the granule aggregate consisting of granules pi filled in container d. Also, β is an adjustment parameter in the simulation of powder compression molding according to the embodiment. Note that the right-hand side of equation (4) is the natural logarithm.

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[0073] Therefore, (c) the relative density ρ1i of the cubic cell di during the consolidation process is calculated based on equation (5).

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[0074] In the yield condition equation for the island-to-large roof structure, for example, we determine the parameters (n, a, m) that minimize the error evaluation formula err in equation (6). n is the number of samples of the measured data.

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[0075] Equation (7) is calculated based on the parameters (n, a, m) determined according to equation (6).

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[0076] After calculating σ￣ based on equation (7), the σ-ρ curve is recreated to confirm the reproducibility of the uniaxial compression test results. The validity of the parameters (n, a, m) is also confirmed by the yield phase or the f-value in equation (2-2) above.

[0077] From the plasticity parameters (a,m) in the yield condition equations for the island-to-large roof, equations (2-2), (2-3), and (7), the correction coefficient α is calculated as shown in equation (8).

[0078] Furthermore, the damping coefficient η of the dashpots 33a and 33b, and the friction coefficient μ of the slider 34b can also be corrected in the same way as the spring constant k of the springs 32a and 32b.

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[0079] The spring constant k' = αk, obtained by multiplying the estimated spring constant k of springs 32a and 32b by α calculated in equation (8), is the spring constant that takes lateral strain (Poisson effect) into consideration.

[0080] By doing as described above, the Poisson effect can be incorporated into the interparticle model M1, allowing us to consider the difference in behavior between a single granule 42 and a group of granules (single granule: compression in only one axis direction; group: compression from all directions of surrounding particles).

[0081] (Variation 3: Adhesion Model) In the above embodiment, the spring constant k was calculated using the interparticle model M1, but the spring constant k can also be calculated using the adhesion model M2 instead of the interparticle model.

[0082] Figure 13 is a schematic diagram of the adhesion model M2. In the adhesion model M2, Fadh is the adhesion force acting from DEM particle 31b to DEM particle 31a. Fadh is expressed as shown in equation (9), where radh is the adhesion force coefficient (0 to 1), Knl is the contact stiffness, sn is the particle overlap distance, and δadh is the adhesion force initiation distance. The contact stiffness is determined by the granule size and Young's modulus (Figure 6), which are input as physical properties.

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[0083] (Variation 4: Parameters to be switched for each mode) In the above embodiment, in the simulation of powder compression molding, the only parameter to be switched for each of the three modes, "(1) granular state", "(2) collapsing", and "(3) primary particle state", was the spring constant k of springs 32a and 32b. However, the simulation is not limited to this; in the simulation of powder compression molding, the damping coefficient η of dashpots 33a and 33b, and the friction coefficient μ of slider 34b can also be set to different values ​​for each of the three modes, similar to the spring constant k, and switched for each mode.

[0084] In other words, the damping coefficient η and the friction coefficient μ may be constants for each mode that are switched according to the displacement of the granules 42 due to compression in the simulation of powder compression molding, the stress that the granules 42 receive due to compression, or the temperature and energy state of the granules 42. Alternatively, the damping coefficient η and the friction coefficient μ may be given as functions for each mode, with variables such as the displacement of the granules 42 based on the collapse behavior of the granules 42 in a uniaxial compression test, the stress that the granules 42 receive due to compression, and the temperature and energy state of the granules 42.

[0085] Although one embodiment has been described above, this is merely an example for the purpose of explaining the present invention and is not intended to limit the scope of the present invention to this embodiment alone. The present invention can be carried out in various other forms. For example, the above embodiment can be combined with one or more modifications as appropriate. [Explanation of Symbols]

[0086] 1: Simulation system, 11: Processor, 12: Memory, 32, 32a, 32b: Springs, 33, 33a, 33b: Dashpots, 34, 34b: Sliders, 42, 42a, 42b: Granules, M1: Interparticle model

Claims

1. A simulation method for a compression molding process of powder or granules, The process includes a simulation step in which the powder or granules are arranged in a predetermined analytical space as multiple particles in a discrete element method (DEM) that uses a model in which the repulsive and attractive forces acting as interactions between two particles when they come into contact are represented by springs, energy dissipation is represented by dashpots, and slip is represented by sliders, and the multiple particles are compressed. The spring constant of the spring, the damping coefficient of the dashpot, and the friction coefficient of the slider are changed according to the displacement of the particles due to the compression, the stress the particles experience due to the compression, or the energy state of the particles. A simulation method characterized by the following:

2. A simulation method according to claim 1, The spring constant, the damping coefficient, and the friction coefficient are given as functions based on the collapse behavior when the particles collapse into primary particles due to the compression. A simulation method characterized by the following:

3. The simulation method according to claim 2, The aforementioned collapse behavior is described in terms of a first mode, a second mode, and a third mode in the process by which the particles collapse into primary particles due to the compression. The spring constant, the damping coefficient, and the friction coefficient are given by the function for each mode. A simulation method characterized by the following:

4. A simulation method according to claim 2 or 3, A uniaxial compression test is performed on one of the aforementioned particles to obtain data relating to the collapse behavior. The function is given based on the acquired data. A simulation method characterized by the following:

5. The simulation method according to claim 4, The acquired data is corrected based on the particle size, The function is given based on the corrected data. A simulation method characterized by the following:

6. The simulation method according to claim 4, The acquired data is corrected based on the Poisson effect in the uniaxial compression test. The function is given based on the corrected data. A simulation method characterized by the following:

7. The simulation method according to claim 6, When considering the Poisson effect, the relative density of each particle is calculated based on the amount of overlap between adjacent particles. The data obtained by performing a uniaxial compression test on one of the particles is corrected based on the calculated relative density. A simulation method characterized by the following:

8. A simulation method according to claim 1, The compression molding step is a step of compressing the powder or granules to form a ceramic molded body. A simulation method characterized by the following:

9. A simulation system for performing a simulation of a compression molding process of powder or granules, The aforementioned simulation system has a processor and memory, The aforementioned processor, The aforementioned powder or granules are arranged as multiple particles in a predetermined analytical space using the Discrete Element Method (DEM), which employs a model in which the repulsive and attractive forces acting as interactions between two particles when they come into contact are represented by springs, energy dissipation is represented by dashpots, and slip is represented by sliders, and a simulation is performed to compress the multiple particles. The spring constant of the spring, the damping coefficient of the dashpot, and the friction coefficient of the slider are changed according to the displacement of the particles due to the compression, the stress the particles experience due to the compression, or the energy state of the particles. A simulation system characterized by the following features.

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