Calculation methods, computing devices, programs, and computational models.

Abstract

The behavior of particles can be easily calculated. [Solution] A computer-implemented method for calculating particle behavior includes setting a spring constant assuming that the particle is a collection of multiple components, two adjacent components are connected by two spring connection elements, and the two spring connection elements have the same spring constant; setting a friction coefficient between the particle and a member external to the particle; and calculating behavior based on the spring constant and the friction coefficient.

Description

[Technical Field]

[0001] This invention relates to a calculation method for calculating the behavior of particles, etc. [Background technology]

[0002] One method for calculating (analyzing) the behavior of particles that make up a material is the Bonded Particle Model (BPM), which is a type of Discrete Element Method (DEM). For example, Patent Document 1 discloses a method for constructing a particle model based on BPM theory. Patent Document 2 also discloses a fracture analysis model consisting of a particle model. [Prior art documents] [Patent Documents]

[0003] [Patent Document 1] Patent No. 6789274 [Patent Document 2] Patent No. 6093717 [Overview of the project] [Problems that the invention aims to solve]

[0004] Conventional BPM has the problem that it requires setting eight interdependent parameters, such as normal stiffness and shear stiffness, to calculate the behavior of particles.

[0005] This invention has been made in view of the above-mentioned problems, and one of its objectives is to make the behavior of particles easily comprehensible. [Means for solving the problem]

[0006] According to a first aspect of the present invention, a computer method for calculating the behavior of a particle includes setting the spring constants by assuming that the particle is an aggregate of multiple components, that two adjacent components are connected by two spring coupling elements, and that the two spring coupling elements have the same spring constant; setting the coefficient of friction between the particle and an external member; and calculating the behavior based on the spring constants and the coefficient of friction. According to a second aspect of the present invention, a computing device for calculating the behavior of a particle includes a processing unit that calculates the behavior based on the spring constant, assuming that the particle is an aggregate of multiple components, two adjacent components are connected by two spring coupling elements, and the two spring coupling elements have the same spring constant, and setting the coefficient of friction between the particle and an external member of the particle. According to a third aspect of the present invention, a program for causing a computer to calculate the behavior of a particle includes setting the spring constants, assuming that the particle is an aggregate of a plurality of components, that two adjacent components are connected by two spring coupling elements, and that the two spring coupling elements have the same spring constant; setting the coefficient of friction between the particle and an external member of the particle; and calculating the behavior based on the spring constants and the coefficient of friction. According to a fourth aspect of the present invention, a computational model for calculating the behavior of a particle comprises a particle as an aggregate of a plurality of constituent elements, a first coupling model having a first spring coupling element where the center of a first constituent element is coupled to the center of a second constituent element adjacent to the first constituent element, and a second coupling model having a second spring coupling element where a coupling point within the first constituent element, separated from the center, is coupled to a coupling point within the second constituent element, separated from the center, wherein the spring constants of the first spring coupling element and the second spring coupling element are the same. [Effects of the Invention]

[0007] According to the present invention, the behavior of particles can be easily calculated. [Brief explanation of the drawing]

[0008] [Figure 1] A diagram showing an example of the configuration of the computational model in the embodiment. [Figure 2] A figure showing an example of a computational model in an embodiment. [Figure 3] An explanatory diagram showing the coupling state of the computational model in the embodiment. [Figure 4] A figure showing an example of a computational model in an embodiment. [Figure 5] A flowchart showing an example of the processing flow in the embodiment. [Figure 6] A figure showing an example of experimental results in an embodiment. [Figure 7] A diagram showing an example of the configuration of a computing device in an embodiment. [Figure 8] A flowchart showing an example of the processing flow in the embodiment. [Figure 9] An explanatory diagram showing the particle model in the embodiment. [Figure 10] An explanatory diagram showing the particle model in the embodiment. [Figure 11] An explanatory diagram showing the particle model in the embodiment. [Figure 12] An explanatory diagram showing the particle model in the embodiment. [Figure 13] Diagram illustrating the effects in the embodiment. [Figure 14] Diagram illustrating the effects in the embodiment. [Figure 15] Diagram illustrating the effects in the embodiment.

[0009] Hereinafter, an example of an embodiment for carrying out the present invention will be described with reference to the drawings. The components described in this embodiment are merely illustrative and are not intended to limit the scope of the present invention to them.

[0010] <Computational Model> Figure 1 shows an example of the configuration of the computational model 1 in an embodiment of the present invention. Calculation Model 1 is an example of a calculation model in the present invention, and may be used, for example, as a model for calculating (analyzing) the behavior of particles during crushing, transportation, or mixing of materials such as minerals or recycled products. Behavior may mean, for example, at least elastic deformation and fracture among elastic deformation, yielding, plastic deformation, and fracture, but is not limited to this. In the following, particles will be denoted with the designation "PTC" and referred to as particle PTC where appropriate.

[0011] Calculation model 1 is composed of a particle PTC, which is an aggregate of multiple components such as one component i and other components k. Component i and component k are coupled via the first coupling model 2(1) and the second coupling model 2(2). In Figure 1, a state in which component i is coupled only with component k is simulated, but component i may be coupled with multiple adjacent other components within the particle PTC, and other components may be coupled with multiple adjacent yet other components. A particle is a mass or a divided mass, and may be an aggregate of component i, component k, and several other components.

[0012] The first coupling model 2(1) is coupled to one center Ci of component i and the other center Ck of component k. The first coupling model 2(1) comprises a first spring coupling element 3(1) and a first damper coupling element 4(1) arranged in parallel. The first spring coupling element 3(1) expands and contracts elastically, and the first damper coupling element 4(1) stabilizes the vibration of the first spring coupling element 3(1). The spring constant of the first spring coupling element 3(1) is K B The damping coefficient of the first damper coupling element 4(1) is η B That is the case.

[0013] The second coupling model 2(2) is coupled to one coupling point Pi located away from the center Ci within component i and to another coupling point Pk located away from the center Ck within component k. The second coupling model 2(2) comprises a second spring coupling element 3(2) and a second damper coupling element 4(2) arranged in parallel. The second spring coupling element 3(2) expands and contracts elastically, and the second damper coupling element 4(2) stabilizes the vibration of the second spring coupling element 3(2). In the calculation model 1 of this embodiment, the spring constant of the second spring coupling element 3(2) is the same K as that of the first spring coupling element 3(1). Band the damping coefficient of the second damper coupling element 4(2) is assumed to be the same damping coefficient η as that of the first damper coupling element 4(1). B is assumed.

[0014] The connection between the components i and k is only through the connections by the first connection model 2(1) and the second connection model 2(2). Also, the connections at the center Ci, center Ck, connection point Pi, and connection point Pk are, for example, pin connections, and no contact force occurs between the component i and the component k. The contact force is a force in a direction perpendicular to the normal connecting the center Ci and the center Ck, or a force in a direction perpendicular to the normal connecting the connection point Pi and the connection point Pk, and refers to a frictional force, a torsional force, etc.

[0015] The distance between the center Ci of the component i and the center Ck of the component k changes elastically. When an external force is applied to the particle PTC from a state where no external force is applied, the distance between the center Ci and the center Ck extends by λ CB and the distance between the connection point Pi and the connection point Pk extends by λ PB and changes.

[0016] In the calculation model 1, contact forces and frictional forces occur between the particle PTC and the member 5 outside the particle PTC. It is assumed that the particle PTC and the member 5 are connected in the same way as in the conventional DEM.

[0017] FIG. 2 is a diagram showing an example of the calculation model 1 in which the component i is connected to four other components. However, the number of other components to which one component is connected is not limited. When a plurality of components are in the closest packing, one component is connected to 12 other components. In the calculation model 1, the normal connection distance r CB between the surface of the component i and the surface of the other component is assumed to be, for example, approximately 0.5 times the radius r CE of the component i. It is unnatural to assume that r CB is less than 0. On the other hand, when r CB is r CESetting it to more than 1 requires considering that component i may combine with other components other than those adjacent to it. Therefore, for example, we can assume it is approximately 0.5 times the average value between 0 and 1. CB For example, r CE It may be 0.2 to 0.8 times, preferably 0.4 to 0.6 times.

[0018] The left side of Figure 3 shows a packed particle PTC, and the right side of Figure 3 shows computational model 1, which models the packed particle PTC. Computational model 1 on the right side of Figure 3 comprises components i, k, s, and t. The left side of Figure 4 shows a porous particle PTC, and the right side of Figure 4 shows a computational model 1 that models the porous particle PTC. Computational model 1 on the right side of Figure 4 comprises components i, k, s, and t. The structure of the particle PTC forming computational model 1 may be either a packed structure or a porous structure. Furthermore, the shape of the components when computational model 1 is formed is not limited.

[0019] <Effects of the computational model> In computational model 1, one component i and other components k are coupled by the first coupling model 2(1) and the second coupling model 2(2), and no contact force is generated between the one component i and the other components k. Therefore, the behavior of particle PTC can be easily calculated by calculating the behavior of the simple computational model 1.

[0020] Furthermore, due to the fact that the spring constant of the first spring coupling element 3(1) and the spring constant of the second spring coupling element 3(2) are the same, the F included in the right-hand side of equations (1) and (5) CB and F PB The spring constant that determines the same K B Setting it to this (see equations (2) and (3)) makes it easier to calculate the behavior based on equations (1) and (5).

[0021] Furthermore, in calculation model 1, because the first coupling model 2(1) and the second coupling model 2(2) are composed of spring coupling elements and damper coupling elements, respectively, no contact force is generated between one component i and other components k, etc. Therefore, the behavior of the particle PTC, which is an aggregate of components, can be easily calculated without considering the coefficient of friction between one component i and other components k, etc. For example, when an external force is applied from an external member 5 to a particle PTC including one component i and other components k, etc., the elastic deformation behavior of the particle can be calculated by setting the coefficient of friction between the particle PTC and the external member 5, and the spring constants of the first coupling model 2(1) and the second coupling model 2(2). Furthermore, by setting the maximum elongation, the fracture behavior of the particle can be calculated, and a load-displacement curve can also be drawn.

[0022] <Calculation method> Figure 5 is a flowchart illustrating an example of the process for realizing the particle behavior calculation method in this embodiment. The process in the flowchart of Figure 5 may be performed by a computer (for example, the processing unit of a computing device described later), and may be realized by reading and executing a program stored in a memory unit (not shown).

[0023] In the flowchart below, each symbol S represents a step. The flowchart described below is merely an example of the processing procedure in this embodiment, and other steps may be added or some steps may be deleted. Alternatively, some of the steps in the flowchart may be rearranged and executed.

[0024] While manual work may be involved, the setting of parameters (parameter values) may be performed by the processing unit. Setting parameters may include, for example, the processing unit storing the parameter values ​​in a memory unit. Alternatively, the processing unit may calculate and set the parameter values, or it may set the parameter values ​​entered by the user based on experimental results, etc.

[0025] First, the processing unit sets the friction coefficient μ between the component and the member 5 (S110). The friction coefficient μ may be determined in the same way as a general DEM. For example, the friction coefficient μ may be determined based on the angle of repose, which is the inclination angle of the surface of the particle group when the friction coefficient determination particles are released from the container, and the outflow velocity when the friction coefficient determination particles are discharged from the container.

[0026] Next, the processing unit determines the spring constant K of the first spring coupling element 3(1) and the second spring coupling element 3(2). B Set the spring constant K (S120). B This can be determined, for example, by drawing a line that fits the elastic deformation curve in the load-displacement curve (horizontal axis is displacement λ, vertical axis is load P) obtained from a compression test using an actual machine, as shown in Figure 6. For example, 10 compression tests are performed and the average value elastic deformation curve is fitted. The fitting can be done, for example, by drawing a graph line such as a quadratic function curve, exponential function curve, logarithmic function curve or straight line on the elastic deformation curve of the compression test using the least squares method. From these graph lines, "K" can be determined. B Let K = P / λ B The spring constant K can be calculated. B This may be determined by a tensile test, if possible.

[0027] Next, the processing unit measures the maximum elongation λ of the first coupled model 2(1) and the second coupled model 2(2). max Set (S130). Maximum extension λ max This can be determined, for example, by adjusting the value corresponding to the displacement λ at the time of failure during a compression test. Failure may be defined as the phenomenon of crack formation or separation that occurs after elastic deformation, yielding, or plastic deformation. Failure may be defined as the state in which the load decreases to approximately 0 in the load-displacement curve from the compression test in Figure 6. λ max This may be determined by a tensile test, if possible.

[0028] Next, the processing unit calculates the deformation and fracture behavior of calculation model 1 based on equations (1) and (2) (S140). The processing unit may also draw a load-displacement curve based on the calculation results.

[0029] For computational model 1, the parallel motion equation for component i used to calculate its behavior is shown in equation (1).

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[0030] Equation (1) is the equation of motion when component i is three-dimensionally bonded with nb other components (including component k), and particle PTC is in contact with nc external members 5, and component i is translated with velocity Vi. In equation (1), mi is the mass of component i, and F CB is the bond force vector of the first bond model 2(1), and F PB is the bond force vector of the second bond model 2(2), and F C is the vector of the contact force with the external member 5, and G is an external force such as gravity.

[0031] F CB is expressed by equation (2), F PB It is expressed by equation (3), and η in equations (2) and (3) B This is expressed by equation (4).

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[0032] In equation (2), K B λ is the spring constant common to the first coupling model 2(1) and the second coupling model 2(2), and λ CB is the extension of the first coupling model 2(1), and η B is the damping coefficient of the first coupling model 2(1), and uCB is the relative velocity between the center Ci of component i and the centers of the other components, and n CB This is the direction vector of the first combined model 2(1). In equation (3), K B λ is the spring constant common to the first coupling model 2(1) and the second coupling model 2(2), and λ PB This is the extension of the second coupling model 2(2), and n PB,n is the normal direction vector of the second combined model 2(2), and n PB,s is the tangential direction vector of the second bond model 2(2), and η B is the damping coefficient of the second coupling model 2(2), and u PB is the relative velocity between the connection point Pi of component i and the connection point of another component, and n PB is the direction vector of the second coupling model 2(2). In equation (3), λ PB <0 represents the case where the distance between connection points is reduced. In equation (4), m is the mass of the constituent element, and in the case of element i, it is mi. According to equation (4), the damping coefficient η B The spring constant K B Determined by the spring constant K B The damping coefficient η B It is determined by [something].

[0033] F in equation (1) C This is determined by the spring constant in the normal direction, the damping coefficient in the normal direction, and the friction coefficient. The spring constant is K B Let the damping coefficient be η B By doing so, if the coefficient of friction μ is determined, then F C The coefficient of friction μ is determined by the angle of repose, etc., as described above.

[0034] As mentioned above, the spring constant K B F CB and F PB The coefficient of friction μ determines F C This is determined. That is, the spring constant K B By defining the coefficient of friction μ, the behavior of the particle PTC can be calculated based on the equation of motion in equation (1).

[0035] For computational model 1, the rotational motion equation for component i used to calculate its behavior is shown in equation (5).

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[0036] Equation (5) is the equation of motion when the particle PTC is in contact with nc external members 5 and the constituent i is in rotational motion with velocity ωi. In equation (5), Ii is the moment of inertia, np is the number of second coupled models 2(2), and T PB is F PB This is the torque vector generated in component i.

[0037] T PB This is expressed by equation (6). In equation (6), r CP is a vector from Ci to Pi, and the symbol "×" represents the cross product of two vectors.

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[0038] Spring constant K B F PB F is determined PB by T PB The determination was made, T PB Equation (5) is determined by this. That is, the spring constant K B By defining this, the deformation behavior of the particle PTC can be calculated based on the equation of motion in equation (5).

[0039] The fracture behavior of particle PTCs is described by equations (1) and (2) as the elongation of the distance between the center Ci of one component i and the center Ck of the other component k, λ. CB , and the extension of the distance between the connection point Pi of one component i and the connection point Pk of the other component k λ PB Determine λ CB When it exceeds the maximum elongation λmax of a real particle PTC, or λ PB When λ exceeds λmax, it is assumed that fracture such as crack formation will occur. CBWhen λ exceeds λmax, and λ PB When λmax exceeds λmax, it may be assumed that fracture such as crack formation occurs. The same λmax is used to determine whether or not fracture has occurred. CB and λ PB It will be used as a point of comparison.

[0040] As described above, after calculating the deformation and fracture behavior of the particle PTC, a load-displacement curve is created and output (e.g., displayed or transmitted) based on the calculation results. The plot of the load-displacement curve is, for example, plotted with the displacement λ on the horizontal axis of the graph. CB or λ PB Correspond to the load P on the vertical axis of the graph, and the right-hand side of equation (1) F C This will be done in correspondence. The creation of the load-displacement curve may be done by a computer. Alternatively, the user may create it manually.

[0041] <Effects of the calculation method> The calculation method of the present invention relates to the coefficient of friction μ and the spring constant K. B By setting these parameters, it is possible to calculate at least the elastic deformation among elastic deformation, yield, plastic deformation, and fracture, and to plot the load-displacement curve. For this reason, the coefficient of friction μ and the spring constant K are used. B By simply setting this as a parameter, you can perform an analysis of elastic deformation.

[0042] Furthermore, the calculation method of the present invention is based on the assumption that the spring constant of the first spring coupling element 3(1) and the spring constant of the second spring coupling element 3(2) are the same K. B The parameters can be set assuming this. Therefore, F is included in the right-hand side of equations (1) and (5). CB and F PB The spring constant that determines the same K B Setting it to this (see equations (2) and (3)) makes it easier to calculate the behavior based on equations (1) and (5).

[0043] Furthermore, the calculation method of the present invention uses the coefficient of friction μ and the spring constant K. BWhen λmax is set as a parameter, the deformation and fracture behavior of particle PTC can be easily calculated based on only three parameters. Therefore, the behavior of minerals, etc., when an external force is applied to them can be easily understood.

[0044] In conventional BPM (Potyondy), eight parameters must be set to calculate the behavior: the normal stiffness of the components, the shear stiffness of the components, the coefficient of friction between components, the normal stiffness of the joints, the shear stiffness of the joints, the tensile strength, the shear strength, and the joint radius. In contrast, the calculation method of the present invention requires fewer parameters to be set compared to conventional BPM, and allows for efficient setting of parameters for calculating deformation and fracture behavior.

[0045] Furthermore, the calculation method of the present invention uses the coefficient of friction μ and the spring constant K as parameters. B Since λmax and λmax can be set to be independent of each other and not dependent on each other, it is not necessary to consider other parameters when determining one parameter, and parameter setting can be done efficiently.

[0046] In conventional BPM, the eight parameters to be set are mutually dependent, making the process of determining the parameters complex. In contrast, the calculation method of the present invention allows for easier and more unique parameter setting compared to conventional BPM, because the three parameters to be set are independent of each other.

[0047] Furthermore, the calculation method of the present invention assumes that the damping coefficients of the first damper coupling element 4(1) and the second damper coupling element 4(2) are the same η B Assuming this is the case, the parameters can be set. Here, by determining a single spring constant, the damping coefficient is also determined to be unique (see equation (4)). For this reason, the F included in the right-hand side of equations (1) and (5) CB and F PB The damping coefficient that determines this is η B This is determined (see equations (2) and (3)), which facilitates the calculation of the behavior based on equations (1) and (5).

[0048] <Computing device> Next, we will describe the computing device used to perform the calculations of the behavior described above. The computing device may also be called a behavior calculation device or a behavior analysis device, etc.

[0049] Figure 7 shows an example of the configuration of the computing device 10 in this embodiment. The computing device 10 includes, for example, a behavior calculation unit 14, a load-displacement curve creation unit 15, and a behavior image generation unit 16. These may, for example, be functional units (functional blocks) of the processing unit (or control unit) of the computing device 10, and may be configured to include processing circuits such as a CPU (Central Processing Unit), GPU (Graphics Processing Unit), DSP (Digital Signal Processor), ASIC (Application Specific Integrated Circuit), FPGA (Field Programmable Gate Array), etc.

[0050] Furthermore, the computing device 10 includes, for example, a friction coefficient storage unit 11, a spring constant storage unit 12, and a maximum extension storage unit 13. These may be configured to include memory such as RAM (Random Access Memory).

[0051] Although not shown in the diagram, the computing device 10 may perform the following processing according to a program stored in memory such as ROM (Read Only Memory).

[0052] The computing device 10 may also be equipped with an output unit that outputs various types of information (for example, display or sound output). The output unit may be, for example, a display device provided by the computing device 10, or a communication unit (including a communication processor, etc.) that provides various types of data, including display data, to a display device connected to the computing device 10 via a communication line.

[0053] Further, the computing device 10 may be provided with an input unit for inputting various types of information. The input unit may be, for example, an input device (e.g., a touch panel integrated with a display device, a keyboard, a pointing device, etc.) operated by a user who uses the computing device 10, or may be a communication unit (including a communication processor) that receives various types of data from an information processing device connected to the computing device 10 via a communication line.

[0054] Also, the computing device 10 realizes a calculation method by a computer based on the calculation model 1, but it is not necessary to draw the calculation model 1 by a computer in order to realize the calculation method. However, the calculation model 1 may be drawn by a computer for the purpose of confirming the underlying calculation model.

[0055] FIG. 8 is a flowchart showing an example of the flow of the behavior analysis process executed by the computing device 10. For the processing of this flowchart, other steps may be added, some steps may be deleted, or some of the steps in the flowchart may be executed after being interchanged.

[0056] The processing unit of the computing device 10 stores the determined friction coefficient μ in the friction coefficient storage unit 11 (S210). The friction coefficient μ may be determined based on the angle of repose or the like in the same manner as S110 in FIG. 5. Also, the processing unit of the computing device 10 stores the determined spring constant K B in the spring constant storage unit 12 (S220). The spring constant K B may be determined based on a physical machine test in the same manner as S120 in FIG. 5. Also, the processing unit of the computing device 10 stores the determined maximum elongation λmax in the maximum elongation storage unit 13 (S230). λmax may be determined based on a physical machine test in the same manner as S130 in FIG. 5.

[0057] Next, the behavior calculation unit 14 performs the calculations of equations (1) and (5) (S240). Specifically, based on the stored friction coefficient μ and spring constant K B for F CB for F PB for FC and T PB are calculated, and F CB , F PB , F C is used to calculate the left side of Equation (1) based on F PB is used to calculate the left side of Equation (5) based on T

[0058] Next, the load-displacement curve creation unit 15 creates and outputs (for example, displays or transmits) a load-displacement curve based on the calculation result of the behavior calculation unit 14 (S250). The plotting of the load-displacement curve is performed by, for example, associating λ CB or λ PB with the displacement λ on the horizontal axis of the graph, and associating F C on the right side of Equation (1) with the load P on the vertical axis of the graph

[0059] Next, the behavior image generation unit 16 generates and outputs (for example, displays or transmits) an image showing the change in the shape of the particle model PTCM due to the compressive load, as an image related to the behavior of the particles (S260). The generation of the image can be performed, for example, based on Equations (1) and (5). Specific images will be described later

[0060] The information such as the image output as described above may be an example of the information related to the behavior of the particles. Other information may be used as long as it is related to the calculated behavior of the particles

[0061] Note that the above processing may be realized by a calculation system (behavior calculation system, behavior analysis system) including two or more devices In this case, for example, a part of the behavior calculation unit 14, the load-displacement curve creation unit 15, and the behavior image generation unit 16 may be provided in the first device, and the others may be provided in the second device, or they may be provided in separate devices (the first device, the second device, the third device). The same applies to the friction coefficient storage unit 11, the spring constant storage unit 12, and the maximum elongation storage unit 13

[0062] <Effects of calculation devices, etc.> The computing device 10 (or computing system) of the present invention enables the calculation method for particle behavior in the present invention to be implemented by a computer. Furthermore, the program of the present invention is stored in the memory unit of the computing device or the like. These features allow the calculation method of the present invention to be processed more efficiently. For example, the behavior image generation unit 16 can visualize the changes in the shape of the particle model PTCM by drawing them, allowing the behavior of the particle model PTCM to be confirmed visually.

[0063] <Comparison of Compression Test Simulation and Actual Compression Test> Figure 9 is a front view of the particle model PTCM used for performing a compression test simulation by the computing device 10 for calculation model 1, and Figure 10 is a plan view of the particle model PTCM. Figure 11 is a front view of the particle replica PTCR used for performing an actual compression test as a comparative test, and Figure 12 is a plan view of the particle replica PTCR. The particle model PTCMs in Figures 9 and 10 are, for example, particle model PTCMs drawn by the behavior image generation unit 16 of the computing device 10.

[0064] The particle model PTCM and the particle replica PTCR have substantially the same contour shape, with a cylindrical shape in the middle section in the vertical direction and curved shapes on the top and bottom surfaces. The particle model PTCM is a random structure composed of an aggregate of multiple components, each component being coupled with 12 other components by the first coupled model 2(1) and the second coupled model 2(2).

[0065] The compression test simulation was performed using the computing device 10. The conditions for the compression test simulation were: density ρ = 2240 kg / m³ for each component. 3 , radius r of each component CE = 0.4 × 10 -3 m, number of components n = 1200, external force G = 9.80665 m / s² 2 The friction coefficient μ = 0.1 between the particle model PTCM and the external member, and the spring constant K B = 1.0 × 10 6 N / m, maximum elongation λmax=1.36×10 -3 It is mm. ρ, rCE n and G are predetermined values ​​that are naturally determined, while μ and K B And λmax are values ​​set as parameters.

[0066] Figure 13 is a graph comparing the load-displacement curves of the compression test simulation and the load-displacement curves of the actual compression test. In Figure 13, the thick line represents the load-displacement curve of the compression test simulation, and the thin line represents the load-displacement curve of the actual compression test. For the actual compression test, load-displacement curves for 10 tests are shown.

[0067] In the elastic deformation portion of the load-displacement curve, the load-displacement curve of the compression test simulation and the load-displacement curve of the actual compression test are in close agreement, and their slopes are also in close agreement. Furthermore, the displacement at the time of failure, when the load drops instantaneously, is in close agreement between the load-displacement curve of the compression test simulation and the load-displacement curve of the actual compression test. Therefore, it can be seen that the compression test simulation based on calculation model 1 can simulate or reproduce the actual compression test.

[0068] Figure 14 shows an image of the particle model PTCM being compressed from above by the compression jig model 21M with the particle model PTCM placed vertically on the compression stand model 20M. The images may be generated by the behavior image generation unit 16 for each mode of change. Figure 15 shows a photograph of the particle replica PTCR being compressed from above by the compression jig 21R with the particle replica PTCR placed vertically on the compression stand 20R using the actual compression test machine. In Figures 14 and 15, Δ is the compression distance in the vertical direction. The compression jig model 21M and the compression jig 21R correspond to the external member 5 (shown in Figure 2).

[0069] Both the particle model PTCM and the particle replica PTCR develop cracks at Δ=0.15mm and produce fragments at Δ=1.5mm. Although not shown in the diagram, when the particle model PTCM and particle replica PTCR are placed horizontally, both develop cracks at Δ=0.15mm and produce fragments at Δ=1.5mm. Furthermore, although not shown in the diagram, when the particle model PTCM and particle replica PTCR are arranged in two layers, with the lower layer horizontal and the upper layer vertical, both develop cracks at Δ=0.30mm. Therefore, the changes in external shape match those observed in the compression test simulation and the actual compression test. From this perspective, it can be seen that the compression test simulation based on calculation model 1 can simulate or reproduce the actual compression test.

[0070] <Variation> Although embodiments of the present invention have been described above with reference to the drawings, the present invention is not limited to those shown.

[0071] For example, the computational model of the present invention may include multiple particles, which are aggregates of multiple constituent elements. In the computational method of the present invention, the internal stress or elastic energy of the particles may be calculated based on computational model 1. Furthermore, the thermal stress when a material is heated may be calculated based on computational model 1.

[0072] Furthermore, the calculation model of the present invention does not necessarily have to include a Dunbar coupling element. In this case, by simplifying equations (2), (3), and (6) and simplifying equations (1) and (5) for calculating the behavior of particle PTCs, it becomes possible to calculate the behavior of particle PTCs more easily.

[0073] Furthermore, in the calculation model of the present invention, the spring constants of the first spring coupling element 3(1) and the second spring coupling element 3(2) do not necessarily have to be the same. If the spring constants are not the same, the behavior of the particle PTC can be calculated by setting five parameters: the coefficient of friction, the spring constant of the first spring coupling element 3(1), the spring constant of the second spring coupling element 3(2), the maximum extension of the first coupling model 2(1), and the maximum extension of the second coupling model 2(2). For example, if these five parameters are set, the deformation behavior of the particle PTC can be calculated using mathematical formulas similar to those in equations (1) and (5), assuming that the spring constants of the first spring coupling element 3(1) and the second spring coupling element 3(2) are different, provided that at least no contact force occurs between the components. Therefore, even when these five parameters are set, it is possible to calculate the behavior of the particle PTC more easily compared to conventional BPM, which requires setting eight parameters. [Explanation of Symbols]

[0074] 1: Computational Model 2(1): First combined model, 2(2): Second combined model 3(1): First spring coupling element, 3(2): Second spring coupling element 4(1): First damper coupling element, 4(2): Second damper coupling element 5: External components 10: Computing device 11: Friction coefficient memory unit, 12: Spring constant memory unit, 13: Maximum extension memory unit, 14: Behavior calculation unit, 15: Load displacement curve creation unit, 16: Behavior image generation unit 20M: Compression stand model, 20R: Compression stand, 21M: Compression jig model, 21R: Compression jig PTC: Particle, PTCM: Particle Model, PTCR: Particle Replica

Claims

1. A method for calculating the behavior of particles performed by a computer, The aforementioned particle is an aggregate of multiple constituent elements, and two adjacent constituent elements are connected by two spring coupling elements, and the spring constant is set assuming that the two spring coupling elements have the same spring constant. Setting the coefficient of friction between the particle and the external member of the particle, The behavior is calculated based on the spring constant and the friction coefficient. Includes, The two spring coupling elements consist of a first spring coupling element to which the center of the first component and the center of the second component adjacent to the first component are coupled, and a second spring coupling element to which a coupling point located away from the center within the first component and a coupling point located away from the center within the second component are coupled. Calculation method.

2. The two spring coupling elements are set to have the same maximum extension, and this includes setting the maximum extension accordingly. The aforementioned behavior is calculated based on the spring constant, the friction coefficient, and the maximum elongation. The calculation method according to claim 1.

3. The spring constant, the friction coefficient, and the maximum elongation are all independent parameters. The calculation method described in claim 2.

4. In calculating the aforementioned behavior, the damping coefficient of the damper coupling element is calculated using the spring constant, assuming that a damper coupling element is provided corresponding to each of the two spring coupling elements having the same spring constant. The calculation method according to any one of claims 1 to 3.

5. A computing device for calculating the behavior of particles, The particle is an aggregate of multiple components, two adjacent components are connected by two spring coupling elements, the spring constant is set assuming the two spring coupling elements have the same spring constant, the coefficient of friction between the particle and an external member is set, and the processing unit calculates the behavior based on the spring constant and the coefficient of friction. The two spring coupling elements consist of a first spring coupling element to which the center of the first component and the center of the second component adjacent to the first component are coupled, and a second spring coupling element to which a coupling point located away from the center within the first component and a coupling point located away from the center within the second component are coupled. computing device.

6. It includes an output unit that outputs information regarding the aforementioned behavior, The computing device according to claim 5.

7. The output unit has a display unit that displays an image relating to the behavior. The computing device according to claim 6.

8. A program that causes a computer to calculate the behavior of particles, The aforementioned particle is an aggregate of multiple constituent elements, and two adjacent constituent elements are connected by two spring coupling elements, and the spring constant is set assuming that the two spring coupling elements have the same spring constant. Setting the coefficient of friction between the particle and the external member of the particle, The behavior is calculated based on the spring constant and the friction coefficient. Includes, The two spring coupling elements consist of a first spring coupling element to which the center of the first component and the center of the second component adjacent to the first component are coupled, and a second spring coupling element to which a coupling point located away from the center within the first component and a coupling point located away from the center within the second component are coupled. program.

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