Simulation device, simulation method, and program

Abstract

To provide a novel simulation device, simulation method and program, which enable analysis of powder behavior in consideration of adhesive force of particles.SOLUTION: A simulation device 20 is provided, comprising a reception unit 31, an adhesive force computation unit 321 for computing adhesive force of particles, and a particle behavior analysis unit 322 configured to analyze behavior of multiple particles using the adhesive force computed by the adhesive force computation unit 321. The adhesive force computation unit 321 computes adhesive force based on a contact radius of a contact surface between a particle and a contacted object in contact with the particle.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a simulation device, a simulation method, and a program. [Background technology]

[0002] Patent Document 1 describes an input device for inputting simulation conditions, an output device for outputting the simulation results; Based on the simulation conditions input from the input device, a plurality of different sizes are a processing device for analyzing the behavior of powder or granular material containing particles, The processing device includes: determining the behavior of the coarse-grained powder or granular material by simulation based on the values ​​of parameters defining the particle size distribution of the powder or granular material to be simulated and the value of a coarse-graining coefficient serving as a criterion for coarse-graining the particles, which are input from the input device; A simulation device for powder and granular materials is disclosed, as disclosed in a simulation device that associates the behavior of particles obtained by simulation with the value of the input coarse-graining coefficient and outputs it to the output device. [Prior art documents] [Patent documents]

[0003] [Patent Document 1] Japanese Patent Publication No. 2020-57135 Summary of the Invention [Problem to be solved by the invention]

[0004] For the purpose of improving processes in factories and reducing testing man-hours when examining manufacturing processes, the behavior of powders (granular materials) containing multiple particles has traditionally been analyzed using discrete element method (DEM) calculations.

[0005] Discrete element method calculation is a simulation technique that describes the movement of the entire powder by solving the equation of motion for each particle.

[0006] In equipment in factories, etc., particles may adhere to the walls of the equipment or particles may aggregate together, causing a granulation phenomenon, depending on the physical properties of the particles, wall surfaces, etc., the processing conditions, etc. However, conventional discrete element method calculations have not been able to fully evaluate the adhesive force acting on particles, and have therefore not been able to appropriately evaluate the above-mentioned phenomenon, for example.

[0007] In view of the problems of the above-mentioned conventional techniques, one aspect of the present invention aims to provide a new simulation device that can analyze the behavior of powder taking into account the adhesive force of particles. [Means for solving the problem]

[0008] In order to solve the above problem, according to one aspect of the present invention, A simulation device for analyzing the behavior of powder containing a plurality of particles, an adhesive force calculation unit that calculates the adhesive force of the particles; a particle behavior analysis unit that analyzes the behavior of the plurality of particles using the adhesive force calculated by the adhesive force calculation unit, The adhesive force calculation unit calculates the adhesive force based on a contact radius of a contact surface between the particle and a contacted object that comes into contact with the particle. and further calculating the adhesive force in the tangential direction of the contact surface between the particle and the contacted object based on the amount of overlap between the particle and the contacted object. A simulation device is provided. [Effects of the Invention]

[0009] According to one aspect of the present invention, it is possible to provide a new simulation device that can analyze the behavior of powder taking into account the adhesive force of the particle surface. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is an explanatory diagram of the adhesive force generated between a particle and a wall surface. [Figure 2]1 is a hardware configuration diagram of a simulation device according to a first embodiment of the present invention. [Figure 3] 1 is a block diagram showing functions of a simulation device according to a first embodiment of the present invention. [Figure 4] FIG. 1 is an explanatory diagram of a reactor used when analyzing the behavior of powder in a first embodiment of the present invention. [Figure 5] FIG. 10 is an explanatory diagram of the analysis results of the behavior of powder when an adhesive force model is used as the adhesive force model. [Figure 6] FIG. 10 is an explanatory diagram of the analysis results of the behavior of powder when a liquid bridge model is used as the adhesive force model. [Figure 7] 1 is an explanatory diagram of a particle group consisting of a plurality of particles and a collision between the particle group and a wall surface. FIG. [Figure 8] 1 is an explanatory diagram of a coarse-grained particle obtained by coarsely graining a particle group made up of a plurality of particles, and the collision of the coarse-grained particle with a wall surface. FIG. [Figure 9] FIG. 10 is a block diagram showing the functions of a simulation device according to a second embodiment of the present invention. [Figure 10] 10 is a flowchart illustrating a simulation method according to a second embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0011] Specific examples of a simulation device, a simulation method, and a program according to an embodiment of the present disclosure (hereinafter referred to as "the present embodiment") will be described below with reference to the drawings. Note that the present invention is not limited to these examples, but is defined by the claims, and is intended to include all modifications within the meaning and scope of the claims. 1. First embodiment [Simulation device] The inventors of the present invention have investigated a model for calculating adhesive force in order to create a new simulation device that can analyze the behavior of powder taking into account the adhesive force of particles. (1) Adhesion model (1-1) Examination of the liquid bridge model The adhesive forces that occur on particle surfaces have been proposed to be due to the force caused by the surface tension of the liquid on the particle surface and the adhesive force caused by the viscous force that accompanies the movement of the liquid on the particle surface as the particles approach each other. Whether surface tension or viscous resistance is dominant is determined by the capillary number. The inventors of this invention conducted an experiment in which resin beads were supplied to a small rotary kiln, and found that the estimated capillary number was on the order of several thousand, and that the liquid bridging force due to viscous resistance was dominant. Therefore, a liquid bridging model due to viscous resistance was investigated as an adhesive force model.

[0012] When particles approach or separate, the viscous resistance of the liquid on the particle surface hinders the particle's movement. The adhesive force between particles originates from this viscous resistance. Adhesion force due to viscous resistance F ad is formulated as the following equation (1-1).

[0013]

number

[0014] However, the above formula (1-1) is expressed as 1 / D, which is the reciprocal of the interparticle distance. s is included in the formula, and the adhesive force F ad is the reciprocal of the interparticle distance, 1 / D s Therefore, when the particle surfaces are in contact, that is, D s = 0, the adhesive force F ad will diverge.

[0015] One way to avoid divergence is to solve the equation of motion in an infinitesimal time step for the discrete element method calculation, but this would significantly increase the calculation time and require an unrealistic calculation time.Another way is to set an upper limit on the adhesive force, but this may change the calculation results.

[0016] Therefore, it is clear that it is difficult to accurately evaluate adhesive force using the liquid bridge model. (1-2) Study of adhesive force model Therefore, a new adhesive force model was investigated. Specifically, it was assumed that the adhesive force originates from the elastic change of the adhesive that occurs on a flat film surface, such as adhesive tape. In this case, the force due to the elastic deformation of the adhesive occurs in the opposite direction to the direction of peeling the tape at the interface where the adhesive tape is peeled. If this is expanded to the adhesive force on a particle, it is thought that the adhesive force occurs on the circumference of the contact surface of the particle. Note that the contact surface means the contact surface between the particle and the object that comes into contact with the particle, and examples of the object that comes into contact with the particle include other particles, wall surfaces, etc. The adhesive force per unit length is defined as A w,n Then, the adhesive force F perpendicular to the contact surface is ad,n can be expressed by the following equation (1-2).

[0017]

number

[0018] As shown in Figure 1(A), when particle 11 is in contact with wall surface 12, if particle 11 moves in the direction of block arrow A1, an adhesive force calculated by the above formula (1-2) is generated in region 131 where particle 11 is in contact with wall surface 12 along block arrow A2, which is the opposite direction to block arrow A1. Note that while the case where particle 11 is in contact with wall surface 12 is described here as an example, the same can be said for the case where particles 11 are in contact with each other. The same applies to the adhesive forces in the rotational and tangential directions described below.

[0019] In addition, the resistance torque T due to the adhesion force in the rotational direction of the particle ad is expressed by the following equation (1-3).

[0020]

number

[0021] As shown in Figure 1(B), when particle 11 is in contact with wall surface 12 and particle 11 rotates in the direction of block arrow B1, a resistance torque, which is an adhesive force that can be calculated by the above equation (1-3), occurs in region 132 where particle 11 is in contact with wall surface 12 along block arrow B2, which is the direction that prevents the rotation of block arrow B1.

[0022] That is, the adhesive force in the direction perpendicular to the contact surface and in the rotational direction of the particle is cont The above formulas (1-2) and (1-3) do not include the reciprocal of the interparticle distance as in the liquid bridge model described above, so even when particles are in contact with each other or are very close to each other, the calculation results of the adhesive force do not diverge and can be appropriately evaluated.

[0023] Since the adhesion force is expressed by the adhesion model here, by specifying that particles roll rather than slide in the tangential direction, an appropriate adhesion force can be calculated without evaluating the adhesion force in the tangential direction. Therefore, the adhesion force can be calculated based on the contact radius at the contact surface.

[0024] However, to evaluate the tangential adhesion force more accurately, the tangential adhesion force F ad,t can be expressed by the following equation (1-4).

[0025]

number

[0026] As shown in Figure 1(C), when particle 11 is in contact with wall surface 12 and particle 11 moves in the direction of block arrow C1, an adhesive force that can be calculated by the above formula (1-4) is generated in region 133 where particle 11 is in contact with wall surface 12 along block arrow C2, which is the opposite direction of block arrow C1.

[0027] In addition to the vertical and rotational adhesion forces calculated based on the contact radius described above, the adhesion force in the tangential direction of the contact surface between the particle and the contacted object can be calculated and taken into account based on the amount of overlap between the particle and the contacted object, thereby enabling a more accurate evaluation of the adhesion force. (2) Simulation equipment The simulation device of this embodiment is a simulation device for analyzing the behavior of powder containing a plurality of particles, and can have the following adhesive force calculation unit and particle behavior analysis unit.

[0028] The adhesive force calculation unit can calculate the adhesive force of the particles.

[0029] The particle behavior analysis unit can analyze the behavior of a plurality of particles using the adhesive force calculated by the adhesive force calculation unit.

[0030] The adhesive force calculation unit can then calculate the adhesive force based on the contact radius of the contact surface between the particle and the contacted object that comes into contact with the particle.

[0031] 2, the simulation device 20 of this embodiment is configured, for example, by an information processing device (computer), and can be physically configured as a computer system including a CPU (Central Processing Unit: processor) 21, which is an arithmetic processing unit, a RAM (Random Access Memory) 22 and a ROM (Read Only Memory) 23, which are main storage devices, an auxiliary storage device 24, an input / output interface 25, and a display device 26, which is an output device. These are interconnected by a bus 27. The auxiliary storage device 24 and the display device 26 may be provided externally.

[0032] The CPU 21 controls the overall operation of the simulation device 20 and performs various information processing. The CPU 21 can execute, for example, a simulation method or a program (simulation program) described later that is stored in the ROM 23 or the auxiliary storage device 24, to calculate adhesive forces and analyze particle behavior.

[0033] The RAM 22 is used as a work area for the CPU 21 and may include a non-volatile RAM for storing main control parameters and information.

[0034] The ROM 23 can store programs (simulation programs) and the like.

[0035] The auxiliary storage device 24 is a storage device such as an SSD (Solid State Drive) or an HDD (Hard Disk Drive), and can store various data, files, etc. required for the operation of the simulation device.

[0036] The input / output interface 25 includes both a user interface such as a touch panel, keyboard, display screen, and operation buttons, and a communication interface that takes in information from an external data recording server or the like and outputs analysis information to other electronic devices.

[0037] The display device 26 is a monitor display, etc. An analysis screen is displayed on the display device 26, and the screen is updated in response to input / output operations via the input / output interface 25.

[0038] Each function of the simulation device 20 shown in FIG. 2 can be realized by reading a program (simulation program) from a main memory device or auxiliary memory device 24, such as RAM 22 or ROM 23, and executing it with CPU 21, thereby reading and writing data in RAM 22, etc., and operating input / output interface 25 and display device 26.

[0039] FIG. 3 shows a functional block diagram of the simulation device 20 of this embodiment.

[0040] 3, the simulation device 20 can have a receiving unit 31, a processing unit 32, and an output unit 33. These units are realized by software and hardware working together when the CPU executes a simulation method or program stored in advance, for example, as described below, in an information processing device such as a personal computer equipped with a CPU, a storage device, various interfaces, etc., which the simulation device 20 has.

[0041] The configuration of each part will be explained below. (A) Reception The reception unit 31 receives input of commands and data from the user related to the processing executed by the processing device 32. Examples of the reception unit 31 include a keyboard or mouse operated by the user to input commands, a communication device for inputting via a network, and a reading device for inputting from various storage media such as a CD-ROM or DVD-ROM. (B) Processing equipment The processing device 32 may include an adhesive force calculation unit 321 and a particle behavior analysis unit 322. The processing device may further include any other components as necessary, such as an initial setting unit and a parameter acquisition unit. (B-1) Adhesion force calculation section As described above, the simulation device 20 of this embodiment can calculate the adhesive force of particles and reflect the adhesive force when analyzing the behavior of multiple particles, thereby making it possible to appropriately evaluate phenomena such as particle aggregation and particle adhesion to wall surfaces.

[0042] As explained in "(1-2) Consideration of Adhesion Model" in "(1) About Adhesion Model," the adhesion calculation unit 321 can use the previously described adhesion model to calculate the adhesion force based on the contact radius at the contact surface between the particle and the contacted object. Specifically, using the previously described equations (1-2) and (1-3), the adhesion force can be calculated based on the contact radius at the contact surface between the particle and the contacted object. Here, because a model expressing adhesion using the adhesion model is used, the particle surface has sufficient adhesion. Therefore, it can be specified that the particle rolls without slipping in the tangential direction. This allows an appropriate adhesion force to be calculated without evaluating the adhesion force in the tangential direction.

[0043] However, to evaluate the tangential adhesive force more accurately, the adhesive force calculation unit can further calculate the tangential adhesive force of the contact surface between the particle and the contacted object based on the overlap amount between the particle and the contacted object. Specifically, the tangential adhesive force can be calculated using the above-mentioned formula (1-4). In this case, the particle behavior analysis unit (described later) will analyze the behavior of the powder by taking into account the tangential adhesive force calculated as described above in addition to the above-mentioned vertical and rotational adhesive forces calculated by the adhesive force calculation unit. (B-2) Particle behavior analysis section The particle behavior analysis unit 322 can analyze the behavior of a plurality of particles using the adhesive force calculated by the adhesive force calculation unit 321. Specifically, the particle behavior analysis unit 322 can perform calculations using the discrete element method to analyze the behavior of the particles. (B-3) Initial setting section The initial setting unit (not shown) initializes the positions of particles constituting the powder to be analyzed, and can set analysis conditions, such as the temperature of the area where the powder is placed as needed. Note that, for example, if the initial conditions are set in advance in a program used to analyze particle behavior in the particle behavior analysis unit 322, the initial setting unit may not be provided. (B-4) Parameter acquisition section A parameter acquisition unit (not shown) can acquire, for example, parameters related to the powder to be analyzed. The acquired parameters can include various parameters required for the analysis in addition to parameters related to the powder. The acquired parameters can be selected depending on the content of the analysis (simulation), so the specific types of parameters are not particularly limited. The acquired parameters include various parameters required for discrete element method calculations, and specifically include one or more types selected from, for example, particle diameter, number of particles, Young's modulus, calculation time step, Poisson's ratio, friction coefficient with a wall surface, friction coefficient between particles, rolling friction coefficient, density, etc.

[0044] The acquired parameters may be data stored in a database or the like, or may be experimental values ​​obtained by conducting experiments in advance. Furthermore, the acquired parameters may be calculated values ​​calculated by fitting experimental results using simulation or the like. Note that, for example, if the necessary parameters are pre-installed in a program or the like used when analyzing particle behavior in the particle behavior analysis unit 322, the parameter acquisition unit may not be provided. (C) Output section The output unit 33 may have a display or the like. The simulation results obtained by the particle behavior analysis unit 322 can be output to the output unit 33. The content of the simulation results to be output is not particularly limited, but for example, the positions of the particles can be output to the output unit 33 as an image in chronological order and displayed.

[0045] Here, an example of the results of an analysis of the behavior of powder carried out using the simulation device of this embodiment will be shown.

[0046] An example of a simulation result of the behavior of multiple particles in a cylindrical reactor 40 shown in Figure 4(A) is shown. Figure 4(B) is a view of the inside of the reactor 40 viewed along the central axis CA of the reactor 40 in Figure 4(A). Figure 4(C) is a side view of the reactor 40 in Figure 4(A), viewed from the inside of the reactor 40 perpendicular to the central axis CA. The reactor 40 has an inner diameter D of 200 mm and a longitudinal length L of 100 mm.

[0047] As shown in Figures 4(B) and 4(C), a plurality of particles 41 were placed in a cylindrical reactor 40. The behavior of the particles 41 was analyzed when the reactor was rotated in one direction around the rotation axis CA.

[0048] The particle conditions used in the analysis are summarized in Table 1.

[0049] [Table 1]

[0050] When the adhesive force model described above is used as the adhesive force model, that is, when analysis is performed using the simulation device of this embodiment, the analysis results are shown in Figures 5(A) to 5(C). Figure 5(A) shows the results 1 second after the start of rotation, Figure 5(B) shows the results 5 seconds after the start of rotation, and Figure 5(C) shows the results 10 seconds after the start of rotation.

[0051] 6(A) to 6(C) show the results of analysis performed in the same manner except that the liquid bridge model described above was used as the adhesive force model. Fig. 6(A) shows the results 1 second after the start of rotation, Fig. 6(B) shows the results 5 seconds after the start of rotation, and Fig. 6(C) shows the results 10 seconds after the start of rotation.

[0052] In FIGS. 5(A) to 5(C) and 6(A) to 6(C), the wall surface 401 of the reactor 40 is indicated by a dotted line.

[0053] It was confirmed that the simulation device of this embodiment can reproduce the occurrence of scaling due to the adhesion of particles 41 to the wall surface 401 as shown in Figures 5(B) and 5(C). It was also confirmed that the calculation results did not diverge and that the behavior of particles could be stably analyzed.

[0054] 6(A) to 6(C), which use a liquid bridge model as the adhesion force model, it was confirmed that the particles 41 are separated from the wall surface 401, and the adhesion force is a non-physical value. This is thought to be because, as mentioned above, in equation (1-1), which is the formula for calculating adhesion force, the adhesion force is proportional to the reciprocal of the distance between particle surfaces, and therefore diverges to infinity when the particle surfaces are in contact.

[0055] From the above results, it was confirmed that the use of the adhesive force model as the adhesion force model provides excellent calculation stability, can reproduce the scaling of the wall surface, and can obtain reasonable results. In other words, it was confirmed that the simulation device of this embodiment can provide a new simulation device that can analyze the behavior of powder taking into account the adhesive force of the particle surface.

[0056] The simulation device of this embodiment described above can simulate the behavior of powder containing a plurality of particles, and its applications are not particularly limited. For example, it can be suitably used to simulate the behavior of powder inside a rotating body such as a kiln. That is, the simulation device of this embodiment can also analyze the behavior of powder inside a rotating body. [Simulation method] Next, the simulation method of this embodiment will be described. The simulation method of this embodiment can be implemented using, for example, the simulation device already described. Therefore, some of the matters already described will not be described again.

[0057] The simulation method of the present embodiment relates to a simulation method for analyzing the behavior of powder containing a plurality of particles. The simulation method of the present embodiment can include the following steps.

[0058] An adhesion force calculation step for calculating the adhesion force of particles.

[0059] A particle behavior analysis step of analyzing the behavior of a plurality of particles using the adhesive force calculated in the adhesive force calculation step.

[0060] In the adhesive force calculation step, the adhesive force can be calculated based on the contact radius of the contact surface between the particle and the contacted object that comes into contact with the particle.

[0061] Each step will be explained below. (1) Adhesion force calculation process The simulation method of this embodiment calculates the adhesive force of particles and can reflect this adhesive force when analyzing the behavior of multiple particles, thereby enabling appropriate evaluation of phenomena such as particle aggregation and particle adhesion to wall surfaces.

[0062] Therefore, in the adhesive force calculation step, as explained in "(1-2) Consideration of Adhesion Model" in "(1) About Adhesion Model," the adhesive force can be calculated based on the contact radius at the contact surface between the particle and the object in contact with the particle using the previously described adhesive force model. Specifically, the adhesive force can be calculated based on the contact radius at the contact surface between the particle and the object in contact with the particle using the previously described equations (1-2) and (1-3). Here, since a model expressing adhesive force using the adhesive force model is used, the particle surface has sufficient adhesive force. Therefore, it can be specified that the particle rolls without slipping in the tangential direction. This allows an appropriate adhesive force to be calculated without evaluating the adhesive force in the tangential direction.

[0063] However, to evaluate the tangential adhesive force more accurately, the adhesive force calculation step can further calculate the tangential adhesive force of the contact surface between the particle and the contacted object based on the overlap amount between the particle and the contacted object. Specifically, the tangential adhesive force can be calculated using the above-mentioned formula (1-4). In this case, the particle behavior analysis step (described later) will analyze the behavior of the powder by taking into account the tangential adhesive force in addition to the above-mentioned vertical and rotational adhesive forces calculated in the adhesive force calculation step. (2) Particle behavior analysis process In the particle behavior analysis step, the behavior of the particles can be analyzed using the adhesive force calculated in the adhesive force calculation step. Specifically, the behavior of the particles can be analyzed by calculation using the discrete element method. (3) Initial setting process The simulation method of this embodiment may further include, for example, an initial setting step. In the initial setting step, the positions of the particles constituting the powder to be analyzed are initialized, and analysis conditions, such as the temperature of the area where the powder is placed, can be set as needed. Note that, for example, if the initial conditions are set in advance in a program or the like used to analyze the behavior of the particles in the particle behavior analysis step, the initial setting step may not be performed. (4) Parameter acquisition process The simulation method of this embodiment may further include, for example, a parameter acquisition step. In the parameter acquisition step, for example, parameters related to the powder to be analyzed may be acquired. The acquired parameters may include various parameters required for the analysis in addition to parameters related to the powder. The acquired parameters can be selected depending on the content of the analysis (simulation), and therefore their specific types are not particularly limited. The acquired parameters include various parameters required for discrete element method calculations, and specifically include one or more types selected from, for example, particle diameter, number of particles, Young's modulus, calculation time step, Poisson's ratio, friction coefficient with a wall surface, friction coefficient between particles, rolling friction coefficient, density, etc.

[0064] The acquired parameters may be data stored in a database or the like, or may be experimental values ​​obtained by conducting experiments in advance. Furthermore, the acquired parameters may be calculated values ​​calculated by fitting experimental results using simulation or the like. Note that, for example, if the necessary parameters are pre-installed in a program or the like used to analyze particle behavior in the particle behavior analysis step, the parameter acquisition step may not be performed. (5) Output process The simulation method of this embodiment may further include, for example, an output step. In the output step, for example, the simulation results obtained in the particle behavior analysis step may be output to an output unit. The content of the simulation results to be output is not particularly limited, but for example, the positions of the particles may be output to the output unit as an image in chronological order and displayed.

[0065] According to the simulation method of the present embodiment described above, the behavior of powder can be analyzed taking into account adhesive forces, which have not been considered in the past. This allows for appropriate evaluation of phenomena such as particle aggregation and particle adhesion to wall surfaces.

[0066] Therefore, the simulation method of this embodiment can provide a new simulation method that can analyze the behavior of powder taking into account the adhesive force of the particle surface. [program] Next, the program of this embodiment will be described.

[0067] The program of this embodiment relates to a program for analyzing the behavior of powder containing a plurality of particles, and can cause a computer to function as an adhesive force calculation unit and a particle behavior analysis unit described below.

[0068] The adhesive force calculation unit can calculate the adhesive force of the particles.

[0069] The particle behavior analysis unit can analyze the behavior of a plurality of particles using the adhesive force calculated by the adhesive force calculation unit.

[0070] The adhesive force calculation unit can then calculate the adhesive force based on the contact radius of the contact surface between the particle and the contacted object that comes into contact with the particle.

[0071] The adhesive force calculation unit can also calculate the adhesive force in the tangential direction of the contact surface between the particle and the contacted object based on the amount of overlap between the particle and the contacted object.

[0072] The program of this embodiment can be stored in various storage media such as the RAM, ROM, and other main or auxiliary storage devices of the simulation device. By loading the program and executing it with the CPU, data can be read and written from and to the RAM, and the input / output interface and display device can be operated and executed. Therefore, the matters already described for the simulation device will not be described here.

[0073] The program of the present embodiment described above may be stored on a computer connected to a network such as the Internet and provided by being downloaded via the network. The program of the present embodiment may also be configured to be provided and distributed via a network such as the Internet.

[0074] The program of this embodiment may be distributed in a state stored on an optical disk such as a CD-ROM or a recording medium such as a semiconductor memory.

[0075] The program of this embodiment described above allows the behavior of powder to be analyzed taking into account adhesive forces, which have not been considered in the past. This allows for appropriate evaluation of phenomena such as particle aggregation and adhesion to wall surfaces.

[0076] Therefore, according to the program of this embodiment, a new program can be provided that can analyze the behavior of powder taking into account the adhesive force of the particle surface.

[0077] 2. Second embodiment Next, we investigated a new simulation device that can analyze the behavior of powders, taking into account the coarse graining and adhesive force of particle groups consisting of multiple particles.

[0078] [Simulation device] (1) Coarse-graining of particles and parameters used to calculate the particle behavior of coarse-grained particles (1-1) Coarse graining of particles Before describing the details of the simulation device of this embodiment, the following describes a method for coarse-graining a particle group consisting of multiple particles, which can be used in the simulation device of this embodiment, and a method for calculating parameters related to the coarse-grained particles, which are coarse-grained particles.

[0079] In discrete element method calculations, the greater the number of particles handled, the greater the calculation load. For this reason, when analyzing the behavior of powder on a large scale, such as in a factory plant, the amount of calculation becomes enormous, making it difficult to carry out the calculations in reality.

[0080] Therefore, when analyzing the behavior of powder containing a large number of particles, in order to reduce the amount of calculation, a coarse-graining technique is required, in which a particle group 71 consisting of multiple particles as shown in Figure 7(A) is treated as a single large particle, a coarse-grained particle 81, as shown in Figure 8(A).

[0081] However, since the specific surface area of ​​individual particles before coarse-graining and the coarse-grained particles differ, some parameters required for calculations will change. Therefore, it is necessary to determine the parameters of the coarse-grained particles appropriately.

[0082] (1-2) Parameters used to calculate the particle behavior of coarse-grained particles In the calculations, two models were used: a case in which a particle group 71 made up of multiple particles before coarse-graining, as shown in Fig. 7(A), collides with a wall surface 72, and a case in which a coarse-grained particle 81, as shown in Fig. 8(A), collides with a wall surface 72. In the following explanation, a method for determining parameters related to coarse-grained particles will be described using the case in which a particle collides with a wall surface as an example, but the same discussion applies to the case in which particles collide with each other, so explanation will be omitted.

[0083] As shown in FIG. 7(A), a particle group 71 consisting of a plurality of particles is arranged in a cubic shape, with two particles in each of the vertical, horizontal, and height directions, for a total of two particles. 3 As will be described later, when these eight particles are grouped together to form one coarse-grained particle, the number of particles aligned in the direction of one side, i.e., 2, is taken as the coarse-graining magnification.

[0084] When a particle group 71 including a plurality of particles 71A and 71B shown in FIG. 7(A) collides with a wall surface 72, a particle 71A located on the wall surface 72 side of the particle group 71 receives a force from the wall surface or an external particle as shown in FIG. 7(B). wAs shown in FIG. 7B, the overlap amount of the particle 71A with the wall surface 72 or the outer particle is δ w The overlap amount of the particle 71B with the adjacent particle 71A is δ p 7(B) is a diagram showing the particle group 71 colliding with the wall surface 72 as viewed from the side.

[0085] In this case, the magnitude of the force applied to the particle group 71 can be expressed by the following formula (2-1).

[0086] In equation (2-1), α is the coarse-graining magnification, which means the number of particles arranged in one direction when particle group 71 is treated as one coarse-grained particle, as described above. When particle group 71 shown in FIG. 7A is treated as one coarse-grained particle 81 shown in FIG. 8A, α=2.

[0087] Also, m is the mass of each particle 71A, 71B, a G is the acceleration of the center of gravity of the particle swarm 71, and η w are viscosity coefficients calculated from the repulsion coefficients between the wall surface 72 or the external particle and the particle 71A. Since the contact force between particles is canceled out according to the law of action and reaction, the force F that particle 71B, which is not in direct contact with the wall surface 72, receives from the adjacent particle 71A is p does not appear in equation (2-1).

[0088]

number

[0089]

number

[0090] Next, as shown in Fig. 8(A), let us assume that particle group 71 consisting of eight particles shown in Fig. 7(A) is one coarse-grained particle 81. In this case, when coarse-grained particle 81 collides with wall surface 72, the force acting on coarse-grained particle 81 can be expressed by the following equation (2-2).

[0091] F in formula (2-2) cw is the force that the coarse-grained particle 81 receives from the wall surface 72 or an external particle, as shown in FIG. 8(B). cw is the amount of overlap between the coarse-grained particle 81 and the wall 72 or the outer particle, and η cw and σ respectively represent the viscosity coefficients calculated from the restitution coefficients between the coarse-grained particle 81 and the wall surface 72 or .... Note that Fig. 8(B) is a side view of the state when the coarse-grained particle 81 collides with the wall surface 72.

[0092]

number

[0093] As described above, coarse-graining is performed to reduce the amount of calculation in the discrete element method calculation. Therefore, the calculation results for the coarse-grained particles 81 and the calculation results for the particle group 71 before being converted into the coarse-grained particles 81 will match.

[0094] Therefore, from the previously described equation (2-1) calculated for particle group 71 and the previously described equation (2-2) calculated for coarse-grained particles 81 obtained by coarsening the particle group, the following equations (2-3) and (2-4) are derived, which indicate that the corresponding parameters are the same.

[0095]

number

[0096]

number

[0097] In addition, the Hertz-Mindlin contact model is used to calculate the particle overlap amount δ w , δ p , δ cw Using the above, the force applied to each particle can be expressed as in the following equations (2-5) to (2-7). w is the spring coefficient between the particle 11A and the wall surface 12 or the external particle, K p is the spring coefficient of the inner particle of particle group 71, K cw means the spring constant between the coarse-grained particle 81 and the wall surface 72 or the external particle, respectively.

[0098]

number

[0099]

number

[0100]

number

[0101] Then, the relationship in the following equation (2-8) can be derived from equations (2-3), (2-5), and (2-7).

[0102]

number

[0103]

number

[0104]

number

[0105] If the centers of gravity of the particle group 71 before coarse-graining and the coarse-grained particles 81 coincide with each other, the relationship of the following formula (2-11) is satisfied.

[0106]

number

[0107] Therefore, K r By appropriately setting the overlap amount δ between the wall surface 72 of the coarse-grained particle 81 and the outer particle, CW It can also be seen that the amount of overlap between particles constituting the particle group 71 before coarse graining can be calculated from the above.

[0108] And K r can be calculated by a characteristic equation that uses the relationship between the elastic energy of the particle group 71 before coarse-graining during a collision and the elastic energy of the coarse-grained particles 81. Specifically, for example, assuming that the elastic energy of the entire particle group 71 before coarse-graining is equal to the elastic energy of the entire coarse-grained particles, a characteristic equation is created to obtain K r can be calculated.

[0109] The elastic energy of particle group 71 and the elastic energy of the coarse-grained particles during collision with wall surface 72 can be calculated by integrating equations (2-5) to (2-7), which represent the forces applied to particles 71A and 71B that make up the particle group 71 described above and the forces applied to the coarse-grained particles, over the overlap distance.

[0110] Therefore, the following formula (2-12) is obtained by using the elastic energy of the entire particle group 71 before coarse-graining and the elastic energy of the entire coarse-grained particles:

[0111]

number

[0112]

number

[0113] Equation (2-13) is the vertical direction K r As is clear from the definition of equation (2-9), K r is a parameter related to the amount of overlap between the coarse-grained particles and the particles that make up the particle group 71 before coarse-graining, and is a parameter that governs the behavior of the coarse-grained particles. r By calculating in advance, it becomes possible to calculate the overlap amount of the pre-coarse-grained particles from the overlap amount of the coarse-grained particles, calculate parameters for the coarse-grained particles, and calculate the behavior of the coarse-grained particles.

[0114] Up to this point, the explanation has been given using the equation of motion in the direction perpendicular to the wall surface 72, but the same can be said for the equation of motion in the tangential direction and the equation of motion of rotation.

[0115] Specifically, the equation of motion in the tangential direction can be expressed by equation (2-14).

[0116] In this case, as shown in equation (2-15), K r When setting δ w , δ p can be expressed as equations (2-16) and (2-17), and if we assume that the elastic energy of the particle group before coarse-graining is equal to the elastic energy of the coarse-grained particles, we obtain equation (2-18). By transforming equation (2-18), we obtain equation (2-19), which is the characteristic equation in the tangential direction. However, a linear spring model was used for the tangential contact model. In this way, the formula for calculating elastic energy differs depending on the contact model, but the elastic energy can be calculated appropriately by changing the characteristic equation as necessary.

[0117]

number

[0118]

number

[0119]

number

[0120]

number

[0121]

number

[0122]

number

[0123] (1-3) Parameters related to the adhesive force of coarse-grained particles The vertical K r When considering adhesive force, the characteristic equation of requires an adhesive force term, which is expressed by the following equation (2-20-1). A in equation (2-20-1) p,n represents the adhesive force coefficient of the internal particles of the particle group before coarse-graining. A in Equation (2-20-1) r is the adhesion coefficient A of the particles that make up the particle group before coarse-graining w,n and the adhesion coefficient A of the coarse-grained particles cw Therefore, it is expressed by equation (2-20-2).

[0124]

number

[0125]

number

[0126] Equation (2-20-1) is the overlap amount δ of the coarse-grained particles. cw Since the equation is a function of , it is necessary to solve the equation in parallel with the calculation using the discrete element method.

[0127] However, solving the characteristic equation simultaneously with calculations using the discrete element method is difficult from the viewpoint of calculation load. Therefore, as an approximate solution, equation (2-20-1) is divided into equations (2-21) and (2-22). Here, equations (2-21) and (2-22) can be solved independently of the overlap amount of the coarse-grained particles. Here, equation (2-21) is the characteristic equation used in this embodiment, and the same characteristic parameters as in the previously described method can be used. On the other hand, with regard to the adhesive force, the solution A of equation (2-22) r and the adhesion coefficient A of the particles that make up the particle group before coarse graining w,n Using the above equation (2-20-2), the adhesive force coefficient A of the coarse-grained particles is calculated. cw That is, the adhesive force of the coarse-grained particles can be calculated using a solution to a characteristic equation that uses the relationship between the adhesive force of the particles that make up the particle group before coarse-graining and the adhesive force of the coarse-grained particles.

[0128]

number

[0129]

number

[0130] Here, the adhesive force before and after coarse graining has been used as an example. However, the same applies to parameters other than adhesive force, and the solution K r , A r The coarse-grained parameters can be calculated using the characteristic equation. For example, the restitution coefficient, friction coefficient, and rolling friction coefficient can also be calculated using the characteristic equation. Note that these coefficients can be adjusted depending on the model applied to the calculation, and can be calculated and converted using the characteristic equation as described above.

[0131] (2) Simulation equipment The simulation device of this embodiment is a simulation device for analyzing the behavior of powder containing multiple particles, and can further have the following first parameter acquisition unit and second parameter acquisition unit in addition to the simulation device described in the first embodiment.

[0132] The first parameter acquisition unit can acquire first parameters including parameters related to powder having a plurality of particles.

[0133] The second parameter calculation unit can calculate the second parameter, which is a parameter for a coarse-grained particle when a particle group made up of a plurality of particles is coarse-grained into one coarse-grained particle.

[0134] Then, the particle behavior analysis unit can analyze the behavior of the coarse-grained particles based on the first parameter and the second parameter.

[0135] Furthermore, the second parameter calculation unit can calculate the second parameter using a solution of a characteristic equation that uses the relationship between the adhesive force of the particles that make up the particle group and the adhesive force of the coarse-grained particles.

[0136] 9 shows a functional block diagram of a simulation device 90 of this embodiment. Note that the hardware can be configured in the same way as the simulation device of the first embodiment, so a description thereof will be omitted.

[0137] 9, the simulation device 90 can have a receiving unit 91, a processing unit 92, and an output unit 93. These units are realized by software and hardware working together when the CPU executes a simulation method or program stored in advance, for example, as described below, in an information processing device such as a personal computer equipped with a CPU, a storage device, various interfaces, etc., which the simulation device 90 has.

[0138] The configuration of each part will be explained below.

[0139] (A) Reception The reception unit 91 receives input of commands and data from the user related to the processing executed by the processing device 92. Examples of the reception unit 91 include a keyboard or mouse operated by the user to input commands, a communication device for inputting via a network, and a reading device for inputting from various storage media such as a CD-ROM or DVD-ROM.

[0140] (B) Processing equipment The processing device 92 can have a first parameter acquisition unit 921, a second parameter calculation unit 922, and a particle behavior analysis unit 923. The processing device can further have any optional components as needed, such as an initial setting unit.

[0141] (B-1) First parameter acquisition unit The first parameter acquisition unit 921 can acquire first parameters including, for example, parameters related to the powder to be analyzed. The first parameters can also include various parameters required for analysis in addition to parameters related to the powder. The first parameter acquisition unit corresponds to the parameter acquisition unit in the first embodiment. The first parameters can be selected depending on the content of the analysis (simulation), so the specific type of the first parameters is not particularly limited. Examples of the first parameters include various parameters required for discrete element method calculations, and specifically include one or more types selected from, for example, particle diameter, number of particles, Young's modulus, calculation time step, Poisson's ratio, friction coefficient with a wall surface, friction coefficient between particles, rolling friction coefficient, density, etc.

[0142] The first parameter may be data stored in a database or the like, or may be an experimental value obtained by conducting an experiment in advance. Alternatively, the first parameter may be a calculated value calculated by fitting the experimental results using a simulation or the like.

[0143] (B-2) Second parameter calculation unit As described above, in the simulation device 90 of this embodiment, in order to reduce the amount of calculation, a particle group consisting of multiple particles in a powder is coarse-grained into a single coarse-grained particle, and calculations can be performed with a reduced number of particles. However, the coarse-grained particle has various parameters, such as mass, that are different from the individual particles that make up the particle group before coarse-graining. Therefore, it is necessary to calculate and set parameters required for calculations for the coarse-grained particle.

[0144] As explained in "(1) Parameters used for calculating the particle behavior of the coarse-grained particles and the particle coarse-grained particles," the second parameter calculation unit 922 calculates K , which is a solution of the characteristic equation derived using the relationship between the elastic energy of the particle group before coarse-graining and the elastic energy of the coarse-grained particles. r And the aforementioned A r The second parameter can be calculated using:

[0145] Specifically, for example, assuming that the elastic energy of the entire particle group 71 before coarse-graining is equal to the elastic energy of the entire coarse-grained particles, the above-mentioned vertical K r The characteristic equations of the particle group 71 before coarse-graining and the coarse-grained particles can be derived as follows: r From the derived equations (2-13), (2-21) and (2-22), the vertical K r , A r Then, the vertical direction K, which is the solution of the characteristic equation shown in the above equation (2-13), can be calculated. r and A, which is the solution of equation (2-22). r The second parameter can be calculated using the above equation (2-19). r Using the characteristic equation of r can be calculated, and the tangential direction K r The second parameter can also be calculated using

[0146] As mentioned above, K r , Ar is a parameter that governs the behavior of coarse-grained particles, and K r , A r By using this, various parameters related to the behavior of coarse-grained particles can be calculated.

[0147] The type of second parameter used in the particle behavior analysis unit described later can be selected depending on the content of the analysis, and is not particularly limited. For example, the second parameter can include the adhesive force of the coarse-grained particles. In this case, the second parameter calculation unit calculates the solution K of the characteristic equation described above from the adhesive force of the particles calculated by the adhesive force calculation unit described in the first embodiment. r , A r The parameters relating to the adhesive force of the coarse-grained particles can be calculated using the following equation: The adhesive force calculation unit described in the first embodiment may be provided separately from the second parameter calculation unit, or may be included in the second parameter calculation unit.

[0148] (B-3) Particle behavior analysis section As with the particle behavior analysis unit described in the first embodiment, the particle behavior analysis unit 923 can analyze the behavior of multiple particles using the adhesive force calculated by the adhesive force calculation unit, specifically, the adhesive force of the coarse-grained particles calculated by the second parameter calculation unit. The particle behavior analysis unit 923 can analyze the behavior of the coarse-grained particles using the first parameter acquired by the first parameter acquisition unit 921 and the second parameter calculated by the second parameter calculation unit 922. Specifically, the behavior of the coarse-grained particles can be analyzed by calculation using the discrete element method. By analyzing the behavior of the coarse-grained particles, the behavior of the powder can be analyzed.

[0149] The behavior referred to here includes not only changes in position due to the movement of the coarse-grained particles, but also changes in state such as temperature changes.

[0150] (B-4) Initial setting section An initial setting unit (not shown) initializes the positions of particles constituting the powder to be analyzed, and can set analysis conditions, such as the temperature of the area where the powder is placed as needed. Note that, for example, if the initial conditions are set in advance in a program or the like used when analyzing the behavior of coarse-grained particles in the particle behavior analysis unit 923, or if the initial conditions are acquired by the first parameter acquisition unit 921, the initial setting unit may not be provided.

[0151] (C) Output section The output unit 93 may have a display or the like. The simulation results obtained by the particle behavior analysis unit 923 can be output to the output unit 93. The content of the simulation results to be output is not particularly limited, but for example, the positions of coarse-grained particles can be output to the output unit 93 as an image in chronological order and displayed.

[0152] The simulation device of this embodiment described above can simulate the behavior of powder containing a plurality of particles, and its applications are not particularly limited. For example, it can be suitably used to simulate the behavior of powder inside a rotating body such as a kiln. That is, the simulation device of this embodiment can also analyze the behavior of powder inside a rotating body.

[0153] According to the simulation device of the present embodiment described above, the amount of calculation can be reduced by treating a particle group consisting of multiple particles as a single coarse-grained particle. Therefore, the amount of calculation can be reduced and calculations can be performed efficiently even for large-scale powder behavior such as in a factory plant.

[0154] Then, the parameter of the coarse-grained particles is the previously mentioned parameter K r , A r Since the calculation is performed using the formula, the calculation can be performed with high accuracy.

[0155] [Simulation method] Next, the simulation method of this embodiment will be described. The simulation method of this embodiment can be implemented using, for example, the simulation device already described. Therefore, some of the matters already described will not be described again.

[0156] The simulation method of this embodiment relates to a simulation method for analyzing the behavior of powder containing a plurality of particles. The simulation method of this embodiment can be carried out according to the flowchart shown in Fig. 10, and can further include the following first parameter acquisition step and second parameter acquisition step in addition to the simulation method described in the first embodiment.

[0157] The first parameter acquisition step can acquire first parameters including parameters related to powder (S1).

[0158] In the second parameter calculation step, when a particle group made up of a plurality of particles is coarse-grained into one coarse-grained particle, the second parameter, which is a parameter for the coarse-grained particle, can be calculated (S2).

[0159] Then, in the particle behavior analysis step, the behavior of the coarse-grained particles can be analyzed based on the first parameter and the second parameter (S3).

[0160] In the second parameter calculation step (S2), the second parameter can be calculated using a solution to a characteristic equation that uses the relationship between the adhesive force of the particles that make up the particle group before coarse-graining and the adhesive force of the coarse-grained particles.

[0161] Each step will be explained below. (1) First parameter acquisition step (S1) In the first parameter acquisition step (S1), first parameters including parameters related to the powder to be analyzed can be acquired. When the above-described simulation device is used, the first parameter acquisition step can be performed, for example, in the first parameter acquisition unit 921. The first parameter acquisition step corresponds to the parameter acquisition step in the first embodiment.

[0162] The first parameter can be selected depending on the content of the analysis, and therefore the specific type is not particularly limited. Examples of the first parameter include various parameters required for discrete element method calculations. Specific examples of the first parameter have already been described in the simulation device, so a description thereof will be omitted here.

[0163] The first parameter may be data stored in a database or the like, or may be an experimental value obtained by conducting an experiment in advance. Alternatively, the first parameter may be a calculated value calculated by fitting the experimental results using a simulation or the like.

[0164] (2) Second parameter calculation step (S2) In the simulation method of this embodiment, in order to reduce the amount of calculation, a particle group consisting of multiple particles contained in the powder is coarse-grained into a single coarse-grained particle, and calculations can be performed with a reduced number of particles.

[0165] Therefore, in the second parameter calculation step (S2), as explained in "(1) Parameters used for calculating the particle behavior of the coarse-grained particles and the particle coarse-grained particles", K is the solution of the characteristic equation derived using the relationship between the elastic energy of the particle group before coarse-graining and the elastic energy of the coarse-grained particles. r And the aforementioned A r Specifically, for example, assuming that the elastic energy and adhesive energy of the entire particle group 71 before coarse-graining are equal to the elastic energy and adhesive energy of the entire coarse-grained particles, the above-mentioned vertical K r , A r The characteristic equations of (2-13), (2-21) and (2-22) are derived, and the vertical K r , A r Then, the vertical direction K, which is the solution of the characteristic equation shown in the above equation (2-13), can be calculated. r and A, which is the solution of equation (2-22). rThe second parameter can be calculated using the above equation (2-19). r Using the characteristic equation of r can be calculated, and the tangential direction K r The second parameter can also be calculated using

[0166] As mentioned above, K r , A r is a parameter that governs the behavior of coarse-grained particles, and K r , A r By using this, various parameters related to the behavior of coarse-grained particles can be calculated.

[0167] When the above-described simulation device is used, the second parameter calculation step can be performed in the second parameter calculation unit 922, for example.

[0168] The type of second parameter used in the particle behavior analysis step described later can be selected depending on the content of the analysis, and is not particularly limited. For example, the second parameter can include the adhesive force of the coarse-grained particles. In this case, in the second parameter calculation step, the solution K of the characteristic equation described above is calculated from the adhesive force of the particles calculated in the adhesive force calculation step described in the first embodiment. r , A r Using this, a parameter related to the adhesive force of the coarse-grained particles can be calculated. Note that although the adhesive force calculation step is not shown in Fig. 10, the adhesive force calculation step may be performed separately from the second parameter calculation step, or may be performed within the second parameter calculation step. When the adhesive force calculation step is performed separately from the second parameter calculation step, the timing of the step is not particularly limited, and it may be performed, for example, after the first parameter acquisition step or before the second parameter calculation step.

[0169] (3) Particle behavior analysis process (S3) In the particle behavior analysis step (S3), similar to the particle behavior analysis step described in the first embodiment, the behavior of multiple particles can be analyzed using the adhesive force calculated in the adhesive force calculation step, specifically, the adhesive force of the coarse-grained particles calculated in the second parameter calculation step. In the particle behavior analysis step, the behavior of the coarse-grained particles can be analyzed using the first parameter obtained in the first parameter acquisition step (S1) and the second parameter calculated in the second parameter calculation step (S2). Specifically, calculations can be performed using the discrete element method to analyze the behavior of the coarse-grained particles. By analyzing the behavior of the coarse-grained particles, the behavior of the powder can be analyzed.

[0170] The behavior referred to here includes not only changes in position due to the movement of the coarse-grained particles, but also changes in state such as temperature changes.

[0171] (4) Initial setting process The simulation method of this embodiment may further include, for example, an initial setting step. In the initial setting step, the positions of the particles constituting the powder to be analyzed are initialized, and analysis conditions, such as the temperature of the area where the powder is placed, can be set as needed. Note that the initial setting step may not be performed, for example, if the initial conditions are set in advance in a program or the like used to analyze the behavior of the coarse-grained particles in the particle behavior analysis step, or if the initial conditions are acquired in the first parameter acquisition step.

[0172] (5) Output process The simulation method of this embodiment can further include, for example, an output step. In the output step, for example, the simulation results obtained in the particle behavior analysis step (S3) can be output to an output unit. The content of the simulation results to be output is not particularly limited, but for example, the positions of coarse-grained particles can be output to the output unit in time series as an image and displayed.

[0173] According to the simulation method of the present embodiment described above, the amount of calculation can be reduced by treating a particle group consisting of multiple particles as a single coarse-grained particle. Therefore, the amount of calculation can be reduced and calculations can be performed efficiently even for large-scale powder behavior such as in a factory plant.

[0174] Then, the parameter of the coarse-grained particles is the previously mentioned parameter K r , A r Since the calculation is performed using the formula, the calculation can be performed with high accuracy.

[0175] [program] Next, the program of this embodiment will be described.

[0176] The program of this embodiment relates to a program for analyzing the behavior of powder containing a plurality of particles, and can cause a computer to function as the following units. Specifically, the program of this embodiment can cause a computer to function so that it further has the following first parameter acquisition unit and second parameter acquisition unit in addition to the units described in the program of the first embodiment.

[0177] The first parameter acquisition unit can acquire first parameters including parameters related to powder.

[0178] The second parameter acquisition unit can calculate the second parameter, which is a parameter for a coarse-grained particle when a particle group made up of a plurality of particles is coarse-grained into one coarse-grained particle.

[0179] Then, the particle behavior analysis unit can analyze the behavior of the coarse-grained particles based on the first parameter and the second parameter.

[0180] The second parameter calculation unit can calculate the second parameter using a solution to a characteristic equation that uses the relationship between the adhesive force of particles that make up the particle group before coarse-graining and the adhesive force of the coarse-grained particles.

[0181] The program of this embodiment can be stored in various storage media such as the RAM, ROM, and other main or auxiliary storage devices of the simulation device. By loading the program and executing it with the CPU, data can be read and written from and to the RAM, and the input / output interface and display device can be operated and executed. Therefore, the matters already described for the simulation device will not be described here.

[0182] The program of the present embodiment described above may be stored on a computer connected to a network such as the Internet and provided by being downloaded via the network. The program of the present embodiment may also be configured to be provided and distributed via a network such as the Internet.

[0183] The program of this embodiment may be distributed in a state stored on an optical disk such as a CD-ROM or a recording medium such as a semiconductor memory.

[0184] According to the program of the present embodiment described above, the amount of calculation can be reduced by treating a particle group consisting of multiple particles as a single coarse-grained particle, which allows for efficient calculations even when analyzing the behavior of large-scale powders, such as those used in factories.

[0185] Then, the parameter of the coarse-grained particles is the previously mentioned parameter K r , A r Since the calculation is performed using the formula, the calculation can be performed with high accuracy. [Explanation of symbols]

[0186] 11, 71A, 71B particles 12, 72 Wall surface (object to be touched) 20, 90 Simulation equipment 321 Adhesion force calculation unit 322, 923 Particle Behavior Analysis Department 921 First parameter acquisition unit 922 Second parameter calculation unit S1 First parameter acquisition process S2 Second parameter calculation process S3 Particle behavior analysis process 71 Particle group 81 Coarse-grained particles

Claims

1. A simulation device for analyzing the behavior of powder containing a plurality of particles, an adhesive force calculation unit that calculates the adhesive force of the particles; a particle behavior analysis unit that analyzes the behavior of the plurality of particles using the adhesive force calculated by the adhesive force calculation unit, The adhesion force calculation unit calculates the adhesion force based on the contact radius at the contact surface between the particle and the contacted object, and further calculates the adhesion force in the tangential direction of the contact surface between the particle and the contacted object based on the amount of overlap between the particle and the contacted object.

2. A simulation method for analyzing behavior of a powder containing a plurality of particles, comprising: an adhesive force calculation step of calculating the adhesive force of the particles; a particle behavior analysis step of analyzing the behavior of the plurality of particles by using the adhesive force calculated in the adhesive force calculation step, In the adhesion force calculation process, the adhesion force is calculated based on the contact radius at the contact surface between the particle and the contacted object, and further, the adhesion force in the tangent direction of the contact surface between the particle and the contacted object is calculated based on the amount of overlap between the particle and the contacted object.

3. A program for analyzing the behavior of a powder containing a plurality of particles, Computer, an adhesive force calculation unit that calculates the adhesive force of the particles; a particle behavior analysis unit that analyzes the behavior of the plurality of particles using the adhesive force calculated by the adhesive force calculation unit; The adhesion force calculation unit is a program that calculates the adhesion force based on the contact radius at the contact surface between the particle and the contacted object, and further calculates the adhesion force in the tangent direction of the contact surface between the particle and the contacted object based on the amount of overlap between the particle and the contacted object.

4. a first parameter acquisition unit that acquires first parameters including parameters related to the powder including the plurality of particles; and a second parameter calculation unit that calculates a second parameter, which is a parameter for a coarse-grained particle when a particle group composed of a plurality of the particles is coarse-grained into a single coarse-grained particle. the particle behavior analysis unit analyzes the behavior of the coarse-grained particles based on the first parameter and the second parameter; The simulation device according to claim 1 , wherein the second parameter calculation unit calculates the second parameter using a solution of a characteristic equation that uses a relationship between the adhesive force of the particle and the adhesive force of the coarse-grained particle.

5. a first parameter acquisition step of acquiring first parameters including parameters related to the powder including the plurality of particles; and a second parameter calculation step of calculating a second parameter, which is a parameter for a coarse-grained particle when a particle group composed of a plurality of the particles is coarse-grained into a single coarse-grained particle. the particle behavior analyzing step analyzes behavior of the coarse-grained particles based on the first parameter and the second parameter; The simulation method according to claim 2 , wherein the second parameter calculation step calculates the second parameter using a solution of a characteristic equation that uses a relationship between the adhesive force of the particle and the adhesive force of the coarse-grained particle.

6. The computer a first parameter acquisition unit that acquires first parameters including parameters related to the powder including the plurality of particles; a second parameter calculation unit that calculates a second parameter, which is a parameter for a coarse-grained particle when a particle group composed of a plurality of the particles is coarse-grained into a single coarse-grained particle, the particle behavior analysis unit analyzes the behavior of the coarse-grained particles based on the first parameter and the second parameter; The program according to claim 3 , wherein the second parameter calculation unit calculates the second parameter using a solution of a characteristic equation that uses a relationship between the adhesive force of the particle and the adhesive force of the coarse-grained particle.

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