JP4899607B2 - Particle behavior simulation apparatus, particle behavior simulation method, and computer program - Google Patents

Description

  The present invention relates to a particle behavior simulation apparatus, a particle behavior simulation method, and a computer program for simulating the behavior of particles having different particle sizes, and particularly when a plurality of interactions acting between particles having different particle sizes need to be considered. The present invention relates to a particle behavior simulation apparatus, a particle behavior simulation method, and a computer program for simulating the behavior of a two-component developer in a development process in an electrophotographic image forming process, for example.

  In recent years, with the rapid progress of computer technology, many behavioral simulation methods for particles such as powders and granules that have been considered to have an excessive processing load have been put into practical use. For example, a simulation method using a method called an individual element method or a discrete element method (hereinafter referred to as DEM) is widely used, and powder behavior analysis using a particle behavior simulator based on DEM is performed. Opportunities have increased.

  However, the particle behavior simulation based on DEM uses a single particle as a calculation unit, so the calculation processing load is very large, and there is an upper limit on the number of particles that can be analyzed. Further, for example, when simulating the behavior of a two-component developer in a laser printer or the like, in addition to the interparticle contact force, external force such as magnetic force, electric force, and interparticle interaction force acting on the developer, toner and carrier particles It is necessary to consider the diameter ratio, and the processing load further increases. Therefore, there is a problem that it is very difficult to accurately execute a simulation at a sufficient particle concentration close to mounting.

Therefore, for example, in Patent Document 1, an effective distance is determined for each of a plurality of interactions depending on the distance between particles, for example, a contact force between particles, a magnetic force, and the like, and an optimum divided region is determined according to the effective distance. Disclosed is a particle behavior calculation method for determining the size of. In Patent Document 1, since the optimum size of the divided region is determined according to the effective distance, unnecessary distance calculation can be minimized, and calculation processing time can be shortened.
JP 2005-122354 A

  In Patent Document 1, since the size of the divided region, that is, the particle search range is determined between the maximum value and the minimum value of the effective distance, unnecessary distance calculation can be omitted for a predetermined interaction. . However, it is difficult to specify an appropriate particle search range for all interactions, and there is still a need to perform unnecessary distance calculations for a given interaction.

  In addition, it is only possible to determine which particle search range is optimal based on the result of simulation calculation, and although the effect of shortening the calculation processing time can be surely obtained, as to whether or not it is the minimum There is no guarantee. In order to optimize the particle search range, the size of the divided cell (region) needs to be changed and it is necessary to perform simulation calculations multiple times, and it is difficult to greatly reduce the total simulation calculation time. Is the current situation.

  Further, when particles having two types of sizes, large and small, coexist, the effective distance varies greatly depending on the particle concentration and particle size ratio in the space where the particles are mixed. In other words, if the particle size ratio is large, an unnecessary distance calculation always occurs even if simulation is performed for one particle search range, so simulation is performed using multiple particle search ranges of different sizes. On the contrary, the calculation processing efficiency may be higher and the calculation processing time may be shortened. Further, even when the simulation calculation is performed without changing the size of the particle search range, it is necessary to optimize the size of the particle search range according to the volume concentration of the mixed particles.

  The present invention has been made in view of such circumstances, and when simulating the behavior of powder using a DEM, the calculation is performed by optimizing the particle search range and simulating according to the particle diameter ratio and particle concentration. It is an object of the present invention to provide a particle behavior simulation apparatus, a particle behavior simulation method, and a computer program that reduce processing load and realize high-speed simulation.

  In order to achieve the above object, the particle behavior simulation apparatus according to the first aspect of the present invention provides a calculation target region for calculating the behavior of particles based on a plurality of interaction forces depending on the distance between particles having different particle diameters. In the apparatus for simulating the behavior of the particles contained in the calculation target area, the particles having the largest particle diameter in the calculation target area are sequentially set as the target particles, and the predetermined size is included in the target particles. Particle search means for searching for particles that are in contact with each other and particles that may be in contact with each other in a small area, means for storing information on the searched particles in the storage means, and calculating the integrated displacement of the particle of interest And a means for judging whether or not the integrated displacement exceeds a predetermined value, and the particle search means is used only when it is judged by the judgment means that the predetermined value has been exceeded. If it is determined that, characterized in that you have to simulate the behavior of the particles, based on the information on the read particles from the storage means.

  The particle behavior simulation apparatus according to the second invention is the particle behavior simulation apparatus according to the first invention, wherein the region is a square region, and the particle size ratio of the particle size of the target particle to the particle size of the particle searched by the particle search means. Is 2.0, and the volume ratio of the particle having the particle diameter different from the particle of interest is 0.030 to 0.333 with respect to the total volume of all the particles in the small area searched by the particle search means. In this case, a means for setting the length of one side of the region to 0.575 to 1.4 times the particle diameter is provided.

  In the particle behavior simulation apparatus according to a third aspect of the present invention, in the first aspect, the region is a square region, and the particle size ratio of the particle size of the particle of interest to the particle size of the particle searched by the particle search means Means for calculating the volume ratio of particles having a particle diameter different from the particle of interest with respect to the total volume of all the particles in the small region searched by the particle search means, and the calculated particle diameter ratio And a means for selecting whether to set the small region as a region having a single size or a region having a plurality of sizes based on the volume ratio, and the small region having a plurality of sizes In the case where the region is set, it is characterized by comprising means for setting the length of one side of the region to be 0.85 to 1.75 times the particle diameter when the volume ratio is near 0.5.

  In the particle behavior simulation apparatus according to a fourth aspect of the present invention, in the first aspect, the region is a square region, and the particle size ratio of the particle size of the particle of interest to the particle size of the particle searched by the particle search means Means for calculating the volume ratio of particles having a particle diameter different from the particle of interest with respect to the total volume of all the particles in the small region searched by the particle search means, and the calculated particle diameter ratio And a means for selecting whether to set the small region as a region having a single size or a region having a plurality of sizes based on the volume ratio, and the small region having a plurality of sizes In the case where the region is set, it is characterized by comprising means for setting the length of one side of the region to 1.1 to 1.8 times the particle diameter when the volume ratio is near 0.1.

  The particle behavior simulation method according to the fifth aspect of the present invention divides a calculation target region for calculating the behavior of particles based on a plurality of interaction forces depending on the distance between particles having different particle diameters into a plurality of regions, In the method of simulating the behavior of the particles included in the target region, the particles having the largest particle diameter in the calculation target region are sequentially selected as the target particles, and the target particles are included in a small region having a predetermined size. Search for particles that are in contact with each other and particles that may be in contact with each other, store information about the retrieved particles in the storage means, calculate the accumulated displacement of the particle of interest, and whether the accumulated displacement exceeds a predetermined value Only when it is determined that the value exceeds the predetermined value, the particle search is performed. When it is determined that the particle value is equal to or less than the predetermined value, the behavior of the particle is determined based on the information regarding the particle read from the storage unit. Characterized in that it emulates.

  In the particle behavior simulation method according to the sixth invention, in the fifth invention, the region is a square region, and the particle size ratio of the particle size of the target particle to the particle size of the searched particle is 2.0. When the volume ratio of the particle having a particle diameter different from that of the target particle is 0.030 to 0.333 with respect to the total volume of all the particles in the searched small region, the length of one side of the region is defined as the particle size. It is characterized by being set to 0.575 to 1.4 times that of.

  Further, in the particle behavior simulation method according to the seventh invention, in the fifth invention, the region is a square region, and the particle size ratio of the particle of interest to the particle size of the searched particle is calculated and searched. Calculate the volume ratio of the particle of the particle size different from the particle of interest to the total volume of all the particles in the small region. Based on the calculated particle size ratio and volume ratio, Selecting whether to set in a region having a plurality of sizes or setting in a region having a plurality of sizes, and setting the small region in a region having a plurality of sizes, when the volume ratio is near 0.5, the region The length of one side is set to 0.85 to 1.75 times the particle diameter.

  Further, in the particle behavior simulation method according to the eighth invention, in the fifth invention, the region is a square region, and the particle size ratio of the particle of interest to the particle size of the searched particle is calculated and searched. Calculate the volume ratio of the particle of the particle size different from the particle of interest to the total volume of all the particles in the small region. Based on the calculated particle size ratio and volume ratio, In the case of selecting whether to set in a region having a plurality of sizes or setting in a region having a plurality of sizes, and setting the small region in a region having a plurality of sizes, when the volume ratio is near 0.1, the region The length of one side is set to 1.1 to 1.8 times the particle diameter.

  The computer program according to the ninth aspect of the present invention divides a calculation target area for calculating the behavior of particles based on a plurality of interaction forces depending on the distance between particles having different particle diameters into a plurality of areas. In the computer program that can be executed by a computer that simulates the behavior of particles contained in the computer, the computer is set as the target particle sequentially from the particle having the largest particle diameter in the calculation target region, and the target particle is Particle search means for searching for particles that are in contact with each other and particles that may be in contact with each other within a small area of a predetermined size contained therein, means for storing information on the searched particles in a storage means, Means for calculating the integrated displacement, determination means for determining whether the integrated displacement exceeds a predetermined value, and when the determination means determines that the predetermined value has been exceeded , Using the particle retrieval means, if it is determined to be equal to or less than a predetermined value, characterized in that to function as a means of simulating the behavior of the particles, based on the information on the read particles from the storage means.

  The computer program according to a tenth aspect of the invention is the computer program according to the ninth aspect, wherein the region is a square region, the particle size of the particle of interest is equal to the particle size of the particle searched by the particle search means. The diameter ratio is 2.0, and the volume ratio of particles having a particle diameter different from that of the target particle is 0.030 to 0.333 with respect to the total volume of all particles in the small region searched by the particle search means. In this case, it is characterized by functioning as means for setting the length of one side of the region to 0.575 to 1.4 times the particle diameter.

  The computer program according to an eleventh aspect of the invention is the computer program according to the ninth aspect, wherein the region is a square region, and the computer is used to determine a particle size of the particle of interest relative to the particle size of the particle searched by the particle search means. Means for calculating the diameter ratio, means for calculating the volume ratio of particles having a particle diameter different from the particle of interest, with respect to the sum of the volumes of all particles in the small region searched by the particle search means, and the calculated particle diameter ratio And a means for selecting whether to set the small region as a region having a single size or a region having a plurality of sizes based on the volume ratio, and the small region having a plurality of sizes In the case of setting in the region, when the volume ratio is in the vicinity of 0.5, the length of one side of the region is functioned as means for setting the length to 0.85 to 1.75 times the particle diameter.

  The computer program according to a twelfth aspect of the invention is the computer program according to the ninth aspect, wherein the region is a square region, and the computer is used to determine the particle size of the particle of interest relative to the particle size of the particle searched by the particle search means Means for calculating the diameter ratio, means for calculating the volume ratio of particles having a particle diameter different from the particle of interest, with respect to the sum of the volumes of all particles in the small region searched by the particle search means, and the calculated particle diameter ratio And a means for selecting whether to set the small region as a region having a single size or a region having a plurality of sizes based on the volume ratio, and the small region having a plurality of sizes In the case where the region is set, when the volume ratio is in the vicinity of 0.1, it functions as means for setting the length of one side of the region to 1.1 to 1.8 times the particle diameter.

  In the first invention, the fifth invention, and the ninth invention, the calculation target region for calculating the behavior of particles based on a plurality of interaction forces depending on the distance between particles having different particle diameters is divided into a plurality of regions, Simulate the behavior of particles contained in the calculation target area. From the particle with the largest particle size within the calculation target area, the target particle is sequentially selected, and the particles that are in contact with each other and the particles that may be in contact with each other are searched within a small area of a predetermined size that includes the target particle. Then, information relating to the retrieved particles is stored in the storage means. Calculates the accumulated displacement of the particle of interest, searches for particles only when the accumulated displacement exceeds a predetermined value, and if the accumulated displacement is less than the predetermined value, simulates the behavior of the particle based on information about the particle read from the storage means To do. As a result, the contact particles are searched in the particle search range based on the particle diameter in order from the particles having the maximum diameter, and only when the amount of movement exceeds a predetermined value, for example, 4% of the particle diameter, the contact particles again. Thus, the number of contact particle search processes can be greatly reduced, and the calculation processing time required for particle behavior simulation can be greatly reduced. Needless to say, the movement distance, which is a criterion for determining whether or not to search for contact particles again, varies depending on the particle movement state, sampling time interval, and the like.

  In the second invention, the sixth invention, and the tenth invention, the region is a square region, the particle size ratio of the particle size of the target particle to the particle size of the searched particle is 2.0, and the searched small size When the volume ratio of the particle of interest and the particle having a different particle diameter to the total volume of all the particles in the region is 0.030 to 0.333, the length of one side of the region is set to 0.575 to 1 of the particle size. Set to 4 times. When the particle size ratio is 2.0 and the volume ratio (particle concentration) is 0.030 to 0.333, the length of one side of the cell (region) is 0.575 to 1.4 times the particle size. It has been experimentally confirmed that the computation processing time required for particle behavior simulation becomes the shortest when set to.

  In the third invention, the fourth invention, the seventh invention, the eighth invention, the eleventh invention and the twelfth invention, the region is a square region, and the particle size ratio of the particle size of the particle of interest to the particle size of the retrieved particle Is calculated, and the volume ratio of the particle having the particle diameter different from that of the target particle is calculated with respect to the total volume of all the particles in the searched small region. Based on the calculated particle diameter ratio and volume ratio, it is selected whether the small region is set as a region having a single size or a region having a plurality of sizes. When the small region is set as a region having a plurality of sizes, when the volume ratio is near 0.5, the length of one side of the region is set to 0.85 to 1.75 times the particle diameter. When the volume ratio is near 0.1, the length of one side of the region is set to 1.1 to 1.8 times the particle diameter.

  This makes it possible to search for particles in a small region based on a more appropriate cell (region) by selecting whether the size of the cell (region) is single or variable depending on the particle diameter ratio and volume ratio. As a whole, the simulation calculation time can be shortened. When the volume ratio is near 0.5, the length of one side of the region is 0.85 to 1.75 times the particle diameter, and when the volume ratio is near 0.1, the length of one side of the region is It has been experimentally confirmed that by setting the cell (region) size to 1.1 to 1.8 times the diameter, the computation processing time required for particle behavior simulation is minimized.

  According to the first invention, the fifth invention, and the ninth invention, the contact particles are searched in order from the particles having the maximum diameter in the particle search range based on the particle diameter, and the moving amount is a predetermined value, for example, particles By searching for contact particles again only when the diameter exceeds 4%, the number of contact particle search processes can be greatly reduced, greatly reducing the computation processing time required for particle behavior simulation. It becomes possible. Needless to say, the movement distance, which is a criterion for determining whether or not to search for contact particles again, varies depending on the particle movement state, sampling time interval, and the like.

  According to the second invention, the sixth invention, and the tenth invention, when the particle diameter ratio is 2.0 and the volume ratio is 0.030 to 0.333, the length of one side of the region is set to the particle diameter. By setting 0.575 to 1.4 times, it is possible to minimize the computation processing time required for particle behavior simulation.

  According to the third invention, the fourth invention, the seventh invention, the eighth invention, the eleventh invention, and the twelfth invention, the size of the cell (region) is made uniform or varies depending on the particle diameter ratio and the volume ratio. By selecting whether or not to perform, particle search can be performed in a small region based on a more appropriate cell (region), and the simulation calculation time can be reduced as a whole. When the volume ratio is near 0.5, the length of one side of the region is 0.85 to 1.75 times the particle diameter, and when the volume ratio is near 0.1, the length of one side of the region is By setting the size of each cell (region) to 1.1 to 1.8 times the diameter, it is possible to minimize the calculation processing time required for particle behavior simulation.

  Hereinafter, a particle behavior simulation apparatus according to an embodiment of the present invention will be specifically described with reference to the drawings.

(Embodiment 1)
FIG. 1 is a block diagram showing a configuration of a particle behavior simulation apparatus 1 according to Embodiment 1 of the present invention. In FIG. 1, the particle behavior simulation apparatus 1 includes at least a CPU (Central Processing Unit) 11, an auxiliary storage unit 12, a RAM 13, a storage unit 14, a communication unit 15, an input unit 16, a display unit 17, an output unit 18, and the above-described unit. The internal bus 19 is connected to the hardware.

  The CPU 11 is connected to the above-described hardware units of the particle behavior simulation apparatus 1 via the internal bus 19. The CPU 11 controls the above-described hardware units and performs various operations according to the computer program 3 stored in the RAM 13. Execute the software function of. The RAM 13 includes an SRAM, a flash memory, and the like, and stores a computer program (load module), temporary data generated when the computer program is executed, and the like.

  The storage unit 14 includes a built-in fixed storage device (hard disk), a ROM, and the like, and a portable recording medium 2 such as a DVD or a CD-ROM. The computer program 3 stored in the storage means 14 is downloaded by the auxiliary storage means 12 from the portable recording medium 2 such as a CD-ROM in which information such as programs and data is recorded, and from the storage means 14 to the RAM 13 at the time of execution. Deploy and execute.

  The communication means 15 is connected to an internal bus 19 and can transmit / receive data to / from an external computer by being connected to an external network such as the Internet, LAN, or WAN. Therefore, it is possible to further reduce the calculation time by executing parallel processing with a plurality of external computers.

  The input means 16 is a data input medium such as a keyboard and a mouse, and the display means 17 is a display device such as a CRT monitor or LCD. The output means 18 is a printing device such as a laser printer or a dot printer.

  Hereinafter, the DEM used in the first embodiment will be described. The DEM is a method for calculating the particle behavior by calculating all the forces acting on each particle forming the powder and sequentially solving the equation of motion of each particle based on the calculated force acting on the particle.

  The force acting on the particle includes not only an external force such as gravity but also a contact force between the wall and the particle and between the particles. The magnitude of the force acting on the particle is determined by the normal speed and the contact state of the particle. In order to calculate the contact state of each particle, it is necessary to calculate the distance between each particle. When calculating the distance between all the particles, if the number of particles is n (n is a natural number), it is necessary to calculate n (n-1) / 2 times, and the calculation is performed when the number of particles n increases. There was a problem that the amount became enormous.

  Therefore, the small area that is the target of distance calculation is changed for each particle. That is, the particles for which the contact determination (distance calculation) is performed are limited to a small area specified by the particle diameter (particle diameter) of the target particle and particles existing in the small area. FIG. 2 is a diagram illustrating an example of a particle limiting method that is a contact determination target by DEM.

  In the example of FIG. 2, a region including the cell 24 including the target particle 21 and the surrounding eight cells is defined as a small region 25, and the particle 22 included in the small region 25 is a target for distance calculation. The particles 23 that are not included in the small region 25 are determined to have no possibility of coming into contact with the target particle 21 and are excluded from the distance calculation target.

  On the other hand, when executing a simulation calculation of developer behavior in electrophotography, not only the force acting by the interparticle contact as described above but also the magnetic attraction force, electrostatic force, van der Worth force, etc. It is necessary to simulate the behavior of For example, the magnetic attractive force is a magnetic force that the target particle 21 receives in a magnetic field due to a magnetic field from another particle or a magnet roller.

  In addition, the electrostatic force includes not only an electrostatic force caused by an electric field generated from a developing electric field and an electrostatic latent image, but also an interparticle force generated by an electric charge caused by contact between particles, friction and the like. For example, an electrostatic attractive force is generated between the toner particles and the carrier particles, and an electrostatic repulsive force is generated between the toner particles, and the magnitude can be obtained by a Coulomb charge equation. Furthermore, the van der Waals force is a universal proximity force that acts between toner particles and carrier particles having different particle diameters.

  3 and 4 are flowcharts showing the procedure of the particle behavior simulation process of the CPU 11 of the particle behavior simulation apparatus 1 according to the first embodiment of the present invention. The CPU 11 of the particle behavior simulation apparatus 1 first acquires various physical parameters necessary for the calculation and calculation conditions such as the initial arrangement of the particles (step S301), and appropriately sets the calculation area to be simulated according to the particle arrangement and the like. It is divided into cells (regions) of a large size (step S302). The CPU 11 sets a particle having the maximum diameter among the existing particles as a target particle (step S303), and sets a small region that is a particle search range based on the particle diameter of the target particle (step S304). The CPU 11 searches for particles that are in contact with the target particle or particles that may be in contact within the set small region (step S305), and stores information (position, particle diameter, etc.) regarding the searched particles. (Step S306).

  The CPU 11 determines whether or not the particle search process has been completed for all particles existing in the calculation area (step S307). If the CPU 11 determines that the CPU 11 has not ended (step S307: NO), the CPU 11 A particle having a large particle diameter is set as a target particle (step S308), the process returns to step S304, and the above-described process is repeated. When it is determined that the CPU 11 has ended (step S307: YES), the CPU 11 calculates a force or the like acting on each stored particle (including the target particle) (step S309), and applies to all the stored particles. It is determined whether or not the acting force has been calculated (step S310).

  When the CPU 11 determines that there are uncalculated particles (step S310: NO), the CPU 11 returns the process to step S309 and calculates the force acting on each particle described above. When the CPU 11 determines that the force acting on all particles has been calculated (step S310: YES), the CPU 11 calculates the acceleration, velocity, and displacement for each particle by solving the equation of motion of each particle (step S310). S311), each particle position is updated (step S312).

  The CPU 11 determines whether or not to end the simulation process (step S313). If the CPU 11 determines to end the simulation process (step S313: YES), the CPU 11 ends the simulation process. The end condition is not particularly limited, and for example, it is determined whether or not to end depending on whether or not the simulation period has elapsed.

  When the CPU 11 determines not to end the simulation process (step S313: NO), the CPU 11 determines whether to execute the particle search process again when the simulation process is executed again. That is, the CPU 11 integrates the displacement of the particle of interest to calculate the integrated displacement from the initial position (step S314), and determines whether the integrated displacement has exceeded a predetermined value (step S315). When the CPU 11 determines that the integrated displacement is equal to or less than the predetermined value (step S315: NO), the CPU 11 reads the stored information regarding the particles, returns the process to step S309, and repeats the above-described process. When the CPU 11 determines that the integrated displacement has exceeded the predetermined value (step S315: YES), the CPU 11 returns the process to step S303 and repeats the above-described process.

  That is, the particle search process is executed again only when the target particle moves more than a predetermined value, and when the target particle does not move more than the predetermined value, there is no need to execute the particle search process again. Therefore, the calculation processing load can be reduced by the amount that the particle search process is not executed, and the execution time of the simulation calculation can be greatly shortened.

  The search process for particles that come into contact with the target particle is executed in the following procedure. In order to simplify the description, first, the procedure of search processing when the particle diameter is single will be described.

In general, the small area is square in two dimensions and cubic in three dimensions. When the number of cells included in one side of the small region is n _s , in the three-dimensional model, the average search cell number n _sc is the cube of the number of cells n _s included in one side of the region as in ( _Equation 1). .

n _sc = n _s ³ (Equation 1)

On the other hand, assuming that the length of one side per cell is r and the coefficient for determining the search target range is λ, the volume V _{c of the} small area to be searched is the cube of n _s · λ · r. Particle number n _c existing in the small area to be searched can be determined by equation (2).

n _c = n · V _c / V (Equation 2)

Therefore, the average value n _{cc of the} number of contact determinations between particles for each small region to be searched can be obtained by (Equation 3).

n _cc = (n _c −1) / 2 (Equation 3)

Accordingly, when the particle search calculation load is K _sc and the contact determination calculation load is K _cc , the length L _pd of one side of the optimal small region to be searched when the particle diameter is single is: (Equation 4) can be calculated. Of course, the means for obtaining the optimum size of the small area is not particularly limited to this.

L _pd = K _sc · n _sc + K _cc · n _cc
= K _sc · n _s ³ + K _cc · (n · V _c / V−1) / 2 (Equation 4)

  FIG. 5 is a schematic diagram showing the relationship between the cell size and the number of contact particles when the particle diameter is single. FIG. 5A shows a state where the size of the cell 24 divided with respect to the particle size of the target particle 21 is large, and FIG. 5B shows the cell divided with respect to the particle size of the target particle 21. The figure which shows a state when the magnitude | size of 24 is small is shown, respectively. As shown in FIG. 5A, when the size of the cell 24 is larger than the particle diameter of the target particle 21, the number of the cells 24 included in the small region 25 to be searched is reduced, and one small region is obtained. The number of particles searched in increases. On the other hand, as shown in FIG. 5B, when the size of the cell 24 is small with respect to the particle diameter of the target particle 21, the number of the cells 24 included in the small region 25 to be searched increases. The number of particles searched in a small area is reduced. Therefore, it is preferable that the size of the cell 24 is larger than the particle diameter of the particle of interest 21 in order to reduce the particle search processing with a relatively large calculation processing load as much as possible in order to shorten the simulation calculation time. Recognize.

Actually, since particles having different particle diameters are mixed, if the size of the small region to be searched is specified based on the size of the cell 24 including the particles 21 having the maximum diameter, the calculation is most performed. Processing load can be reduced. FIG. 6 is a diagram illustrating a method of determining the small region 25 to be searched based on the particle diameter. When the diameter of the particle of interest 21 is r1, the diameter of the other particles is r2, and the diameter of the particle having the maximum diameter is r _max , the length L _s of one side of the small region to be searched by (Equation 5) To decide.

L _s = ri ± r _max (Equation 5)
Where i is a natural number

  Since the size of the cell 24 is specified to be a constant size depending on the particle diameter of the target particle 21, the cells 24 and 24 included in the small region 25 to be searched according to the size of the diameter of the target particle 21. The number of ... varies. In the example of FIG. 6, the small region 61 indicates a small region specified when the target particle 21 is a particle having a large particle size, and the small region 62 is a particle in which the target particle has a small particle size. A small area specified in a certain case is shown. That is, as is clear from (Equation 5), when the target particle 21 is a particle having a large particle diameter, the small region 61 to be searched for contact particles becomes wider.

  Since the number of small areas included in the calculation area is minimized by specifying the small areas that are the search target areas of the particles in the order in which the small areas 61 that are the search targets of the contact particles are wide, the arithmetic processing The particle search process with a relatively large load can be reduced as much as possible, and the simulation calculation time can be shortened.

  FIG. 7 is a diagram showing the degree of variation in simulation time with respect to the number of particles per cell in the particle behavior simulation method according to the first embodiment. In FIG. 7, the horizontal axis indicates the number n of particles contained in one cell, and the vertical axis indicates the particle search processing time for searching for particles in contact with each other as a ratio R to the shortest processing time. Show. In addition, simulation calculation of particle search processing uses 1.6 GHz of IBM PowerPC (PowerPC) 970 (R) as a CPU, 2 GB of memory, and “X-Fortlan (XLFortran)” manufactured by IBM as a compiler. Version 9.1 ”was used and the particle size ratio and the number of particles per cell were varied.

  In FIG. 7, when particles having different particle diameters are mixed, the particle diameter ratio is 2.0 (marked by □) in order to confirm whether or not the time required for the particle search process varies due to the difference in the particle diameter ratio. The time required for the particle search process in the case of 4.0 (◯ mark), 6.0 (Δ mark), 8.0 (▽ mark), and 10.0 (x mark) is plotted. As is clear from the results of FIG. 7, it can be seen that the length of time required for the particle search process does not depend on the particle size ratio but rather depends on the number n of particles contained in one cell. .

  Therefore, it can be confirmed that the number of particles per cell is 1.0 to 5.0 in the fluctuation time width within 5% from the time required for the particle search processing is the shortest. This is because when the cell is a square region, the particle diameter ratio is 2.0, and the volume ratio is 0.030 to 0.333, the length of one side of the cell is the particle diameter (the diameter of the particle having the maximum diameter). It is equivalent to 0.575 to 1.4 times the value. By setting a cell as a size of such a range and setting a small region as a particle search target, it is possible to minimize the simulation calculation time.

(Embodiment 2)
Hereinafter, the particle behavior simulation apparatus 1 according to Embodiment 2 of the present invention will be specifically described with reference to the drawings. Since the configuration of the particle behavior simulation apparatus 1 according to the second embodiment is the same as that of the first embodiment, detailed description thereof will be omitted by attaching the same reference numerals. The second embodiment is different from the first embodiment in that the size of a small region to be a particle search target is changed based on the particle diameter ratio of mixed particles and the volume ratio in the mixed state.

  The particle size ratio of the mixed particles is calculated as the particle size ratio of the retrieved particle size to the particle size of the target particle. For example, when two types of particles having a particle size of r1 and r2 (r1> r2) are mixed, when the target particle is a particle having a particle size of r1, the particle size ratio r1 / r2 of the particle having the particle size of r2 is set to adopt.

  Further, the volume ratio is the volume ratio of particles having a particle diameter different from that of the target particle with respect to the total volume of all contained particles for each small region, that is, a particle size smaller than the target particle (hereinafter referred to as a small particle). Calculated as volume ratio). For example, when two types of particles having a particle size of r1 and r2 (r1> r2) are mixed, when the target particle is a particle having a particle size of r1, the particle size r1 of the volume V2 of the particle having the particle size of r2 The ratio V2 / (V1 + V2) to the sum of the volume V1 of the particle of interest and the volume V2 of the particle having the particle diameter r2 is employed as the small particle volume ratio.

  FIG. 8 is a diagram schematically showing the relationship between cells and small areas that are search target ranges. FIG. 8A shows a case where the cell having the one size shown in the first embodiment is used, and a small region in which particle search can be most efficiently performed when the particle diameter is single. Can be specified. However, in actuality, as shown in FIG. 8B, particles having different particle diameters are mixed, and when they are evenly mixed, a particle search can be efficiently performed even if a cell having one size is used. Although it may occur that a small region that can be specified can be specified, optimization by the method using cells having one size is difficult as long as the degree of mixing varies.

  Thus, as shown in FIG. 8B, two types of cells, a cell having a size for a particle having a large particle size and a cell having a size for a particle having a small particle size, are used in combination. As described in the first embodiment, when the cell size is larger than the particle size of the target particle, the number of cells included in the small area to be searched is reduced, and the search is performed in one small area. The number of particles increases. On the other hand, when the cell size is small with respect to the particle diameter of the target particle, the number of cells included in the small area to be searched increases, and the number of particles searched in one small area decreases. Therefore, in order to reduce the particle search processing with a relatively large calculation processing load as much as possible in order to shorten the simulation calculation time, it is preferable that the cell size is larger than the particle size of the particle of interest.

  However, even if the cell size is larger than the particle size of the target particle, there is almost no target particle in the specific cell, and the distribution state is equal to the presence of only the small particle size particle. Some cells also exist. For example, in the cell 81, the target particle is present at the center, but the cell 82 is mostly occupied by particles having a particle diameter smaller than that of the target particle.

  In this case, rather than using a small region determined based on the particle of interest, the search efficiency is improved when the small region is determined based on the particle having a small particle diameter and the particle search is performed. Therefore, based on the volume concentration of particles having a small particle diameter, a small region is specified based on only one size cell as in the first embodiment, or a small region is specified using a plurality of types of cells. By selecting or selecting, the simulation calculation efficiency can be further increased, and the calculation processing time can be further shortened.

  FIG. 9 is a diagram showing the degree of variation in simulation time with respect to the number of particles per cell in the particle behavior simulation method according to the second embodiment. In FIG. 9, the horizontal axis indicates the number n of particles contained in one cell, and the vertical axis indicates the particle search processing time for searching for particles in contact with each other as a ratio R to the shortest processing time. Show. In addition, simulation calculation of particle search processing uses 1.6 GHz of IBM PowerPC (PowerPC) 970 (R) as a CPU, 2 GB of memory, and “X-Fortlan (XLFortran)” manufactured by IBM as a compiler. Version 9.1 ”was used and the particle size ratio and the number of particles per cell were varied.

  In FIG. 9, when particles having different particle diameters are mixed, the particle diameter ratio is 2.0 (marked by □) in order to confirm whether or not the time required for the particle search process varies due to the difference in the particle diameter ratio. The time required for the particle search process in the case of 4.0 (◯ mark), 6.0 (Δ mark), 8.0 (▽ mark), and 10.0 (x mark) is plotted. As is clear from the results of FIG. 9, the time ratio R of the particle search process is substantially the same even when the particle diameter ratio is different in a portion where R is smaller than 1.3. In the portion where R is larger than 1.3, a slight variation is observed due to the difference in particle diameter ratio.

  This indicates that in the case where the particle search process is accelerated by 1.3 times or more, the particle search process using a single size cell decreases the calculation processing efficiency due to the difference in particle diameter ratio, When speeding up the particle search process by 1.3 times or more, it is suggested that performing the particle search process using a plurality of cells having different sizes further increases the calculation processing efficiency. FIG. 10 is a diagram illustrating the degree of variation in the simulation time of the particle search process with respect to the particle diameter ratio and the small particle volume ratio. The simulation calculation uses 1.6 GHz of IBM PowerPC 970 (R) as the CPU, 2 GB of memory, and “XLFortran version 9.1” manufactured by IBM as the compiler. The particle diameter ratio and the small particle volume ratio were varied.

  In FIG. 10, when particles having different particle sizes are mixed, the time required for the particle search process varies depending on the density of the particles, for example, the small particle volume ratio, which is the ratio of particles having small particle sizes. In order to confirm whether or not, the particle size ratio is 2.0 (□ mark), 4.0 (◯ mark), 6.0 (△ mark), 8.0 (▽ mark), 10.0 (X mark) In this case, the time ratio R required for the particle search process is plotted. In the portion 101 where the time ratio R of the particle search processing is smaller than 1.3, as in the first embodiment, the case where the small region is specified based on the size of a single cell and the particle search processing is executed. There is no difference in the time required for the particle search process from when the particle search process is executed by specifying a small region by changing the cell size.

  On the other hand, in the portion 102 where the time ratio R of the particle search process is larger than 1.3, when the particle size ratio is different, the time ratio R of the particle search process varies greatly depending on the size of the small particle volume ratio. Therefore, in the example of FIG. 10, when the particle size ratio is 2.0, the size of a single cell is set by setting the size of the cell and the size of the small region according to the small particle volume ratio. The particle search process can be greatly speeded up and the simulation calculation time can be further shortened compared to the case where the particle search process is executed by specifying a small region based on the above.

  FIG. 11 is a diagram showing the relationship between the small particle volume ratio and the time ratio R of the particle search process. Curve 111 is the time ratio of the particle search processing corresponding to the number of particles per cell when the small particle volume ratio is 0.5, and curve 112 is the small particle volume ratio of 0.091, respectively. R is shown. In addition, simulation calculation of particle search processing uses 1.6 GHz of IBM PowerPC (PowerPC) 970 (R) as a CPU, 2 GB of memory, and “X-Fortlan (XLFortran)” manufactured by IBM as a compiler. Version 9.1 ”was used and the particle size ratio and the number of particles per cell were varied.

  As is clear from FIG. 11, in the fluctuation time width within 5% of the time required for the particle search processing is the shortest, when the small particle volume ratio is near 0.5, 0.5 to 0.5 in one small region. The simulation time can be minimized by setting the cell to a size in which four particles exist. This corresponds to setting the length of one side of the cell to 0.85 to 1.75 times the particle diameter when the cell is a square region. Further, when the small particle volume ratio is near 0.1, the simulation time can be minimized by setting the small region to a size in which 0.2 to 0.8 particles exist in one small region. it can. This corresponds to setting the length of one side of the cell to 1.1 to 1.8 times the particle diameter when the cell is a square region.

  12 and 13 are flowcharts showing the procedure of the particle behavior simulation process of the CPU 11 of the particle behavior simulation apparatus 1 according to the second embodiment of the present invention. The CPU 11 of the particle behavior simulation apparatus 1 first obtains various physical parameters necessary for calculation, calculation conditions such as initial arrangement of particles (step S1201), and appropriately sets a calculation region to be simulated according to the arrangement of particles and the like. It is divided into cells (regions) of a large size (step S1202). The CPU 11 sets a particle having the maximum diameter among the existing particles as a target particle (step S1203), and sets a small region that is a particle search range based on the particle diameter of the target particle (step S1204). The CPU 11 searches for particles that are in contact with the target particle in the set small region or particles that may be in contact (step S1205).

  The CPU 11 calculates a particle size ratio between the target particle and other particles (step S1206), and calculates a small particle volume ratio that is a volume ratio of particles with a small particle size searched for each small region (step S1207). . The CPU 11 determines whether or not the cell size should be changed based on the particle diameter ratio and the small particle volume ratio (step S1208), and when the CPU 11 determines that the cell size should be changed (step S1208). (S1208: YES), the CPU 11 changes the size of the cell (step S1209), returns the processing to step S1204, and repeats the above-described processing.

  When the CPU 11 determines that there is no need to change the cell size (step S1208: NO), the CPU 11 stores information (position, particle diameter, etc.) regarding the retrieved particles (step S1210). The CPU 11 determines whether or not the particle search process has been completed for all particles existing in the calculation area (step S1211). If the CPU 11 determines that the CPU 11 has not ended (step S1211: NO), the CPU 11 A particle having a large particle diameter is set as a target particle (step S1212), the process returns to step S1204, and the above-described process is repeated. When it is determined that the CPU 11 has ended (step S1211: YES), the CPU 11 calculates a force or the like acting on each stored particle (including the target particle) (step S1213), and applies to all stored particles. It is determined whether or not the acting force has been calculated (step S1214).

  When the CPU 11 determines that there are uncalculated particles (step S1214: NO), the CPU 11 returns the process to step S1213 and calculates the force acting on the above-described particles. When the CPU 11 determines that the force acting on all the particles has been calculated (step S1214: YES), the CPU 11 calculates the acceleration, velocity, and displacement for each particle by solving the equation of motion of each particle (step S1214: YES). S1215), the respective particle positions are updated (step S1216).

  The CPU 11 determines whether or not to end the simulation process (step S1217). When the CPU 11 determines to end the simulation process (step S1217: YES), the CPU 11 ends the simulation process. The end condition is not particularly limited, and for example, it is determined whether or not to end depending on whether or not the simulation period has elapsed.

  When the CPU 11 determines not to end the simulation process (step S1217: NO), the CPU 11 determines whether to execute the particle search process again when the simulation process is executed again. That is, the CPU 11 integrates the displacement of the particle of interest to calculate the integrated displacement from the initial position (step S1218), and determines whether the integrated displacement exceeds a predetermined value (step S1219). When the CPU 11 determines that the integrated displacement is equal to or less than the predetermined value (step S1219: NO), the CPU 11 reads the stored information on the particles, returns the process to step S1213, and repeats the above-described process. When the CPU 11 determines that the integrated displacement has exceeded the predetermined value (step S1219: YES), the CPU 11 returns the process to step S1203 and repeats the above-described process.

  As described above, according to the second embodiment, by selecting whether the cell size is single or variable according to the particle diameter ratio and the volume ratio, a smaller area based on a more appropriate cell can be obtained. Thus, the particle search can be performed, and the simulation calculation time can be shortened as a whole. When the volume ratio is near 0.5, the length of one side of the region is 0.85 to 1.75 times the particle diameter, and when the volume ratio is near 0.1, the length of one side of the region is By setting the cell size to 1.1 to 1.8 times the diameter, the computation processing time required for particle behavior simulation can be minimized.

  In addition, this invention is not limited to the said Example, It cannot be overemphasized that various deformation | transformation, substitution, etc. are possible if it is description in a claim.

It is a block diagram which shows the structure of the particle behavior simulation apparatus which concerns on Embodiment 1 of this invention. It is a figure which shows an example in the particle | grain limitation method used as the contact determination object by DEM. It is a flowchart which shows the procedure of the simulation process of the particle behavior of CPU of the particle behavior simulation apparatus which concerns on Embodiment 1 of this invention. It is a flowchart which shows the procedure of the simulation process of the particle behavior of CPU of the particle behavior simulation apparatus which concerns on Embodiment 1 of this invention. It is a schematic diagram which shows the relationship between the magnitude | size of a cell in case a particle diameter is single, and the number of contact particles. It is a figure which shows the method of defining the small area | region used as search object based on a particle diameter. It is a figure which shows the degree of the fluctuation | variation of the simulation time with respect to the particle number per cell in the particle | grain behavior simulation method which concerns on this Embodiment 1. FIG. It is a figure which shows typically the relationship between a cell and the small area | region which is a search object range. It is a figure which shows the degree of the fluctuation | variation of the simulation time with respect to the number of particles per cell in the particle behavior simulation method which concerns on this Embodiment 2. FIG. It is a figure which shows the degree of the fluctuation | variation of the simulation time of the particle | grain search process with respect to a particle diameter ratio and a small particle volume ratio. It is a figure which shows the relationship between the small particle volume ratio and the time ratio R of a particle search process. It is a flowchart which shows the procedure of the simulation process of the particle behavior of CPU of the particle behavior simulation apparatus which concerns on Embodiment 2 of this invention. It is a flowchart which shows the procedure of the simulation process of the particle behavior of CPU of the particle behavior simulation apparatus which concerns on Embodiment 2 of this invention.

Explanation of symbols

1 Particle behavior simulation device 11 CPU
12 Auxiliary memory 13 RAM
14 storage means 15 communication means 16 input means 17 display means 21 particle of interest 24 cell 25 small region

Claims (12)

Divide the calculation target area to calculate the behavior of particles based on multiple interaction forces depending on the distance between particles with different particle diameters, and simulate the behavior of particles contained in the calculation target area In the device
The particles having the largest particle diameter in the calculation target region are sequentially set as the target particles, and the particles that are in contact with each other and the particles that may be in contact in a small region of a predetermined size that includes the target particles. Particle search means for searching;
Means for storing information about the retrieved particles in a storage means;
Means for calculating the cumulative displacement of the particle of interest;
And a judging means for judging whether or not the integrated displacement exceeds a predetermined value,
The particle search unit is used only when the determination unit determines that the predetermined value is exceeded, and when it is determined that the value is equal to or less than the predetermined value, the behavior of the particle is simulated based on the information about the particle read from the storage unit. A particle behavior simulation apparatus characterized by being configured to do so. The region is a square region;
The particle diameter ratio of the particle diameter of the particle of interest to the particle diameter of the particle searched by the particle search means is 2.0, and the total volume of all the particles in the small area searched by the particle search means When the volume ratio of the particle having a particle diameter different from that of the target particle is 0.030 to 0.333, means for setting the length of one side of the region to 0.575 to 1.4 times the particle diameter. The particle behavior simulation apparatus according to claim 1, further comprising: The region is a square region;
Means for calculating the particle diameter ratio of the particle diameter of the particle of interest to the particle diameter of the particles searched by the particle search means;
Means for calculating a volume ratio of particles having a particle diameter different from the particle of interest, with respect to the total volume of all particles in the small region searched by the particle search means;
Based on the calculated particle size ratio and volume ratio, a means for selecting whether to set a small region in a region having a single size or a region having a plurality of sizes,
In the case where the small region is set as a region having a plurality of sizes, when the volume ratio is close to 0.5, means for setting the length of one side of the region to 0.85 to 1.75 times the particle diameter; The particle behavior simulation apparatus according to claim 1, further comprising: The region is a square region;
Means for calculating the particle diameter ratio of the particle diameter of the particle of interest to the particle diameter of the particles searched by the particle search means;
Means for calculating a volume ratio of particles having a particle diameter different from the particle of interest, with respect to the total volume of all particles in the small region searched by the particle search means;
Based on the calculated particle size ratio and volume ratio, a means for selecting whether to set a small region in a region having a single size or a region having a plurality of sizes,
In the case where the small region is set as a region having a plurality of sizes, when the volume ratio is near 0.1, means for setting the length of one side of the region to 1.1 to 1.8 times the particle diameter; The particle behavior simulation apparatus according to claim 1, further comprising: Divide the calculation target area to calculate the behavior of particles based on multiple interaction forces depending on the distance between particles with different particle diameters, and simulate the behavior of particles contained in the calculation target area In the method
The particles having the largest particle diameter in the calculation target region are sequentially set as the target particles, and the particles that are in contact with each other and the particles that may be in contact in a small region of a predetermined size that includes the target particles. Search and
Storing information about the retrieved particles in a storage means;
Calculate the cumulative displacement of the particle of interest,
Judge whether the accumulated displacement exceeds the predetermined value,
The particle search is performed only when it is determined that the predetermined value is exceeded, and the behavior of the particle is simulated based on the information on the particle read from the storage unit when it is determined that the particle is less than the predetermined value. Particle behavior simulation method. The region is a square region;
The particle size ratio of the particle size of the particle of interest to the particle size of the retrieved particle is 2.0, and the particle size of the particle of which the particle size is different from the particle of interest with respect to the total volume of all the particles in the retrieved small region 6. The particle behavior simulation method according to claim 5, wherein when the volume ratio is 0.030 to 0.333, the length of one side of the region is set to 0.575 to 1.4 times the particle diameter. . The region is a square region;
Calculate the particle size ratio of the particle size of the particle of interest to the particle size of the searched particle,
Calculate the volume ratio of the particle of interest and the particle size different from the total volume of all the particles in the searched small region,
Based on the calculated particle size ratio and volume ratio, select whether to set a small region in a region having a single size or a region having a plurality of sizes,
When the small region is set as a region having a plurality of sizes, when the volume ratio is near 0.5, the length of one side of the region is set to 0.85 to 1.75 times the particle diameter. 6. The particle behavior simulation method according to claim 5, wherein: The region is a square region;
Calculate the particle size ratio of the particle size of the particle of interest to the particle size of the searched particle,
Calculate the volume ratio of the particle of interest and the particle size different from the total volume of all the particles in the searched small region,
Based on the calculated particle size ratio and volume ratio, select whether to set a small region in a region having a single size or a region having a plurality of sizes,
When the small region is set as a region having a plurality of sizes, when the volume ratio is near 0.1, the length of one side of the region is set to 1.1 to 1.8 times the particle diameter. 6. The particle behavior simulation method according to claim 5, wherein: Divide the calculation target area to calculate the behavior of particles based on multiple interaction forces depending on the distance between particles with different particle diameters, and simulate the behavior of particles contained in the calculation target area In a computer program that can be executed on a computer,
The computer,
The particles having the largest particle diameter in the calculation target region are sequentially set as the target particles, and the particles that are in contact with each other and the particles that may be in contact in a small region of a predetermined size that includes the target particles. Particle search means to search,
Means for storing information about the retrieved particles in a storage means;
Means for calculating the cumulative displacement of the particle of interest;
Only when it is determined that the integrated displacement exceeds a predetermined value, and when the determination means determines that the predetermined displacement exceeds the predetermined value, the particle search means is used, A computer program that functions as means for simulating the behavior of particles based on information about particles read from a storage means. The region is a square region;
The computer,
The particle diameter ratio of the particle diameter of the particle of interest to the particle diameter of the particle searched by the particle search means is 2.0, and the total volume of all the particles in the small area searched by the particle search means When the volume ratio of the particle having a particle diameter different from that of the target particle is 0.030 to 0.333, the length of one side of the region is set to 0.575 to 1.4 times the particle diameter. The computer program according to claim 9, wherein the computer program is made to function. The region is a square region;
The computer,
Means for calculating the particle diameter ratio of the particle diameter of the particle of interest to the particle diameter of the particles searched by the particle search means;
Means for calculating a volume ratio of a particle having a particle diameter different from the particle of interest, with respect to a total volume of all particles in the small area searched by the particle search means;
Based on the calculated particle diameter ratio and volume ratio, a means for selecting whether to set a small region as a region having a single size or a region having a plurality of sizes, and a plurality of the small regions When the volume ratio is in the vicinity of 0.5, the length of one side of the region is made to function as a means for setting the length to 0.85 to 1.75 times the particle diameter. The computer program according to claim 9. The region is a square region;
The computer,
Means for calculating the particle diameter ratio of the particle diameter of the particle of interest to the particle diameter of the particles searched by the particle search means;
Means for calculating a volume ratio of a particle having a particle diameter different from the particle of interest, with respect to a total volume of all particles in the small area searched by the particle search means;
Based on the calculated particle diameter ratio and volume ratio, a means for selecting whether to set a small region as a region having a single size or a region having a plurality of sizes, and a plurality of the small regions When the volume ratio is in the vicinity of 0.1, it is made to function as a means for setting the length of one side of the region to 1.1 to 1.8 times the particle diameter. The computer program according to claim 9.

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