JP5079765B2 - Particle behavior analysis apparatus, particle behavior analysis method, and computer program - Google Patents

Description

  The present invention relates to a particle behavior analysis device, a particle behavior analysis method, and a computer program, and is particularly suitable for use in analyzing particle behavior.

  Conventionally, the behavior of particles has been analyzed in various fields. For example, in blast furnace operation in the steel industry, when iron ore and coke are layered from the top of the furnace, the charge layer surface is inclined downward from the furnace periphery toward the center in the furnace radial direction, Because iron ore and coke having different specific gravities and particle sizes are alternately charged, iron ore and coke behave in a complicated manner in a blast furnace. The distribution of charge in the blast furnace affects the flow of reducing gas generated at the tuyere, the pressure distribution and the temperature distribution in the furnace. Therefore, accurate analysis of the behavior of iron ore and coke charged in the blast furnace is important for stable operation of the blast furnace.

As a technique for analyzing the behavior of particles such as iron ore and coke in the blast furnace, there is DEM (Discrete Element Method). In DEM, the shape of a particle is determined, a force generated in the particle when the particles come into contact with each other, and the behavior of the particle in the analysis time is obtained at predetermined time intervals based on the force. In order to accurately analyze the behavior of particles by DEM, it is important to determine a shape that reflects actual particles as faithfully as possible. This is particularly important when analyzing the behavior of particles with various non-spherical shapes, such as iron ore and coke.
There exists a technique of patent document 1 as a technique of evaluating the shape of particle | grains. In Patent Document 1, a projected image of a particle is photographed, and its circularity (= peripheral length of a circle having the same projected area as the projected image of the particle / perimeter length of the projected image of the particle) is obtained, and −1 / log (circular) The shape of the particle is evaluated based on the value of degree.

JP 2004-239645 A

However, since the technique described in Patent Document 1 uses a projected image of particles, the shape of the particles can be evaluated only two-dimensionally. Therefore, the shape of the particle to be evaluated differs depending on the direction of projection, and it is difficult to evaluate the unevenness of the surface of the particle that is not reflected in the projected image.
As described above, the technique described in Patent Document 1 has a problem that it is difficult to accurately determine the shape of the particles used for the analysis of the behavior by the DEM according to the actual particles.
The present invention has been made in view of such problems, and an object of the present invention is to make it possible to more accurately determine the shape of particles used when analyzing the behavior with a DEM.

  The particle behavior analysis apparatus according to the present invention is a particle behavior analysis apparatus that analyzes the behavior of a plurality of particles under a predetermined condition by a discrete element method, an image acquisition unit that acquires an image of the particle, and an image of the particle A particle surface coordinate deriving means for deriving the three-dimensional coordinates of the plurality of points on the surface of the particle, and the three-dimensional coordinates of the plurality of points on the surface of the particle. Based on the particle centroid derivation means for deriving the centroid of the particle, and among the plurality of points on the surface of the particle, a position vector from the centroid of the particle toward the vertex of the polyhedron having the same centroid as the centroid of the particle A particle surface representative point deriving unit for deriving the closest point for each vertex of the polyhedron, and a polyhedron for generating a polyhedron having the point derived by the particle surface representative point deriving unit as a vertex as an analysis particle A contact area setting means for setting a spherical contact area centered on a straight line connecting the vertex of the particle for analysis and the center of gravity of the particle for each of the vertex of the particle for analysis; And the force generated in the analysis particle when it is determined that the analysis particle is in contact with the other region, assuming that the contact region set with respect to the vertex of the analysis particle is in contact with the other region. It is characterized by having particle behavior analysis means for analyzing the behavior of each analysis particle under a predetermined condition by deriving from each analysis particle.

  The particle behavior analysis method of the present invention is a particle behavior analysis method for analyzing the behavior of a plurality of particles under a predetermined condition by a discrete element method, an image acquisition step of acquiring an image of the particle, and an image of the particle A particle surface coordinate deriving step for deriving the three-dimensional coordinates of the plurality of points on the surface of the particle, and the three-dimensional coordinates of the plurality of points on the surface of the particle. Based on a particle centroid derivation step of deriving the centroid of the particle, and among a plurality of points on the surface of the particle, a position vector from the centroid of the particle toward a vertex of a polyhedron having the same centroid as the centroid of the particle A particle surface representative point deriving step for deriving the closest point for each of the vertices of the polyhedron, and a polyhedron for generating a polyhedron having the point derived by the particle surface representative point deriving step as a vertex as an analysis particle A contact region setting step of setting a spherical contact region centered on a straight line connecting the vertex of the particle for analysis and the center of gravity of the particle with respect to each vertex of the particle for analysis And the force generated in the analysis particle when it is determined that the analysis particle is in contact with the other region, assuming that the contact region set with respect to the vertex of the analysis particle is in contact with the other region. And a particle behavior analysis step of analyzing the behavior of each analysis particle under a predetermined condition by deriving from each analysis particle.

  The computer program of the present invention is a computer program for causing a computer to analyze the behavior of a plurality of particles under a predetermined condition by a discrete element method, and an image acquisition step of acquiring an image of the particles; A plurality of points designated on the basis of the image of the particle, and a particle surface coordinate deriving step for deriving three-dimensional coordinates of the plurality of points on the surface of the particle; and a plurality of points on the surface of the particle Based on the three-dimensional coordinates, a particle centroid derivation step for deriving the centroid of the particle, and among a plurality of points on the surface of the particle, from the centroid of the particle to the vertex of a polyhedron having the same centroid as the centroid of the particle A particle surface representative point deriving step for deriving a point closest to the heading position vector for each vertex of the polyhedron, and a point derived by the particle surface representative point deriving step A polyhedron generating step of generating a polyhedron as an apex as an analysis particle, and a spherical contact region whose center is located on a straight line connecting the apex of the analysis particle and the center of gravity of the particle, The contact area setting step that is set for each of the vertices, and the contact area that is set for the vertex of the analysis particle is in contact with another area, and the analysis particle is in contact with the other area. A particle behavior analysis step of analyzing the behavior of each analytical particle under a predetermined condition by deriving the force generated in the analytical particle when determined The computer is executed.

  According to the present invention, among the plurality of points on the surface of the particle, the point closest to the position vector from the center of gravity of the particle toward the vertex of the polyhedron having the same center of gravity as the center of gravity of the particle is the vertex of the polyhedron. And a polyhedron having the point as a vertex is taken as a particle for analysis. In addition, a spherical contact region whose center is located on a straight line connecting the vertex of the particle for analysis and the center of gravity of the particle is set for each vertex of the particle for analysis. The behavior of the plurality of analysis particles under a predetermined condition is derived using the analysis particles and the contact region thus obtained. Therefore, the shape of the particles used when analyzing the behavior by the discrete element method can be determined more accurately than before, and the behavior of the particles can be reproduced more accurately than before.

It is a figure which shows embodiment of this invention and shows an example of a functional structure of a particle behavior analyzer. It is a figure which shows embodiment of this invention and shows an example of a mode that X-rays are irradiated to particle | grains. It is a figure which shows embodiment of this invention and shows an example of an X-ray CT image. It is a figure which shows embodiment of this invention and shows an example of a mode that the several point was designated on the outline of the cross section of the particle | grains represented by the X-ray CT image. It is a figure which shows embodiment of this invention and shows an example of the point on the surface of particle | grains, and the gravity center of the said particle | grain. It is a figure which shows embodiment of this invention and demonstrates an example of the method of selecting the point nearest to the position vector which goes to the vertex of the said dodecahedron from the gravity center of the dodecahedron. It is a figure which shows embodiment of this invention and shows an example of the polyhedron produced | generated as a particle for analysis. It is a figure which shows embodiment of this invention and shows an example of the polyhedron produced | generated using the actual lump ore, the polyhedron produced | generated using the icosahedron, and the icosahedron. It is a figure which shows embodiment of this invention and demonstrates an example of the method of setting the contact area | region 910 with respect to the vertex of the polyhedron which is an analysis particle. It is a figure which shows embodiment of this invention, and shows notionally an example of the mode of the contact area | region of the particle | grains for two analysis which are contacting each other, and an example of the behavior of the particle | grains for analysis. It is a flowchart which shows embodiment of this invention and demonstrates an example of a process of a particle behavior analyzer. It is a flowchart which shows embodiment of this invention and demonstrates an example of the particle | grain determination process in step S1 of FIG. FIG. 13 is a flowchart illustrating the embodiment of the present invention and continuing from FIG. 12. The figure which shows embodiment of this invention and is a figure which shows an example of the result of having analyzed the behavior of the particle for analysis which set the shape as a sphere by DEM, and the result of having analyzed the behavior of the particle for analysis which set the shape as a polyhedron by DEM is there. It is a figure which shows embodiment of this invention and shows the angle of repose (sphere) in Fig.14 (a), the angle of repose (polyhedron) in FIG.14 (b), and an actual angle of repose (experimental result).

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
FIG. 1 is a diagram illustrating an example of a functional configuration of the particle behavior analysis apparatus 100. The particle behavior analysis apparatus 100 can be realized by using, for example, an information processing apparatus (personal computer) including a CPU, ROM, RAM, HDD, various interfaces, a display, and the like. Below, the function with which the particle behavior analysis apparatus 100 is provided is demonstrated in detail.

(Particle cross-sectional image acquisition unit 101)
The particle cross-sectional image acquisition unit 101 acquires cross-sectional images at a plurality of positions of a plurality of particles to be analyzed for behavior. In the present embodiment, the particle cross-sectional image acquisition unit 101 acquires an X-ray CT (Computed Tomography) image as a cross-sectional image. The particle cross-sectional image acquisition unit 101 may directly acquire an X-ray CT image from an X-ray CT apparatus, or may read and acquire an X-ray CT image stored in a portable storage medium, X-ray CT images may be received and acquired from an external device via a network.
FIG. 2 is a diagram conceptually illustrating an example of a state in which the particle 201 is irradiated with the X-ray 202. FIG. 3 is a diagram illustrating an example of the X-ray CT image 301.
2 and 3, when the particle 201 is irradiated with X-rays 202, X-ray CT images 301a to 301l representing cross sections of the particle 201 at positions 203a to 203l are obtained, respectively.
The particle cross-sectional image acquisition unit 101 is realized, for example, when the CPU stores the data of the X-ray CT images 301a to 301l in an HDD or the like via various interfaces. The particle cross-sectional image acquisition unit 101 may acquire cross-sectional images for all particles to be analyzed for behavior, or a cross section for a plurality of representative particles among all particles to be analyzed for behavior. An image may be acquired.

(Particle selection unit 102)
The particle selection unit 102 selects one of a plurality of particles to be analyzed for behavior in a predetermined order.
The particle selection unit 102 is realized, for example, when the CPU executes such a selection process and stores the execution result in a RAM or the like. The particle selection unit 102 may select one of a plurality of particles to be analyzed for behavior based on a user interface operation by the user.
(Particle cross-sectional image selection unit 103)
The particle cross-sectional image selection unit 103 sequentially selects any one of the plurality of X-ray CT images 301a to 301l of the particles selected by the particle selection unit 102 in a predetermined order.
The particle cross-section image selection unit 103 is realized by, for example, the CPU executing such a selection process and storing the execution result in a RAM or the like. The particle cross-sectional image selection unit 103 may select any one of the plurality of X-ray CT images 301a to 301l based on a user interface operation by the user.

(Particle contour extraction unit 104)
The particle contour extraction unit 104 displays the X-ray CT image 301 selected by the particle cross-sectional image selection unit 103 on the display. The user designates a plurality of points on the outline of “the cross section of the particle 201” represented in the X-ray CT image 301 displayed on the display using the user interface. FIG. 4 is a diagram illustrating an example of a state in which a plurality of points are designated on the outline of the “cross section of the particle 201” represented in the X-ray CT image 301. As illustrated in FIG. 4, the user designates a plurality of points 401 a to 401 q on the outline of “the cross section of the particle 201” represented in the X-ray CT image 301. It is preferable that the number of points specified here is as large as possible within a range in which the subsequent calculation load does not increase. The particle contour extraction unit 104 stores information on the position of the designated point.

In the particle contour extraction unit 104, for example, the CPU performs processing for displaying the X-ray CT image 301, the display displays the X-ray CT image 301, and the CPU further performs processing on the X-ray CT image 301. The position of the designated point is acquired by identifying the operation content of the user interface, and the acquired position information is stored in a RAM or the like.
Here, the case where the user designates a plurality of positions on the contour of the cross section of the particle 102 has been described as an example, but this is not necessarily required. That is, a plurality of positions may be automatically specified on the contour of the cross section of the particle 102 according to preset conditions. Here, the X-ray CT images 301 are displayed one by one on the display so that the user designates a plurality of points on the cross-sectional contour of the particle 201. However, a plurality of X-ray CT images 301 are simultaneously displayed. You may make it display on a display and make a user designate the some point on the outline of the cross section of the particle | grain 201 about each of these some X-ray CT images 301. FIG.

(Particle surface coordinate deriving unit 105)
The particle surface coordinate deriving unit 105 derives and stores the three-dimensional coordinates of the “point on the surface of the particle 201” corresponding to the “point on the contour of the cross section of the particle 201” stored by the particle contour extracting unit 104. To do.
The particle surface coordinate deriving unit 105 is realized, for example, when the CPU executes such a derivation process and stores the execution result in a RAM or the like.
(Particle Gravity Deriving Unit 106)
The particle centroid derivation unit 106 derives the three-dimensional coordinates of the centroid of the particle 201 based on the “three-dimensional coordinates of a point on the surface of the particle 201” derived by the particle surface coordinate derivation unit 105.
The particle centroid derivation unit 106 is realized, for example, when the CPU executes such a derivation process and stores the execution result in a RAM or the like.

  FIG. 5 conceptually shows an example of a point on the surface of a particle (circle filled with black) and the center of gravity of the particle (open circle). For example, the particle surface coordinate deriving unit 105 rearranges a plurality of X-ray CT images 301 a to 301 l each having a plurality of points 401 designated at positions 203 a to 203 l, and three-dimensionals the point 401 when rearranged. By deriving the coordinates with the predetermined position as the origin, the three-dimensional coordinates of “the point on the surface of the particle 201” corresponding to “the point on the contour of the cross section of the particle 201” can be derived. Note that the origins of the three-dimensional coordinates described in this specification are all the same.

(Particle surface representative point deriving unit 107)
The particle surface representative point deriving unit 107 first sets a regular dodecahedron having the same center of gravity as the center of gravity derived by the particle center of gravity deriving unit 106. The orientation and size of the regular dodecahedron can be arbitrarily set. Next, the particle surface representative point deriving unit 107 extracts the regular tens from the center of gravity of the set icosahedron among the “points on the surface of the particle 201” from which the three-dimensional coordinates are derived by the particle surface coordinate deriving unit 105. The point closest to the position vector toward the vertex of the dihedron is selected for each of the 20 vertices of the regular dodecahedron.
FIG. 6 is a diagram for explaining an example of a method for selecting the point 605 closest to the position vector 604 from the center of gravity 602 of the regular dodecahedron 601 toward the vertex 603 of the regular dodecahedron 601.
First, as illustrated in FIG. 6A, the particle surface representative point deriving unit 107 derives, for example, a position vector 604 from the center of gravity 602 of the regular dodecahedron 601 toward the vertex 603 of the regular dodecahedron 601.

Next, as illustrated in FIG. 6B, the particle surface representative point deriving unit 107 includes a regular dodecahedron out of position vectors 606 from the center of gravity 602 of the regular dodecahedron 601 to the point 605 on the surface of the particle. A position vector 606 having the smallest angle θ formed by the position vector 604 from the center of gravity 602 of the 601 to the vertex 603 of the regular dodecahedron 601 is selected. Then, the particle surface representative point deriving unit 107 moves the “point 605 on the surface of the particle 201” indicated by the selected position vector 606 from the center of gravity 602 of the regular dodecahedron 601 to the vertex 603 of the regular dodecahedron 601. The point closest to the position vector 604 is selected, and the three-dimensional coordinate of the selected point is stored as the three-dimensional coordinate of the representative point on the surface of the particle 201.
In the particle surface representative point deriving unit 107, for example, the CPU reads ““ the three-dimensional coordinates of the center of gravity of the particle 201 ”and“ the three-dimensional coordinates of the point on the surface of the particle 201 ”stored in the RAM or the like. This is realized by executing the arithmetic processing and storing the execution result in a RAM or the like.

(Polyhedron generator 108)
The polyhedron generation unit 108 generates a polyhedron having 20 points derived from the particle surface representative point deriving unit 107 as vertices for analysis. Specifically, the polyhedron generating unit 108 derives the points derived by the particle surface representative point deriving unit 107 for the vertices of the regular dodecahedron and the particle surface representative point deriving unit 107 for the vertices adjacent to the vertex. A polyhedron is generated by connecting the formed points with a straight line, and the three-dimensional coordinates of each vertex of the polyhedron are stored.
FIG. 7 shows an example of a polyhedron 701 generated as analysis particles.
In the polyhedron generation unit 108, for example, the CPU reads “three-dimensional coordinates of the representative point of the surface of the particle 201” stored in the RAM or the like, executes the above-described arithmetic processing, and stores the execution result in the RAM or the like. Is realized.

Here, the reason for using the regular dodecahedron 601 as shown in FIG. 6A when generating the polyhedron (particle for analysis) 701 as shown in FIG. 7 will be described. FIG. 8 shows an actual block ore 801 (FIG. 8A), a polyhedron 802 generated using an icosahedron (FIG. 8B), and a polyhedron 803 generated using an icosahedron ( It is a figure which shows an example of FIG.8 (c)).
As shown in FIG. 8, the polyhedron 802 shown in FIG. 8 (b) is closer to the actual block ore 801 shown in FIG. 8 (a) than the polyhedron 803 shown in FIG. 8 (c). I understand. This is because the number of vertices of the regular icosahedron is 20 while the number of vertices of the regular icosahedron is 20. That is, when a polyhedron having a large number of vertices is used, a polyhedron having a shape close to an actual particle can be generated as an analysis particle. However, if a polyhedron with too many vertices or a polyhedron other than a regular polyhedron is used, the calculation load may increase. Therefore, in the present embodiment, as described above, the analysis particles are generated using the regular dodecahedron. However, the polyhedron can be appropriately set according to the actual shape of the particle and the calculation ability. That is, it can be a polyhedron having 8 or more vertices (including a regular polyhedron), preferably a polyhedron having 12 or more vertices (including a regular polyhedron), more preferably a vertex. Can be a polyhedron (including regular polyhedrons) of 20 or more.

(Contact area setting unit 109)
The contact area setting unit 109 sets spherical virtual small particles as contact areas for each of the 20 vertices of the polyhedron (analysis particle) 701 generated by the polyhedron generation unit 108, and the size of the contact area is set. (Eg radius) is stored. In the present embodiment, when a contact region set in a polyhedron (analysis particle) is in contact with a contact region set in another polyhedron (analysis particle) in the analysis by DEM described later, Are determined to be in contact with each other. In addition, when a contact region set for a polyhedron (analysis particle) contacts a wall, it is determined that the analysis particle contacts the wall. Thus, the contact region set for the analysis particles is a region where the analysis particles can come into contact with other regions (analysis particles, walls, etc.) in the analysis by DEM.

FIG. 9 is a diagram for explaining an example of a method for setting the contact region 910 for the vertex 901 of the polyhedron 701 that is the particle for analysis.
As illustrated in FIG. 9A, the contact determination region generation unit 108 is located on the inner side of the polyhedron 701 with respect to the vertex 901 so that the vertex 901 of the polyhedron (particle for analysis) 701 and the peripheral surface overlap (coincide with) each other. And a sphere 904 having a center 903 positioned on a straight line connecting the gravity center 902 of the particle 201 and the vertex 901 of the polyhedron is set as a contact region. The radius of the sphere 904 can be appropriately set so as to match the actual particle contact state. For example, the average value of the shortest distances between “each point on the surface of the particle 201 (circle filled in black) and the center of gravity of the particle 201 (open circle)” shown in FIG. This value can be used as the radius of the sphere 904.

When the contact area setting as described above is performed for each of the 20 vertices of the polyhedron 701, contact areas 910a to 910l and the like are obtained as shown in FIG. 9B. In FIG. 9B, the region that protrudes outside the polyhedron 701 in the contact region 910 is shown in black.
In the contact area setting unit 109, for example, the CPU reads ““ polyhedron 701 information (three-dimensional coordinates of each vertex of the polyhedron 701) ”and“ three-dimensional coordinates of the center of gravity of the particle 201 ”from the RAM, etc. This is realized by executing processing and storing the execution result in a RAM or the like. If the contact region 910 is set inside the polyhedron 701 with respect to the vertex 901 so that the vertex 901 of the polyhedron (particle for analysis) 701 overlaps with the peripheral surface of the contact region 910 in this way, the vertex 901 is set. It is preferable because the contact region does not protrude outward, but it is not always necessary that the center 903 is located on a straight line connecting the gravity center of the particle 201 (the white circle in FIG. 5) and the vertex 901 of the polyhedron. It is not necessary for the apex 901 of the polyhedron (analysis particle) 701 and the peripheral surface of the contact region 910 to overlap. For example, the center 903 is positioned on a straight line connecting the gravity center of the particle 201 (the white circle in FIG. 5) and the vertex 901 of the polyhedron so that at least a part of the region protrudes outside the polyhedron 701. The contact area can be set to do so.

(Particle information storage unit 110 for analysis)
The analysis particle information storage unit 110 includes the three-dimensional coordinates of each vertex of the “polyhedron (analysis particle) 701” generated by the polyhedron generation unit 108, and the “contact region 910” set by the contact region setting unit 109. The size and the “three-dimensional coordinates of the center of gravity of the particle 201” derived by the particle centroid derivation unit 106 are stored as information on the particle for analysis.
In the particle information storage unit 110 for analysis, for example, the CPU reads ““ polyhedral (particles to be analyzed) 701 three-dimensional coordinates of each vertex ”and“ size of the contact area 910 ”from the RAM or the like and stores it in the HDD or the like. This is realized by memorizing.

(Particle setting end determination unit 111)
The particle setting end determination unit 111 generates information on the polyhedron (analysis particle) 701 and the contact region 901 for all the particles 201 that should generate the analysis particle 701 among the plurality of particles 201 to be analyzed for behavior. It is determined whether or not. As a result of this determination, when the information of the polyhedron (analysis particle) 701 and the contact region 901 is not generated for all the particles for which the analysis particle 701 should be generated, the plurality of particles 201 are not yet selected. The particle selection unit 102 is instructed to select particles. As a result, the particle selection unit 102 selects particles that have not been selected in a predetermined order. Then, in the same manner as described above, analysis particles and contact areas for the particles are generated.
In the particle setting end determination unit 111, for example, the CPU recognizes a particle to be analyzed for behavior from the X-ray CT image 301 stored in the HDD or the like, and stores the “polyhedron (analysis) stored in the HDD or the like. This is realized by recognizing the presence / absence of particles that have not yet been selected from the information of “particles for use” 701 and contact area 901 ”.

(Particle behavior analysis unit 112)
Using the “analysis particle 701 and contact region 901” obtained as described above, the particle behavior analysis unit 112 analyzes the behavior of the analysis particle 701 under a predetermined condition using a DEM. For example, the particle behavior analysis unit 112 reads information on analysis particles corresponding to the particles 201 whose behavior is to be analyzed, and places each analysis particle at a desired position. Then, the particle behavior analysis unit 112 determines whether or not each analysis particle is in contact with another analysis particle, a wall, or the like. As described above, in the present embodiment, the particle behavior analysis unit 112 determines that the analysis particles are in contact with each other when the contact region of one analysis particle overlaps the contact region of another analysis particle. To do. As described above, when the analysis particle is in contact with another region, the repulsive force in the normal direction and the shear direction in the contact region 901 is obtained to solve the translational motion equation, and the center of gravity in the contact region 901 is The moment of force is obtained to solve the equation of rotation, and each analysis particle is moved based on the result. Such contact determination processing and movement processing for each analysis particle are performed at predetermined time intervals. And the behavior in the analysis time of each particle for analysis is obtained from the result. Note that the analysis particles move by providing a condition that breaks the balance of the forces generated between the analysis particles during the analysis time.

Specifically, the particle behavior analysis unit 112 obtains the repulsive force F _{n, ij} in the normal direction in the contact region of the analysis particles i and j by the following equation (1), for example, and the following equation (2) To obtain the repulsive force F _{t, ij} in the shear direction in the contact region of the analytical particles i and j, solve the translational equation of motion of the following equation (3), and the rotational equation of motion by the following equation (4): solve.

FIG. 10 conceptually shows an example of the state of contact areas 1001 and 1002 of two analysis particles in contact with each other (FIG. 10A) and an example of the behavior of analysis particles (FIG. 10B). FIG. The parameters of equations (1) to (4) will be described with reference to FIG.
In the equation (1), K _n is a spring constant in the normal direction, and can be set according to the distance H or δ _n in FIG. However, K _n can be set to a predetermined constant value. Δu _{n, ij} is a relative translational displacement in the normal direction of the center of gravity between the two particles i and j. η _n is a viscosity constant in the normal direction and is set in advance. n _ij is a unit vector in the normal direction. Δt is a predetermined time interval and is set in advance.

In the equation (2), min [A, B] means that the smaller one of A and B is adopted. μ is a coefficient of friction and can be set to a preset value. However, μ can be varied depending on the state or the like. t _ij is a unit vector in the shear direction. K _t is a spring constant in the shear direction, and can be set according to, for example, the distance H, δ _n , or δ _t in FIG. However, K _t may also be a preset fixed value. Δut _{, ij} is the relative translational displacement in the shear direction of the center of gravity between the two particles i, j. [Delta] [phi _ij is the relative rotational displacement of the contact area caused by the rotation of the particles, for example, by the difference between the rotational displacement phi _j rotational displacement phi _i and the contact region 1002 of the contact area 1001 shown in FIG. 10 (a) Can be represented. η _t is a viscosity constant in the shear direction and is set in advance. Δt is a predetermined time interval and is set in advance.

In the formula (3), v is the velocity of the particles (see FIG. 10). * on v represents time differentiation. F is the total sum of the repulsive forces in the shear direction and the normal direction. m is the mass of the particles and is set in advance. g is a gravitational acceleration. When the analysis particles are not in contact with other analysis particles or walls, the first term on the right side of the equation (3) is 0 (zero).
In the equation (4), ω is the angular velocity of the particles (see FIG. 10). * on ω indicates time differentiation. M is the total sum of moments of force, and is obtained from the repulsive forces F _{n, ij} and F _{t, ij in} the shear direction and the normal direction. I is a moment of inertia and is set in advance.
In addition, after the analysis particles are determined, a method for analyzing the behavior of the analysis particles (an analysis method executed by the particle behavior analysis unit 112) includes various known analysis methods for the behavior of particles in the DEM. It can be applied and is not limited to the method using the above-described equations (1) to (4).
The particle behavior analysis unit 112 is realized, for example, when the CPU reads information on particles for analysis from the HDD or the like, executes the arithmetic processing described above, and stores the execution result in the HDD or the like.

(Particle behavior display section 113)
The particle behavior display unit 113 displays “the behavior of each analysis particle” analyzed by the particle behavior analysis unit 112 on the display.
In the particle behavior display unit 113, for example, the CPU performs processing for reading out information on the analysis result of the behavior of each analysis particle from the HDD or the like and displaying the information on the display. This is realized by displaying the behavior of particles.

Next, an example of processing of the particle behavior analysis apparatus 100 will be described with reference to the flowchart of FIG.
First, in step S1, particle determination processing for determining analysis particles is performed. Details of the particle determination process will be described later with reference to FIGS.
Next, in step S2, the particle behavior analysis unit 112 analyzes the behavior of the analysis particles determined in step S1.
Next, in step S <b> 3, the particle behavior display unit 113 displays “analysis particle behavior” analyzed in step S <b> 2 on the display.

Next, an example of the particle determination process in step S1 of FIG. 11 will be described with reference to the flowcharts of FIGS.
First, in step S11, the particle cross-sectional image acquisition unit 101 acquires X-ray CT images 301a to 301l at a plurality of positions 203a to 203l of a plurality of particles 201 to be analyzed for behavior (see FIGS. 2 and 3). ).
As described above, in the present embodiment, for example, an example of an image acquisition unit is realized by performing the process of step S11.
Next, in step S <b> 12, the particle selection unit 102 selects one of the plurality of particles 201 to be analyzed for behavior in a predetermined order.
Next, in step S13, the particle cross-sectional image selection unit 103 selects any one of the plurality of X-ray CT images 301a to 301l of the particle 201 selected in step S12 in a predetermined order.

Next, in step S14, the particle contour extraction unit 104 displays the X-ray CT image 301 selected in step S13 on the display.
Next, in step S15, the particle contour extraction unit 104 stands by until a point 401 on the contour of “cross section of the particle 201” in the X-ray CT image 301 displayed in step S14 is designated by the user. Then, when the point 401 on the contour of the cross section of the particle 201 is designated, the process proceeds to step S16, and the particle contour extraction unit 104 stores information on the position of the designated point 401 (see FIG. 4).
As described above, in the present embodiment, for example, an example of a particle contour extracting unit is realized by performing the processes of steps S14 and S15.
Next, in step S17, the particle contour extraction unit 104 determines whether or not the designation of the point 401 on the contour of the “cross section of the particle 201” in the X-ray CT image 301 displayed in step S14 has ended. The determination is made based on the operation of the user interface. As a result of this determination, if the designation of the point 401 on the contour of the cross section of the particle 201 has not been completed, the process returns to step S15.

On the other hand, when the designation of the point 401 on the contour of the cross section of the particle 201 is completed, the process proceeds to step S18. In step S18, the particle contour extraction unit 104 finishes specifying the point 401 on the cross-sectional contour of the particle 201 for all of the plurality of X-ray CT images 301a to 301l of the particle 201 selected in step S12. It is determined whether or not. As a result of this determination, if the designation of the point 401 on the cross-sectional contour of the particle 201 has not been completed for all of the plurality of X-ray CT images 301a to 301l of the particle 201 selected in step S12, step S13 is performed. Return to.
On the other hand, when the designation of the point 401 on the contour of the cross section of the particle 201 is completed for all of the plurality of X-ray CT images 301a to 301l of the particle 201 selected in step S12, the process proceeds to step S19.

In step S19, the particle surface coordinate deriving unit 105 derives the three-dimensional coordinates of the “point on the surface of the particle 201” corresponding to the “point on the contour of the cross section of the particle 201” stored in step S16. (See FIG. 5). The process of step S19 is performed individually for all particles selected in step S12.
As described above, in the present embodiment, for example, an example of a particle surface coordinate deriving unit is realized by performing the process of step S19.
Next, in step S20, the particle centroid derivation unit 106 derives the three-dimensional coordinates of the centroid of the particle 201 based on the “three-dimensional coordinates of the point on the surface of the particle 201” derived in step S19. Remember.
As described above, in the present embodiment, for example, an example of a particle gravity center deriving unit is realized by performing the process of step S20.
Next, in step S21 of FIG. 13, the particle surface representative point deriving unit 107 sets a regular dodecahedron 601 having the same center of gravity as the center of gravity derived in step S20 (see FIG. 6A).
Next, in step S22, the particle surface representative point deriving unit 107 selects one of the vertices of the regular dodecahedron 601 set in step S21 in a predetermined order.

Next, in step S23, the particle surface representative point deriving unit 107 determines the center of gravity of the regular dodecahedron 601 set in step S21 among the “points on the surface of the particle 201” from which the three-dimensional coordinates are derived in step S19. From 602, a point 605 closest to the position vector 604 toward the vertex 603 selected in step S22 is derived (see FIG. 6).
As described above, in this embodiment, for example, an example of a particle surface representative point deriving unit is realized by performing the processing of steps S21 to S23.
Next, in step S24, the particle surface representative point deriving unit 107 determines whether all of the vertices 603 of the regular dodecahedron 601 set in step S21 have been selected. If all the vertices 603 of the regular dodecahedron 601 have not been selected as a result of this determination, the process returns to step S22.
On the other hand, if it is determined in step S24 that all the vertices 603 of the regular dodecahedron 601 have been selected, the process proceeds to step S25. In step S25, the polyhedron generation unit 108 generates the polyhedron 701 having the 20 points derived in step S23 as vertices as analysis particles, and stores the three-dimensional coordinates of each vertex of the polyhedron 701. (See FIG. 7).
As described above, in the present embodiment, for example, an example of a polyhedron generation unit is realized by performing the process of step S24.

Next, in step S26, the contact area setting unit 109 sets a spherical contact area 910 for each of the 20 vertices of the polyhedron (analysis particle) 701 generated in step S25, and the contact area The size (for example, radius) of 910 is stored (see FIG. 9).
As described above, in the present embodiment, for example, an example of the contact area setting unit is realized by performing the process of step S26.
Next, in step S27, the analysis particle information storage unit 110 displays the three-dimensional coordinates of each vertex of the “polyhedron (analysis particle) 701” generated in step S25 and the “contact region 910” set in step S26. And the “three-dimensional coordinates of the center of gravity of the particle 201” derived in step S20 are stored as information on the particle for analysis of the particle 201 selected in step S12.
Next, in step S <b> 28, the particle setting end determination unit 111 generates analysis particle information for all the particles 201 for which the analysis particles 701 should be generated among the plurality of particles 201 to be analyzed for behavior. It is determined whether or not. As a result of this determination, if the information on the particles for analysis has not been generated for all the particles for which the particles for analysis 701 should be generated, the process returns to step S12. On the other hand, if the analysis particle information is generated for all of the particles for which the analysis particles 701 are to be generated, the processing according to the flowchart of FIG. 12 is terminated, and the process proceeds to step S2 of FIG.

  FIG. 14 shows the result of analyzing the behavior of analysis particles set as a sphere by DEM (FIG. 14A) and the behavior of analysis particles set as a polyhedron as in this embodiment by DEM. It is a figure which shows an example of the result (FIG.14 (b)) analyzed. FIG. 15 is a diagram showing the angle of repose (sphere) in FIG. 14A, the angle of repose (polyhedron) in FIG. 14B, and the actual angle of repose (experimental result). Here, the analysis target of the behavior is a lump ore, and the analysis particles accumulated in the box are changed to the condition other than the analysis particles after a predetermined time elapses after one side of the box is opened. It is the result of analyzing with the same. However, in FIG. 14A, the friction coefficient is adjusted so as to match the actual behavior as much as possible. As shown in FIG. 14, when all the particles for analysis are made into a sphere, the motion of the particles for analysis does not stop below the slope and does not match the actual behavior of the particles. Further, if the analysis particles are all spheres, the gaps between the particles and the filling structure are greatly different from those of the actual particles, so that the consistency with the actual angle of repose becomes low as shown in FIG. On the other hand, when the shape of the particle for analysis is made to be a polyhedron as in this embodiment, such a problem is solved, and it can be seen that the angle of repose is close to the actual value as shown in FIG.

  As described above, in the present embodiment, based on the three-dimensional coordinates of the points on the surface of the particle 201, the three-dimensional coordinates of the center of gravity of the particle 201 are derived, and the regular dodecahedron 601 having the same center of gravity as the center of gravity is obtained. Set. Then, among the points on the surface of the particle 201, the point 605 closest to the position vector 604 from the center of gravity 602 of the regular dodecahedron 601 to the vertex 603 of the regular dodecahedron 601 is selected, and the selected 20 points A polyhedron 701 having a vertex 605 is used as an analysis particle. A spherical contact region 910 is set for each of the 20 vertices of the polyhedron 701. Based on the polyhedron (analysis particle) 701 and the contact region 910 obtained in this way, the behavior of the analysis particle 701 is analyzed by DEM. Therefore, the shape of the particle 201 used when analyzing the behavior by DEM can be determined more accurately than before, and the behavior of the particle 201 can be reproduced more accurately than before by DEM. .

In addition, what kind of thing may be sufficient as the particle used as the application object of the particle behavior analysis apparatus 100 of this embodiment. For example, it is possible to analyze the behavior of iron ore and coke in a blast furnace, analyze the behavior of particles in a kneader, and analyze the behavior of toner particles in a printer.
Further, in the present embodiment, the case where the cross-sectional images 301 at a plurality of positions of the plurality of particles 201 to be analyzed for behavior are described as an example, but the surface of the particle 201 is obtained using the image of the particle 201. If the three-dimensional coordinates can be acquired, the cross-sectional image 301 is not necessarily acquired. For example, the 3D coordinates of the surface of the particle 201 may be acquired using a 3D image of the particle 201.

The embodiment of the present invention described above can be realized by a computer executing a program. Further, a means for supplying the program to the computer, for example, a computer-readable recording medium such as a CD-ROM recording such a program, or a transmission medium for transmitting such a program may be applied as an embodiment of the present invention. it can. A program product such as a computer-readable recording medium that records the program can also be applied as an embodiment of the present invention. The programs, computer-readable recording media, transmission media, and program products are included in the scope of the present invention.
In addition, the embodiments of the present invention described above are merely examples of implementation in carrying out the present invention, and the technical scope of the present invention should not be construed as being limited thereto. Is. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features thereof.

DESCRIPTION OF SYMBOLS 100 Particle behavior analysis apparatus 101 Particle cross-section image acquisition part 102 Particle selection part 103 Particle cross-section image selection part 104 Particle outline extraction part 105 Particle surface coordinate deriving part 106 Particle center of gravity deriving part 107 Particle surface representative point deriving part 108 Polyhedron generation part 109 Contact Region setting unit 110 Particle information storage unit for analysis 111 Particle setting end determination unit 112 Particle behavior analysis unit 201 Particle 301 X-ray CT image 401 Point on the contour of the cross section of the particle 601 Dodecahedron 602 Gravity of the dodecahedron ( Particle center of gravity)
603 vertex of regular dodecahedron 604 position vector 701 polyhedron (particle for analysis)
910 Contact area

Claims (11)

A particle behavior analyzer for analyzing the behavior of a plurality of particles under a predetermined condition by a discrete element method,
Image acquisition means for acquiring an image of the particles;
Particle surface coordinate deriving means for deriving three-dimensional coordinates of a plurality of points specified on the image of the particle and on the surface of the particle;
Particle centroid derivation means for deriving the centroid of the particle based on the three-dimensional coordinates of a plurality of points on the surface of the particle;
A particle surface that derives, for each of the vertices of the polyhedron, a point closest to a position vector from the centroid of the particle toward the vertex of the polyhedron having the same centroid as the centroid of the particle among a plurality of points on the surface of the particle Representative point deriving means;
A polyhedron generating means for generating a polyhedron with the point derived by the particle surface representative point deriving means as an apex as an analysis particle;
A contact area setting means for setting a spherical contact area centered on a straight line connecting the vertex of the particle for analysis and the center of gravity of the particle with respect to each vertex of the particle for analysis;
Assuming that the contact region set with respect to the vertex of the analysis particle is in contact with another region, the force generated in the analysis particle is derived when it is determined that the analysis particle is in contact with the other region. And a particle behavior analysis means for analyzing the behavior of each analysis particle under a predetermined condition by performing the operation on each analysis particle.   The contact area setting means is arranged inside the analysis particle with respect to the vertex so that the vertex and peripheral surface of the analysis particle overlap each other, and the vertex of the analysis particle and the center of gravity of the particle 2. The particle behavior analysis apparatus according to claim 1, wherein a spherical contact region whose center is located on a straight line connecting the two is set for each vertex of the particle for analysis. A particle contour extracting unit that extracts a plurality of points designated for the cross-sectional contour of the particle based on the cross-sectional image of the particle for each of the cross-sectional images of the particle; ,
The image acquisition means acquires images of a plurality of cross sections of the particles,
The particle surface coordinate deriving means derives three-dimensional coordinates of a point on the surface of the particle based on a plurality of points designated with respect to a cross-sectional contour of the particle. 2. The particle behavior analysis apparatus according to 2.   The particle behavior analysis apparatus according to any one of claims 1 to 3, wherein the number of vertices of a polyhedron having the same centroid as the centroid of the particles is 20 or more.   The particle behavior analysis apparatus according to any one of claims 1 to 4, wherein the polyhedron having the same center of gravity as the particle center is a regular polyhedron. A particle behavior analysis method for analyzing the behavior of a plurality of particles under a predetermined condition by a discrete element method,
An image acquisition step of acquiring an image of the particles;
A particle surface coordinate deriving step of deriving three-dimensional coordinates of a plurality of points designated based on the image of the particle and the plurality of points on the surface of the particle;
A particle centroid derivation step of deriving the centroid of the particle based on the three-dimensional coordinates of a plurality of points on the surface of the particle;
A particle surface that derives, for each of the vertices of the polyhedron, a point closest to a position vector from the centroid of the particle toward the vertex of the polyhedron having the same centroid as the centroid of the particle among a plurality of points on the surface of the particle A representative point derivation process;
A polyhedron generating step of generating a polyhedron with the point derived by the particle surface representative point deriving step as a vertex as an analysis particle;
A contact area setting step for setting a spherical contact area whose center is located on a straight line connecting the vertex of the particle for analysis and the center of gravity of the particle with respect to each vertex of the analysis particle;
Assuming that the contact region set with respect to the vertex of the analysis particle is in contact with another region, the force generated in the analysis particle is derived when it is determined that the analysis particle is in contact with the other region. And a particle behavior analysis step of analyzing the behavior of each analysis particle under a predetermined condition by performing the operation on each analysis particle.   The contact region setting step is arranged inside the analysis particle with respect to the vertex so that the vertex and peripheral surface of the analysis particle overlap each other, and the vertex of the analysis particle and the center of gravity of the particle The particle behavior analysis method according to claim 6, wherein a spherical contact region whose center is located on a straight line connecting the particles is set for each vertex of the particle for analysis. A particle contour extracting step of extracting a plurality of points designated for the cross-sectional contour of the particle based on the cross-sectional image of the particle for each of the cross-sectional images of the particle; ,
The image acquisition step acquires images of a plurality of cross sections of the particles,
The particle surface coordinate deriving step derives three-dimensional coordinates of a point on the surface of the particle based on a plurality of points designated with respect to a cross-sectional contour of the particle. 8. The particle behavior analysis method according to 7.   The particle behavior analysis method according to any one of claims 6 to 8, wherein the number of vertices of a polyhedron having the same centroid as the centroid of the particles is 20 or more.   The particle behavior analysis method according to any one of claims 6 to 9, wherein the polyhedron having the same centroid as the centroid of the particle is a regular polyhedron. A computer program for causing a computer to analyze the behavior of a plurality of particles under a predetermined condition by a discrete element method,
An image acquisition step of acquiring an image of the particles;
A particle surface coordinate deriving step of deriving three-dimensional coordinates of a plurality of points designated based on the image of the particle and the plurality of points on the surface of the particle;
A particle centroid derivation step of deriving the centroid of the particle based on the three-dimensional coordinates of a plurality of points on the surface of the particle;
A particle surface that derives, for each of the vertices of the polyhedron, a point closest to a position vector from the centroid of the particle toward the vertex of the polyhedron having the same centroid as the centroid of the particle among a plurality of points on the surface of the particle A representative point derivation process;
A polyhedron generating step of generating a polyhedron with the point derived by the particle surface representative point deriving step as a vertex as an analysis particle;
A contact area setting step for setting a spherical contact area whose center is located on a straight line connecting the vertex of the particle for analysis and the center of gravity of the particle with respect to each vertex of the analysis particle;
Assuming that the contact region set with respect to the vertex of the analysis particle is in contact with another region, the force generated in the analysis particle is derived when it is determined that the analysis particle is in contact with the other region. A computer program that causes a computer to execute a particle behavior analysis step of analyzing the behavior of each analysis particle under a predetermined condition by performing the operation on each analysis particle.

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