JP2006343876A - Particle behavior analysis device, particle behavior analysis method, program, and storage medium - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a particle behavior analysis method which computes the behavior of a particle in consideration of the influence of unevenness in shape, physical value or physical quantity of a particle on a surface. <P>SOLUTION: A particle 601 has a particle standard axis 605, and its surface is divided into two sites 603 and 604. When the site 603 contacts a structure 602, a contact force of tangential direction, which acts on the particle 601, is computed from a maximum static friction coefficient μ<SB>01</SB>, which is set to the site 603, and a kinetic friction coefficient μ<SB>f1</SB>. When the site 604 contacts the structure 602, a contact force of tangential direction, which acts on the particle 601, is computed from a maximum static friction coefficient μ<SB>02</SB>, which is set to the site 604, and a kinetic friction coefficient μ<SB>f2</SB>. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a particle behavior analysis device, a particle behavior analysis method, a program, and a storage medium, and more particularly, to a particle behavior analysis device and a particle behavior analysis method for analyzing the behavior of particles in a device that stirs and conveys particles in a container. More specifically, the behavior of the particles in the container is analyzed when the physical property values and / or physical quantities of the particles are non-uniform or when the particles have an irregular shape such as a non-spherical shape. The present invention relates to a particle behavior analysis apparatus and a particle behavior analysis method.

  For example, in a copying machine or a printer using electrophotographic technology, a visible image made of toner is formed on the surface of a photoreceptor by a developing device. At this time, in the developing device, development is performed by supplying fine toner particles appropriately to the development site.

  By the way, in recent years, particle behavior analysis for analyzing the stirring / conveying state of the particles in the container is being performed, and the analysis result is being used for optimizing the configuration of the stirring / conveying unit in the container.

  In the state of stirring and transporting the particles, the particles are always in contact with each other, and the particles and the container wall are always in contact with each other. Therefore, in the particle behavior analysis, it is necessary to determine the contact state between particles and between the particle and the container wall, especially the contact force, and the discrete element method (DEM) that can simulate a system in which the contact force is dominant is generally used. (For example, refer nonpatent literature 1.).

  In this DEM, as shown in FIG. 16, the contact force between individual particles constituting the granular material is decomposed into a normal contact force and a tangential contact force as basic elements. The sum of the elastic force, the viscous damping force, and the sliding friction acting when the two particles are in contact with each other is taken as the contact force. Therefore, the contact force (normal contact force, tangential contact force) between the two separated particles is modeled using the virtual spring 1301, the dashpot 1302, and the friction slider 1303, respectively. Specifically, the spring 1301 models an elastic repulsion force among the interparticle acting forces, the dashpot 1302 models viscous damping accompanied by energy dissipation, and the friction slider 1303 slides. It models force.

  In this DEM, a contact force acting between two spheres in the case where two spheres made of a uniform isotropic elastic body and having the same radius are in contact is considered. Hereinafter, the subscript n indicates a value in the normal direction with respect to the contact surface, and the subscript t indicates a value in the tangential direction.

  For example, the contact force acting in the normal direction that the particle i receives from the particle j is represented by the sum of the elastic force in the normal direction and the viscous damping force, and the relative velocity from the particle i to the particle j is expressed by the following formula (1). When the unit vector in the normal direction from the particle i to the particle j is represented by the following formula (2), it is represented by the following formula (3).

Here, the spring constant k _n in the normal direction and the viscosity reduction coefficient η _n in the normal direction at the contact point are expressed by the following equations (4) and (5), respectively. Also, δ _n is the deformation amount in the normal direction at the contact point, E _s is the Young's modulus of each particle, σ _s is the Poisson ratio of the particle, m is the mass of each particle, α is the coefficient of restitution coefficient in the collision between particles. Show.

  Further, the contact force acting in the tangential direction that the particle i receives from the particle j is represented by the sum of the elastic force in the tangential direction and the viscous damping force, and the amount of deformation in the tangential direction is expressed by the following equation (6). When the slip velocity vector for the particle j of i is represented by the following formula (7), it is represented by the following formula (8).

Here, the tangential spring constant k _t and the tangential viscous damping coefficient η _t are expressed by the following equations (9) and (10), respectively. G _s indicates the transverse elastic modulus.

However, the contact force acting in the tangential direction determined by the above equation (8) is the maximum static friction force represented by the product of the contact force acting in the normal direction of the above equation (3) and the maximum static friction coefficient (the following equation) When larger than (see (11)) (see the following formula (12)), it is considered that the two particles are slipping each other, and the dynamic friction force represented by the following formula (13) is working. Here, μ ₀ is the maximum static friction coefficient, and μ _f is the dynamic friction coefficient.

  Further, the displacement in the tangential direction at that time is represented by the following formula (14).

  In the DEM described above, the equation of motion is solved based on the contact force acting in the normal direction that the particle i receives from the particle j and the contact force acting in the tangential direction that the particle i receives from the particle j, and each particle after a minute time has passed. The acceleration, speed, and position of the are calculated. Also, in the contact between the particle and the container wall, the particle behavior analysis can be performed by applying the same model as the interparticle contact shown in FIG. That is, the stirring / conveying state of particles can be analyzed by using DEM.

  Further, in the contact determination between two particles, in order to facilitate the contact determination, the particles are regarded as a circle, a cylinder, or a sphere, and a contact distance δ between the two particles is set. Then, contact determination between two particles is performed using the set distance.

  FIG. 17 is a diagram showing the set contact distance, where (A) shows the contact distance between the two particles, and (B) shows the contact distance between the particles and the structure. Here, the contact distance between the two particles is the length of the overlapping portion of the particles on a straight line connecting the centers of the two particles, and the contact distance between the particles and the structure is perpendicular to the structure surface from the center of the particles. It is the overlap length of particles and structures on the intersecting straight line. Here, the center of the particle is usually defined by the center of a circle or sphere having a radius of curvature of the contact portion or the closest portion.

  Further, when calculating the behavior of charged particles, it is necessary to consider the electrostatic force acting on the particles, but the center-to-center vector of the particles 1401 and 1402 is expressed by the following equation (15), and the particles are generally uniform. In many cases, the following equation (16) is used to obtain the electrostatic force when it is assumed that the particle is charged and the charge of the particle is at the center of the particle.

Here, q ₁ is the charge amount of the particle 1401, q ₂ is the charge amount of the particle 1402, and ε ₀ is the dielectric constant of vacuum.

  Next, the structure of a typical processing program for particle behavior analysis and the concept of calculation will be described.

  FIG. 18 is a diagram showing a program configuration schematically showing the configuration of a typical processing program for particle behavior analysis.

  In FIG. 18, a program 10 includes a control unit 100, an initial condition setting unit 111, a particle property value setting unit 1511, a particle / structure acting force calculation unit 1512, an interparticle action force calculation unit 1513, a particle external force calculation unit 115, A particle displacement calculation unit 116 and a particle behavior display unit 117 are included.

  The control unit 100 controls the entire program 2. The initial condition setting unit 111 sets calculation conditions, for example, the initial arrangement and radius of particles, the shape, size and position of the structure constituting the analysis region, time step, and physical property values such as Young's modulus. The particle property value setting unit 1511 sets particle property values such as Young's modulus, Poisson's ratio, and friction coefficient. The particle-structure interaction force calculation unit 1512 calculates the contact force, adhesion force, electrostatic force, and magnetic force, which is the interaction force between the particle and the structure such as a container wall arranged in association with the particle. . The interparticle action force calculation unit 1513 calculates contact force, adhesion force, electrostatic force, and magnetic force, which are action forces between two particles. The particle external force calculation unit 115 calculates an external force acting on the particles, such as gravity. The particle displacement calculator 116 solves the equation of motion based on the force acting on the particle, and calculates the velocity, parallel displacement, and rotational displacement of the particle. The particle behavior display unit 117 displays the positions of particles and structures at each time step.

In the actual calculation, the particle property value setting unit 1511, the particle / structure interaction force calculation unit 1512, the particle interaction force calculation unit 1513, the particle external force calculation unit 115, and the particle displacement calculation unit 116 repeat processing, Find the behavior of.
"Direct Numerical Simulation of Granular Plug Flow in a Horizontal Pipe (Without Adhesive Force)" (Toshiaki Tanaka, Toshiya Ishida, Hiroshi Tsuji, Transactions of the Japan Society of Mechanical Engineers (Part B), Vol. 57, No. 534 B, 1991 , pp. 456-463.)

  Normally, toner particles are made of various materials such as external additives and fixing resins, and the surface state and physical properties are not always uniform. Further, the shape of the toner particles is not necessarily spherical, but is often indefinite, such as when the surface is uneven or non-spherical.

  Further, it is known that the surface physical properties and shape of toner particles have a great influence on the fluidity and aggregation properties of toner particles. Further, since the toner is an insulator, it is considered that electric charges are distributed on the surface. Here, it is considered that the distribution of the charge amount on the particle surface has a great influence on the electrostatic force between the toner particles or between the toner particles and the structure.

  However, in the conventional particle behavior analysis method, since the physical property value is set for each particle, it is necessary to regard the particle as a homogeneous material, and the case where the particle surface state, physical property value, or physical quantity is not uniform is taken into consideration. I can't put it in.

  Further, since the particles are represented by a circle, a cylinder, or a sphere for easy contact determination, it is difficult to calculate the difference in the behavior of the particles due to irregular shapes such as irregular shapes and non-spherical shapes.

  The present invention provides a particle behavior analysis apparatus, a particle behavior analysis method, a program, and a storage medium capable of calculating particle behavior in consideration of the influence of the shape, physical property value, or physical quantity nonuniformity on the surface of the particle. It is in.

  In order to achieve the above object, a particle behavior analysis apparatus according to the present invention is a particle behavior analysis apparatus for analyzing the behavior of particles in an environment where particles and structures exist, and the surface of the particles is divided into several particles. Based on at least one of the physical property value and the physical quantity set by the site condition setting unit that is divided into sites and sets at least one of the physical property value and the physical quantity at each divided particle site. Based on at least one of the physical property value and the physical quantity set by the site condition setting unit, the site-structure interaction force calculation unit that calculates the interaction force between the particle site and the structure, And an inter-site action force calculation unit for calculating an action force between the particle sites.

  In order to achieve the above object, the particle behavior analysis method of the present invention is a particle behavior analysis method for analyzing the behavior of the particle in an environment where the particle and the structure exist. A particle site condition setting step that divides into sites and sets at least one of the physical property value and the physical quantity at each of the divided particle sites; and at least the physical property value and the physical quantity set in the site condition setting step Based on at least one of the physical property value and the physical quantity set in the particle site / structure acting force calculating step for calculating the acting force between the particle site and the structure based on the one, and the site condition setting step And an action force calculation step between the particle sites for calculating an action force between the particle sites.

  In order to achieve the above object, a program according to the present invention is a program for causing a computer to execute a particle behavior analysis method for analyzing the behavior of the particles in an environment where the particles and structures exist. A particle site condition setting module that divides the particle site and sets at least one of the physical property value and the physical quantity at each of the divided particle sites; the physical property value set by the site condition setting module; and Based on at least one of the physical quantities, the particle site / structure acting force calculation module for calculating the acting force between the particle sites and the structure, and at least the physical property value and the physical quantity set by the site condition setting module. Based on one, the force calculation module between the particle sites is calculated. Characterized in that it comprises a Yuru.

  In order to achieve the above object, a storage medium of the present invention stores the above program.

  According to the present invention, the particle surface is divided into several particle sites, at least one of a physical property value and a physical quantity is set for each particle site, and based on at least one of the physical property value and the physical quantity set for the particle site. Since the acting force is calculated, the particle behavior can be calculated in consideration of the influence of the nonuniformity of the shape, physical property value, or physical quantity on the surface of the particle.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

  First, the particle behavior analysis apparatus and the particle behavior analysis method according to the first embodiment of the present invention will be described. In the particle behavior analysis apparatus and the particle behavior analysis method according to the present embodiment, the particle surface is divided into sites (hereinafter, each region of the divided particle surface is divided) in an environment where a plurality of particles or particles and structures are in contact with each other. (Referred to as “particle site”), and the acting force between the closest particle sites or between the closest particle site and the structure with respect to the structure. In the present embodiment, when particles and structures are arranged in a two-dimensional cross section, that is, particle behavior calculation in a two-dimensional model is performed as a representative example, considering the contact force based on DEM as an acting force, The sliding friction coefficient is considered as a physical property value.

  FIG. 1 is a block diagram showing a schematic configuration of the particle behavior analysis apparatus according to the present embodiment.

  In FIG. 1, the particle behavior analysis apparatus 1 includes a CPU 400, a RAM 401, a display device 402, an input unit 403, an external storage device 404, and a bus 405.

  The RAM 401 includes a program storage unit 401a, an initial condition data storage unit 401b, a particle data storage unit 401c, a site data storage unit 401d, a structure data storage unit 401e, and particles that store external force acting on the particles, for example, gravity data. External force data storage unit 401f, particle contact position data storage unit 401g for storing the contact position of particles, two-object contact distance data storage unit 401h for storing the contact distance between two objects, particle action for storing the acting force acting on the particles A force data storage unit 401i and a particle reference axis data storage unit 401j that stores a reference axis of particles are provided.

  The CPU 400 is a central processing unit and controls each unit connected via the bus 405. Each storage unit 401a to 401j of the RAM 401 includes a program shown in FIG. 2 described later, initial condition data, particle data, site data, structure data, particle external force data, particle contact position data, two-object contact distance data, and particle action. Force data and particle reference axis data are stored.

  The display device 402 includes a display, a printer, and the like, and displays data to be displayed under the control of the CPU 400. The input unit 403 includes a keyboard, a mouse, and the like, and inputs externally input data into the particle behavior analysis apparatus 1. The external storage device 404 is composed of a hard disk or the like and stores various data.

  Hereinafter, each data stored in each of the storage units 401a to 401j of the RAM 401 will be described. The initial condition data is a value related to calculation conditions such as a time step and a calculation actual time. The particle data is a physical property value such as a parallel displacement, a rotational displacement, a position coordinate, a velocity, and a radius of each particle. Site data includes the number of particle sites divided, Young's modulus set at each particle site, physical properties such as Poisson's ratio, friction coefficient and specific gravity, charge amount of each particle site, magnetization, magnetic moment, electric dipole moment and adsorption. It is a physical quantity such as a moisture content, an angle with respect to each particle site, that is, information on an angle formed by each particle site and the reference axis of each particle, and representative point information of each particle site. The structure data includes the position, shape, and dimensions of the structure such as the container wall, speed information when the structure moves, and physical property values such as the Young's modulus and friction coefficient of the structure. The particle external force data is information such as gravity that is an external force acting on the particle. The particle contact position data includes the contact angle θc from the particle reference axis to the contact position when the particle contacts the structure, that is, the angle θc formed by the line segment from the particle center to the contact position with respect to the particle reference axis. Is the value of The contact distance data between two objects is a contact distance between particles or between a particle and a structure, and is a value defined by the length of an overlapping portion of two objects. The particle acting force data is a value obtained by combining the contact forces, which are acting forces acting on each particle site. The particle reference axis data is an axis representing the rotational displacement of the particle, and is data relating to the reference axis of the particle fixed to the particle and rotating together with the particle.

  FIG. 2 shows the configuration of a program corresponding to the calculation of particle behavior in which the particle surface is divided into particle sites and the non-uniformity of at least one of the physical property value and physical quantity on the particle surface is taken into account in the present embodiment. FIG.

  In FIG. 2, the program 2 includes a control unit 100, an initial condition setting unit 111, a site condition setting unit 112, a site / structure acting force calculation unit 113, an intersite action force calculation unit 114, a particle external force calculation unit 115, a particle A displacement calculation unit 116 and a particle behavior display unit 117 are included. Among these, the control unit 100, the initial condition setting unit 111, the particle external force calculation unit 115, the particle displacement calculation unit 116, and the particle behavior display unit 117 are the same as the components in the program of FIG. A description of the components is omitted.

  The particle site condition setting unit 112 includes the particle site division number, Young's modulus, Poisson's ratio, sliding friction coefficient, rolling friction coefficient, specific gravity and other physical property values of each particle site, angle information for each particle site, and each particle site. Set initial conditions for particle sites such as representative points. The physical property values are individually set for each particle site. The site / structure interaction force calculator 113 calculates the contact force between the particle site and the structure that are in contact with each other. The inter-site action force calculation unit 114 calculates the contact force between the particle sites that are in contact with each other.

  In the actual calculation, the initial condition setting unit 111, the site condition setting unit 112, the site / structure interaction force calculation unit 113, the site interaction force calculation unit 114, the particle external force calculation unit 115, and the particle displacement calculation unit 116 are processed. By repeating the above, it is possible to calculate the particle behavior at each timing in consideration of the non-uniformity of physical properties (physical property values and physical quantities) on the particle surface by dividing the particle surface into particle sites.

  Hereinafter, the site-structure interaction force calculator 113 and the site interaction force calculator 114 will be described in detail.

  FIG. 3 is a diagram showing a configuration of a program corresponding to the site-structure acting force calculation unit in FIG.

  In FIG. 3, the site / structure interaction force calculation unit 113 includes a particle / structure contact determination unit 201, a particle reference axis calculation unit 202, a particle / structure contact position calculation unit 203, a contact site identification unit 204, and a contact. It comprises a site-structure interaction force calculation unit 205.

Particles and structures between the contact determination unit 201 determines the contact distance [delta] ₁ between the particles and the structure, a determination of the contact / non-contact between the particles and the structure based on the contact distance [delta] _1. The contact / non-contact determination uses DEM as in the conventional method described above. The particle reference axis calculation unit 202 calculates the particle reference axis based on the rotational displacement of the particles. The particle / structure contact position calculation unit 203 calculates a contact angle θc from the reference axis of the particle to the contact position. The contact site specifying unit 204 specifies the contacted particle site based on the contact angle θc calculated by the particle / structure contact position calculating unit 203 and the particle site information. The contact site / structure interaction force calculation unit 205 calculates the contact force between the particle site and the structure that are in contact with each other based on the contact distance δ ₁ between the particle and the structure and the physical property value of the particle site. To do. Specifically, the contact force is obtained by substituting the physical property value of the particle site in contact with the above-described formulas (1) to (14).

  FIG. 4 is a diagram showing a configuration of a program corresponding to the inter-site action force calculation unit in FIG.

  In FIG. 4, the intersite action force calculation unit 114 includes an interparticle contact determination unit 301, a particle reference axis calculation unit 302, a particle contact position calculation unit 303, a contact site specifying unit 304, and a contact site interacting force calculation unit 305. .

The interparticle contact determination unit 301 determines the contact distance [delta] ₂ between the particles, determination of the contact / non-contact between the particles based on the contact distance [delta] _2. The contact / non-contact determination uses DEM as in the conventional method described above. The particle reference axis calculation unit 302 calculates the reference axis of the particle based on the rotational displacement of the particle in each particle. The particle contact position calculation unit 303 calculates the contact angle θc from the reference axis of the particle to the contact position for each particle. The contact site specifying unit 304 specifies the contacted particle site based on the contact angle θc calculated by the particle contact position calculation unit 303 and the particle site information. The contact site acting force calculation unit 305 calculates the contact force between the particle sites in contact with each other based on the contact distance δ ₂ between the particles and the physical property value of the particle site. Specifically, the contact force is obtained by substituting the physical property value of the particle site in contact with the above-described formulas (1) to (14).

  FIG. 5 is a flowchart of site-structure interaction force calculation processing as a particle behavior analysis method according to the present embodiment. 5 is executed by the site-structure acting force calculator 113.

  First, the particle / structure contact determination unit 201 determines the contact between the target particle and the structure (steps S501 and S502). Specifically, the contact / non-contact determination is performed by DEM as in the conventional particle behavior analysis method described above.

  If the target particle and the structure are not in contact with each other, the process proceeds to step S507. If the target particle and the structure are in contact with each other, the particle reference axis calculation unit 202 stores the particle stored in the particle data storage unit 401c. The particle reference axis is calculated based on the rotational displacement, the calculated particle reference axis is stored in the particle reference axis data storage unit 401j (step S503), and the particle-structure contact position calculation unit 203 stores the particle The contact angle θc from the reference axis to the contact position is calculated, and the calculated contact angle θc is stored in the particle contact position data storage unit 401g (step S504).

  Next, the contact site specifying unit 204 is stored in the contact angle θc stored in the particle contact position data storage unit 401g in step S504, the particle data stored in the particle data storage unit 401c, and the site data storage unit 401d. It is specified which particle site is in contact with the structure based on the existing site data (step S505). Specifically, the angle information of the particle site and the contact angle θc are compared, and the particle site to which the contact site belongs is specified.

  Next, the contact site / structure acting force calculation unit 205 stores the particle data stored in the particle data storage unit 401c, the site data stored in the site data storage unit 401d, and the structure data storage unit 401e. The contact force is calculated based on the structure data being stored and the contact distance data between the two objects stored in the contact distance data storage unit 401h between the two objects, and the calculated contact force is stored in the particle action force data storage unit. 401i is stored (step S506). Specifically, in the formulas (1) to (14) shown in the conventional example, the physical property value of the contacting particle, the physical property value of the particle site, and the physical property value of the structure are represented by the site data storage unit 401d, the particle The contact force is calculated by substituting with reference to the data storage unit 401c and the structure data storage unit 401e.

  Thereafter, it is determined whether or not the contact force has been calculated for all target structures and particles (steps S507 and S508). If the contact force has not been calculated for all structures or particles, the process proceeds to step S501. Returning, when the contact force has been calculated for all the structures and particles, this process is terminated.

  FIG. 6 is a flowchart of the inter-particle site force calculation process as the particle behavior analysis method according to the present embodiment. The processing of FIG. 6 is executed by the inter-particle site force calculation unit 114.

  First, the interparticle contact determination unit 301 determines contact between the target particle and other particles (steps S509 and S510). Specifically, the contact / non-contact determination is performed by DEM as in the conventional particle behavior analysis method described above.

  If the target particle and other particles are not in contact, the process proceeds to step S515. If the target particle and other particles are in contact, the particle reference axis calculation unit 302 stores each particle in the particle data storage unit 401c. The particle reference axis is calculated based on the rotational displacement of the particles being stored, the calculated particle reference axis is stored in the particle reference axis data storage unit 401j (step S511), and the particle contact position calculation unit 303 The contact angle θc from the particle reference axis to the contact position is calculated, and the calculated contact angle θc is stored in the particle contact position data storage unit 401g (step S512).

  Next, the contact site identification unit 304 is stored in the contact angle θc stored in the particle contact position data storage unit 401g in step S512, the particle data stored in the particle data storage unit 401c, and the site data storage unit 401d. Based on the existing site data, which particle site is in contact with other particles in the target particle is specified (step S513). Specifically, the angle information and contact angle θc of each particle site are compared, and the particle site to which the contact site belongs is specified.

  Next, the contact site interaction force calculation unit 305 stores the particle data stored in the particle data storage unit 401c, the site data stored in the site data storage unit 401d, and the contact distance data storage unit 401h between the two objects. Based on the contact distance data between the two objects, the contact force is calculated, and the calculated contact force is stored in the particle action force data storage unit 401i (step S514). Specifically, in the equations (1) to (14) shown in the conventional example, the physical property value of each particle in contact and the physical property value of each particle site are stored in the site data storage unit 401d and the particle data storage unit 401c. The contact force is calculated by reference and substitution.

  Thereafter, it is determined whether or not the contact force has been calculated for all target particles and other particles of interest (steps S515 and S516). If the contact force has not been calculated for all target particles or other particles, step Returning to S509, if the contact force has been calculated for all the particles of interest and other particles, this process ends.

FIG. 7 is a diagram showing calculation of sliding frictional force at the time step in contact with the particle and structure divided into two sites in this embodiment, and (A) shows t = t ₁ [sec. Is a diagram showing the calculation of the sliding frictional force in FIG. 7, and (B) is a diagram showing the calculation of the sliding frictional force at t = t ₂ [sec]. In FIG. 7, the case where one particle and a structure are in contact with each other is considered for ease of explanation.

  7A and 7B, a particle 601 has a particle reference axis 605 and its surface is divided into two sites 603 and 604. The particles 601 are in contact with the structure 602. In the figure, an arrow 606 indicates a normal direction contact force acting on the particle 601, and an arrow 607 indicates a tangential contact force acting on the particle 601.

  Here, the site 603 is in the range from 0 ° to 180 ° clockwise with respect to the particle reference axis 605 of the particle 601, and the site 604 is 180 ° to 360 clockwise with respect to the particle reference axis 605 of the particle 601. Range up to °. The clockwise contact angle with respect to the particle reference axis 605 means an angle formed by a line segment from the center of the particle 601 toward the contact position with respect to the particle reference axis 605. Hereinafter, this is simply referred to as “contact angle”. That's it.

Further, the maximum static friction coefficient μ ₀₁ and the dynamic friction coefficient μ _f1 of the site 603 are set to μ ₀₁ = μ _f1 = 0.5, and the maximum static friction coefficient μ ₀₂ and the dynamic friction coefficient μ _f2 of the site 604 are set to μ ₀₂ = μ _f2 Set to = 1.0. Further, at t = t ₁ , t ₂ [sec], the particle 601 comes into contact with the structure 602, and the force acting on the particle calculated by the above-described equations (1) to (10) is assumed to be unchanged. The contact force 606 in the normal direction acting on the particle 601 calculated based on (3) is 1.0 [N], and the contact force 607 in the tangential direction acting on the particle 601 calculated based on the above equation (8). Is 0.75 [N].

  In FIG. 7A, the particle 601 and the structure 602 are in contact with each other, the contact angle of the particle 601 is 135 °, and the site 603 is in contact with the structure 602. Here, the maximum static frictional force is 0.5 [N] from the above equation (11), and the tangential contact force 607 acting on the particle 601 is larger than the maximum static frictional force, so that the particle 601 is regarded as slipping. It is. At this time, the dynamic friction force is 0.5 [N] from the above equation (13).

  In FIG. 7B, the particle 601 and the structure 602 are in contact with each other, the contact angle of the particle 601 is 225 °, and the site 604 is in contact with the structure 602. Here, the maximum static frictional force is 1.0 [N] from the above formula (11), and the tangential contact force 607 acting on the particle 601 is smaller than the maximum static frictional force, so that the particle 601 is regarded as not slipping. . At this time, the dynamic friction force is 0.75 [N] from the above equation (13).

  That is, even if the tangential contact force acting on the particle 601 calculated from the above formulas (1) to (10) is the same, the friction coefficient is small when the site 603 is in contact with the structure 602. The particles 601 slide, and when the site 604 is in contact with the structure 602, the friction coefficient is large, so the particles 601 do not slip.

  As described above, according to the present embodiment, in the particle behavior analysis, the particle surface is divided into several particle sites, and a physical property value (sliding friction coefficient) is set for each divided particle site. Since the acting force (contact force in the tangential direction) is obtained based on the above formulas (1) to (10) using the set physical property value, it depends on the nonuniformity of the physical property value (sliding friction coefficient) on the particle surface. It is possible to calculate the behavior of particles considering the influence.

  In the present embodiment described above, the sliding friction coefficient in the particle is set as the physical property value of the particle surface, but the set physical property value is not limited to the sliding friction coefficient, for example, a physical property value used in DEM, Specifically, Young's modulus, Poisson's ratio, radius of curvature, coefficient of restitution, specific gravity, rolling friction coefficient, etc. may be set as the physical property values on the particle surface.

  Further, in the present embodiment described above, the contact force is calculated as the acting force, but the calculated acting force is not limited to the contact force, for example, an adhesive force such as a van der Waals force or a liquid crosslinking force. Can also be calculated. In particular, when calculating the van der Waals force, the Hamaker constant, surface roughness, Young's modulus, and the like may be set as physical property values. In addition, although the adhesion force works even without contact, in the case of non-contact, the adhesion force is calculated as an action force between the closest particle sites or between the structure and the closest particle site. The distance between the target particle site and the nearest particle site can be calculated by the method described above, or by using another particle site with the shortest distance from the representative point of the target particle site as the closest particle site. it can.

  Further, in the present embodiment, for each divided particle site, an index indicating the shape and physical quantity of the surface of the particle (for example, the amount of adsorbed water necessary for calculating the liquid crosslinking force) is set instead of the physical property value, By calculating the acting force by the same method as described above, in the particle behavior analysis, the behavior of the particles can be calculated in consideration of the influence of the shape and physical quantity non-uniformity on the surface of the particles.

  In the present embodiment, the particles are divided into particle sites of the same size. However, the size of the particle sites to be divided is not limited to this, and the particles may be divided into particle sites of different sizes. Good. At that time, it is possible to specify the particle site in contact using the contact position of the particle and the structure, and the coordinate information of the particle site.

  In this embodiment, the number of particle site divisions is described as 2, but the number of site divisions is not limited to this. For example, any number of divisions such as 16 divisions, 32 divisions, 100 divisions, etc. may be used in the present invention. Is applicable.

  Note that the number of site divisions does not have to be the same for all particles, and may be different for each particle. For example, a method of changing the number of divisions depending on the particle size may be used, and at this time, the size of the particle site can be set uniformly.

  Further, in this embodiment, the physical property values are individually set for each particle site, but the method for setting the physical property values is not limited to this, for example, a value indicating an average value and variation of the physical property value or physical quantity on the particle surface. Based on the above, at least one of the physical property value and physical quantity of each particle site in each particle may be set using a random number.

  In this embodiment, the physical property values are set for all the particle sites. However, it is not necessary to set the physical property values for all the particle sites. For example, the physical property values or physical quantities are different in a partial region of the particle surface. In this case, it is only necessary to set physical property values or physical quantities only at the particle sites corresponding to these regions, thereby saving the capacity of a memory (not shown) included in the particle behavior analysis apparatus 1.

  In this embodiment, an example in which the present invention is applied to a two-dimensional model is described. However, the present invention may be applied to a three-dimensional model. In this case, the acting force based on the physical property value of each particle site in the three-dimensional model can be calculated by a method similar to the method described above, and thereby the particle behavior in the three-dimensional model can be simulated. In this case, as a method for determining the contact position in the particle, a method for obtaining a three-dimensional position such as a method using a solid angle or a method using a rotation angle in the xyz direction can be applied. In the three-dimensional model, as a method of dividing a three-dimensional sphere, a method of dividing a sphere in three dimensions, such as a method using a regular polyhedron or a method using a quasi-regular polyhedron, can be applied.

  Hereinafter, particle behavior and charge amount analysis in the developing device of the electrophotographic apparatus to which the particle behavior analysis method according to the present embodiment is applied will be described.

  FIG. 8 is a diagram showing a schematic configuration of an image forming apparatus in an electrophotographic apparatus to which the particle behavior analysis method according to the present embodiment is applied.

  In FIG. 8, an image forming apparatus 700 includes a photosensitive drum 701, a charging member 702, a developing device 703, a developing roller 704, an elastic roller 705, an elastic blade 706, a developing container 707, a transfer roller 708, a cleaning blade 709, and a waste toner container 710. , Toner 711 and paper 712.

  The developing device 703 is located in a developing container 707 that stores toner 711 as a one-component developer, and an opening extending in the longitudinal direction (depth direction in the drawing) of the developing container 707, and faces the photosensitive drum 701. A developing roller 704 serving as a developer carrying member is provided, and the electrostatic latent image on the photosensitive drum 701 is developed and visualized.

  In the developing container 707, an elastic blade 706 that is a developer regulating member abuts against the developing roller 704 to regulate the amount of the toner 711 that is carried out, thereby forming a thin layer of the toner 711.

  In recent years, in the developing device 703, in order to realize stable agitation / conveyance of toner particles, toner constituent materials and shapes are positively designed, and the particle behavior analysis method according to the present embodiment is applied to the developing device 703. By using the toner, the shape, dimensions, relative position, etc. of the developing roller and the elastic blade when the toner having non-uniform surface physical properties or the toner having an irregular shape such as an irregular shape or a non-spherical surface shape is used. The toner agitation / conveyance state at the time of the change can be predicted by a computer or the like.

  Next, a particle behavior analysis apparatus and a particle behavior analysis method according to the second embodiment of the present invention will be described.

This embodiment is basically the same in configuration and operation as the first embodiment described above,
The only difference is that the acting force acting not only in the vicinity of the particle site but also in the distance is considered. Therefore, the description of the duplicated configuration and operation is omitted, and the description of the different configuration and operation is given below.

  Further, the particle behavior analysis apparatus and the particle behavior analysis method according to the present embodiment divide the particle surface into sites in an environment where a plurality of particles or particles and structures are in contact with each other, and between the particle sites or between the particle sites and the structure. Find the working force between objects. In this embodiment, when particles and structures are arranged in a two-dimensional section, that is, particle behavior calculation in a two-dimensional model is performed as a representative example, and electrostatic force between particle sites is taken into consideration as an acting force. Consider the amount of charge as a physical quantity.

  FIG. 9 is a block diagram showing a schematic configuration of the particle behavior analysis apparatus according to the present embodiment.

  In FIG. 9, the particle behavior analysis device 3 includes a CPU 400, a RAM 401, a display device 402, an input unit 403, an external storage device 404, and a bus 405.

  The RAM 401 includes a program storage unit 401a, an initial condition data storage unit 401b, a particle data storage unit 401c, a site data storage unit 401d, a structure data storage unit 401e, a particle external force data storage unit 401f, and a particle action force data storage unit 401i. , A particle site representative point / structure vector data storage unit 1001a and a particle site representative point vector data storage unit 1001b.

  Here, the CPU 400, display device 402, input unit 403, external storage device 404 and bus 405, program storage unit 401a in the RAM 401, initial condition data storage unit 401b, particle data storage unit 401c, site data storage unit 401d, structure Since the object data storage unit 401e, the particle external force data storage unit 401f, and the particle action force data storage unit 401i are the same as the components in the particle behavior analysis apparatus 1 of FIG. 1 described above, explanations of these components will be given. Omitted.

  Hereinafter, each data stored in the particle site representative point / structure vector data storage unit 1001a and the particle site representative point vector data storage unit 1001b of the RAM 401 will be described. The particle site representative point / structure vector data is a vector value from the particle site representative point to the structure. The particle site representative point vector data is a vector value from the representative point of the particle site to the representative point of another particle site.

  FIG. 10 shows the configuration of a program corresponding to the calculation of particle behavior in which the particle surface is divided into particle sites and the non-uniformity of at least one of the physical property value and the physical quantity on the particle surface is considered in the present embodiment. FIG.

  10, the program 4 has basically the same configuration as the program 2 of FIG. 2, and instead of the site-structure acting force calculator 113 and the site-site acting force calculator 114, the site-structure acting force is used. The only difference is that the calculation unit 501 and the inter-site action force calculation unit 502 are provided. Therefore, only the site-structure interaction force calculator 501 and the site interaction force calculator 502 will be described in detail below.

  FIG. 11 is a diagram showing a configuration of a program corresponding to the site-structure acting force calculation unit in FIG.

  In FIG. 11, the site / structure interaction force calculation unit 501 includes a site representative point calculation unit 801, a site / structure vector calculation unit 802, and a contact site / structure interaction force calculation unit 803.

  The site representative point calculation unit 801 calculates a representative point of each particle site based on the rotational displacement and parallel displacement of the particles. Specifically, based on the rotational displacement and parallel displacement of the particle, the amount of movement from the time step before the particle site representative point to the current time step is obtained, and the position of the representative point of the particle site at the current time step is determined. Ask. The site / structure vector calculator 802 calculates a particle site representative point / structure vector represented by the following equation (17).

  The contact site / structure interaction force calculation unit 803 calculates the particle site and the structure based on the particle site representative point / structure vector (the above formula (17)), the physical quantity of each particle site, and the physical quantity of the structure. The electrostatic force is calculated as the acting force between. Specifically, using a mirror image method, it is assumed that a mirror image charge having an opposite polarity to the charge set at each particle site exists in the structure, and an electrostatic force (mirror force) acting on each particle site is obtained. For example, the image force for a planar conductor is calculated by the following equation (18).

Here, q _i is the charge amount of the particle site, and q _m is the mirror image charge.

  In addition, torque acts on the particle due to the mirror image force between the particle site and the structure. The torque acting on the particle is further expressed by a vector from the particle center to the particle site representative point by the following equation (19). When the mirror image force acting on the particle site representative point is defined by the following equation (20), it is calculated by the following equation (21).

  FIG. 12 is a diagram showing a configuration of a program corresponding to the inter-site acting force calculation unit in FIG.

  In FIG. 12, the intersite action force calculation unit 502 includes a site representative point calculation unit 901, an intersite vector calculation unit 902, and a contact site interacting force calculation unit 903.

  The site representative point calculation unit 901 calculates, for each particle, a representative point of each particle site based on the rotational displacement and parallel displacement of the particle. Specifically, in each particle, based on the rotational displacement and parallel displacement of the particle, the amount of movement from the time step before the particle site representative point to the current time step is obtained to represent the particle site at the current time step. Find the position of a point. The inter-site vector calculation unit 902 calculates a particle site representative point vector represented by the following formula (22).

  The interaction force calculation unit 903 between the contact sites is based on the vector between the particle site representative points (the above formula (22)), the physical quantity of each particle site, and the position of the representative point of each particle site. Calculate the electrostatic force. Specifically, the calculated electrostatic force is calculated by the following equation (23) using the vector between the representative points of the particle sites (the above equation (22)) and the charge amount of the particle sites.

Here, q _d1 and q _d2 are the charge amounts of the particle sites.

  Further, torque acts on the particles due to electrostatic force between the particle sites. The torque acting on the particles is defined by the following equation (25) when the electrostatic force between the particle sites is defined by the following equation (24). Calculated.

  FIG. 13 is a flowchart of the site-structure interaction force calculation process as the particle behavior analysis method according to the present embodiment. The site / structure interaction force calculation unit 501 executes the process of FIG.

  The site representative point calculation unit 801 calculates the position data of the representative point of the particle site based on the rotational displacement and parallel displacement of the particle stored in the particle data storage unit 401c, and the calculated position data is used as the site data. The data is stored in the storage unit 401d (step S1101). Specifically, based on the rotational displacement and parallel displacement of the particle, the movement amount from the time step before the particle site representative point to the current time step is obtained, and the position data of the representative point of the particle site at the current time step And the calculated position data is stored in the site data storage unit 401d.

  Next, the site-structure vector calculation unit 802 is stored in the position data of the representative points of the particle sites calculated in step S1101 and stored in the site data storage unit 401d, and the structure data storage unit 401e. Based on the position data of the structure, the particle site representative point / inter-structure vector is obtained, and the obtained particle site representative point / inter-structure vector is stored in the particle site representative point / inter-structure vector data storage unit 1001a. (Step S1102).

  Next, the contact site / structure interaction force calculation unit 803 is based on the particle site representative point / structure vector calculated in step S1102 and stored in the particle site representative point / structure vector data storage unit 1001a. Then, the mirror image force is calculated as the acting force between the particle site and the structure (step S1103). Specifically, using the mirror image method, assuming that a mirror image charge exists in the conductor structure, the mirror image force is obtained according to the above equation (18).

  Thereafter, it is determined whether or not the image force has been calculated for all target particle sites, structures and particles (steps S1104, S1105 and S1106), and the image force is calculated for all particle sites, structures and particles. If not, the process returns to step S1101, and if the image force has been calculated for all the particle sites, structures, and particles, this process ends.

  FIG. 14 is a flowchart of the inter-site acting force calculation process as the particle behavior analysis method according to the present embodiment. The process of FIG. 14 is executed by the inter-site action force calculation unit 502.

  The site representative point calculation unit 901 calculates the position data of the representative point of the particle site in each particle based on the rotational displacement and parallel displacement of the particle stored in the particle data storage unit 401c, and the calculated position Data is stored in the site data storage unit 401d (step S1107). Specifically, in each particle, based on the rotational displacement and parallel displacement of the particle, the amount of movement from the time step before the particle site representative point to the current time step is obtained to represent the particle site at the current time step. The point position data is calculated, and the calculated position data is stored in the site data storage unit 401d.

  Next, the inter-site vector calculation unit 902 obtains a particle site representative point vector based on the position data of the representative point of the particle site calculated in step S1107 and stored in the site data storage unit 401d. The particle site representative point vector is stored in the particle site representative point vector data storage unit 1001b (step S1108).

  Next, the interaction force between contact sites is calculated by the contact site interaction force calculation unit 903 based on the particle site representative point vector stored in the particle site representative point vector data storage unit 1001b in step S1108. The electrostatic force is calculated (step S1109). Specifically, the electrostatic force is calculated by substituting the physical quantity of each particle site of the target particle and other particles stored in the site data storage unit 401d into the above equation (23).

  Thereafter, it is determined whether or not the electrostatic force has been calculated for all target particle sites, target particles, and other particles (steps S1110, S1111, S1112, and S1113), and all the particle sites, target particles, and other particles are charged with static electricity. If the force has not been calculated, the process returns to step S1107. If the electrostatic force has been calculated for all the particle sites, the target particle, and other particles, this process ends.

  FIG. 15 is a diagram illustrating a method for calculating electrostatic force when two particles divided into two sites are contacted in the present embodiment. In FIG. 15, a charge amount is set as a physical quantity at each particle site in each particle.

  In FIG. 15, the particle i has a particle site m, and the particle site m has a representative point 1205. The particle j has a particle site n, and the particle site n has a representative point 1206. The particle i and the particle j are not in contact.

  In addition, an arrow 1207 in the figure indicates a particle site representative point vector from the representative point 1205 to the representative point 1206 represented by the following formula (26), and an arrow 1208 indicates a particle represented by the following formula (27). The particle center / representative point vector from the center of i to the representative point 1205 is shown.

When the charge amount at the particle site m is set as q _d (i, m) and the charge amount at the particle site N is set as q _d (j, n), the electrostatic force that the representative point 1205 receives from the representative point 1206 is It is calculated by the following equation (28), and the electrostatic force applied to the particles i is calculated by the following equation (29).

  The electrostatic force calculated by the above equation (29) is different from the electrostatic force calculated by the above equation (16) in the conventional particle behavior analysis method described above. That is, in this embodiment, the electrostatic force can be calculated in consideration of the charge amount distribution on the particle surface.

  Moreover, the torque by the electrostatic force between the particle sites concerning the particle | grain i is calculated by following formula (30).

  The torque calculated by the above equation (30) is 0 except for special cases such as when the particle j has no charge or when the particle sites m and n have the same amount of charge. As a result, torque is applied to the particles and the particles rotate. On the other hand, assuming that the charge of the particle is at the center of the particle as in the conventional particle behavior analysis method described above, torque is not generated because a force is applied to the center of the particle. That is, in the present embodiment, generation of torque due to electrostatic force can be considered by dividing the particle surface into sites.

  As described above, according to the present embodiment, in the particle behavior analysis, the particle surface is divided into several particle sites, the charge amount is set for each divided particle site, and the set object charge is set. Since the acting force (electrostatic force applied to the particle) is obtained based on the above formulas (17) to (29) using the amount, the effect of nonuniformity of the physical quantity (charge amount) on the surface of the particle is considered. Behavior can be calculated. Specifically, in the behavioral analysis of particles, it is possible to consider the electrostatic force acting on the particles and the torque resulting from the electrostatic force in consideration of the influence due to the nonuniformity of the charge amount distribution on the particle surface.

  When the total charge amount of two particles has the same sign (positive or negative), it is assumed that the particle charge is at the center of the particle as in the conventional particle behavior analysis method described above. Since force always occurs, no attractive force is generated between the two particles. However, when the total charge amount of the two particles has the same sign (positive or negative), if charges with different signs are distributed on the particle surface, the same sign charge of other particles and the different sign charge of the own particle Depending on the distance between them, an attractive force may be generated between the two particles. In the present embodiment described above, by dividing the particle surface into sites and considering the electrostatic force at each site, the charge amount distribution can be accurately determined even when charges with different signs are distributed on the particle surface. It can be reproduced, and this can cope with the case where an attractive force is generated between two particles.

  In the present embodiment described above, the representative point of each particle site is present on the particle surface. However, the location of the particle site is not limited to this, and for example, the representative point of the particle site may exist inside the particle. .

  In the present embodiment described above, the representative portion of each particle site is set as a point. However, the location of the representative portion of each particle site is not limited to this, and for example, a surface or a volume may be used.

  In the above-described embodiment, the electrostatic force is calculated as the acting force. However, the calculated acting force is not limited to the electrostatic force, and for example, a magnetic force can be calculated. In particular, when the magnetic force is calculated, magnetization or the like may be set as a physical quantity.

  In the present embodiment described above, the amount of charge in the particle is set as the physical quantity of the particle surface. However, the set physical quantity is not limited to the amount of charge. For example, when electrostatic force is considered as the acting force When considering an electric dipole moment and a magnetic force as an acting force, a magnetization amount, a magnetic moment, etc. may be set as a physical quantity of the particle surface.

  In this embodiment, the physical quantity is set for each particle site, but the physical property value may be set for each particle site. For example, when the electrostatic force is considered as the acting force, the relative dielectric constant is set. When magnetic force is considered as the acting force, relative permeability or the like may be set.

  In the present embodiment, the particles are divided into particle sites of the same size. However, the size of the particle sites to be divided is not limited to this, and the particles may be divided into particle sites of different sizes. Good. At that time, it is possible to specify the particle site in contact using the contact position of the particle and the structure, and the coordinate information of the particle site.

  In this embodiment, the number of particle site divisions is described as 2, but the number of site divisions is not limited to this. For example, any number of divisions such as 16 divisions, 32 divisions, 100 divisions, etc. may be used in the present invention. Is applicable.

  Note that the number of site divisions does not have to be the same for all particles, and may be different for each particle. For example, a method of changing the number of divisions depending on the particle size may be used, and at this time, the size of the particle site can be set uniformly.

  In this embodiment, the physical quantity is individually set for each particle site. However, the physical quantity setting method is not limited to this. For example, the physical quantity is based on the average value of physical quantity or physical property value on the particle surface and a value indicating variation. Thus, at least one of a physical quantity and a physical property value of each particle site in each particle may be set using a random number.

  In this embodiment, an example in which the present invention is applied to a two-dimensional model is described. However, the present invention may be applied to a three-dimensional model. In this case, the acting force based on the physical quantity of each particle site in the three-dimensional model can be calculated by a method similar to the above-described method, whereby the particle behavior in the three-dimensional model can be simulated. In this case, as a method for calculating the representative point in the particle, a method for obtaining a three-dimensional position such as a method using a solid angle or a method using a rotation angle in the xyz direction can be applied. In the three-dimensional model, as a method of dividing a three-dimensional sphere, a method of dividing a sphere in three dimensions, such as a method using a regular polyhedron or a method using a quasi-regular polyhedron, can be applied.

  In the present embodiment, the physical quantity is set for all the particle sites, but it is not necessary to set the physical quantity for all the particle sites.For example, when the physical quantity or the physical property value is different in a partial region of the particle surface, It is only necessary to set a physical quantity or a physical property value at the particle sites corresponding to these regions, thereby saving the capacity of a memory (not shown) included in the particle behavior analysis device 3.

  In this embodiment, physical quantities are set as initial conditions for each particle site. However, various calculation results may be set for each particle site. For example, in each time step, each particle site and structure A charge amount as a result of simulating a charging phenomenon due to contact of an object may be set at each particle site.

  Examples of the storage medium for supplying the program code include RAM, NV-RAM, floppy (registered trademark) disk, hard disk, optical disk, CD-ROM, MO, CD-R, CD-RW, DVD (DVD). -ROM, DVD-RAM, DVD-RW, DVD + RW), magnetic tape, nonvolatile memory card, other ROM, etc., as long as they can store the program code. Alternatively, the program code may be supplied by downloading from another computer or database (not shown) connected to the Internet, a commercial network, a local area network, or the like.

  Further, by executing the program code read by the computer, not only the functions of the above-described embodiments are realized, but also an OS (operating system) running on the computer based on the instruction of the program code. A case where part or all of the actual processing is performed and the functions of the above-described embodiments are realized by the processing is also included.

  Further, after the program code read from the storage medium is written in a memory provided in a function expansion board inserted into the computer or a function expansion unit connected to the computer, the function expansion is performed based on the instruction of the program code. This includes the case where the CPU or the like provided in the board or the function expansion unit performs part or all of the actual processing, and the functions of the above-described embodiments are realized by the processing.

  The form of the program code may be in the form of object code, program code executed by an interpreter, script data supplied to an OS (operating system), and the like.

It is a block diagram showing a schematic structure of a particle behavior analysis device concerning a 1st embodiment of the present invention. It is a figure which shows the structure of the program corresponding to the calculation of the particle | grain behavior in consideration of the nonuniformity of the physical property value and physical quantity in the particle | grain surface in this Embodiment in consideration of at least one of the physical property value and the physical quantity. It is a figure which shows the structure of the program corresponding to the site-structure interaction force calculation part in FIG. It is a figure which shows the structure of the program corresponding to the site force calculation part in FIG. It is a flowchart of the site-structure interaction force calculation process as a particle behavior analysis method according to the present embodiment. It is a flowchart of the interaction force calculation process between particle sites as a particle behavior analysis method according to the present embodiment. In this embodiment, a diagram showing per time step to calculate the sliding friction force when the contact sites divided particles and structures to the two, sliding friction in the (A) is t = t ₁ [sec] It is a figure which shows calculation of force, (B) is a figure which shows calculation of the sliding frictional force in t = t < ₂ > [sec]. 1 is a diagram illustrating a schematic configuration of an image forming apparatus in an electrophotographic apparatus to which a particle behavior analysis method according to an embodiment is applied. It is a block diagram which shows schematic structure of the particle behavior analyzer which concerns on the 2nd Embodiment of this invention. It is a figure which shows the structure of the program corresponding to the calculation of the particle | grain behavior in consideration of the nonuniformity of the physical property value and physical quantity in the particle | grain surface in this Embodiment in consideration of at least one of the physical property value and the physical quantity. It is a figure which shows the structure of the program corresponding to the site-structure interaction force calculation part in FIG. It is a figure which shows the structure of the program corresponding to the site force calculation part in FIG. It is a flowchart of the site-structure interaction force calculation process as a particle behavior analysis method according to the present embodiment. It is a flowchart of an inter-site action force calculation process as a particle behavior analysis method according to the present embodiment. It is a figure which shows the calculation method of the electrostatic force at the time of the contact of the two particle | grains divided into two in this Embodiment. It is a figure which shows the contact force between each particle | grains in DEM. It is a figure which shows the set contact distance, (A) shows the contact distance between 2 particle | grains, (B) shows the contact distance of particle | grains and a structure. It is a figure which shows the program structure which shows roughly the structure of the typical processing program of particle behavior analysis.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Particle behavior analyzer 2, 4 Program 100 Control part 111 Initial condition setting part 112 Site condition setting part 113 Site-structure action force calculation part 114 Intersite action force calculation part 115 Particle external force calculation part 116 Particle displacement calculation part 117 Particle behavior display unit 201 Particle / structure contact determination unit 202 Particle reference axis calculation unit 203 Particle / structure contact position calculation unit 204 Contact site identification unit 205 Contact site / structure interaction force calculation unit 301 Interparticle contact determination unit 302 Particle Reference Axis Calculation Unit 303 Particle Contact Position Calculation Unit 304 Contact Site Identification Unit 305 Contact Site Interacting Force Calculation Unit 400 CPU
401 RAM
402 Display device 403 Input unit 404 External storage device 405 Bus 401a Program storage unit 401b Initial condition data storage unit 401c Particle data storage unit 401d Site data storage unit 401e Structure data storage unit 401f Particle external force data storage unit 401g Particle contact position data storage Unit 401h two-object contact distance data storage unit 401i particle action force data storage unit 401j particle reference axis data storage unit 501 site / structure interaction force calculation unit 502 site interaction force calculation unit 601 particle 602 structure 603, 604 site 605 Particle reference axis 606 Normal contact force 607 Tangential contact force 700 Image forming device 701 Photoconductive drum 702 Charging member 703 Developing device 704 Developing roller 705 Elastic roller 706 Elastic blade 707 Developing container 708 Transfer roller 70 9 Cleaning blade 710 Waste toner container 711 Toner 712 Paper 801, 901 Site representative point calculation unit 802 Site / structure vector calculation unit 803 Contact site / structure interaction force calculation unit 902 Site-site vector calculation unit 903 Contact site interaction Force calculation unit 1001a Particle site representative point / inter-structure vector data storage unit 1001b Particle site representative point vector data storage unit 1205, 1206 Representative point 1207 Particle site representative point vector 1208 Particle center representative point i, j Particle m, n Particle site

Claims (18)

A particle behavior analyzer for analyzing the behavior of particles in an environment where particles and structures exist,
A site condition setting unit that divides the surface of the particle into several particle sites, and sets at least one of a physical property value and a physical quantity at each of the divided particle sites;
Based on at least one of the physical property value and the physical quantity set by the site condition setting unit, a site-structure interaction force calculation unit that calculates an interaction force between the particle site and the structure,
A particle behavior analysis apparatus comprising: an inter-site action force calculation unit that calculates an action force between the particle sites based on at least one of the physical property value and the physical quantity set by the site condition setting unit .   The particle site closest to the structure or other particle is specified, and the acting force is calculated using at least one of the physical property value and the physical quantity set in the specified particle site. The particle behavior analysis apparatus according to claim 1.   A relative position between a representative point of the particle site of the structure or another particle and a representative point of the particle site is obtained, and the obtained relative position and at least one of the physical property value and the physical quantity of the particle site are used. The particle behavior analyzing apparatus according to claim 1, wherein the acting force is calculated.   The site condition setting unit sets at least one of the physical property value and the physical quantity at the particle site based on a value indicating an average value and variation of at least one of the physical property value and the physical quantity of the particle site. 2. The particle behavior analysis apparatus according to claim 1, wherein   The said acting force is represented by at least 1 parameter selected from the parameter group which consists of contact force, adhesion force, electrostatic force, and magnetic force, The Claim 1 characterized by the above-mentioned. Particle analysis behavior device.   The physical property value is at least selected from a parameter group consisting of Young's modulus, Poisson's ratio, sliding friction coefficient, rolling friction coefficient, restitution coefficient, radius of curvature, specific gravity, relative permittivity, Hamaker constant, surface roughness, and relative permeability. The particle behavior analysis device according to any one of claims 1 to 5, wherein the particle behavior analysis device is represented by one parameter.   The physical quantity is represented by at least one parameter selected from a parameter group consisting of a charge amount, a magnetization amount, a magnetic moment, an electric dipole moment, and an adsorbed moisture amount. 2. The particle behavior analysis apparatus according to item 1.   Particles and structures as a developer for forming a visible image on the surface of a carrier on which a latent image is formed, contained in a container, and pressed on the developer carrier to be on the developer carrier At least particles and structures existing in a developing device provided with a developer regulating member that regulates the amount of the developer, and particles and structures present in the stirring unit or the developing unit in which the developer is stirred and mixed. The particle behavior analysis apparatus according to any one of claims 1 to 7, wherein one behavior is analyzed. A particle behavior analysis method for analyzing the behavior of particles in an environment where particles and structures exist,
A particle site condition setting step of dividing the particle surface into several particle sites, and setting at least one of the physical property value and the physical quantity at each of the divided particle sites;
A particle site / structure interaction force calculation step for calculating an interaction force between the particle site and the structure based on at least one of the physical property value and the physical quantity set in the site condition setting step;
A particle behavior comprising: a step of calculating an action force between the particle sites based on at least one of the physical property value and the physical quantity set in the site condition setting step. analysis method.   The particle site closest to the structure or other particle is specified, and the acting force is calculated using at least one of the physical property value and the physical quantity set in the specified particle site. The particle behavior analysis method according to claim 9.   A relative position between a representative point of the particle site of the structure or another particle and a representative point of the particle site is obtained, and the obtained relative position and at least one of the physical property value and the physical quantity of the particle site are used. The particle behavior analysis method according to claim 9, wherein the acting force is calculated.   The particle site condition setting step includes setting at least one of the physical property value and the physical quantity at the particle site based on an average value and a value indicating variation of at least one of the physical property value and the physical quantity of the particle site. The particle behavior analysis method according to claim 9.   The said acting force is represented by at least 1 parameter selected from the parameter group which consists of contact force, adhesion force, electrostatic force, and magnetic force, The Claim 1 characterized by the above-mentioned. Particle analysis behavior method.   The physical property value is at least selected from a parameter group consisting of Young's modulus, Poisson's ratio, sliding friction coefficient, rolling friction coefficient, restitution coefficient, radius of curvature, specific gravity, relative permittivity, Hamaker constant, surface roughness, and relative permeability. The particle behavior analysis method according to any one of claims 9 to 13, wherein the particle behavior analysis method is represented by one parameter.   The physical quantity is represented by at least one parameter selected from a parameter group consisting of a charge amount, a magnetization amount, a magnetic moment, an electric dipole moment, and an adsorbed moisture amount. 2. The particle behavior analysis method according to item 1.   Particles and structures as a developer for forming a visible image on the surface of a carrier on which a latent image is formed, contained in a container, and pressed on the developer carrier to be on the developer carrier At least particles and structures existing in a developing device provided with a developer regulating member that regulates the amount of the developer, and particles and structures present in the stirring unit or the developing unit in which the developer is stirred and mixed. 16. The particle behavior analysis method according to claim 9, wherein one behavior is analyzed. A program for causing a computer to execute a particle behavior analysis method for analyzing the behavior of the particles in an environment where particles and structures exist,
A particle site condition setting module that divides the surface of the particle into several particle sites and sets at least one of the physical property value and the physical quantity at each of the divided particle sites;
A particle site / structure interaction force calculation module that calculates an interaction force between the particle site and the structure based on at least one of the physical property value and the physical quantity set by the site condition setting module;
A program comprising: an action force calculation module between particle sites for calculating an action force between the particle sites based on at least one of the physical property value and the physical quantity set by the site condition setting module.   A computer-readable storage medium storing the program according to claim 17.

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