JP2006300651A - Particle behavior analyzer and analytical method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an particle behavior analyzer and analytical method capable of finding a difference in a compression condition such as a deformed amount and elastic energy of an individual particle due to a physical property of the particle or a structure in detail, in particle behavior analysis using a discrete element method. <P>SOLUTION: In this particle behavior analyzer having the particle and the structure arranged related thereto, and for finding the behavior thereof by the discrete element method, the individual deformed amount and elastic energy of the particle or the structure are individually obtained, as a deformed condition of the particle or the structure, using an approach amount between the two contacting bodies and the respective physical properties, in a contact part between the particle and the particle or patrticle and the structure. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a particle behavior analysis apparatus and a particle behavior analysis method using a discrete element method, and more specifically, a compression state of particles in a contact portion using a property value of a particle such as a developer or a structure such as a container. The present invention relates to a particle behavior analysis apparatus and a particle behavior analysis method for obtaining a physical quantity to be expressed.

  For example, in a copying machine or a printer using an electrophotographic technique, a visible image made of toner is formed on the surface of a photoreceptor by a developing device. Fine toner particles are supplied into the developing device, and the toner particles are appropriately supplied to the development site for development. In the two-component development method, the toner adheres to a carrier that is a magnetic material, and is stirred and conveyed in the developing device. Thus, in the developing machine, particles of various particle sizes and materials such as external additives and resins are mixed in addition to toner particles and carriers. In addition, it is known that toner particles are deteriorated by rubbing and compression in a series of processes in which toner particles are supplied and then transferred onto a paper surface, and this toner deterioration has a great influence on image quality.

  In the field of handling powders and granular materials as described above, it is an important issue to understand the behavior of particles. In recent years, many simulations using the discrete element method (DEM) have been performed for such problems.

  Regarding DEM, a specific calculation method is described in Non-Patent Document 1 and the like, and only features will be briefly described here. DEM is a method for obtaining the behavior of a particle at each time by solving a motion equation based on the force acting on the particle. As a contact force acting between two objects, an elastic repulsive force based on a spring-dashpot model is used. Define viscous damping force.

  Hereinafter, a method for obtaining the contact force in the DEM will be described with reference to FIGS.

  The acting force between the particles is modeled using an elastic spring, dashpot in the normal direction, and an elastic spring, dashpot, slider in the tangential direction as shown in FIG. δ is defined, and contact / non-contact determination and contact force calculation are performed using the distance. In addition, a model similar to the contact between particles can be applied to the contact portion between the particle and a structure such as a container wall. As a result, the behavior of the particles in the powder or granular material can be analyzed using the DEM. Of these, the definition of the approaching amount is as shown in FIG. 8, and the approaching amount between two particles (the length of the overlapping portion of the particles in a straight line connecting the centers of the particles) is shown in FIG. FIG. 8B shows the approach amount between the particle and the structure (the overlapping length of the particle and the structure in a straight line perpendicular to the structure surface from the center of the particle). Here, the center of the particle is defined by the center of a circle or a sphere having a radius of curvature of the normal contact portion or the closest portion.

  Hereinafter, an example of a typical program configuration of the particle behavior analysis apparatus will be described with reference to FIG.

  In the figure, reference numeral 100 denotes a control unit that controls the overall processing of the program.

  Reference numeral 111 denotes an initial condition setting unit, which sets a calculation time and a time step as an initial arrangement of particles, a radius, a physical property value, a shape, a dimension, a physical property value of a rigid structure constituting an analysis region, and a calculation condition. Reference numeral 112 denotes an acting force calculation unit between particles, which obtains an acting force such as a contact force or an adhesion force acting between two particles. Reference numeral 113 denotes an acting force calculation unit for the particle and the structure, which obtains an acting force such as a contact force and an adhesion force acting between the particle and the structure. Reference numeral 115 denotes a calculation unit for an external force acting on the particle, and calculates an acting force such as gravity, magnetic force, electrostatic force, etc. acting on the particle. Reference numeral 116 denotes a particle displacement calculator, which solves the equation of motion based on the acting force acting on the particle and obtains the velocity and displacement of the particle. Reference numeral 117 denotes a particle behavior display unit that displays the positions of particles and structures at each time. In the actual calculation, the behavior of the particles can be obtained by repeatedly performing the processes 112 to 116.

  On the other hand, in the particle behavior analysis using the DEM method, there is a method of using the deformation amount of the toner due to compression or elastic energy as an index of toner deterioration. The following shows an example in which the deformation amount and elastic energy of particles are used as indices in the DEM technique.

Non-patent document 2 specifically describes the DEM technique using the deformation amount of particles as an index. In this way, between the particles on the basis of the approaching amount [delta] of two bodies, or determine the contact force between the particles and the structure, and the particles are plastically deformed when the amount close exceeds the elastic limit amount [delta] _L.

A DEM technique using elastic energy as an index is reported in Non-Patent Document 3 and the like. In this method, the elastic energy in the normal direction and the tangential direction is obtained by the following equation based on the approach amount δ _n δ _t between particles or between particles and structures.

The elastic energy stored in each particle is considered to be divided into two equal parts and stored in the contact part between the particles, and the total elastic energy is stored in the particles between the particles and the structure. Yes.
Tanaka et al., Proceedings of the Japan Opportunity Society (Part B), 57, 534, 60 (1991) Nakayama et al., Fuji Xerox Technical Report, 12, 103 (1998) Transactions of the Japan Society of Mechanical Engineers: 64, 625, (1998), 323

  However, since the above method uses the approach amount that is the sum of the deformation amounts of the particles and structures to determine the deformation amount and elastic energy in the compressed state of the particles, the physical property values such as the size and Young's modulus of the contact particles If they are equal, the value is correct, but if they are different, the deformation amount and elastic energy of each particle cannot be obtained correctly.

For example, FIG. 9 is a diagram showing a contact state between particles and a structure, where reference numeral 901 denotes particles and reference numeral 902 denotes a structure. Here, as in FIG. 9 (a), taken describes the case amount approaching of the particles and the structure was [delta] _n the example. In an ordinary DEM, if the approach amount δ _n is obtained as shown in FIG. 9A, the elastic force due to contact is obtained, but the respective deformation amounts of the particles and the structure are not obtained separately. However, when the particles are sufficiently softer than the structure as shown in FIG. 9B, it is considered that the structure hardly deforms and only the particles deform. Conversely, as shown in FIG. 9C, when the particles are sufficiently harder than the structure, the particles are hardly deformed and only the structure is deformed.

  Thus, even in the same approach amount in the DEM, the compressed state of the particles is completely different depending on the physical properties of the particles and structures.

  The present invention has been made in view of such problems, and in particle behavior analysis using the discrete element method, particle behavior analysis that can accurately determine the deformation amount and elastic energy of each particle as the compression state of the particle. An object is to provide an apparatus and an analysis method.

  In order to solve such a problem, a particle behavior analysis apparatus according to the present invention includes a particle and a structure arranged in association with the particle, and the particle behavior analysis apparatus obtains the behavior by a discrete element method. Alternatively, at the contact part between the particle and the structure, the deformation amount of each particle or structure and the elastic energy can be obtained as the deformation state of the particle or structure by using the approaching amount between the two contacting bodies and the respective physical property values. Is obtained individually.

  In addition, the particle behavior analysis apparatus of the present invention is in pressure contact with particles in a container containing developer as particles for forming a visible image on the surface of the carrier on which the latent image is formed, and the developer carrier. Particles of a developing device equipped with a developer regulating member that regulates the amount of developer on the developer carrier, particles in the agitator and developer where the developer is agitated and mixed, developer carrier and intermediate transfer At least particles in a transfer device that transfers developer as particles represented by a contact portion of the body, and particles in a cleaning device having a cleaning blade provided to remove unnecessary particles on the developer carrier after transfer It is used to analyze one behavior.

  The particle behavior analysis method of the present invention includes a particle and a structure arranged in relation to the particle, and the particle behavior analysis method for obtaining the behavior by a discrete element method. In the contact part, the amount of deformation and elastic energy of each particle or structure are individually determined as the deformation state of the particle or structure using the approaching amount between the two bodies in contact with each other and the respective physical property values. It is characterized by.

  In addition, the particle behavior analysis method of the present invention is brought into pressure contact with particles in a container containing developer as particles for forming a visible image on the surface of the carrier on which the latent image is formed, and the developer carrier. Particles of a developing device equipped with a developer regulating member that regulates the amount of developer on the developer carrier, particles in the agitator and developer where the developer is agitated and mixed, developer carrier and intermediate transfer At least particles in a transfer device that transfers developer as particles represented by a contact portion of the body, and particles in a cleaning device having a cleaning blade provided to remove unnecessary particles on the developer carrier after transfer It is used to analyze one behavior.

  According to the present invention, in the particle behavior analysis apparatus using the discrete element method, it is possible to obtain in detail the difference in compression state such as the deformation amount and elastic energy of each particle due to the physical property value of the particle or structure. became.

  In addition, by using this method, the compression state of particles can be obtained in more detail without changing the behavior of particles with normal DEM.

  Further, by applying the present invention to the developer behavior analysis of an electrophotographic apparatus, a transfer device in which the intermediate transfer member and the photosensitive member are in contact with each other, a cleaning device having a cleaning blade for removing transfer residual toner, and an elastic blade are used. For devices that control the behavior of the developer using a structure, such as a regulating part that coats the magnetic roller with a thin layer of toner, and a development nip part of a toner cartridge in the contact development method, Elastic energy can be predicted more precisely.

  The present invention is not limited to the above-described embodiments, and it goes without saying that modifications and combinations can be appropriately made within the scope of the gist of the present invention.

  Hereinafter, a preferred embodiment of the present invention will be described in detail with reference to the drawings as necessary.

  First, the whole structure of the particle | grain behavior analyzer by this invention is demonstrated using FIG. 1, FIG.

  FIG. 1 is a schematic program configuration diagram showing a preferred example of the processing program of the particle behavior analysis apparatus.

  Reference numerals 100, 111 to 113, and 115 to 117 are the same as those in FIG.

  Reference numeral 114 is a particle deformation amount and elastic energy calculation unit, and separately determines the deformation amount of each particle or structure from the approaching amount of the contacting particle or structure and the physical property value of the particle or structure. The elastic energy of each particle is calculated from the obtained deformation amount.

  FIG. 2 is a block diagram of an apparatus representing a preferred example according to the present invention.

  The configuration of this apparatus will be described in detail. The CPU 200 is a central processing unit and controls the above-described units connected via the bus 205. The storage units 201a to 201f of the RAM 201 store the program, calculation condition data, particle data, structure data, deformation amount data, and elastic energy data shown in FIG. The display device 202 includes a display, a printer, and the like, and displays data to be displayed under the control of the CPU 200. The input unit 203 includes a keyboard, a mouse, and the like, and inputs input data from the outside into the apparatus. The external storage device 204 is composed of a hard disk or the like and stores various data.

  Here, the contents of each data in the RAM 201 will be described. The calculation condition data stores values related to calculation conditions such as time step and actual calculation time. In the particle data, the position coordinates of each particle and physical property values such as particle size, Young's modulus, Poisson's ratio, friction coefficient, specific gravity and the like are stored. The structure data stores values such as the shape, dimensions, physical property values, position coordinates, and movement speed of the structure part. In the deformation amount data, the value of the deformation amount of each particle is stored. The elastic energy data stores the elastic energy value of each particle.

  Here, the detailed concept of the method and the specific processing flow will be described with reference to FIGS. 3 to 6 for the deformation amount of the particles and the elastic energy calculation unit 114 which are the features of the present invention.

  First, the concept of a contact model between particles will be described with reference to FIGS.

FIGS. 5 (a) modulus of elasticity used in conventional DEM shown in k _n, elastic spring represented by k _t is equivalent to that bound particles 1, the elastic spring of the particles 2 in series, by this method The behavior of the obtained particles is exactly the same as that of a normal DEM.

  FIGS. 6A and 6B are diagrams showing the deformation amount and the deformation force in the normal direction and the tangential direction at the contact portion between the particles. Reference numeral 601 indicates the particle 1 and reference numeral 602 indicates the particle 2. Here, how to obtain the deformation amount, deformation force, and elastic energy of the particles 1 is shown. The particle 2 can be obtained by the same method.

  Hereinafter, R represents the radius of the particle. C represents the stiffness constant of each member, and is obtained from the Young's modulus E and Poisson's ratio ν of each member by the following formula.

  Further, the deformation amount and elastic energy of the particle can be obtained in the contact portion between the particle and the structure in the same way as the contact portion between the particles. Specifically, the amount of deformation of the particles and the structure and the elastic energy of the particles are obtained by substituting the physical property values and particle diameters of the particles 2 with the physical property values and the curvature radius of the structures in the formulas (7) to (9). I can do it.

  Next, the deformation amount of the particles at the contact portion between the particles and the specific processing flow in the elastic energy calculation unit 114 will be described.

  FIG. 3 is a block diagram illustrating a preferred example of processing in the deformation amount and elastic energy calculation unit 114 of the particles. FIG. 4 is a flowchart showing a preferred example of the deformation amount of the particles and the flow of processing in the elastic energy calculation unit 114. The flow of processing for calculating the acting force of particles and structures using the above apparatus will be described with reference to FIGS.

1) The contact determination unit 311 performs contact determination between particles or between a particle and a structure based on the particle data 201c by the same method as a normal DEM, and obtains the approach amounts δ _n and δ _t (step S401). ).

  2) The stiffness constant calculation unit 312 obtains the stiffness constant of each particle and structure using the equations (4) and (6) based on the particle data 201c and the structure data 201d (step S402).

  3) In the deformation amount calculation unit 313, the deformation amount of each particle is obtained from the approach amount obtained in 1) and the stiffness constant obtained in 2) using equations (7) and (8), and the deformation amount data 201e is obtained. Save (step S403).

  4) The elastic energy calculation unit 314 calculates the elastic energy of each particle using the equation (9) from the deformation amount obtained in 3), and stores it in the elastic energy data 201f. (Step S404).

  5) The processes 1) to 4) are performed on all particles and structures (step S405).

Based on the above description, an example in which this method is applied when the approaching amount of two particles having the same particle diameter is δ _n = 100 μm as shown in FIG.

  11A and 11B are examples of the results of calculating the deformation amount and elastic energy of the particles when the Young's modulus of the particles 2 is fixed and the Young's modulus of the particles 1 is changed.

  FIG. 11A is an example of the result of the deformation amount of the particle when the Young's modulus of the particle 1 is changed. In this result, the smaller the rigidity of the particle 1, the larger the deformation amount of the particle 1, and the smaller the deformation amount of the particle 2. Further, as the rigidity of the particle 1 increases, the deformation amount of the particle 1 decreases and the deformation amount of the particle 2 increases.

  FIG. 11B shows the elastic energy of the particles 1 and 2 and the elastic energy of the particles 1 and 2 in the conventional DEM. In the conventional DEM, even if the relationship between the Young's modulus of the particle 1 and the particle 2 is changed, the elastic energy of the particle 1 and the particle 2 is the same value. As the amount changes, each elastic energy shows a different value, and its magnitude relationship also changes.

  As shown in the above results, using this method, in the particle behavior analysis device by the discrete element method, the deformation amount and elastic energy of each particle are considered in consideration of the physical property value and particle size of each particle or structure. It became possible to ask for.

  In this embodiment, the deformation amount of the particles is obtained, and the elastic energy is obtained based on the deformation amount. However, when only the elastic energy is obtained, the same as the equation (9) from the rigidity and the approach amount of each particle. Elastic energy can be obtained. In this case, the elastic energy of each particle is obtained using the following equation.

  Further, if the deformation amount and elastic energy of the particles obtained in this embodiment are obtained simultaneously when the acting force is calculated in the acting force calculator 112 between the particles and the acting force calculator 113 between the particle and the structure, contact determination and rigidity It can be shared with the calculation of constants.

  Hereinafter, as one specific application example of the present invention, a developer behavior analysis in a primary transfer portion of an electrophotographic apparatus using an intermediate transfer method will be described.

  FIG. 10 shows a part of an apparatus constituting the image forming apparatus in the electrophotographic apparatus. In the figure, 1011 is a charging member, 1012 is a photosensitive drum, 1013 is a coating member, 1014 is a magnetic roller, 1015 is a developing container, 1016 is a toner bottle, 1017 is a conveying screw, 1018 is an intermediate transfer member, and 1019 is a paper conveying roller. Reference numeral 1020 denotes a cleaning device, and reference numeral 1021 denotes a cleaning member. In the transfer part that transfers the toner image on the photosensitive drum to the intermediate transfer member, it is said that the toner is plastically deformed due to compression as a cause of transfer failure, and the intermediate transfer member for realizing stable transfer is a design item. It is one of.

  By applying the present invention to the primary transfer portion (contact portion between the photosensitive drum and the intermediate transfer member), the deformation amount and elastic energy of the toner in the transfer portion can be predicted by a computer, and the image defect It can be used to elucidate the cause and design the transcription part.

  In the electrophotographic apparatus, in addition to the primary transfer portion, a cleaning member 1021 for cleaning the developer that has not been transferred by the developer cleaning apparatus, and a coating member 1013 for coating the magnetic roller 1014 with a uniform thin layer of toner. Various structures such as a contact developing type developing roller are used to control the behavior of the developer, and the analysis apparatus according to the present invention is applicable to them.

Schematic program configuration diagram showing a preferred example of the overall configuration of the processing program in the particle behavior analysis apparatus of the present invention 1 is a block diagram of a discrete element method analyzer according to an embodiment of the present invention. The block diagram which shows a suitable example of the processing amount in the deformation amount and elastic energy calculation part of the particle concerning the Example of this invention The flowchart showing a suitable example of the flow of the deformation | transformation amount of the particle concerning the Example of this invention, and the flow of a process in an elastic energy calculation part (A) Normal DEM contact model (b) Diagram showing a contact model according to an embodiment of the present invention (A) The figure explaining the relationship between the deformation amount and deformation force of the normal direction in the contact part of the particle | grains concerning the Example of this invention (b) The tangential direction in the contact part of the particle | grains concerning the Example of this invention The figure explaining the relationship between the amount of deformation and the deformation Program configuration diagram for schematically explaining the overall configuration of a processing program in an apparatus for analyzing the behavior of particles according to a conventional example Explanatory diagram for schematically explaining the concept of contact calculation in an apparatus for analyzing the behavior of particles according to a conventional example Explanatory drawing explaining the deformation amount of both in the contact part of particle and structure structure Explanatory drawing which shows a part of electrophotographic apparatus concerning the Example of this invention The figure showing an example of the result regarding the typical sectional view of an example which calculated the compression state of the elastic particle in the two-dimensional section in the contact part of the particles concerning the example of the present invention, and the amount of deformation of an elastic structure

Explanation of symbols

Step S401 to Step S405 Block 100 Represents Processing Control Blocks 111 to 117, 311 to 314 Block 200 Represents CPU
201 RAM
202 Display device 203 Input unit 204 External storage device 205 Bus

Claims (4)

In a particle behavior analyzer that has particles and structures arranged in relation to them, and obtains their behavior by the discrete element method,
The amount of deformation of each particle or structure as the deformation state of the particle or structure using the approach amount between the two bodies in contact with each other and the respective physical property values at the contact portion of the particle and particle or particle and structure. A particle behavior analysis device characterized by obtaining individual and elastic energy. The particle behavior analysis apparatus according to claim 1,
Particles in a container containing a developer as particles for forming a visible image on the surface of the carrier on which the latent image is formed, and the developer on the developer carrier in contact with the developer carrier Particles of a developing device equipped with a developer regulating member that regulates the amount, particles of the agitating unit and developing unit in which the developer is agitated and mixed, and particles represented by the contact part of the developer carrying member and the intermediate transfer member Used to analyze at least one behavior of particles in a transfer device for transferring developer and particles in a cleaning device having a cleaning blade provided to remove unnecessary particles on the developer carrier after transfer. A particle behavior analysis apparatus characterized by that. In the particle behavior analysis method, which has particles and structures arranged in relation to them, and obtains their behavior by the discrete element method,
The amount of deformation of each particle or structure as the deformation state of the particle or structure using the approach amount between the two bodies in contact with each other and the respective physical property values at the contact portion of the particle and particle or particle and structure. A particle behavior analysis method characterized by individually obtaining elastic energy. The particle behavior analysis method according to claim 3,
Particles in a container containing a developer as particles for forming a visible image on the surface of the carrier on which the latent image is formed, and the developer on the developer carrier in contact with the developer carrier Particles of a developing device equipped with a developer regulating member that regulates the amount, particles of the agitating unit and developing unit in which the developer is agitated and mixed, and particles represented by the contact part of the developer carrying member and the intermediate transfer member Used to analyze at least one behavior of particles in a transfer device for transferring developer and particles in a cleaning device having a cleaning blade provided to remove unnecessary particles on the developer carrier after transfer. A particle behavior analysis method characterized by the above.