JP2007249076A - Information processor and information processing method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To analyze behavior of a particle coming into contact with a member while taking a geometric shape of set surface roughness into consideration by setting the surface roughness when a surface of the member has the surface roughness. <P>SOLUTION: The information processor having a member data storage section storing data including property values of a movable member and a particle data storage section storing property data of particles put in a container having the movable member, and computing behavior of a particle coming into contact with the movable member based upon data read out of the data storage sections is equipped with a data setting section which sets data on intervals and height of unevenness as the surface roughness of the movable member in a surface roughness data storage section, a calculation section which calculates relative position data between the particle and movable member based upon data read out of the member data storage section and particle data storage section, a calculation section which calculates an uneven part coming into contact with the particle based upon the calculated position data and interval and height data on the unevenness, and an arithmetic section which finds contact force at the calculated uneven part coming into contact with the particle and computes the behavior of the particle based upon operation of the contact force. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to an information processing technique for analyzing the behavior of toner particles in a container.

  In electrophotographic copying machines and printers, a developer forms a visible image with toner on the surface of a photoreceptor. Fine toner particles are supplied into the developing device. In order to appropriately supply the toner particles to the development site and perform development, the surface of the member for conveying the toner is given a surface roughness, and a large number of toner particles can be stably conveyed by the unevenness of the surface. Has been done.

  In recent years, particle behavior analysis has been performed to analyze the state of toner particle transport and stirring in a container containing toner, and the analysis result is being utilized for optimization of the container configuration and the like. In the state of conveying and stirring the particles, the particles and the particles and the container wall are always in contact with each other. Therefore, in the particle behavior analysis, it is necessary to obtain the contact force between the particles or between the particles and the container wall. A discrete element method (DEM) that can model a system in which the contact force is dominant and calculate the contact force by numerical calculation is generally used.

  For DEM, for example, a specific calculation method is described in Non-Patent Document 1, and only features will be briefly described here.

  DEM is a method for determining the behavior of a particle at each time by modeling the particle and solving the equation of motion of the force acting on the particle. As the contact force between particles and between particle and container wall, elastic repulsion force, viscous damping force and friction force based on spring (elastic element) -dashpot (viscous damping element) model are defined, and the equation of motion is solved. This is to analyze the behavior of particles.

FIG. 12 is a diagram illustrating a model in which the contact force of two objects (1210, 1220) in contact is separated into a normal direction and a tangential direction. The contact force is modeled by an elastic repulsive force represented by a spring 1201 and a viscous damping force represented by a dash pot 1202. Further, a sliding friction force represented by a friction slider 1203 is further applied to the tangential direction of the two objects. These functions only when two objects are in contact.
“Tanaka et al., Proceedings of the Japan Opportunity Society (Part B), 57,534,60 (1991)”

  However, when the surface of the sleeve is provided with a surface roughness, such as a developing roller used in electrophotography, it is necessary to consider the surface roughness because the state of particle transfer varies depending on the size and shape of the surface roughness. is there. In order to realize this with a conventional DEM, a method using a large value as a friction coefficient of sliding friction is employed. However, since the sliding friction force in the DEM is modeled as a force acting in the tangential direction of the particles, for example, the force acts in a direction different from the force that the convex portion of the surface roughness gives to the particles. Therefore, particularly when the surface roughness is equal to or larger than the particle size, it is difficult to accurately represent the influence of the surface roughness only by the sliding frictional force.

  In view of the above-described problems, the present invention provides an information processing technique for setting the surface roughness of a member and analyzing the behavior of particles in contact with the member considering the set surface roughness geometry. The purpose is to do.

An information processing apparatus according to the present invention includes:
Data read from each data storage unit, including a member data storage unit that stores data including physical property values of the movable member, and a particle data storage unit that includes physical property data of particles contained in the container having the movable member Based on the information processing apparatus for calculating the behavior of the particles in contact with the movable member,
Data setting means for setting the data of the unevenness interval and height as the surface roughness of the movable member in the surface roughness data storage unit;
Relative position calculation means for calculating relative position data between the particles and the movable member based on the data read from the member data storage unit and the particle data storage unit;
Contact for calculating the concavo-convex portion in contact with the particles based on the position data calculated by the relative position calculation means and the data of the concavo-convex interval and height set in the surface roughness data storage unit. Position calculating means;
And calculating means for calculating a behavior of the particles by the action of the contact force by obtaining a contact force at the uneven portion that contacts the particles calculated by the contact position calculating means.

  According to the present invention, it is possible to set the surface roughness of a member and analyze the behavior of particles in contact with the member considering the set surface roughness geometry.

(First embodiment)
Hereinafter, a first embodiment of the present invention will be described with reference to the accompanying drawings.

  In the present embodiment, the particle behavior calculation in the case where a member having particles and surface roughness is arranged in a two-dimensional cross section is described as an example, but the same three-dimensional behavior also applies to three-dimensional particle behavior. Analysis is possible by using a model. Further, as shown in FIG. 4, the member having the surface roughness is assumed to have a linear shape, and isosceles triangles 405a to 405d defined by the surface roughness interval λ and the height a are repeated on the surface of the member 401. The surface roughness is expressed as Further, as the member information, one end point of the member is defined as a reference point 402, and the number of unevenness counted from the reference point 402 is defined as an unevenness number. Further, a unit vector Ut403 in the tangential direction of the member and a unit vector Un404 in the normal direction are defined, and the concavo-convex part is set in the direction of the unit normal vector Un.

(Configuration of particle behavior analysis program)
FIG. 1A is a diagram showing a configuration of a particle behavior analysis program module that executes analysis in an information processing device that executes particle behavior analysis (hereinafter also referred to as “particle behavior analysis device”). Means (control unit 100, acting force between particles and surface roughness member) for executing specific processing in cooperation with particle behavior analysis program module and hardware resource (for example, CPU 200 in FIG. 2) Part 115) is constructed.

  The control unit 100 controls the entire particle behavior analysis process. The initial condition setting unit 111 sets the initial conditions of particles, physical property values such as radius and specific gravity, and the calculation conditions such as the shape, size, position, and time step of the members constituting the analysis region.

  Further, the initial condition setting unit 111 further sets information on the surface roughness of the member, such as whether or not the surface roughness is present, the interval and height of the surface roughness, and which surface of the member is to define the surface roughness. Is possible.

  The acting force calculation unit 112 between particles calculates a contact force that is an acting force between two particles. The acting force calculation unit 113 between the particles and the member calculates a contact force that is an acting force between the particles and a member such as a container wall arranged in association with the particles. The external force calculator 114 acting on the particles calculates external forces such as gravity, magnetic force and electrostatic force acting on the particles. The particle displacement calculation unit 116 solves the equation of motion based on the force acting on the particle, and calculates the velocity and displacement of the particle. The particle behavior display unit 117 displays the positions of particles and members at each time.

  The particle-to-particle action force calculation unit 112 and the particle-to-member action force calculation unit 113 define a contact distance δ between two objects, and use the distance to determine contact / non-contact, as well as contact distance and tangent. Calculate contact force determined by displacement and relative speed. At this time, in many cases, the geometric information of the member is generally defined by a straight line, a circular arc, a three-dimensional analysis, a plane, a cylinder, a sphere, or the like.

  Based on the position of each particle, the calculation unit 115 for the acting force between the particle and the member having the surface roughness obtains the position of the concavo-convex portion representing the surface roughness in the vicinity of the particle, and the acting force between it and the particle Perform the calculation.

  By repeating the processing of the particle force calculator 112 to the particle displacement calculator 116, the behavior of the particles at each time can be obtained.

  Next, an operation force calculation unit 115 (hereinafter referred to as a “particle member operation force calculation unit”) 115 between the particles that execute the processing characteristic of the present embodiment and a member having a surface roughness will be described with reference to FIG. A description will be given with reference to FIGS.

  FIG. 1B is a diagram illustrating a configuration of a processing unit that constitutes the particle member acting force calculation unit 115. The particle member acting force calculation unit 115 includes “a concavo-convex part setting unit 118 that can be contacted” and “ It has an uneven part and a particle contact calculation part 119 ”.

  The setting part 118 of the uneven part with a possibility of contact defines the position of the uneven part in the vicinity of the closest particle based on the relative position of the particle and the member. FIG. 5A is a diagram for explaining the calculation of the relative positions of the particles and the members, and FIG. 5B is a diagram for explaining the definition of the concavo-convex portion that may be contacted.

  As shown in FIG. 5A, the distance X from the reference point 402 of the member to the particle 501 is determined, and the unevenness number n of the unevenness portion closest to the particle is determined by the following equation (1).

n = int (X / λ) +1 (1)
Here, int is a function for extracting an integer value in the parentheses.

  λ represents a surface roughness interval (for example, an interval between convex portions).

  As the concavo-convex portions that may come into contact with the particles, the concavo-convex portion 502a with the concavo-convex number n obtained by the equation (1), and the concavo-convex portion 502b with the concavo-convex number n + 1 and the concavo-convex portion 502c with the concavo-convex number n-1 before and after that Define coordinates.

  Specifically, based on the equation representing the member and the coordinates of the reference point 402, on which surface of the member the uneven portion is defined, the distance X from the reference point, the surface roughness interval λ and the height a The coordinates of the vertices constituting the triangle modeling the surface roughness such as 503 are obtained.

  The unevenness / particle contact calculation unit 119 calculates the contact between the three unevenness portions 502a to 502c defined by the setting portion 118 of the unevenness with possibility of contact and the calculation of the contact force as the contact calculation between the particle and the member. I do. This may be achieved by modeling the contact force in the tangential direction and the normal direction using a method similar to the ordinary discrete element method (DEM).

  FIG. 2 is a diagram showing the configuration of the particle behavior analysis apparatus. As shown in FIG. 2, this apparatus includes a CPU 200, a RAM 201, a display device 202, an input unit 203, an external storage device 204, and a bus 205.

  The RAM 201 includes a program storage unit 201a, a calculation condition data storage unit 201b, a particle data storage unit 201c, a member data storage unit 201d, and a surface roughness data storage unit 201e. Further, the RAM 201 includes a distance data storage unit 201f from the reference point to the particle, a nearest unevenness number data storage unit 201g, a possibly uneven surface data storage unit 201h, and a force data storage unit 201i acting on the particles. ing.

  The configuration of each unit will be described in detail. The CPU 201 is a central processing unit, and can control the above-described units connected via the bus 201.

  The storage units 201a to 201d of the RAM 201 store the program modules (111 to 119), calculation condition data, particle data, and member data shown in FIG. Each of the storage units 201e to 201i of the RAM 201 has surface roughness data, distance data from the reference point to the particle, nearest unevenness number data, unevenness data with possibility of contact, and force data acting on the particles. Stored.

  The display device 202 includes a display, a printer, and the like, and can display data to be displayed under the control of the CPU 201. The input unit 203 includes a keyboard, a mouse, and the like, and can input external input data into the apparatus. The external storage device 204 is composed of a hard disk or the like, and can store various data.

  Here, as the contents of each data stored in the RAM 201, the calculation condition data is data including a value related to the calculation condition such as a time step and a calculation actual time. The particle data is data including physical coordinates such as position coordinates, velocity, radius, mass, Young's modulus, and friction coefficient of each particle. The member data is data including physical properties such as the position, shape and dimensions of a member such as a container wall, speed information when the member moves, Young's modulus and friction coefficient. Surface roughness data is the presence or absence of the surface roughness of the member, the interval and height of the unevenness portion of the surface roughness, the type of uneven shape representing the surface roughness, information on which surface of the member has roughness, Data including the coordinates of the reference point of the member. The distance data from the reference point to the particle is data relating to the distance from the designated particle to the reference point. Further, the nearest unevenness number data is data of the number of the unevenness closest to the particle, and is specifically a value obtained by Expression (1). The concavo-convex part data that can be contacted is position data of three concavo-convex parts that may come into contact with the particle, and is defined as position data of coordinates constituting three triangles in this embodiment. The force data acting on the particles is a value obtained as a resultant force such as contact force and gravity acting on each particle.

  FIG. 3 is a flowchart for explaining the flow of processing in the acting force calculation unit (particle member acting force calculation unit) 115 between particles and a member having surface roughness. Hereinafter, the flow of processing for calculating the acting force between the particles and the member having the surface roughness will be described with reference to FIGS. 3 and 5. This process is executed by the control unit 100, the particle member acting force calculation unit 115 (the uneven portion setting unit 118 that may be contacted, the uneven portion and particle contact calculation unit 119) under the overall control of the CPU 200. The

  Specifically, the setting unit 118 of the concavo-convex part that may be contacted executes steps S301 to S303 described below.

  First, in step S301, a relative distance X (FIG. 5) from the reference point 402 to the particle 501 is calculated based on the particle data 201c and the surface roughness data 201e. Then, the distance X from the reference point 402 to the particle 501 is stored in the distance data storage unit 201f.

  Next, in step S302, based on the distance data 201f from the reference point to the particle and the surface roughness data 201e, the uneven number n of the uneven portion at the closest position to the particle is calculated using Equation (1). And stored in the nearest unevenness number data 201g.

  In step S303, based on the nearest unevenness number data 201g and surface roughness data 201e, the vertex coordinates of the three uneven portions 502a to 502c that may come into contact with the particle 501 are obtained, and the unevenness that may be contacted. Stored in the copy data 201h.

  For example, the coordinates of the point 503 that may come into contact with the particles shown in FIG. 5B can be obtained by equation (2).

Point 503 coordinate = P coordinate + (n + 0.5) λUt + aUn (2)
Next, the uneven | corrugated | grooved part and particle | grain contact calculation part 119 performs the process of step S304 demonstrated below.

  In step S304, based on the irregularity data 201h that may be in contact with the particle data 201c, the contact determination between the particle 501 and the three irregularities 502a to 502c and the calculation of the contact force are based on the discrete element method (DEM). Do. Then, the obtained contact force value is added to the force data 201i acting on the particles.

  In step S305, when there is the next particle (S305-Yes), the process returns to step S301, and the same process is repeated. If there is no next particle (S305-No), the process ends.

  The characteristics of the processing of the particle member acting force calculation unit 115 are to model the surface roughness of the member, and determine the contact between the member having the surface roughness and the particle only by setting the interval between the irregularities and the height of the irregularities. The contact force can be calculated.

  As an example of calculation, particle contact determination and contact force calculation will be described by taking as an example a case where the surface of a member having a length of 1 mm has a surface roughness of 5 μm intervals.

  Assuming that the surface roughness is represented by repeating triangles as shown in FIG. 4, the number of triangles is 200. In order to perform contact calculation based on the discrete element method (DEM), an equation representing a member is required. Therefore, it is necessary to set coordinate data of vertices constituting a triangle by the number of triangles. In addition, it is necessary to calculate contact determination with 200 triangles.

  However, by using the processing of the particle member acting force calculation unit 115 according to the embodiment of the present invention, the positions of three triangles that may come into contact with the particle can be specified from the relative positions of the particle and the member. Since only the contact calculation between the three specified triangles and the particles needs to be performed, the calculation load for determining the behavior of the particles can be reduced.

  FIG. 14 is a diagram visualizing the state of particle transport based on the calculation results when the surface of the member constituting the container has and does not have surface roughness. FIG. 14 shows a state in which four particles on a linear member are transported in Δt seconds as the member moves in the right direction (x direction) in the drawing. 14A shows a case where there is no surface roughness, FIG. 14B shows a case where there is a surface roughness having a height of 1/10 of the particle size, and FIG. 14C shows a case where the surface roughness is 1/2. It shows a case where there is a surface roughness having a height.

  Both the surface roughness intervals (λ) in FIGS. 14B and 14C are the same as the particle diameter. In addition, all the calculation conditions except the surface roughness are set to be the same in all calculations. Further, in order to make the conveyance distance easy to understand visually, the movement position (L) of the member for Δt seconds is indicated by a dotted line in the figure.

  In FIG. 14A in which there is no surface roughness, the transport distance of the particles is about 1/6 of the transport distance (L) of the member, and the particles slip about (5L / 6) on the surface of the member.

  In FIG. 14B with a surface roughness that is 1/10 of the particle size, the transport distance is about twice (= L / 3) compared to the case where there is no surface roughness. It slips about (2L / 3) on the surface of the member.

  On the other hand, in FIG. 14C where the surface roughness is 1/2 the particle size, the particles have the same transport distance (L) as the member, and no slip occurs between the member. As described above, in the embodiment of the present invention, since the height and interval of the surface roughness of the member surface can be modeled and reflected in the calculation of the particle behavior, the particle considering the difference in the surface roughness size and shape It is possible to calculate the behavior of

  This makes it possible to easily set the surface roughness data, especially when the size of the member is larger than the size of the surface roughness, and also reduces the contact calculation load between the member having the surface roughness and the particle. be able to.

  In the present embodiment, since the surface roughness interval and height values can be set, for example, the behavior of particles can be calculated based on various surface roughnesses defined in JIS standards. In this case, as the surface roughness, values of arithmetic average roughness Ra, maximum height Ry, ten-point average roughness Rz, unevenness average interval Sm, and local peak sum average interval S can be used. Thereby, it becomes possible to evaluate the calculation corresponding to the actual measurement data of the member.

  FIG. 14 illustrates an example in which the shape of the member is a straight line, but the shape of the member is not limited to a straight line, and the embodiment of the present invention can be applied to other shapes. Since the irregular shape of the surface roughness can be defined along the shape of the member, it can be applied to members of various shapes constituting the container. For example, an arc-shaped member 601 indicated by a broken line as shown in FIG. 6 can perform the same processing as a straight line by defining the uneven shapes 602a to 602e along the arc. At that time, the calculation of the unevenness number can be obtained not by the equation (1) but by the equation (3) using the angle θ from the reference point 402 to the particle 501 and the angle θλ corresponding to the surface roughness interval. .

n = int (θ / θλ) +1 (3)
Here, int is a function for extracting an integer value in the parentheses.

  Further, in the above description, modeling is performed using an isosceles triangle as the uneven shape of the surface roughness, but for example, an inequilateral triangle 701 shown in FIG. 7A and an example shown in FIG. It can also be defined by an arc 702. In the case of an unequal side triangle (FIG. 7A), in addition to the information of the surface roughness interval (λ) and the height (a), for example, the ratio of two sides (b1: b2) and the degree of eccentricity are set. This can be realized by setting the values (c1, c2) to be expressed. Thereby, the uneven | corrugated shape close | similar to the shape of the surface roughness actually measured can be selected. For the purpose of modeling the surface roughness, an isosceles triangle, an unequal triangle, and an arc are taken as examples for the purpose of the present invention. However, the present invention is not limited to this, and the surface roughness interval ( Any shape can be used as long as (λ) and height (a) can be specified.

  In the above description, an example in which the surface roughness is modeled by the interval (λ) and the height (a) in the two-dimensional cross section is described, but the present invention is also applied to the three-dimensional particle behavior calculation. It is possible to apply the embodiment. In this case, the surface roughness can be modeled in a three-dimensional space by a triangular prism shape, a cylindrical shape, or a visual cone shape.

  7C is a diagram showing an example in which the surface roughness is modeled by a triangular prism shape 703, FIG. 7D is a cylindrical shape 704, and FIG. 7E is a quadrangular pyramid 705. In the case of a quadrangular pyramid shape (FIG. 7e), by defining the sides of the xy plane to different lengths, the surface roughness is modeled by setting different surface roughness intervals (λ1, λ2) in the xy plane. It is also possible to do.

  In the above example (FIGS. 7A to 7E), the height of the surface roughness is described as being constant. For example, the height of the surface roughness is set to a different height (for example, It is also possible to model by setting (see a1 and a2 in FIG. 7E).

  In the above description, the process when the member moves is not mentioned, but the reference point coordinates at each time, the unit normal vector, the unit tangent vector, and the like may be updated based on the velocity information of the member. . As a result, the present invention can also be applied to the case where the member in contact with the particles sequentially moves due to the interaction force with the particles.

(Application to electrophotographic image forming devices)
Next, as one specific application example of the embodiment of the present invention, a developer behavior analysis in a developing unit of an electrophotographic image forming apparatus (hereinafter simply referred to as “image forming apparatus”) will be described.

  FIG. 13 is a diagram schematically illustrating the configuration of the developing unit in the image forming apparatus. In the figure, 1311 is a photosensitive drum, 1312 is a developing device, 1313 is a transfer member, 1314 is a cleaning device, and 1315 is a charging member. In the developing device 1312, a developing roller 1316 for transporting toner as a developer to the photosensitive drum 1311 is provided. The surface of the developing roller 1316 is provided with a surface roughness in order to stably convey the toner. By applying the present invention, it is possible to predict with a computer the developer conveyance state when the physical properties and dimensions of the developing roller, the fineness of the surface roughness (interval and height), and the like are changed. The analysis result can be used for designing the developing device configuration.

  According to the present embodiment, in the case where the surface of the member has surface roughness, the surface roughness is set, and the particles that come into contact with the member in consideration of the set surface roughness geometric shape (interval, height) Analysis of behavior becomes possible.

  In addition, it is possible to provide an image forming apparatus including a developing device capable of transporting a developer by a movable member having a surface roughness set based on the result of particle behavior analysis.

(Second Embodiment)
In the first embodiment, as the shape of the surface roughness of the member, the surface roughness is modeled by repeating uneven portions having the same shape. The actual surface of the member has variations in the height and interval of the unevenness, and this variation cannot be taken into consideration in the first embodiment.

  In this embodiment, it is assumed that the surface roughness is periodically repeated in the member surface, and one or more uneven portions having different dimensions and shapes are defined in the reference region, and the reference region is defined on the member surface. The variation is modeled as being repeated.

  Further, in the contact calculation, a method is used in which a reference area close to the particle is obtained based on the relative position between the particle and the member, the position information of the particle with respect to the reference area is obtained, and the contact force of the particle is obtained using the information. . This makes it possible to calculate the contact force when there are variations in the surface roughness interval, height, and shape.

  Hereinafter, a second embodiment of the present invention will be described with reference to the drawings. Since the configuration of the second embodiment is basically the same as that of the first embodiment, the description of the overlapping contents is omitted. Further, as an example of modeling, a case where particles and a member having a varying surface roughness are arranged in a two-dimensional cross section as in the example described in the first embodiment will be described as a representative example. . Note that the gist of the present embodiment is not limited to an example modeled in a two-dimensional section, but a three-dimensional model as described in FIGS. 7C to 7E of the first embodiment. The same can be applied to the conversion.

  FIG. 8A is a diagram exemplifying the modeling of the surface roughness configured in the reference region (region where the reference length is L in the x direction). As shown in FIG. 8A, a reference area having a length L includes four isosceles triangles 801a to 801d having different surface roughness intervals (λ1 to λ4) and heights (a1 to a4). The surface roughness within the region is modeled. In addition, the average height of the four isosceles triangles is defined as an.

  As shown in FIG. 8B, the member having the surface roughness is assumed to be linear, and on the surface of the member 401, four isosceles triangles 801a to 801d in the reference region shown in FIG. Suppose it is repeated. Further, the number of reference areas counted from the reference point 402 is defined as a reference area number. Further, as the member information, a unit vector Ut403 in the tangential direction of the member and a unit vector Un404 in the normal direction are defined, and the concavo-convex portion of the isosceles triangle is in the direction of the unit normal vector Un.

(Configuration of particle behavior analysis program)
FIG. 16 is a diagram illustrating a configuration of a particle behavior analysis program that executes analysis in an information processing apparatus that executes particle behavior analysis according to the second embodiment. Since the control unit 100, the particle force acting force calculation unit 112 to the particle behavior display unit 117, which are program modules in the figure, are the same as those in FIG. 1, the description thereof is omitted here.

  The initial condition setting unit 1611 sets particle calculation conditions, calculation conditions such as the overall shape, size, and position of the member. Further, the initial condition setting unit 1611 provides information on the surface roughness of the member, such as the reference length, the average value and variation of the surface roughness interval and height, and on which surface of the member the surface roughness is defined. Can be further set.

  The setting unit 1620 for the concavo-convex portion in the reference region is based on the reference length, the average value of the surface roughness interval and the height, and the value representing the variation, and the number of concavo-convex portions in the reference region, Set the position, spacing and length. Specifically, the value obtained by dividing the reference length by the average interval of the surface roughness is used as the number of irregularities, and a random number is used so as to follow a normal distribution or the like, and the intervals and heights of the irregularities are determined.

  By repeating the processing of the acting force calculation unit 112 to the particle behavior display unit 117 between the particles, the behavior of the particles can be obtained for each time Δt of the analysis step.

Next, a detailed description will be given of the calculation unit 115 for the acting force between the particles that execute the processing that is the characteristic of the second embodiment and the member having the surface roughness.
First, the content of the calculation part of the acting force between the particles and the member having the surface roughness will be described with reference to FIG. 1B and FIGS.

  The program configuration constituting the calculation unit 115 of the acting force between the particles and the member having the surface roughness is the same as that of FIG. 1B, but the processing contents of the setting unit 118 of the uneven portion that may be contacted are the same. Since it is different, it will be specifically described below.

  FIG. 9 is a diagram for explaining the calculation of the relative positions of the particles and the members and the concavo-convex portions that may be contacted in the second embodiment. As shown in FIG. 9A, the distance X from the reference point 402 of the member to the particle 501 is obtained, and the reference region number m closest to the particle 501 is obtained by equation (4).

m = int (X / L) +1 (4)
Here, int is a function for extracting an integer value in the parentheses.

  Next, the positions of the reference region of the reference region number m and the reference regions (m−1, m + 1) before and after the reference region number m are determined as the concavo-convex portions that may come into contact with the particles. The coordinates of the uneven portions 801a to 801l are defined (FIG. 9B). Specifically, based on the equation representing the member and the coordinates of the reference point 402, on which surface of the member the uneven part is defined, the distance X from the reference point, and the position of the uneven part in the reference region Can be obtained.

  The concavo-convex part and particle contact calculation unit 119 performs contact determination and calculation of the contact force between the twelve concavo-convex parts 801a to 801l defined by the setting part 118 of the concavo-convex part that can be contacted. This can be calculated by using a method similar to a normal discrete element method (DEM).

  FIG. 11 is a flowchart for explaining the flow of processing in the acting force calculator (particle member acting force calculator) 115 between the particles and the member having the surface roughness. Hereinafter, the flow of processing for calculating the acting force between particles and a member having surface roughness will be described with reference to FIGS. 11 and 9 and FIG. 10 showing the apparatus configuration.

  This process is executed by the control unit 100, the particle member acting force calculation unit 115 (the uneven portion setting unit 118 that may be contacted, the uneven portion and particle contact calculation unit 119) under the overall control of the CPU 200. The

  Specifically, the setting unit 118 for the concavo-convex portion that may be contacted executes steps S301, S1101, and S303 described below.

  First, in step S301, the distance X (FIG. 9) from the reference point 402 to the particle 501 is calculated based on the particle data 201c and the surface roughness data 201e, and the distance X from the reference point 402 to the particle is stored as distance data. Stored in the unit 201f.

  Next, in step S1101, based on the distance data 201f from the reference point 402 to the particle 501 and the surface roughness data 201e, the reference region number m of the reference region at the closest position to the particle 501 is expressed by Equation (4). Use to find. And it stores in the uneven | corrugated | grooved part data storage part 1001 in a reference | standard area | region.

  In step S303, three reference regions that may come into contact with the particles 501 are obtained based on the uneven portion data 1002 and surface roughness data 201e in the reference region and the uneven portion data 1001 in the reference region. And each vertex coordinate of 12 uneven | corrugated | grooved parts 801a-801l in three reference area | regions is calculated | required, and it stores in the uneven | corrugated | grooved part data storage part 201h (FIG. 10) with a possibility of contact.

  At this time, the calculation of the coordinates that may come into contact with the particles can be obtained by the equation (2) described in the first embodiment.

  Next, the uneven | corrugated | grooved part and particle | grain contact calculation part 119 performs the process of step S304 demonstrated below.

  In step S304, based on the irregularity data 201h that may contact the particle data 201c, the contact determination between the particle 501 and the twelve irregularities 801a to 801l and the calculation of the contact force are based on the discrete element method (DEM). Do it. Then, the obtained contact force value is added to the force data 201i acting on the particles.

  In step S305, when there is the next particle (S305-Yes), the process returns to step S301, and the same process is repeated. If there is no next particle (S305-No), the process ends.

  FIG. 15 is a diagram visualizing the transport state of particles in a two-dimensional cross section when there is variation in the surface roughness of the members constituting the container.

  FIG. 15 shows a state in which four particles on a linear member are transported in Δt seconds as the member moves in the right direction (x direction) in the figure.

  In this example, a case where there is a surface roughness having an average height of 3/10 of the particle diameter of the particle 501 is calculated, and the average interval of the surface roughness is the same as the particle diameter. The calculation conditions excluding the surface roughness are set to be the same as those in FIG. Further, in order to make the conveyance distance easy to understand visually, the movement position (L) of the member for Δt seconds is indicated by a dotted line in the figure.

  In the initial state of FIG. 15 (a), four particles are connected, but at the moving position after Δt seconds, as shown in FIG. 15 (b), due to the difference in height of the surface roughness with which the particles are in contact. Variations are observed in the transport state. That is, the transport distance varies between the particles (1501, 1502) and the particles (1503, 1504) in Δt seconds. As described above, in this embodiment, since the height of the surface roughness and the variation in the interval can be taken into account, it is possible to calculate the behavior of the particles in consideration of more specific conditions.

  Further, in the above description, the case where the concave and convex shapes in the reference region are connected is described, but this is not necessarily required, and the embodiment of the present invention can also be applied when the concave and convex shapes are separated from each other. It is.

  For example, as shown in FIG. 17A, the inside (L) of the reference region is modeled by the concave portions (1701a, c) and the convex portions (1701b, d), and the concave portion 1701c is formed between the convex portions 1701b and 1701d. It is also possible to model such that

  In the contact calculation, as shown in FIG. 17 (b), a concavo-convex region indicated by hatching in the drawing is defined in the reference region, and the contact calculation is performed depending on whether or not particles are included in the region. It is also possible to switch between. For example, when the particle is included in the uneven portion region (1703a in FIG. 17B), contact calculation with the uneven portion is performed. Further, when it is not included in the region (1703b in FIG. 17B), contact calculation with the member shape before defining the uneven portion shape is performed. If particles are included in both regions (1803c in FIG. 17B), the contact calculation of both cases (1703a, 1703b) is performed, and the position of the uneven portion is irregular. It becomes possible to make contact calculation easy.

  In the above description, the case where the shape of the member is a straight line is described as an example. However, the gist of the present invention is not limited to this, and can be applied to various shapes of members constituting the container. . In order to achieve this, apart from the coordinate system for particle behavior calculation, a local coordinate system for the reference region is defined, and the uneven coordinates of the local coordinate system are mapped to the coordinate system for particle behavior calculation. This can be easily realized by mapping the position back to the local coordinate system.

  In addition, although an isosceles triangle is used as the concavo-convex shape, it can also be defined by an unequal triangle or an arc. Thereby, the uneven | corrugated shape close | similar to the shape of the surface roughness actually measured can be selected. Furthermore, by defining a triangular prism shape, a cylindrical shape, a quadrangular pyramid shape, or the like, it can be applied to a three-dimensional particle behavior calculation. Further, in order to model the uneven shape having the surface roughness shown above, two or more types of shape models can be mixed. As a result, it is possible to consider the shape of the surface roughness close to the actual shape.

  According to the present embodiment, in the case where the surface of the member has surface roughness, the surface roughness is set, and the particles that come into contact with the member in consideration of the set surface roughness geometric shape (interval, height) Analysis of behavior becomes possible.

  Here, it is assumed that the variation in surface roughness is periodically repeated in the member surface, and a plurality of uneven portions having different dimensions and shapes are modeled in the reference region. In the calculation, the average value of the surface roughness average interval and height, the variation (for example, a random number for setting the interval and height of the surface roughness according to the normal distribution), and the reference length are set. By setting these values, it is possible to calculate contact between the member and the particle in consideration of the uneven surface roughness dimension and the uneven shape without setting the position of the uneven shape on the entire member surface.

(Other embodiments)
Needless to say, the object of the present invention can also be achieved by supplying a storage medium storing software program codes for realizing the functions of the above-described embodiments to a system or apparatus. Needless to say, this can also be achieved by the computer (or CPU or MPU) of the system or apparatus reading and executing the program code stored in the storage medium.

  In this case, the program code itself read from the storage medium realizes the functions of the above-described embodiments, and the storage medium storing the program code constitutes the present invention.

  As a storage medium for supplying the program code, for example, a flexible disk, a hard disk, an optical disk, a magneto-optical disk, a CD-ROM, a CD-R, a nonvolatile memory card, a ROM, or the like can be used.

  Further, the functions of the above-described embodiment are realized by executing the program code read by the computer. In addition, an OS (operating system) running on a computer performs part or all of actual processing based on an instruction of a program code, and the above-described embodiment is realized by the processing. Needless to say.

(a) is a figure which shows the structure of the particle behavior analysis program module which performs a particle behavior analysis. (B) is a figure which shows the structure of the process part which comprises the particle member action force calculation part 115. FIG. It is a figure which shows the structure of the information processing apparatus (particle behavior analysis apparatus) which concerns on 1st Embodiment of this invention. It is a flowchart explaining the flow of a process in the calculation part 115 of the acting force of the particle | grains and member with surface roughness which concern on 1st Embodiment of this invention. It is a figure explaining an example which defines the surface roughness which concerns on 1st Embodiment of this invention by the data of a space | interval and height. It is a figure explaining the calculation of the relative position of the particle | grains and member in 1st Embodiment, and the uneven | corrugated | grooved part with a contact possibility. It is a figure explaining an example which defines the surface roughness which concerns on 1st Embodiment of this invention by the data of a space | interval and height. It is a figure explaining an example of a definition of surface roughness concerning an embodiment of the present invention. It is a figure explaining an example of the definition of surface roughness concerning a 2nd embodiment of the present invention. It is a figure explaining the uneven | corrugated | grooved part with calculation of the relative position of particle | grains and a member and contact possibility in 2nd Embodiment. It is a figure which shows the structure of the information processing apparatus (particle behavior analysis apparatus) which concerns on 2nd Embodiment of this invention. It is a flowchart explaining the flow of the process in the calculation part (particle member action force calculation part) 115 of the action force of the particle | grains and member with surface roughness concerning 2nd Embodiment of this invention. It is a figure which illustrates the discrete element model which isolate | separated the contact force of the two objects (1210, 1220) which are contacting into the normal line direction and the tangential direction. 2 is a diagram schematically illustrating a configuration of a developing unit in the image forming apparatus. FIG. It is the figure which visualized the mode of the conveyance of the particle | grains based on a calculation result about the case where the surface of the member which comprises a container has surface roughness. It is the figure which visualized the conveyance state of the particle | grains in a two-dimensional cross section in case there exists dispersion | variation in the surface roughness of the member which comprises a container. It is a figure which shows the structure of the particle behavior analysis program which performs an analysis in the information processing apparatus which performs the particle behavior analysis which concerns on 2nd Embodiment of this invention. It is a figure explaining an example of the definition of surface roughness concerning a 2nd embodiment of the present invention.

Claims (19)

Data read from each data storage unit, including a member data storage unit that stores data including physical property values of the movable member, and a particle data storage unit that includes physical property data of particles contained in the container having the movable member Based on the information processing apparatus for calculating the behavior of the particles in contact with the movable member,
Data setting means for setting the data of the unevenness interval and height as the surface roughness of the movable member in the surface roughness data storage unit;
Relative position calculation means for calculating relative position data between the particles and the movable member based on the data read from the member data storage unit and the particle data storage unit;
Contact for calculating the concavo-convex portion in contact with the particles based on the position data calculated by the relative position calculation means and the data of the concavo-convex interval and height set in the surface roughness data storage unit. Position calculating means;
An information processing apparatus comprising: an operation unit that obtains a contact force at the uneven portion in contact with the particle calculated by the contact position calculation unit and calculates a behavior of the particle by the action of the contact force.   The said setting means models the surface roughness of the said movable member by setting multiple shapes on the said movable member specified by the data of the space | interval and height of the said unevenness | corrugation. The information processing apparatus described.   The setting means divides the surface of the movable member into a plurality of regions, sets data of different unevenness intervals and different heights for the plurality of uneven shapes included in the region, and the surface roughness The information processing apparatus according to claim 1, wherein the information processing apparatus is modeled.   The setting unit divides the surface of the movable member into a plurality of regions, sets a region that does not include the uneven shape and a region that includes the uneven shape in the region, and models the surface roughness. The information processing apparatus according to any one of claims 1 to 3, wherein the information processing apparatus is characterized in that:   The contact position calculating means is based on the position data calculated by the relative position calculating means, and the particles are located in a first region including the uneven shape or in a second region not including the uneven shape. 5. The information processing apparatus according to claim 1, wherein the information processing apparatus determines whether or not it is located in both of the first and second regions.   The information processing apparatus according to claim 1, wherein the calculation unit switches calculation of the contact force based on determination by the contact position calculation unit. 7. The surface roughness height data includes at least one of arithmetic average roughness Ra, maximum height Ry, and ten-point average roughness Rz. The information processing apparatus according to item 1.   The information according to any one of claims 1 to 6, wherein the data of the surface roughness interval includes at least one of an average interval Sm of unevenness and an average interval S of local peaks. Processing equipment. Data read from each data storage unit, including a member data storage unit that stores data including physical property values of the movable member, and a particle data storage unit that includes physical property data of particles contained in the container having the movable member Based on the information processing method in the information processing apparatus for calculating the behavior of the particles in contact with the movable member,
A data setting step for setting the data of the interval and height of the unevenness as the surface roughness of the movable member in the surface roughness data storage unit,
Relative position calculation step for calculating relative position data between the particles and the movable member based on the data read from the member data storage unit and the particle data storage unit,
Contact for calculating the uneven portion that contacts the particle based on the position data calculated by the relative position calculating step and the data of the interval and height of the unevenness set in the surface roughness data storage unit. A position calculating step;
An information processing method comprising: a calculation step of obtaining a contact force at the concave and convex portion in contact with the particle calculated by the contact position calculation step, and calculating a behavior of the particle by the action of the contact force.   10. The surface roughness of the movable member is modeled by setting a plurality of shapes specified by the interval and height data of the unevenness on the movable member in the setting step. The information processing method described.   The setting step divides the surface of the movable member into a plurality of regions, sets data of different unevenness intervals and different heights for the plurality of uneven shapes included in the region, and the surface roughness The information processing method according to claim 9, wherein the information processing method is modeled.   The setting step divides the surface of the movable member into a plurality of regions, sets a region that does not include the uneven shape and a region that includes the uneven shape in the region, and models the surface roughness. The information processing method according to claim 9, wherein the information processing method is any one of claims 9 to 11.   In the contact position calculation step, the particles are located in a first region including the uneven shape or in a second region not including the uneven shape based on the position data calculated by the relative position calculation step. 13. The information processing method according to claim 9, wherein it is determined whether or not it is located in both of the first and second regions.   The information processing method according to claim 9 or 13, wherein the calculation step switches the calculation of the contact force based on the determination in the contact position calculation step. 15. The surface roughness height data includes at least one of arithmetic average roughness Ra, maximum height Ry, and ten-point average roughness Rz. The information processing method according to item 1.   The information according to any one of claims 9 to 14, wherein the data on the surface roughness interval includes at least one of an average interval Sm of unevenness and an average interval S of local peaks. Processing method. A developing device having a movable member having a surface roughness set based on a calculation result of the information processing method according to any one of claims 9 to 16,
Image forming means for forming an image based on the developer conveyed by the movable member of the developing device;
An image forming apparatus comprising:   A program for causing a computer to execute the information processing method according to any one of claims 9 to 16.   A computer-readable storage medium storing the program according to claim 18.

Images