JP4827427B2 - Particle behavior analysis apparatus, control method, and program - Google Patents

Description

  The present invention relates to a particle behavior analysis apparatus, a control method, and a program suitable for obtaining the behavior of particles moving in a region to which a magnetic field is applied.

  In general, in an image forming apparatus such as a copying machine or a printer that performs image formation using electrophotographic technology, a developer (toner) is attached to a latent image formed on the surface of a photoreceptor by a developing device, and developed. A visible image is formed. A magnet roller is generally used in order to control the behavior of the toner and perform appropriate development in the developing device. Magnetic force acts on the toner itself, which is magnetic particles, or carrier particles for conveying the toner, by a magnetic field formed by a rotating magnet roller, and the behavior of the toner and carrier particles is appropriately controlled by the magnetic force.

  By the way, in recent years, particle behavior calculation has been performed to analyze the behavior of particles in the state where the magnetic field as described above is applied, and it is being utilized for elucidating the phenomenon of electrophotography and optimizing the structure of the developing device. . In particle behavior calculations that analyze the behavior of magnetic particles in a magnetic field, a method is generally used to determine the behavior of particles along the time series based on the forces acting on each particle, such as magnetic force and interparticle contact force. However, since the behavior of particles varies depending on the applied magnetic field, it is necessary to accurately determine the magnetic force acting on the particles.

  As a method for obtaining the magnetic force acting on the particles, there is a method for obtaining the magnetization and magnetic force of each magnetic particle based on magnetic field data obtained by numerical calculation such as a finite element method. At that time, a method is used in which the calculation is performed by dividing the magnetic force received by the particle from the applied magnetic field and the magnetic interaction force between the particles. In many cases, the applied magnetic field during the particle behavior calculation is treated as not changing.

  A specific method for calculating the magnetic force acting on the particles will be briefly described with reference to FIG.

  FIG. 13 is a diagram schematically showing a configuration example of a processing program for the entire particle behavior calculation according to the conventional example.

  In FIG. 13, the processing program includes a control unit 1100, an initial condition setting unit 1111, a magnetic force calculator 1112 acting on the magnetic particles, a force calculator 1113 other than the magnetic force acting on the magnetic particles, a particle displacement calculator 1114, A particle behavior display unit 1115 is provided.

  The control unit 1100 controls the entire processing of the program. The initial condition setting unit 1111 sets initial particle arrangement, physical property values, analysis regions, applied magnetic field data, and calculation conditions. The magnetic force calculator 1112 acting on the magnetic particles calculates the magnetic force acting on the particles. A force calculation unit 1113 other than the magnetic force acting on the magnetic particles performs calculations such as gravity acting on the particles. The particle displacement calculator 1114 updates the velocity and displacement of each particle by solving the equation of motion based on all forces acting on each particle. The particle behavior display unit 1115 displays the positions of particles and structures along the time series.

On the other hand, the technique regarding the specific calculation method of the magnetic force which a particle | grain receives from an applied magnetic field mentioned above and the magnetic interaction force of particle | grains is disclosed (for example, refer nonpatent literature 1).
Nagai et al., JapanHardcopy '99 Proceedings, 185 (1999)

  However, the magnetic field applying unit for applying a magnetic field rotates or moves within a predetermined apparatus, such as when the magnet roller for toner replenishment provided in the developing device of the image forming apparatus shown in the above-described conventional example rotates about its axis. For example, it is necessary to calculate the behavior of the magnetic particles using the magnetic field data at the position of the magnetic field application unit at each time.

  In order to realize the calculation of the behavior of magnetic particles in the above conventional example, it is necessary to prepare a plurality of magnetic field data corresponding to the rotation and movement of the magnetic field application unit in advance. There is a problem that the data becomes enormous. In addition, when the magnetic field application unit arbitrarily moves during the particle behavior calculation, magnetic field data cannot be prepared in advance.

  In addition, a method of sequentially performing a magnetic field calculation considering the position of the magnetic field application unit during the execution of the particle behavior analysis can be considered, but this is not a practical method from the viewpoint of calculation time.

  In addition, regarding the display of the calculation result, it is required to display the particle conveyance state and the like in the magnetic field data by simultaneously displaying the particles and the magnetic field data. To that end, a method of holding a combination of particle behavior data and magnetic field data for each time is conceivable, but there is a problem that the data becomes enormous.

  The object of the present invention is to make it possible to easily and accurately calculate the behavior of magnetic particles in consideration of changes in the magnetic field due to the movement and rotation of the magnetic field application unit, and to analyze the particle behavior as the analysis result and the magnetic field data at that time. An object of the present invention is to provide a particle behavior analysis apparatus, a control method, and a program that can be easily displayed.

In order to achieve the above-described object, the particle behavior analysis apparatus of the present invention is a particle behavior analysis apparatus for analyzing the behavior of particles moving within a region to which a magnetic field is applied by a magnetic field applying means, wherein a basic magnetic field application position is provided. A magnetic field calculation means for calculating the magnetic field data in the coordinate system after displacement of the magnetic field application means, by mapping the magnetic field data in the coordinate system of the basic applied magnetic field from the coordinate system after displacement of the magnetic field application means ; and the magnetic force calculating means for calculating a magnetic force acting on the basis of the magnetic field data after mapping calculated by serial magnetic field calculating means to said particles, acts on the particles other than the magnetic force and the magnetic energy calculated by said magnetic force calculation means And a particle behavior analysis means for analyzing the velocity and displacement, which are the behavior of the particles, by solving the equation of motion based on the force .

The particle behavior analysis device of the present invention is a particle behavior analysis device analyze behavior of particles moving within a region where the magnetic field is applied by the magnetic field applying means, the particles located in the coordinate system of the basic magnetic field applied A magnetic field calculation means for calculating the magnetic field data in the coordinate system after displacement of the magnetic field application means by mapping and inversely mapping the magnetic field data at the particle position to the coordinate system after displacement of the magnetic field application means; and the magnetic force calculating means for calculating a magnetic force acting magnetic field data after the inverse mapping calculated by the magnetic field calculating means to the particles based on, acts on the particles other than the magnetic force and the magnetic energy calculated by said magnetic force calculation means And a particle behavior analysis means for analyzing the velocity and displacement, which are the behavior of the particles, by solving the equation of motion based on the force .

  According to the present invention, when the magnetic field applying means is displaced, the behavior of the particles considering the change of the magnetic field by the magnetic field applying means can be simply and based on the basic applied magnetic field data and the magnetic field data after the displacement of the magnetic field applying means. It is possible to calculate with high accuracy.

Further, the magnetic field calculation means having a short calculation time is selected from the magnetic field calculation means and the second magnetic field calculation means in accordance with the size of the magnetic field data or the number of particles, and the magnetic field data calculated by the selected magnetic field calculation means is selected. Since the magnetic force acting on the particles is calculated based on the base, it is possible to reduce the time required for calculating the whole particle behavior.

  Moreover, the magnetic field data which changes with the displacement of the magnetic field applying means and the particle behavior which is the analysis result can be easily displayed.

  Also, by applying the present invention to the developer behavior analysis of an electrophotographic image forming apparatus, the developer behavior in the developer replenishing means of the image forming apparatus and the developer behavior in the developer cleaning means of the image forming apparatus are predicted. can do.

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

[First Embodiment]
In the first embodiment of the present invention, in a particle behavior analysis apparatus that analyzes the behavior of particles moving in a region to which a magnetic field is applied by a magnetic field application unit, particles in a two-dimensional cross section, a magnetic field application unit, and related The particle behavior calculation based on the member will be described. Here, it is assumed that the magnetic field application unit rotates around a certain axis. The magnitude of magnetization of the magnetic particles is constant for each particle. The magnetic field data is expressed by a finite element model composed of nodes and elements.

  FIG. 1 is a diagram schematically illustrating a configuration example of a processing program of a particle behavior analysis apparatus according to the present embodiment, where (a) is a diagram illustrating a processing program for the entire particle behavior calculation, and (b) is a diagram illustrating particles. It is a figure which shows the processing program which comprises the calculation part of the working magnetic force.

  In FIG. 1A, the processing program includes a control unit 100, an initial condition setting unit 111, a magnetic force calculation unit 112a acting on the magnetic particles, a force calculation unit 113 other than the magnetic force acting on the magnetic particles, and a particle displacement calculation. Unit 114 and particle behavior display unit 115. The configuration of FIG. 1A is basically the same as the configuration of FIG. 13 except for the magnetic force calculator 112a acting on the magnetic particles, and will be described briefly.

  The initial condition setting unit 111 is an initial particle arrangement, radius, specific gravity, physical property values such as magnetic characteristics, the shape, size, position, and applied magnetic field data (such as magnetic field and spatial differentiation of the magnetic field) of the structure constituting the analysis region, In addition, calculation conditions such as time steps, and movement information of a magnetic field application unit (not shown) are set. The magnetic force calculator 112a acting on the magnetic particles calculates the magnetic force acting on the particles based on the magnetic characteristics (magnetization, magnetic moment, etc.) of each magnetic particle and the applied magnetic field data.

  The force calculation unit 113 other than the magnetic force acting on the magnetic particles performs calculations such as gravity acting on the particles. The particle displacement calculator 114 updates the velocity and displacement of each particle by solving the equation of motion based on all the forces acting on each particle. The particle behavior display unit 115 displays the positions of particles and structures along the time series.

  In the actual calculation, the behavior of the particles can be obtained by repeating the processing by the initial condition setting unit 111 and the calculation unit 112a to the particle behavior display unit 115 of the magnetic force acting on the magnetic particles.

  Below, each part which comprises the calculation part 112a of the magnetic force which acts on the magnetic particle shown in FIG.1 (b) is demonstrated.

  In FIG. 1B, the magnetic force calculating unit 112a acting on the magnetic particles includes a coordinate system setting unit 116 after the magnetic field applying unit is moved, a magnetic field data mapping calculating unit 117, a particle magnetization calculating unit 118, A magnetic force calculation unit 119 by an applied magnetic field and a magnetic force calculation unit 120 by particles are provided.

  The coordinate system setting unit 116 after the movement of the magnetic field application unit obtains the coordinate system after the movement of the magnetic field application unit based on the current time and the movement information of the magnetic field data. The magnetic field data mapping calculation unit 117 maps the node coordinates and magnetic field data by the finite element method or the like at the basic magnetic field application position from the basic applied magnetic field coordinate system to the coordinate system after movement of the magnetic field application unit. Magnetic field data after the movement of the magnetic field application unit is created.

  The particle magnetization calculator 118 obtains the magnetization vector and magnetic moment of each particle. Here, since it is assumed that the magnitude of the magnetization of the particles is constant, the value may be used. The magnetic force calculation unit 119 by the applied magnetic field calculates the magnetic force acting on each particle by using the magnetic moment of each particle and the magnetic field applied to the particle. The magnetic force calculation unit 120 by particles obtains the magnetic force acting on each particle using the magnetic moment of each particle.

  In addition, in the calculation unit 119 of the magnetic force by the applied magnetic field and the calculation unit 120 of the magnetic force by the particle, a specific calculation method of the magnetic force that the particle receives from the applied magnetic field and the magnetic interaction force between the particles is, for example, Non-Patent Document 1 and the like. The formula described in Non-Patent Document 1 is shown below.

f_ex(i)、f_in(i) は、それぞれ、粒子ｉに働く印加磁界から受ける磁気力と他の粒子から受ける磁気力を表し、M(i)は、粒子ｉの磁気モーメントを表し、H₀(i)、H(j)は、粒子ｉの位置における磁界印加部が形成する磁界と粒子ｊが形成する磁界を表している。なお、H(j)は、粒子ｊの磁気モーメントM(j)の関数である。式１、式２から分かるように、粒子に働く磁気力を求めるためには、各粒子の磁気モーメントと粒子の位置における磁界の空間微分が必要となる。

f _ex (i) and f _in (i) represent the magnetic force received from the applied magnetic field acting on the particle i and the magnetic force received from other particles, respectively, M (i) represents the magnetic moment of the particle i, H ₀ (i) and H (j) represent the magnetic field formed by the magnetic field application unit at the position of the particle i and the magnetic field formed by the particle j. H (j) is a function of the magnetic moment M (j) of the particle j. As can be seen from Equations 1 and 2, in order to obtain the magnetic force acting on the particles, the magnetic moment of each particle and the spatial differentiation of the magnetic field at the particle position are required.

  Next, the coordinate system setting unit 116 and the magnetic field data mapping calculation unit 117 after the movement of the magnetic field application unit, which is a feature of the present embodiment, will be described in detail with reference to FIGS. Prior to detailed description, the configuration of the particle behavior analysis apparatus will be described first.

  FIG. 2 is a block diagram illustrating a configuration example of the particle behavior analysis apparatus.

  In FIG. 2, the particle behavior analysis 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. Further, the RAM 201 includes a program storage unit 201a, a calculation condition data storage unit 201b, a particle data storage unit 201c, a current time data storage unit 201d, a magnetic field data storage unit 201e at the basic magnetic field application position, and a magnetic field application unit after the movement. A coordinate system data storage unit 201f, a particle magnetization state data storage unit 201g, an applied magnetic field data storage unit 201h after mapping, a particle center magnetic field data storage unit 201j, and a force data storage unit 201k acting on particles are provided.

  The configuration of each unit will be described in detail. The CPU 200 is a central processing unit and controls each unit connected via the bus 205. The CPU 200 controls the execution of the processing program shown in FIG. 1 and causes the processing shown in each flowchart described later to be executed. In each of the storage units 201a to 201k of the RAM 201, the processing program, the calculation condition data, the particle data, the current time data, the magnetic field data at the basic magnetic field application position, and the table after the movement of the magnetic field application unit shown in FIG. System data, particle magnetization state data, applied magnetic field data after mapping, particle center magnetic field data, and force data acting on particles are stored.

  The display device 202 includes a display or the like, and displays data to be displayed related to particle behavior analysis under the control of the CPU 200. In addition, data related to particle behavior analysis can be printed out by a printer (not shown). The input unit 203 includes a keyboard, a mouse, and the like, and inputs data externally input by the operator into the apparatus. The external storage device 204 is composed of a hard disk or the like and stores various data.

  Here, the content of each data stored in each said storage part 201a-201k is demonstrated. The calculation condition data is a value related to calculation conditions such as time step and calculation real time. The particle data refers to physical properties such as magnetic properties such as position coordinates, velocity, radius, mass, and relative magnetic permeability of each particle, Young's modulus, and friction coefficient. The current time data is time representing the current state in the time series. The magnetic field data at the basic magnetic field application position is the coordinate system of the basic magnetic field application position, the magnetic field data such as the magnetic field or the spatial differentiation of the magnetic field previously obtained by the finite element method, the movement of the magnetic field application unit such as the rotation speed and the rotation center, etc. Information.

  The coordinate system data after movement of the magnetic field application unit is a coordinate system after movement of the magnetic field application unit obtained based on the coordinate system of the basic applied magnetic field and the movement information of the magnetic field application unit. The magnetization state data of particles is the magnetization vector or magnetic moment of each particle. The applied magnetic field data after mapping is magnetic field data after mapping obtained by mapping the magnetic field data at the basic magnetic field application position to the coordinate system after the magnetic field application unit is moved. The magnetic field data at the particle center is magnetic field data acting on the particle center obtained using the applied magnetic field data after mapping. The force data acting on the particles is a value obtained as a resultant force such as magnetic force, contact force, and gravity acting on each particle.

  FIG. 3 is a flowchart showing a procedure of processing executed by the coordinate system setting unit 116 and the magnetic field data mapping calculation unit 117 after the movement of the magnetic field application unit shown in FIG.

  In FIG. 3, the processing procedure for setting the coordinate system after moving the magnetic field application unit and calculating the mapping of the magnetic field data will be described with reference to the configuration of the particle behavior analysis apparatus shown in FIG.

  (1) First, in the coordinate system setting unit 116 after movement of the magnetic field application unit, the magnetic field is based on the data stored in the current time data storage unit 201d and the magnetic field data storage unit 201e at the basic magnetic field application position, respectively. The coordinate system after the movement of the magnetic field application unit is obtained using the rotation center coordinates and the rotation angle of the application unit, and stored in the coordinate system data storage unit 201f after the movement of the magnetic field application unit (step S301).

  (2) Next, in the magnetic field data mapping calculation unit 117, based on the data respectively stored in the magnetic field data storage unit 201e at the basic magnetic field application position and the coordinate system data storage unit 201f after the movement of the magnetic field application unit. Then, the node coordinates of the magnetic field data, the magnetic field vector on the node, and the spatial differentiation of the magnetic field are mapped to the coordinate system after the magnetic field application unit is moved, and stored in the applied magnetic field data storage unit 201h after the mapping (steps S302 to S303). ).

  (3) The processing from step S302 to step S303 is repeated for the number of nodes (step S304).

  (4) Next, in the magnetic field data mapping calculation unit 117, based on the data stored in the magnetic field data storage unit 201e at the basic magnetic field application position and the coordinate system data storage unit 201f after movement of the magnetic field application unit, respectively. Then, the magnetic field vector on the element and the spatial differential of the magnetic field are mapped to the coordinate system after the magnetic field application unit is moved and stored in the applied magnetic field data storage unit 201h after the mapping (steps S305 to S306). Specifically, the vector value on the element is mapped by mapping the coordinates defining the vector (such as the barycentric coordinates of the element).

  (5) Steps S305 to S306 are repeated by the number of elements (step S307).

  In general, since the magnetic field vector and the spatial differentiation of the magnetic field are defined only at the nodes or elements, either step S303 or step S306 may be performed in the above processing procedure.

  The feature of this embodiment is that magnetic field data that changes with movement and rotation of the magnetic field application unit is obtained by mapping the basic applied magnetic field data to the coordinate system after the movement of the magnetic field application unit. Hereinafter, this process will be described in more detail with reference to FIGS.

  4A and 4B are diagrams illustrating a state in which the magnetic field formed by the magnetic field application unit changes as the magnetic field application unit rotates. FIG. 4A illustrates the magnetic field data of the basic magnetic field application coordinate system, and FIG. It is a figure which shows the applied magnetic field data after rotating the magnetic field application part 60 degree | times clockwise centering on the center coordinate of an application part.

  In FIG. 4, 401 represents a magnetic field application unit such as a magnet roll disposed in an apparatus to be subjected to particle behavior analysis, 402 represents magnetic field data formed by the magnetic field application unit, and 403 represents particles. ing.

  5A and 5B are diagrams for explaining mapping calculation of magnetic field data. FIG. 5A is a diagram showing magnetic field data of the basic magnetic field application coordinate system, and FIG. 5B is a diagram showing the magnetic field application unit around the center coordinates of the magnetic field application unit. It is a figure which shows the applied magnetic field data after rotating around 60 degree | times.

  In FIG. 5, 501 represents an element division model, 502 represents a magnetic field vector defined at the center of gravity of each element, 401 represents a magnetic field application unit, and 403 represents particles.

  Thus, using the coordinate system of the basic applied magnetic field in FIG. 4A and the coordinate system after the rotation of 60 degrees in FIG. 4B, the basic applied magnetic field data in FIG. By mapping to the coordinate system, the applied magnetic field data after 60 degrees rotation is obtained. And the magnetic force which considers rotation of a magnetic field application part can be easily calculated | required by calculating | requiring the magnetic force which acts on particle | grains using the magnetic field data after mapping.

  Further, the particle behavior display unit 115 shown in FIG. 1 can display the magnetic field data along the time series on the display device 202 in addition to displaying the particles along the time series. Also in this case, the calculation of the applied magnetic field data of the present embodiment can be applied.

  Specifically, in addition to the position information of the particles at each time, the position information of the magnetic field application unit or the movement information of the magnetic field application unit at each time is used to display the applied magnetic field data at the time to be displayed in the coordinate system after rotation. The basic applied magnetic field data is obtained by mapping the data, and the contour lines and contours of the data are displayed on the display device 202 simultaneously with the particles.

  FIG. 6 is a diagram illustrating an example of a particle behavior display when the magnetic field application unit rotates 60 degrees.

  In FIG. 6, reference numeral 601 denotes a particle group after being rotated by 60 degrees displayed on the display device 202. By using the display method, it is not necessary to prepare the applied magnetic field data for each time in advance, and only the particle behavior calculation result and the basic applied magnetic field data are prepared. 202 can be displayed. Also, the magnetic force acting on each particle can be displayed on the display device 202 by the same method.

  In the above description, the example in which the magnetic field application unit rotates has been described. However, when the displacement of the magnetic field application unit is known, such as translational movement or both translational and rotational movements, the method of the present embodiment described above is used. It is possible to apply.

  In the above description, the applied magnetic field data is mapped every time the magnetic force of the particle is calculated. However, the time step is smaller than the speed of the magnetic field application unit, and the change in the magnetic field accompanying the movement of the magnetic field application unit is ignored. If possible, it is not necessary to perform the mapping calculation every time. For example, the number of mapping calculations is reduced, such as a method of performing mapping calculation once every 10 steps of particle calculation, or a method of performing mapping calculation only when the total moving distance of the magnetic field application unit after mapping calculation exceeds a threshold. As a result, the calculation real time can be shortened.

  In the above description, the particle behavior calculation in two dimensions has been described. However, it can be easily applied to the particle behavior calculation in three dimensions.

  The method of the present embodiment described above can also be applied to the case where the particle is magnetized by an applied magnetic field or a magnetic field formed by surrounding particles, such as when the particle is a soft magnetic material. Specifically, the particle magnetization calculator 118 obtains the magnetic field at the position of each particle using the magnetic field data mapped to the coordinate system after the magnetic field applying unit is moved.

The magnetic moment M (i) and the magnetization J _m (i) of the particles may use the following formulas described in Non-Patent Document 1, for example.

ここで、V(i) は粒子ｉの体積を表し、μ0とμ（i）は真空の透磁率と粒子ｉの比透磁率を表している。なお、式４は粒子を球形として求めた磁化である。

Here, V (i) represents the volume of the particle i, and μ0 and μ (i) represent the vacuum permeability and the relative permeability of the particle i. Equation 4 is the magnetization obtained by determining the particles as spherical.

  Next, as a specific example of the particle behavior analysis of the present embodiment, a developer behavior analysis in an electrophotographic image forming apparatus will be described.

  FIG. 7 is a schematic diagram illustrating a configuration of a main part of an electrophotographic image forming apparatus.

  In FIG. 7, the image forming apparatus includes a photosensitive drum 1211, a developing device 1212, a transfer member 1213, a cleaning device 1214, a charging member 1215, a developing hopper 1216, and a magnet roller 1217.

  The photosensitive drum 1211 forms a latent image on the drum surface by laser light. The developing device 1212 develops and visualizes the latent image on the photosensitive drum 1211 with toner as a developer. The transfer member 1213 transfers the visible image on the photosensitive drum 1211 to a sheet. The cleaning device 1214 cleans the toner remaining on the photosensitive drum 1211. The charging member 1215 charges the photosensitive drum 1211 to a predetermined potential.

  The developing hopper 1216 contains replenishing toner. The developing hopper 1216 is provided with a magnet roller 1217 for replenishing toner, and the toner is replenished into the developing device 1212 by rotating the magnet roller 1217. By applying the particle behavior analysis by the above-described particle behavior analyzer to the magnet roller 1217, it is possible to predict the toner conveyance state in the developing hopper 1216 and the developing device 1212.

  In the electrophotographic image forming apparatus, a rotating magnet roller may be disposed in the cleaning device 1214, and the particle behavior analysis by the particle behavior analysis device described above is applied to the magnet roller. It is possible.

  As described above, according to the present embodiment, when the magnetic field application unit rotates, by using the basic applied magnetic field data and the rotation information of the magnetic field application unit, the change of the magnetic field accompanying the rotation of the magnetic field application unit can be reduced. It is possible to easily and accurately calculate the behavior of the magnetic particles in consideration.

  In particular, in the particle behavior calculation, since the time step of calculation is generally small and the number of calculation steps is often enormous, magnetic field data for each time is required to calculate the particle behavior more accurately. Even in such a case, it is possible to obtain magnetic field data at each time with high accuracy, and as a result, the behavior of particles can be obtained easily and with high accuracy.

  Also, since the applied magnetic field data can be changed following the movement of the magnetic field application unit, the movement of the magnetic field application unit cannot be predicted in advance, such as when the magnetic field application unit moves by receiving a force from a particle or member. In addition, by obtaining the coordinate system after the movement of the magnetic field application unit, the magnetic field data after the movement of the magnetic field application unit can be obtained with high accuracy.

  Moreover, the magnetic field data which changes with the movement of the particle | grain behavior and magnetic field application part which are analysis results can be displayed easily.

  Further, by applying the present invention to the developer behavior analysis of an electrophotographic image forming apparatus, a developer using a magnet roller such as a developing hopper having a rotatable magnet roller, a developing apparatus, or a cleaning apparatus is used. The developer behavior can be predicted for a device that controls the behavior of the developer.

[Second Embodiment]
In the second embodiment of the present invention, instead of performing the mapping of the basic applied magnetic field data described in the first embodiment, the particles are mapped so that the movement of the magnetic field applying unit is taken into account. It is possible to obtain the magnetic force acting on the

  In the first embodiment described above, the magnetic field that changes with the movement of the magnetic field application unit is obtained by mapping the basic applied magnetic field data to the coordinate system after the movement of the magnetic field application unit. However, when the number of nodes and the number of elements of the basic applied magnetic field data is large, time is required for one mapping calculation, and thus the time required for the entire calculation may be enormous. In particular, in particle behavior calculation, since the time step of calculation is generally small and the number of calculation steps is often enormous, the total calculation time can be shortened by reducing the time required for one mapping calculation as much as possible. Desired. This embodiment is for solving such a problem.

  Since the configuration of the particle behavior analysis apparatus and the processing program of the present embodiment is basically the same as that of the first embodiment described above, the common portion uses the configuration of the first embodiment. In the present embodiment, similarly to the first embodiment described above, the particle behavior calculation based on the particles in the two-dimensional cross section, the magnetic field application unit, and the related members is performed. The magnetic field application unit Is rotated around a certain axis, and magnetic field data is represented by a finite element model composed of nodes and elements.

  FIG. 8 is a diagram schematically showing a configuration example of a processing program of the particle behavior analysis apparatus according to the present embodiment, where (a) is a diagram showing a processing program for the entire particle behavior calculation, and (b) is a diagram of particles. It is a figure which shows the processing program which comprises the calculation part of the working magnetic force.

  8A, the processing program includes a control unit 100, an initial condition setting unit 111, a magnetic force calculation unit 112b acting on the magnetic particles, a force calculation unit 113 other than the magnetic force acting on the magnetic particles, and a particle displacement calculation. Unit 114 and particle behavior display unit 115. Since the elements other than the magnetic force calculator 112b acting on the magnetic particles are the same as those in the first embodiment (FIG. 1A) described above, description thereof is omitted.

  In FIG. 8B, the magnetic force calculating unit 112b acting on the magnetic particles includes a coordinate system setting unit 116 after moving the magnetic field applying unit, a particle magnetization calculating unit 118, a particle magnetic field data calculating unit 711, and an application. A magnetic force calculation unit 119 using a magnetic field and a magnetic force calculation unit 120 using particles are provided. Since the elements other than the particle magnetic field data calculation unit 711 are the same as those in the first embodiment (FIG. 1B) described above, the description thereof is omitted.

  The particle magnetic field data calculation unit 711 maps the particle position to the coordinate system of the basic applied magnetic field, and reversely maps the magnetic field data at the particle position after mapping to the coordinate system after the movement of the magnetic field application unit, thereby applying the magnetic field. Magnetic field data in the coordinate system after moving the part is obtained.

  FIG. 9 is a block diagram illustrating a configuration example of the particle behavior analysis apparatus.

  In FIG. 9, the particle behavior analysis 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. Since elements other than the particle image data storage unit 201m after mapping included in the RAM 201 are the same as the corresponding ones in the first embodiment (FIG. 2) described above, description thereof is omitted.

  The particle coordinate data storage unit 201m after mapping stores coordinates obtained by mapping particle coordinates from the coordinate system after movement of the magnetic field applying unit to the coordinate system of the basic applied magnetic field.

  Next, the processing of the magnetic force calculation 112b acting on the particles, which is a feature of the present embodiment, will be described in detail with reference to FIGS.

  FIG. 10 is a flowchart showing a procedure of processes executed by the magnetic force calculator 112b acting on the magnetic particles.

  In FIG. 10, the processing procedure for calculating the magnetic force acting on the particles will be described with reference to the configuration of the particle behavior analysis apparatus shown in FIG.

  (1) First, in the coordinate system setting unit 116 after movement of the magnetic field application unit, the magnetic field is based on the data stored in the current time data storage unit 201d and the magnetic field data storage unit 201e at the basic magnetic field application position, respectively. The coordinate system after the movement of the magnetic field application unit is obtained using the rotation center coordinates and the rotation angle of the application unit, and stored in the coordinate system data storage unit 201f after the movement of the magnetic field application unit (step S301).

  (2) Next, in the particle magnetic field data calculation unit 711, after the movement of the magnetic field application unit, based on the data stored in the particle data storage unit 201 c and the coordinate system data storage unit 201 f after the movement of the magnetic field application unit, respectively. The particle coordinates are mapped from the coordinate system to the coordinate system of the basic applied magnetic field, and stored in the particle coordinate data storage unit 201m after the mapping (step S901).

  (3) Next, in the particle magnetic field data calculation unit 711, based on the data respectively stored in the basic applied magnetic field data storage unit 201e and the mapped particle coordinate data storage unit 201m, the magnetic field data in the mapped particle coordinates Spatial differentiation is obtained and stored in the applied magnetic field data storage unit 201h after mapping (step S902).

  (4) Next, in the magnetic field data calculation unit 711 of the particles, the magnetic field data storage unit 201e at the basic magnetic field application position, the coordinate system data storage unit 201f after movement of the magnetic field application unit, and the applied magnetic field data storage unit 201h after mapping Based on the data stored in each, the spatial differential of the applied magnetic field after mapping is inversely mapped to the coordinate system after movement of the magnetic field application unit, thereby obtaining the spatial differential of the applied magnetic field at the coordinates of the particle before mapping, The data is stored in the magnetic field data storage unit 201j at the particle center (step S903).

  (5) Next, in the calculation unit 119 of the magnetic force by the applied magnetic field, the particle by the applied magnetic field is converted based on the data respectively stored in the magnetization state data storage unit 201g of the magnetic particles and the magnetic field data storage unit 201j at the particle center. The acting magnetic force is calculated and added to the force data storage unit 201k acting on the particles (step S904).

  (6) The processes in steps S901 to S904 are repeated for the number of particles (step S905).

  The feature of this embodiment is that by mapping the particle coordinates to the coordinate system of the basic applied magnetic field, magnetic field data at the particle position in the coordinate system of the basic applied magnetic field is obtained, and the magnetic field data is the coordinates after moving the magnetic field applying unit. By inversely mapping to the system, the magnetic force in consideration of the movement of the magnetic field application unit is obtained. Hereinafter, this process will be described in more detail with reference to FIGS.

  11A and 11B are diagrams for explaining calculation of mapping of magnetic field data. FIG. 11A is a diagram showing mapping of particle positions on the coordinate system of the basic applied magnetic field, and FIG. 11B is a diagram showing the coordinate system of the magnetic field application unit after movement. It is a figure which shows the reverse mapping of the magnetic field data.

  In FIG. 11, 401 represents a magnetic field application unit, and 403 represents particles before mapping. Reference numeral 501 represents an element division model, and 502 represents a magnetic field vector defined at the center of gravity of each element. Reference numerals 1001 and 1003 denote particles and magnetic field data (spatial differential of the magnetic field) mapped to the coordinate system of the basic applied magnetic field, and reference numerals 1002 and 1004 denote particles and magnetic field data inversely mapped to the coordinate system after movement of the magnetic field application unit ( (Spatial differential of magnetic field).

  The relative position between the particle 1001 after mapping and the magnetic field application unit 401 calculated using the method of the present embodiment is the same as the relative position between the particle 403 and the magnetic field application unit 401 shown in FIG. Therefore, the spatial differential of the magnetic field at the position of the particle 1001 is obtained, and it is reverse-mapped to the coordinate system after the movement of the magnetic field application unit (coordinate system rotated 60 degrees clockwise around the center coordinate of the magnetic field application unit). Thus, the spatial differentiation of the magnetic field at the position of the particle 403 shown in FIG. 4B can be obtained.

  Further, when the particle behavior display unit 115 obtains a magnetic field at an arbitrary position, the calculation of the applied magnetic field data of the present embodiment can be applied. Specifically, by performing the mapping calculation and the inverse mapping calculation of the present embodiment based on the movement information of the magnetic field application unit and the time and position data to be obtained, the magnetic field data at an arbitrary position at each time is obtained. It can be obtained.

  In the above description, the applied magnetic field data is mapped for each particle magnetic force calculation at each time step. However, when the time step is smaller than the speed of the magnetic field application unit, or when the particle moves per time step. If the magnetic field change per time step is negligible, such as when it is small, there is no need to perform mapping calculation every time. For example, a method of performing mapping calculation once every 10 steps of particle calculation, a method of performing mapping calculation only when the total moving distance of the magnetic field application unit after mapping calculation or the maximum moving distance of particles exceeds a threshold, etc. It is possible to shorten the calculation real time by reducing the number of mapping calculations.

  As described above, according to the present embodiment, the magnetic force acting on the particles according to the magnetic field data that changes with the rotation of the magnetic field applying unit, the basic applied magnetic field data and the movement information of the magnetic field applying unit are prepared. Thus, it can be easily obtained.

  In particular, in this embodiment, by performing the mapping calculation and the inverse mapping calculation as many times as the number of particles, it is possible to calculate the particle behavior considering the change in the magnetic field accompanying the rotation of the magnetic field application unit. As a result, when the number of particles is small compared to the applied magnetic field data amount and the time required for the particle mapping calculation is short compared to the magnetic field data mapping, the total calculation is performed as compared with the above-described first embodiment. Time can be shortened.

[Third Embodiment]
In the third embodiment of the present invention, the processing program of the particle behavior analysis apparatus includes the calculation unit 112a for the magnetic force acting on the magnetic particles in the first embodiment described above, and the above-described second embodiment. A method of selecting a method with a short calculation time is realized by including both the magnetic force calculation unit 112b acting on the magnetic particles, and using both calculation units according to the magnitude of the applied magnetic field data and the number of particles.

  FIG. 12 is a diagram schematically illustrating a configuration example of a processing program of the particle behavior analysis apparatus according to the present embodiment.

  In FIG. 12, the processing program includes a control unit 100, an initial condition setting unit 111, a magnetic force calculation method selection unit 1311, a magnetic force calculation unit 112a acting on magnetic particles, a magnetic force calculation unit 112b acting on magnetic particles, and a magnetic force. A force calculation unit 113 other than the magnetic force acting on the particles, a particle displacement calculation unit 114, and a particle behavior display unit 115 are provided. Elements other than the selection unit 1311 of the magnetic force calculation method are the same as the corresponding ones of the first embodiment (FIG. 1A) and the second embodiment (FIG. 8A) described above. Description is omitted.

  The magnetic force calculation method selection unit 1311 compares the number of calculated particles with the number of nodes and the number of elements of the magnetic field data, and selects a method with a short calculation time. Specifically, the prediction calculation time estimated from the number of particles and the prediction calculation time estimated from the magnetic field data amount may be compared to select a method with a short prediction calculation time.

  The magnetic force calculation method selection unit 1311 may be performed once in the pre-processing of the particle calculation. However, when the number of particles changes during the calculation, the selection of the magnetic force calculation method is performed when the number of particles changes. By performing processing by the selection unit 1311, it is possible to always select a method with a short calculation time.

  As described above, according to the present embodiment, it is possible to select a magnetic force calculation method with a short calculation time according to the magnetic field data amount and the number of particles, and as a result, the time required for calculating the entire particle behavior is reduced. It can be shortened.

[Other embodiments]
In addition, an object of the present invention is to supply a storage medium storing software program codes for realizing the functions of the embodiments to a system or apparatus, and a computer (or CPU, MPU, etc.) of the system or apparatus as a storage medium. This can also be achieved by reading and executing the stored program code.

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

  Examples of the storage medium for supplying the program code include a floppy (registered trademark) disk, a hard disk, a magneto-optical disk, a CD-ROM, a CD-R, a CD-RW, a DVD-ROM, a DVD-RAM, and a DVD. -RW, DVD + RW, magnetic tape, nonvolatile memory card, ROM, etc. can be used. Alternatively, the program code may be downloaded via a network.

  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 function expansion unit performs part or all of the actual processing, and the functions of the above-described embodiments are realized by the processing.

  Further, by executing the program code read out by the computer, not only the functions of the above-described embodiments are realized, but also the OS running on the computer based on the instruction of the program code is actually Needless to say, the present invention also includes a case in which the functions of the above-described embodiments are realized by performing part or all of the processing and the processing.

  In this case, the program is supplied by downloading directly from a storage medium storing the program or from another computer or database (not shown) connected to the Internet, a commercial network, a local area network, or the like.

  The form of the program 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.

BRIEF DESCRIPTION OF THE DRAWINGS It is a figure which shows roughly the structural example of the processing program of the particle behavior analyzer which concerns on the 1st Embodiment of this invention, (a) is a figure which shows the processing program of the whole particle behavior calculation, (b) is particle | grains It is a figure which shows the processing program which comprises the calculation part of the magnetic force which acts on. It is a block diagram which shows the structural example of a particle behavior analyzer. It is a flowchart which shows the procedure of the process performed by the setting part of the coordinate system after the movement of a magnetic field application part, and the calculation part of the mapping of magnetic field data. It is a figure which shows the state in which the magnetic field which a magnetic field application part forms with rotation of a magnetic field application part, (a) is a figure which shows the magnetic field data of a basic magnetic field application coordinate system, (b) is the center of a magnetic field application part It is a figure which shows the applied magnetic field data after rotating the magnetic field application part 60 degree | times clockwise centering on a coordinate. It is a figure explaining the mapping calculation of magnetic field data, (a) is a figure which shows the magnetic field data of a basic magnetic field application coordinate system, (b) is 60 degree | times clockwise with a magnetic field application part centering on the center coordinate of a magnetic field application part. It is a figure which shows the applied magnetic field data after rotating. It is a figure which shows the example of a particle behavior display when a magnetic field application part rotates 60 degree | times. 1 is a schematic diagram illustrating a configuration of a main part of an electrophotographic image forming apparatus. It is a figure which shows roughly the example of a structure of the processing program of the particle behavior analyzer which concerns on the 2nd Embodiment of this invention, (a) is a figure which shows the processing program of the whole particle behavior calculation, (b) is particle | grains It is a figure which shows the processing program which comprises the calculation part of the magnetic force which acts on. It is a block diagram which shows the structural example of a particle behavior analyzer. It is a flowchart which shows the procedure of the process performed in the calculation part of the magnetic force which acts on a magnetic particle. It is a figure explaining the mapping calculation of magnetic field data, (a) is a figure which shows the mapping of the particle position to the coordinate system of a basic applied magnetic field, (b) is the magnetic field data to the coordinate system of the magnetic field application part after a movement. It is a figure which shows a reverse mapping. It is a figure which shows roughly the structural example of the processing program of the whole particle behavior calculation which concerns on the 3rd Embodiment of this invention. It is a figure which shows roughly the structural example of the processing program of the whole particle behavior calculation which concerns on a prior art example.

Explanation of symbols

112a Calculation unit of magnetic force acting on magnetic particles 112b Calculation unit of magnetic force acting on magnetic particles 115 Particle behavior display unit (display means)
116 Coordinate system setting unit (coordinate system setting means) after movement of magnetic field application unit
117 Calculation section of magnetic field data mapping (magnetic field calculation means)
118 Calculation Unit for Magnetization of Particles 119 Calculation Unit for Magnetic Force by Applied Magnetic Field (Magnetic Force Calculation Means)
120 Calculation unit of magnetic force by particle 711 Magnetic field data calculation unit of particle (magnetic field calculation means)
1211 Photosensitive drum (carrier)
1214 Cleaning device (developer cleaning means)
1217 Magnet roller (magnetic field applying means, developer supply means)
1311 Selection part of magnetic force calculation method

Claims (11)

A particle behavior analyzer for analyzing the behavior of particles moving within a region to which a magnetic field is applied by a magnetic field applying means,
Magnetic field calculation for calculating magnetic field data in the coordinate system after displacement of the magnetic field applying means by mapping the magnetic field data at the basic magnetic field application position from the coordinate system of the basic applied magnetic field to the coordinate system after displacement of the magnetic field applying means Means,
Magnetic force calculation means for calculating the magnetic force acting on the particles based on the magnetic field data after mapping calculated by the magnetic field calculation means;
Particle behavior analysis means for analyzing the velocity and displacement of the particles by solving a motion equation based on the magnetic force calculated by the magnetic force calculation means and the force acting on the particles other than the magnetic force. ,
A particle behavior analysis apparatus comprising: A particle behavior analyzer for analyzing the behavior of particles moving within a region to which a magnetic field is applied by a magnetic field applying means,
The magnetic field in the coordinate system after the displacement of the magnetic field applying means is mapped by mapping the particle position to the coordinate system of the basic applied magnetic field and inversely mapping the magnetic field data at the particle position to the coordinate system after the displacement of the magnetic field applying means. A magnetic field calculation means for calculating data;
Magnetic force calculation means for calculating the magnetic force acting on the particles based on the magnetic field data after reverse mapping calculated by the magnetic field calculation means;
Particle behavior analysis means for analyzing the velocity and displacement of the particles by solving a motion equation based on the magnetic force calculated by the magnetic force calculation means and the force acting on the particles other than the magnetic force. ,
A particle behavior analysis apparatus comprising:   The particle behavior analysis apparatus according to claim 1 or 2, further comprising coordinate system setting means for obtaining a coordinate system after displacement of the magnetic field applying means. In the coordinate system after displacement of the magnetic field applying means, the particle position is mapped to the coordinate system of the basic applied magnetic field, and the magnetic field data at the particle position is inversely mapped to the coordinate system after displacement of the magnetic field applying means. Second magnetic field calculation means for calculating magnetic field data;
According to the magnitude of the magnetic field data or the number of particles, the magnetic field calculation means and the second magnetic field calculation means, further comprising a selection means for selecting a magnetic field calculation means having a short calculation time,
2. The particle behavior analysis apparatus according to claim 1, wherein the magnetic force calculation means calculates a magnetic force acting on the particles based on magnetic field data calculated by the magnetic field calculation means selected by the selection means.   3. The particle behavior analysis apparatus according to claim 1, further comprising display means for displaying the magnetic field data calculated by the magnetic field calculation means and the behavior of the particles analyzed by the behavior analysis means.   The particles whose behavior is analyzed by the particle behavior analyzer are visualized by a developer on a latent image formed on a carrier, and a developer in a developer replenishing unit of an image forming apparatus that forms an image or a developer cleaning of the image forming apparatus. 6. The particle behavior analysis apparatus according to claim 1, wherein the particle behavior analysis apparatus is a developer in the means.   4. The particle behavior analyzing apparatus according to claim 1, wherein the displacement of the magnetic field applying means is selected from a group including rotation, movement, rotation and movement. A control method of a particle behavior analyzer for analyzing the behavior of particles moving within a region to which a magnetic field is applied by a magnetic field applying means,
Magnetic field calculation for calculating magnetic field data in the coordinate system after displacement of the magnetic field applying means by mapping the magnetic field data at the basic magnetic field application position from the coordinate system of the basic applied magnetic field to the coordinate system after displacement of the magnetic field applying means Process,
A magnetic force calculation step of calculating a magnetic force acting on the particles based on the magnetic field data after mapping calculated by the magnetic field calculation step;
A particle behavior analysis step of analyzing the velocity and displacement of the particles by solving an equation of motion based on the magnetic force calculated by the magnetic force calculation step and the force acting on the particles other than the magnetic force; ,
A control method comprising: A control method of a particle behavior analyzer for analyzing the behavior of particles moving within a region to which a magnetic field is applied by a magnetic field applying means,
The magnetic field in the coordinate system after the displacement of the magnetic field applying means is mapped by mapping the particle position to the coordinate system of the basic applied magnetic field and inversely mapping the magnetic field data at the particle position to the coordinate system after the displacement of the magnetic field applying means. A magnetic field calculation process for calculating data;
A magnetic force calculation step for calculating a magnetic force acting on the particles based on the magnetic field data after reverse mapping calculated by the magnetic field calculation step;
A particle behavior analysis step of analyzing the velocity and displacement of the particles by solving an equation of motion based on the magnetic force calculated by the magnetic force calculation step and the force acting on the particles other than the magnetic force; ,
A control method comprising: A computer-readable program for causing a computer to execute a control method of a particle behavior analysis apparatus that performs behavior analysis of particles moving within a region to which a magnetic field is applied by a magnetic field application means,
Magnetic field calculation for calculating magnetic field data in the coordinate system after displacement of the magnetic field applying means by mapping the magnetic field data at the basic magnetic field application position from the coordinate system of the basic applied magnetic field to the coordinate system after displacement of the magnetic field applying means Procedure and
A magnetic force calculation procedure for calculating a magnetic force acting on the particles based on the magnetic field data after mapping calculated by the magnetic field calculation procedure;
A particle behavior analysis procedure for analyzing the velocity and displacement of the particles by solving a motion equation based on the magnetic force calculated by the magnetic force calculation procedure and the force acting on the particles other than the magnetic force; ,
A program that causes a computer to execute. A computer-readable program for causing a computer to execute a control method of a particle behavior analysis apparatus that performs behavior analysis of particles moving within a region to which a magnetic field is applied by a magnetic field application means,
The magnetic field in the coordinate system after the displacement of the magnetic field applying means is mapped by mapping the particle position to the coordinate system of the basic applied magnetic field and inversely mapping the magnetic field data at the particle position to the coordinate system after the displacement of the magnetic field applying means. Magnetic field calculation procedure for calculating data,
A magnetic force calculation procedure for calculating the magnetic force acting on the particles based on the magnetic field data after inverse mapping calculated by the magnetic field calculation procedure;
A particle behavior analysis procedure for analyzing the velocity and displacement of the particles by solving a motion equation based on the magnetic force calculated by the magnetic force calculation procedure and the force acting on the particles other than the magnetic force; ,
A program that causes a computer to execute.

Images