JP4343766B2 - Analysis method, program for executing the analysis method, and information processing apparatus - Google Patents

Description

  The present invention relates to a technique for analyzing a potential distribution of a device having electric field dependency of conductivity.

  An image forming apparatus using electrophotographic technology such as a printer, a copying machine, and a facsimile is composed of five processes of charging, exposure, development, transfer, and cleaning.

  Of these, the transfer process is a process of transferring a toner image formed on the image carrier to a transfer medium. In order to obtain a high-resolution image, it is important to increase the transfer efficiency and transfer to a transfer medium while suppressing toner scattering during transfer. For this purpose, it is important to optimize various parameters such as an image carrier (photosensitive drum), toner, transfer medium, and transfer conditions.

  In particular, with the spread of colorization in recent years, a transfer method using an intermediate transfer member such as an intermediate transfer belt is becoming mainstream in the transfer process. In the transfer system using an intermediate transfer member, first, four color toner images formed on a photosensitive member are sequentially superimposed to temporarily perform primary transfer onto the intermediate transfer belt. Finally, a final image is formed by performing a secondary transfer onto a final transfer medium such as a transfer sheet all at once. Therefore, two transfer processes are required to obtain the final image. In this case, the transfer efficiency in the two transfer processes is determined by intertwining many parameters such as the transfer conditions of the photoconductor, toner, intermediate transfer belt, transfer paper, primary transfer, and secondary transfer.

  Conventionally, optimization of various parameters in this transfer process has been carried out mainly by experiments using a prototype. However, in recent years, analysis using a computer has also been performed.

  For example, Patent Document 1 (Japanese Patent Laid-Open No. 2003-262617) discloses a method and apparatus for obtaining a potential distribution of a transfer device in consideration of current flowing in a conductor, discharge, and movement of an object. . According to this, the two-dimensional analysis region is first divided into a plurality of small cells. Based on the Poisson equation, the potential of each cell is calculated using a difference method. From the obtained potential distribution and the resistance of each member based on Ohm's law, the movement (advection) of charges accompanying the surface movement of the photosensitive drum, intermediate transfer belt, etc. is calculated. Next, the potential of each cell after the charge is transferred is calculated, and the charge transfer due to the discharge is calculated from the Paschen's discharge law and the capacitor theory from the potential distribution. Among the above steps, the transfer electric field is obtained by repeating the steps after the cell division until the potential distribution is stabilized.

  Here, the handling of the movement (advection) of charges accompanying the motion of the object will be described in detail. The change in charge based on the motion of the object and the Ohm's law can be solved by solving the equation (1) in which the advection term is added to the charge transfer based on the charge conservation law and Ohm's law. Where φ is potential, ρ is charge density, ε is dielectric constant, σ is conductivity,

Is a motion velocity vector of the object, and t is time.

  However, it is generally complicated to solve this equation, and it is difficult to obtain a stable solution. On the other hand, in an object having a constant conductivity, electric charges exist only on the surface. Therefore, conventionally, the conductivity of a conductive object is treated as constant, and when the movement is considered, the calculation is performed by moving the charge on the surface in the movement direction.

  FIG. 12 is a schematic diagram when the transfer device is viewed from the axial direction of the photoreceptor. It is assumed that the transfer paper 273 and the photosensitive drum 272 are moved from left to right in the transfer area. The toner 270 is negatively charged, the substrate of the photosensitive drum 272 is grounded, and a positive voltage is applied to the core 50 of the transfer roller. Thus, an electric field is formed between the photosensitive drum and the transfer roller, and the toner is transferred to the transfer paper.

In contrast to the transfer apparatus shown in FIG. 12, conventionally, the analysis area of the transfer apparatus model is divided into cells for applying the difference method. FIG. 12 is a diagram showing the location where each variable is defined in the cell. The potential and the charge amount are defined at the center of the cell, and the dielectric constant and conductivity are defined at the boundary between the cells.
JP 09-309665 A

  However, the following problems remain in the prior art.

  In general, the conductivity of materials such as a transfer roller and an intermediate transfer belt has a dependency on an electric field, which is known to have a great influence on a potential distribution. According to the above prior art, since the electric field dependency of conductivity cannot be taken into account, the electric field dependency must be ignored, and as a result, an accurate potential distribution cannot be obtained. This is due to the fact that the above technique simulates the movement of an object by moving a charge located on the surface in the direction of movement of the surface. In other words, in the case of a material with uniform conductivity, the electric charge located on the material is only on the surface, but when the conductivity has electric field dependence, the conductivity in the object is not uniform. Since charge is accumulated in the inside, the movement of the charge could not be considered.

  By the way, some materials such as transfer paper and photoconductors have non-uniform properties due to unevenness in the paper and pinholes, and this induces disturbance of the electric field and causes abnormalities in the image formed by the toner. It is known to cause.

  The present invention has been made in view of the above problems, and an object of the present invention is an analysis method that takes into account the electric field dependence of conductivity and the non-uniformity of material physical properties in an object, and a program thereof, and It is to provide an information processing apparatus.

In order to achieve the above-described object, a readable / writable storage means and a simulation model of a device having electric field dependency of conductivity are divided into meshes, and data of each element obtained by the division is stored in the storage means. An analysis method executed by an information processing apparatus for analyzing a potential distribution of the device, the input means meshing a simulation model of the device A step of dividing and storing the data of each element obtained by the division in the storage means, and a total analysis obtained by discretizing Poisson's equation for calculating the potential distribution by the finite element method. the entire node first equation simultaneous a linear equation holds in the region, to calculate the potential of each element by substituting the initial value of the dielectric constant and the charge of each element, the potential Calculated conductivity so as to have a field strength dependency of the elements from the electric field intensity of each element obtained from the distribution, the dielectric in the electric field strength dependence the entire nodal first equation conductivity and the potential with each element The amount of change in charge of each element is calculated by substituting into the equation using conductivity instead of the rate, the charge of each element after a lapse of a minute time is calculated from the amount of change in charge, and the amount of change in each element By substituting the electric charge after the lapse of time for the previous node 's first equation instead of the previous electric charge, the process of calculating the electric potential of each element after the lapse of a minute time is repeated until the steady state is obtained, and the electric potential of each element is calculated And an analysis method for executing the step.

  It becomes possible to accurately analyze the potential distribution of a device having electric field dependency of conductivity.

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

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

  FIG. 1 is a block diagram showing an information processing apparatus according to this embodiment. The computer 20 includes an overall control module that performs various determinations and processes, a data input module that detects data input, a toner dielectric analysis module, a toner charge analysis module, a discharge analysis module, a toner behavior analysis module, a calculation result output module, and the like. Is executed based on a software program, a central processing unit (CPU) 21, a ROM 22 storing the software program and fixed data, a readable / writable RAM 23 storing processing data, and an external storage device. It comprises an input / output circuit (I / O) 24 that communicates. In the information processing apparatus 20, input data 30 is input via the I / O 24, and a calculation result processed by the information processing apparatus 20 is output as output data 31 via the I / O 24.

  FIG. 2 shows the configuration of modules executed by the software program of this embodiment.

  The control module B100 controls the whole for analyzing the transfer process. Specifically, it controls a data input module, a conductor charge transfer analysis module, a discharge analysis module, an object motion analysis module, and a calculation result output module to be described.

  The data input module B110 is for creating mesh data necessary for the analysis performed in the present embodiment and data files of various parameters and storing them in the RAM 23. The mesh data refers to data obtained by dividing the analysis region of the transfer device made of a dielectric or a resistor into minute regions, such as a difference mesh and a finite element mesh, depending on the method of calculating the electric field. In addition, various parameters include dielectric constant, conductivity, charge distribution, potential as boundary condition, speed of moving object, designation of surface where charge can accumulate (referred to as charge surface), discharge The designation of the surface to be generated, the toner diameter, the initial toner arrangement, the toner charge amount, the toner dielectric constant, the calculation step time, the calculation end time, and the like are input.

  The in-conductor charge transfer analysis module B150 calculates the charge transfer in the conductor according to Ohm's law. The conductor charge transfer analysis module B150 includes an electrostatic field calculation module B151 and a transfer charge calculation module B152.

  In the electrostatic field calculation module B151, the potential distribution is calculated by solving Poisson's equation (2). In the mobile charge calculation module B152, the amount of change in charge is calculated from Equation 3 which is Ohm's law and charge conservation law based on the obtained potential distribution, and the charge distribution is updated. Here, φ is potential, ρ is charge density, ε is dielectric constant, σ is conductivity, and t is time. Note that when the mobile charge calculation module B152 is executed, the conductivity corresponding to the electric field is used as the conductivity value in consideration of the electric field (= −gradφ) obtained from the result of Equation 2.

  The discharge analysis module B160 determines the occurrence of various discharges, and calculates the movement of charges due to the discharge and the potential distribution after the discharge.

  The object motion analysis module B180 analyzes the movement of charges accompanying the motion of the object.

  The calculation result output module B200 outputs the obtained results of potential distribution, charge amount distribution, toner behavior, toner charge distribution, discharge distribution, and the like in the calculated region.

  The flow of simulation operation processing in this embodiment will be described. FIG. 3 is a flowchart for executing simulation by executing each module shown in FIG.

  In step S100, first, input data is read (data input module). At this time, an initial charge distribution such as a latent image on the photosensitive drum is also set. Next, a sub charge surface is generated in a member whose conductivity is dependent on the electric field by using the sub charge surface extraction module B 181 and is registered in the RAM 23. The above processing is positioned as A: Pre-preparation step of calculation accompanying time change to be started.

  Next, in step S302, the charge transfer calculation in the conductor is performed using the charge transfer analysis module B150 in the conductor. In this processing, first, the electric potential distribution is obtained by the electrostatic field calculation module B151, the electric charge moved by the moving electric charge calculation module B152 is calculated, and the electric charge distribution data is updated. Here, the process by the electrostatic field calculation module B151 is called an electrostatic field calculation process, and the process by the mobile charge calculation module B152 is called a mobile charge calculation process. The process of step S302 is positioned as B: a conductor charge transfer consideration process.

  Next, in step S402, the discharge charge and the potential distribution after the occurrence of the discharge are obtained using the discharge analysis module B160. This process is positioned as C: discharge consideration process.

  Next, in step S600, the movement analysis of charges accompanying the movement of the object is performed using the surface charge transfer module B182. This process is positioned as D: surface charge transfer step.

  In step S800, if the preset simulation end time is not reached, the process returns to step S300 to execute the simulation at the time obtained by adding Δt to the time from the start of the previously analyzed simulation. The above process is repeated until. In step S900, when the calculation end time is reached, a simulation result is output.

(Analysis by the finite element method)
Here, an example when the finite element method is adopted as a technique for performing electric field calculation in the analysis method in the present embodiment described above will be described. Here, the description is limited to the two-dimensional analysis.

  When the Poisson equation of Equation 2 is solved by the finite element method, the potential φ and the charge (including the polarization charge) Q are the values of the nodes that are the vertices of the mesh-divided element, and the dielectric constant ε and the conductivity σ are Defined as a value. The electric field strength is defined as an element value, and here, the value at the element center is calculated.

  The processing of the main module shown in FIG. 1 when applied to the analysis by the finite element method will be specifically described.

  First, the in-conductor charge transfer analysis step B150 will be described. Equation 4 is a simultaneous linear equation that is obtained by discretizing the Poisson equation of Equation 2 by the finite element method and is established in the entire analysis region. This equation is called the whole node first equation, and n is the number of nodes. In the electrostatic field calculation module B151, the potential distribution {φ} is obtained by solving the equation (4) based on given boundary conditions such as permittivity and charge.

  On the other hand, the left side of Equation 3 is nothing but the dielectric constant ε of the left side of Equation 2 replaced with conductivity σ. Therefore, the mobile charge calculation module B152 substitutes the potential distribution {φ} obtained in Equation 4 for Equation 5 obtained by using σ instead of ε depending on K in Equation 4 to obtain the charge at each node. Find the amount of change. Note that the matrix [L] of Equation 5 is a matrix obtained by using σ instead of ε in the process of creating the matrix [K] of Equation 4.

  As described above, the electrical conductivity σ generally has electric field strength dependency in many cases. If the value according to the electric field strength (= −gradφ) obtained at the stage of solving Equation 4 is used as the electrical conductivity σ used here, the electric field strength dependency of the electrical conductivity is considered. That is, by applying Equation 5, the amount of change in the charge at each node can be calculated very easily. Using this amount of change of charge per unit time, it can be substituted into Equation 4 to obtain the potential distribution {φ} after the lapse of minute time (note that the charge at each node on the charge planes A and B and the sub-charge plane) , The initial value of the charge at each node is given as 0).

  Next, the object motion analysis module B180 will be described. In an object with a constant conductivity, charge is present only on its surface. Therefore, here, the surface of such an object is called a charge surface. When considering the movement of an object having a constant conductivity, it is only necessary to move the charge in the direction of movement of the object between nodes constituting the charge surface as in the prior art.

  FIG. 4 shows an example of the charge surface. FIG. 4A is a schematic diagram in which a photosensitive member portion of an actual transfer process apparatus to be analyzed is substituted with a roller. In FIG. 4A, a roller 51, a core metal 50, and a sheet material 52 are main constituent units of the transfer process apparatus. In this apparatus, in actual operation, the two rollers 51 rotate with the sheet material interposed therebetween, and a voltage is applied to both rollers. On the other hand, as shown in FIG. 4B, in the simulation model of the transfer process apparatus, six charge surfaces 53 are defined as the surface of the object of the analysis object. Although the roller and the sheet are actually in close contact, it is assumed that there is a minute gap 54. In the object motion analysis module, simulation is executed by moving the true charge on the charge surface in the direction of motion of the object.

  Only when the conductivity has electric field dependence, electric charges are held not only on the surface of the object but also inside. Therefore, when considering the movement of charges accompanying the movement of the object, the surface charge transfer module B182 needs to move not only the charges on the object surface but also the charges inside. Therefore, in this process, for an object whose electrical conductivity depends on the electric field, the analyst sets the internal finite element substantially parallel to the surface of the object (that is, perpendicular to the normal direction of the surface). This can be dealt with by providing a division model in which elements are divided into layers so that the charge plane is automatically generated within the program by the sub charge plane extraction module B181. A specific example is shown using the division model of FIG.

The simulation model 60 is obtained by dividing an element of a roller-like object whose conductivity has electric field dependency. In FIG. 5, only half of the roller is modeled and divided. The roller surfaces 61 and 62 are referred to as charge surface A and charge surface B, respectively, and have movement speeds ν _A and ν _B. For the two charge surfaces A and B, the inside of the object is divided into layers so as to be perpendicular to the normal direction of these surfaces.

In the sub charge surface extraction module B181, the charge surface 63 is automatically generated at the boundary between these layers. The generated charge surface is referred to herein as a sub-charge surface. Then, the motion speed of each of the sub-charge surfaces is determined by linearly interpolating ν _A and ν _B based on the distance from the charge surfaces A and B. In the surface charge transfer module B182, charge transfer is performed in the same manner as a general charge surface.

  For a moving member whose electric conductivity depends on the electric field, an analysis with higher accuracy can be performed by solving based on Equation 1 considering the advection term. By providing the secondary charge surface, the movement of charges due to the movement of the member is simplified, and the same analysis as when stationary is possible. By such an analysis method, it is possible to handle the conductive characteristics at rest by the above-described charge-in-conductor analysis module B150 for a member having electric field dependency of conductivity, and the motion of the motion is analyzed by the object motion analysis module B180. The handling is made possible.

  As described above, the dependency of the conductivity of the transfer roller, intermediate transfer belt, etc. on the electric field can be taken into account, and accurate analysis can be performed.

  In the present embodiment, calculation is performed according to the flowchart of FIG. 3 using the module of FIG. 2 described above. As a result, it is possible to perform a transfer analysis in consideration of current and discharge flowing in a conductor whose electric conductivity depends on the electric field.

  An example of the result of simulating the primary transfer portion using the transfer paper as an intermediate transfer belt using the analysis method in the transfer device model shown in FIG. 12 will be described with reference to FIGS.

  FIGS. 6 and 7 are graphs showing the electric field dependence of the conductivity of the three types of intermediate transfer belts (referred to as belts A, B, and C) used for the calculation and the transfer roller, respectively. The value of each axis is standardized and displayed. FIG. 8 shows the calculation result obtained by applying this analysis method, and shows the relationship between the voltage and current applied to the transfer roller in FIG. 12 when there is no toner on the photosensitive drum.

  FIG. 8 shows the experimental results and analysis results of the transfer roller when applied to the three types of intermediate transfer belts A, B, and C shown in FIG. Since it is difficult to actually measure the electric field in the experiment, the experimental result and the analysis result are compared based on the relationship between the voltage applied to the transfer roller and the current.

  The white plot shows the experimental result, and the black plot shows the calculation result. It can be seen that all the belts are in good agreement with the experiment, but this was reproduced for the first time in consideration of the electric field dependence of the conductivity of the intermediate transfer belt and the transfer roller.

  FIG. 9 is a three-dimensional graph of the state of the discharge light at that time for belts A and C, and FIG. 10 is a comparison based on the results calculated by the analysis method described above. Other conditions are fixed as shown in Table 1. 9 and 10, the relationship between the ITB in-plane direction and the discharge intensity is graphed around the nip portion between the drum and the intermediate transfer belt (referred to as ITB). In FIG. 10, the discharge intensity is normalized and displayed. In the experiment, discharge is observed only for belt C upstream from the nip. On the other hand, a slight discharge is observed for both belts A and C on the downstream side. On the other hand, it can be seen that the same is reproduced in the calculation. In the above description, since the focus is on the electric field dependence of the conductivity of the intermediate transfer belt and the transfer roller, the description of the influence of the toner charge is omitted.

  The conditions set in FIGS. 9 and 10 are as shown in Table 1.

  In general, it is very important to be able to predict the discharge because the discharge greatly affects the scattering of the toner in the transfer process.

(Calculation by difference method)
In this embodiment, an example in which a difference method is used for electric field calculation will be described. In the difference method cell, the location where each variable is defined is the same as in FIG. 12 described in the section of the prior art. In addition, here, the description will focus on the differences from the finite element method, and the same parts will be omitted.

  In this embodiment, in order to distinguish from the finite element division model, a portion corresponding to an element of the finite element method in the difference mesh is referred to as a cell.

First, the process performed by the conductor charge transfer analysis module B150 will be described. In the electrostatic field calculation module B151, an orthogonal mesh is generated in a Cartesian coordinate system (xy coordinate system), and coordinates are converted into a general coordinate system (ζη coordinate system) using Equations 7 and 8. Then, the Poisson equation of Equation 6 is solved in this general coordinate system to obtain the potential distribution. Here, ζ ¹ = ζ, ζ ² = η, g ^ij is a metric tensor, √g is a coordinate transformation Jacobian, q is a volume charge density, ε is a dielectric constant, and φ is a potential.

  Next, in the processing by the mobile charge calculation module B152, the amount of change in charge of each cell is calculated by substituting the obtained potential of each cell into Equation 9 corresponding to Equation 3, and the charge distribution is updated. Here, σ represents electrical conductivity.

  In addition, when substituting the potential φ into Equation 9, by using a value corresponding to the electric field strength (= −grad φ) obtained at the stage of solving Equation 6 as the conductivity σ, the electric field strength dependence of the electric conductivity is determined. Therefore, it is possible to obtain the amount of change in charge in consideration of the characteristics. In this case only, charges are retained not only on the surface of the object but also on the inside, but as in the case of the finite element method, a mesh divided in layers so as to be substantially parallel to the surface of the object is given. This is dealt with by automatically generating a charge surface inside the program.

  Next, the object motion consideration module B180 will be described. Here, a set of cells on the surface of an object where charges can be accumulated is called a charge plane. First, in the sub charge surface extraction module B181, the sub charge surface is extracted in the preparatory step as in the analysis by the finite element method. Then, in the surface charge transfer module B182, the charge is moved between the cells constituting the charge surface and the sub charge surface for every elapsed time of the simulation by the amount that the object moves during the calculation step time. Other processing is the same as the analysis by the finite element method.

  Also by the method using the difference method for the electric field calculation as in this embodiment, the transfer analysis in consideration of the current and discharge flowing in the conductor whose electric conductivity depends on the electric field can be performed by the flowchart of FIG. Since the present embodiment is based on the difference method, the physical meaning of the calculation contents is easy to understand and the calculation can be performed at high speed.

  Here, as shown in FIG. 12, the difference method for defining the potential and the charge amount at the center of the cell and the dielectric constant and the conductivity at the boundary between the cells has been described, but the case where the position of this definition is changed is described. It is obvious that the method can be easily applied, and the same can be applied to the case where another calculation method such as an integration method is used as the electric field calculation.

(Other embodiments)
In the above-described embodiment, the moving object has the characteristic that the material physical property is uniform with respect to the moving direction, and the movement of the object is moved by moving the surface and the internal charges by the object movement analysis module B180. I was doing a simulation. In the present embodiment, in actual product development, an object having a material that is inhomogeneous in the direction of motion often becomes a problem, and this is a form of an analysis method that takes such material into consideration.

  For example, a hollow region may be generated inside the moving object, and the influence of the region on the electric field may be a problem. Specifically, there is a known problem that a charging device has a small hollow called a pinhole in a photosensitive member, and discharge is concentrated therein, resulting in non-uniform charging. Further, in the paper of the transfer apparatus shown in FIG. 12, a hollow due to paper unevenness may occur, and toner scattering may occur due to disturbance of the transfer electric field.

  In many cases, the influence of the minute unevenness of the surface of the moving object on the electric field becomes a problem. More specifically, charging and transfer electric fields are affected by the unevenness on the surface of the charging roller, the photoconductor, the intermediate electrophotographic belt, the transfer roller, and the like, and the characteristics thereof deteriorate.

  In the present embodiment, a method of handling an object having non-uniform material characteristics in the moving direction in a relatively simple manner will be described. Here, the case where a hollow exists in a moving object will be described as an example using a method in which electric field calculation is performed by the finite element method described above.

  FIG. 11 shows a part of element division of an object having a hollow. A grid-like solid line is a line indicating a boundary of the element 70 obtained by mesh division. Reference numeral 250 denotes a hollow existing in the object. Here, since the movement of the object is simulated by the movement of charges on the surface and inside, it is necessary to move only the hollow 250 with respect to the dividing element. Here, in each calculation time step, hollow movement is taken into account by setting the material physical property of the element in the hollow position to a hollow value. In addition, the material physical property of an element is determined from the ratio of the area which a hollow occupies in the area of an element.

For example, in FIG. 11, small circles 71 present in each element are points (called grid points) arranged at regular intervals in the element's local coordinate system. The lattice points that are not included in the hollow portion 250 are indicated by white circles, and the lattice points that are included are indicated by black circles. For example, in the case of a dielectric constant ε, the material characteristic having the hollow portion 250 can be obtained by Expression 10. Here, n ₀ is the number of white circle points that are not included in the element, and n ₁ is the number of black points that are included.

Here, ε _mat is a dielectric constant of the object, and ε _void is a hollow dielectric constant. Similarly, in the case of a triangular element or a secondary element, the dielectric constant can be defined from the proportion of lattice points included in the hollow. Here, the material property may be conductivity σ. The hollow does not necessarily need to be air, and the shape does not need to be a circle. In this way, by performing this processing on all elements of the object including the hollow inside, the dielectric constant distribution of the element considering the existence of the hollow can be obtained.

  When the transfer analysis is performed in consideration of the existence of the hollow, a module that takes this material non-uniformity into consideration may be added to the block diagram showing the configuration of the electric field calculation unit shown in FIG.

  Specifically, such processing may be executed as pre-processing in step S302 of the flowchart shown in FIG. In this way, the analysis application range for various materials is expanded by considering the hollows existing in the moving object.

  In addition, here, an example in which an object having non-uniform material characteristics in the direction of motion is taken into account, taking the case of a hollow case as an example, the surface roughness of the object, the influence of foreign matter mixed in the object, etc. The same applies to cases.

  Furthermore, it goes without saying that this method of considering an object having non-uniform material characteristics in the direction of motion is also applicable to the case where a difference method is used for electric field calculation.

  As described above, the transfer process analysis according to the embodiment of the present invention has been described. However, the present invention can be applied not only to the transfer process but also to a charging process and a development process. That is, in the current charging process of an electrophotographic apparatus, a method using a contact type charging roller is mainly used. In this method, the drum surface is charged by generating a discharge between the charging roller and the photosensitive drum. The conductivity of the charging roller used here also has an electric field dependency, but this can be easily dealt with by the above-described analyzer. In the development process, the charged electric toner is moved from the developing roller to the photosensitive drum by the developing electric field. This process is very similar to the transfer process in the sense that the toner is moved onto a different medium. Can also be easily handled by the analysis apparatus according to the present embodiment.

  Furthermore, the present invention is not particular about the analysis of the electrophotographic process. That is, as a method for simulating a potential distribution with respect to general problems including resistance and movement of an object, it can be applied unexpectedly to an electrophotographic process.

  In addition, although the case of the two-dimensional analysis is illustrated here, it is obvious that the present invention can be easily applied to the three-dimensional analysis.

  In the above embodiment, the method using the finite element method and the difference method has been described for the electric field calculation. However, as is apparent from the above description, the present invention is not limited to such an electric field calculation method. The present invention can be similarly applied to other methods, for example, an integration method.

1 is a block diagram of an information processing apparatus. The figure which shows the structure of the module of the program performed in information processing apparatus. The figure which shows the analysis processing flowchart of information processing apparatus. (A) The figure which shows an example of an actual analysis target processing apparatus, (b) The figure which shows an example of the simulation model of an analysis target processing apparatus. The figure which shows an example of the mesh division | segmentation of the model of a transfer roller. The figure which shows the relationship between the electric field strength of the transfer belt AC, and electrical conductivity. The figure which shows the relationship between the electric field strength of a transfer roller, and electrical conductivity. The figure which shows the comparison with the experimental result and analysis result of the relationship between the applied voltage with respect to a transfer roller, and an electric current. The figure which shows the experimental result of the discharge light of a transfer roller. The figure which shows the calculation result of the discharge light of a transfer roller. Explanatory drawing for calculating the dielectric constant of an element in a non-uniform material. The schematic diagram of a transfer apparatus. The figure which shows an example of the definition of the parameter of an element.

Claims (4)

Read / write storage means, meshing of a simulation model of a device having electric field dependence of conductivity, input means for storing data of each element obtained by the division in the storage means, and potential of each element And an analysis method executed by an information processing device that analyzes a potential distribution of the device,
The input means mesh-dividing the simulation model of the device, and storing the data of each element obtained by the division in the storage means;
The analysis means adds a dielectric constant and a charge of each element to a first equation of whole node which is a simultaneous linear equation established in all analysis regions obtained by discretizing Poisson's equation for calculating a potential distribution by a finite element method. The electric potential of each element is calculated by substituting the initial value, and the electric conductivity is obtained from the electric field strength of each element obtained from the distribution of the electric potential so as to have the electric field strength dependency of each element. By substituting the electric conductivity having dependency and the electric potential into an equation using electric conductivity instead of the dielectric constant in the first equation of the whole node, the amount of change in charge of each element is calculated. the elements of the charge is calculated from the change amount of the charge, the potential of each element after minute time by substituting the charges after the lapse of the short time of each element in the overall nodal first equation in place of the previous charge Analysis method repeats the process of calculating until a steady state, and a step of calculating the potential of each element. The entire nodal first equation, K matrices, node the n number, potential phi, when the charge Q,

And
The equation using the conductivity instead of the dielectric constant in the first whole node first equation is a matrix L obtained by using the conductivity instead of the dielectric constant in the process of creating K.

The analysis method according to claim 1, wherein:   A program for causing a computer to execute the analysis method according to claim 1 or 2. A readable / writable storage means;
An input unit that meshes a simulation model of a device having electric field dependency of conductivity, and stores data of each element obtained by the division in the storage unit;
Substitute the initial values of the dielectric constant and charge of each element into the first equation of the whole node, which is a simultaneous linear equation that is established in all analysis areas obtained by discretizing the Poisson equation for calculating the potential distribution by the finite element method. Thus, the electric potential of each element is calculated, the electric conductivity is obtained from the electric field strength of each element obtained from the distribution of the electric potential so as to have the electric field strength dependency of each element, and the electric conductivity having the electric field strength dependency of each element is obtained. The amount of change in the charge of each element is calculated by substituting the rate and the potential into an equation using conductivity instead of the dielectric constant in the first equation of the whole node, and the charge of each element after a lapse of a minute time is calculated. calculated from the change of the charge, the process of calculating the potential of each element after elapse minute time by substituting the charges after the lapse of the short time of each element in the overall nodal first equation in place of the previous charge Repeat until the steady state, the analysis device having an analysis means for calculating the potential of each element.