JP4298590B2 - Analysis method, program for executing the analysis method, and information processing apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To enhance the analyzing precision of a discharge phenomenon in an analyzing technique for analyzing the discharge of a certain apparatus. <P>SOLUTION: This analyzing method has a potential difference calculating step for calculating the potential difference between each of nodal points on the first surface of a simulation model subjected to mesh division and each of the nodal points on the second surface thereof on the basis of the predetermined charge quantity before discharge of each of the nodal points and the dielectric constant of each of the elements of the simulation model, a memory step for storing the data, which is related to the nodal point pair wherein potential difference exceeding the Paschen voltage determined from the distance between the respective nodal points is calculated, in a memory and an analyzing step for analyzing the charge quantity moved by discharge and a potential distribution after discharge on the basis of the data related to the stored nodal point pair and the charge quantity before discharge of each nodal point to store them in the memory. <P>COPYRIGHT: (C)2006,JPO&amp;NCIPI

Description

  The present invention relates to an analysis method for analyzing a discharge of a certain device.

  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 of electric charges accompanying the movement of the surface 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.

  By the way, in the actual nip portion, the dielectric property of the toner layer affects the transfer electric field. According to Patent Document 1, modeling is performed by providing a virtual dielectric layer corresponding to the toner layer in the nip. . The toner charge assumes that the toner transfer efficiency is 100%, and is present on the surface of the photosensitive drum before the transfer nip, and is assumed to be completely transferred onto the transfer sheet after the nip. . Further, ignoring the size of the toner, charges are set on the surfaces of the photosensitive drum and the transfer paper, respectively.

  On the other hand, in order to evaluate the transfer performance, it is extremely important to know the behavior of the toner particles. Although it is not a part of the transfer process, the toner on the paper on the paper transfer belt is calculated by calculating the scattering of the toner due to the disturbance of the electric field due to the peeling discharge. "Release Discharge in Belt System", Japan Opportunity Association [No01-251], 13th Electromagnetic Force Related Symposium Proceedings, pp 469 (2001) ".

JP 09-309665 A Kamonaga et al., “Release Discharge in Electrophotographic Paper Conveyance Transfer Belt System”, The Japan Opportunity Society [No01-251], Proceedings of the 13th Electromagnetic Force Related Dynamics Symposium, pp 469 (2001)

  However, the following problems remain in the prior art.

  First, the determination of the occurrence of discharge in Patent Document 1 lacks strictness because the potential is defined at the center of the cell. Further, in order to suppress the influence to the minimum, each value must be calculated by making the cells on the surface of these objects finer, and the calculation time becomes longer.

  And since the setting method regarding discharge differs in patent document 1 according to the surface shape of an object, designation | designation is needed according to a model, and an operator is forced to complicated operation. Further, it is known that the charge amount of the toner changes when it is discharged, but Patent Document 1 does not consider such discharge for the toner.

  Further, in Patent Document 1, the calculation of the amount of electric charge that is moved by discharge uses the theory of a capacitor composed of parallel plates, so that the material distribution of the model is uniform in the direction of the lines of electric force. Applicable only when layered.

  In general, a member using a corona discharge such as a static elimination needle is often used in a transfer process. However, Patent Document 1 does not consider an analysis assuming a static elimination needle.

  In an actual transfer system, the toner has an individual charge and moves independently. Since it is necessary to evaluate the quality of the transfer device based on the transfer efficiency produced by the toner and the image produced by the toner, it is extremely important to know the behavior of each toner.

  According to Patent Document 1, as described above, the behavior and physical properties of individual toners are not taken into account, and if the assumption of toner motion is incorrect, accurate analysis cannot be performed. Further, the dielectric characteristics and electric charge of the toner are not considered in the electric field calculation, and the simulation reliability is low in a region where the toner is dense, such as a transfer nip.

  The present invention aims to solve such problems.

In order to solve the above-described problem, the present invention provides an analysis method for analyzing a discharge in an information processing apparatus having a readable / writable storage device, wherein each node on the first surface of the simulation model divided by mesh and the second The potential difference from each node of the surface is calculated by the control means of the information processing device based on the predetermined amount of charge before discharge of each node and the dielectric constant of each element constituted by each node of the simulation model a calculation step, of the potential difference obtained from the calculation step, a storage step of storing the information about the nodes pair most above potential difference is asked to Paschen voltage determined from the distance between each node in the storage device, the storage Based on the information about the node pair stored in the step and the amount of charge before the discharge of each node, it is moved by the discharge. That the charge amount and analyzing the potential distribution after discharge, to provide an analysis method characterized by having, an analysis step of storing in the storage device.

An analysis method for analyzing a discharge in an information processing apparatus having a readable / writable storage device, the potential difference between each cell on the first surface and each cell on the second surface of the mesh-divided simulation model, a calculation step of calculating by the control unit of the information processing apparatus based on the dielectric constant determined by the predetermined amount of charge and before Symbol each cell before discharge of each cell, among the potential difference obtained from the calculation step, A storage step of storing in the storage device information on a cell pair for which a potential difference exceeding a Paschen voltage determined from a distance between the cells is determined; information on the cell pair stored in the storage step; and before discharge of each cell Analyzing the amount of charge transferred by discharge based on the amount of charge and the potential distribution after discharge and storing it in the storage device Provides an analysis method characterized by comprising the steps, a.

  According to the present invention, the determination of the occurrence of discharge is strict because the determination is based on the relationship between the distance between the nodes / cells on the two charge surfaces and the potential difference, and even if the element division of the surface of the object is relatively rough, it is accurate. High discharge calculation can be performed.

  In addition, analysis of objects with complex surface shapes can be handled.

  In addition, the behavior of the particles attached to the surface can be accurately calculated in consideration of the size, dielectric characteristics, and electric charge of the particles.

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

  A feature of the discharge analysis method in the present embodiment is to obtain a potential distribution when discharge does not first occur, extract a discharge occurrence point (discharge node pair) from the result, and prevent the Paschen voltage from being exceeded. Is to determine how much charge should be transferred. Equations (3) and (4), which will be described later, are created from the potential distribution when no discharge occurs, and this equation is solved by coupling it with the equation for electric field calculation.

On the other hand, a method of solving a plurality of types of equations by coupling is generally already performed.
For example, when the deformation of a structural structure associated with the flow of fluid is solved, or when a relational condition is imposed on the displacement between different nodes in the structural analysis.

  However, these conventional methods solve a plurality of unknown quantities (for example, fluid pressure and structure displacement) in a coupled manner, or add conditions to the relationship between the unknown quantities. The analysis method in the present embodiment is a method in which the conditional expression is obtained in advance by a similar electric field calculation. In this respect, it is clearly different from the old one, and cannot be solved by the old method.

  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, the data input module, toner dielectric constant analysis module, toner charge analysis module, charge transfer analysis module in the conductor, discharge analysis module, toner behavior analysis module, object motion analysis module, and calculation result output module to be described will be controlled. To do.

  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 toner dielectric constant analysis module B120 calculates data in which the dielectric constant of the toner is added to the distribution of the dielectric constant in the mesh data based on the position, shape (diameter), and dielectric constant data of each toner.

  The toner charge analysis module B130 calculates data in which the distribution of the charge of the toner is added to the distribution of the true charge in the mesh data.

  The in-conductor charge transfer analysis module B150 calculates the charge transfer in the conductor according to Ohm's law.

  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 discharge analysis module B160 includes a discharge extraction module B161 between opposing surfaces, a discharge extraction module B162 between pointed members, a discharge charge amount calculation module B163, and a toner charge update module B164.

The counter-surface discharge extraction module B161 searches for the presence or absence of discharge between two opposing planes according to Paschen's discharge rule, and executes a process of extracting a portion to be discharged. The search for the occurrence of this discharge is the part defining the potential as an unknown variable in the mesh data (this is here called the potential definition segment, or simply the segment. For example, the cell center in the difference method described in the prior art) In the case of the finite element method, this refers to the node on the surface where the discharge is searched for or near the surface, and the discharge definition segment on the opposite surface that exceeds the Paschen voltage for each potential definition segment. This is done by extracting. Here, the segment on or near the surface used for the search is referred to as a discharge search segment, the extracted potential definition segment is referred to as a discharge segment, and a pair with a discharge partner is referred to as a discharge segment pair. As the Paschen voltage _Vpa , some of which are indicated by an approximate curve have been proposed, and any of them may be used. d is the gap length.

  Note that, in the inter-surface discharge extraction module B161, when the surface is covered with the toner layer deposited thereon, the covered potential definition segment is excluded from the search. Then, instead of the excluded one, the potential definition segment (this potential definition segment is particularly referred to as a toner segment) close to the toner in the toner layer deposited on the surface corresponds to the toner positioned on the surface layer. The toner segment is used to search for discharge occurrence.

  In the peak member discharge extraction module B162, a pair of discharge segments is extracted based on an experimental result indicating a relationship between a gap length and a discharge start voltage between two bodies that do not follow Paschen's discharge law, such as a static elimination needle. In the discharge charge amount calculation module B163, the discharge start voltage expressed by the equations 3 and 4 and the relational expression of the charge transfer expressed by the equations 3 and 4 with respect to all the discharge segment pairs extracted in the Poisson equation of the equation 2 are coupled and solved, thereby The potential after the generation and the discharge charge amount are obtained.

Here, i and j are potential definition segment numbers, V _th ^(ij) is the discharge start voltage between i and j, Q _i and Q _j are the charge amounts of i and j before discharge, Q ′ _i , Q ′ _j is the amount of charge of i and j after discharge, and ΔQ _ij is the amount of charge transfer due to discharge between i and j. α is a coefficient indicating the ratio of the potential between both segments after discharge to the discharge start voltage, and is generally set to 1. Detailed examples of specific coupled equations will be described in the following examples. The charge amount of the discharge segment other than the toner segment is updated by adding the discharge charge amount obtained here.

  The toner charge update module B164 is the source of the toner segment extraction when the potential definition segment where the discharge is generated is the toner segment in the discharge charge amount obtained by the discharge charge amount calculation module B163. The toner is renewed by adding its charge amount by the amount of discharge charge.

  The toner behavior analysis module B170 updates Newton's equation of motion based on the force acting on the toner such as electrostatic force, gravity, adhesion force, air resistance force, etc., and updates the toner position to the position after the calculation interval. is there.

  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.

  A processing flow of the information processing apparatus when the transfer apparatus is simulated in the present 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. In step S102, the toner is set to the initial position according to the input data conditions. The above processing is positioned as A: Pre-preparation step of calculation with time change starting from now.

  Next, in step S300, a dielectric constant distribution setting considering the toner is performed using the toner dielectric constant analysis module B120. In step S301, the toner charge analysis module B130 is used to set a true charge distribution considering the toner charge. In step S302, the charge transfer calculation in the conductor is performed from the obtained dielectric constant distribution, true charge distribution, and dielectric polarization distribution using the charge transfer analysis module B150 in the conductor. The processing of S300 to S302 is positioned as B: charge transfer analysis step in the conductor.

  Next, in step S400, a discharge segment pair extraction process in which the discharge location between the parallel surfaces and the discharge destination are paired is executed by the process of the inter-face discharge extraction module B161. Further, in step S401, a discharge segment pair extraction process in which the discharge location between the peak members and the discharge destination is paired is executed by the processing of the peak member discharge extraction module B162. In step S402, the charge of all potential definition segments is obtained (discharge charge amount calculation module B163). In step S403, the charge amount of the discharged toner is updated (toner charge update module B164). The process of S400-S403 is positioned as C: discharge analysis process.

  In step S500, the toner behavior calculation after a predetermined time is calculated using the toner behavior analysis module B170. Then, the toner position obtained by the toner behavior calculation is updated to the obtained position. This process is positioned as D: toner behavior analysis step.

  In step S600, the movement of the charge accompanying the movement of the object (referring to each unit of the toner or paper transport device) is performed (object movement analysis module B180). The object motion analysis module B180 will be described later in detail. The process of S600 is positioned as E: object motion analysis 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 polarization charge) Q are defined as node values described later, and the dielectric constant ε and conductivity σ are defined as element values. The electric field strength is defined as an element value, and here, the value at the element center is calculated.

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

  First, the object motion analysis module B180 will be described. Charge is generally present only on the surface of the object. The surface of an object on which charges can be accumulated is called a charge surface. When considering the movement of the object, the charge may be moved in the direction of movement of the object between the nodes constituting the charge surface. FIG. 4 shows an example of the charge surface. FIG. 4A is a schematic diagram in which a photoconductor of an actual transfer process apparatus to be analyzed is replaced 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, the simulation is executed by moving the true charge on the charge surface in the motion direction of the object.

  Next, the toner dielectric constant analysis module B120 will be described. The dielectric constant of each element is determined from the ratio of the area occupied by the toner to the area of the element. FIG. 5 shows an example in which the dielectric constant is set using the quadrangular element 70.

FIG. 5A shows an element (quadrangle element 70) in the local coordinate system, and points 71 indicated by ◯ are regularly arranged at regular intervals inside the element. The regularly arranged points 71 are referred to as lattice points here. The grid points are arranged at positions indicated by ◯ in the finite element in FIG. 5B by converting them into values (x _s , y _s ) in the model coordinate system using (Equation 5). Here, Mn is the number of nodes constituting the element, N _l is the shape function of the element, and (x ₁ , y ₁ ) is the coordinates of each node constituting the element.

Here epsilon _air is the dielectric constant of air, epsilon _Toner is the dielectric constant of the toner. In this way, the dielectric constant of an element can be accurately defined based on the proportion of the toner model in an element. Similarly, in the case of a triangular element or a secondary element, it is possible to define a constant dielectric constant from the ratio of the points included in the toner particles, assuming regular regularly spaced points inside. In the toner dielectric constant analysis module B120, this process is performed on all elements of the material in which the toner moves, so that an accurate dielectric constant distribution of each element in consideration of the dielectric constant of the toner can be obtained.

  In the above description, the case where the toner has only one type of dielectric constant has been described. However, it is obvious that a plurality of types can be easily handled.

Next, the toner charge analysis module B130 will be described. In the processing of this module, when toner having a charge is present, the charge is distributed from the central point of the toner to a node near the central point. An example in which the toner charge is distributed to the nodes will be described in detail with reference to FIG. In FIG. 6, an element 70 divided into meshes, a node 80 constituting the element, and a circle 72 indicating toner are shown. A center point 81 indicates the center point of the toner. Here, it is assumed to have a charge amount Q _T to the toner. For the element including the center point 81 of the toner, this charge is distributed to each node 80 constituting the element. Expression 7 is used for the distribution process.
Q _l = N _l Q _T (Equation 7)
Here, Q _l is the amount of charge distributed to the l-th node, and N _l is the shape function of the l-th node of the element including the center of the toner. In the toner charge analysis module B130, such distribution is performed for all the toners, and the charge amount of the corresponding node is updated to the toner charge.

  Next, the discharge analysis module B160 will be described. In the finite element method, since the potential is defined by a node, the above-described potential definition segment is a node. Therefore, here, the above-described discharge segment is called “discharge node”, the discharge search segment to be analyzed for discharge is called “discharge search node”, the discharge segment pair is called “discharge node pair”, and the toner segment is called “toner node”. I will decide.

  First, the inter-surface discharge extraction module B161 will be described. First, the operator designates in advance, on the simulation model of the transfer process apparatus, two surfaces of the charge surface that may cause a discharge between the surfaces. Then, a portion where discharge between the two surfaces may occur is extracted based on the potential distribution for each execution time of the simulation.

The method for extracting the discharge occurrence point will be specifically described with reference to FIG. In FIG. 7, an element 70 obtained by dividing the mesh, and charge surfaces 90 and 91 for charging the process apparatus indicated by bold lines are surfaces that may be discharged between the surfaces designated by the operator. The node 80 exists on these charge surfaces 90 and 91, the circle mark indicates a node on the charge surface 90, and the triangle mark indicates a node on the charge surface 91. As shown in FIG. 7, the potential φ _{i of the} node i indicated by 92 on the charge surface 90 (the dielectric constant obtained from the toner dielectric constant analysis module B120 and the charge obtained from the toner charge analysis module B130 are expressed by Obtained from the node 1 on the charge surface 91 (the dielectric constant obtained from the toner dielectric constant analysis module B120 and the charge obtained from the toner charge analysis module B130). Potential difference φ _i −φ ₁ with respect to the potential φ _l ). If the potential difference φ _i −φ ₁ is larger than the Paschen voltage V _pa ^(il) determined from the distance (gap length) between the two nodes expressed by Equation 1, it is determined that a discharge has occurred between the two. This operation is examined for all the nodes 80 on the charge surface 91, and the node 1 exceeding the Paschen voltage is registered in the potential difference RAM 23 as a node where discharge occurs between the node i, that is, a discharge node pair. By performing such an operation on all the nodes on the charge surface 90, all the discharge node pairs between the two surfaces are extracted.

  In the above description, the processing when the positional relationship of the registered discharge node pair is not restricted has been described. However, the charge surface in which the straight line connecting the two nodes is included within a predetermined angle with respect to the normal direction of the charge surface 90 There may be a restriction that only the nodes on 91 are targets for calculating the potential difference. This is because it has been found by the inventor's examination that the treatment for the strange discharge generated when the electric field in the gap is complicated can be suppressed, and a more realistic result can be obtained. Specifically, according to the inventor's study, it has been found that an effective discharge can be extracted while eliminating the processing for strange discharge by adopting only the angle within 30 °.

In addition, when performing a simulation in which toner is deposited on the charge surface, in the portion where the toner is deposited, a discharge search is performed for a node located on the outermost layer portion of the toner instead of the node on the charge surface. A node. An example of extracting discharge search nodes in consideration of toner will be described with reference to FIG. In FIG. 8, each symbol indicates an element 70, a node 80 on the charge surface of the simulation model of the process apparatus, and a charge surface 90 indicated by a thick line. Further, a node 80 indicated by a triangular mark indicates a node on the charge surface, spherical portions 72 and 73 indicate toner, and an X mark 81 indicates the center of the toner. Here, the toner is assumed to be a sphere, and is displayed as a circle in the drawing. The discharge search node is extracted by the following procedure.
(1) All nodes on the charge surface are registered in advance as discharge search nodes.
(2) The toner located on the surface is extracted from the toner deposited on each charge surface. In FIG. 8, the extracted surface toner is indicated by a shaded circle 73, and the other internal toner is indicated by a white circle 72.
(3) Of the nodes on each toner surface, the node closest to the position farthest from the charge surface is extracted as a toner node. In the case of the figure, four nodes 100 indicated by stars are extracted. Then, the extracted toner node is added as a discharge search node.

  Then, nodes on the charge surface covered with toner, that is, nodes on the charge surface indicated by hatched triangles, are excluded from the discharge search nodes. After all, in the case of FIG. 8, the nodes indicated by triangles Δ and stars ☆ without hatching are discharge search nodes on the charge surface.

  Based on the discharge search nodes thus extracted, the discharge node pairs are extracted as described above.

  Next, processing by the peak-to-point member discharge extraction module B162 will be described. The Paschen's discharge law described above is established in an equal electric field such as parallel electrodes, and cannot be applied in an unequal electric field. In particular, the discharge of a member often used in an electrophotographic apparatus having a pointed shape such as a static elimination needle uses corona discharge and cannot use the same law. For such a simulation model of a member to which Paschen's discharge law cannot be applied, a discharge node pair is extracted using a gap length dependency curve of a discharge start voltage obtained from an experiment. An explanation will be given below by taking the case of a static elimination needle as an example.

  FIG. 9 is an example of an element division model of the static elimination needle portion. In FIG. 9, each symbol is an element 70 obtained by dividing the mesh, a charge removal needle 111, a charge surface 90 on the surface of the charge removal needle, and a charge surface 91 opposite to the charge removal needle are nodes 80 constituting two charge surfaces. Yes, among the nodes 80, the circles indicate nodes on the surface of the static elimination needle, and the triangles indicate nodes on the opposite surface.

  In addition, the static elimination needle 111 is regarded as a perfect conductor, and the internal element division | segmentation is not performed. As in the case of the discharge according to Paschen's discharge law, the nodes on the charge surface 90 of the static elimination needle and the charge surface 91 opposite thereto are used as discharge search nodes, that is, the nodes indicated by ○ and △ in the figure are as follows. A discharge node pair is extracted by examining the discharge between both charge planes.

  A method for extracting a discharge node pair will be described. FIG. 11 is a gap dependence curve with the charge surface of the discharge start voltage of the static elimination needle, and this curve is a plot of experimental results. There are two curves in the figure. This is because the discharge characteristics differ when the polarity of the static elimination needle is made positive and when it is made negative. In other words, the two are used separately based on the potential difference between the static elimination needle and the discharge destination. If the potential difference between the two discharge search nodes exceeds the voltage of the selected curve, it is registered in the RAM 23 as a discharge node pair.

  Since the charge removal needle is considered to cause discharge at the pointed tip, only the pointed point from the shape of the charge surface is designated and considered as the discharge search node. In FIG. 9, only the circled nodes 112 with hatching are candidates for discharge search nodes. As a result, a more rapid and accurate electric field result of the discharge of the needle is obtained.

  In the above description of the inter-facing surface discharge extraction module B161 and the peak member discharge extraction module B162, the description has been given only for one charge surface that may cause a discharge on one charge surface. Also, in practice, there is often a possibility that discharge occurs between a plurality of charge surfaces with respect to one charge surface. However, according to the above-described method, it is possible to easily search for the possibility of discharge between each node on the charge surface and the nodes of the plurality of charge surfaces and extract a discharge node pair. The present invention is also effective with respect to curved surfaces.

  Next, the discharge charge amount calculation module B163 will be described. As a premise of the processing of this module, the nodal point pair that causes the discharge between the parallel surfaces and between the peak members has already been extracted by the inter-face discharge extraction module B161 and the peak member discharge extraction module B162, and is registered in the RAM 23. It shall be. Here, the amount of electric charge transferred by the discharge between the discharge node pairs is obtained.

  FIG. 10 is a diagram for explaining an example of obtaining the amount of electric charge moved by discharge. In the figure, 70, 80, 90 and 91 are the same as those in FIG. It is assumed that the node 131 on the charge surface 90 and the node 132 on the charge surface 91 form a discharge node pair, and the node numbers are i and j, respectively. The amount of charge that is moved by the discharge at this discharge node pair is calculated as follows.

  (Equation 8) is a simultaneous linear equation obtained by discretizing the Poisson equation of (Equation 2) by the finite element method, and is an equation after rearranging by substituting boundary conditions. This equation is called the whole node second equation, and m is the number of nodes whose potential is unknown.

Here, the potential vector before discharge is {φ}, the charge vector is {Q}, and those after discharge are {φ ′} and {Q ′}, respectively. For the discharge node pair i, j in the figure, the amount of charge before discharge is Q _i , Q _j , and the electric charge moves from node i to node j by discharge by ΔQ _ij, so that the potential difference between the two nodes becomes αV _th . Shall be. Here, V _th ^(ij) is a discharge start voltage in the gap length between both nodes, and in the case of the node pair extracted in the inter-surface discharge extraction module B161, it is extracted by the Paschen voltage, and the peak member discharge extraction module B162. In the case of the paired nodes, this is the discharge start voltage obtained from the above experimental results. α is a coefficient indicating the ratio of the potential drop to the Paschen voltage after discharge. In general, α is 1.

The potentials φ _i ′ and φ _j ′ of the nodes i and j after discharge have the relationship of (Equation 3). The charge amounts Q _i ′ and Q _j ′ can be expressed by (Equation 4). By incorporating (Equation 3) and (Equation 4) into (Equation 8), the electric field equation after discharge of Equation 9 is obtained.

  Here, “...” In the (m + 1) th row is all zero.

Then, ΔQ _{ij of the} right side vector is shifted to the left side matrix to obtain (Equation 10).

  Here, “...” in the (m + 1) th row and “...” in the (m + 1) th column are all 0. Further, K in Equations 9 and 10 is a coefficient depending on the left side of Equation 2.

The matrix on the left-hand side is symmetrical to the matrix of (Equation 8) with the addition of one row where the columns of the two discharge node numbers are 1 and −1 and the other elements are 0. Is one column added. By solving this equation, the potential distribution {φ ′} after discharge and the amount of charge ΔQ _ij transferred by the discharge can be obtained.

  Here, the case where there is only one discharge node pair has been described. However, when there are a large number of discharge node pairs, rows and columns outside the m × m in this matrix are represented by the number of discharge node pairs in the same manner. By increasing, it is possible to calculate the potential distribution {φ ′} after discharge and the charge amount {ΔQ} transferred by the discharge. That is, for each discharge node pair, the row and column values of the node numbers are 1 and −1, and a matrix in which the number of discharge node pairs is added with 0 rows and columns otherwise.

  In the discharge charge amount calculation module B163, after calculating the amount of charge that moves due to discharge by the above method, among the discharge nodes, the nodes other than the toner nodes, that is, the nodes on the charge surface, are calculated from Equation 4 Obtain the charge amount and update the value.

  Since the matrix on the left side in Equation 10 is a symmetric matrix, Equation 10 can be easily solved by a method such as the skyline method and the ICCG method as in the case of a general finite element method.

  In the above-described discharge analysis module B160, it is assumed that there is one discharge destination node for one node. However, when there are multiple segment pairs of Paschen voltage (discharge start voltage for discharge from pointed member), it is easy to cause discharge from one node to multiple nodes by making them all analysis targets. Can be changed. According to the inventor's investigation, it is known that a discharge result closer to the reproduction of the experimental result can be calculated particularly when the discharge occurs from the pointed member.

  As described above, the occurrence of discharge is determined by searching for a node on the opposite charge surface that satisfies the most discharge condition for each node on the charge surface. Thereby, even if the discharge region is widened as in the case of discharge between the rollers, the conventional problem does not occur.

  Further, since the nodes on the two charge surfaces are used, the determination can be made with high accuracy. In addition, it is possible to extract discharge points with high accuracy even if the element division on the surface of the object is rough. Moreover, it becomes possible to deal with an object having a complicated surface shape. In addition, the location where the discharge occurs is automatically performed within the program using the relationship between the distance between both nodes and the discharge start voltage, regardless of the surface shape of the object, so there is no need to specify the model according to the shape of the model. It will be possible to provide an easy-to-use program.

  In addition, since the discharge charge amount directly calculates the field satisfying (Equation 3) and (Equation 4), it is possible to obtain a highly accurate potential distribution and discharge charge amount. It can also be applied to any model material distribution. Further, it is not necessary to separately provide data necessary for calculating the amount of electric charge moved by discharge, and a program that is extremely easy to use from the viewpoint of the operator can be provided.

  Further, it becomes possible to handle discharge of a member that does not follow Paschen's discharge law such as a static elimination needle, and the practical level increases by analyzing the actual transfer system as it is.

  Here, the toner analysis module B164 will be described. In this module, of the discharge charge amount obtained by the discharge charge amount calculation module B163, when the node where the discharge is generated is a toner node, for the toner that is the basis of the toner node extraction, The charge amount is updated by adding the discharge charge amount ΔQ. At this time, a correspondence table from the toner node to the toner number is required, but this can be easily prepared by the above-described counter-surface discharge extraction module B161, and may be prepared.

  Next, the toner behavior analysis module B170 will be described. As the toner, a spherical object that is independent of the finite element method division model used in the electric field calculation is assumed. In this means, the toner position is updated to a position after the calculation step time by taking into consideration the electrostatic force, gravity, adhesion force, and air resistance force acting on the toner.

The electrostatic force F _e (t) received by the toner at time t is obtained by Equation 11. Here, Q _T (t) and E (t) are the charge amount of the toner at time t and the electric field intensity at the toner center position, respectively.

The total force acting on the toner obtained by adding gravity, adhesion, air resistance, etc. to the electrostatic force F _e (t) received by the toner is defined as F (t). When the toner velocity at time t is represented by v (t), the toner position x (t + dt) after the calculation step time (dt) is obtained from Equation 12 from Newton's equation of motion. In Equation 12, v (t + dt) is the speed after the calculation step time, and m is the weight of the toner.

  The behavior of the toner can be calculated using Equations 11 and 12. Specific methods include a method called a hard sphere model using a relational equation of momentum conservation law and rebound, and an individual element method. There is a method called a typical soft sphere model, and either of them may be adopted here.

  The toner dielectric constant analysis module B120, the toner charge analysis module B130, the toner charge update module B164, and the toner behavior analysis module B170 are used to accurately calculate the behavior of the toner in consideration of the size, dielectric characteristics, and charge of each toner. become able to. As a result, it becomes possible to evaluate the transfer efficiency and directly evaluate the image formed by the toner, and to directly examine the cause / process leading to the formation of the image. In particular, the discharge to the toner that has a very serious influence on the transferred image and the change in the charge amount of the discharged toner can be obtained by calculation, and the image can be accurately predicted at the design stage.

  FIG. 13 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.

  An example of the result of simulating the primary transfer portion using the transfer method as the intermediate transfer belt in the transfer device model shown in FIG. 13 will be described with reference to FIGS.

  FIG. 14 is a graph 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 FIG. 15 is a graph showing the electric field dependence of the conductivity of the transfer roller. is there. The values for each axis are standardized and displayed.

  FIG. 16 is a three-dimensional graph of the state of the discharge light for belts A and C, and FIG. 17 is a comparison based on the results calculated by the analysis method described above. 16 and 17, the relationship between the ITB in-plane position and the discharge intensity is graphed around the nip portion between the drum and the intermediate transfer belt (referred to as ITB). In FIG. 17, the discharge intensity is standardized. 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.

  18 and 19 show the relationship between the voltage and current when the voltage is actually applied to the transfer roller device of FIG. 13 and when the simulation is performed. The white plot shows the experimental result, and the black plot shows the calculation result. FIG. 18 and FIG. 19 show the relationship between the transfer voltage and current when toner is not transferred and when toner is transferred, and the results of three types of intermediate transfer belts A, B, and C are displayed. Thus, both calculations are in good agreement with the experiment for all belts.

  In FIG. 19, the current rising from around 600 V is due to the occurrence of discharge on the toner layer. Due to the discharge to the toner layer, some of the toner has its charge polarity reversed. That is, all the toner is negatively charged before transfer, but some toner changes to positive charge in the process of passing through the nip. As a result, the toner whose polarity is reversed remains on the drum without being transferred. The upper diagram shows that the ratio of the toner remaining on the drum is accurately calculated due to the polarity reversal. As a result, the discharge to the toner according to the present embodiment is calculated appropriately. is there. FIG. 20 shows the relationship between the voltage applied to the transfer roller device and the transfer efficiency. According to FIG. 20, it is understood that the transfer efficiency is lowered when the applied voltage at which discharge starts is 600 V or higher.

  In addition, the setting of the conditions in FIGS.

  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.

(Analysis by difference method)
Here, an example in which the difference method is used for electric field calculation will be described. In addition, in the cell of the difference method, the location where each variable is defined is as shown in FIG. That is, the potential φ and the charge Q are defined as the center of gravity of the cell, and the conductivity σ and the dielectric constant ε are defined as the midpoint of the side between the cells. In addition, here, the description will focus on the differences from the finite element method, and the same parts will be omitted.

  Here, 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.

  The object motion analysis module B180 will be described. The collection of cells on the surface of the model of the device where charge can accumulate is called the charge plane. In this process, as in the finite element method, the true charge and the polarization charge are moved between the cells constituting the charge surface by the amount that the object moves every predetermined time from the start time in the simulation.

  The toner dielectric constant analysis module B120 will be described. Here, as in the finite element method, first, the dielectric constant of each cell is obtained by the method shown in FIG. Based on this, the dielectric constant at the boundary of each cell employs the average value of the dielectric constants of the cells on both sides.

  The toner charge analysis module B130 will be described. It is assumed that the toner has a charge at the center position, and the charge is added to the cell closest to the center point. By performing this process for all toners, the charge distribution in the cell in consideration of the toner charge is obtained.

  The discharge analysis module B160 will be described. In the difference method described here, since the potential is defined at the center of the cell, the above-described potential definition segment is a cell. Therefore, here, the above-described discharge segment is called a discharge cell, a discharge search segment to be extracted is called a discharge search cell, a discharge segment pair is called a discharge cell pair, and a toner segment is called a toner cell.

  First, the inter-surface discharge extraction module B161 will be described. Among the charge planes, two planes that may cause a discharge between the planes are designated in advance, and a discharge occurrence point between the two planes is extracted from the potential distribution at each simulation time step. Since this processing is intended for cells, the analysis processing is the same as in the case of the finite element method although the nodes and positions in the finite element method are different. That is, all discharge cell pairs having a voltage higher than the Paschen voltage are extracted from the potential relationship with the cells on the charge surface facing each cell on the charge surface, and registered in the RAM 23. The discharge search cell in this case is a cell on two charge planes.

Here, in the portion where the toner is deposited on the charge surface, a cell located in the outermost layer portion of the toner is set as a discharge search cell instead of the cell on the charge surface. The discharge search cell is extracted as follows.
(1) First, all cells on the charge surface are registered as discharge search cells.
(2) The toner located on the surface is extracted from the toner deposited on each charge surface.
(3) A process of extracting a toner cell and excluding a toner-covered charge surface cell is executed. Specifically, for the toner on each surface, a cell closest to the position farthest from the charge surface (having a cell center) is extracted as a toner cell. The extracted toner cell is added as a discharge search cell. Instead, cells on the charge surface covered with toner are excluded from discharge search cells.

  Based on the discharge search cell thus extracted, the discharge cell pair is extracted as described above.

  Also, in the process of the peak-to-point member discharge extraction module B162, the potential difference between the two discharge search cells is determined by the gap length between the static elimination needle and the discharge destination and the potential difference, and the voltage of the discharge start curve specified by the operator. In the case of exceeding, it is registered in the RAM 23 as a discharge cell pair.

  Further, in the discharge charge amount calculation module B163, by the process of the discharge extraction module B161 between the opposing surfaces and the discharge extraction module B162 between the peak members, the discharge between the parallel surfaces and between the pair of cells causing the discharge between the peak members is performed. Find the amount of charge to move.

In the difference method, 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 Expressions 14 and 15. Then, the Poisson equation of Equation 13 can be 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.

  Expression 16 represents Expression 13 as a simultaneous linear equation established in all analysis regions, and m is the number of cells with unknown potential.

Here, the potential vector before discharge is {φ}, the charge vector is {Q}, and those after discharge are {φ ′} and {Q ′}, respectively. Then, regarding the discharge cell pair i, j, the charge amount before discharge is Q _i , Q _j , and the electric charge moves from the cell i to the cell j by the discharge by _{ΔQ ij,} so that the potential difference between the two cells becomes αV _th . Suppose that Here, V _th ^(ij) is the discharge start voltage in the gap length between the two cells. In the case of the cell pair extracted by the inter-surface discharge extraction means B161, it is extracted by the Paschen voltage, and the peak member discharge extraction means B162. In the case of such a cell pair, this is the discharge start voltage obtained from the above experimental results. α is a coefficient indicating the ratio of the potential drop to the Paschen voltage after discharge. In general, α is 1.

The potentials φ _i ′ and φ _j ′ of the nodes i and j after discharge have a relationship of Equation 3. The charge amounts Q _i ′ and Q _j ′ can be expressed by Equation 4. By incorporating Equations 3 and 4 into Equation 16, the electric field equation after discharge of Equation 17 is obtained.

  Here, “...” in the (m + 1) th row is all zero.

The right side vector ΔQ _ij is shifted to the left side matrix to obtain Equation 18.

  Here, “...” in the (m + 1) th row and “...” in the (m + 1) th column are all 0. Further, M in Expression 17 and Expression 18 is a coefficient depending on the left side of Expression 2.

  In the matrix on the left side, two rows of the discharge cell number columns 1 and −1 and the other elements of 0 are added to the matrix of Formula 16, and one symmetric column is 1 A column has been added. When there are a large number of discharge cell pairs, the number of rows and columns outside m × m in this matrix increases by the number of discharge cell pairs. By solving this equation, the electric potential {φ ′} and the discharge charge amount {ΔQ} after discharge are obtained. Of the discharge cells, for the cells other than the toner cells, that is, the cells on the charge surface, the charge amount after discharge is obtained from Equation 4, and the value is updated.

  Note that since the matrix on the left side in Equation 18 is a symmetric sparse matrix, it can be easily solved at high speed.

  Further, in the processing of the toner charge update module B164, when the cell in which discharge is generated out of the discharge charge amount obtained by the discharge charge amount calculation module B163 is a toner cell, it becomes a basis for the extraction of the toner cell. The toner is renewed by adding its charge amount to the discharge charge. At this time, a correspondence table from the toner cell to the toner number is required, and this is prepared in advance in the processing of the above-described opposed surface discharge extraction module B161.

  Next, the toner behavior analysis module B170 is the same as the processing described in the finite element method except that the electric field result obtained by the difference method is used for calculating the electric field strength at the toner center position in (Equation 11). Therefore, the description is omitted here.

  As in the present embodiment, even by a method using a difference method for electric field calculation, a transfer analysis is performed in consideration of the behavior of current, discharge, and toner flowing in a conductor according to the flowchart of FIG. 3 using the module configuration of FIG. be able to. In particular, since the present embodiment is based on the difference method, the physical meaning of the calculation content is easier to understand than the finite element method, and the calculation can be performed at high speed.

  Here, as shown in FIG. 18, the difference method for defining the potential and the charge amount at the center of the cell and the dielectric constant and conductivity at the boundary between the cells has been described, but the case where the position of this definition is changed is described. Is also easily applicable.

  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 object processing apparatus schematic diagram, (b) The figure which shows an example of the simulation model of an analysis object processing apparatus. FIG. 5 is an explanatory diagram for defining a dielectric constant of an element in consideration of a dielectric constant of toner. The figure for demonstrating distribution of the electric charge of a toner with respect to each node. The figure for demonstrating the method of analyzing the discharge between two surfaces. Explanatory diagram when toner accumulation is taken into account when analyzing discharge The figure for demonstrating the method to analyze the discharge from the model of pointed members, such as a static elimination needle. The figure which shows an example of the relationship between the discharge start voltage of a pointed member, and gap length. The figure for demonstrating the method of analyzing the discharge between two surfaces. The figure which shows an example of the definition of the parameter of an element. The schematic diagram of a transfer apparatus. 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 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. The figure which shows the calculation of an amount of discharge, and an experimental result when the toner of a transfer roller has not adhered. The figure which shows the calculation and experiment result of the amount of discharge when the toner of a transfer roller has adhered. The figure which shows the relationship between the applied voltage of a transfer roller, and transfer efficiency.

Claims (8)

An analysis method for analyzing a discharge in an information processing apparatus having a readable / writable storage device,
The potential difference between each node on the first surface and each node on the second surface of the mesh-divided simulation model is configured by a predetermined amount of charge before discharge at each node and each node of the simulation model. A calculation step of calculating by the control means of the information processing device based on the dielectric constant of each element;
A storage step of storing in the storage device information on the node pair for which the potential difference exceeding the Paschen voltage determined from the distance between the nodes among the potential differences obtained from the calculating step is determined;
An analysis step of analyzing the amount of charge moved by the discharge and the potential distribution after the discharge based on the information on the node pair stored in the storage step and the amount of charge before the discharge of each node, and storing in the storage device; The analysis method characterized by having.   2. The calculation model according to claim 1, wherein in the calculation step, the simulation model is a simulation model of a member having a pointed shape on the first surface, and each of the second surfaces from a node corresponding to the pointed head of the simulation model. A potential difference from a node is calculated, and in the storing step, information relating to a node pair corresponding to a potential difference exceeding a voltage of a gap length dependency curve of a discharge start voltage obtained in advance is stored in the storage device. analysis method.   2. The calculation model according to claim 1, wherein, in the calculation step, the simulation model is a simulation model in which charged particles are deposited on the first and second surfaces, and a node located in a surface layer portion of the particle is calculated as a potential difference. An analysis method characterized by being a target of the above.   The analysis method according to claim 3, wherein, in the calculation step, the charge of the particle is distributed as a charge of a node located in a surface layer portion of the particle.   2. The analysis method according to claim 1, wherein, in the calculating step, a node of the second surface included within a predetermined angle with respect to a normal direction of the first surface is a target for calculating a potential difference. .   4. The analysis method according to claim 3, wherein the dielectric constant of the simulation model of each element is defined based on a ratio occupied by the particles. An information processing apparatus for analyzing discharge,
A potential difference between each node on the first surface and each node on the second surface of the mesh-divided simulation model is configured by a predetermined amount of charge before discharge at each node and each node of the simulation model. Control means for calculating based on the dielectric constant of each element
Storage means for storing information on a node pair for which a potential difference that exceeds the Paschen voltage determined from the distance between the nodes among the calculated potential differences is determined;
The control means analyzes the information on the node pair stored in the storage means and the amount of electric charge moved by the discharge and the potential distribution after the discharge based on the amount of electric charge before the discharge of each node, and stores it in the storage means An information processing apparatus characterized by: An information processing apparatus for analyzing discharge,
A potential difference defined by each cell on the first and second surfaces of the mesh-divided simulation model is calculated based on a predetermined charge amount before discharge of each cell and a dielectric constant of each cell of the simulation model. Control means to
Storage means for storing information on a cell pair for which a potential difference exceeding the Paschen voltage determined from the distance between the cells among the potential difference obtained from the calculation step is obtained;
The information processing apparatus according to claim 1, wherein the control unit analyzes the amount of charge moved by the discharge and the potential distribution after the discharge based on the information about the stored cell pair and the amount of charge before the discharge of each cell.

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