JP4732105B2 - Analysis method, analysis apparatus, and analysis program - Google Patents

Description

  The present invention relates to an analysis method, an analysis apparatus, and an analysis program for predicting the degree of toner scattering in an electrophotographic process.

  An image forming apparatus using electrophotographic technology such as a copying machine or a laser beam printer forms an image from six processes including charging, exposure, development, transfer, fixing, and cleaning. FIG. 18 is a diagram schematically showing six processes for charging, exposure, development, transfer, fixing, and cleaning related to image formation in the image forming apparatus. FIG. 18 shows a cross section viewed from the axial direction of the photosensitive drum. In FIG. 18, 1 is a photosensitive drum, 2 is a transfer medium (paper), 3 is a transfer roller, 5 is a charging roller, 6 is a developing sleeve, 7 is a fixing roller, 8 is a cleaning blade, and toner is a black circle as 4. displayed.

  First, in the charging process, the surface of the photosensitive drum 1 is uniformly negatively charged by pressing the charging roller 5 to which a negative voltage is applied to the photosensitive drum 1. In the exposure process, light is applied to a portion where an image is formed to remove negative charges, and a latent image is formed. In the developing process, the negatively charged toner 4 is brought close to the developing sleeve 6 and the toner 4 is placed on the latent image portion. In the transfer process, a positive voltage is applied to the transfer roller 3 to transfer the toner 4 to the paper 2. Further, in the fixing process, the toner 4 is fixed to the paper 2. In the cleaning process, the toner 4 remaining on the photosensitive drum 1 is scraped off and prepared for the next process that starts again.

  When forming a color image, the image on the photosensitive drum formed for each color is stacked on paper by a transfer process. Also, depending on the system, the electrical polarity may be reversed, but the principle is the same.

  Among such electrophotographic processes, in the transfer process, a large number of members such as a photoreceptor, a transfer medium, a toner, a transfer roller, etc. appear, and it is necessary to optimize their materials, configuration, voltage conditions, etc. The design work takes a very long time. In particular, the charged individual toners tend to scatter during the transfer process because of their repulsive forces. Therefore, scattering is suppressed by applying a large transfer electric field, but if the transfer electric field is large, a discharge occurs and adversely affects the image. In particular, in the case of a color image, it becomes extremely difficult due to the necessity to superimpose the toner on the toner.

  Among the scattering of toner in such a transfer process, there is one caused by toner transfer (pre-transfer) before the nip (portion where the transfer medium contacts the drum). In particular, it is known that this is remarkable in the case of a line image in the process direction (hereinafter referred to as a vertical line).

  FIG. 19 is a view for explaining scattering of vertical lines of toner in the transfer process. In addition, the code | symbol of each part in FIG. 19 is the same as the code | symbol of each part shown in FIG. In FIG. 19, the vertical line image formed on the photosensitive drum 1 is transferred to the transfer medium, the toner at the end of the transferred line image is scattered by pre-transfer, and the line is thick as indicated by 4A. Also, the image becomes blurred. This is particularly problematic when forming a color image that requires toner to be superimposed on the toner on the transfer medium.

  FIG. 20 is a diagram for explaining using an index defined in ISO 13660 as an index for quantifying the degree of blurring due to image scattering. In FIG. 20, the light reflectance profile based on the presence or absence of toner on the line crossing the line image is measured and added to the line image with the scattering indicated by the symbol A as shown by the broken line. , Get the reflectance distribution of the line. The distribution chart shown in FIG. 20 means the distribution of toner existence probability. In the distribution diagram shown in FIG. 20, the width B of the portion of the line image with the tails drawn is used as the scattering index value for evaluation of the degree of scattering.

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

  For example, in Non-Patent Document 1, the current flowing through the transfer portion is analyzed using a one-dimensional layer structure model. FIG. 21 is an enlarged view of the transfer process portion from the axial direction of the photoreceptor. In FIG. 21, the photosensitive drum 1, the transfer medium 2, and the transfer roller 3 are rotated or moved in the directions of arrows, respectively. In Non-Patent Document 1, it is assumed that the lines of electric force are substantially perpendicular to the surfaces of the photosensitive drum 1, the transfer medium 2, and the transfer roller 3. Then, as the one-dimensional layer configuration model moves with time, the one-dimensional model is deformed assuming that it moves to t0, t1, t2, t3, t4, t5, t6, t7, t8. (Each layer expands and contracts). Then, the movement of charges in the one-dimensional line is calculated based on Ohm's law and Paschen's discharge law. Thus, it is possible to estimate the toner transfer position from the electric field distribution obtained by this calculation.

  Further, according to Patent Document 1, the orientation of the transfer medium (paper) in the transfer process is obtained by calculation using the two-dimensional sectional view seen from the direction shown in FIG. A design support apparatus that uses this to calculate a transfer electric field in the same cross section and predicts the toner scattering state from the electric field distribution is disclosed.

  Further, according to Non-Patent Document 2, based on Ohm's law, Paschen's discharge law, and Newton's law, the potential distribution of the transfer device and the toner A method and apparatus for determining motion is disclosed.

Furthermore, Non-Patent Document 3 uses a three-dimensional parallel plate to consider the change in the transfer electric field due to the change in the gap and the discharge, and the toner scatters as the photoreceptor and transfer medium gradually approach. However, it is disclosed that the transfer state is calculated by calculation.
JP 2002-149715 A Ito, Kawamoto, "Electrophotographic Roller Transfer Process Simulation", Proceedings of the Japan Opportunity Society (C), 65, 637, p. 81-88 (1999) Sasaki et al., “Two-dimensional transfer process simulation considering toner”, Japan Hard Copy 2004, Proceedings, p. 287 (2004) Kamonaga, “Simulation of transcription process”, Journal of the Imaging Society of Japan, 43, 3, p. 171-179 (2004)

  However, the conventional toner scattering calculation technique as described above has the following drawbacks.

  First, in the method of Non-Patent Document 1, since the calculation is one-dimensional and only the toner is regarded as a layer, the degree of toner scattering cannot be quantitatively predicted. Also, in the method of Patent Document 1, since the toner is not considered as particles in the calculation, the degree of scattering cannot be predicted.

  Furthermore, in the method of Non-Patent Document 2, since the model is a two-dimensional section viewed from the axial direction of the photosensitive drum, the scattering of the vertical lines cannot be calculated. Further, since the presence of toner cannot be calculated as a probability distribution, the result cannot be obtained as the scattering index as described above. Furthermore, in the method of Non-Patent Document 3, although the analysis is performed in three dimensions, the current flow is handled in one dimension. Therefore, the influence of the electric charge injected from the transfer roller in the vicinity of the transfer nip portion is not taken into consideration, and there is a problem in its accuracy. In addition, since a three-dimensional electric field calculation is performed, there is a problem in that it takes a calculation time and is used for design.

  As described above, Non-Patent Document 1 discloses that in the transfer system, the region between the photosensitive drum and the transfer roller is moved to the analysis region by moving the photosensitive drum as the photosensitive drum rotates. As known. Further, a method for calculating an electric field distribution while taking into account a charge transfer due to electric conduction or discharge for a two-dimensional problem is known as disclosed in Patent Document 2. However, in the former one-dimensional model, the spatial spread of the electric field cannot be taken into account, and therefore the scattering of the toner cannot be calculated. In the latter case, the two-dimensional cross section is always perpendicular to the central axis of the drum, and the scattering of the vertical lines in the axial direction of the photosensitive drum cannot be calculated. Therefore, conventionally, the only way to calculate the scattering of toner in a vertical line image is to directly solve a three-dimensional problem.

  The present invention has been made in view of such circumstances, and provides an analysis method, an analysis apparatus, and an analysis program capable of accurately predicting toner scattering according to various conditions in a transfer process. Objective.

In order to solve the above-mentioned problems, the present invention models a two-dimensional analysis object cross section parallel to the central axis of the photosensitive drum of a device including the photosensitive drum to the transfer roller, and controls toner movement in the electrophotographic process. An analysis method for analyzing,
An initial position setting step for setting an initial position of toner on the photosensitive drum;
A model shape changing step of changing a layer thickness of the analysis target cross section including a plurality of layers including a photoreceptor layer, an air layer, a transfer medium layer, and a roller layer in accordance with a change in the analysis target cross section due to rotation of the photosensitive drum; ,
In consideration of charge transfer due to electric conduction and discharge, an electric field calculation step of calculating an electric field distribution in the analysis target cross section when the layer thickness of the analysis target cross section is changed,
And a toner motion calculation step of calculating the motion of the toner in the cross section to be analyzed in accordance with the calculated electric field distribution.

  In the analysis method according to the present invention, the model shape change step, the electric field measurement step, and the toner movement step are repeatedly executed according to the passage of time, thereby calculating the movement state of the toner with the passage of time. It is characterized by doing.

  In this way, the analysis area is a two-dimensional section parallel to the central axis of the photosensitive drum and extending from the photosensitive drum to the transfer roller, and this analysis area is moved as the photosensitive drum rotates, resulting in a two-dimensional problem. . Then, the shape change of the two-dimensional section (change in thickness of each layer) with time progress was taken into account by the model shape changing step, and the movement of electric charges due to electric conduction and discharge was taken into consideration by the electric field calculation step. Thereby, it is possible to calculate the toner movement in the cross-sectional surface which is particularly problematic when the vertical lines are scattered by the toner movement calculation process.

  Further, in the analysis method according to the present invention, a plurality of models having different arrangements are prepared as the initial position of the toner on the photosensitive drum, and the medium after transfer by the analysis method is performed for the toner in each arrangement state. The toner position on the top is calculated, and the toner presence distribution on the medium is calculated for each model. A scattering index calculation step of calculating a toner presence probability distribution on the medium by adding all the calculated toner presence distributions in the respective arrangement states and calculating a toner scattering index from the toner presence probability distribution. Furthermore, it is characterized by having.

  As described above, by preparing a plurality of toners on the photosensitive drum before transfer that have different arrangements using random numbers or the like, it is possible to calculate a result that depends on the probability such as the scattering index.

  Furthermore, the analysis method according to the present invention is characterized in that the initial position of the toner on the photosensitive drum uses an arrangement state calculated using the analysis method. The result of the above-described scattering index may greatly depend on the arrangement of the toner on the photosensitive drum, but in this analysis method, by executing the arrangement from the development calculation, it is closer to the actual phenomenon, The accuracy of the result is improved.

  Furthermore, when looking at the movement of charges in a general transfer system, the charge is dominantly injected from the transfer roller through the nip to the transfer medium. That is, the electric lines of force always pass through the contact portion between the transfer roller and the transfer medium. Therefore, in the analysis method according to the present invention, the two-dimensional cross section includes the contact portion. This improves the accuracy of electric field calculation and toner movement.

  According to the present invention, toner scattering according to various conditions in the transfer process can be accurately predicted.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings. FIG. 2 is a block diagram showing a schematic configuration of an analysis apparatus according to an embodiment of the present invention. The analysis apparatus shown in FIG. 2 includes an input data creation unit B11, a scattering index calculation unit B12, and a result display unit B13.

  The input data creation unit B11 creates mesh data necessary for analysis performed in the present embodiment and data files of various parameters. The mesh data is data obtained by dividing the analysis region of the transfer device made of a dielectric or a resistor into minute regions in accordance with a method for performing electric field calculation such as a difference mesh or a finite element mesh. Various parameters include material dielectric constant, conductivity, charge distribution (including latent image), potential as boundary conditions, time variation of thickness of each material layer, toner diameter, toner charge amount, toner dielectric Rate, further calculation time, and calculation end time.

  The scatter index calculation unit B12 calculates the electric field distribution and toner motion in the calculation area, outputs the result data to a file, and calculates the scatter index from these results. For this calculation, the scattering index calculation unit B12 is based on, for example, Ohm's law, Poisson's equation, Paschen's discharge law, and Newton's equation of motion.

  The result display unit B13 reads the result file output from the scatter index calculation unit B12 and displays it in a state that can be visually recognized by an operator or the like.

  The input data creation unit B11 and the result display unit B13 shown in FIG. 2 are generally referred to as pre-posts, and are well-known techniques, and thus description thereof is omitted.

  FIG. 3 is a block diagram showing a hardware configuration of a computer constituting the scattering index calculation unit B12 of the analysis apparatus according to the present embodiment. The computer 20 includes a central processing unit (CPU) 21 that performs various determinations and processes, and a ROM 22 as processing process storage means that stores each processing program and fixed data. The computer 20 also includes a RAM 23 as parameter storage means that is a data memory for storing processing data, and an input / output circuit (I / O) 24 as means for exchanging data with the external storage device 30. . Input data 31 as a product of the input data creation unit B11 is input to the computer 20 via the I / O 24. Then, the calculation result processed by the computer 20 and the input data of the result display unit B13 is output as the output data 32 via the I / O 24.

  Next, a detailed configuration of the scattering index calculation unit B13 will be described. FIG. 4 is a block diagram showing a detailed configuration of the scattering index calculation unit B13 of the analysis apparatus according to the embodiment of the present invention. In FIG. 4, B100 is an overall control unit that controls the entire scattering index calculation, and controls the operation of each of the six units described below.

  First, B110 is a toner initial position setting unit, which obtains the initial position of toner on the photosensitive drum before transfer based on the mesh data and various parameters created by the input data creation unit B11 described above and obtains the external storage device 30. Save to. The initial arrangement of the toner is performed on the latent image set on the photosensitive drum. In addition, the toner initial position setting unit B110 uses a random number, for example, so that the stacking state is different each time it is executed.

  B120 is a transfer calculation unit that calculates how the toner on the photosensitive drum is transferred to the transfer medium, and stores the result in the external storage device 30, the details of which will be described later with reference to FIGS. To do. The post-transfer toner position reading unit B130 reads a plurality of post-transfer toner position distribution results created by the transfer calculation unit B120 from the external storage device and stores them in the RAM 23. The toner presence distribution calculation unit B140 converts the individual toner position distribution into a toner presence distribution indicating whether or not toner exists at each position of the transfer medium. Further, the toner presence probability distribution calculation unit B150 obtains a distribution indicating the toner presence probability at each position of the transfer medium by adding all the obtained toner presence distributions. Furthermore, the scattering index calculation unit B160 calculates a scattering index from the toner presence probability distribution.

  Next, a process for obtaining the scattering index by calculation will be described. FIG. 5 is a flowchart for explaining the scattering index calculation processing step by the analyzing apparatus according to the embodiment of the present invention.

  First, when the process is started (step S100), the toner position on the photosensitive drum is set using the toner initial position setting unit B110 as a toner initial position setting step (step S110). Next, as a transfer calculation step, the transfer calculation unit B120 obtains the toner position when the toner on the photoconductor is transferred to the transfer medium (step S120). Each of the above steps (steps S110 and S120) is repeated, for example, 10 times or more until the number of transfer results is sufficiently accumulated (step S122). Further, in the toner initial position setting step (step S110), the toner is arranged in a different stacked state on the photosensitive drum every time, so that the result of the toner position after the main transfer is different every time.

  If the toner transfer result is sufficiently accumulated in step S122 (Yes), the process proceeds to a post-transfer toner position reading step. In this step, the post-transfer toner position reading unit B130 is used to read all post-transfer toner position results stored in the external storage device 30 (step S130). Then, as a toner presence distribution calculation step, the toner presence distribution calculation unit B140 converts the toner position result after each transfer into a toner presence distribution on the medium (step S140). Further, in the toner presence probability distribution calculation step, the toner presence probability distribution calculation unit B150 obtains the toner presence probability distribution on the transfer medium (step S150). Finally, in the scattering index calculation step, the scattering index calculation unit B160 is used to obtain the scattering index and display it to the analyst (step S160).

  Next, the transfer calculation unit B120 will be described in detail. FIG. 6 is a block diagram showing a detailed configuration of the transfer calculation unit B120 in the analysis apparatus according to the embodiment of the present invention. The transfer calculation unit B120 controls calculation of the transfer process, and includes an input data reading unit B210, a model shape changing unit B220, an electric field calculation unit B230, a toner motion calculation unit B240, and a calculation result output unit B250 described below. Control processing.

  First, the input data reading unit B210 reads the mesh data and various parameters created by the input data creation unit B11 and the toner initial position data on the photosensitive drum created by the toner initial position setting unit B110 and stores them in the RAM 23. . The model shape changing unit B220 changes the shape of the read mesh data according to the elapsed time and stores it in the RAM 23. This can be easily realized by moving the node positions of the mesh data according to the model shape (thickness of each layer) or by re-dividing the elements.

  The electric field calculation unit B230 calculates an electric field distribution in consideration of charge movement and discharge in the conductor and stores the electric field distribution in the RAM 23. FIG. 7 is a flowchart for explaining the processing procedure of the electric field calculation unit B230 of the analysis apparatus according to the embodiment of the present invention. The electrostatic field can be obtained by solving Poisson's equation shown in Equation (1). In addition, for the charge transfer in the conductor, when Ohm's law is established as a conduction mechanism, the equation (2) can be used.

  In equations (1) and (2), ε is the dielectric constant, σ is the conductivity, φ is the potential, and ρ is the charge density. In the electric field calculation, first, Equation (1) is solved by the electrostatic field calculation step to obtain the distribution of potential φ (step S310). Next, in the charge transfer calculation step of the conductor, the obtained potential φ is substituted into the equation (2) to obtain the change in charge density per calculation step time, and the charge distribution in the analysis region is updated (step S320). ). Then, the electrostatic field calculation step is performed again to obtain the potential distribution after the charge transfer due to electrical conduction (step S330). Further, in the charge transfer calculation process by discharge, the discharge occurrence location is extracted based on the obtained potential distribution and Paschen's discharge rule, and the charge transfer amount by discharge and the potential distribution after discharge are obtained (step S340). The details of this method are disclosed in Non-Patent Document 2 described above.

  In FIG. 6, the toner motion calculation unit B240 calculates the toner motion in the electric field and stores it in the RAM 23. As a method for calculating the movement of the toner, for example, assuming that there is an electric charge at the center position of the toner, the electrostatic force F (t ) Then, the velocity v (t) and the position x (t) are obtained from the Newton equation of motion by the equation (4).

Here, Q _T and m are the charge and weight of the toner, respectively.

  There are a method using a momentum conservation law and a method using a DEM (discrete element method) for toner collision, and an appropriate method may be used depending on the problem.

  In FIG. 6, the post-transfer toner position output unit B <b> 250 outputs the obtained post-transfer toner position to the external storage device 30.

  Next, the processing flow of the transfer calculation unit B120 will be described in detail. FIG. 8 is a flowchart for explaining the processing procedure of the transfer calculation unit B120 of the analysis apparatus according to the embodiment of the present invention.

  When the process is started (step S200), first, in the input data reading step, data is read using the input data reading unit B210 (step S210). Then, time t is set to 0 (step S212). Next, in the model shape changing step, the mesh data is changed to the shape at that time (the thickness of each layer) by the model shape changing unit B220 (step S220). Then, in the electric field calculation step, the electric potential distribution after the calculation time step Δt is obtained by the electric field calculation unit B230 using the changed mesh data (step S230). Further, in the toner motion calculation step, the toner motion calculation unit B240 is used to update the toner position to that after the calculation time step Δt (step S240). Steps S220 to S240 described above are repeated until the toner passes through a portion where the roller and the photosensitive drum are in contact with each other with the transfer medium interposed therebetween (hereinafter referred to as “nip portion”) (steps S242 and S244). Thereafter, in the post-transfer toner position output step, the post-transfer toner position output unit B250 outputs the result to a file (step S250).

  In addition, since the photosensitive drum, the transfer medium, and the transfer roller move (the thickness of each layer changes) as the cross section changes over time, it is necessary to move the charges on each surface accordingly (advection). . Further, the toner on the surface of the photosensitive drum and the surface of the transfer medium also needs to be moved with the movement of the surface. These processes are performed by moving the charge and toner on the surface in accordance with the movement of the surface in the model shape changing step (step S220).

  Next, the analysis model used in the present invention will be described.

  FIG. 9 is a diagram showing a potential distribution near the nip portion. In FIG. 9, 91 is a photosensitive layer, 92 is a transfer medium, 93 is the surface of the transfer roller, and 94 is a nip portion. The thick lines in the figure indicate the contour lines of each member, and the thin lines indicate the equipotential lines. Each of the photosensitive drum, the transfer medium, and the transfer roller moves in the direction of the arrow, and FIG. 9 shows the upstream portion of the nip. The electric lines of force intersect perpendicularly with the equipotential lines. Therefore, it can be seen that the lines of electric force from the transfer roller to the photosensitive drum surface near the nip portion tend to pass through the contact portion between the roller and the transfer medium. This tendency is remarkable in the case of a transfer medium having a low resistance and a large ratio of charge injected from the roller to the transfer medium. Yes. Although the potential distribution in the upstream portion of the nip is shown here, the same applies to the downstream portion.

  FIG. 10 is a diagram showing a two-dimensional analysis region handled by the analysis apparatus according to the embodiment of the present invention. In FIG. 10, a two-dimensional cross section for calculating the scattering of vertical lines is indicated by a broken line substantially along the lines of electric force in FIG. In other words, regardless of the elapsed time t0 to t8, the calculated cross section passes through the shortest course including a contact portion between the roller and the transfer medium as a part thereof. When a three-dimensional problem is reduced to a two-dimensional problem, generally, the electric field needs to be uniform in the depth direction of the analysis region. In this case, although it cannot be said that it is completely uniform, since it can be seen from FIG. 9 that the state is close to that, the error due to this approximation is considered to be small.

  FIG. 1 is a diagram illustrating an example of a two-dimensional analysis region (analysis target cross section) and toner arrangement used by the scattering index calculation unit B100 of the analysis apparatus according to an embodiment of the present invention. The mesh data is obtained by finely dividing FIG. FIG. 1 shows the state of transfer as seen from the process direction as indicated by the viewpoint position in FIG. 19, and the transfer process is modeled by a two-dimensional section parallel to the central axis of the photosensitive drum. This corresponds to the broken line in FIG. In FIG. 1, 11 is a photoreceptor layer, 12 is a transfer medium layer, 13 is a transfer roller layer, 110 is the surface of the photoreceptor, 120 is the surface of the transfer medium, 40 is toner on the photoreceptor, and 41 is toner on the medium. Indicates. In the figure, the thickness of the air layer and the thickness of the transfer medium layer are changed by the model shape changing unit B220 with the passage of time. Further, the thickness of the photoreceptor layer is unchanged, and the thickness of the roller layer can be handled as unchanged if the deformation due to the pressing of the roller is ignored.

For example, in FIG. 10, the radius of the photosensitive drum is R, and the angle formed by the line connecting the drum center and the roller center at the photosensitive drum surface position at each time is θ. In this case, the thickness D _air of the air layer and the thickness D _{media of the} medium layer at each time are expressed by the equations (5) and (6).

Note that, .theta.1 the angle portion where the transfer medium and the roller starts to contact, T is the thickness of the transfer medium, D _Toner represents the thickness of the toner layer.

  The above-described processing flow is an example, and it is not necessary to strictly stick to the order. In addition, when the positional relationship between the drum and the roller is different from that shown in FIG.

  Next, an example in which the vertical toner scattering index is actually calculated using the analysis method according to the present embodiment will be described in detail.

<Example 1>
FIG. 11 is a diagram illustrating a result calculated by the transfer calculation unit B120 of the analysis apparatus according to the embodiment of the present invention. That is, the toner on the photosensitive member is transferred to the transfer medium as time passes. In the figure, the black circles represent the toner on the photosensitive drum, and the white circles represent the toner on the transfer medium, simulating the scattering of the toner when transferring the black circle toner vertical lines over the vertical lines of the white circle toner. It is a thing. In FIG. 11, since only the vicinity of the toner is displayed, a part of the transfer roller and the transfer medium is not displayed on the screen. In FIG. 11, the background lines indicate equipotential lines. In FIG. 11, (a) represents before nip, (b) represents immediately before nip, (c) represents during nip, and (d) represents after nip. In FIG. 10, (a) corresponds to t0, t1, (b) to t2, (c) to t3, t4, t5, and (d) to t6 and thereafter.

  Here, the toner lamination state on the drum surface in FIG. 11A is obtained by the toner initial position setting unit B110. Here, the toner initial position setting unit B110 is specifically placed on the drum in a state where the toner is freely dropped and stacked using the discrete element method. According to this method, by setting the initial position where the toner is allowed to fall freely using a random number, different stacked states on the drum can be easily generated. In addition, a positive charge for carrying the toner is arranged in a portion where the toner is present on the surface of the transfer medium.

  And the change in the thickness of the air layer with the passage of time is dealt with by changing the mesh data according to the equation (5) by the model shape changing unit B220. It can be seen from FIG. 11 that the toner is scattered when the toner is transferred from the photosensitive drum to the transfer medium. The correctness of this result has been confirmed by comparing with the result of observing how the actual toner is transferred.

  Next, FIG. 12 is a diagram illustrating an example of the toner distribution on the medium according to the first exemplary embodiment. In this figure, the toner presence distribution on the transfer medium is obtained by the toner presence distribution calculation unit B140 from the result of the toner position on the medium obtained by the transfer calculation unit B120. The transfer medium surface is divided into sections about the diameter of the toner, and the presence distribution of the toner is determined by whether or not toner exists in each section.

  FIG. 13 is a diagram illustrating a result of changing the initial arrangement of the toner on the drum in the first embodiment. That is, FIG. 13 collectively illustrates the steps shown in FIGS. 11 and 12 in which the toner lamination state on the photosensitive drum is changed. In FIG. 13, those obtained by changing the toner lamination state on the photosensitive drum are displayed as calculation numbers 1 and 2. As shown in the figure, different transfer results and toner distributions are obtained.

  FIG. 14 is a diagram illustrating a toner presence probability distribution according to the first exemplary embodiment. First, in FIG. 14A, the calculation of FIG. 13 is performed for 20 initial arrangements, and the obtained toner presence distributions are all added by the toner presence probability distribution unit B150 to normalize the values. Thus, the toner existence probability distribution is obtained. This figure corresponds to the scattering distribution of the toner. In this example, the toner line width (vertical line width) on the drum was 200 μm, but it was scattered over a width of about 400 μm. I understand.

  FIG. 14B shows the curve shown in FIG. 14B obtained by approximating the existence probability distribution line with the Gaussian distribution curve by the scattering index calculation unit B160. Although the approximation is performed using a Gaussian distribution curve here, the approximation may be performed using a cubic curve or the like. Similar to the method shown in FIG. 20, the scatter index calculation unit B160 calculates the scatter index from the spread width B of the skirt in the main curve. In this case, the width of B may be different on the left and right. In this case, for example, averaging may be performed. As a result, in this case, a value of the scattering index of 75 μm is obtained.

  FIG. 15 is a diagram illustrating an example of the presence establishment distribution of the toner when the position of the transfer roller in the first exemplary embodiment is changed. That is, FIG. 15 shows the result corresponding to FIG. 14 when the position of the transfer roller is shifted to the downstream side with respect to the nip portion of the photosensitive drum and the transfer medium, and the scattering index is 38 μm. From this result, it is understood that the toner scattering index is improved by providing the shift amount. In addition, this agrees well with the experimental results, indicating that it can be applied to an actual design.

  As described above, according to the first embodiment, since the motion of each toner is calculated and the two-dimensional plane in which the vertical lines scatter is the analysis target, the degree to which the toner forming the vertical lines scatters is quantified. Can now be predicted. In particular, since the scattering index can be calculated from a plurality of results obtained by changing the initial arrangement of the toner on the photosensitive drum as input data, the transfer performance can be evaluated extremely objectively. Note that this calculation is always performed on a cross section along the lines of electric force, and since electric conduction in the conductor is taken into account, the solution is highly accurate and can be calculated in a short time because two-dimensional calculation is sufficient. be able to.

<Example 2>
In the toner initial position setting unit B110 of Example 1 described above, as the initial position of the toner on the photoconductor, a toner that is freely dropped and stacked is used. However, it is difficult to form an appropriate toner layer for the latent image on the drum. Therefore, in the second embodiment, a method of performing a simple development calculation by applying the method of the first embodiment and using the result as input data for transfer calculation will be described.

  FIG. 16 is a diagram illustrating a developing unit in Example 2 in which a part of FIG. 18 is enlarged. The reference numerals in FIG. 16 are the same as those in FIG. In FIG. 16, similarly to the transfer process calculation in the first embodiment, the calculation is modeled by a two-dimensional section parallel to the central axis of the photosensitive drum. That is, as time passes, as shown by broken lines t0 to t6 in FIG. 16, the cross section of the line connecting the drum surface and the sleeve surface with the shortest line is two-dimensionalized as an analysis region.

  FIG. 17 is a diagram illustrating an example of a two-dimensional calculation model according to the second embodiment. In FIG. 17, 1 is the photosensitive layer, and 6 is the surface of the developing sleeve. In this model, similar to the transfer process calculation flow in FIG. 8, the thickness of the air layer is changed with time by the model shape changing step (step S220). Then, the electric field calculation step (step S230) and the toner motion calculation step (step S240) are repeated until the development is completed to obtain the final toner position distribution on the drum.

  The toner initial position setting unit B110 calculates the toner distribution on the drum as input data for the transfer process calculation by performing the development calculation as described above. In this calculation, it is easy to generate a toner with a different toner lamination state by shifting the phase of the AC component applied to the developing sleeve or changing the initial position of the toner before development. can do.

  As described above, according to the second embodiment, since the toner can be accurately arranged on the latent image on the drum, a highly reliable solution can be obtained.

<Other embodiments>
In the present invention, a software program (in the embodiment, a program corresponding to the flowchart shown in the drawing) that realizes the functions of the above-described embodiments is directly or remotely supplied to a system or apparatus. In addition, this includes a case where the system or the computer of the apparatus is also achieved by reading and executing the supplied program code.

  Accordingly, since the functions of the present invention are implemented by computer, the program code installed in the computer also implements the present invention. In other words, the present invention includes a computer program itself for realizing the functional processing of the present invention.

  In that case, as long as it has the function of a program, it may be in the form of object code, a program executed by an interpreter, script data supplied to the OS, or the like.

  Examples of the recording medium for supplying the program include the following. Floppy (registered trademark) disk, hard disk, optical disk, magneto-optical disk, MO, CD-ROM, CD-R, CD-RW, magnetic tape, nonvolatile memory card, ROM, DVD (DVD-ROM, DVD-R) .

  As another program supply method, the program can be supplied by downloading it from a homepage on the Internet to a recording medium such as a hard disk using a browser of a client computer. That is, it connects to a homepage and downloads the computer program itself of the present invention or a compressed file including an automatic installation function from the homepage. It can also be realized by dividing the program code constituting the program of the present invention into a plurality of files and downloading each file from a different homepage. That is, a WWW server that allows a plurality of users to download a program file for realizing the functional processing of the present invention on a computer is also included in the present invention.

  Further, the program of the present invention is encrypted, stored in a storage medium such as a CD-ROM, and distributed to users. Then, the user who has cleared the predetermined condition is allowed to download key information for decryption from the homepage via the Internet. It is also possible to execute the encrypted program by using the key information and install the program on a computer.

  Further, the functions of the above-described embodiments are realized by the computer executing the read program. In addition, the function of the above-described embodiment can be realized by an OS running on the computer based on an instruction of the program and performing part or all of the actual processing.

  Further, the functions of the above-described embodiments are realized even after the program read from the recording medium is written in a memory provided in a function expansion board inserted into the computer or a function expansion unit connected to the computer. That is, the functions of the above-described embodiments are realized by performing a part or all of the actual processing by the CPU or the like provided in the function expansion board or function expansion unit based on the instructions of the program.

  Thus, the analysis program according to the present invention can be distributed or obtained in a state where it is recorded on a recording medium such as a CD-ROM. In addition, the analysis program can be placed and distributed or received via a transmission medium such as a public telephone line, a dedicated line, or another communication network for a signal transmitted by a predetermined transmission device. Available. At the time of distribution, it is sufficient that at least a part of the computer program is transmitted in the transmission medium. That is, it is not necessary for all data constituting the computer program to exist on the transmission medium at one time. The signal carrying the program is a computer data signal embodied on a predetermined carrier wave including the computer program. Further, the transmission method for transmitting a computer program from a predetermined transmission device includes a case where data constituting the program is transmitted continuously and a case where it is transmitted intermittently.

It is a figure which shows an example of arrangement | positioning of the two-dimensional analysis area | region and toner which the scattering index calculation part B100 of the analyzer which concerns on one Embodiment of this invention uses. It is a block diagram which shows schematic structure of the analyzer which concerns on one Embodiment of this invention. It is a block diagram which shows the hardware constitutions of the computer which comprises the scattering index calculation part B12 of the analyzer which concerns on this embodiment. It is a block diagram which shows the detailed structure of the scattering index calculation part B13 of the analyzer which concerns on one Embodiment of this invention. It is a flowchart for demonstrating the calculation process process of a scattering index | exponent by the analyzer which concerns on one Embodiment of this invention. It is a block diagram which shows the detailed structure of the transcription | transfer calculation part B120 in the analyzer which concerns on one Embodiment of this invention. It is a flowchart for demonstrating the process sequence of electric field calculation part B230 of the analyzer which concerns on one Embodiment of this invention. It is a flowchart for demonstrating the process sequence of the transcription | transfer calculation part B120 of the analyzer which concerns on one Embodiment of this invention. It is the figure which displayed the electric potential distribution of the nip part vicinity. It is a figure which shows the two-dimensional analysis area | region which the analyzer which concerns on one Embodiment of this invention handles. It is a figure which shows the result calculated by transcription | transfer calculation part B120 of the analyzer which concerns on one Embodiment of this invention. 6 is a diagram illustrating an example of a toner distribution on a medium in Embodiment 1. FIG. 6 is a diagram illustrating a result of changing the initial arrangement of toner on the drum in Embodiment 1. FIG. 7 is a diagram illustrating a toner presence probability distribution in Embodiment 1. FIG. 6 is a diagram illustrating an example of toner presence establishment distribution when the position of the transfer roller is changed in Embodiment 1. FIG. FIG. 19 is a diagram illustrating a developing unit in Example 2 in which a part of FIG. 18 is enlarged. FIG. 6 is a diagram illustrating an example of a two-dimensional calculation model in the second embodiment. FIG. 5 is a diagram schematically illustrating six processes of charging, exposure, development, transfer, fixing, and cleaning related to image formation in the image forming apparatus. FIG. 10 is a diagram for explaining scattering of vertical lines of toner in a transfer process. It is a figure for demonstrating using what is prescribed | regulated to ISO13660 as a parameter | index which quantifies the blurring degree by the scattering of an image. FIG. 4 is a diagram showing an enlarged portion of a transfer process from the axial direction of the photoreceptor.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Photosensitive drum 2 Transfer medium 3 Transfer roller 4 Toner 5 Charging roller 6 Developing sleeve 7 Fixing roller 8 Cleaning blade

Claims (7)

An analysis method for modeling the movement of a toner in an electrophotographic process by modeling a two-dimensional analysis object cross section parallel to the central axis of the photosensitive drum of a device including a photosensitive drum to a transfer roller,
An initial position setting step for setting an initial position of toner on the photosensitive drum;
A model shape changing step of changing a layer thickness of the analysis target cross section including a plurality of layers including a photoreceptor layer, an air layer, a transfer medium layer, and a roller layer in accordance with a change in the analysis target cross section due to rotation of the photosensitive drum; ,
In consideration of charge transfer due to electric conduction and discharge, an electric field calculation step of calculating an electric field distribution in the analysis target cross section when the layer thickness of the analysis target cross section is changed,
A toner motion calculation step of calculating a motion of the toner in the analysis object cross section according to the calculated electric field distribution. 2. The toner motion state with the passage of time is calculated by repeatedly executing each model shape changing step, the electric field calculation step, and the toner motion calculation step with the passage of time. Analysis method described.   As the initial position of the toner on the photosensitive drum, a plurality of models having different arrangements are prepared, and the position of the toner on the medium after the transfer is calculated by the analysis method for each arrangement state toner, The toner presence distribution on the medium is calculated for each model, and the toner presence probability distribution on the medium is calculated by adding all the calculated toner presence distributions in the respective arrangement states. The analysis method according to claim 1, further comprising a scattering index calculation step of calculating a toner scattering index from the toner.   The analysis method according to claim 3, wherein the initial position of the toner on the photosensitive drum is an arrangement state calculated using the analysis method according to claim 1.   5. The analysis method according to claim 1, wherein a contact portion between the transfer roller and a transfer medium is included in the analysis target section. 6. An analysis device that models a two-dimensional analysis target cross section parallel to the central axis of the photosensitive drum of a device including the photosensitive drum to the transfer roller, and analyzes toner movement in an electrophotographic process,
Initial position setting means for setting an initial position of toner on the photosensitive drum;
Model shape changing means for changing the layer thickness of the analysis object cross section composed of a plurality of layers including a photoreceptor layer, an air layer, a transfer medium layer, and a roller layer in accordance with a change in the analysis object cross section due to rotation of the photosensitive drum. ,
Electric field calculation means for calculating the electric field distribution in the analysis target cross section when the layer thickness of the analysis target cross section is changed in consideration of charge transfer due to electric conduction and discharge,
An analysis apparatus comprising: toner movement calculation means for calculating movement of the toner in the cross section to be analyzed in accordance with the calculated electric field distribution. An analysis for modeling a two-dimensional cross section to be analyzed parallel to the central axis of the photosensitive drum of the device including the photosensitive drum to the transfer roller in the computer, and causing the computer to analyze the movement of the toner in the electrophotographic process. A program comprising:
An initial position setting procedure for setting an initial position of toner on the photosensitive drum;
A model shape changing procedure for changing a layer thickness of the analysis target cross section including a plurality of layers including a photosensitive layer, an air layer, a transfer medium layer, and a roller layer in accordance with a change in the analysis target cross section due to rotation of the photosensitive drum; ,
An electric field calculation procedure for calculating an electric field distribution in the analysis target cross section when the layer thickness of the analysis target cross section is changed in consideration of charge transfer due to electric conduction and discharge,
An analysis program for executing a toner motion calculation procedure for calculating a motion of the toner in the cross section to be analyzed according to the calculated electric field distribution.

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