JP2017142323A - Analyzer and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide an analyzer and a program that can reduce the amount of calculation compared with one that analyzes a behavior of a transfer part with developer as particles.SOLUTION: The present analyzer is an analyzer in an image forming apparatus that sandwiches a recording medium 18 at a transfer part to which a voltage is applied to transfer a toner image to the recording medium 18, and comprises: first calculation means that calculates an electrostatic force on the toner image in a concave part of the recording medium 18 while regarding the toner image as a layer; second calculation means that calculates an electrostatic force on the toner image in a convex part projecting compared with the concave part of the recording medium 18 while regarding the toner image as a layer; and output means that outputs a first result from the first calculation means and a second calculation result from the second calculation means.SELECTED DRAWING: Figure 4

Description

  The present invention relates to an analysis apparatus and a program.

  Patent Document 1 discloses a potential distribution analysis method for calculating a potential distribution according to a parameter that affects a potential distribution, a calculation region dividing step of dividing a calculation region to form a plurality of cells, and a calculation region dividing step. The potential calculation step for calculating the potential of each cell, the advection charge amount calculation step for calculating the amount of charge flowing into or out of each cell obtained in the calculation region division step, and the inflow into each cell obtained in the calculation region division step Or a potential difference transfer charge amount calculating step for calculating the amount of charge flowing out, and a discharge charge amount calculating step for calculating the amount of charge flowing into or out of each cell obtained in the calculation region dividing step. At least one of the advection charge amount calculation step and the potential difference transfer charge amount calculation step discloses an invention characterized in that a calculation by a difference method considering a cell shape conversion operator is executed.

  Patent Document 2 discloses a potential difference between each node on the first surface and each node on the second surface of the mesh-divided simulation model, the charge amount before discharge at each predetermined node, and the simulation model. A step of calculating a potential difference based on a dielectric constant of each element of the element, and storing, in the memory, information relating to a node pair for which a potential difference exceeding a Paschen voltage determined from a distance between the nodes is calculated. And an analysis step of analyzing the amount of charge moved by discharge and the potential distribution after discharge based on the information on the stored node pair and the amount of charge before discharge of each node, and storing in the memory An invention characterized by having the following is disclosed.

  Non-Patent Document 1 presents a model resulting from unevenness in the transfer rate caused by the distribution of the transfer electric field corresponding to the unevenness of the paper as a density unevenness generation model, and simulates the three-dimensional transfer behavior in consideration of the surface shape of the paper. We disclose that we verified by.

JP 2003-262617 A JP-A-2005-345120

Jun Nakamura et al., “Analysis of Print Density Phenomenon in Transfer on Paper”, Imaging Conference Japan 2012 Proceedings, June 2012, p. 193-196

  The technique shown in the above prior art document has a problem that the calculation amount is large, including motion analysis of developer particles, electric field calculation using a fine mesh corresponding to the size of the developer particles, and the like.

  An object of the present invention is to provide an analysis apparatus and a program that can reduce the amount of calculation compared to the case of analyzing the behavior of a transfer portion using developer as particles.

  The present invention according to claim 1 is an analysis apparatus of an image forming apparatus for transferring a toner image to a recording medium by sandwiching the recording medium in a transfer portion to which a voltage is applied, wherein the recording is performed by regarding the toner image as a layer. First calculating means for calculating an electrostatic force for the toner image in a concave portion of the medium, and calculating an electrostatic force for the toner image in a convex portion protruding from the concave portion of the recording medium by regarding the toner image as a layer. It is an analyzer having a second calculation means, and an output means for outputting a first calculation result by the first calculation means and a second calculation result by the second calculation means.

  The present invention according to claim 2 is the analysis apparatus according to claim 1, wherein the first calculation means and the second calculation means calculate an electrostatic force by changing a voltage applied to the transfer portion.

  According to a third aspect of the present invention, at the same applied voltage, the output means has a minimum difference between the electrostatic force calculated by the first calculating means and the electrostatic force calculated by the second calculating means. The analysis apparatus according to claim 2, wherein the voltage of the transfer portion is output.

  According to a fourth aspect of the present invention, the output means is calculated by the second calculation means with the maximum electrostatic force calculated by the first calculation means and a voltage value at which the electrostatic force is maximum. The analysis apparatus according to claim 2, wherein a difference from the electrostatic force is output.

  According to a fifth aspect of the present invention, there is provided a program for causing a computer to perform an analysis of an image forming apparatus that transfers a toner image onto a recording medium with a recording medium sandwiched between transfer portions to which a voltage is applied. A first calculation step for calculating an electrostatic force for the toner image in the concave portion of the recording medium, and for the toner image in a convex portion protruding from the concave portion of the recording medium by regarding the toner image as a layer A program comprising: a second calculation step for calculating an electrostatic force; and an output step for outputting a first calculation result obtained by the first calculation step and a second calculation result obtained by the second calculation step. .

  According to the first aspect of the present invention, it is possible to provide an analysis apparatus capable of reducing the amount of calculation as compared with the analysis of the behavior of the transfer portion using developer as particles.

  According to the second aspect of the present invention, in addition to the effect of the first aspect of the present invention, it is possible to perform an analysis according to the voltage change of the transfer portion.

  According to the third aspect of the present invention, in addition to the effect of the second aspect of the present invention, it is possible to present the voltage of the transfer section that can minimize density unevenness.

  According to the present invention of claim 4, in addition to the effect of the present invention of claim 2, density unevenness can be evaluated.

  According to the fifth aspect of the present invention, it is possible to provide a program capable of reducing the amount of calculation as compared with the case of analyzing the behavior of the transfer portion using developer as particles.

It is sectional drawing which shows an example of the transfer apparatus of the image forming apparatus used as the object of the analyzer of this invention. It is a block diagram which shows the analyzer which concerns on embodiment of this invention. 2 is a structural analysis diagram of a transfer device of the image forming apparatus according to the embodiment of the present invention. In the embodiment of the present invention, it is a schematic diagram showing a transfer device of the image forming apparatus when the toner is a layer. It is a flowchart which shows the program for analyzing a density nonuniformity in the analyzer which concerns on embodiment of this invention. It is a graph which shows the electrostatic force change of a paper recessed part. It is a graph which shows the electrostatic force maximum value change of each paper recessed part and convex part at the time of changing bias voltage. It is a graph which shows the change of the density nonuniformity parameter | index at the time of changing a bias voltage. It is a graph which shows the maximum value change of the paper recessed part electrostatic force at the time of changing bias voltage.

  Next, embodiments of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a schematic diagram illustrating an example of a transfer device 10 of an image forming apparatus to be analyzed.

  The transfer apparatus 10 is provided with a transfer roll 12 and a backup roll 14 facing each other. An intermediate transfer belt 16 is disposed between the transfer roll 12 and the backup roll 14. The paper (recording medium) 18 is conveyed toward a nip (transfer section) 20 where the transfer roll 12 and the backup roll 14 face each other, and is sandwiched between the intermediate transfer belt 16 and the transfer roll 12 at the nip 20.

  The intermediate transfer belt 16 conveys a toner image transferred from a photoconductor (not shown) on the upstream side of the transfer device 10. The toner is negatively charged, for example, and adheres with electrostatic force to the lower surface of the intermediate transfer belt 16 in FIG.

  A positive bias voltage is applied to the transfer roll 12 and the backup roll 14 is grounded. An electric field is generated between the transfer roll 12 and the intermediate transfer belt 16, and the toner adhering to the intermediate transfer belt 16 in the process of the recording medium 18 passing through the nip 20 is applied to the recording medium 18 by electrostatic force (Coulomb force). Moved and transcribed.

  In the transfer roll 12, a rubber layer 12b such as foamed silicone rubber is formed around a mandrel 12a such as stainless steel. A conductive material such as carbon black is dispersed in the rubber layer 12b.

  In the backup roll 14, a conductive layer 14 b such as hard silicone rubber is formed around a mandrel 14 a such as stainless steel. Similar to the transfer roll 12, a conductive material such as carbon black is dispersed in the conductive layer 14b.

  The intermediate transfer belt 16 is configured by dispersing a conductive material such as carbon black in polyimide or the like.

  A pressure in a direction facing each other is applied between the transfer roll 12 and the backup roll 14. Due to this pressure, the rubber layer 12b of the transfer roll 12 is elastically deformed. In this specification, a portion where the transfer roll 12 is elastically deformed is defined as a nip 20.

  In the transfer device 10 as described above, density unevenness may occur in an image transferred onto a sheet. One of the causes of uneven density is the unevenness of the paper. Since the electric field differs between the concave portion and the convex portion of the paper, a difference occurs in the electrostatic force acting on the toner, and the difference in electrostatic force acting on the toner causes density unevenness.

  In the analysis, a known value can be used for the unevenness of the paper when the paper type is specified, and when the paper type is not specified, the air permeability test and the surface roughness test are used. The obtained value may be used.

  Next, an analysis apparatus that analyzes density unevenness will be described.

FIG. 2 is a block diagram showing the analysis device 24.
The analysis device 24 is composed of, for example, a computer. That is, in the analysis device 24, a CPU 26, a RAM 28 that can temporarily store data, a ROM 30 such as a flash memory, an input interface 32, and an output interface 34 are connected via a control bus 36.

  The CPU 26 executes a predetermined process based on the control program stored in the ROM 30 and controls the analysis device 24. Connected to the input interface 32 is an input device 38 composed of a mouse and a keyboard. Connected to the output interface 34 is an output device 40 composed of a display and a printer.

In analyzing density unevenness, a structural analysis around the nip 20 is performed in advance.
In the structural analysis, as shown in FIG. 3, the transfer roll 12, the backup roll 14, the intermediate transfer belt 16, and the paper 18 are divided into fine cells, the diameter of the transfer roll 12, the thickness of the rubber layer 12b, and the bulk modulus. In addition, the diameter of the backup roll 14 and the like are input and analyzed using, for example, a finite element method. This structural analysis result (air gap data for each layer position or a table) may be stored in the RAM 28 described above.

A numerical value necessary for the calculation is input by the input device 38. As numerical values necessary for calculation, there are a bias voltage Vb, a volume resistivity ρ _i of each layer, a dielectric constant ε _{i of} each layer, and the like. These bias voltage V, volume resistivity ρ, dielectric constant ε, etc. are stored in the RAM 28.

  In analyzing the density unevenness, the toner is handled not as particles but as layers, and an electrostatic force analysis of the layer structure is performed. The electrostatic force analysis is a one-dimensional analysis in the stacking direction (y direction perpendicular to the process direction). However, the process direction (x direction) can be scanned and analyzed two-dimensionally. The electrostatic force analysis is performed once for each of the concave and convex portions of the paper.

  That is, as shown in FIG. 4, the toner is a layer facing the intermediate transfer belt 16, and the case where the concave portion of the paper (for example, the gap with the toner layer is 10 μm) and the convex portion of the paper (for example, the gap with the toner layer) Electrostatic force analysis is performed for the case of 1 μm).

  FIG. 5 is a flowchart showing a program of the analysis device 24.

  First, in step S10, input data (bias voltage Vb, volume resistivity ρ, dielectric constant ε, etc.) stored in the RAM 28 is read.

  In the next step S12, the air gap data (table) stored in the RAM 28 is read.

と書けるから、電荷保存則は式（３）のように表される。

また、放電計算には、（４）式で示すパッシェン（Ｐａｓｃｈｅｎ）則を用いて計算する。

ただし、Ｖpasはトナー層と用紙との間の放電電位、ｄはトナー層と用紙との間のギャップである。

そして、（５）式で示すクーロンの法則を用いてトナー層に作用する静電力を求める。Qt(t)，Et(t)をそれぞれトナー層の電荷、トナー層の電界(たとえばトナー層中央部として)とすると静電力は（５）式のように表わされる：
Ｆ(t)＝Ｑ_t(t)Ｅ_t(t)・・・・・（５） The next step S14 mainly executes electric field / discharge calculation.
That is, first, the air gap data read in step S12 is referred to, or each layer thickness is calculated by geometric calculation. In particular, the air gap such as the distance between the toner layer and the paper and the distance between the paper and the intermediate transfer belt is calculated.
Next, the electric field calculation in the y direction is performed at the start time t0 (time before the nip entry time) or at the start position x0 (position before the nip entry position). For the electric field calculation, a one-dimensional Poisson equation expressed by equation (1) is solved.
dE (y) / dy = ρ / ε (1)
At the same time, the charge conservation law is applied to each layer boundary in order to obtain the charge flow in the layer (the current density flowing into the boundary and the sum of the outgoing current densities are equal to the time derivative of the boundary charge density. It is assumed that Ohm's law holds (the current density in the layer is proportional to the electric field, and the proportionality constant is conductivity = 1 / volume resistivity).
From the charge conservation law, the time change of the charge density σi, i + 1 at the boundary between the i-th layer and the (i + 1) -th layer is equal to the difference between the current densities J of the preceding and subsequent layers. Here, the current density Ji of the i-th layer is expressed by Ohm's law when the conductivity of the i-th layer is written as γi.

Therefore, the law of conservation of charge is expressed as shown in Equation (3).

In addition, the discharge is calculated using the Paschen law expressed by the equation (4).

Where Vpas is a discharge potential between the toner layer and the paper, and d is a gap between the toner layer and the paper.

Then, the electrostatic force acting on the toner layer is obtained using Coulomb's law expressed by the equation (5). If Qt (t) and Et (t) are the charge of the toner layer and the electric field of the toner layer (for example, as the central portion of the toner layer), the electrostatic force is expressed as follows:
F (t) = Q _t (t) E _t (t) (5)

In the next step S16, it is determined whether or not the calculation has been performed up to the final time or the final position. The final time is a time after a predetermined time from the time of leaving the nip, and the final position is a position after a predetermined interval from the position of leaving the nip.
If it is determined in step S16 that the position is before the final position, the process returns to step S14, and the electric field / discharge calculation at the next time or position is executed.
That is,
t = t0, t = t0 + Δt, t = t0 + 2Δt,
Or x = x0, x = x0 + vΔt, x = x0 + v2Δt (v is the process speed)
Then, the calculation is repeated until the final position, and the calculation result is stored in the RAM 28.

  If it is determined in step S16 that the calculation has been completed up to the final position, the process proceeds to the next step S18. In step S18, a current (integrated value of charge amount) J is calculated.

  In the next step S20, it is determined whether or not constant current calculation is set in the first place. If it is determined that the constant current calculation is set, the process proceeds to the next step S22. In step S22, it is determined whether or not J≈set value. When the current J substantially matches the set value, it is determined that the bias voltage is appropriate. However, since the bias voltage is not appropriate for the current J to be a value different from the set value, the next step S24 is performed. The bias voltage is corrected at step S14, step S16, step S18, step S20, step S22, and step S24. The process is executed until the current value J becomes a substantially constant current value.

  If it is determined in step S20 that the constant current calculation is not set, or if it is determined in step S22 that the current J≈the set value, the process proceeds to step S26, and the calculation result is output to the output device 40. The calculation results in step S26 include analysis results such as charge, electric field, and potential difference.

  Next, an embodiment relating to output will be described.

In the first embodiment, a bias voltage with the least density unevenness is obtained by the following procedure.
1. Electric field calculation of the paper recess (gap = δ μm) is performed with respect to the bias voltage N level (V1,... VN) (δ> 1 μm, where δ = 10 μm).
2. The electrostatic force (maximum value in the nip) acting on the toner at each bias voltage level is calculated. 6 shows the relationship between (position (Position mm) and electrostatic force (electrostatic force Fc N / m ³ ) when the pressure is 4 kV in the concave portion of the sheet. This is stored as F10_max and plotted at each bias voltage level as shown by the solid line in FIG.
That is, it is calculated as Fe (Vi, 10) _max = [(Q ₁₀ + δQ) × E ₁₀ ] _max .
3. Electric field calculation of the paper convex portion (contact portion, gap = 1 μm) is performed with respect to the bias voltage N level (V1,... VN).
4). The electrostatic force (maximum value in the nip) acting on the toner at each bias voltage level is calculated. This is indicated by a one-dot chain line in FIG.
That is, it is calculated as Fe (Vi, 1) _max = [(Q ₁ + δQ) × E ₁ ] _max .
5. The unevenness index is index_mottle = [Fe (Vi, 1) _max− Fe (Vi, 10) _max ] / Fe (Vi, 1) _max, and the bias voltage at which index_mottle is minimized is set to the optimum value (see FIG. 8). .

In the second embodiment, density unevenness is evaluated by the following procedure.
1. Electric field calculation of the paper recess (gap = δ μm) is performed with respect to the bias voltage N level (V1,... VN) (δ> 1 μm, where δ = 10 μm).
2. The electrostatic force (maximum value in the nip) acting on the toner at each bias voltage level is calculated. The result is shown in FIG.
That is, Fe (Vi, 10) _max = [(Q + δQ) × E] _max is calculated.
3. The bias voltage at which Fe (Vi, 10) _max is maximized is set to the optimum value (in this case, 2.75 kV from FIG. 9).
4). Fe (2.75 kV, 1) _max is calculated for the convex portion of the paper.
5. Fe (2.75 kV, 1) _max −Fe (Vi, 10) _max or [Fe (2.75 kV, 1) _max −Fe (Vi, 10) _ma ] / Fe (2.75 kV, 1) _max And

In the third embodiment, the optimum transfer configuration is calculated by the following procedure.
1. The optimum bias voltage shown in the first or second embodiment is calculated while changing the resistance or thickness of the rubber layer 12b of the transfer roll 12 or the resistance or thickness of the conductive layer 14 of the backup roll 14. To do.
2. An optimum transfer configuration can be obtained by determining the resistance or thickness of the rubber layer 12b of the transfer roll 12 or the resistance or thickness of the conductive layer 14 of the backup roll 14 so that the density unevenness index is minimized.

  In addition to the above embodiment, density unevenness can be evaluated by changing, for example, a toner supply amount or a charge amount. Further, an optimum transfer configuration can be obtained by changing the resistance or thickness of the intermediate transfer belt.

10: transfer device 12: transfer roll 12b: rubber layer 14: backup roll 14b: conductive layer 16: intermediate transfer belt 18: recording medium 20: transfer unit 24: analysis device 26: CPU
38: Input device 40: Output device

Claims (5)

An analysis apparatus for an image forming apparatus for transferring a toner image to a recording medium by sandwiching the recording medium in a transfer portion to which a voltage is applied,
First calculating means for calculating the electrostatic force for the toner image in the concave portion of the recording medium by regarding the toner image as a layer;
A second calculating means for calculating an electrostatic force for the toner image at a convex portion protruding from the concave portion of the recording medium by regarding the toner image as a layer;
An output means for outputting a first calculation result by the first calculation means and a second calculation result by the second calculation means;
Analyzing device.   The analysis apparatus according to claim 1, wherein the first calculation unit and the second calculation unit calculate an electrostatic force by changing a voltage applied to the transfer unit.   3. The analysis according to claim 2, wherein the output unit outputs a voltage of the transfer unit that minimizes a difference between the electrostatic force calculated by the first calculation unit and the electrostatic force calculated by the second calculation unit. apparatus.   The output means outputs a difference between the maximum electrostatic force calculated by the first calculation means and the electrostatic force calculated by the second calculation means at a voltage value at which the electrostatic force is maximum. Item 3. The analysis device according to Item 2. A program for causing a computer to execute an analysis of an image forming apparatus that transfers a developer onto a recording medium with a recording medium sandwiched between transfer portions to which a voltage is applied,
A first calculation step that regards the toner image as a layer and calculates an electrostatic force for the toner image in a recess of the recording medium;
A second calculation step of calculating an electrostatic force with respect to the toner image at a convex portion protruding from the concave portion of the recording medium by regarding the developer as a layer;
An output step of outputting the first calculation result by the first calculation step and the second calculation result by the second calculation step;
A program with

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