JP2003162156A - Method for simulating transfer mechanism - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To accurately analyze various information useful for transfer performance such as transfer efficiency of toner while taking the time wise change of electric fields associated with the movement of members into consideration. <P>SOLUTION: Each member of a toner carrier, the toner, printed matter and a transfer material which are used for the transfer mechanism of an electrophotography system and clearance parts between respective members are approximated with a finite element model divided into many elements by the finite number of nodes. Initial conditions and boundary conditions are set by inputting required data in each element. Electric field distribution between the members is calculated by using the equation of Poisson from the distribution of electric charges at each node when applying voltage between respective members. The moving amount of the electric charges is calculated by using the Ohm's law from electric fields generated between respective members. The toner is assumed to the charged particles, and the moving amount of the toner is calculated according to a potential difference between the toner and the members by using the moving diffusion equation of the particles, then the positions of the nodes are changed following the positional movements of the members. The moving amounts of the electric charges and toner are calculated moment by moment in the same way, and the transfer performance is analyzed by a finite element method. <P>COPYRIGHT: (C)2003,JPO

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a transfer mechanism simulating method, and more specifically, it accurately predicts and analyzes an actual transfer mechanism in consideration of positional movement of members and toner charging.

[0002]

2. Description of the Related Art In developing a transfer mechanism such as an intermediate transfer belt used in an electrophotographic device such as a printer, a copying machine, a facsimile device, an electrostatic recording device, etc., design and trial manufacture,
The method of conducting experiments and evaluations and further making prototypes of improved products was repeated. However, the method of repeating trial manufacture has a low development efficiency because of the cost and cost of trial manufacture.

Therefore, in order to save the cost and time of trial production, product development using simulation without trial production has been proposed, and the numerical value by the finite element method is also used in the transfer mechanism of the electrophotographic apparatus as described above. With the introduction of simulations, it has become possible to predict product performance to some extent, such as the charging status of each member.

[0004]

However, it is difficult to consider the shape movement of a member such as a belt or the like which is to be simulated, the position movement due to rotation, and the movement of charged toner. There is a problem that it cannot be predicted and analyzed. Further, depending on the setting conditions of the model, it is necessary to remake the model when the transfer condition or the shape of the member is changed, and a simulation method having high versatility is desired.

As described above, in the conventional simulation of the transfer mechanism, it has not been possible to analyze the transfer efficiency of toner in the actual transfer mechanism using the intermediate transfer belt or the like. In particular, in order to achieve high image quality, it is important to optimize various parameters such as belt, toner, transfer conditions, etc. Therefore, a simulation method that can predict the electric field condition between members and the transfer efficiency of toner is required. There is.

The present invention has been made in view of the above problems, and accurately analyzes various information useful for transfer performance such as toner transfer efficiency in consideration of the time change of the electric field due to the position movement of the member. An object of the present invention is to provide a simulation method of a transfer mechanism that can be performed.

[0007]

In order to solve the above-mentioned problems, the present invention provides a toner carrier, a toner, a material to be printed, each member of a transfer material used in a transfer mechanism, and a finite space between each member. Approximate with a finite element model divided into a large number of elements by each node, set the initial condition and boundary condition by inputting the required data to each element, the charge of each node when applying voltage to each member The electric field distribution between the members and the members is calculated from the distribution using Poisson's equation, and the amount of charge transfer is calculated using Ohm's law from the electric fields generated between the members and the members. Assuming that the movement amount of toner is calculated from the potential difference between the toner and the member using the movement diffusion equation of particles, the position of the node is changed according to the position movement of the member, and the movement amount of the charge and toner is changed in the same manner as above. The finite element method by momentarily repeatedly calculated provides a simulation method of a transfer mechanism, wherein the parsing the transfer performance.

As described above, the present invention uses the finite element model to change the positions of the nodes according to the position movements of the above-mentioned members, calculate the amount of movement of the charge and the toner repeatedly every moment, and change the electric field and the toner. The transfer efficiency, etc. of is analyzed by the finite element method. Therefore, it is possible to dynamically express the change in the gap between the members due to the position movement of the members, the movement of the toner and the electric charge, and the time change of the electric field distribution accompanying the movement. Various information useful for transfer performance can be accurately obtained. In addition, by changing the positional relationship of each member at each time, it is possible to easily perform simulation with changing the speed condition of the member, and to easily optimize the shape, feed speed, material, etc. of the member. You can Therefore, in a transfer mechanism such as an electrophotographic device or an electrostatic recording device, useful information can be obtained without making a prototype, so that development efficiency can be improved.

In the present invention, a toner carrier such as an intermediate transfer belt, a material to be printed such as toner and paper, a member of a transfer material such as a transfer roller, and a space between the members are formed by a finite number of nodes. It is approximated by a finite element model that is mesh-divided into elements. In the finite element model, the number of members, the direction of position movement of the members, and the number of voids are set, and the moving distance of each member is analyzed moment by moment. In addition, in the shape data of the finite element model, a double node is formed between each member to form a void portion, and in the void portion, the electric charge moves between the double nodes of the initial shape. The position of the initial node is determined by the initial shape of the member and the moving distance of the member at time 0. At each time, the node of each member is set to move according to the given moving distance. Linear interpolation is performed between them. Further, in each member, it is preferable to divide the element so that the interval between the nodes becomes narrow in the vicinity of the printing object such as paper, and in the void portion, the element is divided into a specified number of elements to prevent the position movement of the member. It is preferable that the distance is always constant regardless of the distance. The required data to be input to each element are the volume charge density q of each member, the relative permittivity ε ′, and the vacuum permittivity ε _0.
Etc., and these data can be set individually for each member.

The finite element model is preferably a one-dimensional model. As a result, modeling can be facilitated, and movement of each modeled member due to rotation can be easily represented. The finite element model may be a two-dimensional model.

In the transfer mechanism of the secondary transfer section, the intermediate transfer belt is used as the toner carrier, the transfer roller is used as the transfer material, and the intermediate transfer belt is formed from the material to be printed such as toner and various papers / films. The simulation of the invention can be used particularly preferably. Since the toner is treated as charged particles and the position movement due to the rotation of the toner carrier can be considered, the intermediate transfer belt on which the toner image is transferred rotates, and the paper or the like supplied between the intermediate transfer belt and the transfer roller. It is useful for analyzing the transfer efficiency of toner when an image is formed by transferring a toner image onto a printing medium and fixing the toner image.

From the distribution of charges at each node when a voltage is applied to each member, the Poisson's equation (Equation 1) below is used to calculate the potential between each member and each member. here,
y is a distance from the lower end of the transfer material, and V is a potential. (Equation 1) Further, the electric field distribution between the members and the members is calculated by using the following Expression 2 from the potential calculated by the Expression 1. Where E
Is the electric field. (Formula 2) By calculating the electric field distribution in this way, the force for moving the electric charge at each node is obtained.

The amount of charge transfer is calculated from the above-mentioned members and the electric field generated between the members using Ohm's law (Equation 3 below). Here, σ is electric conductivity and t is time. (Formula 3) Further, the toner is regarded as charged particles, and the migration of the toner is caused by the potential difference between the toner and the member (the material to be printed and the toner, or the transfer material and the toner) using the particle diffusion equation (Equation 4 below). The amount is calculated. Here, N is the number of types of particles, Ni is the particle number density of particle i, Ci is a coefficient representing the transition from particle j to particle i, vi is the moving speed of particle i, Di is the diffusion coefficient of particle i, Fi is a function consisting of the number of particles, their spatial differentiation and particle velocity. (Equation 4) In this way, the movement amount of the charge and the toner can be obtained from the electric field and the potential difference. Here, the charge at each node of the toner carrying member such as a belt, the printing target, and the transfer material such as the roller and the charge different from that of the toner are set, and the moving range of the toner is the toner carrying member and the printing target. It is assumed that the discharge phenomenon does not occur because it is limited to the space between them. Also,
The toner is present at the nodes on the surface of the toner carrier.
It should be noted that, by applying a voltage, the electric charge is stored at the lower end of the transfer material up to a constant voltage, and then the electric charge is set to flow to each member as needed.

After obtaining the charge and toner movement amounts as described above, the positions of the nodes are changed again with the movement of the member, and the charge and toner movement amounts are repeatedly calculated in the same manner as above. The change in electric field and the transfer efficiency of toner are analyzed by the finite element method. In this way, by appropriately changing the positions of contact points and gaps of the member model in accordance with the rotational movement of the toner carrier such as the belt, and calculating the amount of movement of electric charge and the like moment by moment, each node after the position movement It is possible to sequentially calculate the electric charges in, and it is possible to perform an analysis in consideration of the position movement of each member. Therefore, the transfer performance can be calculated from various patterns according to the distance and the moving speed between the toner carrier such as the belt and the transfer material such as the printing medium and the roller.

It is preferable that the voltage difference causing the discharge is set in correspondence with the interval between the above-mentioned members, and the discharge charge amount is calculated by Paschen's law. Specifically, as shown in the following formulas 5 and 6, when the gap between the members is set to g [μm], discharge occurs at a voltage difference ΔV [V] or more below. (Equation 5) The discharge charge amount at that time is, when the thickness of each member is di, the dielectric thickness of the discharge electrode is D, the relative permittivity is εi ′, and when the surface potential of the member changes from V1 to V2 due to discharge,
From Equation 6, (i = 1, 2 ...) (D = 1 element length) (Equation 6) Can be defined as As a result, it is possible to obtain how much the electric charge has been discharged, and it is possible to accurately obtain information such as a change in the electric field due to a change in the resistance value of the transfer material such as the transfer roller. In addition, in the simulation of the present invention, the gap g between the members is set to a value that is infinitely small, but is set so as not to be 0, and it is possible to assume a case where the transfer material is a sponge roll. it can.

That is, the movement of charges in the same substance is considered by Ohm's law, and the movement of charges between different substances is considered by Paschen's law. Even if the discharge phenomenon does not occur and the printing material is not charged, the toner may be moved if the toner carrier and the transfer material come close to each other.

Further, various objects of analysis include various transfer mechanisms including a toner carrier, toner, a material to be printed, and a transfer material, which can be applied to both primary transfer and secondary transfer.
In particular, the transfer mechanism of the secondary transfer section using the intermediate transfer belt can be preferably analyzed.

Examples of the material of the toner carrier and the transfer material such as the intermediate transfer belt used in the transfer mechanism include various conductive rubbers, resins and elastomers, which are appropriately combined with a filler and the like. But good. Specific examples thereof include an ion conductive polymer, a polymer containing powder of a metal oxide, a conductive filler such as carbon black, and the like.

[0019]

DETAILED DESCRIPTION OF THE INVENTION Embodiments of the present invention will be described below with reference to the drawings. The simulation method of the transfer mechanism of the present invention is performed by executing the simulation program by a simulation device including a storage device in which the program of the simulation method of the present invention is stored, a computer including a CPU, and the like.

FIG. 1 shows a flow chart of a transfer mechanism simulation method of the present invention. First, each member of the transfer material such as a toner carrier such as a belt used for an electrophotographic transfer mechanism, a toner, an object to be printed, a roller, and the space between each member are formed into a large number of elements by a finite number of nodes. The initial conditions and boundary conditions are set by approximating with the divided finite element model and inputting required data to each element.

Next, the electric field distribution between each member is calculated by a simulation using the finite element method using the Poisson's equation from the charge distribution at each node when a voltage is applied to each member. . Then, from the electric field generated between each member and the member, the amount of charge transfer is calculated using Ohm's law, and the toner is regarded as a charged particle, and the potential difference between the toner and the member is calculated using the particle transfer diffusion equation. The toner movement amount is calculated by. that time,
The voltage difference at which discharge occurs is set in correspondence with the interval between the above-mentioned members, and the discharge charge amount is calculated according to Paschen's law.

After that, the positions of the nodes are changed again with the movement of the member, and the movement amounts of the charge and the toner are repeatedly calculated in the same manner as described above, and the change of the electric field and the transfer efficiency of the toner are finite elements. It is analyzed by the method.

In the present embodiment, as shown in FIG. 2, in the image forming apparatus for the color printer in which the intermediate transfer belt 10 as the toner carrier is mounted, the transfer mechanism of the secondary transfer portion is simulated. . This image forming apparatus includes an intermediate transfer belt 10, which is a toner carrier, a charging roller 11, a photoconductor 12, a transfer roller (sponge roller) 13, which is a transfer material, a fixing roller 14, and four color toners 1.
5 (15a to 15d), a mirror 16, and a metal roller 19 as an earth roller.

When an image is formed by this image forming apparatus, first, the photoconductor 12 rotates in the direction of the arrow in the figure, and the photoconductor 12 is charged by the charging roller 11 and then the laser beam is passed through the mirror 16. 17 is exposed on the photoreceptor 12. Thereafter, the four-color toners 15 are respectively supplied onto the photoconductor 12 as needed, and the toners 15 are developed.
Next, the toner image is primarily transferred onto the intermediate transfer belt 10 passing between the photoconductor 12 and the transfer roller 13, the intermediate transfer belt 10 is rotated, and the toner image on the intermediate transfer belt 10 is transferred to the intermediate transfer belt 10. The secondary transfer is performed on the paper 18 passing between the transfer roller 13 and the transfer roller 13. After that, the paper 18 is conveyed in the direction of the arrow in the figure, and the toner image is fixed on the paper 18 by the fixing roller 14.

FIG. 3 shows a detailed state of the secondary transfer portion to be analyzed. The metal roller 19 is grounded, and a voltage can be applied to the transfer roller 13 by the power source E and the metal shaft 13A. While the metal roller 19 and the transfer roller 13 rotate in the direction of the arrow in the figure, the toner 1
The intermediate transfer belt 10 carrying 5 and the paper 18 are also moved, and the charged toner 15 is transferred onto the paper 18 according to each member and the electric field state between the members.

In carrying out the analysis, specifically, first,
As an analysis target of the simulation, in the initial state, as shown in FIGS. 4 and 5, the intermediate transfer belt 10 (hereinafter, also simply referred to as the belt 10), the toner 15, the paper 18,
A one-dimensional finite element in which each member of the transfer roller 13 (hereinafter also simply referred to as the roller 13) and the void portion 20 (20, 20B) between each member are divided into a large number of quadrilateral elements Y by a finite number of nodes S. It is approximated by a model. In the present embodiment, the number of nodes of the belt is 42, the number of elements is 20, the number of nodes of the roller is 324, the number of elements is 161, the number of paper nodes is 22, the number of elements is 10, and the number of voids is 12 and the number of elements is 5. The numerical value at the right end of the model in the figure indicates the height from the origin (unit: mm).

The belt 10, the paper 18, and the roller 13 are quadrangular finite element models, and the belt 10,
Toner 15 and voids 20 are formed on the surface of the belt 10 on the side of the paper 18.
They are arranged on the same line so that the paper 18 is provided via A and the roller 13 is provided via the space 20B. Roller 13
And the paper 18, and the space 2 between the paper 18 and the belt 10.
0 is formed and is a double node. The toner 15 is assumed to be located at a node on the surface of the belt 10. Further, the voids 20 are divided into five elements and are evenly arranged at each time.
The element Y is divided so that the interval between the nodes S becomes narrower in the vicinity of the element 8.

The position of the initial node S is determined by the initial shape of each member and the moving distance of the member at time 0. At each time, the node S of each member is set to move according to the given moving distance. Is performed, and linear interpolation is performed during the time. That is, in the above finite element model, the number of members, the direction of movement, and the number of voids are set, and the moving distance of each member is analyzed moment by moment. Specifically, as shown in FIG. The belt 10, the paper 18, and the roller 13 are
While the position is changed and the shape of the void portion 20 is changed according to the change of time, the toner transfer mechanism of the secondary transfer portion is analyzed every moment.

In the above finite element model, material characteristic data necessary for analysis are input. Specifically, in this embodiment, the physical properties of each member are set as shown in Table 1 below. The dielectric constant of the voids is the vacuum dielectric constant.

[0030]

[Table 1]

In order to perform the simulation by the finite element method, first, the belt 10 is set to 0 V, and the initial charge is applied so that the voltage of 1000 V is generated at the node at the lower end of the roller 13 which is the transfer material. By applying the initial charge, the roller 13, the paper 18, the belt 10, and the gap 20 between the members.
An electric field is generated in the electric field, and the electric field causes electric charges to move from the nodes at the lower end of the roller 13 to the positions of the nodes of each member.
Then, the electric field distribution between the members is further calculated from the charge distribution at each node and the position of each node using Poisson's equation. Here, the lower end of the roller 13 is 1000
The setting is such that the electric charge is discharged after the V voltage is stored. Then, the amount of charge movement is calculated from the electric field generated between the respective members using Ohm's law, and the toner 15 is regarded as charged particles that can move to the surface of the paper 18, and the toner 15 and the toner 15 are calculated using the movement diffusion equation of the particles. The movement amount of the toner 15 onto the paper 18 is calculated from the potential difference between the members. Here, the moving range of the toner 15 is limited to the space between the belt 10 and the paper 18.

At this time, the voltage difference causing the discharge is set in correspondence with the interval between the respective members, and the discharge charge amount is calculated by Paschen's law. Specifically, if the discharge charge amount is determined by the potential difference and the dielectric constant, and if the conditions for causing the discharge are adjusted, the charges are moved at a stroke in the space between the roller 13 and the paper 18, and the space between the paper 18 and the toner 15, and the discharge Discharge is performed so that the amount of charge at each node is the same. That is, the movement of charges in the same substance is considered by Ohm's law, and the movement of charges between different substances is considered by Paschen's law. After that, the positions of the nodes are changed again with the movement of the member, and the movement amounts of the electric charge and the toner are repeatedly calculated every moment as in the above.

As described above, the belt 10, the toner 15, the paper 18, and the roller 13 are modeled by using the finite element model, the positions of the nodes S are changed as the above-mentioned members move, and the flow of the electric charge is accompanied. Since the electric field distribution is changed from time to time and the amount of movement of the charge and the toner 15 is repeatedly calculated every moment, it is possible to dynamically express the time change of the electric field distribution between the respective members. Therefore, various information useful for transfer performance such as the change in electric field and the transfer efficiency of the toner 15 can be accurately obtained.

An example of the simulation of the transfer mechanism of the present invention will be described in detail below. The transfer mechanism of the secondary transfer section using the intermediate transfer belt was analyzed by the same method as in the first embodiment. The voltage applied to the shaft of the transfer roller is 1
The electrical characteristics of each member were set as shown in Table 2 below. For the roller, the volume resistivity is logΩ =
Three patterns of 6, 7, and 8 were prepared. The outer diameter of the roller is φ2
It was set to 0 mm and rotated at 100 rpm. The analysis result and the actual measurement result are shown in FIGS. The software used is JMAG-Studio Ver. 6 Use computer is NEC MA80T

[0035]

[Table 2]

FIG. 7 shows the moving state of each member with time, and shows the change with time of each position of the lower end of the belt, the upper and lower ends of the paper, and the upper end of the roller due to the rotational movement. 0.015
The distance between the paper, the belt and the roller was the smallest in the range of 0.02 seconds. Further, FIG. 8 shows a simulation result in which the change of the toner transfer rate with the passage of time is analyzed for each volume resistivity of the roller. 0.015
From about 0.02 seconds, the transfer efficiency is drastically improved.
After that, as the belt and the roller were separated from the paper, the curve became a gentle curve and became a constant value. In addition, the measured values of the transfer ratio of each toner when three rollers are used are also shown on the graph.

As shown in FIG. 8, in any of the analysis results of the simulation and the actually measured values, the higher the volume resistivity of the roller, the lower the transfer rate. The relative change could be analyzed accurately. Further, regarding the resistance of each roller, the final value of the transfer rate in the analysis result of the simulation is almost the same as or slightly smaller than the actually measured value, and the absolute value of the transfer efficiency can be accurately predicted. From this, it was confirmed that by using the simulation of the present invention, it is possible to predict useful information regarding transfer performance such as a toner transfer ratio.

[0038]

As is apparent from the above description, according to the present invention, each member of the toner carrier, the toner, the material to be printed, and the transfer material is modeled using the finite element model, and the movement of each member is performed. Along with this, the positions of the nodes are changed, and the electric field distribution is changed at any time in accordance with the flow of electric charges, and the movement amounts of electric charges and toner are repeatedly calculated every moment. Therefore, the time change of the electric field distribution between each member can be dynamically expressed,
It is possible to accurately obtain various information useful for transfer performance, such as changes in electric field and toner transfer efficiency.

Further, by changing the positional relationship of each member at each time, it becomes possible to easily carry out a simulation in which the speed condition of the member is changed.
The feed speed and material can be optimized. Further, by calculating the discharge charge amount between the members, the analysis accuracy can be further improved.

Therefore, in the transfer mechanism such as the intermediate transfer belt or the like, useful information can be obtained without making a trial, so that the development efficiency can be improved. Especially in the secondary transfer section of the image forming apparatus using the intermediate transfer belt,
It can be suitably used for analysis of the transfer efficiency of toner on the intermediate transfer belt to the printing medium.

[Brief description of drawings]

FIG. 1 is a view showing a flowchart of a transfer mechanism simulation method of the present invention.

FIG. 2 is a diagram showing an image forming apparatus for a color printer using an intermediate transfer belt.

FIG. 3 is a schematic enlarged view of a secondary transfer portion to be analyzed.

FIG. 4 is a diagram showing a finite element model of each member to be simulated.

FIG. 5 is a diagram showing a nodal point of each member, a division state of the element, and a temporal change of each member.

FIG. 6 is a diagram showing a transfer state of toner according to movement of each member.

FIG. 7 is a diagram showing a temporal change of each member and a positional relationship thereof.

FIG. 8 is a diagram showing an analysis result of simulation.

[Explanation of symbols]

10 Intermediate transfer belt 13 Transfer roller 15 toner 18 paper S node Y element

   ─────────────────────────────────────────────────── ─── Continued front page    (72) Inventor Akira Kadoro             3-6-9 Wakihama-cho, Chuo-ku, Kobe-shi, Hyogo               Sumitomo Rubber Industries, Ltd. (72) Inventor Akio Miyoro             3-6-9 Wakihama-cho, Chuo-ku, Kobe-shi, Hyogo               Sumitomo Rubber Industries, Ltd. (72) Inventor ▲ Tani ▼ Koji             1-5-8 Shinmachi, Nishi-ku, Osaka-shi, Osaka             Inside the Japan Research Institute (72) Inventor Yasuhito Taniguchi             1-5-8 Shinmachi, Nishi-ku, Osaka-shi, Osaka             Inside the Japan Research Institute F-term (reference) 2H134 QA01                 2H200 FA16 GB50 JB10 JC04

Claims (3)

[Claims] 1. A finite element model in which each member of a toner carrier, a toner, an object to be printed, and a transfer material used in a transfer mechanism and a space between each member are divided into a large number of elements by a finite number of nodes. Then, the initial conditions and boundary conditions are set by inputting the required data to each element, and the electric field distribution between the members and the members using the Poisson's equation from the charge distribution at each node when voltage is applied to the above members. Is calculated, and the amount of charge transfer is calculated from each member and the electric field generated between the members using Ohm's law.At the same time, the toner is regarded as charged particles, and the transfer diffusion equation of particles is used to calculate the difference between the toner and the member. After calculating the toner movement amount from the potential difference, the position of the node is changed according to the position movement of the above member, and the movement amount of the charge and toner is repeatedly calculated in the same manner as above. A method for simulating a transfer mechanism, which is characterized by analyzing transfer performance. 2. The transfer mechanism simulation method according to claim 1, wherein a voltage difference at which discharge occurs is set corresponding to an interval between the respective members, and the discharge charge amount is calculated by Paschen's law. 3. The toner carrier is an intermediate transfer belt, the transfer material is a transfer roller, and the transfer efficiency of the toner on the intermediate transfer belt to the printing medium is analyzed by a one-dimensional finite element model. The method of simulating a transfer mechanism according to claim 1 or 2.