JPH10260159A - Method and device for simulating behavior of grain in container - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method and a device for simulating behavior of grains in a container by which the quantity of static electricity generating in a container housing powder and grain accompanied with mixing/agitating of powder and grain can be estimated and grasped, trial-and-error experiment be reduced greatly and an index for optimal control design be obtained. SOLUTION: The changing positions of grains housed in a container are obtained every fine time elapse on the basis of container shape, mixing/agitating condition, physical property value of the grain, and physical property value of wall surface of the container. The quantity of static electricity generating in the grains 10 and 11 or on the wall surface of the container due to mixing/ agitating operation in the container is obtained assuming that it depends on the contact area between the grains 10 and 10 or between the grain and wall surface of the container.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION The present invention relates to a method for reducing the number of particles contained in a container based on the shape of the container, mixing and stirring conditions, physical characteristics of the particles, and physical characteristics of the walls of the container. TECHNICAL FIELD The present invention relates to a method and apparatus for simulating the behavior of particles in a container, which calculates and displays the position of each minute time period, and particularly relates to a computer which measures the amount of static electricity generated during mixing and stirring of powders and granules represented by an electrophotographic process. The present invention relates to a method and an apparatus for numerically simulating by using.

[0002]

2. Description of the Related Art In the field of handling particles such as powders and granules, it is important to understand the behavior of the particles. Conventionally, the behavior of such particles has been grasped through trial and error experiments and the like. Therefore, the labor was enormous in terms of time and economy.

In order to avoid such trial and error experiments, for example, Japanese Patent Application Laid-Open No. 7-84792 discloses a simulation device for particle behavior in a rotating mixing vessel.

In this simulation apparatus, regarding the particles contained in the rotating mixing vessel, the three-dimensional shape of the inner wall of the rotating mixing vessel, the rotation speed of the rotating mixing vessel, the friction characteristics between the inner wall and the particles, the attitude with respect to the direction of gravity, etc. With the factor as a factor, it is possible to simulate the state of change in the position of the particles in the rotary mixing vessel over time.

For example, in a rotary mixing vessel, a particle diameter of 1-2
500 to 800 particles of about mm
The state when a predetermined time has elapsed after rotating the rotary mixing container at 回 転 30 rpm can be displayed.

[0006]

However, the above-described conventional apparatus for simulating the behavior of particles in a rotary mixing vessel can simulate the position in the behavior of particles, but cannot simulate the amount of static electricity generated in the behavior of particles. have.

That is, in the field of handling particles such as powders, mixing and agitation generally occur during the operation, and static electricity is generated due to this. The mechanism of the generation of static electricity has not been theoretically elucidated yet, and the prediction, control, and determination of the method of suppressing the amount of electrostatic charge have been performed based only on many trial and error experiments and empirical intuition. As a result, much time and effort is spent on experiments aimed at optimal control design.

In particular, in the field using electrophotographic process technology such as a copying machine and a laser printer, a mixing and stirring operation of powders and granules is performed in the apparatus, and the powders are promptly adjusted to an optimal charge amount for the process. It is required to be charged. on the other hand,
In fields such as pneumatic transportation of powder, mixing and agitation occur during transportation, and static electricity is generated due to friction with the equipment wall, which hinders pneumatic transportation such as aggregation and adhesion of the powder to the wall. Occurs.

However, at this time, the amount and location of the generation of static electricity in the powder and granules depend on the constituents of the powder and granules and the wall material of the apparatus, physical characteristic values such as surface conditions, environmental conditions such as temperature and humidity, and environmental conditions such as temperature and humidity. Although it largely depends on the state of filling of the powder and the like, the mechanism of generation of static electricity is unclear, and it is difficult to predict in advance.

Further, even if the amount of static electricity generated is measured by an experiment, in most cases, very poor reproducibility results can be obtained due to minute fluctuations in the experimental environment. The present invention has been made in view of the above-described conventional problems, and its purpose is to predict the amount of static electricity generated due to the mixing and stirring operation in the container containing the granular material,
An object of the present invention is to provide a method and apparatus for simulating the behavior of particles in a container, which can significantly reduce trial and error experiments and provide an index for optimal control design.

[0011]

According to a first aspect of the present invention, there is provided a method for simulating the behavior of particles in a container. In the method of simulating the behavior of particles in a container, which is obtained and displayed based on the stirring conditions, the physical characteristic values of the particles, and the physical characteristic values of the container wall, static electricity generated on the particles or the container wall due to the mixing and stirring operation The amount is determined between particles and particles based on the position of the particles over time.
It is characterized in that the prediction is made based on the contact area between the container wall surfaces.

When the particles are agitated in the container, charges move between the particles constituting the particles and at the contact interface between the particles and the wall of the container, and the charges remain after separation, so that the particles and the wall of the container are left behind. Charging occurs and static electricity is generated. Therefore, the amount of generated static electricity can be calculated as depending on the contact area between the particles and between the particles and the wall surface of the container.

Therefore, in the above invention, the amount of static electricity of the particles or the particles generated on the container wall surface due to the mixing and stirring operation is predicted based on the contact area between the particles and between the particles and the container wall surface. ing.

As a result, the number of trial and error experiments can be reduced and the effects of various parameters can be tested on a computer as compared with the prior art, so that the development period can be significantly reduced and development costs can be reduced.

Further, by applying the present invention to a simulation of stirring and charging of a two-component developer, it is possible to reproduce a generally well-known charging curve of an electrophotographic two-component developer. For this reason, it is expected that the number of experiments conventionally performed to achieve the required charging characteristics will be reduced.

According to a second aspect of the present invention, there is provided a method for simulating the behavior of particles in a container, wherein the method for simulating the behavior of particles in a container according to the first aspect comprises the steps of: It is characterized in that it is performed based on the sliding friction area obtained from the contact area between the particles and the particle-container wall surface.

It has been experimentally confirmed that the amount of charge increases when slippage occurs at the contact interface during contact. From a microscopic perspective, it can be fully imagined that the material on the particle surface is scraped off by the sliding friction and loses the charge it holds by adhering to the partner particle, and the effect of the surface roughness is offset by the sliding friction. Therefore, it can be imagined that an increase in the actual contact area facilitates the movement of charges on the contact surface.

Therefore, in the above invention, the amount of static electricity generated on the particles or the wall of the container due to the mixing and stirring operation is calculated as follows:
The prediction is made based on the sliding friction area obtained from the contact area between the particles and between the particles and the container wall.

Thus, depending on the conditions of mixing and stirring,
In many cases, the force in the direction that causes slippage is more dominant than the contact force between particles in the direction of the center of gravity, but even in such a case, it is possible to accurately simulate the amount of static electricity generated.

According to a third aspect of the present invention, there is provided a method for simulating the behavior of particles in a container. In the method for simulating the behavior of particles in a container, which is obtained and displayed based on the characteristic value and the physical characteristic value of the container wall surface, the amount of static electricity generated on the particles or the container wall surface due to the mixing and stirring operation is determined between the particles and between the particles. -It is characterized in that it is predicted based on the required contact time required from contact between container walls to separation.

The moving speed of the electric charge generated at the contact interface at the time of contact depends on its material, surface condition, and the like.
Although it cannot be specified unconditionally, in the case of a powder made of a resin material having a very high electric resistance such as a toner used in an electrophotographic process, it takes some time for the transfer of electric charge at the contact interface to take some time. Can be easily assumed.

Therefore, in the above invention, the amount of static electricity generated on the particles or the wall surface of the container due to the operation of mixing and stirring is calculated as follows:
The prediction is made based on the required contact time from the contact between the particles and between the particle and the container wall to the separation.

This enables accurate simulation of static electricity generation due to mixing and stirring performed under a material condition such as a polymer having a very high electric resistance.

According to a fourth aspect of the present invention, there is provided an apparatus for simulating the behavior of particles in a container.
Based on the physical characteristic values of the particles contained in the container, the shape of the container, the mixing and stirring conditions, and the physical characteristic values of the container wall surface, the temporal position of the particles in the container is obtained, stored in the storage means, and then displayed in the container. In the particle behavior simulation device, the contact area between the particles and between the particles and the vessel wall is determined from the position of the particles over time, and based on the determined contact area, the particles are generated on the particles or the vessel wall due to the mixing and stirring operation. It is characterized by comprising calculating means for calculating the amount of static electricity, and display means for displaying the amount of static electricity calculated by the calculating means and the temporal position of the particles stored in the storage means.

According to the above invention, the amount of static electricity generated on the particles or the container wall surface due to the mixing and stirring operation is calculated by the calculation means based on the contact area between the particles and the particle-container wall surface. The position of each particle and the amount of generated static electricity calculated by the calculating means are displayed on the display means.

As a result, it is possible to predict and grasp the charge amount of each particle accompanying the mixing and stirring operation in the container accommodating the granular material. In addition, this makes it possible to provide a device for simulating the behavior of particles in a container, which can greatly reduce trial and error experiments and can provide an index for optimal control design.

According to a fifth aspect of the present invention, there is provided an apparatus for simulating the behavior of particles in a container.
According to a fourth aspect of the present invention, in the apparatus for simulating the behavior of particles in a container, the calculation means obtains an amount of static electricity based on a sliding friction area obtained from a contact area between the particles and between the particles and the container wall.

According to the above invention, the amount of static electricity generated on the particles or on the container wall due to the mixing and stirring operation is calculated by the calculating means based on the contact area between the particles and between the particles and the container wall. It is calculated based on the friction area.

As a result, a container capable of accurately simulating the amount of generated static electricity even under the condition of mixing and agitation in which the force in the direction of causing slip is more dominant than the contact force in the direction of the center of gravity of the particles. An apparatus for simulating the behavior of internal particles can be provided.

According to a sixth aspect of the present invention, there is provided an apparatus for simulating the behavior of particles in a container.
Based on the physical characteristic values of the particles contained in the container, the shape of the container, the mixing and stirring conditions, and the physical characteristic values of the container wall surface, the temporal position of the particles in the container is obtained, stored in the storage means, and then displayed in the container. In the particle behavior simulation device, the required contact time required from contact between the particles and between the particle and the container wall to separation is determined, and based on the determined required contact time, the particles or the container wall surface are caused by the mixing and stirring operation. A calculator for calculating the amount of generated static electricity; and a display unit for displaying the amount of static electricity calculated by the calculator and the temporal position of the particles stored in the storage unit. .

According to the above-mentioned invention, the amount of static electricity generated on the particles or the container wall surface due to the mixing and stirring operation by the calculation means is determined by the contact required between the contact between the particles and between the particle and the container wall surface to the separation. Based on the required time, it is calculated in correspondence with the position of each particle over time, and the position of each particle and the amount of generated static electricity calculated by this calculating means are displayed on the display means.

As a result, it is possible to provide an apparatus for simulating the behavior of particles in a container capable of accurately simulating the generation of static electricity due to mixing and stirring performed under a material condition such as a polymer having an extremely high electric resistance.

[0033]

BEST MODE FOR CARRYING OUT THE INVENTION

[Embodiment 1] An embodiment of the present invention will be described below with reference to FIGS.

In the method for simulating the behavior of particles in a container according to the present embodiment, the contact between the individual particles constituting the granular material is based on the contact force between two spheres as a basic element, as shown in FIG. Is modeled using the spring 1, the dashpot 2, and the friction slider 3.

The above-mentioned spring 1 models the elastic repulsive force of the inter-particle acting force, the dashpot 2 models viscous damping with energy dissipation, and the friction slider 3 models sliding friction. Things. Note that these functions only when the two balls are in contact with each other.

The spring constant k of the spring 1 giving elastic repulsion
Is calculated from the Young's modulus, Poisson's ratio, particle size, etc. of the particles based on Hertz's contact theory, and the viscous damping coefficient η of the dashpot 2 that gives viscous damping is calculated from the repulsion coefficient of the particles. The repulsive force P and the viscous damping force D acting between the spheres or against the wall surface are defined as the values obtained from a shear test or the like of the particle layer, respectively. Expressions (1) to (4) shown below are given for each of the linear direction and the tangential direction.

[0037]

(Equation 1)

Here, δ is the approach distance of the particles, ν is the Poisson's ratio of the material, E is the Young's modulus (longitudinal modulus) of the material, G is the transverse modulus of the material, r is the particle radius, V is the particle velocity, m is a particle mass, c is a dimensionless constant, and μ is a kinetic friction coefficient relating to tangential slip, and it is assumed that slip occurs at the contact point when | P _t |> μ · | P _n | is satisfied. In addition, the suffixes A and B indicate particles, the suffix n indicates the normal direction from the contact point to the particle center of gravity, and the suffix t indicates the tangential direction at the contact point. In the case of contact between a sphere and a wall surface, one particle radius r is set to ∞ (infinity).

The above Hertzian contact theory is based on the theory that when two solids come into contact with each other and receive a load, the contact portion elastically deforms to form a contact region, and a contact pressure is generated in that region. It is. In Hertzian contact theory, when the contact area is small enough for a solid, the contact is Hertzian c
For example, in a contact between a sphere and a sphere, when a sphere having a radius of curvature r _A · r _B is in contact under a normal force (normal force) P _n , the contact area is circular. The radius a and the approach distance δ _n between the two spherical surfaces are expressed by the following equations (5) and (6), respectively.

[0040]

(Equation 2)

Next, after modeling the contact force between the two spheres as described above, as shown in FIG. 3, all the particles 5, 6, 7, 8, 9, which are in direct contact with the particle 4 of interest. , The distance between the centers of gravity is calculated, and the amount of approach δ _n between each particle 5, 6, 7, 8, 9 and the particle of interest 4 is calculated. Then, each of the approach amounts δ _n obtained here and the spring constant k determined earlier,
By substituting the viscous damping coefficient η into the above-described equations (1) to (4) for obtaining the above-described repulsive force P and viscous damping force D, the distance between the particle 4 of interest and each particle 5, 6, 7, 8, 9. The repulsive force P and the viscous damping force D in the normal direction and the tangential direction are determined.

Based on the thus obtained repulsion force P and viscous damping force D, the normal contact force f _n and the tangential direction between the target particle 4 and each of the particles 5, 6, 7, 8, 9. Contact force f
_{and t} . The normal contact force f _n and the tangential contact force f _t are represented by the following equations (7) and (8). However, the contact force f _n and the tangential contact force _ft are vector quantities having different directions for each of the particles 5, 6, 7, 8, and 9 in contact.

[0043]

(Equation 3)

Then, the normal contact force f _n (vector amount) and the tangential contact force f _t between all the particles 5, 6, 7, 8, 9 directly in contact with the target particle 4 (Vector quantity), and in addition to the sum of the contact forces,
These forces are added together in consideration of forces such as gravity, and this is used as a force vector F acting on the particle 4 of interest.

By sequentially calculating all particles as the focused particle 4 by the above-described method, the force vector F received by each particle due to another particle, a wall surface, gravity, or the like can be calculated.

The equation of motion is solved based on the thus obtained force vector F acting on each particle, and information such as acceleration, velocity and position of each particle after a lapse of a minute time is calculated by the following equation.

[0047]

(Equation 4)

Here, the vector x is the position of the particle centroid, Δ
t is a minute time step. The dots on the symbols indicate differentiation with time, and the two dots indicate second-order differentiation.

In the above-described method, the positions of all particles after a lapse of a short period of time have been determined. Since the displacement of each particle is determined, a new external force is obtained based on the displacement.
By repeatedly performing the above-described method, the position of every particle in the region at every minute time is obtained.

Then, information on the position, speed, acceleration, etc. of every particle in the area obtained at every elapse of a minute time is recorded in an auxiliary storage device such as a hard disk as needed, thereby obtaining the behavior of the particles. To track. The above is the simulation method of the basic discrete element method for obtaining the temporal position.

In the behavior simulation method of the present embodiment, the simulation of the discrete element method
Furthermore, a model for generating static electricity due to contact between particles and between particles and a wall surface is introduced.

The model of generation of static electricity due to contact here is a model in which the amount of static electricity generated by mixing and stirring particles depends on the contact area when the particles come into contact. That is, as shown in FIG. 1, the area (contact area) of the contact surface formed when two particles 10 and 11 represented by two spheres come into contact is determined, and the amount of charge depending on the contact area is determined. It is said that the movement occurs between the two particles, and after the two particles separate, an amount of static electricity depending on the contact area is generated between the two particles.

The contact area between the two particles is determined in the same manner as described above using the model of the contact force between the two spheres in FIG. Sometimes, the force acting on each particle is calculated, and this can be obtained based on the Hertzian contact theory described above, which gives the relationship between the force when the two spheres come into contact and the radius of the contact surface.

More specifically, similarly to the above, as shown in FIG. 3, the distance between the centers of gravity is calculated for all the particles 5, 6, 7, 8, and 9 that are in direct contact with the particle 4 of interest. Then, the approach amount δ _n between each of the particles 5, 6, 7, 8, 9 and the target particle 4 is obtained.

Then, each of the approach distance δ _n obtained here and the spring constant k determined above are substituted into the above-described equation (1) for obtaining the repulsive force P _n in the normal direction, so that the target particle 4 The repulsion _Pn in the normal direction between the particles 5, 6, 7, 8, and 9 is obtained. By substituting the thus obtained repulsion force P _n in the normal direction into the above-described equation (5), the target particle 4 and each of the particles 5, 6, 7, 8
• Determine the radius a of each contact surface between 9 and determine the area of each contact surface.

Next, the determined target particle 4 and each particle 5.6
Based on the area of each contact surface between 7, 8, and 9, the amounts of static electricity generated by individual contacts are calculated and summed up to obtain the amount of static electricity generated in the particle 4 of interest.

The amount of static electricity generated when each particle comes into contact with another particle or the wall surface of the container is calculated by sequentially calculating all particles as the particle of interest 4 using the above method.

In the above method, the amount of generated static electricity is obtained based on the contact area of all the particles for a certain time. The displacement of each particle is obtained by the above-described method of obtaining the position of the particles over time. Therefore, a new external force is obtained based on this displacement to obtain a new contact, and the amount of static electricity generated corresponding to the temporal position of the particle can be obtained by repeatedly calculating the above method based on the contact area at that position. .

Then, the amount of static electricity generated corresponding to the position with the passage of time for all the particles in the obtained region is recorded in an auxiliary storage device such as a hard disk. Thereafter, each recorded data is read using a program capable of displaying a particle position, a charge amount, and the like by graphics, visualized, and a calculation result is displayed.

Actually, in the case of insulator particles that cause charging, the charge transferred in the previous contact acts to prevent the transfer of the charge in the next contact, so that different types of particles A and particles and each q _Amax · q _Bmax saturation charge amount obtained in contact with the B, and the charge amount of immediately before contact with the q _a · q _B, the amount of charge transfer Δq _a · Δq _B caused by this contact, the following equation It can be represented by (9).

[0061]

(Equation 5)

Here, α is a physical characteristic value of the particles A and B (in the case of contact with the container, the particles and the wall surface of the container) and the particles A and B
This is a function that depends on the contact area between the particles (in the case of contact with the container, the contact area between the particles and the wall surface of the container), and can be expressed by the following equation (10).

[0063]

(Equation 6)

Here, Q _s is the charge transfer amount per unit contact area, S is the contact area, V _e is the charge transfer speed at the contact interface, R is the charge transfer resistance at the contact interface, β
₁ is a constant.

It is easy to imagine that even when particles of the same kind come into contact with particles of the same kind having different charge amounts, the charge moves in a direction in which the difference in charge amount is reduced. Since the amount of movement becomes large, the amount of charge transfer Δq _A1 · Δq _A2 at the time of contact between the same kind of particles A1 and A2 can be expressed by the following equation (11).

[0066]

(Equation 7)

Here, q _A1 and q _A2 are the respective charge amounts immediately before the contact, and α is the physical characteristic value of the particles A1 and A2 and the particles A1 and A2.
It is a function that depends on the contact area between the two.

Therefore, the amount of static electricity generated by the contact is determined depending on the contact area. However, in practice, of course, the movement of the charge due to the amount of charge between the particles at the position or between the particle and the wall surface of the container. Is predicted based on the likelihood of occurrence (or the likelihood of occurrence). This is the same in other embodiments described below.

Next, a description will be given of a simulation apparatus capable of performing the above-described display by performing the above-described behavior simulation method of the particles in the container. The simulation device according to the present embodiment is configured by, for example, a personal computer, and as shown in FIG. 4, a storage device 21 for physical property values of particles, a three-dimensional shape storage device 2 for a container in which particles are stored.
2, storage device for mixing and stirring conditions 23, storage device 24 for physical property values of container walls, particle position calculation unit 25, static electricity amount calculation unit 26, calculated particle position storage unit 27, calculated static electricity amount storage unit 28, and display means Static electricity / particle position display device 2
9.

Storage device 21 for physical property values of the above particles
Stores physical characteristic values such as Young's modulus, Poisson's ratio, particle size, viscous damping coefficient, and friction coefficient of the particles described above.

The storage unit 24 of the physical property value of the container wall stores physical property values such as Young's modulus, Poisson's ratio, particle size, viscous damping coefficient and friction coefficient related to the material constituting the container wall. I have.

Further, the particle position calculation section 25 and the static electricity amount calculation section 26 constitute calculation means of the present invention.

The operation of the simulation apparatus having the above configuration will be described with reference to flowcharts shown in FIGS. 5 and 6 and FIGS. 3 and 4. First, the shape of the container, the mixing and stirring conditions, the fluid and the physical characteristic values of the container wall surface are stored in the respective storage devices 21 to 24, and the initial state is set (S
1). Next, the spring constants (normal and tangential directions) required for the calculation of the contact force are calculated from the Young's modulus and Poisson's ratio of the material, and the viscous damping coefficients (normal and tangential directions) are calculated.
Is calculated by the coefficient of restitution of the particles, and a constant required for the simulation is calculated (S2).

When the above processing is completed, attention is paid to one particle in the container, and the contact of the particle 4 of interest with another particle is determined (S3). The contact is determined by comparing the distance between the particles and the sum of the particle radii.

As described above, for the particles whose contact has been confirmed in the contact determination in step S3 (in some cases, the wall surface of the container), the distance between the centers of gravity of the contact particles 5, 6, 7, 8, and 9 and the target particle 4 is determined as described above. Calculation (S4), the distance between the centers of gravity is calculated, and the above-described calculation is performed to calculate the repulsive force and the viscous damping force, respectively (S5).
The contact force between all the particles 5, 6, 7, 8, and 9 in contact with the target particle 4 is calculated (S6).

When the contact force is calculated in this way, the target particle 4 obtained in S5 and all the particles 5 in contact with the target particle 4
The contact area is determined based on each repulsive force between 6, 7, 8, and 9, and as a function depending on the contact area,
At this position, the amount of static electricity generated in the target particle 4 is obtained (S7).

Next, the above-described calculation processing is performed for each particle as a target particle 4 for each particle. At this time, it is first determined whether or not all particles have been completed (S11). Focusing on the next particle (S9), S3
Return to Then, the above processing is repeated.

When it is confirmed in S8 that the calculation has been completed for all the particles, the acceleration, velocity, etc., and the particle position of the target particle 4 are calculated based on the contact force calculated in S6. (S10 / S11) Then, the calculated particle position and static electricity amount are recorded (S12).

Finally, after it is determined whether or not the step of the specified time has been completed (S13), if the process of the predetermined time remains, the time step is advanced by one (S14).
Returning to S3, the above-mentioned processes S3 to S12 are repeated.

Thereafter, the particle position and the amount of static electricity recorded in the auxiliary storage device are read by the static electricity amount / particle position display device 29 shown in FIG. 4 and visualized and displayed by graphics.

As shown in FIG. 6, the display operation of the static electricity amount / particle position display device 29 is as follows. First, the outline of the container is displayed (S21), and then the reading of the particle position and the static electricity amount is performed. Perform (S22). Next, the particles are displayed at the calculated particle positions (S23), and the particles are colored and displayed according to the amount of static electricity (S24). Thus, the processing of one time step is completed.

Next, after determining whether or not the specified time step has been completed (S25), if there is a next time step, the time step is advanced (S26), and S21 is performed.
And the processing of S21 to S24 is repeated. Thus, the position of the particles and the amount of static electricity in the container for each time step can be sequentially grasped.

As described above, in the method for simulating the behavior of particles in a container according to the present embodiment, the amount of static electricity generated on the particles or on the wall surface of the container due to the operation of mixing and stirring is determined between the particles and between the particles and the wall surface of the container. It is determined as depending on the contact area.

As a result, the number of trial and error experiments can be reduced and the effect of various parameters can be tested on a computer as compared with the prior art, so that the development period can be significantly reduced and development costs can be reduced.

Further, by applying the present embodiment to the simulation of the stirring and charging of the two-component developer, it is possible to reproduce the generally well-known charging curve of the electrophotographic two-component developer. For this reason, it is expected that the number of experiments conventionally performed to achieve the required charging characteristics will be reduced.

In the apparatus for simulating the behavior of particles in a container according to the present embodiment, the particle position calculating unit 25 and the static electricity amount calculating unit 26 use the container shape, mixing and stirring conditions, physical property values of the particles, and the wall surface of the container. Based on the physical property values, the amount of generated static electricity is calculated in accordance with the position of each particle over time.

The positions of the particles and the amount of static electricity calculated by the particle position calculator 25 and the static electricity amount calculator 26 are displayed on the static electricity / particle position display device 29.

As a result, it is possible to predict and grasp the amount of static electricity generated by each particle due to the mixing and stirring operation in the container containing the granular material. In addition, this makes it possible to provide a device for simulating the behavior of particles in a container, which can greatly reduce trial and error experiments and can provide an index for optimal control design.

In this embodiment, the mixing and stirring operation in the container containing the granular material is dealt with. However, the present invention is not limited to this. The present invention is also applicable to transportation in pipes in various fields and powders in other devices.

[Second Embodiment] The following will describe another embodiment of the present invention with reference to FIG. For the sake of convenience, members having the same functions as those shown in the drawings of the first embodiment are denoted by the same reference numerals, and description thereof is omitted.

Experimentally, it has been confirmed that when slippage occurs at the contact interface during contact, the charge amount increases. From a microscopic perspective, it can be fully imagined that the material on the particle surface is scraped off by the sliding friction and loses the charge it holds by adhering to the partner particle, and the effect of the surface roughness is offset by the sliding friction. It can also be imagined that an increase in the true contact area facilitates the movement of charges on the contact surface.

Therefore, the behavior simulation method of the present embodiment is a model in which the amount of static electricity generated by mixing and stirring particles depends on the flow friction area obtained from the contact area when the particles come into contact. That is, as shown in FIG. 1, the area (contact area) of a contact surface formed when two particles 10 and 11 represented by two spheres come into contact is determined, and from this contact area, as shown in FIG. The area of the flow friction surface is determined, and an amount of charge transfer depending on the area occurs between the two particles, and after separation, an amount of static electricity is generated between the two particles.

More specifically, the target particle 4 and each of the particles 5, 6,.
The respective sliding friction areas are determined based on the area of each contact surface between 7, 8, and 9, and the amount of static electricity generated in each individual contact is calculated based on the sliding friction area, and the sum is calculated. 4 (see FIG. 3).

Thus, depending on the conditions of mixing and stirring,
There are many conditions in which the force in the direction that causes slippage is more dominant than the contact force in the direction between the centers of gravity of particles, but even in such a case, the amount of generated static electricity can be accurately simulated.

As described above, in practice, of course, the transfer of charges due to the charge amount between the particles at the position or between the particles and the wall surface of the container (probability of occurrence).
Predict based on also. Here, the above equations (9) and (11)
Is represented by (10) as in the first embodiment. Here, S is a sliding friction area.

[Embodiment 3] The following will describe still another embodiment of the present invention with reference to FIG. For the sake of convenience, members having the same functions as those shown in the drawings of the first embodiment are denoted by the same reference numerals, and description thereof is omitted.

The speed of movement of the electric charge generated at the contact interface at the time of contact depends on the material, surface condition, and the like.
Although it cannot be specified unconditionally, it is easy for a powder made of a resin material having a very high electric resistance, such as a toner used in an electrophotographic process, to take some time for the transfer of electric charge at a contact interface. Can be assumed.

Therefore, in the behavior simulation method according to the present embodiment, a model in which the amount of static electricity generated by mixing and stirring particles depends on the time required for contact from contact of the particles to separation (required contact time). It is. That is, by calculating and tracking the position of the particles at each elapse of a minute time, as shown in FIG. 8, the contact time required from contact to separation when the two particles 10 and 11 come into contact is measured, and the required time is calculated. It is said that a time-dependent amount of charge moves and generates static electricity.

Specifically, the target particle 4 and each of the particles 5, 6,.
The respective required contact times between 7.8, 9, and 9 are obtained, and the amounts of static electricity generated by the individual contacts are calculated based on the required contact times and summed up to obtain the amount of static electricity generated in the target particle 4 ( (See FIG. 3).

As a result, it is possible to accurately simulate the generation of static electricity due to mixing and stirring performed under a material condition such as a polymer having a very high electric resistance.

As described above, in practice, of course, the transfer of electric charge due to the amount of electric charge between particles or between the particle and the wall surface of the container at the position (probability of occurrence).
Predict based on also. Here, the above equations (9) and (11)
Is represented by the following equation (12).

[0102]

(Equation 8)

Here, Q _T is the amount of charge transfer per unit contact time, T is the required contact time, V _e is the charge transfer speed at the contact interface, R is the charge transfer resistance at the contact interface, and β ₂ is a constant. is there.

[0104]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS As an embodiment of the method and apparatus for simulating the behavior of particles in a container according to the present invention, a cylindrical stirring member is disposed in a rectangular parallelepiped container, and toner (small particles) and carrier (large particles) are mixed. Two types of particles, large and small, were filled and stirred, and the change with time in the amount of static electricity generated by contact was observed. Here, it is assumed that the generation of static electricity due to the contact occurs only when the toner, which is two kinds of large and small particles, and the carrier are in contact, and no static electricity is generated when the toner particles or the carrier are in contact with each other.

Further, in order to know the relationship between the mixture ratio of large and small particles and the amount of generated static electricity, simulation was performed on five samples A, B, C, D, and E having different mixture ratios as shown in FIG. Was.

The calculation is performed for up to 10 seconds, visualized and displayed by graphics, and in order to more accurately grasp the amount of static electricity generated quantitatively, the amount of static electricity of each of the toner and the carrier (charge amount: cumulative amount of generated electrostatic amount) Value) was created based on the obtained value of the generated static electricity.

The calculation conditions are as shown in Table 1.

[0108]

[Table 1]

FIG. 10 shows the change over time in the charge amount of the toner.
FIG. 11 shows the change over time in the charge amount of the carrier.

When attention is paid to the toner, roughly, the lower the toner mixture ratio, the more rapidly the amount of static electricity generated in the toner increases, but it can be confirmed that if the mixture ratio is extremely low, the degree of rise is rather slow.

[0111]

According to the method for simulating the behavior of particles in a container according to the first aspect of the present invention, as described above, the amount of static electricity generated on the particles or the wall surface of the container due to the mixing and stirring operation is determined by determining the position of the particles over time. This is a prediction method based on the contact area between the particles and the contact area between the particles and the container wall surface determined based on the base.

Therefore, as compared with the prior art, the number of trial and error experiments can be reduced, and the effects of various parameters can be tested on a computer.

Further, by applying the present invention to a simulation of stirring and charging of a two-component developer, it is possible to reproduce a generally well-known charging curve of an electrophotographic two-component developer. For this reason, it is expected that the number of experiments performed conventionally to achieve the required charging characteristics will be reduced.

According to the method for simulating the behavior of particles in a container according to the second aspect of the present invention, as described above, the method for simulating the behavior of particles in a container according to the first aspect includes the step of predicting the amount of static electricity between particles and between particles. -This method is performed based on the sliding friction area obtained from the contact area between the container wall surfaces.

Therefore, in addition to the effect of the first aspect of the invention, depending on the conditions of the mixing and stirring, there is also a condition in which the force in the direction of causing slip is more dominant than the contact force in the direction of the center of gravity of the particles. Although there are many, even in such a case, there is an effect that the amount of generated static electricity can be simulated more accurately.

According to the method for simulating the behavior of particles in a container according to the third aspect of the present invention, as described above, the amount of static electricity generated on the particles or on the wall surface of the container due to the mixing and stirring operation is determined as follows.
This is a method of estimating based on the required contact time required from contact between particles and between particles and the wall of the container to separation.

Therefore, in the same manner as the effect of the invention according to claim 1, the number of trial and error experiments can be reduced and the effect test of various parameters on a computer can be carried out, and the development period can be greatly reduced. Expected to be shorter and development costs reduced.

Further, by applying the present invention to a simulation of stirring and charging of a two-component developer, it is possible to reproduce a generally well-known charging curve of an electrophotographic two-component developer. For this reason, it is expected that the number of experiments conventionally performed to achieve the required charging characteristics will be reduced.

In addition, there is an effect that it is possible to accurately simulate the generation of static electricity due to mixing and stirring performed under a material condition such as a polymer having a very high electric resistance.

According to the fourth aspect of the present invention, the behavior simulation apparatus for particles in a container obtains the contact area between particles and between particles and the wall surface of the container from the aging position of the particles as described above.
Calculating means for calculating the amount of static electricity generated on the particle or container wall due to the mixing and stirring operation based on the determined contact area; and the amount of static electricity calculated by the calculating means and stored in the storage means. Display means for displaying the position of the particles over time.

Therefore, it is possible to predict and grasp the amount of static electricity generated in the container accompanying the mixing and stirring operation in the container containing the granular material. In addition, this makes it possible to significantly reduce the number of trial and error experiments and to provide an apparatus for simulating the behavior of particles in a container that can provide an index for optimal control design.

According to a fifth aspect of the present invention, there is provided an apparatus for simulating the behavior of particles in a container according to the fourth aspect of the present invention, wherein the calculating means comprises an inter-particle and a particle-container. In this configuration, the amount of static electricity is obtained based on a sliding friction area obtained from a contact area between wall surfaces.

Therefore, it is possible to more accurately simulate the amount of generated static electricity even under the condition of mixing and stirring in which the force in the direction of causing slip is more dominant than the contact force in the direction of the center of gravity of the particles. The effect of being able to provide a behavior simulation device for particles in a container is provided.

The behavior simulation device for particles in a container according to the invention according to claim 6 determines the contact time required from contact between particles and between particles and the wall surface of the container to separation, and obtains the required contact time as described above. Calculating means for calculating the amount of static electricity generated on the particles or the wall of the container due to the operation of mixing and stirring, based on Display means for displaying the position.

Therefore, it is possible to predict and grasp the amount of static electricity generated in the container accompanying the mixing and stirring operation in the container containing the granular material. Further, there is an effect that it is possible to provide an apparatus for simulating the behavior of particles in a container, which can accurately simulate the generation of static electricity due to mixing and stirring performed under a material condition such as a polymer having an extremely large electric resistance.

[Brief description of the drawings]

FIG. 1 shows a first embodiment of a method for simulating the behavior of particles in a container according to the present invention,
FIG. 4 is an explanatory diagram showing a model in which the amount of static electricity generated when two particles come into contact depends on the contact area.

FIG. 2 is a conceptual diagram of a contact force model for calculating a repulsive force, a viscous damping force, and a frictional force between two particles, which are basic elements for tracking the behavior of a granular material.

FIG. 3 is a conceptual diagram illustrating a method of calculating a contact force with neighboring particles that is considered when calculating a force acting on a particle of interest.

FIG. 4 is a block diagram showing a configuration of a simulation device used in the method for simulating the behavior of particles in a container.

FIG. 5 is a flowchart showing a method of calculating particle behavior and the amount of generated static electricity in the method of simulating the behavior of particles in a container.

FIG. 6 is a flowchart showing a method for displaying a particle position and an amount of static electricity in the behavior simulation method for particles in a container.

FIG. 7 illustrates a second embodiment of the method for simulating the behavior of particles in a container according to the present invention, and illustrates a model in which the amount of static electricity generated when two particles come into contact depends on the sliding friction area. FIG.

FIG. 8 shows a third embodiment of the method for simulating the behavior of particles in a container according to the present invention,
FIG. 4 is an explanatory diagram showing a model in which the amount of static electricity generated when two particles come into contact depends on the required contact time.

FIG. 9 is an explanatory view showing each sample of an example of the amount of static electricity generated by the method for simulating the behavior of particles in a container according to the present invention.

FIG. 10 is a graph showing the change over time in the charge amount of the toner as a result of the example of the amount of static electricity generated by the method for simulating the behavior of particles in a container according to the present invention.

FIG. 11 is a graph showing the change over time in the charge amount of a carrier, which is the result of an example of the amount of static electricity generated by the method for simulating the behavior of particles in a container according to the present invention.

[Explanation of symbols]

21 Storage Device for Physical Property Value of Particles 24 Storage Device for Physical Property Value of Container Wall (Container Wall Charge Amount Storage Means) 25 Particle Position Calculation Unit (Calculation Means) 26 Static Electricity Calculation Unit (Calculation Means) 29 Static Electricity / Particle position display device (display means)

Claims (6)

[Claims] 1. The time-dependent position of particles contained in a container is determined and displayed based on the shape of the container, mixing and stirring conditions, physical property values of the particles, and physical property values of the container wall surface. In the behavior simulation method, it is necessary to predict the amount of static electricity generated on the particles or the container wall surface due to the operation of mixing and agitation based on the contact area between the particles and the particle-container wall surface obtained based on the temporal position of the particles. Characteristic behavior simulation method of particles in a container. 2. The method for simulating the behavior of particles in a container according to claim 1, wherein the prediction of the amount of static electricity is performed based on a sliding friction area obtained from a contact area between particles and between a particle and a wall surface of the container. . 3. The time-varying position of the particles contained in the container is determined and displayed based on the shape of the container, mixing and stirring conditions, physical property values of the particles, and physical property values of the wall surface of the container. In the behavior simulation method, the amount of static electricity generated on particles or the container wall due to the operation of mixing and stirring is predicted based on the contact time required from contact between particles and between particles and container wall to separation. Simulation method for behavior of particles in a container. 4. A physical property value of particles contained in the container,
Based on the shape of the container, the mixing and stirring conditions, and the physical property values of the container wall surface, the aging position of the particles in the container is determined and stored in the storage means and displayed after the particle behavior simulation device. Calculating means for calculating the contact area between the particles and between the particles and the wall surface of the container, and calculating, based on the determined contact area, the amount of static electricity generated on the particles or the wall surface of the container due to the mixing and stirring operation; A behavior simulation apparatus for particles in a container, comprising: display means for displaying the amount of static electricity calculated by the means and the temporal position of the particles stored in the storage means. 5. The apparatus according to claim 4, wherein said calculating means calculates the amount of static electricity based on a sliding friction area obtained from a contact area between the particles and a contact area between the particles and the container wall. . 6. A physical property value of the particles contained in the container,
A device for simulating the behavior of particles in a container, which is obtained based on the shape of the container, the mixing and stirring conditions, and the physical property values of the container wall surface, and which displays the time-dependent positions of the particles in the container and stores them in the storage means, and displays the results. Calculating means for determining a required contact time required from contact between the wall surfaces to separation, and calculating, based on the determined required contact time, an amount of static electricity generated on the particles or the container wall surface due to the mixing and stirring operation; A behavior simulation apparatus for particles in a container, comprising: display means for displaying the amount of static electricity calculated by the means and the temporal position of the particles stored in the storage means.