JP4125111B2 - Behavior analysis apparatus, behavior analysis method, and program - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a behavior analysis apparatus, a behavior analysis method, and a program, and more particularly, to a behavior analysis apparatus that analyzes the behavior of an elastic structure and particles contained in a container, and the behavior of the elastic structure and particles contained in a container. The present invention relates to a behavior analysis method to be analyzed, and a program for causing a computer to execute the behavior analysis method.
[0002]
The elastic structure is in the form of a sheet for stirring and transporting the particles in the container, and the elastic structure is bent by contact with the particles and the container by the behavior analysis apparatus, behavior analysis method, and program. The behavior of particles and elastic structures in the phenomenon of stirring and conveying particles is analyzed.
[0003]
[Prior art]
In general, in a copying machine or a printer using electrophotographic technology, a visible image made of toner is formed on the surface of a photosensitive member by a developing device.
[0004]
Fine toner particles are supplied from an external container into the developing unit. To supply the toner particles into the developing unit and perform appropriate development, the toner particles in the container are mixed with a sheet-like stirring member. And stirring.
[0005]
Incidentally, in recent years, particle behavior analysis is being performed in order to analyze the stirring state of particles in a container stirred by a stirring member, and this analysis result is being used for optimizing the structure of a stirring device.
[0006]
In the stirring state of the particles, the particles and the particles and the container wall are always in contact with each other. Therefore, in the particle behavior analysis, it is necessary to obtain a contact force between particles or between a particle and a container wall, and a discrete element method (DEM) that can calculate a system in which the contact force is dominant is generally used.
[0007]
As for the discrete element method (DEM), a specific calculation method is described in Non-Patent Document 1, for example, and only its features will be briefly described here.
[0008]
The discrete element method (DEM) is a method for obtaining the behavior of a particle for each time by solving an equation of motion based on the force acting on the particle. As a contact force acting between two objects, a spring-dashpot model is used. Based on the elastic repulsive force and viscous damping force. Further, in the contact with the container wall or the like by the particle, the contact between the particle and the container wall can be handled by applying the same model as the contact between particles.
[0009]
By using such a discrete element method (DEM), the stirring state of the particles by the stirring member can be analyzed.
[0010]
A configuration example and a calculation concept of a typical processing program for conventional particle behavior analysis will be described below with reference to FIGS. FIG. 14 is a program configuration diagram schematically showing a configuration example of a conventional processing program, and FIG. 15 is a diagram showing a concept of conventional contact calculation.
[0011]
In FIG. 14, reference numeral 100 denotes a control unit that controls the entire processing of the program.
[0012]
Reference numeral 111 denotes an initial condition setting unit that sets initial conditions of particles, physical property values such as radius and specific gravity, and the calculation conditions such as the shape, size, position, and time step of the rigid structure constituting the analysis region.
[0013]
Reference numeral 112 denotes an acting force calculation unit between particles, which calculates a contact force that is an acting force between two particles.
[0014]
Reference numeral 113 denotes an acting force calculation unit between the particle and the member, and calculates a contact force that is an acting force between the particle and a member such as a container wall arranged in association with the particle.
[0015]
Reference numeral 114 denotes a calculation unit for an external force acting on the particle, and calculates an external force such as gravity, magnetic force, and electrostatic force acting on the particle.
[0016]
Reference numeral 118 denotes a particle displacement calculator that solves the equation of motion based on the force acting on the particle and calculates the velocity and displacement of the particle.
[0017]
Reference numeral 1311 denotes a particle behavior display unit, which displays the positions of particles and members at each time.
[0018]
The particle-to-particle force calculation unit 112 and the particle-to-member force calculation unit 113 determine a contact distance δ between two objects, determine contact / non-contact using the distance, Calculate contact force determined by tangential displacement and relative speed. Among these, as for the contact distance, the contact distance δ between the two particles is the length of the overlapping portion of the particles on a straight line connecting the centers of the two particles 1411 and 1412 as shown in FIG. As shown in FIG. 15B, the contact distance between the particle 1411 and the member 1413 on a straight line perpendicular to the surface of the member 1413 from the center of the particle 1411 is obtained as shown in FIG. Ask for it. Here, the center of the particle is defined by the center of a circle or a sphere having a radius of curvature of the normal contact portion or the closest portion.
[0019]
In the actual calculation, the behavior of the particles can be obtained by repeating the processing by the setting unit 111, the calculation units 112 to 114, and the calculation unit 118 in FIG.
[0020]
By the way, when the stirring member is an elastic structure that can undergo large elastic deformation, such as a sheet-like stirring member, the elastic structure bends due to contact with particles or a container. It was necessary to dynamically consider the deflection of the object. In particular, the behavior of the elastic structure changes depending on the physical properties such as the mass and Young's modulus of the particles, the arrangement of the particles in the container, and the hardness and dimensions of the elastic structure. It was necessary to solve the behavior in a coupled manner.
[0021]
For calculating the behavior of an elastic structure, methods using a finite element method or a spring-mass model are known. In particular, as described in Non-Patent Document 2, for example, the latter is represented by a plurality of mass points connected by a rotary spring and an expansion spring, and by solving the equation of motion of the mass points, the elastic structure is obtained. This is a method that can calculate the behavior of each time in consideration of the deflection, and can realistically calculate the behavior of the elastic structure.
[0022]
[Non-Patent Document 1]
Tanaka et al., Transactions of the Japan Society of Mechanical Engineers (B), 57, 534, 60 (1991)
[0023]
[Non-Patent Document 2]
Noro et al., Proceedings of the 10th Annual Meeting of the Japan Society of Mechanical Engineers, 105 (1997)
[0024]
[Problems to be solved by the invention]
By the way, when the finite element method is used to analyze the elastic structure (stirring member) and the particle behavior, the finite element based on the position of the particle at each time step is used. It is necessary to create and calculate the division, which is not practical in terms of the time required for the calculation.
[0025]
On the other hand, when the spring-mass model is used for the analysis of the elastic structure, the calculation time can be shortened. However, when the spring-mass model is used, there is a problem in that it is necessary to perform contact determination and calculation of contact force between the elastic structure represented by the mass point and the particle.
[0026]
Further, in the display of the calculation result, it is required to display the stirring state and the contact state by simultaneously displaying the particles and the elastic structure. In general display of elastic structure behavior, a method is used in which the mass points are connected with line segments. However, since this display method does not represent the thickness of the elastic structure, the elastic structure and particles or container walls are displayed. There was a problem that it was not possible to accurately represent the state of contact with the.
[0027]
The present invention has been made in view of such problems, and provides a behavior analysis apparatus, a behavior analysis method, and a program that make it possible to easily and accurately analyze the behavior of an elastic structure and particles. For the purpose.
[0028]
It is another object of the present invention to provide a behavior analysis apparatus, a behavior analysis method, and a program that can easily display the behavior of an elastic structure and particles as analysis results.
[0029]
[Means for Solving the Problems]
  In order to achieve the above object, according to the behavior analysis apparatus of the present invention, the processing device executes a program read from the memory, thereby causing particle displacement calculation means, elastic force calculation means, acting force calculation means, and In the behavior analysis apparatus that realizes the function of the mass displacement calculation means and displays the behavior of the elastic structure and particles contained in the container on the display means, the memory includes:Stores thickness data of the elastic structure, particle data, force data acting on the particles, spring-mass model data representing the elastic structure, and mass point connecting line segment data connecting the mass points of the spring-mass model.The particle displacement calculation means includes:Having particle data stored in the memoryForce acting on particlesAs a result, contact force acting on each particle and resultant force including gravityBased on,The displacement of the particles along the time seriesUsing the equation of motionAnd the elastic force calculation meansSpring-mass points stored in the memoryBased on the model, bending spring force and elastic spring force acting on each mass point as the elastic force of the elastic structureTheAnd the acting force calculation meansUsing the position data of the mass point connecting line segment stored in the memory and the thickness data of the elastic structure, the relative position between the mass point connecting line segment and the particle is obtained, and the acting force according to the relative position is obtained. calculateWhen,Work on each mass pointBy the elastic force calculation meansCalculationElastic force and acting force calculation meansCalculationBased on the applied force, the displacement of the mass point representing the elastic structure is changed along the time series.Using the equation of motionThe behavior of the particles and the elastic structure is calculated on the basis of the mass point displacement calculating means for calculating, the displacement of the particles calculated by the particle displacement calculating means and the displacement of the mass points calculated by the mass point displacement calculating means.Along the time seriesDisplay means for displayingThe
[0030]
  In order to achieve the above object, the present inventionBehavior analysis deviceAccording to the behavior analysis method, processing of the particle displacement calculation step, elastic force calculation step, acting force calculation step, mass displacement calculation step, and display step is realized by the processing device executing the program read from the memory. And display the behavior of the elastic structure and particles contained in the container on the display device.Behavior analysis deviceIn the behavior analysis method,Has particle data stored in memoryForce acting on particlesAs a result, contact force acting on each particle and resultant force including gravityBased on,The displacement of the particles along the time seriesUsing the equation of motion, the processorIn the elastic force calculation step,Based on a spring-mass model representing the elastic structure stored in the memory, the processing device generates a bending spring force and an expansion spring force acting on each mass point as the elastic force of the elastic structure.And in the acting force calculation step,The relative position between the mass point connecting line segment and the particle is obtained using the position data of the mass point connecting line segment connecting the mass points representing the elastic structure stored in the memory and the thickness data of the elastic structure. The processing device applies an acting force according to the relative position.CalculationShiThe mass point displacement calculating stepWork on each mass pointThe elastic force calculation stepInCalculated elastic force, in the acting force calculation stepLeaveBased on the calculated acting force, the displacement of the mass point representing the elastic structure is changed along the time series.Using the equation of motion, the processorWhen calculated, in the display step, based on the displacement of the particle calculated by the particle displacement calculation step and the displacement of the mass point calculated by the mass point displacement calculation step,Depends on display deviceBehavior of the particles and the elastic structureThe processor controls the display of the time series ofIt is characterized byThe
[0031]
  In order to achieve the above object, the present inventionLet the computer execute the behavior analysis methodAccording to the program, in a program for causing a computer to execute a behavior analysis method for causing a display device to display the behavior of an elastic structure and particles contained in a container.Has particle data stored in memoryForce acting on particlesAs a result, contact force acting on each particle and resultant force including gravityBased on,The displacement of the particles along the time seriesUsing the equation of motion, the processorA particle displacement calculation step to be calculated;Based on a spring-mass model representing the elastic structure stored in the memory, the processing device generates a bending spring force and an expansion spring force acting on each mass point as the elastic force of the elastic structure.An elastic force calculation step to calculate,The relative position between the mass point connecting line segment and the particle is obtained using the position data of the mass point connecting line segment connecting the mass points representing the elastic structure stored in the memory and the thickness data of the elastic structure. The processing device applies an acting force according to the relative position.An action force calculating step to calculate;Work on each mass pointThe elastic force calculation stepInCalculated elastic force, in the acting force calculation stepLeaveBased on the calculated acting force, the displacement of the mass point representing the elastic structure is changed along the time series.Using the equation of motion, the processorBased on the mass point displacement calculation step to be calculated, the particle displacement calculated by the particle displacement calculation step and the mass point displacement calculated by the mass point calculation step,Depends on display deviceBehavior of the particles and the elastic structureThe time series display ofAnd a display step controlled by the processing device.
[0032]
DETAILED DESCRIPTION OF THE INVENTION
Hereinafter, embodiments of the present invention will be described with reference to the drawings.
[0033]
[First Embodiment]
The first embodiment of the present invention will be described below. Here, calculation of particle behavior based on particles, elastic structures, and related members in a two-dimensional cross section will be described.
[0034]
FIG. 1 is a program configuration diagram showing a schematic overall configuration of a processing program of a particle behavior analysis apparatus when an analysis region has an elastic structure. Note that the constituent parts denoted by reference numerals 100 to 114 and 118 are the same as those already described with reference to FIG.
[0035]
However, in the initial condition setting unit 111, in addition to the calculation conditions of the particles and members in the initial condition setting unit shown in FIG. 14, the position, size, physical property value of the elastic structure, the number of mass points representing the elastic structure (longitudinal direction) Information about the elastic structure such as the number of divisions) is further set. Based on these values, the size of the elastic structure represented by one mass point is determined, and the mass and position of the mass point and the spring constants of the bending spring and the expansion spring are obtained.
[0036]
Reference numeral 115 denotes an elastic force calculation unit of the elastic structure, which calculates a bending spring force and an expansion spring force acting on each mass point based on the spring-mass point model. The spring-mass model calculation that is normally performed can be applied to this calculation.
[0037]
Reference numeral 116 denotes an elastic structure and particle acting force calculation unit, which performs contact determination and contact force calculation based on the position of the mass point representing the elastic structure, the thickness of the elastic structure, and the position and radius of the particle. .
[0038]
Reference numeral 117 denotes an acting force calculation unit for the elastic structure and the member, which performs contact determination and contact force calculation based on the position of the mass point representing the elastic structure, the thickness of the elastic structure, and the position of the member.
[0039]
Reference numeral 119 denotes a displacement calculation unit of the elastic structure. By solving the equations of motion based on the forces acting on the respective mass points obtained by the elastic force calculation unit 115, the action force calculation unit 116, and the action force calculation unit 117, Find the speed and displacement of the mass point. In this case, the method usually used in the spring-mass model calculation can be applied.
[0040]
By repeating the processes of the initial condition setting unit 111 and the calculation units 112 to 119, the behavior of the mass points representing the particles and the elastic structure at each time can be obtained.
[0041]
Reference numeral 120 denotes a behavior display unit for the particles and the elastic structure, and displays the behavior of the particles and the members and the elastic structure along the time series.
[0042]
In the present embodiment, the behavior of the particles and the elastic structure is coupled and solved by calculating the contact force between the elastic structure and the particles and members in contact with the elastic structure.
[0043]
The elastic structure and particle action force calculation unit 116 and the elastic structure and member action force calculation unit 117 will be described in detail below.
[0044]
First, the contents of the elastic structure and particle acting force calculation unit 116 will be described with reference to FIGS.
[0045]
FIG. 2 is a program configuration diagram showing an outline of the processing that constitutes the elastic structure and the acting force calculation unit 116 for particles.
[0046]
Reference numeral 211 denotes a defining part of mass point connecting line segments, and a connecting line segment connecting adjacent mass points is represented by, for example, a straight line equation and coordinates of both end points. At this time, the number of mass point connecting line segments is (N−1), where N is the number of mass points.
[0047]
Reference numeral 212 denotes a contact determination unit between the mass point connection line segment and the particle, and the contact distance between the mass point connection line segment and the particle is determined based on the relative position between the mass point connection line segment and each particle and the thickness of the elastic structure. The contact / non-contact is determined based on the distance.
[0048]
FIG. 3 is an explanatory diagram for explaining the concept of contact determination.
[0049]
As shown in FIG. 3A, using the distance ΔL between the mass point connecting line segment 312 and the center of the particle 313, the particle radius r, and the distance h which is ½ of the thickness of the elastic structure, To obtain the contact distance δ.
[0050]
δ = r + h−ΔL
When the contact distance δ is positive and the line segment 314 shifted by the distance h in the direction perpendicular to the mass point connecting line segment 312 and the particle 313 intersect, the mass point connecting line segment 312 and the particle 313 are in contact with each other. It is determined that
[0051]
Returning to FIG. 2, reference numeral 213 denotes a mass point connecting line segment and a particle force calculation unit. When the contact determination unit 212 determines that they are in contact with each other, similarly to the normal discrete element method (DEM). The contact force is obtained based on the contact distance, tangential displacement, and relative speed. At this time, the mass point at which the contact force acts is, for example, the mass point closer to the particle among the two end mass points constituting the mass point connecting line segment.
[0052]
Reference numeral 214 denotes an end mass point / particle contact determination unit, which determines the contact distance between the end line segment and the particle based on the position and thickness of the end mass point, and determines contact / non-contact based on the distance. Specifically, as shown in FIG. 3 (b), an end portion that is perpendicular to the mass point connecting line segment 312 of the end mass point, has a length 2h of the elastic structure, and has an end mass point at the center. This is represented by a line segment 315. Further, using the distance ΔL between the end line segment 315 and the center of the particle 313 and the particle radius r, the contact distance δ is obtained based on the following equation.
[0053]
δ = r−ΔL
When the contact distance δ is positive and the end line segment 315 and the particle 313 intersect, it is determined that the end line segment 315 and the particle 313 are in contact.
[0054]
Reference numeral 215 denotes an end mass point and particle force calculation unit. When the contact determination unit 214 determines that the contact is made, the contact distance, the tangential displacement, and the like, as in the normal discrete element method (DEM), The contact force is obtained based on the relative speed.
[0055]
FIG. 9 is a block diagram showing the configuration of the particle behavior analysis apparatus according to the first embodiment of the present invention. Before describing the processing in the elastic structure and particle acting force calculation unit 116 with reference to FIG. 4, the configuration of the particle behavior analysis apparatus will be described first.
[0056]
As illustrated in FIG. 9, the particle behavior analysis apparatus includes a CPU 900, a RAM 901, a display device 902, an input unit 903, an external storage device 904, and a bus 905. The RAM 901 further includes a program storage unit 901a, a calculation condition data storage unit 901b, a particle data storage unit 901c, a rigid structure data storage unit 901d, an elastic structure data storage unit 901e, a mass point-spring model data storage unit 901f, and a mass point connection. Line segment data storage unit 901g, mass particle data storage unit 901h, contact distance data storage unit 901j between two objects, tangential displacement data storage unit 901k between two objects, and relative velocity data storage unit 901m between two objects, acting on particles A force data storage unit 901n and a force data storage unit 901p acting on the mass point are provided.
[0057]
The configuration of each part will be described in detail. The CPU 900 is a central processing unit that controls each part connected via the bus 905. In each of the storage units 901a to 901p of the RAM 901, the program, calculation condition data, particle data, rigid structure data, elastic structure data, mass point-spring model data, mass point connection line segment data, mass point particle data, Contact distance data between two objects, tangential displacement data between two objects, relative velocity data between two objects, force data acting on particles, and force data acting on mass points are stored. The display device 902 includes a display, a printer, and the like, and displays data to be displayed under the control of the CPU 900. The input unit 903 includes a keyboard, a mouse, and the like, and inputs input data from the outside into the apparatus. The external storage device 904 includes a hard disk and stores various data.
[0058]
Here, the contents of each data will be described.
[0059]
The calculation condition data is a value related to calculation conditions such as time step and calculation real time. The particle data is physical property values such as position coordinates, velocity, radius, mass, Young's modulus, and friction coefficient of each particle. The rigid structure data is a physical property value such as a position, a shape and a dimension of a member such as a container wall, speed information when the member moves, a Young's modulus and a friction coefficient. The elastic structure data includes the position and size of an elastic structure such as a sheet, a speed value when a speed is applied to the elastic structure, and physical property values such as Young's modulus and specific gravity. The mass point-spring model data is the number of mass points, the position and speed of each mass point, the mass, and the constants of the bending spring and the expansion spring that connect the mass points, and can be obtained using elastic structure data. The mass point connecting line segment data is an equation of line segments connecting adjacent mass points and position information of the end portions. The mass particle data is a value of the mass position and the center position and radius of the mass particle represented by 1/2 of the thickness of the elastic structure. The contact distance between two objects is a contact distance between particles, a particle and a member, an elastic structure and a particle, or an elastic structure and a member, and is a value obtained from the length of an overlapping portion of two objects. The tangential displacement between two objects is a displacement in the tangential direction of the two objects in contact, and is obtained as an integral value of the tangential component of the relative velocity between the two objects by the discrete element method (DEM). The relative speed between the two objects is a relative value of the speed between the two objects. The force acting on the particles is a value obtained as a resultant force such as contact force acting on each particle, gravity and the like. The force acting on the mass point is a value obtained as a resultant force of the contact force acting on each mass point and the force such as gravity.
[0060]
FIG. 4 is a flowchart showing a procedure of processes executed by the elastic structure and particle action force calculation unit 116 shown in FIG. With reference to the particle behavior analysis apparatus shown in FIG. 9, the procedure for calculating the acting force between the elastic structure and the particles will be described.
[0061]
1) First, the mass point connecting line segment defining unit 211 uses the mass point coordinates stored in the mass point-spring model data storage unit 901f to use the equation of the straight line of the mass point connecting line connecting adjacent mass points and the coordinates of both end points. Are stored in the mass point connecting line segment data storage unit 901g (step S401).
[0062]
2) Next, in the contact determination unit 212 of the mass point connecting line segment and the particle, one of the mass point connecting line segments is determined based on the data stored in the particle data storage unit 901c and the mass point connecting line segment data storage unit 901g. A contact distance δ with one particle is obtained, stored in the contact distance data storage unit 901j between two objects, and contact / non-contact determination is performed based on the distance (steps S402 and S403). As described above, the contact distance δ is expressed as follows using the distance ΔL between the mass point connecting line segment and the center of the particle, the particle radius r, and the distance h that is ½ of the thickness of the elastic structure. Obtained by the formula.
[0063]
δ = r + h−ΔL
The distance ΔL can be obtained mathematically from a straight line equation and the coordinates of the center point.
[0064]
When the contact distance δ is positive and the line segment and the particle shifted by ½ of the thickness of the elastic structure in the direction perpendicular to the mass point connection line intersect the particle, the mass point connection line and the particle Is determined to be in contact.
[0065]
In addition, the distance between both mass points of the mass point connecting line segment and the particle center is obtained, and the material point with the shorter distance is considered to be in contact with the particle.
[0066]
3) When it is determined in step S403 that the mass point connecting line segment and the particle are in contact, the particle point connecting line segment and the particle action force calculation unit 213 have the particle data storage unit 901c and the mass-spring model data storage unit 901f. A contact distance data storage unit 901j between two objects, a tangential displacement data storage unit 901k between two objects, and a relative velocity data storage unit 901m for storing relative velocity data between two objects obtained from the velocity values of particles and mass points. Based on the stored data, the normal and tangential elastic repulsive force and viscous damping force are obtained according to the discrete element method (DEM) as the contact force acting between the mass point and the particle. Then, the value of the contact force obtained in the force data acting on the contacting particle stored in the force data storage unit 901n acting on the particle and the force data acting on the mass point stored in the force data storage unit 901p acting on the mass point are obtained. Are added together (step S404).
[0067]
4) The processes in steps S402 to S404 are repeated by the number of mass point connecting line segments (step S405).
[0068]
5) Next, in the end mass point / particle contact determination unit 214, based on the data stored in the particle data storage unit 901c and the mass point-spring model data storage unit 901f, the end line segment and the particle contact distance Is stored in the contact distance data storage unit 901j between two objects, and contact / non-contact determination is performed based on the distance (steps S406, S407, S403a). The end line segment is expressed, for example, as a line segment that is perpendicular to the mass point connecting line segment of the end mass point, has a length 2h of the elastic structure, and has the center as the end mass point. Further, using the distance ΔL between the end line segment and the particle center and the particle radius r, the contact distance δ is obtained based on the following equation.
[0069]
δ = r−ΔL
The distance ΔL can be obtained mathematically from a straight line equation and the coordinates of the center point.
[0070]
When the contact distance δ is positive and the end line segment and the particle intersect, it is determined that the end line segment and the particle are in contact.
[0071]
6) When it is determined in step S403a that the end line segment and the particle are in contact, the end mass point and the particle action force calculation unit 215 include a particle data storage unit 901c, a mass point-spring model data storage unit 901f, A contact distance data storage unit 901j between two objects, a tangential displacement data storage unit 901k between two objects, and a relative velocity data storage unit 901m that stores relative velocity data between two objects obtained from the velocity values of particles and mass points. Based on the stored data, the normal and tangential elastic repulsive force and viscous damping force are obtained based on the discrete element method (DEM) as the contact force acting between the end mass and the particle. . Then, the obtained contact force is added to the force data acting on the contacting particle stored in the force data storage unit 901n and the force data acting on the mass stored in the data storage unit 901p, respectively (step S404a). ).
[0072]
7) The processes in steps S407, S403a, and S404a are performed on the material points at both ends (step S408).
[0073]
8) The processing in steps S402 to S408 is performed for all particles (step S409).
[0074]
Next, the contents of the elastic structure and member acting force calculator 117 shown in FIG. 1 will be described with reference to FIGS.
[0075]
FIG. 5 is a program configuration diagram showing the program configuration of the elastic structure and member acting force calculation unit 117, FIG. 6 is a diagram showing mass points and members of the elastic structure, and FIG. 7 is an elastic structure. It is a flowchart which shows the procedure of the process performed in the applied force calculation part 117 of an object and a member.
[0076]
FIG. 5A is a program configuration diagram showing a program configuration of the elastic structure and member acting force calculation unit 117 in the first embodiment.
[0077]
In FIG. 5A, reference numeral 511 denotes a mass particle defining portion, and a spherical mass particle having a radius half the thickness of the elastic structure and having a mass coordinate as a center is defined for each mass point. .
[0078]
Reference numeral 512 denotes a contact determination unit between the particle particle and the rigid body structure, and performs contact / non-contact determination based on the center position and radius of the particle particle and the position and size of the rigid body structure (member).
[0079]
Specifically, as shown in FIG. 6A, using the distance ΔL between the center of the mass particle 611 and the member 612 and the mass particle radius h, the mass particle 611 and the member 612 are based on the following equation. The contact distance δ is obtained. FIG. 6A is a diagram showing the mass particle 611 and the member 612 in the first embodiment.
[0080]
δ = h−ΔL
When the contact distance δ is positive and the member 612 and the mass particle 611 intersect, it is determined that the mass particle 611 and the member 612 are in contact.
[0081]
Reference numeral 513 is an action force calculation unit for the mass particle and the rigid component member. When it is determined by the contact determination unit 512 that the contact is made, the contact distance, tangential displacement, Calculate contact force determined by relative speed.
[0082]
Note that the processing in the contact determination unit 512 between the particle particle and the rigid component and the processing in the acting force calculation unit 513 of the material particle and the rigid component member are the same as the processing in the acting force calculation unit 113 in FIG. Done.
[0083]
FIG. 7 is a flowchart showing a procedure of processing executed by the acting force calculator 117 of the elastic structure and member shown in FIG. Hereinafter, the process performed in the acting force calculation unit 117 will be described with reference to FIGS.
[0084]
1) First, in the particle particle definition unit 511, based on the data stored in the mass-spring model data storage unit 901f, the mass representing the elastic structure is the center, and ½ of the thickness of the elastic structure is the radius. The particle particles to be defined are defined and stored in the particle particle data storage unit 901h (step S701).
[0085]
2) Next, in the contact determination unit 512 between the mass particle and the rigid body structure, one mass particle and a member are based on the data stored in the rigid structure data storage unit 901d and the mass particle data storage unit 901h, respectively. The contact distance δ is obtained and stored in the contact distance data storage unit 901j between the two objects, and contact / non-contact determination is performed based on the contact distance δ (steps S702 and S403b). The contact distance δ is obtained by the following equation using the distance ΔL between the center of the particle particle and the member and the particle radius h.
[0086]
δ = h−ΔL
The distance ΔL can be obtained mathematically from a straight line equation and the coordinates of the center point.
[0087]
When the contact distance δ is positive and the member and the mass particle intersect, it is determined that the mass particle and the member are in contact.
[0088]
3) When it is determined in step S403b that the particle particle and the member are in contact with each other, in the acting force calculator 513 of the particle particle and the rigid component, the rigid structure data storage unit 901d, the mass point-spring model data storage unit 901f A contact distance data storage unit 901j between two objects, a tangential displacement data storage unit 901k between two objects, and a relative velocity data storage unit 901m that stores relative velocity data between two objects obtained from the velocity values of a member and a mass point. Based on the stored data, the normal and tangential elastic repulsion and viscous damping force are obtained based on the discrete element method (DEM) as the contact force acting between the mass point and the member. Then, the obtained contact force is added to the force data storage unit 901p that stores force data acting on the contacting mass point (step S404b).
[0089]
4) Steps S702, S403b, and S404b are repeated by the number of mass points (step S703).
[0090]
5) The processes in steps S702, S403b, S404b, and S703 are repeated by the number of members (step S704).
[0091]
Next, the display of the particle | grains and elastic structure performed by the particle | grain and elastic structure behavior display part 120 shown in FIG. 1 is demonstrated with reference to FIG. 10, FIG.
[0092]
FIG. 10 is a diagram illustrating an example in which the positions and thicknesses of the respective mass points constituting the elastic structure are expressed by circles, cylinders, spheres, and line segments connecting them.
[0093]
(A) shows a model in which each mass point of the elastic structure is represented by a circle 1011 in the two-dimensional calculation, and (b) expresses each mass point of the elastic structure in the three-dimensional calculation by a cylinder 1013, and the torsion in the depth direction is represented. A spring-mass model not taken into consideration is shown, and (c) represents a spring-mass model in which each mass point of the elastic structure is represented by a sphere 1015 in three-dimensional calculation and a twist in the depth direction is taken into consideration. Note that the line segments 1012, 1014, and 1016 that connect the mass points represent springs by lines of mountains and valleys. Also, the radius of the circle or cylinder representing the mass point is made equal to ½ of the thickness of the elastic structure.
[0094]
FIG. 11 is a diagram illustrating another display example of the elastic structure.
[0095]
In FIG. 11, the elastic structure is represented by a straight line or a rectangular parallelepiped obtained from the adjacent mass point and the thickness of the elastic structure. The models shown in FIGS. 11 (a), 11 (b), and 11 (c), respectively, similarly to FIGS. 10 (a), (b), and (c), take into account two-dimensional calculation, three-dimensional calculation without considering twist, and twist. Each can be used for three-dimensional calculation.
[0096]
By using these display methods, each mass point position and thickness of the elastic structure can be expressed. Therefore, by visually displaying the elastic structure at the same time as the particles, the contact state with the particles and members can be visually confirmed. Can do.
[0097]
Next, the agitation state of particles analyzed and displayed by the particle behavior analyzer will be described with reference to FIG. FIG. 12 is a schematic cross-sectional view showing the stirring state of the particles in the two-dimensional cross section when the elastic structure stirring member is present in the container.
[0098]
In the figure, reference numeral 1211 denotes a stirring member for an elastic structure, 1212 denotes a container, and 1213 denotes particles. (A), (b), (c), (d) shows each position along the time series of particle | grains and an elastic structure in this order. Note that the elastic structure 1211 is displayed using the two-dimensional calculation model display method shown in FIG.
[0099]
In FIG. 12 (a), since the elastic structure 1211 is not in contact with the particles or the container 1212, the elastic structure 1211 is basically in a free state and kept straight, but (b), ( In (c) and (d), it can be seen that the elastic structure 1211 bends due to the resistance against rotation caused by contact with the particles and the container 1212, and that the particles are pushed out by this deflection.
[0100]
That is, the elastic member 1211 rotates counterclockwise (counterclockwise) in the figure, and FIG. 12B shows a state in which the particles stored in the lower part of the container 1212 start to be pushed out while contacting the wall of the container 1212. Has been. FIG. 12C shows the state when the elastic member 1211 further rotates, and it can be seen that the extruded particles have reached the upper part of the rotation axis. FIG. 12D shows a state where the elastic member 1211 further rotates and particles that have exceeded the rotation axis fall again to the lower part of the container 1212 and start to be stored in the space after passing through the elastic member 1211. ing. Thereafter, when the elastic member 1211 further rotates, the particles positioned in the advancing direction of the elastic member 1211 are pushed out by the elastic member 1211, and the elastic member 1211 receives the force received by pushing the particles (the force pushing the particles and the inner wall of the container). In the relationship between the friction force between the elastic member 1211 and the like and the force that the elastic member 1211 tries to return to the free state, when the latter force is won, the bent state returns to the straight initial state due to the spring force.
[0101]
As described above, the behavior of the particles and the elastic structure can be coupled and solved by considering the acting force of the elastic structure and the particles, and the elastic structure and the member (container). For this reason, by using the present invention, it is possible to calculate the dynamic deflection of the elastic structure in the container when the stirring member of the elastic structure is in the container. In addition, since the contact force of the particle with the elastic structure can be obtained by a spring-dashpot model based on the discrete element method (DEM), the contact with the particle or the elastic structure can be accurately expressed. The stirring state can be obtained with high accuracy.
[0102]
Since the normal spring-mass point model deals only with the position information of the mass point, a method of performing contact determination from the relative position of the mass point and the particle can be considered. However, this method cannot accurately determine contact and define the contact distance in consideration of the thickness of the elastic structure. Therefore, the difference in the contact state according to the thickness of the elastic structure cannot be determined. On the other hand, in the present invention, using the position of the mass point representing the elastic structure and the thickness of the elastic structure, the relative position between each mass point and the particle is obtained, and the contact force according to the relative position is calculated. . Thereby, it is possible to handle the contact state of the elastic structure with high accuracy.
[0103]
In addition, when the distance between the mass points is longer than the diameter of the particle or the size of the member, the contact determination based on the relative position between the mass point and the particle causes a calculation problem that the particle or the member passes between the mass points. There is a case. In the present invention, by calculating the contact between the mass point connecting line segment connecting the mass points and the particle, even when the particle moves between the mass points, the contact between the mass point and the particle can be expressed. It is possible to prevent computational inconsistencies that cause particles to slip through.
[0104]
In the above description, a member refers to a structure such as a container wall that has higher rigidity and less elastic deformation than an elastic structure.
[0105]
In the above description, a structure composed of particles, an elastic structure, and members related thereto is taken as an example, but it is not always necessary to be composed of all of them. For example, in the structure composed of particles and an elastic structure, or the structure in which the elastic structure and the member cannot be contacted at all, the acting force calculator 117 of the elastic structure and the member in FIG. 1 is excluded. It is possible to analyze the behavior of particles and elastic structures using a processing program. Similarly, even in the case of having only an elastic structure and members, the behavior of the elastic structure can be easily and accurately analyzed using the processing program configuration excluding the elastic structure and the particle action force calculation unit 116 shown in FIG. Is possible.
[0106]
In the above description, the behavior of the particle and the elastic structure is coupled and solved. However, the present invention can be easily applied to a case where a member that is a rigid structure moves due to a force received from the particle or the elastic structure. It is possible to analyze the coupled behavior of both easily and accurately. Specifically, by determining the displacement of the member using the force acting on the member obtained by the acting force calculator 113 of the particle and the member and the acting force calculator 116 of the elastic structure and the member, the particle and the elastic structure It becomes possible to calculate the coupled behavior of objects and members. In this case, the member behavior calculation may be performed by a method used in normal particle behavior calculation.
[0107]
In the above description, the behavior of the particle and the elastic structure in the two-dimensional cross section is described. However, the three-dimensional particle behavior calculation and the three-dimensional spring-mass model are performed in the same manner as the above method. It is possible to perform a three-dimensional particle behavior calculation by performing the calculation in a coupled manner. At this time, as a method of the spring-mass point model, any model that can express an elastic structure with a mass point, such as a method that does not consider twist or a method that considers twist, is applicable. In the contact calculation with the elastic structure particles, by using a connecting flat plate instead of the mass point connecting line segment, and in the contact calculation with the elastic structure member, by expressing the particle particles with a cylinder or a sphere, Contact calculation can be easily performed in three-dimensional calculation.
[0108]
In addition, in the above description, the mass point connecting line segment and the end line segment are represented by straight lines, but the curve is represented by a curve passing through three mass points or the arc is represented by an arc. It is also possible to use. This makes it possible to accurately represent the deflection of the elastic structure. In that case, a method according to the definition of the line segment may be used as the contact distance or contact determination.
[0109]
In the case where there are a plurality of elastic structures in the container, for example, the particles of the present invention can be treated as contact between the mass point of one elastic structure and the mass point connecting line segment of the other elastic structure. It is possible to apply a contact calculation between a mass point connecting line segment and a mass point connecting line segment.
[0110]
Further, in the above description, the depth width in the elastic structure having a two-dimensional cross section is not mentioned, but the unit length in the depth direction is set in order to align the units of the magnitude of the force in the spring-mass model and the particle behavior calculation. Need to be the same. Therefore, the representative particle size of the particle behavior calculation is made equal to the depth length of the spring-mass model.
[0111]
In the above description, the contact force acts on the mass point closer to the particle among the two end mass points constituting the mass point connecting line segment, but the contact force is distributed according to the distance between the particle and the two mass points. It is also possible to apply other methods such as
[0112]
In the above description, the line segment passing through the end mass point is defined as the end line segment. However, when the end mass point is at a position different from the end of the elastic structure, the line passing through the end of the elastic structure is used. Minutes can be used.
[0113]
In the above description, the contact force is used as the action force between the elastic structure and the particles or between the members. However, the present invention is not limited to the contact force. For example, it is known that an adhesion force such as a VanDerWals force acts between two objects, and this force depends on a separation distance between the objects. The present invention can also be applied to such a force acting between objects in a non-contact state, and the separation distance (reverse sign of the contact distance) is obtained from the contact distance obtained in the present invention, It is possible to calculate the force that works.
[0114]
Hereinafter, as one specific application example of the present invention, a case where the present invention is applied to a developer behavior analysis in a developing unit of an electrophotographic apparatus will be described.
[0115]
FIG. 13 is a diagram illustrating a part of an image forming apparatus in an electrophotographic apparatus.
[0116]
In the figure, 1511 is a photosensitive drum, 1512 is a developing device, 1513 is a transfer member, 1514 is a cleaning device, 1515 is a charging member, and 1516 is a developing container. In the developing container 1516, an agitating member 1517 for agitating and conveying the toner as the developer is provided. Recently, a sheet-like elastic member may be used as the stirring member 1517, thereby achieving stable stirring.
[0117]
By applying the present invention to the developing container 1516, it is possible to predict the stirring state of the developer when the physical properties, shape, and dimensions of the stirring member 1517, the shape and relative position of the developing container 1516, and the like are changed. . And this analysis result can be utilized for the design of a stirring structure, etc.
[0118]
In the electrophotographic apparatus, in addition to the developing container 1516, an elastic structure for controlling the behavior of the developer, for example, an elastic regulating member 1518 for regulating the thickness of the developer on the developing roller, and a cleaning device 1514. In this case, a cleaning member 1519 for cleaning the developer that has not been transferred, a conveying member 1520 made of an elastic member for feeding the developer into the cleaning container, and the like are used. The device is applicable.
[0119]
In the present invention, the interaction force includes a force selected from the group consisting of contact force, adhesion force, magnetic force, and electrostatic force. Among the above, it is desirable to further consider contact force and adhesion force as contact force and adhesion force, and examples thereof include friction force, electrostatic force, intermolecular force, and magnetic force. In addition, it is preferable to consider the contact force as the interaction force.
[0120]
[Second Embodiment]
In the first embodiment, the contact between the elastic structure and the particle is obtained using the mass point connecting line segment, and the contact between the elastic structure and the member is obtained using the material particle. However, when the member is smaller than the distance between the mass points, the member may be expected to pass through the mass points, resulting in inconsistent calculation results. Similarly, slipping between mass points may occur at the end of the elastic structure.
[0121]
The second embodiment is for solving such a problem, and the contact calculation using the mass point connecting line segment described in the first embodiment is applied to the contact between the elastic structure and the member. Applicable.
[0122]
That is, as a contact calculation means between the elastic structure and the member, there are two methods of contact calculation using the mass point connecting line segment and contact calculation using the mass particle, and the thickness of the elastic structure and the distance between the mass points, Depending on the size of the particle or member, both are used properly, thereby preventing problems such as slipping through the mass points and accurately representing the contact between the elastic structure and the member.
[0123]
Since the configuration of the second embodiment is basically the same as that of the first embodiment, the configuration of the first embodiment is used in the description of the second embodiment.
[0124]
FIG. 5B is a program configuration diagram showing a program configuration of the elastic structure and member acting force calculation unit 117 in the second embodiment.
[0125]
In the figure, the definition unit 511, the contact determination unit 512, and the action force calculation unit 513 are the same as the definition unit 511, the contact determination unit 512, and the action force calculation unit 513 of the first embodiment shown in FIG. The definition unit 211 is the same as the definition unit 211 of the first embodiment shown in FIG. Therefore, description is abbreviate | omitted here.
[0126]
Reference numeral 520 denotes a calculation method selection unit. When the size of the rigid structure (member) is larger than the distance between the mass points of the elastic structure or the thickness of the elastic structure, the calculation method using the mass particle is selected. If the size of the rigid structure is smaller than the distance between the mass points of the elastic structure or the thickness of the elastic structure, or if it is a contact calculation with the end of the elastic structure, the calculation method using the mass point connecting line select.
[0127]
Reference numeral 514 denotes a contact determination unit between the mass point connection line segment and the rigid body structure. Based on the relative position between the mass point connection line segment and the member (rigid body structure) and the thickness of the elastic structure, the mass point connection line segment and the member The contact distance is obtained and contact / non-contact is determined based on the distance.
[0128]
Reference numeral 515 denotes an acting force calculation unit for the mass point connecting line segment and the rigid body component. When the contact determination unit 514 determines that the contact is made, the contact distance and the tangent are determined in the same manner as in the normal discrete element method (DEM). Contact force is calculated using displacement and relative speed. At this time, the mass point at which the contact force acts is, for example, the mass point closer to the particle among the two end mass points constituting the mass point connecting line segment.
[0129]
Reference numeral 516 denotes an end mass point / member contact determination unit that obtains a contact distance between the end line segment and the member represented by the position and thickness of the end mass point, and determines contact / non-contact based on the distance. Do.
[0130]
Reference numeral 517 denotes an end mass point and a member acting force calculation unit. When the contact determination unit 516 determines that they are in contact, the contact force is obtained using the contact distance, the tangential displacement, and the relative speed.
[0131]
The processes in the contact determination unit 514, the action force calculation unit 515, the contact determination unit 516, and the action force calculation unit 517 are the contact determination unit 212, the action force calculation unit 213, and the contact determination unit in the first embodiment shown in FIG. 214 and the action force calculation unit 215 correspond to processing when the particles are replaced with members (rigid bodies), respectively.
[0132]
In the following, when the calculation method selection unit 520 selects the calculation method using the mass point connection line segment, the process of calculating the acting force between the mass point connection line segment and the member will be described with reference to FIGS. 8, 5 (b), and 9. Will be described with reference to FIG. FIG. 8 is a flowchart illustrating a procedure of processes performed in the elastic structure and member acting force calculation unit 117 according to the second embodiment.
[0133]
1) First, the mass point connecting line segment defining unit 211 uses the mass point coordinates stored in the mass point-spring model data storage unit 901f to use the equation of the straight line of the mass point connecting line connecting adjacent mass points and the coordinates of both end points. And is stored in the mass point connecting line data storage unit 901g (step S401a).
[0134]
2) Next, in the contact determination unit 514 between the mass point connection line segment and the rigid structure, based on the data stored in the rigid structure data storage unit 901d and the mass point connection line data storage unit 901g, respectively, the mass point connection line segment The contact distance δ between one of the two and the rigid structure is obtained, stored in the contact distance data storage unit 901j between the two objects, and contact / non-contact determination is performed based on the distance (steps S801 and S403c). The contact distance δ is obtained based on the following equation using a distance ΔL between the mass point connecting line segment and the rigid structure, and a distance h that is ½ of the thickness of the rigid structure.
[0135]
δ = h−ΔL
The distance ΔL can be obtained mathematically from a straight line equation and the coordinates of the center point.
[0136]
When the contact distance δ is positive and the line segment shifted by ½ of the thickness of the rigid structure in the direction perpendicular to the mass point connecting line intersects with the rigid structure, they are in contact with each other. It is determined that
[0137]
At the same time, the distance between both mass points of the mass point connecting line segment and the rigid structure is obtained, and the material point with the shorter distance is considered to be in contact with the member.
[0138]
3) If it is determined in step S403c that the mass point connecting line segment and the rigid structure are in contact, the mass point connecting line segment and the rigid structure acting force calculation unit 515 include the rigid structure data storage unit 901d, the mass point A spring model data storage unit 901f, a contact distance data storage unit 901j between two objects, a tangential displacement data storage unit 901k between two objects, and a relative storage for storing relative velocity data between two objects obtained from the value of the velocity of the material member. Based on the data stored in the velocity data storage unit 901m, as the contact force acting between the mass point and the rigid structure, based on the discrete element method (DEM), the elastic repulsive force in the normal direction and the tangential direction Find the viscous damping force. Then, the obtained contact force is added to the force data storage unit 901p acting on the contacting mass point (step S404c).
[0139]
4) The processes of steps S801, S403c, and S404c are repeated by the number of mass point connecting line segments (step S405a).
[0140]
5) Next, in the end mass point / member contact determination unit 516, based on the data stored in the rigid structure data storage unit 901d and the mass point-spring model data storage unit 901f, respectively, the end line segment and the rigid structure The contact distance between the two objects is stored in the contact distance data storage unit 901j between the two objects, and contact / non-contact is determined based on the distance (steps S406a, S802, and S403d). The end line segment is, for example, a line segment that is perpendicular to the mass point connecting line segment of the end mass point, has a thickness 2h of the rigid structure, and has a center at the end mass point. Further, using the distance ΔL between the end line segment and the rigid structure, the contact distance δ is obtained by the following equation.
[0141]
δ = △ L
The distance ΔL can be obtained mathematically from a straight line equation and the coordinates of the center point.
[0142]
When the end line segment and the member intersect, it is determined that the end line segment and the member are in contact with each other.
[0143]
6) When it is determined in step S403d that the end line segment is in contact with the member, the end line segment and member acting force calculation unit 517 includes a rigid structure storage unit 901d, a mass-spring model data storage unit. 901f, the contact distance data storage unit 901j between the two objects, the tangential displacement data storage unit 901k between the two objects, the relative velocity data storage unit 901m that stores the relative velocity data between the two objects obtained from the velocity values of the material point members. Based on the data stored in each, the contact force acting between the material point of the end and the member, based on the discrete element method (DEM), the elastic repulsive force and the viscous damping force in the normal and tangential directions Ask for. Then, the contact force is added to the force data storage unit 901p acting on the contacting mass point (step S404d).
[0144]
7) Steps S802, S403d, and S404d are performed on the material points at both ends (step S408a).
[0145]
8) The processes in steps S801 to S408a are performed on all members (step S704a).
[0146]
The contact determination described above will be described with reference to specific examples shown in FIGS.
[0147]
FIG. 6A shows the case where the distance between the mass points is shorter than that of the member. In this case, the selection unit 520 in FIG. 5 selects the method for calculating the contact between the mass particle and the member, and the first embodiment shown in FIG. The contact calculation is performed according to the same processing procedure as in the flowchart in FIG.
[0148]
FIG. 6B shows a case where the distance between the mass points is longer than that of the member. In this case, the selection unit 520 in FIG. 5 selects the contact calculation method between the mass point connecting line segment and the member, and the contact calculation is performed according to the flowchart in FIG. Done.
[0149]
As described above, in the second embodiment, the elastic structure is obtained by properly using the calculation method using the mass particle and the calculation method using the mass connection line segment depending on the relative size difference between the elastic structure and the member. Regardless of the length, the thickness, the number of mass points, the size of the member, etc., it is possible to reliably determine contact between the two. Thereby, it can respond to various container shapes, dimensions of elastic structures, and the like.
[0150]
In the above description, the contact distance δ between the mass point connecting line segment and the rigid structure is represented by h−ΔL. However, when the mass point connecting line segment and the rigid structure intersect, the contact distance δ is Correction is made using a distance h that is ½ of the thickness of the rigid structure.
[0151]
In the second embodiment, two calculation methods are applied to contact calculation between the elastic structure and the member. However, the present method can also be applied to contact calculation between the elastic structure and the particle.
[0152]
[Other embodiments]
An object of the present invention is to supply a storage medium storing software program codes for realizing the functions of the embodiments to the system or apparatus, and the computer of the system or apparatus (or CPU, MPU, etc.) stores it. It is also achieved by reading and executing the program code stored on the medium.
[0153]
In this case, the program code itself read from the storage medium realizes the functions of the above-described embodiments, and the storage medium storing the program code constitutes the present invention.
[0154]
Examples of the storage medium for supplying the program code include a floppy (registered trademark) disk, a hard disk, a magneto-optical disk, a CD-ROM, a CD-R, a CD-RW, a DVD-ROM, a DVD-RAM, and a DVD. -RW, DVD-R, magnetic tape, nonvolatile memory card, ROM, etc. can be used.
[0155]
Further, by executing the program code read by the computer, not only the functions of the above embodiments are realized, but also an OS (operating system) running on the computer based on the instruction of the program code Includes a case where the function of the above-described embodiment is realized by performing part or all of the actual processing.
[0156]
Further, after the program code read from the storage medium is written in a memory provided in a function expansion board inserted into the computer or a function expansion unit connected to the computer, the function expansion is performed based on the instruction of the program code. This includes a case where the CPU or the like provided in the board or the function expansion unit performs part or all of the actual processing and the functions of the above-described embodiments are realized by the processing.
[0157]
As described above, various embodiments of the present invention have been shown and described. Examples of embodiments of the present invention are listed below.
[0158]
[Embodiment 1] In a behavior analysis apparatus for analyzing the behavior of an elastic structure and particles contained in a container,
Particle displacement calculation means for calculating the displacement of the particles along a time series based on the force acting on the particles;
Elastic force calculation means for calculating the elastic force of the elastic structure based on a spring-mass model;
An action force calculating means for calculating an action force acting between the elastic structure and the particles;
Based on the elastic force calculated by the elastic force calculation means and the action force calculated by the action force calculation means, the mass point displacement calculation means for calculating the displacement of the mass point representing the elastic structure along a time series; and
Display means for displaying the behavior of the particles and the elastic structure on the basis of the displacement of the particles calculated by the particle displacement calculation means and the displacement of the mass points calculated by the mass point displacement calculation means;
A behavior analysis apparatus characterized by comprising:
[0159]
[Embodiment 2] The acting force calculation means obtains a relative position between each mass point of the elastic structure and the particle using the position of each mass point representing the elastic structure and the thickness of the elastic structure. The behavior analysis apparatus according to the first embodiment, wherein an acting force corresponding to the relative position is calculated.
[0160]
[Embodiment 3] The acting force calculation means defines a mass point connecting line segment that connects each mass point representing the elastic structure, and uses the position of the mass point connecting line segment and the thickness of the elastic structure, The behavior analysis apparatus according to embodiment 1, wherein a relative position between the mass point connecting line segment and the particle is obtained, and an acting force according to the relative position is calculated.
[0161]
[Embodiment 4] The acting force calculation means defines a mass particle having a mass representing the elastic structure as a center and having a radius of 1/2 of the thickness of the elastic structure, and the mass particle, the particle, The behavior analysis apparatus according to the first embodiment, wherein a relative position is obtained and an acting force corresponding to the relative position is calculated.
[0162]
[Embodiment 5] In the case of calculating the behavior of a particle and an elastic structure in a two-dimensional cross section, the depth direction length of the elastic structure is defined to be the same as the representative diameter of the particle. Item 1. The behavior analysis apparatus according to item 1.
[0163]
[Embodiment 6] The display means includes a circle, a cylinder, or a sphere defined by a position of a mass point representing the elastic structure and a thickness of the elastic structure, and a line segment that connects the circle, the cylinder, or the sphere. The elastic structure is displayed, or the elastic structure is displayed by a line segment or a rectangular parallelepiped defined and connected by the position of a mass point representing the elastic structure and the thickness of the elastic structure. The behavior analysis apparatus according to the first aspect.
[0164]
[Embodiment 7] In a behavior analysis apparatus for analyzing the behavior of the elastic structure in an elastic structure and a member arranged in association with the elastic structure,
Elastic force calculation means for calculating the elastic force of the elastic structure based on a spring-mass model;
Using the position of each mass point representing the elastic structure and the thickness of the elastic structure, the relative position between each mass point and the member is obtained, and according to the relative position, the elastic structure and the member Acting force calculating means for calculating acting force acting between,
A displacement calculating means for calculating a displacement of a mass point representing the elastic structure along a time series based on the elastic force calculated by the elastic force calculating means and the acting force calculated by the acting force calculating means;
Display means for displaying the behavior of the elastic structure based on the displacement of the mass point calculated by the displacement calculation means;
A behavior analysis apparatus characterized by comprising:
[0165]
[Embodiment 8] The acting force calculation means defines a mass point connecting line segment that connects each mass point representing the elastic structure, and uses the position of the mass point connecting line segment and the thickness of the elastic structure, The behavior analysis apparatus according to the seventh embodiment, wherein a relative position between the mass point connecting line segment and the member is obtained, and an acting force according to the relative position is calculated.
[0166]
[Embodiment 9] The acting force calculation means defines a mass particle having a mass representing the elastic structure as a center and a radius of 1/2 of the thickness of the elastic structure, and the mass particle, the particle, The behavior analysis apparatus according to the first embodiment, wherein a relative position is obtained and an acting force corresponding to the relative position is calculated.
[0167]
[Embodiment 10] The display means includes a circle, a cylinder, or a sphere defined by a position of a mass point representing the elastic structure and a thickness of the elastic structure, and a line segment that connects the circle, the cylinder, or the sphere. The elastic structure is displayed, or the elastic structure is displayed by a line segment or a rectangular parallelepiped defined and connected by the position of a mass point representing the elastic structure and the thickness of the elastic structure. The behavior analysis apparatus according to the first aspect.
[0168]
[Embodiment 11] In a behavior analysis apparatus for analyzing the behavior of an elastic structure and particles contained in a container,
Particle displacement calculation means for calculating the displacement of the particles along a time series based on the force acting on the particles;
Elastic force calculation means for calculating the elastic force of the elastic structure based on a spring-mass model;
First action force calculating means for calculating an action force acting between the elastic structure and the particles;
A second acting force calculating means for calculating an acting force acting between the elastic structure and the container;
Based on the elastic force calculated by the elastic force calculating means, the acting force calculated by the first acting force calculating means, and the acting force calculated by the second acting force calculating means, the elastic structure is A mass displacement calculating means for calculating the displacement of the representing mass along the time series, and
Display means for displaying the behavior of the particles and the elastic structure on the basis of the displacement of the particles calculated by the particle displacement calculation means and the displacement of the mass points calculated by the mass point displacement calculation means;
A behavior analysis apparatus characterized by comprising:
[0169]
[Embodiment 12] The first acting force calculation means uses the position of each mass point representing the elastic structure and the thickness of the elastic structure to calculate the relative mass points of the elastic structure and the particles. The position is obtained, the acting force according to the relative position is calculated, and the second acting force calculation means uses the position of each mass point representing the elastic structure and the thickness of the elastic structure to calculate the elasticity. The behavior analysis apparatus according to embodiment 11, wherein a relative position between each mass point of the structure and the container is obtained, and an acting force corresponding to the relative position is calculated.
[0170]
[Embodiment 13] The first acting force calculation means defines a mass point connecting line segment connecting each mass point representing the elastic structure, and uses the position of the mass point connecting line segment and the thickness of the elastic structure. And calculating the acting force according to the relative position, and the second acting force calculating means connects the material points representing the elastic structure. Defining a connecting line segment, using the position of the mass point connecting line segment and the thickness of the elastic structure, the relative position between the mass point connecting line segment and the container is obtained, and the acting force according to the relative position is determined. The behavior analysis device according to embodiment 11, wherein the behavior analysis device is calculated.
[0171]
[Embodiment 14] The first acting force calculation means defines a mass particle having a mass representing the elastic structure as a center and a radius of 1/2 of the thickness of the elastic structure, and the mass particle A relative position with respect to the particle is obtained, and an acting force according to the relative position is calculated, and the second acting force calculating means has a mass point representing the elastic structure as a center and a thickness of 1 of the elastic structure. The behavior analysis apparatus according to claim 11, wherein a particle having a radius of / 2 is defined, a relative position between the particle and the container is obtained, and an acting force according to the relative position is calculated.
[0172]
[Embodiment 15] In the case of calculating the behavior of a particle and an elastic structure in a two-dimensional cross section, the depth direction length of the elastic structure is defined to be the same as the representative diameter of the particle. Item 11. The behavior analysis apparatus according to item 11.
[0173]
[Embodiment 16] The display means includes a circle, a cylinder, or a sphere defined by a position of a mass point representing the elastic structure and a thickness of the elastic structure, and a line segment that connects the circle, the cylinder, or the sphere. The elastic structure is displayed, or the elastic structure is displayed by a line segment or a rectangular parallelepiped defined and connected by the position of a mass point representing the elastic structure and the thickness of the elastic structure. The behavior analysis apparatus according to the eleventh aspect.
[0174]
[Embodiment 17] The embodiment 1 to the embodiment, wherein the acting force calculated by the acting force calculation means is based on at least one of contact force, adhesion force, magnetic force, and electrostatic force. The behavior analysis apparatus according to any one of aspects 16.
[0175]
[Embodiment 18] Particulate developer contained in a developing device for forming a visible image with a developer on the surface of a carrier on which a latent image is formed, and elasticity for stirring or conveying the developer Structure, elastic structure for regulating the thickness of particulate developer deposited on the developing roller in the developing device, and the particle, unnecessary developer after transfer on the developer carrier in the developing device At least one of the elastic structure for removing particles and the particles, and the elastic structure for sending unnecessary developer particles from a container for storing unnecessary developer particles in the developing device and the particles The behavior analysis apparatus according to any one of Embodiments 1 to 17, wherein the behavior of two combinations is analyzed.
[0176]
[Embodiment 19] In a behavior analysis method for analyzing the behavior of an elastic structure and particles contained in a container,
A particle displacement calculating step for calculating a displacement of the particle along a time series based on a force acting on the particle;
An elastic force calculating step for calculating an elastic force of the elastic structure based on a spring-mass model;
A first acting force calculating step for calculating an acting force acting between the elastic structure and the particles;
A second action force calculating step for calculating an action force acting between the elastic structure and the container;
Based on the elastic force calculated by the elastic force calculating step, the operating force calculated by the first applied force calculating step, and the applied force calculated by the second applied force calculating step, the elastic structure is A mass displacement calculation step for calculating the displacement of the mass point to be represented along the time series, and
A display step for displaying the behavior of the particle and the elastic structure based on the displacement of the particle calculated by the particle displacement calculation step and the displacement of the mass point calculated by the mass point displacement calculation step;
The behavior analysis method characterized by having.
[0177]
[Embodiment 20] In the first acting force calculation step, the position of each mass point representing the elastic structure and the thickness of the elastic structure are used to calculate the relative mass points of the elastic structure and the particles. A position is obtained, and an acting force according to the relative position is calculated, and the second acting force calculating step uses the position of each mass point representing the elastic structure and the thickness of the elastic structure to calculate the elasticity. The behavior analysis method according to embodiment 19, wherein a relative position between each mass point of the structure and the container is obtained, and an acting force according to the relative position is calculated.
[0178]
[Embodiment 21] In the first acting force calculation step, a mass point connecting line segment connecting each mass point representing the elastic structure is defined, and the position of the mass point connecting line segment and the thickness of the elastic structure are used. Then, a relative position between the mass point connecting line segment and the particle is obtained, and an acting force according to the relative position is calculated, and the second acting force calculating step includes a mass point that connects the mass points representing the elastic structure. Defining a connecting line segment, using the position of the mass point connecting line segment and the thickness of the elastic structure, the relative position between the mass point connecting line segment and the container is obtained, and the acting force according to the relative position is determined. The behavior analysis method according to embodiment 19, wherein the behavior analysis method is calculated.
[0179]
[Embodiment 22] In the first acting force calculation step, a particle having a mass representing the elastic structure as a center and having a radius of ½ of the thickness of the elastic structure is defined. A relative position with respect to the particle is obtained, and an acting force according to the relative position is calculated, and the second acting force calculating step has a mass of 1 representing the elastic structure as a center, with the mass representing the elastic structure as a center. The behavior analysis method according to claim 19, wherein a particle having a radius of / 2 is defined, a relative position between the particle and the container is obtained, and an acting force according to the relative position is calculated.
[0180]
[Embodiment 23] In the case of calculating the behavior of a particle and an elastic structure in a two-dimensional cross section, the length in the depth direction of the elastic structure is defined to be the same as the representative diameter of the particle. 19. The behavior analysis method according to 19.
[0181]
[Embodiment 24] The display step includes a circle, a cylinder, or a sphere defined by a position of a mass point that represents the elastic structure and a thickness of the elastic structure, and a line segment that connects the circle, the cylinder, or the sphere. The elastic structure is displayed, or the elastic structure is displayed by a line segment or a rectangular parallelepiped defined and connected by the position of a mass point representing the elastic structure and the thickness of the elastic structure. The behavior analysis method according to aspect 19.
[0182]
[Embodiment 25] The action force calculated in the first and second action force calculation steps is based on at least one of contact force, adhesion force, magnetic force, and electrostatic force. The behavior analysis method according to any one of Embodiments 19 to 24.
[0183]
[Embodiment 26] Particulate developer contained in a developing device for forming a visible image with a developer on the surface of a carrier on which a latent image is formed, and elasticity for stirring or conveying the developer Structure, elastic structure for regulating the thickness of particulate developer deposited on the developing roller in the developing device, and the particle, unnecessary developer after transfer on the developer carrier in the developing device At least one of the elastic structure for removing particles and the particles, and the elastic structure for sending unnecessary developer particles from a container for storing unnecessary developer particles in the developing device and the particles The behavior analysis method according to any one of Embodiments 19 to 25, wherein the behavior of one combination is analyzed.
[0184]
[Embodiment 27] In a program for causing a computer to execute a behavior analysis method for analyzing the behavior of an elastic structure and particles contained in a container,
The behavior analysis method is
A particle displacement calculating step for calculating a displacement of the particle along a time series based on a force acting on the particle;
An elastic force calculating step for calculating an elastic force of the elastic structure based on a spring-mass model;
A first acting force calculating step for calculating an acting force acting between the elastic structure and the particles;
A second action force calculating step for calculating an action force acting between the elastic structure and the container;
Based on the elastic force calculated by the elastic force calculating step, the operating force calculated by the first applied force calculating step, and the applied force calculated by the second applied force calculating step, the elastic structure is A mass displacement calculation step for calculating the displacement of the mass point to be represented along the time series, and
A display step for displaying the behavior of the particle and the elastic structure based on the displacement of the particle calculated by the particle displacement calculation step and the displacement of the mass point calculated by the mass point displacement calculation step;
The program characterized by having.
[0185]
[Embodiment 28] In a computer-readable storage medium storing a behavior analysis method for analyzing the behavior of an elastic structure and particles contained in a container as a program,
The behavior analysis method is
A particle displacement calculating step for calculating a displacement of the particle along a time series based on a force acting on the particle;
An elastic force calculating step for calculating an elastic force of the elastic structure based on a spring-mass model;
A first acting force calculating step for calculating an acting force acting between the elastic structure and the particles;
A second action force calculating step for calculating an action force acting between the elastic structure and the container;
Based on the elastic force calculated by the elastic force calculating step, the operating force calculated by the first applied force calculating step, and the applied force calculated by the second applied force calculating step, the elastic structure is A mass displacement calculation step for calculating the displacement of the mass point to be represented along the time series, and
A display step for displaying the behavior of the particle and the elastic structure based on the displacement of the particle calculated by the particle displacement calculation step and the displacement of the mass point calculated by the mass point displacement calculation step;
A storage medium comprising:
[0186]
【The invention's effect】
As described above in detail, according to the present invention, an elastic structure and particles can be accurately and easily obtained by coupling and solving a spring-mass model for calculating the behavior of an elastic structure and a particle behavior calculation. The behavior of can now be analyzed.
[0187]
In addition, by determining the contact / non-contact between the elastic structure and the particle, the elastic structure and the member (container), and calculating the contact force in consideration of the thickness of the elastic structure, the elastic structure and the particle The behavior can be analyzed easily and more accurately.
[0188]
Also, by properly using the two calculation methods according to the size of the particles and members for the elastic structure, it is possible to handle accurate contact regardless of the size and number of points of the elastic structure, the size and shape of the member, etc. I can do it now.
[0189]
In addition, by displaying elastic structures using circles, cylinders, spheres, line segments, rectangular parallelepipeds, etc., defined by the thickness of the elastic structure, the behavior of the elastic structures and particles that are the analysis results is displayed in an easy-to-understand manner. I can do it now.
[0190]
Also, by applying the present invention to the developer behavior analysis of an electrophotographic apparatus, a developer container having a sheet stirring member, a developer having an elastic regulating member for regulating the developer thickness on the developing roller, and a transfer residual toner Developer for a device that controls the behavior of the developer using an elastic structure, such as a cleaning device having a cleaning blade for removing the toner and a delivery device for delivering the removed toner to the container The behavior can be predicted.
[Brief description of the drawings]
FIG. 1 is a program configuration diagram showing a schematic overall configuration of a processing program of a particle behavior analysis apparatus when an analysis region has an elastic structure.
FIG. 2 is a program configuration diagram showing an outline of processing that constitutes an “elastic structure and particle acting force calculation unit”;
FIG. 3 is an explanatory diagram for explaining a concept of contact determination.
FIG. 4 is a flowchart showing a processing procedure in the “elastic structure and particle acting force calculator” shown in FIG. 1;
FIG. 5 is a program configuration diagram showing a program configuration of an “elastic structure and member acting force calculation unit”.
FIG. 6 is a diagram showing mass points and members of an elastic structure.
FIG. 7 is a flowchart showing a procedure of processing performed in an “elastic force structure and member acting force calculation unit”.
FIG. 8 is a flowchart illustrating a procedure of processes performed in an “elastic force structure and member acting force calculation unit” according to the second embodiment.
FIG. 9 is a block diagram showing the configuration of the particle behavior analysis apparatus according to the first embodiment of the present invention.
FIG. 10 is a diagram showing an example in which positions and thicknesses of respective parts constituting an elastic structure are expressed by circles, cylinders, spheres, and line segments connecting them.
FIG. 11 is a diagram showing another display example of the elastic structure.
FIG. 12 is a schematic cross-sectional view showing a stirring state of particles in a two-dimensional cross section when an elastic structure stirring member is present in a container.
FIG. 13 is a diagram illustrating a part of an image forming apparatus in an electrophotographic apparatus.
FIG. 14 is a program configuration diagram schematically showing a configuration example of a conventional processing program.
FIG. 15 is a diagram showing a concept of conventional contact calculation.
[Explanation of symbols]
100: Control unit
900: CPU
901: RAM
902: Display device
903: Input unit
904: External storage device
905: Bus

Claims (12)

By executing the program read from the memory by the processing device, the functions of the particle displacement calculation means, elastic force calculation means, acting force calculation means, and mass point displacement calculation means are realized, and the elastic structure enclosed in the container In the behavior analysis device that displays the behavior of particles and particles on the display means,
The memory includes thickness data of the elastic structure, particle data, force data acting on the particles, spring-mass model data representing the elastic structure, and mass point connecting line segment data connecting the mass points of the spring-mass model. Store
The particle displacement calculating means, as the force acting on particles having a particle data stored in the memory, based on the resultant force including the contact force and the gravity acting on each particle, the equation of motion along the particle displacement in time series Calculate using
The elastic force calculation means calculates a bending spring force and an expansion spring force acting on each mass point as an elastic force of the elastic structure based on a spring-mass point model stored in the memory ,
The acting force calculating means obtains a relative position between the mass point connecting line segment and the particle using the position data of the mass point connecting line segment stored in the memory and the thickness data of the elastic structure, Calculate the acting force according to the position,
The mass displacement calculation means, based on the acting force calculated by the calculated elastic force and the acting force calculation means by said resilient force calculation means acting respectively on the mass point, the displacement of the mass point representing the elastic structure in time series Along with the equation of motion ,
The display means, based on the particle displacement calculated by the particle displacement calculation means and the mass point displacement calculated by the mass point displacement calculation means, shows the behavior of the particles and the elastic structure along a time series. A behavior analysis device characterized by displaying. The acting force calculation means includes:
  Centering on a mass point representing the elastic structure, a mass particle having a radius of 1/2 of the thickness of the elastic structure is defined, a relative position between the mass particle and the particle is obtained, and the relative position is determined. The behavior analysis apparatus according to claim 1, wherein an acting force is calculated. The acting force calculation means includes:
  The length of the elastic structure in the depth direction is defined to be the same as the representative particle diameter of the particle when calculating the behavior of the particle and the elastic structure in a two-dimensional cross section. Behavior analysis device. The display means includes
  Displaying the elastic structure by a circle, cylinder, or sphere defined by the position of the mass point representing the elastic structure and the thickness of the elastic structure, and a line connecting the circle, cylinder, or sphere, or 2. The behavior analysis apparatus according to claim 1, wherein the elastic structure is displayed by a line segment or a rectangular parallelepiped defined and connected by a position of a mass point representing the elastic structure and a thickness of the elastic structure. By executing the program read from the memory, the processing unit executes the particle displacement calculation step, elastic force calculation step, acting force calculation step, mass point displacement calculation step, and display step, and is contained in the container. In the behavior analysis method of the behavior analysis device that displays the behavior of the elastic structure and particles on the display device,
In the particle displacement calculation step, as a force acting on the particles having the particle data stored in the memory, based on a resultant force including contact force and gravity acting on each particle, the displacement of the particle is expressed by an equation of motion along a time series. The processor calculates using
In the elastic force calculation step, based on a spring-mass model representing the elastic structure stored in the memory, a bending spring force and an expansion spring force acting on each mass as the elastic force of the elastic structure are processed in the processing device. There is calculated,
In the acting force calculation step, using the position data of the mass point connecting line connecting the mass points representing the elastic structure stored in the memory and the thickness data of the elastic structure, the mass point connecting line segment and the obtains the relative position of the particles, the action force corresponding to said relative position is said processing unit calculates,
Wherein the mass displacement calculating step, the elastic force calculated in the elastic force calculation step acting respectively on the mass point, based on said action force calculated Oite the action force calculation step, time mass displacement representing the elastic structure The processor calculates using the equation of motion along the sequence ,
In the display step, based on the particle displacement calculated in the particle displacement calculation step and the mass point displacement calculated in the mass point displacement calculation step, a time series of the behavior of the particles and the elastic structure by the display device The behavior analysis method of the behavior analysis device, characterized in that the processing device controls the display . In the acting force calculation step,
Centering on a mass point representing the elastic structure, a mass particle having a radius of 1/2 of the thickness of the elastic structure is defined, a relative position between the mass particle and the particle is obtained, and the relative position is determined. 6. The behavior analysis method of the behavior analysis apparatus according to claim 5, wherein the processing device calculates an acting force of the behavior analysis apparatus. When calculating the behavior of particles and elastic structures in a two-dimensional section,
6. The behavior analysis method of the behavior analysis apparatus according to claim 5, wherein the processing device defines the length of the elastic structure in the depth direction as the same as the representative particle size of the particles. In the display step,
The elastic structure is displayed on the display device by a circle, a cylinder, or a sphere defined by the position of the mass point representing the elastic structure and the thickness of the elastic structure, and a line segment connecting the circle, the cylinder, or the sphere. Or the processing device controls display of the elastic structure by a line segment or a rectangular parallelepiped defined and connected by a position of a mass point representing the elastic structure and a thickness of the elastic structure. Item 6. A behavior analysis method of the behavior analysis apparatus according to Item 5 . In a program for causing a computer to execute a behavior analysis method for displaying on a display device the behavior of an elastic structure and particles contained in a container,
Based on the resultant force including contact force and gravity acting on each particle as the force acting on the particle having particle data stored in the memory, the processor calculates the displacement of the particle along the time series using the equation of motion. A particle displacement calculation step;
An elastic force calculation step in which the processing device calculates a bending spring force and an elastic spring force acting on each mass point as an elastic force of the elastic structure based on a spring-mass model representing the elastic structure stored in the memory. When,
The relative position between the mass point connecting line segment and the particle is obtained using the position data of the mass point connecting line segment connecting the mass points representing the elastic structure stored in the memory and the thickness data of the elastic structure. An action force calculating step in which the processing device calculates an action force according to the relative position ;
Elastic force calculated in the elastic force calculation step acting respectively on the mass point, based on the acting force calculated Oite the acting force calculation step, the equations of motion along the displacement time series of mass representing the elastic structure A mass displacement calculating step that the processing device calculates using ,
Based on the particle displacement calculated in the particle displacement calculation step and the mass point displacement calculated in the mass point displacement calculation step, the processing displays the time series display of the behavior of the particles and the elastic structure on the display device. A display step controlled by the device ;
A program for causing a computer to execute a behavior analysis method characterized by comprising: In the acting force calculation step,
Centering on a mass point representing the elastic structure, a mass particle having a radius of 1/2 of the thickness of the elastic structure is defined, a relative position between the mass particle and the particle is obtained, and the relative position is determined. The program for causing a computer to execute the behavior analysis method according to claim 9, wherein the processing device calculates the utility of the behavior analysis device. When calculating the behavior of particles and elastic structures in a two-dimensional section,
The processing apparatus determines that the length of the elastic structure in the depth direction is the same as the representative particle size of the particles. The program which makes a computer perform the behavioral analysis method of Claim 9 characterized by the above-mentioned. In the display step,
The elastic structure is displayed on the display device by a circle, a cylinder, or a sphere defined by the position of the mass point representing the elastic structure and the thickness of the elastic structure, and a line segment connecting the circle, the cylinder, or the sphere. Or the processing device controls the display of the elastic structure by a line segment or a rectangular parallelepiped defined and connected by the position of the mass point representing the elastic structure and the thickness of the elastic structure. A program for causing a computer to execute the behavior analysis method according to Item 9 .

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