JP2011081530A - Discrete element method analysis simulation method for particle model, discrete element method analysis simulation program and discrete element method analysis simulation device - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a discrete element method analysis simulation method, a discrete element method analysis simulation program and a discrete element method analysis simulation device, wherein a polygonal particle model introduced with rolling resistance, i.e., rotary motion of polygonal particles is introduced. <P>SOLUTION: This discrete element method analysis simulation method for analyzing behavior of a large number of analysis target particles includes: a step of imparting a physical property value to a virtual particle; a virtual particle arrangement step of arranging the virtual particles; and a behavior simulation step of simulating the behavior of the analysis target particles. The behavior simulation step includes a step of measuring a particle attitude angle between the analysis target particles and/or the virtual particles. In the behavior simulation step, about the analysis target particles and/or the virtual particles, the behavior of each particle is obtained by solving a motion equation formulated based on the rotary motion. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a discrete element method analysis simulation method, a discrete element method analysis simulation program, and a discrete element method analysis simulation apparatus for the behavior of polygonal particles into which rolling resistance of particles is introduced.

  In the field of handling particles such as powder and granules, it is important to understand the behavior of the particles. Conventionally, the behavior of such particles has often been grasped by trial and error experiments. In such a case, the behavior analysis of desired particles cannot be performed unless the composition of the particles actually used, the experimental apparatus, and the experimental environment are prepared. In addition, every time these specifications were changed, an experiment had to be performed, and time and cost had to be taken into consideration each time.

  In recent years, it has been widely used to simulate particle behavior analysis on a computer by formulating or modeling particle behavior analysis rather than experimentally, and simulating the behavior of a system governed by almost the same law. By using a simulation technique, the behavior of particles can be predicted. Further, by repeatedly performing the same simulation calculation while changing the conditions and parameters for introducing particles (powder), it is possible to evaluate the performance of various particle compositions, device designs and control bodies.

  As a means for simulating powder behavior analysis in the case of formulas, a discrete element method (Discrete Elements Method or Distinct Elements Method) analysis simulation method for analyzing the behavior of each powder (hereinafter referred to as DEM in this specification). And a method of analyzing the behavior by modeling the shape of the particle to be analyzed.

  The principle of DEM simulation is that the contact force between balls in the normal direction (see FIG. 1 (a)) and the shearing direction (see FIG. 1 (b)) acting between two balls considered as spherical particles is shown in FIG. As shown, the forked model is composed of springs 2 and 4 representing elastic properties, dashpots 3 and 5 representing inelastic properties, and a slider 6 (shear direction) representing frictional properties between the balls 1. Explained by The forked model determines the contact between the wall of the cylindrical container and the ball, the contact between the balls, the normal between the ball and the wall or the balls when they are in contact, the contact force and the friction force in the shear direction. Is calculated based on the Forked model shown in FIGS. 1A and 1B, and the elastic coefficients of the springs 2 and 4 are obtained from Hertz's elastic contact theory, and the viscous damping coefficient (normal line) of the dashpots 3 and 5 is calculated. Direction) and coefficient of friction (shear direction) can be obtained by experiments. Based on the contact force, the acceleration, velocity, and displacement of all the balls are calculated at each discretization time, and by repeating this calculation, the motion behavior of the entire ball group at an arbitrary time is simulated.

  According to the DEM simulation, collision determination between particles can be easily performed and the calculation load can be reduced. Examples of particle behavior analysis using DEM simulation include particle behavior analysis used for toner as disclosed in JP-A-2006-259911 (see Patent Document 1).

  However, the shape of the particles is often not a sphere in reality, and assuming a sphere, the problem is that the contact angle is not formed with high accuracy and the powder flow is estimated to be larger than the actual one. It is. Moreover, since the method described in Patent Document 1 assumes that the particles are spherical, and does not consider point or surface contact between the particles, for example, for the closest packing (high concentration packing) of metal particles Not suitable.

  On the other hand, as an improvement measure of particle behavior analysis by conventional DEM simulation, for example, a non-spherical particle proposed by Matsushima et al. (See Non-Patent Document 1) and a non-spherical particle model based on DEM simulation based on a cluster model. There is a spherical particle behavior analysis method. In the method described in Non-Patent Document 1, compared to the conventional DEM simulation as in Patent Document 1, it is possible to estimate the flow of the model powder closer to the actual powder, but the cluster model is used. Therefore, the problem is that the calculation system is small, that is, the number of model powders per region is estimated to be small.

  In recent years, there is a model proposed by John-Paul Latham, et al (see Non-Patent Document 2) that combines a DEM simulation and a polygonal particle model. The method described in Non-Patent Document 2 has solved the problem that the contact (particle orientation) angle between the particle and the wall surface is not accurately formed as compared with the conventional DEM simulation. Since the rotational motion of the sphere must be taken into account, there is a problem that a calculation load is applied.

JP 2006-259911 A

Matsushima et al. (Journal of Aerospace Engineering, 2009, pp. 15-23. Journal of Aerospace Engineering, 2009). John-Paul Latham et al., Minerals Engineering, 21 (2008), 797-805.

  The desired solution to the above-mentioned problem is to use spherical particles in the calculation to introduce the rolling resistance of the particles, ie the rotational movement of polygonal particles.

  In view of the above circumstances, the present invention provides a polygonal particle model that introduces rolling resistance, that is, a discrete element method analysis simulation method and a discrete element method analysis simulation of a polygonal particle model that introduces rotational motion of polygonal particles. A program and a discrete element method analysis simulation apparatus are provided.

  The object of the present invention is a discrete element method analysis simulation method for analyzing the behavior of a large number of analysis target particles, the step of giving physical properties to virtual particles, the virtual particle arrangement step of arranging the virtual particles, A behavior simulation step of simulating the behavior of the analysis target particle, and the behavior simulation step includes a step of measuring a particle posture angle between the analysis target particle and / or the virtual particle, and the analysis target particle and / or Alternatively, for virtual particles, this is effectively achieved by determining the behavior of individual particles by solving a motion equation based on translational motion.

  Further, the physical property value given to the virtual particle is at least one of Young's modulus, viscous damping coefficient, and friction coefficient, or the analysis target particle is a polygonal particle, or the analysis target particle And / or in the step of measuring the particle posture angle between the virtual particles, when the particle posture angle between the analysis target particle and / or the virtual particle is 0, the particles are determined to be in surface contact, or When it is determined that the particles are in surface contact with each other, an equation of motion is established based on the rotational motion, and the rotational angle is calculated in consideration of the contact surface between the particles in the calculation of the rotational moment and angular acceleration based on the information on the particle attitude angle. And determining the behavior of individual particles, or measuring the particle orientation angle between the analysis target particles and / or virtual particles, When the particle posture angle between the child and / or virtual particles is measured, when the particles are determined to be in point contact, or when the particles are determined to be in point contact, based on rotational motion More effective by establishing equation of motion, calculating rotation moment and angular acceleration based on information on particle attitude angle, calculating rotation angle considering particle contact point and contact force, and determining individual particle behavior Is achieved.

  The present invention also provides a discrete element method analysis simulation program for executing the discrete element method analysis simulation method, a recording medium on which the discrete element method analysis simulation program is recorded, or a discrete element method equipped with the recording medium. An analysis simulation apparatus, comprising: means for giving a physical property value to virtual particles; virtual particle arrangement means for arranging the virtual particles; and behavior simulation means for simulating the behavior of the analysis target particles; The behavior simulation means is effectively achieved by comprising means for measuring a particle posture angle between the analysis target particles and / or virtual particles.

  The discrete element method analysis simulation method of the present invention can easily determine the surface or point contact between particles by measuring the particle attitude angle, and can accurately simulate the flow of powder.

  Further, it is possible to simulate the behavior of the powder with a calculation load comparable to that of the conventional DEM simulation.

This is a forked model that dynamically simulates a DEM simulation in the prior art. It is a flowchart which shows the pre-processing before performing the particle behavior analysis of this invention. It is a flowchart of the DEM simulation method in this invention. It is the schematic of the polygon (regular hexagon) type | mold virtual particle in embodiment of this invention.

  Hereinafter, embodiments for carrying out the present invention will be described with reference to the drawings.

  FIG. 2 is a flowchart showing the flow of pre-processing before performing particle behavior analysis in the present invention.

  First, before conducting behavioral analysis, a physical property value is given to a simulation particle necessary for the present invention, that is, a virtual particle (step S1). Specifically, a spring constant, a viscous damping coefficient, and a friction coefficient are given to the virtual particles. Regarding the spring constant, there are a linear spring and a non-linear spring. For non-linear springs, enter Young's modulus.

  Next, a process for generating virtual particles is performed (step S2). As in the conventional DEM simulation, the processing procedure inputs a range in which virtual particles are arranged, and sets a virtual particle average diameter and a virtual particle average interval.

  Next, the number of virtual particles is set (step S3), the setting of the diameter of each virtual particle, the setting of the coordinate position where each virtual particle is arranged, and the diameter and coordinate position of each virtual particle are output (step S4). The process ends.

  FIG. 3 shows a processing procedure of particle behavior analysis in the present invention in the form of a flowchart. FIG. 4 shows a schematic diagram of a two-dimensional polygonal (regular hexagonal) type virtual particle in the embodiment of the present invention. In FIG. 4, regular hexagonal virtual particles are shown. However, when the simulation method of the present invention is actually used, the shape of the particles is not particularly limited.

  First, initial conditions are given to each particle to be analyzed, and initialization is performed (step S11). The initial condition referred to here is a physical property value or the like calculated in advance in the above-described virtual particle processing. Next, the contact (collision) between particles is determined (step S12). Here, the determination is performed assuming spherical particles (see “calculation” in patterns A and B in FIG. 4).

  The particles referred to here include both analysis target particles and virtual particles shown in FIG. The analysis target particles and the virtual particles can be simulated without particular limitation if they are powders such as metals, drugs, and toners.

  Next, when contact between particles is detected (determined), by further measuring the particle posture angle (step S13), when the particle posture angle θ (see FIG. 4 for θ) is 0, It is determined as surface contact (step S131), and when θ is observed, it is determined as point contact (step S132). In calculating the rotational motion, the method of calculating the rotational moment is changed between the case of surface contact and the case of point contact.

  As shown in FIG. 4, the particle orientation angle θ here refers to the side AB and the side in the regular hexagon ABCDEF and the regular hexagon A′B′C′D′E′F ′ when the particle is regarded as a plane. The case where A′B ′ overlaps (see pattern A “assumed” in FIG. 4) is defined as θ = 0, that is, surface contact, and point A contacts side A′B ′ (see pattern B “assumed” in FIG. 4). In this case, the angle is measured with the angle BAB ′ = θ and is defined as a point contact.

  After measuring the particle posture angle in step S13, step S131, and step S132, the distance between the particles is calculated (step S14), and the acting force such as the elastic repulsion force or the viscous force due to the contact is calculated (step S15). Furthermore, the rotational motion is calculated, and the angular velocity and the particle attitude angle of the particle are calculated. These calculation processes (steps S13 to S15) are repeated until the calculation for the contact particles is completed (step S16).

  If contact is not determined in step S12, the process proceeds to step S17 described later.

  Next, the external force acting on the particles is calculated (step S17). The external force mentioned here includes gravity, van der Waals force, and the like.

  And the process of step S13-S17 is repeatedly performed about all the particles (step S18).

  Next, an equation of motion is established for each particle to be analyzed, and the respective acceleration, velocity, and displacement are calculated (step S19). The equation of motion used in the present invention is as follows (see the following formula 1).

上記数１にて、並進運動は、ニュートンの第二法則より、式（Ａ）のように表される。ここで、式（Ａ）におけるＦ_Ｃ及びＦ_ｇは、接触力及び重力である。

In the above equation 1, the translational motion is expressed as in equation (A) by Newton's second law. Here, F _C and F _g in the formula (A) are contact force and gravity.

Next, the contact force F _C is expressed by the equations (1) and (2) of the above formula 1 for the normal direction component F _Cn and the tangential direction component F _Ct , respectively. In equations (1) and (2), k, δ, η, v, r, and ω are a spring constant, displacement, viscous damping coefficient, velocity, particle radius, and angular velocity, respectively. The subscripts n and t mean a normal direction component and a tangential direction component.

On the other hand, in the above equation 1, the rotational motion is expressed as the equation (3) in the above equation 1. Here, I is the moment of inertia, and r and F _Ct are defined by the equations (1) and (2) as described above.

  When solving the equation of motion in step S19, if the particles are determined to be in surface contact (step S131), the rotational motion is calculated in consideration of the surface contact. The rotational motion is calculated using Equation (3) in consideration of surface contact. In calculating the angular acceleration in surface contact, the contacted surface and the contact force acting on it are considered.

  In solving the equation of motion in step S19, when it is determined that the particles are in point contact (step S132), the contact point and the contact force are considered when calculating the angular acceleration in the point contact. Furthermore, the particle attitude angle is taken into account in the calculation of the rotational motion. This means that, for example, in the case of point contact of two particles, if the contact vertex is not on a straight line connecting the center of gravity of the particle, it rotates. This cannot be done assuming a spherical shape.

  Then, the processes in steps S12 to S19 are repeatedly executed until the time step ends (step S20).

  According to the present embodiment, since various physical property values are given to the analysis target particle and various physical property values are also given to the virtual particle, the equation of motion is calculated in step S19 and the mechanical interaction between the particles is calculated. When obtaining the action, the effect received by the particles can be reproduced, and the behavior of the particles to be analyzed can be analyzed with high accuracy.

  In the present embodiment, the behavioral analysis of a regular hexagonal particle having a two-dimensional system has been described. However, the present invention is not limited to this configuration. If the particle posture angle can be specified, a particle having a small rolling resistance, that is, a regular dodecagon, etc. Simulation of polygonal particles is also possible. Application to a three-dimensional system model is also possible.

  The program for executing the discrete element method analysis simulation method according to the present invention (hereinafter referred to as “discrete element method analysis simulation program”) is an arbitrary recording medium (CD-ROM, flash memory, etc.) external to the device, or the device. It is stored in an internal recording medium (such as a hard disk or memory), and is read and executed by the device. The apparatus here may be an information processing apparatus capable of controlling the execution of the discrete element method analysis simulation program, such as a personal computer, and a general-purpose hardware configuration can be applied. The discrete element method analysis simulation program according to the present invention and the recording medium and apparatus for recording the program are not limited to the types and numbers. The loading (storage) of the program can be changed as appropriate according to the form of the apparatus.

  In addition, the apparatus includes means for giving a physical property value to virtual particles, virtual particle placement means for placing the virtual particles, and behavior simulation means for simulating the behavior of the analysis target particles, Although means for measuring a particle posture angle between the analysis target particles and / or virtual particles is provided, the mounting method of the recording medium in which the discrete element method analysis simulation program is recorded can be appropriately changed.

  By using the simulation method of the present invention, it is expected to analyze the behavior of powders handled in the closest packing of metal particles, toner particles, pharmaceuticals and the like.

1 Ball 2 Normal Spring 3 Normal Dash Pot 4 Shear Spring 5 Shear Dash Pot 6 Slider

Claims (10)

A discrete element method analysis simulation method for analyzing the behavior of a large number of particles to be analyzed,
Giving physical properties to virtual particles;
A virtual particle placement step of placing the virtual particles;
A behavior simulation step of simulating the behavior of the analysis target particle,
The behavior simulation step includes a step of measuring a particle posture angle between the analysis target particle and / or the virtual particle, and solves a motion equation based on a rotational motion for the analysis target particle and / or the virtual particle. A discrete element method analysis simulation method characterized in that the behavior of individual particles is obtained.   The discrete element method analysis simulation method according to claim 1, wherein the physical property value given to the virtual particles is at least one of a spring constant, a viscous damping coefficient, and a friction coefficient.   The discrete element method analysis simulation method according to claim 1, wherein the analysis target particle is a polygonal particle.   In the step of measuring the particle posture angle between the analysis target particles and / or virtual particles, when the particle posture angle between the analysis target particles and / or virtual particles is 0, the particles are determined to be in surface contact. The discrete element method analysis simulation method according to any one of claims 1 to 3.   When it is determined that the particles are in surface contact with each other, an equation of motion is established based on the rotational motion, and the rotational angle is calculated in consideration of the contact surface between the particles in the calculation of the rotational moment and angular acceleration based on the information on the particle attitude angle. The discrete element method analysis simulation method according to claim 4, wherein the behavior of each particle is obtained.   In the step of measuring the particle posture angle between the analysis target particle and / or virtual particle, when the particle posture angle between the analysis target particle and / or virtual particle is measured, the particles are determined to be in point contact. The discrete element method analysis simulation method according to any one of claims 1 to 3.   When it is determined that the particles are in point contact with each other, an equation of motion is established based on the rotational motion, and the contact point and the contact force between the particles are considered in the calculation of the rotational moment and the angular acceleration based on the information on the particle attitude angle. 7. The discrete element method analysis simulation method according to claim 6, wherein the rotation angle is obtained to obtain the behavior of each particle.   A discrete element method analysis simulation program for executing the discrete element method analysis simulation method according to any one of claims 1 to 7.   A recording medium on which the discrete element method analysis simulation program according to claim 8 is recorded.   A discrete element method analysis simulation apparatus equipped with the recording medium according to claim 9, wherein the apparatus provides a physical property value to a virtual particle, a virtual particle arrangement unit that arranges the virtual particle, and the analysis target A behavioral simulation means for simulating the behavior of particles, and the behavioral simulation means comprises means for measuring a particle posture angle between the analysis target particles and / or virtual particles. Simulation device.

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