JP2013023698A - Method for analyzing particle behavior - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a calculation method and a method for analyzing particle behavior that achieve high-speed calculation without decreasing accuracy in calculation of behavior of a great number of particles in a large-scale facilities.SOLUTION: In order to simplify calculation related to a collision process between particles in the analysis of particle behavior of a multiparticle system, a velocity of one particle is replaced with a predictive velocity at the time of tin the relative velocity between two particles, which provides viscous force at the time of tin the normal direction of the contact surface between the collided two particles. The viscous force in the normal direction acting on a particle 1 is assumed to be the force, η×(V-E), proportional to the difference between the predictive value Eof the velocity in the normal direction Vat the time of tand the velocity in the normal direction Vat the time of tof the other particle 2, and the viscous force in the normal direction acting on the particle 2 is represented by the force, η×(V-E), proportional to the difference between the predictive value Eof the velocity in the normal direction of the particle 2 at the time of tand the velocity in the normal direction Vat the time of t.

Description

  The present invention relates to a particle behavior calculation method using a discrete element method and its application to the steelmaking field.

  As shown in the outline of the sintering material classification equipment in Fig. 7, the sintering material is loaded into the surge hopper from the shuttle conveyor, cut out from the drum feeder, and dropped onto the lower pallet by dropping it over the fluid. Is done. The arrangement of these devices is designed so that a sintered material having a large particle size is distributed at the bottom of the loading layer on the pallet and a sintered material having a small particle size is distributed at the top. However, the classified sintered material is not necessarily arranged with the particle size distribution as described above. In such a case, as the sintered raw material is dispensed, the aggregate of the raw materials tends to collapse into an indeterminate shape, which hinders efficient raw material dispensing, or the sintered raw material diffuses and cracks. In some cases, there was concern about a serious decline in production efficiency and environmental impact.

  In addition, when designing a sintering material charging device that consists of elements such as shuttle conveyors, surge hoppers, drum feeders, and sieves, and for the purpose of distributing the sintering materials, the arrangement of each machine element through experience and trial and error There were many cases to decide. In performing the optimum design of such an apparatus, it is effective to perform a computer experiment with high accuracy using a simulation using a computer. The discrete element method shown in Non-Patent Document 1 is often used for behavior analysis of particle groups in such a simulation. In the discrete element method, individual particles constituting a particle group are used as elements, and the dynamic behavior of the aggregate is numerically analyzed on the condition that each element satisfies the equation of motion with respect to the aggregate of elements. It is a technique. The numerical calculation is performed with the step time as Δt and the equation of motion as the difference equation.

  In the discrete element method, the behavior of many particles is analyzed. If there is no external field, the particles move repeatedly with collision and constant velocity. If there is an external field such as gravity or an electric field, the movement by the force of the external field is added to such movement. There, the collision of many particles is basically the collision of two particles. In order to obtain an accurate result, the collision process from the collision of the particles to the separation needs to be calculated finely to improve the accuracy, and the step time Δt for calculating the movement needs to be fine.

In the discrete element method, the outline of handling two colliding particles is as follows. Hereinafter, the time index p is introduced. p is an integer, and the value of p increases by 1 as time advances by Δt. The time at the time index p represented by t ^p. Similarly, a specific physical quantity (for example, V) at the time index ^p is represented as V ^p .

Assume that two particles colliding at time t ^p are particle 1 and particle 2. When each particle collides, it is considered that the particles are sunk into each other. ^{Let the} amount of sinking at that time be δ ^p . This is illustrated in FIG. The force received by each particle is determined by dividing the force in the normal direction of the contact surface formed by the indentation and the component in the in-plane (tangential) direction. As shown in FIG. 2, the force in either direction is represented by a force due to the parallel connection of a spring having a spring constant k and a dashpot having a viscosity coefficient η. For example, the force in the normal direction of the contact surface that the particle 1 receives is represented by the sum of the repulsive force by the spring proportional to the amount of penetration and the viscous force proportional to the relative velocity of the two colliding particles. If a time t ^p, respectively V ₁ direction normal velocity of particles 1 and particle 2 in ^p, V ₂ ^p, the particle 1, the normal force F ₁ ^p experienced by the collision at time t ^p is It is expressed as follows.
F ₁ ^p = −k × δ ^p + η × (V ₂ ^p −V ₁ ^p )
The first term on the right side of the above formula is the repulsive force due to the spring, and the second term is the viscous force due to the dashpot. If there is an external field such as gravity, such a term will be added. Similarly, the force received by the particle 2 is expressed by changing the subscript 1 to the subscript 2 in the above equation.

Normal motion is obtained by substituting the force of the above equation into Newton's equation of motion. The calculation is performed discretely with a step time Δt. Accordingly, the motion of the particle 1 in the normal direction, that is, the temporal change in velocity and position can be obtained by solving the following discrete motion equation.
m ₁ (V ₁ ^{p + 1} −V ₁ ^p ) / Δt = F ₁ ^p
x ₁ ^{p + 1} = x ₁ ^p + V ₁ ^p Δt
Here, m ₁ is the mass of the particle 1, and x ₁ ^p is a contact surface normal direction component at the center position of the particle 1 at time t ^p . The particle 2 is obtained in the same manner, and in this way, the speed and position change at every step time Δt. When the distance between the centers of the two particles becomes larger than r ₁ + r ₂ which is the sum of the respective radii, the collision process ends, and the movement proceeds to a constant velocity motion or a free motion in the external field.

  The force in the in-plane direction (tangential direction) of the contact surface is also expressed by a similar model, and its motion is obtained in the same manner. In addition, the rotational motion of the particles is taken into account and analyzed as a comprehensive particle motion.

  In this way, the behavior of the particle group is analyzed with high accuracy. Even when a particle collides with a plurality of particles, the collision may be divided into two particles as described above, and the resultant force may be obtained to solve the equation of motion. Further, for the elastic coefficient k and the viscosity coefficient η, non-patent document 2 and non-patent document 3 disclose display formulas that can be calculated accurately and efficiently.

  Moreover, in patent document 1, it discloses that the turning chute | shoot for the raw material charging apparatus to a blast furnace is designed using a discrete element method.

  However, when trying to clarify the macroscopic behavior of flowing powder using the discrete element method, it is necessary to track the collision process as described above for a large number of particles, and the calculation of all motions is completed. There is a problem that it takes an enormous amount of time. In order to shorten the calculation time, increasing the step time Δt to reduce the number of calculation steps to a rough time scale is one effective measure for reducing the calculation time. However, in that case, there is no big problem when the particles are moving freely, but for the motion analysis when the particles collide, as shown above, unless the collision process is traced in fine steps, It turns out that a big error will arise. That is, if the step time Δt is increased, a very large error is generated in the calculation of the collision process, and the calculation accuracy is greatly reduced.

  There have been some disclosures of techniques for reducing the calculation time. In Patent Document 2, the behavior of a transported material such as coal or ore conveyed by a conveyor belt is analyzed using the discrete element method. However, in order to shorten the time, the behavior of the transported material such as a belt transport surface is directly measured. Only the part that influences is described and analyzed. Patent Document 3 discloses that a space area to be calculated is divided and calculation is performed on representative particles in the divided area. Further, Patent Document 4 discloses an example of behavior analysis of toner used in a copying machine, but particles with a large amount of movement are subject to high-precision calculations, and particles with a small amount of movement are low-precision. It is supposed to be the target of calculation. Here, as a low-accuracy calculation method, it is disclosed that the determination of contact between particles is omitted or the calculation amount is reduced by increasing the calculation interval.

  In other words, in the conventional technique, it is necessary to determine the position and amount of movement of the particle to be analyzed, and to apply calculations with different accuracy. There was a concern that the error of the particles became large and the behavior of the particles could not be analyzed correctly.

  As a measure for avoiding such a concern, a calculation method capable of reducing the amount of calculation while maintaining accuracy is required.

JP 2007-262453 A JP 2001-139116 A JP 2007-286514 A JP 2010-79493 A

Hideo Kiyama, Takashi Fujimura, Proceedings of the Japan Society of Civil Engineers, No. 333, 137-146 (1983) S.P.Timoshenko and J.N.Goodier, Theory of Elasticity, p409, McGraw-Hill p409 (1970) Edited by Powder Engineering Society, Introduction to Powder Simulation, Sangyo Tosho Co., Ltd. p33 (1998)

  The present invention relates to a calculation method for speeding up the calculation without reducing accuracy when calculating the behavior of a large number of particles in a large-scale facility, and the behavior of particles in a short time by using such a calculation method. It is an object of the present invention to provide a particle behavior analysis method capable of analyzing the above.

In the case of the particle behavior analysis of the multiparticulate system targeted by the present invention, the present inventors consider that contact or collision between particles is very large, and the calculation load can be reduced if calculations regarding such a collision process can be omitted. It was. While maintaining accuracy, we investigated the calculation method that can omit the collision process by increasing the time step. As a result, the velocity of one particle is replaced with the predicted velocity at time t ^{p + 1} in the relative velocity between the two particles giving the viscous force at time t ^p in the normal direction of the contact surface between the collided two particles. It was found that the purpose was achieved.

The gist of the present invention is as follows.
(1) A method for calculating the motion from the collision of any two particles to the separation in the calculation of the particle motion, wherein the normal direction of the contact surface of the two particles colliding at time t ^p (hereinafter, The force acting on the “normal direction”) is an elastic repulsive force −k × δ ^p whose elastic coefficient is k and proportional to the amount δ ^p of the particles at time t ^p .
And expressed as the sum of viscous drag forces with viscosity coefficient η,
Of one of the particles 1, the time t ^p than just time step Δt advanced time t ^{p +} direction normal velocity V ₁ ^{p + 1} in the ^first prediction value E ₁ ^{p + 1} and law at the time t ^p of the other particles 2 Force proportional to the difference from linear velocity V ₂ ^p η × (V ₂ ^p −E ₁ ^{p + 1} )
Is the normal direction viscous force acting on the particle 1, and the normal direction viscous force acting on the other particle 2 is also the predicted value E ₂ ^{p +} of the normal direction velocity of the particle 2 at time t ^{p + 1} . force eta × proportional to the difference between the normal direction velocity V ₁ ^p at ¹ and the time _{^{t p (V 1 p -E 2}} p + 1)
The calculation method of the motion of the normal direction until it leaves | separates after the two particles collide characterized by expressing by.
Here, the time index p is an integer, and the value of p increases by 1 when the time advances by Δt. The upper right subscript p means the physical index in the time index p.
(2) Predicted normal direction velocity E ₁ ^{p + 1} of particle ¹ and predicted normal direction velocity of particle 2 at time t ^{p + 1} , where the mass of particle ₁ is m ₁ and the mass of particle 2 is m ₂ E ₂ ^{p + 1} respectively
as well as
The method for calculating the motion in the normal direction from the collision of the two particles to the separation, as described in (1) above.
(3) At the time t ^p , normal forces F ₁ ^p and F ₂ ^{p received} by the particles 1 and 2 from the collision are obtained.
as well as
The calculation method of the motion of the normal direction until it leaves | separates after the two particle | grains as described in said (1) or (2) collide, characterized by these.
(4) A particle behavior analysis method for analyzing the behavior of multiparticulate particles, wherein the motion of each particle is calculated by the discrete element method using the equation of motion, and any two particles collide with each other. A particle behavior analysis characterized by using the method of calculating the motion in the normal direction until the two particles collide after they collide with each other for the calculation of the motion until they move away from each other (1) to (3) Method.
(5) The particle behavior analysis method described in (4) above is used to obtain the particle distribution of the sintered raw material that has been put into the surge hopper from the shuttle conveyor, cut out from the drum feeder, and dropped over the sieve. A method for analyzing the distribution of particles in a sintered material.

It is a figure in which particles collide. It is a figure explaining the force of the normal direction which acts on the particle | grains which are colliding. It is a figure of the collision process of particle | grains. It is a figure of the collision process of particle | grains. It is a figure of the collision process of particle | grains. It is a flowchart which calculates the motion of multiple particles. It is a figure of a sintering raw material classification equipment outline. It is a figure explaining particle behavior calculation.

[First embodiment]
(Determination of particle collision and amount of retraction)
The shape of the target particle is not particularly limited, but here, a case where it is a sphere will be described as an example. Particle 1 is a sphere of radius r _1, of determining whether the two particles of a particle 2 of radius r ₂ are in contact, there are various methods, the distance for example of particles 1 center and particles 2 center If it is r ₁ + r ₂ or less, it may be determined that the contact is made. If the particle is not a sphere, the center of gravity of the particle may be the center and the average radius may be the radius.

The amount of penetration is determined by the difference in the center-to-center distance between the two particles that are in contact with r ₁ + r ₂ . When used for calculation, a value obtained by further dividing the difference thus obtained by the above-mentioned r ₁ + r ₂ may be used.

If the amount of penetration between particle 1 and particle 2 is δ and the positions of the centers of the two particles measured on the line connecting the centers are x ₁ and x ₂ , the center distance between the two particles is | x ₁ −x ₂ | These change over time. If the right shoulder subscript ^p indicates that each amount is a value at time t ^p, the amount δ ^p of indentation at time t ^p can be expressed as follows. An example of indentation is shown in FIG.
δ ^p = {(r ₁ + r ₂ ) − | x ₁ ^p −x ₂ ^p |} / (r ₁ + r ₂ ) [Formula 1]

  When contact determination of two particles is performed at a certain time, the center distance between the two particles is much smaller than the sum of the radii of the particles determined to be in contact, that is, the amount of retraction is often large. When such dents are large, the repulsive force is also large, and unless the time step is taken finely, the particles are repelled rapidly by the large repulsive force, and the calculation may become unstable.

(Force acting in the normal direction of the contact surface)
The force acting in the normal direction to the contact surface (hereinafter referred to as contact normal force) has a great influence on the collision process until the two particles in contact with each other are separated. In other words, the collision process ends quickly if the contact surface is largely retracted along the normal line. Therefore, the collision process can be omitted by adjusting the force acting in the normal direction. Here, the transition of the time is assumed to change by the increment time Δt. That is, at time t ^p , time has elapsed from time index p = 0 by pΔt.

In Non-Patent Document 1, as the force acting on the two particles in contact at time t ^p in the normal direction of the contact surface, when focusing on the particle 1, (1) repulsive force proportional to the amount of penetration -Keideruta ^p, and is given as the sum of (2) viscous force is proportional to the relative velocity of the two _{^{particles, η (V 2 p -V 1}} p). Here, the subscript p on the right shoulder represents a time index. δ ^p is the amount of penetration of particles 1 and 2 at time t ^p . V ₁ ^p and V ₂ ^p are the contact surface normal direction velocities of the particles 1 and 2 at time t ^p , respectively. K and η are proportional coefficients. As shown in FIG. 2, these are represented by a model in which a spring having a spring constant k and a dashpot having a viscosity coefficient η are connected in parallel. That is, as described in Non-Patent Document 1, in the prior art, the contact normal force F ₁ ^p acting on the particle 1 is F ₁ ^p = −kδ ^p + η (V ₂ ^p −V ₁ ^p ) [Formula 2]
It is expressed. Further, the normal force acting on the particle 2 may be obtained by replacing the subscripts 1 and 2 in [Formula 2].

If the time step Δt is increased, even if contact determination is made at time t ^p , the particles are immediately separated, the collision process can be omitted, and the calculation can be speeded up. However, the repulsive force term of the above [Equation 2] becomes large, As will be described later, the speed of the particles becomes too high, and the calculation becomes unstable or the error becomes large. Therefore, in the prior art, it is necessary to calculate Δt finely and track the collision process at fine time intervals. The inventors paid attention to the expression of the viscous force in (2) above. Therefore, the normal line direction velocity V ₁ ^p at the time t ^p of the particle 1 is the replaced velocity at time t ^{p + 1} of the particle 1, that is, V ₁ ^{p + 1.} Here, the time t ^{p + 1} is a time advanced from the time t ^p by the increment time Δt. However, at time t ^p, since it is difficult to grasp the precise rate at time _{^{t p + 1, V 1 p}} + 1 is represented by a predicted value E ₁ ^{p + 1} at time t ^{p + 1.} That is, in the present invention, the contact normal force F ₁ ^p acting on the particle 1 replaces V ₁ ^p in the above [Equation 2] with E ₁ ^{p + 1} ,
_{^{F 1 p = -kδ p + η}} (V 2 p -E 1 p + 1) [ Equation 3]
It is expressed. For the contact normal force F ₂ ^p acting on the particle 2, the subscripts 1 and 2 in [Formula 3] may be interchanged. That is, F ₂ ^p = −kδ ^p + η (V ₁ ^p −E ₂ ^{p + 1} ) [Formula 4]
It expresses.

There are several methods for calculating the predicted normal direction velocity. For example, according to the calculation method according to the present invention, even if coarser increment Δt time, even if the collision at time t ^p, at time t ^{p + 1} particles often are separated, and even repulsive force It was found that the calculation amount was reduced while maintaining accuracy without being too large, and the calculation time was ¼ or less compared to the case of the prior art using [Formula 2]. Here, it should be noted that the normal-direction viscous force acting on the particle 2 is usually the reaction force of the viscous force acting on the particle 1 and is therefore a force of the same magnitude and in the opposite direction. There is a relationship, and the sum is zero. In the present invention, [Formula 4] is obtained, which is not necessarily the same size as [Formula 3]. Therefore, in the two particles that are in contact, the sum of the viscous forces in the normal direction is not zero, but the residual force has a finite value, and the relationship between action and reaction is not satisfied. Does not give a correct picture. However, it has been found that the error caused by that is negligibly small. Furthermore, when considering the collision of a large number of particles, it has been found that such a residual force has a random direction and magnitude, and as a result, the sum is further reduced and has little influence on accuracy.

(Predicted normal direction velocity)
The predicted normal velocity E ₁ ^{p + 1} of the particle 1 is considered as the normal velocity of the particle 1 at time t ^{p + 1 when} the particle 1 moves with the force received only from the particle 2 with which the particle 1 collides. Therefore, it is obtained from the following discrete equation of motion.
m ₁ (E ₁ ^{p + 1} −V ₁ ^p ) / Δt = F ₁ ^p [Formula 5]

Substituting [Formula 3] into F ₁ ^p in the above formula and organizing it,
Is obtained.

By substituting [Formula 6] into [Formula 3] again, the normal direction force that the particle 1 receives from the particle 2 at time t ^p is:
It becomes. Similarly, the predicted normal velocity E ₂ ^{p + 1} and the normal direction force F ₂ ^p for the particle 2 are expressed by the following [Equation 8] and [Equation 9].

Thus, the prediction direction normal speed E ₁ ^{p + 1} and E ₂ ^{p + 1} is indicated by an amount of time t ^p, because it was shown by the normal direction force value be at time t ^p, efficient program creation can and will Furthermore, as described above, the calculation time can be shortened while maintaining the accuracy.

(Omission of calculation of collision motion after contact of particles judged to be in contact)
A conceptual diagram of the progress of the subsequent collision process when two particles are in contact at time t ^p is shown in FIGS. When the normal force is expressed by [Formula 2], which is the prior art, it is necessary to finely calculate the collision process until the particles are separated as shown in FIG. For example, as shown in FIG. 4, in the collision process when Δt is multiplied several times with the same normal direction force, the particles after contact are greatly sunk in the next step, and the next step is a repulsive force. Each rebounds at a high speed, making the calculation unstable and increasing the error. Next, when the present invention of [Equation 3] is used with the large time increment Δt, as shown in FIG. 5, the contact is depressed to some extent in the next step as shown in FIG. The calculation of the collision process can be omitted. This is because, when [Equation 3] is used, the amount of penetration increases, and even if the repulsive force increases considerably, the viscous force acting in the reverse direction also increases and is balanced moderately. That is, if [Equation 3] is used, it is possible to shorten the calculation speed by taking a large time step while maintaining accuracy and omitting the collision process.

  Because of the significant omission of the above calculation steps, when using the calculation method according to the present invention, the accuracy of the calculation results hardly change even if the time increment Δt is 4 to 10 times the time increment in the case of the prior art. I understood. That is, it has been found that the calculation time is ¼ to 1/10 with the same accuracy as that of the calculation according to the prior art.

(Motion of contact particles)
In a particle group composed of a large number of particles, one particle often collides with a plurality of particles at the same time. Even in this case, for each collision of two particles, the normal force is obtained and the resultant force is considered to act on the particles.

For example, a certain target particle i is fixed, and it is determined whether another opposing particle j collides with the particle i. For those determined to collide, the normal direction force between the two particles represented by [Equation 7] and [Equation 9] is obtained for each contact surface. When this operation is repeated and all collision particles are obtained for the particle i, a similar search is performed focusing on other particles, and the collision particles and the normal force in each collision are obtained for all particles, and the sum of these is obtained. Ask for. However, since the contact surface normal is directed in a different direction in each collision, it is necessary to obtain a vector-like sum. For example, if N counter particles j collide with the target particle i, the normal velocities in different directions are considered for each collision of i and j, and the above [Equation 3] to [Equation 9] are Apply. That is, the predicted speed E _ji ^{p + 1} at the time t ^{p + 1} of the particle i in the normal direction of each contact surface with the opposing particle j of the target particle i may be considered in the same manner as in [Equation 6]
It becomes. Here, [delta] _ij ^p is weight sinking due to the collision of the particles i, j at time t ^p, V _ij ^p is the particle j at time t ^p, the velocity component of the contact surface normal to the direction of the particles i, j. Similarly, V _ji ^p is a velocity component in the normal direction of the contact surface of the particle i at time t ^p .

Therefore, the force F _ji ^{p in the} normal direction that the particle i receives from the collision between the particle i and the particle j at the time t ^p is expressed as follows in the same manner as in [Equation 7].

As described above, this force is the amount in the normal direction with respect to the contact surface of the particle i and the particle j at the time t ^p , and when the unit vector in the normal direction is represented by e _ji ^p , 11] is a vector indicating the direction of the force.

The resultant force of each normal direction force that the particle i receives from the N collisions at the time t ^p is obtained by summing the opposing particle j with the force represented by [Equation 11] as a vector having the direction e _ji ^p. obtain.

Further, the force in the tangential direction of the contact surface in each collision and the rotational moment due to each collision are also obtained, and the resultant force is obtained. Here, the tangential force and rotational moment of each contact surface can be calculated using the prior art as described in Non-Patent Document 1. That is, the force in the tangential direction of the contact surface is calculated on the assumption that an elastic spring that gives shear resistance and a viscous dashpot are arranged in parallel, and shear deformation near the contact point is mainly caused by frictional force between elements. The rotational moment can be obtained by a numerical analysis based on a difference method in the same way as the displacement equation of motion, with the equation of motion of the moment of rotation established for each element. Once these resultant forces are obtained, the discrete equation of motion is solved in the same manner as in the prior art, and the velocity and position at time t ^{p + 1} are obtained. A flowchart of the above steps is shown in FIG.

(Particle behavior analysis method)
In the particle behavior analysis method for analyzing the behavior of multiparticulate particles, the method for calculating the motion in the normal direction from the collision of the two particles of the present invention to the separation thereof can be used. In the particle behavior analysis method, the motion of each particle is calculated by a discrete element method using a motion equation. With respect to all the particles existing in a predetermined space region, numerical calculation is performed with the step time being Δt and the equation of motion of each particle as a difference equation. For particles that do not collide with other particles, if there is no external field, a constant-velocity linear motion, and if there is an external field such as gravity or an electric field, motion due to external field force is added to such motion. Here, the calculation method of the motion in the normal direction from the collision of the two particles of the present invention to the separation of the two particles is used for the calculation of the motion from the collision of any two particles to the separation of the two particles.

  After setting the initial conditions and boundary conditions of the system, perform the behavior analysis for all the particles that make up the multiparticulate particles according to the above procedure, and see how the target multiparticulate particles as a whole over time. It is possible to clarify whether to exercise.

Using the calculation method and device according to the present invention, a group of particles composed of particles of different sizes passes through various devices under gravitational acceleration until it finally stops moving. In addition, it is possible to obtain the spatial particle size distribution of the particles in the lump finally formed by the particle group. At this time, mechanical elements such as shuttle conveyors, hoppers, drum feeders, and sieves are virtually arranged as devices through which the particle groups pass, so that the particle groups have a particle size distribution simulating the particles of the sintering raw material. By deciding, an actual sintering raw material charging apparatus can be modeled. As the final particle size distribution of the particles, it is desirable in terms of work efficiency that a distribution in which large particles are below and small particles are on top is formed. However, as described above, there are many cases where a distribution deviating from such a desirable distribution is generated depending on the spatial positional relationship and operation conditions of the machine elements. By using the calculation method and analysis method according to the present invention, the sintered raw material apparatus can be modeled and the spatial particle size distribution finally formed can be obtained. Furthermore, an ideal spatial particle size distribution can be obtained by changing the position of the machine element and operating conditions and performing the calculation. In other words, the design of the sintering raw material charging apparatus and the determination of the operating conditions can be performed at a remarkably high speed.
(Sintering raw material particle distribution analysis method)
That is, the particle behavior analysis method of the present invention can be used as a particle arrangement distribution analysis method for sintered raw materials. In the sintering material classification equipment as shown in FIG. 7, the material is put into the surge hopper 2 from the shuttle conveyor 1, cut out from the drum feeder 3, falls down on the fluid 4, and becomes a deposit 6 on the pallet 5. The particle distribution of the sintered raw material obtained is determined by the particle behavior analysis method of the present invention. First, the shuttle conveyor 1, the surge hopper 2, the drum feeder 3, and the sieve 4 are arranged in the space, and the boundary condition when each particle comes into contact with each device is determined. Next, the particle distribution of the sintered raw material mounted in the shuttle conveyor is given as an initial condition. After making the above preparations, a numerical equation is calculated for all particles (elements) existing in the system as a difference equation with a ticking time Δt. In that case, the calculation method of the motion of the normal direction until it leaves | separates after the two particle | grains of this invention collide is used.

  As a result of such calculations, it is possible to clarify the particle distribution of the sintered raw material that has been thrown from the shuttle conveyor into the surge hopper, cut out from the drum feeder, and dropped over the fluid over time. it can.

(Coefficient for force in the normal direction of the contact surface)
The coefficients k and η used in [Equation 3] can be considered as an elastic coefficient and a viscosity coefficient, respectively, but as disclosed in Non-Patent Document 2, Non-Patent Document 3, etc., rather than simple constants. By setting as follows, accurate calculation can be performed efficiently.

  The two particles that collide are defined as particle i and particle j.

Here, each variable is expressed as follows.
1 / E ^* = (1−ν _i ² ) / E _i + (1−ν _j ² ) / E _j [Formula 15]
^{1 / r * = 1 / r} i + 1 / r j [ Equation 16]
1 / m ^* = 1 / m _i + 1 / m _j [Formula 17]
Within the range of [Equation 13] to [Equation 18], E is Young's modulus, ν is Poisson's ratio, r is the radius of the collision particle, m is the mass of the collision particle, e is the coefficient of restitution, and π is the circumference. Represent.

(Analysis using image processing processor GPU)
A general-purpose computer that uses a normal central processing unit (CPU) as a computer used for the calculation of particle behavior analysis when it is calculated by a graphics processing unit (GPU), which is an arithmetic unit for high-speed image processing. It was found that the calculation time can be shortened to 1/50 or less in comparison with the same calculation using. That is, when a program created using the calculation method according to the present invention is applied to the GPU, the calculation time is reduced to 1/200 or less compared to the case where the program using the calculation method of the prior art is applied to the CPU. It can be done. However, when implemented on a GPU, the program form executed by the computer is different from the program form applied to the CPU, so the program form must be changed. However, the calculation algorithm is the same, and it is the same that the algorithm that becomes the calculation method according to the present invention is used. Therefore, even if the calculation is performed using the GPU, it is apparent that the present invention is achieved. In addition, the calculation method according to the present invention has no factor that hinders parallel calculation, which is a feature of calculation by GPU. Therefore, it is possible to efficiently extract the characteristics of calculation by GPU.

[Example 1] (Analysis using a general-purpose computer)
Using the coefficients shown in [Equation 13] to [Equation 18], a particle group consisting of 5 types of spherical particles and 2 × 10 ⁴ particles in a time increment of Δt = 10 ⁻⁶ seconds is obtained as a hopper. The calculation of falling onto the pallet was simulated using a general-purpose computer. The simulation performed in the conventional technique was completed in about 50 hours. A similar simulation was carried out at a time step of 50 × 5 × 10 ⁻⁵ seconds. However, the prior art did not provide an accurate solution. However, if the calculation method according to the present invention is used with the time step kept at 5 × 10 ⁻⁵ , the simulation is completed in about 5 hours, and the particle is almost the same as the calculation performed in the time step of 10 ⁻⁶ in the prior art. Distribution was obtained. That is, it was found that the error due to the “predicted speed” can be almost ignored. Furthermore, it was found that the calculation time was shortened to 1/10 while maintaining accuracy by the program according to the present invention.

[Example 2]
(Comparison between analysis using a general-purpose computer and analysis using a processing unit GPU for image processing)
The calculation of the behavior of a particle group consisting of 2 × 10 ⁵ particles was simulated using a conventional calculation method at a time interval of 1 × 10 ⁻⁶ seconds using a general-purpose computer, and it took about 98 days to complete the calculation. It was. A similar calculation was performed using the calculation method of the present invention with a time step of 5 × 10 ⁻⁵ seconds, and it took about 8 days. In a time step of 5 × 10 ⁻⁵ seconds, a program to which the calculation method of the present invention was applied was converted to operate on a device using a GPU and calculated on a device having a GPU. As a result, the calculation was completed in 12 hours, and almost the same result as in the case of the time increment of 1 × 10 ⁻⁶ seconds was obtained by the conventional method. Accordingly, the calculation time is reduced to about 1/200 while maintaining the accuracy with respect to the conventional technique using a general-purpose computer.

[Example 3]
The particle motion according to the present invention is used for simulating the distribution of the sintered raw material that has been thrown into the surge hopper 2 from the shuttle conveyor 1, cut out from the drum feeder 3, and dropped over the fluid 4 using the apparatus shown in FIG. 7. This calculation method was simulated using a general-purpose computer. First, a shuttle conveyor, a surge hopper, a drum feeder, and a sieve were arranged in the space, and boundary conditions when each particle contacted each device were determined. Subsequently, the particle arrangement distribution of the sintering raw material mounted in the shuttle conveyor was given as an initial condition. After making the above preparations, numerical calculations were performed on all particles (elements) present in the system as a difference equation with a ticking time Δt. At that time, the calculation method of the motion in the normal direction from the collision of the two particles of the present invention to the separation of the two particles was used.

FIG. 8 shows the calculation results of the particle behavior in the apparatus in which the sieve part is composed of a plate and a plurality of strips. The fallen particles accumulate on the lower pallet. The lower pallet moves from the right to the left in the figure at a predetermined speed, and the deposited particles are transported to the left in the figure and proceed to the next step. In the calculation, three types of particles were considered (large particles (the brightest, white particle diameter 6 mm), medium particles (the darkest, black particle diameter 5 mm), and small particles (intermediate brightness, gray particle diameter 3 mm). )). Each particle had the same weight density, 3.3 g / cm ³ . The interval between the strips is wider at the tip (lower right), and the larger particles fall from the right. The fallen large particles roll to the right on the slope of the deposit and are easily caught in the bottom of the deposit from the right end of the slope. On the other hand, small particles fall from around the root of the sieve and fall on the upper surface of the sediment in the lower bullet. As a result, it was found that sediments were classified from the bottom into large particles (lightest, white), medium particles (darkest, black), and small particles (intermediate brightness, gray). The calculation time required to obtain this result was 10 hours. Furthermore, when similar particle behavior was calculated with a similar apparatus configuration using a general-purpose computer using the conventional discrete element method, it took about 100 hours. It can be seen that the efficiency is improved by the method of the present invention.

[Example 4]
The program according to the present invention used in Example 3 was ported to a dedicated computer for image processing using a GPU, and calculations were performed with the same element arrangement as in Example 3. At this time, the same result as in Example 3 was obtained, but the time required for the calculation was 2 hours, which was 1/50 or less compared to Example 3 using a general-purpose computer. Furthermore, since a computer dedicated to image processing is used, the intermediate results and final results can be displayed efficiently, and the design efficiency is remarkably improved.

[Example 5]
Using a computer dedicated to image processing using a GPU, the calculation was performed by changing the length and angle of the plate and the opening angle of the strip in an apparatus in which the fluid part is composed of a plate and a plurality of strips. As a result, the distribution of the deposited particles should be in the range of 0.5 to 1.0 m for the plate length, 40 to 50 degrees for the angle, and 1.5 to 4.0 degrees for the strip opening angle. I understood.

DESCRIPTION OF SYMBOLS 1 Shuttle conveyor 2 Surge hopper 3 Drum feeder 4 Fluid 5 Pallet 6 Deposit

Claims (5)

This is a method of calculating the motion from the collision of any two particles to the separation in the calculation of the motion of the particle, and the normal direction of the contact surface of the two particles colliding at time t ^p (hereinafter referred to as “normal”). The force acting in the “direction”) is an elastic repulsive force −k × δ ^p whose elastic coefficient is k and proportional to the amount of particle δ ^p at time t ^p .
And expressed as the sum of viscous drag forces with viscosity coefficient η,
Of one of the particles 1, the time t ^p than just time step Δt advanced time t ^{p +} direction normal velocity V ₁ ^{p + 1} in the ^first prediction value E ₁ ^{p + 1} and law at the time t ^p of the other particles 2 Force proportional to the difference from linear velocity V ₂ ^p η × (V ₂ ^p −E ₁ ^{p + 1} )
Is the normal direction viscous force acting on the particle 1, and the normal direction viscous force acting on the other particle 2 is also the predicted value E ₂ ^{p +} of the normal direction velocity of the particle 2 at time t ^{p + 1} . force eta × proportional to the difference between the normal direction velocity V ₁ ^p at ¹ and the time _{^{t p (V 1 p -E 2}} p + 1)
The calculation method of the motion of the normal direction until it leaves | separates after the two particles collide characterized by expressing by.
Here, the time index p is an integer, and the value of p increases by 1 when the time advances by Δt. The upper right subscript p means the physical index in the time index p. Assume that the mass of particle 1 is m ₁ and the mass of particle 2 is m ₂ , the predicted normal direction velocity E ₁ ^{p + 1} of particle ¹ and the predicted normal direction velocity E ₂ ^{p of} particle 2 at time t ^{p + 1} . ⁺¹ each
as well as
The calculation method of the motion of the normal direction until it leaves | separates after the two particles collide of Claim 1 characterized by the above-mentioned. At time t ^p , normal forces F ₁ ^p and F ₂ ^{p received} by the particles 1 and 2 from the collision are obtained.
as well as
The calculation method of the motion of the normal direction until it leaves | separates after the two particles collide of Claim 1 or 2 characterized by these.   A particle behavior analysis method for analyzing the behavior of multiparticulate particles, where the motion of each particle is calculated by the discrete element method using the equation of motion, until any two particles collide and then leave A particle behavior analysis method using the method for calculating the motion in the normal direction from the collision of two particles to the separation of the two particles according to any one of claims 1 to 3.   The particle behavior analysis method according to claim 4 is used to determine the particle distribution of the sintered raw material that has been put into a surge hopper from a shuttle conveyor, cut out from a drum feeder, and dropped over a sieve. The particle arrangement distribution analysis method of the sintering raw material.