Simulation device and program

Abstract

To provide a simulation device and a program which can simulate behavior of a spherical medium within a mill container in a vibration ball mill device.SOLUTION: A simulation device determines a relative coordinate position (MB) of a mill container wall surface, calculates a contact direction (H1) of spherical mediums at contact point positions with the wall surface of the respective spherical mediums, calculates a vibration velocity vector (V1) of the wall surface at the contact point and a motion velocity vector (VT) of the wall surface, calculates a force (J0) which is such a force that the spherical mediums receive from the wall surface, calculates a contact direction (H2) between the respective spherical mediums, calculates a motion velocity vector (VP) at contact point position between the spherical mediums, determines a motion velocity vector (V) and minute time deviation (U) of the spherical medium, based on the force (J0), the force (JP), gravity (G) and minute unit time (Δt), determines medium center coordinates (P) after the minute unit time (Δt) from the minute time deviation (U), and updates the motion velocity vector (V) and the medium center coordinates (P).SELECTED DRAWING: Figure 7

Description

[Technical Field]

[0001] The present invention relates to a simulation device and a program for simulating the behavior of spherical media in a mill vessel of a vibratory ball mill. [Background technology]

[0002] There are various types of ball mills for grinding or mixing workpieces, including a container-rotating type rolling ball mill, a stirring ball mill with a rotating agitator, a rotary mill in which the mill container is driven to rotate around a fixed rotation axis, and a rotary rocking mill in which the mill container is rocked while rotating.

[0003] A medium behavior simulation device that simulates the behavior of spherical media in a container in a rotary rocking mill is disclosed, for example, in Patent Document 1. The medium behavior simulation device disclosed in Patent Document 1 simulates the behavior of spherical media in a mill container in a rotary rocking mill in which the mill container is rotated and the rotation shaft is rocked.

[0004] This medium behavior simulation device uses a discrete element method as a simulation technique, which calculates the force acting on each particle at every minute time interval, calculates the equation of motion differentially based on the calculation results, and sequentially performs numerical analysis of the particle displacement. Note that a specific calculation method for the discrete element method is disclosed in, for example, Non-Patent Document 1. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Laid-Open No. 2009-119433 [Non-patent literature]

[0006] [Non-Patent Document 1] Transactions of the Japan Society of Mechanical Engineers (Part B), Vol. 57, No. 534, 60, 1991 Summary of the Invention [Problem to be solved by the invention]

[0007] In recent years, among ball mills, vibration ball mills have been attracting attention for their superior productivity compared to tumbling ball mills, and for use in grinding inorganic materials and flattening metal powders such as silver and copper powders.

[0008] A vibratory ball mill is equipped with an unbalanced weight, the mill container is installed in an eccentric position, and vibration is generated by the rotation of a motor. As mentioned above, in order to support the mill container while achieving vibration, a spring is provided on the underside where the mill container is installed, and the vibration is mainly a periodic motion such as a circular motion. The vibration amplitude of the vibratory ball mill can be adjusted by changing the weight or position of the unbalanced weight.

[0009] On the other hand, as mentioned above, a vibrating ball mill has many parts, and the mill vessel itself is essentially floating, so factors such as the grinding media, type of material to be ground, amount of material charged, vibration frequency, unbalanced weight, spring, etc. have a complex influence, and the vibration of the mill vessel is not a perfect circular motion; the length and inclination of the major and minor axes of the circular motion also vary depending on the conditions. One factor that makes it difficult to simulate the behavior of spherical media inside the mill vessel is the complex vibration shape of a vibrating ball mill.

[0010] In view of the above circumstances, an object of the present invention is to enable easy and accurate sequential simulation of the behavior of spherical media in a mill vessel of a vibration ball mill apparatus. [Means for solving the problem]

[0011] The gist and configuration of the present invention to achieve the above object are as follows.

[0012] (1) A simulation device for simulating the behavior of a large number of spherical media in a vibration ball mill device that vibrates an axisymmetric mill container filled with the spherical media, the simulation device comprising: a control unit; The control unit Inputting, as initial parameters, the medium center coordinates (P) which are the coordinates of the center position of the spherical medium in an absolute coordinate system (K1) which is a coordinate system with a fixed coordinate center, the motion velocity vector (V) of the spherical medium in the absolute coordinate system (K1), the infinitesimal unit time (Δt) for performing the numerical analysis, and the radius (R) of the spherical medium, The XY coordinates of the center of the Z-axis direction of the mill container in the absolute coordinate system (K1) are determined as mill center coordinates (M), and the relative coordinate position (MB) of the wall surface of the mill container is determined based on the mill center coordinates (M); Based on the medium center coordinates (P), the radius (R) of the spherical medium, and the relative coordinate position (MB), a contact point coordinate (D) is determined for each of the multiple spherical media, which is the coordinate of the contact point position with the wall surface, and a contact direction (H1) of the spherical medium at the contact point position in the absolute coordinate system (K1) is calculated from the contact point coordinates (D) and the medium center coordinates (P); A vibration velocity vector of the wall surface in the absolute coordinate system (K1) due to the vibration motion of the wall surface at the contact point position is calculated as a wall vibration velocity vector (V1), and a motion velocity vector of the wall surface at the contact point position in the absolute coordinate system (K1) is calculated from the vibration velocity vector (V1) as a wall motion velocity vector (VT); Calculating a force (J0) that the spherical medium receives from the wall surface based on the motion velocity vector (V), the contact direction (H1), and the wall surface motion velocity vector (VT); determining a center-to-center distance (L) between each of the spherical media from the medium center coordinates (P), determining contact between the spherical media from the center-to-center distance (L) and the radius (R) of the spherical media, and calculating a contact direction (H2) between the spherical media from the medium center coordinates (P) based on the determination; In the absolute coordinate system (K1), a motion velocity vector (VP) at a contact point position between the spherical media is calculated based on the motion velocity vector (V); Calculating a force (JP) that the spherical medium receives from another spherical medium based on the contact direction (H2) and the motion velocity vector (VP); a motion equation is numerically analyzed based on the force (J0), the force (JP), gravity (G), and the infinitesimal unit time (Δt), thereby determining a motion velocity vector (V) and infinitesimal time displacement (U) of the spherical medium after the infinitesimal unit time (Δt), determining a medium center coordinate (P) of the spherical medium after the infinitesimal unit time (Δt) from the infinitesimal time displacement (U), and updating the motion velocity vector (V) and the medium center coordinate (P); Simulation device.

[0013] (2) The control unit The major axis radius (A), minor axis radius (B), and tilt (DW) of the elliptical vibration orbit of the mill center coordinate (M), and the vibration frequency (C) of the mill container are input as initial parameters; The parametric representation of the ellipse is

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[0014] (3) A program for causing a computer to function as the simulation device described in (1) or (2) above. [Effects of the Invention]

[0015] According to the present invention, it is possible to easily and accurately sequentially simulate the behavior of spherical media in a mill vessel of a vibratory ball mill. [Brief explanation of the drawings]

[0016] [Figure 1] FIG. 1 is a diagram showing the configuration of a vibration ball mill device. [Figure 2] 1 is a block diagram illustrating an example of the configuration of a simulation device according to an embodiment. [Figure 3] FIG. 2 is a block diagram illustrating an example of the configuration of a control unit in the simulation device according to an embodiment. [Figure 4] FIG. 10 is a diagram showing an elliptical vibration orbit of the mill center coordinates in an absolute coordinate system. [Figure 5] FIG. 1 is a diagram showing an elliptical vibration orbit of the mill center coordinates and a mill container in an absolute coordinate system. [Figure 6A] FIG. 1 is a diagram showing a model of compressive force in the Voigt model. [Figure 6B] FIG. 1 is a diagram showing a model of shear force in the Voigt model. [Figure 7] 10 is a flowchart showing an example of a simulation operation. [Figure 8] 10 is a diagram showing the results of simulating the behavior of spherical media using a simulation device and the state of the spherical media using a vibration ball mill device under condition 1. FIG. [Figure 9] 10 is a diagram showing the results of simulating the behavior of spherical media using a simulation device and the state of the spherical media using a vibration ball mill device under condition 2. FIG. [Figure 10] 10 is a diagram showing the results of simulating the behavior of spherical media using a simulation device and the state of the spherical media using a vibration ball mill device under condition 3. FIG. [Figure 11] 10 is a diagram showing the results of simulating the behavior of spherical media using a simulation device and the state of the spherical media using a vibration ball mill device under condition 4. FIG. DETAILED DESCRIPTION OF THE INVENTION

[0017] Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

[0018] The present invention involves performing computational analysis of the behavior of a plurality of spherical media within a vibratory ball mill device, and sequentially simulating the behavior of the spherical media.

[0019] The configuration of a vibration ball mill is shown in Figure 1. The vibration ball mill 6 shown in Figure 1 includes a mill container 7 in which a plurality of spherical media (balls) 8 such as SUS balls and a workpiece (metal powder) 9 are loaded, a vibration drive unit (motor) 10 having an unbalanced weight 11, and a spring 12 that supports the mill container 7.

[0020] The vibration ball mill device 6 can efficiently grind or mix the workpiece 9 in the mill container 7 by subjecting the axisymmetric mill container 7 to periodic vibration, such as circular motion, at high speed in a short period of time. Because the mill container 7 performs vibration motion, the multiple spherical media 8 in the mill container 7 behave in the X-, Y-, and Z-axis directions due to the vibration motion.

[0021] Fig. 2 shows an example of the configuration of a simulation device according to an embodiment. The simulation device 1 shown in Fig. 2 includes an input unit 2, a storage unit 3, a control unit 4, and an output unit 5. In order to simulate the behavior of spherical media 8 moving three-dimensionally in a mill container 7, the simulation device 1 defines an absolute coordinate system K1, which is a coordinate system with a fixed coordinate center.

[0022] The input unit 2 includes at least one input interface. The input interface may be, for example, a physical key, a capacitance key, a pointing device, or a touch screen integrated with a display. The input unit 2 accepts an operation to input data used in the operation of the simulation device 1. The input unit 2 may be connected to the simulation device 1 as an external input device instead of being provided in the simulation device 1. As the connection interface, any interface compatible with standards such as USB (Universal Serial Bus), HDMI (High-Definition Multimedia Interface, registered trademark), or Bluetooth (registered trademark) may be used.

[0023] The storage unit 3 includes at least one semiconductor memory, at least one magnetic memory, at least one optical memory, or any combination thereof. The semiconductor memory is, for example, a random access memory (RAM), a read only memory (ROM), or a flash memory. The RAM is, for example, a static random access memory (SRAM) or a dynamic random access memory (DRAM). The ROM is, for example, an electrically erasable programmable read only memory (EEPROM). The flash memory is, for example, a solid-state drive (SSD). The magnetic memory is, for example, a hard disk drive (HDD). The storage unit 3 functions as, for example, a main storage device, an auxiliary storage device, or a cache memory. The storage unit 3 stores initial parameters used in the operation of the simulation device 1, information obtained by the operation of the simulation device 1, etc.

[0024] The control unit 4 may be configured with dedicated hardware such as an ASIC (Application Specific Integrated Circuit) or an FPGA (Field-Programmable Gate Array), or may be configured with a processor, or may be configured with both. The control unit 4 uses the discrete element method to sequentially simulate the behavior of each spherical medium 8 loaded in the mill vessel 7 of the vibration ball mill apparatus 6. A specific calculation method for the discrete element method is disclosed, for example, in Non-Patent Document 1.

[0025] The output unit 5 includes at least one output interface. The output interface is, for example, a display, a speaker, or a printer, and presents data input from the control unit 4 to the user. The display is, for example, an LCD (liquid crystal display) or an organic EL (electro luminescent) display. The output unit 5 may be connected to the simulation device 1 as an external output device instead of being provided in the simulation device 1. As the connection interface, any interface compatible with standards such as USB, HDMI, Bluetooth, etc. may be used.

[0026] 3 shows an example configuration of the control unit 4. The control unit 4 includes an initial parameter input unit 41, a wall surface relative coordinate position derivation unit 42, a first contact direction derivation unit 43, a velocity vector derivation unit 44, a first force derivation unit 45, a second contact direction derivation unit 46, a second force derivation unit 47, a behavior analysis unit 48, and an analysis result output unit 49.

[0027] The initial parameter input unit 41 inputs initial parameters via the input unit 2. If the initial parameters are stored in the storage unit 3, the initial parameter input unit 41 acquires the initial parameters from the storage unit 3. The initial parameters include, for example, a medium center coordinate P, which is the coordinate of the center position of the spherical medium in an absolute coordinate system K1, which is a coordinate system with a fixed coordinate center, a motion velocity vector V of the spherical medium 8 in the absolute coordinate system K1, a major axis radius A, a minor axis radius B, and a tilt DW of an elliptical vibration orbit described below, a vibration frequency C of the mill container 7, a minute unit time Δt for performing the numerical analysis, a radius R of the spherical medium 8, and a medium identification index F for identifying the spherical medium 8. Of these, the medium center coordinate P and the motion velocity vector V are parameters that are updated by simulation.

[0028] The wall surface relative coordinate position derivation unit 42 determines the XY coordinates M of the center of the mill container 7 in the Z-axis direction in the absolute coordinate system K1 (hereinafter referred to as the "mill center coordinates"). A specific example of a method for calculating the mill center coordinate M will be described later. Then, based on the mill center coordinate M, the wall surface relative coordinate position derivation unit 42 determines the relative coordinate position MB of the mill container wall surface 7A (hereinafter referred to as the "wall surface relative coordinate position").

[0029] The first contact direction derivation unit 43 determines contact between each spherical medium 8 and the mill container wall surface 7A based on the medium center coordinate P, the radius R of the spherical medium 8, and the wall surface relative coordinate position MB. Then, based on the contact determination result, the first contact direction derivation unit 43 calculates the contact point coordinate D, which is the coordinate of the contact point position d between the spherical medium 8 and the mill container wall surface 7A. Next, the first contact direction derivation unit 43 calculates the contact direction H1 at the contact point position d in the absolute coordinate system K1 of the spherical medium 8 from the contact point coordinate D, the medium center coordinate P, and the medium identification index F.

[0030] The velocity vector derivation unit 44 calculates a vibration velocity vector (hereinafter referred to as "wall vibration velocity vector") V1 in the absolute coordinate system K1 due to the vibration motion of the mill vessel wall surface 7A at the contact point position d. Then, based on the wall vibration velocity vector V1, the velocity vector derivation unit 44 calculates a motion velocity vector (hereinafter referred to as "wall motion velocity vector") VT in the absolute coordinate system K1 of the mill vessel wall surface 7A at the contact point position d.

[0031] The first force derivation unit 45 calculates the force J0 that the spherical medium 8 receives from the mill container wall surface 7A based on the motion velocity vector V, the contact direction H1 calculated by the first contact direction derivation unit 43, and the wall motion velocity vector VT calculated by the velocity vector derivation unit 44.

[0032] The second contact direction derivation unit 46 calculates the center-to-center distance L between each spherical medium 8 from the medium center coordinate P and the medium identification index F, and determines contact between the spherical media 8 from the center-to-center distance L and the radius R of the spherical media. Then, the second contact direction derivation unit 46 calculates the contact direction H2 between each spherical medium 8 from the medium center coordinate P based on the contact determination between the spherical media 8.

[0033] The second force derivation unit 47 calculates, in the absolute coordinate system K1, a motion velocity vector VP (motion velocity vector at the contact point position between the spherical media 8) that a spherical medium 8 receives from another spherical medium 8, based on the motion velocity vector V. Then, the second force derivation unit 47 calculates a force JP that a spherical medium 8 receives from another spherical medium 8, based on the contact direction H2 calculated by the second contact direction derivation unit 48 and the motion velocity vector VP.

[0034] The behavior analysis unit 48 analyzes the behavior of the spherical media 8 in the mill vessel 7 by repeating numerical calculations at intervals of minute time Δt using the discrete element method. Specifically, the behavior analysis unit 48 numerically analyzes the equation of motion based on the force J0 calculated by the first force derivation unit 45, the force JP calculated by the second force derivation unit 47, the gravity G acting on the spherical media 8, and the minute unit time Δt, to determine the motion velocity vector V of the spherical media 8 after the minute unit time Δt and the minute time displacement U. The motion velocity vector V calculated here is the motion velocity vector acting on one spherical media 8, including all influences from the mill vessel wall surface 7A and other spherical media 8. The behavior analysis unit 48 then determines the medium center coordinate P of the spherical media 8 after the minute unit time Δt from the minute time displacement U.

[0035] The analysis result output unit 49 stores the movement speed vector V and the medium center coordinate P calculated by the behavior analysis unit 48 in the storage unit 3. As a result, the movement speed vector V and the medium center coordinate P are updated.

[0036] (Mill center coordinates) FIG. 4 shows the elliptical vibration orbit 13 of the mill center coordinate M in the absolute coordinate system K1. Note that in this specification, "ellipse" includes a circle. The simulation device 1 performs accurate simulations by reproducing the elliptical shape shown in FIG. 4. In the XY coordinate system in the Z-axis direction in the absolute coordinate system K1, the simulation device 1 sets the vibration center Q0 so that the entire mill container 7 is located in the first quadrant based on the input mill radius (radius of the mill container 7) CE and major axis radius A. Vibration is assumed to cause the mill center coordinate M (Xm, Ym) to move in the direction of the arrow on the elliptical vibration orbit 13 shown in FIG. 4. In the XY coordinate system in the Z-axis direction in the absolute coordinate system K1, the mill container wall surface 7A is located at a distance equal to the mill radius CE from the mill center coordinate M (Xm, Ym). The mill vessel wall surface 7A is located in the Z-axis direction in the range from Z1=0 to the mill barrel length (the barrel length of the mill vessel 7) OH, and is located on a plane parallel to the XY plane at Z1=0 and Z1=mill barrel length OH.

[0037] In reproducing the elliptical shape, the simulation device 1 assumed that the vibration caused the center of the axis of the mill container 7 to move, and that the mill container 7 also moved simultaneously. When the major axis radius of the elliptical vibration orbit 13 is A and the minor axis radius is B (A≧B), the parametric representation of the ellipse is shown in Equation (1).

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[0038] Since the X and Y coordinates at angle φ can be found from the parametric representation, the simulation device 1 sets equation (2) so that angle φ varies with frequency C and time t. At this time, φ indicates the angle moving per second, and when φ>2π, 2π is subtracted so that the elliptical oscillation orbit 13 falls within the positive coordinate range.

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[0039] The simulation device 1 sets the center coordinates M (Xm, Ym) of the mill vibrating ellipse by giving this ellipse a tilt DW. As shown in equation (3), the tilt DW is given to the ellipse by multiplying equation (1) by a rotation matrix that rotates by the tilt DW.

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[0040] When performing a simulation, setting negative values ​​to the coordinates complicates the calculations, so the simulation device 1 sets the initial coordinates as the mill center coordinate M (Xm, Ym) and the medium center coordinate P of all spherical media 8 plus the mill radius CE and major axis radius A.

[0041] Figure 5 shows the elliptical vibration orbit 13 of the mill center coordinate M and the mill container 7 in the absolute coordinate system. The simulation device 1 uses equation (3) to set the elliptical vibration orbit 13 of the mill center coordinate M as shown in Figure 5. For simplicity, in the present invention, A and B in equation (3) correspond to the major axis radius A and the minor axis radius B, respectively.

[0042] The simulation device 1 calculates the wall vibration velocity vector V1 at time t using the mill center coordinates M1 (Xm1, Ym1) at time t and the mill center coordinates M2 (Xm2, Ym2) at the previous time step t-Δt, according to equation (4).

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[0043] The Voigt model, a commonly known viscoelastic mechanical model, may be used as the mechanical model acting on the spherical medium 8. Figure 6 shows a conceptual diagram of the Voigt model. Figure 6A shows compression force, and Figure 6B shows shear force. The Voigt model represents the force acting on the spherical medium 8 by connecting in parallel a spring 14, which represents the elastic properties of the spherical medium 8, and a dashpot 15, which represents the inelastic properties (viscosity). For shear force, a friction slider 16 is installed as the tangential component of the interaction force to represent the frictional interaction accompanying the contact of a group of spherical media 8.

[0044] The simulation device 1 applies the Voigt model to the discrete element method to simulate the behavior of spherical media 8 in a mill vessel 7 having an elliptical orbit.

[0045] (Operation of the simulation device) Next, the operation of the simulation device 1 equipped with the above-described control unit 4 will be described with reference to Fig. 7. The simulation device 1 sets an absolute coordinate system K1 for the coordinate information of the spherical media 8, and the control unit 4 uses the discrete element method to repeat numerical calculations at short time intervals Δt according to the procedure shown in Fig. 7 to simulate the behavior of the spherical media 8 in the mill container 7, and outputs the results from the output unit 5.

[0046] In step S101, the simulation apparatus 1 defines an absolute coordinate system K1, which is a coordinate system with a fixed coordinate center, for the vibration ball mill apparatus 6.

[0047] In step S102, the simulation device 1 inputs initial parameters such as material constants and vibration conditions required for performing the numerical analysis via the input unit 2, and stores them in the storage unit 3.

[0048] The material constants used in the numerical analysis are, for example, the density ρ, Young's modulus G, Poisson's ratio v, radius R, friction coefficient μ, rolling friction coefficient μr, charge weight W, medium identification index F, and number of spheres N for the spherical medium 8. The number of spheres N is calculated using the charge weight W, density ρ, and radius R.

[0049] The vibration conditions for performing the numerical analysis include, for example, the mill radius CE, the mill body length OH, the minute unit time Δt for performing the numerical analysis, the major axis radius A, the minor axis radius B, the tilt DW, the vibration frequency C, the medium center coordinate P of the spherical medium 8, and the motion velocity vector V of the spherical medium 8. The motion velocity vector V of the spherical medium 8 input as an initial parameter is usually "0" or an extremely small value.

[0050] In step S103, the simulation device 1 determines the mill center coordinate M of the mill container 7 and the wall surface relative coordinate position MB in the absolute coordinate system K1, and stores these in the storage unit 3 for each spherical medium 8.

[0051] In step S104, the simulation device 1 determines whether the spherical medium 8 has come into contact with the mill vessel wall surface 7A for each of the multiple spherical mediums 8, based on the medium center coordinate P, the spherical medium radius R, and the wall surface relative coordinate position MB. The simulation device 1 determines that the spherical medium 8 has come into contact with a predetermined position on the mill vessel wall surface 7A when the distance between the medium center coordinate P and the wall surface relative coordinate position MB is equal to or less than the radius R of the spherical medium 8.

[0052] In step S105, the simulation apparatus 1 determines the contact point coordinate D, which is the coordinate of the contact point position d between the spherical medium 8 and the mill vessel wall surface 7A in the absolute coordinate system K1, based on the contact determination of the spherical medium 8 with the mill vessel wall surface 7A.

[0053] In step S106, the simulation apparatus 1 calculates the contact direction H1 of the spherical medium 8 at the contact point position d in the absolute coordinate system K1 based on the contact point coordinate D, using the medium center coordinate P and the medium identification index F.

[0054] In step S107, the simulation device 1 calculates, based on the contact point coordinate D, a wall vibration velocity vector V1 of the mill vessel wall 7A at the contact point position d due to the vibration motion of the mill vessel 7.

[0055] In step S108, the simulation device 1 calculates the wall motion velocity vector VT at the contact point position d in the absolute coordinate system K1 from the wall vibration velocity vector V1.

[0056] In step S109, when there are a large number of spherical media 8 and mutual collisions cannot be ignored, the simulation device 1 calculates the center-to-center distance L between each spherical medium 8 from the medium center coordinates P and the medium identification index F. Then, the simulation device 1 determines contact between the spherical media 8 using the center-to-center distance L and the radius R of the spherical media 8 stored in the memory unit 3.

[0057] In step S110, the simulation apparatus 1 calculates the contact direction H2 between the spherical media 8 from the medium center coordinates P and the medium identification index F based on the contact determination between the spherical media 8.

[0058] In step S111, the simulation apparatus 1 calculates a motion velocity vector VP that a spherical medium 8 receives from another spherical medium 8 in the absolute coordinate system K1.

[0059] In step S112, the simulation device 1 calculates a first force J0 that the spherical media 8 receive from the mill vessel wall surface 7A based on the motion velocity vector V, the contact direction H1 of the spherical media 8 on the mill vessel wall surface 7A, and the wall motion velocity vector VT. The simulation device 1 also calculates a second force JP that the spherical media 8 receive from other spherical media 8 based on the contact direction H2 between the spherical media 8 and the motion velocity vector VP.

[0060] In step S113, the simulation device 1 calculates the motion velocity vector V and the minute time displacement U of each spherical medium 8 by numerically analyzing the equation of motion based on the first force J0, the second force JP, the gravity G acting on the spherical medium 8, and the minute unit time Δt.

[0061] In step S114, the simulation apparatus 1 stores the motion velocity vector V and the minute time displacement U of each spherical medium 8 in the storage unit 3 in sequence.

[0062] In step S115, the simulation device 1 outputs the simulation results of the behavior of the spherical medium 8 in the mill container 7 through the output unit 5 based on the infinitesimal time displacement U of the entire spherical medium 8. Note that the operation of the simulation device 1 does not necessarily have to follow the order shown in FIG. 7, and the processing order can be changed within a consistent range. For example, the simulation device 1 may calculate the first force J0 immediately after step S108.

[0063] (Simulation results) Next, the results of simulating the behavior of the spherical media 8 using the simulation device 1 will be compared with the state of the spherical media 8 using the vibration ball mill device 6. Tables 1 and 2 show the parameters used in the simulation.

[0064] [Table 1]

[0065] [Table 2]

[0066] Specifically, a 5.9 kg load of spherical media 8 (5 mm diameter SUS balls) was loaded into a Chuo Kakoki Shoji B-1 stainless steel cylindrical pot (inner diameter 14.65 cm, body length 19 cm, internal volume 3.2 L). The mill vessel 7 was driven under specified operating conditions, and the behavior of the spherical media 8 over time was compared. To obtain a more accurate picture of the behavior of the spherical media 8, the comparative experiment was conducted without placing any workpiece inside the mill vessel 7. Amplitude and frequency were measured using a Sinfonia Technology V-Checker. The movement of the spherical media 8 inside the mill vessel 7 was observed using a Novitec Phantom Miro C110 high-speed camera.

[0067] 8 to 11 show the results of a simulation of the behavior of the spherical media 8 using the simulation device 1 under conditions 1 to 4 shown in Table 2, respectively, and the state of the spherical media 8 in the vibration ball mill device 6. Here, the ball charge weight is set to 5.9 kg, and the behavior of the spherical media 8 is shown from the start of operation until the mill container 7 makes two rotations. When performed under condition 1, the time required for the mill container 7 to make one rotation is 0.076 seconds, and FIG. 8 shows the behavior of the spherical media 8 in the mill container 7 after 0 seconds, 0.03 seconds, 0.06 seconds, 0.09 seconds, 0.12 seconds, and 0.15 seconds. When carried out under conditions 2 to 4, the time required for the mill container 7 to rotate once is 0.050 seconds, and Figures 9 to 11 show the behavior of the spherical media 8 in the mill container 7 after 0 seconds, 0.02 seconds, 0.04 seconds, 0.06 seconds, 0.08 seconds, and 0.10 seconds.

[0068] 8 to 11, regardless of the conditions under which the mill vessel 7 is driven, the simulation device 1 is able to accurately simulate the behavior of the spherical media 8 that closely resembles the actual state in the vibration ball mill 6. In other words, the present invention defines an absolute coordinate system K1 with a fixed coordinate center, and makes it possible to easily and accurately sequentially simulate the behavior of a large number of spherical media 8 that move three-dimensionally within the mill vessel 7 of the vibration ball mill 6 by applying the discrete element method.

[0069] (program) A computer capable of executing program instructions can also be used to function as the above-described simulation device 1. Here, the computer may be a general-purpose computer, a dedicated computer, a workstation, a PC, a mobile terminal, etc. The program instructions may be program code, code segments, etc. for performing the necessary tasks.

[0070] The control unit 4 is a processor such as a CPU (Central Processing Unit), MPU (Micro Processing Unit), GPU (Graphics Processing Unit), DSP (Digital Signal Processor), or SoC (System on a Chip), and may be configured with multiple processors of the same or different types. The processor performs the above-mentioned processing by reading and executing a program from the storage unit 3. Note that at least a part of the processing content may be realized by hardware.

[0071] The program may be recorded on a computer-readable recording medium. Using such a recording medium, the program can be installed on a computer. Here, the recording medium on which the program is recorded may be a non-transitory recording medium. The non-transitory recording medium is not particularly limited, and may be, for example, a CD-ROM, a DVD-ROM, or a USB (Universal Serial Bus) memory. Furthermore, the program may be downloaded from an external device via a network.

[0072] Although the above-described embodiments have been described as typical examples, it will be apparent to those skilled in the art that many modifications and substitutions can be made within the spirit and scope of the present invention. Therefore, the present invention should not be construed as being limited by the above-described embodiments, and various modifications or alterations are possible without departing from the scope of the claims. For example, with regard to the constituent blocks or processing steps described in the embodiments, multiple blocks or processing steps can be combined into one, or one block or processing step can be divided into multiple blocks. [Explanation of symbols]

[0073] 1 Simulation device 2 Input section 3 Storage section 4. Control section 5 Output section 6. Vibration ball mill equipment 7 Mill container 7A Mill vessel wall 8 Spherical media (balls) 9 Workpiece (metal powder) 10 Vibration drive unit 11 Unbalanced weight 12 Spring 13 Elliptical vibration orbit around the center of the mill 14 Spring 15 Dashpot 16 Friction Slider 41 Initial parameter input section 42 Wall relative coordinate position derivation unit 43 First contact direction derivation part 44 Velocity vector derivation section 45 1st force derivation part 46 Second contact direction derivation part 47 2nd force derivation part 48 Behavior Analysis Department 49 Analysis result output section

Claims

1. A simulation device for simulating the behavior of a large number of spherical media in a vibration ball mill device that vibrates an axisymmetric mill container filled with the spherical media, the simulation device comprising: a control unit; The control unit Inputting, as initial parameters, medium center coordinates (P) which are the coordinates of the center position of a spherical medium in an absolute coordinate system (K1) which is a coordinate system with a fixed coordinate center, a motion velocity vector (V) of the spherical medium in the absolute coordinate system (K1), a minute unit time (Δt) for performing numerical analysis, and a radius (R) of the spherical medium, The XY coordinates of the center of the mill container in the Z-axis direction in the absolute coordinate system (K1) are determined as mill center coordinates (M), and the relative coordinate position (MB) of the wall surface of the mill container is determined based on the mill center coordinates (M); Based on the medium center coordinates (P), the radius (R) of the spherical medium, and the relative coordinate position (MB), contact point coordinates (D), which are the coordinates of the contact point position with the wall surface, are obtained for each of the multiple spherical media, and a contact direction (H1) of the spherical medium at the contact point position in the absolute coordinate system (K1) is calculated from the contact point coordinates (D) and the medium center coordinates (P); A vibration velocity vector of the wall surface in the absolute coordinate system (K1) due to the vibration motion of the wall surface at the contact point position is calculated as a wall vibration velocity vector (V1), and a motion velocity vector of the wall surface at the contact point position in the absolute coordinate system (K1) is calculated from the vibration velocity vector (V1) as a wall motion velocity vector (VT); Calculating a force (J0) that the spherical medium receives from the wall surface based on the motion velocity vector (V), the contact direction (H1), and the wall surface motion velocity vector (VT); determining a center-to-center distance (L) between each of the spherical media from the medium center coordinates (P); determining contact between the spherical media from the center-to-center distance (L) and the radius (R) of the spherical media; and calculating a contact direction (H2) between the spherical media from the medium center coordinates (P) based on the determination; In the absolute coordinate system (K1), a motion velocity vector (VP) at a contact point position between the spherical media is calculated based on the motion velocity vector (V); Calculating a force (JP) that the spherical medium receives from another spherical medium based on the contact direction (H2) and the motion velocity vector (VP); a motion equation is numerically analyzed based on the force (J0), the force (JP), gravity (G), and the infinitesimal unit time (Δt) to determine a motion velocity vector (V) and infinitesimal time displacement (U) of the spherical medium after the infinitesimal unit time (Δt), and a medium center coordinate (P) of the spherical medium after the infinitesimal unit time (Δt) is determined from the infinitesimal time displacement (U), and the motion velocity vector (V) and the medium center coordinate (P) are updated; Simulation device.

2. The control unit The major axis radius (A), minor axis radius (B), and inclination (DW) of the elliptical vibration orbit of the mill center coordinate (M), and the vibration frequency (C) of the mill container are input as initial parameters; The parametric representation of the ellipse is [Equation 1] The angle φ at the frequency (C) is changed by the following equation. [Equation 2] and multiplying it by a rotation matrix that rotates by the tilt (DW) by the following equation: [Equation 3] 2. The simulation device according to claim 1, wherein the components (Xm, Ym) of the mill center coordinates (M) are calculated by the following equation.

3. A program for causing a computer to function as the simulation device according to claim 1.

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