Flattening prediction method, flattening prediction apparatus, and program

Abstract

To predict a flattening processing time for flattening a metal powder by a ball media mill.SOLUTION: A flattening prediction method includes the steps of: measuring a rate R of change of a BET specific surface area value of a metal powder under a condition n; obtaining a flattening rate constant Yn with respect to a flattening processing time Tn under the condition n by (R*1) / Tn; obtaining a prediction coefficient Z by Yn / En using a collision energy En obtained by simulation for movement of balls in the ball media mill under the condition n; obtaining a predicted flattening rate constant Ym under a condition m by Em×Z, using a collision energy Em under the condition m different from the condition n; and obtaining, by [(b / a)*1] / Ym, a predicted processing time Tm required to obtain a metal powder having a BET specific surface area value b by flattening-processing a metal powder having a BET specific surface area value a under the condition m.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present invention relates to a flattening prediction method, a flattening prediction device, and a program. [Background technology]

[0002] Metal powders are manufactured by flattening them using a ball mill depending on their intended use. However, metal powders are aggregates of individual particles that repeatedly disperse and aggregate. This makes it difficult to derive the relationship between the individual particles, and it is difficult to treat them as a continuum, as in fluid dynamics simulations.

[0003] Therefore, a method is known in which a mechanical model is set for each particle and the discrete behavior of individual particles is numerically analyzed based on the mechanical model. In particular, it has been proposed to simulate the movement of powder based on the discrete element method (distinct element method), which sets a viscoelastic mechanical model between particles, calculates the forces acting on each particle over a short period of time, and based on this, calculates the equation of motion differentially to sequentially numerically analyze the displacement of the particles (see, for example, Non-Patent Document 1).

[0004] Recently, the motion of balls and powder in a ball media mill has been analyzed by the discrete element method to theoretically clarify the milling phenomenon (see, for example, Non-Patent Documents 2 and 3).

[0005] In the discrete element method, the mechanical model acting on the particles (balls and powder) is the most important, and the Voigt model is used as a viscoelastic mechanical model. In the Voigt model, the force acting on the particles is expressed by a spring that represents elastic properties and a dashpot that represents inelastic properties, and the acting force can be obtained by sequentially analyzing the particle center coordinates and the particle center coordinate displacement over a small time period.

[0006] Using this discrete element method, the behavior of the balls and powder in a ball media mill is typically analyzed by computer using the following procedure. First, initial parameters indicating the characteristics of the particles (balls and powder) are input into the computer, and contact between the particle and the container (cylinder) wall is determined and the initial position of the ball is set. Next, when a particle of interest that is not in contact with the container wall comes into contact with a nearby particle, the contact force (acting force) between the particle of interest and the contacting particle is calculated. Then, the average values ​​of the particle's acceleration, velocity, and displacement are calculated based on the contact force, thereby simulating the particle's motion characteristics. Furthermore, if the particle is in contact with the container wall when contact between the particle and the container wall is determined, the acting force is calculated, and the average values ​​of the particle's acceleration, velocity, and displacement are calculated based on the contact force, thereby simulating the particle's motion characteristics.

[0007] Patent Document 1 also discloses that the motion of balls in a ball media mill is simulated by a discrete element method using a viscoelastic mechanical model, the kinetic energy of all balls at the start of collision is calculated, and the degree of amorphization of inorganic powder is calculated based on the kinetic energy, and the amorphization treatment time required to bring the inorganic powder to a predetermined degree of amorphization is calculated. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] Japanese Patent Application Publication No. 11-207203 [Non-patent literature]

[0009] [Non-Patent Document 1] PACundall and OLStrack, “A discrete numerical model for granular assemblies”, Geotechnique, No.29, p.47-65, 1979. [Non-patent document 2] Junya Kano, Fumiyoshi Saito et al., Bulletin of the Materials Research Institute, Tohoku University, Vol. 52, No. 1, 2, pp. 112-125 [Non-patent document 3] Junya Kano, Naoki Chujo and Fumio Saito, “Advanced Power Technology”, Vol.8, No.1, p.39-51, 1997. Summary of the Invention [Problem to be solved by the invention]

[0010] Patent Document 1 discloses a method for predicting the amorphization of inorganic powders using a ball media mill, but does not disclose the flattening behavior of metal powders. Furthermore, the ball media mill described in Patent Document 1 has a small capacity of about 10 L and uses large balls with a diameter of 10 mm, making it difficult to apply the flattening treatment of metal powders to mass production.

[0011] In recent years, in order to meet more advanced needs, there has been a demand for predicting the flattening treatment time required to obtain metal powder with an optimum flattening degree.

[0012] In view of the above circumstances, an object of the present invention is to predict the flattening processing time of metal powder when the metal powder is flattened by a ball media crusher. [Means for solving the problem]

[0013] The gist and configuration of the present invention to achieve the above object are as follows.

[0014] (1) In a flattening process in which balls and metal powder are placed in a mill container of a ball media mill and the metal powder is flattened by stirring the inside of the mill container, a step of measuring a rate of change R of the BET specific surface area value of the metal powder under flattening treatment conditions n (BET specific surface area value after flattening treatment / BET specific surface area value before flattening treatment); Using the change rate R, the flattening processing time T nThe flattening rate constant Y n of Y n =(R-1) / T n and The flattening rate constant Y n and the collision energy E obtained by simulation using a discrete element method using a viscoelastic dynamics model for the ball movement in the ball media mill under the flattening treatment condition n. n Using and, the prediction coefficient Z is Z=Y n / E n and The prediction coefficient Z and the collision energy E obtained by the simulation for the movement of the ball in the ball media crusher under flattening treatment condition m, which is different from the flattening treatment condition n. m Using the above, the predicted flattening rate constant Y under the flattening treatment condition m is calculated. m of Y m =E m ×Z and the predicted flattening rate constant Y m Using the above, the predicted processing time T required to obtain a metal powder having a BET specific surface area value of b by flattening a metal powder having a BET specific surface area value of a under the flattening processing conditions m is calculated. m of T m =[(b / a)-1] / Y m and A flattening prediction method comprising:

[0015] (2) The flattening prediction method according to (1), wherein the metal powder is selected from copper powder, silver powder, silver-coated copper powder, and silver-coated alloy.

[0016] (3) The flattening prediction method according to (1) or (2), wherein in the simulation, the diameter of the ball is set to be at least one time and at most two times the diameter of the ball actually used.

[0017] (4) A flattening prediction method described in any one of (1) to (3), wherein in the simulation, the cross-sectional shape of the mill container is set to be approximately the same as the cross-sectional shape of an actual mill container, and the body length of the mill container is set to be 10 times or more the diameter of the balls actually used.

[0018] (5) The flattening prediction method according to any one of (1) to (4), wherein the number of balls in the simulation is set to be between 10,000 and 1,000,000.

[0019] (6) The flattening prediction method according to any one of (1) to (5), wherein the capacity of the mill container of the ball media mill is 0.4 L or more and 150 L or less.

[0020] (7) A flattening prediction device including a control unit, which predicts a processing time when flattening metal powder using a ball media crusher, The control unit Using the measured value of the change rate of the BET specific surface area value of the metal powder under the flattening treatment condition n (BET specific surface area value after flattening treatment / BET specific surface area value before flattening treatment) R, the flattening treatment time T n The flattening rate constant Y n of Y n =(R-1) / T n It is calculated by The flattening rate constant Y n and the collision energy E obtained by simulation using a discrete element method using a viscoelastic dynamics model for the ball movement in the ball media mill under the flattening treatment condition n. n Using and, the prediction coefficient Z is Z=Y n / E n It is calculated by The prediction coefficient Z and the collision energy E obtained by the simulation for the movement of the ball in the ball media crusher under flattening treatment condition m, which is different from the flattening treatment condition n. m Using the above, the predicted flattening rate constant Y under the flattening treatment condition m is calculated.m of Y m =E m ×Z It is calculated by the predicted flattening rate constant Y m Using the above, the predicted processing time T required to obtain a metal powder having a BET specific surface area value of b by flattening a metal powder having a BET specific surface area value of a under the flattening processing conditions m is calculated. m of T m =[(b / a)-1] / Y m The flattening prediction device calculates the flattening.

[0021] (8) A program for causing a computer to function as the flattening prediction device according to (7). [Effects of the Invention]

[0022] According to the present invention, when flattening metal powder using a ball media crusher, it is possible to predict the processing time required for flattening metal powder. [Brief explanation of the drawings]

[0023] [Figure 1] FIG. 1 is a diagram showing the configuration of a ball media crusher. [Figure 2] 1 is a block diagram illustrating an example of the configuration of a flattening prediction device according to an embodiment. [Figure 3A] FIG. 1 is a diagram showing a model of compressive force in a Voigt model as a viscoelastic mechanical model of the discrete element method employed in the method for predicting flattening of metal powder of the present invention. [Figure 3B] FIG. 1 is a diagram showing a model of shear force in the Voigt model, which is a viscoelastic mechanical model of the discrete element method employed in the method for predicting flattening of metal powder of the present invention. [Figure 4] 10 is a flowchart illustrating an example of the operation of a flattened prediction method according to an embodiment. [Figure 5] 10 is a graph showing the simulation results when the actual ball diameter is 1.6 mm and the collision energy is calculated with the ball diameter set to 3 mm and 10 mm. [Figure 6] 1 is a graph showing the rate of change in BET specific surface area value for each actual treatment time. DETAILED DESCRIPTION OF THE INVENTION

[0024] Hereinafter, one embodiment will be described in detail with reference to the drawings.

[0025] The present invention predicts the flattening time when metal powders such as silver powder, copper powder, silver-coated copper powder, and silver-coated alloy powder are flattened using a ball media mill using collision energy obtained based on a simulation of ball movement in the mill. The present invention has discovered that the degree of flattening of metal powder can be expressed as the rate of change in the BET specific surface area of ​​the metal powder with respect to the flattening time (BET specific surface area after flattening / BET specific surface area before flattening). It has also been discovered that, given a set of measured values ​​for the rate of change with respect to flattening time under given conditions, the following simulation can be used to predict the flattening time under other conditions. Furthermore, the cross-sectional shape of the mill vessel used in the simulation is set to be approximately the same as the cross-sectional shape of the actual mill vessel. In the present invention, "approximately the same" refers to, for example, when the cross-sectional shape of the actual mill vessel is a segmented circle, the cross-sectional shape of the vessel used in the simulation is set by matching the diameter and central angle of the cross-section of the actual mill vessel.

[0026] Figure 1 shows the configuration of a ball media mill. The agitation method for the mill container of a ball media mill is not limited, and may be a rolling method or a vibration method. The ball media mill 6 shown in Figure 1 is a vibration type mill, and includes a mill container 7 in which spherical media (balls) 8 such as SUS balls and a workpiece (metal powder) 9 are loaded, a vibration drive unit 10 with an unbalanced weight 11, and a spring 12 that supports the mill container 7. The ball media mill 6 is used for various purposes, such as crushing the workpiece 9 to a predetermined particle size.

[0027] Ball media mills 6 that can be simulated by the present invention can be divided into dry mills and wet mills. Dry mills include planetary ball mills, rocking ball mills, tumbling ball mills, and vibrating ball mills. Wet mills include attritors and bead mills. In the case of wet mills, it is advisable to add parameters for fluid resistance and buoyancy to the equation of motion to reproduce fluid behavior.

[0028] 2 shows an example of the configuration of a flattening prediction device according to an embodiment. The flattening prediction device 1 shown in FIG. 2 includes an input unit 2, a storage unit 3, a control unit 4, and an output unit 5.

[0029] The input unit 2 includes at least one input interface. The input interface is, 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 for the operation of the flattening prediction device 1. The input unit 2 may be connected to the flattening prediction device 1 as an external input device instead of being provided in the flattening prediction 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.

[0030] 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 flattening prediction device 1, information obtained by the operation of the flattening prediction device 1, etc.

[0031] 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 to include both. The control unit 4 executes processes related to the operation of the flattening prediction device 1 while controlling each part of the flattening prediction device 1.

[0032] Specifically, the control unit 4 includes an initial parameter input unit 41, a contact determination unit 42, a collision energy calculation unit 43, a flattening processing time prediction unit 44, and an analysis result output unit 45, and analyzes the movement behavior of the balls 8 within the mill container 7 of the ball media grinder 6.

[0033] 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 the density of the balls 8, the Young's modulus and Poisson's ratio derived from the material of the balls 8, the diameter of the balls 8, a medium identification index for identifying the balls 8, the coefficient of friction, the charge weight of the balls 8, the number of balls 8, the width of the mill container 7, the body length of the mill container 7, the amplitude of the mill container 7, the frequency of the mill container 7, absolute coordinate information of the center of the balls 8 in the absolute coordinate system, motion vector information of the balls 8, and a small unit time. In this embodiment, the coefficient of friction was set to 0.8 based on Figure 3.56 (relationship between the angle of repose of the pulverized sample and the friction coefficient in the simulation) described in Non-Patent Document 3.

[0034] The contact determination unit 42 uses a known method to determine whether the balls 8 are in contact with the mill vessel wall surface 7A and whether the balls 8 are in contact with each other. Contact determination is described in, for example, Reference 1 below, and therefore a detailed description thereof will be omitted. [Reference document 1] Japanese Patent Application Publication No. 11-147048

[0035] The collision energy calculation unit 43 calculates the collision energy received by the ball 8 per unit time by a discrete element method using a Voigt model as a viscoelastic dynamic model. A specific calculation method will be described later.

[0036] The flattening process time prediction unit 44 calculates the flattening process time T measured under any flattening process condition n in the flattening process in which the metal powder 9 is flattened by stirring the inside of the mill container 7. nThe "flattening treatment conditions" include the material of the balls 8 and the mill container wall surface 7A, the diameter of the balls 8, the density of the balls 8, the weight of the balls 8, the number of balls 8, the amount of the metal powder 9, the width and length of the mill container 7, the vibration frequency of the mill container 7, the amplitude of the mill container 7, the treatment time, etc. The flattening treatment time prediction unit 44 then uses the rate of change in the BET specific surface area and the collision energy calculated by the collision energy calculation unit 43 to predict the treatment time T required to flatten silver powder having a BET specific surface area value a to obtain silver powder having a BET specific surface area value b under flattening treatment conditions m, which are different from the flattening treatment conditions n. m The specific calculation method will be described later.

[0037] The analysis result output unit 45 outputs the predicted processing time T m The data obtained by the operation of the flattening prediction device 1 is output to the storage unit 3 or the output unit 5.

[0038] 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 the data input from the analysis result output unit 45 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 flattening prediction device 1 as an external output device instead of being provided in the flattening prediction device 1. The connection interface may be any interface compatible with standards such as USB, HDMI, or Bluetooth.

[0039] (Calculation of collision energy) FIG. 3 shows a conceptual diagram of the Voigt model. FIG. 3A shows compression force, and FIG. 3B shows shear force. In the Voigt model, a spring 14 representing the elastic properties of the balls 8 and a dashpot 15 representing the inelastic properties (viscosity) are connected in parallel to represent the force acting on the balls 8. In the case of shear force, a friction slider 16 is inserted as a tangential component of the interaction force to represent the frictional interaction accompanying the contact of a group of balls 8. In such a Voigt model, when a pair of balls 8 collide, one of the balls 8 is focused on. i , the other is the target ball 8 j As a result, the focus is on ball 8 i The radius of r i , target ball 8 j The radius of r j , the center distance between both balls 8 is r ij Then, when the two balls 8 start to collide, the following equation (1) is established. r i +r j =r ij ···(1)

[0040] The force acting at the contact point of a pair of balls 8 generated by the movement of the ball media crusher 6 is defined as the compression force f n (The subscript n indicates the compression direction) and a pair of shear forces f due to the friction coefficient s1 and f s2 (The subscripts s1 and s2 indicate the shear direction, respectively.) The compressive force f at time t n and shear force f s1 ,f s2 is expressed as the sum of the elastic force e based on the spring 14 and the viscous force d according to the Voigt model, as shown in equation (2). f n =e n (t)+d n (t) f s1 =e s1 (t)+d s1 (t) (2) f s2 =e s2 (t)+d s2 (t)

[0041] Here, the elastic force e and the viscous force d due to the spring 14 are determined by the overlap distance r between the balls 8. d and the relative displacement velocity (Δu / Δt) over a short time period. Therefore, the elastic force e(t) based on the spring 14 at time t is a function of the compression elastic constant K of the spring 14. n and shear constant K s Based on this, for each direction, it is expressed by equation (3). e n (t)=K n Δu n e s1 (t)=e s1 (t-Δt)+K s1 Δu s1 e s2 (t)=e s2 (t-Δt)+K s2 Δu s2 ···(3)

[0042] The viscous force d(t) due to the spring 14 at time t is expressed as the compressive viscosity coefficient η of the dashpot 15. n and shear viscosity coefficient η s Based on this, for each direction, it is expressed by equation (4). d n (t)=η n (Δu n / Δt) d s1 (t)=η s1 (Δu s1 / Δt) d s2 (t)=η s2 (Δu s2 / Δt) (4)

[0043] Overlap distance r between colliding balls 8 d is the center distance r shown in Eq. (1) ij and the distance between the balls, it is expressed by equation (5). r d =r ij -Ball distance (5)

[0044] Δu n is the center coordinate u of the two colliding balls 8. ni ,u nj The relative displacement over a small time period is given by equation (6). Δu n =u ni -u nj ···(6)

[0045] Therefore, in the simulation of the movement of the balls in the container using the Voigt model, the force acting on the powder (metal powder 9) by the balls 8 in the ball media grinder 6 can be obtained by sequentially analyzing the center coordinates of the balls 8 and the displacement of the ball center over a short period of time.

[0046] Compression elastic constant K of spring 14 incorporating ball center coordinates ni―j and shear elastic constant K si―j is the Young's modulus E of the material of the ball 8 based on Hertz's elastic contact theory. i ,E j , Poisson's ratio v i ,v j It is expressed by equation (7) as follows. i , δ j is the amount of compression between the balls, b i―j is the contact width, s is the compressive elastic modulus K n represents the coefficient of shear modulus Ks for

number

[0047] In addition, the compressive viscosity coefficient η of the dashpot 15 incorporating the ball center coordinates ni-j and shear viscosity coefficient η si-j is expressed by equation (8), which is the condition for critical damping. η ni-j =2√(mK ni-j ) η si-j =η ni-j √s (8)

[0048] In addition, when the ball 8 contacts the wall surface 7A of the mill vessel, the compression elastic constant K ni-w and shear elastic constant K si-w is the Young's modulus E derived from the material of the mill vessel wall 7A. w , Poisson's ratio v w Therefore, it is expressed by equation (9).

number

[0049] Dashpot 15 compression viscosity coefficient η ni-w and shear viscosity coefficient η si-w is expressed by equation (10), which is the condition for critical damping. η ni-w =2√(mK ni-w ) η si-w =η ni-w √s (10)

[0050] The above Young's modulus and Poisson's ratio must be values ​​derived from the material, but the Young's modulus may be a value lower than the theoretical value of the material, preferably from 0.1 MPa to about 1 / 100 of the actual physical value.

[0051] In addition, the unit time Δt (amount of time interval) of calculation in this discrete element method must satisfy the condition described in equation (11) in terms of the convergence and stability of the difference solution. The unit time Δt is calculated by dividing the weight m of one ball 8 and the compressible elastic constant K n Therefore, increasing the ball diameter not only reduces the number of calculation particles but also increases the unit time Δt, thereby further shortening the calculation time. Δt≦2√(m / K n ) ···(11)

[0052] In this way, in order to simulate the movement of the balls 8 in the ball media crusher 6 using the Voigt model and predict the flattening of the metal powder 9, first, the collision energy E per unit time Δt at the start of collision of all the balls 8 in the ball media crusher 6 is calculated. In this case, in the Voigt model, i The velocity of motion is u i , target ball 8 j The velocity of motion is u j Then, the relative velocity of both balls is u ij is expressed by equation (12). u ij =u i -u j ····(12)

[0053] Featured Ball 8 i The mass of m i , target ball 8 j The mass of m j Then, the collision energy ε at the start of the collision between the two balls is expressed by equation (13).

number

[0054] The total collision energy E per unit time Δt when all N balls 8 in the ball media crusher 6 collide in pairs is expressed by equation (14).

number

[0055] However, in this case, the target ball is 8. i Target ball 8 j Considering only the collision energy when the ball collides with the target ball 8 j Focused on ball 8 iThe collision energy when the balls collide with each other is ignored. The degree of flattening of the metal powder 9 (the amount of change in the BET specific surface area) and the flattening process time are calculated based on the collision energy E per unit time Δt at the start of collision of all the balls 8 in the ball media mill 6 obtained in this way. Note that a detailed calculation method for the collision energy is described in the following Reference 2. However, while Reference 2 explains a calculation method using a two-dimensional model, in the present invention, the calculation is performed using an improved three-dimensional model. [Reference 2] "Introduction to Powder Simulation," edited by the Society of Powder Technology, pp. 29-44, 1998

[0056] (Flattening prediction method) Next, a flattening prediction method (a method for predicting the flattening process time of the metal powder 9) according to one embodiment will be described with reference to FIG.

[0057] In step S101, balls 8 and metal powder 9 are placed in the mill container 7 of the ball media mill 6, and the metal powder 9 is flattened by stirring the inside of the mill container 7. In this flattening process, the measurer measures the BET specific surface area (m 2 The rate of change R of the specific surface area (BET specific surface area after flattening treatment / BET specific surface area before flattening treatment) (i.e., the change in specific surface area after flattening treatment / BET specific surface area before flattening treatment) is actually measured using a specific surface area measuring device.

[0058] In step S102, the control unit 4 calculates the flattening processing time T under the flattening processing condition n using the change rate R. n The flattening rate constant Y n (s -1 ) is calculated using equation (15). n may be determined by the least squares method from the rate of change in the BET specific surface area value for a plurality of treatment times under the flattening treatment condition n. Y n =(R-1) / T n ···(15)

[0059] In step S103, the control unit 4 calculates the collision energy E n Calculate (J / s).

[0060] In step S104, the control unit 4 calculates the flattening speed constant Y n and the collision energy E under the flattening treatment condition n n Using this, the prediction coefficient Z(J -1 ) is calculated using equation (16). The prediction coefficient Z may be calculated not only under one condition but also under multiple conditions, using the slope of the regression line obtained by the least squares method between the flattening rate constant calculated under each condition and the collision energy under each condition. Z=Y n / E n ···(16)

[0061] In step S105, the control unit 4 calculates the collision energy E m Calculate (J / s).

[0062] In step S106, the control unit 4 calculates the prediction coefficient Z and the collision energy E m Using this, the predicted flattening rate constant Y under flattening treatment condition m is m is calculated using equation (17). Y m =E m ×Z (17)

[0063] In step S107, the control unit 4 calculates the predicted flattening rate constant Y m Using equation (18), the predicted processing time T required to obtain metal powder with a BET specific surface area value b by flattening metal powder with a BET specific surface area value a under flattening processing conditions m is calculated. m Ask for. T m =[(b / a)-1] / Y m ···(18)

[0064] Under large-scale conditions, such as a mill container 7 with a capacity of 3 L or more and 700 or more balls 8 loaded, it would take a long time (e.g., 5 to 7 days) to calculate the collision energy through a simulation using a ball diameter that is the same as the actual ball diameter. Furthermore, if the ball diameter is set to more than twice the actual diameter, the resulting collision energy value would differ significantly. Therefore, in the simulation, the ball diameter is preferably set to between 1 and 2 times the diameter of the balls 8 actually used, and more preferably between 1.5 and 2 times the actual diameter.

[0065] FIG. 5 shows the simulation results when the impact energy was calculated for ball diameters of 3 mm and 10 mm when the actual ball diameter was 1.6 mm. The correlation coefficient between the values ​​calculated for the actual ball diameter of 1.6 mm and a ball diameter of 3 mm, which is 1.9 times the actual ball diameter, was 0.998, and the correlation coefficient between the values ​​calculated for the actual ball diameter of 1.6 mm and a ball diameter of 10 mm, which is 6.3 times the actual ball diameter, was 0.976. Furthermore, the slope of the regression line calculated by the least squares method under each condition was 1.19 for a ball diameter of 3 mm and 1.75 for a ball diameter of 10 mm, which was more than 1.5 times larger than the impact energy calculated for the actual ball diameter of 1.6 mm. Based on these results, in this embodiment, the ball diameter in the simulation was set to 3 mm, which is 1.9 times the actual size.

[0066] In the simulation of this embodiment, the mill vessel is assumed to be cylindrical, the cross-sectional shape of the mill vessel is set to be approximately the same as the cross-sectional shape of the actual mill vessel 7, and the body length of the mill vessel is set to be 10 times or more the diameter of the balls 8 that are actually used. If the body length of the mill vessel is 10 times or more the diameter of the balls 8, this is preferable because it shortens the calculation time and improves the accuracy of the calculation of the collision energy.

[0067] In the simulation of this embodiment, the number of balls is set to between 10,000 and 1,000,000. If the number of balls is within this range, it is preferable because the simulation can be performed efficiently and accurately.

[0068] In this embodiment, the capacity of the mill container 7 of the ball media mill 6 that can be predicted is from 0.4 L to 150 L. If the capacity of the mill container 7 is within this range, it is preferable because it allows efficient and accurate simulations from small to large capacities.

[0069] (Experimental results) The processing time required to reach a desired degree of flattening was predicted when silver powders B to G shown in Table 1 were pulverized and flattened using a vibration ball mill and a tumbling ball mill as the ball media mill 6. The BET specific surface area (SSA) values ​​in this embodiment were measured by the BET single-point method using nitrogen adsorption using a specific surface area measuring device (Macsorb HM-model 1210, manufactured by MOUNTECH Co., Ltd.). The measurement conditions for the BET specific surface area were a sample weight of 3.0 g, a N2 / He (30 / 70) mixed gas mixture, a gas flow rate of 25 mL / min, and degassing at 60°C for 10 minutes before measurement.

[0070] [Table 1]

[0071] To determine the prediction coefficient Z, the flattening rate constant Y1 under flattening treatment condition 1 shown in Table 2 was determined using silver powder A shown in Table 1. Specifically, silver powder A (BET value: 0.22 m 2 / g, D50: 5.2 μm) 1.5 kg, and balls (SUS304, ball diameter 1.6 mm, ball density 7.81 g / cm 3 12 kg of silver powder was placed in a mill container 7 of a ball media mill 6 (manufactured by Chuo Kakoki, B-1), and the BET values ​​of each silver powder were measured after 900 seconds, 1800 seconds, and 3600 seconds at a vibration frequency of 1200 rpm.

[0072] Figure 6 shows a graph in which the rate of change R, calculated by dividing the BET specific surface area value after flattening treatment by the BET specific surface area value before flattening treatment (the BET specific surface area value of the raw powder), is plotted on the vertical axis, and the treatment time is plotted on the horizontal axis. In Figure 6, there is a good correlation between the flattening rate R and the treatment time, and the flattening rate constant Y1 (= 1.17 × 10) was determined from the slope of the regression line by the least squares method. -4 ) was sought.

[0073] [Table 2]

[0074] The collision energy E1 of silver powder A under flattening treatment condition 1 shown in Table 2 was calculated using the parameters shown in Tables 3 and 4 (ball diameter 3 mm, ball density 7.81 g / cm 3 The calculation was performed with the following settings: the ball's friction coefficient 0.8, Young's modulus 0.193 GPa, and Poisson's ratio 0.3. The obtained impact energy E1 was 55.2 (J / s), and the prediction coefficient Z obtained from equation (16) was 2.13 × 10 -6 (J -1 The ball diameter of 3 mm in this simulation is 1.9 times the actual ball diameter of 1.6 mm.

[0075] [Table 3]

[0076] [Table 4]

[0077] Next, for each of the silver powders A to G shown in Table 1, the predicted flattening rate constant Y m The predicted coefficient Z and the collision energy E calculated by the simulation m The results are shown in Table 5. The collision energy E mThe parameters shown in Tables 3 and 4 were used to calculate the above. Note that, for condition 2, the same ball media crusher 6 (manufactured by Chuo Kakoki Co., Ltd., B-1) as for condition 1 was used, and for conditions 3 to 6, the ball media crusher 6 was FVR-20 manufactured by Chuo Kakoki Co., Ltd.

[0078] [Table 5]

[0079] (Confirmation of simulation results) Under the flattening treatment conditions 2 to 8 shown in Table 2, the actual flattening treatment time T n and BET specific surface area value, and the flattening treatment time T n The rate of change R of the BET specific surface area was calculated. Next, the predicted treatment time T m , the predicted flattening rate constant Y m The results are shown in Table 6.

[0080] [Table 6]

[0081] As shown in Table 6, the calculated estimated processing time T m and the flattening processing time T actually required to reach a desired flattening degree. n The difference between the measured and actual values ​​is within 20%. Therefore, it can be seen that the flattening treatment time can be predicted according to the present invention. Furthermore, by predicting the flattening treatment time, it becomes possible to flatten metal powder efficiently and economically.

[0082] (program) A computer capable of executing program instructions can also be used to function as the above-described flattening prediction 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 necessary tasks.

[0083] 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.

[0084] 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.

[0085] 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]

[0086] 1 Flattening prediction device 2 Input section 3 Storage section 4. Control section 5 Output section 6 Ball Media Grinding Machine 7 Mill container 7A Mill vessel wall 8 Spherical media (balls) 9 Workpiece (metal powder) 10 Vibration drive unit 11 Unbalanced weight 12 Spring 14 Spring 15 Dashpot 16 Friction Slider 41 Initial parameter input section 42 Contact determination section 43 Collision energy calculation unit 44 Flattening processing time prediction unit 45 Analysis result output section

Claims

1. a step of measuring a rate of change R (BET specific surface area value after flattening treatment / BET specific surface area value before flattening treatment) of the BET specific surface area value of the metal powder under flattening treatment condition n in a flattening process in which balls and metal powder are placed in a mill container of a ball media grinder and the mill container is stirred to flatten the metal powder; Using the change rate R, the flattening processing time T under the flattening processing condition n is calculated. ｎ The flattening rate constant Y ｎ of Y ｎ =(R-1) / T ｎ and The flattening rate constant Y ｎ and the collision energy E obtained by simulation using a discrete element method using a viscoelastic dynamics model for the ball movement in the ball media crusher under the flattening treatment condition n. ｎ Using this, the prediction coefficient Z is Z=Y ｎ / E ｎ and The prediction coefficient Z and the collision energy E obtained by the simulation for the movement of the ball in the ball media crusher under a flattening treatment condition m different from the flattening treatment condition n. ｍ Using the above, the predicted flattening rate constant Y under the flattening treatment condition m is calculated. ｍ of Y ｍ =E ｍ ×Z and The predicted flattening rate constant Y ｍ Using the above, the predicted processing time T required to flatten a metal powder having a BET specific surface area value of a under the flattening processing conditions m to obtain a metal powder having a BET specific surface area value of b is calculated. ｍ of T ｍ =[(b / a)-1] / Y ｍ and A flattening prediction method comprising:

2. The method of claim 1 , wherein the metal powder is selected from copper powder, silver powder, silver-coated copper powder, and silver-coated alloy.

3. The flattening prediction method according to claim 1 , wherein in the simulation, the diameter of the ball is set to be equal to or greater than one time and equal to or less than two times the diameter of a ball actually used.

4. The flattening prediction method described in claim 1, wherein in the simulation, the cross-sectional shape of the mill container is set to be approximately the same as the cross-sectional shape of the actual mill container, and the body length of the mill container is set to be 10 times or more the diameter of the balls actually used.

5. The flattening prediction method according to claim 1 , wherein the number of balls in the simulation is set to be equal to or greater than 10,000 and equal to or less than 1,000,000.

6. The flattening prediction method according to claim 1 , wherein the capacity of the mill container of the ball media mill is 0.4 L or more and 150 L or less.

7. A flattening prediction device including a control unit, which predicts a processing time when flattening metal powder using a ball media crusher, The control unit Using the measured value of the change rate of the BET specific surface area value of the metal powder under the flattening treatment condition n (BET specific surface area value after the flattening treatment / BET specific surface area value before the flattening treatment), R, the flattening treatment time T ｎ The flattening rate constant Y ｎ of Y ｎ =(R-1) / T ｎ It is calculated by The flattening rate constant Y ｎ and the collision energy E obtained by simulation using a discrete element method using a viscoelastic dynamics model for the ball movement in the ball media crusher under the flattening treatment condition n. ｎ Using this, the prediction coefficient Z is Z=Y ｎ / E ｎ It is calculated by The prediction coefficient Z and the collision energy E obtained by the simulation for the movement of the ball in the ball media crusher under a flattening treatment condition m different from the flattening treatment condition n. ｍ Using the above, the predicted flattening rate constant Y under the flattening treatment condition m is calculated. ｍ of Y ｍ =E ｍ ×Z It is calculated by The predicted flattening rate constant Y ｍ Using the above, the predicted processing time T required to flatten a metal powder having a BET specific surface area value of a under the flattening processing conditions m to obtain a metal powder having a BET specific surface area value of b is calculated. ｍ of T ｍ =[(b / a)-1] / Y ｍ The flattening prediction device calculates the flattening.

8. A program for causing a computer to function as the flattening prediction device according to claim 7.

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