Grinding medium design program and method, and information processing system

Abstract

To design a grinding medium used in a grinder so as to improve grinding efficiency.SOLUTION: The grinding medium design method includes (A) a step of setting a shape of an inner wall of a pod in a grinder, (B) a step of setting a shape of a grinding medium in the grinder, and (C) a step of virtually generating a first contact between the grinding media having the set shape and a second contact between the grinding medium and the inner wall of the pod having the set shape a plurality of times at random. The method includes: a step of calculating an area on a reference surface, wherein the distance between the surfaces of both the pulverization media in a contact state is within a range determined by the diameter of a particle to be pulverized; a step (D) of calculating an evaluation value of a shape set for the pulverization media from the area obtained by a plurality of pulverization operations; and a step (E) of determining the shape of the pulverization media on the basis of a plurality of evaluation values obtained by repeatedly executing the step of setting the shape of the pulverization media, the step of calculating the area on the reference surface, and the step of calculating the evaluation value.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a design technique for grinding media used in a grinder. [Background technology]

[0002] Ball mills are common grinding machines used in many fields (ore dressing, cement, pharmaceuticals, etc.). Ball mills generally use spherical grinding media. Shapes other than spherical, such as Cylpebs and Cubes, have been proposed, but as disclosed in Non-Patent Document 1, for example, there are reports that they are not very effective in improving grinding efficiency, and they have not become widespread.

[0003] Furthermore, although there are documents that mention grinding media of various shapes (for example, Patent Document 1), there is no mention of how to design the shape of the grinding media to improve grinding efficiency.

[0004] The crushing process in ore dressing consumes a huge amount of energy, accounting for approximately 2% of the world's total energy consumption. However, the efficiency of a typical crusher is said to be less than 5%, and the efficiency of a typical crusher, a ball mill, is said to be less than 1%, so there is a need to improve crushing efficiency. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Laid-Open No. 2010-119915 [Non-patent literature]

[0006] [Non-Patent Document 1] Shahbazi, et al., Miner. Eng. 157, 106490 (2020) Summary of the Invention [Problem to be solved by the invention]

[0007] Therefore, according to one aspect, an object of the present invention is to provide a technique for designing grinding media used in a grinder so as to improve grinding efficiency. [Means for solving the problem]

[0008] The grinding media design method of the present invention includes the steps of: (A) setting the shape of the inner wall of a pod in a grinding mill; (B) setting the shape of the grinding media in the grinding mill; (C) virtually randomly generating a first contact between grinding media having the set shape and a second contact between the grinding media and the inner wall of a pod having the set shape multiple times, and calculating the area on a reference plane where the distance between the surfaces of the two grinding media in the contacting state is within a range determined by the diameter of the particles to be ground; (D) calculating an evaluation value of the shape set for the grinding media from the areas measured multiple times; and (E) determining the shape of the grinding media based on the multiple evaluation values ​​obtained by repeatedly executing the steps of setting the shape of the grinding media, calculating the area on the reference plane, and calculating the evaluation value. [Effects of the Invention]

[0009] According to one aspect, it becomes possible to design the grinding media used in the grinder so as to improve the grinding efficiency. [Brief explanation of the drawings]

[0010] [Figure 1] FIG. 1 is a diagram showing an overview of an information processing system according to an embodiment of the present invention. [Figure 2] FIG. 2 is a diagram illustrating a processing flow of the processing executed by the information processing system. [Figure 3] FIG. 3 is a diagram showing a processing flow of the contact simulation processing. [Figure 4] FIG. 4 is a diagram for explaining the distance and the proximity area when two spheres are in contact with each other. [Figure 5A]FIG. 5A (a) is a front view of the output shape of the grinding media, and (b) is a reference front view. [Figure 5B] FIG. 5B (a) is a right side view of the output shape of the grinding media, and (b) is a reference right side view. [Figure 5C] FIG. 5C (a) is a left side view of the output shape of the grinding media, and (b) is a reference left side view. [Figure 5D] FIG. 5D (a) is a plan view of the output shape of the grinding media, and (b) is a reference plan view. [Figure 5E] FIG. 5E (a) is a bottom view of the output shape of the grinding media, and (b) is a reference bottom view. [Figure 5F] FIG. 5F (a) is a rear view of the output shape of the grinding media, and (b) is a reference rear view. [Figure 5G] FIG. 5G is a reference perspective view of the grinding media output configuration. [Figure 6A] FIG. 6A is a reference front view of the grinding media output shape showing its difference from a simple ellipsoid. [Figure 6B] FIG. 6B is a reference right side view of the grinding media output shape showing the difference from a simple ellipsoid. [Figure 6C] FIG. 6C is a reference left side view of the grinding media output shape showing the difference from a simple ellipsoid. [Figure 6D] FIG. 6D is a reference plan view of the output shape of the grinding media, showing its difference from a simple ellipsoid. [Figure 6E] FIG. 6E is a reference bottom view of the grinding media output shape, showing its difference from a simple ellipsoid. [Figure 6F] FIG. 6F is a reference rear view of the grinding media output shape showing the difference from a simple ellipsoid. [Figure 7] FIG. 7 shows the experimental results regarding the output shape of the grinding media. [Figure 8] FIG. 8 is a diagram illustrating an example of a functional configuration of a computer. DETAILED DESCRIPTION OF THE INVENTION

[0011] [Embodiment 1] In a ball mill, the material to be ground is sandwiched between the grinding media or between the grinding media and the wall of the pod (also called the mill container), and is subjected to compressive and shear forces, resulting in grinding. In this embodiment, the shape of the grinding media is designed with a focus on the area that sandwiches the material between the grinding media or between the grinding media and the wall of the pod.

[0012] FIG. 1 shows an example of the configuration of an information processing system 100 for designing the shape of grinding media.

[0013] The information processing system 100 includes an input unit 110, an input data storage unit 120, a shape optimization unit 130, and an output unit 140. The input unit 110 accepts inputs such as the number of processing iterations, the processing termination conditions, the particle size of the object to be pulverized (particle size before pulverization), the shape of the inner wall of the pod (e.g., the inner diameter in the case of a cylindrical pod), conditions regarding the grinding media (e.g., the approximate size and basic shape of the grinding media), and the number of grinding media to be used, and stores these in the input data storage unit 120. The shape optimization unit 130 uses the data stored in the input data storage unit 120 to perform the process described below to optimize the shape of the grinding media. The output unit 140 outputs the processing results of the shape optimization unit 130 to an output device such as a display device or to another device (e.g., another information processing device connected to a network).

[0014] The shape optimization unit 130 has and controls a shape generation unit 131, a contact simulation unit 132, an evaluation unit 133, a first data storage unit 134, and a second data storage unit 135. The shape generation unit 131 virtually generates the shape of the grinding media and the shape of the inner wall of the pod, and stores the data in the first data storage unit 134. The contact simulation unit 132 randomly generates virtual contact between grinding media and between the grinding media and the inner wall of the pod multiple times, calculates the proximity area (described below) for each contact, and stores the calculated area in the second data storage unit 135. The evaluation unit 133 uses the data stored in the second data storage unit 135 to evaluate one virtually generated shape of the grinding media and also evaluates multiple virtually generated shapes of the grinding media.

[0015] Next, the processing contents of the information processing system 100 shown in FIG. 1 will be described with reference to FIGS.

[0016] First, the input unit 110 receives input from the user, such as the number of times the contact simulation is repeated, the termination conditions for the process, the particle size d of the object to be pulverized (particle size before pulverization), the shape of the inner wall of the pod, data on the pulverization media, and the number of pulverization media to be used, and stores these in the input data storage unit 120 (FIG. 2: step S1). The termination conditions for the process include, for example, the number of different shapes of the pulverization media and the target value for the proximity area.

[0017] Next, the shape generation unit 131 of the shape optimization unit 130 sets the shape of the pod's inner wall based on the data about the grinding media (e.g., the approximate size of the grinding media) stored in the input data storage unit 120 and the shape of the pod's inner wall, and generates a model of that shape (step S3). For example, if the ratio of the approximate size of the grinding media to the pod's inner diameter is less than a threshold, the pod's inner wall is set to be flat. On the other hand, if this ratio is equal to or greater than the threshold, a curved surface that curves at the pod's inner diameter is generated. Note that if the pod's inner wall is not cylindrical, a curved surface is generated that imitates the actual shape. Alternatively, whether the surface is flat or curved may be determined based on a difference rather than a ratio. The data of the generated model is stored in the first data storage unit 134.

[0018] The shape generation unit 131 then determines the shape of the grinding medium based on data about the grinding medium stored in the input data storage unit 120 and generates two models of that shape (step S5). For example, the shape of the grinding medium is determined based on conditions such as the use of a combination of spherical harmonic functions as the basic shape of the grinding medium and the specification of the approximate size of the grinding medium. Spherical harmonic functions are equivalent to a three-dimensional Fourier series, and various three-dimensional shapes can be expressed by combining spherical harmonic functions. Therefore, multiple types of shapes can be created by combining spherical harmonic functions in different ways. The types of spherical harmonic functions to be combined and in different ways are changed each time step S5 is executed. Note that the method is not limited to using spherical harmonic functions; for example, a method that can transform the data into multiple types of three-dimensional shapes by changing the values ​​of multiple parameters may also be used. The data of the generated models is stored in the first data storage unit 134.

[0019] Then, the contact simulation unit 132 executes a contact simulation process (step S7), which will be described with reference to FIGS.

[0020] The contact simulation unit 132 determines whether the contact is between the grinding media or between the inner wall of the pod and the grinding media based on the data stored in the input data storage unit 120 (e.g., the number of grinding media to be used) (FIG. 3: step S21).

[0021] Assuming that the greater the number of grinding media to be used, the greater the frequency of contact between the grinding media. A probability function is prepared so that the greater the number of grinding media to be used, the higher the probability of contact between the grinding media (i.e., the probability of contact between the grinding media). Then, from the probability function, the probability of contact between the grinding media according to the number of grinding media to be used this time is identified, and it is determined which of two types of contact will occur at that occurrence probability.

[0022] When it is determined that contact between the grinding media has occurred (step S23), the contact simulation unit 132 independently and randomly rotates the two grinding media models (step S25). The contact simulation unit 132 then positions the centers of the two grinding media models in the rotated orientation on the same axis (for example, on the Z axis) with a predetermined distance between them (step S27). The contact simulation unit 132 then moves one of the grinding media models on the axis to bring it into contact with the other grinding media model (step S29).

[0023] The contact simulation unit 132 calculates the distance D on a straight line parallel to an axis (for example, the Z axis) between each surface point of one of the grinding media models and a surface point of the other model in the contact state (step S31).

[0024] For ease of explanation, an example of two spheres will be explained using Figure 4. Figure 4 shows an example in which two spheres, which are grinding media and whose centers are on the Z axis, are in contact. At the point of contact, the distance D between the surfaces of the two spheres is 0, and the distance D increases as the distance from the point of contact increases.

[0025] The contact simulation unit 132 then calculates the area A on a plane R (also referred to as a reference plane) perpendicular to an axis (e.g., the Z axis) where the distance D is equal to or less than a threshold Dth based on the particle size d before crushing, and stores the area A in the second data storage unit 135 (step S33). The threshold Dth based on the particle size d before crushing may be, for example, the particle size d itself, or a value adjusted from the particle size d according to a predetermined rule. In the example of FIG. 4, the region where the distance D is equal to or less than the threshold Dth is the range that includes the point where the two spheres contact and is surrounded by a thick line on the spheres, and calculates the area A of the region α where the distance D is equal to or less than the threshold Dth projected onto the plane R perpendicular to the Z axis. The process then returns to the original process.

[0026] On the other hand, if it is determined that contact will occur between the grinding media and the inner wall of the pod, rather than between the grinding media themselves (step S23: No route), the contact simulation unit 132 randomly rotates one model of the grinding media (step S35).

[0027] The contact simulation unit 132 also positions the center of the grinding medium model in the post-rotation posture at a predetermined distance from the model of the inner wall of the pod in the normal direction of the inner wall model (step S37). Furthermore, the contact simulation unit 132 moves the grinding medium model on the normal line of the model of the inner wall of the pod to bring it into contact with the model of the inner wall of the pod (step S39).

[0028] Then, the contact simulation unit 132 calculates the distance D on a straight line parallel to the normal to the surface of the pod inner wall model for each point on the surface of the grinding medium model in the contact state (step S41).

[0029] Finally, the contact simulation unit 132 calculates the area A on a plane R (also called the reference plane) perpendicular to the normal line, where the distance D is equal to or less than the threshold Dth based on the particle size d before crushing, and stores the area A in the second data storage unit 135 (step S43). Then, the process returns to the calling process.

[0030] In this embodiment, the area A is called the proximity area, and the larger this area is, the more efficiently the object to be crushed can be crushed.

[0031] If the shape of the pod's inner wall is flat or cylindrical, the model of the pod's inner wall does not need to be rotated randomly. However, if a different shape is set, the model of the pod's inner wall is rotated randomly, for example, around the pod's rotation axis (e.g., the Y axis). The grinding media model is then placed in the rotated position on a predetermined Z axis and then moved to contact the pod's inner wall model. In this case, the plane perpendicular to the Z axis is used as the reference plane.

[0032] Furthermore, although the distance D is set to be equal to or smaller than the threshold value Dth, a lower limit other than 0 may be separately set for convenience of calculation, etc. In other words, a section from the threshold value Dths to the threshold value Dth may be set.

[0033] 2, the shape optimization unit 130 determines whether the contact simulation process has been executed a predetermined number of times (for example, the number of repetitions of the contact simulation stored in the input data storage unit 120) (step S9). If the contact simulation process has not been executed the predetermined number of times, the process returns to step S7.

[0034] On the other hand, when the contact simulation process has been executed a predetermined number of times, the evaluation unit 133 calculates, as an evaluation value, an average value of the proximity areas A for the predetermined number of times stored in the second data storage unit 135 (step S11). The average value is an example of an evaluation value.

[0035] The evaluation unit 133 also determines whether or not the termination condition for the process stored in the input data storage unit 120 is satisfied (step S13). The termination condition for the process may be defined, for example, by the number of types of shapes of the grinding media to be subjected to the contact simulation process, by a target value for the average value of the proximity area A, or by both.

[0036] If the termination condition of the process is not satisfied, the process returns to step S5. On the other hand, if the termination condition of the process is satisfied, the shape optimization unit 130 instructs the output unit 140 to output data on the shape of the grinding medium that maximizes the average value of the adjacent area A to an output device or the like (step S15).

[0037] This allows us to search for the shape of the grinding media with the largest average value of the proximity area A, which is an evaluation value, while taking into consideration not only contact between the grinding media but also contact with the inner wall of the pod. In other words, it is expected that the grinding efficiency will improve.

[0038] When setting the shape of the grinding media in step S5, simply doing it randomly may result in poor efficiency, so it may be done according to an appropriate optimization algorithm.

[0039] For example, a genetic algorithm may be used as the optimization algorithm. In this case, the following process is carried out. · Make it possible to express the shape of the grinding media as a gene sequence. In the first generation, a certain number of shapes (for example, 100) are randomly selected, and the average value of the proximity area A for each is calculated. From the first generation, a certain number of types (for example, 100) of second generation types are set through selection (selecting multiple excellent shapes with large average values ​​of adjacent area A as "parents"), crossover (mixing the genes of the selected multiple parents to create "child" genes), and mutation (randomly changing part of the child's genes). Repeat the above process (for example, 10 generations). The final generation will adopt a grinding media shape with the largest average value of the adjacent area A.

[0040] It is also possible to calculate the average value of the proximity area A due to contact between grinding media and the average value of the proximity area A due to contact between grinding media and the inner wall of the pod separately, and then select as parents a shape with a large average value of the proximity area A due to contact between grinding media and the inner wall of the pod and a shape with a large average value of the proximity area A due to contact between grinding media and the inner wall of the pod, and then intertwine them.

[0041] Furthermore, instead of a genetic algorithm, a simulated annealing (SA), a tabu search (TS), a particle swarm optimization (PSO), or the like may be employed.

[0042] [Modification of the first embodiment] In the above example, the particle size d before crushing is specified as a single value, but there are also cases where the particle size before crushing is specified as a range such as d1 or more and d2 or less.

[0043] In such a case, thresholds Dth1 and Dth2 of the distance D may be set for each of a plurality of diameter values ​​representing that section, for example, for each of the lower limit values ​​d1 and d2, to calculate the proximity areas A(Dth1) and A(Dth2), and the average value Aave of the proximity areas A(Dth1) and A(Dth2) may be calculated as the second evaluation value. Then, a further average value of the average values ​​Aave for the number of executions of the contact simulation process is calculated as the evaluation value.

[0044] However, the multiple diameter values ​​representing the range of particle diameters before crushing are not limited to the upper and lower limits, but may be intermediate values ​​of the range, or if the frequency distribution of particle diameters before crushing is known, a value other than the intermediate value may be used as the threshold value Dthx accordingly.Furthermore, if the frequency distribution of particle diameters before crushing is known, a weighted average of the proximity areas A of each threshold value may be calculated as the second evaluation value according to the frequency distribution.

[0045] [Example] As described above, approximately 5,500 different grinding media shapes were randomly generated using a combination of spherical harmonics, and the shape with the largest average value of the proximity area A (hereinafter referred to as the output shape) was identified. Six-sided views of this output shape are shown in Figures 5A to 5F (a). Figures 5A to 5F (b) show the surface meshed with triangles, with two axes passing through the center indicated. Figure 5G also shows a reference perspective view of the surface meshed with triangles.

[0046] The shape index of this output shape is as follows: The axes that intersect with the three axes that are orthogonal to each other at the center are called the long axis, the middle axis, and the short axis in descending order. ·Long axis length / middle axis length 1.14 ·Long axis length / short axis length 1.24 ·Sphericity 0.993

[0047] The output shape is an irregular shape, like a slightly squashed ellipsoid, and cannot be created intentionally by humans. Figures 6A to 6F show diagrams in which a dotted line representing a certain ellipsoid is superimposed on the output shape. The certain ellipsoid has a major axis length the same as that of the output shape, a median axis length the same as that of the output shape, and a minor axis length the same as that of the output shape. In each diagram, it can be seen that the ellipsoid includes both a portion that is more bulging than the ellipsoid and a portion that is more truncated than the ellipsoid.

[0048] We also conducted experimental verification using a ball mill with grinding media having this output shape. Alumina N-99 was machined to create 10 spherical grinding media with a diameter of 20 mm and 10 grinding media with the output shape. The grinding media with the output shape were sized to have the same volume as the 20 mm spherical grinding media. Each type of media was placed in a small magnetic mill (inner diameter 100 mm, length 120 mm) and grinding experiments were conducted. As shown in Figure 7, grinding experiments were conducted for five cases, A to E, each of which was carried out under conditions specified by the sample, sample particle size, sample input amount, ball mill rotation speed, and ball mill grinding time.

[0049] To evaluate the grinding results, we measured the weight ratio of fine particles (here, particles with a diameter of 90 μm or less) generated as a result of grinding under the same conditions for the spherical and output shapes. As shown in Figure 7, the fine particle ratio b for the output shape grinding media was approximately 10% higher than the fine particle ratio a for the spherical grinding media, and statistical significance was also confirmed. In other words, we confirmed that the grinding efficiency of the output shape grinding media was more than 10% higher than that of a typical spherical shape. After the same grinding time had elapsed, there was no significant difference in the amount of wear or damage between the spherical and output shapes.

[0050] For iron media made by casting, the manufacturing cost is the same whether it is spherical or output-shaped. Therefore, by adopting the output shape, it is possible to improve the crushing efficiency by 10% or more without increasing the manufacturing cost. This has the effect of reducing the energy used for crushing (i.e., cost and CO2 generation) by 10% or more.

[0051] Although the embodiments of the present invention have been described above, the present invention is not limited to these. For example, the functional configuration example of the information processing system shown in Figure 1 is an example and may differ from the program configuration example. Furthermore, the processing flows shown in Figures 2 and 3 are also examples, and the processing order may be changed or multiple steps may be executed simultaneously as long as the same processing results can be obtained.

[0052] In addition to the ball mill, the present invention can be applied to mills that use spherical media, such as a bead mill, a planetary mill, a hardening mill, a vibration mill, and an agitation mill.

[0053] Furthermore, although the average value of the proximity area A is shown above as an example of the evaluation value, the reciprocal of the average value may be used as the evaluation value, and the shape of the grinding medium with the lowest evaluation value may be selected.

[0054] The information processing system 100 described above is, for example, a computer device as shown in FIG. 8 , in which a memory 2501, a CPU 2503, a hard disk drive (HDD) 2505 (which may be a solid state drive (SDD)), a display control unit 2507 connected to a display device 2509, a drive device 2513 for a removable disk 2511, an input device 2515, and a communication control unit 2517 for connecting to a network are connected via a bus 2519. An operating system (OS) and an application program for carrying out the processing of this embodiment are stored in the HDD 2505 and are read from the HDD 2505 to the memory 2501 when executed by the CPU 2503. The CPU 2503 controls the display control unit 2507, the communication control unit 2517, and the drive device 2513 according to the processing content of the application program to perform predetermined operations. Data during processing is mainly stored in the memory 2501, but may also be stored in the HDD 2505. In an embodiment of the present invention, an application program for performing the above-described processing is distributed by being stored on a computer-readable removable disk 2511, and is installed from the drive device 2513 onto the HDD 2505. It may also be installed onto the HDD 2505 via a network such as the Internet and the communication control unit 2517. Such a computer device realizes the above-described various functions through organic cooperation between hardware such as the CPU 2503 and memory 2501 described above and programs such as the OS and application programs.

[0055] Furthermore, instead of implementing all of the functions of the information processing system 100 in one computer device, the functions may be shared among multiple computer devices. Note that whether the information processing system 100 is implemented in one computer device or multiple computer devices, the entire system will be referred to as an information processing system.

[0056] The above-described embodiment can be summarized as follows.

[0057] The grinding media design method according to this embodiment includes the steps of: (A) setting the shape of the inner wall of a pod in a grinding mill; (B) setting the shape of the grinding media in the grinding mill; (C) virtually randomly generating a first contact between grinding media having the set shape and a second contact between the grinding media and the inner wall of a pod having the set shape multiple times, and calculating the area on a reference plane where the distance between the surfaces of the two grinding media in the contacting state is within a range determined by the diameter of the particles to be ground; (D) calculating an evaluation value of the shape set for the grinding media from the areas measured multiple times; and (E) determining the shape of the grinding media based on the multiple evaluation values ​​obtained by repeatedly executing the steps of setting the shape of the grinding media, calculating the area on the reference plane, and calculating the evaluation value.

[0058] By calculating the above area based on the contact between the grinding media and the contact between the grinding media and the inner wall of the pod in this way, the shape of the grinding media can be appropriately evaluated, and a shape that will result in higher grinding efficiency can be selected.

[0059] The first contact and the second contact may be generated with a probability based on the number of grinding media used in the grinding mill, for example, since the more grinding media there are, the more contact between the grinding media will occur, and this is intended to simulate such a situation.

[0060] Furthermore, in the step of setting the shape of the inner wall of the pod described above, either a flat surface or a curved surface that curves in accordance with the internal shape of the pod may be set based on the relationship between the inner diameter of the pod and the size of the grinding media. For example, if the size of the grinding media is small compared to the inner diameter of the pod, there is no problem in regarding the inner wall of the pod as a flat surface, and calculation costs can be reduced.

[0061] Furthermore, if a range is set for the diameter of the particles to be pulverized, the area on the reference surface may be calculated by setting the range for each of multiple diameter values ​​representing the range. In this case, in the step of calculating the shape evaluation value, a second evaluation value may be calculated from the area for each of the multiple diameter values ​​for each of multiple runs, and the evaluation value of the shape set for the grinding media may be calculated from the second evaluation values ​​for multiple runs. The multiple diameter values ​​representing the range may be, for example, upper and lower limits, but may also include intermediate values ​​between the upper and lower limits. The second evaluation value may be a simple average, or, for example, a weighted average based on the frequency distribution of particle diameters before pulverization may be used.

[0062] A program for causing a processor to perform the above-described processing can be created, and the program is stored in a computer-readable storage medium or storage device, such as a flexible disk, an optical disk such as a CD-ROM (Read Only Memory), a magneto-optical disk, a semiconductor memory (e.g., a ROM), a hard disk, etc. Data during processing is temporarily stored in a storage device such as RAM (Random Access Memory). [Explanation of symbols]

[0063] 110 Input section 120 Input data storage section 130 Shape optimization section 140 Output section 131 Shape generation unit 132 Contact simulation unit 133 evaluation unit 134 first data storage unit 135 second data storage unit

Claims

1. Setting the shape of the inner wall of the pod in the grinder; setting the shape of the grinding media in the grinder; a step of virtually randomly generating a first contact between the grinding media having the set shape and a second contact between the grinding media and the inner wall of the pod having the set shape multiple times, and calculating an area on a reference plane where the distance between the surfaces of the two in contact falls within a range determined by the diameter of the particles to be crushed; A step of calculating an evaluation value of the shape set for the grinding medium from the area for the plurality of times; A step of determining the shape of the grinding medium based on a plurality of evaluation values ​​obtained by repeatedly executing the step of setting the shape of the grinding medium, the step of calculating the area on the reference surface, and the step of calculating the evaluation value; A computer-implemented method for designing grinding media, comprising:

2. The first contact and the second contact are caused to occur with a probability based on the number of grinding media used in the grinding machine. The grinding media design method according to claim 1.

3. In the step of setting the shape of the inner wall of the pod, Based on the relationship between the inner diameter of the pod and the size of the grinding media, either a flat surface or a curved surface that conforms to the internal shape of the pod is set. The grinding media design method according to claim 1.

4. When a range is set for the diameter of the particles to be pulverized, setting the range for each of a plurality of diameter values ​​representing the section and calculating the area on the reference surface; In the step of calculating an evaluation value of the shape, A second evaluation value is calculated from the area for each of the plurality of diameter values ​​for each of the plurality of times, and an evaluation value for the shape set for the grinding medium is calculated from the second evaluation values ​​for the plurality of times. The grinding media design method according to claim 1.

5. A program for causing a computer to execute the grinding medium design method according to any one of claims 1 to 4.

6. a means for setting the shape of the inner wall of the pod in the crusher; a means for setting the shape of the grinding media in the grinder; a means for virtually randomly generating a first contact between grinding media having the set shape and a second contact between the grinding media and the inner wall of a pod having the set shape multiple times, and calculating an area on a reference plane where the distance between the surfaces of the two in contact falls within a range determined by the diameter of the particles to be crushed; a means for calculating an evaluation value of the shape set for the grinding medium from the area for the plurality of times; A means for determining the shape of the grinding medium based on a plurality of evaluation values ​​obtained by repeatedly operating the means for setting the shape of the grinding medium, the means for calculating the area on the reference surface, and the means for calculating the evaluation value; An information processing system having the above.

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