Particle size distribution determination method

Abstract

To provide a grain size distribution measurement method capable of precisely calculating a grain size distribution of a mixed particle size accumulated body.SOLUTION: A first grain size distribution of a first grain sample is calculated for each first grain size distribution (ST1), a second grain size distribution of a mixed particle size accumulated body with which a particle that belongs to a second grain size section is mixed is calculated (ST2), the second grain size distribution is approximated by a linear combination of the first grain size distribution (ST3), the total number distribution of the mixed particle size accumulated body is calculated from coefficients of the linear combination by using a surface probability model (ST5), the entire mass distribution of the mixed particle size accumulated body is calculated based on the entire number distribution (ST6), a first grain size distribution is calculated based on the entire mass distribution (ST7), a first cumulative mass distribution obtained by accumulating the first grain size distribution (ST8), the first cumulative mass distribution is approximated by an approximation function that expresses a grain size distribution rule (ST9), a second cumulative mass distribution is calculated based on the approximation function (ST10), and a second grain size distribution is calculated based on the second cumulative mass distribution (ST11).SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a method for measuring the particle size distribution of particles such as coke, sintered ore, and more particularly to a particle size distribution measuring method capable of accurately calculating the particle size distribution, which is the relationship between particle size classes and the mass fraction of all particles in each particle size class of a mixed particle size deposit (a deposited particle group) containing particles belonging to multiple particle size classes (classifications determined by particle size, which is an index of particle size). [Background technology]

[0002] Blast furnace raw materials such as coke and sintered ore are transported in piles on a belt conveyor and charged into the blast furnace. It is known that the particle size (an index that represents the degree of particle size) of the particles that make up the raw materials affects the productivity of blast furnace operation. For this reason, it is desirable to continuously measure the particle size distribution of the raw materials during the raw material transportation process to maintain quality.

[0003] The particle size of blast furnace raw materials is generally measured by taking samples (sampling) from a belt conveyor at regular intervals, dividing the samples every four or eight hours, and then sieving them. Therefore, even if the particle size distribution of the raw materials fluctuates over a short period of time due to variations in raw material quality or malfunctions in production equipment, intermittent measurements using sieves after sampling make it impossible to accurately capture temporal fluctuations in the particle size distribution because the time intervals are too long.

[0004] As a method capable of continuously measuring particle diameters in a non-contact manner, for example, the method described in Non-Patent Document 1 has been proposed. The method described in Non-Patent Document 1 is a measurement method using a light-section type 3D camera in which a laser light source that emits linear laser light and an area scan camera are integrated. In the method described in Non-Patent Document 1, a moving distance detection device such as a rotary encoder in contact with the belt conveyor is used. A 3D camera measures the position of the upper edge of the cross section of particles deposited on the belt conveyor every time the belt conveyor moves a certain distance. This generates a distance image (sometimes called a 3D image or depth image) in which the pixel value of each pixel indicates the distance from a reference position (e.g., the distance from the 3D camera). Near the boundaries of stacked particles, the irradiated laser light is interrupted and dark, and the unevenness of the particles increases. Therefore, in the distance image, the pixel values ​​of pixel regions corresponding to the boundaries of particles tend to differ from the pixel values ​​of other pixel regions. The method described in Non-Patent Document 1 utilizes this characteristic to determine particle boundaries, identify each particle, and calculate the particle size of each particle. The dimensions of stacked particles with portions hidden by other particles are smaller than their actual dimensions. For this reason, in the method described in Non-Patent Document 1, height information of each particle (height from the bottom of the conveyor belt) that can be calculated using a 3D camera is used to preferentially extract surface particles (hereinafter referred to as "surface particles" as appropriate), and the diameter of the minor axis of each surface particle in the range image when it is considered as an ellipse is used as the particle size.

[0005] As a method capable of continuously measuring particle diameters in a non-contact manner, the methods described in Non-Patent Document 2 and Patent Document 1 have also been proposed, which use a 3D camera in the same way as the method described in Non-Patent Document 1. Non-Patent Document 2 and Patent Document 1 describe in detail an edge detection method for identifying each particle and an image processing method for recognizing surface particles, and Patent Document 1 in particular also describes a method for speeding up measurement.

[0006] In the method described in Non-Patent Document 2, image processing is performed on a distance image acquired of deposited particles to extract surface particles in the surface layer with little overlap, the particle size of each surface particle is sorted into particle size categories determined by the mesh size of a sieve, and the number distribution of surface particles (surface number distribution), which is the relationship between the particle size categories and the number of surface particles in each particle size category, is calculated. The method described in Non-Patent Document 2 then estimates the number distribution of all deposited particles, including not only surface particles but also hidden particles, using a surface probability model, which represents the degree of surface visibility and appearance in the surface layer according to particle size, i.e., a model that estimates the number distribution of all deposited particles (total number distribution) from the number distribution of surface particles. Furthermore, the method described in Non-Patent Document 2 estimates the distribution of the mass fraction of all deposited particles (total mass distribution) using the volume ratio (or mass ratio) for each particle size category.

[0007] The inventors applied the method described in Non-Patent Document 2 to a mixed particle size deposit in which particles (coke particles) belonging to multiple particle size classes are mixed and deposited at a predetermined mass ratio, and conducted a confirmation test to determine whether the overall mass distribution can be accurately estimated. As a result of this confirmation test, it was found that even if the sample was a single-grained sample consisting only of particles with the same grain size, in the case of irregular particles such as coke or sintered ore, the grain size distribution of the single-grained sample would be broader than the grain size distribution because the grain size of the surface layer particles varies depending on the particle orientation. For this reason, it was found that simply sorting the grain sizes of the surface layer particles measured with a 3D camera into grain size divisions determined by a sieve, counting the number of surface layer particles for each grain size division, and applying the method described in Non-Patent Document 2 would result in a blurred grain size distribution (total mass distribution) that did not accurately match the results measured using a sieve. [Prior art documents] [Patent documents]

[0008] [Patent Document 1] Japanese Patent Application Publication No. 2019-174155 [Non-patent literature]

[0009] [Non-Patent Document 1] MJ Thurley, "Automated, On-line, Calibration-Free, Particle Size Measurement using 3D Profile Data", Measurement and Analysis of Blast Fragmentation: Workshop Hosted by FRAGBLAST 10 - The 10th International Symposium on Rock Fragmentation by Blasting, 2013, pp.23-32 [Non-patent document 2] MJ Thurley, "Three Dimensional Data Analysis for the Separation and Sizing of Rock Piles in Mining", Ph.D. Thesis, Monash University, December 2002, chapter 4, pp.27-60 Summary of the Invention [Problem to be solved by the invention]

[0010] The present invention aims to provide a particle size distribution measurement method that can accurately calculate the particle size distribution, which is the relationship between particle size classifications and the mass proportion of the total particles in each particle size classification of a mixed particle size deposit containing particles belonging to multiple particle size classifications (classifications determined by particle size, which is an index representing the degree of particle size), with respect to the mixed particle size deposit. [Means for solving the problem]

[0011] To solve the above-mentioned problems, the inventors conducted extensive research and came up with the particle size distribution measurement method described in Japanese Patent Application No. 2021-078603. In this particle size distribution measurement method, single-grain size samples are prepared for each of the multiple grain size classes to which particles constituting a mixed-grain size sediment belong. The particle size of the surface layer of each single-grain size sample is measured using a 3D camera or the like to calculate a first particle size distribution that indicates the relationship between the particle size and number of particles in the surface layer of the single-grain size sample. Furthermore, the particle size of the surface layer of a mixed-grain size sediment containing particles belonging to the multiple grain size classes is measured using a 3D camera or the like to calculate a second particle size distribution that indicates the relationship between the particle size and number of particles in the surface layer of the mixed-grain size sediment. The calculated second particle size distribution is then approximated by a linear sum of the calculated first particle size distributions, and each coefficient of this linear sum is considered to represent the number ratio of different particle size classes in the surface layer of the mixed-grain size sediment, assuming that the mixed-grain size sediment is composed of a combination of single-grain size samples of multiple grain size classes. Thereafter, the coefficients are used to calculate the overall mass distribution in the same procedure as the method described in Non-Patent Document 2.

[0012] The particle size distribution measurement method described in Patent Application No. 2021-078603 gives as a specific example three particle size categories: particle size category 1 (25 mm < particle size ≦ 38 mm), particle size category 2 (38 mm < particle size ≦ 50 mm), and particle size category 3 (50 mm < particle size ≦ 75 mm), and gives a case in which a mixed particle size laminate is made up of particles belonging to these three particle size categories blended in any mass ratio, and single particle size samples are prepared for the same three particle size categories. In this example, the particle size distribution measurement method described in Patent Application No. 2021-078603 makes it possible to calculate a highly accurate particle size distribution (total mass distribution) that closely matches the results measured using a sieve.

[0013] However, when the inventors added particle size category 4 (75 mm < particle size ≦ 100 mm), which includes particle sizes larger than particle size category 3, to the above three particle size categories 1 to 3, and conducted confirmation tests on the particle size distribution measurement method described in Patent Application No. 2021-078603, they found that in some cases the results did not fully match those measured using a sieve.

[0014] Figure 1 shows an example of the results of the above-mentioned confirmation test. Figure 1(a) shows the particle size distribution (first particle size distribution) of surface particles measured using a 3D camera for single-grain size samples of grain size categories 1 to 4. Figure 1(b) shows the total mass distribution calculated using the particle size distribution measurement method described in Japanese Patent Application No. 2021-078603 for a mixed-grain size deposit containing single-grain size samples of grain size categories 1 to 4 blended at mass ratios of 10%, 15%, 45%, and 30% (hereinafter referred to as the "mixed-grain size deposit of Example 1"). Figure 1(c) shows the total mass distribution calculated using the particle size distribution measurement method described in Japanese Patent Application No. 2021-078603 for a mixed-grain size deposit containing single-grain size samples of grain size categories 1 to 4 blended at mass ratios of 15%, 20%, 45%, and 20% (hereinafter referred to as the "mixed-grain size deposit of Example 2"). In Figures 1(b) and 1(c), the graphs indicated by "3D" are data calculated using the particle size distribution measurement method described in Patent Application No. 2021-078603, and the graphs indicated by "Sieve" are data measured using a sieve (total mass proportion reflecting the actual state of the blended particles). As can be seen from Figures 1(b) and 1(c), when particle size category 4, which includes particle sizes larger than particle size category 3, is added, even the particle size distribution measurement method described in Patent Application No. 2021-078603 may not fully match the results measured using sieves. This is partly because particles belonging to particle size category 4 (75 mm < particle size ≦ 100 mm) have large irregularities. When particle sizes are measured using a 3D camera, the unevenness is mistakenly recognized as particle boundaries, making it difficult to distinguish between the particle sizes measured for particles belonging to particle size category 3 (50 mm < particle size ≦ 75 mm). Therefore, as shown in Figure 1(a), there is a large overlap between the particle size distribution measured for a single particle size sample in particle size category 3 and the particle size distribution measured for a single particle size sample in particle size category 4. As a result, the overall mass distribution does not fully match the results measured using sieves, as shown in Figures 1(b) and 1(c).

[0015] When there is a large overlap in the particle size distributions measured for a single particle size sample, as in the case of particle size categories 3 and 4 above, there is a problem in that the accuracy of the overall mass distribution calculated for a mixed particle size deposit in which this single particle size sample is mixed in a specified mass ratio will be poor. Furthermore, for example, for particle size category 0 (0 mm < particle size ≦ 25 mm), which contains particle sizes smaller than particle size category 1, the particle sizes of the surface particles are so small that they cannot be accurately measured using a 3D camera.As a result, for single-particle-size samples of this particle size category 0, the particle size distribution as shown in Figure 1(a) cannot be accurately measured, and as a result, there is a problem that the overall mass distribution cannot be accurately calculated for mixed-particle-size deposits in which this single-particle-size sample is mixed in a specified mass ratio.

[0016] Therefore, the inventors conducted further intensive research to improve the particle size distribution measurement method described in Japanese Patent Application No. 2021-078603. As a result, they first considered preparing single-particle-size samples consisting of only multiple particle size categories (e.g., the aforementioned particle size categories 1-3) in which the effect of particle size distribution overlap can be ignored, and calculating the overall mass distribution (e.g., the overall mass distribution for the aforementioned particle size categories 1-3) in the same manner as the particle size distribution measurement method described in Japanese Patent Application No. 2021-078603. Next, they calculated a first particle size distribution by expanding this overall mass distribution to multiple particle size categories (e.g., the aforementioned particle size categories 0-4) that include particles of the mixed-particle-size deposit. They then calculated a first cumulative mass distribution, which is the relationship between this first particle size distribution and the cumulative mass fraction of the entire particles of the mixed-particle-size deposit. They found that this first cumulative mass distribution could be accurately approximated by an approximation function that represents a particle size distribution law, such as the Rosin-Rammler distribution equation. It was then found that by calculating a second cumulative mass distribution, which is the relationship between the particle sizes included in multiple particle size divisions (for example, the aforementioned particle size divisions 0 to 4) of the mixed particle size deposit body and the cumulative mass proportion of each particle size division, based on this approximate function, it is possible to accurately calculate the particle size distribution (second particle size distribution), which is the relationship between the particle size divisions and the mass proportion of the total particles in each particle size division of the mixed particle size deposit body, based on this second cumulative mass distribution. The present invention was completed based on the findings of the inventors described above.

[0017] That is, in order to solve the above-mentioned problem, the present invention provides a first particle size distribution calculation method that prepares single-particle size samples, which are samples consisting of only particles having the same particle size in a first particle size division, which is a particle size division determined by the size of the particle, for a plurality of first particle size divisions, images of the surface layers of the single-particle size samples of the plurality of first particle size divisions are taken while changing the deposition state of the single-particle size samples, distance images are obtained that show the distance from a reference position to the particles in the surface layer, and a first particle size distribution that shows the relationship between the particle size and the number of particles in the surface layer of the single-particle size sample is calculated for each of the plurality of first particle size divisions based on the distance images. a second particle size distribution calculation step of imaging a surface layer of a mixed-grain size deposit body, the surface layer of which is a blend of particles belonging to a plurality of second particle size divisions including a particle size division different from the plurality of first particle size divisions, while changing the deposition state of the mixed-grain size deposit body, obtaining a distance image showing the distance from a reference position to the particles in the surface layer, and calculating a second particle size distribution showing the relationship between particle size and number of particles in the surface layer of the mixed-grain size deposit body based on the distance image; and a coefficient calculation step of approximating the second particle size distribution with a linear sum of the first particle size distributions for each of the plurality of first particle size divisions, and calculating a coefficient of the linear sum. an overall number distribution calculation step of calculating an overall number distribution, which is a relationship between the first particle size division and the overall number ratio of particles in each of the first particle size divisions in the mixed particle size deposit body, from the coefficients of the linear sum using a surface probability model that estimates the number distribution of all deposited particles from the number distribution of particles in the surface layer; an overall mass distribution calculation step of calculating an overall mass distribution, which is a relationship between the first particle size division and the overall mass ratio of particles in each of the first particle size divisions in the mixed particle size deposit body, based on the overall number distribution and the volume ratio calculated from the first particle size divisions; a first particle size distribution calculation step of calculating a first particle size distribution, which is a relationship between particle sizes in a range including the second particle size division and a mass ratio of all particles in the mixed particle size deposit body; a first cumulative mass distribution calculation step of calculating a first cumulative mass distribution, which is a relationship between particle sizes in a range including the plurality of second particle size divisions and a cumulative mass ratio obtained by accumulating the mass ratio of all particles in the mixed particle size deposit body in the first particle size distribution; an approximation step of approximating the first cumulative mass distribution with an approximation function representing a particle size distribution law; and a particle size in a range including the plurality of second particle size divisions based on the approximation function.The particle size distribution measuring method includes: a second cumulative mass distribution calculating step of calculating a second cumulative mass distribution which is a relationship between the cumulative mass proportion for each of the second particle size classes; and a second particle size calculating step of calculating a second particle size distribution which is a relationship between the second particle size classes and the mass proportion of all particles for each of the second particle size classes of the mixed particle size deposit based on the second cumulative mass distribution.

[0018] In the present invention, a "distance image" refers to an image in which the pixel value of each pixel indicates the distance from a reference position (e.g., the distance from the distance image acquisition means). The "distance image" acquired in the first particle size distribution calculation step is an image showing the distance from the reference position to the particles in the surface layer of the single-grain-size sample, and the "distance image" acquired in the second particle size distribution calculation step is an image showing the distance from the reference position to the particles in the surface layer of the mixed-grain-size deposit. The distance image acquisition means for acquiring the distance image is not particularly limited as long as it can acquire the distance to the target surface layer, but examples include a light-section type 3D camera that combines a laser light source that emits linear laser light with an area scan camera. The reference position can be set to any position, and for example, the position of the distance image acquisition means can be used as the reference position. Once a "distance image" can be acquired, it is possible to calculate the particle size and number of particles by performing calculations based on the "distance image" using a calculation device connected to the distance image acquisition means, for example, by using the method described in Non-Patent Document 2. Furthermore, the "surface probability model" is synonymous with the surface probability model described in Non-Patent Document 2, and is a model that represents the degree of likelihood of appearance or visibility in the surface layer according to particle size. In other words, the surface probability model is a model that relates the number distribution of particles in the surface layer for each particle size classification to the number distribution of all deposited particles, and is a model that estimates the number distribution of all deposited particles from the number distribution of particles in the surface layer. Furthermore, the "volume ratio" refers to the value obtained by dividing the volume calculated from one particle size division by the reference volume, where the volume calculated from another particle size division is taken as the reference volume.

[0019] According to the present invention, in the first particle size distribution calculation step, a first particle size distribution is calculated based on the overall mass distribution calculated in a manner similar to the particle size distribution measurement method described in Japanese Patent Application No. 2021-078603. The first particle size distribution is the relationship between the particle sizes in a range including multiple second particle size classes (particle size classes of the mixed-grain-size deposit body including particle size classes different from the first particle size class of the single-grain-size sample) and the mass fraction of all particles in the mixed-grain-size deposit body. In other words, a first particle size distribution is calculated by expanding the overall mass distribution to include multiple second particle size classes including particles of the mixed-grain-size deposit body. Next, in the first cumulative mass distribution calculation step, a first cumulative mass distribution is calculated, which is the relationship between the particle sizes in a range including the multiple second particle size classes and the cumulative mass fraction obtained by accumulating the mass fraction of all particles in the mixed-grain-size deposit body in the first particle size distribution. Based on the aforementioned findings of the inventors, this first cumulative mass distribution can be approximated by an approximation function representing the particle size distribution law. Therefore, by approximating the first cumulative mass distribution in the approximation step and calculating the second cumulative mass distribution, which is the relationship between the particle sizes in the range including the plurality of second particle size classes and the cumulative mass fraction for each second particle size class, based on this approximation function in the second cumulative mass distribution calculation step, it is possible to calculate the second particle size distribution, which is the relationship between the second particle size class and the mass fraction of the total particles in each second particle size class of the mixed particle size sediment body, based on the second cumulative mass distribution in the second particle size calculation step. In other words, even if the second particle size class of the mixed particle size sediment body includes a particle size class different from the first particle size class of the single particle size sample, it is possible to accurately calculate the mass fraction of the total particles in each second particle size class by preparing only the plurality of first particle size classes as the single particle size sample, in which the effect of particle size distribution overlap can be ignored.

[0020] In the first particle size distribution calculation step and the second particle size distribution calculation step of the present invention described above, particle size distributions (first particle size distribution and second particle size distribution) showing the relationship between the particle size and the number of particles in the surface layer are calculated, respectively. However, according to the knowledge of the present inventors, one parameter of the relationship shown in the particle size distribution is not necessarily limited to the number of particles in the surface layer, and instead, even if a particle size distribution showing the relationship between the particle size and the area or volume of particles in the surface layer is used, the total mass distribution, and therefore the second particle size distribution, can be calculated with high accuracy. Therefore, in the first particle size distribution calculation step, instead of the first particle size distribution showing the relationship between the particle size and the number of particles in the surface layer of the single particle size sample, a second particle size distribution showing the relationship between the particle size and the area of ​​the particles in the surface layer of the single particle size sample is calculated, and in the second particle size distribution calculation step, particle size Instead of the second particle size distribution showing the relationship between the particle size and the number of particles in the surface layer of the deposit, particle size A second particle size distribution indicating the relationship between the particle size and area of ​​the particles in the surface layer of the deposit may be calculated. Alternatively, in the first particle size distribution calculation step, instead of the first particle size distribution showing the relationship between the particle size and the number of particles in the surface layer of the single particle size sample, a first particle size distribution showing the relationship between the particle size and the volume of particles in the surface layer of the single particle size sample is calculated, and in the second particle size distribution calculation step, particle size Instead of the second particle size distribution showing the relationship between the particle size and the number of particles in the surface layer of the deposit, particle size A second particle size distribution indicating the relationship between the particle size and the volume of the particles in the surface layer of the deposit may be calculated.

[0021] In the total number distribution calculation step of the present invention, when calculating the total number distribution of the mixed-grain-size deposit body using the surface probability model, it is necessary to input the height of the mixed-grain-size deposit body (the height (bulk height) when the particle size of the particles in the surface layer is measured in the second particle size distribution calculation step) into the surface probability model. When measuring the particle size of the particles in the surface layer of the mixed-grain-size deposit body in the second particle size distribution calculation step, if the mixed-grain-size deposit body is deposited in a tray, i.e., if it is deposited in an area that is partitioned in four directions when viewed from above, the height of the mixed-grain-size deposit body is stable and can be grasped relatively easily, so a preset fixed value can be used. However, when the mixed-grain-size deposit body is deposited and transported on a belt conveyor, the height is likely to fluctuate during transport, so it is preferable to actually measure the height.

[0022] That is, in the present invention, it is preferable to have a height calculation step, in which, in the second particle size distribution calculation step, the second particle size distribution is calculated while the mixed-grain size deposit body in a state where it has been piled up on a belt conveyor is transported by the belt conveyor, and the positions of the upper edges of the cross section of the mixed-grain size deposit body and the belt conveyor are measured, in the height calculation step, the cross-sectional area of ​​the mixed-grain size deposit body is calculated based on the positions of the upper edges of the cross section of the mixed-grain size deposit body and the belt conveyor and the previously measured position of the upper edge of the cross section of the belt conveyor in a state where the mixed-grain size deposit body has not been piled up, the cross section of the mixed-grain size deposit body is considered to be a trapezoid and the height of the mixed-grain size deposit body is calculated based on the cross-sectional area, and in the overall number distribution calculation step, the overall number distribution is calculated from the coefficients of the linear sum and the height of the mixed-grain size deposit body calculated in the height calculation step using the surface probability model.

[0023] The cross section of a typical belt conveyor used to transport particles such as coke and sintered ore is trapezoidal, and therefore the cross section of the mixed-grain pile deposited on the belt conveyor can often be approximated as a trapezoid as well. According to the above-described preferred method, by measuring the positions of the upper edges of the cross sections of the mixed-grain-size deposit body and the belt conveyor in the second particle size distribution calculation step, the cross-sectional area of ​​the mixed-grain-size deposit body can be calculated in the height calculation step. Then, by approximating the cross section of the mixed-grain-size deposit body as a trapezoid, the height of the mixed-grain-size deposit body can be calculated from the cross-sectional area of ​​the mixed-grain-size deposit body. By using the calculated height of the mixed-grain-size deposit body in the surface probability model in the overall number distribution calculation step, the overall number distribution of the mixed-grain-size deposit body can be calculated with high accuracy, even when the mixed-grain-size deposit body is piled up and transported on a belt conveyor. Consequently, the overall mass distribution of the mixed-grain-size deposit body can be calculated with high accuracy in the overall mass distribution calculation step. In order to measure the positions of the upper edges of the cross sections of the mixed-grain size deposit and the belt conveyor, it is conceivable to use a distance image acquisition means used to acquire a distance image of the mixed-grain size deposit in combination. [Effects of the Invention]

[0024] According to the present invention, for a mixed-grain-size sediment containing particles belonging to multiple grain size classes, it is possible to accurately calculate a grain size distribution (second grain size distribution), which is the relationship between the grain size classes and the mass proportions of all particles in each grain size class of the mixed-grain-size sediment. In particular, according to the present invention, even if multiple single-grain-size samples corresponding to the multiple grain size classes (second grain size classes) of the mixed-grain-size sediment are prepared, and there is a large overlap in the grain size distributions measured for the multiple single-grain-size samples, or even if the grain sizes of surface layer particles cannot be measured accurately because the second grain size class includes small grain sizes, it is possible to accurately calculate the second grain size distribution simply by preparing single-grain-size samples of multiple grain size classes (first grain size classes) in which the effect of overlap in grain size distributions is negligible. [Brief explanation of the drawings]

[0025] [Figure 1] FIG. 1 is a diagram showing an example of the results of a confirmation test regarding the particle size distribution measurement method described in Patent Application No. 2021-078603. [Figure 2] FIG. 1 is a flow chart showing steps of a particle size distribution measuring method according to one embodiment of the present invention. [Figure 3] FIG. 3 is an explanatory diagram for schematically explaining step ST1 shown in FIG. 2. [Figure 4] FIG. 3 is an explanatory diagram that schematically explains steps ST2 to ST4 shown in FIG. 2. [Figure 5] FIG. 3 is an explanatory diagram that schematically explains steps ST7 to ST11 shown in FIG. [Figure 6] 1 shows the second particle size distribution and linear sum of the mixed particle size deposit of Example 1 calculated in the examples. [Figure 7] 1 shows the surface number distribution, total number distribution, and total mass distribution of the mixed particle size deposit of Example 1 calculated in the examples. [Figure 8] 1 shows a first particle size distribution calculated in an example. [Figure 9] 1 shows the first cumulative mass distribution, the approximate function Q(x'), and the second cumulative mass distribution calculated in the example. [Figure 10] 1 shows the second particle size distribution calculated in the examples. [Figure 11] FIG. 10 is an explanatory diagram illustrating a method for calculating the height of a mixed particle size deposit accumulated and transported on a belt conveyor. [Figure 12] FIG. 10 is an explanatory diagram illustrating a method for calculating the height of a mixed particle size deposit accumulated and transported on a belt conveyor. [Figure 13] FIG. 2 is a diagram for explaining the deposition state of surface layer particles. [Figure 14] For the examples, the first particle size distribution of a single particle size sample related to the area of ​​surface particles and the first particle size distribution of a mixed particle size sediment calculated using the first particle size distribution and the second particle size distribution related to the area of ​​surface particles are shown. [Figure 15] For the examples, the first cumulative mass distribution, approximate function Q(x'), and second cumulative mass distribution of the mixed grain size deposit calculated using the first grain size distribution and second grain size distribution related to the area of ​​surface grains are shown. [Figure 16] For the examples, the second particle size distribution calculated when the first particle size distribution and the second particle size distribution related to the area of ​​the surface layer particles are used is shown. [Figure 17] In the examples, the first cumulative mass distribution, approximate function P(x'), and second cumulative mass distribution calculated for a mixed-grain sediment body further containing particles belonging to grain size category 0 (0 mm < grain size ≦ 25 mm) using the first grain size distribution and second grain size distribution related to the number of surface layer particles are shown. [Figure 18] In the examples, the second particle size distribution calculated for a mixed particle size deposit further containing particles belonging to particle size category 0 (0 mm<particle size≦25 mm) is shown when the first particle size distribution and the second particle size distribution related to the number of surface particles are used. [Figure 19] In the examples, the first cumulative mass distribution, approximate function P(x'), and second cumulative mass distribution calculated for a mixed particle size deposit further containing particles belonging to particle size category 0 (0 mm < particle size ≦ 25 mm) using the first particle size distribution and second particle size distribution related to the area of ​​surface particles are shown. [Figure 20]In the examples, the second particle size distribution calculated using the first particle size distribution and the second particle size distribution related to the surface particle area is shown for a mixed particle size deposit further containing particles belonging to particle size category 0 (0 mm < particle size ≦ 25 mm). DETAILED DESCRIPTION OF THE INVENTION

[0026] Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings. Fig. 2 is a flow diagram showing steps included in a particle size distribution measuring method according to one embodiment of the present invention. Fig. 3 is an explanatory diagram that schematically explains step ST1 shown in Fig. 2. Fig. 4 is an explanatory diagram that schematically explains steps ST2 to ST4 shown in Fig. 2. Fig. 5 is an explanatory diagram that schematically explains steps ST7 to ST11 shown in Fig. 2. 2, the particle size distribution measuring method according to this embodiment includes steps ST1 to ST11. Each step will be described below in order. Note that this embodiment will be described taking as an example a case where the particle size distribution (second particle size distribution) of a mixed particle size laminate containing particles belonging to four or five particle size classes is measured, but the present invention is not limited to this and can also be applied to a mixed particle size laminate containing particles belonging to three particle size classes or six or more particle size classes.

[0027] <Process ST1> In step ST1 (corresponding to the first particle size distribution calculation step of the present invention), single particle size samples, which are samples consisting only of particles having particle sizes in the same particle size class (first particle size class), are prepared for multiple first particle size classes. It is possible to know in advance which particle size classes the particles belong to in a mixed particle size laminate containing particles belonging to multiple second particle size classes (i.e., particles of various particle sizes). In this embodiment, the particle size distribution of a mixed particle size laminate containing particles belonging to, for example, four particle size classes (second particle size classes) blended at arbitrary mass ratios is measured. The single particle size samples are prepared for, for example, three of the four particle size classes of the mixed particle size laminate, for which the influence of overlapping particle size distributions can be ignored. Specifically, in this embodiment, as shown in Fig. 3(a), single particle size samples are prepared for a total of three first particle size classes: particle size class 1, which includes particles that pass through a 38 mm mesh sieve but not a 25 mm mesh sieve (i.e., particles with a particle size of 25 mm < particle size ≦ 38 mm); particle size class 2, which includes particles that pass through a 50 mm mesh sieve but not a 38 mm mesh sieve (i.e., particles with a particle size of 38 mm < particle size ≦ 50 mm); and particle size class 3, which includes particles that pass through a 75 mm mesh sieve but not a 50 mm mesh sieve (i.e., particles with a particle size of 50 mm < particle size ≦ 75 mm). Specifically, for example, one tray T's worth of samples is prepared as shown in Fig. 3(a).

[0028] In step ST1, distance image acquisition means (in this embodiment, a 3D camera 1 using a light-section method using a linear laser beam L as shown in FIG. 3(a)) is used above each of the three single-particle-size samples of the first particle size range. Images are repeatedly captured while changing the deposition state of each single-particle-size sample to acquire distance images, and a computing device (not shown) connected to the distance image acquisition means performs computations to measure the particle size of the surface particles of each single-particle-size sample. To acquire the distance images, the tray T is moved relative to the 3D camera 1 in a direction perpendicular to the direction of the linear laser beam L (the horizontal direction in FIG. 3(a)), which serves as the light-section line. In this embodiment, the minor axis diameter of the surface particles in the distance image, when the surface particles are regarded as ellipses, is used as the particle size of the surface particles. The deposition state can be changed by mixing and stirring that occurs when each single-particle-size sample is transferred between the tray T and another container (not shown). It is preferable that the number of repeated measurements of each single-particle-size sample is the same. As a result, a first particle size distribution showing the relationship between the particle size (x) and number of surface particles in the single-particle-size sample is calculated for each of the three first particle size divisions, as shown in Figure 3(b). In Figure 3(b), A(x) is the first particle size distribution calculated for the single-particle-size sample in particle size division 1, B(x) is the first particle size distribution calculated for the single-particle-size sample in particle size division 2, and C(x) is the first particle size distribution calculated for the single-particle-size sample in particle size division 3.

[0029] <Process ST2> In step S2 (corresponding to the second particle size distribution calculation step of the present invention), a mixed-grain-size deposit is formed by blending particles belonging to multiple second particle size classes (e.g., particle size classes 1-4) at arbitrary mass ratios, including the three first particle size classes (particle size classes 1-3) and a different particle size class (e.g., particle size class 4 (75 mm<particle size≦100 mm) that passes through a 100 mm mesh sieve but not a 75 mm mesh sieve). Using a distance image capture device (in this embodiment, a 3D camera 1 shown in FIG. 4(a)), the mixed-grain-size deposit is repeatedly photographed while changing its deposition state to obtain distance images. A computing device (not shown) connected to the distance image capture device then performs calculations to measure the particle size of the surface particles of the mixed-grain-size deposit. In this embodiment, the minor axis diameter of the surface particles in the distance image, when considered as an ellipse, is used as the particle size of the surface particles. As in the case of single-grain samples, when a mixed-grain sediment is piled up in tray T and the grain size of the surface layer particles is measured, the change in the sediment state can be achieved by the mixing and stirring that occurs when the mixed-grain sediment is transferred between tray T and another container. The number of repeated measurements of the mixed-grain sediment does not necessarily have to be the same as the number of repeated measurements of each single-grain sample. When measuring the particle size of the surface particles of a mixed-grain size deposit that is accumulated and transported on a belt conveyor, the measurement can be repeated assuming that different deposition states of mixed-grain size deposits mixed in the same mass ratio are unfolding on the belt conveyor. As a result, a second particle size distribution, which shows the relationship between the particle size (x) and the number of particles in the surface layer of the mixed-grain-size sediment body, is calculated as shown in Fig. 4(b). In Fig. 4(b), F(x) shown by the solid line is the second particle size distribution calculated for the mixed-grain-size sediment body.

[0030] <Process ST3> In step ST3 (corresponding to the coefficient calculation step of the present invention), in order to quantify the extent to which the number of surface layer particles of each particle size division appears in the second particle size distribution F(x) of the mixed-grain size sediment body (the number of surface layer particles of the mixed-grain size sediment body), as shown in FIG. 4(b), the particle size distribution F(x) of the mixed-grain size sediment body is linearly summed C(x) of the first particle size distributions A(x), B(x), and C(x) for each of the three first particle size divisions. a A(x)+Cb B(x)+C c Approximate by C(x) and the coefficient of the linear sum C a , C b , C c In Fig. 4(b), the linear sum is indicated by a dashed line. Approximation using the linear sum can be performed using a known approximation method such as the least squares method.

[0031] <Process ST4> Coefficient C of the linear sum calculated in step ST3 a can be considered to be a value proportional to the number of surface particles belonging to grain size category 1 that appear in the mixed-grain sediment. Similarly, the coefficient C of the linear sum b can be considered to be a value proportional to the number of surface particles belonging to grain size category 2 that appear in the mixed-grain sediment. Similarly, the coefficient C of the linear sum c can be considered to be a value proportional to the number of surface particles belonging to grain size category 3 that appear in the mixed-grain sediment. For this reason, in step ST4, each coefficient C a , C b , C c are regarded as the surface number ratios, which are the number ratios of surface particles belonging to grain size classes 1, 2, and 3 of each single grain size sample in the mixed-grain sediment, and the surface number distribution showing the relationship between the first grain size class and the surface number ratio for each first grain size class is calculated for the mixed-grain sediment, as shown in Figure 4(c).

[0032] <Process ST5> In step ST5 (corresponding to the overall number distribution calculation step of the present invention), the surface number distribution as shown in Figure 4(c) calculated in step ST4 and the surface probability model are used to calculate the overall number distribution, which is the relationship between the first particle size division and the total number proportion of particles in each first particle size division of the mixed particle size deposit body. The surface number distribution is not equal to the total number distribution, which is the distribution of the number ratio of all deposited particles. This is because the frequency with which particles appear in the surface layer varies depending on particle size, with larger particles appearing more frequently in the surface layer, so the surface number distribution will count more large particles than the total number distribution. For this reason, to calculate the total number distribution, a surface probability model is required that represents the degree of likelihood of particles appearing in the surface layer or being visible depending on particle size and that can estimate the number distribution of all deposited particles from the number distribution of surface particles. The surface probability model is explained below.

[0033] The surface probability P of particles of size class i appearing on the surface layer i is expressed by the following equation (1).

number

[0034] The surface probability Pi of equation (1) is expressed by the following equation (2), and more specifically by the following equations (3) to (6).

number

number

number

number

number

[0035] In step ST5, the overall number distribution is calculated using the surface probability model described above. Specifically, the total number of particles Ni is calculated by an iterative method using the following formula (1') obtained by modifying the formula (1) of the surface probability model. Note that in this embodiment, the ratio of the total number of particles to the total number of particles is calculated, rather than the total number of particles themselves.

number

[0036] In the iterative method, the following steps (1) to (5) are carried out. (1) First, N j The initial value of N1 is set to a value obtained by dividing 1 by the number of granularity divisions. In this embodiment, since the number of granularity divisions (first granularity divisions) is 3, N1 = N2 = N3 = 1 / 3. (2)N j Substitute the initial value of into the right-hand side of equation (1') and update N i Ask for. (3) Updated N i About N i is normalized by 1. That is, N i N so that the sum of N1+N2+N3 is 1. i The ratio N i Replace with / (N1+N2+N3). (4) Normalized N j Substituting into the right-hand side of equation (1'), the updated N i Ask for. (5) Repeat steps (1) to (4) i converges (N before update i and the updated N i Repeat this process until the absolute value of the difference between the number and the number becomes equal to or less than a certain value, and calculate the final total number of particles (number ratio) N i Ask for. This gives the particle size class i and the total particle number ratio N i The overall number distribution, which is the relationship between

[0037] <Process ST6> In step ST6 (corresponding to the total mass distribution calculation step of the present invention), the total number distribution calculated in step ST5 and the volume ratio V calculated from each of the three first particle size divisions are i Based on the above (see Table 1), the total mass distribution, which is the relationship between the particle size division and the mass ratio of the whole particles in each particle size division of the mixed particle size sediment, is calculated. Specifically, as shown in the following formula (7), the number ratio of all particles N i and volume ratio V i Multiply by and calculate the ratio as the mass fraction of the whole particles m i It is calculated as follows.

number

[0038] <Process ST7> In step ST7 (corresponding to the first particle size distribution calculation step of the present invention), a first particle size distribution is calculated based on the overall mass distribution calculated in step ST6. This first particle size distribution is the relationship between the particle size x' (25 mm<particle size x'≦100 mm) in the range including multiple second particle size ranges (particle size ranges 1 to 4) and the mass fraction of all particles in the mixed particle size sediment body, as shown by the bar graph in Figure 5(a). Specifically, in step ST6, the mass fraction of all particles in each of the first particle size ranges (particle size ranges 1 to 3) of the mixed particle size sediment body is calculated. However, since the particle size distribution of particle size range 3 overlaps significantly with that of particle size range 4, making it difficult to distinguish between them (see Figure 1(a)), the overall mass fraction of particle size range 3 calculated in step ST6 is replaced with the overall mass fraction of particle size ranges 3 and 4 (50 mm<particle size x'≦100 mm) (the overall mass fractions of particle size ranges 1 and 2 calculated in step ST6 are used as is).

[0039] <Process ST8> In step ST8 (corresponding to the first cumulative mass distribution calculation step of the present invention), a first cumulative mass distribution is calculated, which is the relationship between the particle size x' (25 mm < particle size x' ≦ 100 mm) in the range including multiple second particle size divisions (particle size divisions 1 to 4), as shown by "◯" in Figure 5(a), and the cumulative mass proportion obtained by accumulating (accumulating in order from smallest to largest particle size) the mass proportion of all particles in the mixed particle size deposit body in the first particle size distribution calculated in step ST7. Specifically, in the example shown in Figure 5(a), the total mass fraction of particle size class 1 is plotted on the vertical axis at the position where the horizontal axis corresponds to the maximum particle size of particle size class 1 (particle size x' = 38 mm), the sum of the total mass fractions of particle size class 1 and particle size class 2 is plotted on the vertical axis at the position where the horizontal axis corresponds to the maximum particle size of particle size class 2 (particle size x' = 50 mm), and the sum of the total mass fractions of particle size class 1 to particle size class 2 (i.e., 100%) is plotted on the vertical axis at the position where the horizontal axis corresponds to the maximum particle size of particle size class 3 and 4 (particle size x' = 100 mm), and this is calculated as the first cumulative mass distribution.

[0040] <Process ST9> In step ST9 (corresponding to the approximation step of the present invention), the first cumulative mass distribution calculated in step ST8 is approximated by an approximation function (approximation function Q(x') shown in FIG. 5(a)) that represents the particle size distribution law. In this embodiment, the Rosin-Rammler distribution equation is used as the approximation function that represents the particle size distribution law. This will be described in detail below.

[0041] The Rosin-Rammler distribution law is known as a particle size distribution law that expresses the particle size distribution of pulverized particles. For example, when the particles are coke, the upper limit of the particle size division is a particle size of 100 mm. Therefore, the inventors have confirmed that if P(x') expressed by the following formula (8), which is normalized based on the Rosin-Rammler distribution formula so that the cumulative mass fraction is 0% at a particle size of 0 mm and 100% at a particle size of 100 mm, applies to the process analysis value of the particle size distribution of coke with relatively high accuracy,

number

[0042] In the example shown in Figure 5(a), the cumulative mass ratio is 0% at a particle size of 25 mm and 100% at a particle size of 100 mm, so Q(x') expressed by the following equation (9) can be used as the approximate function for step ST9.

number

[0043] <Process ST10> In step ST10 (corresponding to the second cumulative mass distribution calculation step of the present invention), based on the approximation function Q(x') determined in step ST9, a second cumulative mass distribution is calculated, which is the relationship between the particle size x' (25 mm < particle size x' ≦ 100 mm) in the range including multiple second particle size divisions (particle size divisions 1 to 4) and the cumulative mass proportion of each second particle size division (each particle size division 1 to 4), as plotted by ``◯'' and ``●'' in Figure 5(b). Specifically, in the second cumulative mass distribution shown in Figure 5(b), the cumulative mass proportion values ​​plotted at particle size x' = 38 mm, 50 mm, and 100 mm (plotted with "○") are the same as those in the first cumulative mass distribution. Because the cumulative mass proportion at particle size x' = 75 mm (the maximum particle size in particle size category 3) is unknown, the value of Q(75) calculated by substituting x' = 75 mm into equation (9) can be estimated as the cumulative mass proportion at particle size x' = 75 mm (estimating the cumulative mass proportion plotted with "●"), thereby enabling the second cumulative mass distribution to be calculated.

[0044] <Process ST11> In step ST11 (corresponding to the second cumulative mass distribution calculation step of the present invention), a second particle size distribution is calculated based on the second cumulative mass distribution calculated in step ST10, which is the relationship between the second particle size classes (particle size classes 1 to 4) and the mass proportion of the total particles in each second particle size class of the mixed particle size deposit, as shown by the bar graph in Figure 5(b). Specifically, in the example shown in FIG. 5(b), 100-Q(75) can be calculated as the total mass fraction of particle size division 4 (75 mm<particle size x'≦100 mm). Furthermore, by subtracting the cumulative mass fraction at particle size x'=50 mm (the cumulative mass fraction calculated in step ST8) from Q(75), the total mass fraction of particle size division 3 (50 mm<particle size x'≦75 mm) can be calculated. For the total mass fractions of particle size division 1 (25 mm<particle size x'≦38 mm) and particle size division 2 (38 mm<particle size x'≦50 mm), the total mass fractions calculated in step ST6 can be used as is. In this way, in step ST11, a second particle size distribution is calculated, which is the relationship between the second particle size divisions (particle size divisions 1-4) and the total mass fractions of particles in each second particle size division of the mixed particle size deposit.

[0045] In the above description of steps ST7 to ST11, the mixed-grain-size sediment body is an example in which particles belonging to four second grain size classes (grain size classes 1 to 4) are blended in arbitrary mass proportions, but in the case of a mixed-grain-size sediment body in which particles belonging to multiple second grain size classes (grain size classes 0 to 4) are blended in arbitrary mass proportions and which further includes grain size class 0 (0 mm<grain size≦25 mm) that does not pass through sieves with a mesh size of less than 25 mm, the second grain size distribution can be calculated as shown in Figures 5(c) and 5(d). Specifically, this is as follows.

[0046] In the case of a mixed particle size deposit in which particles belonging to particle size classes 0 to 4 are blended in any mass ratio, in step ST7, a first particle size distribution is calculated, which is the relationship between the particle size x' (0 mm < particle size x' ≦ 100 mm) in the range that includes multiple second particle size classes (particle size classes 0 to 4) and the mass ratio of the total particles in the mixed particle size deposit, as shown by the bar graph in Figure 5(c). In step ST8, a first cumulative mass distribution is calculated, which is the relationship between the particle size x' (0 mm < particle size x' ≦ 100 mm) in the range including multiple second particle size classes (particle size classes 0 to 4), as shown by "◯" in Figure 5(c), and the cumulative mass proportion obtained by accumulating (accumulating in order from smallest to largest particle size) the mass proportion of all particles in the mixed particle size deposit in the first particle size distribution calculated in step ST7. In step ST9, the first cumulative mass distribution calculated in step ST8 is approximated by an approximation function representing the particle size distribution law. Specifically, as in the case shown in FIG. 5(a), the first cumulative mass distribution is first approximated by the approximation function Q(x') expressed by the aforementioned equation (9) (specifically, the values ​​of the parameters a and b in equation (9) are determined). Next, an approximation function P(x') expressed by equation (8) with the parameters a and b having the same values ​​as the determined values ​​of the parameters a and b in equation (9) is determined. In the case of a mixed-grain-size sediment body in which particles belonging to particle size classes 0 to 4 are blended at an arbitrary mass ratio, the cumulative mass ratio is 0% at a particle size of 0 mm and 100% at a particle size of 100 mm. Therefore, the approximation function finally determined in step ST9 is the approximation function P(x'). In step ST10, based on the approximation function P(x') determined in step ST9, a second cumulative mass distribution is calculated, which is the relationship between the particle size x' (0 mm < particle size x' ≦ 100 mm) in the range including multiple second particle size divisions (particle size divisions 0 to 4) and the cumulative mass fraction for each second particle size division (each particle size division 0 to 4), as plotted with "◯" and "●" in Figure 5(d). Specifically, since the cumulative mass fraction at particle size x' = 25 mm (the maximum particle size in particle size division 0) is unknown, the value of P(25) calculated by substituting x' = 25 mm into equation (8) is estimated as the cumulative mass fraction at particle size x' = 25 mm (the cumulative mass fraction plotted with "●" is estimated). Similarly, since the cumulative mass fraction at particle size x' = 75 mm (the maximum particle size of particle size category 3) is unknown, the value of P(75) calculated by substituting x' = 75 mm into formula (8) is estimated as the cumulative mass fraction at particle size x' = 75 mm (the cumulative mass fraction plotted with "●" is estimated). Also, the cumulative mass fraction values ​​plotted at particle size x' = 38 mm and 50 mm (plotted with "○") in the second cumulative mass distribution shown in Figure 5(d) are not the same as those in the first cumulative mass distribution shown in Figure 5(c), and considering the addition of particle size category 0, a conversion similar to that used to change the approximation function Q(x') to the approximation function P(x') is required. Specifically, the cumulative mass fraction at particle size x' = 38 mm in the first cumulative mass distribution (hereinafter referred to as "Q m ") is reduced by a factor of (1-P(25) / 100) by the amount of particle size division 0 added, and P(25) is added to this to determine the cumulative mass ratio of particle size x' = 38 mm in the second cumulative mass distribution (hereinafter referred to as "P m In other words, the cumulative mass ratio Q of particle size x' = 38 mm in the first cumulative mass distribution must be m , P m =Q m According to (1-P(25) / 100)+P(25), the cumulative mass fraction P of particle size x'=38 mm in the second cumulative mass distribution m The same applies to the cumulative mass fraction of particle size x' = 50 mm. In step ST11, based on the second cumulative mass distribution calculated in step ST10, a second particle size distribution, which is the relationship between the second particle size classes (particle size classes 0 to 4) and the mass proportion of the total particles in each second particle size class of the mixed particle size deposit, as shown by the bar graph in Figure 5(d), is calculated.

[0047] According to the particle size distribution measurement method of this embodiment described above, when multiple single particle size samples corresponding to multiple particle size divisions (second particle size divisions) of a mixed particle size deposit are prepared, even if there is a large overlap in the particle size distributions measured for the multiple single particle size samples or if the particle sizes of surface particles cannot be measured accurately because the second particle size division contains small particle sizes, the second particle size distribution can be calculated accurately simply by preparing single particle size samples of multiple particle size divisions (first particle size divisions) in which the effect of overlap in particle size distributions can be ignored.

[0048] <Example> Hereinafter, as an example, an example of the results of calculating the second particle size distribution by the particle size distribution measuring method according to this embodiment will be described.

[0049] In this example, a Sick Ruler E1200 (area scan camera pixel count: 1024 x 512, measurement speed: 10,000 cross sections / second) was used as the 3D camera 1, and the height from the bottom of tray T to the 3D camera 1 was adjusted so that the entire tray T (500 x 500 x 100 mm) on which coke particles had accumulated was within the field of view. Tray T was also mounted on a belt-driven traveling cart, and a rotary encoder installed on the traveling cart was used to detect the travel distance. The cart was set up to capture one distance image when it had traveled the length of tray T.

[0050] In step ST1 of this example, one tray T's worth (approximately 8 kg) of single particle size samples sieved into particle size range 1 (25 mm<particle size≦38 mm), particle size range 2 (38 mm<particle size≦50 mm), and particle size range 3 (50 mm<particle size≦75 mm) was prepared, and the measurement was repeated 20 times while changing the deposition state of each single particle size sample in tray T, and the number of surface layer particles was tallied for each particle size range at 5 mm intervals to calculate the first particle size distribution of each single particle size sample. The particle size distributions of the surface layer particles for particle size ranges 1 to 3 shown in Fig. 1(a) above represent the first particle size distributions of each single particle size sample calculated in this example.

[0051] Next, in step ST2 of this example, particles belonging to four particle size divisions 1 to 4, namely, particle size division 1 (25 mm<particle size≦38 mm), particle size division 2 (38 mm<particle size≦50 mm), particle size division 3 (50 mm<particle size≦75 mm), and particle size division 4 (75 mm<particle size≦100 mm), were blended in mass proportions of 10%, 15%, 45%, and 30%, respectively, and deposited in tray T to obtain a "mixed particle size deposit body of Example 1." Similarly, particles belonging to four particle size divisions 1 to 4 were blended in mass proportions of 15%, 20%, 45%, and 20%, respectively, and deposited in tray T to obtain a "mixed particle size deposit body of Example 2." Then, as with the single particle size sample, the deposition state of the mixed particle size deposit body in tray T was changed and measurement was repeated 50 times. The number of surface particles was counted for each particle size range at 5 mm intervals, and a second particle size distribution of the mixed particle size deposit body was calculated. Then, in step ST3 of this embodiment, the second particle size distribution F(x) of the mixed particle size sediment body is calculated by the least squares method as a linear sum C of the first particle size distributions A(x), B(x), and C(x) of each single particle size sample. a A(x)+C b B(x)+C c Approximate by C(x) and calculate each coefficient C of the linear sum. a , C b , C c was calculated. FIG. 6 shows the second particle size distribution and linear sum of the mixed particle size deposit of Example 1 calculated in this example.

[0052] Next, in step ST4 of this embodiment, each coefficient C a , C b , Cc The surface number distribution was calculated by regarding these as the surface number ratios, which are the number ratios of surface particles belonging to grain size classes 1, 2, and 3 in the mixed-grain sediment body. Figure 7 shows the surface number distribution, total number distribution, and total mass distribution of the mixed-grain size deposit of Example 1, calculated in this example. Figure 7(a) shows the surface number distribution, Figure 7(b) shows the total number distribution, and Figure 7(c) shows the total mass distribution. The surface number ratio on the vertical axis of the surface number distribution shown in FIG. 7(a) is calculated by adjusting each coefficient C calculated in step ST3 so that the sum of the surface number ratios corresponding to each particle size division 1 to 3 is 100%. a , C b , C c is expressed as a percentage.

[0053] Next, in step ST5 of this example, the surface number distribution shown in Fig. 7(a) and the surface probability model were used to calculate the total number distribution shown in Fig. 7(b). The total number ratio on the vertical axis of the total number distribution shown in Fig. 7(b) is the number ratio of all particles that make up the mixed-grain-size deposit, and is a value expressed as a percentage so that the sum of the total number ratios corresponding to grain size categories 1 to 3 is 100%.

[0054] Next, in step ST6 of this embodiment, the total number distribution shown in FIG. 7(b) and the volume ratio V i (See Table 1) and the overall mass distribution shown in Fig. 7(c) was calculated. The overall mass fraction on the vertical axis of the overall mass distribution shown in Fig. 7(c) is the mass fraction of all particles that make up the mixed-grain sediment, and is expressed as a percentage so that the sum of the overall mass fractions corresponding to each grain size class is 100%.

[0055] Next, in step ST7 of this embodiment, based on the overall mass distribution shown in Figure 7(c), a first particle size distribution was calculated, which is the relationship between the particle sizes in the range including multiple second particle size classes (particle size classes 1 to 4) and the mass proportion of the entire particles in the mixed particle size deposit. FIG. 8 shows the first particle size distribution calculated in this example. FIG. 8(a) shows the first particle size distribution of the mixed particle size deposit body of Example 1, and FIG. 8(b) shows the first particle size distribution of the mixed particle size deposit body of Example 2. The graph shown as "3D" in FIG. 8 shows the first particle size distribution, and the graph shown as "Sieve" shows data measured using a sieve (total mass proportion reflecting the actual state of the blended particles). As shown in FIG. 8, it can be seen that the first particle size distribution calculated in step ST7 is close to the total mass proportion reflecting the actual state.

[0056] Next, in step ST8 of this embodiment, a first cumulative mass distribution was calculated, which is the relationship between the particle size range including multiple second particle size classes (particle size classes 1 to 4) and the cumulative mass proportion obtained by accumulating (accumulating in order from smallest to largest particle size) the mass proportion of all particles in the mixed particle size deposit body in the first particle size distribution shown in Figure 8. Next, in step ST9 of this embodiment, the first cumulative mass distribution calculated in step ST8 was approximated by the approximation function Q(x') expressed by the above-mentioned equation (9). Next, in step ST10 of this embodiment, based on the approximation function Q(x') determined in step ST9, a second cumulative mass distribution was calculated, which is the relationship between the particle sizes in the range including multiple second particle size classes (particle size classes 1 to 4) and the cumulative mass proportions of each second particle size class (particle size classes 1 to 4). Figure 9 shows the first cumulative mass distribution, approximate function Q(x'), and second cumulative mass distribution calculated in this example. Figure 9(a) shows the first cumulative mass distribution, approximate function Q(x'), and second cumulative mass distribution for the mixed-grain-size sediment body of Example 1, and Figure 9(b) shows the first cumulative mass distribution, approximate function Q(x'), and second cumulative mass distribution for the mixed-grain-size sediment body of Example 2.

[0057] Finally, in step ST11 of this embodiment, based on the second cumulative mass distribution shown in Figure 9, a second particle size distribution was calculated, which is the relationship between the second particle size classes (particle size classes 1 to 4) and the mass proportion of the total particles in each second particle size class of the mixed particle size deposit. FIG. 10 shows the second particle size distribution calculated in this example. FIG. 10(a) shows the second particle size distribution of the mixed particle size deposit of Example 1, and FIG. 10(b) shows the second particle size distribution of the mixed particle size deposit of Example 2. The graph shown as "3D" in FIG. 10 shows the second particle size distribution, and the graph shown as "Sieve" shows data measured using a sieve (total mass proportion reflecting the actual state of the blended particles). As shown in FIG. 10, the second particle size distribution calculated in step ST11 differs from the total mass distribution calculated using the particle size distribution measurement method described in Japanese Patent Application No. 2021-078603 shown in FIGS. 1(b) and 1(c), and is closer to the total mass proportion reflecting the actual state.

[0058] Although this embodiment has been described as an example of measuring the particle size distribution (second particle size distribution) of a mixed-particle-size deposit body deposited in tray T, the present invention can also measure the particle size distribution of a mixed-particle-size deposit body deposited and transported on a belt conveyor. However, in the case of a mixed-particle-size deposit body deposited and transported on a belt conveyor, unlike a mixed-particle-size deposit body deposited in tray T, the height H of the mixed-particle-size deposit body used in the surface probability model is likely to fluctuate during transport, so it is preferable to actually measure the height H. An example of a method for measuring (calculating) the height H will be described below.

[0059] 11 and 12 are explanatory diagrams for explaining a method for calculating the height of the mixed-grain size deposit accumulated and transported on the belt conveyor, and show a cross section perpendicular to the transport direction of the belt conveyor. To calculate the height of the mixed-grain-size deposit piled up and transported on the belt conveyor, as shown in FIG. 11(a), in step ST2 described above, the distance image acquisition means (3D camera 1) is used to repeatedly measure the particle size of the surface particles of the mixed-grain-size deposit pile, and the positions of the cross-sectional upper edge E1 (shown by the dashed line in FIG. 11(a)) of the mixed-grain-size deposit pile and the belt conveyor BC are repeatedly measured. Meanwhile, as shown in FIG. 11(b), the position of the cross-sectional upper edge E2 (shown by the dashed line in FIG. 11(b)) of the belt conveyor BC when no mixed-grain-size deposit pile has been piled up is measured in advance and stored. Then, based on the positions of the cross-sectional upper edges E1 and E2, the cross-sectional area S of the mixed-grain-size deposit pile is calculated as shown in FIG. 11(c). Specifically, after aligning the end points A and B of the upper edge E1 of the cross section with the end points A' and B' of the upper edge E2 of the cross section, the vertical coordinate of the upper edge E2 of the cross section is subtracted from the vertical coordinate of the upper edge E1 of the cross section, and this is integrated in the horizontal direction (the left-right direction in Figure 11), thereby calculating the cross-sectional area S. As mentioned above, since the position of the upper edge E1 of the cross section is repeatedly measured, the cross-sectional area S is also repeatedly calculated. Therefore, the cross-sectional area S used to calculate the height H of the mixed-grain-size deposit can be, for example, the average value of the repeatedly calculated cross-sectional areas S.

[0060] Here, the cross section of a general belt conveyor BC used to transport particles such as coke and sintered ore is a trapezoid (isosceles trapezoid), so the cross section of the mixed-grain pile can often be approximated as a trapezoid as well. Therefore, as shown in Figure 12, the cross section of the mixed-grain sediment body is approximated as a trapezoid of height H. As shown in Figure 12, if the width of the bottom of the belt conveyor BC is W and the inclination angle of the side of the belt conveyor BC (the inclination angle relative to the up-down direction) is θ, the area of ​​the trapezoid is expressed as (W + H tan θ) H. If we consider the area of ​​this trapezoid to be equal to the cross-sectional area S of the mixed-grain sediment body, then the following equation (10) holds.

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[0061] Various modified examples of the particle size distribution measuring method according to this embodiment will be described below. In the particle size distribution measuring method according to this embodiment, the diameter of the surface layer particles is determined by the minor axis diameter when the surface layer particles in the distance image are regarded as ellipses, but as will be described below, it is also possible to calculate the particle size by determining the deposition state of the surface layer particles. Also, in the particle size distribution measuring method according to this embodiment, in step ST1, a first particle size distribution showing the relationship between the particle size and the number of surface layer particles in a single particle size sample is calculated, and in step ST2, a mixed particle size distribution is calculated. particle size The second particle size distribution, which shows the relationship between the particle size and number of surface particles in the sediment, is calculated. However, as described below, instead of this, the first particle size distribution, which shows the relationship between the particle size and area of ​​the surface particles of the single-grain sample, is calculated. particle size The second particle size distribution, which shows the relationship between the particle size and area of ​​the surface layer particles of the sediment body, or the first particle size distribution, which shows the relationship between the particle size and volume of the surface layer particles of a single particle size sample, is calculated. particle size It is also possible to calculate a second particle size distribution, which indicates the relationship between the particle size and volume of the surface particles of the sediment.

[0062] FIG. 13 is a diagram for explaining the deposition state of surface layer particles. As shown in the left diagram of Figure 13(a), if the height from the bottom of the belt conveyor BC, obtained by subtracting the vertical coordinate of the bottom of the belt conveyor BC directly below the surface particle from the vertical coordinate of the top of the surface particle, is greater than the minor axis diameter of the surface particle, it can be determined that the surface particle is resting on top of another particle group. In this case, as shown in the right diagram of Figure 13(b), since the vertical diameter (height diameter) of the surface particle is unknown because it is buried in the particle group, it can be assumed to be the same as the minor axis diameter, and is calculated as (major axis diameter) x (minor axis diameter). 2 is the volume of the surface particle, and the minor axis diameter is the particle diameter of the surface particle. In this case, the surface particle is regarded as a spheroid whose height diameter is the same as the minor axis diameter.

[0063] As shown in the left diagram of Figure 13(b), if the height from the bottom of the belt conveyor BC, calculated by subtracting the vertical coordinate of the bottom of the belt conveyor BC directly below the surface particle from the vertical coordinate of the top of the surface particle, is equal to or less than the minor axis diameter of the surface particle, it can be determined that the surface particle is directly resting on the belt conveyor BC. In this case, the height diameter of the surface particle is considered to be the same as the height from the bottom of the belt conveyor BC, and the volume of the surface particle is calculated as (major axis diameter) × (minor axis diameter) × (height diameter). Furthermore, as shown in the right diagram of Figure 13(b), considering the case where the surface particle passes through the sieve mesh at a 45° angle, the particle diameter d can be calculated using the following equation (12), where b is the minor axis diameter and c is the height diameter.

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[0064] In either case, if the surface particle is considered to be an ellipsoid, the volume is precisely (major axis diameter) x (minor axis diameter) 2 However, when the particle size distributions related to the volume of surface layer particles are calculated in steps ST1 and ST2, this coefficient is multiplied by both particle size distributions, and is canceled when the coefficient of the linear sum is calculated in step ST3, so it can be omitted. In either case, the surface particle area can be calculated as the product of the major axis diameter and the minor axis diameter of the surface particle. To accurately calculate the area of ​​a surface particle when the surface particle in the range image is considered to be an ellipse, the product of the major axis diameter and the minor axis diameter must be multiplied by a coefficient of π / 4. However, this coefficient can be omitted because it is multiplied by both particle size distributions when particle size distributions related to the surface particle area are calculated in steps ST1 and ST2 and is canceled out when the coefficient of the linear sum is calculated in step ST3.

[0065] Hereinafter, an example will be described in which, in steps ST1 and ST2, the particle size distribution is calculated based on the area of ​​the surface layer particles instead of the number of surface layer particles. Figure 14 shows the first particle size distribution of a single particle size sample related to the surface particle area, and the first particle size distribution of a mixed-grain size sediment body calculated using the first and second particle size distributions related to the surface particle area for the aforementioned examples. Figure 14(a) shows the first particle size distribution, Figure 14(b) shows the first particle size distribution of the mixed-grain size sediment body of Example 1 calculated using the first particle size distribution shown in Figure 14(a), and Figure 14(c) shows the first particle size distribution of the mixed-grain size sediment body of Example 2 calculated using the first particle size distribution shown in Figure 14(a). In Figures 14(b) and 14(c), the graphs labeled "3D" show the first particle size distribution, and the graphs labeled "Sieve" show data measured using a sieve (total mass proportion reflecting the actual state of the blended particles). As shown in Figure 14(a), the first particle size distribution of the single-grain-size sample related to the area of ​​surface particles is such that the particle size distribution of the larger particle size fraction is lifted up on the vertical axis compared to the first particle size distribution of the single-grain-size sample related to the number of surface particles shown in Figure 1(a). However, by setting the second particle size distribution of the mixed-grain-size sediment calculated in step ST2 to a particle size distribution based on the same standard (area of ​​surface particles), the first particle size distribution calculated in step ST7 can be made to be similar to the first particle size distribution shown in Figure 8, as shown in Figures 14(b) and 14(c). It can be seen that the first particle size distribution calculated in step ST7 is close to the total mass fraction that reflects the actual state.

[0066] Figure 15 shows the first cumulative mass distribution, approximate function Q(x'), and second cumulative mass distribution of the mixed-grain-size deposit body calculated using the first and second particle size distributions related to the surface layer particle area for the aforementioned examples. Figure 15(a) shows the first cumulative mass distribution, approximate function Q(x'), and second cumulative mass distribution for the mixed-grain-size deposit body of Example 1, and Figure 15(b) shows the first cumulative mass distribution, approximate function Q(x'), and second cumulative mass distribution for the mixed-grain-size deposit body of Example 2. Figure 16 shows the second particle size distribution calculated when the first particle size distribution and the second particle size distribution related to the surface layer particle area are used for the aforementioned Examples. Figure 16(a) shows the second particle size distribution of the mixed particle size sediment body of Example 1, and Figure 16(b) shows the second particle size distribution of the mixed particle size sediment body of Example 2. The graph shown as "3D" in Figure 16 shows the second particle size distribution, and the graph shown as "Sieve" shows data measured using a sieve (total mass proportion reflecting the actual state of the blended particles). As shown in Fig. 16, even when the first particle size distribution and the second particle size distribution related to the area of ​​the surface layer particles are used, the second particle size distribution calculated in step ST11 can be made to be a distribution similar to the second particle size distribution shown in Fig. 10. It can also be seen that the second particle size distribution calculated in step ST11 has a value close to the total mass fraction that reflects the actual state.

[0067] 17A and 17B show the first cumulative mass distribution, approximate function P(x'), and second cumulative mass distribution calculated for a mixed-grain-size deposit body further blended with particles belonging to grain size category 0 (0 mm<grain size≦25 mm) in the aforementioned example, using the first and second grain size distributions related to the number of surface layer particles. Fig. 17A shows the first cumulative mass distribution, approximate function P(x'), and second cumulative mass distribution for a mixed-grain-size deposit body obtained by further blending particles belonging to grain size category 0 into the mixed-grain-size deposit body of Example 1 (hereinafter referred to as the "mixed-grain-size deposit body of Modification 1"), and Fig. 17B shows the first cumulative mass distribution, approximate function P(x'), and second cumulative mass distribution for a mixed-grain-size deposit body obtained by further blending particles belonging to grain size category 0 into the mixed-grain-size deposit body of Example 2 (hereinafter referred to as the "mixed-grain-size deposit body of Modification 2") Fig. 18 shows the second particle size distribution calculated using the first particle size distribution and the second particle size distribution related to the number of surface layer particles for the mixed-grain size deposit body further blended with particles belonging to particle size category 0 (0 mm<grain size≦25 mm) in the above-mentioned example. Fig. 18(a) shows the second particle size distribution for the mixed-grain size deposit body of Modification Example 1, and Fig. 18(b) shows the second particle size distribution for the mixed-grain size deposit body of Modification Example 2. As shown in Figure 18, the particle size distribution measurement method of this embodiment makes it possible to calculate a second particle size distribution, which is the relationship between particle size classes 0 to 4 and the total mass proportion of each particle size class 0 to 4 of the mixed particle size deposit, even for a mixed particle size deposit containing particles belonging to particle size classes 0 to 4.

[0068] 19 shows the first cumulative mass distribution, approximate function P(x'), and second cumulative mass distribution calculated for a mixed-grain-size deposit body further containing particles belonging to grain size category 0 (0 mm<grain size≦25 mm) in the aforementioned example, when the first and second grain size distributions related to the surface layer grain area are used. Fig. 19(a) shows the first cumulative mass distribution, approximate function P(x'), and second cumulative mass distribution for the mixed-grain-size deposit body of Modification Example 1, and Fig. 19(b) shows the first cumulative mass distribution, approximate function P(x'), and second cumulative mass distribution for the mixed-grain-size deposit body of Modification Example 2. Fig. 20 shows the second particle size distribution calculated using the first particle size distribution and the second particle size distribution related to the surface particle area for the mixed-grain size deposit body further blended with particles belonging to particle size category 0 (0 mm<grain size≦25 mm) in the aforementioned example. Fig. 20(a) shows the second particle size distribution for the mixed-grain size deposit body of Modification Example 1, and Fig. 20(b) shows the second particle size distribution for the mixed-grain size deposit body of Modification Example 2. As shown in Figure 20, according to the particle size distribution measurement method of this embodiment, even when using the first particle size distribution and the second particle size distribution related to the area of ​​surface particles for a mixed particle size deposit containing particles belonging to particle size classes 0 to 4, it is possible to calculate the second particle size distribution, which is the relationship between the particle size classes 0 to 4 and the total mass proportion of each particle size class 0 to 4 of the mixed particle size deposit. [Explanation of symbols]

[0069] 1. 3D camera (means for acquiring distance images) BC···Belt conveyor ST1 process (first particle size distribution calculation step) ST2... process (second particle size distribution calculation step) ST3... process (coefficient calculation step) ST4...Process ST5... process (total number distribution calculation step) ST6... process (total mass distribution calculation step) ST7 process (first particle size distribution calculation step) ST8... process (first cumulative mass distribution calculation step) ST9... process (approximation step) ST10... process (second cumulative mass distribution calculation step) ST11 process (second particle size calculation step) T···Tray

Claims

1. a first particle size distribution calculation step of preparing single-particle size samples, which are samples consisting only of particles having the same particle size in a first particle size division, which is a particle size division determined by particle size, for a plurality of first particle size divisions, taking images of the surface layers of the single-particle size samples of the plurality of first particle size divisions while changing the deposition state of the single-particle size samples, obtaining distance images showing the distance from a reference position to the particles in the surface layer, and calculating a first particle size distribution showing the relationship between particle size and number of particles in the surface layer of the single-particle size sample for each of the plurality of first particle size divisions based on the distance images; a second particle size distribution calculation step of imaging a surface layer of a mixed-grain size deposit body, the surface layer of which is a blend of particles belonging to a plurality of second particle size divisions including a particle size division different from the plurality of first particle size divisions, while changing the deposition state of the mixed-grain size deposit body, obtaining a distance image showing the distance from a reference position to the particles in the surface layer, and calculating a second particle size distribution showing the relationship between particle size and number of particles in the surface layer of the mixed-grain size deposit body based on the distance image; a coefficient calculation step of approximating the second particle size distribution by a linear sum of the first particle size distributions for the plurality of first particle size ranges and calculating a coefficient of the linear sum; an overall number distribution calculation step of calculating, from the coefficients of the linear sum, an overall number distribution, which is a relationship between the first particle size division and the overall number ratio of particles in each of the first particle size divisions in the mixed particle size deposit body, using a surface probability model that estimates the number distribution of all deposited particles from the number distribution of particles in the surface layer; an overall mass distribution calculation step of calculating an overall mass distribution, which is a relationship between the first particle size division and the mass ratio of all particles in each of the first particle size divisions of the mixed particle size deposit body, based on the overall number distribution and the volume ratio calculated from the first particle size divisions; a first particle size distribution calculation step of calculating a first particle size distribution, which is a relationship between particle sizes in a range including the plurality of second particle size classes and a mass ratio of all particles in the mixed particle size deposit body, based on the total mass distribution; a first cumulative mass distribution calculation step of calculating a first cumulative mass distribution, which is a relationship between a particle size range including the plurality of second particle size divisions and a cumulative mass ratio obtained by accumulating the mass ratios of all particles in the mixed particle size deposit body in the first particle size distribution; an approximation step of approximating the first cumulative mass distribution with an approximation function representing a particle size distribution law; a second cumulative mass distribution calculation step of calculating a second cumulative mass distribution, which is a relationship between particle sizes in a range including the plurality of second particle size divisions and the cumulative mass ratio for each of the second particle size divisions, based on the approximation function; a second particle size calculation step of calculating a second particle size distribution, which is a relationship between the second particle size division and the mass ratio of the whole particles in each of the second particle size divisions of the mixed particle size deposit body, based on the second cumulative mass distribution; A particle size distribution measuring method comprising the steps of:

2. In the first particle size distribution calculation step, instead of a first particle size distribution showing the relationship between particle size and number of particles in the surface layer of the single particle size sample, a first particle size distribution showing the relationship between particle size and area of ​​particles in the surface layer of the single particle size sample is calculated, 2. The particle size distribution measuring method according to claim 1, wherein in the second particle size distribution calculation step, a second particle size distribution showing the relationship between particle size and area of ​​particles in the surface layer of the mixed particle size deposit is calculated instead of a second particle size distribution showing the relationship between particle size and number of particles in the surface layer of the mixed particle size deposit.

3. In the first particle size distribution calculation step, instead of a first particle size distribution that indicates the relationship between particle size and number of particles in the surface layer of the single particle size sample, a first particle size distribution that indicates the relationship between particle size and volume of particles in the surface layer of the single particle size sample is calculated, 2. The particle size distribution measuring method according to claim 1, wherein in the second particle size distribution calculation step, instead of a second particle size distribution showing the relationship between particle size and number of particles in the surface layer of the mixed particle size deposit, a second particle size distribution showing the relationship between particle size and volume of particles in the surface layer of the mixed particle size deposit is calculated.

4. a height calculation step; In the second particle size distribution calculation step, the second particle size distribution is calculated while the mixed particle size deposit in a state where it is deposited on a belt conveyor is being conveyed by the belt conveyor, and positions of the upper edges of the cross sections of the mixed particle size deposit and the belt conveyor are measured; In the height calculation step, a cross-sectional area of ​​the mixed-grain size deposit is calculated based on the positions of the upper edges of the cross sections of the mixed-grain size deposit and the belt conveyor and the position of the upper edge of the cross section of the belt conveyor when the mixed-grain size deposit is not deposited, and the cross section of the mixed-grain size deposit is regarded as a trapezoid and a height of the mixed-grain size deposit is calculated based on the cross-sectional area.

4. The particle size distribution measuring method according to claim 1, wherein in the total number distribution calculation step, the total number distribution is calculated using the surface probability model from the coefficients of the linear sum and the height of the mixed particle size deposit calculated in the height calculation step.

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