JP7610119B2 - Particle size distribution measurement method - Google Patents

Description

The present invention relates to a method for measuring the particle size distribution of particles such as coke and sintered ore. In particular, the present invention relates to a particle size distribution measurement method that can accurately calculate the overall mass distribution, which is the relationship between the particle size classes and the mass ratio of the whole 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).

Blast furnace raw materials such as coke and sintered ore are transported in a piled state on a conveyor belt and charged into the blast furnace. It is known that the particle size of the particles that make up the raw materials (an index that shows the degree of distribution of particle size, which is the diameter of the particles) 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 in order to maintain quality.

The particle size of blast furnace raw materials is generally measured by taking samples (sampling) from a conveyor belt at regular intervals, dividing the samples every 4 or 8 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 the quality of the raw materials or malfunctions in the production equipment, intermittent measurements using sieves after sampling result in large time intervals, making it impossible to accurately capture the temporal fluctuations in the particle size distribution.

As a method capable of continuously measuring particle diameters in a non-contact manner, for example, a 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 means such as a rotary encoder in contact with the belt conveyor is used to measure the position of the upper edge of the cross section of the particles deposited on the belt conveyor with a 3D camera every time the belt conveyor advances a certain distance, thereby generating a distance image (sometimes called a 3D image or a depth image) in which the pixel value of each pixel indicates the distance from a reference position (for example, the distance from the 3D camera). In the vicinity of the boundary between the piled up particles, the irradiated laser light is interrupted and darkened, and the unevenness of the particles becomes large, so that the pixel value of the pixel area corresponding to the vicinity of the particle boundary in the distance image is likely to be different from the pixel value of the other pixel areas. In the method described in Non-Patent Document 1, this characteristic is used to determine the particle boundary to identify each particle, and the particle size of each particle is calculated. The dimensions of the piled up particles having a part hidden by other particles are smaller than the 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 by a 3D camera is used to preferentially extract surface particles (hereinafter referred to as "surface particles" as appropriate), and the minor axis diameter of each surface particle in the distance image when it is regarded as an ellipse is taken as the particle size.

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 been proposed, which use a 3D camera in the same manner as the method described in Non-Patent Document 1.
Non-Patent Document 2 and Patent Document 1 provide detailed descriptions of an edge detection method for identifying each particle and an image processing method for recognizing surface particles. In particular, Non-Patent Document 2 describes a method for increasing the speed of measurement.

In the method described in Non-Patent Document 2, image processing is performed on the distance image acquired for the deposited particles, surface particles in the surface layer with little overlap are extracted, the particle size of each surface particle is divided into particle size categories determined by the mesh size of the sieve, and the number distribution of surface particles (surface number distribution), which is the relationship between the particle size category and the number of surface particles in each particle size category, is calculated. In addition, in the method described in Non-Patent Document 2, the number distribution of the entire deposited particles, including not only surface particles but also hidden particles, is estimated using a surface probability model, which is a model that represents the degree of appearance and visibility on the surface layer according to particle size, that is, a model that estimates the number distribution of the entire deposited particles (total number distribution) from the number distribution of surface particles. Furthermore, in the method described in Non-Patent Document 2, the volume ratio (or mass ratio) of each particle size category is used to estimate the distribution of the mass ratio of the entire deposited particles (total mass distribution).

The inventors applied the method described in Non-Patent Document 2 to a mixed-grain deposit in which particles (coke particles) belonging to multiple grain size categories are mixed in a predetermined mass ratio and deposited, and conducted a confirmation test to determine whether the overall mass distribution of the deposit could be accurately estimated.
FIG. 1 is an explanatory diagram for explaining the details of the above-mentioned confirmation test.
As shown in Fig. 1(a), in the above confirmation test, first, single-grain-size samples, which are samples consisting of particles having the same particle size, were prepared and piled up for a plurality of particle size classes. Specifically, a single-grain-size sample of particle size class 1 consisting of particles that pass through a 38 mm mesh sieve but not a 25 mm mesh sieve (i.e., particles with a diameter of about 25 mm < diameter ≦ 38 mm), a single-grain-size sample of particle size class 2 consisting of particles that pass through a 50 mm mesh sieve but not a 38 mm mesh sieve (i.e., particles with a diameter of about 38 mm < diameter ≦ 50 mm), and a single-grain-size sample of particle size class 3 consisting of particles that pass through a 75 mm mesh sieve but not a 50 mm mesh sieve (i.e., particles with a diameter of about 50 mm < diameter ≦ 75 mm) were prepared in a tray T of a predetermined size. Then, each single-particle-size sample was blended in a predetermined mass ratio (single-particle-size sample of particle size category 1 was P1 [%], single-particle-size sample of particle size category 2 was P2 [%], and single-particle-size sample of particle size category 3 was P3 [%]) to prepare one tray T's worth of mixed-particle-size deposit (in this case, a sample blended with particles belonging to three particle size categories 1 to 3, in which the particles belonging to each particle size category were blended in arbitrary mass ratios P1, P2, and P3, respectively; this also includes the case where there is only a single-particle-size sample in which any one of P1, P2, and P3 is 100%).

Next, in the above confirmation test, as shown in FIG. 1(b), for the same mixed-grain-size deposit, the deposition state in the tray T was changed each time due to mixing and stirring that occurred when the mixed-grain-size deposit was transferred between the tray T and another container C, and the particle size measurement of the surface layer particles was repeated 10 times using a 3D camera 1 placed above the tray T and using a light cutting method with a linear laser light L. When measuring the particle size, a distance image showing the distance from a reference position to the surface layer particles was obtained while moving the tray T relative to the 3D camera 1 in a direction perpendicular to the direction in which the linear laser light L that becomes the light cutting line extends (the left-right direction in FIG. 1(b)). Then, based on this distance image, a calculation device (not shown) such as an image processing device connected to the 3D camera 1 performed calculations to measure the particle size of the surface layer particles.
1(c), the number of surface particles was counted for each particle size division using each surface particle identified when calculating the particle size measured each time, and the surface number distribution was calculated from the sum of the numbers from the 10 measurements. After that, the total number distribution was calculated using the procedure described in Non-Patent Document 2 using a surface probability model, and finally the total mass distribution was calculated.

Fig. 2 is a diagram showing an example of the results of the above-mentioned confirmation test. In Fig. 2, the graph indicated with "sieve" is data measured using a sieve (mass ratio reflecting the actual state of the blended particles), and the graph indicated with "3D" is data calculated by the method described in Non-Patent Document 2 using a 3D camera 1.
Figures 2(a) to 2(c) show the total mass distributions obtained for the single-grain-size samples of each grain size division. Specifically, Figure 2(a) shows the total mass distribution obtained for the single-grain-size sample of grain size division 1 (P1=100%), Figure 2(b) shows the total mass distribution obtained for the single-grain-size sample of grain size division 2 (P2=100%), and Figure 2(c) shows the total mass distribution obtained for the single-grain-size sample of grain size division 3 (P3=100%).
Figures 2(d) and 2(e) show the total mass distributions obtained for a mixed-grain-size deposit containing two single-grain-size samples of different grain sizes. Specifically, Figure 2(d) shows the total mass distribution obtained for a mixed-grain-size deposit containing single-grain-size samples of grain sizes 1 and 3 in a given mass ratio (P1 = P3 = 50%), and Figure 2(e) shows the total mass distribution obtained for a mixed-grain-size deposit containing single-grain-size samples of grain sizes 1 and 3 in a different mass ratio (P1 = 25%, P3 = 75%).
FIG. 2(f) shows the total mass distribution obtained for a mixed-grain pile containing single-grain samples of the three grain size classes in predetermined mass proportions (P1=15%, P2=20%, P3=65%).

As can be seen from Figures 2(a) to 2(c), the method described in Non-Patent Document 2 results in a result indicating the presence of particles (total mass ratio > 0%) in other particle size fractions that should not actually exist (total mass ratio = 0%). Also, as can be seen from Figures 2(d) to 2(f), the method described in Non-Patent Document 2 calculates total mass distributions that are spread across all particle size fractions, so that it is not possible to distinguish, by looking at these total mass distributions alone, whether the resulting mixture is a mixed-grain-size deposit made up of single-grain-size samples of two particle size fractions or a mixed-grain-size deposit made up of single-grain-size samples of three particle size fractions.
As described above, if the particle sizes of surface particles measured by the 3D camera 1 are simply assigned to particle size classifications determined by the mesh size of the sieve, as in the method described in Non-Patent Document 2, the calculation result will include particles that belong to a particle size classification that should not actually exist, and the particle size distribution (total mass distribution) will become blurred, making it difficult to distinguish differences in particle size distribution.

FIG. 3 is a diagram showing another example of the results of the above-mentioned confirmation test (corresponding to Example 1 described later). Specifically, FIG. 3 shows a particle size distribution (first particle size distribution) calculated from the sum of the number of surface layer particles in each particle size range (specifically, 5 mm intervals) smaller than the particle size range included in each particle size range, using the particle size of the surface layer particles measured each time for the single particle size sample of each particle size division as described above, and calculated from the sum of the number of particles in 10 measurements. FIG. 3(a) is a particle size distribution obtained for a single particle size sample of particle size division 1, FIG. 3(b) is a particle size distribution obtained for a single particle size sample of particle size division 2, and FIG. 3(c) is a particle size distribution obtained for a single particle size sample of particle size division 3. For example, the data point plotted at the particle size 25 mm position on the horizontal axis of FIG. 3 means the number of surface layer particles whose particle size measured by the 3D camera 1 is 20 mm<particle size≦25 mm. 3 indicates the number of surface layer particles having a particle size of 25 mm<particle size≦30 mm measured by the 3D camera 1. The same applies to the other data points.
As shown in Fig. 3, the particle size distribution obtained by the particle size measurement using the 3D camera 1 is wider in both the larger and smaller particle size directions than the particle size range indicated by the dashed line. There are two possible reasons for this.

Fig. 4 is an explanatory diagram for explaining the cause of obtaining the result shown in Fig. 3. Fig. 4(a) is a plan view of a particle, which is conveniently simulated as a rectangular parallelepiped, viewed from the optical axis direction of the 3D camera 1, and Fig. 4(b) is a side view of the particle, which is conveniently simulated as a rectangular parallelepiped, viewed from a horizontal direction perpendicular to the optical axis direction of the 3D camera 1.
The first reason is as follows. In the method described in Non-Patent Document 2, the minor axis diameter when the particle is considered as an ellipse in the distance image acquired by the 3D camera 1 is regarded as the particle size. Therefore, it is considered that the particle shown in the upper diagram of FIG. 4(a) is imaged by the 3D camera 1 at an angle as shown in the lower diagram of FIG. 4(a), and the minor axis diameter may be calculated to be larger than the actual minor axis diameter shown in the upper diagram. In other words, it is considered that the particle size measured by the 3D camera 1 (minor axis diameter in the lower diagram of FIG. 4(a)) may be larger than the particle size measured using a sieve (minor axis diameter in the upper diagram of FIG. 4(a)). In this case, it is considered that the particle size distribution obtained by the 3D camera 1 spreads in the direction of larger particle size than the particle size division.
The second cause is as follows. As shown in the left diagram of FIG. 4(b), a part of the particle of interest in the vertical direction (optical axis direction of the 3D camera 1) is often buried and hidden among other accumulated particle groups, and is not captured by the 3D camera 1. Therefore, in the method described in Non-Patent Document 2, the diameter (height diameter) of the particle in the vertical direction is considered to be the same as the minor axis diameter. However, in reality, as shown in the right diagram of FIG. 4(b), the height diameter of the particle is larger than the minor axis diameter, and the particle does not pass through the mesh of the sieve, so that the particle size measured by the 3D camera 1 (minor axis diameter in the left diagram of FIG. 4(b)) may be smaller than the particle size measured using the sieve (height diameter of the particle in the right diagram of FIG. 4(b)). In this case, it is considered that the particle size distribution obtained by the 3D camera 1 spreads in the direction of smaller particle size than the particle size division.
In this way, due to differences in the orientation of surface layer particles, it is thought that the particle size distribution obtained from the particle sizes measured by the 3D camera 1 becomes wider than the particle size divisions determined by the sieve.

As described above, in the case of amorphous particles such as coke and sintered ore, the particle size of the surface particles varies depending on the particle's posture, and the particle size distribution is wider than the particle size divisions. For this reason, it was found that simply dividing the particle sizes of the surface particles measured with the 3D camera 1 into particle size divisions determined by the sieve, counting the number of surface particles for each particle size division, and applying the method described in Non-Patent Document 2 would result in a blurred particle size distribution (total mass distribution) that does not accurately match the results measured using the sieve.

JP 2019-174155 A

M. J. 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 M. J. 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

The objective of the present invention is to provide a method for measuring particle size distribution that can accurately calculate the overall mass distribution, which is the relationship between the particle size classifications and the overall mass proportion of 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).

In order to solve the above problem, the inventors have conducted extensive research. First, single-grain-size samples (samples consisting of only particles having the same grain size) were prepared for each of the multiple grain size classes to which the particles constituting the mixed-grain-size deposit belong, and the grain size of the surface layer of each single-grain-size sample was measured to calculate a first grain size distribution showing the relationship between the grain size and the number of particles in the surface layer of the single-grain-size sample. In addition, the grain size of the surface layer of the mixed-grain-size deposit containing particles belonging to the multiple grain size classes was measured to calculate a second grain size distribution showing the relationship between the grain size and the number of particles in the surface layer of the mixed-grain-size deposit. We then found that if the calculated second particle size distribution is approximated by a linear sum of the calculated first particle size distributions, and each coefficient of this linear sum is considered to be the number ratio of different particle size fractions of the particles in the surface layer of the mixed-size deposit when it is considered that the mixed-size deposit is composed of a combination of single-size samples of multiple particle size fractions, then the coefficients can be used to calculate the overall mass distribution in a similar procedure to the method described in Non-Patent Document 2, and it is possible to obtain a highly accurate calculation that closely matches the results measured using a sieve.
The present invention has been completed based on the findings of the present inventors.

That is, in order to solve the above problem, the present invention provides a first particle size distribution calculation step of preparing single-grain-size samples, which are samples consisting of only particles having the same particle size for a particle size division, which is a division determined by the size of the particle size, for a plurality of particle size divisions, imaging the surface layers of the single-grain-size samples of the plurality of particle size divisions while changing the deposition state of the single-grain-size samples, obtaining a distance image showing the distance from a reference position to the particles of the surface layer, and calculating a first particle size distribution showing the relationship between the particle size and the number of particles in the surface layer of the single-grain-size sample for each of the plurality of particle size divisions based on the distance image, and a second particle size distribution calculation step of imaging the surface layer of a mixed-grain-size deposit body in which particles belonging to the plurality of particle size divisions are blended 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 of the surface layer, and calculating a first particle size distribution showing the relationship between the particle size and the number of particles in the surface layer of the single-grain-size sample for each of the plurality of particle size divisions based on the distance image. A particle size distribution measurement method is provided, which includes a second particle size distribution calculation step of calculating a second particle size distribution that indicates the relationship between the particle size and the number of particles in the surface layer of the deposit, 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 particle size divisions and calculating the coefficients of the linear sum, an overall number distribution calculation step of calculating an overall number distribution that is the relationship between the particle size division and the overall number ratio of particles in each of the particle size divisions of the mixed particle size deposit from the coefficients of the linear sum using a surface probability model that estimates the number distribution of all the deposited particles from the number distribution of particles in the surface layer, and an overall mass distribution calculation step of calculating an overall mass distribution that is the relationship between the particle size division and the overall mass ratio of particles in each of the particle size divisions of the mixed particle size deposit based on the overall number distribution and the volume ratio calculated from the particle size division.

In the present invention, the "distance image" means an image in which the pixel value of each pixel indicates the distance from a reference position (for example, the distance from a distance image acquisition means), and the "distance image" acquired in the first particle size distribution calculation step is an image indicating the distance from the reference position to the particles in the surface layer of the single particle size sample, and the "distance image" acquired in the second particle size distribution calculation step is an image indicating the distance from the reference position to the particles in the surface layer of the mixed particle size deposit. The distance image acquisition means for acquiring the distance image is not particularly limited as long as it is a means capable of acquiring the distance to the target surface layer, and for example, a light-cutting type 3D camera in which a laser light source that emits linear laser light and an area scan camera are integrated can be mentioned. The reference position can be set at any position, and for example, the position of the distance image acquisition means can be set as the reference position. If the "distance image" can be acquired, for example, by using the method described in Non-Patent Document 2, it is possible to calculate the particle size and the number of particles by performing calculations based on the "distance image" with a calculation device connected to the distance image acquisition means.
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 appearance and 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 class to the number distribution of all the deposited particles, and is a model that estimates the number distribution of all the deposited particles from the number distribution of particles in the surface layer.
Furthermore, the "volume ratio" refers to a value obtained by dividing a volume calculated from one particle size division by a reference volume, where the volume calculated from another particle size division is taken as the reference volume.

According to the present invention, in the coefficient calculation step, the second particle size distribution of the mixed-grain-size deposit calculated in the second particle size distribution calculation step is approximated by a linear sum of the first particle size distributions obtained from each single-grain-size sample calculated in the first particle size distribution calculation step, and the coefficient of the linear sum is calculated. Based on the above-mentioned knowledge of the inventor, the coefficient of this linear sum can be considered to be the number ratio of particles in the surface layer belonging to the particle size division of each single-grain-size sample in the mixed-grain-size deposit. Therefore, in the total number distribution calculation step, a total number distribution, which is a relationship between the particle size division and the total number ratio of each particle in the mixed-grain-size deposit, is calculated from the calculated coefficient using a surface probability model similar to the method described in Non-Patent Document 2, and in the total mass distribution calculation step, a total mass distribution, which is a relationship between the particle size division and the total mass ratio of each particle in the mixed-grain-size deposit, is calculated.
As described above, in the present invention, the coefficient of the linear sum is regarded as the number ratio of different grain size fractions of particles in the surface layer of a mixed-grain-size deposit when the mixed-grain-size deposit is considered to be composed of a combination of single-grain-size samples of multiple grain size fractions, and this coefficient is used to finally calculate the overall mass distribution, so that it is possible to accurately calculate the overall mass distribution, as discovered by the inventors above.

In the first particle size distribution calculation step and the second particle size distribution calculation step of the present invention described above, a particle size distribution (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 is 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, the entire mass distribution can be calculated with high accuracy even if a particle size distribution showing the relationship between the particle size of the particles in the surface layer and the area or volume is used.
Therefore, in the first particle size distribution calculation step, instead of a first particle size distribution showing the relationship between the particle size and the number of particles in the surface layer of the single-grain size sample, a first particle size distribution showing the relationship between the particle size and the area of particles in the surface layer of the single-grain size sample may be calculated, and in the second particle size distribution calculation step, instead of a second particle size distribution showing the relationship between the particle size and the number of particles in the surface layer of the mixed- grain size deposit, a second particle size distribution showing the relationship between the particle size and the area of particles in the surface layer of the mixed-grain size deposit may be calculated.
Alternatively, in the first particle size distribution calculation step, instead of a first particle size distribution showing the relationship between the particle size and the number of particles in the surface layer of the single-grain 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-grain size sample may be calculated, and in the second particle size distribution calculation step, instead of a second particle size distribution showing the relationship between the particle size and the number of particles in the surface layer of the mixed- grain size deposit, a second particle size distribution showing the relationship between the particle size and the volume of particles in the surface layer of the mixed-grain size deposit may be calculated.

In the total number distribution calculation step of the present invention, when calculating the total number distribution of the mixed grain size deposit using the surface probability model, it is necessary to input the height of the mixed grain size deposit (the height (bulk height) when the grain size of the surface layer particles is measured in the second grain size distribution calculation step) to the surface probability model. In the second grain size distribution calculation step, when measuring the grain size of the surface layer particles of the mixed grain size deposit, if the mixed grain size deposit is deposited in a tray, i.e., if it is deposited in an area partitioned in four directions in a plan view, the height of the mixed grain size deposit is stable and can be grasped relatively easily, so a fixed value set in advance can be used. However, when the mixed grain size deposit is deposited on a belt conveyor and transported, the height is likely to fluctuate during transportation, so it is preferable to actually measure the height.

That is, in the present invention, it is preferable to have a height calculation step, and in the second particle size distribution calculation step, the second particle size distribution is calculated while the mixed particle size deposit piled up on the belt conveyor is transported by the belt conveyor, and the positions of the upper edge of the cross section of the mixed particle size deposit and the belt conveyor are measured. In the height calculation step, the cross-sectional area of the mixed particle size deposit is calculated based on the positions of the upper edge of the cross section of the mixed particle size deposit and the belt conveyor and the position of the upper edge of the cross section of the belt conveyor in a state where the mixed particle size deposit is not piled up, which is measured in advance. The cross section of the mixed particle size deposit is regarded as a trapezoid, and the height of the mixed particle size deposit is calculated based on the cross-sectional area. In the total number distribution calculation step, the total number distribution is calculated from the coefficient of the linear sum and the height of the mixed particle size deposit calculated in the height calculation step using the surface probability model.

A typical belt conveyor for transporting particles such as coke and sintered ore has a trapezoidal cross section, and therefore the cross section of the mixed-grain pile piled up on the belt conveyor can often be approximated as a trapezoid as well.
According to the above-mentioned preferred method, in the second particle size distribution calculation step, the positions of the cross-sectional upper edges of the mixed-grain-size deposit and the belt conveyor are also measured, so that in the height calculation step, the cross-sectional area of the mixed-grain-size deposit can be calculated. Then, if the cross-section of the mixed-grain-size deposit is approximated as a trapezoid, the height of the mixed-grain-size deposit can be calculated from the cross-sectional area of the mixed-grain-size deposit. In the total number distribution calculation step, by using the calculated height of the mixed-grain-size deposit in the surface probability model, even when the mixed-grain-size deposit is deposited and transported on the belt conveyor, the total number distribution of the mixed-grain-size deposit can be calculated with high accuracy, and thus the total mass distribution of the mixed-grain-size deposit can be calculated with high accuracy in the total mass distribution calculation step.
In order to measure the positions of the upper edge of the cross section of the mixed-grain size deposit and the belt conveyor, it is possible to use a distance image acquisition means for acquiring a distance image of the mixed-grain size deposit in combination.

According to the present invention, for a mixed-grain sediment containing particles belonging to multiple grain size classes, it is possible to accurately calculate the overall mass distribution, which is the relationship between the grain size classes and the total mass proportion of the particles in each grain size class of the mixed-grain sediment.

FIG. 1 is an explanatory diagram for explaining the content of a confirmation test for confirming the measurement accuracy of the method described in Non-Patent Document 2. FIG. 2 is a diagram showing an example of the results of the confirmation test described in FIG. 1. FIG. 2 is a diagram showing another example of the results of the confirmation test described in FIG. 1 . FIG. 4 is an explanatory diagram for explaining the cause of obtaining the results shown in FIG. 3; FIG. 1 is a flow diagram showing steps of a particle size distribution measuring method according to one embodiment of the present invention. FIG. 6 is an explanatory diagram for explaining steps ST1 to ST4 shown in FIG. 5 . 1 shows the particle size distribution and linear sum of the mixed particle size deposit calculated in Example 1. 4 shows the surface number distribution, total number distribution, and total mass distribution of the mixed grain size deposit calculated in Example 1. The overall mass distribution calculated in Examples 1 to 3 is shown. FIG. 13 is an explanatory diagram illustrating a method for calculating the height of a mixed-grain size deposit accumulated and transported on a belt conveyor. FIG. 13 is an explanatory diagram illustrating a method for calculating the height of a mixed-grain size deposit accumulated and transported on a belt conveyor. FIG. 2 is a diagram for explaining a typical deposition state of surface layer particles. 1 shows a first particle size distribution of a single particle size sample regarding the area or volume of surface layer particles calculated in step ST1 of Example 1. In steps ST1 and ST2 of Examples 1 to 3, when the particle size distribution related to the area of the surface layer particles is calculated, the total mass distribution calculated in step ST6 is shown. In steps ST1 and ST2 of Examples 1 to 3, when the particle size distribution related to the volume of surface layer particles is calculated, the total mass distribution calculated in step ST6 is shown.

Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings.
Fig. 5 is a flow diagram showing steps of the particle size distribution measuring method according to the present embodiment. Fig. 6 is an explanatory diagram for explaining steps ST1 to ST4 shown in Fig. 5.
As shown in Fig. 5, the particle size distribution measuring method according to this embodiment includes steps ST1 to ST6. Each step will be described below in order. Note that, in this embodiment, an example will be described in which the particle size distribution (total mass distribution) of a mixed particle size laminate containing particles belonging to three particle size classes is measured, but the present invention is not limited thereto, and can also be applied to a mixed particle size laminate containing particles belonging to two particle size classes or four or more particle size classes.

<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 of only particles having the same particle size distribution, are prepared for a plurality of particle size distributions. It is possible to know in advance which particle size distributions the particles in a mixed particle size laminate in which particles belonging to a plurality of particle size distributions (i.e., particles of various particle sizes) are mixed. In this embodiment, in order to measure the particle size distribution of a mixed particle size laminate in which particles belonging to three particle size distributions are mixed at any mass ratio, the single particle size samples are also prepared for the same three particle size distributions as the mixed particle size laminate. Specifically, in this embodiment, as in the above-mentioned confirmation test described with reference to Figures 1 to 3, the mixed particle size laminate is mixed with particles belonging to a total of three particle size classes, namely, particle size class 1, which includes particles that pass through a sieve with a mesh size of 38 mm but not a sieve with a mesh size of 25 mm (i.e., particles with a particle size of about 25 mm < particle size ≦ 38 mm), particle size class 2, which includes particles that pass through a sieve with a mesh size of 50 mm but not a sieve with a mesh size of 38 mm (i.e., particles with a particle size of about 38 mm < particle size ≦ 50 mm), and particle size class 3, which includes particles that pass through a sieve with a mesh size of 75 mm but not a sieve with a mesh size of 50 mm (i.e., particles with a particle size of about 50 mm < particle size ≦ 75 mm), in any mass ratio. For this reason, single particle size samples are prepared for these three particle size classes (particle size classes 1 to 3). Specifically, for example, one tray T's worth is prepared as in the case shown in Figure 1 (a).
In step ST1, the distance image acquisition means (in this embodiment, the 3D camera 1 similar to that shown in FIG. 1(b)) arranged above each single-particle-size sample of the three particle size divisions is used to repeatedly capture images of each single-particle-size sample while changing the deposition state of the sample, and distance images are acquired. A calculation device (not shown) connected to the distance image acquisition means performs calculations to measure the particle size of the surface layer particles of each single-particle-size sample. In this embodiment, the minor axis diameter of the surface layer particles in the distance image, which is considered to be an ellipse, is used as the particle size of the surface layer 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 C, as in the case shown in FIG. 1(b). It is preferable that the number of repeated measurements of each single-particle-size sample is the same. As a result, as shown in FIG. 6(a), a first particle size distribution showing the relationship between the particle size (x) and the number of surface particles of the single-particle-size sample is calculated for each of the three particle size divisions. In FIG. 6( a ), A(x) is the first particle size distribution calculated for a single particle size sample in particle size category 1, B(x) is the first particle size distribution calculated for a single particle size sample in particle size category 2, and C(x) is the first particle size distribution calculated for a single particle size sample in particle size category 3.

<Process ST2>
In step S2 (corresponding to the second particle size distribution calculation step of the present invention), a distance image acquisition means (in this embodiment, a 3D camera 1 similar to that shown in FIG. 1(b)) is placed above a mixed-grain-size deposit in which particles belonging to the three particle size categories 1 to 3 are mixed in an arbitrary mass ratio, and distance images are acquired by repeatedly capturing images of the mixed-grain-size deposit while changing the deposition state of the mixed-grain-size deposit, and a calculation device (not shown) connected to the distance image acquisition means 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 they are regarded as ellipses is used as the particle size of the surface particles.
In the case of measuring the particle size of the surface layer particles by piling a mixed-grain-size sediment in tray T as in the case of the single-grain-size sample, the change in the state of the pile can be achieved by mixing and stirring that occurs when transferring the mixed-grain-size sediment between tray T and another container C, as in the case shown in Fig. 1(b). The number of repeated measurements of the mixed-grain-size sediment does not necessarily have to be the same as the number of repeated measurements of each single-grain-size sample.
When measuring the particle size of surface particles of a mixed-grain deposit accumulated and transported on a belt conveyor, the measurement can be repeated assuming that different pile states of mixed-grain deposits mixed in the same mass ratio are developed on the belt conveyor.
In this way, 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 deposit, is calculated as shown in Fig. 6(b) . In Fig. 6(b) , F(x) shown by the solid line is the second particle size distribution calculated for the mixed-grain-size deposit.

<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) (the number of surface layer particles of the mixed particle size deposit body) of the mixed particle size deposit body, as shown in Fig. 6(b), the particle size distribution F(x) of the mixed particle size deposit body is approximated by a linear sum C _a · A(x) + C _b · B(x) + C _c · C(x) of the first particle size distributions A(x), B(x), and C(x) for each of the three particle size divisions, and the coefficients C _a , C _b , and C _c of the linear sum are calculated. In Fig. 6(b), the linear sum is shown by a dashed line. The approximation by the linear sum can be performed using a known approximation method such as the least squares method.

<Process ST4>
The coefficient C _a of the linear sum calculated in step ST3 can be considered to be a value proportional to the number of surface layer particles belonging to grain size division 1 that appear in the mixed-grain-size deposit. Similarly, the coefficient C _b of the linear sum can be considered to be a value proportional to the number of surface layer particles belonging to grain size division 2 that appear in the mixed-grain-size deposit. Similarly, the coefficient C _c of the linear sum can be considered to be a value proportional to the number of surface layer particles belonging to grain size division 3 that appear in the mixed-grain-size deposit.
For this reason, in step ST4, each coefficient C _a , C _b , and C _c is regarded as a surface number ratio, which is the number ratio of surface particles belonging to grain size classes 1, 2, and 3 of each single grain size sample in the mixed grain size deposit body, and a surface number distribution, which shows the relationship between the grain size classes and the surface number ratio for each grain size class, is calculated for the mixed grain size deposit body, as shown in Figure 6 (c).

<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 6 (c) calculated in step ST4 and the surface probability model are used to calculate the overall number distribution, which is the relationship between the particle size classification and the total number proportion of particles in each particle size classification 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 the deposited particles. This is because the frequency of particles appearing in the surface layer varies depending on the particle size, and the larger the particle size, the more frequently they appear in the surface layer, so the surface number distribution will count more large particles than the total number distribution. For this reason, in order 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 the particle size, and that estimates the number distribution of all the deposited particles from the number distribution of surface particles. The surface probability model will be explained below.

式（１）のｉは粒度区分を示す添え字であり、本実施形態では、ｉ＝１が粒度区分１（２５ｍｍ＜粒径≦３８ｍｍ）、ｉ＝２が粒度区分２（３８ｍｍ＜粒径≦５０ｍｍ）、ｉ＝３が粒度区分３（５０ｍｍ＜粒径≦７５ｍｍ）に対応する。式（１）の右辺のｊはｉと同じく粒度区分を示す添え字であり、粒度区分ｉの表面確率Ｐ_ｉが、粒度区分ｉ自体のみならず、他の粒度区分の変数にも依存することを示す。Ｘ_ｉは測定の各回における粒度区分ｉに属する表層粒子の個数で、Ｅ（Ｘ_ｉ）は全測定回数における表層粒子の個数の平均値を表している。本実施形態に係る粒度分布測定方法では、直接Ｘ_ｉを扱うことなく、工程ＳＴ４で算出した表面個数分布を用いる。具体的には、Ｅ（Ｘ_ｉ）（ｉ＝１～３）の値を工程ＳＴ３で算出した各係数Ｃ_ａ、Ｃ_ｂ、Ｃ_ｃに置き換える。すなわち、Ｅ（Ｘ_１）＝Ｃ_ａ、Ｅ（Ｘ_２）＝Ｃ_ｂ、Ｅ（Ｘ_３）＝Ｃ_ｃとする。
また、式（１）の右辺のＰ_ｉの変数であるＨは混合粒度堆積体の高さ（嵩高さ）を表し、Ｎ_ｊは粒度区分ｊに属する粒子全体の個数を表す。Ｄ_ｊは粒度区分ｊの粒度の中間値を表す。本実施形態では、Ｄ_１＝（２５＋３８）／２＝３１．５ｍｍ、Ｄ２＝（３８＋５０）／２＝４４ｍｍ、Ｄ３＝（５０＋７５）／２＝６２．５ｍｍとなる。 The surface probability P _i that particles of the particle size class i appear on the surface layer is expressed by the following formula (1).

In formula (1), i is a subscript indicating the particle size division, and in this embodiment, i=1 corresponds to particle size division 1 (25 mm<particle size≦38 mm), i=2 corresponds to particle size division 2 (38 mm<particle size≦50 mm), and i=3 corresponds to particle size division 3 (50 mm<particle size≦75 mm). The j on the right side of formula (1) is a subscript indicating the particle size division like i, and indicates that the surface probability P _i of particle size division i depends not only on the particle size division i itself but also on the variables of other particle size divisions. X _i is the number of surface particles belonging to particle size division i in each measurement, and E(X _i ) represents the average value of the number of surface particles in all measurements. In the particle size distribution measurement method according to this embodiment, the surface number distribution calculated in step ST4 is used without directly dealing with X _i . Specifically, the values of E(X _i ) (i=1 to 3) are replaced with the coefficients C _a , C _b , and C _c calculated in step ST3. That is, E( _X1 )= _Ca , E( _X2 )= _Cb , and E( _X3 )= _Cc .
In addition, H, which is a variable of P _i on the right side of the formula (1), represents the height (bulk height) of the mixed grain size deposit, N _j represents the total number of particles belonging to grain size class j, and D _j represents the median grain size of grain size class j. In this embodiment, D ₁ = (25 + 38)/2 = 31.5 mm, D 2 = (38 + 50)/2 = 44 mm, and D 3 = (50 + 75)/2 = 62.5 mm.

式（２）の右辺のＭ_ｉは、粒度区分ｉに属する粒子が表層にあるとき、この表層粒子の下の空間に存在する粒子の平均個数に、この表層粒子自体の個数１個を加えた個数であり、式（３）のように表される。式（３）のＶ_Ｍは、表層にある粒度区分ｉに属する粒子の面積と高さＨとの積で表される体積の空間に存在する粒子の平均体積であり、式（４）のように表される。式（３）のＶ_ｉと式（４）のＡ_ｉは、それぞれ粒度区分ｉにおける体積比と面積比であり、Ｖ_１＝１としたときの中間値Ｄ_ｉの三乗の比、Ａ_１＝１としたときの中間値Ｄ_ｉの二乗の比となっている。本実施形態では、体積比Ｖ_ｉ及び面積比Ａ_ｉは、以下の表１に示す値となる。

式（２）のｇ（ｉ）は、式（５）及び式（６）で表され、粒度区分ｉに属する粒子の見えやすさを示す。 The surface probability Pi of formula (1) is expressed by the following formula (2), and more specifically by the following formulas (3) to (6).

M _i on the right side of formula (2) is the average number of particles present in the space below the surface layer particles when the particles belonging to the particle size division i are present in the surface layer, plus one for the surface layer particles themselves, and is expressed as in formula (3). V _M in formula (3) is the average volume of particles present in the space whose volume is represented by the product of the area and height H of the particles belonging to the particle size division i in the surface layer, and is expressed as in formula (4). V _i in formula (3) and A _i in formula (4) are the volume ratio and area ratio in the particle size division i, respectively, and are the ratio of the cube of the intermediate value D _i when V ₁ =1, and the ratio of the square of the intermediate value D _i when A ₁ =1. In this embodiment, the volume ratio V _i and the area ratio A _i have the values shown in Table 1 below.

g(i) in formula (2) is expressed by formulas (5) and (6) and indicates the visibility of particles belonging to particle size class i.

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 total number of particles is not calculated, but the ratio of the number of particles to the total number of particles is calculated.

In the iterative method, the following steps (1) to (5) are carried out.
(1) First, set the initial value of _Nj to a value obtained by dividing 1 by the number of granularity classes. In this embodiment, since the number of granularity classes is 3, _N1 = _N2 = _N3 = 1/3.
(2) The initial value of N _j is substituted into the right-hand side of equation (1') to obtain the updated N _i on the left-hand side.
(3) For the updated N _i , normalize N _i by 1. That is, replace N i with the ratio N _i /(N ₁ +N ₂ +N ₃ ) so that the sum N ₁ +N ₂ +N ₃ of _{N i} becomes 1.
(4) Substitute the normalized N _j into the right-hand side of equation (1') to obtain the updated N _i on the left-hand side.
(5) The steps (1) to (4) are repeated until N _i converges (the absolute value of the difference between N _i before the update and N _i after the update becomes equal to or less than a certain value), and the final total number (number ratio) N _i of particles is obtained.
This allows the calculation of the total number distribution, which is the relationship between the particle size class i and the number ratio N _i of the total particles for each particle size class i.

<Step ST6>
In step ST6 (corresponding to the overall mass distribution calculation step of the present invention), the overall mass distribution, which is the relationship between the particle size divisions and the total mass fraction of particles in each particle size division of the mixed particle size deposit, is calculated based on the overall number distribution calculated in step ST5 and the volume ratio V _i (see Table 1) calculated from each of the three particle size divisions.
Specifically, as shown in the following formula (7), the number ratio N _i of all particles is multiplied by the volume ratio V _i , and the resulting ratio is calculated as the mass ratio m _i of all particles.

According to the particle size distribution measuring method of the present embodiment described above, in step ST3, the particle size distribution F(x) of the mixed particle size deposit calculated in step ST2 is approximated by a linear sum C a ·A( _x ) + C _b ·B(x) + C _c ·C(x) of the particle size distributions A(x), B(x), and C(x) of each single particle size sample calculated in step ST1, and the coefficients C _a , C _b , and C _c of the linear sum are calculated. Next, in a fourth step ST4, the calculated coefficients C _a , C _b , and C _c of the linear sum are regarded as surface number ratios, which are the number ratios of surface layer particles belonging to the particle size divisions of each single particle size sample in the mixed particle size deposit, and a surface number distribution showing the relationship between the particle size divisions and the surface number ratios for each particle size division is calculated. Thereafter, using a surface probability model in the same manner as in the method described in Non-Patent Document 2, in step ST5, the calculated surface number distribution and the surface probability model are used to calculate an overall number distribution, which is the relationship between the grain size classification and the total number proportion of particles in each grain size classification of the mixed grain size deposit body, and in step ST6, an overall mass distribution, which is the relationship between the grain size classification and the total mass proportion of particles in each grain size classification of the mixed grain size deposit body, is calculated.
In this way, the coefficients C _a , C _b , and C _c of the linear sum are regarded as the surface number ratio, which is the number ratio of surface particles belonging to the grain size classification of each single-grain sample in the mixed-grain sediment body, to calculate the surface number distribution, and this surface number distribution is finally used to calculate the total mass distribution, so that the total mass distribution can be calculated with high accuracy.

Example 1
Hereinafter, as Example 1, an example of the results of calculating the total mass distribution by the particle size distribution measuring method according to this embodiment will be described.

In Example 1, a Sick Ranger-E50 (area scan camera pixel count: 1536 x 512, measurement speed: 35,000 cross sections/second) was used as the 3D camera 1, and the height from the bottom of the tray T (500 x 500 x 100 mm) on which the coke particles had accumulated was adjusted so that the entire tray T was within the field of view. The tray T was also mounted on a belt-driven traveling cart, and the travel distance was detected by a rotary encoder installed on the traveling cart. The cart was set up to capture one distance image when it had traveled the length of the tray T.

In step ST1 of Example 1, a tray T full of single-particle-size samples (approximately 8 kg) was prepared, which were sieved into each of the particle size categories of 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). The measurement was repeated 10 times by changing the stacking state of each single-particle-size sample in the tray T, and the number of surface particles was counted for each particle size range at 5 mm intervals to calculate the first particle size distribution of each single-particle-size sample. The above-mentioned FIG. 3 shows the first particle size distribution of each single-particle-size sample calculated in Example 1. FIG. 3(a) shows the first particle size distribution A(x) of the single-particle-size sample of particle size category 1, FIG. 3(b) shows the first particle size distribution B(x) of the single-particle-size sample of particle size category 2, and FIG. 3(c) shows the first particle size distribution C(x) of the single-particle-size sample of particle size category 3.

Next, in step ST2 of Example 1, particles belonging to the three particle size classes 1 to 3 were blended in mass ratios of 15%, 20%, and 65%, respectively, and deposited in tray T to obtain a mixed particle size deposit. Then, similarly to the case of the single particle size sample, the measurement was repeated 10 times while changing the deposition state of the mixed particle size deposit in tray T, and the number of surface layer particles was counted for each particle size range at 5 mm intervals to calculate the second particle size distribution of the mixed particle size deposit.
Next, in step ST3 of Example 1, the particle size distribution F(x) of the mixed-grain-size deposit was approximated by the linear sum _Ca.A (x) + _Cb.B (x) + Cc.C(x) of the particle size distributions A(x), B(x), and _C (x) of each single-grain-size sample using the least squares method, and the coefficients _Ca , _Cb , and _Cc of the linear sum were calculated.
Fig. 7 shows the second grain size distribution and linear sum of the mixed grain size deposit calculated in Example 1. The solid line in Fig. 7 is the second grain size distribution F(x) of the mixed grain size deposit, and the dashed line is the linear sum C _a · A(x) + C _b · B(x) + C _c · C(x). As shown in Fig. 7, the coefficients are C _a = 0.16833, C _b = 0.225909, and C _c = 0.644118.

Next, in step ST4 of Example 1, the coefficients C _a , C _b , and C _c were regarded as surface number ratios, which are the number ratios of surface layer particles belonging to grain size classes 1, 2, and 3 in the mixed grain size deposit, respectively, to calculate the surface number distribution.
8 shows the surface number distribution, total number distribution, and total mass distribution of the mixed grain size deposit calculated in Example 1. Fig. 8(a) shows the surface number distribution, Fig. 8(b) shows the total number distribution, and Fig. 8(c) shows the total mass distribution.
The surface number ratio on the vertical axis of the surface number distribution shown in FIG. 8(a) is a value obtained by expressing each of the coefficients C _a , C _b , and C _c as a percentage so that the sum of the surface number ratios corresponding to each grain size class is 100%.

Next, in step ST5 of Example 1, the surface number distribution shown in FIG. 8(a) and the surface probability model were used to calculate the total number distribution shown in FIG. 8(b). The total number ratio on the vertical axis of the total number distribution shown in FIG. 8(b) is the total number ratio of the 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 each grain size category is 100%.

Finally, in step ST6 of Example 1, the overall mass distribution shown in Fig. 8(c) was calculated based on the overall number distribution shown in Fig. 8(b) and the volume ratio V _i (see Table 1). The overall mass ratio on the vertical axis of the overall mass distribution shown in Fig. 8(c) is the mass ratio of all the particles constituting the mixed grain size deposit, and is a value expressed as a percentage so that the sum of the overall mass ratios corresponding to each grain size class is 100%.
As shown in Fig. 8(c), the total mass percentage of particle size category 1 was 13.40129%, the total mass percentage of particle size category 2 was 24.05432%, and the total mass percentage of particle size category 3 was 62.54439%. As described above, the mixed particle size deposit was made by mixing particles belonging to the three particle size categories 1 to 3 in mass percentages of 15%, 20%, and 65%, respectively, so that the results shown in Fig. 8(c) can be said to be close to the mass percentages that were actually mixed.

Example 2
In Example 2, the overall mass distribution of the mixed grain size deposit was calculated in the same manner as in Example 1, except that in step ST2, a mixed grain size deposit was used in which particles belonging to the three grain size categories 1 to 3 were blended in mass proportions of 0%, 50%, and 50%, respectively.

Example 3
In Example 3, the overall mass distribution of the mixed grain size deposit was calculated in the same manner as in Example 1, except that in step ST2, a mixed grain size deposit was used in which particles belonging to the three grain size categories 1 to 3 were blended in mass proportions of 15%, 55%, and 30%, respectively.

Fig. 9 shows the total mass distributions calculated in Examples 1 to 3. Fig. 9(a) shows the total mass distribution calculated in Example 1, Fig. 9(b) shows the total mass distribution calculated in Example 2, and Fig. 9(c) shows the total mass distribution calculated in Example 3. The graphs indicated with "3D" in Fig. 9 show data calculated in each Example, and the graphs indicated with "sieve" show data measured using a sieve (mass ratio reflecting the actual state of the blended particles). The graph indicated with "3D" in Fig. 9(a) is the same as the graph shown in Fig. 8(c).
As shown in FIG. 9 , in all of Examples 1 to 3, the calculated total mass distribution is close to the mass ratio reflecting the actual state, and it can be seen that the measurement was performed with higher accuracy than the result calculated by the conventional method described with reference to FIG. 2 .

In Examples 1 to 3, the particle size distribution of a mixed-grain-size deposit piled up in a tray T is measured, but the present invention can also measure the particle size distribution of a mixed-grain-size deposit piled up and transported on a belt conveyor. However, in the case of a mixed-grain-size deposit piled up and transported on a belt conveyor, unlike a mixed-grain-size deposit piled up in a tray T, the height H of the mixed-grain-size deposit 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.

10 and 11 are explanatory diagrams for explaining a method for calculating the height of a mixed-grain size deposit pile accumulated and transported on a belt conveyor, and are shown in a cross section perpendicular to the transport direction of the belt conveyor.
When calculating the height of the mixed-grain deposit accumulated and transported on the belt conveyor, as shown in FIG. 10(a), in the above-mentioned step ST2, the particle size of the surface layer particles of the mixed-grain deposit is repeatedly measured using a distance image acquisition means (3D camera 1), and the positions of the cross-sectional upper edge E1 (shown by a dashed line in FIG. 10(a)) of the mixed-grain deposit and the belt conveyor BC are repeatedly measured. Meanwhile, as shown in FIG. 10(b), the position of the cross-sectional upper edge E2 (shown by a dashed line in FIG. 10(b)) of the belt conveyor BC in a state in which the mixed-grain deposit is not accumulated 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 deposit is calculated as shown in FIG. 10(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 the result is integrated in the horizontal direction (the left-right direction in FIG. 10 ), thereby calculating the cross-sectional area S. As described 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 deposit can be, for example, the average value of the repeatedly calculated cross-sectional areas S.

式（８）をＨについて解けば、以下の式（９）が成立する。

幅Ｗ及び傾斜角θは既知の値であるため、混合粒度堆積体の断面積Ｓ（断面積Ｓの平均値）を算出すれば、式（９）によって混合粒度堆積体の高さＨを算出することができる。
以上のようにして、ベルトコンベアＢＣ上に堆積して搬送される混合粒度堆積体の高さＨを算出し、これを工程ＳＴ５において表面確率モデルに用いることで、トレイＴ内に堆積した混合粒度堆積体の場合と同様に、混合粒度堆積体の全体個数分布を算出することができ、工程ＳＴ６において全体質量分布を算出可能である。 Here, the cross section of a general belt conveyor BC for transporting particles such as coke and sintered ore is a trapezoid (isosceles trapezoid), and therefore, in many cases, the cross section of the mixed grain size pile can also be approximated as a trapezoid.
Therefore, as shown in Fig. 11, the cross section of the mixed-grain deposit is approximated as a trapezoid of height H. As shown in Fig. 11, 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 with respect to the up-down direction) is θ, the area of the trapezoid is expressed as (W + H tan θ) H. If the area of this trapezoid is considered to be equal to the cross-sectional area S of the mixed-grain deposit, the following formula (8) is established.

By solving equation (8) for H, the following equation (9) is obtained.

Since the width W and the inclination angle θ are known values, by calculating the cross-sectional area S of the mixed-grain-size deposit body (average value of the cross-sectional area S), the height H of the mixed-grain-size deposit body can be calculated using equation (9).
In the above manner, the height H of the mixed-grain size deposit piled up and transported on the belt conveyor BC is calculated, and by using this in the surface probability model in step ST5, the overall number distribution of the mixed-grain size deposit piles can be calculated, as in the case of the mixed-grain size deposit piles piled up in the tray T, and the overall mass distribution can be calculated in step ST6.

A modified example of the particle size distribution measuring method according to this embodiment will be described below.
In the particle size distribution measuring method according to the present embodiment, the minor axis diameter of the surface layer particles in the distance image is used as the particle size of the surface layer particles, but it is also possible to calculate the particle size by judging the deposition state of the surface layer particles, as described below. In addition, in the particle size distribution measuring method according to the present embodiment, in step ST1, a first particle size distribution showing the relationship between the particle size and the number of surface layer particles of a single particle size sample is calculated, and in step ST2, a second particle size distribution showing the relationship between the particle size and the number of surface layer particles of a mixed particle size deposit is calculated, but instead of these, as described below, it is also possible to calculate a second particle size distribution showing the relationship between the particle size and the area of the surface layer particles of a mixed particle size deposit together with the first particle size distribution showing the relationship between the particle size and the area of the surface layer particles of a single particle size sample, or to calculate a second particle size distribution showing the relationship between the particle size and the volume of the surface layer particles of a mixed particle size deposit together with the first particle size distribution showing the relationship between the particle size and the volume of the surface layer particles of a single particle size sample.

FIG. 12 is a diagram for explaining the deposition state of surface layer particles.
As shown in the left diagram of Fig. 12(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 on top of another particle group. In this case, as shown in the right diagram of Fig. 12(b), the vertical diameter (height diameter) of the surface particle is buried in the particle group and is unknown, so it is considered to be the same as the minor axis diameter, and (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 considered to be a spheroid whose height diameter is the same as the minor axis diameter.

As shown in the left diagram of FIG. 12(b), 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 equal to or less than the minor axis diameter of the surface particle, it can be determined that the surface particle is directly 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 (major axis diameter x minor axis diameter x height diameter). In addition, as shown in the right diagram of FIG. 12(b), the particle diameter of the surface particle can be calculated by the following formula (10) when the minor axis diameter is b and the height diameter is c, taking into account the case where the surface particle passes through the mesh of the sieve in the 45° direction.

In any of the above cases, when the surface layer particles are regarded as ellipsoids, the volume must be calculated by multiplying (major axis diameter × minor axis diameter) ² by a coefficient of π/6 to be precise. However, this coefficient is multiplied by both particle size distributions when the particle size distributions related to the volume of the surface layer particles are calculated in steps ST1 and ST2, and is cancelled out when the coefficient of the linear sum is calculated in step ST3, so that it can be omitted.
In any of the above cases, the surface particle area can be calculated by the product of the major axis diameter and the minor axis diameter of the surface particle. When the surface particle in the distance image is regarded as an ellipse, the area needs to be calculated by multiplying the product of the major axis diameter and the minor axis diameter by a coefficient of π/4. However, this coefficient can be omitted because it is multiplied by both particle size distributions when the particle size distributions related to the surface particle area are calculated in steps ST1 and ST2 and is cancelled when the coefficient of the linear sum is calculated in step ST3.

Hereinafter, an example will be described in which, in steps ST1 and ST2, instead of the number of surface layer particles, a particle size distribution relating to the area or volume of surface layer particles is calculated as the particle size distribution.
Fig. 13 shows the first particle size distribution of the single particle size sample related to the area or volume of the surface layer particles calculated in step ST1 of Example 1. Fig. 13(a) shows the first particle size distribution related to the area of the surface layer particles, and Fig. 13(b) shows the first particle size distribution related to the volume of the surface layer particles. In Fig. 13, the first particle size distributions of the single particle size samples of particle size classes 1 to 3 are displayed in an overlapping manner.
Compared to the first particle size distribution of the single-particle-size sample relating to the number of surface particles shown in Figure 3, the first particle size distribution of the single-particle-size sample relating to area or volume shown in Figure 13 has the particle size distribution of the larger particle size range lifted up on the vertical axis. However, by also setting the second particle size distribution of the mixed-particle-size deposit calculated in step ST2 to a particle size distribution based on the same criteria (number of surface particles, area or volume), the overall mass distribution finally calculated in step ST6 can be made to be similar to the overall mass distribution shown in Figure 9 described above.

Fig. 14 shows the total mass distribution calculated in step ST6 when the particle size distribution related to the area of the surface layer particles is calculated in steps ST1 and ST2 of Examples 1 to 3. Fig. 14(a) shows the total mass distribution corresponding to Example 1, Fig. 14(b) shows the total mass distribution corresponding to Example 2, and Fig. 14(c) shows the total mass distribution corresponding to Example 3. The graphs shown with "3D" in Fig. 14 show data corresponding to each Example, and the graph shown with "sieve" shows data measured using a sieve (mass ratio reflecting the actual state of the blended particles).
As shown in Figure 14, for all of Examples 1 to 3, the overall mass distribution calculated using the particle size distribution related to the area of the surface particles is close to the mass ratio reflecting the actual state, and it can be seen that the measurement was performed with the same high accuracy as the overall mass distribution calculated using the particle size distribution related to the number of surface particles shown in Figure 9.

Fig. 15 shows the total mass distribution calculated in step ST6 when the particle size distribution related to the volume of surface layer particles is calculated in steps ST1 and ST2 of Examples 1 to 3. Fig. 15(a) shows the total mass distribution corresponding to Example 1, Fig. 15(b) shows the total mass distribution corresponding to Example 2, and Fig. 15(c) shows the total mass distribution corresponding to Example 3. The graphs shown with "3D" in Fig. 14 show data corresponding to each Example, and the graph shown with "sieve" shows data measured using a sieve (mass ratio reflecting the actual state of the blended particles).
As shown in Figure 15, for all of Examples 1 to 3, the overall mass distribution calculated using the particle size distribution related to the volume of surface particles is close to the mass ratio reflecting the actual state, and it can be seen that the measurement was performed with the same high accuracy as the overall mass distribution calculated using the particle size distribution related to the number of surface particles shown in Figure 9.

1...3D camera (distance image acquisition means)
BC... Belt conveyor ST1... Process (first particle size distribution calculation step)
ST2...Step (second particle size distribution calculation step)
ST3...Process (coefficient calculation step)
ST4: Step ST5: Step (total number distribution calculation step)
ST6: Process (total mass distribution calculation step)
T: Tray

Claims (4)

a first particle size distribution calculation step of preparing single-particle-size samples, which are samples consisting of only particles having the same particle size for a particle size division, which is a division determined by the particle size, for a plurality of particle size divisions, imaging the surface layers of the single-particle-size samples for the plurality of 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 the particle size and the number of particles in the surface layer of the single-particle-size sample for each of the plurality of 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 containing particles belonging to the plurality of particle size classes while changing the deposition state of the mixed-grain-size deposit body, acquiring a distance image showing the distance from a reference position to the particles of the surface layer, and calculating a second particle size distribution showing the relationship between the particle size and the number of particles of 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 each of the plurality of particle size ranges and calculating a coefficient of the linear sum;
a total number distribution calculation step of calculating a total number distribution, which is a relationship between the particle size divisions and the total number ratio of particles in each particle size division of 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 the 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 particle size divisions and the mass ratios of all particles in each particle size division of the mixed particle size deposit body, based on the overall number distribution and a volume ratio calculated from the particle size divisions;
The particle size distribution measuring method according to claim 1, In the first particle size distribution calculation step, a first particle size distribution showing a relationship between particle size and area of the particles in the surface layer of the single particle size sample is calculated instead of a first particle size distribution showing a relationship between particle size and number of the particles in the surface layer of the single particle size sample,
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 indicating the relationship between the particle size and area of the particles in the surface layer of the mixed particle size deposit is calculated instead of a second particle size distribution indicating the relationship between the particle size and number of particles in the surface layer of the mixed particle size deposit. In the first particle size distribution calculation step, a first particle size distribution showing a relationship between particle size and volume of particles in the surface layer of the single particle size sample is calculated instead of a first particle size distribution showing a relationship between particle size and number of particles in the surface layer of the single particle size sample,
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 indicating the relationship between the particle size and volume of particles in the surface layer of the mixed particle size deposit is calculated instead of a second particle size distribution indicating the relationship between the particle size and number of particles in the surface layer of the mixed particle size deposit. A height calculation step is provided,
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 transported by the belt conveyor, and the positions of the cross-sectional upper edges 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, which is measured in advance, and a height of the mixed-grain size deposit is calculated based on the cross-sectional area, assuming that the cross section of the mixed-grain size deposit is a trapezoid;
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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