JP5529682B2 - Pore continuity analysis apparatus, porous body manufacturing method, pore continuity analysis method and program thereof - Google Patents

Description

  The present invention relates to a pore continuity analyzer, a porous body manufacturing method, a pore continuity analysis method, and a program thereof.

  As one method for analyzing the pores of a porous body, a method for obtaining the pore diameter by cross-sectional observation by CT scan has been proposed (see Patent Document 1). In this method, a cross section of a porous body is imaged by CT scan, and the distribution of internal pore diameters in the cross section is measured. As the internal pore diameter, the cross-sectional area of each internal pore in each imaging cross section of the CT scan is measured, and the diameter of a circle having an area corresponding to the cross-sectional area is adopted.

JP 2004-261644 A (paragraph 0041)

  However, although the above-described method can determine the internal pore diameter, it cannot know whether the pores are three-dimensionally continuous inside the porous body, that is, the continuity of the pores.

  The present invention has been made to solve such problems, and its main object is to investigate the continuity of pores in a porous body.

  The pore continuity analysis apparatus, the porous body manufacturing method, the pore continuity analysis method, and the program thereof according to the present invention employ the following means in order to achieve the main object described above.

The pore continuity analyzer of the present invention is
Position information indicating the position of a pixel obtained by a three-dimensional scan of the porous body is associated with pixel type information indicating whether the pixel is a space pixel or an object pixel indicating an object. Data storage means for storing porous body data;
Referring to the porous body data, virtual spheres having various diameters are arranged so that spherical pixels which are pixels occupied by the virtual spheres do not overlap the object pixels and fill the spatial pixels. Sphere positioning means;
Continuity deriving means for deriving continuity of pores from one exposed surface of the porous body to the other exposed surface based on information on the virtual sphere arranged by the virtual sphere arranging means;
It is equipped with.

  In this pore continuity analysis apparatus, the data storage means is a spatial pixel representing the position of a pixel obtained by three-dimensional scanning of the porous body and a pixel representing a space, or an object pixel representing that the pixel is an object Porous material data in association with pixel type information representing the above is stored. Then, by referring to the porous body data, virtual spheres having various diameters are arranged so as not to overlap the object pixels and to fill the space pixels. That is, the pores having a constant diameter and a complicated shape are replaced with a plurality of virtual spheres having various diameters. Then, the continuity of the pores from one exposed surface of the porous body to the other exposed surface is derived based on the information regarding the arranged virtual sphere. As described above, since the pores in the porous body are regarded as a collection of three-dimensional virtual spheres, it can be easily determined whether or not the pores are continuous depending on whether or not the virtual spheres are connected. The “information about the virtual sphere” refers to information such as the center coordinates and diameter of the virtual sphere, for example.

  In the pore continuity analyzing apparatus of the present invention, the virtual sphere arranging means may be means for arranging the virtual spheres so that the centers of the virtual spheres are not the same. Even if a plurality of virtual spheres having the same center are arranged, one virtual sphere having the same or smaller diameter is not necessary for deriving the continuity of the pores. By preventing the placement of such virtual spheres, the virtual spheres can be placed efficiently.

  In the pore continuity analyzing apparatus of the present invention, the virtual sphere arrangement means may be a means for preferentially arranging a virtual sphere having a large sphere diameter, or the virtual sphere arrangement means may be a virtual sphere having a predetermined minimum sphere diameter. By temporarily repeating the process of temporarily arranging the virtual sphere so as not to overlap the object pixel and the process of enlarging the sphere diameter of the temporarily arranged virtual sphere as much as possible within a range not overlapping the object pixel. It is good also as a means to arrange | position. In this way, the spatial pixels can be filled with a virtual sphere having a sphere diameter as large as possible.

  In the pore continuity analyzing apparatus of the present invention, the virtual sphere arranging means may be means for arranging the virtual spheres so that the spherical pixels of the virtual spheres do not overlap each other. In this way, the position where the virtual sphere can be placed is more limited, and therefore the processing time required to place the virtual sphere can be shortened compared to the case where the overlapping of the spherical pixels is allowed.

  In the pore continuity analyzing apparatus of the present invention, the continuity deriving means determines whether or not there is a path to reach the other exposed surface by following virtual spheres adjacent to or overlapping each other from the one exposed surface. If the determination is positive and the determination is affirmative, a plurality of virtual spheres constituting the route may be regarded as a passage in which the continuity of the pores is ensured. In this way, the continuity of the pores can be easily determined. In this case, when the continuity deriving unit determines that there is a path that reaches the other exposed surface by following virtual spheres that are adjacent to or overlap each other from the one exposed surface, When there is a branch path that is a path branched from one exposed surface to the other exposed surface, the main branch path may be specified among the branched paths. Further, in this case, the continuity deriving means determines the smallest virtual sphere having the smallest sphere diameter among the virtual spheres constituting the branch path for each branch path when identifying the main branch path among the branch paths. The branch path having the largest sphere diameter of the smallest virtual sphere among the branch paths may be specified as the main branch path, and in specifying the main branch path among the branch paths, The average sphere diameter of the virtual sphere constituting the branch path may be derived for each branch path, and the branch path having the maximum average sphere diameter among the branch paths may be specified as the main branch path. In identifying the main branch path among the branch paths, the branch direction for each branch path is specified by the direction of the straight line connecting the center points of the virtual spheres that are adjacent to each other or overlap, and the main branch path is determined based on the branch direction. It may be a means for identifying the 岐経 path. Here, if the fluid passes through the porous body from one exposed surface to the other exposed surface, if there is a branch path, the fluid does not necessarily pass through all of the branch paths, so the fluid actually passes through. It is necessary to specify the route to be performed. By specifying the main branch path as described above, the main branch path can be regarded as a path through which the fluid actually passes. When the main branch path is specified, the virtual sphere constituting the main branch path is regarded as a path in which the continuity of the pores is ensured, and the virtual sphere constituting the branch path other than the main branch path The sphere may not be regarded as a passage in which the continuity of the pores is ensured.

  In the pore continuity analyzing apparatus of the present invention, the continuity deriving means determines whether or not there is a path to reach the other exposed surface by following virtual spheres adjacent to or overlapping each other from the one exposed surface. In the case of affirmative determination, a plurality of virtual spheres constituting the route and a virtual sphere that can be reached from the plurality of virtual spheres constituting the route by following the virtual spheres adjacent to each other or overlapping each other It is good also as a means to regard as the channel | path where the continuity of this is ensured. In this way, not only the virtual sphere that forms the path from one exposed surface to the other exposed surface, but also the virtual sphere that branches off from the virtual sphere that configures the path but has a dead end. Can be regarded as a passage in which the continuity of the pores is ensured.

  The pore continuity analyzing apparatus of the present invention is configured such that a plurality of virtual spheres existing in a passage that is regarded as ensuring the continuity of the pores derived by the continuity deriving unit are adjacent to each other from the one exposed surface. A first detection process for detecting a virtual sphere that can be reached by following only a virtual sphere having a diameter larger than a predetermined threshold among the virtual spheres that overlap or overlap each other from or overlap with the other exposed surface A second detection process for detecting a virtual sphere that can be reached by following only a virtual sphere having a diameter larger than the threshold among the virtual spheres, and at least one of the first detection process and the second detection process. It is good also as what was provided with the effective path | route identification means which pinpoints the path | route in which the virtual sphere detected in either exists as an effective path | route. In this way, among the virtual spheres present in the passages that are assumed to have continuity of the pores, an object having a size equal to or smaller than a predetermined threshold (for example, a particle having a diameter equal to or smaller than the predetermined threshold) is one of the virtual spheres. Only passages that can be reached when entering from the exposed surface and the other exposed surface can be identified as effective passages. In this case, the pore continuity analyzing apparatus according to the present invention provides a surface area of the effective passage based on the spherical pixel and the spatial pixel that constitute the effective passage and the spherical pixel or the object pixel adjacent to the spatial pixel. It is good also as what has the surface area calculation means which computes. For example, after a porous body is manufactured, if it is desired to coat an object of a predetermined threshold size on the surface, the coating can be performed only on the surface of a passage that the object can reach from one exposed surface or the other exposed surface. Absent. In such a pore continuity analysis apparatus, in such a case, the surface area capable of coating an object having a size equal to or smaller than a predetermined threshold can be calculated by calculating the surface area of the effective passage.

  The pore continuity analyzing apparatus of the present invention may include a pore volume calculating means for calculating the pore volume of the porous body based on the volume of each virtual sphere. In this way, not only the continuity of the pores can be derived by the virtual sphere, but also the pore volume of the porous body can be calculated by the virtual sphere.

  The pore continuity analyzing apparatus according to the present invention is based on the volume of a plurality of virtual spheres existing in a passage that is considered to have the pore continuity secured by the continuity deriving unit. A passage pore volume calculating means for calculating a certain passage pore volume may be provided. In this way, not only the continuity of the pores is derived by the virtual sphere, but also the passage pore volume, which is the volume of the passage in which the derived continuity is ensured, can be calculated by the virtual sphere. When the main branch path is specified as described above, the passage pore volume of only the main branch path may be calculated, or the passage pores of the passage excluding the branch paths other than the main branch path may be calculated. The volume may be calculated.

The method for producing the porous body of the present invention comprises:
A method for producing a porous body using a pore continuity analyzer comprising the passage pore volume calculating means,
(A) forming a porous body under predetermined conditions;
(B) acquiring the porous body data by performing a three-dimensional scan of the porous body formed in the step (a), and storing the acquired porous body data in the data storage unit;
(C) the pore continuity analyzer calculating the passage pore volume based on the porous body data stored in the data storage means;
(D) The predetermined condition is changed based on the passage pore volume calculated in the step (c), and the steps (a) to (c) are repeated to form a porous body having a desired passage pore volume. Steps,
Is included.

  In this porous body manufacturing method, a porous body is formed under predetermined conditions, porous body data is obtained by three-dimensional scanning the formed porous body, and the obtained porous body data is stored as data. Store in the storage means. Subsequently, the pore continuity analyzer of the present invention calculates the passage pore volume based on the porous body data stored in the data storage means. Then, a predetermined condition is changed based on the passage pore volume, and a porous body having a desired passage pore volume is formed by repeating porous body formation, acquisition and storage of porous body data, and calculation of the passage pore volume. To do. By doing so, since the porous body is formed by changing the predetermined conditions based on the calculated passage pore volume, a porous body having a desired passage pore volume can be efficiently manufactured. If the passage pore volume can be calculated, the passage porosity as a proportion of the passage pore volume in the total volume of the porous body can also be calculated. Therefore, a porous body having a desired passage porosity can be efficiently produced. be able to. Here, in existing methods such as mercury porosimeter and Archimedes method for observing the porosity, open pores (pores partially open toward the exposed surface) and closed pores (all of the pores on the exposed surface) Is not open and is completely isolated from the exposed surface), but it cannot be determined whether the open pore penetrates from one exposed surface to another. It was. In the case of a porous body used for a filter or the like, how many open pores exist in the porous body (that is, the porosity value) (ie, how many pores pass through this porous body) The value of the passage pore volume and passage porosity is important because it directly affects the filter characteristics, and the passage pore volume (or passage porosity) that directly affects the filter characteristics is desired only by the manufacturing method of the present invention. A filter with a value of can be made.

The pore continuity analysis method of the present invention comprises:
Position information indicating the position of a pixel obtained by a three-dimensional scan of the porous body is associated with pixel type information indicating whether the pixel is a space pixel or an object pixel indicating an object. A method for analyzing pore continuity of a porous body using porous body data,
(A) Referring to the porous body data, virtual spheres having various diameters are arranged such that spherical pixels that are pixels occupied by the virtual spheres do not overlap the object pixels and fill the spatial pixels. Placing step;
(B) deriving pore continuity from one exposed surface of the porous body to the other exposed surface based on information on the virtual sphere arranged in the step (a);
Is included.

  In this pore continuity analysis method, position information representing the position of a pixel obtained by a three-dimensional scan of a porous body and a pixel representing whether the pixel is a space pixel representing an area or an object pixel representing an object With reference to the porous body data associated with the type information, virtual spheres having various diameters are arranged so as not to overlap the object pixels and to fill the spatial pixels. That is, the pores having a constant diameter and a complicated shape are replaced with a plurality of virtual spheres having various diameters. Then, the continuity of the pores from one exposed surface of the porous body to the other exposed surface is derived based on the information regarding the arranged virtual sphere. As described above, since the pores in the porous body are regarded as a collection of three-dimensional virtual spheres, it can be easily determined whether or not the pores are continuous depending on whether or not the virtual spheres are connected. Note that the pore continuity analysis method of the present invention may include a step for realizing the function of any of the above-described pore continuity analysis apparatuses.

  The program of this invention is for making each step of the pore continuity analysis method described above realize one or more computers. This program may be recorded on a computer-readable recording medium (for example, hard disk, ROM, FD, CD, DVD, etc.) or from a computer via a transmission medium (communication network such as the Internet or LAN). It may be distributed to another computer, or may be exchanged in any other form. If this program is executed by a single computer or if each step is shared and executed by a plurality of computers, each step of the above-mentioned pore continuity analysis method is executed. The following effects can be obtained.

It is a lineblock diagram of user personal computer 20 of a 1st embodiment. 2 is a front view of a honeycomb filter 30 including a porous partition wall 44. FIG. It is AA sectional drawing of FIG. 3 is a conceptual diagram of porous body data 60. FIG. It is explanatory drawing of the data file. It is a flowchart which shows an example of the analysis process routine of 1st Embodiment. It is a flowchart which shows an example of a virtual sphere arrangement | positioning process. It is explanatory drawing which shows an example of a virtual sphere table. It is explanatory drawing of arrangement | positioning of a virtual sphere. It is a flowchart which shows an example of a continuity derivation process. It is explanatory drawing which shows an example of a continuous pore table. It is explanatory drawing of a continuity derivation process. It is a block diagram of the user personal computer 120 of 2nd Embodiment. It is a flowchart which shows an example of the analysis process routine of 2nd Embodiment. 3 is a conceptual diagram of porous body data 60. FIG. It is explanatory drawing of the continuity derivation | leading-out process of 2nd Embodiment. It is explanatory drawing of arrangement | positioning of a virtual sphere. It is explanatory drawing which shows an example of a continuous pore table. It is explanatory drawing of an effective channel | path specific process. It is explanatory drawing of a surface area calculation process. It is explanatory drawing showing a mode that the virtual boundary surface was set. It is explanatory drawing showing a mode that the spherical pixel and space pixel which comprise an effective channel | path were selected. It is another flowchart of a virtual sphere arrangement | positioning process. It is explanatory drawing which shows an example of the cross section of the porous body data after virtual sphere arrangement | positioning. It is explanatory drawing of branch angle Fd-Id. It is explanatory drawing which shows a mode that step S630 of a modification is performed.

  Next, modes for carrying out the present invention will be described with reference to the drawings.

[First Embodiment]
FIG. 1 is a block diagram showing an outline of the configuration of a user personal computer (PC) 20 which is a first embodiment of the pore continuity analyzer of the present invention. The user PC 20 includes a CPU 22 that executes various processes, a ROM 23 that stores various processing programs such as an analysis processing program 23a, a virtual sphere arrangement program 23b, and a continuity derivation program 23c, and a RAM 24 that temporarily stores data. Controller 21 and HDD 25, which is a large-capacity memory for storing various data such as three-dimensional pixel data of the porous body. The user PC 20 includes an input device 27 such as a display 26 for displaying various information on a screen and a keyboard for a user to input various commands. This user PC 20 can perform analysis processing based on the three-dimensional pixel data of the porous body stored in the HDD 25. In addition, although mentioned later in detail, an analysis process is a process which mainly analyzes about the continuity of the pore in a porous body based on the three-dimensional pixel data of a porous body.

  Here, the porous body analyzed by the user PC 20 will be described. FIG. 2 is a front view of the honeycomb filter 30 including the porous partition walls 44 that are porous bodies, and FIG. 3 is a cross-sectional view taken along the line AA of FIG.

The honeycomb filter 30 is a diesel particulate filter (DPF) having a function of filtering particulate matter (particulate matter (PM)) in exhaust gas from a diesel engine. The honeycomb filter 30 includes a large number of cells 34 partitioned by porous partition walls 44 (see FIG. 3). The material of the porous partition wall 44 is preferably a ceramic material such as Si-bonded SiC or cordierite from the viewpoint of strength and heat resistance. The thickness of the porous partition wall 44 is preferably 200 μm or more and less than 600 μm, and is 300 μm in the first embodiment. The porous pores 44 preferably have an average pore diameter (by mercury intrusion method) of 10 μm or more and less than 60 μm, and a porosity of 40% or more and less than 65%. As shown in FIG. 3, the large number of cells 34 formed in the honeycomb filter 30 include an inlet open cell 36 in which an inlet 36a is opened and an outlet 36b is sealed with an outlet sealing material 38, and an inlet 40a is an inlet seal. There is an outlet open cell 40 which is sealed by a stopper 42 and the outlet 40b is opened. These inlet open cells 36 and outlet open cells 40 are alternately provided so as to be adjacent to each other. The cell density is preferably 15 cells / cm ² or more and less than 65 cells / cm ² .

  The honeycomb filter 30 is mounted on the downstream side of a diesel engine (not shown), for example, and is used for purifying exhaust gas containing PM and releasing it to the atmosphere. In addition, the arrow of FIG. 3 has shown the flow of the waste gas at this time. The exhaust gas containing PM from the diesel engine flows into the inlet open cell 36 from the inlet 36a of the honeycomb filter 30 and then flows into the adjacent outlet open cell 40 through the porous partition wall 44. It is discharged into the atmosphere from the outlet 40b. Here, since the exhaust gas containing PM is collected from the inlet open cell 36 through the porous partition wall 44 and flows into the outlet open cell 40, the exhaust gas flowing into the outlet open cell 40 is PM. Clean exhaust gas that does not contain. The pores in the porous partition wall 44 are coated with an oxidation catalyst such as platinum (not shown), and the trapped PM is oxidized to prevent the porosity of the porous partition wall 44 from decreasing and the pressure loss from rising rapidly. doing.

  The honeycomb filter 30 can be manufactured using, for example, a clay or slurry prepared by mixing a base material, a pore former, and a dispersing material. As the substrate, the above-described ceramic material can be used. For example, in the case of using SiC as a base material, a mixture of SiC powder and metal Si powder at a mass ratio of 80:20 can be used. As the pore former, those that burn after firing are preferable. For example, starch, coke, foamed resin, and the like can be used. As the dispersing material, a surfactant such as ethylene glycol can be used. There is no restriction | limiting in particular in the means to prepare a kneaded material, For example, the method of using a kneader, a vacuum kneader, etc. can be mentioned. For example, this clay is extruded into a shape shown in FIGS. 2 and 3 using a mold having a shape in which the cells 34 are arranged side by side, and the cells 34 are formed by the outlet sealing material 38 and the inlet sealing material 42. After sealing, the honeycomb filter 30 including the porous partition walls 44 can be manufactured by performing drying treatment, calcination treatment, and firing treatment. The outlet sealing material 38 and the inlet sealing material 42 may use raw materials that form the porous partition walls 44. Further, the calcination process is a process of burning and removing organic components contained in the honeycomb filter 30 at a temperature lower than the firing temperature. The firing temperature can be 1400 ° C. to 1450 ° C. for cordierite raw material, and 1450 ° C. for Si-bonded SiC. Through such steps, the honeycomb filter 30 including the porous partition walls 44 can be obtained.

  The HDD 25 of the user PC 20 stores three-dimensional pixel data of the porous partition wall 44 obtained by performing a CT scan on the honeycomb filter 30. In the first embodiment, the XY plane represented by the X direction and the Y direction shown in FIG. 3 is taken as an imaging section, and a plurality of imaging sections are taken in the Z direction shown in FIG. It has gained. The resolution in each of the X, Y, and Z directions is 1 μm, and the resulting cube having one side of 1 μm is the minimum unit of three-dimensional pixel data, that is, a pixel. Each pixel has its position represented by the X, Y, and Z coordinates, and is added with type information for specifying whether the pixel is a space (pore) or an object (a constituent material of the porous partition wall 44). Are stored in the HDD 25. In the first embodiment, a pixel representing space (spatial pixel) is added with value 0 as type information, and a pixel representing an object (object pixel) is added with value 9 as type information. Actually, the data obtained by the CT scan is, for example, luminance data for each of the X, Y, and Z coordinates. The pixel data used in the first embodiment can be obtained by binarizing the luminance data with a predetermined threshold value and determining whether the pixel is a spatial pixel or an object pixel for each coordinate. The predetermined threshold value may be determined so that, for example, the porosity of the porous partition wall 44 obtained by measurement is substantially equal to the porosity in the pixel data after binarization. Such a CT scan can be performed using, for example, SMX-160CT-SV3 manufactured by Shimadzu Corporation.

  An example of the pixel data is shown in FIG. FIG. 4A is a conceptual diagram of porous body data 60 as pixel data obtained by CT scanning the porous partition wall 44 in the region 50 of FIG. The porous body data 60 is obtained by extracting pixel data of a cubic portion having a side of 300 μm from the pixel data of the porous partition wall 44, and an analysis process described later is performed on the porous body data 60. The porous body data 60 includes an inflow surface 61 (see FIG. 3) in which two of the six surfaces of the cube are the boundary surfaces between the porous partition wall 44 and the inlet open cell 36, and the porous partition wall 44 and the outlet in the region 50. It is an outflow surface 62 (see FIG. 3) which is a boundary surface with the open cell 40, and the remaining four surfaces are cross sections of the porous partition wall 44. FIG. 4B is an XY plane (imaging cross section) 63 and a partially enlarged view 64 of the porous body data 60 at the position where the Z coordinate is a value of 3. As shown in the enlarged view 64, the XY plane 63 is composed of an array of pixels each having a side of 1 μm, and each pixel is represented by either a spatial pixel or an object pixel. Note that, as shown in FIG. 4B, the imaging section obtained by the CT scan is data of a plane having no thickness in the Z direction, but each imaging section has a thickness corresponding to the interval (1 μm) in the Z direction of the imaging section. That is, as described above, each pixel is treated as a cube having one side of 1 μm. The porous body data 60 includes a porous body table 71 in which XYZ coordinates and type information are associated with each other as shown in FIG. 5, and an inflow / outflow table 72 representing the inflow surface 61 and the outflow surface 62. The data file 70 that is included is stored in the HDD 25. Note that “X = 1” in the inflow / outflow table 72 is a plane of X = 1 in the XYZ coordinate system, and represents the inflow surface 61 as shown in FIG. “X = 300” similarly represents the outflow surface 62. The HDD 25 stores not only the data file 70 but also a plurality of other data files representing pixel data of the porous partition walls 44 other than the region 50 described above.

  Next, an analysis process performed on the data file 70 by the user PC 20 will be described. FIG. 6 is a flowchart of the analysis processing routine. This analysis processing routine is performed when the CPU 22 executes the analysis processing program 23 a stored in the ROM 23 when the user instructs to perform the analysis processing via the input device 27. In the following, the case where the analysis process of the data file 70 is performed will be described, but the analysis process can be similarly performed for other data files. Which data file is to be analyzed may be determined in advance or specified by the user.

  When the analysis processing routine is executed, the CPU 22 first reads the data file 70 stored in the HDD 25 and stores it in the RAM 24 (step S100). Then, the virtual wall surface of the porous body data 60 represented by the read data file 70 is set (step S110). Specifically, the user designates the distance from the porous body data 60, which is a cube having a side of 300 μm, to the virtual wall surface covering the periphery, via the input device 27, and the CPU 22 accepts it and stores it in the RAM 24. . For example, if the distance to the virtual wall surface is specified as 1 μm, the CPU 22 has a virtual wall surface 1 μm outside from each surface of the porous body data 60 in the X, Y, and Z directions, and object pixels are all arranged on the outside. It is considered to be. That is, since the porous body data 60 has one side of 300 μm, the porous body data 60 is regarded as being covered with a cubic virtual wall surface having one side of 302 μm. Subsequently, a virtual sphere placement process, which is a process of placing a virtual sphere in the space pixels inside the virtual wall set in step S110, is executed (step S120).

  Here, the description of the analysis processing routine is interrupted, and the virtual sphere arrangement processing will be described. FIG. 7 is a flowchart of the virtual sphere arrangement process. This virtual sphere arrangement processing is performed by the CPU 22 executing the virtual sphere arrangement program 23b stored in the ROM 23.

  When the virtual sphere placement process is executed, the CPU 22 first sets the diameter R of the virtual sphere to the maximum value Rmax (step S200), and among the spatial pixels inside the virtual wall set in step S110, the virtual R having the diameter R is set. A position where the sphere can be arranged is searched (step S210). The virtual sphere having a diameter R is a virtual sphere having a diameter of R μm and a center at the center of any pixel. The position where the virtual sphere having the diameter R can be arranged is searched for as follows, for example. First, one of the spatial pixels at that time (a pixel whose type information is 0) is selected. When a virtual sphere with a diameter R centered on the selected pixel is arranged, if the virtual sphere overlaps with an object pixel or a virtual sphere already arranged, another virtual pixel is selected again. If one of the spatial pixels is selected sequentially and the virtual sphere does not overlap the object pixel and does not overlap the already arranged virtual sphere, the position is a position where a virtual sphere having a diameter R can be placed. Is determined. If the virtual sphere overlaps the object pixel or the already-arranged virtual sphere regardless of which of the spatial pixels at that time is selected as the center, it is determined that there is no position where the virtual sphere having the diameter R can be disposed. . The order of selecting the central pixel may be random or may be performed in order from the pixel on the inflow surface 61 toward the pixel on the outflow surface 62. Moreover, the value of Rmax should just be a value more than the maximum value of the pore diameter normally existing in the porous partition wall 44. For example, the value can be set with reference to numerical values obtained by experiments. If it is determined in step S210 that there is a place that can be placed, one virtual sphere with a diameter R is placed there (step S220). Specifically, in the porous body table 71 stored in the RAM 24 in step S100, the type information corresponding to the pixel occupied by the virtual sphere when the virtual sphere having the diameter R is arranged is occupied by the virtual sphere. It is updated to a value of 5 indicating that it is a spherical pixel. In the first embodiment, when a volume of 50% or more of the pixels is occupied by the virtual sphere, the pixel is a sphere pixel. However, only a pixel that is completely included in the virtual sphere may be a sphere pixel. However, when a part of the pixel is occupied in the virtual sphere, the pixel may be a sphere pixel. Subsequently, the CPU 22 associates the center coordinates of the virtual sphere arranged in step S220, the diameter R, and the sphere identification code and stores them as a virtual sphere table (step S230). The sphere identification code is a code for individually identifying a plurality of virtual spheres stored in the virtual sphere table, and any code such as a number may be used. The virtual sphere table is stored in a predetermined area of the RAM 24.

  Then, the CPU 22 determines whether 99% or more of the spatial pixels have been replaced with spherical pixels (step S240). Specifically, this determination is made by referring to the type information of each pixel included in the porous body table 71 stored in the RAM 24 and the number of pixels whose type information is 0 and the number of pixels whose value is 5. The number of pixels whose type information is 5 is 99% or more with respect to the total number. The determination threshold value is not limited to 99%, and other values may be used. If a negative determination is made in step S240, the process returns to step S210, and the processes of steps S210 to S240 are repeated as long as a virtual sphere with a diameter R can be arranged. If a virtual sphere with a diameter R cannot be placed, a negative determination is made in step S210, the diameter R is decreased by 1 (step S250), and the processing in steps S210 to S240 is repeated in the same manner. If a positive determination is made in step S240, for each virtual sphere stored as the virtual sphere table in step S230, the sphere identification code of another adjacent virtual sphere is stored in the virtual sphere table as adjacent information ( Step S260), the virtual sphere arrangement process is terminated. Here, “adjacent” means a state in which a virtual sphere whose diameter of the virtual sphere is increased by 1 μm (1 pixel) occupies a spherical pixel derived from another virtual sphere (a pixel whose type information is 5). The virtual sphere derived from the occupied spherical pixel is defined as an adjacent virtual sphere.

  By this virtual sphere arrangement processing, the sphere identification code of the arranged virtual sphere, the center coordinates and diameter of the virtual sphere, and the adjacent information of the virtual sphere (the sphere identification code of the virtual sphere adjacent to the virtual sphere) are associated with each other. A virtual sphere table is stored in the RAM 24, and space pixels are replaced with sphere pixels by the arranged virtual spheres. FIG. 8 shows an example of the virtual sphere table created. In the virtual sphere table of FIG. 8, for example, a virtual sphere with a sphere identification code of value 1 has a center coordinate of (X1, Y1, Z1), a diameter of R1 μm, and a sphere identification code of values 3 and 8. (When the diameter of a virtual sphere with a sphere identification code value 1 is increased by 1 μm, the sphere pixel of the virtual sphere with a sphere identification code value 3 and 8 is occupied). FIG. 9A shows an example of the porous body data 60 before the virtual sphere is arranged, and FIG. 9B shows an example of the porous body data 60 after the virtual sphere is arranged. Here, FIG. 9 shows one cross section of the porous body data 60, and in FIG. 9B, the virtual sphere (sphere pixel) is shown as a circle, but in reality, a three-dimensional image is shown in the XYZ coordinate system as a sphere. Are arranged. As shown in FIG. 9B, the virtual sphere is arranged so as not to overlap the object pixel and other virtual spheres by the virtual sphere placement processing. The virtual wall surface 65 is set in step S110 described above, and the virtual sphere is arranged in a range that does not protrude outward from the virtual wall surface 65. Although not shown in FIG. 9B, 99% or more of the spatial pixels are actually replaced with spherical pixels, and a virtual sphere having a smaller diameter than the virtual sphere shown in FIG. Many are arranged. However, for the sake of convenience, the following description will be made assuming that only the virtual sphere shown in FIG. 9B is arranged.

  Returning to the description of the analysis processing routine of FIG. When the virtual sphere arrangement process in step S120 is completed, the CPU 22 executes a continuity derivation process for deriving the continuity of pores in the porous partition wall 44 based on the arranged virtual sphere (step S130).

  Here, the description of the analysis processing routine is interrupted, and the continuity derivation processing is described. FIG. 10 is a flowchart of the continuity derivation process. This continuity derivation process is performed by the CPU 22 executing the continuity derivation program 23 c stored in the ROM 23.

  When the continuity derivation process is executed, the CPU 22 first selects one unselected virtual sphere including the inflow surface 61 (step S300). Whether or not the virtual sphere includes the inflow surface 61 is determined based on the center coordinates and diameter of each virtual sphere stored in the virtual sphere table created by the virtual sphere arrangement process and the inflow stored in the inflow / outflow table 72. It can be determined by a mathematical expression (X = 1) representing the surface 61. Subsequently, the virtual spheres continuous with the selected virtual sphere are sequentially traced and all of them are selected (step S310). Specifically, based on the adjacent information stored in the virtual sphere table, all other virtual spheres adjacent to the selected virtual sphere are selected as continuous virtual spheres. Then, all virtual spheres continuing to the newly selected virtual sphere are selected in the same manner, and this is repeated until it is determined that there are no other virtual spheres continuing. When the process of step S310 is performed, it is determined whether or not there is a virtual sphere including the outflow surface 62 in the selected virtual sphere (step S320). The method for determining whether or not the virtual sphere includes the outflow surface 62 is the same as the determination as to whether or not the inflow surface 61 is included. If a negative determination is made, all the virtual spheres selected in step S310 cannot be selected (step S330).

  On the other hand, if an affirmative determination is made in step S320, only the virtual spheres that exist on the path from the virtual sphere including the inflow surface 61 to the virtual sphere including the outflow surface 62 among the selected virtual spheres have pore continuity. It memorize | stores in a continuous pore table as a secured channel | path (step S340). Here, the path from the virtual sphere including the inflow surface 61 to the virtual sphere including the outflow surface 62 is obtained by sequentially connecting the central points of the virtual sphere including the inflow surface 61 with the virtual straight line. When the center point of the virtual sphere including the outflow surface 62 is reached, it is imaged as a virtual straight line path from the center point of the virtual sphere including the inflow surface 61 to the center point of the virtual sphere including the outflow surface 62. . Therefore, the determination as to whether or not the virtual sphere exists on the route is performed as follows, for example. First, for the virtual sphere selected in step S310, the center points of only the virtual spheres that are continuous from the center point of the virtual sphere including the inflow surface 61 are connected by a virtual straight line. When a path connecting the virtual sphere including the inflow surface 61 to the virtual sphere including the outflow surface 62 can be drawn, all the virtual spheres having the center point on the path are virtual spheres existing on the path. These virtual spheres are stored in the continuous pore table as a passage in which the continuity of the pores is ensured. The continuous pore table is stored in a predetermined area of the RAM 24, and includes a passage identification code for identifying the passage and a plurality of virtual spheres determined as passages in which the continuity of the pores is ensured. This is associated with an identification code. The sphere identification code is stored in the continuous pore table as data that can specify how the virtual sphere forms a passage. An example of the continuous pore table is shown in FIG. Details of FIG. 11 will be described later.

  When the process of step S330 or S340 is performed, it is determined whether there are other selectable virtual spheres other than the virtual spheres including the inflow surface 61 and stored in the continuous pore table (step S350). ). And if affirmation determination is carried out, it will progress to step S300 and will repeat the process of step S300-S350. If a negative determination is made in step S350, this routine is terminated.

  Here, how the continuity deriving process is performed on the virtual sphere arranged as shown in FIG. 9B will be described with reference to FIG. FIG. 12 shows only the virtual spheres, the inflow surface 61, and the outflow surface 62 in FIG. 9B. The following description will be made assuming that a sphere identification code is attached. First, in step S300, one of virtual spheres A1, B1 to B3, C1, and C2 that are virtual spheres including the inflow surface 61 is selected. If the virtual sphere C1 is selected here, the virtual spheres C2 and C3 continuous with the virtual sphere C1 are also selected in step S310. Subsequently, since none of the virtual spheres C1 to C3 includes the outflow surface 62, a negative determination is made in step S320. Then, in step S330, the virtual spheres C1 to C3 are in a non-selectable state and are not selected in the subsequent continuity derivation process.

  Subsequently, returning to step S300, assuming that the virtual sphere B1 is selected from the virtual spheres A1, B1 to B3, in step S310, the virtual spheres continuous to the virtual sphere B1 are sequentially traced and all of them are selected. That is, the virtual spheres B1 to B32 are selected. Subsequently, since the selected virtual sphere includes virtual spheres B31 and B32 including the outflow surface 62, an affirmative determination is made in step S320. And only the virtual sphere which exists on the path | route from the inflow surface 61 to the outflow surface 62 is memorize | stored in a continuous pore table by step S340. Here, the path from the inflow surface 61 to the outflow surface can be drawn by connecting the center lines of continuous virtual spheres from any one of the virtual spheres B1 to B3 to any one of the virtual spheres B32 and 33 with a straight line. Therefore, the virtual sphere existing on this route is stored in the continuous pore table. For example, since the virtual sphere B9 is on the path from the virtual sphere B3 to the virtual sphere B31 or B32, it is stored in the continuous pore table. Further, for the virtual spheres B5 and B6, it is not possible to draw a path connecting the inflow surface 61 to the outflow surface 62 while passing through the center points of the virtual spheres B5 and B6. Therefore, the virtual spheres B5 and B6 are not regarded as passages in which the continuity of the pores is ensured, and are not stored in the continuous pore table. The same applies to the virtual spheres B14 to B16. Further, regarding the virtual spheres B27 and B28, if an attempt is made to draw a path from the inflow surface 61 to the outflow surface 62 while passing through the center points of the virtual spheres B27 and B28, the virtual sphere B26 is passed twice. In the first embodiment, even when the same virtual sphere passes through the same path twice or more times, it is determined that the path connects the inflow surface 61 to the outflow surface 62, and the virtual spheres B27 and B28 are determined. Is also stored in the continuous pore table. Such a virtual sphere may not be determined as a path connecting the inflow surface 61 to the outflow surface 62. In step S340, in this way, it is determined whether or not all of the selected virtual spheres B1 to B32 are virtual spheres existing on the path connecting the inflow surface 61 to the outflow surface 62. Thereby, virtual spheres other than the virtual spheres B5, B6, B14 to B16 among the virtual spheres B1 to B32 are stored in the continuous pore table.

  Then, the process proceeds to step S350, since there is still a selectable virtual sphere A1 including the inflow surface 61, a positive determination is made, and the virtual sphere A1 is selected in step S300. Thereafter, as described above, all the virtual spheres A1 to A17 are selected in step S310, and since the virtual spheres A15 and A17 including the outflow surface 62 are selected, an affirmative determination is made in step S320, and step S340 is performed. Thus, virtual spheres other than the virtual spheres A9 to A12 among the virtual spheres A1 to A17 are stored in the continuous pore table. Then, a negative determination is made in step S350, and the continuity derivation process ends. An example of the continuous pore table created in this way is shown in FIG. As shown in the figure, the sphere identification codes of a series of consecutive virtual spheres B1 to B32 (except for the virtual spheres B5, B6, B14 to B16) are stored in association with the passage identification code “1”, and another continuous virtual sphere is stored. The sphere identification codes of the spheres A1 to A17 (except for the virtual spheres A9 to A12) are associated with the path identification code “2”. Further, as described above, the sphere identification code is stored in the continuous pore table so that it can be specified how the virtual sphere forms the passage. In addition, although the structure of the passage is conceptually shown in FIG. 11, the actual data structure is obtained by associating the identification code of the virtual sphere continuous with the virtual sphere for each sphere identification code of the virtual sphere constituting the passage. Any data structure can be used.

  Returning to the description of the analysis processing routine of FIG. When the continuity derivation process in step S130 is completed, the CPU 22 calculates necessary data based on the data file, virtual sphere table, and continuous pore table stored in the RAM 24 by the above-described process (step S140). For example, the continuity of the pores from the inflow surface 61 to the outflow surface 62 in the porous body data 60 is ensured by calculating and summing the volume of the virtual sphere stored in the continuous pore table based on the virtual sphere table. From the inflow surface 61 in the porous body data 60, the passage pore volume, which is the volume of the passage, is derived, or the average value of the diameter of the virtual sphere stored in the continuous pore table is calculated based on the virtual sphere table. It is possible to calculate a passage average pore diameter that is an average pore diameter of a passage in which the continuity of the pores to the outflow surface 62 is ensured. Further, the total value of the volume of the virtual sphere obtained by summing the number of sphere pixels in the porous body table of the data file is calculated as the pore volume that is the total value of the pore volume in the porous body data 60. The average pore diameter of the porous body data 60 can be calculated as the average value of the diameters of all the virtual spheres stored as the virtual sphere table. In addition, the porosity, which is the ratio of the pores in the porous body data 60, is calculated based on the total number of pixels and the number of spherical pixels in the porous body data 60, or based on the total number of pixels in the porous body data 60. The passage porosity, which is the porosity of only the passage, can be calculated based on the total volume of the porous body data 60 calculated in this way and the passage pore volume. The passage pore volume and the passage average pore diameter can be derived for each different passage, that is, for each different passage identification code.

  Then, the data file, virtual sphere table, continuous pore table, and various data calculated in step S140 are stored together in the HDD 25 as an analysis result file (step S150), and this routine is terminated. As a result, the user can perform performance evaluation of the porous partition wall 44 based on the contents of the analysis result file. For example, since the porous partition wall 44 purifies the exhaust gas that passes through, not all of the pores affect the purification of the exhaust gas, and the volume of the passage through which the exhaust gas actually passes from the inflow surface 61 to the outflow surface 62 It is necessary to evaluate the purification performance of exhaust gas by the pore diameter. The values of the passage pore volume, passage average pore diameter, and passage porosity calculated in this analysis processing routine can be used for the evaluation of such purification performance.

  Further, this analysis result file can also be used in manufacturing a porous partition wall having a desired passage pore volume. For example, first, a porous partition wall is manufactured by the above-described method by mixing a base material having a predetermined particle size and a pore former having a predetermined particle size at a predetermined blending weight ratio, and a CT scan is performed on the manufactured porous partition wall. The above-described analysis processing routine is performed on the three-dimensional pixel data obtained by performing the above. And based on the passage pore volume contained in the obtained analysis result file, the particle size of the base material, the particle size of the pore former, and the blending weight ratio are appropriately changed to produce the porous partition wall again, and this is repeated. Thus, a porous partition wall having a desired passage pore volume can be obtained. In this case, for example, if the passage pore volume obtained from the analysis file is smaller than the desired value, the blending weight ratio of the pore former is increased. Based on the passage pore volume obtained by the analysis, By appropriately changing the particle size and blending weight ratio of the pore material, a porous partition wall having a desired passage pore volume can be efficiently produced. In addition, since the passage porosity can be calculated based on the passage pore volume as described above, when a porous partition wall having a desired passage porosity is desired, the same method is used for efficient production. can do.

As an example of manufacturing a porous partition wall having a desired passage porosity used for a filter by using the above analysis result file, a case of manufacturing a porous partition wall having an average pore diameter of 13 μm and a passage porosity of 50%. This will be described with reference to Table 1. First, a mixture of SiC powder having an average particle diameter of 40 μm and metallic Si powder having an average particle diameter of 4 μm at a mass ratio of 80:20 is used as a base material, and the pore former A having an average particle diameter of 30 μm is used as the base material. The porous body 1 of Table 1 was manufactured by the method mentioned above using what mixed (starch) with the mass ratio of 100: 30. And when the average pore diameter and porosity of this porous body 1 were measured with a mercury porosimeter, as shown in Table 1, the average pore diameter was 13 μm and the porosity was 50%. In addition, one of the porous body data having a side of 300 μm is extracted from the pixel data obtained by performing the CT scan of the porous body 1, and the above-described data file is created. As a result, as shown in Table 1, the passage pore volume was 12.7 × 10 ⁶ μm ³ and the passage porosity was 47% (= passage pore volume / 300 ³ μm ³ × 100). The porosity of the mercury porosimeter is less than 50% while the porosity of the passage is less than 50%. The porosity of the mercury porosimeter is that all open pores (a part of the pores are open to the exposed surface). ), The passage porosity is calculated from the porosity of only the pores that constitute the passage in which the continuity from one exposed surface to the other exposed surface is ensured among the open pores. This is because. Subsequently, since the passage porosity of the porous body 1 was lower than the target value of 50%, the pore former B (starch) having an average particle diameter of 20 μm was added to the same amount of the base material and the pore former A as the porous body 1. The porous material 2 shown in Table 2 was produced by further mixing at a mass ratio of base: pore-forming material B = 100: 10. As for the porous body 2, the average pore diameter, passage pore volume, and passage porosity were derived in the same manner as the porous body 1, and as shown in Table 1, both the average pore diameter and passage porosity were larger than the target values. It became. Therefore, in order to reduce the pore former A, the mass ratio of the base material and the pore former A is set to 100: 25, and other than that, the base material and the pore formers A and B are mixed under the same conditions as the porous body 2. The porous body 3 shown in Table 1 was manufactured. Then, when the average pore diameter, the passage pore volume, and the passage porosity were derived in the same manner as the porous bodies 1 and 2, the average pore diameter was 13 μm and the passage porosity was 50% as shown in Table 1. A bulkhead could be obtained. Thus, a desired porous partition can be efficiently manufactured by changing suitably the particle size and compounding weight ratio of a pore making material based on the numerical value obtained from an analysis result file. In addition, the porosity by the mercury porosimeter in the porous body 3 was 53%. In this way, in the porous partition wall where the porosity of the passage represented by the filter is an important factor, the porosity by the mercury porosimeter includes the open pores that are not communicated from one exposed surface to the other exposed surface. The evil that it becomes becomes cannot be excluded. That is, the relationship between the conventional filter characteristics and the porosity includes such inevitable errors. To obtain the desired filter characteristics by performing more precise measurement, the above-described analysis result file is used. Thus, it can be seen that a method of manufacturing a porous partition wall having a desired passage porosity is optimal. As described above, what is changed as appropriate is not limited to the particle size and the blending weight ratio of the pore former, but the desired particle size and the mixing weight ratio of the SiC powder and the metal Si powder are appropriately changed to obtain the desired porosity. A quality partition can also be obtained. Further, in the above example, one piece of porous body data having a side of 300 μm is extracted from the pixel data obtained from the manufactured porous body, and the passage porosity is derived. However, a plurality of pieces of porous body data are extracted. You may repeat manufacture of a porous body so that the average value of each channel | path porosity may become a desired value.

  According to the first embodiment described in detail above, the X, Y, Z coordinates representing the pixel position obtained by the three-dimensional scan of the porous partition wall 44 and the type information representing whether the pixel is a spatial pixel or an object pixel are obtained. A data file 70 as the associated porous body data 60 is stored in the HDD 25. Then, by the virtual sphere arrangement process, the data file 70 is referred to and virtual spheres having various diameters are arranged so as not to overlap the object pixels and to fill the space pixels. Then, through the continuity deriving process, the continuity of the pores from the inflow surface to the outflow surface of the porous partition wall 44 is derived based on the virtual sphere table that is information on the arranged virtual spheres. As described above, since the pores in the porous body are regarded as a collection of three-dimensional virtual spheres, it can be easily determined whether or not the pores are continuous depending on whether or not the virtual spheres are connected. Further, since the virtual sphere placement process is a process of placing the virtual sphere with priority from the one having the largest diameter, the spatial pixels can be filled with the virtual sphere having the largest diameter. In other words, if a spatial pixel is filled with a virtual sphere with a small diameter, the error between the average pore diameter derived from the diameter of the virtual sphere and the actual average pore diameter may increase, but this is prevented. it can. Furthermore, in the virtual sphere placement processing, each virtual sphere is placed so that the sphere pixels do not overlap each other, so the positions where the virtual sphere can be placed are more limited, and the virtual sphere placement processing is compared to the case where the overlap of the sphere pixels is allowed. Can be shortened. Furthermore, in step S320, it is determined whether or not there is a path that traces a continuous virtual sphere from the inflow surface and reaches the outflow surface. If the determination is affirmative, a plurality of virtual spheres existing on the path are defined as pores. Therefore, the continuity of the pores can be easily determined. Furthermore, the pore volume and the passage pore volume can be calculated based on the volume of the virtual sphere.

[Second Embodiment]
Next, a second embodiment of the pore continuity analyzer of the present invention will be described. FIG. 13 is a configuration diagram illustrating a schematic configuration of a user personal computer (PC) 120 according to the second embodiment. Note that, in the user PC 120 of the second embodiment, the same components as those of the user PC 20 of the first embodiment are denoted by the same reference numerals, and description thereof is omitted.

  As illustrated in FIG. 13, the user PC 120 includes a CPU 22, a controller 121 including a ROM 123 and a RAM 24 that stores various processing programs, an HDD 25, a display 26, and an input device 27. The ROM 123 stores an analysis processing program 123a, a virtual sphere arrangement program 23b, a continuity derivation program 123c, an effective passage identification program 123d, and a surface area calculation program 123e. As will be described in detail later, the user PC 120 saves the porous three-dimensional pixel data (data file representing the pixel data of the porous partition wall 44 such as the data file 70) stored in the HDD 25 in the same manner as in the first embodiment. Based on this, it is possible to analyze the continuity of the pores in the porous pair, determine the effective passage of the continuous pores, and calculate the surface area of the effective passage.

  Next, an analysis process performed by the user PC 120 on the data file 70 stored in the HDD 25 will be described. FIG. 14 is a flowchart of an analysis processing routine. In FIG. 14, the same steps as those of the analysis processing routine of FIG. This analysis processing routine is performed by the CPU 22 executing the analysis processing program 123 a stored in the ROM 123 when the user instructs to perform the analysis processing via the input device 27. In the following, the case where the analysis process of the data file 70 is performed will be described, but the analysis process can be similarly performed for other data files. Which data file is to be analyzed may be determined in advance or specified by the user.

  When this analysis processing routine is executed, the CPU 22 first executes the processes of steps S100 to S120. This is the same as the processing described in the first embodiment. As a result, the data file 70 is read from the HDD 25, a virtual wall surface is set, and the virtual sphere placement program 23b is executed to place the virtual sphere in the spatial pixels inside the virtual wall surface and create the virtual sphere table of FIG. Processing is performed. An example of the porous body data 60 after the virtual sphere arrangement is shown in FIG. In FIG. 15, one cross section different from that in FIG. 9 is shown in the porous body data 60. In FIG. 15, as in FIG. 9B, 99% or more of the spatial pixels are actually replaced with spherical pixels, but only the virtual sphere shown in FIG. 15 is arranged for convenience of explanation. The following description will be made assuming that

  When the process of step S120 ends, the CPU 22 executes a continuity derivation process (step S130a).

  Here, the description of the analysis processing routine is interrupted, and the continuity derivation processing is described. FIG. 16 is a flowchart of the continuity derivation process. This continuity derivation process is performed by the CPU 22 executing the continuity derivation program 123 c stored in the ROM 123. In FIG. 16, the same step number is assigned to the same process as the continuity derivation process of FIG. 10 of the first embodiment, and the description thereof is omitted.

  As shown in FIG. 16, the continuity derivation process of the second embodiment is based on the point that step S340a is performed instead of the above-described step S340 and the selection of virtual spheres up to that point when a negative determination is made in step S350. 10 is the same as the continuity derivation process of FIG. 10 except that the continuity derivation process is terminated after performing step S360 to cancel. In step S340a, the continuity of the pores is ensured between the virtual sphere existing on the path from the virtual sphere including the inflow surface 61 to the virtual sphere including the outflow surface 62 and the virtual sphere continuous to the virtual sphere. The process which memorize | stores in a continuous pore table as a channel | path is performed. That is, in step S340, only the virtual spheres existing on the path from the virtual sphere including the inflow surface 61 to the virtual sphere including the outflow surface 62 are used as the passages in which the continuity of the pores is ensured. On the other hand, in step S340a, a virtual sphere that does not exist on the path from the virtual sphere including the inflow surface 61 to the virtual sphere including the outflow surface 62 (for example, a virtual sphere in a passage where the branch destination is a dead end). Even if it exists, the virtual sphere continuing to the virtual sphere on the path is a passage in which the continuity of the pores is ensured. In other words, the process of step S340a is a process in which, when an affirmative determination is made in step S320, all the virtual spheres selected in the immediately preceding step S310 are passages in which the continuity of the pores is ensured.

  Here, how the continuity deriving process of FIG. 16 is performed on the virtual sphere arranged as shown in FIG. 15 will be described with reference to FIG. FIG. 17 shows only the virtual spheres, the inflow surface 61, and the outflow surface 62 of FIG. 15, and the sphere identification codes a1 to a14 and b1 to b16 are attached to the virtual spheres as illustrated. This will be described below. First, in step S300, any one of virtual spheres a1, b1, and b2 that are virtual spheres including the inflow surface 61 is selected, and all virtual spheres continuous to the virtual sphere selected in step S310 are selected. For example, when the virtual sphere a1 is selected in step S300, the virtual spheres a1 to a14 are selected in step S310. Since the selected virtual sphere includes the virtual sphere a14 including the outflow surface 62, a positive determination is made in step S320. Subsequently, in step S340a, a virtual sphere that exists on the path from the virtual sphere including the inflow surface 61 to the virtual sphere including the outflow surface 62, that is, the virtual spheres a1 to a9, a12 to a14, and the virtual sphere continuously. The virtual spheres, that is, the virtual spheres a10 and a11 are stored in the continuous pore table as a passage in which the continuity of the pores is ensured. In step S350, since there are still selectable virtual spheres b1 and b2 including the inflow surface 61, an affirmative determination is made, and the processes in and after step S300 are performed. Thereafter, similarly, the virtual sphere b1 or the virtual sphere b2 is selected in step S300, and the virtual spheres b1 to b16 are selected in step S310. Subsequently, since the virtual sphere b16 including the outflow surface 62 is selected, an affirmative determination is made in step S320, and the virtual spheres b1 to b16 are stored in the continuous pore table in step S340a. Then, a negative determination is made in step S350, the process of step S360 is performed, and the continuity derivation process is terminated. An example of the continuous pore table created in this way is shown in FIG. As shown in the figure, the sphere identification codes of a series of consecutive virtual spheres a1 to a14 are stored in association with the path identification code “1”, and the sphere identification codes of other consecutive virtual spheres b1 to b16 are stored as the path identification code “ 2 ”. Note that this continuous pore table conceptually shows the configuration of the passage similarly to the continuous pore table of FIG. 11, and the actual data structure may be any data structure.

Returning to the description of the analysis processing routine of FIG. When the continuity derivation process in step S130a is completed, the CPU 22 performs an effective passage specifying process for specifying an effective passage among the passages stored in the continuous pore table (step S132). The effective passage is a passage that can be reached when an object having a diameter of the threshold value Rref enters the inflow surface 61 and the outflow surface 62 among the passages stored in the continuous pore table. is there. In the second embodiment, the threshold value Rref is a maximum value (for example, 2 μm) of the particle size distribution of alumina (Al ₂ O ₃ ) supporting platinum as an oxidation catalyst that coats the pores in the porous partition wall 44. ). The reason for this will be described later.

  Here, the description of the analysis processing routine is interrupted, and the effective passage specifying process will be described. FIG. 19 is a flowchart of the effective path specifying process. This effective passage specifying process is performed by the CPU 22 executing the effective passage specifying program 123 d stored in the ROM 123.

  When the effective passage specifying process is executed, the CPU 22 first selects one unselected path among the paths stored in the continuous pore table in the continuity derivation process in step S130a (step S600). Then, for the virtual sphere including the inflow surface 61 in the selected passage, it is determined whether or not there is an unselected virtual sphere whose diameter R is larger than the threshold value Rref (step S610). As to which of the selected passages is a virtual sphere including the inflow surface 61, the virtual sphere constituting the selected passage is specified by the continuous pore table, and the virtual sphere table is determined for this virtual sphere in the same manner as in step S300. And can be determined by the inflow / outflow table 72. Alternatively, when the continuous pore table is stored in the RAM 24 in step S340a, information indicating which virtual sphere including the inflow surface 61 among the virtual spheres constituting the passage may be stored together. .

  If a positive determination is made in step S610, the CPU 22 selects one of the unselected virtual spheres including the inflow surface 61 that has been determined positive in step S610 (step S620). Subsequently, among the virtual spheres that are continuous with the selected virtual sphere, a virtual sphere that can be reached by sequentially tracing only unselected virtual spheres having a diameter R larger than the threshold value Rref is selected (step S630). This process is performed in the same manner as the process of step S310 except that only virtual spheres whose diameter R is larger than the threshold value Rref are sequentially traced. And if the process of step S630 is performed, it will return to step S610 and will repeat the process of step S610-S630 until it makes negative determination in step S610.

  If a negative determination is made in step S610, the CPU 22 determines whether or not there is an unselected virtual sphere having a diameter R larger than the threshold Rref for the virtual sphere including the outflow surface 62 in the selected passage (step S640). ). This process is the same as step S610 described above except that the process is performed for a virtual sphere including the outflow surface 62. Subsequently, when a positive determination is made in step S640, one is selected from the unselected virtual spheres including the outflow surface 62 that has been determined positive in step S640 (step S650). Then, among the virtual spheres that are continuous with the selected virtual sphere, a virtual sphere that can be reached by sequentially tracing only unselected virtual spheres having a diameter R larger than the threshold value Rref is selected (step S660). The processing in step S660 is the same as that in step S630 described above except that the starting virtual sphere is a virtual sphere including the outflow surface 62. If the process of step S660 is performed, the process returns to step S640, and the processes of steps S640 to S660 are repeated until a negative determination is made in step S640.

  If a negative determination is made in step S640, the CPU 22 stores the virtual sphere selected in at least one of steps S610 to S660 as a virtual sphere in the effective path (step S670). Specifically, among the virtual spheres stored in the virtual sphere table, an effective code indicating that the virtual sphere in the effective path is a virtual sphere identification code of the virtual sphere selected in at least one of steps S610 to S660 (for example, A process of associating value 1) is performed. Subsequently, it is determined whether there are other unselected passages (step S680). If a positive determination is made, the process returns to step S600 and the processes of steps S600 to S680 are repeated. If a negative determination is made in step S680, the selection of all virtual spheres is canceled (step S690), and the effective path specifying process is terminated.

  Here, how the effective passage specifying process is performed will be described with reference to FIG. Of the virtual spheres a1 to a14 and b1 to b16, the virtual spheres a10, b10, and b13 have a diameter R that is less than or equal to the threshold value Rref, and the other virtual spheres have a diameter R that is greater than the threshold value Rref. When the effective passage specifying process is executed, none of the passages stored in the continuous pore table in FIG. 18 (passage having the passage identification code “1” and “2”) is selected. Select. For example, if the passage having the passage identification code “1” is selected, in step S610, the virtual sphere a1 that is a virtual sphere including the inflow surface 61 among the passages having the passage identification code “1” has a diameter R of the threshold value Rref. Since it is large, a positive determination is made. Subsequently, in step S620, the virtual sphere a1 that has been positively determined in step S610 is selected. In step S630, a virtual sphere that can be reached by sequentially tracing only unselected virtual spheres having a diameter R larger than the threshold Rref is selected from the virtual spheres that are continuous with the virtual sphere a1. Here, as can be seen from FIG. 18, with regard to the virtual spheres a2 to a9 and a12 to a14, all of the virtual spheres that can reach the virtual sphere a1 by sequentially following only the virtual sphere having a diameter R larger than the threshold value Rref. It is. On the other hand, the virtual sphere a10 is not selected because the diameter R is equal to or smaller than the threshold value Rref. The virtual sphere a11 is continuous only with the virtual sphere a10 although the diameter R is larger than the threshold value Rref. Therefore, the virtual sphere a11 cannot be reached by following only the virtual sphere having the diameter R larger than the threshold value Rref from the virtual sphere a1, and the virtual sphere a11 is not selected. As described above, in step S630, the virtual spheres a1 to a9 and a12 to a14 are selected. Since there is no virtual sphere including the inflow surface 61 other than the already selected virtual sphere a1 in the passage with the passage identification code “1”, a negative determination is made in step S610. Even in the subsequent step S640, since there is no virtual sphere including the outflow surface 62 other than the already selected virtual sphere a14, a negative determination is made. If a negative determination is made in step S640, in step S670, the selected virtual spheres a1 to a9 and a12 to a14 are set as virtual spheres in the effective path, and the sphere identification codes of these virtual spheres are set to the virtual spheres in the effective path. Corresponding to a valid code indicating that there is. When the process of step S670 is performed, since a path with the path identification code “2” in the continuous pore table is not selected, a positive determination is made in step S680.

  If an affirmative determination is made in step S680, a passage having the passage identification code “2” is not selected in step S600, and is selected. Subsequently, in step S610, the virtual spheres b1 and b2, which are virtual spheres including the inflow surface 61 among the selected passages, both make a positive determination because the diameter R is larger than the threshold value Rref. In step S620, an unselected virtual sphere b1 or virtual sphere b2 is selected, and in any case, virtual spheres b3 to b9 are selected in step S630. Since the virtual sphere b10 has a diameter R that is equal to or smaller than the threshold value Rref, the virtual spheres b10 to b16 cannot reach only the unselected virtual spheres whose diameter R is larger than the threshold value Rref sequentially, and in step S630 Not selected. Since both of the virtual spheres b1 and b2 including the inflow surface 61 are selected in step S630, a negative determination is made in the next step S610. In subsequent step S640, since there is an unselected virtual sphere b16 including the outflow surface 62, an affirmative determination is made, and in step S650, the virtual sphere b16 is selected. Subsequently, in Step S660, since the diameter R of the virtual sphere b13 is equal to or less than the threshold value Rref, the virtual spheres b14 to b16 are selected. Since there is no virtual sphere including the outflow surface 62 other than the already selected virtual sphere a16, a negative determination is made in step S640. In the subsequent step S670, the effective codes are associated with the sphere identification codes of the selected virtual spheres b1 to 9 and b14 to b16, and a negative determination is made in step S680. In step S690, the selection of all virtual spheres is canceled, and the valid passage specifying process is terminated.

  By performing the effective path specifying process as described above, among the virtual spheres a1 to a14 and b1 to b16, the virtual spheres other than the virtual spheres a10, a11, and b10 to b13 are associated with effective codes, Specified as a virtual sphere. On the other hand, the virtual spheres a10, a11, b10 to b13 are specified as virtual spheres that are not in the effective path. Although the shape of the passage in the porous partition wall 44 (the shape of the boundary between the space pixel and the object pixel) is complicated, the diameter R of the virtual sphere is compared with the threshold value Rref by the effective passage specifying process in this way, and the inside of the effective passage is By determining whether or not the virtual sphere is, it is possible to easily identify the effective path.

  Returning to the description of the analysis processing routine of FIG. When the effective passage specifying process in step S132 ends, the CPU 22 performs a surface area calculation process for calculating the surface area of the effective passage (step S134).

  Here, the description of the analysis processing routine is interrupted, and the surface area calculation processing will be described. FIG. 20 is a flowchart of the surface area calculation process. This surface area calculation process is performed by the CPU 22 executing the surface area calculation program 123e stored in the ROM 123.

  When this surface area calculation process is executed, the CPU 22 is first a virtual boundary surface between the effective path and a path other than the effective path for the paths stored in the continuous pore table in the continuity derivation process in step S130a. A virtual boundary surface is set (step S700). This virtual boundary surface identifies a virtual sphere that is adjacent to a virtual sphere in the effective passage and is not in the effective passage, and is set as a plane that passes through the center point of the virtual sphere. For example, in the passage having the passage identification code “1” in FIG. 18, the virtual sphere adjacent to the virtual sphere in the effective passage and not in the effective passage is the virtual sphere a10 adjacent to the virtual sphere a9. Therefore, a virtual boundary surface passing through the center point of the virtual sphere a10 is set. The situation at this time is shown in FIG. FIG. 21 is an enlarged view around the virtual sphere a10 in FIG. As illustrated, the virtual sphere a10 is adjacent to the virtual spheres a9 and a11 in the effective path. At this time, the virtual boundary surface intersects with a straight line connecting the center points of the virtual spheres a9 and a11 and is set as a surface passing through the center of the virtual sphere a10. Similarly, in the passage having the passage identification code “2”, a virtual boundary surface that intersects the straight line connecting the center points of the virtual spheres b9 and b11 perpendicularly and passes through the center point of the virtual sphere b10, and the virtual sphere b12 , B14 perpendicular to the straight line connecting the central points of b14 and a plane passing through the central point of the virtual sphere b13. The setting of the virtual boundary surface is specifically a value 3 indicating that the type information of the spatial pixel or the spherical pixel in the position overlapping the virtual boundary surface in the porous body table 71 is the virtual boundary surface. It is done by updating to.

  Subsequently, the CPU 22 selects all the spherical pixels and spatial pixels that constitute the effective path (step S710). Here, the selection of the spherical pixel or the spatial pixel constituting the effective path is performed as follows. First, a sphere pixel constituting a virtual sphere associated with an effective code is selected. Next, spatial pixels or spherical pixels that are continuous with the selected spherical pixel are sequentially traced, and spatial pixels and spherical pixels that can be traced are selected. Thereby, all the spherical pixels and spatial pixels surrounded by the object pixel and the virtual boundary surface around the effective path are selected as the effective path. FIG. 22 shows a state in which the spherical pixel and the spatial pixel constituting the effective path are selected in FIG.

When the process of step S710 is performed, the CPU 22 calculates the surface area of the effective passage for each passage (step S720), stores the calculated surface area in association with the passage identification code of the continuous pore table (step S730), and the surface area. The calculation process ends. The surface area of the effective passage is calculated, for example, by calculating the number of surfaces that contact the spherical pixel, the spatial pixel, and the surrounding object pixel selected in step S710, and the area per pixel surface (this embodiment) Then, it can be calculated by multiplying by 1 μm ² ). Note that the shape of the surface in contact with the spherical pixel and the spatial pixel selected in step S710 and the surrounding object pixel is approximated so as to be a shape close to the surface of the actual porous partition wall 44, and the approximate surface area is obtained. It may be the surface area.

  Returning to the description of the analysis processing routine of FIG. When the surface area calculation process in step S134 is completed, the CPU 22 calculates necessary data based on the data file, virtual sphere table, and continuous pore table stored in the RAM 24 by the above-described process (step S140a). In this process, the passage pore volume, the passage average pore diameter, and the like are calculated in the same manner as step S140 of the analysis processing routine of the first embodiment, and the effective passage surface area for each passage stored in the continuous pore table by the surface area calculation processing is calculated. Calculate the total value.

The data file, virtual sphere table, continuous pore table, and various data calculated in step S140a are stored together in the HDD 25 as an analysis result file (step S150a), and this routine is terminated. Thereby, the user can perform the performance evaluation of the porous partition wall 44 and the like based on the contents of the analysis result file as in the first embodiment. Further, the performance evaluation of the porous partition wall 44 can be performed based on the calculated surface area of the effective passage. This will be described below. The porous partition wall 44 is coated with the oxidation catalyst by immersing the porous partition wall 44 in alumina (Al ₂ O ₃ ) supporting the oxidation catalyst. For this reason, the coating is made only in the porous partition wall 44 that can be reached when alumina enters from the inflow surface 61 and the outflow surface 62. In the second embodiment, the value of the threshold value Rref is set to the maximum value of the particle size distribution of the alumina used for this coating. Therefore, the passage through which the alumina can reach can be specified as the effective passage by the effective passage specifying process. And by the surface area calculation process, the coatable area can be calculated as the surface area of the effective passage. The ability to oxidize the collected PM (regeneration ability) of the porous partition wall 44 can be evaluated based on the surface area.

  According to the second embodiment described in detail above, in the continuity derivation process, it is determined whether or not there is a path that reaches the outflow surface by following a virtual sphere that is continuous from the inflow surface. In the case of an affirmative determination, the continuity of the pores is ensured between a plurality of virtual spheres constituting the route and a virtual sphere that can be reached by following a continuous virtual sphere from the plurality of virtual spheres constituting the route. It is considered a passage. For this reason, not only a virtual sphere that forms a path from one exposed surface to the other exposed surface, but also a virtual sphere that branches off from the virtual sphere that configures the path but has a dead end. It can be regarded as a passage in which the continuity of the pores is secured.

  Further, in the effective passage specifying process of the second embodiment, for a plurality of virtual spheres existing in the passage that are considered to have maintained the continuity of the pores in the continuity derivation process, Among these, the processes of steps S610 to S630 for selecting a virtual sphere that can be reached by following only a virtual sphere having a diameter R larger than the threshold value Rref are performed. In addition, the process of steps S640 to S660 is performed to select a virtual sphere that can be reached by tracing only a virtual sphere having a diameter R larger than the threshold value Rref among the virtual spheres continuous from the outflow surface. Then, the passage in which the virtual sphere selected in at least one of steps S610 to S660 is present is specified as an effective passage. As a result, among the virtual spheres present in the passages where the continuity of the pores is ensured, only effective passages that can be reached when particles having a size of the threshold Rref enter from the inflow surface and the outflow surface Can be specified as Furthermore, the surface area calculation process of the second embodiment can calculate the surface area of the effective passage based on the spatial pixels and sphere pixels constituting the effective passage and the object pixels adjacent thereto.

Here, the correspondence between the components of the first and second embodiments and the components of the present invention will be clarified. The HDD 25 of the first embodiment and the second embodiment corresponds to the data storage means of the present invention, and the CPU 22 that executes the virtual sphere arrangement program 23b in the first embodiment and the second embodiment and performs the virtual sphere arrangement processing is virtual. The CPU 22 corresponding to the sphere arrangement means, which executes the continuity derivation processing by executing the continuity derivation programs 23c and 123c, corresponds to the continuity derivation means, and executes the analysis processing programs 23a and 123a to execute step S140 of the analysis processing routine. The CPU 22 for executing the processing corresponds to the pore volume calculating means and the passage pore volume calculating means. Further, the CPU 22 that executes the effective path specifying program 123d in the second embodiment and performs the effective path specifying process corresponds to the effective path specifying means, and executes the surface area calculating program 123e in the second embodiment to perform the surface area calculating process. The CPU 22 corresponds to surface area calculation means.
In addition, in 1st Embodiment and 2nd Embodiment, an example of the pore continuity analysis method of this invention is clarified by demonstrating operation | movement of user PC20,120.

  Needless to say, the present invention is not limited to the above-described first and second embodiments, and can be realized in various modes as long as they belong to the technical scope of the present invention.

  For example, in the first embodiment and the second embodiment described above, the virtual sphere placement processing is performed by placing the virtual pixels from the virtual sphere having a large diameter in the space pixel. However, the virtual sphere placement processing illustrated in FIG. You may perform a virtual sphere arrangement | positioning process with a flowchart. When the virtual sphere arrangement process of FIG. 23 is executed, the CPU 22 first sets the diameter R of the virtual sphere to the minimum value Rmin (step S400), and randomly selects one of the pixels selected from the porous body data 60 A virtual sphere with a diameter R centered at is temporarily arranged (step S410). Specifically, the type information of the porous body table 71 stored in the RAM 24 in step S100 is not changed, and the center coordinates of the virtual sphere, the diameter R, and the sphere identification code are associated with each other and stored in the virtual sphere table of the RAM 24. To do. Note that the value of Rmin is smaller than the minimum value of the pore diameter normally present in the porous partition wall 44, and can be obtained by experiment (for example, 3 μm). Subsequently, it is determined whether or not the pixel occupied by the virtual sphere temporarily arranged in step S410 overlaps the object pixel or the sphere pixel of the already arranged virtual sphere (step S420). This determination can be made based on the center coordinates and the diameter R stored in step S410. If a positive determination is made, the virtual sphere cannot be placed at the temporarily placed position, so the center coordinates and the diameter R of the temporarily placed virtual sphere are deleted from the virtual sphere table in the RAM 24 (step S430), and step Return to S410. On the other hand, if a negative determination is made in step S420, whether or not the diameter R is increased by 1 without changing the center coordinates of the temporarily arranged virtual sphere is overlapped with the object pixel or the spherical pixel of the already arranged virtual sphere. Determination is made (step S440). This determination is performed, for example, by calculating from the center coordinates and the diameter R the pixel that the virtual sphere will occupy when the diameter R is increased by 1, and determining whether or not the object pixel or the sphere pixel is included therein. It can be carried out. If a negative determination is made, the diameter R of the temporarily placed virtual sphere stored in the virtual sphere table is increased by 1 (step S450), and the process returns to step S440. Thereby, the processing of steps S440 to S450 is repeated until a positive determination is made in step S440, and the diameter R of the temporarily arranged virtual sphere is set to a size that can be arranged in a range that does not overlap the object pixel without changing the center coordinates. A process of incrementing by 1 is performed. If the determination in step S440 is affirmative, if the diameter R of the temporarily arranged virtual sphere is increased by 1 and the center coordinate is moved by one pixel, does it overlap the object pixel or the spherical pixel of the already arranged virtual sphere? It is determined whether or not (step S460). Note that the direction in which the center coordinate is moved by one pixel may be any of the X, Y, and Z directions (total of 6 directions). If the diameter R is increased by 1, the object pixel is moved regardless of which direction the virtual sphere is moved. Alternatively, an affirmative determination is made in step S460 only when it is considered that it overlaps with a spherical pixel of the already arranged virtual sphere. If a negative determination is made in step S460, the diameter R of the temporarily arranged virtual sphere is increased by 1 and the center coordinates of the temporarily arranged virtual sphere are overlapped with the object pixel or the spherical pixel of the already arranged virtual sphere. The value is shifted by one pixel in the direction that does not appear (step S470). In addition, when there can be a plurality of such direction candidates, any one of them may be used, for example, a direction may be selected at random. Then, the process returns to step S440, and the processes of steps S440 to S470 are repeated until an affirmative determination is made in step S460. If an affirmative determination is made in step S460, it is considered that the diameter R of the virtual sphere cannot be increased any more while avoiding overlapping with the object pixel or the spherical pixel of the already-arranged virtual sphere. The arrangement is confirmed (step S480). Specifically, in the porous body table 71 stored in the RAM 24 in step S100, the type information corresponding to the pixel of the coordinate occupied by the temporarily placed virtual sphere is updated to a value 5 indicating that it is a sphere pixel. To do. Then, the same determination as in step S240 of FIG. 7 is performed (step S490). If a negative determination is made, the process returns to step S400 to repeat the above-described steps S400 to S490. If an affirmative determination is made in step S490, the adjacent information is stored in the virtual sphere table as in step S260 of FIG. 7 (step S500), and the virtual sphere placement process is terminated. In this virtual sphere placement process, a process of temporarily placing a virtual sphere having a diameter of the minimum value Rmin so as not to overlap the object pixel and the sphere pixel of the already placed virtual sphere is performed in steps S400 to S430. A process of enlarging the diameter R as much as possible is performed in steps S440 to S450 within a range where the sphere does not overlap the object pixel and the sphere pixel of the already-arranged virtual sphere. Are arranged in spatial pixels. By doing so, the spatial pixels can be filled with a virtual sphere having a diameter as large as possible. Also, when a negative determination is made in step S460, that is, if the diameter R can still be increased if the center coordinate is moved by one pixel, the diameter R is increased while moving the center coordinate in step S470. Spatial pixels can be filled with virtual spheres with larger diameters. In addition to the above-described FIG. 7 or FIG. 23, the virtual sphere arrangement processing may be performed by other methods.

  In the first embodiment and the second embodiment described above, in the virtual sphere arrangement processing of FIG. 7, the virtual sphere is arranged so as not to overlap the object pixel and the sphere pixel of the already arranged virtual sphere. Any virtual sphere may be arranged so as to fill the space pixel without overlapping the object pixel. For example, the virtual spheres may be allowed to overlap each other. Even in this case, the pore volume can be calculated by adding up the number of spherical pixels in the porous body table of the data file, as in the first embodiment described above. When the pore volume is derived based on the virtual sphere table, the volume of the overlapping portion between the virtual spheres is calculated from the center coordinates and diameter of the virtual sphere, and the overlap is calculated from the simple total value of the volumes of each virtual sphere. By reducing the volume of the portion, the pore volume can be calculated similarly. Also in the continuity derivation process, not only adjacent virtual spheres but also virtual spheres with overlapping spherical pixels are regarded as continuous virtual spheres, thus ensuring the continuity of pores as well. Identified passages can be identified. Further, in the case where the virtual spheres are allowed to overlap with each other as described above, the virtual spheres may be arranged so that the centers of the virtual spheres are not the same. In this way, virtual spheres can be arranged efficiently.

  In the first embodiment and the second embodiment described above, the user PC 20 performs the above-described processing on the pixel data obtained by performing the CT scan on the porous partition wall 44 of the honeycomb filter 30 used for purification of the exhaust gas, and thus the pores are obtained. However, the present invention is not limited to this. Porous material obtained by three-dimensional scanning of a porous body and associated with position information representing the position of a pixel and pixel type information representing whether the pixel is a spatial pixel representing a space or an object pixel representing an object The pore continuity may be analyzed for any material data. In the first embodiment and the second embodiment, the continuity of the pores from the inflow surface 61 to the outflow surface 62 when exhaust gas passes is analyzed, but from one surface exposed to the outside to the other exposure What is necessary is just to derive the continuity of the pores to the surface. Further, although the user PC 20 (120) analyzes the continuity of the pores with a single device, the processing may be performed by distributing the processing to a plurality of computers.

  In the first embodiment and the second embodiment described above, the porous body data 60 is assumed to be a cube having one side of 300 μm. However, the length of one side may be any value, and the cube Instead, it may have any shape such as a rectangular parallelepiped or a cylinder. In addition, although each pixel in the porous body data 60 is a cube having one side of 1 μm, the length of one side may be smaller or larger than 1 μm. Each pixel does not have to be a cube, such as 1 μm in the XY direction and 2 μm in the Z direction. Furthermore, although the distance from the porous body data 60 to the virtual wall surface is set to 1 μm in step S110, the distance is not limited to this, and any value may be used. In each direction of XYZ and each surface of the porous body data 60, It may be a different value. For example, the length of one side of the porous body data 60 may be selected from a range of 10 μm to 1 mm, and the length of one side of each pixel may be selected from a range of 0.1 to 5 μm.

  In the first embodiment described above, in step S140, data such as passage pore volume, passage average pore diameter, passage porosity, and the like are calculated based on the continuous pore table and the virtual sphere table. Other data may be calculated based on the continuous pore table and the virtual sphere table. For example, the passage surface area that is the surface area of the passage in which the continuity of the pores from the inflow surface 61 to the outflow surface 62 is ensured may be calculated based on the continuous pore table and the virtual sphere table. In this case, among the object pixels stored in the virtual sphere table, an object pixel that is adjacent to the spatial pixel or the sphere pixel and is located on the passage in which the continuity of the pores is secured is identified, and the identified object pixel A value obtained by multiplying the number of pixels by the area of one surface of the object pixel may be calculated as the passage surface area. Further, after the continuity deriving process of the first embodiment, the effective passage specifying process and the surface area calculating process of the second embodiment may be performed to derive the surface area of the effective path.

  In the first embodiment described above, when the route stored in the continuous pore table in step S340 is branched in the middle, that is, when there is a branch route, the main branch route may be specified from among the branch routes. . Hereinafter, an example of a technique for identifying main branch paths will be described with reference to FIG. FIG. 24 shows an example of the cross section of the porous body data after the virtual sphere arrangement, as in FIG. 9B. In FIG. 24, a virtual sphere E1 including the inflow surface 161 and virtual spheres F6, G3, H5, and I6 including the outflow surface 162 exist, and a path from the inflow surface 161 to the outflow surface 162 branches from the virtual sphere E3 in the middle. doing. Therefore, the path from the virtual sphere E3 to the outflow surface 162 includes a branch path that passes through the virtual spheres F1 to F6 (hereinafter referred to as a branch path F) and a branch path that passes through the virtual spheres G1 to G3 (hereinafter referred to as the branch path G). ), Branch paths (hereinafter referred to as branch paths H) via the virtual spheres H1 to H5, and branch paths (hereinafter referred to as branch paths I) via the virtual spheres I1 to I6. The minimum diameter of the branch path F is the sphere diameter of the virtual sphere F1 among the virtual spheres F1 to F6, and the minimum diameter of the branch path G is the sphere diameter of the virtual sphere G1 among the virtual spheres G1 to G3. The minimum diameter of H is the spherical diameter of the virtual sphere H1 among the virtual spheres H1 to H5, and the minimum diameter of the branch path I is the spherical diameter of the virtual sphere I1 of the virtual spheres I1 to I6. The spherical diameters of the virtual spheres F1, G1, H1, and I1 are 7 μm, 10 μm, 5 μm, and 8 μm, respectively.

  The main branch path may be specified as follows. That is, the comparison diameter of each branch path may be derived, and the branch path having the largest comparison diameter may be specified as the main branch path. Here, the comparative diameter of the branch path may be an average value or a minimum diameter value of the virtual spheres constituting the branch path, or a virtual sphere immediately after the branch, that is, the first virtual sphere constituting the branch path (for example, In the case of the branch path F, it may be derived as the spherical diameter of the virtual sphere F1). For example, when the minimum diameter value of the branch path is used as the comparative diameter of the branch path, the largest value among the minimum diameters of the branch paths F to I is the spherical diameter value 10 μm of the virtual sphere G1. Is identified as the main branch path.

  The main branch path may be specified as follows. That is, branch routes are selected in order from the branch route with the larger diameter for comparison, and the branch route selected until the total value of the comparison diameters of the selected branch routes exceeds the comparison diameter of the route before branching is selected. It may be specified as a main branch path. Here, the comparison diameter of the path before branching may be derived as the spherical diameter of the virtual sphere immediately before branching (for example, the virtual sphere E3 in the case of FIG. 24), or the virtual sphere immediately before branching in the path before branching. May be derived as the sphere diameter of a virtual sphere immediately before (for example, virtual sphere E2 in the case of FIG. 24), or virtual spheres constituting the path before branching (for example, virtual spheres E1 to E3 in the case of FIG. 24). ) May be derived as an average value or a minimum value of the sphere diameters. For example, in FIG. 24, the comparison diameter of the path before branching is the sphere diameter of the virtual sphere E3 that is the virtual sphere immediately before branching (value is 24 μm), and the comparison diameter of the branch paths F to I is the virtual diameter immediately after branching. The case where the spherical diameters of the spheres F1, G1, H1, and I1 are used will be described. In this case, when branch paths are selected in order from a branch path having a larger diameter for comparison, the total diameter of the selected branch paths when the branch paths are selected in the order of branch paths G, I, and F is 25 μm. The diameter of the path before branching exceeds 24 μm. Therefore, the branch paths F, G, and I are specified as main branch paths.

  The main branch path may be specified as follows. That is, the branch direction for each branch path may be specified based on the direction of the straight line connecting the center points of the virtual sphere, and the main branch path may be specified based on the branch direction. For example, a branch path whose angle between the branch direction and the X-axis (axis in the direction from the inflow surface to the outflow surface) direction is closest to 0 ° may be specified as the main branch path. Here, the branch direction may be, for example, a straight line direction from the center point of the virtual sphere immediately before branching to the center point of the virtual sphere immediately after branching. In this case, in the branch paths F to I in FIG. 24, the direction of the straight line from the center point of the virtual sphere E3 to the center point of the virtual sphere F1 becomes the branch direction of the branch path F, and from the center point of the virtual sphere E3 to the virtual sphere G1. The direction of the straight line toward the center point of the virtual path is the branch direction of the branch path G, the direction of the straight line from the center point of the virtual sphere E3 to the center point of the virtual sphere H1 is the branch direction of the branch path H, and the center point of the virtual sphere E3 The direction of the straight line from the center to the center point of the virtual sphere I1 is the branch direction of the branch path I. Since the angle between the branch direction and the X-axis direction is the closest to 0 ° is the branch direction of the branch path G as can be seen from FIG. 24, the branch path G is identified as the main branch path. In addition, a branch angle, which is an angle between the direction of the path before branching and the branching direction, is derived based on the direction of the path before branching and the branching direction, and the branch path whose branch angle is closest to 0 ° is determined as the main branch. A route may be specified. Here, the direction of the route before branching may be, for example, the direction of a straight line from the center point of the virtual sphere immediately before the branching point in the route before branching to the center point of the virtual sphere immediately before branching. In this case, in FIG. 24, the direction of the path before branching is the direction of a straight line from the center point of the virtual sphere E2 to the center point of the virtual sphere E3, and the branch direction of the branch path F is the virtual sphere from the center point of the virtual sphere E3. The branch direction of the branch path G is the direction of the straight line from the center point of the virtual sphere E3 to the center point of the virtual sphere G1, and the branch direction of the branch path H is the center of the virtual sphere E3. The direction of the straight line from the point toward the center point of the virtual sphere H1 is the direction of the straight line from the center point of the virtual sphere E3 to the center point of the virtual sphere I1. Therefore, the branch angles Fd to Id of the branch paths F to I are as shown in FIG. 25 is an enlarged view of the virtual spheres E2, E3, F1, G1, and H1 in FIG. As can be seen from FIG. 25, the branch angle Gd has the branch angle closest to 0 ° among the branch angles Fd to Id, and therefore the branch path G is specified as the main branch path. Further, the main branch path may be specified by comparing the branch angle with a predetermined threshold value and determining whether or not the main branch path. For example, when the branch angles Fd to Id are 130 °, 15 °, 30 °, and 70 °, respectively, and the threshold is 120 °, the branch paths G, H, and I having the branch angle less than the threshold are mainly used. It may be specified as a branch path. The threshold value is not limited to 120 ° and may be set as appropriate.

  Although the description of the identification of the main branch path has been made so far with reference to FIG. 24, the branch path from the virtual sphere B10 in FIG. In the case where the branch path merges later, such as the branch path configured by the virtual sphere B13 and the branch path configured by the virtual spheres B17 to B23, the above-described method for specifying the main branch path is used. May be. Further, the identification of the main branch route is not limited to the example described above, and any method may be used. For example, the main branch paths may be specified by combining the above-described methods. Furthermore, depending on the Reynolds number of the fluid flowing from the inflow surface to the outflow surface, it is determined depending on the nature of the fluid flowing from the inflow surface to the outflow surface, such as determining which method to select the branch path according to the above-described method. A method for specifying a branch path may be selected.

  When the main branch path is specified as described above, at least one of the passage pore volume, the passage average pore diameter, the passage porosity, and the passage surface area of only the main branch path may be calculated in step S140 described above. Then, at least one of the passage pore volume, the passage average pore diameter, the passage porosity, and the passage surface area of the passage excluding the branch passages other than the main branch passage may be calculated. Further, when the main branch path is specified, the virtual sphere constituting the main branch path is regarded as a passage in which the continuity of the pores is ensured, and stored in the continuous pore table in step S340, and the main branch path The virtual spheres constituting the other branch paths may not be stored in the continuous pore table in step S340 on the assumption that the continuity of the pores is not regarded as a passage.

  In the effective path specifying process of the second embodiment described above, not only the diameter R of the virtual sphere and the threshold value Rref are compared, but also the size of the virtual boundary surface may be considered. For example, in steps S630 and S660, a virtual sphere that can be reached by sequentially tracing only unselected virtual spheres having a diameter R larger than the threshold Rref is selected from the virtual spheres that are continuous with the selected virtual sphere. At the same time, regarding a virtual sphere having a diameter R equal to or smaller than the threshold Rref among the virtual spheres that are continuous with the selected virtual sphere, the virtual boundary is assumed to have a diameter equal to or larger than the threshold Rref. When the object can pass through, the virtual sphere may be selected. Hereinafter, steps S630 and S660 of this modification will be described with reference to FIG. FIG. 26A shows an example of the cross section of the porous body data after the virtual sphere arrangement as in FIG. In FIG. 26A, virtual spheres c1 to c6 are arranged as illustrated. The diameter R of the virtual spheres c1, c2, c4 to c6 is larger than the threshold value Rref, and the diameter R of the virtual sphere c3 is equal to or smaller than the threshold value Rref. When the effective passage specifying process is performed on the porous body data, an affirmative determination is made in step S610, the virtual sphere c1 is selected in step S620, and then step S630 of the modified example is executed. In step S630 of this modification, virtual spheres c2 and c6 that are continuous with the virtual sphere c1 and whose diameter R is larger than the threshold value Rref are selected. Here, since the diameter R of the virtual sphere c3 is equal to or smaller than the threshold value Rref, a virtual boundary surface of the virtual sphere c3 is assumed as shown in FIG. The assumption of the virtual boundary surface is performed in the same manner as in step S700 described above. That is, since the virtual sphere c3 is continuous with the virtual spheres c2 and c4, a virtual boundary surface is assumed as a plane that intersects perpendicularly with a straight line connecting the center points of the virtual spheres c2 and c4 and passes through the center of the virtual sphere c3. . Then, it is determined whether or not an object having a diameter equal to or larger than the threshold value Rref can pass through the virtual boundary surface. FIG. 26B shows a cross-sectional view (viewed as B) when the porous body data of FIG. 26A is cut along the virtual boundary surface of the virtual sphere c3. As shown in FIG. 26B, the diameter of the largest inscribed circle occupying the assumed virtual boundary surface is calculated, and it is determined whether or not this diameter is larger than the threshold value Rref. Whether or not an object having the following diameter can pass can be determined. Note that the maximum inscribed circle occupying the virtual boundary surface can be calculated in the same manner as the virtual sphere arrangement processing of FIG. 7, for example. That is, it is determined whether or not a circle with a diameter R can be arranged on the virtual boundary surface while sequentially decreasing the diameter R from the maximum value Rmax by a value of 1, and is calculated as the value of the diameter R when an affirmative determination is made for the first time. be able to. When it is determined that an object having a diameter equal to or smaller than the threshold Rref can pass through the virtual boundary surface, the virtual sphere c3 is also selected in the same manner as the virtual sphere having the diameter R larger than the threshold Rref. In this case, the unselected virtual spheres that are further continuous from the virtual sphere c3 are sequentially followed. That is, the virtual spheres c4 and c5 whose diameter R is larger than the threshold value Rref are also selected. On the other hand, when it is determined that an object having a diameter equal to or smaller than the threshold Rref cannot pass through the virtual boundary surface, the virtual sphere c3 is not selected, and the virtual spheres c4 and c5 continuous to the virtual sphere c2 are not sequentially traced. As described above, in step S630 of the modified example, even if the diameter R of the virtual sphere is equal to or smaller than the threshold value Rref, whether or not an object having a diameter equal to or smaller than the threshold value Rref can pass is determined based on the size of the virtual boundary surface. . This makes it possible to more appropriately determine whether an object having a diameter equal to or smaller than the threshold value Rref can actually pass through the passage. In step S630 of this modified example, it is determined whether or not an object having a diameter equal to or smaller than the threshold value Rref can be passed assuming a virtual boundary surface. Unlike step S700, a spatial pixel or a position at a position overlapping the virtual boundary surface or The type information of the spherical pixel is not updated to the value 3. However, when it is determined that an object having a diameter equal to or smaller than the threshold Rref cannot pass through the assumed virtual boundary surface, the type information of the spatial pixel or the spherical pixel at the position overlapping the virtual boundary surface is updated to the value 3. Also good. Note that step S660 of the modified example is the same as step S630 of the modified example, except that the virtual sphere that is the starting point to follow is a virtual sphere including the outflow surface 262.

  In the second embodiment described above, in step S700 of the surface area calculation process, the virtual boundary surface specifies a virtual sphere that is adjacent to the virtual sphere in the effective passage and is not in the effective passage, and the center point of this virtual sphere. However, the virtual boundary surface may be set by another method. For example, a virtual sphere adjacent to a virtual sphere in the effective passage and not in the effective passage may be identified and set as a plane that passes through the contact point between the virtual sphere and the virtual sphere in the adjacent effective passage. . For example, in the passage having the passage identification code “1” in FIG. In this case, the virtual boundary surface may be set so as to intersect perpendicularly with a straight line connecting the center points of the virtual sphere a9 and the virtual sphere a10.

  20, 120 User personal computer (PC), 21, 121 controller, 22 CPU, 23, 123 ROM, 23a, 123a Analysis processing program, 23b Virtual sphere placement program, 23c, 123c Continuity derivation program, 24 RAM, 25 HDD, 26 Display, 27 input device, 30 honeycomb filter, 34 cell, 36 inlet open cell, 36a inlet, 36b outlet, 38 outlet sealant, 40 outlet open cell, 40a inlet, 40b outlet, 42 inlet sealant, 44 porous Partition, 50 region, 60 porous body data, 61, 161, 261 inflow surface, 62, 162, 262 outflow surface, 63 XY plan view, 64 enlarged view, 65 virtual wall surface, 70 data file, 71 porous body table, 72 Inflow / outflow table, 123d Effective passage identification program, 123e surface area calculation program, A1-A17, B1-B32, C1-C3, E1-E3, F1-F6, G1-G3, H1-H5, I1-I6, a1-a14, b1-b16, c1 to c6 Virtual sphere, Fd, Gd, Hd, Id Branch angle.

Claims (18)

Position information indicating the position of a pixel obtained by a three-dimensional scan of the porous body is associated with pixel type information indicating whether the pixel is a space pixel or an object pixel indicating an object. Data storage means for storing porous body data;
Referring to the porous body data, virtual spheres having various diameters are arranged so that spherical pixels which are pixels occupied by the virtual spheres do not overlap the object pixels and fill the spatial pixels. Sphere positioning means;
Continuity deriving means for deriving continuity of pores from one exposed surface of the porous body to the other exposed surface based on information on the virtual sphere arranged by the virtual sphere arranging means;
Equipped with a,
The information regarding the virtual sphere includes at least information regarding the diameter of the virtual sphere,
Pore continuity analyzer. The virtual sphere arrangement means is means for arranging the virtual spheres so that the centers of the virtual spheres are not the same.
The pore continuity analyzer according to claim 1. The virtual sphere arrangement means is a means for preferentially arranging a virtual sphere having a large sphere diameter.
The pore continuity analyzer according to claim 1 or 2. The virtual sphere placement means is capable of temporarily placing a virtual sphere having a predetermined minimum sphere diameter so as not to overlap the object pixel, and the sphere diameter of the temporarily placed virtual sphere within a range not overlapping the object pixel. It is means for arranging the virtual sphere by alternately repeating the process of enlarging as much as possible,
The pore continuity analyzer according to claim 1 or 2. The virtual sphere arranging means is a means for arranging the virtual spheres so that the spherical pixels of the virtual spheres do not overlap each other.
The pore continuity analyzer according to any one of claims 1 to 4. The continuity deriving means determines whether or not there is a path to reach the other exposed surface by following virtual spheres adjacent to or overlapping each other from the one exposed surface. It is a means of regarding a plurality of virtual spheres constituting a path as a passage in which continuity of the pores is ensured.
The pore continuity analyzer according to any one of claims 1 to 5. When the continuity deriving means determines that there is a path that reaches the other exposed surface by following virtual spheres adjacent to or overlapping each other from the one exposed surface, the one exposed surface in the path When there is a branch path that is a path branched from the other exposed surface to the other exposed surface, it is a means for identifying a main branch path among the branch paths.
The pore continuity analyzer according to claim 6. The continuity deriving means specifies, for each branch path, a minimum virtual sphere having the smallest sphere diameter among virtual spheres constituting the branch path when specifying a main branch path among the branch paths. A means for identifying a branch path having a maximum sphere diameter of the smallest virtual sphere among the paths as the main branch path;
The pore continuity analyzer according to claim 7. The continuity deriving means derives an average sphere diameter of virtual spheres constituting the branch path for each branch path when specifying a main branch path among the branch paths, and the average sphere diameter of the branch paths Is a means for identifying the largest branch path as the main branch path.
The pore continuity analyzer according to claim 7. The continuity deriving means specifies a branch direction for each branch path based on a direction of a straight line connecting the center points of virtual spheres adjacent to or overlapping each other when specifying a main branch path among the branch paths. Means for identifying the main branch path based on the branch direction;
The pore continuity analyzer according to claim 7. The continuity deriving means determines whether or not there is a path to reach the other exposed surface by following virtual spheres adjacent to or overlapping each other from the one exposed surface. A passage in which the continuity of the pores is secured between a plurality of virtual spheres constituting the route and a virtual sphere that can be reached from the plurality of virtual spheres constituting the route by following virtual spheres that are adjacent to each other or overlapping each other Is a means to consider,
The pore continuity analyzer according to any one of claims 1 to 5. It is a pore continuity analysis device according to any one of claims 6 to 11,
With respect to a plurality of virtual spheres existing in a passage that is considered to have secured the continuity of pores derived by the continuity deriving means, a predetermined one of the virtual spheres adjacent to or overlapping each other from the one exposed surface A first detection process for detecting a virtual sphere that can be reached by following only a virtual sphere having a diameter larger than a threshold; and a diameter larger than the threshold among virtual spheres adjacent to or overlapping each other from the other exposed surface A second detection process for detecting a virtual sphere that can be reached by tracing only the virtual sphere possessed by the presence of the virtual sphere detected by at least one of the first detection process and the second detection process Effective passage specifying means for specifying a passage to be performed as an effective passage
Stoma continuity analyzer with The pore continuity analyzer according to claim 12,
A surface area calculating means for calculating a surface area of the effective passage based on the spherical pixel and the spatial pixel constituting the effective passage and the spherical pixel or the object pixel adjacent to the spatial pixel;
Stoma continuity analyzer with It is a pore continuity analyzer of any one of claims 1 to 13,
A pore volume calculating means for calculating a pore volume of the porous body based on a volume of each virtual sphere;
Stoma continuity analyzer with It is a pore continuity analyzer of any one of claims 1 to 13,
A passage pore volume that calculates a passage pore volume, which is a pore volume of the passage, based on a volume of a plurality of virtual spheres existing in the passage considered to have the pore continuity secured by the continuity deriving means. Calculation means,
Stoma continuity analyzer with A method for producing a porous body using the pore continuity analyzer according to claim 15,
(A) forming a porous body under predetermined conditions;
(B) acquiring the porous body data by performing a three-dimensional scan of the porous body formed in the step (a), and storing the acquired porous body data in the data storage unit;
(C) the pore continuity analyzer calculating the passage pore volume based on the porous body data stored in the data storage means;
(D) The predetermined condition is changed based on the passage pore volume calculated in the step (c), and the steps (a) to (c) are repeated to form a porous body having a desired passage pore volume. Steps,
The manufacturing method of the porous body containing this. Position information indicating the position of a pixel obtained by a three-dimensional scan of the porous body is associated with pixel type information indicating whether the pixel is a space pixel or an object pixel indicating an object. A method for analyzing pore continuity of a porous body using porous body data,
(A) Referring to the porous body data, virtual spheres having various diameters are arranged such that spherical pixels that are pixels occupied by the virtual spheres do not overlap the object pixels and fill the spatial pixels. Placing step;
(B) deriving pore continuity from one exposed surface of the porous body to the other exposed surface based on information on the virtual sphere arranged in the step (a);
Only including,
The information regarding the virtual sphere includes at least information regarding the diameter of the virtual sphere,
Stomatal continuity analysis method.   A program that causes one or more computers to realize each step of the pore continuity analysis method according to claim 17.

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