JP6681221B2 - Structure analysis device, structure analysis method, and three-dimensional woven fiber material manufacturing method - Google Patents

Description

  The present invention relates to a structure analysis device, a structure analysis method, and a three-dimensional woven fiber material manufacturing method, and is suitable for application to, for example, inspection of fiber-reinforced composite materials.

  In recent years, fiber-reinforced composite materials have begun to be used in various fields. A fiber-reinforced composite material is a composite material manufactured by combining fibers and a support material, and has superior material properties such as light weight and high strength as compared with a single material, so it is a component for aircraft, automobiles, etc. Is attracting attention as. Fiber-reinforced composite materials include, for example, CMC (Ceramic Matrix Composites) and FRP (Fiber Reinforced Plastics), which are appropriately used depending on the environment and purpose of use.

  In such a fiber-reinforced composite material, the orientation of the fiber bundle greatly affects the strength. Therefore, the fiber bundle of the finished fiber-reinforced composite material is meandering at a position that should be straight, is deflected by being totally displaced from the reference axis where it should be originally arranged, or is broken in the middle. If so, the strength of the fiber-reinforced composite material is reduced. For this reason, it is necessary to inspect the orientation of the fiber bundles of the completed fiber-reinforced composite material component. For example, the internal structure is analyzed using three-dimensional volume data (CT image) of the component imaged by CT (Computed Tomography) scan. Is considered to do.

  In Patent Document 1, based on a second step of binarizing an input three-dimensional image to obtain a binary image and an orientation detection filter having a parameter for giving anisotropy to the shape of a detection cross section, 2 Regarding the third step of estimating the orientation of each foreground pixel in the value image, the fourth step of extracting the central pixel indicating the center of the fiber bundle from the foreground pixel group of which the orientation is estimated, and the extracted central pixel group A fifth step of connecting the central pixels showing the same or similar orientation as the same fiber bundle and connecting the central pixels showing the same fiber bundle, and meandering of the central pixel group showing the same connected fiber bundle. A sixth step of calculating a quantity, and an image analysis apparatus are disclosed.

Japanese Unexamined Patent Application Publication No. 2015-067552

  However, detailed imaging by CT scanning takes time, and in particular, it is not realistic to capture a detailed CT image with a small voxel size for a large part. Further, although binarization processing is often performed in the analysis of CT images, CT images often include noise, and when binarization processing is performed, the boundary between the object and the background is Some areas are not judged properly. Especially in a low-resolution image with a large voxel size, since there are many intermediate gradations, the important geometric information that characterizes the fabric structure is lost when binarization processing is performed, which may make it difficult to recognize the orientation of the fiber bundle. is there.

  The present invention has been made in consideration of the above points, and a structure analysis device and a structure capable of analyzing the structure of a fiber-reinforced composite material from a three-dimensional image of the fiber-reinforced composite material without using a binarization process. It is intended to provide an analysis method.

  In order to solve such a problem, the structural analysis device of the present disclosure calculates the eigenvector in the minimum direction of the change in the gradation value at each grid point of the coordinates in the three-dimensional image in which the three-dimensional woven fiber material is photographed, A lattice point orientation calculation unit that is the orientation of each of the lattice points, and the orientation of the points in the image is calculated based on the orientation of the lattice points around the points, and the direction of the calculated orientation. A boundary curve calculating unit that repeatedly calculates the orientation in the same manner for the new point moved to, and calculates a boundary curve that is the stretching direction of the fiber bundle.

  Further, the apparatus operating method of the present disclosure, at each grid point of the coordinates in the three-dimensional image in which the three-dimensional woven fiber material is photographed, the eigenvector in the minimum direction of the change in gradation value is the orientation of each grid point. , The orientation of a point in the image is calculated based on the orientation of the grid points around the point, and the orientation is the same for the new point moved in the direction of the calculated orientation. Is a structural analysis method in which the boundary curve that is the stretching direction of the fiber bundle is calculated by repeating

  Further, the three-dimensional woven fiber material manufacturing method of the present disclosure is a three-dimensional woven fiber material, in which a three-dimensional woven fiber material is molded, and the molded three-dimensional woven fiber material is inspected using the above-described structural analysis method. It is a manufacturing method.

  According to the present disclosure, the structure of a fiber-reinforced composite material can be analyzed from a three-dimensional image of the fiber-reinforced composite material without using a binarization process.

It is a figure which shows the hardware constitutions of the structure analysis apparatus which concerns on this embodiment. It is a figure showing the functional block of the analysis processing part of a structure analysis device. It is a flow chart of structural analysis processing concerning this embodiment. It is a figure which shows simulated about the three-dimensional woven fiber material used as the object of structural analysis in this embodiment. It is a figure which represents typically about the orientation of the lattice point calculated from a gradient vector. It is a flow chart which shows lattice point orientation calculation processing. It is a schematic diagram for explaining calculation of a boundary curve. 3 is a CT image showing a cross section of a three-dimensional woven fiber material of SiC fiber. 9 is an image in which a boundary curve searched by applying a boundary curve calculation process to the CT image in FIG. 8 is superimposed on the CT image in FIG. 8. It is an image in which a different gradation value is assigned to each direction component with respect to the orientation obtained by the boundary curve calculation process. FIG. 11 is an enlarged view of a portion surrounded by a square in FIG. 10. FIG. 3 is a diagram showing vector fields u and v and isosurfaces that are scalar fields s and t in two dimensions. It is a flowchart of a fiber bundle surface calculation process. It is a figure of an example which represented the isosurface of s, t, and f obtained by the fiber bundle surface calculation processing by the three-dimensional image.

  Hereinafter, an embodiment of the present invention will be described in detail with reference to the drawings. In the following description, similar elements will be denoted by the same reference symbols, without redundant description.

(1) Configuration of Structural Analysis Apparatus According to this Embodiment FIG. 1 is a diagram showing a hardware configuration of a structural analysis apparatus 100 according to this embodiment. As shown in this figure, the structural analysis device 100 includes a CPU (Central Processing Unit) 101, a volatile storage unit 102 such as a RAM (Random Access Memory), a non-volatile storage unit 103 such as a hard disk or a flash memory, and a network 201. A network connection unit 104 for connecting to an external memory, an external device connection unit 105 such as a USB (Universal Serial Bus) connector for connecting the external memory 202, an input device 106 such as a keyboard and a mouse, and a liquid crystal display screen. It may be composed of the display device 107. Here, the CPU 101, the volatile storage unit 102, and the non-volatile storage unit 103 configure an analysis processing unit 150 that operates by software. The structural analysis device 100 may be configured by a computer system in which computer devices having a hardware configuration as shown in FIG. 1 are network-connected.

  FIG. 2 is a diagram showing a configuration of the analysis processing unit 150 of the structural analysis device 100. As shown in this figure, the analysis processing unit 150 determines the minimum eigenvector of the change in gradation value at each grid point at each grid point of the coordinates in the image in which the cross section of the three-dimensional woven fiber material is photographed. The lattice point orientation calculation unit 151 for the orientation and the orientation of an arbitrary point in the image are calculated based on the orientations of the surrounding lattice points, and similarly for a new point moved in the direction of the calculated orientation. A boundary curve calculation unit 152 that calculates a boundary curve that is the stretching direction of the fiber bundle by repeatedly calculating the orientation, and a fiber bundle surface calculation unit 153 that calculates the surface of the layer formed by the family of fiber bundles from the boundary curve. And have.

(2) Structural Analysis Processing FIG. 3 is a flowchart of structural analysis processing S100 according to the present embodiment. As shown in this flowchart, in the structural analysis process S100, first, in step S110, a three-dimensional image captured by an external CT scanning device or the like is input via the network 201, the external memory 202, or the like. Next, the lattice point orientation calculation processing S120 by the lattice point orientation calculation unit 151 and the boundary curve calculation processing S130 by the boundary curve calculation unit 152 are performed using the results of the lattice point orientation calculation processing. After that, the fiber bundle surface calculation unit 153 performs the fiber bundle surface calculation process S140, and the structural analysis process S100 ends. Here, the fiber bundle surface calculation process S140 may not be performed. Details of each process will be described below. In the following description, it is assumed that the three-dimensional image is a CT image captured by a CT scanning device, and its gradation value is called a CT value. However, even when a three-dimensional image that is not a CT image is used. A gradation value can be applied as the CT value.

  FIG. 4 is a diagram schematically showing a three-dimensional woven fiber material which is a target of structural analysis in the present embodiment. As shown in FIG. 4, the three-dimensional woven fiber material is formed by stacking thin plates of plain woven fibers composed of X yarns 11 and Y yarns 12 and binding a plurality of thin plates with Z yarns 13.

ここで、距離ｒは、δをＣＴ画像のボクセルサイズとし、αを定数とすると、α×δで表される。αは１．５〜３に設定されることが望ましい。ｗ_jは、格子点ｑ_jにおける重みであり、以下の式（２）で定義することとしてもよい。

ここで、ｄ_jは、ｐ_iからｑ_jまでの距離である。勾配ベクトルｇ_jはＣＴ値の変化を示し、最小固有値の固有ベクトルｅ_1iはＣＴ値の最小変化方向を意味する。したがって、分散共分散行列Ｍの最小固有値の固有ベクトルｅ_1iをｐ_iにおける配向とする（Ｓ１２３）。ここで、距離ｒは、繊維束と繊維束との間の距離以下とすることができる。またその中でも最も大きい値とすることが好ましく、繊維束と繊維束との間の距離としてもよい。また格子点の配向の算出では、ハリス（Harris）のコーナー検出法を用いることとしてもよい。 (3) Lattice point orientation calculation process In the lattice point orientation calculation process S120 by the lattice point orientation calculation unit 151, it is assumed that the minimum direction of change in CT value is the orientation in the CT image, and the orientation is calculated using the gradient vector. To do. Figure 5 is a grating in the CT image in which the yarn 31 and 32 is a fiber bundle is reflected, and the gradient vector g _i of the lattice point q _j in the lattice point p _i within the distance r, which is calculated from the gradient vector g _i It is a figure which represents typically about the orientation (eigenvector _e1i ) of the point p _i . FIG. 6 is a flowchart showing the lattice point orientation calculation processing S120. The lattice point orientation calculation processing S120 will be described with reference to FIGS. The lattice point orientation calculation unit 151 first calculates the gradient vector g _i at all lattice points in the CT image (S121). Next, for each point p _i whose orientation is to be detected, the variance-covariance matrix M shown in Equation (1) for the lattice point q _i within the predetermined distance r is calculated (S122).

Here, the distance r is represented by α × δ, where δ is the voxel size of the CT image and α is a constant. It is desirable that α is set to 1.5 to 3. w _j is a weight at the lattice point q _j , and may be defined by the following equation (2).

Here, d _j is the distance from p _i to q _j . The gradient vector g _j indicates the change in CT value, and the eigenvector e _{1i of the} minimum eigenvalue means the minimum change direction of the CT value. Therefore, the eigenvector e _1i of the minimum eigenvalue of the variance-covariance matrix M is set as the orientation in p _i (S123). Here, the distance r can be equal to or less than the distance between the fiber bundles. In addition, the largest value is preferable, and the distance between the fiber bundles may be used. The Harris corner detection method may be used to calculate the orientation of the lattice points.

(4) Boundary Curve Calculation Process Next, the boundary curve calculation process S130 by the boundary curve calculation unit 152 will be described. FIG. 7 is a schematic diagram for explaining the calculation of the boundary curve. In the boundary curve calculation process S130, first, the orientation e _j of the point a _j is calculated by triple linear interpolation of the eigenvector {e _1i } of the surrounding grid points p _i . Next, a point b which is separated from the point a _{j in the} e _j direction by a distance ε is calculated. Further, the same processing is repeated by setting the point b to a _{j + 1} , and the process of advancing by a minute distance according to the orientation is repeated. At this time, if the point b satisfies any of the following conditions, the process may be terminated.
Condition 1: The curvature of the boundary curve is not less than a predetermined value.
Condition 2: The eigenvector e _2j of the second eigenvalue at the point b is significantly different from the eigenvector of the second eigenvalue at the point a _j .

The reason for providing conditions 1 and 2 is to avoid the influence of noise in the CT image, and in particular, the CT value of the air portion at the intersection of the X yarn and the Y yarn becomes a value higher than expected and becomes unclear. This is because the direction of the gradient of does not behave as expected, and when the traveling direction is determined only by e _1i , there is a possibility that the fiber bundle may follow a fiber bundle extending in a different direction. In order to avoid such an erroneous search, the next point b is added to the next curve only when there is no large change in the bending direction. Specifically, for condition 1, the predetermined value of the curvature can be determined based on the maximum curvature and its allowable intersection in the assumed shape, and for condition 2, the second eigenvector of point a and the second eigenvector of b. The threshold value of the difference in the rate of change (first derivative) from the eigenvector of can be determined on the basis of the amount of change in curvature and its allowable intersection.

  FIG. 8 is a CT image showing a cross section of a three-dimensional woven fiber material of SiC fiber. The overlapping portion of the X yarns and the Y yarns has a pillar structure, and an array of 2 × 2 pillars is called a unit cell, which is treated as a minimum structural unit of a three-dimensional woven fiber material. In FIG. 8, the unit cell is observed as a white square. FIG. 9 is an image in which the boundary curve searched by applying the boundary curve calculation process S130 is superimposed on the CT image of FIG. 8 on the CT image of FIG. As shown in this figure, it is confirmed that the boundaries of the X yarn and the Y yarn are accurately searched.

In FIG. 10, a lattice point orientation calculation process S120 and a boundary curve calculation process S130 are performed on a CT image showing a cross section of a three-dimensional woven fiber material of SiC fiber, and e _1i = (e _x , e of each point a _i It is an image in which different gradation values are assigned to _y , _ez ). FIG. 11 is an enlarged view of a portion surrounded by a square in FIG. As shown in these figures, it can be confirmed that the boundary of each yarn is shown. Actually, by assigning the colors (R (red), G (green), B (blue)) to e _1i = (e _x , e _y , e _z ) and displaying them in color, The extending direction can be displayed more easily.

(5) Fiber bundle surface calculation processing Uniform and accurate arrangement of the unit cells is an important element in parts molded from a three-dimensional woven fiber material such as CMC. In the fiber bundle surface calculation processing S140 of the present embodiment, the layer boundary is represented as a surface for the purpose of evaluating the crossing shape of the X yarn and the Y yarn of each layer. These faces that approximate a family of yarns are represented as isosurfaces of a scalar function whose gradient direction corresponds to the yarn direction of this family. The scalar fields s, t and f can be considered as X, Y and Z yarns, respectively. These scalar fields can be obtained by solving three independent Poisson equations for the scalar function. FIG. 12 is a diagram showing this concept in two dimensions. The arrows indicate the vectors belonging to the vector fields u and v corresponding to the X and Y threads, respectively. The isosurfaces that are the scalar fields s and t are shown by solid lines. By obtaining the isosurface, the unit cell 50, which is a set of squares, appears surrounded by the isosurface.

  FIG. 13 shows a flowchart of the fiber bundle surface calculation processing S140. For simplicity, u, v and w are approximated to the X, Y and Z yarn directions, respectively. The input of this algorithm is the set of curves and the two vectors resulting from the boundary curve calculation process. The two vector sets are provided as u and v target directions.

  As shown in this flowchart, first, the boundary curve is divided into short segments (S141). Next, the direction of the segment is compared with the target direction to determine which of u and v the segment belongs to (S142). The orientation of the segment is determined, for example, to match the orientation of the target direction of the vector field specified in step S142, or to be the direction with the highest degree of coincidence among some candidates (S143). In addition, a lattice structure that covers the object in the CT image is generated, and three vectors u, v, and w are assigned to each lattice point (S144). In this allocation, a normalization vector, which is the average of the plurality of normalization vectors obtained in step S143 and obtained by normalizing the plurality of segments, may be allocated. Further, this average may be applied to a segment closer to the grid point than the predetermined distance. If there is no segment sufficiently close to the grid point, it may be expanded to other grid points to obtain the vector of the grid point under consideration. The vector field w is defined by the outer product u × v. Finally, the three Poisson expressions of ∇s = u, ∇t = v and ∇f = w are independently solved (S145) to obtain three scalar fields s, t and f, and The value plane is output (S146).

  FIG. 14 is a diagram showing an example in which the isosurfaces of s, t, and f obtained by the fiber bundle surface calculation processing S140 are represented by a three-dimensional image. As shown in this figure, the shape and arrangement of the unit cells can be confirmed.

  In addition, the orientation of the above-mentioned lattice points, the boundary curve and the surface of the fiber bundle is examined using at least one of the surfaces of the three-dimensional woven fiber material, for example, if it is determined that the strength is insufficient, it is determined to be defective, In other cases, product inspection such as processing as a non-defective product may be performed. The inspection step can be one of the steps of manufacturing a three-dimensional woven fiber material.

(6) Effects of the present embodiment The structural analysis device 100 according to the present embodiment is configured such that at each grid point of the coordinates in the three-dimensional image in which the three-dimensional woven fiber material is photographed, the minimum direction of the change in the gradation value is detected. A lattice point orientation calculation unit 151 that calculates an eigenvector and determines the orientation of each lattice point, and calculates the orientation of points in the image based on the orientation of the lattice points around the points, and moves in the direction of the calculated orientation. And a boundary curve calculation unit 152 that calculates a boundary curve that is the stretching direction of the fiber bundle by repeatedly calculating the orientation for the new point, without using the binarization process. The structure of the fiber-reinforced composite material can be analyzed from the three-dimensional image of the fiber-reinforced composite material.

  The present disclosure can be applied to the inspection of fiber reinforced composite materials.

100 Structural Analysis Device 101 CPU
102 Volatile storage unit 103 Nonvolatile storage unit 104 Network connection unit 105 External device connection unit 106 Input device 107 Display device 150 Analysis processing unit 151 Lattice point orientation calculation unit 152 Boundary curve calculation unit 153 Fiber bundle surface calculation unit 201 Network 202 External memory

Claims (11)

At each grid point of the coordinates in the three-dimensional image in which the three-dimensional woven fiber material is photographed, the eigenvector of the minimum direction of the change in gradation value is calculated, and the grid point orientation calculation unit is set as the orientation of each grid point. ,
The orientation of a point in the image is calculated based on the orientation of the grid points around the point, and the orientation is similarly set for the new point moved in the direction of the calculated orientation. A structure analysis apparatus, comprising: a boundary curve calculation unit that repeatedly calculates and calculates a boundary curve that is a stretching direction of the fiber bundle. In the structural analysis device according to claim 1,
The lattice point orientation calculation unit,
Of the grid points , a gradient vector g _j at a grid point q _j within a distance r from the grid point p _i is calculated,
The weights in the lattice points q _j as w _j, the following expression of the covariance matrix M for said lattice points q _j (1):

And then
The eigenvector e _{1i of the} smallest eigenvalue is the orientation at the grid point p _i ,
Structural analysis equipment. In the structural analysis device according to claim 2,
The distance r is represented by α × δ, where δ is the length of one side of the pixel of the image, and α is 1.5 to 3. In the structural analysis device according to claim 2 or 3,
The weight w _j is expressed by the following formula (2), where d _j is the distance from the grid point p _i to the grid point q _j.

Structural analysis device represented by. In the structural analysis device according to claim 2 or 3,
The structure analysis device, wherein the distance r is equal to or less than a distance between fiber bundles. The structural analysis device according to any one of claims 1 to 5,
The structural analysis device, wherein calculation based on the orientation of the lattice points around the points is performed by triple linear interpolation. The structural analysis device according to any one of claims 1 to 6,
The repetition is
Condition 1: The curvature of the boundary curve formed by adding the new point is not less than a predetermined value, and Condition 2: the second vector of eigenvalues of the new point and the second vector of the immediately preceding point. Is significantly different from the vector of eigenvalues of,
A structural analysis device that terminates processing when either of the above is satisfied. The structural analysis device according to any one of claims 1 to 7,
The structural analysis device further comprising a fiber bundle surface calculation unit that calculates a surface of a layer formed by the family of fiber bundles from the boundary curve. In the structural analysis device according to claim 8,
The fiber bundle surface calculation unit allocates the vectors u, v and w respectively corresponding to the X yarns, the Y yarns and the Z yarns to the respective lattice points based on the boundary curve, and the Poisson's equation ∇s = u, ∇t = V and ∇f = w are independently solved, and the obtained s, t, and f isosurfaces are output. At each grid point of the coordinates in the three-dimensional image where the three-dimensional woven fiber material is photographed, the eigenvector of the minimum direction of the change in gradation value is the orientation of each grid point
The orientation of a point in the image is calculated based on the orientation of the grid points around the point, and the orientation is similarly set for the new point moved in the direction of the calculated orientation. A structural analysis method, wherein a boundary curve that is a stretching direction of a fiber bundle is calculated by repeating calculation. Mold three-dimensional woven fiber material,
A method for producing a three-dimensional woven fiber material, comprising inspecting the formed three-dimensional woven fiber material using the structural analysis method according to claim 10.

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