Design support device for periodic structures, processing support device for objects to be processed, design support method, and design support program

Abstract

This invention provides a design support technology that allows for the determination of whether or not a closed cavity exists inside a periodic object when it is fabricated using additive manufacturing, with less computational effort. [Solution] The design support device 10 for supporting the design of periodic structures fabricated using a layered structure comprises a data acquisition unit 12 that acquires data showing the spatial distribution of the shapes of structures within some of the unit cells among all the unit cells constituting the periodic structure, and a state variable calculation unit 14 that calculates virtual state variables of structures within some of the unit cells using a virtual physical model with partial differential equations. The state variables indicate whether or not a closed cavity exists inside the periodic structure.

Description

[Technical Field]

[0001] The present invention relates to a design support device for periodic structures, a processing support device for objects to be processed, a design support method, and a design support program. [Background technology]

[0002] Techniques have been proposed to perform topology optimization so that the geometric features of a structure satisfy the geometric constraints in additive manufacturing (e.g., Patent Document 1). In addition, design support techniques have been proposed to determine whether or not a closed cavity exists inside a structure fabricated by additive manufacturing (e.g., Patent Document 2). [Prior art documents] [Non-patent literature]

[0003] [Patent Document 1] International Publication No. 2019 / 216221 [Patent Document 2] Japanese Patent Publication No. 2022-105478 [Overview of the project] [Problems that the invention aims to solve]

[0004] Additive manufacturing methods, such as the powder bed method, involve spreading metal powder and irradiating the area to be fabricated with a laser or electron beam, repeatedly melting and solidifying it to create a structure. In this case, it is necessary to remove any unsolidified metal powder after the fabrication process is complete.

[0005] However, if a closed cavity exists inside the fabricated structure that does not connect to the outside, it becomes impossible to remove the metal powder from this cavity. It is not impossible to drill holes (through-holes) in such cavities to remove the metal powder after the structure is completed. However, such work generally complicates the manufacturing process and degrades the performance of the structure. In particular, if multiple closed cavities are nested inside the structure, it is extremely difficult to drill through-holes afterward. Therefore, it is desirable to design the structure so that no such closed cavities exist before starting the fabrication process.

[0006] The technology described in Patent Document 1 can perform topology optimization so that the geometric features of a structure satisfy the geometric constraints in additive manufacturing. However, this technology cannot determine at the design stage whether or not there are closed cavities within the structure that do not have through-holes that connect to the outside.

[0007] The technology described in Patent Document 2 provides design support by calculating a state variable that indicates whether or not a closed cavity exists inside a structure using a virtual physical model based on partial differential equations. While this method is very useful, it has the drawback of requiring a large amount of computation because it performs calculations regardless of whether or not the target structure has periodicity.

[0008] This invention was made in view of these circumstances, and its purpose is to provide a design support technology that can determine, with less computation, whether or not a closed cavity exists inside a periodic structure (i.e., a periodic structure) when fabricating it using additive manufacturing. [Means for solving the problem]

[0009] To solve the above problems, a design support device according to one aspect of the present invention is a design support device for supporting the design when fabricating a periodic structure of two-dimensional or three-dimensional shape composed of unit cells arranged periodically using a laminated structure, comprising: a data acquisition unit that acquires data showing the spatial distribution of the shape of the structure in some of the unit cells among all the unit cells constituting the periodic structure; and a state variable calculation unit that calculates a virtual state variable of the structure in some of the unit cells using a virtual physical model with partial differential equations. The state variable indicates whether or not a closed cavity exists inside the periodic structure, the data acquisition unit acquires data showing the spatial distribution of the shape of the structure in some of the unit cells using a finite element method that divides the space including some of the unit cells into a mesh, and the state variable is a virtual temperature distribution p, a p χ is the thermal diffusion coefficient at each point in the space containing structures within some unit cells, χ is a characteristic function that takes a value of 1 when the mesh is a point of a structure within some unit cells and a value of 0 when the mesh is not a point of a structure within some unit cells, and the partial differential equation is

number

[0010] In one embodiment, the periodic structure takes the form of a two-dimensional lattice structure, and some unit cells may consist of four adjacent unit cells.

[0011] In one embodiment, the periodic structure takes the form of a three-dimensional lattice structure, and some unit cells may consist of eight adjacent unit cells.

[0012] In one embodiment, a p ￣ is the diffusion coefficient in the non-structural space within some unit cells, and ε p is the diffusion coefficient in some of the structures within a unit cell, and a p The value of ￣ is ε p Larger than the value of , L is a value that characterizes the space including structures within some unit cells, and the thermal diffusion coefficient ap may be represented by [Number] In some embodiments, the design support device may further include a determination unit that determines the quality of the design of the periodic structure based on the state variables.

[0013] In some embodiments, the determination unit may calculate the maximum value of the state variables, and if the calculated maximum value of the state variables is smaller than a predetermined threshold value, determine that the design of the periodic structure is good.

[0014] In some embodiments, the determination unit may calculate the maximum value of the state variables, and if the calculated average value of the state variables is smaller than a predetermined threshold value, determine that the design of the periodic structure is good.

[0015] Another aspect of the present invention is a design support method. This method is a design support method for supporting the design when forming a periodic structure having a two-dimensional shape or a three-dimensional shape in which unit cells are periodically arranged using a stacking structure, and includes a step of obtaining data indicating the spatial distribution of the shape of the structure in some of the unit cells among all the unit cells constituting the periodic structure using a data acquisition unit, and a step of calculating virtual state variables of the structure in some of the unit cells by a virtual physical model using a partial differential equation using a state variable calculation unit. The state variable indicates whether or not there is a closed cavity inside the structure in some of the unit cells, the data acquisition unit obtains data indicating the spatial distribution of the shape of the structure in some of the unit cells using the finite element method in which the space including the structure in some of the unit cells is divided into meshes, the state variable is a virtual temperature distribution p, a

[0016] is the heat diffusion coefficient at each point in the space including the structure in some of the unit cells, χ is a characteristic function that takes the value 1 when the mesh is a point of the structure in some of the unit cells and takes the value 0 when the mesh is not a point of the structure in some of the unit cells, and the partial differential equation is p is the heat diffusion coefficient at each point in the space including the structure in some of the unit cells, χ is a characteristic function that takes the value 1 when the mesh is a point of the structure in some of the unit cells and takes the value 0 when the mesh is not a point of the structure in some of the unit cells, and the partial differential equation is

number

[0017] A further aspect of the present invention is a design support program. This program is a design support program for assisting in the design of a periodic structure having a two-dimensional or three-dimensional shape, composed of unit cells arranged periodically, using a laminated structure, and causes the computer to perform the following steps: acquire data showing the spatial distribution of the shapes of structures within some of the unit cells among all the unit cells constituting the periodic structure using a data acquisition unit; and calculate virtual state variables of the structures within some of the unit cells using a virtual physical model with partial differential equations using a state variable calculation unit. The state variables indicate whether or not there are closed cavities inside the structures within some of the unit cells, the data acquisition unit acquires data showing the spatial distribution of the shapes of structures within some of the unit cells using a finite element method that divides the space containing the structures within some of the unit cells into a mesh, and the state variables are a virtual temperature distribution p, a p χ is the thermal diffusion coefficient at each point in the space containing structures within some unit cells, χ is a characteristic function that takes a value of 1 when the mesh is a point of a structure within some unit cells and a value of 0 when the mesh is not a point of a structure within some unit cells, and the partial differential equation is

number

[0018] Another aspect of the present invention is a design support device. This device is a periodic structure having a two-dimensional or three-dimensional shape in which unit cells are arranged periodically, and is a design support device for supporting the design of a periodic structure connected to a fixed surface. The device includes a data acquisition unit that acquires data indicating the spatial distribution of the shape of the structure within some of the unit cells that make up the periodic structure, and a state variable calculation unit that calculates the virtual state variables of the structure within some of the unit cells using a virtual physical model based on partial differential equations. The state variable indicates whether or not there is a surface connected to the fixed surface in the periodic structure. The data acquisition unit acquires data indicating the spatial distribution of the shape of the structure within some of the unit cells using the finite element method in which the space including the structure within some of the unit cells is divided into meshes. The state variable is a virtual temperature distribution p, a p is the heat diffusion coefficient at each point in the space including the structure within some of the unit cells, χ is a characteristic function that takes the value 0 when the mesh is a point of the structure within some of the unit cells and takes the value 1 when the mesh is not a point of the structure within some of the unit cells, and the partial differential equation is

Equation

[0019] A further aspect of the present invention is a processing support device. This device is a processing support device for supporting the processing of the inner wall surface of a periodic processing object having a two-dimensional or three-dimensional shape, in which unit cells are arranged periodically, from a specific direction, and comprises a data acquisition unit that acquires data showing the spatial distribution of the shapes of structures in some of the unit cells among all the unit cells constituting the periodic processing object, and a state variable calculation unit that calculates a virtual state variable of the structure in some of the unit cells using a virtual physical model with partial differential equations. The state variable indicates whether or not there is a hole facing a specific direction in the periodic processing object, the data acquisition unit acquires data showing the spatial distribution of the shapes of structures in some of the unit cells using a finite element method that divides the space including the structures in some of the unit cells into a mesh, the state variable is a virtual temperature distribution p, ap is the thermal diffusion coefficient at each point in the space including the structures in some of the unit cells, χ is a characteristic function that takes a value of 0 when the mesh is a point of the structure in some of the unit cells and a value of 1 when the mesh is not a point of the structure in some of the unit cells, and the partial differential equation is

number

[0020] Furthermore, any combination of the above components, as well as conversions of the expression of the present invention between devices, methods, systems, recording media, computer programs, etc., are also valid embodiments of the present invention. [Effects of the Invention]

[0021] According to the present invention, when fabricating a periodic structure using additive manufacturing, it is possible to determine whether or not a closed cavity exists inside the structure with less computational effort. [Brief explanation of the drawing]

[0022] [Figure 1]This is a diagram of a structure with a closed cavity inside. (a) is a perspective view of the structure as seen from the outside. (b) is a perspective view of the structure cut across a plane. (c) is an enlarged view of the cross-section of the structure cut across a plane. [Figure 2] This is a diagram of a structure that does not have any closed cavities inside. (a) is a perspective view of the structure as seen from the outside. (b) is a perspective view of the structure cut through a plane. (c) is an enlarged view of the cross-section of the structure cut through a plane. [Figure 3] This is a photograph showing an example of a lattice structure. [Figure 4] This is a functional block diagram of the design support device according to the first embodiment. [Figure 5] This figure shows four adjacent unit cells in a two-dimensional lattice structure. [Figure 6] Figure 5 shows the closed cavity portion determined based on the state variables calculated by the state variable calculation unit, within the region of Figure 5. [Figure 7] This figure shows another example of four adjacent unit cells in a two-dimensional lattice structure. [Figure 8] Figure 7 shows the closed cavity portion determined based on the state variables calculated by the state variable calculation unit in the region. [Figure 9] This figure shows an example of eight adjacent unit cells in a three-dimensional lattice structure. [Figure 10] This is a functional block diagram of the design support device according to the second embodiment. [Figure 11] This flowchart shows the processing procedure for the design support method according to the third embodiment. [Figure 12] This is a schematic diagram illustrating the fifth embodiment. (a) shows a structure connected to the bottom surface and a structure floating above the bottom surface. (b) shows the structure in (a) when a state variable is applied. [Figure 13]This is a schematic diagram illustrating the sixth embodiment. (a) shows a workpiece with a hole facing a specific direction and a workpiece without a hole facing a specific direction. (b) shows the state when a state variable is applied to the workpiece in (a). [Modes for carrying out the invention]

[0023] The present invention will be described below with reference to the drawings, based on preferred embodiments. The embodiments are illustrative and not limiting. Not all features or combinations thereof described in the embodiments are necessarily essential to the invention. The same or equivalent components, members, and processes shown in each drawing are denoted by the same reference numerals, and redundant explanations are omitted as appropriate. Furthermore, the scale and shape of each part shown in each drawing are set for convenience to facilitate explanation and are not to be interpreted restrictively unless otherwise specified. Also, when terms such as "first," "second," etc. are used in this specification or claims, unless otherwise specified, these terms do not indicate any order or importance, but are merely for distinguishing one configuration from another. In addition, some components that are not important for explaining the embodiments are omitted from the drawings.

[0024] Before describing the specific implementation methods, let's explain the underlying knowledge by referring to Figures 1 and 2. Both Figures 1 and 2 show three-dimensional structures fabricated using additive manufacturing.

[0025] The structure 1 shown in Figure 1 has a closed cavity inside. Figure 1(a) is a perspective view of structure 1 from the outside. In this figure, it is not immediately apparent whether or not a closed cavity exists inside structure 1. Figure 1(b) is a perspective view of structure 1 cut by a plane P1 with constant z. This figure shows that a closed cavity exists within cross-section P1. Figure 1(c) is an enlarged view of the cross-section when structure 1 is cut by a plane with constant z. In this cross-section, five closed cavities H1, H2, H3, H4, and H5 are nested together. After the fabrication of structure 1, the metal powder remaining in these five cavities H1, H2, H3, H4, and H5 cannot be removed. In this sense, structure 1 is not a desirable design.

[0026] The structure 2 shown in Figure 2 does not have any closed cavities inside. Figure 2(a) is a perspective view of structure 2 from the outside. In this figure, it is not immediately apparent whether or not there are closed cavities inside structure 2. Figure 2(b) is a perspective view of structure 2 cut by a plane P2 with constant z. From this figure, it can be seen that there are no closed cavities in the cross section P2. Figure 2(c) is an enlarged view of the cross section of structure 1 when cut by a plane with constant z. In this cross section, there are three cavities H11, H12, and H13. These three cavities H11, H12, and H13 have through holes O11, O12, and O13, respectively. After the fabrication of structure 2, the metal powder remaining in these three cavities H11, H12, and H13 can be removed through the through holes O11, O12, and O13. In this sense, structure 2 is a desirable design.

[0027] As described above, structures fabricated using additive manufacturing can be considered desirable designs if they do not contain any closed cavities inside. In other words, structures fabricated using additive manufacturing can be considered desirable designs if they either have no cavities inside at all, or if cavities exist but these cavities have through-holes that connect to the outside.

[0028] The inventors, after diligent research, discovered that it is possible to determine whether or not a closed cavity exists inside a structure by using a virtual physical model. This physical model includes a scalar-valued function p(x,y,z) defined in a three-dimensional region containing the structure. Hereafter, this scalar-valued function p(x,y,z) will be referred to as the "state variable." For simplicity, the state variable p(x,y,z) may also be abbreviated as simply p. The state variable p(x,y,z) is a scalar field representing a physical quantity related to each point in space. This state variable p(x,y,z) takes a value of 0 in a closed cavity inside the structure and a non-zero value at other points. Therefore, for example, if p(x,y,z)=0 at all points in the region under consideration, then there is no closed cavity inside the structure, and it can be judged that the design is desirable. Conversely, if there is a point in the region under consideration where p(x,y,z)≠0, then there is a closed cavity inside the structure, and it can be judged that the design is not desirable.

[0029] Furthermore, the inventors discovered that this state variable p satisfies the following partial differential equation.

number

number

number

[0030] The state variable p can be likened to a hypothetical temperature distribution in space (though not the temperature itself). In this case, the parameter a in equation (1) p This can be interpreted as the thermal diffusion coefficient of the system. Parameter a pThis is defined at each point. According to equation (2), in a structure (where there is no heat source), heat diffusion is slow, so the temperature rises (heat accumulates), while in a space that is not a structure (where there is a heat source), heat diffusion is fast, so the temperature does not rise (heat does not accumulate). However, parameter a p ￣(a with macron) p ) indicates the thermal diffusion coefficient in a space that is not a structure, and ε p This represents the thermal diffusion coefficient in the structure. χ, defined in equation (3), is also called the characteristic function and determines the geometric shape of the structure. From the above, it can be seen that the state variable p, which can be likened to a hypothetical temperature distribution, has its distribution determined according to equation (1) based on the balance between the diffusion coefficient and the heat source. This invention determines whether or not a closed cavity exists inside a structure, based on the above principle discovered by the inventor, in order to judge the quality of the structure's design.

[0031] (Lattice structure) Here, we will describe a lattice structure as an example of a periodic structure (hereinafter referred to as a "periodic structure"). A lattice structure is a structure in which unit cells (hereinafter referred to as "unit cells") are arranged periodically. Figure 3 is a photograph showing an example of a lattice structure. As shown in this photograph, a lattice structure allows for hollow interiors, making it easy to reduce weight without changing the shape. By adopting such a lattice structure, it is possible to artificially create composite materials with properties different from homogeneous materials (such as ultralightness). Furthermore, the grid-like shape of a lattice structure has excellent properties in terms of strength, elasticity, breathability, and cooling effect. For these reasons, lattice structures are expected to have applications in various industrial fields, starting with the medical and sporting goods fields.

[0032] Another excellent characteristic of lattice structures is that the structure is simple because the unit cells are arranged periodically. This offers the advantage that, for example, when calculating state variables using the method described above, calculations only need to be performed on a very limited number of unit cells, rather than performing calculations on the entire periodic structure (lattice structure) in question. As a result, the amount of computation can be significantly reduced.

[0033] [First Embodiment] Figure 4 shows the functional blocks of the design support device 10 according to the first embodiment. The design support device 10 includes a data acquisition unit 12 and a state variable calculation unit 14.

[0034] Hereafter, when we refer to a periodic structure, we mean a two-dimensional or three-dimensional periodic structure composed of unit cells arranged periodically.

[0035] The data acquisition unit 12 acquires data showing the spatial distribution of the shapes of structures within some of the unit cells that make up the periodic structure. For example, if the target periodic structure is a two-dimensional periodic structure composed of 1000 unit cells, the data acquisition unit 12 acquires data showing the spatial distribution of the shapes of structures within four adjacent unit cells from among those 1000 unit cells. Data showing the spatial distribution of shapes is data showing the distribution of the presence or absence of shapes in space. Such data includes pixel data of shapes, voxel data, and polygon data in STL format, for example. Such data may be input by a user using an input means, or it may be automatically input by a computer-controlled data input means.

[0036] The state variable calculation unit 14 calculates virtual state variables of the structure within the unit cell from which data was acquired, using a virtual physical model based on partial differential equations. The state variables calculated in this way indicate whether or not a closed cavity exists within the portion of the periodic structure in which the unit cell from which data was acquired exists. By arranging and reconstructing the portions in which the presence or absence of a closed cavity has been revealed according to the periodicity of the periodic structure, it is possible to determine whether or not a cavity exists throughout the entire periodic structure.

[0037] Here, the inventors have found that if the periodic structure takes the form of a two-dimensional lattice structure, then the unit cells used to acquire data only need to be four adjacent unit cells.

[0038] Figure 5 shows four adjacent unit cells in a two-dimensional lattice structure. In Figure 5, the areas shown in black are where material is present, and the areas shown in white are where material is absent. A slight outer boundary is provided around the perimeter of the region enclosed by the four unit cells, and this boundary is used as the boundary condition to evaluate whether a closed cavity exists within that region.

[0039] Figure 6 shows the closed cavities determined by the state variable calculation unit 14 based on the state variables calculated for the region shown in Figure 5. As shown in Figure 6, there are four closed cavities in the structure within this region. By arranging and reconstructing the regions where the presence or absence of closed cavities has been revealed in this way, according to the periodicity of the periodic structure, it is possible to determine whether or not cavities exist throughout the entire original periodic structure.

[0040] Thus, even in the case of a two-dimensional periodic structure composed of a large number of unit cells, such as 1000, it is possible to determine the presence or absence of closed cavities in the entire periodic structure by calculating state variables for only four adjacent unit cells from among those 1000 unit cells. In other words, in the case of a two-dimensional shape, it is sufficient to calculate state variables for four unit cells arranged two adjacently in the x direction and two adjacently in the y direction.

[0041] Figure 7 shows four adjacent unit cells in a two-dimensional lattice structure, a different example from that in Figure 5. Figure 8 shows the closed cavities determined by the state variable calculation unit 14 based on the state variables calculated for the region in Figure 7. As shown in Figure 8, there are four closed cavities in this region.

[0042] Furthermore, the inventors have discovered that when a periodic structure takes the form of a three-dimensional lattice structure, the unit cells from which data is acquired only need to be eight adjacent unit cells. Figure 9 shows eight adjacent unit cells in a three-dimensional lattice structure. That is, as shown in Figure 9, in the case of a three-dimensional shape, state variables are calculated for eight unit cells arranged in a sequence of two adjacent units in the x-direction, two adjacent units in the y-direction, and two adjacent units in the z-direction.

[0043] According to this embodiment, when fabricating a periodic structure with a two-dimensional or three-dimensional shape, composed of unit cells arranged periodically, using additive manufacturing, it is possible to determine whether or not a closed cavity exists inside with a small amount of computation.

[0044] In one embodiment, the data acquisition unit 12 may acquire data showing the spatial distribution of the shapes of structures within a unit cell using a finite element method that divides the space containing the unit cell into a mesh. The space containing the unit cell may be any shape, such as a cube, a rectangular prism, a triangular pyramid, a sphere, or a spheroid. The shape of the mesh may be any simple shape that can be mathematically represented, such as a triangle or quadrilateral in two dimensions, or a tetrahedron or hexahedron in three dimensions.

[0045] According to this embodiment, even if the unit cells have a complex shape, data showing their spatial distribution can be flexibly acquired.

[0046] In one embodiment, the state variables are a hypothetical temperature distribution p and a thermal diffusion coefficient at each point in the space including the structure within the unit cell. p Let the characteristic function χ be a function that takes a value of 1 when the mesh is a point of a structure within this unit cell and a value of 0 when the mesh is not a point of a structure within this unit cell. In this case, the aforementioned partial differential equation is

number

[0047] According to this embodiment, a design support device can be configured by specifically defining partial differential equations.

[0048] In one embodiment, the diffusion coefficient in the non-structural space within the unit cell is a p The diffusion coefficient in the structure within the unit cell is ε p Let L be the value that characterizes the space containing the structure within the unit cell. However, a p The value of ￣ is ε p It is greater than the value of a. At this time, the thermal diffusion coefficient is a p teeth,

number

[0049] According to this embodiment, the thermal diffusion coefficient can be specifically defined, and a design support device can be configured accordingly.

[0050] [Second Embodiment] Figure 10 shows the functional blocks of the design support device 20 according to the first embodiment. The design support device 10 comprises a data acquisition unit 12, a state variable calculation unit 14, and a determination unit 22. In other words, the design support device 20 includes the determination unit 22 in addition to the configuration of the design support device 10 in Figure 3. The other configurations and operations of the design support device 20 are the same as those of the design support device 10. Hereafter, explanations of parts that overlap with the design support device 10 will be omitted as appropriate, and the explanation will focus on the differences.

[0051] The judgment unit 22 determines the quality of the design of the periodic structure based on the state variables calculated by the state variable calculation unit 14. As mentioned above, the calculated state variables take a value of 0 within closed cavities inside the periodic structure and a non-zero value where they are not. Therefore, the closer the physical quantity within the region under consideration is to 0, the fewer closed cavities there are inside the periodic structure, and thus the better the design can be judged. Conversely, the further the physical quantity within the region under consideration is from 0, the more closed cavities there are inside the periodic structure, and thus the worse the design can be judged. In other words, the judgment unit 22 determines the quality of the design based on the magnitude of the calculated state variables.

[0052] According to this embodiment, the quality of the design of a periodic structure can be judged based on the calculated physical quantities.

[0053] In one embodiment, the determination unit 22 calculates the maximum value of the state variable, and if the calculated maximum value of the state variable is smaller than a predetermined threshold, it determines that the design of the periodic structure is good. Generally, the calculated state variable takes different values ​​at each point. Therefore, by comparing the values ​​of all the calculated state variables, if the maximum value is smaller than a predetermined threshold, it can be determined that the design of the periodic structure is good.

[0054] According to this embodiment, since the quality of the periodic structure is determined by considering all calculated state variables, an accurate judgment can be obtained.

[0055] In one embodiment, the determination unit 22 determines that the design of the periodic structure is good if the average value of the calculated state variables is smaller than a predetermined threshold. In this embodiment, instead of comparing the values ​​of all the calculated state variables, the design of the periodic structure is determined to be good by comparing its average value with a predetermined threshold. This has the advantage of requiring less computation compared to the case where the maximum value of the state variables is used.

[0056] According to this embodiment, the quality of a periodic structure can be determined with less computation, thus enabling faster determination or requiring fewer computing resources.

[0057] [Third Embodiment] Figure 11 shows a flowchart illustrating the processing procedure of a design support method according to the third embodiment. This design support method comprises step S1 and step S2.

[0058] In step S1, this method uses a data acquisition unit to acquire data showing the spatial distribution of the shapes of structures within some of the unit cells that make up the periodic structure.

[0059] In step S2, this method uses a state variable calculation unit to calculate virtual state variables for structures within some unit cells using a virtual physical model based on partial differential equations. The state variables indicate whether or not a closed cavity exists inside the structure.

[0060] The data acquisition unit uses a finite element method to divide the space containing structures within some unit cells into a mesh and acquires data showing the spatial distribution of the shapes of structures within some unit cells. The state variable is a hypothetical temperature distribution p. p χ is the thermal diffusion coefficient at each point in the space containing structures within some unit cells. χ is a characteristic function that takes a value of 1 when the mesh is a point in the structure within some unit cells, and a value of 0 when the mesh is not a point in the structure within some unit cells. The partial differential equation is:

number

[0061] According to this embodiment, it is possible to determine whether or not a closed cavity exists inside a periodic structure fabricated by additive manufacturing.

[0062] [Fourth Embodiment] The fourth embodiment is a computer program. This program causes the computer to execute steps S1 and S2.

[0063] In step S1, the program uses the data acquisition unit to acquire data showing the spatial distribution of the shapes of structures within some of the unit cells that make up the periodic structure.

[0064] In step S2, the program uses a state variable calculation unit to calculate virtual state variables for some of the structures within a unit cell using a virtual physical model based on partial differential equations. The state variables indicate whether or not a closed cavity exists inside the structure.

[0065] The data acquisition unit uses a finite element method to divide the space containing structures within some unit cells into a mesh and acquires data showing the spatial distribution of the shapes of structures within some unit cells. The state variable is a hypothetical temperature distribution p. p χ is the thermal diffusion coefficient at each point in the space containing structures within some unit cells. χ is a characteristic function that takes a value of 1 when the mesh is a point in the structure within some unit cells, and a value of 0 when the mesh is not a point in the structure within some unit cells. The partial differential equation is:

number

[0066] According to this embodiment, a computer can be used to determine whether or not a closed cavity exists inside a periodic structure fabricated by additive manufacturing.

[0067] [Fifth Embodiment] When designing structures, it is sometimes necessary that the structure be connected to a fixed surface such as the ground or a wall. For example, a freestanding building or object must be connected to the ground so that it can stand on its own. Or, shelves or signs must be connected to a wall so that they can be fixed in place. In such cases, the structure must not be floating above the fixed surface, but must be connected to a fixed surface in some way. This is equivalent to the condition in the aforementioned embodiment of additive manufacturing, where there must be no completely closed void inside the structure, and there must always be a through-hole somewhere that connects to the outside.

[0068] Using Figure 12, we will explain the principle that supports the design of self-supporting structures. Structure 3, shown in Figure 12(a), is connected to the base surface G1 via a connecting surface G2. On the other hand, structures 4 and 5 are floating above the base surface G1. In order to realize a self-supporting structure on the base surface G1, it is necessary to select structure 3 and eliminate structures 4 and 5 during the design phase.

[0069] Figure 12(b) schematically shows what happens when the state variable p is applied to the structure in Figure 12(a). However, in this embodiment, the cavities in the additive manufacturing process described above are replaced with regions where the structure exists. That is, the through-holes in the additive manufacturing process correspond to the connection surfaces between the structure and the fixed surface in this embodiment. If the state variable p is likened to a hypothetical temperature distribution in space, as shown in Figure 12(b), heat is diffused to the bottom surface G1 through the connection surface G2 in structure 3. On the other hand, in structures 4 and 5, there are no connection surfaces, so heat is trapped.

[0070] Based on the above findings, a fifth embodiment will be described using Figure 4. The fifth embodiment is a design support device for assisting in the design of periodic structures connected to fixed surfaces such as the ground or walls. Figure 4 shows the functional blocks of the design support device 10 according to the fifth embodiment. The design support device 10 comprises a data acquisition unit 12 and a state variable calculation unit 14.

[0071] The data acquisition unit 12 acquires data showing the spatial distribution of the shapes of structures within some of the unit cells that make up the periodic structure. The state variable calculation unit 14 calculates virtual state variables for the structures within these some unit cells using a virtual physical model based on partial differential equations. At this time, the calculated state variables indicate whether or not there are surfaces connected to fixed surfaces in the periodic structure.

[0072] As before, the state variable is assumed to be a hypothetical temperature distribution p, and the thermal diffusion coefficient at each point in the space containing the structure within the unit cell is a. p Let's assume that the partial differential equation in p is

number

number

[0073] According to this embodiment, with regard to the design of a periodic structure connected to a fixed surface, it is possible to determine whether or not there is a surface on the structure that is connected to the fixed surface.

[0074] [Sixth Embodiment] When processing the inner wall surface of a structure that is partially enclosed by walls using a tool, it is necessary to insert the processing tool into the interior of the structure toward the surface to be processed. For example, when processing the inner wall surface by milling, an end mill is inserted toward the processing surface; when spray painting the inner wall surface, a nozzle is inserted toward the painting surface; and when cleaning the inner wall surface, a cleaner is inserted toward the cleaning surface. In such cases, the wall on the side facing the surface to be processed is not closed, and there must be a hole for inserting the tool. This corresponds to the aforementioned embodiment of additive manufacturing, where there is no completely closed cavity inside the structure, and there is always a through-hole that connects to the outside. However, while the through-hole for removing metal powder in additive manufacturing could face any direction, the hole in this embodiment must face a specific direction (i.e., toward the processing surface).

[0075] Using Figure 13, we will explain the principle that supports machining the inner wall surface of a workpiece from a certain direction. Here, we consider a milling operation in which the end mill 8 is inserted in the y-axis direction, given that the x and y axes are defined as shown in the figure. In the workpiece 6 shown in Figure 13(a), there is a hole H100 near the center into which the end mill 8 can be inserted in the y-axis direction. On the other hand, the workpiece 7 does not have a hole into which the end mill 8 can be inserted in the y-axis direction (however, there is a hole H200 facing the x-axis direction, so it is possible to insert the end mill 8 in the x-axis direction and machine in the x-axis direction).

[0076] Figure 13(b) schematically shows what happens when the aforementioned state variable p is applied to the structure in Figure 13(a). However, in this case, the thermal diffusivity coefficient of the state variable p represents only thermal diffusion in the y-axis direction. In other words, the thermal diffusivity coefficient in this embodiment is anisotropic, not isotropic. In this case, the hole H100 in the y-axis direction of the workpiece corresponds to a through hole in additive manufacturing. If we liken the state variable p to a hypothetical temperature distribution in space, as shown in Figure 13(b), in workpiece 6, heat diffuses from the space below the hole H100 through the hole H100, but heat is trapped in the space below the part outside the hole H100. On the other hand, in workpiece 7, there is no hole facing the y-axis direction, so heat does not diffuse in the y-axis direction, and heat is trapped throughout the entire space. Therefore, when considering machining in which the end mill 8 is inserted in the y-axis direction, it can be seen that there are unmachinable regions in workpiece 6 and workpiece 7 as shown in Figure 13(b).

[0077] Based on the above findings, a sixth embodiment will be described using Figure 4. The sixth embodiment is a processing support device for assisting in processing the inner wall surface of an object to be processed from a specific direction. Figure 4 shows the functional blocks of the processing support device 10 according to the fifth embodiment (in Figure 4, "design support device" should be read as "processing support device"). The processing support device 10 comprises a data acquisition unit 12 and a state variable calculation unit 14.

[0078] The data acquisition unit 12 acquires data showing the spatial distribution of the shapes of structures within some of the unit cells that make up the object to be periodically processed. The state variable calculation unit 14 calculates virtual state variables for the structures within some of the unit cells using a virtual physical model based on partial differential equations. The state variables calculated at this time indicate whether or not there are holes facing a specific direction in the object to be periodically processed.

[0079] As mentioned above, the state variables are the hypothetical temperature distribution p and the thermal diffusion coefficient at each point in the space including the structure within the unit cell, a. pLet the characteristic function χ be a function that takes a value of 0 when the mesh is a point of a structure within a unit cell and a value of 1 when the mesh is not a point of a structure within a unit cell. In this case, the aforementioned partial differential equation is

number

[0080] According to this embodiment, it is possible to determine whether or not processing is possible when processing the inner wall surface of an object to be periodically processed from a specific direction. In particular, this embodiment is considered to be extremely useful when it is not possible to directly perceive, such as with the naked eye or ultrasound, whether or not there is a hole for inserting a processing tool.

[0081] In the above example, the machining direction was assumed to be the y-axis direction. However, it is not limited to this, and the machining direction can be any direction. That is, the diffusion coefficient a p By changing the direction of heat diffusion represented by , the processing direction can be taken in any direction. In particular, the diffusion coefficient a p By setting multiple heat diffusion directions represented by [a specific formula / method] and repeatedly applying them, it is possible to determine whether machining is feasible from multiple directions. This method can be applied, for example, to multi-axis machining, and is therefore extremely useful in industry.

[0082] The present invention has been described above based on examples. These examples are illustrative, and it will be understood by those skilled in the art that various modifications are possible in combinations of their components and processing processes, and that such modifications also fall within the scope of the present invention.

[0083] In the above embodiment, the state variable p was likened to a hypothetical temperature distribution in space. However, the state variable p is not limited to this, and may be likened to any suitable distribution of physical quantities, such as a hypothetical potential distribution, pressure distribution, or strain distribution in space. In this case, an appropriate partial differential equation corresponding to each physical quantity is applied.

[0084] The modified form produces the same functions and effects as the embodiment.

[0085] Any combination of the embodiments and modifications described above is also useful as an embodiment of the present invention. The new embodiments resulting from these combinations possess the combined effects of each of the embodiments and modifications that are combined. [Explanation of Symbols]

[0086] 1...Structure 2...Structures 3...Structures 4...Structures 5...Structures 6. Object to be processed 7. Object to be processed 8 End Mills 10...Design support equipment 12. Data Acquisition Unit 14. State Variable Calculation Unit 22... Judgment Department 20...Design support equipment S1... A step to obtain data showing the spatial distribution of the shape of the structure. S2 - Step to calculate the virtual state variables of the structure. H1·Cavity H2·Cavity H3·Cavity H4··Hollow H5·Cavity H11·Cavity H12·Cavity H13·Cavity O11...Through hole O12...Through hole O13...Through hole G1...Fixed surface G2 connection surface H100...hole H200··hole

Claims

1. A design support device for assisting in the design of a periodic structure with a two-dimensional or three-dimensional shape, which is composed of unit cells arranged periodically, when fabricating it using a layered structure, A data acquisition unit that acquires data showing the spatial distribution of the shapes of structures within some of the unit cells that constitute the periodic structure, The system includes a state variable calculation unit that calculates virtual state variables of structures within some of the unit cells using a virtual physical model based on partial differential equations, The aforementioned state variable indicates whether or not a closed cavity exists inside the periodic structure. The data acquisition unit acquires data showing the spatial distribution of the shapes of structures within the partial unit cells using a finite element method that divides the space including the partial unit cells into a mesh. The aforementioned state variable is a hypothetical temperature distribution p, a ｐ This is the thermal diffusion coefficient at each point in the space including the structure within some of the unit cells, χ is a characteristic function that takes a value of 1 when the mesh is a point of a structure within the unit cell, and a value of 0 when the mesh is not a point of a structure within the unit cell. The aforementioned partial differential equation is [Math 1] A design support device characterized by being represented as such.

2. The aforementioned periodic structure takes the form of a two-dimensional lattice structure. The design support device according to claim 1, characterized in that the aforementioned part of the unit cells are four adjacent unit cells.

3. The aforementioned periodic structure takes the form of a three-dimensional lattice structure. The design support device according to claim 1, characterized in that the aforementioned part of the unit cells are eight adjacent unit cells.

4. a p ￣ is the diffusion coefficient in the non-structural space within the aforementioned part of the unit cell, ε p This is the diffusion coefficient in the structure within the aforementioned part of the unit cell, a p The value of ￣ is ε p Greater than the value, L is a value that characterizes the space including the structures within some of the unit cells, The thermal diffusion coefficient a ｐ teeth [Math 2] The design support device according to claim 1, characterized by being represented as follows.

5. The design support device according to claim 1, further comprising a determination unit that determines whether the design of the periodic structure is good or bad based on the state variables.

6. The design support device according to claim 5, characterized in that the determination unit calculates the maximum value of the state variable, and if the calculated maximum value of the state variable is smaller than a predetermined threshold, it determines that the design of the periodic structure is good.

7. The design support device according to claim 5, characterized in that the determination unit calculates the average value of the state variables, and if the calculated average value of the state variables is smaller than a predetermined threshold, it determines that the design of the periodic structure is good.

8. A design support method for assisting in the design of a periodic structure with a two-dimensional or three-dimensional shape, composed of unit cells arranged periodically, when fabricating it using a layered structure, The steps include: using a data acquisition unit to acquire data showing the spatial distribution of the shapes of structures within some of the unit cells that constitute the periodic structure; The system includes a step of using a state variable calculation unit to calculate virtual state variables of structures within some of the unit cells using a virtual physical model based on partial differential equations, The aforementioned state variable indicates whether or not a closed cavity exists inside the periodic structure. The data acquisition unit acquires data showing the spatial distribution of the shapes of the structures within the unit cells using a finite element method that divides the space including the structures within the unit cells into a mesh. The aforementioned state variable is a hypothetical temperature distribution p, a ｐ This is the thermal diffusion coefficient at each point in the space including the structure within some of the unit cells, χ is a characteristic function that takes a value of 1 when the mesh is a point of a structure within the unit cell, and a value of 0 when the mesh is not a point of a structure within the unit cell. The aforementioned partial differential equation is [Math 1] A design support method characterized by being represented as follows.

9. A design support program for assisting in the design of a periodic structure with a two-dimensional or three-dimensional shape, composed of unit cells arranged periodically, when fabricating it using a layered structure, The steps include: using a data acquisition unit to acquire data showing the spatial distribution of the shapes of structures within some of the unit cells that constitute the periodic structure; The computer is instructed to perform the following steps: using a state variable calculation unit, calculate virtual state variables of the structures within some of the unit cells using a virtual physical model based on partial differential equations; The aforementioned state variable indicates whether or not a closed cavity exists inside the periodic structure. The data acquisition unit acquires data showing the spatial distribution of the shapes of the structures within the unit cells using a finite element method that divides the space including the structures within the unit cells into a mesh. The aforementioned state variable is a hypothetical temperature distribution p, a ｐ This is the thermal diffusion coefficient at each point in the space including the structure within some of the unit cells, χ is a characteristic function that takes a value of 1 when the mesh is a point of a structure within the unit cell, and a value of 0 when the mesh is not a point of a structure within the unit cell. The aforementioned partial differential equation is [Math 1] A design support program characterized by being represented as follows.

10. A design support device for assisting in the design of a periodic structure having a two-dimensional or three-dimensional shape, composed of unit cells arranged periodically, and connected to a fixed surface, A data acquisition unit that acquires data showing the spatial distribution of the shapes of structures within some of the unit cells that constitute the periodic structure, The system includes a state variable calculation unit that calculates virtual state variables of structures within some of the unit cells using a virtual physical model based on partial differential equations, The state variable indicates whether or not there is a surface in the periodic structure that is connected to the fixed surface. The data acquisition unit acquires data showing the spatial distribution of the shapes of the structures within the unit cell using a finite element method that divides the space including the structures within the unit cell into a mesh. The aforementioned state variable is a hypothetical temperature distribution p, a ｐ is the thermal diffusion coefficient at each point in the space including the structure within the unit cell, χ is a characteristic function that takes a value of 0 when the mesh is a point of a structure within the unit cell, and a value of 1 when the mesh is not a point of a structure within the unit cell. The aforementioned partial differential equation is [Math 1] A design support device characterized by being represented as such.

11. A processing support device for assisting in the processing of the inner wall surface of a periodically processed object having a two-dimensional or three-dimensional shape, in which unit cells are arranged periodically, from a specific direction, A data acquisition unit that acquires data showing the spatial distribution of the shapes of structures within some of the unit cells among all the unit cells that constitute the object to be periodically processed, The system includes a state variable calculation unit that calculates virtual state variables of structures within some of the unit cells using a virtual physical model based on partial differential equations, The state variable indicates whether or not there is a hole facing the specific direction in the object to be periodically processed. The data acquisition unit acquires data showing the spatial distribution of the shapes of the structures within the unit cell using a finite element method that divides the space including the structures within the unit cell into a mesh. The aforementioned state variable is a hypothetical temperature distribution p, a ｐ This is the thermal diffusion coefficient at each point in the space including the structure within the unit cell, χ is a characteristic function that takes a value of 0 when the mesh is a point of a structure within the unit cell, and a value of 1 when the mesh is not a point of a structure within the unit cell. The aforementioned partial differential equation is [Math 1] A processing support device characterized by being represented as such.

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