WO2018221722A1

WO2018221722A1 - 3d model generation device, 3d model generation method, 3d model generation program, structure, and structure manufacturing method

Info

Publication number: WO2018221722A1
Application number: PCT/JP2018/021161
Authority: WO
Inventors: 裕之安河内; 建太郎添田; 博祐鈴木
Original assignee: 国立大学法人東京大学
Priority date: 2017-06-01
Filing date: 2018-06-01
Publication date: 2018-12-06

Abstract

Provided is a 3D model generation device that generates 3D model data of a structure which has a cross-section shape that is suited to layered shaping and which has a density distribution that continuously changes according to the amount of voids. The 3D model generation device comprises: a determination unit that determines the value of a first parameter which varies spatially so that the value decreases as the density of a structure 100 increases and the value increases as the density decreases; and a generation unit that generates, in accordance with an inequality containing a periodic function in which the value is determined depending on the first parameter using a coordinate value that indicates a point in space as a variable, 3D model data which designates whether to layer a shaping material at the point in space.

Description

3D model generation device, 3D model generation method, 3D model generation program, structure and method of manufacturing structure

The present invention relates to a 3D model generation device, a 3D model generation method, a 3D model generation program, a structure, and a method for manufacturing the structure.

Conventionally, in order to optimize the structure of a structure according to the stress distribution etc., the size and shape of the structure may be optimized, or the phase (topology) such as the number of holes in the structure may be optimized. .

The following Patent Document 1 describes a design support device that analyzes a rigid structure by a finite element method and a phase optimization process so as to suppress thermal deformation of a resin molded product constrained at at least one restraint point. Yes.

JP 2012-226630 A

In recent years, so-called 3D printers, which manufacture structures by laminating molding materials such as resins, have begun to spread. By using a 3D printer, it is possible to manufacture a structure having a three-dimensionally complicated structure, which has been difficult to manufacture by injection molding or machining.

∙ A three-dimensionally complex structure may be designed with the aid of a computer. For example, assuming a model in which the density of a structure changes continuously, an optimal density distribution may be obtained according to a stress distribution or the like.

However, even when an optimum density distribution is obtained, it is difficult to actually manufacture a structure having a density distribution that continuously changes. In addition, the meat is often thinned so as to approximately reproduce the optimum density distribution. However, with such a structure, the expected performance may not be obtained. In addition, a structure that has been roughly cut out may have isolated points in the cross section, and may not always be suitable for manufacturing by a 3D printer.

Therefore, the present invention provides a 3D model generation apparatus, a 3D model generation method, and a 3D model, which generate 3D model data of a structure having a cross-sectional shape suitable for additive manufacturing and having a density distribution that continuously changes depending on the number of voids. A generation program, a structure, and a method for manufacturing the structure are provided.

The 3D model generation device according to one aspect of the present invention includes a determination unit that determines the value of the first parameter that changes spatially so that the value is smaller as the density of the structure is larger and as the density is smaller. A generating unit that generates 3D model data for specifying whether or not to stack a modeling material on a spatial point according to an inequality including a periodic function in which a coordinate value representing the spatial point is a variable and a value is determined depending on a first parameter; .

According to this aspect, the value of the first parameter is determined according to the density of the structure, and the 3D model data is generated according to the inequality including the periodic function whose value is determined depending on the first parameter. 3D model data of a structure having a suitable cross-sectional shape and having a density distribution that continuously changes depending on the number of voids is generated.

In the above aspect, the first parameter includes a plurality of components corresponding to a plurality of directions, and the determining unit determines that the higher the density is, the smaller the geometric mean value of the plurality of components of the first parameter is; The generating unit determines a plurality of components of the first parameter based on a first condition that relates the density and the plurality of components of the first parameter so that a geometric mean value of the plurality of components of one parameter increases. The 3D model data may be generated according to an inequality including a periodic function in which the coordinate value is a variable and the value is determined depending on a plurality of components of the first parameter.

According to this aspect, the geometric average value of the plurality of components of the first parameter is determined according to the density of the structure, and the 3D model is included according to the inequality including the periodic function whose value is determined depending on the plurality of components of the first parameter. By generating data, 3D model data of a structure having a larger number of voids at a portion where the density is desired to be reduced and a smaller number of voids at a portion where the density is desired to be increased is generated.

In the above aspect, the coordinate value in the orthogonal coordinate system is represented as (x, y, z), and the plurality of components of the first parameter are represented by Tx (x, y, z), Ty (x, y, z), Tz (x , Y, z), the density distribution is represented as D (x, y, z), and the minimum period that can be modeled when stacking the modeling material is expressed as T _min .

It may be expressed as

In the above aspect, the determining unit has a smaller geometric mean value of the plurality of components of the first parameter at a location where the Mises stress calculated from the stress distribution of the structure is large, and a plurality of components of the first parameter at a location where the Mises stress is small. The plurality of components of the first parameter are determined based on the second condition that relates the Mises stress and the plurality of components of the first parameter so that the geometric mean value of The coordinate value may be a variable, and may be generated according to an inequality including a periodic function whose value is determined depending on a plurality of components of the first parameter.

According to this aspect, the geometric mean value of the plurality of components of the first parameter is determined according to the Mises stress applied to the structure, and the periodic function whose value is determined depending on the plurality of components of the first parameter is included. By generating the 3D model data according to the inequality, 3D model data of a structure having a smaller gap at a portion where the Mises stress is smaller and a smaller void at a portion where the Mises stress is larger is generated.

In the above aspect, the coordinate value in the orthogonal coordinate system is represented as (x, y, z), and the plurality of components of the first parameter are represented by Tx (x, y, z), Ty (x, y, z), Tz (x , Y, z), Mises stress is represented by σ _vm (x, y, z), and the conversion coefficient is represented by R (σ _vm ), the second condition is

May be expressed.

In the above aspect, the determination unit may determine the plurality of components of the first parameter based on the third condition relating the anisotropy of the elastic modulus distribution of the structure and the ratio of the plurality of components of the first parameter. Good.

According to this aspect, the ratio of the plurality of components of the first parameter is determined based on the anisotropy of the elastic modulus distribution of the structure, and the periodic function whose value is determined depending on the plurality of components of the first parameter is included. By generating 3D model data according to the inequality, 3D model data of a structure having a desired anisotropic elastic modulus is generated.

In the above aspect, when the plurality of vertical components of the elastic modulus distribution are expressed as Kx (x, y, z), Ky (x, y, z), Kz (x, y, z), the third condition is

May be expressed.

In the above aspect, the determination unit may determine the plurality of components of the first parameter based on the fourth condition relating the anisotropy of the stress distribution of the structure and the ratio of the plurality of components of the first parameter. .

According to this aspect, the ratio of the plurality of components of the first parameter is determined based on the anisotropy of the stress distribution applied to the structure, and the periodic function whose value is determined depending on the plurality of components of the first parameter By generating 3D model data according to an inequality including, 3D model data of a structure having a smaller elastic modulus in a direction in which applied stress is larger is generated.

In the above aspect, when the shear stress distribution of the structure is expressed as σxy (x, y, z), σyz (x, y, z), σzx (x, y, z), the fourth condition is

May be expressed.

In the above aspect, the determining unit determines the second parameter based on the stress distribution of the structure so that the second parameter is smaller as the stress distribution is larger and the second parameter is larger as the stress distribution is smaller. The generation unit may generate the 3D model data according to an inequality in which a plurality of terms are weighted by the second parameter.

According to this aspect, the second parameter is determined based on the stress distribution applied to the structure, and the 3D model data is generated according to the inequality in which the plurality of terms are weighted by the second parameter, thereby applying the applied stress. 3D model data of a structure whose elastic modulus changes spatially according to the distribution is generated.

In the above aspect, the second parameter includes a plurality of components corresponding to a plurality of directions, and the determining unit determines whether the stress distribution anisotropy and the ratio of the values of the plurality of components of the second parameter are related to the fifth condition. Based on this, a plurality of components of the second parameter may be determined.

According to this aspect, the ratio of the plurality of components of the second parameter is determined based on the anisotropy of the stress distribution applied to the structure, and the plurality of terms are weighted by the plurality of components of the second parameter. By generating the 3D model data according to the inequality, the 3D model data of the structure whose elastic modulus changes anisotropically according to the anisotropy of the applied stress distribution is generated.

In the above aspect, the coordinate value in the orthogonal coordinate system is represented as (x, y, z), and the plurality of components of the second parameter are represented by Bx (x, y, z), By (x, y, z), Bz (x , Y, z), and when the vertical stress distribution of the structure is represented as σxx (x, y, z), σyy (x, y, z), σzz (x, y, z), the fifth condition is

May be expressed.

In the above aspect, the coordinate value in the orthogonal coordinate system is represented as (x, y, z), and the plurality of components of the first parameter are represented by Tx (x, y, z), Ty (x, y, z), Tz (x , Y, z), a periodic function of the period T as F, and a plurality of components of the second parameter as Bx (x, y, z), By (x, y, z), Bz (x, y, z), and when the third parameter equal to or greater than 0 is represented as A (x, y, z), the inequality is

May be expressed.

In the above aspect, the 3D model data may include designation of a drawing width when stacking modeling materials.

According to this aspect, the width of the modeling material when the modeling materials are stacked can be specified by specifying the drawing width, and the density of the structure can be adjusted from a viewpoint different from the first parameter and the like.

In the above aspect, the generation unit may generate the 3D model data according to a plurality of inequalities having different values of at least the first parameter.

According to this aspect, by generating 3D model data according to a plurality of inequalities, it is possible to generate 3D model data of a structure in which a plurality of characteristics are superimposed.

In the above aspect, the periodic function may be a function representing a sine wave or a triangular wave.

In the above aspect, a conversion unit that performs coordinate conversion may be further provided before the value of the first parameter is determined by the determination unit.

In the above aspect, the conversion unit may perform coordinate conversion so as to diagonalize the stress distribution of the structure.

In the 3D model generation method according to another aspect of the present invention, the step of determining the value of the first parameter that varies spatially is such that the smaller the density of the structure is, the larger the density is. Generating 3D model data for designating whether or not to stack a modeling material on a spatial point according to an inequality including a periodic function whose value depends on a first parameter, with coordinate values representing the spatial point as variables. including.

A 3D model generation program according to another aspect of the present invention is such that a computer provided in a 3D model generation apparatus has a smaller first parameter value that varies spatially as the density of a structure increases, and the density decreases. A decision unit that decides to be larger as a location, and 3D model data that specifies whether or not to stack a modeling material on a spatial point, a coordinate value representing the spatial point as a variable, and a value depending on the first parameter It functions as a generation unit that generates according to an inequality including a determined periodic function.

In the structure according to another aspect of the present invention, the coordinate value in the orthogonal coordinate system is represented as (x, y, z), and the plurality of components of the first parameter are represented by Tx (x, y, z), Ty (x, y, z), Tz (x, y, z), a periodic function of the period T as F, and a plurality of components of the second parameter as Bx (x, y, z), By (x, y, z). ), Bz (x, y, z), and when the third parameter of 0 or more is represented as A (x, y, z), the inequality

There is a modeling material in a location that satisfies the condition, and there is a void in a location that does not satisfy the inequality.

According to this aspect, a structure having a cross-sectional shape suitable for additive manufacturing and having a density distribution continuously changing due to the number of voids is formed.

In the structure according to another aspect of the present invention, in any cut surface, the modeling material is continuously present, and in the cut surface, there is a gap between the modeling materials, and the gap is open to the outside. When the cut surface is continuously shifted in an arbitrary direction, the distribution of the modeling material continuously changes, and the modeling material and the gap exist in a spatially changing period.

In the above aspect, the surface of the modeling material may be coated with a material different from the modeling material.

According to this aspect, by forming the skeleton of the structure with the modeling material and covering the surface with a material different from the modeling material, it is possible to obtain a structure having various characteristics that are difficult to realize with only the modeling material.

In the method of manufacturing a structure according to another aspect of the present invention, a coordinate value in an orthogonal coordinate system in which the stacking direction is z is represented as (x, y, z), and a plurality of components of the first parameter are represented by Tx (x , Y, z), Ty (x, y, z), Tz (x, y, z), a periodic function of the period T as F, and a plurality of components of the second parameter as Bx (x, y, z). z), By (x, y, z), Bz (x, y, z), and z representing the height in the stacking direction when the third parameter of 0 or more is represented as A (x, y, z). The value of the inequality

And the step of laminating a modeling material at a location (x, y) that satisfies the inequality is included.

According to this aspect, by manufacturing the structure according to the above inequality, the layered modeling can be easily performed in the step of stacking the modeling material, and the structure in which the density distribution continuously changes due to the number of gaps is manufactured. Is done.

According to the present invention, a 3D model generation apparatus, a 3D model generation method, and a 3D model that generate 3D model data of a structure that has a cross-sectional shape suitable for additive manufacturing and whose density distribution continuously changes due to the number of voids. A generation program, a structure, and a method for manufacturing the structure can be provided.

It is a network block diagram of the 3D model production | generation apparatus which concerns on embodiment of this invention. It is a functional block diagram of the 3D model production | generation apparatus which concerns on embodiment of this invention. It is a flowchart of the process which determines the 1st parameter performed by the 3D model production | generation apparatus which concerns on embodiment of this invention. It is a flowchart of the process which produces | generates the 3D model performed by the 3D model production | generation apparatus which concerns on embodiment of this invention. It is a perspective view of the 3D model produced | generated by the 3D model production | generation apparatus which concerns on embodiment of this invention. It is a top view of the 3D model produced | generated by the 3D model production | generation apparatus which concerns on embodiment of this invention. It is a flowchart which shows the manufacturing method of the structure which concerns on embodiment of this invention. It is a figure which shows the structure which concerns on embodiment of this invention.

Embodiments of the present invention will be described with reference to the accompanying drawings. In addition, in each figure, what attached | subjected the same code | symbol has the same or similar structure.

FIG. 1 is a network configuration diagram of a 3D model generation apparatus 10 according to an embodiment of the present invention. The 3D model generation device 10 generates a 3D model for layered modeling of the structure 100 by the 3D printer 30. The 3D model (three-dimensional model) is a model indicating the three-dimensional structure of the structure 100, and may be described in an arbitrary data format and may include data related to settings of the 3D printer 30. The 3D model generation device 10 may be configured by a general-purpose or dedicated computer including at least one memory and at least one hardware processor, and the 3D model of the structure 100 according to the 3D model generation program stored in the memory. Is generated.

The 3D model generation device 10 is connected to the communication network N, generates a 3D model in response to an instruction from the user terminal device 20, and provides the 3D model to the 3D printer 30. Note that the 3D model generation device 10 may be configured integrally with the user terminal device 20 or may be configured integrally with the 3D printer 30.

The user terminal device 20 is a computer terminal, and may be a personal computer or a smartphone, for example. The 3D printer 30 manufactures the structure 100 by laminating laminated materials. The 3D printer 30 only needs to be capable of layering the structure 100, and the method of layering is arbitrary and is not limited.

FIG. 2 is a functional block diagram of the 3D model generation apparatus 10 according to the embodiment of the present invention. The 3D model generation device 10 includes a reception unit 11, a conversion unit 12, a storage unit 13, a determination unit 14, and a generation unit 15. The receiving unit 11 receives an instruction to generate a 3D model from the user terminal device 20 or receives a condition for generating a 3D model. The conditions for generating the 3D model include all or part of the designation of the density distribution that the structure 100 should have, the designation of the stress distribution applied to the structure 100, and the designation of the elastic modulus distribution that the structure should have. It's okay.

The conversion unit 12 performs coordinate conversion before the determination unit 14 determines the value of the first parameter. Here, the conversion unit 12 may perform coordinate conversion so as to diagonalize the stress distribution of the structure 100. That is, the conversion unit 12 may perform coordinate conversion so that the coordinate axis coincides with the main stress axis of the structure 100. Further, the conversion unit 12 may perform coordinate conversion so that a specific component among the plurality of components of the elastic modulus distribution of the structure 100 is zero.

The determination unit 14 determines the value of the first parameter that varies spatially so that it is smaller as the density of the structure 100 is higher, and is higher as the density is lower. Here, the first parameter may include a plurality of components corresponding to a plurality of directions in the space. The 3D model generation device 10 according to the present embodiment receives the characteristics that the structure 100 should have from the user terminal device 20, determines various parameters so as to realize the characteristics, and based on the determined parameters, the 3D model Is generated. The first parameter is one type of such various parameters.

The generation unit 15 uses 3D model data for designating whether or not a modeling material is laminated at a spatial point, a coordinate function representing the spatial point as a variable, and an inequality including a periodic function whose value is determined depending on the first parameter. Generate. The generation unit 15 generates 3D model data by deforming a curved surface called a gyroid. Here, the gyroid is a minimally curved surface having periodicity in three directions connected infinitely. When the coordinate value in the Cartesian coordinate system is expressed as (x, y, z), the gyroid is implicitly expressed as sin (x) cos (y) + sin (y) cos (z) + sin (z) cos (x) = 0. Approximately expressed by a yield equation.

The 3D model generation apparatus 10 according to the present embodiment generates 3D model data using an inequality obtained by modifying an implicit equation representing a gyroid. More specifically, the period of the sine function or cosine function is replaced with a first parameter that changes spatially, and the weighting of the three terms of the implicit equation representing the gyroidal is changed to a second parameter that changes spatially. Replace the equal sign of the implicit equation representing the gyroidal with an inequality sign, replace the right side of the implicit equation representing the gyroidal with a spatially changing third parameter, and replace the sine and cosine functions with a general periodic function Thus, the inequality for generating the 3D model data is obtained by transforming the implicit equation representing the gyroid.

More specifically, the coordinate value in the orthogonal coordinate system is expressed as (x, y, z), and the plurality of components of the first parameter are expressed as Tx (x, y, z), Ty (x, y, z), Tz. (X, y, z), and a plurality of components of the second parameter are represented as Bx (x, y, z), By (x, y, z), Bz (x, y, z), and zero or more When the third parameter is represented as A (x, y, z) and the periodic function of the period T is represented as F, the inequality for generating 3D model data by the 3D model generation apparatus 10 according to the present embodiment is as follows: It is expressed by Equation (9).

By determining the value of the first parameter according to the density of the structure 100 and generating 3D model data according to an inequality including a periodic function whose value is determined depending on the first parameter, a cross-sectional shape suitable for additive manufacturing is obtained. And 3D model data of the structure 100 in which the density distribution continuously changes depending on the number of voids.

The storage unit 13 is configured such that the geometric mean value of the plurality of components of the first parameter is smaller as the density of the structure 100 is higher, and the geometric average value of the components of the first parameter is larger as the density is lower. A first condition 13a relating the density and a plurality of components of the first parameter is stored. More specifically, the coordinate value in the orthogonal coordinate system is expressed as (x, y, z), and the plurality of components of the first parameter are expressed as Tx (x, y, z), Ty (x, y, z), Tz. It is expressed as (x, y, z), the density distribution of the structure 100 is expressed as D (x, y, z), and the minimum period that can be modeled when stacking modeling materials is expressed as T _min . The condition 13a is expressed by the following mathematical formula (10).

Incidentally, T _min the minimum period possible shaping when stacking the modeling material is a value defined by the performance of the 3D printer 30, it is also possible for the user to specify. The determination unit 14 may determine a plurality of components of the first parameter based on the first condition 13a. The generation unit 15 may generate the 3D model data according to an inequality including a periodic function in which the coordinate value (x, y, z) is a variable and the value is determined depending on a plurality of components of the first parameter.

A geometric mean value of a plurality of components of the first parameter is determined according to the density of the structure 100, and 3D model data is generated according to an inequality including a periodic function whose value depends on the plurality of components of the first parameter. Thus, 3D model data of a structure having a larger number of voids in a portion where the density is desired to be reduced and a smaller number of voids in a portion where the density is desired to be increased is generated.

The storage unit 13 has a smaller geometric mean value of a plurality of components of the first parameter at a location where the Mises stress calculated from the stress distribution of the structure 100 is larger, and a synergy of the components of the first parameter at a location where the Mises stress is smaller. A second condition 13b that associates the Mises stress with a plurality of components of the first parameter is stored so that the average value becomes large. More specifically, the coordinate value in the orthogonal coordinate system is expressed as (x, y, z), and the plurality of components of the first parameter are expressed as Tx (x, y, z), Ty (x, y, z), Tz. When expressed as (x, y, z), Mises stress is expressed as σ _vm (x, y, z), and conversion coefficient is expressed as R (σ _vm ), the second condition 13b is expressed by the following formula (11). expressed. The Mises stress σ _vm refers to σ _vm = [(σ ₁ −σ ₂ ) ² + (σ ₂ −σ ₃ ) ² + (σ ₃ −) when principal stresses are expressed as σ ₁ , σ ₂ , and σ _3. It is a scalar represented by σ ₁ ) ² ] / 2. Further, the conversion coefficient R (σ _vm ) may be a function of the Mises stress σ _vm .

It should be noted that an upper limit value and a lower limit value may be provided on the right side of Equation (11) according to the resolution of the 3D printer 30. The determination unit 14 may determine a plurality of components of the first parameter based on the second condition 13b. The generation unit 15 may generate the 3D model data according to an inequality including a periodic function in which the coordinate value (x, y, z) is a variable and the value is determined depending on a plurality of components of the first parameter.

The geometric mean value of the plurality of components of the first parameter is determined according to the Mises stress applied to the structure 100, and the 3D model data according to an inequality including a periodic function whose value is determined depending on the plurality of components of the first parameter By generating the 3D model data of the structure 100, the portion having a smaller Mises stress has more voids and the portion having a larger Mises stress has fewer voids.

The storage unit 13 stores a third condition 13c that relates the anisotropy of the elastic modulus distribution of the structure 100 and the ratio of the plurality of components of the first parameter. More specifically, when the plurality of vertical components of the elastic modulus distribution are expressed as Kx (x, y, z), Ky (x, y, z), Kz (x, y, z), the third condition 13c Is represented by the following formula (12).

Note that an upper limit value and a lower limit value may be set for each of the plurality of components of the first parameter. The upper limit value and the lower limit value may be determined by the resolution of the 3D printer 30. The determination unit 14 may determine a plurality of components of the first parameter based on the third condition. The generation unit 15 may generate the 3D model data according to an inequality including a periodic function in which the coordinate value (x, y, z) is a variable and the value is determined depending on a plurality of components of the first parameter.

The ratio of the plurality of components of the first parameter is determined based on the anisotropy of the elastic modulus distribution of the structure 100, and the 3D model data according to an inequality including a periodic function whose value depends on the plurality of components of the first parameter Is generated, 3D model data of the structure 100 having a desired anisotropic elastic modulus is generated.

The storage unit 13 stores a fourth condition 13d that relates the anisotropy of the stress distribution of the structure 100 and the ratio of the plurality of components of the first parameter. More specifically, when the shear stress distribution of the structure 100 is expressed as σxy (x, y, z), σyz (x, y, z), σzx (x, y, z), the fourth condition 13d is: It is represented by the following formula (13).

The determination unit 14 may determine a plurality of components of the first parameter based on the fourth condition 13d. The generation unit 15 may generate the 3D model data according to an inequality including a periodic function in which the coordinate value (x, y, z) is a variable and the value is determined depending on a plurality of components of the first parameter.

The ratio of the plurality of components of the first parameter is determined based on the anisotropy of the stress distribution applied to the structure 100, and 3D according to an inequality that includes a periodic function whose value depends on the plurality of components of the first parameter. By generating model data, 3D model data of the structure 100 having a smaller elastic modulus in a direction in which applied stress is larger is generated. That is, 3D model data of the structure 100 is generated that is harder in the direction in which the applied stress is larger and softer in the direction in which the applied stress is smaller. As a result, a lightweight structure 100 having sufficient hardness to withstand stress can be manufactured.

The determination unit 14 may determine the second parameter based on the stress distribution of the structure 100 such that the second parameter is smaller as the stress distribution is larger and the second parameter is larger as the stress distribution is smaller. . The generation unit 15 may generate the 3D model data according to an inequality in which a plurality of terms are weighted by the second parameter.

The second parameter is determined based on the stress distribution applied to the structure 100, and the 3D model data is generated according to the inequality in which a plurality of terms are weighted by the second parameter, so that the elasticity is obtained according to the applied stress distribution. 3D model data of the structure 100 whose rate varies spatially is generated.

The storage unit 13 stores a fifth condition 13e relating the anisotropy of the stress distribution and the ratio of the values of the plurality of components of the second parameter. More specifically, the coordinate value in the orthogonal coordinate system is represented as (x, y, z), and the plurality of components of the second parameter are represented as Bx (x, y, z), By (x, y, z), Bz. (X, y, z), and when the vertical stress distribution of the structure 100 is expressed as σxx (x, y, z), σyy (x, y, z), σzz (x, y, z), the fifth The condition 13e is expressed by the following mathematical formula (14).

The determination unit 14 determines the ratio of the plurality of components of the second parameter according to the fifth condition 13e, and further Bx (x, y, z) × By (x, y, z) × Bz (x, y, z). The value of the plurality of components of the second parameter may be determined under the condition = 1. The generation unit 15 may generate 3D model data according to an inequality in which a plurality of terms are weighted by the second parameter.

A ratio of a plurality of components of the second parameter is determined based on anisotropy of a stress distribution applied to the structure, and the 3D model data is obtained according to an inequality in which a plurality of terms are weighted by the plurality of components of the second parameter. By generating, 3D model data of the structure 100 whose elastic modulus changes anisotropically according to the anisotropy of the applied stress distribution is generated.

The inequality used by the generation unit 15 to generate the 3D model will be described in more detail. The inequality is expressed by Equation (9) above.

When the structure 100 is layered by the 3D printer 30, a value of (x, y) that satisfies the inequality by substituting the value of z representing the height in the stacking direction into the inequality represented by the formula (9) A molding material is laminated on the substrate.

By manufacturing the structure 100 according to such an inequality, the layered modeling can be easily performed in the step of stacking the modeling materials, and the structure 100 in which the density distribution continuously changes due to the number of gaps is manufactured. .

The periodic function F included in the inequality may be a function representing a sine wave or a triangular wave. For example, when F (x) = sin (x), since the period T of the periodic function F is T = 2π, the inequality is expressed by the following equation (15).

The 3D model data generated by the 3D model generation apparatus 10 may include designation of a drawing width when stacking modeling materials. The designation of the drawing width may change for each space coordinate value. By specifying the drawing width, the width of the modeling material when the modeling material is stacked can be specified, and the density of the structure can be adjusted from a viewpoint different from the first parameter or the like.

The designation of the drawing width designates the drawing width by the 3D printer 30 when the structure 100 is layered, and designates the cross-sectional width of the mesh structure of the structure 100. On the other hand, the third parameter A (x, y, z) appearing on the right side of the inequality is a parameter that specifies the thickness of the network structure of the structure 100.

The generation unit 15 may generate the 3D model data according to a plurality of inequalities having different values of at least the first parameter. In this case, the 3D printer 30 substitutes the value of z representing the height in the stacking direction into a plurality of inequalities having different parameter values, and stacks the modeling material at a location (x, y) that satisfies at least one of the inequalities. Will be. By generating 3D model data according to a plurality of inequalities, 3D model data of the structure 100 in which a plurality of characteristics are superimposed can be generated.

FIG. 3 is a flowchart of processing for determining the first parameter executed by the 3D model generation device 10 according to the embodiment of the present invention. First, the 3D model generation device 10 determines whether or not to directly specify the density distribution of the structure 100 (S10). The determination as to whether or not to directly specify the density distribution of the structure 100 may be made based on an instruction from the user terminal device 20.

When directly specifying the density distribution of the structure 100 (S10: Yes), the 3D model generation device 10 receives the specification of the density distribution from the user terminal device 20 (S11). Thereafter, based on the first condition 13a, a geometric mean value of a plurality of components of the first parameter is determined (S12). Note that the 3D model generation apparatus 10 may perform coordinate conversion by the conversion unit 12 before determining the geometric mean value of the plurality of components of the first parameter.

Furthermore, the 3D model generation device 10 determines whether or not to specify the elastic modulus distribution of the structure 100 (S13). The determination as to whether or not to specify the elastic modulus distribution of the structure 100 may be made based on an instruction from the user terminal device 20.

When designating the elastic modulus distribution of the structure 100 (S13: Yes), the 3D model generation device 10 receives designation of the elastic modulus distribution from the user terminal device 20 (S14). Thereafter, the ratio of the plurality of components of the first parameter is determined based on the third condition 13c (S15).

On the other hand, when the elastic modulus distribution of the structure 100 is not specified (S13: No), the 3D model generation device 10 receives the specification of the stress distribution from the user terminal device 20 (S16). Thereafter, the ratio of the plurality of components of the first parameter is determined based on the fourth condition 13d (S17).

Further, when the density distribution of the structure 100 is not directly designated (S10: No), the 3D model generation device 10 receives the designation of the stress distribution from the user terminal device 20 (S18). In this case, the 3D model generation device 10 calculates Mises stress based on the received stress distribution, and determines the geometric mean value of the plurality of components of the first parameter based on the second condition 13b (S19). Furthermore, the 3D model generation device 10 determines the ratio of the plurality of components of the first parameter based on the fourth condition 13d (S17). Note that the 3D model generation apparatus 10 may perform coordinate conversion by the conversion unit 12 before determining the geometric mean value of the plurality of components of the first parameter. Thus, the process for determining the first parameter ends.

FIG. 4 is a flowchart of a process for generating a 3D model executed by the 3D model generation apparatus 10 according to the embodiment of the present invention. The process of generating the 3D model is a process performed after the process of determining the first parameter, and includes a process of determining the second parameter and a process of determining the third parameter.

First, the 3D model generation device 10 determines whether to specify a stress distribution (S20). The determination as to whether or not to specify the stress distribution may be made based on an instruction from the user terminal device 20.

When the stress distribution is designated (S20: Yes), the 3D model generation device 10 receives the stress distribution from the user terminal device 20 (S21). Thereafter, the 3D model generation device 10 determines a plurality of components of the second parameter based on the fifth condition 13e (S22).

On the other hand, when the stress distribution is not designated (S20: No), the 3D model generation device 10 accepts designation of a plurality of components of the second parameter (S23). For example, it is possible to accept the designation that all the plurality of components of the second parameter are 1.

The 3D model generation device 10 receives the designation of the third parameter (S24). Also, designation of the drawing width when stacking the modeling materials is accepted (S25). The 3D model generation apparatus 10 generates 3D model data based on, for example, the inequality represented by Expression (15) using the parameters determined by the above processing (S26).

FIG. 5 is a perspective view of the 3D model M generated by the 3D model generation apparatus 10 according to the embodiment of the present invention. In the lower left of FIG. 5, the x axis, the y axis, and the z axis are shown.

FIG. 6 is a top view of the 3D model M generated by the 3D model generation apparatus 10 according to the embodiment of the present invention. FIG. 6 illustrates the 3D model M from the z-axis direction, and the x-axis and the y-axis are illustrated in the upper left of FIG.

The 3D model M generates a structure 100 that is easily deformed in the x-axis direction but difficult to deform in the y-axis direction and the z-axis direction. As can be read from FIG. 5 and FIG. 6, the structure 100 manufactured based on the 3D model M has the modeling material continuously present at an arbitrary cut surface. That is, there is no isolated point on any cut surface, and layered modeling is easy.

Further, in the structure 100, a gap exists between the modeling materials at any cut surface, and the gap communicates with the outside. The structure 100 is constituted by a single continuous film-like structural material, and forms a three-dimensional network structure. Further, in the structure 100, when the cut surface is continuously shifted in an arbitrary direction, the distribution of the modeling material continuously changes. For example, in the case of a jungle gym-shaped structure, the distribution of the modeling material may change discontinuously when the cut surface is continuously shifted in an arbitrary direction. Since the structure 100 does not discontinuously change the distribution of the modeling material when the cut surface is continuously shifted in an arbitrary direction, it is easy to ensure the strength when performing layered modeling.

Also, the modeling material and the gap exist with a spatially changing period. The spatially changing period of the modeling material and the gap is defined by the first parameter, and realizes the density distribution specified directly or indirectly. With the 3D model M, it is possible to manufacture a structure 100 that has a cross-sectional shape suitable for additive manufacturing and whose density distribution changes continuously due to the number of gaps.

FIG. 7 is a flowchart showing a method for manufacturing the structure 100 according to the embodiment of the present invention. The manufacture of the structure 100 is executed by the 3D printer 30 based on the 3D model data generated by the 3D model generation apparatus 10.

First, the 3D printer 30 reads the 3D model data generated by the 3D model generation device 10 (S30). Thereafter, the 3D printer 30 initializes the height in the stacking direction (S31). For example, the 3D printer 30 may initialize the height in the stacking direction by z = 0, where z is the height in the stacking direction in the orthogonal coordinate system (x, y, z).

The 3D printer 30 determines whether there is a coordinate (x, y) that satisfies the inequality given by the 3D model data (S32). Here, the inequality may be given by, for example, Expression (15). When there is a coordinate (x, y) that satisfies the inequality (S32: Yes), the modeling material is stacked at the coordinate (x, y) with the drawing width specified by the 3D model data (S33). After the modeling material is laminated at the coordinates (x, y) and when there is no coordinate (x, y) that satisfies the inequality (S32: No), it is determined whether or not there is an update of the height z in the lamination direction ( S34). When there is an update of the stacking direction height z (S34: Yes), the stacking direction height z is updated by a predetermined update width (S35). The update width of the height z in the stacking direction may be set based on the rules of the 3D printer 30.

The 3D printer 30 repeats the above process, and if it is determined that the height z in the stacking direction has not been updated (S34: No), the process ends.

FIG. 8 is a diagram showing the structure 100 according to the embodiment of the present invention. In the figure, a photograph taken so that the structure 100 is viewed from above is shown. The modeling material of the structure 100 is a resin. By using the modeling material as a resin, the structure 100 can be reduced in weight.

The structure 100 shown in FIG. 8 has a columnar shape, and is formed such that the period of the network structure is shorter as it approaches the end surface, and the period of the network structure is longer as it is closer to the center. With such a structure, while maintaining a sufficient strength against the force applied from the outside of the structure 100, the gap in the center can be relatively increased, and the structure 100 having both strength and lightness can do. Moreover, it can be set as the structure suitable for rotational motion by making a network structure into circular symmetry.

The structure 100 may be one in which the surface of the modeling material is coated with a material different from the modeling material. When the modeling material is a resin, the structure 100 may have a metal, ceramic, or glass coating on the surface of the resin. For example, the structure 100 shown in FIG. 8 may be immersed in a plating agent and metal plating may be performed on the surface of the modeling material. In that way, it is difficult to realize the structure 100 alone by forming the skeleton of the structure 100 with a modeling material such as resin and covering the surface with a material different from the modeling material such as metal, ceramics, or glass. A structure 100 having various characteristics can be obtained. For example, the structure 100 having high rigidity and light weight can be obtained by forming the skeleton of the structure 100 with a resin and covering the surface with a metal.

The embodiment described above is for facilitating the understanding of the present invention, and is not intended to limit the present invention. Each element included in the embodiment and its arrangement, material, condition, shape, size, and the like are not limited to those illustrated, and can be changed as appropriate. In addition, the structures shown in different embodiments can be partially replaced or combined.

For example, a coordinate value in the orthogonal coordinate system is represented as (x, y, z), and a plurality of components of the first parameter are represented by Tx (x, y, z), Ty (x, y, z), Tz (x, y). , Z), a plurality of components of the second parameter are represented as Bx (x, y, z), By (x, y, z), Bz (x, y, z), and a third parameter of 0 or more is represented. A (x, y, z) is represented, a periodic function of the period T is represented by F, a center coordinate of a predetermined voxel [i, j, k] is represented by (x _i , y _j , z _k ), When the fourth parameter corresponding to the voxel [i, j, k] is expressed as W _ijk (x, y, z), the inequality for generating the 3D model data by the 3D model generation device 10 according to the present embodiment is: It may be expressed by the following mathematical formula (16). Here, the predetermined voxel [i, j, k] may be a plurality of voxels, for example, [1, 2, 3] (i = 1, j = 2, k = 3) or [10, 10, 10] (i = 10, j = 10, k = 10) or the like.

Here, the sum Σ _{i, j, k} is performed over a predetermined voxel. Thus, even if the density distribution D (x, y, z) of the structure 100 is not necessarily a symmetric distribution centered at (x, y, z) = (0, 0, 0), the structure The 3D model data can be generated so that the material and the void continuously exist at an appropriate period.

The plurality of components of the first parameter are Tx (x, y, z) = 1, Ty (x, y, z) = 1, Tz (x, y, z) = 1, and the plurality of second parameters. Are Bx (x, y, z) = 1, By (x, y, z) = 1, Bz (x, y, z) = 1, F (x) = sin (x), When the period T of the periodic function F is T = 2π, an inequality for generating 3D model data by the 3D model generation apparatus 10 may be expressed by the following Expression (17). Here, D _base is an average of D (x, y, z), and W _base (x, y, z) = 1−Σ _{i, j, k} W _ijk (x, y, z).

The function form of W _ijk (x, y, z) is arbitrary. For example, when the length of one voxel piece is expressed as s, it may be expressed by the following mathematical formula (18).

Further, for a given voxel [i, j, k], a three-dimensional rotation matrix R ^{i, j, k} is defined according to the direction in which the stress is applied, and is used in the inequality shown in Equation (16) or Equation (17). The coordinate value may be replaced from (x, y, z) to R ^{i, j, k} (x, y, z) ^t .

Claims

A determination unit that determines the value of the first parameter that varies spatially to be smaller as the density of the structure is smaller, and larger as the density is lower;
Generation that generates 3D model data that specifies whether or not to stack a modeling material on a spatial point, according to an inequality including a periodic function whose value depends on the first parameter, with the coordinate value representing the spatial point as a variable And
A 3D model generation device comprising:
The first parameter includes a plurality of components corresponding to a plurality of directions,
The determination unit is
The higher the density, the smaller the geometric mean value of the plurality of components of the first parameter, and the smaller the density, the greater the geometric mean value of the plurality of components of the first parameter. Determining a plurality of components of the first parameter based on a first condition relating a plurality of components of one parameter;
The generating unit generates the 3D model data according to the inequality including the periodic function in which the coordinate value is a variable and the value is determined depending on a plurality of components of the first parameter.
The 3D model generation apparatus according to claim 1.
The coordinate value in the orthogonal coordinate system is represented as (x, y, z), and the plurality of components of the first parameter are represented by Tx (x, y, z), Ty (x, y, z), Tz (x, y). when z) and represents, it represents the distribution of the density D (x, y, z) and, representing the minimum period possible modeling and T min when stacking the modeling material,
The first condition is:

Expressed as
The 3D model generation apparatus according to claim 2.
The determination unit has a smaller geometric mean value of the plurality of components of the first parameter for a portion where the Mises stress calculated from the stress distribution of the structure is large, and a plurality of the first parameter for a portion where the Mises stress is small. Determining a plurality of components of the first parameter based on a second condition relating the Mises stress and the plurality of components of the first parameter so that a geometric mean value of the components is increased;
The generating unit generates the 3D model data according to the inequality including the periodic function in which the coordinate value is a variable and the value is determined depending on a plurality of components of the first parameter.
The 3D model generation apparatus according to claim 1.
The coordinate value in the orthogonal coordinate system is represented as (x, y, z), and the plurality of components of the first parameter are represented by Tx (x, y, z), Ty (x, y, z), Tz (x, y). , Z), the Mises stress as σ vm (x, y, z), and the conversion coefficient as R (σ vm ),
The second condition is:

Expressed as
The 3D model generation apparatus according to claim 4.
The determination unit is
Determining a plurality of components of the first parameter based on a third condition relating the anisotropy of the elastic modulus distribution of the structure and the ratio of the plurality of components of the first parameter;
The 3D model generation device according to any one of claims 2 to 5.
When the plurality of vertical components of the elastic modulus distribution are expressed as Kx (x, y, z), Ky (x, y, z), Kz (x, y, z),
The third condition is:

Expressed as
The 3D model generation apparatus according to claim 6.
The determination unit is
Determining a plurality of components of the first parameter based on a fourth condition relating anisotropy of stress distribution of the structure and a ratio of the plurality of components of the first parameter;
The 3D model generation device according to any one of claims 2 to 5.
When the shear stress distribution of the structure is represented as σxy (x, y, z), σyz (x, y, z), σzx (x, y, z),
The fourth condition is:

Expressed as
The 3D model generation apparatus according to claim 8.
The determination unit sets the second parameter based on the stress distribution of the structure so that the second parameter is smaller as the stress distribution is larger and the second parameter is larger as the stress distribution is smaller. Decide
The generation unit generates the 3D model data according to the inequality in which a plurality of terms are weighted by the second parameter.
The 3D model generation apparatus according to any one of claims 1 to 9.
The second parameter includes a plurality of components corresponding to a plurality of directions,
The determining unit determines a plurality of components of the second parameter based on a fifth condition relating anisotropy of the stress distribution and a ratio of values of the plurality of components of the second parameter;
The 3D model generation apparatus according to claim 10.
The coordinate value in the orthogonal coordinate system is represented as (x, y, z), and the plurality of components of the second parameter are represented by Bx (x, y, z), By (x, y, z), Bz (x, y). , Z), and when the vertical stress distribution of the structure is expressed as σxx (x, y, z), σyy (x, y, z), σzz (x, y, z),
The fifth condition is:

Expressed as
The 3D model generation apparatus according to claim 11.
The coordinate value in the orthogonal coordinate system is represented as (x, y, z), and the plurality of components of the first parameter are represented by Tx (x, y, z), Ty (x, y, z), Tz (x, y). , Z), the periodic function of the period T as F, and the plurality of components of the second parameter as Bx (x, y, z), By (x, y, z), Bz (x, y, z), and when the third parameter equal to or greater than 0 is represented as A (x, y, z),
The inequality is

Expressed as
The 3D model generation device according to any one of claims 10 to 12.
The 3D model data includes designation of a drawing width when laminating the modeling material,
The 3D model generation device according to any one of claims 1 to 13.
The generation unit generates the 3D model data according to a plurality of the inequalities having different values of at least the first parameter.
The 3D model generation apparatus according to any one of claims 1 to 14.
The periodic function is a function representing a sine wave or a triangular wave.
The 3D model generation apparatus according to any one of claims 1 to 15.
Before determining the value of the first parameter by the determination unit, further comprising a conversion unit for performing coordinate conversion;
The 3D model generation device according to any one of claims 1 to 16.
The conversion unit performs coordinate conversion so as to diagonalize the stress distribution of the structure,
The 3D model generation apparatus according to claim 17.
Determining the value of the first parameter that varies spatially so that the density of the structure is small as the density is high, and the density is low as the density is low.
Generating 3D model data for designating whether or not a modeling material is to be stacked on a spatial point according to an inequality including a periodic function whose value depends on the first parameter, with the coordinate value representing the spatial point as a variable When,
A 3D model generation method including:
A computer provided in the 3D model generation device
A determination unit that determines a value of the first parameter that varies spatially to be smaller as the density of the structure is smaller and larger as the density is lower, and whether or not the modeling material is stacked on the spatial point. A generating unit that generates 3D model data to be specified according to an inequality including a periodic function in which a coordinate value representing the spatial point is a variable and a value is determined depending on the first parameter;
3D model generation program to function as
A coordinate value in the orthogonal coordinate system is represented as (x, y, z), and a plurality of components of the first parameter are represented by Tx (x, y, z), Ty (x, y, z), Tz (x, y, z). ), A periodic function of the period T is represented as F, and a plurality of components of the second parameter are represented as Bx (x, y, z), By (x, y, z), Bz (x, y, z). , When a third parameter equal to or greater than 0 is expressed as A (x, y, z),
Inequality

There is a modeling material in a place that satisfies, and there is a gap in a place that does not satisfy the inequality,
Structure.
In any cut surface, the modeling material exists continuously,
In the cut surface, a gap exists between the modeling materials, the gap leads to the outside,
When the cut surface is continuously shifted in an arbitrary direction, the distribution of the modeling material continuously changes,
The modeling material and the gap exist in a spatially changing cycle.
Structure.
The surface of the modeling material is coated with a material different from the modeling material,
The structure according to claim 21 or 22.
A coordinate value in the orthogonal coordinate system in which the stacking direction is z is represented as (x, y, z), and a plurality of components of the first parameter are represented by Tx (x, y, z), Ty (x, y, z), Tz. (X, y, z), a periodic function of the period T as F, and a plurality of components of the second parameter as Bx (x, y, z), By (x, y, z), Bz (x, y, z), and when a third parameter equal to or greater than 0 is represented as A (x, y, z),
The inequality of the value of z representing the height in the stacking direction

Substituting for and forming a modeling material at a location (x, y) that satisfies the inequality,
A method of manufacturing a structure.