WO2019160095A1

WO2019160095A1 - Mold manufacturing method

Info

Publication number: WO2019160095A1
Application number: PCT/JP2019/005618
Authority: WO
Inventors: 石川慎介; 藤川武; 大西有希; 平井義彦; 飯田達矢; 渡辺謙太
Original assignee: 株式会社ダイセル; 国立大学法人東京工業大学; 公立大学法人大阪府立大学
Priority date: 2018-02-19
Filing date: 2019-02-15
Publication date: 2019-08-22

Abstract

Provided is a method for manufacturing a mold which is to be used for molding a resin through an imprinting method and which enables formation of a highly-precise molded body through compensation for contraction deformation associated with hardening or solidification of the resin. This method is for manufacturing a mold for manufacturing, through molding of a resin, molded bodies having a variety of aspect ratios and having conical shapes, pyramid shapes, frustum shapes, circular cylindrical shapes, prismatic shapes, imperfect spherical shapes, or linear shapes having a rectangular, trapezoidal, triangular, or imperfect spherical cross-section in a plane perpendicular to the longitudinal direction. The method is characterized by determining a prediction function regarding deformation that occur when a resin having an arbitrarily-defined rate of dimensional change is molded into a molded body having an arbitrarily-defined aspect ratio, calculating a correction function for compensating deformation from the prediction function, and designing a mold using the correction function.

Description

Mold manufacturing method

The present invention relates to a method for producing a mold used for molding a resin, a molded body using the mold produced by the method, and the mold design program. This application includes Japanese Patent Application No. 2018-27433, filed in Japan on February 19, 2018, Japanese Patent Application No. 2018-1000085, filed in Japan on May 25, 2018, and Japan on September 18, 2018. Claims the priority of Japanese Patent Application No. 2018-174309, filed in Japanese Patent Application No. 2018-174309, the contents of which are incorporated herein by reference.

Imprint is a microfabrication technology that can transfer nano-sized patterns by a very simple process of forming using a mold. If imprint is used, it can be mass-produced at low cost, and has been put to practical use in various fields such as semiconductor devices and optical members.

For example, a micromirror array is an optical member in which a large number of square pillars or pyramids having a side of 1-1000 μm are arranged in a lattice shape, and two adjacent side surfaces of the four side surfaces of the solid shape are used as orthogonal mirrors. Therefore, an accurate angle and high flatness are required.

However, when the resin is molded by the imprint method, it is difficult to obtain a molded body in which the shape of the mold is accurately transferred due to shrinkage accompanying the curing or solidification of the resin. For this reason, it is necessary to correct the dimension and shape of the mold in accordance with the shrinkage of the resin. However, this requires repeated trial and error, and enormous costs and time are required to create the mold prototype.

Patent Document 1 describes that a reduction in line width due to resin shrinkage can be corrected by a specific function for a mold used for forming a wiring pattern by molding a resin by an imprint method.

JP 2012-183692 A

However, in Patent Document 1, no consideration is given to the fact that the side surface of the wiring is curved, and even if a mold corrected using the above function is used, the side surface of the obtained wiring pattern is not curved. It was found that the surface accuracy was low.

Accordingly, an object of the present invention is to produce a mold capable of forming a highly accurate molded body by compensating for shrinkage deformation accompanying the curing or solidification of the resin for a mold used for molding a resin by an imprint method. It is to provide a method.
Another object of the present invention is to provide a method for producing a high-precision molded article made of a cured or solidified resin using the mold.
Another object of the present invention is to provide a mold capable of accurately producing a desired molded body by molding a resin.
Another object of the present invention is to provide a mold design program that uses a computer to predict deformation associated with hardening or solidification of a resin and to design a mold for obtaining a molded body with very little deformation based on the predicted deformation. There is to do.

As a result of intensive studies to solve the above-mentioned problems, the present inventors have found that when a resin is molded to produce a desired molded body, the dimensional change rate of the resin and the aspect ratio of the desired molded body are included. The inventors have found a specific function capable of deriving a mold shape in which deformation is compensated, and found that a molded body having excellent surface accuracy can be obtained by using a mold having a shape obtained by the function. The present invention has been completed based on these findings.

That is, the present invention is formed by molding a resin to have various aspect ratios, a cone shape, a pyramid shape, a truncated cone shape, a truncated pyramid shape, a cylindrical shape, a prism shape, a spherical shape, or a plane perpendicular to the longitudinal direction A method for producing a mold for producing a linear shaped product having a rectangular, trapezoidal, triangular, or ball-shaped cross section, wherein a resin having an arbitrary dimensional change rate is formed into a molded product having an arbitrary aspect ratio. A method for manufacturing a mold is provided, wherein a prediction function of deformation at the time of molding is obtained, a correction function for compensating for deformation is calculated from the prediction function, and a mold is designed using the correction function. To do.
Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. When the molded body is placed so as to be bilaterally symmetric by a cut surface that includes a point that includes the axis and the y-axis and that indicates the maximum height of the molded body, the height in the y-axis direction on the cut surface and the horizontal plane Dimensional change rate: If the resin is light or thermosetting resin, it is the volume change rate before and after curing. If the resin is a thermoplastic resin, “(thermal It is a value calculated by “Glass transition temperature of plastic resin (° C.) − Scheduled environment temperature (° C.)) × Linear expansion coefficient”.

The present invention also provides a linear molded body having a rectangular or trapezoidal cross section in a plane perpendicular to the longitudinal direction, wherein a resin having a dimensional change rate of α ₀ is molded and the aspect ratio defined below is A. Provided is a mold manufacturing method for manufacturing, wherein a mold recess shape is set to the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is set to be bilaterally symmetric in the plane including the x axis and the y axis.
The shape of the upper surface of the space formed by the recess is a curve represented by the following formula (1-1), and the shape of the side surface of the space is represented by the following formula (1-2). Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. The height in the y-axis direction at the cut surface when the molded body is placed so as to be bilaterally symmetric by a cut surface including a point that includes the x axis and the y axis and indicates the maximum height of the molded body. Dimensional change rate: If the resin is light or a thermosetting resin, it is the volume change rate before and after curing, and if the resin is a thermoplastic resin , “(Glass transition temperature (° C) of thermoplastic resin-Expected ambient temperature ( Is a value calculated by)) × linear expansion coefficient "

(Where α ₀ is the dimensional change rate of the resin, b is a parameter related to the ratio of the elastic modulus of the resin and the force in the width direction, x includes the x-axis and the y-axis of the space formed by the recesses, and The half width of the cut surface including the point indicating the maximum height of the space, c is a parameter relating to the ratio of the shrinkage in the height direction and the shrinkage in the width direction, and ε _x is the horizontal stretching correction factor)

(Where α ₀ is the dimensional change rate of the resin, y is the height of the space, τ _s is the relaxation coefficient of side shrinkage, A is the aspect ratio, and ε _y is the stretching correction coefficient in the vertical direction)

The present invention also provides a mold for producing a molded article having a prismatic shape or a truncated pyramid shape, in which a resin having a dimensional change rate of α ₀ is molded and the aspect ratio defined below is A. A method for manufacturing a mold, characterized in that the concave shape of the mold is the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is set to be bilaterally symmetric in the plane including the x axis and the y axis.
The upper surface of the space formed by the horizontal surface and the concave portion and including the bottom surface, the four side surfaces, and the upper surface is indicated by a continuous curve in the z-axis direction represented by the following formula (1-1).
The four side surfaces of the space are respectively shown by continuations in the x-axis direction or z-axis direction of the curves represented by the following formulas (1-2-1) to (1-2-4), respectively.
The shape of the corner formed by two adjacent side surfaces is a point 1 on the curve representing the corner end of one side surface and a point on the curve representing the corner end of the other side surface, A straight line, a polygonal line, or an arc connecting the point 1 and the point 2 having the same y-axis value;
The shape of the corner formed by the side surface parallel to the plane including the x-axis and the y-axis and the top surface is the point 1 ′ on the curve representing the corner-side end portion of the side surface and the curve representing the corner-side end portion of the top surface. A straight line, a polygonal line, or an arc connecting the point 1 ′ and the point 2 ′ having the same x-axis value,
The shape of the corner formed by the side surface and the upper surface parallel to the plane including the y-axis and the z-axis is the point 1 ″ on the curve representing the corner end of the side surface and the curve representing the corner end of the upper surface. A straight line, a polygonal line, or an arc connecting the point 1 ″ and the point 2 ″ having the same z-axis value. Aspect ratio: One direction on the horizontal plane is the x axis, and the horizontal plane The direction perpendicular to the x-axis is the z-axis, the direction perpendicular to the x-axis and the z-axis is the y-axis, the molded body formed of a mold is on a horizontal plane, includes the x-axis and the y-axis, and the maximum height of the molded body is Dimensional change is the ratio of the height in the y-axis direction at the cut surface to the width of the cut surface in the x-axis direction in contact with the horizontal plane when the molded body is placed so as to be symmetrical with the cut surface including the indicated point Rate: If the resin is light or thermosetting resin, it is the volume change rate before and after curing, and if the resin is a thermoplastic resin , - is a value calculated by "(glass transition temperature of the thermoplastic resin (℃) scheduled use environment temperature (℃)) × linear expansion coefficient"

(Where α ₀ is the dimensional change rate of the resin, y is the height of the space, τ _s is the relaxation coefficient of side shrinkage, A is the aspect ratio, k ₁ is the correction coefficient for the shrinkage rate in the x-axis direction, k ₂ represents a correction coefficient for the contraction rate in the z-axis direction, and k ₁ and k ₂ are the same or different and are numbers of 1.0 to 2.0)

In the present invention, the molded body is a pyramidal trapezoidal shape, a prismatic shape having an aspect ratio of A, or a linear structure having a rectangular or trapezoidal cross section in a plane perpendicular to the longitudinal direction. A method for producing the mold having a shape fixed to a base surface at a bottom surface is provided.

The present invention also provides the method for producing the mold, wherein b is represented by a function represented by the following formula (b-1).

(A in the formula is the same as above, b ₁ is a number from 0.21 to 0.84, b ₂ is a number from 0.3 to 0.9, b ₃ is a number from 1.5 to 2.5, b ₄ is a number from 0.06 to 0.24)

The present invention also provides the method for producing the mold, wherein c is represented by a function represented by the following formula (c-1).

(A in the formula is the same as above. C ₁ is a number from 0.2 to 0.8, c ₂ is a number from 2.5 to 3.5, and c ₃ is a number from 0.5 to 2.0. )

The present invention is also, tau _s is indicated by the function represented by the following formula (tau _s -1), provides a method of manufacturing the mold.

(A in the formula is the same as above. Τ _s1 is a number between 0.12 and 0.46)

The present invention also provides the method for producing the mold, wherein the stretching correction coefficients ε _x and ε _y are derived by the following procedures 1 to 5.
1. y = f _uy (x) = α ₀ bx ² + α ₀ (1−α ₀ ) c + (1−α ₀ ) ² , and x = f _sx (y) = (1−α ₀ (1−e− ^{y / τs (A)} ) / 2A
Find the intersection (x ₀ , y ₀ ) of
2. The temporary correction shape g _u (x) of the upper surface and the temporary correction shape g _s (y) of the side surface are calculated from the following equations.
g _u (x) = 1 / f _uy (x)
g _s (y) = (1 / 2A) ² / f _sx (y)
4). Next, the horizontal height y ₁ = g _u (x ₀ ) of the provisional correction shape and the half width x ₁ = g _s (y ₀ ) of the provisional correction shape are obtained.
5. The horizontal direction correction coefficient ε _x and the vertical direction correction coefficient ε _y of the provisional correction shape are calculated from the following equations.
ε _x = x ₁ / x ₀
ε _y = y ₁ / y ₀

The present invention also molds a resin having a dimensional change rate of α ₀ to produce a linear shaped product having a triangular cross section in a plane perpendicular to the longitudinal direction and having an aspect ratio A defined below. There is provided a method for manufacturing a mold for manufacturing a mold, wherein the concave shape of the mold is the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In a state where the concave portion is opened so as to open on the horizontal plane side, the x-axis and the y-axis are included, and the concave portion is installed so as to be symmetrical on the plane including the point indicating the maximum depth of the concave portion.
The shape of the hypotenuse when the space formed by the horizontal plane and the concave portion and including the bottom surface and the two inclined surfaces is cut by a plane including the x-axis and the y-axis, the x-coordinate is expressed by the following formula (2-1), and y A coordinate is a curve formed by collecting points represented by the following formula (2-2). Aspect ratio: one direction on the horizontal plane is the x axis, and on the horizontal plane, the direction perpendicular to the x axis is the z axis, the x axis The y-axis is the direction perpendicular to the z-axis, and the molded body is symmetrical on the horizontal plane by the cutting plane that includes the point that includes the x-axis and y-axis and indicates the maximum height of the molded body. Is the ratio of the height in the y-axis direction at the cut surface and the width of the cut surface in the x-axis direction in contact with the horizontal plane in the case where it is installed. Dimensional change rate: When the resin is light or thermosetting resin , The volume change rate before and after curing, and when the resin is a thermoplastic resin, Is a value calculated by the scheduled use environment temperature (℃)) × linear expansion coefficient "- Temperature (℃)

(Where k _t is the following formula (k _t −1)

For q that satisfies the above, the range is 0.9q ≦ k _t ≦ 1.1q. α ₀ is the dimensional change rate of the resin, y is the height of the space, τ _t is the relaxation coefficient of side shrinkage, and A is the aspect ratio)

The present invention also provides a mold manufacturing method for manufacturing a quadrangular pyramid-shaped molded article having an aspect ratio of A by molding a resin having a dimensional change rate of α ₀ , wherein the concave shape of the mold is defined as follows: Provided is a method for producing a mold, characterized by having a shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the case where the concave portion is opened on the horizontal plane side, and the concave portion is set so as to be symmetric with respect to the plane including the point indicating the maximum depth of the concave portion,
The bottom surface of the space formed by the horizontal plane and the recess is a quadrangle, the four sides of the bottom surface are parallel to the x axis or the z axis, and the four side surfaces of the space have one side of the bottom surface as the bottom side, X of a curve formed by collecting points on the x-coordinate, y-coordinate, and z-coordinate represented by the following formulas (5-1) to (5-4) that connect the base and the vertex of the space. Indicated in the axial direction or continuous in the z-axis direction,
The shape of the corner formed by two adjacent side surfaces is a point 1 on the curve representing the corner end of one side surface and a point on the curve representing the corner end of the other side surface, A method of manufacturing a mold, wherein the mold is a straight line, a polygonal line, or an arc connecting the point 1 and a point 2 having the same y-axis value.
Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. X-axis in contact with the height in the y-axis direction on the cut surface and the horizontal plane when the molded product is placed on a horizontal plane so that the molded product is symmetrical with the cut surface including the point indicating the maximum height of the molded product Dimensional change rate: If the resin is a light or thermosetting resin, it is the volume change rate before and after curing. If the resin is a thermoplastic resin, “(thermoplastic resin The glass transition temperature (° C) minus the expected environmental temperature (° C) x linear expansion coefficient "

(Wherein, alpha ₀ is the dimensional change of the resin, y is the height of the space, tau _s relaxation coefficient aspect shrinkage, A is .k _t indicating the aspect ratio is a correction coefficient of contraction of the y-axis direction, The following formula (k _t -1)

(With respect to q satisfying 0.9q ≦ k _t ≦ 1.1q)

In the present invention, the molded body is a pyramid shape having an aspect ratio of A, or a linear structure having a triangular cross section in a plane perpendicular to the longitudinal direction, and the structure is fixed to the base surface at the bottom surface. There is provided a method for manufacturing the mold having a shaped shape.

The present invention is also, tau _t is indicated by the function represented by the following formula (tau _t -1), provides a method of manufacturing the mold.

(Where τ _t1 is a number from 1.0 to 2.0 and τ _t2 is a number from 0.2 to 1.0. A is the same as above)

The present invention also molds a resin having a dimensional change rate of α ₀ to produce a linear molded body having a spherical section in a plane perpendicular to the longitudinal direction and having an aspect ratio A defined below. There is provided a method for manufacturing a mold, characterized in that the shape of the concave portion of the mold is the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is left-right symmetrical on the plane including the x axis and the y axis and including the point indicating the maximum depth of the mold.
The cross-sectional shape of the sphere-shaped side surface when a space including a bottom surface and a sphere-shaped side surface formed by a horizontal plane and a concave portion is cut by a plane including the x-axis and the y-axis, 3-1), and the y-coordinate is a curve formed by collecting points represented by the following formula (3-2). Aspect ratio: One direction on the horizontal plane is the x-axis, and the x-axis is on the horizontal plane. The vertical direction is the z-axis, the direction perpendicular to the x-axis and the z-axis is the y-axis, and the molded body by the mold includes a point that includes the x-axis and the y-axis on the horizontal plane and indicates the maximum height of the molded body. This is the ratio of the height in the y-axis direction at the cut surface and the width of the cut surface in the x-axis direction in contact with the horizontal plane when the molded body is placed symmetrically by the cut surface. In the case of a light or thermosetting resin, it is the volume change rate before and after curing, and when the resin is a thermoplastic resin, Is a value calculated by the scheduled use environment temperature (℃)) × linear expansion coefficient "- glass transition temperature of the thermoplastic resin (℃)

(Where α ₀ is the rate of dimensional change of the resin, r is the radius of the sphere, and y is the height of the space. Y ₀ is on the y-axis at the center of the sphere that is part of the molded product to be produced. Τ _c is the side shrinkage relaxation coefficient, A is the aspect ratio, and k _c is the following formula:

(For p that satisfies 0.9p ≦ k _c ≦ 1.1p)

The present invention is also a mold manufacturing method for manufacturing a notched molded article having an aspect ratio of A by molding a resin having a dimensional change rate of α ₀ , wherein the concave shape of the mold is Provided is a method for producing a mold, characterized by having a shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the case where the concave portion is opened on the horizontal plane side, and the concave portion is set so as to be symmetric with respect to the plane including the point indicating the maximum depth of the concave portion,
The bottom surface of the space formed by the horizontal plane and the concave portion is a circle, and when the circle is divided into four arcs by the xy plane and the zy plane, points on the four arcs, The line connecting the vertices is a curve formed by collecting points on the x, y, and z coordinates represented by the following formulas (4-1) to (4-4). Aspect ratio: on the horizontal plane A direction perpendicular to the x-axis on the horizontal plane is a z-axis, a direction perpendicular to the x-axis and the z-axis is a y-axis, and the compact includes the x-axis and the y-axis. The height of the cut surface in the y-axis direction and the cut surface in the x-axis direction in contact with the horizontal surface when the molded body is placed on a horizontal plane so as to be symmetrical with the cut surface including the point indicating the maximum height of Dimensional change rate: The ratio of volume change before and after curing when the resin is light or thermosetting resin. For RESIN, - is a value calculated by "(glass transition temperature of the thermoplastic resin (℃) scheduled use environment temperature (℃)) × linear expansion coefficient"

(For p that satisfies 0.9p ≦ k _c ≦ 1.1p)

In the present invention, the molded body is a sphere-shaped structure having an aspect ratio of A, or a line-shaped structure having a sphere-shaped cross section in a plane perpendicular to the longitudinal direction. A method of manufacturing the mold having a shape fixed to the mold is provided.

The present invention is also, tau _c is represented by the function represented by the following formula (tau _c -1), it provides a method of manufacturing the mold.

( _Wherein τ _c10 is a number from 0.05 to 0.2, τ _c11 is a number from 0.005 to 0.02, τ _c12 is a number from 2.5 to 10, τ _c13 is a number from 10 to 40, τ _c14 is a number from 2 to 8. A is the same as above)

The present invention also provides a mold obtained by the method for producing the mold.

The present invention also provides a mold manufacturing apparatus for manufacturing a mold by the mold manufacturing method.

The present invention also provides a molded body for producing a molded body made of a cured product or a solidified product of the resin through a step of manufacturing a mold by the mold manufacturing method and molding a resin using the obtained mold. A manufacturing method is provided.

The present invention also provides a molded body obtained by the method for producing the molded body.

The present invention also provides a molded body obtained by manufacturing a mold by the mold manufacturing method and obtaining a molded body made of a cured or solidified product of the resin through a step of molding a resin using the obtained mold. A manufacturing apparatus is provided.

The present invention also provides a linear molded body having a rectangular or trapezoidal cross section in a plane perpendicular to the longitudinal direction, wherein a resin having a dimensional change rate of α ₀ is molded and the aspect ratio defined below is A. Provided is a mold for manufacturing, wherein the concave shape of the mold is the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is set to be bilaterally symmetric in the plane including the x axis and the y axis.
The shape of the upper surface of the space formed by the recess is a curve represented by the following formula (1-1), and the shape of the side surface of the space is represented by the following formula (1-2). Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. The height in the y-axis direction at the cut surface when the molded body is placed so as to be bilaterally symmetric by a cut surface including a point that includes the x axis and the y axis and indicates the maximum height of the molded body. Dimensional change rate: If the resin is light or a thermosetting resin, it is the volume change rate before and after curing, and if the resin is a thermoplastic resin , “(Glass transition temperature (° C) of thermoplastic resin-Expected ambient temperature ( Is a value calculated by)) × linear expansion coefficient "

The present invention also provides a mold for molding a resin having a dimensional change rate of α ₀ and manufacturing a quadrangular prism shape or a truncated pyramid shaped product having an aspect ratio A defined below. In addition, a mold is provided in which the concave shape of the mold is the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is set to be bilaterally symmetric in the plane including the x axis and the y axis.
The upper surface of the space formed by the horizontal surface and the concave portion and including the bottom surface, the four side surfaces, and the upper surface is indicated by a continuous curve in the z-axis direction represented by the following formula (1-1).
The four side surfaces of the space are respectively shown by continuations in the x-axis direction or z-axis direction of the curves represented by the following formulas (1-2-1) to (1-2-4), respectively.
The shape of the corner formed by two adjacent side surfaces is a point 1 on the curve representing the corner end of one side surface and a point on the curve representing the corner end of the other side surface, A straight line, a polygonal line, or an arc connecting the point 1 and the point 2 having the same y-axis value;
The shape of the corner formed by the side surface parallel to the plane including the x-axis and the y-axis and the top surface is the point 1 ′ on the curve representing the corner-side end portion of the side surface and the curve representing the corner-side end portion of the top surface. A straight line, a polygonal line, or an arc connecting the point 1 ′ and the point 2 ′ having the same x-axis value,
The shape of the corner formed by the side surface and the upper surface parallel to the plane including the y-axis and the z-axis is the point 1 ″ on the curve representing the corner end of the side surface and the curve representing the corner end of the upper surface. A straight line, a polygonal line, or an arc connecting the point 1 ″ and the point 2 ″ having the same z-axis value. Aspect ratio: One direction on the horizontal plane is the x axis, and the horizontal plane The direction perpendicular to the x-axis is the z-axis, the direction perpendicular to the x-axis and the z-axis is the y-axis, the molded body formed of a mold is on a horizontal plane, includes the x-axis and the y-axis, and the maximum height of the molded body is Dimensional change is the ratio of the height in the y-axis direction at the cut surface to the width of the cut surface in the x-axis direction in contact with the horizontal plane when the molded body is placed so as to be symmetrical with the cut surface including the indicated point Rate: If the resin is light or thermosetting resin, it is the volume change rate before and after curing, and if the resin is a thermoplastic resin , - is a value calculated by "(glass transition temperature of the thermoplastic resin (℃) scheduled use environment temperature (℃)) × linear expansion coefficient"

The present invention also molds a resin having a dimensional change rate of α ₀ to produce a linear shaped product having a triangular cross section in a plane perpendicular to the longitudinal direction and having an aspect ratio A defined below. There is provided a mold characterized in that the concave shape of the mold is the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In a state where the concave portion is opened so as to open on the horizontal plane side, the x-axis and the y-axis are included, and the concave portion is installed so as to be symmetrical on the plane including the point indicating the maximum depth of the concave portion.
The shape of the hypotenuse when the space formed by the horizontal plane and the concave portion and including the bottom surface and the two inclined surfaces is cut by a plane including the x-axis and the y-axis, the x-coordinate is expressed by the following formula (2-1), and y A coordinate is a curve formed by collecting points represented by the following formula (2-2). Aspect ratio: one direction on the horizontal plane is the x axis, and on the horizontal plane, the direction perpendicular to the x axis is the z axis, the x axis The y-axis is the direction perpendicular to the z-axis, and the molded body is symmetrical on the horizontal plane by the cutting plane that includes the point that includes the x-axis and y-axis and indicates the maximum height of the molded body. Is the ratio of the height in the y-axis direction at the cut surface and the width of the cut surface in the x-axis direction in contact with the horizontal plane in the case where it is installed. Dimensional change rate: When the resin is light or thermosetting resin , The volume change rate before and after curing, and when the resin is a thermoplastic resin, Is a value calculated by the scheduled use environment temperature (℃)) × linear expansion coefficient "- Temperature (℃)

(Where k _t is the following formula (k _t −1)

The present invention is also a mold for molding a resin having a dimensional change rate of α ₀ and manufacturing a quadrangular pyramid shaped article having an aspect ratio of A, and the concave portion of the mold has the following shape. A mold is provided.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the case where the concave portion is opened on the horizontal plane side, and the concave portion is set so as to be symmetric with respect to the plane including the point indicating the maximum depth of the concave portion,
The bottom surface of the space formed by the horizontal plane and the recess is a quadrangle, the four sides of the bottom surface are parallel to the x axis or the z axis, and the four side surfaces of the space have one side of the bottom surface as the bottom side, X of a curve formed by collecting points on the x-coordinate, y-coordinate, and z-coordinate represented by the following formulas (5-1) to (5-4) that connect the base and the vertex of the space. Indicated in the axial direction or continuous in the z-axis direction,
The shape of the corner formed by two adjacent side surfaces is a point 1 on the curve representing the corner end of one side surface and a point on the curve representing the corner end of the other side surface, A method of manufacturing a mold, wherein the mold is a straight line, a polygonal line, or an arc connecting the point 1 and a point 2 having the same y-axis value.
Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. X-axis in contact with the height in the y-axis direction on the cut surface and the horizontal plane when the molded product is placed on a horizontal plane so that the molded product is symmetrical with the cut surface including the point indicating the maximum height of the molded product Dimensional change rate: If the resin is a light or thermosetting resin, it is the volume change rate before and after curing. If the resin is a thermoplastic resin, “(thermoplastic resin The glass transition temperature (° C) minus the expected environmental temperature (° C) x linear expansion coefficient "

(With respect to q satisfying 0.9q ≦ k _t ≦ 1.1q)

The present invention also molds a resin having a dimensional change rate of α ₀ to produce a linear molded body having a spherical section in a plane perpendicular to the longitudinal direction and having an aspect ratio A defined below. There is provided a mold characterized in that the concave shape of the mold is the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is left-right symmetrical on the plane including the x axis and the y axis and including the point indicating the maximum depth of the mold.
The cross-sectional shape of the sphere-shaped side surface when a space including a bottom surface and a sphere-shaped side surface formed by a horizontal plane and a concave portion is cut by a plane including the x-axis and the y-axis, 3-1), and the y-coordinate is a curve formed by collecting points represented by the following formula (3-2). Aspect ratio: One direction on the horizontal plane is the x-axis, and the x-axis is on the horizontal plane. The vertical direction is the z-axis, the direction perpendicular to the x-axis and the z-axis is the y-axis, and the molded body by the mold includes a point that includes the x-axis and the y-axis on the horizontal plane and indicates the maximum height of the molded body. This is the ratio of the height in the y-axis direction at the cut surface and the width of the cut surface in the x-axis direction in contact with the horizontal plane when the molded body is placed symmetrically by the cut surface. In the case of a light or thermosetting resin, it is the volume change rate before and after curing, and when the resin is a thermoplastic resin, Is a value calculated by the scheduled use environment temperature (℃)) × linear expansion coefficient "- glass transition temperature of the thermoplastic resin (℃)

(For p that satisfies 0.9p ≦ k _c ≦ 1.1p)

The present invention is also a mold for producing a spherically shaped molded body having an aspect ratio of A by molding a resin having a dimensional change rate of α ₀ , and the concave portion of the mold has the following shape. A mold is provided.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the case where the concave portion is opened on the horizontal plane side, and the concave portion is set so as to be symmetric with respect to the plane including the point indicating the maximum depth of the concave portion,
The bottom surface of the space formed by the horizontal plane and the concave portion is a circle, and when the circle is divided into four arcs by the xy plane and the zy plane, points on the four arcs, The line connecting the vertices is a curve formed by collecting points on the x, y, and z coordinates represented by the following formulas (4-1) to (4-4). Aspect ratio: on the horizontal plane A direction perpendicular to the x-axis on the horizontal plane is a z-axis, a direction perpendicular to the x-axis and the z-axis is a y-axis, and the compact includes the x-axis and the y-axis. The height of the cut surface in the y-axis direction and the cut surface in the x-axis direction in contact with the horizontal surface when the molded body is placed on a horizontal plane so as to be symmetrical with the cut surface including the point indicating the maximum height of Dimensional change rate: The ratio of volume change before and after curing when the resin is light or thermosetting resin. For RESIN, - is a value calculated by "(glass transition temperature of the thermoplastic resin (℃) scheduled use environment temperature (℃)) × linear expansion coefficient"

(For p that satisfies 0.9p ≦ k _c ≦ 1.1p)

The present invention can also be obtained by molding a resin to have various aspect ratios, such as a cone shape, a pyramid shape, a truncated cone shape, a truncated pyramid shape, a cylindrical shape, a prismatic shape, a spherical shape, or a plane perpendicular to the longitudinal direction. A mold design program for causing a computer to execute a mold design for manufacturing a molded product having a rectangular, trapezoidal, triangular, or spherical shape in cross section, and having a desired molded product shape and aspect ratio A and a first step of inputting a dimensional change rate α ₀ of the resin to be formed
A second step of causing the computer to select a correction function in accordance with the desired shape of the molded body from the input shape of the desired molded body, the aspect ratio A, and the dimensional change rate α ₀ of the resin to be formed; And a third step of causing the computer to execute correction of the concave shape of the mold by the selected correction function.
Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. When the molded body is placed so as to be bilaterally symmetric by a cut surface that includes a point that includes the axis and the y-axis and that indicates the maximum height of the molded body, the height in the y-axis direction on the cut surface and the horizontal plane Dimensional change rate: If the resin is light or thermosetting resin, it is the volume change rate before and after curing. If the resin is a thermoplastic resin, “(thermal It is a value calculated by “Glass transition temperature of plastic resin (° C.) − Scheduled environment temperature (° C.)) × Linear expansion coefficient”.

In the present specification, unless otherwise specified, the “cut surface” and “cross section” of the molded body are one direction on the horizontal plane as the x axis, and the direction perpendicular to the x axis on the horizontal plane as the z axis, The molded body is set so that the direction perpendicular to the x-axis and the z-axis is the y-axis, and the horizontal plane is symmetrical with respect to the plane including the x-axis and the y-axis, and the point indicating the maximum height is on the y-axis. It is a surface that includes a point that includes the x-axis and the y-axis and indicates the maximum height of the molded body when installed.

According to the mold manufacturing method of the present invention, the design of a silicone mold, which has been conventionally performed by repeating trial manufacture and spending enormous time and cost, predicts deformation by calculation using a function and performs necessary corrections. By adding to the design, it can be done faster and more reliably.
In addition, since the mold obtained by the mold manufacturing method of the present invention has a shape in which the expected deformation is compensated, if the mold is used, the molding has excellent shape accuracy (particularly excellent surface accuracy). The body can be obtained efficiently and inexpensively.
Therefore, the manufacturing method of the present invention optically inserts fine structures such as optical members such as micromirror arrays, semiconductor lithography, polymer MEMS, flat screens, holograms, waveguides, and precision machine parts that require high surface accuracy. It is suitably used for manufacturing by printing.

It is a figure which shows the analysis system of the shrinkage deformation accompanying hardening or solidification of the linear-shaped molded object whose cross section is a rectangle. It is a function of the figure which shows the correction | amendment line based on the cross-sectional shape of the deform | transformed upper surface and side surface after hardening of the linear-shaped molded object whose cross section is a rectangle, and the said deformed upper surface and side surface shape. It is the figure which extended | stretched the correction | amendment line of the linear shaped molded object whose cross section is a rectangle. It is a figure which shows the prediction of a deformation | transformation of the molded object of a linear shape whose cross section is an isosceles triangle. It is a figure which shows the prediction of a deformation | transformation of the linear shaped molded object whose cross section is spherical. It is a figure which shows the change of b accompanying the change of the aspect ratio by the finite element analysis of the linear shaped molded object whose cross section is a rectangle. It is a figure which shows the change of c accompanying the change of the aspect ratio by the finite element analysis of the linear shaped molded object whose cross section is a rectangle. Figure showing the change in τ _{s with} the change in aspect ratio and the change in k _s with the change in aspect ratio (8-a) by finite element analysis of a linear shaped product with a rectangular cross section (8) -b). It shows a section along a finite element analysis of the linear shaped body of an isosceles triangle, graph showing changes in the associated tau _t change the aspect ratio (9-a), a change in the k _t with changes in aspect ratio (9-b). It is a figure which shows the change of (tau) _c accompanying the change of an aspect-ratio by the finite element analysis of the linear shaped molded object where a cross section is a spherical shape. It is a schematic diagram which shows the correction | amendment effect of the molded object of a linear shape whose cross section is a rectangle. It is a schematic diagram which shows the correction effect of the molded object of a linear shape whose cross section is an isosceles triangle. It is a schematic diagram which shows the correction | amendment effect of the linear shaped molded object whose cross section is a spherical part. Figure (14-a) showing the mean square error σ of the deformed upper surface shape predicted value after curing, and the figure showing the mean square error σ of the side surface shape predicted value (14-b) ). It is a figure which shows the mean square error (sigma) of the deformed side surface shape prediction value after hardening of the molded object of a linear shape whose cross section is an isosceles triangle. It is a figure which shows the mean-square error (sigma) of the deformed side surface shape prediction value after hardening of the linear shaped body with a spherical section. It is a figure which shows the analysis system of the shrinkage deformation of an upper surface and a side surface accompanying hardening or solidification of a quadratic prism shape molded object. It is a figure which shows the correction | amendment method of the angle | corner formed by the side surface (6-1) and the side surface (6-2) which contracted and deform | transformed with hardening or solidification of a square columnar shaped molded object, (1) is a side surface (6- The point (Rb) on the curve representing the corner end of 1) and the point (Rc) on the curve representing the corner end of the side surface (6-2) are connected by an arc, (2) (3) is a diagram connecting with a straight line instead of the arc, (4) is a diagram (4) extending the side surface (6-1) in the x-axis direction, FIG. 6B is a diagram in which 6-2) is extended in the z-axis direction and a line intersecting the both side surfaces is a corner (or an end side). FIG. 5 is a diagram showing an analysis system for shrinkage deformation of four side surfaces (5-1) to (5-4) accompanying hardening or solidification of a quadrangular pyramid shaped body. It is a figure which shows the analysis system of the shrinkage deformation accompanying hardening or solidification of a spherical notch-shaped molded object. It is a schematic diagram which shows the correction effect of a molded object of a quadrangular pyramid shape. It is a schematic diagram which shows the correction effect of a molded object of a quadrangular pyramid shape.

[Mold manufacturing method]
The method for producing a mold of the present invention comprises forming a resin and having various aspect ratios, such as a cone shape, a pyramid shape, a truncated cone shape, a truncated pyramid shape, a cylindrical shape, a prismatic shape, a spherical shape, or a longitudinal direction. A method for producing a mold for producing a linear shaped body having a rectangular, trapezoidal, triangular or spherical cross section in a vertical plane (for example, molding with an aspect ratio in the range of 0.01 to 5 below) Calculate the aspect ratio dependency of the deformation by simulating the shrinkage deformation of the body accompanying the hardening or solidification of the resin using the finite element analysis method. Based on this, the resin having an arbitrary dimensional change rate can be arbitrarily selected. Obtaining a prediction function of deformation at the time of forming into a molded article having an aspect ratio of the above, calculating a correction function for compensating the deformation from the prediction function, and designing a mold using the correction function And butterflies.
Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis (that is, the height direction) is the y-axis. The body (i.e., the body desired to be molded by the mold) is symmetric on the horizontal plane by a cutting plane that includes a point that includes the x-axis and y-axis and indicates the maximum height of the molded body. Is the ratio of the height in the y-axis direction at the cut surface and the width of the cut surface in the x-axis direction in contact with the horizontal plane when the resin is installed in the above manner. Dimensional change rate: When the resin is light or thermosetting resin, The rate of volume change before and after curing. If the resin is a thermoplastic resin, the value is calculated as “(Glass transition temperature of the thermoplastic resin (° C.) − Scheduled environment temperature (° C.)) × Linear expansion coefficient”. Is

In this specification, the sphere notch or the sphere notch shape is a three-dimensional shape obtained by cutting the sphere along one plane.
The “scheduled environment temperature (° C.)” is a temperature in an area or environment where the molded product formed by the mold of the present invention is planned to be used. is there. In Japan, it is usually 25 ° C.

The material of the mold in the present invention is not particularly limited, and examples thereof include metal, quartz, sapphire, silicone, cycloolefin polymer, and fluorine polymer.

In the present invention, the resin is fixed to the base surface at the bottom, and deformation is predicted as shrinkage deformation occurs at a constant rate in the same direction as the resin hardens or solidifies.

[Embodiment 1: Mold production method for producing a linear shaped body having a rectangular or trapezoidal cross section in a plane perpendicular to the longitudinal direction]
For example, a linear shaped body having a rectangular or trapezoidal cross section in a plane perpendicular to the longitudinal direction due to shrinkage deformation of the resin [preferably, a cross section in a plane perpendicular to the longitudinal direction having an aspect ratio of A is rectangular or trapezoidal. Prediction of the shape of a shaped product that is a linear structure and has a shape in which the structure is fixed to the base surface on the bottom surface can be performed by the analysis system illustrated in FIG. In the present invention, the shapes of the upper surface and the side surface of the molded body are examined.

It is considered that the upper surface of the molded body is deformed by a force generated in the vertical direction and a force generated in the horizontal direction. Therefore, the prediction function for the deformation of the upper surface height is expressed by the following equation (1-1) ′.

(Where α ₀ is the dimensional change rate of the resin, b is a parameter related to the ratio of the elastic modulus of the resin and the force in the width direction, x includes the x-axis and y-axis of the space formed by the recesses, and The half width of the cut surface including the point indicating the maximum height of the space, c is a parameter relating to the ratio of the contraction in the height direction to the contraction in the width direction)

It is considered that the side surface of the molded body is deformed by the force generated in the lateral direction with the base surface interface portion fixed to the base surface. Therefore, the prediction function of the deformation of the side surface width is expressed by the following formula (1-2) ′.

(Where α ₀ is the resin dimensional change rate, y is the height of the space, τ _s is the side-shrinkage relaxation coefficient, k _s is the x-axis direction shrinkage correction coefficient, and A is the aspect ratio)

In the above formula, b, c, τ _s, k _s are obtained by fitting, for example, compacts having various aspect ratios by finite element analysis. Here, the finite element analysis can be performed using, for example, structural analysis software “MARC” (manufactured by MSC Software) or the like. The finite element analysis results are shown in FIGS.

In addition, the deformation of the side surface of the molded body may be obtained by using, for example, an actual measurement value in addition to the simulation using the structural analysis software “MARC” (manufactured by MSC Software Co., Ltd.).

From FIG. 6, b is represented by a function represented by the following formula (b-1). Further, as shown in FIG. 14, since the prediction error is reduced in a range where the aspect ratio is large, according to the method of the present invention, a molded body having a larger aspect ratio (aspect ratio is preferably 0.1 or more). In this case, it can be seen that better prediction accuracy can be exhibited and the error can be extremely reduced.

In the above formula (b-1), b ₁ is a number of 0.21 to 0.84, preferably 0.42. b ₂ is a number of 0.3 to 0.9, preferably 0.6. b ₃ is a number of 1.5 to 2.5, preferably 2.0. b ₄ is a number from 0.06 to 0.24, preferably 0.12. A is the same as above.

From FIG. 7, c is represented by a function represented by the following formula (c-1).

In the formula, c ₁ is a number of 0.2 to 0.8, preferably 1.0. c ₂ is a number from 2.5 to 3.5, preferably 3.0. c ₃ is a number of 0.5 to 2.0, preferably 1.0. A is the same as above.

From FIG. 8, τ _s is represented by a function represented by the following formula (τ _s −1). Further, k _s is in a range of 0.9r ≦ k _s ≦ 1.1r with respect to r satisfying the following formula (k _s −1).

In the formula, τ _s1 is a number between 0.12 and 0.46, preferably 0.23. A is the same as above.

The stretching correction coefficients ε _x and ε _y can be derived, for example, by the following procedure using the prediction function.
1. y = f _uy (x), determining the point of intersection of _{x = f sx (y) (} x 0, y 0).
2. The temporary correction shape g _u (x) of the upper surface and the temporary correction shape g _s (y) of the side surface are calculated from the following equations.
g _u (x) = 1 / f _uy (x)
g _s (y) = (1 / 2A) ² / f _sx (y)
4). Next, the horizontal height y ₁ = g _u (x ₀ ) of the provisional correction shape and the half width x ₁ = g _s (y ₀ ) of the provisional correction shape are obtained.
5. The horizontal stretching ratio ε _x and the vertical stretching ratio ε _y of the provisional correction shape are calculated from the following equations.
ε _x = x ₁ / x ₀
ε _y = y ₁ / y ₀
6). As described above, the upper surface correction function (1-1) and the side surface correction function (1-2) are obtained as follows.
Fu ⁻¹ (x) = g _u (x / ε _x ) Domain (−x ₁ ≦ x ≦ x ₁ ) (1-1)
Fs ⁻¹ (y) = g _s (y / ε _y ) range (−y ₁ ≦ y ≦ y ₁ ) (1-2)
Here, the stretching ratio is a constant value in the horizontal and vertical directions, but may be changed depending on the horizontal and vertical positions. The rate of change includes proportional stretching and moderate stretching.

Furthermore, the cross-sectional shape of the mold after correction is obtained by connecting Fu ⁻¹ and Fs ⁻¹ (see FIGS. 2 and 3).

From the above, the following method is preferable as the mold manufacturing method in the case of the present embodiment [1].
That is,
A mold for manufacturing a resin having a dimension change rate of α ₀ and manufacturing a linear shaped body having a rectangular or trapezoidal cross section in a plane perpendicular to the longitudinal direction and having an aspect ratio A defined below. A method for manufacturing a mold, characterized in that the shape of the recess of the mold is the following shape [1].
Mold concave shape [1]: One direction on the horizontal plane is the x axis, the direction perpendicular to the x axis is the z axis, and the direction perpendicular to the x and z axes is the y axis, and the mold is on the horizontal plane In addition, the cut surface of the upper surface of the space formed by the recess when the recess of the mold is installed so as to open to the horizontal plane and the recess is installed symmetrically on the plane including the x-axis and the y-axis And the shape of the side surface of the space at the cut surface is a curve represented by the following formula (1-2) Aspect ratio: one direction on the horizontal plane X axis, a direction perpendicular to the x axis on the horizontal plane as a z axis, a direction perpendicular to the x axis and the z axis as a y axis, and a molded product by a mold including the x axis and the y axis on the horizontal plane, and The molded body is left by the cut surface including the point indicating the maximum height of the molded body. It is the ratio between the height in the y-axis direction at the cut surface and the width of the cut surface in the x-axis direction in contact with the horizontal plane when installed so as to be right-symmetric. Dimensional change rate: resin is light or thermosetting resin Is the volume change rate before and after curing, and when the resin is a thermoplastic resin, “(Glass transition temperature of the thermoplastic resin (° C.) − Scheduled environment temperature (° C.)) × Linear expansion coefficient” Is the calculated value

Mold for producing a linear shaped body having a rectangular or trapezoidal cross section in a plane perpendicular to the longitudinal direction, which is obtained by the above method and molded with a resin having a dimensional change rate of α ₀ and an aspect ratio of A. Has the concave shape [1].

[Embodiment 2: Method for producing a mold for producing a quadrangular prism shape or a truncated pyramid shaped body]
For example, a quadrangular prism shape or a truncated pyramid shaped molded body by shrinkage deformation of a resin [preferably, a quadrangular prism shape or a truncated pyramid shape structure having an aspect ratio of A, and the structure is The shape prediction of the formed body having a shape fixed to the base surface at the bottom surface can be performed by the analysis system shown in FIG. In the present invention, the shapes of the upper surface and the four side surfaces of the molded body are examined.

Consider a quadrangular prism shaped compact with −1 / 2A ≦ x ≦ 1 / 2A, 0 ≦ y ≦ 1, and −1 / 2A ≦ z ≦ 1 / 2A.
As shown in FIG. 17, the upper surface and the four side surfaces are considered to be gradually contracted toward the center of the surface.

The prediction function of the upper surface deformation is expressed by the following formula (1-1) ′.

It is considered that the four side surfaces (6-1) to (6-4) of the molded body are deformed by a force generated in the horizontal direction and the vertical direction in a state where the base surface interface portion is fixed to the base surface. Therefore, the prediction function of the deformation of the side surface width is expressed by the following formulas (1-2-1) ′ to (1-2-4) ′.

In addition, the deformation of the side surface of the molded body may be performed using, for example, an actual measurement value in addition to the simulation using the structure analysis software “MARC” (manufactured by MSC Software Co., Ltd.).

And, the correction function of the upper surface and the side surface of the mold can be derived using the prediction function.

Further, the corners of the mold are corrected as shown in (1) to (4) of FIG.
The corners formed by two adjacent side surfaces are a point on the curve representing the corner end of one side surface and a point on the curve representing the corner end of the other side surface, And a point having the same y-axis value are connected by a straight line, a polygonal line, an arc, or two adjacent side surfaces are extended, and a line intersecting the both side surfaces is defined as a corner (or an end side). .
The shape of the corner formed by the side surface parallel to the plane including the x-axis and the y-axis and the top surface is on the curve representing the corner-side end portion of the side surface and the curve representing the corner-side end portion of the top surface. A point that is the same as the point and has the same x-axis value is connected by a straight line, a polygonal line, or an arc.
The shape of the corner formed by the side surface and the upper surface parallel to the surface including the y-axis and the z-axis is on the curve representing the corner-side end portion of the side surface and the curve representing the corner-side end portion of the upper surface. The points that are the same as the z-axis value are connected by straight lines, polygonal lines, or arcs.

As mentioned above, as a mold manufacturing method in the case of this embodiment [2], the following method is preferable.
That is,
A method for producing a mold for producing a molded article having a dimensional change rate of α ₀ and having an aspect ratio defined below of A, a quadrangular prism shape, or a truncated pyramid shape, A method for producing a mold, characterized in that the concave shape of the mold is the following shape [2].
Mold concave shape [2]: One direction on the horizontal plane is the x axis, the direction perpendicular to the x axis is the z axis, and the direction perpendicular to the x and z axes is the y axis, and the mold is on the horizontal plane In the case where the concave portion of the mold is installed so as to open on the horizontal plane side, and the concave portion is set to be symmetrical in the plane including the x axis and the y axis,
The upper surface of the space formed by the horizontal surface and the concave portion and including the bottom surface, the four side surfaces, and the upper surface is indicated by a continuous curve in the z-axis direction represented by the following formula (1-1).
The four side surfaces of the space are respectively shown by continuations in the x-axis direction or z-axis direction of the curves represented by the following formulas (1-2-1) to (1-2-4), respectively.
The shape of the corner formed by two adjacent side surfaces is a point 1 on the curve representing the corner end of one side surface and a point on the curve representing the corner end of the other side surface, A straight line, a polygonal line, or an arc connecting the point 1 and the point 2 having the same y-axis value;
The shape of the corner formed by the side surface parallel to the plane including the x-axis and the y-axis and the top surface is the point 1 ′ on the curve representing the corner-side end portion of the side surface and the curve representing the corner-side end portion of the top surface. A straight line, a polygonal line, or an arc connecting the point 1 ′ and the point 2 ′ having the same x-axis value,
The shape of the corner formed by the side surface and the upper surface parallel to the plane including the y-axis and the z-axis is the point 1 ″ on the curve representing the corner end of the side surface and the curve representing the corner end of the upper surface. Which is a straight line, polygonal line, or arc connecting the point 1 ″ and the point 2 ″ having the same z-axis value.

In the above formulas (1-1) and (1-2-1) to (1-2-4), b is represented by a function represented by the following formula (b-1). c is represented by a function represented by the following formula (c-1). τ _s is expressed by a function represented by the following formula (τ _s −1). Further, the stretching correction coefficient ε _x is derived by the same procedure as in the case of a shaped body having a rectangular or trapezoidal cross section in a plane perpendicular to the longitudinal direction and having an aspect ratio of A, using the prediction function. can do.

A mold for producing a molded article having a square columnar shape or a truncated pyramid shape, which is obtained by the above method and is molded by molding a resin having a dimensional change rate of α ₀ and having an aspect ratio of A, has the above concave shape [ 2].

[Embodiment 3: Mold production method for producing a linear shaped product having a triangular cross section in a plane perpendicular to the longitudinal direction]
For example, a linear shaped product having a triangular cross section in the plane perpendicular to the longitudinal direction due to shrinkage deformation of the resin [preferably, the aspect ratio is A and the cross section in the plane perpendicular to the longitudinal direction is triangular (equilateral triangle or The shape prediction of the molded body having a shape in which the structure is fixed to the base surface at the bottom surface] can be performed by the analysis system illustrated in FIG. The molded body contracts in the vertical direction, the contraction is zero at the most distal end, and the contraction in the height direction is gradually increased toward the center. Therefore, the x coordinate of the prediction function is expressed by the following formula (2-1) ′, and the y coordinate of the prediction function is expressed by the following formula (2-2) ′.

(Where α ₀ is the dimensional change rate of the resin, y is the height of the space, τ _t is the relaxation coefficient of side shrinkage, A is the aspect ratio, and k _t is the following formula (k _t − 1)

(With respect to q satisfying 0.9q ≦ k _t ≦ 1.1q)

In the above equation, τ _t is a coefficient related to the aspect ratio, and _kt is a correction value for compensating for shrinkage in the x-axis direction. This is obtained by fitting a molded body having various aspect ratios by finite element analysis. The finite element analysis results are shown in FIG.

From FIG. 9, τ _t is represented by a function represented by the following formula (τ _t −1). K _t is in the range of 0.9q ≦ k _t ≦ 1.1q with respect to q satisfying the above formula (k _t −1). Further, as shown in FIG. 15, since the prediction error is reduced in the range where the aspect ratio is small, according to the method of the present invention, the molded body having a larger aspect ratio (for example, an aspect ratio of 0.7 or less) is obtained. In this case, it can be seen that better prediction accuracy can be exhibited and the error can be extremely reduced.

Τ _t1 in the formula is, for example, a number from 1.0 to 2.0, and preferably 1.5. Further, τ _t2 in the formula is, for example, a number from 0.2 to 1.0, and preferably 0.5. A is the same as above.

From FIG. 9, the cross-section f _ty (x) of the compact after shrinkage deformation is determined.

The mold correction function F _ty ⁻¹ (x) can be derived by the following equation using the prediction function.
F _ty ⁻¹ (x) = F _ty ² / f _ty (x)

As mentioned above, as a mold manufacturing method in the case of this embodiment [3], the following method is preferable.
That is,
Mold manufacturing method for molding a resin having a dimensional change rate of α ₀ and manufacturing a linear shaped product having a triangular cross section in a plane perpendicular to the longitudinal direction and having an aspect ratio of A defined below A method for manufacturing a mold, wherein the concave shape [3] of the mold is the following shape.
Mold concave shape [3]: One direction on the horizontal plane is the x axis, the direction perpendicular to the x axis is the z axis, and the direction perpendicular to the x axis and the z axis is the y axis, and the mold is on the horizontal plane In addition, when the concave portion of the mold is installed so as to open to the horizontal plane side, the concave portion is set to be bilaterally symmetric in the plane including the x axis and the y axis and including the point indicating the maximum depth of the concave portion. ,
The shape of the hypotenuse when the space formed by the horizontal plane and the concave portion and including the bottom surface and the two inclined surfaces is cut by a plane including the x-axis and the y-axis, the x-coordinate is expressed by the following formula (2-1), and y It is a curve formed by collecting points whose coordinates are represented by the following formula (2-2)

Where k _t is the following formula (k _t −1)

For q that satisfies the above, the range is 0.9q ≦ k _t ≦ 1.1q.

In the formula, α ₀ represents the dimensional change rate of the resin, y represents the height of the space, and A represents the aspect ratio. τ _t is a relaxation coefficient of side contraction.

A mold for producing a linear shaped product having a triangular cross section in a plane perpendicular to the longitudinal direction, which is obtained by the above method and is molded by a resin having a dimensional change rate of α ₀ and an aspect ratio of A, It has the said recessed part shape [3], It is characterized by the above-mentioned.

[Embodiment 4: Mold production method for producing a quadrangular pyramid shaped body]
For example, a linear shaped product having a triangular cross section in a plane perpendicular to the longitudinal direction due to shrinkage deformation of the resin [preferably a quadrangular pyramid structure with an aspect ratio of A, and the structure is The shape prediction of the molded body having a shape fixed to the base surface] can be performed by the analysis system shown in FIG.

Four points on the x, y, z coordinate axes [(x, y, z) = (0, 1, 0), (−1 / 2A, 0, 1 / 2A), (1 / 2A, 0, 1 / 2A), (1 / 2A, 0, -1 / 2A), (-1 / 2A, 0, -1 / 2A)] are considered as quadrangular pyramid shaped compacts.

It is considered that the four side surfaces (5-1) to (5-4) of the molded body are deformed by the force generated in the horizontal direction and the vertical direction with the base surface interface portion fixed to the base surface. Therefore, the x coordinate of the prediction function is expressed by the following formula (2-1) ′, and the y coordinate of the prediction function is expressed by the following formula (2-2) ′.

(Wherein, y represents the height of the space, tau _t represents a relaxation coefficient aspect shrinkage, A .k _t indicating the aspect ratio is represented by the following formula (k _t -1)

For q that satisfies the above, the range is 0.9q ≦ k _t ≦ 1.1q.

τ _t is represented by a function represented by the following formula (τ _t −1).

The mold correction function can be derived using the prediction function.

As mentioned above, as a mold manufacturing method in the case of this embodiment [4], the following method is preferable.
That is,
A mold manufacturing method for manufacturing a quadrangular pyramid-shaped molded body having an aspect ratio of A by molding a resin having a dimensional change rate of α ₀ , wherein the concave shape of the mold is the following shape [4]. The manufacturing method of the mold characterized by the above-mentioned.
Mold concave shape [4]: One direction on the horizontal plane is the x axis, the direction perpendicular to the x axis is the z axis, and the direction perpendicular to the x and z axes is the y axis, and the mold is on the horizontal plane In the case where the concave portion of the mold is opened on the horizontal plane side, and the concave portion is set so as to be symmetric with respect to the plane including the point indicating the maximum depth of the concave portion,
The bottom surface of the space formed by the horizontal plane and the recess is a quadrangle, the four sides of the bottom surface are parallel to the x axis or the z axis, and the four side surfaces of the space have one side of the bottom surface as the bottom side, X of a curve formed by collecting points on the x-coordinate, y-coordinate, and z-coordinate represented by the following formulas (5-1) to (5-4) that connect the base and the vertex of the space. Indicated in the axial direction or continuous in the z-axis direction,
The shape of the corner formed by two adjacent side surfaces is a point 1 on the curve representing the corner end of one side surface and a point on the curve representing the corner end of the other side surface, A method of manufacturing a mold, wherein the mold is a straight line, a polygonal line, or an arc connecting the point 1 and a point 2 having the same y-axis value.

(With respect to q satisfying 0.9q ≦ k _t ≦ 1.1q)

A mold for producing a quadrangular pyramid-shaped molded article obtained by molding the resin having a dimensional change rate of α ₀ and having an aspect ratio of A has the concave shape [4]. Features.

[Embodiment 5: Mold production method for producing a linear shaped product having a spherical cross section in a plane perpendicular to the longitudinal direction]
For example, a linear shaped article having an aspect ratio of A and a section perpendicular to the longitudinal direction and having a sphere-shaped cross section due to shrinkage deformation of the resin [preferably, on a surface perpendicular to the longitudinal direction and having an aspect ratio of A The shape prediction of a shaped body having a shape in which the cross-section is a spherical shape and the structure is fixed to the base surface at the bottom surface can be performed by the analysis system shown in FIG. The molded body shrinks in the vertical direction, the shrinkage is zero at the most distal end, and the shrinkage is considered to gradually increase toward the center. Therefore, the x coordinate of the prediction function is expressed by the following formula (3-1) ′, and the y coordinate of the prediction function is expressed by the following formula (3-2) ′.

In the formula, α ₀ is the rate of dimensional change of the resin, r is the radius of the spherical surface, y is the height of the space, and y ₀ is on the y-axis at the center of the sphere that includes the molded product to be produced. The y coordinate is shown. τ _c is the relaxation coefficient of the spherical surface, and A is the aspect ratio. k _c is the following formula

For p satisfying the above condition, 0.9p ≦ k _c ≦ 1.1p. .

In the above formula, r represents the radius of the spherical surface and satisfies the following formula.
r = 1/2 [(1 / 2A) ² +1]
(Where A represents the aspect ratio)

In the above equation, τ _c is a parameter relating to the ratio of the shrinkage in the height direction and the shrinkage in the width direction, and this can be obtained by fitting a molded body having various aspect ratios by finite element analysis. A finite element analysis result is shown in FIG.

From FIG. 10, τ _c is represented by a function represented by the following formula (τ _c −1). Further, as shown in FIG. 16, since the prediction error is reduced in the range where the aspect ratio is small, according to the method of the present invention, the molded body having a small aspect ratio (for example, an aspect ratio of 0.3 or less) is obtained. In this case, it can be seen that better prediction accuracy can be exhibited and the error can be extremely reduced.

In the formula (τ _c −1), τ _c1 is a number of 1.0 to 2.0, preferably 1.6. τ _c2 is a number from 0.2 to 1.0, preferably 0.6. A is the same as above.

From FIG. 10, the molded product cross section f _cy (x) after shrinkage deformation is determined.

The mold correction function F _cy ⁻¹ (x) can be derived from the following equation using the prediction function.
F _cy ⁻¹ (x) = F _cy ² / f _cy (x)

As mentioned above, as a mold manufacturing method in the case of this embodiment [5], the following method is preferable.
That is,
Manufacturing a mold for molding a resin having a dimensional change rate of α ₀ and manufacturing a linear molded body having a cross section of a sphere in a plane perpendicular to the longitudinal direction and having an aspect ratio A defined below. It is a method, Comprising: The manufacturing method of the mold characterized by making the recessed part shape of a mold into the following shape [5].
Mold concave shape [5]: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. In addition, when the concave portion of the mold is installed so as to open on the horizontal plane side, the concave portion is set to be bilaterally symmetrical on the plane including the x axis and the y axis and including the point indicating the maximum depth of the mold.
The cross-sectional shape of the sphere-shaped side surface when a space including a bottom surface and a sphere-shaped side surface formed by a horizontal plane and a concave portion is cut by a plane including the x-axis and the y-axis, 3-1) is a curve formed by collecting points whose y-coordinate is expressed by the following formula (3-2).

(With respect to q satisfying 0.9q ≦ k _t ≦ 1.1q)

A mold for producing a linear shaped product having a cross section of a sphere with a cross section in a plane perpendicular to the longitudinal direction, which is obtained by the above-described method, is molded with a resin having a dimensional change rate of α ₀ and an aspect ratio is A. And having the concave shape [5].

[Embodiment 6: Mold manufacturing method for manufacturing a spherically shaped molded body]
For example, a spherically-shaped molded article having an aspect ratio of A due to shrinkage deformation of a resin [preferably a spherically-shaped structure having an aspect ratio of A, and the structure is fixed to the base surface at the bottom surface The shape prediction of the formed body having the formed shape] can be performed by the analysis system shown in FIG. It is considered that the shrinkage of the molded body gradually increases toward the center.

Therefore, the x coordinate of the prediction function is expressed by the following formula (4-1-1), the y coordinate of the prediction function is expressed by the following formula (4-1-2), and the z coordinate of the prediction function is expressed by the following formula (4) -1-3).

(For p that satisfies 0.9p ≦ k _c ≦ 1.1p)

The mold correction function can be derived using the prediction function.

As mentioned above, as a mold manufacturing method in the case of this embodiment [6], the following method is preferable.
That is,
A mold manufacturing method for molding a resin having a dimensional change rate of α ₀ and manufacturing a spherically-shaped molded body having an aspect ratio of A, wherein the concave shape of the mold is the following shape [6]. The manufacturing method of the mold characterized by the above-mentioned.
Mold concave shape [6]: One direction on the horizontal plane is the x axis, the direction perpendicular to the x axis is the z axis, and the direction perpendicular to the x and z axes is the y axis, and the mold is on the horizontal plane In the case where the concave portion of the mold is opened on the horizontal plane side, and the concave portion is set so as to be symmetric with respect to the plane including the point indicating the maximum depth of the concave portion,
The bottom surface of the space formed by the horizontal plane and the concave portion is a circle, and when the circle is divided into four arcs by the xy plane and the zy plane, points on the four arcs, The line connecting the vertices is a curve formed by collecting points on the x, y, and z coordinates represented by the following formulas (4-1) to (4-4).

(For p that satisfies 0.9p ≦ k _c ≦ 1.1p)

τ _c is represented by a function represented by the above formula (τ _c −1).

A mold obtained by the above method for molding a resin having a dimensional change rate of α ₀ and producing a spherically-shaped molded body having an aspect ratio of A has the concave shape [6]. And

According to the mold manufacturing method of the present invention, it is possible to appropriately predict shrinkage deformation due to hardening or solidification of a resin for a molded body having various aspect ratios by calculation using a specific function. If a mold is originally designed (or a mold for producing a mold is designed) and a mold is manufactured based on the design, a molded body having a desired shape with a high accuracy in a very short time compared to the conventional case. (For example, a molded article having a shape error of 5% or less (preferably 3% or less, particularly preferably 1% or less, particularly preferably 0.5% or less) using a resin having a dimensional change rate of 10%) You can definitely get it.

[Mold manufacturing equipment]
The mold manufacturing apparatus of the present invention molds a resin and has various aspect ratios, such as a cone shape, a pyramid shape, a truncated cone shape, a truncated pyramid shape, a cylindrical shape, a prism shape, a spherical shape, or a longitudinal direction. An apparatus for manufacturing a mold for manufacturing a linear shaped body having a rectangular, trapezoidal, triangular, or sphere-shaped cross section in a vertical plane, wherein a resin having an arbitrary dimensional change rate has an arbitrary aspect ratio A prediction function of deformation at the time of forming into a molded body is obtained, a correction function for compensating for deformation is calculated from the prediction function, and a mold is designed using the correction function.

The mold manufacturing apparatus of the present invention obtains a prediction function of deformation when molding a resin having an arbitrary dimensional change rate into a molded body having an arbitrary aspect ratio, and compensates the deformation from the prediction function. The correction function is calculated, and the mold is designed and manufactured using the correction function (for example, the mold of the mold is designed using the correction function, and the mold is manufactured using the obtained mold). The configuration is not particularly limited as long as it has a function.

If the mold manufacturing apparatus of the present invention is used, shrinkage deformation accompanying the hardening or solidification of the resin is accurately predicted, and the mold is manufactured based on this, so that a mold with deformation compensation can be manufactured. The mold thus obtained is very useful since it can reliably produce a molded body having a desired shape.

[Mold design program]
The mold design program of the present invention forms a resin and has various aspect ratios, such as a cone shape, a pyramid shape, a truncated cone shape, a truncated pyramid shape, a cylindrical shape, a prism shape, a spherical shape, or perpendicular to the longitudinal direction. A mold design program for causing a computer to execute a mold design for manufacturing a molded product having a rectangular, trapezoidal, triangular, or spherically shaped cross section in a simple plane, the shape of a desired molded product, A first step of inputting an aspect ratio A and a dimensional change rate α ₀ of the resin to be formed;
A second step of causing the computer to select a correction function in accordance with the desired shape of the molded body from the input shape of the desired molded body, the aspect ratio A, and the dimensional change rate α ₀ of the resin to be formed; And a third step of causing the computer to perform correction of the concave shape of the mold by the selected correction function.

The second step is a step of selecting a correction function according to a desired shape of the molded body,
For example, the desired molded body is made of a cured or solidified resin having a dimensional change rate of α ₀ , an aspect ratio of A, a prismatic shape, a truncated pyramid shape, or a rectangular section in a plane perpendicular to the longitudinal direction. Alternatively, in the case of a trapezoidal linear shaped product, the concave shape of the mold is set such that one direction on the horizontal plane is the x axis, the direction perpendicular to the x axis is the z axis, and the x axis and the z axis are perpendicular to the horizontal plane. The direction is the y axis, and the mold is recessed on the cutting plane including the x axis and the y axis in a state where the mold is opened on the horizontal plane so that the concave portion of the mold opens to the horizontal plane, and the point indicating the maximum depth of the mold. When the cross-sectional shape of the upper surface of the space formed by the concave portion is a curve represented by Formula (1-1), and the side surface of the space is The cross-sectional shape is expressed by formula (1-2) Let the curve be
For example, the desired molded body is made of a cured or solidified resin having a dimensional change rate of α ₀ , has an aspect ratio of A, a pyramid shape, or a linear cross section in a plane perpendicular to the longitudinal direction. In the case of a molded body, the concave shape of the mold is an x-axis in one direction on the horizontal plane, a z-axis in a direction perpendicular to the x-axis on the horizontal plane, and a y-axis in a direction perpendicular to the x-axis and z-axis, In a state where the mold is placed on a horizontal plane so that the concave portion of the mold opens to the horizontal plane side, the concave portion is symmetrical on the cutting plane including the x axis and the y axis and including the point indicating the maximum depth of the mold. Let the cross-sectional shape in the said cut surface of the side surface of the space formed by the recessed part be a curve represented by Formula (2).
For example, the desired molded body is formed of a cured or solidified resin having a dimensional change rate of α ₀ , has a spherical shape with an aspect ratio of A, or a line with a spherical surface in a cross section perpendicular to the longitudinal direction. In the case of a molded body having a shape, the concave shape of the mold is defined as an x-axis in one direction on the horizontal plane, a z-axis in a direction perpendicular to the x-axis on the horizontal plane, and a y-axis in a direction perpendicular to the x-axis and z-axis. The recesses are symmetrical on the cutting plane including the x-axis and the y-axis and the point indicating the maximum depth of the mold in a state where the mold is placed on the horizontal plane so that the recesses of the mold open to the horizontal plane side. In this case, the cross-sectional shape of the side surface of the space formed by the concave portion in the cut surface is a curve represented by Expression (3).

The computer is not particularly limited as long as it is a device that can perform necessary calculations, and for example, an electronic computer or the like is preferably used. A numerically controlled machine tool is preferably used, and a three-dimensional cutting machine having a multi-axis control function is suitable as the numerically controlled machine tool.

The mold design program of the present invention can perform the design of the mold with trial and error very efficiently by causing the computer to execute the program.

[Method for producing molded article]
The method for producing a molded article of the present invention is a molded article comprising a cured product or a solidified product of the resin, through a step of producing a mold by the above-described mold production method and molding a resin using the obtained mold. It is characterized by obtaining.

The molded body has various aspect ratios, such as a cone shape, a pyramid shape, a truncated cone shape, a truncated pyramid shape, a cylindrical shape, a prismatic shape, a spherical shape, or a cross section in a plane perpendicular to the longitudinal direction, a trapezoid, There is no particular limitation as long as it is a triangular or spherically shaped molded body. For example, a micromirror array etc. are mentioned as a truncated pyramid shape or a prism-shaped molded object. The micromirror array is an optical member in which a large number of three-dimensional patterns of rectangular pillars and pyramids having a height of 1 to 1000 μm are arranged in a grid pattern (for example, arranged in a grid pattern with an interval of 1 to 1000 μm).

For example, when a micromirror array is manufactured, the mold preferably has a configuration in which a large number of concave portions having a truncated pyramid shape or a prismatic inverted shape are arranged in a lattice shape.

Examples of the method for molding the resin include the following methods (1) and (2).
(1) A method in which a resin is applied to a mold, a substrate is pressed from above, the resin is cured or solidified, and then the mold is peeled off. (2) The mold is applied to the resin applied on the base surface (or substrate). Method of releasing the mold after pressing and molding, and curing or solidifying the resin

As the resin, any resin that can form a molded body by curing or solidification can be used without particular limitation. Examples of the resin include light or thermosetting resin and thermoplastic resin.

The light or thermosetting resin is a resin that forms a cured product by light irradiation or heat treatment, and contains a curable compound and a polymerization initiator. In addition, known and commonly used additives (for example, solvents, antioxidants, surface conditioners, photosensitizers, antifoaming agents, leveling agents, coupling agents, surfactants, flame retardants, UV absorbers as necessary) , Coloring agents, etc.).

The curable compound includes a cationic polymerizable compound and a radical polymerizable compound, and the cationic polymerizable monomer includes, for example, an epoxy compound, an oxetane compound, a vinyl ether compound, and the like. Further, the radical polymerizable compound includes, for example, an olefin monomer, a (meth) acrylic monomer, a styrene monomer, and the like.

As the resin in the present invention, for example, when a molded body having excellent heat resistance is desired, it is preferable to use a light or thermosetting resin, and in particular, optical characteristics (particularly transparency), high hardness, and When a molded article having heat resistance is desired, an epoxy resin [particularly, an epoxy group composed of two adjacent carbon atoms and oxygen atoms constituting an alicyclic ring such as a cyclohexene oxide group (that is, an aliphatic group) It is preferable to use a compound having a cyclic epoxy group, for example, a compound represented by the following formula (i).

In the above formula (i), X represents a single bond or a linking group (a divalent group having one or more atoms). Examples of the linking group include a divalent hydrocarbon group, an alkenylene group in which part or all of a carbon-carbon double bond is epoxidized, a carbonyl group, an ether bond, an ester bond, a carbonate group, an amide group, and the like. And a group in which a plurality of are connected. In addition, the substituent (for example, alkyl group etc.) may couple | bond with the cyclohexene oxide group in Formula (i).

Representative examples of the compound represented by the above formula (i) include 3,4-epoxycyclohexylmethyl (3,4-epoxy) cyclohexanecarboxylate, (3,4,3 ′, 4′-diepoxy) biphenyl. Cyclohexyl, bis (3,4-epoxycyclohexylmethyl) ether, 1,2-epoxy-1,2-bis (3,4-epoxycyclohexane-1-yl) ethane, 2,2-bis (3,4-epoxy) And cyclohexane-1-yl) propane and 1,2-bis (3,4-epoxycyclohexane-1-yl) ethane.

[Molded product manufacturing equipment]
The apparatus for producing a molded body of the present invention is formed of a resin, and has various aspect ratios, a cone shape, a pyramid shape, a truncated cone shape, a truncated pyramid shape, a cylindrical shape, a prismatic shape, a spherical shape, or a longitudinal direction. Is a device for manufacturing a linear shaped product having a rectangular, trapezoidal, triangular, or spherical notched cross section in a plane perpendicular to the surface, and molding a resin having an arbitrary dimensional change rate into a molded product having an arbitrary aspect ratio. A deformation prediction function is obtained, a correction function for compensating the deformation is calculated from the prediction function, a mold is designed and manufactured using the correction function, and the resin is obtained using the obtained mold. It is characterized by molding.

The apparatus for producing a molded body of the present invention obtains a prediction function of deformation when molding a resin having an arbitrary dimensional change rate into a molded body having an arbitrary aspect ratio, and compensates the deformation from the prediction function. The correction function is calculated, the mold is designed and manufactured using the correction function (for example, the mold of the mold is designed using the correction function, and the mold is manufactured using the obtained mold. The structure is not particularly limited as long as it has a function and a function of molding a resin using the obtained mold.

If the manufacturing apparatus of the molded body of the present invention is used, shrinkage deformation accompanying resin curing or solidification is accurately predicted, and an ultraviolet curable composition is molded using a mold manufactured based on this, A molded body having a desired shape can be reliably produced.

<Explanation of simulation results>
Next, a simulation method and results for each embodiment will be described below.

Embodiment [1]
According to the following procedure, the shape of the molded body after curing shrinkage is verified by computer simulation, and the design of the mold is changed using this.
Procedure 1: Extract parameters based on the results calculated using commercially available software for structural analysis (“MARC”, MSC Software) (FIGS. 6-8)
Step 2: Determine the desired aspect ratio of the molded body and the dimensional change rate of the resin to be used. Procedure 3: Extract b and c from the parameters (FIGS. 6 and 7), and the cross-sectional shape of the upper surface of the molded body after shrinkage Step 4: Extract τ _s and k _s from the parameters (Fig. 8) to determine the approximate function of the cross-sectional shape of the side surface of the compact after shrinkage deformation. Shrinkage accompanying hardening or solidification according to the above-mentioned method Using the prediction function, the shape of the deformed molded body (a molded body having a linear shape with a rectangular cross section in the plane perpendicular to the longitudinal direction and the structure fixed to the base surface at the bottom) is used. The correction function was calculated using this, and the mold design was changed.
The results are shown in FIGS. From FIG. 11, when a resin having a shrinkage deformation rate of about 10% due to curing or solidification is used, the shape error can be suppressed to about 0.29% (σ value) by performing mold correction by the above method. I understood.

Embodiment [2]
The mold was corrected as described in FIGS.
The results are shown in FIG. From FIG. 21, when the correction was not performed, the side wall surface was distorted, but the distortion was reduced by the correction. The mean square error of the distance between the target surface and the surface after contraction without correction is 4.3 when the height of the structure is 1 (dimensionless) with respect to the contraction ratio of 10%. % Error was reduced to 0.1% by applying the correction.

Embodiment [3]
Procedure 1: Extract parameters based on the results calculated using commercially available software for structural analysis ("MARC", manufactured by MSC Software) (Fig. 9)
Step 2: the aspect ratio of the desired molded body, steps to determine the dimensional change of the resin to be used 3: Parameters extracts from tau _t and k _t (FIG. 9), approximation shaped body the cross-sectional shape after shrinking Determine the function According to the method described above, the compact after shrinkage deformation due to hardening or solidification (a linear structure with a cross section in the plane perpendicular to the longitudinal direction isosceles triangles, and the structure on the bottom surface The shape of the molded body having a fixed shape) was calculated using a prediction function, and a correction function was calculated using this, thereby changing the mold design.
The results are shown in FIGS. From FIG. 12, when a resin having a shrinkage deformation rate of about 10% due to hardening or solidification is used, the shape error (σ value; standard deviation in the y-axis direction) is obtained by correcting the mold by the above method. It turned out that it can suppress to 1.6 * 10 ^<-2 >.

Embodiment [4]
As shown in FIG. 19, the mold was corrected.
The results are shown in FIG. As shown in FIG. 22, when the correction is not performed, the side wall surface is distorted, but the distortion is eliminated by the correction. When the correction is not performed, the mean square error with respect to the target surface has an error of 17.1% when the height of the structure is 1 (non-dimensional) with respect to the contraction ratio of 10%. It was reduced to 0.3% by applying the correction.

Embodiment [5]
Procedure 1: Extract parameters based on the results calculated using commercially available software for structural analysis ("MARC", manufactured by MSC Software) (Fig. 10)
Step 2: Determine the desired aspect ratio of the molded body and the dimensional change rate of the resin to be used. Procedure 3: Extract τ _c from the parameter (Fig. 10) and determine an approximate function of the cross-sectional shape of the molded body after shrinkage. According to the above-mentioned method, the molded body after shrinkage deformation accompanying hardening or solidification (a linear structure having a cross section in a plane perpendicular to the longitudinal direction and having the structure fixed to the base surface on the bottom surface) The shape of the formed body) was calculated using a prediction function, and the correction function was calculated using this to change the design of the mold.
The results are shown in FIGS. From FIG. 13, when a resin having a shrinkage deformation rate of about 10% due to curing or solidification is used, the shape error (σ value; standard deviation in the y-axis direction) is obtained by correcting the mold by the above method. It turned out that it can suppress to 1.9 * 10 ^<-2 >.

According to the manufacturing method of the present invention, it is possible to quickly and surely design a mold used for manufacturing a fine structure such as a micromirror array by optical imprinting. Moreover, if the mold obtained in this way is used, a fine structure excellent in shape accuracy can be efficiently produced.

I Cut shape of the desired molded body
II Cut surface shape after shrinkage deformation due to hardening or solidification
III Spatial sectional shape of mold recess that compensates for shrinkage deformation due to hardening
IV Cross-sectional shape of a molded product obtained using a mold that compensates for shrinkage deformation due to hardening or solidification

Claims

Molded resin with various aspect ratios, cone shape, pyramid shape, truncated cone shape, truncated pyramid shape, cylindrical shape, prismatic shape, spherical notch shape, or rectangular cross section in the plane perpendicular to the longitudinal direction, trapezoid A method of manufacturing a mold for manufacturing a linear shaped product having a triangular or spherical shape, wherein a resin having an arbitrary dimensional change rate is deformed when formed into a molded product having an arbitrary aspect ratio. A method for manufacturing a mold, comprising: obtaining a prediction function, calculating a correction function for compensating for deformation from the prediction function, and designing the mold using the correction function.
Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. When the molded body is placed so as to be bilaterally symmetric by a cut surface that includes a point that includes the axis and the y-axis and that indicates the maximum height of the molded body, the height in the y-axis direction on the cut surface and the horizontal plane Dimensional change rate: If the resin is light or thermosetting resin, it is the volume change rate before and after curing. If the resin is a thermoplastic resin, “(thermal It is a value calculated by “Glass transition temperature of plastic resin (° C.) − Scheduled environment temperature (° C.)) × Linear expansion coefficient”.
A mold for forming a resin having a dimension change rate of α 0 and manufacturing a linear shaped body having a rectangular or trapezoidal cross section in a plane perpendicular to the longitudinal direction and having an aspect ratio A defined below. A method for manufacturing a mold, characterized in that the concave shape of the mold is the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is set to be bilaterally symmetric in the plane including the x axis and the y axis.
The shape of the upper surface of the space formed by the recess is a curve represented by the following formula (1-1), and the shape of the side surface of the space is represented by the following formula (1-2). Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. The height in the y-axis direction at the cut surface when the molded body is placed so as to be bilaterally symmetric by a cut surface including a point that includes the x axis and the y axis and indicates the maximum height of the molded body. Dimensional change rate: If the resin is light or a thermosetting resin, it is the volume change rate before and after curing, and if the resin is a thermoplastic resin , “(Glass transition temperature (° C) of thermoplastic resin-Expected ambient temperature ( Is a value calculated by)) × linear expansion coefficient "

(Where α 0 is the dimensional change rate of the resin, b is a parameter related to the ratio of the elastic modulus of the resin and the force in the width direction, x includes the x-axis and the y-axis of the space formed by the recesses, and The half width of the cut surface including the point indicating the maximum height of the space, c is a parameter relating to the ratio of the shrinkage in the height direction and the shrinkage in the width direction, and ε x is the horizontal stretching correction factor)

(Where α 0 is the dimensional change rate of the resin, y is the height of the space, τ s is the relaxation coefficient of side shrinkage, A is the aspect ratio, and ε y is the stretching correction coefficient in the vertical direction)
A method for producing a mold for producing a molded article having a dimensional change rate of α 0 and having an aspect ratio A defined as follows: A method for manufacturing a mold, wherein the concave shape of the mold is as follows.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is set to be bilaterally symmetric in the plane including the x axis and the y axis.
The upper surface of the space formed by the horizontal surface and the concave portion and including the bottom surface, the four side surfaces, and the upper surface is indicated by a continuous curve in the z-axis direction represented by the following formula (1-1).
The four side surfaces of the space are respectively shown by continuations in the x-axis direction or z-axis direction of the curves represented by the following formulas (1-2-1) to (1-2-4), respectively.
The shape of the corner formed by two adjacent side surfaces is a point 1 on the curve representing the corner end of one side surface and a point on the curve representing the corner end of the other side surface, A straight line, a polygonal line, or an arc connecting the point 1 and the point 2 having the same y-axis value;
The shape of the corner formed by the side surface parallel to the plane including the x-axis and the y-axis and the top surface is the point 1 ′ on the curve representing the corner-side end portion of the side surface and the curve representing the corner-side end portion of the top surface. A straight line, a polygonal line, or an arc connecting the point 1 ′ and the point 2 ′ having the same x-axis value,
The shape of the corner formed by the side surface and the upper surface parallel to the plane including the y-axis and the z-axis is the point 1 ″ on the curve representing the corner end of the side surface and the curve representing the corner end of the upper surface. A straight line, a polygonal line, or an arc connecting the point 1 ″ and the point 2 ″ having the same z-axis value. Aspect ratio: One direction on the horizontal plane is the x axis, and the horizontal plane The direction perpendicular to the x-axis is the z-axis, the direction perpendicular to the x-axis and the z-axis is the y-axis, the molded body formed of a mold is on a horizontal plane, includes the x-axis and the y-axis, and the maximum height of the molded body is Dimensional change is the ratio of the height in the y-axis direction at the cut surface to the width of the cut surface in the x-axis direction in contact with the horizontal plane when the molded body is placed so as to be symmetrical with the cut surface including the indicated point Rate: If the resin is light or thermosetting resin, it is the volume change rate before and after curing, and if the resin is a thermoplastic resin , - is a value calculated by "(glass transition temperature of the thermoplastic resin (℃) scheduled use environment temperature (℃)) × linear expansion coefficient"

(Where α 0 is the dimensional change rate of the resin, b is a parameter related to the ratio of the elastic modulus of the resin and the force in the width direction, x includes the x-axis and the y-axis of the space formed by the recesses, and The half width of the cut surface including the point indicating the maximum height of the space, c is a parameter relating to the ratio of the shrinkage in the height direction and the shrinkage in the width direction, and ε x is the horizontal stretching correction factor)

(Where α 0 is the dimensional change rate of the resin, y is the height of the space, τ s is the relaxation coefficient of side shrinkage, A is the aspect ratio, k 1 is the correction coefficient for the shrinkage rate in the x-axis direction, k 2 represents a correction coefficient for the contraction rate in the z-axis direction, and k 1 and k 2 are the same or different and are numbers of 1.0 to 2.0)
The shaped body is a truncated pyramid shape, prismatic shape, or a linear structure having a rectangular or trapezoidal cross section in a plane perpendicular to the longitudinal direction with an aspect ratio of A, and the structure is fixed to the base surface at the bottom surface The method for producing a mold according to claim 2 or 3, wherein the mold has a shaped shape.
The method for producing a mold according to any one of claims 2 to 4, wherein b is represented by a function represented by the following formula (b-1).

(A in the formula is the same as above, b 1 is a number from 0.21 to 0.84, b 2 is a number from 0.3 to 0.9, b 3 is a number from 1.5 to 2.5, b 4 is a number from 0.06 to 0.24)
The method for producing a mold according to any one of claims 2 to 5, wherein c is represented by a function represented by the following formula (c-1).

(A in the formula is the same as above. C 1 is a number from 0.2 to 0.8, c 2 is a number from 2.5 to 3.5, and c 3 is a number from 0.5 to 2.0. )
The method for producing a mold according to any one of claims 2 to 6, wherein τ s is represented by a function represented by the following formula (τ s -1).

(A in the formula is the same as above. Τ s1 is a number between 0.12 and 0.46)
The method for producing a mold according to any one of claims 2 to 7, wherein the stretching correction coefficients ε x and ε y are derived by the following procedures 1 to 5.
1. y = f uy (x) = α 0 bx 2 + α 0 (1−α 0 ) c + (1−α 0 ) 2 , and x = f sx (y) = (1−α 0 (1−e− y / τs (A) ) / 2A
Find the intersection (x 0 , y 0 ) of
2. The temporary correction shape g u (x) of the upper surface and the temporary correction shape g s (y) of the side surface are calculated from the following equations.
g u (x) = 1 / f uy (x)
g s (y) = (1 / 2A) 2 / f sx (y)
4). Next, the horizontal height y 1 = g u (x 0 ) of the provisional correction shape and the half width x 1 = g s (y 0 ) of the provisional correction shape are obtained.
5. The horizontal direction correction coefficient ε x and the vertical direction correction coefficient ε y of the provisional correction shape are calculated from the following equations.
ε x = x 1 / x 0
ε y = y 1 / y 0
Mold manufacturing method for molding a resin having a dimensional change rate of α 0 and manufacturing a linear shaped product having a triangular cross section in a plane perpendicular to the longitudinal direction and having an aspect ratio of A defined below And the manufacturing method of the mold characterized by making the recessed part shape of a mold into the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In a state where the concave portion is opened so as to open on the horizontal plane side, the x-axis and the y-axis are included, and the concave portion is installed so as to be symmetrical on the plane including the point indicating the maximum depth of the concave portion.
The shape of the hypotenuse when the space formed by the horizontal plane and the concave portion and including the bottom surface and the two inclined surfaces is cut by a plane including the x-axis and the y-axis, the x-coordinate is expressed by the following formula (2-1), and y A coordinate is a curve formed by collecting points represented by the following formula (2-2). Aspect ratio: one direction on the horizontal plane is the x axis, and on the horizontal plane, the direction perpendicular to the x axis is the z axis, the x axis The y-axis is the direction perpendicular to the z-axis, and the molded body is symmetrical on the horizontal plane by the cutting plane that includes the point that includes the x-axis and y-axis and indicates the maximum height of the molded body. Is the ratio of the height in the y-axis direction at the cut surface and the width of the cut surface in the x-axis direction in contact with the horizontal plane in the case where it is installed. Dimensional change rate: When the resin is light or thermosetting resin , The volume change rate before and after curing, and when the resin is a thermoplastic resin, Is a value calculated by the scheduled use environment temperature (℃)) × linear expansion coefficient "- Temperature (℃)

(Wherein, k t is a correction coefficient of contraction of the y-axis direction, the following formula (k t -1)

For q that satisfies the above, the range is 0.9q ≦ k t ≦ 1.1q. α 0 is the dimensional change rate of the resin, y is the height of the space, τ t is the relaxation coefficient of side shrinkage, and A is the aspect ratio)
A mold manufacturing method for manufacturing a quadrangular pyramid-shaped molded body having an aspect ratio of A by molding a resin having a dimensional change rate of α 0 , wherein the concave shape of the mold is as follows: A method for manufacturing a mold.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the case where the concave portion is opened on the horizontal plane side, and the concave portion is set so as to be symmetric with respect to the plane including the point indicating the maximum depth of the concave portion,
The bottom surface of the space formed by the horizontal plane and the recess is a quadrangle, the four sides of the bottom surface are parallel to the x axis or the z axis, and the four side surfaces of the space have one side of the bottom surface as the bottom side, X of a curve formed by collecting points on the x-coordinate, y-coordinate, and z-coordinate represented by the following formulas (5-1) to (5-4) that connect the base and the vertex of the space. Indicated in the axial direction or continuous in the z-axis direction,
The shape of the corner formed by two adjacent side surfaces is a point 1 on the curve representing the corner end of one side surface and a point on the curve representing the corner end of the other side surface, A method of manufacturing a mold, wherein the mold is a straight line, a polygonal line, or an arc connecting the point 1 and a point 2 having the same y-axis value.
Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. X-axis in contact with the height in the y-axis direction on the cut surface and the horizontal plane when the molded product is placed on a horizontal plane so that the molded product is symmetrical with the cut surface including the point indicating the maximum height of the molded product Dimensional change rate: If the resin is a light or thermosetting resin, it is the volume change rate before and after curing. If the resin is a thermoplastic resin, “(thermoplastic resin The glass transition temperature (° C) minus the expected environmental temperature (° C) x linear expansion coefficient "

(Wherein, alpha 0 is the dimensional change of the resin, y is the height of the space, tau s relaxation coefficient aspect shrinkage, A is .k t indicating the aspect ratio is a correction coefficient of contraction of the y-axis direction, The following formula (k t -1)

(With respect to q satisfying 0.9q ≦ k t ≦ 1.1q)
The shaped body is a pyramid shape having an aspect ratio of A, or a linear structure having a triangular cross section in a plane perpendicular to the longitudinal direction, and the structure is fixed to the base surface at the bottom surface. The method for producing a mold according to claim 9 or 10.
The method for producing a mold according to any one of claims 9 to 11, wherein τ t is represented by a function represented by the following formula (τ t -1).

(Where τ t1 is a number from 1.0 to 2.0 and τ t2 is a number from 0.2 to 1.0. A is the same as above)
Manufacturing a mold for molding a resin having a dimensional change rate of α 0 and manufacturing a linear molded body having a cross section of a sphere in a plane perpendicular to the longitudinal direction and having an aspect ratio of A defined below. It is a method, Comprising: The manufacturing method of the mold characterized by making the recessed part shape of a mold into the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is left-right symmetrical on the plane including the x axis and the y axis and including the point indicating the maximum depth of the mold.
The cross-sectional shape of the sphere-shaped side surface when a space including a bottom surface and a sphere-shaped side surface formed by a horizontal plane and a concave portion is cut by a plane including the x-axis and the y-axis, 3-1), and the y-coordinate is a curve formed by collecting points represented by the following formula (3-2). Aspect ratio: One direction on the horizontal plane is the x-axis, and the x-axis is on the horizontal plane. The vertical direction is the z-axis, the direction perpendicular to the x-axis and the z-axis is the y-axis, and the molded body by the mold includes a point that includes the x-axis and the y-axis on the horizontal plane and indicates the maximum height of the molded body. This is the ratio of the height in the y-axis direction at the cut surface and the width of the cut surface in the x-axis direction in contact with the horizontal plane when the molded body is placed symmetrically by the cut surface. In the case of a light or thermosetting resin, it is the volume change rate before and after curing, and when the resin is a thermoplastic resin, Is a value calculated by the scheduled use environment temperature (℃)) × linear expansion coefficient "- glass transition temperature of the thermoplastic resin (℃)

(Where α 0 is the rate of dimensional change of the resin, r is the radius of the sphere, and y is the height of the space. Y 0 is on the y-axis at the center of the sphere that is part of the molded product to be produced. Τ c is the side shrinkage relaxation coefficient, A is the aspect ratio, and k c is the following formula:

(For p that satisfies 0.9p ≦ k c ≦ 1.1p)
A mold manufacturing method for manufacturing a spherically shaped molded body having an aspect ratio of A by molding a resin having a dimensional change rate of α 0 , wherein the concave portion of the mold has the following shape: A method for manufacturing a mold.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the case where the concave portion is opened on the horizontal plane side, and the concave portion is set so as to be symmetric with respect to the plane including the point indicating the maximum depth of the concave portion,
The bottom surface of the space formed by the horizontal plane and the concave portion is a circle, and when the circle is divided into four arcs by the xy plane and the zy plane, points on the four arcs, The line connecting the vertices is a curve formed by collecting points on the x, y, and z coordinates represented by the following formulas (4-1) to (4-4). Aspect ratio: on the horizontal plane A direction perpendicular to the x-axis on the horizontal plane is a z-axis, a direction perpendicular to the x-axis and the z-axis is a y-axis, and the compact includes the x-axis and the y-axis. The height of the cut surface in the y-axis direction and the cut surface in the x-axis direction in contact with the horizontal surface when the molded body is placed on a horizontal plane so as to be symmetrical with the cut surface including the point indicating the maximum height of Dimensional change rate: The ratio of volume change before and after curing when the resin is light or thermosetting resin. For RESIN, - is a value calculated by "(glass transition temperature of the thermoplastic resin (℃) scheduled use environment temperature (℃)) × linear expansion coefficient"

(Where α 0 is the rate of dimensional change of the resin, r is the radius of the sphere, and y is the height of the space. Y 0 is on the y-axis at the center of the sphere that is part of the molded product to be produced. Τ c is the side shrinkage relaxation coefficient, A is the aspect ratio, and k c is the following formula:

(For p that satisfies 0.9p ≦ k c ≦ 1.1p)
The molded body has a spherical shape with an aspect ratio of A, or a linear structure with a spherical section in a plane perpendicular to the longitudinal direction, and the structure is fixed to the base surface at the bottom surface. The manufacturing method of the mold of Claim 13 or 14 which has.
The method for producing a mold according to any one of claims 13 to 15, wherein τ c is represented by a function represented by the following formula (τ c -1).

( Wherein τ c10 is a number from 0.05 to 0.2, τ c11 is a number from 0.005 to 0.02, τ c12 is a number from 2.5 to 10, τ c13 is a number from 10 to 40, τ c14 is a number from 2 to 8. A is the same as above)
A mold obtained by the mold manufacturing method according to any one of claims 1 to 16.
A mold manufacturing apparatus for manufacturing a mold by the mold manufacturing method according to any one of claims 1 to 16.
A molding comprising a cured product or a solidified product of the resin through a step of producing a mold by the method for producing a mold according to any one of claims 1 to 16 and molding a resin using the obtained mold. The manufacturing method of the molded object which obtains a body.
A molded body obtained by the method for producing a molded body according to claim 19.
A molding comprising a cured product or a solidified product of the resin through a step of producing a mold by the method for producing a mold according to any one of claims 1 to 16 and molding a resin using the obtained mold. An apparatus for producing a molded body for obtaining a body.
A mold for molding a resin having a dimensional change rate of α 0 and manufacturing a linear shaped body having a rectangular or trapezoidal cross section in a plane perpendicular to the longitudinal direction and having an aspect ratio A defined below. The mold is characterized in that the concave shape of the mold is the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is set to be bilaterally symmetric in the plane including the x axis and the y axis.
The shape of the upper surface of the space formed by the recess is a curve represented by the following formula (1-1), and the shape of the side surface of the space is represented by the following formula (1-2). Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. The height in the y-axis direction at the cut surface when the molded body is placed so as to be bilaterally symmetric by a cut surface including a point that includes the x axis and the y axis and indicates the maximum height of the molded body. Dimensional change rate: If the resin is light or a thermosetting resin, it is the volume change rate before and after curing, and if the resin is a thermoplastic resin , “(Glass transition temperature (° C) of thermoplastic resin-Expected ambient temperature ( Is a value calculated by)) × linear expansion coefficient "

(Where α 0 is the dimensional change rate of the resin, b is a parameter related to the ratio of the elastic modulus of the resin and the force in the width direction, x includes the x-axis and the y-axis of the space formed by the recesses, and The half width of the cut surface including the point indicating the maximum height of the space, c is a parameter relating to the ratio of the shrinkage in the height direction and the shrinkage in the width direction, and ε x is the horizontal stretching correction factor)

(Where α 0 is the dimensional change rate of the resin, y is the height of the space, τ s is the relaxation coefficient of side shrinkage, A is the aspect ratio, and ε y is the stretching correction coefficient in the vertical direction)
A mold for manufacturing a resin having a dimensional change rate of α 0 and manufacturing a quadrangular prism shape or a truncated pyramid shape molded body having an aspect ratio of A defined below, and a concave portion of the mold A mold having the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is set to be bilaterally symmetric in the plane including the x axis and the y axis.
The upper surface of the space formed by the horizontal surface and the concave portion and including the bottom surface, the four side surfaces, and the upper surface is indicated by a continuous curve in the z-axis direction represented by the following formula (1-1).
The four side surfaces of the space are respectively shown by continuations in the x-axis direction or z-axis direction of the curves represented by the following formulas (1-2-1) to (1-2-4), respectively.
The shape of the corner formed by two adjacent side surfaces is a point 1 on the curve representing the corner end of one side surface and a point on the curve representing the corner end of the other side surface, A straight line, a polygonal line, or an arc connecting the point 1 and the point 2 having the same y-axis value;
The shape of the corner formed by the side surface parallel to the plane including the x-axis and the y-axis and the top surface is the point 1 ′ on the curve representing the corner-side end portion of the side surface and the curve representing the corner-side end portion of the top surface. A straight line, a polygonal line, or an arc connecting the point 1 ′ and the point 2 ′ having the same x-axis value,
The shape of the corner formed by the side surface and the upper surface parallel to the plane including the y-axis and the z-axis is the point 1 ″ on the curve representing the corner end of the side surface and the curve representing the corner end of the upper surface. A straight line, a polygonal line, or an arc connecting the point 1 ″ and the point 2 ″ having the same z-axis value. Aspect ratio: One direction on the horizontal plane is the x axis, and the horizontal plane The direction perpendicular to the x-axis is the z-axis, the direction perpendicular to the x-axis and the z-axis is the y-axis, the molded body formed of a mold is on a horizontal plane, includes the x-axis and the y-axis, and the maximum height of the molded body is Dimensional change is the ratio of the height in the y-axis direction at the cut surface to the width of the cut surface in the x-axis direction in contact with the horizontal plane when the molded body is placed so as to be symmetrical with the cut surface including the indicated point Rate: If the resin is light or thermosetting resin, it is the volume change rate before and after curing, and if the resin is a thermoplastic resin , - is a value calculated by "(glass transition temperature of the thermoplastic resin (℃) scheduled use environment temperature (℃)) × linear expansion coefficient"

(Where α 0 is the dimensional change rate of the resin, b is a parameter related to the ratio of the elastic modulus of the resin and the force in the width direction, x includes the x-axis and the y-axis of the space formed by the recesses, and The half width of the cut surface including the point indicating the maximum height of the space, c is a parameter relating to the ratio of the shrinkage in the height direction and the shrinkage in the width direction, and ε x is the horizontal stretching correction factor)

(Where α 0 is the dimensional change rate of the resin, y is the height of the space, τ s is the relaxation coefficient of side shrinkage, A is the aspect ratio, k 1 is the correction coefficient for the shrinkage rate in the x-axis direction, k 2 represents a correction coefficient for the contraction rate in the z-axis direction, and k 1 and k 2 are the same or different and are numbers of 1.0 to 2.0)
A mold for producing a linear shaped product having a triangular cross section in a plane perpendicular to the longitudinal direction, in which a resin having a dimensional change rate of α 0 is molded and the aspect ratio defined below is A. The mold is characterized in that the concave shape of the mold is the following shape.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In a state where the concave portion is opened so as to open on the horizontal plane side, the x-axis and the y-axis are included, and the concave portion is installed so as to be symmetrical on the plane including the point indicating the maximum depth of the concave portion.
The shape of the hypotenuse when the space formed by the horizontal plane and the concave portion and including the bottom surface and the two inclined surfaces is cut by a plane including the x-axis and the y-axis, the x-coordinate is expressed by the following formula (2-1), and y A coordinate is a curve formed by collecting points represented by the following formula (2-2). Aspect ratio: one direction on the horizontal plane is the x axis, and on the horizontal plane, the direction perpendicular to the x axis is the z axis, the x axis The y-axis is the direction perpendicular to the z-axis, and the molded body is symmetrical on the horizontal plane by the cutting plane that includes the point that includes the x-axis and y-axis and indicates the maximum height of the molded body. Is the ratio of the height in the y-axis direction at the cut surface and the width of the cut surface in the x-axis direction in contact with the horizontal plane in the case where it is installed. Dimensional change rate: When the resin is light or thermosetting resin , The volume change rate before and after curing, and when the resin is a thermoplastic resin, Is a value calculated by the scheduled use environment temperature (℃)) × linear expansion coefficient "- Temperature (℃)

(Where k t is the following formula (k t −1)

For q that satisfies the above, the range is 0.9q ≦ k t ≦ 1.1q. α 0 is the dimensional change rate of the resin, y is the height of the space, τ t is the relaxation coefficient of side shrinkage, and A is the aspect ratio)
A mold for producing a quadrangular pyramid shaped article having an aspect ratio of A by molding a resin having a dimensional change rate of α 0 , wherein the mold has a concave shape of the following shape .
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the case where the concave portion is opened on the horizontal plane side, and the concave portion is set so as to be symmetric with respect to the plane including the point indicating the maximum depth of the concave portion,
The bottom surface of the space formed by the horizontal plane and the recess is a quadrangle, the four sides of the bottom surface are parallel to the x axis or the z axis, and the four side surfaces of the space have one side of the bottom surface as the bottom side, X of a curve formed by collecting points on the x-coordinate, y-coordinate, and z-coordinate represented by the following formulas (5-1) to (5-4) that connect the base and the vertex of the space. Indicated in the axial direction or continuous in the z-axis direction,
The shape of the corner formed by two adjacent side surfaces is a point 1 on the curve representing the corner end of one side surface and a point on the curve representing the corner end of the other side surface, A method of manufacturing a mold, wherein the mold is a straight line, a polygonal line, or an arc connecting the point 1 and a point 2 having the same y-axis value.
Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. X-axis in contact with the height in the y-axis direction on the cut surface and the horizontal plane when the molded product is placed on a horizontal plane so that the molded product is symmetrical with the cut surface including the point indicating the maximum height of the molded product Dimensional change rate: If the resin is a light or thermosetting resin, it is the volume change rate before and after curing. If the resin is a thermoplastic resin, “(thermoplastic resin The glass transition temperature (° C) minus the expected environmental temperature (° C) x linear expansion coefficient "

(Wherein, alpha 0 is the dimensional change of the resin, y is the height of the space, tau s relaxation coefficient aspect shrinkage, A is .k t indicating the aspect ratio is a correction coefficient of contraction of the y-axis direction, The following formula (k t -1)

(With respect to q satisfying 0.9q ≦ k t ≦ 1.1q)
This is a mold for molding a resin having a dimensional change rate of α 0 and manufacturing a linear shaped molded article having a spherical cross section in a plane perpendicular to the longitudinal direction and having an aspect ratio A defined below. The mold has a concave shape as described below.
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the state where the concave portion is installed so as to open to the horizontal plane side, the concave portion is left-right symmetrical on the plane including the x axis and the y axis and including the point indicating the maximum depth of the mold.
The cross-sectional shape of the sphere-shaped side surface when a space including a bottom surface and a sphere-shaped side surface formed by a horizontal plane and a concave portion is cut by a plane including the x-axis and the y-axis, 3-1), and the y-coordinate is a curve formed by collecting points represented by the following formula (3-2). Aspect ratio: One direction on the horizontal plane is the x-axis, and the x-axis is on the horizontal plane. The vertical direction is the z-axis, the direction perpendicular to the x-axis and the z-axis is the y-axis, and the molded body by the mold includes a point that includes the x-axis and the y-axis on the horizontal plane and indicates the maximum height of the molded body. This is the ratio of the height in the y-axis direction at the cut surface and the width of the cut surface in the x-axis direction in contact with the horizontal plane when the molded body is placed symmetrically by the cut surface. In the case of a light or thermosetting resin, it is the volume change rate before and after curing, and when the resin is a thermoplastic resin, Is a value calculated by the scheduled use environment temperature (℃)) × linear expansion coefficient "- glass transition temperature of the thermoplastic resin (℃)

(Where α 0 is the rate of dimensional change of the resin, r is the radius of the sphere, and y is the height of the space. Y 0 is on the y-axis at the center of the sphere that is part of the molded product to be produced. Τ c is the side shrinkage relaxation coefficient, A is the aspect ratio, and k c is the following formula:

(For p that satisfies 0.9p ≦ k c ≦ 1.1p)
A mold for producing a spherically shaped molded body having an aspect ratio of A by molding a resin having a dimensional change rate of α 0 , wherein the concave shape of the mold is the following shape .
Mold concave shape: x direction is one direction on the horizontal plane, z axis is the direction perpendicular to the x axis on the horizontal plane, y axis is the direction perpendicular to the x and z axes, and the mold is molded on the horizontal plane. In the case where the concave portion is opened on the horizontal plane side, and the concave portion is set so as to be symmetric with respect to the plane including the point indicating the maximum depth of the concave portion,
The bottom surface of the space formed by the horizontal plane and the concave portion is a circle, and when the circle is divided into four arcs by the xy plane and the zy plane, points on the four arcs, The line connecting the vertices is a curve formed by collecting points on the x, y, and z coordinates represented by the following formulas (4-1) to (4-4). Aspect ratio: on the horizontal plane A direction perpendicular to the x-axis on the horizontal plane is a z-axis, a direction perpendicular to the x-axis and the z-axis is a y-axis, and the compact includes the x-axis and the y-axis. The height of the cut surface in the y-axis direction and the cut surface in the x-axis direction in contact with the horizontal surface when the molded body is placed on a horizontal plane so as to be symmetrical with the cut surface including the point indicating the maximum height of Dimensional change rate: The ratio of volume change before and after curing when the resin is light or thermosetting resin. For RESIN, - is a value calculated by "(glass transition temperature of the thermoplastic resin (℃) scheduled use environment temperature (℃)) × linear expansion coefficient"

(Where α 0 is the rate of dimensional change of the resin, r is the radius of the sphere, and y is the height of the space. Y 0 is on the y-axis at the center of the sphere that is part of the molded product to be produced. Τ c is the side shrinkage relaxation coefficient, A is the aspect ratio, and k c is the following formula:

(For p that satisfies 0.9p ≦ k c ≦ 1.1p)
Molded resin with various aspect ratios, cone shape, pyramid shape, truncated cone shape, truncated pyramid shape, cylindrical shape, prismatic shape, spherical notch shape, or rectangular cross section in the plane perpendicular to the longitudinal direction, trapezoid , A mold design program for causing a computer to execute a mold design for producing a molded product having a triangular shape or a spherical shape, and a resin to be formed. A first step of inputting a dimensional change rate α 0 of
A second step of causing the computer to select a correction function in accordance with the desired shape of the molded body from the input shape of the desired molded body, the aspect ratio A, and the dimensional change rate α 0 of the resin to be formed; And a third step of causing the computer to correct the concave shape of the mold by the selected correction function.
Aspect ratio: One direction on the horizontal plane is the x-axis, the direction perpendicular to the x-axis on the horizontal plane is the z-axis, and the direction perpendicular to the x-axis and z-axis is the y-axis. When the molded body is placed so as to be bilaterally symmetric by a cut surface that includes a point that includes the axis and the y-axis and that indicates the maximum height of the molded body, the height in the y-axis direction on the cut surface and the horizontal plane Dimensional change rate: If the resin is light or thermosetting resin, it is the volume change rate before and after curing. If the resin is a thermoplastic resin, “(thermal It is a value calculated by “Glass transition temperature of plastic resin (° C.) − Scheduled environment temperature (° C.)) × Linear expansion coefficient”.