JP2002108954A - Method for designing shape - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a general method for preparing a shape between two known shapes or preparing a shape obtained by extrapolating these shapes, to numerically express the provided shape by using the smoothness/complexity of the shape as the quantity of differences from original shapes and to use the prepared shape for evaluating moldability in production or the like. SOLUTION: In a shape changing method for generating an intermediate shape when a product shape A and the plate or cylinder of an initial material shape are given, a change expression to move in the normal direction of the shape is used corresponding to the difference between the curvature values of individual points (or a fixed curvature values) on the product shape and the curvature values of the individual points on the initial material shape. The final shape after repeatedly applying this change expression becomes the initial material shape and a shape gradually changing from the product shape to the initial material shape can be provided. Since the curvature value of the plate or cylinder which are popular as initial material shapes is fixed, the shape is converged to that value.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for designing a surface shape of an object, such as a processed shape of a forged product or a die shape for shape processing. In particular, the present invention relates to a shape designing method suitable for automatic design of a plastic working surface using CAD / CAM.

[0002]

2. Description of the Related Art In the processing of a die for a forged product, an intermediate die is used when it is difficult to simultaneously form a product shape from an initial shape of a material. The design of the intermediate mold shape is made by selecting a close shape from the product shape of similar products manufactured in the past and the intermediate mold shape used at the time of manufacture, and using an empirical method or some numerical processing method The way to design was done. For example, Japanese Patent Application Laid-Open No. 10-2549
No. 26 discloses that when determining the intermediate shape of a new forged product,
A method of designing a new forged product shape, a forged product shape similar to the new forged product, and a shape of the pre-process of the pre-forged product in advance, and designing a shape of the pre-process of the new forged product by a synthetic calculation of the three. Is disclosed. In that case, it was assumed that there was a similar shape in the past that served as a reference. If there is no similar shape in the past, there is a problem that an intermediate shape cannot be automatically designed.

[0003] The smoothness and complexity of the product shape has a strong influence on the difficulty of the molding process and the complexity of the molding process. The surface shape that influences the surface characteristics is expressed in a unified form, and there is no index that can be used for estimating the formability or evaluating the machined surface to be designed.

[0004]

SUMMARY OF THE INVENTION The present invention solves the above-mentioned problems, and can create a reasonable surface shape in the intermediate stage of processing without a similar shape based on past experience, and also has a good formability in production processing. It is an object of the present invention to obtain a surface shape designing method capable of obtaining a unified index of a surface shape suitable for estimating a surface to be designed and evaluating a machined surface to be designed.

[0005]

According to a first aspect of the present invention, there is provided a method for designing a shape, the method comprising the steps of: The point where each point on the surface is moved by a distance including the proportionality of curvature of each point is set as a new surface, and a three-dimensional shape is created using the surface obtained by repeating this process. Design method.

[0006] The second invention described in claim 2 is a
A method of designing a shape, in which a surface constituting a three-dimensional shape is divided into a plurality of sections, and a total value obtained by calculating a product of an area of each section and an amount proportional to a curvature is defined as a design of the three-dimensional shape. A shape design method characterized by being used as an index.

[0007]

The first invention is based on a new idea of using a virtual curved surface (hereinafter referred to as a moving surface) in which a surface having a known shape continuously moves and changes in designing a three-dimensional shape. As an equation describing the movement of the moving surface, an equation in which the moving speed changes according to the local curvature value of the surface constituting the shape is used. The magnitude of the moving speed of the moving surface is given by Equation (1), where Km is the curvature of a point on the curved surface, V is the moving speed, and V ^* is the moving speed at the reference curvature K ^* . V ^* , K ^*
Is a constant given arbitrarily, and V may include another constant term. The direction of the moving speed is the direction of the normal to the surface, and there are a direction inside the radius of curvature (toward the center of the radius of curvature) and an outside direction, and either one is selected. From theoretical analysis of surface tension, etc.,
If the cross section is a curve and the initial curve is smooth and does not self-intersect, it can be seen that the moving surface has the characteristic that it continues to be smooth and becomes convex even if it moves according to equation (1). I have. Also, the moving surface described by this equation is
Since the entire surface is continuously changed, it is possible to apply the present invention to plastic working that does not involve material removal such as forging.

The constant of the equation (1) may be determined according to the direction in which the surface is moved and the shape of the surface that the moving surface reaches (hereinafter referred to as the reaching surface). If the surface before moving is possible by plastic working, the moving surface is a surface that can be realized by plastic working. Can be selected. The reaching surface can be arbitrarily selected from the ideal shape designed by another means or the material shape planned for manufacturing the product, so even if there is no similar shape or intermediate shape based on past experience, At least one known surface that is given in advance (a surface that gives the initial value of the moving surface)
, A reasonable intermediate shape can be designed.

According to a second aspect of the present invention, the surface created by the mechanical processing is composed of a flat surface and a curved surface. The larger the curvature, that is, the smaller the radius of curvature, and the more the curved surface is compared with the flat surface. It is based on the fact that the more the more, the more complicated the surface. When the surface forming the three-dimensional shape is considered to be composed of a curved surface and a partial section of a plane, the amount proportional to the curvature increases as the curvature of the curved surface portion increases, and the total value obtained by calculating the product of the area and the area is The value increases as the area of the curved surface portion increases. The plane is a surface that is relatively easy to machine and has only a small contribution to the total value because the curvature of the plane is zero. Therefore, by calculating the sum of the curvature of the surface and the product of the area and the area, a uniform index (parameter indicating the state of the surface) having a characteristic that increases in accordance with the complexity of the surface can be obtained. . On the other hand, a surface created by processing has an industrial characteristic value obtained for each surface, and a correlation can be obtained by associating this characteristic value with an index. Thus, the index enables industrial evaluation of the designed surface.

[0010]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS When designing a continuously moving surface using a digital computer, a method of approximation by repetitive calculation divided into minute sections or minute times is generally used. In this case, in order to obtain the moving surface according to the first aspect of the present invention, the surface constituting the shape is first divided into small sections (hereinafter, referred to as surface elements) to obtain the position (representative point) and curvature (surface element) of each surface element. Average curvature) is determined. Next, using a small time interval, the distance to move in the normal direction of the surface element at a speed calculated using the curvature and constant of the surface element is calculated, and a new position of each surface element representative point is obtained. . Next, by connecting the moved representative points, a moving surface having a new shape related to the shape before the movement can be obtained.

FIGS. 1 and 3 show a first embodiment of the present invention.
It will be explained by. The present embodiment is a method of designing a shape, and based on two surfaces constituting a given three-dimensional shape, one surface is set as a movement start surface, the other surface is set as a reaching surface, and A point where each point has moved by a distance including the curvature proportional amount of each point is defined as a new surface, and a plurality of three-dimensional shapes are created using a surface obtained by repeating this process. It is a design method. The two shapes are surfaces to be processed by forging, the starting surface of movement is a given product shape surface, and the reaching surface is a material initial shape surface. Actual processing is the direction in which the product shape is formed from the initial shape of the material, but in the shape design of the present embodiment, it is easy to calculate from the complicated product shape to the direction of the relatively simple material shape, The calculation of the moving plane is performed in the reverse direction.

FIG. 1 shows an example of a shape change in which a plurality of surfaces are extracted from the moving surface obtained in this embodiment. It is assumed that the positions of both end points are constrained. The left side of FIG. 1 is a plate having an initial material shape, and the right side of FIG. 1 is a half cylinder. This embodiment uses two shapes, namely, a product shape and a material initial shape. Thereafter, an intermediate shape is obtained by performing the following numerical processing using a computer or the like. The flowchart is shown in FIG.

The algorithm for calculating the moving plane from the product shape to the initial material shape is as follows. A spline curve formed by passing points that are unequal to the initial shape of the material (arriving surface shape) is described by a straight line vector sequence, and the i-th normal direction of the vector end point and the curvature Gi (the curvature value may be constant). Ask for. A spline curve formed by unequal passing points of the current product shape is described by a straight line vector sequence, and the i-th normal direction of the vector end point and the curvature Ki are obtained. The coordinates are set in the normal direction according to the difference from the curvature value Gi of the initial shape of the material.
Move

[0014]

(Equation 1)

In the equation (2), C is a constant having a unit of a moving amount having a small value, and Go is a typical curvature value of the material initial shape (generally, the maximum value of the curvature, or 1). A spline curve is regenerated by passing the end point of the moved line segment vector. In addition, in the case of controlling the area to be constant, an equation of constant growth that enlarges / reduces while maintaining the shape feature is also executed. This is done by correcting ΔVi obtained by Expression (2) by Expression (3).

[0016]

(Equation 2)

In the equation (3), Sk is the area of the changing shape, and Sg is the area of the material initial shape. By repeating this, the moving surface converges to the material initial shape (attainment surface shape) having the specified curvature.

For the purpose of associating the curvature of each point of the two shapes, the curves are polylined into the same number. Here, if the curvature value of each point of the curve is obtained analytically, it is not necessary to make the curve multiline. The curvature value of the final shape may be a constant curvature value such as a flat plate or a circle. FIG. 1 shows a two-dimensional curve,
A similar method can be used to evaluate a dimensional curved surface.

A second embodiment of the present invention will be described with reference to FIG. According to the method of the first invention, a shape that extrapolates a known shape can be obtained based on a given three-dimensional shape.
In FIG. 2, the shape of the lowermost stage is the movement start surface (right C in FIG. 1), and the sign of the coefficient C is reversed using the equation (2), so that the surface moved upward is the middle stage and the upper stage. It is a moving surface. Under the condition that the positions of both end points are fixed, Go in equation (2) uses a cylindrical surface, so that the moving surface has a convex shape at both ends bulging compared to the starting surface. This can be used, for example, when designing a new shape by further improving the characteristics of the product shape (in FIG. 1, the stress uniformity of the cross-sectional shape of the shape to which a bending load is applied). Note that when extrapolating a shape, there is no guarantee that the shapes will not self-intersect, and the shape will change near the product shape.

The third embodiment of the present invention is according to the second invention, and will be described with reference to equations (4) and (5).
The present embodiment is a method of designing a shape, in which a surface constituting a three-dimensional shape is divided into a plurality of sections, and a total value obtained by calculating a product of an area of each section and an amount proportional to a curvature is calculated. Is used as a design index of the three-dimensional shape, wherein the formulas (4) and (4) ^* are continuous formulas, and the formulas (5) and (5) ^* are discrete formulas. Total value (C
The expression for D) is shown.

[0021]

(Equation 3)

In the formula (4), Area: area of the curved surface, K _x : curvature in the X direction on the small area dA, K _x0 : X
Representative curvature value of the direction of arrival-sectional shape (Material initial shape) (or curvature values on the corresponding micro-area dA), K _y: curvature in the Y direction on the small area dA, Ky 0: _Y direction reaches sectional shape ( The representative curvature value of the material initial shape (or the curvature value on the corresponding minute area dA), L: the representative length of the curved surface.

The equation (4) indicates that the surface constituting the three-dimensional shape is constituted by an orthogonal coordinate system, and the curvature of the surface constituting the three-dimensional shape is obtained by using the minute area dA provided by dividing the area of the curved surface. (K _x , K _y ) is defined by the curvature (K) of the surface constituting the arrival surface shape.
_x0 , _Ky0 ) in the form of _calculating the sum of the standard deviations. The reference surface is a surface where CD = 0, and a relatively simple plane / cylindrical surface or the like as compared with the processed surface can be applied. (4) ^* expression (4) ^* in formula, in order to be independent of the CD value in feature sizes, the representative length of the curved surface L
And the product of

The CD value of the expression (4) can be applied to the shapes A to F in FIG. 1 and can be used as a parameter indicating the characteristics of the smoothness and complexity of the shapes A to F. Although the coordinate system of Expression (4) is shown using the rectangular coordinate system, an arbitrary coordinate system can be set based on the characteristics of the shape. In addition, although it is in the form of adding two coordinate systems,
Only a single coordinate system may be calculated.

Formulation example when calculating from discrete data
Then (5), (5)^* It becomes an expression.

[0026]

(Equation 4)

[0027] (5), ^{(5) *} formula, Div: division number of the curve (2 or more divisions), L: is a representative length of the curve.

Equation (5) is an example of an equation that gives an example of obtaining the total value (CD) for the cross-sectional shape (curve on two dimensions) of the surface constituting the three-dimensional shape. The curve showing the cross-sectional shape is
Div is evenly divided at the same interval as the reference curve (which may be a straight line), and the difference between the curvature Ki of the cross section at the i-th division point and the curvature Gi at the same division point of the reference surface is obtained. Is a formula for calculating the total value in the form of a standard deviation using (5) ^* Eq. (5) is the product of the representative length L of the shape in order to make the shape independent of the shape size in Eq. (5).

FIG. 4 shows an example of calculating the CD by the equation (5) for the shapes shown on the right side (shapes A to F converging on a half cylinder) of FIG. When the shape changes from the product shape A to the material shape F, the CD simply decreases from the large value 1 to the small value 0. The value of CD according to equation (5) depends on the number of divisions Div of the curve, but by using a sufficiently large number of divisions depending on the complexity of the shape, the value approaches CD and approaches the convergence value as the Div increases.

The CD value is expressed as a difference from the curvature of the final shape (attained shape), and does not depend on the size of the shape (the same parameter value if the shape is the same even if the size of the shape is different). That is, the expression method is preferable. Therefore,
As a method of expressing the smoothness / complexity of a shape, the deviation or dispersion of the curvature of each point of the shape to be changed and the curvature of each point of the final shape is used, and the smoothness / complexity of the shape is independent of the size of the shape. In order to obtain a value of only the length, a product with (for example, the representative length L) is used. For example, when the final shape is a semicircle, the shape size is a diameter r or a radius r which is １ ／ thereof.
And the product with this. FIG. 5 shows the relationship between Div and 2r and CD ^* . The upper diagram in FIG. 5 shows that in the shape shown in FIG. 1 (right), if the number of divisions is 200 or more, all the shapes have the same value regardless of the number of divisions. The figure below shows that equation (5) ^* is not dependent on the shape size.

This CD has the same value even if the cross-sectional shape is reversed left and right.

Although the CD value of the shape A is normalized by setting it to 1, it is not inevitable. Further, although the formulas (4) and (5) use the form of the standard deviation, the form of the variance or the sum of the absolute values of the differences between the curvature values of the points may be used.

A fourth embodiment of the present invention will be described with reference to FIG. In the present embodiment, C is calculated by using the equation (5).
This is an example in which D is used for evaluation of a forging load on a surface to be designed in designing an intermediate mold in forging.

The present CD value indicates the complexity of the shape, and a shape having a high CD basically has low productivity. For example, in the case of molding by forging, in the case of a complicated shape that cannot be molded to a product shape by one molding, molding is performed in multiple stages, and a mold having an intermediate shape is required. It is possible to use the CD value in selecting the preferred intermediate shape. FIG. 6 is a view showing the relationship between the maximum forming load value P and the CD value obtained by the plastic deformation simulation from the cross-sectional shape before and after the processing in the cross-sectional shape shown in FIG. 1 (right side). First, the difference between the CD value of the product shape A and the CD value of the semi-cylindrical shape F, which is the material, is determined by the equation (5) and is set as CD1 (full scale on the horizontal axis). The load is obtained by simulation and set as P1 (full scale on the vertical axis). Next, the CD value of each surface obtained by the expression (5) for several surfaces obtained by the expression (2) including B to G of the moving surfaces in the middle stage of the product shape and the material initial shape is CD2, and the same movement is performed. The forming load obtained by the simulation when the surface is processed into the product shape F is summarized as P2. In FIG. 6, since each point is substantially on a straight line, C
It can be seen that the ratio of D is substantially proportional to the square of the ratio of the forging load. Therefore, the forging load value can be estimated from the CD value selected as the intermediate shape. Using Fig. 6, it is possible to evaluate the moving surface by the forging load value. For example, in order to maximize the forging load of the equipment in order to improve efficiency, a moving surface with a large forging load is adopted as an intermediate shape. Alternatively, if it is necessary to use a two-stage intermediate shape, it can be rational to use an intermediate shape at a point that divides the horizontal axis into three equal parts.

Since the CD value of the present invention indicates the smoothness and complexity of the surface shape forming the three-dimensional shape, a method for evaluating the surface characteristic value using the CD as a guide for generating the intermediate shape is used. Is obtained.

The CD value of the present invention indicates the smoothness of the shape from the definition method. In addition, since the product shape is generally complicated and the initial material shape is simple, the obtained intermediate shape indicates the complexity from the initial material shape. Smoothness is less harmful to the user who handles the product shape and design, while complexity is more complicated when the product shape is complicated and you want to create a slightly simpler shape for production. It can be used as a parameter value for shape selection, such as a method of determining an intermediate mold shape when molding is difficult.

As the CD value of the present invention, a CD value of a moving surface which is a candidate for an intermediate press shape such as a press die is obtained, and an appropriate one giving a CD value is selected from these candidates. Thus, a method for automatically generating an intermediate press shape can be obtained. FIG. 7 shows an example of generating a hook-shaped intermediate shape (three-dimensional shape). The initial shape is lightweight but complex, so the forging load value is high. By using this as the original shape and generating a smooth (not complicated) intermediate shape using the CD value as a guide, a shape with a reduced forging load value can be obtained. Alternatively, the degree of wrinkles, which is one of the evaluations of the formability of a thin plate press, can be estimated by the CD value.

Further, in generating a product shape, it is possible to obtain a method of treating the complexity of a solid as one unit based on the CD value of the present invention and using it as integrated data in design and manufacturing.

[0039]

When two shapes, for example, a product shape and a material initial shape are determined, an intermediate shape can be determined without a shape based on past experience. The intermediate shape can be expressed as a parameter indicating the smoothness / complexity of the shape as a difference from the original shape, and this can be used to estimate productivity, for example, a forging load value.

[Brief description of the drawings]

FIG. 1 is a diagram showing a state (two-dimensional shape) of generating an intermediate shape according to the present invention.

FIG. 2 is a diagram showing a shape obtained by extrapolating the shape of the present invention.

FIG. 3 is a flowchart showing a method of calculating a shape according to the present invention.

FIG. 4 is a diagram illustrating a relationship between a cross-sectional shape and a curvature deviation amount indicating complexity of the shape according to the present invention.

FIG. 5 is a diagram showing the relationship between the curvature deviation amount, the number of shape divisions, and the shape size according to the present invention.

FIG. 6 is a diagram showing a relationship between a curvature deviation amount and a forging load according to the present invention.

FIG. 7 is a diagram showing a state (three-dimensional shape) of generating an intermediate shape according to the present invention.

[Explanation of symbols]

CD Curvature deviation amount (amount indicating shape smoothness / complexity) CD ^* Curvature deviation amount (amount indicating shape smoothness / complexity, independent of shape size) Div Number of shapes L Size of shape Depth (representative length of curved surface and curve) r Radius of cylindrical shape CD1 Curvature deviation of product shape CD2 Curvature deviation of intermediate shape P1 Material forming load value from initial shape to product shape P2 Material Molding load value from initial shape to intermediate shape

Claims (2)

[Claims] 1. A method for designing a shape, wherein each point on a surface is determined based on a surface constituting a predetermined three-dimensional shape.
A shape designing method, characterized in that a point moved by a distance including a curvature proportional amount of each point is used as a new surface, and a three-dimensional shape is created using a surface obtained by repeating this process. 2. A method for designing a shape, comprising dividing a surface forming a three-dimensional shape into a plurality of sections, and calculating a total value obtained by calculating a product of an area of each section and an amount proportional to a curvature. A shape designing method, which is used as a design index for the three-dimensional shape.