JP2000084620A - Method for comparing shape of curved surface - Google Patents

Abstract

PROBLEM TO BE SOLVED: To obtain information adapted to an actual work by digitizing the shape of two or more curved surfaces to be compared, calculating the characteristic values of the shape about the numerical values of each curved surface or the difference between the numerical values of each curved surface and executing the comparison and judgement of the shape of the curved surface using the obtained characteristic values of the shape. SOLUTION: The positions of representative points on the curved surface are beforehand decided as the numerical values by which the shape of the curved surface is expressed and the distance (height) from the reference surface at those points is used. As the representative points on the curved surface, a total of nine points of four vertexes of a rectangle, midpoints of four sides and center are adopted. Even these nine points are enough to digitize the shape of the curved surface in the case of a simple shape. As the representative shapes (deformation mode), five deformation modes are used. The mode 1 respectively expresses bending deformation in the X-axis direction, mode 2 bending deformation in the Y-axis direction, mode 3 bending deformation (twist) in the diagona direction, mode 4 inclination in the X-axis direction and mode 5 inclination in the Y-axis direction. The shape used practically can be approximately expressed by these characteristic values.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a curved surface shape comparison method for comparing curved surface shapes before and after a metal plate is bent or the like.

[0002]

2. Description of the Related Art In the field of shipbuilding and the like, a curved surface forming process is performed in which a steel plate is subjected to thermal deformation such as pressing or heating to form a curved surface. In particular, a heating method in which a part of a steel sheet is heated and a curved surface is formed using thermal deformation is widely used because it has a greater degree of freedom in curvature and the like than in press working. This method was previously performed manually, but has been automated in view of the need for skill and work efficiency.

In the case of a curved surface forming process, when a final shape cannot be obtained by a single process, the shape may be first processed into a certain shape and then processed into the next shape. In that case,
The machining method will be examined by comparing the shapes of the two curved surfaces.

As a method for comparing the shapes of curved surfaces, a sum of squares of the difference between the heights of two curved surfaces is generally used. Here, the difference between the heights of the curved surfaces is measured at a representative point or an intersection of meshes. Alternatively, two surfaces are developed into a two-dimensional Fourier series, and the difference between the coefficients (Fourier coefficients)
Sum of squares may be used.

Japanese Patent Application Laid-Open No. 10-58052 proposes a method for bending a plate by linear heating. This technique converts the height of a representative point into a characteristic value to determine the condition of linear heating. Specifically, the height of the representative point is represented by a vector a _j , and this is multiplied by a transformation matrix P _ij to obtain a characteristic value b _j . Then, the position of the line heating linear, the slope or the like, determined using the equation of the characteristic values b _j, performs linear heating.

[0006]

A conventional method for comparing the shapes of curved surfaces is to numerically express the similarity or difference between two curved surfaces in a mathematical sense. Therefore, the curved surfaces are not compared from the viewpoint of forming the curved surfaces, that is, from the viewpoint of the classification by the forming method. Therefore,
Even if similar curved surfaces are determined in the related art, it cannot be said that those curved surfaces can always be machined in the same machining mode.

For example, in roll bending or press bending, only a curved surface consisting of a group of straight lines such as a cylindrical surface or a U-shape can be realized, so that a curved surface having no straight line group cannot be machined even if the curved surface has a small difference. . After all, in the prior art, it can be said that the processing method and conditions for deforming one of the two curved surfaces from one to the other largely depend on experience.

The present invention provides a curved surface shape comparison method capable of presenting information according to actual work by determining a curved surface shape in accordance with a processing method and conditions.

[0009]

SUMMARY OF THE INVENTION The present invention provides a method for comparing 2
Digitize the shape of one or more curved surfaces and calculate the characteristic value of the shape by separating the numerical value of each curved surface or the difference between the numerical values of each curved surface into a plurality of formable shape components. This is a curved surface shape comparison method for comparing curved surface shapes using values.

In the present invention, as numerical values representing the shape of a curved surface, a plurality of representative point positions on the curved surface are determined.
The distance (height) from the reference plane at those points can be used. Hereinafter, a set of numerical values of these plural points will be referred to as a shape vector. Shape vectors are measured for two or more curved surfaces to be compared, and each or a difference between the vectors is separated into a plurality of shape components.

The plurality of shapes that can be formed are representative shapes that can be deformed by a forming method or a tool or means. For example, they can be said to be basic deformation modes such as bending and torsion. The number of deformation modes is appropriately determined depending on the deformation mode used. Here, separating into a plurality of shape components means separating a shape vector into these deformation mode components. This is because, by displaying the deformation mode component as a vector, the inner product with the shape vector is obtained, whereby the deformation mode component can be extracted.

If the shape vector is orthogonal to the vector of the deformation mode component, the inner product becomes 0, and it can be determined that the shape is completely different. If both are parallel, the inner product will be the maximum and it can be determined that they have the same shape. In this way, it is possible to determine what deformation mode component the shape of a certain curved surface is composed of based on the value of the inner product of the shape vector.

As described above, if the value of the inner product for each deformation mode component is considered as a characteristic value of the shape, the shape of the curved surface can be classified and evaluated from the viewpoint of the forming method. For example, it can be said that two curved surfaces having similar shape characteristic values have similar shapes and are easily deformed from one to the other. Further, the difference between the characteristic values of the shapes of the two curved surfaces is 1
If it falls within one of the deformation mode components, it can be determined that the deformation modes are mutually deformable.

It is desirable that the representative shapes (deformation modes) are independent of each other. This is because, when the deformation mode components are displayed as vectors, the vectors can be selected so as to be orthogonal.

[0015]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Numerical representation of the shape of a curved surface is based on the fact that the distance of a curved surface from a reference surface at a representative point is a _j and the shape of the curved surface is represented by a numerical value a _j . This numerical value a _j
It is converted to a simple numerical value by the following conversion, and expressed as n _j . further,
The shape of the curved surface in the representative shape (deformation mode) i is represented by n _ij
And a matrix N is _{created in} which this n _ij is the component of the i-th row and the j-th column.

The shape x _j measured for an arbitrary curved surface X
_Is multiplied by the matrix N _ij from the left. X
_{Expressed as i} . (X _i ) = (n _ij ) (x _j ) (1)

Obtained result X _i (shape characteristic vector)
Is that when the shape x _j is close to the machining mode i, the value of X _i becomes large, and when it is orthogonal, it becomes 0. Here, “to be orthogonal” means that the shape vector (x _j ) representing the curved surface X and the machining mode i
Is that the shape vector (n _j ) is orthogonal.

In particular, the shape vector (n
_j ) If the elements themselves are selected so as to be orthogonal to each other, the value of the shape characteristic vector X _i represents the expansion coefficient of the curved surface X based on the base vector.

The shape characteristic vectors are calculated for two curved surface shapes X and Y and compared. Assuming that the shape vectors of the curved surface shapes X and Y are (x _j ) and (y _j ), (X _i ) = (n _ij ) (x _j ) (Y _i ) = (n _ij ) (y _j ) (2) Become.

Next, the evaluation amount σ (X, Y) is defined as follows. σ (X, Y) = Σ _i (X _i −Y _i ) ² (3) Here, Σ _i represents the sum of machining mode i. For example, to determine which of the two curved surface shapes X and X ′ is closer to the curved surface shape Y, the evaluation amounts σ (X, Y) and σ
(X ′, Y) is calculated. If σ (X ′, Y) <σ (X, Y) (4), it can be determined that X ′ is closer to Y than X.

In the above discussion, the conversion matrix
Each row of (n _ij ) may be multiplied by a constant for dimensionless or normalization. In the definition formula of the evaluation amount σ (X, Y), the sum of the absolute values of the differences may be used instead of the sum of the squares of the differences, and any value that is called a norm in mathematics may be used.

Instead of calculating the shape characteristic vector for each of the two curved surface shapes X and Y, the difference between the two curved surface shapes may be calculated first and then converted using the conversion matrix (n _ij ). In this case, if the difference between the shape vectors is represented by z _j , the shape vectors (x _j ) and (y _j ) of the curved surface shapes X and Y are expressed as follows. z _j = x _j −y _j (5)

The difference between the shape vectors is as follows, considering the shape characteristic vector. (Z _i ) = (n _ij ) (z _j ) σ = Σ _i Z _i ² (6)

Similarly, regarding the curved surface shape X ′, a shape characteristic vector is considered from the difference (z ′ _j ) from the curved surface shape Y. (Z ′ _i ) = (n _ij ) (z ′ _j ) σ ′ = Σ _i Z _i ² (7) Here, if σ ′ <σ, it can be determined that X ′ is closer to Y than X. .

It should be noted that the conversion result of the difference between the curved surface shapes is as described above.
By looking at each mode component Z _i for (Z _i ), it is possible to know which deformation mode is better to use.

[0026]

A description will now be given of an example in which four vertices of a rectangle, four midpoints, and a total of nine points at the center are taken as representative points on a curved surface. Here, if the number of points to be digitized is increased, it is possible to digitize a complicated shape, but the subsequent calculation processing is also complicated. Even at these nine points, a simple shape such as a quadratic surface is sufficient for numerically expressing the shape of the curved surface.

FIG. 1 shows points (measurement points) for digitizing the shape of the curved surface. The numbers in the figure are the numbers j of these points
Is shown. As the shape of the curved surface, a distance from a reference surface such as a surface plate is used. The distances of the curved surface from the reference surface at these points are defined as a _j : a _{1 to} a ₉ . As an example of a representative shape (deformation mode), five deformation modes as shown in FIG. 2 will be described.

Here, each deformation mode will be described. Mode 1 is bending deformation in the X-axis direction, mode 2 is bending deformation in the Y-axis direction, mode 3 is bending deformation in the diagonal direction (torsion), and mode 4 is the X-axis bending deformation. The inclination in the direction and the mode 5 represent the inclination in the Y-axis direction, respectively. Since the shape used for practical use can be almost expressed by these characteristic values, it is possible to digitize the shape of the curved surface.

First, the numerical values a _{1 to} a ₉ of the shape of the curved surface in these deformation modes are converted into simple numerical values by an appropriate linear transformation, and are expressed as n _{1 to} n ₉ . For example, deformation modes 1 to 5 (i =
1-5), (n _j ) = (1, -2, 1, 1, -2, 1, 1, -2, 1), i = 1 (n _j ) = (1, 1, 1 , -2, -2, -2, 1, 1, 1), i = 2 (n _j ) = (1, 0, -1, 0, 0, 0, -1, 0, 1), i = 3 (n _j ) = (-1, 0, 1, -1, 0, 1, -1, 0, 1), i = 4 (n _j ) = (-1, -1, -1, 0, 0, 0, 1, 1, 1), i = 5 (8). In this example, (n _j ) are orthogonal to each other.

A matrix (n _ij ) having these (n _j ) as rows becomes a transformation matrix. When the matrix is newly written, the following is obtained.

[0031]

(Equation 1)

As examples of the shape comparison, the following three shapes X,
Consider X ', Y. These are a convex shape at the center, a shape belonging to mode 1, and a flat plate, respectively, and the height at the representative point is as follows. X: (0, 0, 0, 0, √6, 0, 0, 0, 0) Center is convex X ': (1, 0, 1, 1, 0, 1, 1, 0, 1) Mode 1 Y: (0, 0, 0, 0, 0, 0, 0, 0, 0) flat plate

By multiplying these by the transformation matrix (n _ij ) of _Equation 1,
When the shape characteristic vector is obtained using Expression (2), (X _i ) = (− 2√6, −2√6, 0, 0, 0) (X ′ _i ) = (6, 0, 0, 0) , 0) (Y _i ) = (0, 0, 0, 0, 0).

Using these shape characteristic vectors to calculate the evaluation amount σ (X, Y) using equation (3), σ (X, Y) = 48 and σ (X ′, Y) = 36 , X ′ are closer to Y than X. Comparing the sum of squares of the height difference according to the conventional method, X and Y,
Both X 'and Y are 6, and there is no difference.

Looking at the components of the shape characteristic vector (component i of the deformation mode), since the first and second components of the shape X are not 0, the first and second components can be formed from the shape Y (flat plate). It can be seen that two deformation modes are required. Similarly, since only the first component of the shape X ′ is not 0, it can be seen that only mode 1 is required for molding.

[0036]

According to the present invention, by comparing the shape of a curved surface with a numerical value and converting it into a plurality of characteristic values, it is possible to easily compare the curved surface shapes. Therefore, according to the present invention, the shape of the curved surface can be determined in accordance with the processing method and conditions, so that information suitable for actual work can be presented.

[Brief description of the drawings]

FIG. 1 is a diagram showing the positions of points (measurement points) for digitizing the shape of a curved surface.

FIG. 2 is a diagram illustrating a shape of a curved surface according to a deformation mode.

Claims (1)

[Claims] 1. The shape of two or more surfaces to be compared is quantified, and the numerical value of each surface or the difference between the numerical values of each surface is calculated.
A curved surface shape comparison method in which a characteristic value of a shape is calculated by separating components of a plurality of shapes that can be formed, and the shape of the curved surface is compared using the characteristic values of the obtained shape.