JP2006263751A - Flat plate working information acquiring method, and flat plate working method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for acquiring flat plate working information capable of reproducing the working procedure by a skilled person as much as possible and necessary for forming a plate having a curved surface shape out of a flat plate, and a flat plate working method. <P>SOLUTION: The method for acquiring flat plate working information necessary for forming a plate having a curved surface shape out of a flat plate comprises a step of functioning the objective curved surface shape, a step of drawing the geodesic line to the functioned curved surface, a step of obtaining the in-plane distortion distribution from the changes in the interval on the geodesic line to satisfy the condition of being parallel on the plane, a step of obtaining the principal curvature distribution and the initial curvature distribution to obtain the objective curved surface shape, and a step of obtaining the curvature distribution to be added from the difference between the principal curvature distribution and the initial curvature distribution. In the flat plate working method, a plate having the curved surface shape is formed out of a flat plate based on the flat plate working information. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a flat plate processing information acquisition method and a flat plate processing method necessary for forming a plate material having a curved shape from a flat plate, which can be used for determining a forming procedure of a shipbuilding outer plate.

  For example, a part of a ship's hull and the outer shells of aircraft, trains, etc. have curved shapes, and conventionally, when these curved surfaces are formed, a developed view in which the curved surface shape is developed on a plane by a specific method is drawn. According to the experience and intuition of highly skilled and experienced technicians, for example, curved surface forming processing by linear heating has been performed.

In recent years, the relationship between the added strain and deformation has been handled as an optimal problem by utilizing the fact that the deformation shape after applying strain to the plate material is obtained by numerical simulation.
On the other hand, when forming a flat plate material into the desired curved surface by linear heating, in order to eliminate the need for finishing cutting after bending, in order to perform accurate chamfering, the inherent strain and inherent deformation of each linear heating in advance. After creating a linear heating method that performs bending when the desired curved surface shape is given, the generated inherent strain distribution is added to the desired curved surface shape and freely deformed A method of developing a curved surface into a planar shape by performing FEM (finite element method) elasticity simulation is known (see, for example, Patent Document 1).
JP 2000-237826 A

  However, in the above prior art, the processing method (processing method) for obtaining the desired curved surface shape is very complicated. In addition, a plurality of directions are required as in-plane strain directions required for curved surface formation, which leaves a problem that it is a very difficult processing method in reality or difficult to cope with large deformation. It was. Moreover, it was very different from the work procedure of skilled workers.

  This invention is made | formed in view of said subject, and it aims at providing the acquisition method of the flat plate processing information which can reproduce the work procedure which a skilled worker performs as much as possible.

The method for obtaining flat plate processing information according to the present invention is as follows.
In the acquisition method of flat plate processing information necessary for forming a plate material having a curved shape from a flat plate,
Functionalizing the desired curved surface shape;
Drawing a geodesic curve on a functionalized surface;
Obtaining an in-plane strain distribution from a change in spacing on a geodesic line that satisfies a parallel condition on a plane;
Obtaining a main curvature distribution and an initial curvature distribution for obtaining a desired curved surface shape;
A step of obtaining a curvature distribution to be added from the difference between the main curvature distribution and the initial curvature distribution;
It is characterized by having.

  The flat plate processing method according to the present invention is characterized in that a plate material having a curved shape is formed from a flat plate based on the flat plate processing information obtained by the flat plate processing information acquisition method.

  The flat processing information acquisition method according to the present invention includes a step of drawing a geodesic line on a functionalized curved surface, a step of obtaining an in-plane strain distribution from a change in an interval on the geodesic line that satisfies a parallel condition on the plane, and Since there are a step of obtaining a main curvature distribution and an initial curvature distribution for obtaining a desired curved surface shape, and a step of obtaining a curvature distribution to be added from a difference between the main curvature distribution and the initial curvature distribution, the work procedure performed by a skilled worker is performed. It can be reproduced as much as possible.

  Embodiments of the present invention will be described below.

To form a curved surface such as a ship's outer plate from a flat plate, (1) drawing a development view on the flat plate (current drawing development), and (2) bending by heating called a roller, a press, or a go iron. Two steps are performed. An unfolded figure that has been flattened by adding bending deformation, torsional deformation, stretching or shrinking deformation to a shape that is not a flat surface, is reconstructed into a curved surface by adding bending, twisting, stretching or shrinking in the opposite direction. For this reason, the original shape cannot be restored unless the amount of deformation applied when the curved surface is developed on a flat surface is known.
It is generally difficult to quantify the amount of deformation required for this development. In particular, it is difficult to quantify the in-plane deformation amount classified as expansion / contraction deformation. When the in-plane deformation amount is not accurate, for example, when a paper is pasted on a spherical surface, a “wrinkle” is always generated somewhere (see FIGS. 2 and 3). If the quantitative distribution of “wrinkles” can be known and removed beforehand, a beautiful curved surface can be formed.

  In the present invention, so that a curved surface can be handled in the computer, (1) a function for approximating the curved surface with a mathematical expression, (2) a function for pasting paper on the approximated curved surface in the computer, and (3) a function for measuring the size of “wrinkles” A computer system equipped with a computer is constructed to handle the curved surface mathematically and mechanically.

  That is, the flat processing information acquisition method according to the present invention includes a step of functionalizing a target curved surface shape, a step of drawing a geodesic line on the functionalized curved surface, and a geodesic line that satisfies a parallel condition on the plane. A step of obtaining an in-plane strain distribution from a change in the distance between the steps, a step of obtaining a main curvature distribution and an initial curvature distribution for obtaining a desired curved surface shape, and a step of obtaining a curvature distribution to be added from a difference between the main curvature distribution and the initial curvature distribution And having.

The flat plate processing information acquisition method according to the present invention will be further described with reference to the flowchart of FIG.
First, for example, the phase shape of the outer shell that becomes a part of the hull of the ship, that is, the target curved surface shape is functionalized to give the target curved surface shape (S10 in FIG. 1).
As the target curved surface shape, for example, discrete spatial coordinates are received from graphic information, and the curved surface is approximated in the form of z = z (x, y). At this time, for example, a neural network using a sigmoid function is used as the function, and learning is performed so that the z coordinate is output with respect to the input of the (x, y) coordinate on the curved surface. Thus, when the (x, y) coordinates are given to the computer, the z coordinates on the curved surface can be known.

Next, a geodesic line is drawn on the functionalized curved surface as follows. That is, the trunk line is drawn discretely by the geodesic line (S12 in FIG. 1), and the branch line is drawn by the geodesic line (S14 in FIG. 1).
For example, in the example shown in FIG. 2, when the paper is pasted on the spherical surface described above, the side AB is first pasted on the spherical surface, and then the adhesive position extending in the vertical direction such as AD and BC is pasted. . Here, the side AB corresponds to the trunk line of the geodesic line, and the lines AD and BC correspond to branch lines of the geodesic line. On the other hand, in the example shown in FIG. 3, the square center point O is first pasted, and then radially pasted from the point O. The resulting “wrinkles” are shown schematically in both figures (a). In these cases, it goes without saying that the square ABCD corresponds to the development of the area ABCD on the spherical surface, and “wrinkles” correspond to the in-plane deformation. In order to perform the processing mechanically, it is convenient to align the direction of “wrinkles” as much as possible. In the case of FIG. 2, the direction of the “wrinkle” is one direction on the development view. Therefore, the method shown in FIG. 2 is preferable because it is not necessary to decompose the in-plane deformation amount into independent orthogonal two-direction components and can be expressed simply.

From the above, the following properties are used to paste paper on a curved surface in a computer. The square shown in FIG. 2B is referred to as a development view.
(1) The bonding portion is a straight line on the development view.
(2) The bonding portion is composed of a single base line (trunk line) and a plurality of branch lines that intersect perpendicularly thereto.
(3) In the developed view, after bonding, the curved surface is in contact with the straight line (1).
(4) A tangent line satisfying the above (3) on the curved surface is a geometrically characteristic line called a geodesic line.
From the above, if a geodesic line corresponding to a base line (trunk line) and a branch line perpendicular to the base line is drawn on the curved surface, this is the bonding position.

Specifically, the geodesic line is drawn by the following procedure.
That is, as shown in FIG. 4, the starting point is determined as a point S (x, y) on the xy plane. If this (x, y) coordinate is given to a function that expresses a curved surface, the z coordinate can be easily obtained, and this is the G ₁ point, which is the starting point of the geodesic line. Point D is the end point of vector SD indicating the direction of drawing a geodesic line on the xy plane. Points S ₁ and S ₂ are determined at equal distances across a point S on a straight line on the xy plane perpendicular to SD. The z coordinate on the curved surface P corresponding to the x and y coordinates of the points S ₁ and S ₂ is obtained by using a curved surface function, and the points h ₁ and f ₁ on the curved surface are determined.
The circles of the same radius that are in the plane perpendicular to the line h ₁ f ₁ and have the centers at the points h ₁ and f ₁ are the points C ₁ and C ₂ . Of the intersections of the circles C ₁ and C ₂ and the curved surface P, the points on the geodesic line traveling direction side are h ₂ and f ₂ .
Furthermore, the circle C _1, of the intersection of the circle and a curved P centered in a plane parallel to the circle C _1, C ₂ to G ₁ at the same size as the C _2, a point in the traveling direction side of the geodesic G ₂ .
When the operations previously performed on the line segment h ₁ f ₁ and the point G ₁ are performed on the line segment h ₂ f ₂ and the point G ₂ , the G point is sequentially obtained and its coordinates are recorded. (X, y, z) coordinates obtained by dividing the points on the geodesic line at equal intervals can be obtained as the discrete coordinates of the geodesic line.
In FIG. 4, the average value theorem is used between the straight line passing through the points h ₁ and h ₂ and the tangent line at the point G ₁ . Therefore, the point S does not necessarily need to be a midpoint between the points S ₁ and S ₂ , and as a special case, the point S may be coincident with either the point S ₁ or S ₂ .

Once a geodesic line has been drawn as a continuous G point in FIG. 4, the operations previously performed on the line h ₁ f ₁ and the point G ₁ are as shown in FIG. When G ₁ G ₃ and point G ₂ are performed and point N ₂ is obtained and N point is obtained repeatedly, the point N on the geodesic line that intersects the previous geodesic line perpendicularly at point G ₂ (x, y, z ) Coordinates can be obtained as discrete coordinates. In the case of FIG. 5, the average value theorem is used between the straight line passing through the points G ₁ and G ₃ and the tangent line at the point G ₂ . Therefore, it is not always necessary to obtain the point N ₂ from the three points G ₁ , G ₂ and G _{3. As} a special case, the point N ₂ (or N ₁ ) is obtained from the two adjacent points G ₁ and G _2. It is also allowed.
Thus, a geodesic line as a base line and a geodesic line as a branch line orthogonal to the base line can be drawn on the curved surface.

Next, the in-plane strain is calculated by measuring the branch line spacing in the trunk direction (S16 in FIG. 1).
“Wrinkles”, or in-plane strain, that occurs when a paper depicting a base line and a branch line is pasted on the curved surface at the position of the base line and the branch line, is a point that is at the same distance from the base line on the adjacent branch line. (e.g. in FIG. 5, _{N 1} and _{N 2)} represented by the change in the spacing of. “Wrinkles” do not need to occur when the distance between branches does not change. In addition, although it has been called only “wrinkles” until now, there is actually a case where “hikitsuri”, that is, paper stretches. Since the coordinates of the points on the geodesic line have already been obtained, the distance between the points on the branch line and the amount of change can be easily known.
Here, in obtaining the in-plane strain distribution necessary for curved surface formation, the in-plane strain on a specific geodesic line on the curved surface is designated as zero, and the in-plane strain necessary for curved surface formation is parallel to the previous geodesic line. Calculated as a strain-only component.
Thereby, a person who performs flat plate processing (user) can designate a place where he / she does not want to give strain, and a processing method can be created as a unidirectional strain distribution desired by the flat plate processing person. This strain distribution can be made to correspond to the triangular work of the conventional work.

  The in-plane strain distribution is calculated from the process of functionalizing the target curved surface shape described above, the process of drawing a geodesic line on the functionalized curved surface, and the change in the interval on the geodesic line that satisfies the parallel condition on the plane. Through the required steps, basic processing information necessary to form a plate with a curved shape from a flat plate can be obtained. Using this processing information as a guide, a plate with a curved shape is formed from a flat plate. can do.

  In the flat plate machining information acquisition method according to the present invention, a step of obtaining a main curvature distribution and an initial curvature distribution for obtaining a target curved surface shape, and a step of obtaining a curvature distribution added from a difference between the main curvature distribution and the initial curvature distribution And having.

Here, the developable surface and the non-expandable surface will be described.
A developable surface is a developable surface, which is a curved surface with a Gaussian curvature of zero and an average curvature that is not zero. In other words, one of the two main curvatures is 0, and more flatly, it is a curved surface that does not “wrinkle” even when paper is attached to the surface, and the side of a cylinder or cone corresponds to this.
A non-developable surface is a curved surface that has two principal curvatures that are not zero, and is a curved surface that has a non-zero Gaussian curvature. The average curvature is a surface that can be interpreted as an undevelopable surface.
In the present invention, since it is assumed that “wrinkles” are caused when paper is pasted on a curved surface, the target curved surface is a non-expandable surface. That is, the curved surface that is the subject of the present invention, that is, the curved surface that is functionalized when the in-plane strain distribution is obtained (S10 in FIG. 1) is a non-developable surface.

Further, the in-plane strain distribution of the torus model will be described.
The shape shown in FIG. 6 is called a torus, and the shape is determined by dimensions R and r in the figure. A point provided for examining a change in length between two points shown in FIG. 5 (a point located at an equal distance from a base line on an adjacent branch line, for example, N ₁ and N ₂ or less in FIG. Draw a development line on the plane and place it so that the trunk line and the xy plane coincide with each other, and move the gauge and the development line on the plane to the torus surface. The gauge points are set on the grid points with an interval of 1.
In the torus, a theoretical solution of strain based on the length of the intersection line between the xy plane and the torus is known.

Based on the above knowledge, the direction and distribution of the initial curvature necessary for curved surface formation are obtained.
Near the arbitrary point on the curved surface is a torus curved surface with two principal curvatures. Even when the main curvature varies depending on the location, it can be treated as a torus curved surface within a sufficiently narrow range.
If a plate is previously bent into a cylindrical shape and an in-plane strain is applied to it, a curved surface can be formed, but even if the in-plane strain is the same, if the radius of the first cylinder is different, it will be completed The main curvature of the curved surface is not the same. For this reason, the initial curvature distribution for shaping the entire curved surface can be obtained by deriving these relationships based on elastic mechanics and calculating the entire curved surface.

The initial curvature cannot be determined unless the principal curvature of the target curved surface and the direction on the curved surface are known. It is necessary to determine the principal curvature and its direction on the approximate curved surface. For this purpose, it is necessary to draw a geodesic line passing through a point where the principal curvature direction is desired on the curved surface at 45 ° intervals. Therefore, first, the curvatures in the four directions R3 to R6 are measured (S20 in FIG. 1) on the functionalized curved surface (S10 in FIG. 1) which is a non-developable surface.
FIG. 7 shows points on the geodesic line obtained discretely at 45 ° intervals. Assuming that the curvature radii calculated from three points on the geodesic line in each direction are R3 to R6, there is a relationship of the following equation between the angle θ formed by the R3 direction and the main curvature direction. From this equation, the main curvature direction can be obtained.

  Also, the principal curvature radii R1 and R2 are given from the following two equations, respectively.

  By repeating this operation on the curved surface, a main curvature distribution is obtained (S22 in FIG. 1).

The curved surface is formed by setting the main curvature of each part on the curved surface to a target principal curvature. In order to obtain the desired principal curvature, it is necessary to apply bending deformation in addition to the application of in-plane strain necessary for curved surface formation. For example, when an in-plane strain is applied to a plate bent into a cylindrical shape, a torus curved surface corresponding to the initially set cylindrical deformation can be obtained. In other words, even if the in-plane strain applied is the same, the target curved surface cannot be obtained unless the initial cylindrical curvature (called initial curvature) is correct.
Therefore, assuming that the initial curvature changes to a different curvature due to the effect of in-plane strain, the main curvature radii for calculation are RT1 and RT2, and the relationship between the initial curvature radii R0 to obtain it Is required.
The main curvatures obtained when in-plane strain is applied to a cylindrical shape with various radii by elastic theory to obtain the desired principal curvature radius is R1 and R2, and the relationship with the initial curvature radius R0 is shown in FIG. Show. Here, RAV is the geometric mean of the target radii of curvature.

In FIG. 8, the horizontal axis represents the ratio between the average curvature RAV and the larger main curvature R1, and the vertical axis represents the ratio between the initial curvature R0 and the average curvature and the ratio between the smaller curvature and the average curvature. ing. A straight line with an inclination of 1 represents R1 itself. When the horizontal axis is 1, the larger curvature and the average curvature are 1, that is, a sphere. The initial curvature at this time is 0. That is, a sphere can be obtained when only an in-plane strain is given without giving an initial curvature. When the horizontal axis is 6 or more, the initial curvature and the larger target curvature are approximately equal. In this case, the larger initial curvature may be given as the initial curvature.
By obtaining R0 of each point from the main curvature distribution on the target curved surface, an initial curvature distribution necessary for curved surface formation is obtained, that is, the initial curvature is estimated (S24 in FIG. 1).
Here, there is a restriction on the initial curvature that can be given to the flat plate. The flat plate cannot be deformed into a shape other than a so-called developable surface shape such as a cylindrical shape or a conical shape.
In the above procedure, an initial curvature distribution that can be expressed as a developable surface is estimated.

Then, the developable surface is fitted from the obtained initial curvature distribution to determine, for example, the initial shape of a cone (S26 in FIG. 1).

By the way, as described above, the initial curvature distribution necessary for forming the target shape, that is, the initial curvature distribution that is a non-developable surface, and the initial curvature distribution that can be given, that is, the initial curvature that can be expressed as a developable surface. It is not the same as the curvature distribution. For this reason, more precisely, the difference in curvature to be added after applying in-plane strain, that is, the curvature as a non-developable surface that is not reflected when determining the initial shape (S26 in FIG. 1) is calculated. (S28 in FIG. 1), curvature information to be partially added is obtained (S30 in FIG. 1). Specifically, the initial curvature distribution that can be given is subtracted as a vector from the initial curvature distribution necessary for forming the target shape to obtain the curvature distribution as a non-expandable surface.
As described above, the initial curvature and the additional curvature are obtained as the processing information required for the curved surface formation.
By performing a series of steps of the flat plate processing information acquisition method according to the present invention described above, information serving as a guide for flat plate processing can be obtained. Moreover, the work procedure performed by the skilled worker can be reproduced as much as possible by performing flat plate processing based on this flat plate processing information.

The target shape is shown in FIG. The shape with the smaller radius of curvature was chosen depending on the location. Further, FIG. 10 shows a shape obtained by obtaining the in-plane strain and giving the in-plane strain to the cone having the initial curvature. FIG. 10 is a comparison of the distribution of curvature in a plurality of branch line directions along one trunk line in FIG. 9 after the deformation calculation. That is, the distribution of the smaller radius of curvature is shown. The solid line is the target curvature radius distribution, the initial curvature given by the circle, and Δ is the deformed shape calculated using the finite element method.
Here, although no additional curvature is given, it can be seen that Δ and the solid line are almost the same.

It is a flowchart for demonstrating the procedure about the acquisition method of the flat plate processing information which concerns on this invention. It is for demonstrating the basic concept of the acquisition method of the flat plate processing information which concerns on this invention, About one method when sticking paper on a spherical surface, (a) is the state which stuck paper on the spherical surface, ( b) is a diagram showing the paper developed on a plane before being attached to a spherical surface. It is for demonstrating the basic concept of the acquisition method of the flat plate processing information which concerns on this invention, About another one method when sticking paper on a spherical surface, (a) shows the state which stuck paper on the spherical surface. (B) is a figure which respectively shows the paper which carried out the plane development before sticking on a spherical surface. It is for demonstrating the method of drawing a geodesic line, and is a figure which shows a geodesic start point. It is a figure for demonstrating the method of drawing a geodesic line, and is a figure which shows the geodesic start point of a perpendicular direction. It is a figure for demonstrating the in-plane distortion distribution of a torus model. It is a figure which shows the state which calculated | required the geodesic line which passes along the point which wants to obtain | require the principal curvature direction on a curved surface discretely at 45 degree intervals. The horizontal axis represents the ratio between the average curvature RAV and the larger main curvature R1, and the vertical axis represents the ratio between the initial curvature R0 and the average curvature and the ratio between the smaller curvature and the average curvature. . It is a figure which shows the target shape of an Example. It is the figure which showed and compared distribution of the smaller curvature radius of the curved surface shape obtained by this invention, and the curved surface shape obtained by another method, respectively.

Claims (2)

In the acquisition method of flat plate processing information necessary for forming a plate material having a curved shape from a flat plate,
Functionalizing the desired curved surface shape;
Drawing a geodesic curve on a functionalized surface;
Obtaining an in-plane strain distribution from a change in spacing on a geodesic line that satisfies a parallel condition on a plane;
Obtaining a main curvature distribution and an initial curvature distribution for obtaining a desired curved surface shape;
Obtaining a curvature distribution to be added from the difference between the main curvature distribution and the initial curvature distribution;
A flat plate machining information acquisition method characterized by comprising: A flat plate processing method comprising forming a plate material having a curved surface shape from a flat plate based on the flat plate processing information obtained by the flat plate processing information acquisition method according to claim 1.