KR101751828B1 - Plate forming method by using mesh generation and planar development of 3d surface - Google Patents

Abstract

A method of machining a yarn using segmentation of a curved surface and flat expansion is disclosed. The method includes: a first step of generating a target curved surface; A second step of dividing the target curved surface into quadrilateral curved surface pieces; A third step of converting the divided surface pieces into divided plane pieces; A fourth step of optimally expanding the divided planar pieces on one and the same plane; And a fifth step of converting the geometric parameters obtained at any one of the second, third, and fourth steps into processing variables and extracting them.

Description

TECHNICAL FIELD [0001] The present invention relates to a three-dimensional surface division method,

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method of curving a three-dimensional curved surface and a method of flattening a curved surface using a flattening method. The present invention is well suited for extracting processing variables in sheet material processing using a heat source using a three-dimensional curved surface segmentation and flattening method.

R & D on the development of general curved surfaces has been carried out in the shipbuilding industry. Since the conventional method is not unique in the year and depends on the processing method, the experience and know-how of skilled workers are combined and consistent automation is not achieved. Also, it is difficult to extract optimal parameters for machining because of lack of connection with machining process, and the process is also complicated. Therefore, considering the machining process, it is necessary to divide the curved surface appropriately according to the curvature, extract the machining variables from the curved machining through optimal development of the simpler process, and provide the extracted parameters to the operator need. This method can minimize the material consumption in the processing step as well as the processing step.

 Conventional surface segmentation techniques include a method of dividing a surface by a finite element method which is not flexible with respect to the state of the surface, that is, the change of curvature, and this method is disclosed in Patent Registration No. 10-044092. In addition, since the conventional development method is based on the experience of the designer in most cases, it is difficult to apply the development method in complex curved surfaces and is not associated with the processing. Therefore, Resulting in unprocessed process variables. In addition, the development method using existing optimization techniques is complicated and the processing parameters are determined from mathematical calculations.

A problem to be solved by the present invention is to provide a method of automatically selecting a portion having a large change in curvature of a target shape, dividing the portion intensively, and obtaining a final processing condition at a similar level without a large difference depending on the position.

According to an aspect of the present invention, there is provided a method of forming a curved surface by using a surface division and a flat expansion, the method including: a first step of creating a target surface; A second step of dividing the target curved surface into quadrilateral curved surface pieces; A third step of converting the divided surface pieces into divided plane pieces; A fourth step of optimally expanding the divided planar pieces on one and the same plane; And converting the geometric parameters obtained from the third step and the fourth step into machining variables and extracting them.

According to one embodiment, the second step uses a distance-based method to divide the target curved surface, wherein the distance-based method is a method of dividing a curved shape of the target curved surface and a machining shape corresponding thereto into a starting point and an ending point, Determining a point on the machining shape as a new machining point when a difference between the curved shape and the machining shape is greatest between the start point and the end point to generate a new machining shape, The above process is repeated using the curved shape and the new machining shape. At this time, when the maximum distance in which the difference between the curved shape and the machining shape is the largest is smaller than a preset reference distance, the process is repeated.

According to another embodiment, in the second step, the angle reference method is used for dividing the target curved surface, wherein the angle reference method comprises the steps of: forming a tangent line at a starting point and a tangent line at a contact moving along the curved shape of the target curved surface, When the angle is less than a preset reference angle, the intersection of the tangent lines is determined as a new forming point, and the process is repeated starting from the new contact point generated in the process.

The fourth step is accomplished by moving each of the planar pieces to minimize energy while translating and rotating by the sum of the force vectors and the moments summed by the springs on the vertex of each of the planar pieces .

The forming angle of the machining parameters in the fifth step may be obtained from the angle formed by two adjacent planar pieces of the planar pieces in the third step. The molding line among the processing parameters of the fifth step may be obtained from the edge of the adjacent flat pieces after the end of the optimum development by the fourth step. The molding line among the machining variables in the fifth step is obtained by averaging the position coordinates of the vertexes of adjacent planar pieces among the planar pieces after optimum development by the fourth step to obtain representative coordinate points, Can be obtained by connecting straight lines. The contraction amount or the expansion amount of the machining variables in the fifth step may be extracted from the distance between vertexes between adjacent flat pieces of the flat pieces after the forefront expansion by the fourth step.

The present invention enables automatic extraction of machining parameters during machining and provides it to the operator. By concentrating the division of the curved surface or curved line at a large curvature change by a geometric approach, Efficiency can be increased, and the complex three-dimensional shape of the curved surface can be divided into several quadrangular pieces having different sizes depending on the curvature. In addition, it is possible to arrange the segmented planar pieces arbitrarily on a two-dimensional plane, and then to optimize the developed shape by a simpler method than the existing optimization method by moving the pieces using the spring principle. The contraction amount or expansion amount can be extracted geometrically immediately from the developed final shape, and the amount of material loss during processing can be reduced since the processing amount is determined using the shrinkage amount or expansion amount. We obtain the position to be machined from the divided curved surface by molding line, extract the angle required for forming through the geometrical angle between curved surfaces when dividing the curved surface, and provide processing variables which are concrete working instructions can do. Further, the present invention can also obtain a variable in a process of flattening a curved plate in a manner similar to the above.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a flow diagram of a method of dividing a surface and expanding a plane for an automatic tiling method according to an embodiment of the present invention; FIG.
2 is a conceptual diagram illustrating a distance-based method that may be used for surface segmentation of FIG.
3 is a conceptual diagram illustrating a process of finding a forming point by a distance-based method;
4 is a conceptual diagram for introducing an angle reference method that can be used for the surface division of Fig.
5 is a conceptual diagram illustrating a process of finding a forming point by an angle-based method.
FIG. 6 is a conceptual diagram for sequentially explaining a process of dividing a curved surface by expanding a two-dimensional curve segmentation into three dimensions and optimally expanding the same into a plane.
7 is a conceptual view for explaining a process of optimally expanding by a method using a virtual spring.
FIG. 8 is a conceptual diagram for explaining the results of optimal development in two forms according to the present invention; FIG.

Hereinafter, embodiments of the present invention will be described in detail with reference to the accompanying drawings. The following embodiments are provided by way of example so that those skilled in the art can fully understand the spirit of the present invention. Therefore, the present invention is not limited to the embodiments described below, but may be embodied in other forms. In the drawings, the width, length, thickness, and the like of the components may be exaggerated for convenience. Like reference numerals designate like elements throughout the specification.

Before describing the embodiments of the present invention, the present invention is a curve dividing technique which is a basis for dividing a processed surface into a plurality of flat pieces for machining into a target shape, Techniques for determining the forming points and forming conditions from the divided pieces, techniques for spreading the divided flat pieces on a two-dimensional plane and introducing virtual springs to optimize the development, and finally, techniques for geometric variables and processing May comprise a technique for constructing a database of variables.

The geometric parameters to be covered in this method may correspond to forming angle, in-plane shrinkage, and molding line. The forming angle is obtained from the angle formed by two adjacent planar pieces after the surface splitting. The molding line becomes the edge of the planar pieces obtained after optimal development and can thus be heated. The spacing between the planes obtained after optimal development corresponds to the in-plane shrinkage to be shrunk. The machining variables are variables required for actual machining, such as torch feed rate, torch-to-specimen distance, and molding line.

Referring to FIGS. 1 and 6 together, the method includes a curved surface creation step S1, a curved surface division step S2, an initial expansion step S3, an optimal expansion step S4, ). As will be described in detail below, the initial development electric field step S3 includes developing the divided three-dimensional curved surface into a two-dimensional plane, and the optimum developing step S5 introduces the spring principle to optimize the two- Development.

Hereinafter, each step of the variable extraction method will be described in more detail. Note that the curved surface segmentation step S2, the initial expansion step S3 and / or the forefront development step S4 of the respective steps constitute the invention by itself.

1. Curved surface creation step (S1)

In this step S1, the target curved surface is generated. The difference between the target shape and the surface to be machined becomes the target surface, and the target surface is obtained by calculating the difference between the target shape and the shape to be machined by mathematical approximation with Beizer surface, SPLINE surface or NURBS surface. The target surface is subjected to the following steps.

2. Surface splitting step (S2)

In this step S2, the target curved surface generated in the previous step S1 is divided into rectangular pieces. The curved surface division is extended from the principle of 'two-dimensional curved plate forming', and a method of reducing the processing parameters is used so that the curvature change is relatively large and the flat pieces are automatically concentrated on the required portion. Here, 'two-dimensional curved plate' means that the shape of the curved plate is symmetrical with respect to one plane, and the curved plate is approximated by assuming a curved line along a symmetrical plane. In the present invention, the following two methods are proposed as a two-dimensional division method of a curve.

2-1. Distance-based method

2 is a diagram schematically showing an example of the distance reference method. The dotted line in Fig. 2, that is, the curve is the target shape and the solid line is the shape to be machined, that is, the molding shape.

In the distance reference method, the maximum distance between the target shape and the molding shape is used as a molding reference, and the procedure is as follows.

A. The starting point P _i and the ending point P _{i + 1 at} which the target shape and the molding shape intersect are defined as the initial molding points.

B. determines the starting point and the target point on the image and the difference h _j is greater when the target shape of the contour between the end points to the new forming point P _{i + 2} and generates a new contour.

C. Repeat the above process using the new machining shape and the target shape to obtain another new forming point. At this time, the maximum distance (the difference between the target shape and the machining shape; h_j) Is less than a preset reference distance, the process is repeated.

D. The angle between the straight line (tangent line) and the straight line (tangent line) in the finally obtained machining shape is determined as the forming angle θ _i required for machining, and the position at that time is determined as the machining position d _i .

FIG. 3 shows a process of finding a forming point using a distance-based method.

2-2. Angular reference method

Fig. 4 is a schematic view showing an example of an angle reference method. Referring to Fig. 4, the angle between two tangents is used as a reference point of a forming point, and the procedure is as follows.

A. When the angle between the tangent at the starting point S _i and the tangent at the moving contact S _j along the target shape is less than a preset reference angle, the intersection of the tangent lines is determined as a new forming point P _i . At this time, a new contact S _{i + 1 is} also generated.

B. Repeat the above procedure with the new contact point as the starting point again to obtain the final forming points.

C. In the finally obtained machining shape, since the reference angle is the forming angle? _I , all of them have a constant forming angle, and the position at that time is determined from the forming position d _i .

FIG. 5 shows a process of finding a forming point using a distance-based method.

In both of the above-described methods, that is, in both the angle-based method and the distance-based method, the molding points are concentrated on the curved portion where the curvature change is large. Applying this method to a three-dimensional curved surface makes it possible to concentrate the dividing line at a portion with a large curvature change. The procedure for applying to a three-dimensional curved surface is shown at the top of FIG.

It is possible to think of a hypothetical straight line connecting the adjacent end points in a three-dimensional curved surface. If this virtual straight line and the actual side (curve) are seen, similarity with the above-mentioned two-dimensional molding method can be found. That is, through the relationship between the virtual straight line and the sides, a desired number of forming points can be generated on the curve. If the forming points are connected to each other by repeating this process while moving at a predetermined interval to the opposite side, can do. By repeating the same method on the other sides, you can create new curves that cross the already created curve. The points where the curves and the curves meet are determined as the forming points in the three-dimensional curved surface, and the curved surfaces are divided by connecting them linearly.

3. Planar piece creation step (S3)

Each surface piece divided in the previous step S2 includes four points. In this step S3, the four points are approximated on one plane through a least square method so as to be placed on one plane. The method of finding the plane equation according to the least squares method is as follows. Here, e is the error with respect to the variable z, and the value represented by the sum of squares is Sr. It is possible to obtain a parameter that minimizes the equation relating to Sr.

The last step in this step is to obtain the geometric parameter, the forming angle. The angle formed by two adjacent plane segments divided by the least squares method is extracted by the forming angle. The calculation is obtained by vector calculation with the normal vector of each plane piece. Compute two vectors on the plane using the three vertices of each plane piece, P ₁ , P ₂ , P _3, and the origin (0,0,0)

,

를 외적(Cross Product)하여 법선 벡터

을 구한다. 이렇게 구한 법선 벡터와 같은 방법으로, 인접한 평면 조각의 법선 벡터

가 이루는 각을 [수학식 3]을 이용하여 성형각도로 결정한다. These two vectors

,

Is cross product, and the normal vector

. In the same manner as the normal vector thus obtained, the normal vector of the adjacent flat piece

Is determined as a forming angle by using Equation (3).

4. Optimal deployment step (S4)

In this step S4, the flat pieces are optimally expanded on one and the same plane. In the three-dimensional space obtained in the previous step, the divided plane pieces are rotated in one plane (X-Y plane) and are laid out in order so as to overlap or not meet each other. At this time, each flat piece is assumed to be a non-deformable rigid body with no mass. In this step S4, as shown in the upper diagram of FIG. 7, the vertexes of the respective planar pieces are connected by the adjacent vertexes and the virtual springs, and the planar pieces are moved little by little in sequence as shown in the figure. When one piece moves, the remaining pieces do not move. When two or more pieces overlap, the piece is moved in contact with each other so as not to overlap, and this process is repeated. In this way we move all the pieces sequentially one by one. At this time, calculate the total energy of all springs and repeat this process until energy is minimum.

By the sum of the force vectors and the sum of the moments due to the springs at the vertices of the respective planar pieces, each planar piece moves to minimize energy while translating and rotating, which is shown in Equation (4).

Where u _i is the distance from one vertex of a planar piece to the vertex of another planar piece adjacent to it. At this time, as a boundary condition, make sure that each plane piece does not overlap with each other. When the optimum development is completed in this way, there is a gap between adjacent pieces, and this space becomes a part to be removed or shrunk to be processed into a three-dimensional shape. This is defined as the amount of shrinkage, and when using a heat source (flame, laser, and induction heating), the principle of shrinkage due to thermal stress is used. The amount of shrinkage is treated as a geometric parameter in the present invention. Another geometrical parameter and machining variable, the forming line, is obtained by averaging the positional coordinates of the vertexes of the adjacent plane segments after the plane optimization is completed, obtaining the representative coordinate point, and then forming the straight line between the points. And the heating proceeds along this molding line.

The constraint is set differently according to the processing method. In the case of the curved processing, the expansion is performed until the flat pieces do not overlap with each other (see the left side of FIG. 8). The opposite planarization can be considered. In the case of planarization, the process is performed until there is no gap between the flat pieces (see the right side of FIG. 8). In the case of the contact-type thin sheet forming by the tool, in the case of the curvature forming, it is repeated until the gap between the flat pieces disappears (see the right side of FIG. 8) (See the left side of FIG. 8). The distance between the optimally arranged planar pieces is a processing variable for machining, which corresponds to the amount of contraction or expansion depending on the machining method.

5. Process variable extraction step (S5)

As mentioned above, the processing parameters required for molding into the three-dimensional target shape include forming angle, molding line, shrinkage, or expansion amount.

The forming angle is in the flat piece creation step (S3). The angle formed by two adjacent planar pieces divided by the least squares method is extracted by the forming angle and obtained by vector calculation with the normal vector of each plane piece. Two vectors are calculated on one plane using the three vertices of each plane piece, P ₁ , P ₂ , P _3, and the origin (0, 0, 0) (see Equation 2).

을 구한다. 이렇게 구한 법선 벡터와 같은 방법으로 구한 인접한 평면 조각의 법선 벡터

가 이루는 각을 성형각도로 결정한다 ([수학식 3 참조]). At this time, the normal vector on the plane is a normal vector, and the two vectors are cross product

. The normal vector of the adjacent flat piece obtained by the same method as the normal vector thus obtained

Is determined as a forming angle (see Equation 3).

As described above, when the curved plate shape at the initial stage of processing is a three-dimensional curved surface, the divided curves at step S2 become the molding line. On the other hand, if the initial shape to be machined is a flat plate, after the flat expansion is completed in step S4, the position coordinates of the vertexes of the adjacent plane pieces are averaged to obtain a representative coordinate point, I ask.

The amount of shrinkage or expansion is determined by the processing method and the distance between adjacent vertices after the end of the optimal expansion corresponds to this value. In the case of machining using thermal stress such as laser machining and ship machining, only the shrinkage amount needs to be taken into consideration. Therefore, in the case of the bending process, the gaps existing between the flat pieces are shrunk for machining into the target shape, Is extracted as a shrinkage amount. In the case of planarization, the amount of shrinkage can be determined from the overlapping optimal expansion plane pieces, and corresponds to the amount of shrinkage at which the overlapping portions of the pieces are to be shrunk for processing into the target shape.

In the case of sheet metal forming using a tool, the amount of expansion must be taken into account in contrast to the method using thermal stress. In the case of blanket processing, the amount of expansion can be determined from the overlapping optimized expansion flat pieces, and must be expanded by this overlap amount for processing into the target shape. In the case of the flattening process, the gaps between the best-flattened flat pieces that are not overlapped can be expanded and processed into the target shape. At this time, the distance between the adjacent vertexes is extracted as the expansion amount.

Since the step S5 is to find the machining conditions necessary for actual machining, it is necessary to convert the geometrical parameters obtained in the above steps into machining parameters. In this step, a database consisting of geometric variables and process variables is established to perform this process. To do this, we first calculate the angle of deflection and the amount of contraction by controlling the distance between the torch and the specimen using the experiment and the FEM analysis. At this time, other heating conditions are kept constant. According to the existing research results and literature, the transfer rate of the torch is inversely proportional to the angle of deformation, and the shrinkage amount also has a similar relationship. These results are combined to complete the data map, which is a database composed of geometric variables and machining variables. Through this data map, it is possible to obtain the feed speed of the torch or the distance between the torch and the specimen, which is a processing condition for the forming angle and the shrinkage amount, and provide it to the user.

S1: Creating a surface S2: Splitting a surface
S3: Initial deployment (flat piece creation) S4: Optimal deployment
S5: Extraction of process variables

Claims (10)

In a method of processing a curved surface using a division of a curved surface and a flat expansion,
A first step of generating a target curved surface;
A second step of dividing the target curved surface into quadrilateral curved surface pieces;
A third step of converting the divided surface pieces into divided plane pieces; And
A fourth step of expanding the divided plane segments onto the same two-dimensional plane; And
And a fifth step of converting the geometric parameters obtained at any one of the second, third, and fourth steps into processing variables and extracting the geometric parameters. 2. The method according to claim 1, wherein the second step uses a distance-based method for dividing the curved surface of interest, wherein the distance-based method is a step of forming a curved shape of the curved surface of interest and a starting point and an end point, Determining a point on the machining shape as a new machining point when a difference between the curved shape and the machining shape is greatest between the start point and the end point to generate a new machining shape, And repeating the process using the curved shape and the new machining shape. 3. The method according to claim 2, wherein the repeat of the process is stopped when the maximum distance between the curved shape and the machining shape is larger than a preset reference distance. The method according to claim 1, wherein the second step uses an angle-based method for dividing the target curved surface, wherein the angle reference method includes a step of forming a tangent line at a starting point and an angle And a step of determining a new forming point at an intersection of the tangent lines when the reference point is less than a preset reference angle, and repeating the process starting from the new contact point generated in the process. [2] The method of claim 1, wherein the second step is to generate a molding point on the sides prior to the distance reference method or the angle reference method, wherein the same number of molding points are generated on the curve on the curve while moving gradually along the curved surface And the remaining steps are repeated to create forming points on the curved surface, and finally the forming points are connected to divide the curved surface. The method according to claim 1, wherein the fourth step comprises: expanding the divided planar pieces on a single plane, then applying a virtual spring to each vertex, And moving to minimize energy while translating and rotating. ≪ RTI ID = 0.0 > 8. < / RTI > The method according to claim 1, wherein the forming angle of the machining parameters is extracted from an angle formed by two adjacent flat pieces of the flat pieces in the third step. delete 2. The method according to claim 1, wherein the molding line of the machining variables is obtained by averaging the position coordinates of the vertexes of adjacent planar pieces of the plane pieces after the development by the fourth step to obtain representative coordinate points, And a plurality of grooves formed in the groove. The method according to claim 1, wherein the contraction amount or the expansion amount of the machining variables is extracted from a distance between vertexes between adjacent flat pieces of the flat pieces after the development by the fourth step.

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