KR100300455B1 - Curve-based Method for NC Processing Path Generation of Polyhedral Models - Google Patents

Abstract

The present invention relates to a curve-based method for generating NC machining paths of a polyhedron model. The present invention relates to a process of assigning topological properties to a polyhedron model that satisfies the vertex sharing rule and has only geometrical properties, and uses topological relationships of edges and vertices. The process of defining geometric characteristics (convex, concave, flat, saddle), the accurate representation of triangular, triangular, cylindrical and spherical trimming surfaces created from triangular, convex edges or vertices, It is possible to calculate accurate CL path data stably and quickly by finding the intersection between possible drive planes and rearranging, trimming, and connecting the curves and segments generated after slicing.

Description

Curve-based Method for NC Path Generation of Polyhedral Models

The present invention relates to a curve-based method for generating a NC machining path of a polyhedron model. More particularly, the present invention relates to a polyhedron model that satisfies a vertex sharing rule. Since the CL curve is generated by removing the parts that may cause interference during trimming operation, convex interference does not occur at all, and the intersections of the concave parts can be accurately obtained, so that the polyhedral model can be processed without errors in 3-axis NC machining. The present invention relates to a curve-based method for generating NC machining paths of polyhedral models.

In general, most of complex shapes such as the fuselage of an aircraft, the exterior of an automobile, and the appearance of home appliances are represented by a compound surface composed of several freeform surfaces. NC machine is usually used to process this compound curved shape. One of the most important problems when generating NC data, which is the input information of the NC machine, is to solve the interference of the tool. Here, the interference of the tool refers to a phenomenon in which the blade portion of the tool overcuts or gougs the machining surface.

Methods for generating tool paths without tool interference have been developed using parametric surfaces, offset surfaces, solid models, z-maps, and polyhedrons.

The conventional polyhedron method was developed by Duncan, Jun, Hwang, and Lee, all of which is a 'point based approach'.

As shown in Figure 1a, for a given tool center axis (x ₁ , y ₁ ), determine the value of z ₁ by lowering the tool until it meets a triangular polyhedron. Another method (Figure 1b) finds the intersection between a given tool center axis and the inverse tool offset surface, and determines the z ₁ value by selecting the highest point along the z axis. The tool center point (x ₂ , y ₂ , z ₂ ) can be obtained by performing the same calculation process at the point moved by the step length to find the next tool center point. When these points are entered into the NC machine, the tool moves along the straight line connecting the two points and cuts them.

However, since the generation of such a tool path in the related art has to calculate the distance to the triangle around all of the contact points of the tool, it takes a lot of calculation time to find the triangle in the vicinity, and convex interference generated when the tool moves between the two points. There is a fundamental limitation in preventing convex gouges and it is difficult to find the sharp-turn point in Figure 1c in the concave area.

Accordingly, the present invention is a 'curve-based method' developed to solve this problem, the phase information is given to the polyhedron model that satisfies the vertex-to-vertex rule to accurately calculate the offset elements, drive plane Since the CL curve is generated by removing the parts that may cause interference when trimming after trimming, the convex interference does not occur at all, and the sharp-turn point in the concave part can be accurately obtained, so the 3-axis NC The goal is to provide a curve-based method for generating NC machining paths for polyhedral models that can be processed without errors during machining (Figure 1c).

On the other hand, in order to achieve the above object, the present invention, in the generation of NC machining path using a computer, the process of providing topological properties to a polyhedral model that satisfies the vertex sharing rule and has only geometric properties, and using the topological relationship edges The process of defining the geometric features of the and vertices (convex, concave, flat, and saddle), the process of accurately representing the triangular, cylindrical, and spherical trims that are generated from triangular, convex edges or convex vertices, It is characterized by consisting of the process of finding the intersection between the offset element and the drive plane capable of intersection, and the process of rearranging, trimming, and connecting curves and line segments generated after slicing.

1 shows the difference between a point-based approach (a, b) and a curve-based approach (c)

2 is a flow chart illustrating an overall procedure for generating CL data in accordance with the present invention.

3 is a view showing a CL data generation process according to the present invention.

4 shows a data structure of a polyhedron model according to the present invention.

Figure 5 shows the properties of the edge according to the invention.

6 is a view for defining the property of the boundary corner in accordance with the present invention.

7 shows the shape of an offset element according to the edge property according to the invention.

8 is a view showing an offset form by an attribute of a vertex in accordance with the present invention.

9 illustrates the attribute definition of a boundary vertex in accordance with the present invention.

10 is a view for explaining the process of defining the properties of the vertices after reconstructing the polyhedron with only convex edges in accordance with the present invention.

11 is an illustration for finding the intersection between a cylindrical trim surface and a plane according to the present invention.

12 is an illustration for finding the intersection between a spherical trim surface and a plane according to the present invention.

Figure 13 shows a CL-path which is a CL-curve and toolpath according to the invention.

Hereinafter, the present invention will be described in detail with reference to the accompanying drawings.

The overall procedure of the method of generating a numerical control (NC) path for processing a polyhedral curved surface according to the present invention is shown in FIG. 2. First, it takes a polyhedral model with only geometry and creates a data structure and gives it a topological relationship.

Then, the polyhedral model is coordinated so that the tool direction is parallel to the x-axis, and the drive planes parallel to the xz plane are defined. Using the polyhedron with topological information, we define the properties of the edges (concave, convex, saddle, flat). Among the elements that form a polyhedron, the triangular plane, the convex edges, and the convex corners are offset, and the intersections with the series of drive planes are obtained at once. By arranging the intersections of one drive plane and overlapping sections, the bottom part (based on the z-axis value) can be removed and then connected to generate the final cutter location data.

In addition, the method of generating CL data according to the present invention is illustrated in FIG. 3.

That is, Figure 3a is to give the phase information to the input polyhedron model and define the properties of the edge, Figure 3b is to define the drive plane after the coordinate transformation of the polyhedral model so that the drive plane is parallel to the xz plane, Figure 3c is a polyhedron CL data is generated by slicing, rearranging, and linking offset elements of the triangle (triangular, cylindrical, and spherical), and FIG. 3D shows the original coordinates. Show the rotationally converted CL data.

Now, let's take a closer look at the important steps in the overall procedure described above.

The polyhedron model inputted to the method according to the present invention is a polyhedron model having only geometric information that satisfies the vertex sharing rule. Each vertex has an edge connected to it (V ₁ : e _1, e ₂ , e ₅ ; V ₂ : e ₂ , e ₃ ; V ₃ : e ₁ , e ₃ , e ₄ ; V ₄ : e ₄ , e ₅ ) Pointer to the corner to find (V ₁ → e ₁ , V ₁ → e ₂ , V ₁ → e ₅ ; V ₂ → e ₂ , V ₂ → e ₃ ; V ₃ → e ₁ , V ₃ → e ₃ , Must have V ₃ → e ₄ ; V ₄ → e ₄ , V ₄ → e ₅ ).

However, if one vertex has pointers to all connected edges, the amount of information is so large that only the pointer to the first edge is available (V ₁ → e ₁ ; V ₂ → e ₂ ; V ₃ → e ₁ ; V ₄ → e ₄ ). And all corners are pointers to two vertices (e ₁ → V ₁ , V ₃ ; e ₂ → V ₁ , V ₂ ; e ₃ → V ₂ , V ₃ ; e ₄ → V ₃ , V ₄ ; e ₅ → Pointers to two triangular planes adjacent to one corner with V ₁ , V ₄ (e ₁ → T ₁ , T ₂ ; e ₂ → T ₁ , NULL; e ₃ → T ₁ , NULL; e ₄ → T ₂ , NULL; e ₅ → T ₂ , NULL).

If there is only one neighboring triangle (boundary edge), the rest of the pointers are NULL. The triangle has pointers to three edges (T ₁ → e ₁ , e ₂ , e ₃ ; T ₂ → e ₁ , e ₄ , e ₅ ), and all triangles, edges, and vertices are closed list structures, respectively. It is.

Now, let's look at how to offset the triangles, edges, and vertices that make up the polyhedron.

First, the offset of the triangular plane becomes a triangular plane in which the triangular plane is parallelly moved by the tool radius in the normal beta direction.

For the edge offset, it is very efficient to use the edge property. Figure 5 shows the properties of the corner is divided as shown in Table 1.

property Justice Convex (CONVEX) If two neighboring triangles are convex, CONCAVE When two neighboring triangles are concave Flat (FLAT) When two neighboring triangles are parallel to each other

Here, the edge property can be easily defined using two neighboring triangles. However, if the edge is located at the boundary of the polyhedron model, a virtual triangular parallel to the edge of the z-axis is created to define the properties of the edge (Fig. 6).

The shape of the offset element according to the property of the edge is shown in FIG. 7, in the case of a convex edge, a cylindrical trim face 7a, and in the case of a concave edge, an intersection line 7b is generated between two neighboring triangular planes. It is shown in form 7c.

Here, the cylindrical trim surface generated at the convex edge is composed of two line segments and two circular arcs, which are represented by a secondary glass Bezier curve or the like.

On the other hand, the attributes of the vertex can be divided into convex (CONVEX), concave (CONCAVE), flat (FLAT), saddle (SADDLE). Here, the offset form according to the property of the vertex is as shown in Figure 8, wherein the convex vertex is created a spherical trim surface, if the concave the intersection between the triangular planes connected to the vertex. And when it is flat, it appears as a vertex. The boundary curve of the spherical surface by the convex vertex in FIG. 8 is the same as the boundary curve of the cylindrical trim surface of the edge connected to this vertex.

Meanwhile, the attributes of the vertices are defined using the attributes of the connected edges, which are summarized in Table 2 showing the attributes of the vertices according to the corner attributes.

Number of corners Corner properties Vertex properties Whether a sphere is created Three All corners are CONVEX CONVEX female All corners are CONCAVE CONCAVE part All corners are FLAT FLAT part Four 3 or more CONVEX edges CONVEX female There are less than three CONVEX corners SADDLE, CONCAVE FLAT part 5 or more If the polyhedron is reconstructed with only convex edges, CONVEX female if not CONCAVE part

Here, when the vertex is located at the boundary of the polyhedron model, two virtual triangular planes parallel to the z-axis are created as shown in FIG. 9, and the properties of the virtual edges are defined using this, and then the vertex properties of the boundary are defined according to Table 2. Can be.

If there are five or more edges connected to the vertex and their properties consist of convex, concave and flat, it is not easy to define the vertex properties. In this case, the process of defining the attributes of the vertices is shown in FIG. 10.

First, the polyhedral model is reconstructed while removing the concave edges from the polyhedron model composed of convex and concave edges as shown in FIG. 10A. Define the properties of the edges of the reconstructed polyhedron model (FIG. 10B). If there is another concave edge in the reconstructed polyhedron model, the above process is repeated until the polyhedral model is formed with only convex edges (FIG. 10C). If there are fewer than three convex edges during this process, they are not convex vertices and do not create a sphere. Once a polyhedron with convex edges is made, these edges are used to obtain the boundary curve of the offset sphere (FIG. 10D).

As described above, in the present invention, the geometrical properties are defined using the topological information of the polyhedron model to accurately represent the offset shapes of the triangular plane, the corners, and the vertices.

Now, let's take a closer look at the problem of the intersection between the offset triangular, cylindrical trim, spherical trim and drive planes described above.

First, find the minimum and maximum values in the y-axis direction for one offset element (triangular face, cylindrical trim face, or spherical trim face). Find the drive planes within the range of minimum and maximum values, find the intersection between these planes and the offset elements (this intersection is called the 'CL-curve') and store for each drive plane. A detailed description of the process of finding the intersection between each offset element and one drive plane is as follows.

In the process of intersection between the offset triangular plane and the plane, the line segment obtained by connecting two intersection points between the plane and the three edges of the plane becomes a CL-curve.

The intersection between the cylindrical trim face and the plane becomes an elliptical arc or line segment. First, the intersections V ₀ and V ₂ between the drive plane and the cylindrical trim surface boundary curve (two line segments and two circular arcs) are calculated (FIG. 11). Obtain SP and EP by projecting V ₀ and V ₂ perpendicular to the base plane of the cylindrical trim face, and use the second point of the second glass Bezier curve to make an arc using these two points and the center point of the circle on the base plane. Find the control point (MP) and weight. Project MP back to the drive plane to find V ₁ . Where the weight of V ₁ is equal to that of MP. If, V _0, when the projection points SP and EP of the V ₂ matches line of intersection is a line segment that connects the V _0, V _2.

On the other hand, the intersection between the spherical trim surface and the plane becomes an arc. First, the intersections V ₀ and V ₂ between the spherical boundary curve (three or more arcs) and the plane are obtained. Next, the center point B of the sphere is projected perpendicular to the drive plane to find the center point C of the circle. At this time, the intersection line (CL-curve) to be obtained is a circular arc having a center point C, a start point V ₀ and an end point V ₂ . This arc is represented by a secondary glass Bezier curve.

The intersections obtained by the above method are stored for each drive plane and overlap in the concave part. Since the CL-curves in each drive plane are listed in random order, they are sorted according to the size of the x-axis value of the starting point for efficient trimming. The intersection point of the next curve is calculated, where overlapping curves are selected at the top with respect to the z axis and the rest are discarded (FIG. 13). In this process, concave gouges are eliminated and one CL-path is obtained by connecting these CL-curves.

The CL-paths thus obtained consist of line segments, arcs or elliptical arcs and can be machined along this path to precisely machine a given polyhedron. The CL-path is post-processed and made into NC data, depending on the type of NC machine.

As described above, the present invention can accurately represent the cylindrical and spherical trim surfaces generated at the convex edges or vertices by defining the properties of edges or vertices using the topological relationship of the polyhedron model. By finding the intersections between possible drive planes at the same time, it is not necessary to find a nearby triangular plane for interference inspection. In addition, by reordering, trimming, and connecting curves and segments generated after slicing, NC data consisting of CL curves rather than CL points can be calculated reliably and quickly, and it is effective to accurately process polyhedral models without errors. .

Claims (1)

In generating a 3-axis NC machining path without tool interference using a computer, The process of assigning topological properties to a polyhedral model that satisfies the vertex sharing law and has only geometric properties, the process of defining the geometric characteristics (convex, concave, flat, saddle) of edges and vertices using topological relationships, The process of accurately expressing faces, triangular planes created from convex edges or vertices, cylindrical trim surfaces, and spherical trim planes, obtaining intersections between the offset elements and possible drive planes at once, and after slicing Curve-based method for generating NC cutting paths of polyhedral models characterized by rearranging, trimming, and connecting curve data.