JP3187813B2 - How to create offset surface data - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention will be described in the following order. A Industrial application field B Outline of the invention C Conventional technology (Figs. 5 and 6) D Problems to be solved by the invention (Figs. 5 to 7) E Means for solving the problems (FIG. 2) F action (FIG. 2) G embodiment (G1) Interpolation of discontinuous spaces SPC ₁ , SPC ₂ , SPC ₃ (FIGS. 1, 3 to 7) (G2) Discontinuous space Interpolation of SPC ₁₂₃ (FIGS. 1 to 7) Effect of the Invention A Field of Industrial Use The present invention relates to a method for creating offset surface data, for example, CAD (computer aided design) or CAM (computer).
This method is suitable when applied to the case where offset surface data for producing a product having an outer shape having the free-form surface is created using data representing the free-form surface generated in, for example, aided manufacturing. B. Summary of the Invention The present invention relates to a method for creating offset surface data representing the trajectory of a tool for two adjacent patches created by a free-form surface creation method, wherein the condition of tangent plane continuity does not hold at the shared boundary. For three patches connected to each other under the condition, in the discontinuous space of the corner where the offset surface data is discontinuous to each other,
By reliably interpolating the offset surface data, it is possible to control the tool of the machine tool not to operate abnormally at the shared boundary position when the tool is moved based on the three discontinuous offset surface data. C Prior Art For example, when designing the shape of an object having a free-form surface using a CAD method (geometric modeling), a designer generally uses a plurality of points in a three-dimensional space through which the surface passes (this is called a node). And a computer calculates a boundary curve network connecting the plurality of designated nodes by using a desired vector function, thereby creating a curved surface represented by a so-called wire frame. Thus, a large number of framework spaces surrounded by boundary curves can be formed (such a process is called a framework process). The boundary curve network formed by such framework processing is
It itself represents the rough shape of the object that the designer intends to design, and uses a boundary curve surrounding each framework space to interpolate a curved surface that can be expressed by a predetermined vector function as the surface shape of the details of the object. If you can
As a whole, a free-form surface (which cannot be defined by a quadratic function) designed by an designer for an object can be generated. Here, the curved surface formed in each frame space forms a basic element constituting the entire curved surface, and this is called a patch. By the way, in order to give a more natural outer shape to the generated free-form surface as a whole, a patch that satisfies the condition of continuation of the tangent plane at the shared boundary is provided in two frame spaces adjacent to each other with the shared boundary therebetween. A free-form surface creation method has been proposed in which a control edge vector around a shared boundary is reset (Japanese Patent Application No. 60-277448). This free-form surface creation method includes, for example, two patches as shown in FIG. Are connected smoothly, the nodes given by the framework processing Based on adjacent patches Control edge vector such that the condition of tangent plane continuity is satisfied at the shared boundary COM1 of Are set, and the internal control points are set by these control edge vectors. The principle is to set again. If such a method is applied to other shared boundaries COM2, COM3, and COM4, the patch will eventually end up. Can be smoothly connected to adjacent patches under the condition of tangential plane continuity. In this specification, the tangent plane means a plane formed by tangent vectors in the u and v directions at each point of the shared boundary. For example, for each point on the shared boundary COM1 in FIG. When the tangent planes are the same, the condition of continuation of the tangent plane holds. That is, a point (0,
The condition of continuation of the tangent plane for v) is determined as shown in FIG. Ie patch , The tangent vector in the direction transverse to the shared boundary COM1 (ie the u-direction) , And the tangent vector in the direction along the shared boundary COM1 (ie, the v direction) Normal vector Is Represented by a patch The tangent vector in the direction across the shared boundary COM1 And the tangent vector in the direction along the common boundary COM1 Normal vector Is It is represented by Under such conditions, in order to be tangent plane continuation,
Tangent vector Must lie on the same plane, so that the normal vector Will face in the same direction. To achieve this, the following equation So that the internal control points Should be set. Where λ (v), μ (v), ν
(V) is a scalar quantity. Also patch Is Vector function consisting of a cubic Bezier equation Is expressed using. u and v are parameters in the u and v directions, and E and F are shift operators. In this specification, control points include nodes and control points that represent boundary curves of the framework space and internal control points that represent curved surfaces inside the patch. D Problems to be Solved by the Invention A large number of patches generated by such a method Consider cutting a product having an outer shape represented by the curved surface data using, for example, a milling machine formed of an NC machine tool. In this case, one patch Offset surface data corresponding to Is And define the center of the tool of the milling machine as offset surface data It may be sufficient to move through the position given by. Equation (5) is the patch to be processed. For position data representing the surface of Offset surface data consisting of a surface translated in the normal direction by the amount of translation represented by Means to generate Here, R represents the distance from the center position of the tool to the cutting edge. Thus, the offset surface data represented by the equation (5) Is input to the control device of the machine tool so that the center of the tool is offset surface data. If the cutting edge is controlled to move on a free-form surface represented by Moving on a curved surface parallel to The curved surface represented by can be cut. By the way, in general, as described above with reference to FIG. The curved surface formed by sequentially connecting
Offset surface data obtained using equation (5) It can be easily cut by using. That is, two patches adjacent to each other Surface data obtained based on To , Two patches adjacent to each other as described above with reference to FIG. If they are connected under the condition of tangent continuity,
Patch at the location of the shared border COM1 Normal vector as well as Are the same as each other, so the translation data input during the cutting operation as well as (Equations (6) and (7)) are equal to each other. Therefore, the tool is a patch Under the same conditions as when cutting the surface, the cutting can be continued so as to smoothly pass the boundary position. However, as shown in FIG. 7, three patches adjacent to each other, for example, at a corner of an object. Are connected in a discontinuous state where the condition of tangent plane continuity does not hold at the shared boundaries COM12, COM23, and COM31, the offset surface data at the positions of the shared boundaries COM12, COM23, and COM31 However, there is a problem in that a discontinuous space is generated near the positions of the shared boundaries COM12, COM23, and COM31. In FIG. Each patch Are shown, and three patches are shown for these control points. Surface data for Is the following equation, Is calculated by Thus, the control points are obtained by the equations (8) to (10). Offset surface data corresponding to Position data representing Is calculated. In such an operation, the shared boundaries COM12, COM23, COM31
Control point representing The normal vectors of the points on the shared boundaries COM12, COM23, and COM31 corresponding to Are different, the offset surface data obtained by the calculations of the equations (8), (9) and (10) accordingly. Location data Represents different positions from each other, and the surface data Location data Represents different positions, and the surface data Location data Represent different positions from each other. Thus, in the tool movement space, the position data Space between SPC ₁ , position data Space between SPC ₂ and position data The space between SPC ₃ and the three patches forming the corner Share points shared by Position and position data With respect to the space SPC ₁₂₃ between them, data specifying the movement trajectory of the tool cannot be obtained (this space SPC ₁ , SPC ₂ ,
SPC ₃ and SPC ₁₂₃ are called discontinuous spaces). In the discontinuous spaces SPC _{1 to} SPC ₃ and SPC ₁₂₃ , a patch There is a risk that a tool that has been cutting to the position of the common boundary COM12, COM23, COM31 may perform an operation that draws an abnormal movement trajectory in the vicinity of the common boundary COM12, COM23, COM31. , The shared boundary of the workpiece
There is a possibility that parts near COM12, COM23, and COM31 will be cut off unnecessarily. The present invention has been made in view of the above points, in particular,
Three patches like corners Offset surface data points When the discontinuous space SPC ₁₂₃ occurs between the tool and the tool, it is possible to prevent the tool from performing an abnormal machining operation on the machining shape being cut in the discontinuous space SPC _{123 at the} corner. It is an object of the present invention to propose an offset surface data creating method capable of easily creating an offset surface data. E. Means for Solving the Problems In order to solve such problems, in the present invention, CAD
The first, second and third patches expressed by a vector function approximated to the shape of an object using the device and which are adjacent to each other in principle , Second and third offset surface data offset by an offset amount based on the shape of the tool, based on a surface representing the shape of the object formed by connecting under the condition of tangent plane continuity In the offset surface data creation method for generating the The offset surface data of the first, second and third patches for the corner where the tangent plane is discontinuous Among the shared points on the first, second and third offset surface data First, second and third normal vectors of the point corresponding to And the intersection of the planes with the first, second and third normal vectors Find the intersection By interpolating the position data of (1) as offset surface data in the discontinuous space generated at the corner, the cutting path can be obtained by controlling the moving path of the tool by the offset surface data generated. F action common point First, second and third patches adjacent to each other at Is connected via shared boundaries COM12, COM23, and COM31 under conditions that do not satisfy the condition of tangent plane continuity, 3
One patch Offset surface data corresponding to Discontinuous space SPC without offset surface data between
₁₂₃ occurs. Regarding the discontinuous space _S123 , Point corresponding to Surface data representing Its normal vector based on Intersection of the planes π _{(01) 123} , π _{(02) 123} , and π _{(03) 123} Is calculated, and this is interpolated as offset surface data. By doing so, the first, second and third offset surface data The tool of the machine tool moved by the When cutting to the position and trying to cross the discontinuous space SPC ₁₂₃ , the tool To the common point of the workpiece It is possible to prevent the possibility of an abnormal operation such as cutting off the portion. G Example Hereinafter, an example of the present invention will be described in detail with reference to the drawings. In the case of this embodiment, the central processing unit (CPU) of the offset curved surface data creating device includes three patches forming a corner portion created in advance by the free curved surface creating device. Data and offset surface data created based on these patch data (FIG. 7) is read as necessary, and the program enters the interpolation calculation program for the offset surface data from step SP1 in FIG. (G1) Interpolation of Discontinuous Spaces SPC ₁ , SPC ₂ , SPC ₃ The offset surface data creating apparatus firstly connects two tangent planes under the condition of discontinuity as shown in FIG.
One patch Offset surface data corresponding to Offset surface data for the discontinuous spaces SPC ₁ , SPC ₂ , and SPC ₃ generated between them (the end faces surrounding the discontinuous spaces are called discontinuous end faces) Is interpolated. That is, in step SP2 of FIG.
12, Normal lines on COM23 and COM31 are patched Check if they are common to each other. If an affirmative result is obtained here, the patch is executed as described above with reference to FIG. Are connected to each other so as to satisfy the condition of tangent plane continuity. In this case, the offset surface data Since there is no discontinuous space in between, the offset curved surface data creating apparatus immediately proceeds to step SP3 and ends the program. On the other hand, if a negative result is obtained in step SP2, the offset surface data creating apparatus proceeds to step SP2.
Moving on to 4, the shared boundaries COM12, COM2 are sequentially described as described below.
3, corresponding discontinuous space using data about COM31
The execution of the interpolation calculation of SPC ₁ , SPC ₂ , and SPC ₃ is started. That is, first, in step SP4, the 0th point among the control points representing the shared boundary COM12 The execution of the interpolation calculation for (FIG. 7) is started. That is, the point of u = 0 and v = 0 About the first patch, as shown in FIG. Surface data for Control points representing the shared boundary COM12 Corresponding points From the data on Vector represented by Ask for. vector Is a point Represents the parallel surface data (the second term of equation (8)) for From the point Up to the difference vector. Also vector Is a vector Position vector represented by U = 0, v = 1 representing the shared boundary COM12 with reference to Offset surface data corresponding to Upper point . Vector obtained in this way Is a patch Surface data related to Of the discontinuous space SPC generated at the shared boundary COM12 ₁
Out of the point Point around Height and point of the end face part enclosed by Represents the inclination of the end face at About If you find the outer product like Point of Normal vector at Can be requested. Thus, the offset curved surface data creating apparatus is provided with the first patch. Offset surface data for 0th point representing the shared boundary COM12 Discontinuity end face based on data near Normal vector representing height and slope of Can be obtained. The offset surface data creating apparatus then proceeds to step SP
Move to 5 and the second patch Offset surface data for From the control point representing the shared boundary COM12 Offset surface data corresponding to Upper point From By performing the operation of From the point Vector up to Find this vector Normal vector in the same direction as Offset surface data Of the discontinuous end faces at the position of the common boundary COM12, that is, the point Point as data representing Normal vector at Can be requested. By the way, this normal vector As shown by the broken line in FIG. Plane at _{(02) 123} (normal vector Is the normal, and this is the normal vector And the offset surface data creating apparatus determines the normal vector in the next step SP6. Face M _{(02) 123} and point Normal vector at Position vector representing the intersection of Is calculated. Points obtained as a result of such calculation Is represented by a shared boundary, as shown in FIG.
Point representing COM12 Patches containing Offset surface data for Upper point The second patch is on a line extending in a direction perpendicular to the discontinuous end face at Offset surface data for Upper point Normal vector In the plane M _{(02) 123} orthogonal to. Therefore, center the tool on the first patch. Offset surface data for Based on the common boundary COM12
Surface on the line represented by = 0 In the process of cutting the curved surface of The center of the tool while machining Upper point When you reach, then patch Point of processing To the center of the tool before starting From the point And then this point From the point To the point of the common boundary COM12 The center of the tool to the first offset surface data Upper point To the second offset surface data Upper point Will be able to be moved. Thus the center of the tool is the first patch Offset surface data for Point of From the second patch Offset surface data for Point of In this case, it is possible to effectively avoid the possibility that the cutting edge of the tool performs an extraordinary operation such as excessively cutting off the workpiece. Eventually the center of the tool will be the second patch On the shared boundary COM12 of Point corresponding to Is reached, the center of the tool will be shifted to the offset surface data By moving up, the second
Patch Point on the boundary COM12 Data that can be restarted from the server. Offset surface data generator After calculating the data of step S7, a point representing the sharing boundary COM12 is similarly obtained in step SP7. By performing a similar operation on, the point corresponding to the discontinuous space SPC ₁ Is calculated based on the same method, and then the process proceeds to step SP8 to obtain the position data obtained by the calculation. Offset surface data Interpolation is performed as surface data representing the moving position of the tool in the discontinuous space SPC ₁ between the two. Thus, the offset surface data generating apparatus performs the offset surface data generation for the discontinuous space SPC ₁ in steps SP4 to SP8 in FIG. Are created and interpolated, and in the following step SP9, the offset surface data for the discontinuous spaces SPC ₂ and SPC ₃ are set in the same manner as described above. Create and interpolate. Consequently offset surface data generating apparatus, in the foregoing step SP4～SP9, discontinuous space SPC _1, SPC _2, SPC ₃
The interpolation program of the offset curved surface data for is ended. By moving the tool of the machine tool using the offset surface data created as described above, Offset surface data corresponding to By moving the center of the tool along Can be individually cut. At the same time, the first, second and third patches Offset surface data for From the state of moving the tool based on the shared boundary CO
Before passing through M12, COM23 and COM31 and proceeding to the processing of offset surface data of another patch, adjacent patches are connected under the condition of tangential plane continuity as described above with reference to FIG. Discontinuous space SPC ₁
If SPC ₂ or SPC ₃ occurs, By interpolating the position data as offset surface data, the object to be processed by the machine tool can be determined by the first, second and third patches. Free surface represented by the above data and the interpolated offset surface data The cutting can be performed smoothly by using. And patch At the positions of the shared boundaries COM12, COM23, and COM31 therebetween, it is possible to effectively prevent the tool from abnormally operating and excessively cutting the workpiece. (G2) Interpolation of discontinuous space SPC ₁₂₃ Next, the offset surface data creation device uses three patches. Share points of Data and three offset surface data A processing program for the discontinuous space SPC _{123 in the} corner portion generated between the steps is executed according to the following procedure. First, in step SP10, the operator checks the generated patch. Display the surface data on the display on the display and share the common points of the corners to be interpolated. After visually checking the Offset surface data around Specify the data representing the discontinuous end face of. In response to this, in the next step SP11, the offset surface data generating device executes the offset surface data generation as shown in FIG. Point representing the discontinuous end face of Data and points Points based on the data Normal vector at Ask for. These normal vectors Is a point Is a point To the translation amount data expressed by the second term of Equations (8), (9), and (10) Occur on an extension of the vector represented by, and thus the normal vector Point of discontinuous space SPC ₁₂₃ Three discontinuous end faces centered at Represents the height and the inclination of. Subsequently, the offset surface data creating apparatus executes step SP
Move to 12 normal vector Intersection of the planes π _{(01) 123} , π _{(02) 123} , and π _{(03) 123} Ask for. Where the normal vector Π _{(01) 123} , π _{(02) 123} , and π _{(03) 123} Normal vector at position And a plane orthogonal to. Therefore, three planes π _{(01) 123} ,
When π _{(02) 123} and π _{(03) 123} intersect each other, the intersection common to these three surfaces Can be specified only at one point. That is, the point where the planes π _{(01) 123} and π _{(02) 123} intersect is
In FIG. 2, it is on the straight line indicated by the broken line L1 and
The intersection of _{(03) 123} and π _{(01) 123} is on the straight line indicated by the broken line L2. Therefore, the intersection of straight lines L1 and L2 Is the intersection of three planes π _{(01) 123} , π _{(02) 123} , and π _{(03) 123} Can be specified to only one point. Subsequently, the offset data creating apparatus proceeds to step SP13, and After the position data is interpolated as offset curved surface data for the discontinuous space SPC ₁₂₃ generated in the corner, the program proceeds to step SP3 and ends the program. In this way three patches Of the offset surface data used when cutting free-form surfaces where the tangent planes are connected to each other under discontinuous conditions adjacent to each other, the discontinuous space SPC
_{When 123} occurs, the intersection in Figure 2 If cutting is performed using interpolation as interpolation data, the cutting edge of the tool This can effectively avoid the possibility of excessively shaving off the corner portion represented by the above. That is, for example, the first patch When moving a tool that is cutting a workpiece across the discontinuous space SPC ₁₂₃ , the cutting edge of the tool The tool center position at one end To move the tool edge to a point. Away from Then the center of the tool is the second (or third) patch To move the tool edge to the point again. After touching the patch Go to the cutting process. Thus, it is possible to effectively prevent the tool from excessively shaving off the workpiece due to the abnormal operation. H Effects of the Invention As described above, according to the present invention, three patches connected under the condition that the condition of continuation of the tangent plane does not hold When cutting off an object having a free-form surface represented by the following formula, offset surface data representing the moving point of the tool at the corner portion is generated when offset surface data representing the moving path of the tool of the machine tool is created. By interpolation, it is possible to effectively prevent the possibility of generating machining data such as abnormally excessive cutting at a corner portion.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a flowchart showing one embodiment of an offset surface data creating method according to the present invention; FIG. 2 is a schematic diagram showing a procedure for creating interpolation data of a discontinuous space at a corner; 3 is a schematic diagram showing offset surface data obtained as a result of the interpolation, FIG. 4 is a schematic diagram showing a procedure for creating interpolation data of a discontinuous space generated between two patches, and FIG. FIG. 6 is a schematic diagram for explaining a condition for connecting two patches to each other according to a tangent plane continuation condition, FIG. 6 is a vector diagram for explaining a tangent plane continuation condition, and FIG. FIG. 11 is a schematic diagram for explaining a discontinuous space generated when offset curved surface data is created for three patches connected under a condition where the condition is not satisfied.

Claims (1)

(57) [Claims] Using a CAD device, the first and second functions that are represented by a vector function approximated to the shape of the object and that are adjacent to each other in principle
First and second offsets by an offset amount based on the shape of the tool, based on the curved surface representing the shape of the object formed by connecting the second and third patches under the condition of continuation of the tangent plane.
And a third offset surface data generation method for generating offset surface data, wherein, among the curved surfaces representing the shape of the object, the first, second, and third corner portions having a discontinuous tangent plane at a common point are used. The first, second, and third normal vectors of the points corresponding to the shared points on the first, second, and third offset surface data among the offset surface data of the patch No. 3 are obtained. 1. Intersection points of the planes having the first, second, and third normal vectors are obtained, and the position data of the intersection points are interpolated as offset surface data in the discontinuous space generated at the corner portion. A method for generating offset curved surface data, characterized in that a cutting surface can be obtained by controlling the movement path of the tool.