JP2003181745A - Three dimensional machining method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To produce a smooth curved surface by integrating a different type of graphic information produced in another system into a formula of a curved surface, in three dimensional machining to be carried out by a programmed computer using a milling machine, etc. <P>SOLUTION: A method for carrying out three dimensional machining for a workpiece by a programmed computer using a cutting tool of which the cutting surface has a quadratic surface of revolution, such as an ellipse, a sphere. A plurality of curved surfaces based on a plurality of different types of graphic information (including an expression defining a curved surface) representing a curved surface and a curve are defined by a unified expression of variables (u), (v). A central travelling point of the cutting tool having tip radii r<SB>p</SB>, r<SB>n</SB>is obtained with respect to a normal vector N at a point S(u, v) calculated by the unified expression. <P>COPYRIGHT: (C)2003,JPO

Description

Description: BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a processing method for performing three-dimensional processing on a workpiece with a machine tool such as a milling machine, and more particularly, to a method in which a cutting surface is a rotating secondary surface. The present invention relates to a three-dimensional processing method including arithmetic control of a curved surface to be cut by a cutting tool having a cutting tool and a locus of a cutting movement center of the cutting tool. 2. Description of the Related Art In recent years, various attempts to perform three-dimensional processing on metal materials using a computer have been developed and put to practical use. In this kind of three-dimensional machining, a 3D machining based on a curved surface (cutting traveling) cut by traveling of a cutting tool is used.
Shaft cutting and 2.5-axis cutting based on the movement center locus (center running) of the cutting tool are roughly classified. [0003] In any of the cutting methods, conventionally, the curved surfaces are individually stretched, and different curved surfaces are continuously cut out by changing over. For example, as shown in FIG. 8, three surfaces #i, #j, and #k are individually defined (u and v for the surface #i, u and v for the surface #j,
Cutting was performed while sequentially moving to u, v) for curved surface #k, curved surface #i, curved surface #k, and curved surface #j. At this time, a series of trajectories were calculated based on the cutting direction γ that is not related to the characteristics (coordinate system) of the curved surface. In this case, cutting is performed irrespective of the characteristics of the curved surface, and depending on the undulation of the curved surface, the cutting becomes coarse or becomes finer than necessary, resulting in unnecessary cutting. Furthermore, a lot of check calculations are made to avoid tool interference when moving over curved surfaces,
There is a problem that the calculation time increases. [0004] In view of this point, the present inventor has disclosed in Japanese Patent Publication No. Hei 8-1.
As described in Japanese Patent No. 5701, a three-dimensional machining method has been proposed in which a plurality of curved surfaces having different characteristics are defined by a fourth-order or lower polynomial to calculate a cut curved surface. According to this method,
The root can be easily obtained by the four arithmetic calculations, and a point on the surface is determined from the variables u and v. Conversely, the orthogonal coordinate values (x,
The determination of u and v from (y, z) can be processed at high speed. However, when a surface equation created by another system is loaded into a computer that executes the above method and is subjected to arithmetic control, the surface is usually Spline, B-spline, N
urbus, Bezier, etc.,
It is not always represented by a polynomial, and some conversion is required. The present inventor has further disclosed in Japanese Patent No. 282442.
As described in Japanese Patent Application Publication No. 4 (1994), a three-dimensional machining method is proposed in which various curved surface definition expressions are defined by one rational expression, and an intersection S (u, v) on the curved surface required for cutting is calculated. did.
This method is attributed to obtaining the roots of rational expressions, and can integrate various types of surface definition expressions into one surface expression relating to variables u and v, thereby reducing the time required for calculating the cutting travel and improving machining accuracy. Was completed. However, at present, various types of surface definition formulas have been adopted, and some of them are represented by analytical functions that cannot be represented by formulas.
One rational expression cannot be integrated. [0006] The present inventor further disclosed in Japanese Patent No. 320175.
As described in Japanese Unexamined Patent Publication No. 1 (1994), whether a plurality of different types of defining expressions representing curved surfaces and curves can be solved by an algebraic method,
Alternatively, it is determined whether a solution can be obtained by an analytical method, and based on the determination result, a plurality of surfaces based on a plurality of defining expressions are defined by a unified expression relating to variables u and v by an algebraic method or an analytical method. A dimension processing method was proposed. According to this method,
Surfaces and curves represented in various forms can be directly handled with each other, and surfaces and curves obtained from a plurality of different types of definition formulas have high accuracy. On the other hand, Japanese Patent Publication No. 4-43726 discloses that
A curved surface processing method using a cutting tool whose cutting curved surface has a rotating quadric surface such as an elliptical sphere is disclosed. According to this processing method, the cutting edge portions having different curvatures are properly used in accordance with the change in the curvature of the processing surface, so that the surface accuracy and the processing efficiency of the processing surface are remarkably improved. Therefore, an object of the present invention is to use a cutting tool in which the above-mentioned cutting surface has a rotating quadratic surface, and based on a plurality of types of different graphic information (including definition expressions) representing curved surfaces and curves, It is an object of the present invention to provide a three-dimensional processing method capable of executing a curved surface processing of a preferable shape by a quick calculation. In order to achieve the above object, a three-dimensional machining method according to the present invention uses a cutting tool whose cutting surface has a rotating quadratic surface by a programmed computer. X orthogonal to each other with respect to the workpiece
In a machining method for performing three-dimensional machining including an axis, a y-axis, and a z-axis, a step of defining a plurality of curved surfaces based on a plurality of types of different graphic information representing curved surfaces and curves by a unified formula regarding variables u and v; , One point S (u, v) obtained using this unified equation
A step of determining by the following formula (1) with respect to the normal vector N, the tip diameter r _p, the central travel point P of the cutting tool having r _n in,
Running the cutting tool according to the center running point P to process the workpiece. [0010] [0011] When _{r = r n / r p d} = √ (1+ (r 2 -1) n 2), P (u, v) = (Px, Py, Pz) Px = Sx + r p nx / d Py = _{sy + r p ny / d Pz} = Sz + r n 2 nz / r p d [0012] in the present invention, a curved surface, a plurality of types of different graphic information representing a curve variables a plurality of curved surfaces on the basis of the (defined formula containing) u, The definition by the unified formula regarding v includes the following method. For example, as described in Japanese Patent Publication No. Hei 8-15701, a plurality of curved surfaces having different characteristics given as graphic information are defined by the following polynomials regarding variables u and v, and are cut as an integrated surface. Calculate the curved surface. And
From the cutting surface defined by the polynomial, the center traveling point P of the cutting tool is obtained using the above equation (1). [0014] Alternatively, as described in Japanese Patent No. 2824424, a plurality of curved surfaces are defined by one rational expression relating to variables u and v based on a plurality of different types of defining expressions representing curved surfaces and curves. From the cutting surface defined by the rational expression, the center traveling point P of the cutting tool is obtained using the above expression (1). Alternatively, as described in Japanese Patent No. 3201751, it is determined whether a solution is obtained by algebraic method or a solution by a plurality of different types of defining expressions representing curved surfaces and curves. Discriminate, and based on the discrimination result, define a plurality of surfaces based on a plurality of definition formulas by an algebraic method or an analytical method by a unified formula relating to variables u and v, and from the cutting surface defined by the unified formula, The center traveling point P of the cutting tool is obtained using the above equation (1). According to the present invention, since a cutting tool having a rotating quadratic surface such as an elliptical sphere is used as a cutting surface, a cutting edge portion having a different curvature is appropriately used in accordance with a change in the curvature of a processing surface. The surface accuracy and processing efficiency of the processing surface are significantly improved. In addition, since the center traveling point P of the cutting tool is obtained by using the above equation (1), it is possible to execute a curved surface processing of a preferable shape by a quick calculation. Embodiments of a three-dimensional processing method according to the present invention will be described below with reference to the accompanying drawings. (Explanation of Apparatus) FIG. 1 shows a schematic configuration of an apparatus for carrying out the processing method of the present invention.
Has a table 3 on a base 2 and a processing head 5 having a cutting tool 6 on a column 4. Table 3 has an X-axis DC motor 10 and a Y-axis DC motor 11
Are moved in the X-axis direction and the Y-axis direction. Processing head 5
Are driven in the Z-axis direction by a Z-axis DC motor 12. Speed control is performed by each control unit 1 to each of the motors 10, 11, and 12.
This is performed by outputting control signals from 5, 16, and 17. On the other hand, the graphic input / control system includes a 16-bit to 32-bit computer 20 and a tape reader 2.
1. It is composed of a control panel 22. Tape reader 21
Is the NC data defined by JIS (Japanese Industrial Standards), especially
Read the G code as the program format.
Graphic information to be cut as three screens or perspective views is input to the computer 20 by the user. The computer 20 transfers a control program stored in a floppy disk 20a as a recording medium to the CPU 24,
The calculation described below is performed. The control panel 22 has a machine operation panel 23 and has a built-in CPU 24, and graphic information and the like from the computer 20 and the tape reader 21 are transferred to an input port a of the CPU 24. The CPU 24 generates cutting data from the input graphic information, and outputs the cutting data b,
The control units 15 and 1 are used as control signals from c and d.
Output to 6,17. Hereinafter, generation of cutting data by the CPU 24 will be described in detail. (Curved Surface) As shown in FIG. 2, a curved surface is defined for two independent variables u and v with respect to a rectangular coordinate system. That is, for u and v satisfying 0 ≦ u ≦ 1 and 0 ≦ v ≦ 1, a reference (function) S for determining one point in space is determined. When the reference S is differentiable (smooth), S is a curved surface. That is, when x = x (u, v) y = y (u, v) z = z (u, v) by the differentiable functions x, y, z concerning u, v, S (u, v) ) = (X, y, z) S is a curved surface and is differentiable, so that ηS / ηu ηS / ηv exists for the normal vector. Further, in the present invention, it is assumed that a Twist vector η ² S / ηuηv exists. In this embodiment, in which the cutting tool 6 shown in FIG. 3, that is, the cutting tool 6 whose cutting curved surface is an elliptical sphere travels to cut the curved surface S, the tip of the tool 6 has constant diameters r _p and r _n.
Having. Assuming that the tip diameter of the tool 6 is simplified to a radius R, the center of the tool cutting portion is located at a position away from the curved surface S by a radius R in the normal direction. That is, in order to determine the center running of the tool 6, the normal vector N must be determined. At one point S (u, v) on the curved surface #s, Then, through S (u, v), Ru,
A plane including Rv is called a tangent plane (a plane hatched in FIG. 2), and a normal vector N is defined as N = Ru × Rv. For this normal vector N, the central travel point P of the tool 6 tip diameter is r _p, r _n is defined by the following equation (1). (Equation 5) [0029] When _{r = r n / r p d} = √ (1+ (r 2 -1) N 2), P (u, v) = (Px, Py, Pz) Px = Sx + r p Nx / d Py = _{Sy + r p Ny / d Pz} = Sz + r n 2 Nz / r p d [0030] by the way, the curved surface #s is u, because v is a differentiable function on, if considered to be differentiable far here necessary, This function can be unifiedly expressed as a rational expression for u and v or as an analytical correspondence. Thereby, the curved surface # for u and v
The roots can be obtained by algebraic or analytical methods to find points on s. For example, a certain curved surface #a is a cubic spline
The surface is defined by the following equation (2). Assuming that another surface #b is defined by the following equation (3): The above equations (2) and (3) are integrated by the following rational equation (4). [Equation 8] When the rational expression (4) is illustrated by a graphic, it is represented as shown in FIG. 4, and a root is found in [a, b]. In this case, a method of analytically converging is adopted. That is, the extremum and inflection point of a rational expression are obtained, and the root is obtained by setting an initial value at one point between them. By the above process, any type of curved surface definition formula can be integrated into one curved surface formula relating to variables u and v, the calculation speed is increased, and the cutting accuracy is improved. Although the surface is represented as a rational expression, this is done for one surface. Therefore, a plurality of curved surfaces are rational expressions defined for unique u and v, respectively. That is, even if it is a rational expression of the same type,
Since the references u and v are different, they are completely different. However, in the present invention, a plurality of these curved surfaces can be simplified as one by defining them as rational expressions for the same u and v. For example, as shown in FIG.
If there are curved surfaces #a and #b defined by the same rational expression, the rational expression is reduced to the curved surface #c by one rational expression. As a result, the number of curved surfaces decreases, and the calculation time for calculating the cutting travel decreases. By the way, the intersection curve is to find the intersection between curved surfaces. That is, a solution of a simultaneous equation using curved surfaces is obtained. Therefore, when a surface a fa (u, v) and a surface b fb (u, v) are obtained, the equation fa (u, v) = fb (u, v)
Becomes the intersection curve. When both fa (u, v) and fb (u, v) are rational, the above method is used. If at least one is not a rational expression, a solution is analytically obtained from the criterion that points on the surface are given to u and v as analytical functions. By converging to a solution sequentially from one value,
You can approach the solution to where you want. (Definition of Curved Surface) A curved surface is basically defined by three drawings or perspective views given by a designer, and is defined while strictly observing these items. In the drawing, a curve, a cross-sectional curve, and the like which are contours of a curved surface are described. Based on these, a curved surface definition net which is the basis of the curved surface is created. A surface definition net is a surface intended by the designer.
An area (patch) that consists of a number of grid points (patches) that create a surface and that requires a surface by this surface definition net
Is divided into First, a rational expression or a correspondence relation for each patch is determined, and a unified expression (rational expression or analysis function) for the entire surface is determined. As for the continuous surface, one surface definition net is created by a unified expression expressing each surface. With this curved surface definition net, a continuous curved surface is expressed as a unified expression for the same characteristic as an integrated surface. More specifically, as shown in FIG. 6, a curved surface and a curve based on other CAD data and CAM data are inputted in a step S1, and a relationship representing the curved surface and the curve is determined in a step S2. That is, all input surfaces and curves are represented by rational formulas, and a solution is obtained by an algebraic method, or at least one surface or curve is not represented by a rational formula, and is solved by an analytical method. Is determined. If everything is represented by a rational expression, a solution is obtained in step S3 using an algebraic method. If a curved surface or curve that is not a rational expression is included, a solution is obtained in step S4 using an analytical method. Step S3
Alternatively, the solution obtained in S4 is defined by a unified formula regarding variables u and v. Next, in step S5, the intersection and the intersection line are calculated, and in step S6, the center traveling point of the tool is obtained, and NC data is generated. . (1. Curved Surface Definition Net) A curved surface is defined from a curve described in the drawing as the designer intends.
In order to determine the shape of the surface, a surface definition net is defined by a number of grid points (patches). According to the characteristics of the curved surface, the curved surface is divided by the curves (u-curve and v-curve) in the u and v directions, and the number of division points is m and n, respectively.
And At this time, with respect to sequence _{u 0 = 0 <u 1 <} ...... <u m = 1 v 0 = 0 <v 1 <...... <v n = 1, u, v pairs (u _j, v _i) to Te defines _{S (u j, v i)} Su (u j, v i) Sv (u j, v i) Suv (u j, v i). Here, Su (u, v) = ηS / ηu Sv (u, v) = ηS / ηv Suv (u, v) = η ² S / ηuηv To define such a surface definition net,
A differentiable correspondence criterion (function) from u and v to one point P in space will be defined. As shown in FIG. 7, the curved surface grasps that the v-curve moves and changes along the u-curve. When a cross-sectional curve is described in a given drawing, that curve is a v-curve. At this time, if the v-curve moves while making a differentiable change along the u-curve, the correspondence S (u, v) to one point P on the curved surface defined for u, v is u , V, Su,
Sv and Suv exist. The change in the v-curve depends on the shape and u-
The position relative to the curve will change. That is, the matrix (direction) for determining the shape and the position changes differentiably. [0047] This correspondence, 0 ≦ if u ≦ 1,0 ≦ v ≦ 1, u, because defined for v, u _j, relative to v _i, curved definition net S (u _j, v _i ) is created. (2. Unified Surface) The area to be cut is determined by the surface definition net. Here, in the region _{u j-1 ≦ u ≦ u} j v i-1 ≦ v ≦ v i, to define a unified type S _ji u, relates v, it defines the curved surface by the binding of these S _ji. The unified formula defined here must comply with the following conditions (A) and (B). (A) Strictly observe the items described in the drawings. That is, the curves, numerical values (dimensions,
Angle, etc.). (B) It must sufficiently reflect the designer's intention when creating the surface definition net. The designer designs the curved surface in consideration of the intended undulation. The unified formula must be consistent with this design. Now, when defining a surface as a unified expression combination in a region, the unified expression combination defined separately for each region must be differentiable at the boundaries of those regions. In the present invention, define a unified expression by (u _j, v _i) in the _{S (u j, v i)} Su (u j, v i) Sv (u j, v i) Suv (u j, v i) I do. These values are immediately obtained from the design surface (cut surface) equation (corresponding standard). By defining a unified expression using these as constraints, a curved surface holding the shape intended by the designer can be defined. In the present invention, S, Su, S at these grid points (patches)
By restricting v and Suv, the whole can be made differentiable. In some drawings, only a passing point is shown. In such a case, Su, Sv, Suv cannot be obtained from the shape intended by the designer. In this case, it is not possible to define a unified expression for each area without regard to the adjacent area. In other words, a unified expression is defined by the interrelationship of all areas. (3. Surface Concatenation) A surface is defined taking advantage of its characteristics (coordinate system). Conventionally, curved surfaces having different characteristics have been defined as different curved surfaces. For this reason, as the cutting surface becomes more complicated, the number of curved surfaces to be defined increases, and the calculation becomes more complicated. In the present invention, curved surfaces having different characteristics are connected to each other, and are expressed again as one curved surface by an analytic function for the same characteristic. It is assumed that the curved surfaces S and S ′ are each represented by a function according to the characteristics. U for surface S
-Let the intersection point P of the curve and the curved surface S 'be 0≤u. At this time, regarding the curved surface S, u ′ and v ′ exist, and P = S ′
(U ', v'). Here, generality is not lost even if {Su (u, v), S′u (u ′, v ′)} ≧ {Su (u, v), S′v (u ′, v ′)}. At this time, u = 0 to u =
Until u, the u-curve of the curved surface S is taken, and from u = u ′ to u = 1
By taking the u′-curve of the curve S ′, the curve is defined again. By defining n such curves and dividing each curve into m, a curved surface definition net extending over the curved surfaces S and S ′ is established. If one curved surface is defined by this curved surface definition net, it becomes an integrated curved surface combining the curved surfaces S and S ′. In addition, the combined curved surfaces maintain the characteristics of the respective curved surfaces S and S ′. (Tool running) When a curved surface is defined, a tool runs on it to perform cutting. In this embodiment, the tip of the tool 6 is rotated quadratic surface diameter r _p, r _n, the position of the tool center is the point P represented by Equation (1). When the tool travels along the curve on the curved surface S, the point P is determined for a point on the curve to determine the tool center travel position. When a curved surface is not represented by a mathematical expression, at least two neighboring points must be obtained, which makes the calculation complicated and time-consuming. [0056] In contrast, in the present invention, determines the curved surface definition net with (u _j, v _i) with respect to Equation (1) determining the point P, the center traveling based on these points Generate a surface definition net as a surface. When the surface definition net is determined, the surface can be defined by a unified expression using the net. Assuming that the surface defined in this way is * S, for all u and v satisfying 0 ≦ u ≦ 1, 0 ≦ v ≦ 1, The unified curved surface formula is determined as follows. The unified formula in the present invention establishes this relationship within a sufficiently small error. As a result, the center of the tool does not need to be obtained from the curved surface S.
(U, v). This is the unified u, v
, Which is extremely simple compared to the conventional method, and the calculation speed is so high that it cannot be compared.

BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a schematic configuration diagram of a cutting device for carrying out the present invention. FIG. 2 is an explanatory diagram of a curved surface definition. FIG. 3 is an explanatory view showing a tip shape and a machining surface of a cutting tool. FIG. 4 is a graph illustrating an analysis method for finding a root of a rational expression. FIG. 5 is an explanatory diagram of simplifying a plurality of curved surfaces. FIG. 6 is a flowchart showing an outline of a control procedure. FIG. 7 is an explanatory diagram of how to hold a curved surface. FIG. 8 is an explanatory view of cutting a plurality of curved surfaces in a conventional three-dimensional processing method. [Description of Signs] 1 ... machine tool main body 3 ... table 5 ... machining head 6 ... cutting tools 15, 16, 17 ... control unit 20 ... computer 22 ... control panel 24 ... CPU

   ────────────────────────────────────────────────── ─── Continuation of front page    (72) Inventor Kenichi Honda             2-1-3-Shigino Nishi, Joto-ku, Osaka City, Osaka Prefecture             No. 606 (72) Inventor Kazunari Teramoto             Aichi-gun Aichi-gun Nagakute-machi             地 の １ Toyota Central Research Laboratory Co., Ltd. F-term (reference) 5H269 AB05 AB19 BB05 CC02 DD01                       QA05 QC01

Claims (1)

Claims: 1. A cubic tool including an x-axis, a y-axis, and a z-axis orthogonal to a workpiece by a programmed computer using a cutting tool whose cutting surface has a rotating quadric surface. In a machining method for performing original machining, a step of defining a plurality of curved surfaces based on a plurality of different types of graphic information representing curved surfaces and curves using a unified formula for variables u and v, and a point determined using the unified formula S (u, v) with respect to the normal vector n at the step of finding the tip diameter r _p, the central travel point P of the cutting tool having r _n by the formula, ## EQU1 ## r = the _{r n / r p d = √} (1+ (r 2 -1) n 2) to, P (u, v) = (Px, Py, Pz) Px = Sx + r p nx / d Py = Sy + r p ny _{/ d Pz = Sz + r n} 2 nz / accordance r _p d the central travel point P is traveling cutting tool, a three-dimensional machining method characterized by comprising a, a step of processing the workpiece.