JPH0815701B2 - Three-dimensional processing method - Google Patents

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a machining method for three-dimensionally machining a workpiece with a machine tool such as a milling machine, and more particularly to arithmetic control of a cutting curved surface by a cutting tool and a cutting movement center locus of the cutting tool.

[0002]

2. Description of the Related Art In recent years, various attempts have been developed and put to practical use for three-dimensional processing of metal materials using a computer. In this type of three-dimensional machining, a curved surface (cutting traveling) cut by traveling of a cutting tool is used as a reference 3
It is roughly classified into axial cutting and 2.5 axial cutting based on the movement center locus (center running) of the cutting tool.

In any of the cutting methods, conventionally, the cut curved surfaces are individually stretched, and different curved surfaces are continuously cut out by transfer cutting. For example, as shown in FIG. 6, three curved surfaces #i, #j, and #k are individually defined (u and v for curved surface #i, u and v for curved surface #j,
The cutting was performed while sequentially moving to u, v) regarding curved surface #k, curved surface #i, curved surface #k, and curved surface #j. At this time, a series of loci was calculated by the cutting direction γ that is not related to the characteristic (coordinate system) of the curved surface. In this case, cutting was performed without depending on the characteristics of the curved surface, and the cutting was rough depending on the undulations of the curved surface, or the cutting was unnecessarily fine and wasted. Furthermore, many check calculations are performed to avoid tool interference when transferring curved surfaces,
It has a problem that the calculation time becomes long.

Further, in order to perform cutting according to the characteristics of the curved surface, the curved surfaces must be cut individually because the directions of the characteristics of the curved surface are different. For this reason, useless running of the tool has occurred. Furthermore, regarding the calculation of center running,
It was always necessary to determine which curved surface the interference had to be checked with, and the operation procedure was complicated. Since the curved surface is determined by the characteristics, the region surrounded by the contour curve serving as the boundary is determined by utilizing the characteristics of these curves. Therefore, curved surfaces having different characteristics cannot be defined as one curved surface.

[0005]

SUMMARY OF THE INVENTION Therefore, an object of the present invention is to provide a three-dimensional processing method capable of rapidly and continuously cutting a plurality of curved surfaces by a simple calculation. In order to achieve the above object, the three-dimensional processing method according to the present invention first defines a plurality of curved surfaces having different characteristics as an integral surface. As shown in FIG. 1, when curved surfaces #i, #j, and #k are given, they are defined as an integral curved surface #s. This curved surface #s is defined by two directions (u, v) showing its characteristics. This direction is unique to curved surface #s,
It is not absolute for all curved surfaces like the Cartesian coordinate system. Conventionally, curved surfaces #i, #j, and #k have different seats.
Although it was defined by the standard system (u, v) , a plurality of curved surfaces are defined by the same direction (u, v) by unifying these directions (u, v). That is, when transferring from the curved surface #i to the curved surface #k, the characteristic curves of the curved surfaces #i and #k are combined. Next, the cutting is performed according to the characteristic (coordinate system) of the curved surface defined as an integral surface. At this time, it is not necessary to check the cutting traveling when transferring between a plurality of curved surfaces, which is required in the conventional machining method, and the traveling calculation speed becomes high.

In the present invention, the idea of the curved surface is that variables u and v are provided in the direction of the characteristic of the curved surface, and points on the curved surface are defined with respect to these u and v. It is the conventional processing method that the correspondence from u, v to the points on the curved surface is determined for each curved surface, and the processing method according to the present invention is that the same correspondence criterion is determined over a plurality of curved surfaces. In the present invention, the correspondence criterion is a polynomial.

[0007]

[Equation 2]

It is expressed by n is 4 or less
Therefore , the polynomial can easily find the root by the four arithmetic operations, and determine the point on the curved surface from u and v, and conversely, the determination of u and v from the orthogonal coordinate values (x, y, z) on the curved surface. It can be processed at high speed.

[0009]

Embodiments of the three-dimensional processing method according to the present invention will be described below with reference to the accompanying drawings. [Description of Apparatus] FIG. 2 shows a schematic configuration of an apparatus for carrying out the processing method of the present invention. The machine tool main body 1 has a table 3 on a base 2 and a processing head having a cutting tool 6 on a column 4. 5 is attached. Table 3 is X-axis DC motor 1
It is moved in the X-axis direction and the Y-axis direction by the 0 and Y-axis DC motors 11. The machining head 5 is driven by the Z-axis DC motor 12 in the Z direction.
Driven axially. The speed control is for each motor 10, 11,
This is performed by outputting a control signal from each control unit 15, 16, 17 to 12.

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 the control panel 22. Tape reader 21
Is NC data defined by JIS (Japanese Industrial Standard),
The G code as the program format is read.
The computer 20 has three views or oblique views depending on the user.
Graphic information to be cut as a view is input. Control panel 2
2 includes a machine operation panel 23 and a built-in CPU 24, and graphic information and the like from the computer 20 and the tape reader 21 are input to the input port a of the CPU 24. The CPU 24 generates cutting data from the inputted graphic information and outputs it as control signals from the output ports b, c and d to the control units 15, 16 and 17.

The generation of cutting data by the CPU 24 will be described in detail below. [Curved Surface] As shown in FIG. 3, a curved surface is defined for two independent variables u and v with respect to the Cartesian coordinate system. That is, 0 ≦ u
For u and v such that ≦ 1, 0 ≦ v ≦ 1, a reference (function) S for determining one point in space is defined.

When this reference S is differentiable (smooth), S is a curved surface. That is, when differentiable functions x, y, and z with respect to u and v are used, x = x (u, v) y = y (u, v) z = z (u, v) When S (u, v) ) = (X, y, z) is a curved surface and is differentiable, so that ηS / ηu ηS / ηv exists with respect to the normal vector. Further, in the present invention, the twist vector η ² S / ηuηv is assumed to exist.

In the present invention in which a cutting tool is run to cut a curved surface, the tip of the tool is a sphere having a constant radius R. Therefore, the center of the tool cutting portion is located at a position separated from the curved surface by the radius R in the normal direction. That is, in order to obtain the center travel of the tool, the normal vector must be determined. At one point S (u, v) on the curved surface #s,

[0014]

(Equation 3)

Then, through S (u, v), Ru,
A plane including Rv is called a tangent plane (a plane with diagonal lines in FIG. 3), and the normal vector N is defined as N = Ru × Rv. With respect to this normal vector N, the tool center traveling point P is defined by the following equation. P = S (u, v) + ε · R · N, where ε ² = 1 (+1 is the front side and −1 is the back side) R: Tool radius

By the way, since the curved surface #s is a differentiable function with respect to u and v, if it is considered that it can be differentiated to a necessary place, this function is u, v according to the Taylor series in analysis theory. Can be approximated as a polynomial for. As a result, u, v
Polynomial to find points on surface #s for

[0017]

[Equation 4]

The value of will be obtained. Conversely, to determine u and v for the Cartesian coordinate system, we reduce to obtaining the roots of the polynomial. Since n is 4 or less, the curved surface is calculated by algebra, the cutting accuracy is improved, and the calculation speed is increased. The surface is represented as a polynomial, but this is done for one surface. Therefore,
For a plurality of curved surfaces, they are polynomials defined for unique u and v, respectively. That is, even if polynomials of the same type are used, they are completely different because u and v, which are their references, are different. However, in the present invention, for multiple curved surfaces these successive, identical u, v
A plurality of curved surfaces is globally defined as one curved surface by defining it as a polynomial for.

[Definition of curved surface] A curved surface is a three-view drawing or perspective view given by a designer.
The items described in the drawings are the basics and are defined while strictly observing them. In the drawings, curved lines, cross-sectional curves, etc., which are contours of curved surfaces, are described. On the basis of these, a curved surface definition net that is the basis of a curved surface is created. A curved surface definition net is a curved surface intended by the designer, and has many grid points that create the curved surface.
(Patch) , and the curved surface definition net divides the curved surface into necessary areas (patches) . First of all
Determine the polynomials for these patches and
Determine the polynomial for the entire surface.

For a continuous curved surface, one curved surface definition net is created by a polynomial expressing each curved surface. By this curved surface definition net, a continuous curved surface is made an integral surface and is expressed by a polynomial for the same characteristic. In particular,
As shown in FIG. 4, drawing description items are input in step S1, and a curved surface definition net is created in step S2. next,
A curved surface is defined by a polynomial in step S3, and if there is no curved surface to be connected, the process is completed in step S5. If there is a curved surface to be connected, a curved surface definition net relating to curved surface connection is created in step S4, and the processing returns to step S3 to define each curved surface as an integral surface by a polynomial.

[1. Curved surface definition net] A curved surface is defined as intended by the designer from a curve which is a drawing description item. In order to determine the shape of the curved surface, a curved surface definition net is defined by many grid points (patches) . According to the characteristics of the curved surface, curves in the u direction and the v direction (u
-Curve, v-curve) divides the curved surface, and the numbers of the dividing points are m and n, respectively. Then, for the sequence u ₀ = 0 <u ₁ <... <u _m = 1 v ₀ = 0 <v ₁ <... <v _n = 1 for the set of u and v (u _j , v _i ), , S (u _j , v _i ) Su (u _j , v _i ) Sv (u _j , v _i ) Suv (u _j , v _i ). Where Su (u, v) = ηS / ηu Sv (u, v) = ηS / ηv Suv (u, v) = η ² S / ηuηv

To define such a curved surface definition net,
A differentiable correspondence standard (function) from u, v to one point P in space will be defined. As shown in FIG. 5, regarding a curved surface, the v-curve moves and changes along the u-curve. When a section curve is drawn in a given drawing, that curve is the v-curve. At this time, if the v-curve moves along the u-curve with a differentiable change, the correspondence S (u, v) to one point P on the curved surface defined for u, v is u. , V, differentiable with respect to Su,
Sv and Suv exist. The change of v-curve depends on the shape and u-
The position relative to the curve will change. That is, the matrix (direction) that determines the shape and the position changes so that it can be differentiated. This correspondence is defined for u and v if 0 ≦ u ≦ 1 and 0 ≦ v ≦ 1. Therefore, for u _j and v _i , the surface definition net S (u _j , v _i ). Is created.

[2. Curved Surface Polynomial] The area to be cut is defined by the curved surface definition net.
Here, in the region u _j-1 ≦ u ≦ u _j v _i-1 ≦ v ≦ v _i , a polynomial S _ji regarding u and v is defined, and a curved surface is defined by the combination of these S _ji . The polynomial defined here must comply with the following conditions (1) and (2).

(1) Strictly observe the matters described in the drawings. That is, the curves, numbers (dimensions,
Corners, etc.) must be represented. (2) It must sufficiently reflect the designer's intention when creating the curved surface definition net. The designer designs the curved surface in consideration of the undulations intended by himself. The polynomial must fit this design.

Now, when defining a curved surface as a combination of polynomials in a region, the combination of polynomials defined separately for each region must be differentiable at the boundaries of those regions. In the present invention, to define the polynomial 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) . These values are immediately obtained from the equation (corresponding standard) of the design surface (cutting surface). By defining a polynomial with these as constraints, a curved surface that holds the shape intended by the designer can be defined. In the present invention, S, Su, S at these lattice points (patches) are
By restricting v and Suv, the whole can be differentiated.

In some drawings, only passing points may be shown. In such a case, Su, Sv, and Suv cannot be obtained from the shape intended by the designer. In this case, a polynomial cannot be determined without relating adjacent regions to each region. That is, a polynomial is defined by the mutual relation of all areas.

[3. Curved Surface Connection] A curved surface is defined by taking advantage of its characteristics (coordinate system). Conventionally, curved surfaces having different characteristics have been defined as different curved surfaces. Therefore, as the cutting surface has a more complicated shape, the number of defined curved surfaces increases, and the calculation becomes more complicated.
In the present invention, curved surfaces having different characteristics are connected, and again expressed as a single curved surface by a polynomial for the same characteristic.

It is assumed that the curved surfaces S and S'are represented by polynomials according to their characteristics. U− regarding the curved surface S
The intersection point P between the curve and the curved surface S ′ is 0 ≦ u. At this time,
With respect to the curved surface S, u ′ and v ′ exist, and P = S ′
(U ', v'). Here, the 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 =
The u-curve of the curved surface S is taken up to u, and u = u 'to u = 1
Up to the above, the curve is redefined by taking the u′-curve of the curved surface S ′. By defining n such curves and dividing each curve into m, a curved surface definition net over the curved surfaces S and S ′ is stretched. If one curved surface is defined by this curved surface definition net, the curved surfaces S and S'are combined to form an integral curved surface. Moreover, the combined curved surfaces maintain the characteristics of the respective curved surfaces S and S '.

[Tool Travel] When a curved surface is defined, the tool travels on it to perform cutting. The tip of the tool is a sphere having a constant radius R, and the position of the center of the tool is a point vertically separated from the curved surface by R. That is, with respect to the curved surface S, the tool center traveling point P is determined by the above formula.

When the tool travels along the curve on the curved surface S, the tool center traveling position is determined by obtaining the point P for the point on the curve. This method is to define a point separated from the curved surface by R, and conventionally, the normal vector N (see FIG. 3) was calculated over all the cutting points. When the curved surface is not expressed by a mathematical expression, at least two neighboring points have to be calculated for calculating the normal vector N, which makes the calculation complicated and time consuming.

On the other hand, in the present invention, the point P is determined by using the above equation for (u _j , v _i ) which defines the curved surface definition net, and based on these points, the center running curved surface is defined. Generate a surface definition net. When this curved surface definition net is defined, a curved surface can be defined by a polynomial by this net. If the surface defined in this way is * S, then for all u, v where 0 ≦ u ≦ 1, 0 ≦ v ≦ 1, * S (u, v) = S (u, v) + ε・ R · N ... Define the curved surface polynomial so that The polynomial in the present invention establishes this relationship within a sufficiently small error. As a result, it is not necessary to obtain the center of the tool from the curved surface S,
For curved surface * S, * S (u, v) for u and v will be obtained. This is a calculation for obtaining values for u and v of the polynomial, which is extremely simple as compared with the conventional method, and the calculation speed is so high that it cannot be compared.

[Brief description of drawings]

FIG. 1 is an explanatory view of defining a plurality of curved surfaces having different given characteristics as an integral surface by a polynomial expression in a three-dimensional processing method according to the present invention.

FIG. 2 is a schematic configuration diagram of a cutting device for carrying out the present invention.

FIG. 3 is an explanatory diagram of curved surface definition in the three-dimensional processing method according to the present invention.

FIG. 4 is a flowchart showing an outline of a control procedure in the three-dimensional processing method according to the present invention.

FIG. 5 is an explanatory diagram of how to grasp a curved surface in the three-dimensional processing method according to the present invention.

FIG. 6 is an explanatory view of cutting a plurality of curved surfaces in a conventional three-dimensional processing method.

[Explanation of symbols]

 1 ... Machine tool main body 3 ... Table 5 ... Machining head 6 ... Cutting tool 15, 16, 17 ... Control unit 20 ... Computer 22 ... Control panel 24 ... CPU

Claims (2)

[Claims] 1. An x-axis and a y-axis orthogonal to each other with respect to a workpiece.
Axis, in the processing method of performing a three-dimensional processing comprising a z-axis, a plurality of different curved surfaces given property as a graphic information,
Defined by the following polynomials for variables u and v
Calculate the cutting surface, 3D processing method characterized by. 2. The three-dimensional processing method according to claim 1.
Then, the normal vector at one point S (u, v) obtained by the polynomial
Center run of a cutting tool with tip radius R against tor N
Determining the line point P by the following equation, P = S (u, v ) + ε · R · N where (front +1, is referred to as back side -1) ε ² = 1 dimensional machining method comprising .