JP2007279937A - Method for machining contour surface and solid by numerical control single cutting tool - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an NC program for machining a contour surface and machining a three-dimensional solid for which the contour surface is a base surface by a non-rotational single cutting tool in one stroke. <P>SOLUTION: A contour is set at the position of the radius R of a C-axis table so as to be machined by a single cutting tool. In the NC machining method of a system of working a contour shape by giving a slight variance and generating cutting motion even while making XY axes perform follow-up motion in synchronism with rotation in order to continuously machine a surface surrounded by the contour thoroughly in one stroke, the NC program of calculating the point sequence of a turning machining path for which a contraction coefficient is added to the machining path of a basic contour shape, successively deciding a circular arc by three points adjacent in the point sequence and successively connecting two points of them by circular interpolation is executed. Also, a basic contour is defined as a base horizontal cross section and a recessed or projected solid in a shape according to a specified definition function is continuously machined in one stroke in an NC machining method. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method of cutting a contoured two-dimensional surface and a three-dimensional solid with a non-rotating single blade, and more particularly, a curved two-dimensional surface at an arbitrary position of a workpiece fixed on a rotating table. The present invention relates to a method for NC processing of a three-dimensional contour surface or a three-dimensional solid.

  A rotating tool, that is, an end mill is often used for normal contour processing. However, when the shape becomes small, a planar method using a non-rotating single blade is required.

  For a curve given by a mathematical expression or a point sequence, it is usual to connect minute line segments by linear interpolation, which is not a heavy load due to the performance improvement of a digitizer or a computer. However, there is a need for a method of calculating a continuous machining path with a single stroke and easily building a high-accuracy program on a personal computer (small computer).

  In view of this, the present inventor, in the patent application of the previous Japanese Patent Application No. 2006-037483 (hereinafter referred to as “Patent Application A”), the C-axis center is O, a quadratic curve offset from the center O, or a similar basic A first step in which a fixed point A is set at the center of the contour shape and the line segment OA is R (mm), and the contour (FA) is arbitrarily divided, with i = 0 to p, a split angle (−θi), and a split A second step of calculating the length q of the line segment ANi at the point (Ni), and a third step of calculating the XY axis system coordinates (Mi) when the dividing point (Ni) is moved by the table rotation (θi). Steps and a fourth step of calculating circles (E0 to Ep) passing through three adjacent M points are sequentially executed, and for each of the circles (Ei), the leading points of the three M points are determined. Circular interpolation command and table motion with start point coordinate value and intermediate point as end point coordinate value It is proposed to create an NC program by the step of creating NC commands that are synchronized with each other and sequentially connecting them, and to execute contour processing by synthetic three-axis simultaneous interpolation processing of XY-axis arc and C-axis straight line. I named it the method.

Japanese Patent Laid-Open No. 11-151635 JP 2000-246614 A Japanese Patent No. 3333679

  Although the technology about the processing of the contour line is disclosed by the patent application A, a method of processing the inside of the contour smoothly as a two-dimensional surface, or a processing method of a three-dimensional solid using the two-dimensional surface as a base surface Improvements remain. For example, if the inside of the contour line is to be finished to a flat surface, contour line processing is forced to create another contour line program with a slightly reduced shape and repeat the processing. Similar complexity and inefficiency remains for three-dimensional solid processing.

  The present invention provides a method for continuously processing the inside of a contour line surrounded by a closed curve with a single stroke to form a contour surface, and a method for continuously processing a three-dimensional solid shape having the contour surface as a base section with a single stroke. To do.

但し、Ｃ軸中心をＯ、輪郭の内部定点をＡ、線分ＯＡをＲ、輪郭を分割した点をＮｉ、線分ＡＮｉの長さをｑｉ、輪郭の分割角度及びＣ軸の旋回角度をθｉとして記述されるとき、
前記基本輪郭面内を単一刃具を用いて隈なく加工するため、[数２]を用いて点列を計算する。
[数２]

但し、Ｆ（θ）を縮み関数であり刃具が輪郭内を回動する際のピッチ幅を決める関数である。θｉを連続回動してＸｉ，Ｙｉの点列が計算される。次いで、隣接する３点を通る円を逐次計算し、該３点のうちの先頭点を始点座標値、中間点を終点座標値とする円弧補間を順次接続する。方式でＸＹ軸円弧補間とＣ軸の３軸合成制御のＮＣプログラムを作り一筆書き方式で輪郭面内を加工する方法とすることにより達成される。 The object of the present invention is as follows: (1) In a machine tool for NC control of the XY axis and the C axis, the basic contour to be machined offset from the center of the C axis is expressed by:
[Equation 1]

However, the center of the C axis is O, the internal fixed point of the contour is A, the line segment OA is R, the point where the contour is divided is Ni, the length of the line segment ANi is qi, the division angle of the contour and the turning angle of the C axis are θi When described as
In order to process the inside of the basic contour plane without any defects using a single cutting tool, a point sequence is calculated using [Equation 2].
[Equation 2]

However, F (θ) is a contraction function and is a function that determines the pitch width when the blade rotates within the contour. The point sequence of Xi and Yi is calculated by continuously rotating θi. Next, circles passing through three adjacent points are sequentially calculated, and circular interpolation with the start point coordinate value as the start point coordinate value and the intermediate point as the end point coordinate value is sequentially connected. This is achieved by creating an NC program for XY-axis circular interpolation and C-axis three-axis synthesis control by a method and processing the contour surface by a one-stroke method.

The object of the present invention is as follows. (2) The shrinkage function F (θ) is an expression,
[Equation 3]
F (θ) = − (q / Q) · ρ · θi
However, Q is the maximum value of the radial segment qi, and ρ is an interval constant (mm / θ) for contour surface machining, which is achieved by the machining method described in (1) above.

但し、Ｃ軸中心をＯ、輪郭の内部定点をＡ、線分ＯＡをＲ、輪郭を分割した点をＮｉ、線分ＡＮｉの長さをｑｉ、輪郭の分割角度及びＣ軸の旋回角度をθｉとして記述し、 被加立体の表面を単一刃具を用いて連続した一筆書きで加工するため式[数４]を用いて点列を計算する。
[数４]

但し、ｑｚ＝ｑｉ＋Ｆ（θ）、 Ｚｏは初期値、Ｚ(ｑｚ)はｑｉとｑｚを変数とする定義関数である。
基底面全域にわたり、θｉを連続回動してＸｉ，Ｙｉの点列を計算し、次いで、隣接する３点を通る円を逐次計算し該３点のうちの先頭点を始点座標値、中間点を終点座標値とする円弧補間を順次接続する方式でＸＹ軸円弧補間とＣ軸の３軸合成制御命令ブロックを作り、更に上記式「Ｚｉ」のＺ軸制御命令を加え４軸合成制御として一筆書き方式で加工する方法。 The above-mentioned object of the present invention is as follows: (3) In a machine tool for NC control of the XYZ axis and the C axis, the contour of the horizontal base section of the solid to be machined offset from the center of the C axis is described by the formula [Equation 1]. When
[Equation 1]

However, the center of the C axis is O, the internal fixed point of the contour is A, the line segment OA is R, the point where the contour is divided is Ni, the length of the line segment ANi is qi, the division angle of the contour and the turning angle of the C axis are θi In order to process the surface of the object to be added with a single stroke using a single cutting tool, the point sequence is calculated using Equation [4].
[Equation 4]

However, qz = qi + F (θ), Zo is an initial value, and Z (qz) is a definition function with qi and qz as variables.
Rotate θi continuously over the entire basal plane to calculate the point sequence of Xi and Yi, then calculate the circle passing through the three adjacent points one after the other. The XY-axis circular interpolation and the C-axis three-axis composition control command block are made by sequentially connecting the circular interpolation with the end point coordinate value as the end-point coordinate value, and the Z-axis control command of the above formula “Zi” is added to make a one-stroke composition control. Processing by writing method.

  Further, the object of the present invention is as follows: (4) The function Z (qz) in the equation “Zi” is calculated from a cross-sectional definition function having θi, qi, and qz as variables. This is achieved by the processing method described in 3).

  With this invention, NC contour surface machining of various closed curves can be performed with high efficiency and high accuracy. Conventionally, the contour processing and surface processing performed by connecting minute line segment segments, using 2out of 3 circular interpolation, and writing with a single stroke, the NC program can be shortened and handled easily on a personal computer. In addition, the check becomes easy, and the NC contour surface machining time is further shortened.

  In addition, according to the present invention, three-dimensional solid processing with a single cutting tool can be performed at an arbitrary position of a part, and a shape based on a three-dimensional solid cross-sectional definition function based on a basic contour surface can be achieved by a one-stroke method. I can do it. The program shortened by the “2out of 3” three-point circle method enables high-speed and high-precision machining.

  The NC processing machine used in the present invention is as shown in FIG. 1. A column base (Y axis) 2 that moves a Y axis by attaching a column 3 on a bed 1 and a rotary table (C rotation axis) centered on O. 6, and a carriage 4 for Z-axis movement is attached to the column 3. The carriage 4 is configured to include a ram 5 that holds the tool rest 9 and moves to the X-axis, and is attached to the tool rest 9. The non-rotating single blade 8 is moved along the XYZ axes, and the workpiece 7 is placed on the C-axis table 6 and turned. The C-axis center O is taken as the origin of the XY axes. The contour FA is machined on the surface of the workpiece 7. Since the contour FA is at a distance away from the axis O, the target contour FA is swung around the origin O as the table rotates. The blade 8 follows the XY composite motion so that the coordinate point M at the tip of the blade does not leave the contour FA as shown in FIG. If the motion of the contour FA and the XY composite motion are exactly the same, the cutting tool 8 does not perform a machining action. Therefore, the condition for processing the contour FA is that there is a motion difference between the C-axis turning motion and the XY composite motion. The locus of this motion difference generates a desired contour shape FA.

  In normal machining, the C-axis motion is taken as the cutting motion and the XYZ-axis motion is taken as the feed motion, so the cutting motion is high speed and high horsepower, and the feed system is low speed and low horsepower. As described above, the contour machining operation described in this specification is a technique that uses the difference between the motions of the axes without distinguishing between the cutting motion and the feed motion. The review of the cutting phenomenon has contributed greatly.

  As described above, the principle of this technology is that the machining progresses by giving a slight difference between the circular motion of the table 6 and the XY axis interpolation motion. Create restrictions. It does not apply to curves with inflection points, those with singular points such as heart shapes and broken lines, and those where the center of curvature changes to the left and right in the direction of travel, such as sine curves. However, the part excluding such inadequate points is applicable. In addition, even if the shape cannot be described in the numerical formula, a point sequence is given and it can be applied if it does not violate the above restriction conditions. Since the outline drawing which is the subject of the present invention is a continuous stroke, it must be closed.

  When an outline FA, for example, an ellipse as shown in FIGS. 5 to 6 is given, a fixed point A is first defined at the center as the first step, and the outline FA is set with UV coordinates with the fixed point A as the origin. Define. Further, the value of the line segment OA is set as the turning radius R. In the case of a quadratic curve that can be calculated, a point where the line segment ANi can be easily calculated is selected as the fixed point A. If the point sequence is given by a computer, digitizer, etc., a fixed point A is selected as an arbitrary point in the center area.

  Next, as a second step, the outline FA defined by the UV axis system is divided in the direction opposite to the C axis rotation, and Ni is assigned to each point. The division may be performed at a certain angle or an arbitrary angle. It is reasonable to divide the portion where the curvature change is large into fine parts and the small part into large parts. Then, the length q of each line segment ANi is calculated. For example, for an ellipse represented by [Equation 5], this step is given by [Equation 6] with θi as a variable. The relationship between θi and qi may be tabulated using a digitizer or CAD.

（但し、a、bは定数）
[数６]

[Equation 5]

(However, a and b are constants)
[Equation 6]

The third step is the calculation of the cutting tool point position M (Xi, Yi) when the table 6 is rotated by the C axis angle θi. Xi and Yi are obtained by substituting qi into [Equation 1].
The cutting tool point position M (Xi, Yi) is a point sequence on the trajectory CM of the XY-axis composite motion.

  The fourth step is to sequentially create a three-point circle Ei from the point group of M points at the blade point position. The three points determine one circle Ei, and the arc centers Xei and Yei and the radius ri are determined. An example of a three-point circle calculation method is shown below.

ただし、α、β及びａ、ｂは計算簡易化のための媒介変数で図３中に記載の通りである。また、この図３の三点円の中心座標などの計算結果の一例は、図７に数値表として示した。 In FIG. 3, the blade trajectory CM is (M ₁ , M ₂ , M ₃ , M ₄ ,... M _p ), and E ₁ = (M ₁ , M ₂ , M ₃ ) and a circle passing through three adjacent points When written as E ₂ = (M ₂ , M ₃ , M ₄ ), the respective center points are E ₁₀ (Xe ₁ , Ye ₁ ) and E ₂₀ (Xe ₂ , Ye ₂ ). Since the coordinate values (Xi, Yi) of each M point are known, Xe ₁ and Ye ₁ can be obtained from [Equation 7] for E ₁₀ . The radius ri of each circle is derived from the center point coordinates.
[Equation 7]

However, α, β and a, b are parameters for simplifying the calculation and are as described in FIG. An example of calculation results such as the center coordinates of the three-point circle in FIG. 3 is shown as a numerical table in FIG.

  Next, the features of the circular interpolation connection method “2 out of 3 method” of the present invention will be described with reference to FIG. In the figure, there are triangular areas M2, Mt, and M3 in sections M2 and M3. Mt is an intersection obtained by extending the line segment M1M2 and the line segment M4M3, respectively, and there is an improper appropriate point in this region. In order to connect the two points M2 and M3, three types of line segment M2M3, arc E2, and arc E3 can be selected, but the portion surrounded by arcs E2 and E3 (shaded hatch) is the most probable region, and the approximation error E3 is determined as the smallest value. The three-point circle method of the present invention is superior to the conventional line segment segment linear interpolation method.

  The NC program is constructed by creating a circular interpolation command from the three-point circle data obtained above and connecting them sequentially. The obtained three-point circle Ei includes the radius ri, the center coordinates Xei, Yei, and the position coordinates of the 3M points, but the circular interpolation command of the NC program includes the three-point circle center coordinates Xei, Yei or the radius ri. The start point and intermediate point data are used.

  NC commands (blocks) constituting the program include a preparation command and a processing command. For the preparation, there are a G code as a coordinate system, instructions X and Y for moving the cutting tool to the machining start point, and further there are a C-axis rotation direction G code and an arc interpolation rotation direction G code as modal instructions. The machining command gives Xi + 1 and Yi of the intermediate point position M point Mi + 1, the radius ri, and the C-axis turning angle θi + 1 as end points in the same block, and adds the motion speed F. The radius ri may be replaced with the center point coordinates Ii and Ji. In the same manner, information on the point Mi + 2 is written in the next block.

  In the program, the first point and intermediate point data are used and the third point is discarded. The data discarded in the next three-point circle is used. Therefore, there is a feature that the two front points are extrapolated at the connection point of the NC command.

[Contour surface processing]
[Calculation of cutting tool point Mi (Xi, Yi)]
In order to process the inside of the basic contour by the four steps described above in a one-stroke drawing method, as shown in FIGS. 8 and 9, the cutter is slightly moved from one point of the basic contour according to the continuous rotation of θi. The cutting tool trajectory along the basic contour line is obtained while being separated one by one. As the third step, the cutting tool point Mi (Xi, Yi) is calculated by the formula [2]. In general, the contraction function F (θi) of the third equation of [Equation 2] becomes [Equation 3]. That is, F (θi) = − (qi / Q) ρθi, Q is the maximum value of the moving radius qi, and ρ is the interval constant of the locus line. F (θi) is a reduction from the basic contour and corresponds to the feed of surface cutting, and (qi / Q) is necessary when machining to the center, but the surface machining reaches the center. If not, F (θi) = ρθi
[Equation 8]
Yi = Rcosθi + qi−ρθi
May be used. FIG. 9 is a diagram in which point sequences obtained by calculation are connected by straight line segments.

(Calculation of three-point circle)
After the point sequence of the cutting tool points Mi is obtained by the above procedure, a three-point circle is calculated. This procedure is the fourth step, and is to sequentially create a three-point circle (Ei) from the point sequence of Mi points. One circle (Ei) is determined by the three points, and the arc center (Xei, Yei) and radius (ri) are calculated. FIG. 8 is the result of smoothing by applying the circular interpolation process described in paragraph [0024] in FIG.

[NC program]
The processing from the three-point circle data to the NC program is performed in the same manner as in the case of the basic contour, and the end processing is performed after reaching the center point.

ただし、ｑｚ＝ｑｉ＋Ｆ(θi)、Ｚｏは初期値である。Ｚ軸制御を加えると図１１を例とする基本輪郭面を断面とする三次元立体が形成される。線分ｑｚは図１１において三次元立体の基本輪郭水平断面（Ａ）のθi線のＺ軸垂直断面（Ｂ）における刃具の位置を与える線分であり、またＺ（ｑｚ）は刃具の基底面からの深さである。そこで曲線（１)〜（２）に定義関数を与えるといろいろな機能を持った凹または凸の立体を形成することが可能になる。定義関数は基本輪郭の定点ＡにたてたＺ軸と線分ｑｉの関数であり直線、二次曲線などを選ぶことが出来るが、必ずしもＺ軸対照である必要はないから片側が（１)〜（２）円弧で反対側（２)〜（３）が直線といった異形状も可能であり機能部品の生産に利用される。 When a Z-axis control motion is added to the processing of the contour surface described above, a three-dimensional solid (unevenness) can be formed.
[Equation 4]

However, qz = qi + F (θi) and Zo are initial values. When the Z-axis control is applied, a three-dimensional solid whose cross section is a basic contour surface as shown in FIG. 11 is formed. A line segment qz is a line segment that gives the position of the cutting tool in the Z-axis vertical section (B) of the θi line of the three-dimensional solid basic contour horizontal section (A) in FIG. 11, and Z (qz) is the base surface of the cutting tool. From the depth. Therefore, if a definition function is given to the curves (1) to (2), it is possible to form a concave or convex solid having various functions. The definition function is a function of the Z-axis and the line segment qi established at the fixed point A of the basic contour, and a straight line, a quadratic curve, or the like can be selected, but one side is not necessarily a Z-axis contrast (1) (2) Different shapes such as arcs and opposite sides (2) to (3) are also possible and are used for the production of functional parts.

  In addition, a definition function can be given not for the Z-axis cross section passing through the fixed point A but for a cross section parallel to the Z-axis cross section of θ = 0, for example, and a so-called kamaboko type three-dimensional shape can be formed. That is, if there is a three-dimensional shape definition, it is possible to create a continuous NC machining program by a one-stroke writing method.

[Example 1]
[Ellipse processing]
As an example, when processing the upper surface of the part 7 by using the above-mentioned standard ellipse formula, [Equation 5] in the paragraph [0018] as a basic contour (FA), the origin (0, 0) of the UV coordinate system is set as the above. The point A of the first step is determined, and the distance OA from the turning center O is R. In the subsequent second step, the basic contour FA defined by the UV axis system is divided in the direction opposite to the C axis turning, and Ni is assigned to each point. Then, the length (q) of each line segment ANi is calculated. That is, (θi) is given as a variable and is given by the equation [Formula 6] A numerical table for calculating the relationship between q and θi is shown in FIG.

  The third step calculates the cutting tool point Mi (Xi, Yi) when the table is rotated by the angle (θi) of the C axis. The calculation uses [Equation 1] in paragraph [0008].

  The fourth step is to sequentially create a three-point circle Ei from the point sequence of the M points. One circle Ei is determined at three points, and the arc center (Xei, Yei) and radius (ri) are calculated. . This has already been described in detail with reference to FIGS.

"Surface machining path"
The surface machining path is a path that circulates along the basic contour while leaving one point of the basic contour. A contraction function F (θ) is added as a third term to the equation Yi in [Equation 1]. As described above, F (θ) is an expression of a function having q and θ as variables,
F (θ) = − (qi / Q) ρθi
Or if only θ is a variable,
F (θ) = − ρθi.
As in the case of the basic contour, the third step is the calculation of the cutting tool point Mi (Xi, Yi) when the table is rotated by the angle (θi) of the C axis. The reduction function F (θ) is added to the equation of [Equation 1], and the calculation is performed by [Equation 2].

   The procedure after the calculation of the three-point circle in the next fourth step is exactly the same as in the case of the basic contour path. The number of surroundings is determined by the size of the basic contour and the value of ρ. In the case of the function F (θ) = − (qi / Q) ρθi of [Equation 3], after reaching the internal fixed point A, the F (θ ) =-[Rho] [theta] i, the termination process is performed by the programmer.

[Structure of NC program]
The NC program is created by connecting the path data of the basic contour path and the surface machining path obtained above. In other words, a circular interpolation command is made with three-point circle data, and is sequentially connected. The obtained three-point circle Ei includes the line segment (ri), the center coordinates (Xei, Yei), and the position coordinates of the 3M points. The circular interpolation command of the NC program includes (Ei) or (ri ), Start point, and intermediate point data. In this way, it is a feature of this method that an NC program is created like a single stroke. A series of calculation processes is illustrated in FIG.

[Example 2]
12 to 13 are compound closed curves whose contours are composed of a parabola, an arc, and a straight line. Each unit curve or straight line touches smoothly and does not have an unsuitable part as described in paragraph [0016]. 12 (1) to (2) are parabolas, (2) to (3) are arcs, (3) to (4) are straight lines, (4) to (5) are arcs, and (5) to (1). Is a parabola, and each connection point is smooth and shares a tangent. Each unit curve or straight line has its own focal point and center point in its own coordinate system, and the point sequence on the contour has its own coordinate value. Therefore, a fixed point A is provided inside the contour as shown in FIG. It can be converted into a coordinate system and integrated. In this way, the fixed point A determined inside the contour of the first step is determined at a convenient position at or near the center of gravity in the case of this composite closed curve, and then the coordinate calculation of the contour division point Ni is performed by coordinate conversion. Do. This calculation process may be simplified by CAD. The position selection of the fixed point A is important in order to keep the cutting edge direction of the cutting tool constant (the line segment qi is perpendicular to the contour line). In the case of a composite graphic, the shape may be lost due to the density of the point sequence on the basic contour graphic, so it is necessary to consider the point sequence pitch to be dense near the unit graphic connection point.

  The surface machining path after the point sequence on the basic contour figure is determined is to create a path that goes around the basic contour while leaving the basic contour, and shrinks to Yi in [Equation 1] F (θi) Is as described in paragraph [0035]. The end point processing and the configuration of the NC program are the same as in paragraphs [0036] and [0037], respectively.

[Example of solid processing with the basic contour surface as the base surface]
Since the present invention is a method for processing a contour surface and a three-dimensional processing method using the contour as a horizontal base section, an embodiment of the three-dimensional processing method will be described next.

  As already described in paragraph [0030], the method of continuously processing the contour surface with a single stroke can be applied to solid processing. The conventional three-dimensional machining technology was (a) machining program for each contour line (b) linear segment line segment linear connection (c) end mill machining, but in the present invention (b) continuous program (b) Three-point circular connection circular interpolation (C) Single cutting tool with excellent quality and efficiency.

  In the example shown in FIGS. 14 to 15, the shape of the solid to be processed is a concave or convex shape and has a specified horizontal base outline shape, and the Z axis is set at a fixed point A in the outline figure, and the point on the outline It has a vertical section defined by a vertical section definition function (hereinafter referred to as a section definition function) Z (qz) having a line segment NiA (qi) as Ni and a line segment qz at the cutting edge current point in the contour as variables. There are two types of vertical cross sections defined. FIG. 14 shows an example of defining a radial vertical section centering on the Z axis at the fixed point A, and the other is a perpendicular of a parallel straight line (PC line) of an arbitrary angle θ on the base contour surface. FIG. 15 shows an example of defining the cross section. The defined cross-sectional shape is a straight line, an arc, a parabola, an ellipse, or the like.

  The cross-sectional definition function of the radial cross section is determined by giving a graphic condition to the relational expression between the line NiA = (qi) of the point Ni on the basic contour graphic and the fixed point A and the cutting edge point qz. The parallel cross-sectional definition function is determined by giving a graphic condition to the relational expression between the intersection (PCn) of the PC line and the base outline graphic and the cutting edge point qz.

[Example 3]
Example 3 is an example in which the radial cross section as shown in FIG. 16 has a straight cross section (B) and the base contour surface (A) is an ellipse. Since the base contour surface is an ellipse, C, Xi, and Yi up to the third equation of [Expression 4] are determined. In the case of this example, the definition function Z (qz) is a linear system in the equation Zi = Z ₀ + Z (qz), and if Z (qz) = β (qi−qz) (where β is a constant), the cross-sectional triangle is similar. Further, if Z (qz) = H (qi−qz) / qi (where H is a constant), a triangle with a constant height is obtained. It should be noted that when the second term of Zi is +, it is a convex shape, and when it is −, it is a concave shape.

[Example 4]
Example 4 is an example in which the radial cross section (B) as shown in FIG. 14 has a parabolic cross section and the base outline (A) is an ellipse. This example gives a parabolic condition to the section definition function. Note that when the basic formula of parabola Z (qz) = σ (qz) ² defines a condition that matches the base contour, the height h (which is also the depth) of the solid is (qi) ² = h / σ. Then, Z (qz) = h * (qz / qi) ² . This solid is a multifocal parabola.

または、

とすれば、

により定義関数Ｚ（ｑｚ）が決定される。 [Example 5]
Example 5 is an example in which the radial cross section shown in FIG. 17 has an arc and the base contour surface is an ellipse. This example gives an arc condition to the section definition function. There are cases where the height of the figure vertex is specified (arc radius changes) and the arc radius is specified (vertex height changes). Since the basal plane is an ellipse, the radial center line is targeted for the fixed point A, and (1), (3) of the three points (1), (2), (3) are determined as shown in FIG. Therefore, the arc is determined by giving the radius r ₀ or the depth h of (3) point.

Or

given that,

Thus, the definition function Z (qz) is determined.

と

を得る。
あらためて線分ｑｅＡｅ＝（ｑｅ）’また、線分ｑｅＡｅ＝（ｑｚ）’とおくと、断面図形の定義関数を得ることができる。 Since the following embodiments have a parallel section, the calculation process will be described with reference to FIG. Returning to step 1 and step 2 again, the angle on the basal plane of the parallel section is defined as α, and a straight line DAD ′ is formed. A straight line E, qz, E ′ that passes through the current point qz of the cutting edge point trajectory running in the base contour plane and parallel to DAD ′ is formed, and the perpendicular from the fixed point A is drawn and the intersection point is set to Ae. If the line segment AAe = G, the angle θ′i and the line segment Aqe are obtained.
A straight line passing through A and Ae is called an Aα line and is a top line of the cross-sectional figure.
The cut surface is at the EE 'line, and

When

Get.
If the line segment qeAe = (qe) ′ and the line segment qeAe = (qz) ′ are set again, a cross-sectional figure definition function can be obtained.

[Example 6]
FIG. 19 of Example 6 is an example in which a parallel section has a straight section and a base outline is a straight line. Refer to the expression in paragraph [0044]
Z (qz) = β (qi−qz)
Z (qz) = H (qi-qz) / qi
When (qe) ′ and (qz) ′ described in paragraph [0047] are cited, the definition function in the case of a parallel section is obtained.
Z (qz) = β (qi′−qz ′) or
Z (qz) = H (qi′−qz ′) / qi ′.

[Example 7]
Example 7 has a parallel section, a parabolic section, and an ellipse of the base outline as shown in FIG. 15 described above. Similar to [0048] in the previous paragraph, [0045] has a radial section and a parabolic section. Formula Z (qz) = h * (qz / qi) ²
Is replaced with Z (qz) = h * (q′z / q′i).
However, it should be noted that the top line is not symmetrical.

[Composition of NC machining program]
In the processing of the three-dimensional solid described in Examples 3 to 7 above, numerical control information about the Z axis is added to the invention related to the processing of the contour surface, and four-axis synchronous control of C, X, Y, and Z (with regard to XY) Is circular interpolation).

  According to the present invention, the NC program uses a one-stroke writing method for processing by numerical control of a curved contour surface using a non-rotating single cutting tool and processing of a three-dimensional solid by a cross-sectional definition function based on the contour surface. It is shortened and can be easily handled by a personal computer, and the processing time is shortened.

The perspective view which shows the basic composition of the 4-axis NC processing machine used for this invention. The top view of the movement locus | trajectory of the blade point M in the processing machine of FIG. Illustration of how to find a three-point circle. Explanatory drawing of the characteristic about the locus | trajectory of a three-point circle. Explanatory drawing of the 2nd step which calculates | requires the length q of a line segment in the case of ellipse processing. Explanatory drawing of the 3rd step which calculates XY point coordinate M when a division point moves in the case of ellipse processing. A calculation table such as the center coordinates of the three-point circle in FIG. Cutting tool trajectory (2 out of 3 method) when machining the inside of the basic contour all the way with a single stroke. The figure which carries out the segment connection of the point sequence of the blade tool locus | trajectory which rotates within an ellipse outline surface. Numerical table of reference example, machining program calculation table for elliptical surface. Explanatory drawing of a three-dimensional cross-section definition function. An example of a composite figure contour surface. Unified coordinate system for compound drawing contours. An example in which the shape of the solid to be processed is convex, the parabolic section is a radial section, and the base outline is an ellipse. An example of a three-dimensional shape to be processed having a convex shape, a parallel cross section and a parabolic cross section. An example of a radial section with a straight section. Explanatory drawing of a definition function when a radial cross section is a circular arc. Explanatory drawing of the blade-tip locus | trajectory calculation process of the base figure of a parallel-shaped cross section. An example of a parallel section with a straight section and a base contour that is an ellipse.

Explanation of symbols

1 bed 2 column base (Y axis)
3 columns
4 Carriage (Z axis)
5 Ram (X axis)
6 Rotary table (C rotary shaft)
7 Workpiece
8 Cutting tools
9 Tool stand
OC center point
A Internal fixed point of the contour
C Table NC control axis
Point where Ni contour is divided
ANi line segment
q Length of line segment
θi Dividing angle, C axis turning angle
R Distance between points A and O
Mi The position Mi (Xi, Yi) of the cutting point of the cutting tool when the value of the NC axis C is θi.
CMM trajectory, cutter trajectory (XY)
Ei 3-point circle made from 3M points
radius of ri Ei
Xei Ei center coordinates
Center coordinates of Yei Ei
ρ Contour processing interval constant
F (θ) shrinkage function

Claims (4)

For machine tools with NC control of the XY and C axes, the basic machining contour offset from the center of the C axis

However, the center of the C axis is O, the internal fixed point of the contour is A, the distance of the line segment OA is R, the point where the contour is divided is Ni, the length of the line segment ANi is qi, the segment segment angle and the C axis swivel When the angle is described as θi, an expression for processing the inside of the basic contour plane without any defects using a single cutting tool,

Use to calculate the sequence of points.
However, F (θ) is a contraction function. Rotate θi continuously to calculate the sequence of points Xi and Yi, then calculate the circles passing through the three adjacent points one after the other, and the start point of these three points is the start point coordinate value and the intermediate point is the end point coordinate value A method of connecting the circular interpolation in order to create an NC program for XY-axis circular interpolation and C-axis three-axis composition control, and processing the contour surface by a single stroke writing method. The contraction function F (θ) is an equation,
F (θ) = − (q / Q) · ρ · θi
However, Q is the maximum value of the line segment qi, and ρ is an interval constant (mm / θ) for contour surface processing. In a machine tool for NC control of the XYZ axis and the C axis, the contour of the solid horizontal base section offset from the center of the C axis is

However, the center of the C axis is O, the internal fixed point of the contour is A, the distance of the line segment OA is R, the point where the contour is divided is Ni, the length of the line segment ANi is qi, the segment segment angle and the C axis swivel When the angle is described as θi,
Formula for processing the basic contour surface without any defects using a single cutting tool,

Is used to calculate the point sequence (Xi, Yi).
However, qz = qi + F (θ), Zo is an initial value, and Z (qz) is a definition function with qi and qz as variables. Rotate θi continuously over the entire basal plane to calculate the sequence of points Xi and Yi, then calculate the circle passing through the three adjacent points one after the other. The XY-axis circular interpolation and C-axis three-axis composition control command block are created by sequentially connecting the circular interpolation as the end point coordinate value, and the Z-axis control command of the above formula “Zi” is added to make a one-stroke composition control. Processing method.    The processing method according to claim 3, wherein the function Z (qz) in the expression “Zi” is calculated from a cross-sectional definition function having qi · qz as a variable.

Images