JP2007018495A - Contour machining method by numerical control single cutting tool - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To carry out cutting of a curved figure based on a planer method using non-rotational single cutter by a simple numerical control program. <P>SOLUTION: In machining of a contour on an optional point of a workpiece on a C-axis table, a fixed point A is defined inside the given contour shape, and the contour is divided into sections, which are an optional number P in number, at a division angle -θi, and a distance between an i-th division point and the fixed point is calculated to be used as a data set (qi-θi) when i ranges from 0 to p. In synchronization with C-axis rotational motion θi of the fixed point A, XY-axis composition motion of the cutter is carried out to follow the rotational motion of the fixed point A, a locus CM, along which composition motion of the XY-axis and the C-axis gives a contour shape FA, on the XY coordinate is found by adding a value corresponding to the distance qi to a Y-axis instruction value. Then, continuous three points are taken out from a point string on the locus CM corresponding to qi, a contour machining program for a circular interpolation NC instruction based on 2-out of-3 method is generated, and machining is carried out. <P>COPYRIGHT: (C)2007,JPO&INPIT

Description

  The present invention relates to a method of cutting a contour shape with a non-rotating single cutting tool, and more particularly to a method of NC processing a contour of a curve at an arbitrary position of a workpiece fixed on a table rotating at a constant speed. .

  A rotating tool, that is, an end mill is often used for normal contour machining. However, when the shape is reduced, the end mill needs to have a small diameter, and the rotational speed increases, which is not satisfactory in terms of accuracy and life.

  Therefore, a lathe system or a shaver system (planar system) technique, that is, a contour machining technique using a non-rotating single blade is applied. Many of the prior arts use a method in which the contour is divided into line segments and the point sequence is connected by linear interpolation. When the contour is only circular, circular interpolation is used without creating a point sequence.

  For a contour surrounded by a curve given by a mathematical expression or a point sequence, it is normal to connect minute line segments by linear interpolation, and this is not a large load accompanying the performance improvement of a digitizer or a computer. However, there is a demand for a technique for easily calculating with a personal computer (small computer) and building a high-accuracy program when processing a large number of contours or when the shape changes (see Patent Documents 1-3). .

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

The following three points need to be considered when using a non-rotating single cutting tool in contour processing by cutting.
1. Appropriate cutting speed 2. Direction of the blade NC program

  The cutting speed of general cutting has gradually increased recently, and has become normal at several hundreds m / min. It is not easy to create a relative speed of the above-mentioned degree when trying to process a contour with a small size (several mm) with a single cutting tool. Fortunately, the progress of NC machine tools in recent years has been remarkable, and the feed rate has reached several meters per minute, and it has become possible to use the feed motion for the cutting motion if the work material is selected appropriately. It has also been reported that a better finish can be obtained at lower speeds, such as lathe turning. In the case of a small shape, high-speed machining of a single cutting tool cannot be expected, and since the cutting force is small, a method of using a feed motion for the cutting motion becomes possible.

  Needless to say, it is desirable that the direction of the cutting tool and the cutting direction match. As shown by the relationship between the non-rotating single cutting tool 8, the cutting direction 8a, and the cutting locus CM in FIG. 16, it is ideal that they coincide like a planar, but the lathe is inclined by the feed amount, Therefore, it is called oblique cutting. In the case of the present invention, oblique cutting may occur depending on the type of curve and the way of selecting the fixed point A, but this is not a problem in the case of low speed and fine cutting. As shown in FIG. 17, in the method in which the tool rotation axis W is provided so as to change the direction of the blade 8 in accordance with the trajectory CM, it is difficult to match the tip of the blade and the turning axis.

  Also, the method of creating an NC program by creating straight line segments from a large number of point sequences and connecting them by linear interpolation is heavy in preparation load, difficult to check the program, and the data volume increases at an accelerated rate when accuracy is important. Since the execution speed of the NC device is slowed, there is a drawback that an appropriate cutting speed cannot be obtained.

  The above-described contour cutting with the non-rotating single cutting tool includes a control device that simultaneously controls the X, Y and C axes, and a non-rotating cutting tool that moves according to the X and Y motion axis coordinate systems. 8 and a table 6 on which the workpiece 7 is mounted and rotated by C-axis drive, a curved line (eg, an ellipse) or a straight line at a distance away from the origin O on the XY plane of the workpiece 7 When an attempt is made to process the contour FA of the composite curve including Thus, the machining object can be achieved by a simple numerical control program. A first step in which a fixed point A is set at the center of the contour shape of a curved line or a complex curve including a straight line, and the line segment OA has a radius R (mm), and the contour FA is arbitrarily divided into division numbers i = 0 to p. Then, the second step of calculating the dividing angle (−θi) and the length q of the line segment ANi at the dividing point Ni, and the XY coordinates Mi (Xi, Yi) when the dividing point Ni is moved by the table rotation (θi). ) And a fourth step of calculating circles Ei to Ep passing through three adjacent M points, and for each of the circles Ei, An NC program is created by an arc interpolation command in which the start point is a start point coordinate value and an intermediate point is an end point coordinate value, and an NC command that synchronizes table rotation motion is generated and sequentially connected. Contour addition by simultaneous three-axis interpolation processing It is intended to perform the work.

  According to the present invention, NC contour machining of various curves can be performed with high efficiency and high accuracy. By using the 2 out of 3 circular interpolation method, which was previously used for contour processing by connecting short line segments, the NC program can be shortened and can be easily handled by a personal computer. The NC contour machining time is further shortened.

  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, a carriage 4 for Z-axis movement is attached to the column 3, a ram 5 is provided on the carriage 4 to hold the blade base 9 and move to the X-axis, and a non-rotating single blade 8 is provided. The workpiece 7 is moved on the XYZ axes, and the workpiece 7 is placed on the C-axis table 6 and rotated. 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. When this motion difference is always a constant value (mm), the contour FA is circular, and the XY composite motion is circular interpolation with a fixed distance offset from the origin O.

  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 that the power and speed are designed appropriately. That is, 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. Even if the appearance of the mechanical device is similar, the design and utilization techniques are different.

  As described above, the principle of this technique is based on the difference between the circular motion of the table 6 and the combined motion of the XY axes 2 and 5, so that the contour that can be machined due to the continuity of both motions and the direction of the cutting tool. The restriction of the shape FA occurs. It does not apply to curves with inflection points, singular points such as heart shapes and broken lines, and sine curves where the center of curvature changes to the left and right in the direction of travel. However, a part excluding such unsuitable points can be processed. A curve that can be defined unconditionally as being possible is a continuous curve that does not have an inflection point and has its center inside, or a curve portion that satisfies the condition.

  When a contour FA satisfying the condition, for example, an ellipse as shown in FIGS. 5 to 6, is given, as a first step, a fixed point A is first defined at the center, and the UV coordinates with the fixed point A as the origin are used. A contour FA is defined. 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. If it is not closed, a fixed point A is selected at the center of the inner area. In order to enable calculation of the line segment q, which will be described later, the fixed point A is preferably placed at a position away from the contour line FA.

  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. In the case of a closed quadratic curve (for example, an ellipse represented by Equation 1), this step is easy and is given by Equation 2 using θi as a variable. If there is no q calculation formula, the relationship between θi and q is tabulated using a computer or CAD.

刃具点位置Ｍ（Ｘ_ｉ、Ｙ_ｉ）はＸＹ軸合成運動の軌跡ＣＭ上の点列である。 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. Since q has already been obtained, Xi and Yi are obtained by substituting q into Equation 3.

The cutting tool point position M (X _i , Y _i ) 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１８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 (Xe1, Ye1) and E ₂₀ (Xe ₂ , Ye ₂ ). Since the coordinate values (X _i , Y _i ) of each M point are known, Xe ₁ and Ye ₁ can be obtained by Equation 4 for E ₁₀ .

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. To connect the two points M2 and M3 in the point sequence M1 to M5, three types of line segment M2M3, arc E2, and arc E3 can be selected, but the part surrounded by arcs E2 and E3 (shaded hatch) is the most certain If the extrapolation of the two front points is considered, E3 is determined as the one with the smallest approximation error.

  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.

[Ellipse processing]
As already described with reference to FIGS. 5 to 6, the first step of taking a fixed point A at the center of the ellipse for obtaining the radius R (mm), dividing the outline of the ellipse into a desired arbitrary number p, A second step for calculating the length qi of the line segment ANi at each dividing point Ni, a third step for calculating the XY point coordinates Mi when the dividing point is moved by the center rotation of the table 6, and three adjacent M points For each of the circles Ei obtained through the fourth step of sequentially calculating the circle Ei passing through the coordinates, the circular interpolation command with the start point coordinate value of the three M points as the start point coordinate value and the intermediate point as the end point coordinate value and Table 6 An NC program synchronized with the rotational motion is created, thereby realizing planar contour NC machining with a non-rotating cutting tool by simultaneous simultaneous interpolation of an XY-axis arc and a C-axis straight line. FIG. 6 shows an example of calculating the elliptical three-point circle and calculating the center coordinates and radius.

[Processing complex figures of parabolas, circles, and straight lines]
7 to 9 show an example in which the contour FA is composed of a composite figure of a parabola-shaped part, a circular arc part, and a straight line part. In the illustrated example, the parabola has a principal axis (x ² = −4σy, focal point (0, σ)), and is a contour locus CM composed of circles λ1 and λ2 and a tangent line L having a radius C in contact therewith, and a second step for obtaining each distance qi in each locus It is explanatory drawing of.

The fixed point A is set as the focal point F, and is set as the origin of the UV axis. The center coordinates of the left and right small circles are U1, V1; -U1, V1. As shown in the drawing, the dividing lines q1, q2,... Qp are drawn from the fixed point A to the trajectory CM at the dividing angle θi (i = 1, 2,. The calculation formula is as follows: the parabola part is Equation 5, the arc section is Equation 6, and the straight section is Equation 7.

  In the above case, the angle θ in the UV coordinate system is opposite to the rotation direction of the C axis. In the case of FIG. 7, the parabola is converted into polar coordinates and angled with respect to the CCW. When the quasi-line U 'is formed, since Q'N' = q in the figure, the above formula 5 is obtained. In the case of a parabola, θ = π and q = ∞, so that there is not only a limit of the angle in the −V direction, but also the cutting edge and the traveling direction do not coincide with each other. .

  FIG. 8 is an example of machining an arc offset from the fixed point A, and since the two sides and one corner are known, the above equation 6 can be easily obtained. FIG. 9 shows a case where there are two linear portions L1 and L2 in the trajectory CM. Both are converted into polar coordinates, the moving radius is qi, and the angle is θi. The angle between the tangent line of the contour and the vector qi is preferably 90 °, but may be inappropriate depending on the shape and the position of the fixed point A. In order to avoid this, the fixed point A should be set at the center.

また、図１０のスパイラルはＣ軸がＣＷに回転するときｒが増加する。この第３ステップに続いて第４ステップの三点円の計算を行い、三点円の始点、中間点、及び半径または三点円の中心座標とを使ってＮＣプログラムを作成することは、前述他の実施例と同様である。 [Spiral processing]
When the contour figure to be given is an Archimedes spiral and is expressed as polar coordinates r = b + aθ, a> 0, the origin of the UV axis is taken as a fixed point A in FIG. Taking q from the V-axis to CCW, the calculation of q in the second step is q = r. Accordingly, Xi and Yi in the third step of Expression 4 are expressed by Expression 8 with respect to the turning angle θi of the C axis. However, a is an increment of r with respect to the angle θ and corresponds to a lathe feed.

In the spiral of FIG. 10, r increases when the C-axis rotates to CW. The third step is followed by the calculation of the three-point circle in the fourth step, and the creation of the NC program using the start point, the middle point, and the radius or the center coordinates of the three-point circle is described above. This is the same as the other embodiments.

[Combination of spiral and outer circle]
Using the Archimedes spiral machining, the inside of the outer circle Ew can be turned flatly (front turning). The lathe only sends the tool toward the center of rotation, but in this case, since the center of the outer circle and the center of rotation are offset, conventionally, many concentric circles have been programmed and processed. It is possible to perform face turning with a single stroke using the spiral machining of the method of the present invention. The NC program is a figure in which the spiral contracts toward the center in the outer circle as shown in FIG.

次に、上記外円Ｅｗの加工に続いて内部スプラインｓｐを数１０により計算すればスパイラルが中心に向って収縮する。

ここで、ｑｉは減少関数であるから、ｑｉ＞０となる範囲を選ぶ。この第３ステップ以下の手続きは前述他の例と同様であり、｛Ｇコード（円弧補間コード）＋ Ｘｉ＋ Ｙｉ＋ ｒｉ（三点円半径）＋ Ｃ軸回転角＋ Ｆコード（運動速度コード）＋ 運動速度値｝を１ブロック内に記入する。加工された結果は円盤形状になる。前記ｒｉ（三点円半径）は、Ｉｉ、Ｊｉ（三点円中心座標）に置き換えても良い。図１５（Ａ）は、その計算結果の例である。ａ＝０．００２ｍｍ、ｗ＝３ｍｍ、Ｒ＝１０ｍｍ、角度θは０〜１５００度までで約４回転して外円からＡ点に達する。図１５（Ａ）において、Ｘｃ、Ｙｃ、ｒａｄｉｕｓ、は三点円の中心座標及び半径である。 First, the outer circle Ew is processed by Equation 9 with w being the radius of the outer circle Ew and R being the distance between the center A of the Ew and the center O of the C axis.

Next, if the inner spline sp is calculated by Equation 10 following the processing of the outer circle Ew, the spiral contracts toward the center.

Here, since qi is a decreasing function, a range where qi> 0 is selected. The procedure after the third step is the same as in the other examples described above: {G code (circular interpolation code) + Xi + Yi + ri (three-point circle radius) + C-axis rotation angle + F code (motion speed code) + motion Speed value} is entered in one block. The processed result is a disk shape. The ri (three-point circle radius) may be replaced with Ii and Ji (three-point circle center coordinates). FIG. 15A shows an example of the calculation result. a = 0.002 mm, w = 3 mm, R = 10 mm, and the angle θ reaches 0 to 1500 degrees, and rotates about 4 times to reach point A from the outer circle. In FIG. 15A, Xc, Yc, and radius are the center coordinates and radius of a three-point circle.

[Synthesis of spiral, outer circle and Z-axis function]
In FIGS. 10 and 11, since the Z axis does not move during the machining, the machining is a flat surface. Machining of a rotating body whose main axis is a Z-axis such as a cone or a sphere is controlled by NC control of the Z-axis motion by a function of Z = f (qi) (qi is the length of the radial diameter of the spiral polar coordinate, It is possible to create various rotating bodies by combining spiral motion and Z-axis motion. However, since the spiral is not a circle, it is not strictly a rotating body and is an approximate rotating body.

[Cone processing]
The above formula 10 is XY axis NC control, but Z axis control is added and XYZ 3 axis control is performed to process the cone (cavity), bottom surface outer diameter 2w, and low angle α in the Z axis cross section of FIG. The projected depth Z of the tip point of the spiral moving radius qi that moves on the bottom surface of the cone with the angle θi as a function is expressed by the following equation (12) with reference to the equation (10).

図１５（Ｂ）の「円錐体」は、この数１３のＺの値を計算した実施例である。この加工の場合、三点円の計算にはＸｉ、Ｙｉのみが使われＺｉ値は使用しない。最終のＮＣプログラムの作成ステップでは刃具運動命令ブロックにおいて、ＸＹＺおよびＣの４軸が同期合成運動するように構成される。 When the Z axis is set at the fixed point A of the spiral in FIG. 11 and the expression of Z in Expression 12 is added to Expression 10, position data (Step 3) of the following XYZ 3-axis control blade tool is obtained.

The “cone” in FIG. 15B is an example in which the value of Z in Equation 13 is calculated. In this processing, only Xi and Yi are used for the calculation of the three-point circle, and the Zi value is not used. In the final NC program creation step, the four axes of XYZ and C are configured to perform synchronous and combined motion in the blade motion command block.

The command block format (code format) is different depending on the calculation method, interpolation method, and output method inside the NC unit, but the XY axis motion is distributed by circular interpolation in the 4-axis synchronous synthetic motion, That is, the C-axis and the Z-axis move synchronously by their command values within that time. Therefore, the following code format is reasonable.
{G (circular interpolation code) + Xi + Yi + ri + G (linear interpolation code) + Ci + Zi + F (motion speed code) + speed value} or {G (circular interpolation code) + Xi + Yi + Ii + Ji + G (linear interpolation code) + Ci + Zi + F (motion speed code) + speed value}
In a general NC device, there are cases where 4-axis interpolation cannot include circular interpolation or a plurality of interpolation codes cannot be included in the same block. It is assumed that multiple linear interpolation axes can be controlled synchronously.

したがって、前記円推体の場合と同様の手順により数１５が得られる。

図１５（Ｂ）の「球面」は、この数１５のＺｉの値を計算した実施例である。この場合の三点円の計算以降の手順は、前記錐体円と全く同様であり、ＮＣ加工命令の構成もまた同様である。 [Spherical processing]
The sphere (cavity) shown in FIG. 13 is processed by the same method as the circular thruster. The depth Zi of the point on the spherical surface on which qi (the position of the cutting tool) is projected when the spiral moving radius qi moves as a function of θi as the outer diameter 2dw and the radius Rs of the sphere is expressed by the following equation 14 in FIG. It is as follows.

Therefore, Equation 15 is obtained by the same procedure as in the case of the circular thruster.

The “spherical surface” in FIG. 15B is an example in which the value of Zi in Formula 15 is calculated. The procedure after the calculation of the three-point circle in this case is exactly the same as that of the cone circle, and the configuration of the NC machining command is also the same.

前記円推体、球体の場合と同様な手順で、数１７に示されるようにＸＹＺ座標値を得る。

この場合の三点円の計算にはＸｉ、Ｙｉのみが使われＺｉ値は使用しないこと、最終のＮＣプログラムの作成ステップで刃具運動命令ブロックがＸＹＺおよびＣの４軸の同期合成運動を可能とすること、など三点円の計算以降の手順は、前記円錐体の加工と全く同様でありＮＣ加工命令の構成もまた同様である。
なお、段落番号［００３３］〜［００３８］までの回転体（三次元）はキャビティをもって説明してきたが、当然凸形状も同様の手続きをもって加工される。すなわち定点Ａに立つＺ軸を主軸とした回転体の創成するのに、ＸＹ平衡上のスパイラル運動とＺ軸函数Ｚ＝ｆ（ｇｉ）を合成して達成され、Ｚ軸断面は円となる立体形状が得られる。 [Processing of rotating paraboloid]
Zi = f (qi) is obtained when the center section of the rotating body having the rotation center Z-axis at the fixed point A is a parabola of x ² = 4σz and the upper surface radius is w as shown in FIG.
In FIG. 11, the spiral radius vector qi is the distance between the parabola focal point F and the vertex O is σ, and the perpendicular PQ standing from the point P on the parabola to the quasi-line y = −σ is the radius vector qi (FP). Since it is equal, it is expressed by Equation 16.

XYZ coordinate values are obtained as shown in Equation 17 by the same procedure as in the case of the circular body and the sphere.

In this case, only Xi and Yi are used for the calculation of the three-point circle, and Zi values are not used. In the final NC program creation step, the tool motion command block can perform four-axis synchronous motion of XYZ and C. The procedure after the calculation of the three-point circle, such as, is exactly the same as the processing of the cone, and the configuration of the NC processing command is also the same.
In addition, although the rotary body (three-dimensional) from the paragraph numbers [0033] to [0038] has been described with the cavity, naturally the convex shape is processed with the same procedure. In other words, the creation of a rotating body with the Z axis as the main axis at the fixed point A is achieved by combining the XY equilibrium spiral motion and the Z axis function Z = f (gi), and the Z axis cross section is a circle. A shape is obtained.

  In the present invention, NC contour machining by a non-rotating single cutting tool can be implemented by a shortened NC program.

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 feature about the locus of a three-point circle. Explanatory drawing of the 2nd step which calculates | requires the length q of line segment ANi in the case of ellipse processing. Explanatory drawing of the 3rd step which calculates XY point coordinate M when a dividing point moves in the case of ellipse processing. Explanatory drawing of the 1st, 2nd step with respect to the parabola part in the case of the outline process of the composite figure which consists of a parabola, a circle, and a straight line. Explanatory drawing of the 1st, 2nd step with respect to the circular part in the case of the outline process of the composite figure which consists of a parabola, a circle, and a straight line. Explanatory drawing of the 1st, 2nd step with respect to the straight line part in the case of the outline process of the composite figure which consists of a parabola, a circle, and a straight line. Explanatory drawing which shows the relationship with the 1-3rd step in the case of spiral processing. Explanatory drawing in the case of the combination figure process which has a spiral and its circumscribed circle. Explanatory drawing at the time of the synthesis | combination of a spiral, a circumcircle, and a Z-axis function, and a cone processing. Explanatory drawing at the time of the synthesis | combination of a spiral, a circumscribed circle, and a Z-axis function, and a spherical body process. Explanatory drawing in the case of the synthesis | combination of a spiral, a circumscribed circle, and a Z-axis function, and a rotating paraboloid processing. (A) is a numerical table of an example of the calculation results of the three-point circle center coordinates and radius in the implementation of FIG. 11, and (B) is the cone processing, sphere processing, and rotational paraboloid processing of FIGS. It is a numerical table of an example of the calculation result of Zi with respect to the three-point circle data at the time of implementation. Explanatory drawing of the relationship between the cutting direction in the case of the cutting process by a non-rotating single blade tool, and a cutting locus. Explanatory drawing of the aspect which provided the tool rotating shaft. The numerical table which shows an example of calculation results, such as the center coordinate of the three-point circle of FIG.

Explanation of symbols

1 bed 2 column base (Y axis)
3 Column 4 Carriage (Z axis)
5 Ram (X axis)
6 Rotary table (C rotary shaft)
7 Workpiece 8 Cutting tool 9 Cutting tool base O C-axis center point A Internal fixed point C of the contour NC control axis Ni of the table Point ANi divided by the segment q Length of the segment qi Segment angle R Division angle R Distance Mi Cutting point position Mi (Xi, Yi) when the value of NC axis C is θi
CMM locus Ei Radius of three-point circle ri Ei made from 3M points

Claims (3)

A control device that simultaneously NC-controls the X, Y, and C axes, a non-rotating cutting tool that moves in accordance with each of the X and Y motion axis coordinate systems, and a table on which a workpiece is placed and rotated by C axis driving In a method of machining a contour of a compound curve including a curve or a straight line at a distance away from an origin O on an XY plane of a workpiece by an NC machine tool comprising:
A first step in which a fixed point A is set at the center of the contour shape of a complex curve including a curve or a straight line, and the line segment OA is R (mm);
A second step of dividing the contour FA into an arbitrary number of divisions i = 0 to p and calculating the length q of each segment angle −θi and the segment ANi at the division point Ni;
A third step of calculating an XY point coordinate Mi when the dividing point is moved by the table rotation θi about the origin O;
A fourth step of calculating circles Ei-Ep passing through three adjacent XY point coordinates Mi, Mi + 1, Mi + 2,
Are executed sequentially,
For each of the circles Ei, an NC command is generated by synchronizing the circular interpolation command with the starting point Mi of the three XY point coordinates Mi as the starting point coordinate value and the intermediate point Mi + 1 as the ending point coordinate value and the table rotation motion. A numerically controlled contour processing method using a non-rotating single cutting tool, wherein an NC program is created by connecting steps, and contour processing is executed by combined three-axis simultaneous interpolation processing of an XY-axis arc and a C-axis straight line. The outline is composed of a circle Ew having a radius w and a spiral having the circle Ew as a circumscribed circle,
A first step in which the center of the circle is a fixed point A and the distance from the C-axis center O is a radius R; and a circle equation in the XY coordinate system

Creating a circular interpolation motion program of XY coordinates of radius R to be
Archimedes spiral equation in XY coordinate system

2. The method according to claim 1, further comprising: a second step of dividing a spiral curve satisfying (where a> 0) sequentially into an arbitrary number of divisions p and calculating a length q of a line segment ANi at each division point. A numerically controlled machining method for a contour surface by the non-rotating single blade according to claim 1. The contour is composed of a circle Ew having a radius w and a spiral curve having the circle Ew as a circumscribed circle,
A first step in which the center of the circle is a fixed point A and the distance from the C-axis center O is a radius R; and a circle equation in the XY coordinate system

Creating a circular interpolation motion program of XY coordinates of radius R to be
Archimedes spiral equation in XY coordinate system

A spiral arc that satisfies (where a> 0) is sequentially divided into an arbitrary number of divisions p, and has a second step of calculating the length q of the line segment ANi at each division point;
Further, after the fourth step of calculating the three-point circle, the circular interpolation command, the table rotational movement, and the position in the Z-axis direction of the blade edge at each position of the circular arc contour (Zi = f (qi)) An NC program is created by the step of synchronizing and creating NC commands in succession, and processing of a rotating body with the Z axis as the main axis by simultaneous synthesis interpolation of the XY axis arc, Z, and C axes. A numerically controlled machining method using a non-rotating single blade according to claim 1.

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