JP2008000844A - Method for controlling surface pattern arrangement formed on machining surface, CAD / CAM, and numerically controlled machine tool - Google Patents

Abstract

【Task】
A method of easily forming the desired regular surface pattern on the machined surface by end milling.
【Solution】
Divide the machining surface with polygonal patches, set the starting position of the tool path from the apex or center of the polygonal patch, and set the tool path to the inside or outside by a certain crossfeed amount with the end mill This can be achieved by selecting the cutting conditions and controlling the phase difference when machining with a spiral stroke in the machining path while shifting.
[Selection] Figure 2

Description

The present invention relates to a method for controlling the arrangement of surface patterns formed on a processed surface by cutting with an end mill using a numerically controlled machine tool, and a method for uniformly forming a target surface pattern on the entire processed surface.

Increasing the number of products that have functions such as improved scratch resistance and anti-slip properties by making the surface uneven by chemical etching, electrical discharge machining, laser machining, machining with NC engraving machines, etc. Yes. In addition, with the development of design development methods using CG and 3D-CAD, products with high design features using uneven patterns, such as interior and exterior wall tiles and accessories of buildings, are becoming more common.

By adjusting the initial processing position of the ball end mill blade at the processing start point of each processing line of the ball end mill, the position of the irregularities is precisely regulated in the feed direction of each processing line on the metal plane, and the feed between the processing lines There is known a method (see Patent Document 1) in which directions are regularly phased and a pattern regularly formed between processing lines can be variably formed.

High-speed and high-feeding has become possible due to the advancement of high-speed, high-precision and high-speed machining technology for machine tools, but in ball end milling with high feed, the cause of uncut material generated by the cutting edge in the feed direction is analyzed. It is found that the uncut material is in the eccentricity between the rotation center of the spindle and the tool axis and the phase difference of the tool cutting edge, and the phase difference of the tool cutting edge on the plane is controlled by the movement time of the tool and the amount of tool eccentricity It is known that a cutting plane diagram 1 having an irregular pattern of an arbitrary shape can be created by setting to an arbitrary value (see Non-Patent Document 1). The phase difference is a difference in the rotation angle of the same tool cutting edge in adjacent passes.

In addition, when the above technique is applied to a curved surface to form a concavo-convex pattern on a cylindrical shape or a spherical surface, if the processing surface radius Rw of the cylindrical surface or spherical surface is known, the curved line portion is approximated by a minute line segment. A method is also known in which a concave / convex pattern can be machined into a surface pattern changed according to the number of blocks b by setting a tool path and setting the number of blocks b in the cutting section and the distance between the blocks in the workpiece coordinate system. (Refer nonpatent literature 2).

JP 2001-71207 A Akinori Saito, Takiaki, Masaomi Tsutsumi, “Control Method of Concave and Finished Patterns in Ball End Mill Processing”, Journal of Precision Engineering, Vol. 66, No. 3, 2000, p419-423. Akinori Saito, Akiaki, and Masaomi Tsutsumi, “Method of forming uneven pattern on curved surface in ball end mill processing”, Journal of Precision Engineering, Vol. 66, No. 12, 2000, p1963-1967.

However, assuming that the purpose of forming a fine concavo-convex pattern is to improve the mechanical properties and designability of a workpiece, in the above-described prior art, in order to form a desired concavo-convex pattern on a freely designed processed surface, Setting of the tool movement time for controlling the phase difference becomes complicated. Therefore, a great deal of time is required to match the intended uneven pattern.

As a method for avoiding the above problem, the inventors divided the machining surface with polygonal patches, created a one-stroke tool path in an arbitrary patch using an end mill, selected cutting conditions, Perform a simulation to display the alignment state of the pattern, output the image of the concavo-convex pattern formed by the cutting edge movement locus as an image file, check the pattern formed in the patch, and check the concavo-convex pattern formed by the cutting conditions The method of selection was adopted.

Using an end mill such as a ball end mill or a bull nose end mill as the cutting tool, and selecting the cutting conditions in the following steps, the phase difference of the cutting edge of the tool is controlled, and the target surface is even and regular. A method for forming an uneven pattern was found. By applying this method to CAD / CAM and numerically controlled machine tools, it becomes possible to control the arrangement of surface patterns formed on the machined surface.

(1) A numerically controlled machine tool using an end mill as a tool, and a method for controlling the arrangement of surface patterns formed by tool cutting edges on a machining surface,
Dividing the entire processing surface in combination with the same regular polygon patch or several different shaped regular polygon patches, and storing it as coordinate data;
A step of setting a one-stroke tool path in a spiral shape with a constant cross-feed amount from one vertex of any one regular polygon patch in the regular polygon patch, parallel to the side;
Tilt the tool or the machining surface, set the machining start point on the tool path, and machining conditions, input the set value into the calculation formula defined for each regular polygon, and each round of the tool path Calculating a phase difference of the tool cutting edge;
The movement trajectory of the tool cutting edge on the tool path is simulated, the image of the pattern arrangement to be formed is displayed on the monitor screen, the processing conditions are adjusted as necessary, and the pattern arrangement in the regular polygon patch is adjusted. Selecting an image and storing the processing conditions;
Setting machining conditions for all regular polygon patches formed on the machining surface, setting a tool path for the entire machining surface, and performing cutting with a numerically controlled machine tool;
The method of controlling the surface pattern arrangement formed on the processed surface.

(2) As the machining conditions, at least the number of blades of the end mill, the rotation speed, the feed rate, the feed amount per blade, the inclination angle with respect to the machining surface of the tool, the cross feed amount, and the outermost peripheral side of the regular polygon patch The method of controlling the surface pattern arrangement | sequence formed in the process surface as described in (1) which is the length of this.

(3) A one-stroke tool path is set in a spiral shape with a constant cross-feed amount from one vertex in the regular polygon patch, and within the revolving tool path, the regular polygon On the tool path parallel to one side, a point where a perpendicular drawn from the center of gravity of the regular polygon intersects is defined as a point on the tool path with the number of laps n, and Pn, and the number of laps (n + 1) ) On the tool path is set to Pn + 1, and by inputting the machining conditions, the rotation angle λn → n + 1 that makes a round in the patch of the tool is calculated from an arithmetic expression defined for each regular polygon. (Rad) is calculated, phase difference (omega) n-> n + 1 (rad) is calculated | required, The method of controlling the surface pattern arrangement | sequence formed in the process surface as described in (1).

(4) The method of controlling the surface pattern arrangement formed on the machined surface according to (1), wherein the end mill has a constant radius of curvature.

(5) A CAD equipped with a function for dividing a machining surface into regular polygon patches and a function for creating an NC program of a spiral-stroke tool path with a constant cross-feed amount in the regular polygon. / CAM.

(6) Function for storing at least machining steps according to claims 1 to 4, controlling set machining conditions, outputting an image file, performing computation by the stored operator, and outputting a control signal to a numerically controlled machine tool Equipped with CAD / CAM.

(7) A numerically controlled machine tool that performs cutting using any of the functions (1) to (6) as a program, software, or CAD / CAM

If you set a spiral one-stroke tool path in a polygonal patch with a machined surface and cut with a constant cross-feed amount, the phase difference of the tool cutting edges in the polygon will be kept constant, A regular and uniform concavo-convex pattern with a tool cutting edge can be formed therein, and a concavo-convex pattern having a designed regular arrangement can be formed on the entire processing surface depending on the purpose of use or decoration.

The inventors divide the machining surface into polygonal patches by the patch division cutting method, machine the inside of the patch with a spiral one-stroke tool path, and the phase difference of the tool cutting edge for each turn of the ball end mill. A simulation and experiment were carried out to control the arrangement of the concavo-convex pattern. In the present invention, since the cutting trace by the tool cutting edge is used for forming a concavo-convex pattern on the processing surface, the target cutting trace cannot be obtained when the end mill is arranged perpendicular to the processing surface. For this reason, in the present invention, the end mill and the machining surface are inclined and the end mill blade tip has a constant radius of curvature in order to form cutting traces on the machining surface for the number of the end mill blades during one rotation of the end mill. An end mill such as a ball end mill or a bull nose end mill is most suitable.

In the patch division cutting method, the machining surface is divided by polygon patches as shown in FIG. 2A, and the inside of each divided polygon is a spiral tool path as shown in FIG. 2B. It is a method of processing with. Machining is performed by using an arbitrary vertex of a polygon or the center of a spiral tool path as a starting point or an ending point of the tool path, and moving the tool path inward or outward by a constant crossfeed amount by an end mill, Machining with a spiral stroke.

Taking a square patch as an example, FIG. 3A shows a tool path for machining one square patch. In this square patch, as shown in FIG. 3B, consider four triangles divided by a straight line connecting the center of gravity G of the patch and each vertex, and pay attention to one triangle ΔGCD. The length of one side of the square patch is L, and the intersections of the perpendicular drawn from the center of gravity to each side and the spiral tool path are P1, P2, P3... Pn from the outside. When the cross feed amount fc (mm) is constant, the tool movement distance Ln → n + 1 (mm) between the adjacent point Pn and the point Pn + 1 can be calculated by Equation 1.

In addition, the time Tn → n + 1 (min) required for the tool to move the distance of Ln → n + 1 can be calculated by Equation 2 when the feed rate is F (mm / min).

Therefore, the rotation angle λn → n + 1 (rad) of the tool from the point Pn to the point Pn + 1 after going through the inside of the patch is expressed by the following equation (3), assuming that the spindle rotation speed is S (min ^-1 ). Desired.

Here, the relationship of Formula 4 holds among the spindle rotation speed S, the feed speed F 1, the number N of end mill blades, and the feed amount ft per blade.

Substituting number (2) into number (3) and further substituting number (1) and number (4) yields number 5.

From this equation 5, the rotation angle λn of the tool from the point Pn to the point Pn + 1 through the patch.
→ n + 1 is an equidistant sequence of initial term d = 2π (4L−3fc) / Nft and tolerance Δλ = −16πfc / Nft with respect to the number n of rounds in the in-patch machining path.

Here, considering the relationship between the concavo-convex pattern on the machined surface and the phase difference, the tool rotation angle λn → n + 1 during one round of the patch is calculated, so the phase difference is λn → n + 1 Can be obtained as a remainder obtained by dividing by 2π.

That is, the phase difference ωn → n + 1 (rad) when machining with a spiral tool path can be expressed by Equation 6.

However, 0 <ωn → n + 1 <2π.

From Equation 6, mod (λn → n + 1, 2π) represents the remainder of (λn → n + 1) / 2π, and J represents the integer part of the quotient. The phase difference ωn → n + 1 increases by Δλ when the number of turns n increases, and when it becomes larger than 2π, the quotient J is added and becomes a value subtracted by 2πJ. That is, it is understood that the increase is repeated by Δλ in the range of 0 to 2π.

In order to form a concavo-convex pattern aligned on a straight line, the phase difference ωn → n + 1 shown in Equation 6 may be constant regardless of the value of the number of turns n. That is, Δλ may be an integer multiple of 2π. In the triangle ΔGCD in FIG. 3, Δλ shown in Table 1 may be set so as to satisfy Equation 7.

That is, if the cross feed amount fc, the feed amount ft per blade, and the number N of blades are determined, finally, only the constant part d of Formula 6 is involved in the phase difference ωn → n + 1. . Substituting d and Expression 7 in Table 1 into Equation 6, the phase difference ωn → n + 1 of the triangle ΔGCD can be calculated by Equation 8, and is constant within the triangle.

To summarize the above, the inside of the patch is processed into a spiral shape with a single stroke using this method, and the three parameters of the feed amount ft, the cross feed amount fc, and the number N of blades are changed to Δλ By adjusting the, a concavo-convex pattern aligned on a straight line can be formed in the triangle of each patch. Further, it can be seen from Equation 8 that if the length L of one side of the patch is changed, the phase difference is changed, so that the inclination in the cross-feed direction of the pattern arranged on the straight line can be changed.

In the four triangles ΔGDA, ΔGCD, ΔGBC, and ΔGAB in the square patch of FIG. 3, the tool rotation angle λn → n + 1 during one round of the patch can be calculated as in Equation 6. In this case, d and Δλ in Equation 6 are as shown in Table 1. Δλ has the same value in the four triangles, and d is decreased from the triangle ΔGDA including the machining start point by −4πfc / Nft in the same direction as the spiral tool path, that is, clockwise.

As described above, if the inside of the patch is processed by the spiral tool path, the phase difference of each triangular region can be easily made constant, so that complicated control of the tool movement time becomes unnecessary. Therefore, a regular uneven pattern is formed in the patch, and a pattern of the patch itself is formed, so that a uniform surface pattern can be generated on the entire processed surface.

Similarly, for regular triangles and regular hexagonal patches other than squares, assuming that the inside of the patch is to be machined with a spiral tool path, a perpendicular line and a spiral line drawn from the center of gravity to each side in the tool path for each turn. The tool movement distance Ln → n + 1 (mm) between Pn and the adjacent Pn + 1 with the tool path is calculated from a different calculation formula for each regular polygon, and the tool rotation angle λn between two adjacent points → n + 1 can be calculated as an equidistant sequence similar to that in the case of a square by substituting the equations (2) to (4) into equation (5). Table 2 shows a summary of Δλ, initial term ds, and clockwise reduction Δd of equilateral triangles and regular hexagons machined by the tool path shown in FIG. Δλ is the same in any triangle as in the square patch.

In order to compare the difference from the pattern due to actual processing, the present inventors have targeted the processing of an inclined plane by a ball end mill as a method of displaying the uneven pattern processed in the patch on the screen by simulation. FIG. 4 is a diagram showing a state in which the point Q on the tool cutting edge where the amount of cut from the machining surface is the largest moves at the feed speed F while rotating at the spindle rotation speed S on the spiral tool path. . There are three types of patch shapes: regular triangles, squares, and regular hexagons. The length L of one side of the patch, the spindle rotation speed S, the feed speed F, and the cross feed amount fc are input values. Each time the tool cutting edge moves for the time required for one rotation of the tool, it can be plotted along the tool path, and the movement locus of the cutting edge formed in the patch can be displayed as an uneven pattern.

The cutting conditions were set to the conditions described in Table 3, a phase difference was calculated, and a simulation was performed in which the movement trajectory of the formed cutting edge was displayed on the monitor screen as an uneven pattern. The length L of one side of the patch was set to 15 mm, 10 mm, and 5 mm in the order of regular triangle, square, and regular hexagon. For each patch, among the three parameters for aligning the concavo-convex pattern shown in the previous chapter on a straight line, the cross feed amount fc is adjusted to change Δλ in Tables 1 and 2, and the phase difference ωn → n The concavo-convex patterns were compared by simulation for the case where +1 changes with each turn and the case where it changes.

As shown in Table 4, the feed amount ft and the cross feed amount fc per blade are set to the same level, and high feed processing is assumed, so that the difference in the uneven pattern due to the change in phase difference can be clearly observed. I made it.

FIG. 5 shows the result of simulation for one patch of regular triangle, square, and regular hexagon when the phase difference changes with each revolution. If each patch is considered to be a triangle with the center of gravity at the top and each side at the bottom, it can be seen that an elliptical arc-shaped uneven pattern is formed inside each triangle of the patch.

FIG. 6 shows the result of simulation with the cross feed amount adjusted so that Δλ is an integer multiple of 2n for the same three types of patches as in FIG. Compared with FIG. 5, the uneven pattern in each triangle of each patch changes from an elliptical arc shape to a pattern aligned on a straight line. From this, it can be seen that if the phase difference is made constant, the inside of each triangle will be an uneven pattern aligned on a straight line.

5 and 6, the movement trajectory of the cutting edge adjacent in the cross-feed direction indicates that the phase is advanced when the phase difference is 0 to π, that is, the tool When the direction of the cutting edge reaches the same position in the feed direction and the previous round, since it is already cut, a movement trajectory of the cutting edge is formed contrary to the feed direction. On the other hand, in the case of π to 2π, the phase is delayed and a moving locus of the cutting edge is formed in the feed direction. In the case of 0 or 2π, since the phase is the same, the moving locus of the cutting edge is formed perpendicular to the feed direction. Further, the moving distance in the feeding direction becomes longer as it is closer to π. According to these, in FIG. 5, the concavo-convex pattern to be formed is not aligned on a straight line because the phase difference fluctuates for each turn.

FIGS. 7 and 8 show the results of calculating the phase difference in the triangle including the processing start point for each of the three types of patches shown in FIGS. Referring to FIG. 7, the phase difference of the equilateral triangular patch indicated by Δ is increased from the first round to the second round, and the phase difference is decreased from the second round to the sixth round. Thus, the movement trajectory of the cutting edge is formed opposite to the feeding direction with respect to the movement trajectory of the outermost cutting edge in the first round, and is formed in the feeding direction from the second round to the fourth round. And it turns out that it forms reverse to a feed direction in the 5th to 6th laps. That is, an elliptical arc-shaped uneven pattern is formed counterclockwise. Considering similarly, since the square patch has an uneven pattern on the elliptical arc in the clockwise direction, and the regular hexagonal patch has a phase difference that fluctuates at π, a zigzag uneven pattern is formed.

On the other hand, as shown in FIG. 8, since the square and hexagonal patches have a constant phase difference of π or more, a concavo-convex pattern on a straight line inclined in the feed direction is formed, and the equilateral triangle patch has a phase difference of 0. It can be seen that an uneven pattern is formed perpendicular to the feed direction. 7 and 5 and FIG. 8 and FIG. 6 respectively compare the uneven pattern alignment state well with the phase difference relationship in the number of laps, and the uneven pattern alignment state is determined by the phase difference. I understand that.

As described above, when the flow of the procedure of the present invention is shown in FIG. 9, first, the processed surface is divided into polygonal patches in order to process the processed surface into an intended alignment pattern. Next, one stroke of the polygonal patch and the center point of the tool path are the starting point or ending point, and the inside of the polygon is parallel to the side, connecting the outer periphery and the center point with a constant crossfeed amount. Create a tool path for. Then, the machining conditions such as the number of end mill blades, cross feed amount, feed amount per blade, etc. are selected, the set numerical value is input to the arithmetic expression, and the phase difference is calculated by the arithmetic unit. The cutting operation is simulated, and an image file of a concavo-convex pattern of the movement locus by the tool cutting edge in the polygon is created and displayed on the monitor screen, and whether or not this pattern is allowed is selected. Create all polygonal tool paths on the machined surface and perform cutting with a numerically controlled machine tool. The operations so far are preferably created as a program and written in CAD / CAM software.

Moreover, it is also possible to provide a database of the alignment patterns that can be formed on the processed surface according to the present invention and provide it as easy-to-operate CAM software so that the user can easily change the contents of the data. For example, the user can click the icon of “Processing data setting” in the database menu to display the details of the processing conditions of the selected alignment pattern image from the alignment pattern image database. Further, the user can also set a new machining condition so that the details of the displayed machining condition can be changed.

Next, a cutting experiment was conducted using a table turning type 5-axis vertical machining center and a solid carbide ball end mill (φ10 mm, number of blades 2). The cutting conditions were the same as the simulation conditions shown in Tables 3 and 4, and the simulation result was compared with the concavo-convex pattern formed by actual processing. FIGS. 10 and 11 show the results of processing by forming regular triangles, squares, and regular hexagonal patches in vertical and horizontal directions on an inclined plane, respectively. FIG. 10 shows the results when the phase difference changes for each turn, and FIG. 11 shows the results when the phase difference is constant.

It can be seen that the pattern of the patch outer shape is formed on the entire processed surface where the patches are continuously formed vertically and horizontally, and the uneven pattern formed in the patch is the same for any patch. It can also be confirmed that each patch is divided into triangles having the center of gravity as the apex and each side as the base. As described above, when m-square patches are continuously processed using the present method, a patch outline pattern and m triangles are formed in each patch on the processed surface, and uniform within each triangle. It was found that an uneven pattern was formed. Comparing FIG. 10 and FIG. 11, the uneven pattern in the triangle of each patch has changed from an elliptical arc shape to an uneven pattern aligned on a straight line, which is in good agreement with the simulation results shown in FIGS. . As a result, if the three parameters are adjusted to make the phase difference constant, an uneven pattern arranged on a straight line is formed on each triangle.

By providing irregularities on the surface, it is possible to provide a product to which functions such as improvement of scratch resistance and prevention of slipping are added. In addition, it is possible to develop products with high design features using uneven patterns, such as interior and exterior wall tiles and accessories of buildings by a design development method using CG or 3D-CAD in the future.

It is a figure which shows the uneven | corrugated pattern of the processing surface by a ball end mill process, and the processing surface pattern calculated by simulation by the conventional uneven | corrugated surface processing method. It is the figure (a) which divides | segments the whole process surface of this invention, and the figure which shows the spiral tool path | route which processes the area | region in a patch of a regular triangle, a square, and a regular hexagon with one stroke. FIG. 4 is a diagram showing four triangles divided by an intersection point P of a spiral tool path in a square patch, a perpendicular drawn on each side from the center of gravity, and a straight line connecting the center of gravity and each vertex. is there. When the simulation of the present invention is performed, the point Q on the cutting edge with the inclined tool and the point Q moves along the tool path by one rotation of the tool when the inside of the square patch is processed into a spiral shape. It is the conceptual diagram which showed the position. In the present invention, in the case of an example in which the phase difference changes for each turn, it is a diagram that displays an image by simulating the uneven pattern in each patch of regular triangle, square, and regular hexagon. In this invention, it is the figure which simulated the uneven | corrugated pattern in each patch of a regular triangle, a square, and a regular hexagon, when the phase difference was the same example for every turn, and displayed the image. It is the figure which plotted the phase difference of the cutting edge calculated for every round by the simulation under the cutting conditions of FIG. It is the figure which plotted the phase difference calculated for every round by the simulation under the cutting conditions of FIG. It is a figure which shows the flow of this invention. Using a table swivel type 5-axis vertical machining center and a solid carbide ball end mill, the process surface of the present invention is divided into regular triangles, squares, and regular hexagonal polygonal patches, each formed vertically and horizontally, It is a processing example in case a phase difference changes for every round, and is a figure which shows the uneven | corrugated pattern formed in the processing surface. Using a table swivel type 5-axis vertical machining center and a solid carbide ball end mill, the process surface of the present invention is divided into regular triangles, squares, and regular hexagonal polygonal patches, each formed vertically and horizontally, It is a processing example in case a phase difference is the same for every round, and is a figure which shows the uneven | corrugated pattern formed in the processing surface.

Claims (7)

A method for controlling an arrangement of surface patterns formed by tool cutting edges on a machining surface using an end mill as a tool in a numerically controlled machine tool,
Dividing the entire processing surface in combination with the same regular polygon patch or several different shaped regular polygon patches, and storing it as coordinate data;
A step of setting a one-stroke tool path in a spiral shape with a constant cross-feed amount from one vertex of any one regular polygon patch in the regular polygon patch, parallel to the side;
Tilt the tool or the machining surface, set the machining start point on the tool path, and machining conditions, input the set value into the calculation formula defined for each regular polygon, and each round of the tool path Calculating a phase difference of the tool cutting edge;
The movement trajectory of the tool cutting edge on the tool path is simulated, the image of the pattern arrangement to be formed is displayed on the monitor screen, the processing conditions are adjusted as necessary, and the pattern arrangement in the regular polygon patch is adjusted. Selecting an image and storing the processing conditions;
Setting machining conditions for all regular polygon patches formed on the machining surface, setting a tool path for the entire machining surface, and performing cutting with a numerically controlled machine tool;
A method of controlling the surface pattern arrangement formed on the processed surface. As the machining conditions, at least the number of blades of the end mill, the rotational speed, the feed rate, the feed amount per blade, the tilt angle with respect to the machining surface of the tool, the cross feed amount, and the length of the outermost peripheral side of the regular polygon patch The method of controlling the surface pattern arrangement formed on the processed surface according to claim 1. A one-stroke tool path is set in a spiral shape with a constant cross-feed amount from one vertex in the regular polygon patch, and parallel to one side of the regular polygon in the circulating tool path. A point where a perpendicular drawn from the center of gravity of the regular polygon intersects on a simple tool path is defined as a point on the tool path with the number of laps n as Pn, and the number of laps (n + 1) in one round of the patch. By setting the point on the tool path to Pn + 1 and inputting the machining conditions, the rotation angle λn → n + 1 (rad) that makes a round in the patch of the tool from the arithmetic expression defined for each regular polygon The method of controlling the surface pattern arrangement formed on the processed surface according to claim 1, wherein the phase difference ωn → n + 1 (rad) is calculated. The method for controlling the surface pattern arrangement formed on the machining surface according to claim 1, wherein the edge of the end mill is an end mill having a constant radius of curvature. A CAD / CAM equipped with a function for dividing a machining surface into regular polygon patches and a function for creating an NC program of a spiral-stroke tool path with a constant cross hood amount in the regular polygon. At least the machining steps described in claims 1 to 4 are stored, and from the input machining conditions, a phase difference is calculated from an arithmetic expression determined for each regular polygon stored in advance, and the movement locus of the tool cutting edge is imaged. CAD / CAM equipped with a function to output as a file. A numerically controlled machine tool that performs cutting using any of the functions described in claims 1 to 6 as a program, software, or CAD / CAM