JP4403662B2 - Curved surface correction polishing system, NC polishing apparatus, NC program generation method for optical component polishing, NC program generation method for polishing, two-dimensional coordinate point group file generation method for NC program, NC program generation method - Google Patents

Description

[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a processing technology for a scanning lens and its mold used in a polygon scanner optical system of a laser beam printer, and based on measurement data, a curved surface cutting technology or a curved surface grinding technology for the purpose of correcting an error in preprocessing. About.
[0002]
[Prior art and problems to be solved by the invention]
As a method for polishing a free curved surface, a method of pressing a small-diameter tool with a constant force and traversing the tool has been conventionally used. 2. Description of the Related Art Conventionally, a technique for improving the shape accuracy of a curved surface or removing undulation by changing the removal depth by changing the traverse speed according to the tool position is known. As the means for determining the traverse condition, many calculation methods have been proposed on the premise that the removal depth by polishing is proportional to the tool residence time which is the reciprocal of the traverse speed, and these are generally used.
[0003]
As a method of generating a polishing trajectory for curved surface polishing, a region to be processed is defined by a rectangle in a two-dimensional plane coordinate system, this is projected onto the surface to be processed, and the projected region is filled with the tool contact surface. A method for setting a locus is known. For example, the techniques disclosed in JP-A-6-83426, JP-A-9-323252, JP-A-10-315111, and the like correspond to this. The polishing trajectory here refers to a path along which the center point of the tool contact area moves. In order to generate this polishing locus, a specific movement locus is given to the tool. If the surface to be machined has a sufficiently large radius of curvature with respect to the flat surface or the radius of curvature of the tool, the movement locus of the tool center and the locus of the tool contact part are almost the same. It can be set easily.
[0004]
However, applying the shape correction technique using the tool residence time to a free-form surface having a relatively small radius of curvature of several tens of mm to several tens of mmR has some problems in ensuring accuracy. That is, when a free curved surface having a relatively small radius of curvature of several tens of mm to several tens of mm R is polished with a tool having a radius of curvature of several mm to several tens of mm, between the movement locus of the tool center and the polishing locus, An offset corresponding to the radius of curvature of the tool exists in a size that cannot be ignored, and the difference between the two loci appears as a large difference.
[0005]
Therefore, even when a tool movement locus is given such that the tool center makes a linear movement, the contact locus is bent, and the contact locus cannot be distributed at a constant interval. As countermeasures, take a longitudinal section at the same pitch with respect to the surface to be machined, set a polishing position command point to specify the polishing locus on this section curve, and set the radius of curvature of the tool in the normal direction at each command point. A method is used in which the tool position command point is calculated by offsetting the polishing position command point by an amount to obtain the tool movement locus. The coordinates of the tool position command point are used as they are as an NC program for machining. According to the above means, the density of the polishing locus can be made uniform to some extent, but since the polishing position command points are arranged on a straight line on the XY plane, there is a limitation on the density uniformity of the polishing locus. However, there remains a problem that the intervals are equal on the straight line of the X and Y axes and not on the curved surface.
[0006]
Since the density of the scanning lines causes surface roughness depending on the location, it is undesirable for high-quality optical component processing. Also, the roughness of the tool contact locus is a factor that changes the removal depth of polishing.As described above, in the construction method that reduces shape error and waviness by residence time control, it is necessary to incorporate the effect of this into the residence time derivation algorithm. is there. Similarly, if the polishing position command points on the polishing locus are coarse and dense, it is necessary to take the influence into the residence time distribution in the NC program for correction processing.
[0007]
In view of the above-described problems in the prior art, the present invention provides a mechanism for easily and accurately converting a correction amount of a shape error and waviness as an NC program, and realizing a highly efficient and highly accurate corrected polishing system. Objective. Also, in the free-form traverse polishing method using a small-diameter polishing tool, a new polishing NC program creation method is provided, which makes it possible to easily generate a tool contact trajectory with a small density distribution on a curved surface and generate a polishing position command point. To do. In addition, assuming that polishing position command points with small unevenness on the curved surface are assumed, shape error and undulation are expressed by a discrete value of a two-dimensional array at the polishing position command points, and corrected from this array data. It is possible to easily calculate a command value to the processing machine such as a dwell time of a tool necessary for processing.
[0008]
[Means for Solving the Problems]
Curved modified polishing system according to claim 1 of the present invention, in order to achieve the above object, the shape error and waviness of the surface to be processed that put the working front of the curved surface polishing step performed in the tool machine, shape measurement In a curved surface correction polishing system that is corrected based on the result and used to reduce the shape error and waviness in the subsequent curved surface polishing process , polishing for instructing the polishing position and polishing path of the processing surface by the tool of the processing machine a command unit, at intervals equally dividing the tool contact path at the tool contact path on passing through the center of the processing region by the tool of the machine within the tool contact path on the processed surface, which is the predetermined with obtaining the plurality of polishing position command point, and the position command point arithmetic unit for generating a two-dimensional coordinate point group file showing the polishing position command point in two-dimensional plane coordinate system, the two-dimensional coordinate point A storage unit for storing a file, and the shape and waviness of the surface to be processed to the previously determined, the shape evaluation unit for extracting based on the shape error and undulation of the machined surface obtained by the shape measurement in the shape measurement result The polishing removal amount of the processing surface necessary for correcting the shape error and waviness of the processing surface extracted by the shape evaluation unit based on the shape measurement result is stored in the storage unit. A polishing amount calculation unit that calculates each position command point obtained from the two-dimensional coordinate point group file and outputs the calculated polishing removal amount to the polishing command unit as a correction value of the tool contact locus ; It is characterized by having.
[0009]
According to the second aspect of the present invention, in order to achieve the above object, in the curved surface correction polishing system according to the first aspect, means for changing the polishing removal depth according to the required removal amount at each of the position command points is provided. a, tool feed rate, tool rotation speed, by changing one of the tool pressing force, characterized in that to put a change in the polishing removal depth.
[0010]
Those according to the third aspect, in order to achieve the above object, according to claim 1 or 2 curved modified polishing system, for processing by modifying the grinding path and the polishing position of the workpiece surface by the tool using an NC program in the polishing command section, format the NC program, including feed speed of the tool in each row to perform a command for polishing position, the reciprocal of the feed rate, tool rotation speed, one of the command value of the polishing load It is characterized by comprising.
[0011]
According to the fourth aspect of the present invention, in order to achieve the above object, in the curved surface correction polishing system according to the third aspect, the polishing position command point in the NC program offsets the contact position of the tool with a two-dimensional plane coordinate. It is a format described without calculation , or a format described only with two-dimensional plane coordinates. The normal vector of the surface to be machined at the polishing position command point or the calculation of the center of curvature of the tool contour is calculated by the NC command value inside the machine. It is characterized in that it is performed by a decoding unit.
[0012]
In order to achieve the above object, the NC polishing apparatus according to the fifth aspect uses the curved surface modified polishing system according to the third aspect and operates according to the NC program.
[0013]
According to the sixth aspect of the present invention, in order to achieve the above object, in the NC polishing apparatus according to the fifth aspect, normal control can be performed so that the normal line of the surface to be processed at the polishing position command point coincides with the tool pressing direction. It is characterized by being.
[0014]
An NC program creation method for polishing an optical component according to claim 7 is an NC program creation method for polishing an optical component used in the curved surface correction polishing system of claim 3 in order to achieve the above object. The coordinates of the polishing position command point in the program are expressed in a two-dimensional plane coordinate system, and the two-dimensional plane coordinate system is set in parallel with a plane showing the optical effective area.
[0015]
According to the eighth aspect of the present invention, in order to achieve the above object, an NC program creating method for polishing an optical part used in the curved surface correction polishing system of the third aspect, wherein a polishing position command point in the NC program is , rectangular long Henma other representing the optical effective region is projecting a center line parallel to one of the short sides on a curved surface, such as to pass through a point that divides equal the resulting curve length tool It is characterized by setting a route.
[0016]
The polishing NC program creation method according to claim 9 is a polishing NC program creation method used for the curved surface correction polishing system according to claim 4 in order to achieve the above-described object. A function that calculates the density of the tool position command points or the density of the tool trajectory existing per unit area with the area corresponding to the contact area as a unit area, and corrects the polishing removal amount at each point by a numerical value representing this density. It is characterized by having.
[0017]
According to the tenth aspect of the present invention, in order to achieve the above object, a polishing NC program creation method used in the curved surface correction polishing system according to the third aspect, wherein an interval between polishing position command points for generating a tool locus is provided. is equal to or less than 1/2 of the wavelength of the swell to be corrected.
[0018]
The method for creating a two-dimensional coordinate point cloud file for NC program according to claim 11 is a method for creating a two-dimensional coordinate point cloud file for NC program used in the curved surface correction polishing system of claim 1 in order to achieve the above object. a is, tool contact path adjacent sets a trajectory so that equal spacing, and sets at equal intervals on as much as possible the position command point on the locus in that.
[0019]
The NC program creation method according to claim 12 is an NC program creation method used in the curved surface correction polishing system according to claim 3 in order to achieve the above object, and the polishing position command point in the NC program is an optical effective area rectangular long Henma other representing the will project a center line parallel to one of the short sides on a curved surface, the tool path so as to pass through the points that divide equal the resulting curve length A tool at each contact point is obtained by obtaining a two-dimensional coordinate point group file obtained by setting and a necessary polishing removal amount corresponding thereto and multiplying a one-dimensional numerical array representing the polishing removal amount by an arbitrary constant. It is converted into any one of the reciprocal of the feed rate, the tool rotation speed, and the tool pressing force, and used as a control command value synchronized with the tool scanning.
[0020]
According to the thirteenth aspect of the present invention, in order to achieve the above object, in the curved surface modified polishing system according to any one of the first to third aspects, the linear motion axis is XYZ of three orthogonal axes, and rotational movement about the X axis is performed. when the a-axis, rotating the B-axis about the Y-axis, the polishing position command point for generating a tool path, on the basis of the normal vector that put on each point, the a-axis or the value of the B-axis component Is set to be constant, and a tool path passing through these points is generated.
[0023]
Curved modified polishing system according to the claims 1 to 4, in order to achieve the above object, the curved surface modified polishing system of claim 1, the polishing removal amount calculation unit for outputting the necessary polishing removal amount at each point, the machining point It has a function of outputting a normal direction component in and a component orthogonal to the plane coordinate system.
[0025]
BEST MODE FOR CARRYING OUT THE INVENTION
Embodiments and examples of the present invention will be described below with reference to the drawings.
This embodiment is an example in which waviness with an amplitude of 100 nm generated in a curved lens is removed by residence time control. In order to employ a method of keeping the tool posture constant with respect to the machining point normal, an NC polishing apparatus capable of simultaneous control of four axes in the XYAB axis direction as shown in FIG. 2 was used. The present embodiment is composed of three elements: a new NC program creation procedure, a dedicated NC program format, and a method for converting a shape correction amount to a residence time using these.
[0026]
FIG. 1 shows the procedure for creating the NC program as the first element. The feature here is to generate evenly on the curved surface with a simpler method than the polishing position command point. In step 1, the curved surface design is first completed. The shape of an optical component such as a lens is expressed by a formula, and the following description will be made on the assumption of this.
[0027]
In step 2, a rectangle for designating a processing area is set on the curved surface. This is an enlargement of the outer periphery of the lens by a few millimeters. This is for avoiding the boundary line of the processing region which tends to be a defect. It is a rectangle on the XY plane. In this example, the long side is set to be parallel to the X axis and the short side is set to be parallel to the Y axis.
[0028]
In step 3, this rectangle is projected onto the work surface. As a result, a boundary line 5 (denoted by reference numeral 5 in FIG. 2) indicating the machining area on the work surface is generated.
[0029]
In step 4, enter the tool path generation conditions. In this machining, as shown by reference numeral 16 or 17 in FIG. 5, the trajectory is scanned in the Y direction, moved slightly by one command point in the X direction and then Y-scanned again, so that the polishing position in the X direction and the Y direction is adopted. Input the pitch of the command point. In particular, the X pitch has a strong correlation with the roughness of the polished surface and is determined based on the shape of the polishing mark of the tool.
[0030]
The above is the part where the present invention and the conventional method share the same procedure. The characteristic procedure of the present invention will be described below.
[0031]
In step 5b of FIG. 1, to set the center line 10 and 9 with respect to FIG. 4 rectangles 4 for machining area designation shown in (1). This is similarly projected on the processing surface to obtain the curves 11 and 12 on the curved surface ((2) in FIG. 4). Subsequently, in the procedure 6b of FIG. 1, a direction to be preferentially divided is determined. This case as the scanning lens type often take more restrictive undulation accuracy. In this example, the X direction corresponding to the length of the lens is used. Therefore, the dividing points 13 are formed so that the length on the curve is equally divided with respect to the center line 12 in the longitudinal direction (FIGS. 4 (1) and (2) ). Subsequently, in the procedure 7b of FIG. 1, a cross-sectional curve 14 is formed by taking an intersection line between the plane 21 including the dividing point 13 and orthogonal to the X axis and the curved surface indicated by the boundary line 5. The number of the cross-sectional curves 14 is the same as the number of dividing points 13 set previously ((3) in FIG. 4). In the shape of the present embodiment, the plane 21 orthogonal to the X axis is used to obtain the cross-sectional curve 13, but a plane orthogonal to the curve 12 may be used depending on the shape. Density of polishing position command points to be finally formed is selected whichever that a small. The dividing points 15 are set in the same manner for all the cross-sectional curves 14. The dividing point 15 becomes the polishing position command point in the above process.
[0032]
5 (a) is one in which a polishing position command point formed by the present embodiment shown in XY plane view. Since they are arranged at equal intervals on the curved surface, in the XY plan view, density is produced in both the X direction and the Y direction. On the other hand, FIG. 5B represents an XY plan view in the case of the conventional method , and the polishing position command points 8 are equally spaced. Polishing paths 17 and 16 can be formed by connecting the polishing position command points 15 and 8 in the manner of a single stroke.
[0033]
Hereinafter, a new format of the NC program which is the second and third elements of the present invention and a method for calculating the residence time will be described with reference to FIG. In the new format, the polishing position command point is represented by XY two-dimensional plane coordinates, and the dwell time at each position is described by a parameter W. The major difference from the conventional method is that the polishing position command point can be directly input without calculating the offset of the tool, and only the XY coordinates, which are the minimum necessary in the NC program, are in XYAB 4-axis control machining. It is a point. In the conventional method, it is necessary to perform offset calculation for obtaining the center position of the curvature of the tool and to describe command values for the number of axes of the processing machine. Furthermore, the derivation of the dwell time for correcting the shape error is often performed using a complicated integration calculation. It became possible because the formula for designating the curved surface was input in advance on the processing machine side, and the offset calculation was performed inside the processing machine.
[0034]
The new format can be used for shape and swell evaluation by replacing the W term at the end of the line with the Z height indicating the shape error. By making the measurement evaluation file and the NC program in a common format in this way, it has become possible to remarkably easily and accurately generate an NC program for correction processing by feeding back error data. Specifically, it is only necessary to convert the above-described sequence of Z heights into the residence time W. As already described, since the polishing position command points are uniformly arranged on the curved surface, this conversion can also be easily converted to W simply by multiplying the value of Z by a specific constant. This constant is determined by the processing trace shape of the polishing tool, the polishing conditions, the tool trajectory, and the interval between the polishing position command points. However, this constant is determined in advance by experimenting with a tool trajectory or by simple simulation. It is what
[0035]
The curved lens type swell removal experiment was performed by the above means. The polishing tool 1 is a foamed polyurethane having a tire shape as shown in FIG. 2 , and diamond slurry is used as abrasive grains. The rotation axis is orthogonal to the pressing direction. The surface to be processed is a Ni-plated surface subjected to diamond cutting. The processing area was 10 × 10 mm square. In the measurement evaluation of the cut surface, the 19 cross-section curve of FIG. 7 was obtained, and a swell of about 100 nm in amplitude was found. The entire processing area is evaluated with a stylus type shape evaluation machine, and the undulation error is 0 . The output was made with XYZ coordinates at 1 mm pitch intervals. This is the same as the format on the right side of FIG. 6 except that the parameters differ between W and Z. The value of Z indicates the necessary removal amount at each point, and the unit is μm. Subsequently, the conversion coefficient K = 3 . 2 was multiplied by Z in each row to convert to residence time W. This file was directly used as an NC program for correction polishing. 20 sectional curves 7 after processing could be reduced to 40% before processing 41nm, and the undulation amplitude. The preparation period of the NC program is 1/3 of the conventional method, and the efficiency as a process is relatively improved.
[0036]
【The invention's effect】
As described above, the invention according to claim 1 is a two-dimensional coordinate stored in the storage unit for polishing removal amount of the processing surface necessary for correcting the shape error and waviness of the processing surface. The position command point obtained from the point cloud file is calculated for each point, and the calculated polishing removal amount is output to the polishing command unit as a correction value of the tool contact locus. By correcting the shape error and waviness by directly writing points, setting the polishing position command points at equal intervals, and implementing the measurement evaluation file and polishing NC program in the same format for position information. From the required removal amount, it is possible to easily and accurately convert the tool residence time or the like into the operation operation of the processing machine.
[0037]
In the invention according to claim 2, as described above, the three parameters have a linear relationship with the polishing depth, and the necessary removal amount at each point is converted into the machine operation only by multiplying a specific constant. Can do.
[0038]
In the invention according to claim 3, as described above, each point of the polishing position command point is individually provided with processing machine operation information necessary for removing a shape error or waviness, thereby connecting the points arbitrarily. The NC program for correction can be easily created by managing only the order. In addition, the number of shape error data Z and the number of correction operations W match, and the correction amount can be easily transferred.
[0039]
In the inventions according to claims 4 and 7, as described above, the measurement evaluation file and the NC program format for polishing can be shared, and the correction amount can be easily and accurately transferred to the NC program.
[0040]
As described above, the invention according to claim 5 can perform the modified polishing process using this system.
[0041]
As described above, the invention according to claim 6 enables accurate load control and peripheral speed control of the tool at the processing point by keeping the tool posture constant with respect to the processing surface normal line. Improvement of accuracy can be realized.
[0042]
In the invention according to the eighth aspect, as described above, when the polishing position command points are accurately and evenly arranged on the curved surface, the uniformity is maintained when it is difficult if the interval is not very small. By specifying the priority order of the locations, it is necessary to place the highest priority on the center line parallel to the scanning direction in the scanning lens. However, it is possible to suppress defects in optical functions due to such inhomogeneities as much as possible. .
[0043]
As described above, the invention according to claim 9 is most effective in correcting the polishing position command point on the basis of the tool contact area since the nonuniformity of the polishing position command point is not completely avoided. Can be corrected.
[0044]
As described above, when the invention according to claim 10 is used for evaluating the undulation amplitude and removing the undulation, it is necessary to make the numerical value range at least, but the number of polishing position command points is not limited. It is efficient in terms of shape evaluation.
[0045]
In the invention according to claim 11, as described above, the polishing position command points are evenly arranged in the length on the curved surface, so that the required removal amount at each point is simply multiplied by a certain constant to stay. It can be converted into processing machine operation such as time.
[0046]
As described above, the invention according to the twelfth aspect can convert the required removal amount into the operation of the processing machine with a simple operation, and can efficiently perform the correction processing.
[0047]
In the invention according to claim 13, as described above, the number of simultaneously controlled axes accompanying the traversing of the polishing tool can be achieved when the specified rule and the uniform arrangement of the polishing position command points can be achieved for a specific shape. It is possible to reduce the machining error associated with the mechanical motion.
[0049]
The invention according to claim 1 4, as has been described above, by its output, five-axis control and four-axis control XYAB of XYZAB keep the polishing system a constant tool attitude relative to the machining point normal, tilt The present invention can be utilized in any machining form of XYZ 3-axis control and XY 2-axis control that do not include control.
[Brief description of the drawings]
FIG. 1 is a flowchart illustrating a procedure for creating an NC program for curved surface shape modification according to the present invention.
FIG. 2 is a perspective view for explaining a specific method of procedures 2 and 3 in the NC program creation procedure of FIG. 1;
FIG. 3 is a diagram for explaining a specific method of procedures 6a and 7a according to the conventional method in the NC program creation procedure of FIG. 1;
[Figure 4] in the NC program generating procedure 1, is a diagram for explaining a procedure 5b, specific methods 6b and 7 b according to the present invention.
FIG. 5 is a diagram for explaining a difference between a polishing position command point generated by the procedure of the present invention and a position coordinate in the case of a conventional method.
FIG. 6 is a diagram showing an example of an NC program format used in the polishing system of the present invention.
FIG. 7 is a diagram showing the result of performing undulation removal processing using the polishing system of the present invention on undulations on a curved surface.
[Explanation of symbols]
DESCRIPTION OF SYMBOLS 1 Polishing tool 2 Polishing spindle 3 Curved lens metal mold 4 Rectangle for processing area designation 5 Boundary line of processing area 6 Plane orthogonal to X axis 7 Y-direction cross section curve 8 Dividing points of equal pitch on Y axis 9 Processing area Rectangular short center line for designation 10 Rectangular long center line for machining area designation 11 Short center line 9 projected on the curved surface
12 Longitudinal center line 10 projected on the curved surface
13 Division point for equally dividing the length of the curve 12 14 Y-axis direction cross section curve 15 Division point for equally dividing the length of the curve 14 16 Polishing locus according to the conventional method 17 Polishing locus according to the present invention 19 Waviness of the processed surface before polishing Sectional curve shown 20 Sectional curve showing waviness reduction effect after polishing 21 Plane passing through the dividing point 13 and orthogonal to the X axis

Claims (14)

The shape error and waviness of the surface to be processed that put the working front of the curved surface polishing step performed in the tool machine, and modified based on the shape measurement result, to reduce the shape error and waviness in curved polishing step working followed In the curved surface correction polishing system used for
A polishing command section for commanding a polishing position and a polishing path of the surface to be processed by the tool of the processing machine;
A plurality of polishing position at intervals equally dividing the tool contact path at the tool contact path on passing through the center of the processing region by the tool of the machine within the tool contact path on the processed surface, which is the predetermined A position command point calculation unit for obtaining a command point and generating a two-dimensional coordinate point group file indicating the polishing position command point in a two-dimensional plane coordinate system ;
A storage unit for storing the 2-dimensional coordinate point group file,
A shape evaluation unit for extracting the shape and waviness of the surface to be processed determined in advance and the shape error and waviness of the surface to be processed obtained by shape measurement based on the shape measurement result ;
The amount of polishing removal of the work surface necessary for correcting the shape error and waviness of the work surface extracted by the shape evaluation unit based on the shape measurement result is stored in the storage unit. A polishing amount calculation unit that calculates each position command point obtained from the dimensional coordinate point cloud file and outputs the calculated polishing removal amount to the polishing command unit as a correction value of the tool contact locus ;
A curved surface correction polishing system comprising: 2. The curved surface correction polishing system according to claim 1, further comprising means for changing the polishing removal depth in accordance with a required removal amount at each of the position command points, and any one of a tool feed speed, a tool rotation speed, and a tool pressing force. A curved surface correction polishing system characterized by changing the polishing removal depth. According to claim 1 or 2 curved modified polishing system, using the NC program in the polishing command section for processing by modifying the grinding path and the polishing position of the workpiece surface by the tool, the NC program, the polishing position curved modified polishing system characterized by comprising a format including feed speed of the tool in each row to perform a command, reciprocal feed rates, tool rotation speed, one of the command value of the polishing load. In the curved surface modified polishing system of claim 3, polishing position command point in the NC program, the contact position of the tool, formatted as described in the two-dimensional plane coordinates without offset calculation or format described by a two-dimensional plane coordinates, A curved surface correction polishing system, wherein calculation of a normal vector of a surface to be processed or a center of curvature of a tool contour at a polishing position command point is performed by an NC command value decoding unit inside the processing machine .   An NC polishing apparatus using the curved surface correction polishing system according to claim 3 and operating according to the NC program.   6. The NC polishing apparatus according to claim 5, wherein the normal control of matching the normal line of the work surface at the polishing position command point with the tool pressing direction is possible.   An NC program creation method for polishing an optical component used in the curved surface correction polishing system according to claim 3, wherein the coordinates of the polishing position command point in the NC program are expressed in a two-dimensional plane coordinate system. An NC program creation method for polishing an optical component, characterized in that the coordinate system is set parallel to a plane showing an optically effective area. A NC program generating method for optical components polishing using in claim 3 curved modified polishing systems, polishing position command point in the NC program, the rectangle representing the optically effective area length Henma other short side NC program creation for polishing optical parts, characterized by projecting a center line parallel to either one onto a curved surface and setting a tool path that passes through points that divide the obtained curve into equal lengths Method.   An NC program creation method for polishing used in the curved surface correction polishing system according to claim 4, wherein the tool position command point existing per unit area is defined as an area corresponding to a contact area of the tool on the processing surface. A polishing NC program creation method characterized by having a function of calculating a density of a tool or a tool locus and correcting a polishing removal amount at each point by a numerical value representing the density. A polishing NC program creation method used in the curved surface modification polishing system of claim 3, the spacing of the polishing position command point for generating a tool path is less than half of the wave length of the undulation to be modified An NC program creation method for polishing characterized by the above. A creation method of claim 1 curved modifications used in the polishing system NC program 2-dimensional coordinate point group files for sets a path to tool contact path adjacent becomes equal intervals, the position on the trajectory on its A method for creating a two-dimensional coordinate point group file for an NC program, characterized in that command points are set to be as evenly spaced as possible. A NC program creation method used in the curved surface modification polishing system of claim 3, polishing position command point in the NC program, a rectangular long Henma other representing the optical effective area is parallel to one of the short sides A two-dimensional coordinate point cloud file obtained by projecting a center line onto a curved surface and setting a tool path that passes through a point that divides the obtained curve into equal lengths and the corresponding polishing removal amount Is converted into any one of the reciprocal of the tool feed speed, the tool rotation speed, and the tool pressing force at each contact point by multiplying a one-dimensional numerical array representing the polishing removal amount by an arbitrary constant. An NC program creation method characterized by being used as a control command value synchronized with scanning. 4. The curved surface correction polishing system according to claim 1, wherein when the linear motion axis is XYZ of three orthogonal axes, the rotational motion around the X axis is A axis, and the rotation around the Y axis is B axis, the polishing position command point for generating, based on the normal vector that put on each point, the value of the a-axis or the B-axis component sets the point where the constant, generating a tool path through these An NC program creation method characterized by: 2. The curved surface corrected polishing system according to claim 1, wherein the polishing removal amount calculation unit that outputs a necessary polishing removal amount at each point has a function of outputting a normal direction component at a processing point and a component orthogonal to the planar coordinate system. Curved surface polishing system characterized by