JP2005088148A - Polishing method, die or optical element or optical scanning unit - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a polishing method for polishing an optical element or a die for forming the optical element by correcting shape errors of the surface to be polished, and further to provide the die or the optical element or an optical scanning unit. <P>SOLUTION: A polishing apparatus 1 polishes a workpiece P so as to give a curved surface by controlling a polishing tool 2, which is attached to a spindle and has a specified radius of curvature, while applying a specified load to the workpiece according to a polishing control command and turning the tool at a specified peripheral speed. The polishing apparatus 1 acquires the removal efficiency variation of the polishing tool 2 for at least one of the polishing time or the moving distance of the polishing tool 2 from the polishing results in the preceding polishing process for the workpiece, the removal efficiency of the polishing tool 2 being defined as the removed depth of the workpiece P by the polishing tool 2 per a unit time. Then, the polishing apparatus 1 generates a polishing control command value in the following polishing process from the shape errors to be removed and the removal efficiency variation. As a result, the polishing process for giving a high shape accuracy is carried out at a reduced number of repetition. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a polishing method, a mold, an optical element, or a scanning optical unit, and more specifically, a polishing method, a mold for polishing an optical element or a mold for molding an optical element by correcting a shape error of a processing surface, and a mold The present invention relates to a mold, an optical element, or a scanning optical unit.

  In recent years, in electrophotographic image forming apparatuses such as copying machines and laser printers, the beam diameter has become smaller and the scanning lens accuracy has become very high as laser scanning has become more dense and colored. It is coming.

  Conventionally, as a processing method for creating an optical element having a free-form surface with high accuracy, ultra-precision cutting represented by diamond cutting, ultra-precision grinding mainly using a diamond grindstone or a CBN grindstone has been known. Then, a so-called shape creation polishing method in which a small diameter polishing tool is made to act in a substantially point contact state and shape creation is performed by controlling the residence time has been frequently used.

  In these methods, the surface shape is created by scanning the entire contact surface of a sufficiently small tool contact area, such as several hundred to several thousandths, as compared with the area of the work surface. In these construction methods, when the tool state, for example, the shape of the tool cutting edge or the removal efficiency, changes during the scanning of the tool, a shape error is directly generated. There was a problem that it became an obstruction factor for shape processing.

  Therefore, conventionally, an NC machining apparatus has been proposed that corrects a machining command by obtaining a shape error in a plurality of machining operations and subtracting the average component from the previous command (see Patent Document 1).

  In this conventional technique, correction by adding or subtracting an error component from an ideal shape and reflecting it in the NC data is generally performed except for an average of errors of a plurality of machining operations. In the construction method of the principle of creating a shape by transferring the tool trajectory such as precision grinding or cutting, it is conventional that the accuracy can be relatively improved by using the above method based on the tool trajectory used in the pre-processing. It has been confirmed from.

  However, the amount of deviation from the ideal shape is treated as a shape error in the pressure transfer type shape creation polishing based on the pre-processed surface. Since there is no equivalent to the above method, sufficient accuracy cannot be obtained by the above-described prior art method.

  That is, shape creation polishing is a method for generating a machining command from a shape error after the previous machining.

  As a processing error suppression method in shape creation polishing under such conditions, for example, there are a curved surface polishing system and a lens mold polishing method previously proposed by the present applicant (see Patent Document 2).

  In this prior art, deterioration of the removal efficiency of the polishing tool is determined in-process from the color of the tool surface, and the polishing conditions are corrected by the amount of change in the removal efficiency.

JP-A-9-57621 JP 2003-39296 A

  However, in the conventional technique described in Patent Document 2, when the fluctuation of the polishing tool removal efficiency is affected not only by the machining time but also by the curvature radius of the surface to be machined, the removal is also included. It is necessary to prepare a database for estimating the efficiency. If this database is insufficient, there is a possibility that a sufficient effect cannot be obtained, and improvement is necessary.

  Therefore, the present invention accurately acquires the removal efficiency variation of the polishing tool from the result of the previous shape creation polishing process, corrects the removal efficiency variation, and greatly reduces the processing error of the shape creation polishing by a simple method. An object of the present invention is to provide a highly accurate polishing method, a mold, an optical element, or a scanning optical unit that can be reduced.

  Specifically, according to the first aspect of the present invention, a polishing tool having a predetermined radius of curvature attached to a rotating shaft is rotated at a constant tool peripheral speed around the rotating shaft while applying a constant load according to a polishing control command. However, when polishing the workpiece into a curved surface, the removal depth of the workpiece per unit time by the polishing tool is defined as the removal efficiency of the polishing tool, and polishing is performed from the previous polishing result for the workpiece. By obtaining the removal efficiency fluctuation of the polishing tool with respect to at least one of the time or the scanning distance of the grinding tool, and generating a polishing control command value in the next polishing process from the shape error amount to be removed and the removal efficiency fluctuation value An object of the present invention is to provide a shape creation polishing method capable of performing polishing processing with high shape accuracy with a small number of repeated processing.

  The invention according to claim 2 is configured such that the polishing control command value is configured by one or a combination of two or more of the dwell time of the polishing tool, the polishing load, and the tool peripheral speed. When the sharpness deteriorates over time, the polishing control command value increases the residence time and increases the machining time, thereby preventing sharpness deterioration by increasing the tool peripheral speed and sacrificing the machining time. Therefore, it is an object of the present invention to provide a shape-generating polishing method that achieves both high processing efficiency and high-precision processing by using high-precision polishing processing and using an appropriate combination of dwell time, polishing load, and tool peripheral speed.

  According to the third aspect of the present invention, the removal efficiency variation of the polishing tool is given by equation (1) when ΔC_out is the change in curvature of the surface to be processed caused by polishing and ΔC_in is the amount of change in curvature as the polishing control command. Even if the measurement data does not wait for a reference in the depth direction, the actual machining amount corresponding to the machining depth is acquired and special measurement is performed. It is another object of the present invention to provide a shape creation polishing method that can perform high-precision processing only by providing a data processing procedure.

  In the invention according to claim 4, when the fluctuation of the removal efficiency of the polishing tool is expressed by the equation (2) when ΔW_out is the change in the waviness amplitude of the work surface caused by the polishing, and ΔW_in is the waviness amplitude as the polishing control command. Even if the measurement data does not wait for a reference in the depth direction, the actual machining amount corresponding to the machining depth is acquired and special measurement is performed. Therefore, it is an object of the present invention to provide a shape creation polishing method capable of performing high-precision processing only by providing a data processing procedure.

  According to the fifth aspect of the present invention, the removal efficiency variation of the polishing tool is given by equation (3), where d_out is the removal depth of the work surface generated by polishing and d_in is the depth of the polishing control command. By using the coefficient N, it is possible to reliably and accurately remove the polishing amount with the removal depth when the optical surface can be extended in the height direction like the edge surface. Grasping efficiency fluctuations, grasping high-frequency changes that change removal efficiency also affects the scanning direction of the polishing tool, and highly accurate when traversing the polishing tool in the main scanning direction, square workpieces, etc. An object of the present invention is to provide a shape creation polishing method capable of performing the above-described processing.

  The invention according to claim 6 acquires the removal depth of the surface to be processed as a point cloud when the surface shape data of the surface to be processed before and after the processing is expressed by XYZ coordinate values. Probe scan for shape measurement by data interpolation by using the orthogonal polynomial or moving average method to determine the difference in Z value at any XY coordinate point on the work surface before and after machining and using it as the removal depth Even if the data is rough and the number of data points is small, accurate removal depth evaluation is performed, and a shape can be created with high accuracy by freely tracking an arbitrary shape to an arbitrary spatial wavelength with an orthogonal polynomial. The object is to provide a polishing method.

  The invention according to claim 7 is the shape creation polishing method, wherein the polishing area of the work surface can be represented by a rectangle, the polishing tool is scanned in the short direction of the rectangle, and the short direction is scanned. The operation of moving in a small amount in the longitudinal direction is repeated to perform polishing, and the state of removal efficiency change is determined by the coefficient M, the coefficient L, the shape creation polishing method according to any one of claims 3 to 5. By obtaining as a value of any one of the coefficients N and setting the change state with respect to the position in the longitudinal direction as the function g (x) given by the equation (5), the removal efficiency deterioration and the processing error are immediately combined to determine the polishing control command value. It is an object of the present invention to provide a shape creation polishing method capable of acquiring correction data and creating NC data more easily and performing machining more easily and with high accuracy.

  The invention according to claim 8 eliminates the function g (x) by setting the order to a high degree within a reproducible range from a plurality of machining results, with the function g (x) being a polynomial represented by the equation (6). To provide a shape creation polishing method that corrects not only the linear regression (linear) component but also higher-order terms for efficiency deterioration, and can perform curved surface processing with higher shape accuracy with fewer polishing. It is aimed.

  According to a ninth aspect of the present invention, a mold for molding an optical element is polished by the shape creation polishing method according to any one of the first to eighth aspects, and the optical element is defined by the first to the third aspects. A high-efficiency and high-precision mold and a high-performance optical element at low cost are provided by using a mold that has been polished by the shape creation polishing method according to any one of Items 8. The purpose is that.

  The invention according to claim 10 is an optical element of a scanning optical unit that irradiates a uniformly charged photoconductor using a plurality of optical elements with a laser beam modulated by image data and emitted from a laser light source. It is an object of the present invention to provide a high-performance scanning optical unit at low cost by molding using a mold polished by the shape creation polishing method according to any one of claims 1 to 8.

  The polishing method according to the first aspect of the present invention is to rotate a polishing tool having a predetermined radius of curvature attached to a rotating shaft around the rotating shaft at a constant tool peripheral speed while applying a constant load according to a polishing control command. In a polishing method for controlling and polishing a workpiece into a curved surface, the removal depth of the workpiece per unit time by the polishing tool is defined as the removal efficiency of the polishing tool, and the previous polishing for the workpiece is performed. From the result, the removal efficiency fluctuation of the polishing tool with respect to at least one of the polishing time or the scanning distance of the polishing tool is acquired, and the polishing control command value in the next polishing process is determined from the shape error amount to be removed and the removal efficiency fluctuation value. The above-mentioned purpose is achieved by generating.

  In this case, for example, as described in claim 2, the polishing control command value may be configured by one or a combination of two or more of the dwell time, polishing load, and tool peripheral speed of the polishing tool. Good.

  For example, as described in claim 3, the removal efficiency variation of the polishing tool is defined as ΔC_out for a change in curvature of the surface to be processed caused by the polishing, and ΔC_in for a change in curvature as a polishing control command. Sometimes, it may be indicated by the coefficient M given by the above equation (1).

  Further, for example, as described in claim 4, the removal efficiency fluctuation of the polishing tool is expressed as follows: ΔW_out is a change in the waviness amplitude of the surface to be processed caused by the polishing, and ΔW_in is a waviness amplitude as a polishing control command. Then, it may be indicated by the coefficient L given by the above equation (2).

  Further, for example, as described in claim 5, the removal efficiency fluctuation of the polishing tool is determined when d_out is a removal depth of the work surface generated by the polishing and d_in is a depth of a polishing control command. The coefficient N may be given by the above equation (3).

  Furthermore, for example, as described in claim 6, the removal depth of the surface to be processed is acquired by a point cloud when surface shape data of the surface to be processed before and after processing is expressed by XYZ coordinate values. Even with the orthogonal polynomial or the moving average method of the above formula (4), even the removal depth generated when machining is performed by obtaining the difference of Z values at arbitrary XY coordinate points on the machining surface before and after machining. Good.

  Further, for example, as described in claim 7, in the shape creation polishing method, the polishing area of the work surface can be represented by a rectangle, the polishing tool is scanned in the short direction of the rectangle, and the short direction When the above scanning is performed, an operation of moving a small amount in the longitudinal direction of the rectangle is repeatedly performed to perform polishing, and the state of the removal efficiency change is the shape according to any one of claims 3 to 5. The function g (x) given by the above equation (5) may be obtained as a value of any one of the coefficient M, the coefficient L, and the coefficient N by the creative polishing method, and the change state with respect to the position in the longitudinal direction.

  Further, for example, as described in claim 8, the function g (x) is a polynomial represented by the above equation (6), and the degree thereof is high within a reproducible range from a plurality of machining results. The order may be set.

  A mold or an optical element according to a ninth aspect of the present invention is a mold for molding an optical element or an optical element molded using the mold, and the mold is as defined in any one of the first to eighth aspects. It is polished by the shape creation polishing method according to any one of the above, and the optical element is molded by using a mold polished by the shape creation polishing method according to any one of claims 1 to 8. Has achieved the above objectives.

  According to a tenth aspect of the present invention, there is provided a scanning optical unit that irradiates a uniformly charged photosensitive member with a laser beam modulated by image data and emitted from a laser light source using a plurality of optical elements. The said optical element has achieved the said objective by shape | molding using the metal mold | die grind | polished by the shape creation grinding | polishing method in any one of Claim 1-8.

  According to the polishing method of the first aspect of the present invention, the polishing tool having a predetermined radius of curvature attached to the rotating shaft is rotated around the rotating shaft at a constant tool peripheral speed while applying a constant load according to the polishing control command. However, when polishing the workpiece into a curved surface, the removal depth of the workpiece per unit time by the polishing tool is defined as the removal efficiency of the polishing tool, and polishing is performed from the previous polishing result for the workpiece. Since the removal efficiency variation of the polishing tool with respect to at least one of the time or the scanning distance of the polishing tool is acquired, and the polishing control command value in the next polishing process is generated from the shape error amount to be removed and the removal efficiency variation value, Polishing processing with high shape accuracy can be performed with a small number of repeated processing.

  According to the polishing method of the second aspect of the present invention, the polishing control command value is configured by one or a combination of two or more of the dwell time of the polishing tool, the polishing load, and the tool peripheral speed. When the sharpness of the polishing tool deteriorates over time, the grinding control command value prevents the sharpness deterioration by increasing the tool peripheral speed by increasing the residence time and increasing the processing time. Without sacrificing time, the polishing can be performed with high accuracy, and the dwell time, polishing load, and tool peripheral speed can be used in appropriate combination to achieve both processing efficiency and high accuracy processing.

  According to the polishing method of the third aspect of the present invention, when the removal efficiency variation of the polishing tool is expressed as ΔC_out for the change in curvature of the work surface caused by the polishing, and ΔC_in for the amount of change in curvature as the polishing control command, Since it is assumed to be indicated by the coefficient M given in (1), even if the measurement data does not wait for the reference in the depth direction, the actual machining amount corresponding to the machining depth can be acquired. High-precision processing can be performed only by providing a data processing procedure without performing a simple measurement.

  According to the polishing method of claim 4, when the removal efficiency variation of the polishing tool is ΔW_out for the change in the waviness amplitude of the work surface caused by the polishing, and the waviness amplitude as the polishing control command is ΔW_in, Since it is assumed to be indicated by the coefficient L given by the equation (2), even if the measurement data does not wait for the reference in the depth direction, the actual machining amount corresponding to the machining depth can be acquired, High-precision processing can be performed only by providing a data processing procedure without performing special measurement.

  According to the polishing method of the fifth aspect of the present invention, when the removal efficiency variation of the polishing tool is defined as d_out as the removal depth of the work surface generated by the polishing and d_in as the depth of the polishing control command, Since it is assumed to be expressed by the coefficient N given in 3), when the reference in the height direction such as the edge surface can be taken for the extension of the optical surface, it is possible to reliably and accurately grasp the polishing amount by the removal depth. It is possible to grasp fluctuations in removal efficiency with high accuracy, and to grasp changes in high frequency such that the change in removal efficiency has an effect on the scanning direction of the polishing tool, and when the polishing tool is traversed in the main scanning direction or square High-precision machining can be performed on workpieces and the like.

  According to the polishing method of the invention described in claim 6, the removal depth of the work surface is acquired by a point cloud when the surface shape data of the work surface before and after the processing is expressed by XYZ coordinate values, The removal depth generated when machining is performed by obtaining the Z value difference at an arbitrary XY coordinate point on the work surface before and after machining by the orthogonal polynomial or moving average method of equation (4). Even if the shape measurement probe scan is rough and the number of data points is small, accurate removal depth evaluation can be performed, and any shape can be freely followed by any spatial wavelength with an orthogonal polynomial to achieve high accuracy. Processing can be performed.

  According to the polishing method of the invention described in claim 7, the shape creation polishing method is such that the polishing area of the work surface can be represented by a rectangle, the polishing tool is scanned in the short direction of the rectangle, and the short direction is scanned. If it carries out, the operation | movement which moves a small amount in the longitudinal direction of the said rectangle will be performed repeatedly, polishing processing will be implemented, and the state of a removal efficiency change will be a coefficient with the shape creation polishing method in any one of Claim 3-5 Since it is obtained as a value of any one of M, coefficient L, and coefficient N and the change state with respect to the position in the longitudinal direction is a function g (x) given by equation (5), polishing is performed by immediately combining removal efficiency deterioration and processing error. Correction data for the control command value can be acquired, NC data can be created more easily, and machining can be performed more easily and with high accuracy.

  According to the polishing method of the invention described in claim 8, the function g (x) is set to a polynomial represented by the equation (6), and the order is set to a high order within a reproducible range from a plurality of processing results. Therefore, the deterioration of the removal efficiency can be corrected not only to the linear regression (linear) component but also to higher-order terms, and curved surface processing with higher shape accuracy can be performed with fewer times of polishing.

  According to the mold or the optical element of the invention described in claim 9, the mold for molding the optical element is polished by the shape creation polishing method according to any one of claims 1 to 8, and optical Since the element is formed by using a mold polished by the shape creation polishing method according to any one of claims 1 to 8, a high-efficiency and high-precision mold and a low cost are high. A performance optical element can be provided.

  According to the scanning optical unit of the invention described in claim 10, scanning optics for irradiating a uniformly charged photosensitive member with a laser beam modulated by image data and emitted from a laser light source using a plurality of optical elements. Since the optical element of the unit is formed using the mold polished by the shape creation polishing method according to any one of claims 1 to 8, a high-performance scanning optical unit is provided at low cost. be able to.

  Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. In addition, since the Example described below is a suitable Example of this invention, various technically preferable restrictions are attached | subjected, However, The scope of the present invention limits this invention especially in the following description. As long as there is no description of the effect, it is not restricted to these aspects.

  FIGS. 1 and 12 are views showing a first embodiment of a polishing method, mold or optical element or scanning optical unit of the present invention, and FIG. 1 shows a polishing method, mold or optical element or scanning of the present invention. It is a principal part front view of polish device 1 to which the 1st example of an optical unit is applied.

  In FIG. 1, a polishing apparatus 1 has a spindle (rotation shaft) (not shown) fixed to the tip of a spindle head (not shown) that is controlled to move in the X-axis, Y-axis, and Z-axis directions. Tool 2 is attached. The polishing tool 2 is formed in a substantially tire shape or a spherical shape, and is driven to rotate clockwise in FIG. 1 at a predetermined rotational speed (a constant tool peripheral speed) by a spindle. The polishing apparatus 1 polishes the workpiece P by moving the polishing tool 2 along the processing surface of the workpiece (workpiece) P while rotating the polishing tool 2 by the spindle.

  The workpiece P is generally placed on a table (not shown) that is movable in the X-axis, Y-axis, and Z-axis directions of the polishing apparatus 1, and the workpiece P is, for example, a laser printer. The optical element used in the scanning optical system, for example, a plastic lens mold.

  Now, let the longitudinal direction of the workpiece P, which is a substantially rectangular lens mold, be the main scanning direction, the short direction is the sub-scanning direction, and the workpiece P, which is a lens mold, as shown in FIG. It is clamped on the table of the polishing apparatus 1 in such a posture that the main scanning direction is parallel to the X axis and the sub scanning direction is parallel to the Y axis.

  That is, the polishing tool 2 is a tire-shaped or spherical-shaped tool having an arc cross section, is rotationally driven by a tool spindle parallel to the XY plane, and further has a constant load in the Z-axis direction that is the cutting direction (indicated by an arrow in FIG. 1). Is pressed against the optical molding surface Pa.

  The workpiece P that is a lens mold is stainless steel, and the optical molding surface Pa is constituted by electroless Ni plating.

  The tip of a cleaning brush (cleaning means) 3 is pressed against the polishing tool 2, and the brush bristles 5 are implanted in the brush holding part 4 of the cleaning brush 3.

  As shown in FIG. 1, the cleaning brush 3 is located at a position displaced in the rotational direction of about 45 degrees from the topmost part of the polishing tool 2 with respect to the rotational direction of the polishing tool 2 (clockwise in FIG. 1). 2 is in contact with 2. The cleaning brush 4 is for suppressing the quality of the surface of the polishing tool 2 from being altered by the accumulation of polishing powder.

  The polishing apparatus 1 suppresses wear of the polishing tool 2 during long-time polishing by supplying processing oil 7 as a lubricating liquid in a properly dropped state from a liquid supply tube 6.

  The polishing tool 2 is a material obtained by kneading urethane resin and wood powder, and the polishing tool 2 itself does not have abrasive grains. Therefore, in the polishing apparatus 1, when the workpiece P is polished with the polishing tool 2, the diamond paste 8 is applied to the entire surface of the optical molding surface Pa in advance, and the abrasive particles are supplied by being rolled together with the scanning of the polishing tool 2. It has become a form.

  The polishing apparatus 1 performs residence time control for scanning the polishing tool 2. In this dwell time control, the height distribution data of the corrected machining amount is converted into the tool dwell time based on the following equation (7) which is a Preston equation.

h = k · P · V · T (7)
In Equation (7), h is the polishing removal depth, k is a proportional constant, P is the polishing pressure, V is the tool speed, and T is the tool residence time.

  Next, the operation of this embodiment will be described. The polishing apparatus 1 of the present embodiment is moved along the optical molding surface Pa of the workpiece P while being attached to the spindle and rotated to polish the workpiece P. As a result of the previous shape creation polishing processing Therefore, the sharpness variation of the polishing tool 2 is accurately grasped, and the sharpness variation of the polishing tool 2 is corrected to easily and greatly reduce the processing error of the shape creation polishing.

  The polishing apparatus 1 is a constant load control in which the polishing pressure P and the tool peripheral speed V are constant and the pressing force is constant. However, when the polishing amount is considered as a removal volume, there is no problem even if it is handled as a constant pressure.

  Then, in the polishing apparatus 1, as shown in the tool path 10 shown in FIG. 1, the polishing is performed by repeating the fine movement of the Y direction scanning and the X direction scanning, and the direction of the polishing load and the normal vector at the processing point always match. As described above, simultaneous 4-axis control of XYZAB is given.

  Now, as shown in FIG. 2, when the polishing apparatus 1 scans the polishing tool 2 in the order of Y-direction scanning and X-direction scanning, the optical effective area Pga and the polishing area Pha on the optical molding surface Pa are as shown in FIG. 2 and the turning operation portion of the polishing tool 2 becomes an incomplete polishing region. Therefore, the polishing region Pha is slightly increased so that the turning operation is outside the optically effective region Pga. Yes.

  In the polishing apparatus 1, the spindle that is the tool rotation axis is not parallel to the Y axis (sub-scanning direction) and has a specific inclination. This is due to the cutting trace in the main scanning direction (X direction). This is to increase the removal effect. The polishing tool 2 is a tool path 10 that scans in the Y direction, then moves (pick feeds) a small amount in the X direction, and repeats scanning in the Y direction again.

  As shown in FIG. 3, the optical molding surface Pa of the workpiece P is represented by a main scanning direction sectional curve Pt and a sub-scanning direction sectional curve Qt, and includes an aspherical surface including even odd-numbered orders as shown in FIG. Expressed as an expression. 3 and 4, the curved surface is defined by defining how the radius of curvature Rs of the sub-scanning direction sectional curve Qt in contact with the curve of the optical molding surface Pa changes in the main scanning direction.

  When the center of the cross section curve Pt in the main scanning direction is X = 0, the X direction distribution of the radius of curvature Rs is given by the following equation (8), and the curvature Cs that is the reciprocal of the radius of curvature Rs is obtained. .

  Here, the procedure for correcting the shape efficiently and with high accuracy according to the mold design shape given by Expression (8) will be described below.

  Now, as an optical molding surface Pa that is a processed surface of the workpiece P before polishing, the optical molding surface Pa is finished by shape creation processing by diamond cutting, and the evaluation of the sub-scanning cross-sectional shape is shown in FIG. As shown in FIG. 5, a plurality of sub-scanning cross-sectional curves Qt are obtained by shape measurement, an approximate arc is obtained for each sub-scanning cross-sectional curve Qt, and the curvature of the approximate arc is the optical processing surface Pa, which is the actual machining surface. Of curvature Cs. A sub-scanning curvature error ΔCs (ΔCs = actual machining surface curvature Cs−design value curvature Cs), which is the difference between the actual machining surface curvature Cs and the design value curvature Cs, is obtained. This sub-scanning curvature error ΔCs is obtained by the number of measured sub-scanning sectional curves Qt.

  In FIG. 5, the X-direction distribution L1 of the sub-scanning curvature error ΔCs before polishing and the X-direction distribution L2 of the sub-scanning curvature error ΔCs after the first polishing are as shown in the figure. In order to correct the X-direction distribution L1 of the error ΔCs, the X-direction distribution L1 of the sub-scanning curvature error ΔCs before polishing is converted into a residence time distribution of the polishing tool 2, and the first correction polishing is performed. The result of the first corrected polishing is the X-direction distribution L2 of the sub-scanning curvature error ΔCs after the first polishing.

  In the conventional polishing method, the second polishing is performed based on the X-direction distribution L2 of the sub-scanning curvature error ΔCs after the first polishing, and the third floor is polished based on the residual. The machining operation is repeatedly performed to gradually reduce the machining error.

  However, as a result of investigating the cause of the error, it has been found that the difference in polishing in the polishing method is mainly due to fluctuations in the removal efficiency of the polishing tool 2 over time.

  The removal efficiency of the polishing tool 2 corresponds to the proportionality constant K of the Preston equation of the above equation (7).

  Therefore, the polishing apparatus 1 of the present embodiment evaluates the fluctuation of the proportional constant K that has occurred in the actual polishing process, and corrects the fluctuation effect of the proportional constant K in the next polishing control command so that it can be accurately performed in a small number of times. Correct shape correction.

  The change rate M of the proportionality constant K is shown as a curve M in FIG. 6 and, as shown in the above formula (1), the curvature change amount ΔC_out of the optical molding surface Pa actually obtained by polishing and the polishing. This is a ratio with the curvature correction amount ΔC_in as the control command value.

  The curvature correction amount ΔC_in as the polishing control command value corresponds to the X-direction distribution L1 of the sub-scanning curvature error ΔCs before polishing, and the curvature change amount ΔC_out actually obtained by polishing is the sub-scanning curvature before polishing. This corresponds to the difference between the X-direction distribution L1 of the error ΔCs and the X-direction distribution L2 of the sub-scanning curvature ΔCs after the first polishing.

  When the machining progresses according to the polishing control command, the change rate M of the proportional constant K becomes 1.0. If the machining is excessive, the change rate M exceeds 1.0, and if the machining is insufficient, the change rate M Since M takes a value less than 1.0, it is ideal that the rate of change M does not vary at 1.0.

  The polishing process is performed from the minus side of the X axis to the plus side. In the initial stage of the process, the curve M does not match 1.0 even in the vicinity of X = −100 because of the proportionality constant K of about 10%. This is because a misunderstanding has occurred.

  In FIG. 6, the curve M has a undulation with a gradual decrease trend, and as a change of the proportionality constant K, it cannot be expected until the undulation amplitude is reproduced. In FIG. 6, correction information M_line (x) indicated by a straight line Mt is used.

  When the correction information M_line (x) is used to determine the removal efficiency deterioration at the main scanning position X and the correction is given, the corrected polishing command L21 shown in FIG. 7 is obtained. This polishing correction command L21 is the first in FIG. The value of the X-direction distribution L2 of the sub-scanning curvature error ΔCs after polishing is divided by the value obtained from the correction information M_line (x). In FIG. 7, the correction command L3 is the conventional second polishing command of FIG.

  The result of performing the second polishing based on this polishing command L21 is shown in FIG. 8, and the sub-scanning curvature error ΔCs is ± 1.0e-5 on the front surface of the optical molding surface Pa, which is the processing surface. If the workpiece P has the same shape and dimensions when the other workpiece P is subsequently processed, the polishing control command value is corrected using the correction information M_line (x). The first polishing can be carried out.

  Further, when the actual processing amount by polishing and the polishing control command value are evaluated by the waviness amplitude of the sub-scanning sectional curve, as shown in FIG. 9, if the waviness amplitude before polishing is ΔW_in, the waviness amplitude generated by the polishing The amount of decrease is as indicated by ΔW_out in FIG.

  In this case, the coefficient L indicated by the above formula (2) is defined as the sharpness variation of the polishing tool 2.

  In this case, both ends of the cross-section curve are excluded because of large variations in amplitude evaluation.

  Further, when the actual processing amount and the command value by polishing are directly evaluated by the removal depth, as shown in FIG. 12 which is an enlarged view in the circle of FIGS. 11 and 11, the workpiece P generated by polishing is shown. If the removal depth of the optical molding surface Pa is d_out and the depth of the polishing control command is d_in, the coefficient N shown in the above equation (3) is defined as the sharpness variation of the polishing tool 2.

  In this case, when the reference Hp for depth evaluation such as the unprocessed polished area of the workpiece P cannot be obtained, the height of the workpiece P shown in FIG. By accurately evaluating, the removal depth d_out generated by polishing can be acquired.

  Further, the removal depth of the optical molding surface Pa of the workpiece P generated by the polishing is d_out, and the surface shape data of the optical molding surface Pa of the workpiece P before and after the processing is expressed in XYZ coordinate values. Acquired by a group, and by obtaining the difference of Z values at arbitrary XY coordinate points on the surface before and after processing by the orthogonal polynomial or moving average method shown by the above equation (4).

  Furthermore, when the polishing area of the optical molding surface Pa of the workpiece P is represented by a rectangle, scanning is performed with the polishing tool 2 in the short direction, and the operation is performed by repeatedly performing a slight movement in the longitudinal direction, The state of sharpness change is obtained as the value of the above formulas (3) to (5), and the change state with respect to the longitudinal position is represented by any one of the above formulas (5).

  In addition, g (x) relating to this is expressed by the polynomial in the above formula (6), and the order is set to a high order within a reproducible range from a plurality of processing results.

  Therefore, the polishing apparatus 1 can be reduced in size, and a workpiece such as a mold can be polished with high accuracy.

  When a plastic lens as an optical element used in a scanning optical system of a laser printer is molded using the mold thus polished, a plastic lens as a highly accurate optical element can be molded.

  In addition, by manufacturing the scanning optical unit using the plastic lens thus molded, a high-quality scanning optical unit can be configured, and a laser printer that forms a high-quality image can be manufactured.

  The invention made by the present inventor has been specifically described based on the preferred embodiments. However, the present invention is not limited to the above, and various modifications can be made without departing from the scope of the invention. Needless to say.

  The present invention can be applied to a polishing method for a mold such as an fθ lens of a laser printer or a digital copying apparatus, a mold, an optical element, or a scanning optical unit.

BRIEF DESCRIPTION OF THE DRAWINGS The principal part perspective view of the grinding | polishing apparatus to which one Embodiment of the grinding | polishing method of this invention, the metal mold | die for optical elements, an optical element, and a scanning optical unit is applied. The figure which shows the relationship between the optical effective area | region and polishing area | region on the optical molding surface of the to-be-processed object of FIG. The figure which shows the detail of the shape of the optical shaping | molding surface of a to-be-processed object with the main scanning direction cross section curve and the subscanning direction cross section curve. FIG. 4 is a detailed view of the radius of curvature of the main scanning direction sectional curve, the sub-scanning direction sectional curve, and the sub-scanning direction sectional curve of FIG. 3. The figure which shows the X direction distribution of the subscanning curvature error before grinding | polishing, and the X direction distribution of the subscanning curvature error after the 1st grinding | polishing. The figure which shows the rate of change of the proportionality constant of Preston's formula. 6 is a diagram illustrating a polishing command in which the X-direction distribution value of the sub-scanning curvature error after the first polishing in FIG. 5 is corrected with the correction information in FIG. 6. The figure which shows the sub-scanning curvature error which performed 2nd grinding | polishing based on the grinding | polishing command of FIG. The figure which shows the waviness amplitude before grinding | polishing in the case of evaluating the actual process amount and command value by grinding | polishing by the waviness amplitude of a subscanning cross-section curve. The figure which shows the amount of reduction | decrease of an amplitude when waviness amplitude before grinding | polishing of FIG. 9 is grind | polished. The figure which shows the to-be-processed object and its processed surface in the case of evaluating the actual processing amount and command value by grinding | polishing directly by the removal depth. The enlarged view in the circle of FIG.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Polishing apparatus 2 Polishing tool 3 Cleaning brush 4 Brush holding part 5 Brush hair 6 Liquid supply tube 7 Processing oil 8 Diamond paste P Workpiece Pa Optical molding surface

Claims (10)

  A polishing tool with a predetermined radius of curvature attached to a rotating shaft is controlled while rotating at a constant tool peripheral speed around the rotating shaft while applying a constant load in accordance with a polishing control command, thereby polishing the workpiece into a curved surface. In the polishing method to be processed, the removal depth of the workpiece per unit time by the polishing tool is defined as the removal efficiency of the polishing tool, and the polishing time or the scanning distance of the polishing tool from the previous polishing result for the workpiece A shape generating polishing method characterized in that a removal efficiency fluctuation of the polishing tool for at least one of the two is acquired, and a polishing control command value in a next polishing process is generated from a shape error amount to be removed and the removal efficiency fluctuation value.   2. The shape generating polishing method according to claim 1, wherein the polishing control command value is configured by one or a combination of two or more of a residence time, a polishing load, and a tool peripheral speed of the polishing tool. The removal efficiency variation of the polishing tool is a coefficient M given by the following equation (1), where ΔC_out is a change in curvature of the work surface caused by the polishing and ΔC_in is a change in curvature as a polishing control command.
M = ΔC_out / ΔC_in (1)
The shape creation polishing method according to claim 1, wherein The removal efficiency variation of the polishing tool is a coefficient L given by the following equation (2), where ΔW_out is a change in the waviness amplitude of the work surface caused by the polishing and ΔW_in is a waviness amplitude as a polishing control command.
L = ΔW_out / ΔW_in (2)
The shape creation polishing method according to claim 1, wherein The removal efficiency variation of the polishing tool is a coefficient N given by the following equation (3), where d_out is the removal depth of the work surface generated by the polishing and d_in is the depth of the polishing control command.
N = d_out / d_in (3)
The shape creation polishing method according to claim 1, wherein The removal depth of the surface to be processed is obtained as a point cloud when the surface shape data of the surface to be processed before and after processing is expressed by XYZ coordinate values, and is an orthogonal polynomial of the following equation (4)

6. The shape creation according to claim 5, which is a removal depth generated when machining is performed by obtaining a difference of Z values at arbitrary XY coordinate points on a machining surface before and after machining by a moving average method. Polishing method. In the shape creation polishing method, the polishing area of the surface to be processed can be represented by a rectangle, the polishing tool is scanned in the short direction of the rectangle, and the scan in the short direction is performed. The operation of moving a small amount is repeatedly performed to perform polishing, and the state of the removal efficiency change is determined by the shape creation polishing method according to any one of claims 3 to 5 with a coefficient M, a coefficient L, and a coefficient N. A function g (x) which is obtained as any value and the change state with respect to the position in the longitudinal direction is given by the following equation (5)
M or L or N = g (x) (5)
A shape creation polishing method, characterized by: The function g (x) is a polynomial represented by the following equation (6).

The shape creation polishing method according to claim 7, wherein the order is set to a high order within a reproducible range from a plurality of processing results.   A mold for molding an optical element or an optical element molded using the mold, wherein the mold is polished by the shape creation polishing method according to any one of claims 1 to 8, 9. A mold or an optical element, wherein the optical element is molded using a mold polished by the shape creation polishing method according to any one of claims 1 to 8. A scanning optical unit that irradiates a uniformly charged photoconductor using a plurality of optical elements with a laser beam modulated by image data and emitted from a laser light source. A scanning optical unit, which is molded using a mold polished by the shape creation polishing method according to claim 8.

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