JP5434001B2 - Polishing method, polishing condition calculation method and polishing apparatus - Google Patents

Description

  The present invention relates to a polishing method, a polishing condition calculation method, and a polishing apparatus.

  When performing mirror polishing to finish the surface (surface to be polished) of an object to be polished such as an optical element, surface roughness of the surface of the object to be polished and waviness that significantly reduces the performance of the object to be polished For the purpose of smoothing cracks and the like, a polishing method and a polishing apparatus for polishing using a polishing tool having a spherical polishing member are known (see, for example, Patent Document 1).

  When performing the above-described polishing, the polishing member is pressed against the surface to be polished, and is linearly moved between the both ends of the surface to be polished along the surface to be polished in the main scanning direction. While moving in the sub-scanning direction perpendicular to the main scanning direction by a predetermined pitch, polishing is performed following the surface to be polished, and polishing is performed while pressing and scanning the polishing member so that the surface to be polished has a desired shape. I do.

In such a polishing method and polishing apparatus, due to the shape of the polishing member, undulation occurs on the surface to be polished when the polishing member is pressed against the surface to be polished and polishing is performed. As a method for reducing this waviness, a method of polishing by reducing the size of the polishing member or the above-mentioned predetermined pitch value is well known.
JP 2007-144568 A

  However, although the waviness can be reduced by reducing the value of the predetermined pitch in the above-described polishing method, the time required for polishing one polishing object by increasing the scanning distance of the polishing member. However, there was a problem that the polishing efficiency was lowered.

  The present invention has been made in view of such problems, and an object thereof is to provide a polishing method, a polishing condition calculation method, and a polishing apparatus that avoid the occurrence of large waviness without reducing polishing efficiency. .

For this purpose achieved, the polishing method according to the first invention, together to press the polished surface of the polishing object while rotating the polishing member spherical, predetermined in the main scanning direction along the polished surface the distance moved relative a polishing method of polishing the surface to be polished while the sub-scanning direction are moved relative to perpendicular to the main scanning direction by a predetermined pitch of the predetermined distance for each finishes relative movement, the predetermined the value of the pitch, an input step of inputting the polishing conditions including the allowable values for waviness representing the unevenness of the polished surface formed by performing the polishing, the polishing condition inputted in the input step a calculation step of calculating the maximum unevenness difference of the undulation on the basis of the maximum unevenness difference of the undulation calculated in said calculating step, an input at said input step To Yes and determining steps were whether the greater than the allowable value. Then, in the determination step, the maximum unevenness difference of the undulation allow polishing when it is determined to be equal to or less than the allowable value, when the maximum unevenness difference of the undulation is determined to be greater than the allowable value Is characterized by not allowing polishing.

The polishing method according to the second invention, together to press the polished surface of the polishing object while rotating the polishing member spherical, are relatively moved a predetermined distance in the main scanning direction along the polished surface a polishing method of polishing the surface to be polished while relatively moved in the sub-scanning direction orthogonal to the main scanning direction by a predetermined pitch of the predetermined distance for each finishes relative movement, was polished by the polishing member a measurement step of obtaining the radius values of the contact circle formed the abrasive member from the measurement results of the surface of the polished surface when the is pressed against the surface to be polished, the contact circle obtained in the measuring step child and calculating step of calculating a swell factor radius represents a value obtained by dividing the value of the predetermined pitch input of the waviness factor calculated in said calculating step, a polishing run Maximum unevenness difference of undulation representing the unevenness of the polished surface formed by is closed and a determination step of determining whether it is within a predetermined range before and after the numerical value becomes a peak. Then , in the determination step, when it is determined that the undulation coefficient is not within the predetermined range, polishing is permitted, and when it is determined that the undulation coefficient is within the predetermined range, the undulation coefficient is determined by a predetermined calculation. It is characterized by correcting.

The polishing condition calculating method according to the present invention, together to press the polished surface of the polishing object while rotating the polishing member spherical, are relatively moved a predetermined distance in the main scanning direction along the polished surface a polishing condition calculation process of polishing of the polished surface while the sub-scanning direction are moved relative to perpendicular to the main scanning direction by a predetermined pitch of the predetermined distance for each finishes relative movement, the Young's modulus of the polishing member and Poisson's ratio, the radius of the polishing member, the value of the pressure for pressing the polishing member to the surface to be polished, as well, the allowable values for waviness representing the unevenness of the polished surface formed by performing polishing an input step of inputting the polishing conditions including, based on the polishing condition inputted in the input step, are formed when the is pressed against the polishing member to the surface to be polished Radius of Sawaen, undulation coefficient representing the value obtained by dividing the radius of the osculating circle at the value of the predetermined pitch, and a first calculation step of calculating the maximum unevenness difference of the undulation, is calculated in the first calculation step And a second calculation step of calculating a maximum pitch value that satisfies the allowable value based on a radius of the contact circle, the undulation coefficient, and the maximum unevenness difference of the undulation .

The polishing apparatus according to a first invention includes a head portion provided so as to polish the object facing the polishing member spherical for polishing said polishing object, rotatable in said head portion a polishing tool held in a rotary drive mechanism for rotating the polishing tool at a predetermined rotational speed, and a pressing mechanism for pressing at a predetermined pressure the abrasive member to the surface to be polished of the polishing object, the pressing a moving mechanism for relatively moving at a predetermined moving speed the polishing member which is pressed against the surface to be polished in the surface to be polished by a mechanism, the rotation driving mechanism, controlling the operation of the pressing mechanism, and the moving mechanism by the while rotating the polishing member with to press the polished surface, said predetermined distance in the main scanning direction along the polished surface are relatively moved, for each finishes relatively moves the predetermined distance And a control unit for performing polishing of the polished surface while relatively moved in the sub-scanning direction orthogonal to the main scanning direction by a constant pitch, gives instructions to the controller, input and output to obtain the output from the control unit It is configured with a device . Then, the control unit, the polishing conditions including the allowable values for waviness representing the value of said predetermined pitch which is input from the input device, the unevenness of the polished surface formed by performing polishing based calculates the maximum unevenness difference of the swell, the maximum unevenness difference of the calculated the undulation determines whether the greater than the allowable value inputted from the input-output device, the maximum unevenness difference of the undulation is the allowable allow polishing if the value below configured not to allow polishing when the maximum unevenness difference of the undulation is larger than the allowable value.

The polishing apparatus according to the second invention includes a head portion provided so as to polish the object facing the polishing member spherical for polishing said polishing object, rotatable in said head portion a polishing tool held in a rotary drive mechanism for rotating the polishing tool at a predetermined rotational speed, and a pressing mechanism for pressing at a predetermined pressure the abrasive member to the surface to be polished of the polishing object, the pressing a moving mechanism for relatively moving at a predetermined moving speed the polishing member which is pressed against the surface to be polished in the surface to be polished by a mechanism, the rotation driving mechanism, controlling the operation of the pressing mechanism, and the moving mechanism Accordingly, said while the polishing member is rotated together to press the polished surface, along said polished surface are relatively moved a predetermined distance in the main scanning direction, Tokoro the predetermined distance for each finishes relative movement And a control unit for performing polishing of the surface to be polished while the sub-scanning direction are moved relative to perpendicular to the main scanning direction by a pitch, gives instructions to the control unit, input and output device for obtaining an output from the control unit It is configured with. Then, the control unit obtains the radius of the contact circle formed in the polishing member from the measurement results of the surface of the polished surface was polished by the polishing member is pressed against the surface to be polished, A waviness coefficient representing a value obtained by dividing the acquired radius of the contact circle by the predetermined pitch value input from the input / output device is calculated, and the calculated waviness coefficient has a peak of the maximum unevenness of the waviness. determines whether it is within a predetermined range before and after the number, the waviness factor permits the polishing if not within the predetermined range, the predetermined operation of the undulation coefficient when the is within a predetermined range It is comprised so that it may correct | amend by.

The polishing apparatus according to a third invention includes a head portion provided so as to polish the object facing the polishing member spherical for polishing said polishing object, rotatable in said head portion a polishing tool held in a rotary drive mechanism for rotating the polishing tool at a predetermined rotational speed, and a pressing mechanism for pressing at a predetermined pressure the abrasive member to the surface to be polished of the polishing object, the pressing a moving mechanism for relatively moving at a predetermined moving speed the polishing member which is pressed against the surface to be polished in the surface to be polished by a mechanism, the rotation driving mechanism, controlling the operation of the pressing mechanism, and the moving mechanism by the while rotating the polishing member with to press the polished surface, said predetermined distance in the main scanning direction along the polished surface are relatively moved, for each finishes relatively moves the predetermined distance And a control unit for performing polishing of the polished surface while relatively moved in the sub-scanning direction orthogonal to the main scanning direction by a constant pitch, gives instructions to the controller, input and output to obtain the output from the control unit It is configured with a device . The control unit receives the Young's modulus and Poisson's ratio of the polishing member input from the input / output device , the radius of the polishing member, the value of the pressure that presses the polishing member against the surface to be polished, and polishing. A radius of a contact circle formed when the polishing member is pressed against the surface to be polished , based on polishing conditions including an allowable value for waviness representing irregularities of the surface to be polished formed by Calculating the undulation coefficient representing the value obtained by dividing the radius of the contact circle by the value of the predetermined pitch and the maximum unevenness difference of the undulation, and calculating the calculated radius of the contact circle, the undulation coefficient, and the maximum unevenness of the undulation. Based on the difference , the largest pitch value that satisfies the allowable value is calculated .

  According to the polishing method, the polishing condition calculation method, and the polishing apparatus according to the present invention, it is possible to avoid the occurrence of large waviness without reducing the polishing efficiency.

  Hereinafter, preferred embodiments of the present invention will be described with reference to the drawings. A schematic configuration of a polishing apparatus 1 to which the present invention is applied is shown in FIG. The polishing apparatus 1 includes an XYZ stage 20 that supports a workpiece 10 that is an object to be polished, a head unit 30 that is provided to face the XYZ stage 20, and a polishing tool 40 that is rotatably held by the head unit 30. The pressing mechanism 50 that presses the polishing member 42 provided at the tip of the polishing tool 40 against the flat upper surface (surface 11 to be polished), the moving speed of the XYZ stage 20, and the rotation of the polishing tool 40 A control unit 60 for controlling the operation of the polishing apparatus 1 such as speed and polishing load by the pressing mechanism 50, an interface 70 for inputting / outputting information to / from the control unit 60, and a surface measurement for measuring the surface profile of the surface 11 to be polished. Part 80 and the like.

  The XYZ stage 20 has a vacuum suction mechanism (not shown) that vacuum-sucks the lower surface of the workpiece 10 and holds the workpiece 10 in a substantially horizontal state so that the surface 11 to be polished faces upward. Here, the direction perpendicular to the surface 11 to be polished is defined as the positive direction of the Z axis, and as shown in FIG. 1, the direction parallel to the longitudinal direction of the polishing tool 40 is the X axis. The direction parallel to and perpendicular to the X axis is taken as the Y axis (see FIGS. 1 to 4). Further, the XYZ stage 20 is configured to be movable in the X, Y, and Z directions using a servo motor, a ball screw, or the like (not shown), and the workpiece 10 sucked and held by the XYZ stage 20 is desired with respect to the polishing tool 40. The position can be relatively moved in the X, Y, and Z directions.

  The head unit 30 includes a head main body 31 and a chuck 32 that is rotatably attached to the head main body 31. The head body 31 incorporates a bearing mechanism (not shown) and the like, and a chuck 32 is rotatably attached. The chuck 32 detachably holds the polishing tool 40, whereby the polishing tool 40 is rotatably held by the head unit 30. A servo motor 33 is attached to the head main body 31, and the servo motor 33 rotates the polishing tool 40 held on the chuck 32 together with the chuck 32.

  As shown in FIG. 2, the polishing tool 40 includes a rod-shaped support member 41 and a spherical polishing member 42. The support member 41 is formed so as to extend in a rod shape, and the polishing member 42 is attached to the distal end portion, and the proximal end portion is connected and held to the chuck 32. Therefore, the polishing tool 40 is held by the head unit 30 in a state where it can be rotated by the servo motor 33 around the central axis A extending in the longitudinal direction of the support member 41, and rotates on the front end side of the support member 41. A polishing process is performed on the surface 11 to be polished by the polishing member 42. The polishing member 42 is formed into a spherical shape using hard urethane having a nonwoven fabric-based continuous foam structure, and is attached to the distal end side of the support member 41 by adhesion or the like.

  The pressing mechanism 50 presses the polishing member 42 of the polishing tool 40 against the surface to be polished 11 of the workpiece 10 by a pneumatic cylinder (not shown) through the head portion 30. The pneumatic cylinder is connected to an air pressure source (not shown) such as an air tank via an electropneumatic regulator (not shown). The electropneumatic regulator is a device capable of electronically controlling the pressure and flow rate of air, and the air pressure-adjusted by the electropneumatic regulator is supplied from a pneumatic source to the pneumatic cylinder. The pressure pressed against the surface 11 to be polished can be adjusted.

  As shown in FIG. 1, the control unit 60 is electrically connected to the XYZ stage 20 (servo motor, etc.) and the servo motor 33 of the head unit 30, and outputs a drive signal to the XYZ stage 20 to The position of the head unit 30 and the polishing tool 40 on the X, Y, and Z axes and the moving speed in the X, Y, and Z directions are controlled, and a rotation drive signal is output to the servo motor 33 to output the servo motor 33. By controlling the rotational speed, the moving speed and rotational speed of the polishing tool 40 pressed by the XYZ stage 20 in the X, Y, and Z directions can be controlled. In addition, the control unit 60 is electrically connected to the pressing mechanism 50, and outputs a pressure control signal to the electropneumatic regulator to control the air pressure supplied to the pneumatic cylinder (polishing load on the workpiece 10). The pressure for pressing the polishing member 42 against the surface 11 to be polished can be adjusted.

  As described above, when a load is applied to the polishing member 42 in the downward direction (−Z direction) by the pressing mechanism 50, the polishing member 42 is pressed against the surface 11 to be polished as shown in FIG. 4. Therefore, when the polishing member 42 is pressed downward (−Z direction) against the surface 11 to be polished, the polishing member 42 is deformed, and a contact circle 81 is formed between the lower surface of the polishing member 42 and the surface 11 to be polished. Is done. Here, the radius of the contact circle 81 is r, and the load applied to the polishing member 42 in the −Z direction is P.

  The surface measurement unit 80 is electrically connected to the control unit 60, measures the surface profile of the surface 11 to be polished before and after polishing, and relates to the unevenness of the surface 11 to be polished such as the radius r of the contact circle 81 described above. Information is taken into the control unit 60.

  In addition, the controller 60 moves the XYZ stage 20 to press and rotate the rotating polishing member 42 against the surface 11 to be polished, thereby polishing the surface 11 to be polished. As shown in FIG. 3, the top moves in the + Y direction from a point 90 which is the lower left end of the surface 11 to be polished. Then, after the polishing member 42 reaches the upper end of the surface 11 to be polished, the polishing member 42 moves in the + X direction by the value of the pitch 82 described in detail later, and then moves in the -Y direction. After the polishing member 42 reaches the lower end of the surface to be polished, it moves in the + X direction by the value of the pitch 82 and then moves in the + Y direction again. Thus, the polishing process is performed by the rotating polishing member 42 moving on the surface 11 to be polished (detailed later).

  The interface 70 includes input / output devices such as an operation screen (not shown) and a keyboard on which an operator inputs data, and the control unit 60 is necessary for polishing based on data input from the interface 70. Performs parameter value calculation processing. Then, the calculation result calculated by the control unit 60 or the execution result when the polishing process is executed is displayed on the screen by the interface 70.

  In the polishing apparatus 1 schematically configured as described above, a value obtained by dividing the radius r of the contact circle formed when the above-described polishing member 42 is pressed against the surface 11 to be polished by the pitch 82 is defined as the undulation coefficient ρ. When the undulation coefficient ρ is an integer multiple of 0.5, the undulation may have a peak value. Therefore, the polishing method according to the present invention is used as a method of performing polishing after adjusting the value of the pitch 82 so that the undulation coefficient ρ does not become an integral multiple of 0.5. The polishing method in the first embodiment will be described below. The first embodiment is a polishing method for determining the validity of the value of the pitch 82 input from the interface 70 and determining whether or not to perform polishing according to the result. The details will be described with reference to FIG. To do.

  First, after the operator inputs the value of the pitch 82 from the interface 70, when both the Young's modulus E representing the material of the polishing member 42 and the Poisson's ratio ν are known (Yes in step S101), the operator The Young's modulus E and Poisson's ratio ν are input from the interface 70. Next, a load P, a pad radius R, and an allowable waviness value (unit%) described later are input from the interface 70 (step S102). Therefore, when the input of the load P, the pad radius R, and the allowable waviness value is completed, the control unit 60 uses the waviness RangeW (serving as an index representing the contact circle radius r, the waviness coefficient ρ, and the waviness size of the contact circle 81 described above. (Unit%) is calculated using the equations (1), (2), and (3) described later (step S103).

  The contact circle radius r, the undulation coefficient ρ, and the undulation RangeW described above are the value of the pitch 82, the Young's modulus E, the Poisson's ratio ν, the maximum value and the minimum value of the polishing removal amount when one workpiece 10 is polished. Using the average values, they can be expressed as equations (1), (2), and (3), respectively. The swell allowable value described above represents the allowable threshold value of the swell RangeW as a percentage in the same manner as the swell RangeW.

ρ＝r /(ピッチ８２の値) （２）
Ｗ＝（(除去量の最大値−除去量の最小値)/（除去量の平均値））×１００ （３）

ρ = r / (value of pitch 82) (2)
W = ((maximum value of removal amount−minimum value of removal amount) / (average value of removal amount)) × 100 (3)

  As described above, after calculating the contact circle radius r, the undulation coefficient ρ, and the undulation RangeW, the control unit 60 determines whether or not the undulation RangeW is larger than the input undulation allowable value (step S104). When the control unit 60 determines that the swell RangeW is larger than the swell allowable value, the control unit 60 provides an interface indicating that the input pitch 82 should be corrected and the optimized pitch 82 value. The screen is output to 70 (step S105). At this time, the optimum value of the pitch 82 is only displayed on the screen of the interface 70, and the polishing process is not started. Further, when the control unit 60 determines that the undulation RangeW is equal to or less than the undulation allowable value, the control unit 60 does not display the optimum value of the pitch 82 on the interface 70 and starts polishing the workpiece 10. (Step S106).

  When the polishing process is started through the above process (step S106), a transfer device (not shown) transfers the workpiece 10 onto the XYZ stage 20, and the XYZ stage 20 holds the workpiece 10 by suction. Thereafter, the control unit 60 moves the XYZ stage 20 to position the workpiece 10 at a predetermined polishing start position. When the workpiece 10 is positioned at the polishing start position, the servo motor 33 presses the point 90 which is the lower left corner of the surface 11 to be polished while rotating the polishing member 42 by the operation control of the control unit 60 (see FIG. 3). ).

  As described above, after the polishing member 42 rotating by the control unit 60 is pressed against the point 90 on the surface 11 to be polished, the control unit 60 moves the XYZ stage 20 downward (−Y direction). Thereby, polishing of the workpiece 10 is started. For example, in the case of FIG. 3, the polishing member 42 relatively moves upward (+ Y direction) from the point 90 which is the lower left end of the surface 11 to be polished. After that, when the polishing member 42 is positioned at the upper end of the surface 11 to be polished, the control unit 60 moves the XYZ stage 20 leftward (−X direction) by the value of the pitch 82. The upper end of the polishing surface 11 is relatively moved in the + X direction by the value of the pitch 82. Thereafter, the polishing member 42 relatively moves in the −Y direction. After the polishing member 42 reaches the lower end of the surface 11 to be polished, the polishing member 42 relatively moves in the + X direction by the value of the pitch 82 and then moves in the + Y direction. Go. As described above, the polishing member 42 repeats relative movement to polish the entire surface 11 to be polished.

  Further, when the operator inputs the value of the pitch 82 from the interface 70 at the time of starting the polishing process, and the values of the Young's modulus E and the Poisson's ratio ν of the polishing member 42 are unknown (in the case of No in step S101). Then, the control unit 60 presses the polishing member 42 against the point 90 which is the lower left end of the surface 11 to be polished, and moves the XYZ stage 20 downward (−Y direction). At this time, the polishing member 42 relatively moves upward (+ Y direction) from the point 90 that is the lower left end of the surface 11 to be polished, and performs polishing until the polishing member 42 reaches the upper end of the surface 11 to be polished. At this time, the surface measurement unit 80 measures the surface profile, and as a result, the control unit 60 acquires the value of the contact circle radius r (step S107), and then calculates the equation (from the value of the pitch 82 and the value of the radius r ( 2) is used to calculate the value of the swell coefficient ρ (step S108).

  After calculating the value of the swell coefficient ρ, the control unit 60 determines whether the value of ρ is in the range of an integral multiple of 0.5 plus or minus 0.05 (step S109). Here, when the control unit 60 determines that the undulation coefficient ρ is in the range of an integral multiple of 0.5 plus or minus 0.05 (Yes in step S109), the control unit 60 determines the undulation coefficient ρ. Correction is performed, and the corrected waviness coefficient ρ ′ is a value obtained by adding 0.2 to ρ. At this time, the value of the pitch 82 is also corrected by the equation (2) using the corrected undulation coefficient ρ ′. Thereafter, polishing is started using the corrected undulation coefficient ρ ′ and the value of pitch 82 as parameters (step S106). In addition, when the control unit 60 determines that the value of the undulation coefficient ρ is not in the range of an integer multiple of 0.5 plus or minus 0.05 (in the case of No in step S109), the control unit 60 performs the swell described above. Polishing is started without correcting the coefficient or the like, using the undulation coefficient ρ before correction and the input pitch 82 value as parameters (step S106).

  A polishing condition calculation method according to the second embodiment of the present invention will be described below with reference to FIG. In the second embodiment, since the same polishing apparatus as that used in the first embodiment is used, the configuration of the polishing apparatus is assigned the same number and the description thereof is omitted. Note that the polishing condition calculation method of the second embodiment described below shows a method of calculating the optimum value of the pitch 82 using a polishing apparatus.

  First, when the values of the Young's modulus E and the Poisson's ratio ν of the polishing member 42 are unknown (No in step S201), the control unit 60 has a message that the value of the pitch 82 cannot be calculated on the interface 70. Is displayed on the screen, and the calculation of the optimum value of the pitch 82 is stopped (step S202). If the values of the Young's modulus E and Poisson's ratio ν of the polishing member 42 are known (Yes in step S201), the operator inputs the Young's modulus E and Poisson's ratio ν from the interface 70, and then , Load P, pad radius R, and waviness tolerance (unit%) are input (step S203). When the input of the load P, the pad radius R, and the allowable waviness value is completed, the control unit 60 sets the contact circle radius r, the waviness coefficient ρ, and the waviness RangeW (unit%) to the above-described equations (1), (2), ( 3) (Step S204). Thus, using the contact circle radius r, the undulation coefficient ρ, and the undulation RangeW calculated in step S204, the control unit 60 calculates the optimum value of the pitch 82, and displays the optimum value of the pitch 82 on the interface 70 (step 70). S205).

  The inventor of the present invention performs a simulation for calculating the undulation RangeW using the polishing method, the polishing condition calculation method, and the polishing apparatus of each of the above-described embodiments. The contents of this simulation will be described below. The Young's modulus E, Poisson's ratio ν, load P, radius R of the polishing member 42, and waviness tolerance are shown below (referred to as polishing condition A).

Young's modulus E of the polishing member 42: 3.00 MPa
Poisson's ratio ν of polishing member 42: 0.35
Radius R of polishing member 42: 50.0 mm
Polishing load P: 2.00kg
Swell tolerance: 5.00%

  As a result of executing the simulation under the above polishing condition A, a graph shown in FIG. From this result, it can be seen that as the value of the pitch 82 decreases and the value of the undulation coefficient ρ increases, the undulation RangeW decreases, but in addition, when the undulation coefficient ρ is an integral multiple of 0.5, It can also be seen that the swell RangeW has a peak value. From this result, if the polishing process is performed after adjusting the value of the pitch 82 so that the waviness coefficient ρ does not become an integral multiple of 0.5 by the polishing method, the polishing condition calculation method, and the polishing apparatus of each embodiment described above, the pitch The value of waviness RangeW can be reduced without reducing the polishing efficiency by reducing the value of 82 more than necessary.

  FIGS. 6 and 7 are graphs showing the amount of polishing removal when the value of the pitch 82 is 2.0 mm and 2.3 mm, respectively, under the polishing condition A described above. In these graphs, the horizontal axis indicates the distance from the left end of the surface 11 to be polished, and the vertical axis indicates the value obtained by standardizing the polishing removal amount. From the graph of FIG. 6, when the value of the pitch 82 is 2.0 mm (the value of the undulation coefficient ρ is 3.0), the undulation RangeW is 9.2%, whereas the pitch 82 is It can be seen that when the value is 2.3 mm (the value of the undulation coefficient ρ is 2.61), the undulation RangeW is 4.2%. As described above, when the pitch 82 value is increased from 2.0 mm to 2.3 mm, the pitch range 82 is increased to increase the polishing efficiency so that the waviness RangeW is decreased from 9.2% to 4.2%. When the value is raised, the value of the waviness RangeW can be reduced.

  As described above, the example in which the undulation RangeW takes a peak value when the undulation coefficient ρ is an integer multiple of 0.5 is shown. However, the present invention also applies to the case where the peak value is taken when the undulation coefficient ρ is not an integer multiple of 0.5. By adjusting the value of the pitch 82 using the polishing method, the polishing condition calculation method, and the polishing apparatus according to the invention, the value of the waviness RangeW can be reduced.

  In each of the above-described embodiments, an example in which the polishing tool 40 is disposed in parallel with the surface to be polished 11 has been described. However, the present invention is not limited thereto, and the head portion 30 is directed upward with respect to the surface to be polished 11 ( The center axis of the polishing tool 40 may be disposed obliquely with respect to the surface 11 to be polished of the workpiece 10 by lifting in the positive direction (Z-axis).

  Further, in each of the above-described embodiments, the polishing member 42 is moved on the surface 11 to be polished by moving the XYZ stage 20 and the workpiece 10. However, the present invention is not limited to this, and the workpiece 10 is fixed. As an alternative, the head unit 30 and the polishing tool 40 may be moved.

  In each of the above-described embodiments, the workpiece 10 having the planar surface 11 to be polished has been described as an object to be polished. However, the present invention is not limited thereto, and the object to be polished 11 has a curved surface. In contrast, polishing can be performed using the polishing method according to the present invention.

1 is a schematic view of a polishing apparatus according to the present invention. It is the enlarged view seen from the polishing tool horizontal direction which shows the vicinity of the polishing tool. It is the enlarged view seen from the polishing tool upper direction which shows the vicinity of the polishing tool. It is an enlarged view in the vicinity of the polishing member 42 on the surface 11 to be polished when polishing. 6 is a graph showing a relationship between a waviness coefficient ρ and a waviness Range W when a simulation is performed under a polishing condition A. It is a graph which shows the grinding | polishing removal amount of the workpiece | work 10 when the value of the pitch 82 is 2.00 mm and the waviness coefficient (rho) is 3.00. It is a graph which shows the grinding | polishing removal amount of the workpiece | work 10 when the value of the pitch 82 is 2.30 mm and the wave | undulation coefficient (rho) is 2.61. It is a flowchart which shows the process which checks the validity of the value of the input pitch 82. FIG. It is a flowchart which shows the process which calculates the optimal value of the pitch.

Explanation of symbols

1 Polishing device 10 Workpiece (polishing object)
11 Surface to be polished 20 XYZ stage (movement mechanism)
30 head part 33 servo motor (rotary drive mechanism)
Reference Signs List 40 polishing tool 41 support member 42 polishing member 50 pressing mechanism 60 control unit 70 interface (input / output device)
80 Surface measurement unit

Claims (17)

Together to press the polished surface of the polishing object while the polishing member is rotated spherical, along said polished surface are relatively moved a predetermined distance in the main scanning direction, the predetermined distance for each finishes relative movement In a polishing method for polishing the surface to be polished while relatively moving in a sub-scanning direction orthogonal to the main scanning direction by a predetermined pitch,
An input step for inputting a polishing condition including a value of the predetermined pitch and an allowable value for waviness representing the unevenness of the surface to be polished formed by performing polishing;
A calculation step of calculating the maximum unevenness difference of the undulation on the basis of the polishing condition inputted in the input step,
A determination step of determining whether a maximum unevenness difference of the undulation calculated in the calculation step is larger than the allowable value input in the input step ;
Polished in the determination step, when the maximum unevenness difference of the undulation allow polishing when it is determined to be equal to or less than the allowable value, the maximum unevenness difference of the undulation is determined to be greater than the allowable value A polishing method characterized by not permitting . 2. The maximum pitch value that satisfies the allowable value is output when the maximum unevenness difference of the undulation is determined to be larger than the allowable value in the determining step . Polishing method. 3. The correction of the value of the predetermined pitch input in the input step is urged when it is determined in the determination step that the maximum unevenness difference of the undulation is larger than the allowable value. The polishing method according to 1. The polishing conditions input in the input step include the value of the predetermined pitch, the Young's modulus and Poisson's ratio of the polishing member, the radius of the polishing member, and the value of the pressure that presses the polishing member against the surface to be polished. The polishing method according to claim 1, wherein the polishing method is an allowable value for the waviness. Wherein the calculation step, by performing a simulation of the polishing based on the polishing condition inputted in the input step, the maximum unevenness difference of the swell, forming the abrasive member when the is pressed against the surface to be polished 5. The polishing method according to claim 1, wherein a undulation coefficient representing a radius of the contact circle and a value obtained by dividing the radius of the contact circle by the value of the predetermined pitch is calculated. Together to press the polished surface of the polishing object while the polishing member is rotated spherical, along said polished surface are relatively moved a predetermined distance in the main scanning direction, the predetermined distance for each finishes relative movement In a polishing method for polishing the surface to be polished while relatively moving in a sub-scanning direction orthogonal to the main scanning direction by a predetermined pitch,
A measurement step of obtaining a value of a radius of a contact circle formed when the polishing member is pressed against the surface to be polished from a measurement result of the surface of the surface to be polished that has been polished by the polishing member ;
A calculation step of calculating a swell coefficient representing a value obtained by dividing the radius of the contact circle obtained in the measurement step by the value of the input predetermined pitch;
Whether or not the undulation coefficient calculated in the calculation step is within a predetermined range before and after the numerical value at which the maximum unevenness of undulation representing the unevenness of the surface to be polished formed by polishing is peaked and a determination step of determining,
In the determination step, when it is determined that the undulation coefficient is not within the predetermined range, polishing is permitted, and when it is determined that the undulation coefficient is within the predetermined range, the undulation coefficient is corrected by a predetermined calculation. A polishing method characterized by the above. Claim, characterized by further comprising a polishing step of polishing while relatively moving to the other end of the surface to be polished along the surface to be polished with to press the abrasive member at one end of the surface to be polished 6. The polishing method according to 6. 8. The polishing method according to claim 6 , wherein in the determination step, it is determined whether or not the undulation coefficient is in a range of an integer multiple of 0.5 ± 0.05 . Together to press the polished surface of the polishing object while the polishing member is rotated spherical, along said polished surface are relatively moved a predetermined distance in the main scanning direction, the predetermined distance for each finishes relative movement In a polishing condition calculation method for polishing the surface to be polished while relatively moving in a sub-scanning direction orthogonal to the main scanning direction by a predetermined pitch,
It represents the Young's modulus and Poisson's ratio of the polishing member, the radius of the polishing member, the value of the pressure that presses the polishing member against the surface to be polished, and the irregularities of the surface to be polished formed by performing polishing. An input step for inputting polishing conditions including a tolerance for waviness;
Based on the polishing conditions input in the input step , the radius of the contact circle formed when the polishing member is pressed against the surface to be polished, and the radius of the contact circle divided by the value of the predetermined pitch. A undulation coefficient representing a value, and a first calculation step of calculating a maximum unevenness difference of the undulation ;
A second calculation step of calculating a maximum pitch value out of the allowable values based on the radius of the contact circle calculated in the first calculation step , the waviness coefficient, and the maximum unevenness difference of the waviness ; A polishing condition calculation method comprising: A head portion provided to face the object to be polished;
A polishing tool having a spherical polishing member for polishing the polishing object, and rotatably held by the head part;
A rotational drive mechanism for rotationally driving the polishing tool at a predetermined rotational speed;
A pressing mechanism for pressing the polishing member against the surface to be polished of the object to be polished with a predetermined pressure;
A moving mechanism for relatively moving the polishing member pressed against the polished surface by the pressing mechanism at a predetermined moving speed on the polished surface;
By controlling the operations of the rotation drive mechanism, the pressing mechanism, and the moving mechanism, the polishing member is pressed against the surface to be polished while rotating, and a predetermined scanning direction is set along the surface to be polished. distance moved relative, and a control unit for performing polishing of the surface to be polished while the sub-scanning direction are moved relative to perpendicular to the main scanning direction by a predetermined pitch of the predetermined distance for each finishes relative movement,
In a polishing apparatus provided with an input / output device for giving an instruction to the control unit and obtaining an output from the control unit,
Wherein, based on the polishing conditions including the allowable values for waviness representing the value of said predetermined pitch which is input from the input device, the unevenness of the polished surface formed by performing polishing The maximum unevenness difference of the undulation is calculated , it is determined whether the calculated maximum unevenness difference of the undulation is larger than the allowable value input from the input / output device, and the maximum unevenness difference of the undulation is equal to or less than the allowable value. In the polishing apparatus, polishing is permitted, and when the maximum unevenness difference of the waviness is larger than the allowable value, polishing is not permitted . The control unit is configured to output a value of a maximum pitch that satisfies the allowable value when it is determined that a maximum unevenness difference of the undulation is larger than the allowable value. Item 11. The polishing apparatus according to Item 10 . The control unit is configured to prompt correction of the value of the predetermined pitch input from the input / output device when it is determined that the maximum unevenness difference of the undulation is larger than the allowable value. The polishing apparatus according to claim 10 or 11 . The polishing conditions input from the input / output device include the value of the predetermined pitch , the Young's modulus and Poisson's ratio of the polishing member, the radius of the polishing member, and the pressure for pressing the polishing member against the surface to be polished . the polishing apparatus according to any one of claims 10 to 12, wherein the value, to be a permissible value for the undulation. The control unit, based on the polishing conditions input from the input / output device , the maximum unevenness difference of the undulation, and the radius of a contact circle formed when the polishing member is pressed against the surface to be polished The polishing apparatus according to claim 10 , wherein a waviness coefficient representing a value obtained by dividing the radius of the contact circle by the value of the predetermined pitch is calculated . A head portion provided to face the object to be polished;
A polishing tool having a spherical polishing member for polishing the polishing object, and rotatably held by the head part;
A rotational drive mechanism for rotationally driving the polishing tool at a predetermined rotational speed;
A pressing mechanism for pressing the polishing member against the surface to be polished of the object to be polished with a predetermined pressure;
A moving mechanism for relatively moving the polishing member pressed against the polished surface by the pressing mechanism at a predetermined moving speed on the polished surface;
By controlling the operations of the rotation drive mechanism, the pressing mechanism, and the moving mechanism, the polishing member is pressed against the surface to be polished while rotating, and a predetermined scanning direction is set along the surface to be polished. distance moved relative, and a control unit for performing polishing of the surface to be polished while the sub-scanning direction are moved relative to perpendicular to the main scanning direction by a predetermined pitch of the predetermined distance for each finishes relative movement,
In a polishing apparatus provided with an input / output device for giving an instruction to the control unit and obtaining an output from the control unit,
The control unit acquires and acquires the radius of a contact circle formed when the polishing member is pressed against the surface to be polished from the measurement result of the surface of the surface to be polished that has been polished by the polishing member . A waviness coefficient representing a value obtained by dividing the radius of the contact circle by the value of the predetermined pitch input from the input / output device is calculated, and the calculated waviness coefficient is formed by performing polishing. maximum unevenness difference of undulation representing the unevenness of the surface is equal to or within a predetermined range before and after the numerical value becomes a peak, to allow polishing when the swell factor is not within the predetermined range, the predetermined A polishing apparatus configured to correct the waviness coefficient by a predetermined calculation when it is within a range . The polishing apparatus according to claim 15 , wherein the control unit is configured to determine whether or not the waviness coefficient is within a range of an integer multiple of 0.5 ± 0.05 . A head portion provided to face the object to be polished;
A polishing tool having a spherical polishing member for polishing the polishing object, and rotatably held by the head part;
A rotational drive mechanism for rotationally driving the polishing tool at a predetermined rotational speed;
A pressing mechanism for pressing the polishing member against the surface to be polished of the object to be polished with a predetermined pressure;
A moving mechanism for relatively moving the polishing member pressed against the polished surface by the pressing mechanism at a predetermined moving speed on the polished surface;
By controlling the operations of the rotation drive mechanism, the pressing mechanism, and the moving mechanism, the polishing member is pressed against the surface to be polished while rotating, and a predetermined scanning direction is set along the surface to be polished. distance moved relative, and a control unit for performing polishing of the surface to be polished while the sub-scanning direction are moved relative to perpendicular to the main scanning direction by a predetermined pitch of the predetermined distance for each finishes relative movement,
In a polishing apparatus provided with an input / output device for giving an instruction to the control unit and obtaining an output from the control unit,
The control unit executes the Young's modulus and Poisson's ratio of the polishing member input from the input / output device , the radius of the polishing member, the value of the pressure pressing the polishing member against the surface to be polished, and polishing A radius of a contact circle formed when the polishing member is pressed against the surface to be polished , based on polishing conditions including an allowable value for waviness representing the unevenness of the surface to be polished formed by A waviness coefficient representing a value obtained by dividing the radius of the contact circle by the value of the predetermined pitch and a maximum unevenness difference of the waviness are calculated, and the calculated radius of the contact circle, the waviness coefficient, and the maximum unevenness difference of the waviness are calculated. Based on this, the polishing apparatus is configured to calculate the largest pitch value out of the allowable values .

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