Polishing Tool, Polishing Head, Polishing Apparatus, And Polishing Method

20250360593 ยท 2025-11-27

    Inventors

    Cpc classification

    International classification

    Abstract

    A polishing tool for polishing a workpiece by holding a polishing material between the workpiece and its polishing surface, the polishing tool including: a main shaft part that has the polishing surface at a front end and that extends along a polishing axis; a plurality of elastic parts that are continuous from the main shaft part and that extend radially outward; and a plurality of seat parts that are continuous to the radially outside of the plurality of elastic parts. A position at which the main shaft part connects to each of the elastic parts and a position at which the corresponding seat part connects thereto are different in a direction of the polishing axis.

    Claims

    1. A polishing tool for polishing a workpiece by holding a polishing material between the workpiece and a polishing surface of the polishing tool, the polishing tool comprising: a main shaft part that has the polishing surface facing the workpiece at a front end and that extends along a polishing axis, the polishing axis being a virtual axis defined as a direction in which a center of the polishing surface approaches or moves away the workpiece; a plurality of elastic parts that are continuous from the main shaft part and that extend in a radially outward direction with respect to the polishing axis; and a plurality of seat parts that are continuous to a radially outside of the plurality of elastic parts, wherein a position at which the main shaft part connects to each of the elastic parts and a position at which the corresponding seat part connects to each of the elastic parts are different in a direction of the polishing axis, and when the respective seat parts are applied with equal amounts of displacement toward a same side that is either a radially inside or radially outside by a tool driving mechanism, the plurality of elastic parts elastically deform and the main shaft part is displaced so as to include an axial component with respect to the polishing axis, whereas when the respective seat parts are applied with different amounts of displacement toward the same side that is either the radially inside or radially outside, or the displacement toward different sides that are the radially outside and the radially inside by the tool driving mechanism, the main shaft part is displaced so as to include a radial component with respect to the polishing axis.

    2. The polishing tool according to claim 1, wherein the plurality of elastic parts and the plurality of seat parts are disposed at equal intervals in a circumferential direction with reference to the polishing axis.

    3. The polishing tool according to claim 2, wherein the number of the elastic parts and the number of the seat parts each are three.

    4. A polishing head having the polishing tool according to claim 1, the polishing head comprising: a tool base; and a tool driving mechanism that is disposed on the tool base to displace or elastically deform the polishing tool, wherein the tool driving mechanism includes a plurality of driving units that are disposed in the plurality of seat parts to radially displace the seat parts.

    5. The polishing head according to claim 4, comprising a tool control device that controls the tool driving mechanism, wherein the tool control device includes a first frequency signal generator that generates a plurality of first frequency signals to periodically reciprocate and displace the plurality of driving units so that increase-decrease cycles of displacement amounts coincide with each other.

    6. The polishing head according to claim 5, wherein: the tool control device further includes a second frequency signal generator that generates a plurality of second frequency signals to periodically reciprocate and displace the plurality of driving units so that the increase-decrease cycles of the displacement amounts coincide with each other, and a signal superimposing unit that generates driving signals for the respective driving units by superimposing the plurality of first frequency signals and the plurality of second frequency signals, wherein: the plurality of first frequency signals generated by the first frequency signal generator coincide with each other in increase-decrease phase; and the plurality of second frequency signals generated by the second frequency signal generator are different from each other in increase-decrease phase.

    7. The polishing head according to claim 5, wherein: the tool control device further includes a second frequency signal generator that generates a plurality of second frequency signals to periodically reciprocate and displace the plurality of driving units so that the increase-decrease cycles of the displacement amounts coincide with each other, and a signal superimposing unit that generates driving signals for the respective driving units by superimposing the plurality of first frequency signals and the plurality of second frequency signals, wherein the first frequency signals have a frequency higher than the frequency of the second frequency signals.

    8. The polishing head according to claim 5, comprising a bias signal generator that generates a bias signal to be superimposed on at least one of the first frequency signals.

    9. The polishing head according to claim 8, comprising a polishing head setting calculation unit that varies the bias signal generated by the bias signal generator by referring to scanning path information for the polishing surface regarding the workpiece and/or shape information on the workpiece.

    10. The polishing head according to claim 1, wherein the tool driving mechanism vibrates the polishing surface along a spiral moving locus.

    11. The polishing head according to claim 10, wherein the tool driving mechanism displaces a spiral axis of the spiral moving locus on the polishing surface.

    12. A polishing apparatus, comprising: a base; the polishing head according to claim 4; a polishing head holding mechanism that is provided on the base to hold the polishing head; a workpiece holding mechanism that is provided on the base to hold the workpiece; and a relative movement mechanism that relatively moves the workpiece and the polishing head in an axial direction of the polishing axis and in a radial direction with reference to the polishing axis.

    13. A polishing method for polishing a workpiece by holding a polishing material between a polishing surface of a polishing tool and the workpiece, the polishing material containing abrasive grains dispersed in a fluid, the polishing method comprising: disposing a plurality of driving units along a circumferential direction with reference to a polishing axis to cause each of the driving units to displace a contact point with the polishing tool in a radial direction with reference to the polishing axis, the polishing axis being a virtual axis defined as a direction in which a center of the polishing surface approaches or moves away the workpiece; generating a synchronization frequency signal to periodically reciprocate and displace the plurality of driving units so that increase-decrease cycles and increase-decrease phases of displacement amounts coincide with each other; generating a plurality of first frequency signals to periodically reciprocate and displace the plurality of driving units so that the increase-decrease cycles of the displacement amounts coincide with each other; generating driving signals for the respective driving units by using at least the plurality of first frequency signals; and displacing the plurality of driving units by the plurality of driving signals so as to displace the polishing surface of the polishing tool in an axial direction and a radial direction with reference to the polishing axis.

    14. The polishing method according to claim 13, wherein: a plurality of second frequency signals are generated to periodically reciprocate and displace the plurality of driving units so that the increase-decrease cycles of the displacement amounts coincide with each other; the plurality of first frequency signals coincide with each other in increase-decrease phase and the plurality of second frequency signals are different from each other in increase-decrease phase; the driving signals for the respective driving units are generated by superimposing the plurality of first frequency signals and the plurality of second frequency signals; and the plurality of driving units are displaced by the plurality of driving signals so as to displace the polishing surface of the polishing tool in the axial direction and the radial direction with reference to the polishing axis.

    15. The polishing method according to claim 13, wherein: the driving signals for the respective driving units are generated by superimposing a bias signal on at least one of the first frequency signals; and the plurality of driving units are displaced by the plurality of driving signals so as to displace the polishing surface of the polishing tool in the axial direction and the radial direction with reference to the polishing axis.

    16. The polishing method according to claim 15, wherein the bias signal is varied by referring to a scanning path information for the polishing surface regarding the workpiece and/or shape information on the workpiece.

    17. The polishing method according to claim 13, wherein the polishing surface is vibrated along a spiral moving locus.

    18. The polishing method according to claim 17, wherein a spiral axis of the spiral moving locus on the polishing surface is displaced.

    19. A polishing method for polishing a workpiece by holding a polishing material between a polishing surface of a polishing tool and the workpiece, the polishing material containing abrasive grains dispersed in a fluid, the polishing method comprising: disposing a plurality of driving units along a circumferential direction with reference to a polishing axis to cause each of the driving units to displace a contact point with the polishing tool in a radial direction with reference to the polishing axis, the polishing axis being a virtual axis defined as a direction in which a center of the polishing surface approaches or moves away the workpiece; generating frequency signals that are at least twice as many as a number of the driving units; inputting a driving signal to each of the driving units, the driving signal being obtained by superimposing at least two frequency signals among the frequency signals; and displacing the plurality of driving units by the plurality of driving signals so as to displace the polishing surface of the polishing tool in an axial direction and a radial direction with reference to the polishing axis.

    Description

    BRIEF DESCRIPTION OF THE DRAWINGS

    [0031] These and other characteristics, features, and advantages of the present invention will become clear from the following description with reference to the accompanying drawings, wherein:

    [0032] FIG. 1 is a side view of a polishing apparatus according to an embodiment of the present invention;

    [0033] FIG. 2A is a front view of a polishing head applied to the polishing apparatus, and FIG. 2B is a side view thereof;

    [0034] FIG. 3 is a partial cross-sectional view of the polishing head as seen from an arrow III-III in FIG. 2A;

    [0035] FIG. 4A is a perspective view of a polishing tool applied to the polishing head, and FIG. 4B is a perspective view illustrating a modification of the polishing surface;

    [0036] FIG. 5A is a front view of the polishing tool, and FIG. 5B is a side view thereof;

    [0037] FIG. 6A is a front view of the polishing tool, FIG. 6B is a side view thereof, and FIG. 6C is a diagram illustrating a composite vector of displacement vectors of the polishing tool;

    [0038] FIGS. 7A and 7B are perspective views illustrating a process of manufacturing the polishing tool;

    [0039] FIG. 8A is a block diagram illustrating the function of a movement control device of the polishing apparatus, and FIG. 8B is a block diagram illustrating the function of a tool control device of the polishing apparatus;

    [0040] FIG. 9A is a diagram illustrating first to third synchronization frequency signals DA, DB, and DC of the tool control device, FIG. 9B is a diagram illustrating first to third phase difference frequency signals QA, QB, and QC, FIG. 9C is a diagram illustrating first to third driving signals KA, KB, and KC, and FIG. 9D is a front view illustrating the operation of a polishing surface 230 by the first to third driving signals KA, KB, and KC;

    [0041] FIG. 10A is a side view illustrating the operation of the polishing surface 230 by the first to third driving signals KA, KB, and KC, and FIG. 10B is a front view thereof;

    [0042] FIG. 11A is a diagram illustrating first to third bias signals EA, EB, and EC of the tool control device, FIG. 11B is a diagram illustrating first to third driving signals KA(t1), KB(t1), and KC(t1), FIG. 11C is a front view illustrating the operation of the polishing surface at the elapsed time t1, FIG. 11D is a front view illustrating the operation of the polishing surface at the elapsed time t2, and FIG. 11E is a front view illustrating the operation of the polishing surface at the elapsed time t3;

    [0043] FIG. 12A is a diagram illustrating first to third bias signals EA, EB, and EC of the tool control device, FIG. 12B is a diagram illustrating first to third driving signals KA(t1), KB(t1), and KC(t1), FIG. 12C is a side view illustrating the operation of the polishing surface at the elapsed time t1, FIG. 12D is a side view illustrating the operation of the polishing surface at the elapsed time t2, and FIG. 12E is a side view illustrating the operation of the polishing surface at the elapsed time t3;

    [0044] FIGS. 13A to 13C are cross-sectional views illustrating the polishing process of the workpiece by the polishing tool;

    [0045] FIG. 14A shows a vibration waveform in the Z-axis direction of the polishing tool, and FIG. 14B shows a vibration waveform in the radial direction with reference to the polishing tool;

    [0046] FIG. 15A is a micrograph in the initial state of the workpiece for verification, and FIG. 15B is a three-dimensional profile thereof;

    [0047] FIG. 16A is a micrograph after polishing the workpiece for verification with the polishing apparatus, and FIG. 16B is a three-dimensional profile thereof;

    [0048] FIG. 17A is a micrograph after polishing the workpiece for verification with a polishing apparatus according to a comparative example, and FIG. 17B is a three-dimensional profile thereof; and

    [0049] FIG. 18 is a diagram illustrating a modification of first to third synchronization frequency signals DA, DB, and DC, first to third phase difference frequency signals QA, QB, and QC, and first to third driving signals KA, KB, and KC of the tool control device.

    DETAILED DESCRIPTION OF THE INVENTION

    [0050] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

    [0051] FIG. 1 illustrates an overall configuration of a polishing apparatus 1 according to the present embodiment. The polishing apparatus 1 includes: a base 10; a polishing head 100; a polishing head holding mechanism 20 that is provided on the base 10 to hold the polishing head 100; a workpiece holding mechanism 30 that is provided on the base 10 to hold a workpiece W; a relative rotation mechanism 33 that relatively rotates the workpiece W and the polishing head 100; a relative movement mechanism 40 that relatively moves the workpiece W and the polishing head 100 in an axial direction and a radial direction R of a polishing axis J, and a polishing material supplying device 35 that supplies a fluid-like polishing material between the workpiece W and the polishing head 100. The polishing apparatus 1 further includes a tool control device 50 that controls a tool driving mechanism 140 in the polishing head 100, and a movement control device 60 that controls the relative movement mechanism 40. Note that the tool control device 50 and the movement control device 60 operate in conjunction with each other.

    [0052] For convenience of explanation, the direction in which the center of the polishing surface of the polishing head 100 approaches or moves away the workpiece W (the left-to-right direction in FIG. 1) is defined as a Z-axis direction. In FIG. 1, a line passing through the center of the polishing surface 230 of the polishing head 100 and parallel to the Z-axis direction is defined as a virtual polishing axis J. Furthermore, a vertical direction perpendicular to the Z-axis direction (the top-to-bottom direction in FIG. 1) is defined as a Y-axis direction, and a direction perpendicular to both the Z-axis direction and the Y-axis direction (the direction perpendicular to the page on which the illustration in FIG. 1 rests) is defined as an X-axis direction. Furthermore, a direction perpendicular to the polishing axis J (or Z-axis) is defined as a radial direction R with reference to the polishing axis, and a circumferential direction around the polishing axis J (or Z-axis) is defined as a circumferential direction S with reference to the polishing axis.

    <Workpiece Holding Mechanism>

    [0053] The workpiece holding mechanism 30 holds a workpiece W to be polished. Although not particularly illustrated, the workpiece holding mechanism 30 includes a chuck that holds the workpiece W such that the surface to be polished on the workpiece W faces in the Z-axis direction.

    <Polishing Head Holding Mechanism>

    [0054] The polishing head holding mechanism 20 serves as a seating for holding the polishing head 100. The polishing head holding mechanism 20 holds the polishing head 100 so that the polishing axis J of the polishing head 100 becomes parallel to the Z-axis direction. Although not particularly illustrated, the polishing head holding mechanism 20 preferably includes a chuck that detachably holds the polishing head 100 so that the polishing surface thereof faces in the Z-axis direction. When a normal cutting tool is equipped instead of the polishing head 100, which is held by the polishing head holding mechanism 20 and by use of a chuck, the entire polishing apparatus 1 changed into a general-purpose cutting apparatus.

    <Relative Rotation Mechanism>

    [0055] The relative rotation mechanism 33 is a rotation mechanism that relatively rotates the workpiece W and the polishing surface 230 about the Z-axis. Herein, the relative rotation mechanism 33 serves as a rotation main axis fixed to the base 10, and rotates the workpiece holding mechanism 30 about the Z-axis.

    <Relative Movement Mechanism>

    [0056] The relative movement mechanism 40 is a mechanism that moves the workpiece W and the polishing head 100 in the X-axis, Y-axis, and Z-axis directions, this movement being relative to the base 10. In the present embodiment, the relative movement mechanism 40 includes: a Y-axis linear motion device 42 that moves the polishing head holding mechanism 20 in the Y-axis direction; a Z-axis linear motion device 44 that moves the Y-axis linear motion device 42 in the Z-axis direction; an X-axis linear motion device 46 that moves the Z-axis linear motion device 44 in the X-axis direction; and a tilt mechanism 48 that tilts the polishing axis J of the polishing head holding mechanism 20 with reference to the Z-axis direction. Note that, in the present embodiment, the structure in which the polishing head 100 is moved relative to the base 10 in the X-axis, Y-axis, and Z-axis direction, and also in a tilt direction has been exemplified, but the present invention is not limited thereto. Some or all of the mechanisms for movement in the X-axis, Y-axis, and Z-axis directions, and the tilt direction may be provided on the side where the workpiece holding mechanism 30 is provided. When the surface to be polished of the workpiece W is a flat surface, the tilt mechanism 48 can be eliminated. On the other hand, when the surface to be polished of the workpiece W has a three-dimensional shape, the polishing head 100 is preferably tilted by the tilt mechanism 48 so that the polishing axis J coincides with the direction vertical to the surface to be polished.

    <Polishing Material Supply Device>

    [0057] The polishing material supply device 35 continuously supplies a fluid-like polishing material between the workpiece W and the polishing surface of the polishing head 100. Specifically, the polishing material supply device 35 includes: a pump (not illustrated); a pipe 36 that guides the polishing material discharged from the pump; a nozzle 37 that is attached to the forefront of the pipe 36 and discharges the polishing material; and a nozzle holding mechanism 38 that holds the nozzle 37 at a predetermined position.

    <Polishing Head>

    [0058] As illustrated in an enlarged view of FIG. 2, the polishing head 100 includes: a tool base 110; a tool driving mechanism 140 that is disposed on the tool base 110; a polishing tool 200 that is held by the tool driving mechanism 140; and a tool control device 50 that controls the tool driving mechanism 140.

    (Tool Base)

    [0059] The tool base 110 is a plate-shaped member that extends in the X-axis and Y-axis directions.

    (Polishing Tool)

    [0060] The polishing tool 200 serves as a tool for polishing a workpiece W by holding the polishing material between its polishing surface 230 and the workpiece W. For convenience of explanation, in the polishing tool 200, the side approaching the workpiece W along the polishing axis J (or the Z axis) is referred to as the front end side, and the side away from the workpiece W is referred to as the base end side. As illustrated in FIG. 4 to FIG. 6, the polishing tool 200 includes a main shaft part 210, a first elastic part 310, a second elastic part 320, a third elastic part 330, a first seat part 410, a second seat part 420, and a third seat part 430.

    [0061] The main shaft part 210 is a rod-shaped member that extends along the polishing axis J (or Z axis), has a polishing surface 230 that is located on the front end side, and faces the workpiece W. More specifically, the main shaft part 210 has a central shaft 210A that extends along the polishing axis J, a first rib 211 that spreads from the central shaft 210A in a first radial direction R1 and extends along the polishing axis J, a second rib 212 that spreads from the central shaft 210A in a second radial direction R2 and extends along the polishing axis J, and a third rib 213 that spreads from the central shaft 210A in a third radial direction R3 and extends along the polishing axis J. The first to third ribs 211 to 213 increase the stiffness of the main shaft part 210. The polishing surface 230 is provided at the front end in the central shaft 210A. Note that the polishing surface 230 is not limited to a flat surface, and as illustrated in FIG. 4B, the polishing surface 230 may be a three-dimensional surface (for example, a convex surface such as a part of a spherical surface).

    [0062] The first elastic part 310 is a member that is continuous from the base end side of the main shaft part 210 and extends from the polishing axis J toward the outside in the first radial direction (R1 direction). The first elastic part 310 is elastically deformed in the polishing axis J direction and/or the first radial direction R1 by an external force. The first seat part 410 is a portion to be provided radially outward of the first elastic part 310, and provides a structural part (here, a seat surface 410A) such as a surface to be supported by the tool driving mechanism 140 described later.

    [0063] Here, as illustrated in FIG. 5, a position at which the main shaft part 210 (polishing axis J) connects to the first elastic part 310 is defined as a main shaft-side continuous point 310A, and a portion of the first seat part 410 (seat surface 410A) in the first elastic part 310 is defined as a seat part-side continuous point 310B. With respect to the main shaft-side continuous point 310A, the seat part-side continuous point 310B is located at a position shifted along the polishing axis J, specifically, on the base end side. When a central axis in an extending direction of the member of the first elastic part 310 is defined as a first arm axis 310J, the first arm axis 310J is an inclined member that is displaced from a front end side to a base end side of the polishing axis J as it extends from the inside toward the outside in the first radial direction R1 of the polishing axis J. The first arm axis 310J may be defined as a straight-line component connecting the main shaft-side continuous point 310A and the seat-side continuous point 310B. As illustrated in FIG. 5B, in the first elastic part 310, a constriction part 310K is formed on the proximal side of the main shaft-side continuous point 310A. The dimension 310Kw in the constriction part 310K in a direction perpendicular to the first arm axis 310J is smaller than the dimension 310Ew of any optional point on the farther side thereto. As a result, the constriction part 310K in the first elastic part 310 has a lower stiffness, so that the constriction part 310K tends to elastically deform. On the inside of the first seat part 410 in the first radial direction R1, a first escape space 410K is formed.

    [0064] In the present embodiment, a case has been illustrated where the main shaft-side continuous point 310A is located on the front end side and the seat part-side continuous point 310B is located on the base end side. However, the present invention is not limited thereto, and a structure in which the main shaft-side continuous point 310A is located on the base end side and the seat part-side continuous point 310B is located on the front end side may be adopted.

    [0065] The first seat part 410 provides a surface that faces outward in the first radial direction R1. The first seat part 410 receives a first external force F1 that is applied from the outside toward the inside in the first radial direction R1. The first seat surface 410A provided on the first seat part 410 is a concave part that is recessed in a partially spherical shape here. When the tool driving mechanism 140 described later is engaged with the first seat surface 410A, the first seat part 410 is supported and pressed from the outside toward the inside in the first radial direction R1. The pressure provided to the first seat part 410 in an initial state serves as a holding pressure (pressurization) to maintain a holding posture of the polishing tool 200.

    [0066] The second elastic part 320 is a member that is continuous from the base end side of the main shaft part 210 and extends from the polishing axis J toward the outside in the second radial direction (R2 direction). The second elastic part 320 is elastically deformed in the polishing axis J direction and/or the second radial direction R2 by an external force. The second seat part 420 is a portion to be provided radially outward of the second elastic part 320, and provides a structural part (here, a seat surface 420A) such as a surface to be supported by the tool driving mechanism 140 described later.

    [0067] Here, as illustrated in FIG. 5, a position at which the main shaft part 210 (polishing axis J) connects to the second elastic part 320 is defined as a main shaft-side continuous point 320A, and a portion of the second seat part 420 (seat surface 420A) in the second elastic part 320 is defined as a seat part-side continuous point 320B. With respect to the main shaft-side continuous point 320A, the seat part-side continuous point 320B is located on the base end side of the polishing axis J. In other words, the main shaft-side continuous point 320A and the seat part-side continuous point 320B are at different positions along the polishing axis J. When a central axis in an extending direction of the member of the second elastic part 320 is defined as a second arm axis 320J, the second arm axis 320J is an inclined member that is displaced from a front end side to a base end side of the polishing axis J as it extends from the inside toward the outside in the second radial direction R2 of the polishing axis J. In the second elastic part 320, a constriction part 320K is formed on the near side of the main shaft-side continuous point 320A. As a result, the constriction part 320K has a lower stiffness, so that the constriction part 320K tends to elastically deform. On the inside of the second seat part 420 in the second radial direction R2, a second escape space 420K is formed.

    [0068] In the present embodiment, a case has illustrated where the main shaft-side continuous point 320A is located on the front end side and the seat part-side continuous point 320B is located on the base end side. However, the present invention is not limited to this configuration, and a structure in which the main shaft-side continuous point 320A is located on the base end side and the seat part-side continuous point 320B is located on the front end side may be adopted.

    [0069] The second seat part 420 provides a surface that faces outward in the second radial direction R2. The second seat part 420 receives a second external force F2 that is applied from the outside toward the inside in the second radial direction R2. The second seat surface 420A provided on the second seat part 420 is a concave part that is recessed in a partially spherical shape here. When the tool driving mechanism 140 described later is engaged with the second seat surface 420A, the second seat part 420 is supported and pressed from the outside toward the inside in the second radial direction R2. The pressure provided to the second seat part 420 in an initial state serves as a holding pressure (pressurization) to maintain a holding posture of the polishing tool 200.

    [0070] The third elastic part 330 is a member that is continuous from the base end side of the main shaft part 210 and extends from the polishing axis J toward the outside in the third radial direction (R3 direction). The third elastic part 330 is elastically deformed in the polishing axis J direction and/or the third radial direction R3 by an external force. The third seat part 430 is a portion to be provided radially outward of the third elastic part 330, and provides a structural part (here, a seat surface 430A) such as a surface to be supported by the tool driving mechanism 140 described later.

    [0071] Here, as illustrated in FIG. 5, a position at which the main shaft part 210 (polishing axis J) connects to the third elastic part 330 is defined as a main shaft-side continuous point 330A, and a portion of the third seat part 430 (seat surface 430A) in the third elastic part 330 is defined as a seat part-side continuous point 330B. With respect to the main shaft-side continuous point 330A, the seat part-side continuous point 330B is located on the base end side of the polishing axis J. In other words, the main shaft-side continuous point 330A and the seat part-side continuous point 330B are at different positions along the polishing axis J. When a central axis in an extending direction of the member of the third elastic part 330 is defined as a third arm axis 330J, the third arm axis 330J is an inclined member that is displaced from the front end to the base end side of the polishing axis J as it extends from the inside toward the outside in the third radial direction R3 of the polishing axis J. In the third elastic part 330, a constriction part 330K is formed on the near side of the main shaft-side continuous point 330A. As a result, the constriction part 330K has a lower stiffness, so that the constriction part 330K tends to elastically deform. On the inside of the third seat part 430 in the third radial direction R3, a third escape space 430K is formed.

    [0072] In the present embodiment, a case has been illustrated where the main shaft-side continuous point 330A is located on the front end side and the seat part-side continuous point 330B is located on the base end side. However, the present invention is not limited to this configuration, and a structure in which the main shaft-side continuous point 330A is located on the base end side and the seat part-side continuous point 330B is located on the front end side may be adopted.

    [0073] The third seat part 430 provides a surface that faces outward in the third radial direction R3. The third seat part 430 receives a third external force F3 that is applied from the outside toward the inside in the third radial direction R3. The third seat surface 430A provided on the third seat part 430 is a concave part that is recessed in a partially spherical shape. When the tool driving mechanism 140 described later is engaged with the third seat surface 430A, the third seat part 430 is supported and pressed from the outside toward the inside in the third radial direction R3. The pressure provided to the third seat part 430 in an initial state serves as a holding pressure (pressurization) to maintain the holding posture of the polishing tool 200.

    [0074] Furthermore, in the present embodiment, the first radial direction R1, the second radial direction R2, and the third radial direction R3 have an angular difference of 120 degrees along the circumferential direction S. Specifically, the first elastic part 310, the second elastic part 320, and the third elastic part 330 are disposed at equal intervals in the circumferential direction S. Similarly, the first seat part 410, the second seat part 420, and the third seat part 430 are disposed at equal intervals in the circumferential direction S. The first elastic part 310, the second elastic part 320, and the third elastic part 330 have a structure of rotational symmetry around the polishing axis J. Similarly, the first seat part 410, the second seat part 420, and the third seat part 430 have a structure of rotational symmetry around the polishing axis J.

    (Manufacturing Method of Polishing Tool)

    [0075] FIG. 7 shows a manufacturing method of the polishing tool 200. As illustrated in FIG. 7A, when a columnar (cylindrical) base metal B is worked by, for example, a wire cutter or the like, a precursor Z having first to third planes B1, B2, and B3 that spread radially with respect to a central axis C is formed as illustrated in FIG. 7B. The first plane B1, the second plane B2, and the third plane B3 of the precursor Z are each further worked by the wire cutter or the like to cut out a portion corresponding to a first rib 211, the first elastic part 310, and the first seat part 410 from the first plane B1, to cut out a portion corresponding to a second rib 212, the second elastic part 320, and the second seat part 420 from the second plane B2, and to cut out a portion corresponding to a third rib 213, the third elastic part 330, and the third seat part 430 from the third plane B3. Through these processes, the precise polishing tool 200 can be produced.

    (Tool Driving Mechanism)

    [0076] As illustrated in FIGS. 2 and 3, the tool driving mechanism 140 includes a first driving unit 510, a second driving unit 520, and a third driving unit 530.

    [0077] The first driving unit 510 serves as a member that supports and displaces the first seat part 410 from the outside toward the inside in the first radial direction R1. The first driving unit 510 includes: a first contact body 510A; a first displacement shaft 510B that holds the first contact body 510A and displaces it in the first radial direction R1; a first driving source 510C that reciprocatingly moves the first displacement shaft 510B in a shaft direction (first radial direction R1); a first bracket 510D that is fixed to a tool base 110 to movably hold the first driving source 510C in the first radial direction R1; and a first position adjusting unit 510E that adjusts the position of the first radial direction R1 in the first driving source 510C.

    [0078] The first position adjusting unit 510E includes a first female screw stand 510E1 that is fixed to the tool base 110, and a first adjusting male screw 510E2 to be threadedly engaged with the female screw of the first female screw stand 510E1. The first adjusting male screw 510E2 can freely move in the first radial direction R1 by adjusting a screwed-in amount of the first adjusting male screw 510E2 with respect to the first female screw stand 510E1. The position of the first driving source 510C in the first radial direction R1 is adjusted by engaging the forefront of the first adjusting male screw 510E2 with the first driving source 510C.

    [0079] The first contact body 510A is a spherical convex part having the same diameter as the spherical concave part of the first seat surface 410A. As a result, the first contact body 510A engaged with the first seat surface 410A functions as a so-called spherical seat. The first contact body 510A supports the first seat part 410 in all directions including the direction of the polishing axis J, the circumferential direction S, and the first radial direction R1. Here, a case has been illustrated where the first contact body 510A is a spherical convex part and the first seat surface 410A is a spherical concave part, and these structures may be reversed. Moreover, without being limited to the spherical seat structure, engagement between the first contact body 510A and the first seat surface 410A may be achieved in other structures.

    [0080] The first driving source 510C, which is a stacked piezoelectric actuator herein, is held by the first bracket 510D so that the first radial direction R1 serves as a displacement axis of the first driving source 510C. The stacked piezoelectric actuator can precisely control the position of the first displacement shaft 510B (first contact body 510A) relative to itself (actuator itself) at high speed with the voltage supplied from the tool control device 50.

    [0081] When the first driving source 510C displaces the first contact body 510A from the outside toward the inside in the first radial direction R1, the first seat part 410 moves in the same direction. At this time, since the first elastic part 310 elastically deforms in the first radial direction R1, the first external force F1 acts between the first contact body 510A and the first seat surface 410A. As the first contact body 510A is displaced more from the outside toward the inside in the first radial direction R1, the first external force F1 becomes larger. Note that the first position adjusting unit 510E has a role of providing pressure between the first contact body 510A and the first seat surface 410A.

    [0082] The second driving unit 520 serves as a member that supports and displaces the second seat part 420 from the outside toward the inside in the second radial direction R2. The second driving unit 520 includes: a second contact body 520A; a second displacement shaft 520B that holds the second contact body 520A and displaces it in the second radial direction R2; a second driving source 520C that reciprocatingly moves the second displacement shaft 520B in a shaft direction (second radial direction R2); a second bracket 520D that is fixed to the tool base 110 to movably hold the second driving source 520C in the second radial direction R2; and a second position adjusting unit 520E that adjusts the position of the second radial direction R2 in the second driving source 520C.

    [0083] The second position adjusting unit 520E includes a second female screw stand 520E1 fixed to the tool base 110, and a second adjusting male screw 520E2 to be threadedly engaged with the female screw of the second female screw stand 520E1. The second adjusting male screw 520E2 can freely move in the second radial direction R2 by adjusting a screwed-in amount of the second adjusting male screw 520E2 with respect to the second female screw stand 520E1. The position of the second driving source 520C in the second radial direction R2 is adjusted by engaging the forefront of the second adjusting male screw 520E2 with the second driving source 520C.

    [0084] The second contact body 520A is a spherical convex part having the same diameter as the spherical concave part of the second seat surface 420A. As a result, the second contact body 520A engaged with the second seat surface 420A functions as a so-called spherical seat. The second contact body 520A supports the second seat part 420 in all directions including the direction of the polishing axis J, the circumferential direction S, and the second radial direction R2. Here, a case has been illustrated where the second contact body 520A is a spherical convex part and the second seat surface 420A is a spherical concave part, and these structures may be reversed. Moreover, without being limited to the spherical seat structure, engagement between the second contact body 520A and the second seat surface 420A may be achieved in other structures.

    [0085] The second driving source 520C, which is a stacked piezoelectric actuator herein, is held by the second bracket 520D so that the second radial direction R2 serves as a displacement axis of the second driving source 520C. The stacked piezoelectric actuator can precisely control the position of the second displacement shaft 520B (second contact body 520A) relative to itself (actuator itself) at high speed with the voltage supplied from the tool control device 50.

    [0086] When the second driving source 520C displaces the second contact body 520A from the outside toward the inside in the second radial direction R2, the second seat part 420 moves in the same direction. At this time, since the second elastic part 320 elastically deforms in the second radial direction R2, the second external force F2 acts between the second contact body 520A and the second seat surface 420A. As the second contact body 520A is displaced more from the outside toward the inside in the second radial direction R2, the second external force F2 becomes larger. Note that the second position adjusting unit 520E has a role of providing pressure between the second contact body 520A and the second seat surface 420A.

    [0087] The third driving unit 530 serves as a member that supports and displaces the third seat part 430 from the outside toward the inside in the third radial direction R3. The third driving unit 530 includes a third contact body 530A; a third displacement shaft 530B that holds the third contact body 530A and displaces it in the third radial direction R3; a third driving source 530C that reciprocatingly moves the third displacement shaft 530B in a shaft direction (third radial direction R3); a third bracket 530D that is fixed to the tool base 110 to movably hold the third driving source 530C in the third radial direction R3; and a third position adjusting unit 530E that adjusts the position of the third radial direction R3 in the third driving source 530C.

    [0088] The third position adjusting unit 530E includes a third female screw stand 530E1 fixed to the tool base 110, and a third adjusting male screw 530E2 to be threadedly engaged with the female screw of the third female screw stand 530E1. The third adjusting male screw 530E2 can freely move in the third radial direction R3 by adjusting a screwed-in amount of the third adjusting male screw 530E2 with respect to the third female screw stand 530E1. The position of the third driving source 530C in the third radial direction R3 is adjusted by engaging the forefront of the third adjusting male screw 530E2 with the third driving source 530C.

    [0089] The third contact body 530A is a spherical convex part having the same diameter as the spherical concave part of the third seat surface 430A. As a result, the third contact body 530A engaged with the third seat surface 430A functions as a so-called spherical seat. The third contact body 530A supports the third seat part 430 in all directions including the direction of the polishing axis J, the circumferential direction S, and the third radial direction R3. Here, a case has been illustrated where the third contact body 530A is a spherical convex part and the third seat surface 430A is a spherical concave part, and these structures may be reversed. Moreover, without being limited to the spherical seat structure, engagement between the third contact body 530A and the third seat surface 430A may be achieved in other structures.

    [0090] The third driving source 530C, which is a stacked piezoelectric actuator herein, is held by the third bracket 530D so that the third radial direction R3 serves as a displacement axis of the third driving source 530C. The stacked piezoelectric actuator can precisely control the position of the third displacement shaft 530B (third contact body 530A) relative to itself (actuator itself) at high speed with the voltage supplied from the tool control device 50.

    [0091] When the third driving source 530C displaces the third contact body 530A from the outside toward the inside in the third radial direction R3, the third seat part 430 moves in the same direction. At this time, since the third elastic part 330 elastically deforms in the third radial direction R3, the third external force F3 acts between the third contact body 530A and the third seat surface 430A. As the third contact body 530A is displaced more from the outside toward the inside in the third radial direction R3, the third external force F3 becomes larger. Note that the third position adjusting unit 530E has a role of providing pressure between the third contact body 530A and third seat surface 430A.

    <Description of Function of Polishing Head>

    [0092] Now, the function of the polishing head will be described. Here, displacement amounts U1, U2, and U3 are exaggerated for the convenience of the illustrated description. As illustrated in FIG. 5, consider a case where the tool driving mechanism 140 generates, for the respective first seat part 410, second seat part 420, and third seat part 430, a first displacement amount (moving amount) U1, a second displacement amount U2, and a third displacement amount U3 in the direction toward the inside in the radial directions R1, R2, and R3 with the magnitude identical to each other. For example, as illustrated in FIG. 5B, the seat part-side continuous point 310B in the first elastic part 310 is applied with the first external force F1 based on the first displacement amount (moving amount) U1, and the main shaft-side continuous point 310A is applied with a combined force FG of the second external force F2 and the third external force F3 in the first radial direction R1 based on the second displacement amount U2 and the third displacement amount U3. Since the first external force F1 and the combined force FG have the same magnitude and their vectors are parallel, the first elastic part 310 elastically deforms like an elastic hinge, so that an inclination angle with respect to the polishing axis J decreases. Since the first seat part 410 is engaged in the direction of the polishing axis J, the main shaft-side continuous point 310A is displaced to the front end side of the polishing axis J, as shown by the state of transition from a chain line to a dotted line. Since elastic deformation of the first elastic part 310 also occurs in the second elastic part 320 and the third elastic part 330 in an exactly the same way, the main shaft part 210 is displaced to the front end side along the polishing axis J, so that the polishing surface 230 approaches the workpiece W. A displacement amount (distance) of the polishing surface 230 can be adjusted by the pressing-in amount of the first seat part 410, the second seat part 420, and the third seat part 430. In other words, the displacement amount (distance) of the polishing surface 230 can be adjusted by the magnitude of the first external force F1, the second external force F2, and the third external force F3. For example, when the first displacement amount (moving amount) U1, the second displacement amount U2, and the third displacement amount U3 are applied so as to coincide with each other in all of the increase-decrease amplitude (displacement width), the increase-decrease cycle, and the increase-decrease phase, the polishing surface 230 reciprocatingly vibrates along the polishing axis J. By making the displacement amounts U1, U2, and U3 unbalanced (unequal), the direction of vibration (vibration axis) of the polishing surface 230 can be inclined (tilted) with respect to the Z axis. Here, a case has been illustrated where the displacement amounts U1, U2, and U3 are applied in the direction toward the inside in the radial directions R1, R2, and R3. However, the present invention is not limited to this. For example, when the first displacement amount (moving amount) U1, the second displacement amount U2, and the third displacement amount U3 are generated in the direction toward the outside in the radial directions R1, R2, and R3 with their magnitude identical to each other, the main shaft-side continuous point 310A is displaced to the base end side in the polishing axis J.

    [0093] Next, as illustrated in FIG. 6, consider a case where the tool driving mechanism 140 generates, for the respective first seat part 410, second seat part 420, and third seat part 430, the first displacement amount U1, the second displacement amount U2, and the third displacement amount U3 in the direction toward the inside in the radial directions R1, R2, and R3 with the magnitude different from each other. Here, assume a case where the first displacement amount U1 is large, and the second displacement amount U2 and the third displacement amount U3 are identical to each other and smaller than the first displacement amount U1. In this case, as illustrated in FIG. 6C, due to the difference in displacement amount, a composite vector UF of displacement vectors corresponding to the first displacement amount U1, the second displacement amount U2, and the third displacement amount U3 remains in the first radial direction R1. As a result, as illustrated in FIG. 6B, while the elastic deformations of the first elastic part 310, the second elastic part 320, and the third elastic part 330 are present, the entire polishing tool 200 is offset in the first radial direction R1 (the direction of the composite vector UF). As a result, the main shaft part 210 and the polishing surface 230 move in the first radial direction R1. The radial displacement of the polishing surface 230 can appropriately be adjusted using the overall balance of the first displacement amount U1, the second displacement amount U2, and the third displacement amount U3. For example, when the first displacement amount (moving amount) U1, the second displacement amount U2, and the third displacement amount U3 are made to coincide with each other in increase-decrease amplitude (displacement width) and increase-decrease cycle, while their increase-decrease phases are shifted by equal intervals (in this case, phase intervals of 120 degrees), the polishing surface 230 turns around a predetermined turning central axis (Z axis) in the circumferential direction S. The turning radius can be controlled by the amplitude (maximum displacement amount) of the first displacement amount U1, the second displacement amount U2, and the third displacement amount U3. Here, a case has been illustrated where the displacement amounts U1, U2, and U3 are applied in the direction toward the inside in the radial directions R1, R2, and R3 with their amounts being different from each other. However, the present invention is not limited to this. For example, the first displacement amount (moving amount) U1, the second displacement amount U2, and the third displacement amount U3 may be generated in the direction toward the outside in the radial directions R1, R2, and R3 with their magnitudes different from each other. Furthermore, a case has been illustrated where all the displacement amounts U1, U2, and U3 are in the direction toward the inside in the radial directions R1, R2, and R3. However, the present invention is not limited to this. For example, the displacement amount U1 may be in the direction toward the inside in the radial directions R1, R2, and R3, and the displacement amount U2 and the displacement amount U3 may be in the direction toward the outside in the radial directions R1, R2, and R3. In short, the first seat part 410, the second seat part 420, and the third seat part 430 are different in displacement from each other in three patterns as shown below. The first pattern is a case where the displacement amounts U1, U2, and U3 are in an identical direction, which is toward the inside or outside in the radial directions R1, R2, and R3 and their displacement amounts are different from each other. The second pattern is a case where the displacement amounts U1, U2, and U3 are in directions different from each other, which are toward the inside or outside in the radial directions R1, R2, and R3, and their displacement amounts are identical to each other. The third pattern is a case where the displacement amounts U1, U2, and U3 are in directions different from each other, which are toward the inside or outside in the radial directions R1, R2, and R3, and their displacement amounts are also different from each other.

    <Movement Control Device>

    [0094] The movement control device 60 includes a driving driver and a calculator for the relative rotation mechanism 33 and the relative movement mechanism 40. As illustrated in FIG. 8A, the movement control device 60 has a movement control unit 62, a scanning path setting unit 64, and a polishing head setting calculation unit 65. The movement control device 60 is loaded with workpiece shape information 300, which is three-dimensional shape data on the surface (surface to be polished) of the workpiece W. Note that all or part of the movement control device 60 may be incorporated to the side of the polishing head 100.

    [0095] The scanning path setting unit 64 sets the scanning path information for the polishing surface 230 of the polishing head 100 with respect to the surface (surface to be polished) of the workpiece W. The scanning path information relates to change in three-dimensional relative coordinates (Xw, Yw, Xw) based on the workpiece W over time (t), and the scanning path information is defined here as N(t). In other words, the scanning path information N(t) can be expressed as positional information (Xw(t), Yw(t), Xw(t)) in the relative coordinates. The scanning path setting unit 64 refers to the workpiece shape information 300 at the time of setting the scanning path information N(t). For example, when the surface to be polished of the workpiece W has a three-dimensional shape that includes irregularities, grooves, or the like, the scanning path information N(t) is also the information along the irregularities or the like. When polishing is performed by rotating the relative rotation mechanism 33, the scanning path setting unit 64 preferably sets spiral scanning path information N(t) for the surface of the workpiece W.

    [0096] The movement control unit 62 controls the relative rotation mechanism 33 and the relative movement mechanism 40 on the basis of the scanning path information N(t) that has been set by the scanning path setting unit 64. As a result, the polishing surface 230 subjected to position control by the relative movement mechanism 40 moves along the scanning path information N(t) with respect to the surface to be polished of the workpiece W that is rotated by the relative rotation mechanism 33. In this case, it is desirable to control so that a separation distance between the workpiece W and the polishing surface 230 is constant (constant is the concept that excludes slight vibration and slight displacement of the polishing surface 230 caused by the tool driving mechanism 140). The movement control unit 62 can also tilt the polishing head 100 so that the polishing axis J is perpendicular to the surface to be polished of the workpiece W by using the relative movement mechanism 40.

    [0097] The polishing head setting calculation unit 65 generates polishing head setting information V, which is a target value relating to slight vibration and/or slight displacement of the polishing surface 230, in conjunction with the scanning path information N(t). The polishing head setting information V is stored in a polishing head setting holding unit 66. Examples of preferable polishing head setting information V to be held may include an amplitude value of the polishing surface 230 in the Z-axis direction, a turning radius of the polishing surface 230 around the Z axis, and instruction information about the amount of slight displacement at a vibration reference position of the polishing surface 230 using bias voltage. This makes it possible to change the vibration amount, the vibration cycle, and the vibration reference position of the polishing surface 230, in conjunction with the location (scanning path) of the polishing surface 230 relative to the workpiece W.

    [0098] For example, the preferable polishing head setting information V may relate to how to slightly vibrate and/or slightly displace the polishing surface 230 of the polishing head 100 in accordance with the position of the polishing surface 230 on the relative coordinates (Xw, Yw, Xw) over the surface to be polished of the workpiece W. In this case, the polishing head setting information V is the position function information V(Xw, Yw, Xw) depending on the relative coordinates (Xw, Yw, Xw).

    [0099] Meanwhile, for example, the preferable polishing head setting information V may relate to how to slightly vibrate and/or slightly displace the polishing surface 230 of the polishing head 100 in accordance with elapsed time (t) of the scanning path information N(t). In this case, the polishing head setting information V is time function information V(t) depending on the elapsed time (t).

    [0100] Specifically, the polishing head setting information V may be instruction information relating to the frequency, phase, and voltage (amplitude) for each signal generated by a first frequency signal generator 53, a second frequency signal generator 55, and a bias signal generator 56, as will be described later. In other words, the polishing head setting information V is the instruction information relating to the frequency, phase, and voltage (amplitude) for each of a first synchronization frequency signal DA, a second synchronization frequency signal DB, a third synchronization frequency signal DC, a first phase difference frequency signal QA, a second phase difference frequency signal QB, a third phase difference frequency signal QC, a first bias signal EA, a second bias signal EB, and a third bias signal EC. This means that all the signals DA, DB, DC, QA, QB, QC, EA, EB, and EC are position function signals DA(Xw, Yw, Xw), DB(Xw, Yw, Xw), DC(Xw, Yw, Xw), QA(Xw, Yw, Xw), QB(Xw, Yw, Xw), QC(Xw, Yw, Xw), EA(Xw, Yw, Xw), EB(Xw, Yw, Xw), and EC(Xw, Yw, Xw) depending on the relative coordinates (Xw, Yw, Xw), or they are time function signals DA(t), DB(t), DC(t), QA(t), QB(t), QC(t), EA(t), EB(t), and EC(t) depending on elapsed time. Here, a case has been illustrated where the relative coordinates (Xw, Yw, Xw) are used, and the relative coordinates may be converted to absolute coordinates (X, Y, X).

    [0101] The polishing head setting calculation unit 65 may receive real-time position information on the polishing head 100 by the movement control unit 62 of the movement control device 60, and may calculate the polishing head setting information V in real time. The polishing head setting information V is transmitted to the tool control device 50 in real time to slightly vibrate the polishing head 100.

    <Tool Control Device>

    [0102] As illustrated in FIG. 8B, the tool control device 50 includes an amplifier type power supply (driver) and a calculator to control the displacement amount and the vibration amount of the stacked piezoelectric actuators constituting the first driving source 510C, the second driving source 520C, and the third driving source 530C. Specifically, the tool driving mechanism 140 includes a first driver 51A that controls the first driving source 510C, a second driver 51B that controls the second driving source 520C, and a third driver 51C that controls the third driving source 530C. The tool control device 50 further includes the first frequency signal generator 53, the second frequency signal generator 55, the bias signal generator 56, and a signal superimposing unit 57.

    [0103] The first frequency signal generator 53 generates a plurality of frequency signals by referring to the polishing head setting holding unit 66. In the present embodiment, in particular, the first frequency signal generator 53 is configured to generate a plurality of synchronization frequency signals that coincide with each other in increase-decrease cycle and increase-decrease phase. Specifically, the first frequency signal generator 53 includes a first first frequency signal generator 53A that generates the first synchronization frequency signal DA for the first driving source 510C, a first second frequency signal generator 53B that generates the second synchronization frequency signal DB for the second driving source 520C, and a first third frequency signal generator 53C that generates the third synchronization frequency signal DC for the third driving source 530C. The first to third synchronization frequency signals DA, DB, and DC are signals identical to each other in all of the increase-decrease amplitude, the increase-decrease cycle, and the increase-decrease phase.

    [0104] The second frequency signal generator 55 generates a plurality of frequency signals by referring to the polishing head setting holding unit 66. In the present embodiment, in particular, the second frequency signal generator 55 is configured to generate a plurality of phase difference frequency signals that are different from each other in increase-decrease phase. Specifically, the second frequency signal generator 55 includes a second first frequency signal generator 55A that generates the first phase difference frequency signal QA for the first driving source 510C, a second second frequency signal generator 55B that generates the second phase difference frequency signal QB for the second driving source 520C, and a second third frequency signal generator 55C that generates the third phase difference frequency signal QC for the third driving source 530C. The first phase difference frequency signal QA, the second phase difference frequency signal QB, and the third phase difference frequency signal QC coincide with each other in increase/decrease amplitude and increase-decrease cycle, and their increase-decrease phases are different from each other by 120 degrees. The amplitude and cycle of these signals are determined on the basis of a turning radius and turning cycle information on the polishing surface 230 in the polishing head setting holding unit 66. The frequency of the first phase difference frequency signal QA, the second phase difference frequency signal QB, and the third phase difference frequency signal QC is preferably set to become smaller than the frequency of the first to third synchronization frequency signals DA, DB, and DC. The amplitude of the first phase difference frequency signal QA, the second phase difference frequency signal QB, and the third phase difference frequency signal QC is preferably set to become larger than the amplitude of the first to third synchronization frequency signals DA, DB, and DC. By setting the frequency of the first to third synchronization frequency signals DA, DB, and DC larger than the frequency of the first to third phase difference frequency signals QA, QB, and QC, the polishing surface 230 vibrates in two vibration modes that are different from each other in frequency.

    [0105] The bias signal generator 56 generates a plurality of bias signals by referring to the polishing head setting holding unit 66. Specifically, the bias signal generator 56 includes a first bias signal generator 56A that generates the first bias signal EA for the first driving source 510C, a second bias signal generator 56B that generates the second bias signal EB for the second driving source 520C, and a third bias signal generator 56C that generates the third bias signal EC for the third driving source 530C. As illustrated in FIG. 11A, the first to third bias signals EA, EB, and EC may have pulsed (linear) waveforms or periodic waveforms such as sinusoidal waves. Note that the units (for example, seconds) of a horizontal axis (time) of the first to third bias signals EA, EB, and EC in FIG. 11A are significantly larger than the units (for example, milliseconds) of the horizontal axis in FIGS. 9A and 9B. In the case of adopting periodic waveforms, their frequency is preferably smaller than the frequency of the first to third synchronization frequency signals DA, DB, and DC and the first to third phase difference frequency signals QA, QB, and QC.

    [0106] The signal superimposing unit 57 includes a first signal superimposing unit 57A, a second signal superimposing unit 57B, and a third signal superimposing unit 57C. The first signal superimposing unit 57A generates a first driving signal KA obtained by superimposing the first synchronization frequency signal DA, the first phase difference frequency signal QA, and the first bias signal EA. The first signal superimposing unit 57A transmits the first driving signal KA to the first driver 51A. As a result, the first driver 51A displaces the first driving source 510C on the basis of the first driving signal KA.

    [0107] The second signal superimposing unit 57B generates a second driving signal KB obtained by superimposing the second synchronization frequency signal DB, the second phase difference frequency signal QB, and the second bias signal EB. The second signal superimposing unit 57B transmits the second driving signal KB to the second driver 51B. As a result, the second driver 51B displaces the second driving source 520C on the basis of the second driving signal KB.

    [0108] The third signal superimposing unit 57C generates a third driving signal KC obtained by superimposing the third synchronization frequency signal DC, the third phase difference frequency signal QC, and the third bias signal EC. The third signal superimposing unit 57C transmits the third driving signal KC to the third driver 51C. As a result, the third driver 51C displaces the third driving source 530C on the basis of the third driving signal KC.

    (Function of Tool Control Device)

    [0109] FIG. 9C schematically shows the first to third driving signals KA, KB, and KC generated by superimposing the first to third synchronization frequency signals DA to DC in FIG. 9A and the first to third phase difference frequency signals QA, QB, and QC in FIG. 9B, respectively. Note that the frequency of the first to third synchronization frequency signals DA to DC in FIG. 9A is 200 Hz. The first phase difference frequency signal QA, the second phase difference frequency signal QB, and the third phase difference frequency signal QC in FIG. 9B are set to have a frequency of 99 Hz, and their reference phases are set to have a phase difference of 120 degrees from each other.

    [0110] The first to third synchronization frequency signals DA, DB, and DC included in the first to third driving signals KA, KB, and KC in FIG. 9C coincide with each other in amplitude and cycle. As a result, as illustrated in FIG. 5B, the polishing surface 230 reciprocatingly vibrates along the polishing axis J at 200 Hz. At the same time, the first to third phase difference frequency signals QA, QB, and QC included in the first to third driving signals KA, KB, and KC in FIG. 9C have a phase difference of 120 degrees. As a result, the mode shown in FIG. 6B periodically changes in the circumferential direction, and as illustrated in FIG. 9D, the polishing surface 230 slightly turns with respect to the center of turning L, which is the vibration reference position, around the Z axis at 99 Hz (5,960 rpm). When the first to third synchronization frequency signals DA, DB, and DC have amplitude difference, the polishing surface 230 can turn in an elliptical orbit, for example. This setting allows the polishing surface 230 to reciprocatingly vibrate along a spiral moving locus with a spiral axis in the Z-axis direction.

    [0111] In FIG. 9, a case has been illustrated where the polishing surface 230 is slightly turned by the first to third phase difference frequency signals QA, QB, and QC. However, the present invention is not limited to this. For example, by appropriately setting the amplitude (voltage) and the phase difference of the first to third phase difference frequency signals QA, QB, and QC, the polishing surface 230 can reciprocatingly vibrate linearly in the Y-axis direction (or in the X-Y plane) without turning (see arrow QM) by the first to third phase difference frequency signals QA, QB, and QC as illustrated in FIG. 10. When the reciprocating vibration (see arrow QM) is made to coincide with the reciprocating vibration in the Z-axis direction (see arrow KM) by the first to third synchronization frequency signals DA, DB, and DC, the polishing surface 230 can reciprocatingly vibrate in the direction inclined with respect to the Z axis (see arrow RM). As a result, when, for example, a normal direction of the surface of the workpiece W is inclined with respect to the Z axis, the vibration direction of the polishing surface 230 (see arrow RM) can be made to coincide with the normal direction of the workpiece W.

    [0112] The first to third driving signals KA(t1), KB(t1), and KC(t1) in FIG. 11B are generated by superimposing the first to third synchronization frequency signals DA to DC in FIG. 9A, the first to third phase difference frequency signals QA, QB, and QC in FIG. 9B, and the first to third bias signals EA, EB, and EC in FIG. 11A, respectively. These first to third driving signals KA(t1), KB(t1), and KC(t1) schematically show the state in the vicinity of elapsed time t1 in FIG. 11A. At elapsed time t1, a bias value Ba1 of the first bias signal EA is present. As a result, the first driving signal KA(t1) has a higher value (higher voltage) by the bias value Ba1 than the second and third driving signals KB(t1) and KC(t1). As illustrated in FIG. 11C, since the first external force F1 (KA(t1)) increases by the bias value Ba1, a vibration reference position (center of turning) L1 is offset by distance O1 as compared with the vibration reference position (center of turning) L0 without a bias. At elapsed time t2 in FIG. 11A, a bias value Bb2 of the second bias signal EB is present. Accordingly, the second external force F2 (KB(t2)) increases as illustrated in FIG. 11D, so that a vibration reference position (center of rotation) L2 is offset by distance O2 as compared with the vibration reference position (center of turning) L without a bias. At elapsed time t3 in FIG. 11A, a bias value Bc3 of the third bias signal EC is present. Accordingly, the third external force F3 (KC(t3) increases as illustrated in FIG. 11D, so that a vibration reference position (center of rotation) L3 is offset by distance O3 as compared with the vibration reference position (center of turning) L without a bias.

    [0113] As is clear from these cases, when the first to third bias signals EA, EB, and EC are set to sine wave signals (frequency signals) with a phase difference of 120 degrees from each other, the vibration reference position (center of turning) L of the polishing surface 230 itself can be turned around the Z axis. Similarly, when the first to third bias signals EA, EB, and EC are appropriately combined, the center of turning L can be offset in any direction and with any amount. In other words, by controlling the first to third bias signals EA, EB, and EC, the spiral axis itself for the spiral moving locus of the polishing surface 230 can be turned around the Z axis or moved in any direction in the XY plane.

    [0114] The first to third driving signals KA(t1), KB(t1), and KC(t1) in FIG. 12B are generated by superimposing the first to third synchronization frequency signals DA, DB, and DC in FIG. 9A, the first to third phase difference frequency signals QA, QB, and QC in FIG. 9B, and the first to third bias signals EA, EB, and EC in FIG. 12A, respectively. These first to third driving signals KA(t1), KB(t1), and KC(t1) schematically show the state in the vicinity of elapsed time t1 in FIG. 12A.

    [0115] As illustrated in FIG. 12A, at elapsed time t1, a bias value Ba1 of the first bias signal EA, a bias value Bb1 of the second bias signal EB, and a bias value Bc1 of the third bias signal EC are concurrently present with their values identical to each other. As a result, the first driving signal KA(t1), the second and third driving signals KB(t1) and KC(t1) have higher values (higher voltage) by the bias values Ba1, Bb1, and Bc1, respectively. As a result, as illustrated in FIG. 12C, the Z-axis coordinate Z(t1) of the vibration reference position L1 of the polishing surface 230 is displaced in the Z-axis direction as compared with the Z-axis coordinate Z(0) of the vibration reference position L0 of the polishing surface 230 without a bias. At elapsed time t2 in FIG. 12A, a bias value Ba2 of the first bias signal EA, a bias value Bb2 of the second bias signal EB, and a bias value Bc2 of the third bias signal EC are present with their values identical to each other, and they are larger than the bias values at elapsed time t1. As a result, as illustrated in FIG. 12D, a Z-axis coordinate Z(t2) of the vibration reference position L2 of the polishing surface 230 is displaced in the Z-axis direction by the bias values as compared with the Z-axis coordinate Z(0) of the vibration reference position L0 of the polishing surface 230 without a bias, and its displacement amount is larger than that in the Z-axis coordinate Z(t1). At elapsed time t3 in FIG. 12A, a bias value Ba3 of the first bias signal EA, a bias value Bb3 of the second bias signal EB, and a bias value Bc3 of the third bias signal EC are present with their values identical to each other, and they are larger than the bias values at elapsed time t2. As a result, as illustrated in FIG. 12E, a Z-axis coordinate Z(t3) of the vibration reference position L3 of the polishing surface 230 is displaced in the Z-axis direction as compared with the Z-axis coordinate Z(0) of the vibration reference position L0 of the polishing surface 230 without a bias, and its displacement amount is larger than that in the Z-axis coordinate Z(t2).

    [0116] As is clear from these cases, the vibration reference position L of the polishing surface 230 can be displaced in the Z-axis direction by concurrently applying the first to third bias signals EA, EB, and EC. By combining the technical concepts shown in FIGS. 11 and 12, the position of the vibration reference position L of the polishing surface 230 can freely be controlled in both the axial and radial directions with the first to third bias signals EA, EB, and EC.

    [0117] The polishing head setting holding unit 66 of the tool control device 50 can automatically change the setting values, such as the amplitude or voltage, frequency, and reference phase of each of the first to third synchronization frequency signals DA, DB, and DC, the first to third phase difference frequency signals QA, QB, and QC, and the first to third bias signals EA, EB, and EC, along the scanning path.

    [0118] For example, as illustrated in FIG. 13A, when part of the surface to be polished of the workpiece W on the scanning path has a flat or convex shape, a turning radius r1 of the polished surface 230 can be set large. This enhances the polishing efficiency. Meanwhile, as illustrated in FIG. 13B, when part of the surface to be polished of the workpiece W on the scanning path has a groove or concave shape, a turning radius r2 of the polishing surface 230 is set smaller to prevent interference between the polishing surface 230 and the surface to be polished. For example, when the workpiece W is a diffractive optics lens using a diffraction optical system or a microlens array, its surface has irregularities. It is therefore preferable to control the turning radius depending on the scanning path. Moreover, as illustrated in FIG. 13C, when the workpiece W is a convex curved surface or a concave curved surface, the first to third bias signals EA, EB, and EC allow the vibration reference position L of the polishing surface 230 to be moved in both the axial and radial directions, so that the distance (polishing gap) between the curved surface of the workpiece W and the polishing surface 230 can be controlled with high precision at high speed. For example, when the workpiece W is rotated at high speed by the relative rotation mechanism 33, it may be difficult to maintain a constant polishing gap against the irregularities of the surface to be polished of the workpiece W due to a response speed limit of the relative movement mechanism 40. In such cases, the first to third bias signals EA, EB, and EC can maintain the polishing gap constant. To achieve such control, the polishing head setting calculation unit 65 in FIG. 8A controls the first to third bias signals EA, EB, and EC on the basis of the scanning path information N(t) and the workpiece shape information 300.

    (Introduction of Modifications)

    [0119] In FIGS. 9 and 10, a case has been illustrated where the first frequency signal generator 53 of the tool control device 50 generates the first to third synchronization frequency signals DA, DB, and DC that coincide with each other in increase-decrease cycle and increase-decrease phase. However, the present invention is not limited to this. The first frequency signal generator 53 may generate the first to third phase difference frequency signals GA, GB, and GC that are different from each other in increase-decrease phase. The polished surface 230 can be vibrated slightly or turned slightly in any direction by freely controlling the phase, frequency, and amplitude of the total six signals including the first to third phase difference frequency signals GA, GB, and GC generated by the first frequency signal generator 53 and the first to third phase difference frequency signals QA, QB, and QC generated by the second frequency signal generator 55.

    [0120] Thus, in the present embodiment, when the number of the driving units is n (n=3 in the present embodiment), the number of the frequency signals to be generated is preferably at least 2n (at least 6 in this case), and a driving signal obtained by superimposing at least two frequency signals is preferably input into each of the driving units. In this manner, when each driving unit is displaced on the basis of two or more frequency signals, the polishing surface of the polishing tool can be displaced concurrently in the axial and radial directions of the polishing axis. When 3n or more (9 or more in this case) frequency signals are generated, in particular, the polishing surface can be displaced with higher precision.

    <Demonstration Experiment 1: Verification of Polishing Head Operation>

    [0121] How the polishing surface 230 was displaced in the single polishing head 100 was verified. Specifically, the first to third synchronization frequency signals DA to DC were set to have a frequency of 200 Hz and their reference phases were all set to 0. The first phase difference frequency signal QA, the second phase difference frequency signal QB, and the third phase difference frequency signal QC were set to have a frequency of 99 Hz, and their reference phases were set to have a phase difference of 120 degrees from each other. The amplitude of these signals was appropriately set in the range of 0 to 4 (V). The input of the first to third bias signals EA, EB, and EC were omitted. Under these conditions, the polishing tool 200 was vibrated by the tool driving mechanism 140, and the displacement of the polishing surface 230 in the Z-axis direction and the displacement of the polishing surface 230 in the radial direction R were measured with confocal chromatic sensors. The results thereof are shown in FIG. 14.

    [0122] As illustrated in FIG. 14A, it was possible to reciprocatingly vibrate the polishing surface 230 with a travel distance of 0.025 mm or less (for example, 0.015 mm) in the Z-axis direction. The reciprocating vibration waveform was a smooth sinusoidal wave of 200 Hz, and the displacement amount normalized by the voltage of the driving signal was 4 m/V.

    [0123] As illustrated in FIG. 14B, it was possible to turnably vibrate the polishing surface 230 in the radial direction R (X-Y plane direction) with a travel distance of 0.025 mm or less (for example, 0.015 mm) so as to be superimposed on the vibration in the Z-axis direction. This reciprocating vibration waveform was approximate to the shape of a seesaw function of 99 Hz, and the normalized displacement amount was 5 m/V. One characteristic feature is that there is almost no crosstalk between the slight vibration in the Z-axis direction and the slight vibration in the radial direction R. This means that even when the polishing tool 200 is displaced in a superimposing manner by the first driving signal KA, the second driving signal KB, and the third driving signal KC using the tool driving mechanism 140, the slight vibration of the polishing surface 230 in the Z-axis direction and the slight vibration in the radial direction R can independently be controlled.

    [0124] Note that this verification procedures can be used as a calibration method for the single polishing head 100. In other words, the setting values of the first to third synchronization frequency signals DA to DC, the first phase difference frequency signal QA, the second phase difference frequency signal QB, and the third phase difference frequency signal QC may be adjusted until a desired slight vibration in the Z-axis direction and a desired slight vibration in the radial direction R can be obtained.

    <Demonstration Experiment 2: Verification of Polishing by Polishing Apparatus>

    [0125] Next, polishing of the workpiece W using the polishing apparatus 1 shown in FIG. 1 was verified. For example, in the case of molding using a metal mold, a hairline-like cutting mark (tool mark), which is a moving locus of a working tool at the time of manufacturing the metal mold, is formed on the surface of the metal mold, and this tool mark may be transferred to an optical element. Similarly, when an optical element is directly worked by cutting, a hairline-like cutting mark (tool mark), which is a moving locus of the cutting tool, remains on the optical element. It was verified whether or not the tool mark could be erased by polishing the surface of the workpiece W by the polishing apparatus 1.

    (Preparation of Polishing Material)

    [0126] As a polishing material, alumina particles of #30000 (particle size of 0.3 to 0.39 m) were mixed into non-Newtonian fluid, which was adjusted to a desired viscosity by setting a mixture ratio between water and starch in the range of 50:50 to 50:30, at a concentration of 40 g/L.

    (Preparation of Workpiece)

    [0127] A disc-shaped (cylindrical) workpiece W plated with electroless nickel was prepared, and its circular surface (surface to be polished) was cut along a hairline-like moving path by diamond turning. The resultant surface state is shown in FIG. 15. As shown by an optical micrograph in FIG. 15A, it was confirmed that hairline-shaped irregularities (grooves or peaks) were formed on the surface to be polished. As shown by a three-dimensional profile measured by a three-dimensional scanner in FIG. 15B, it was confirmed that hairline-shaped irregularities (grooves or peaks) were formed on the surface to be polished. The surface roughness measured using the three-dimensional profile was 0.24 nmRa. A line pitch (distance) of the hairline-like irregularities (grooves or peaks) was about 20 m.

    (Setting of Polishing Apparatus)

    [0128] In the polishing apparatus 1, the polishing surface 230 was a circular plane with a diameter of 2 mm. The first to third synchronization frequency signals DA to DC were set to have a frequency of 1,000 Hz and their reference phases were all set to 0. The first phase difference frequency signal QA, the second phase difference frequency signal QB, and the third phase difference frequency signal QC were set to have a frequency of 100 Hz, and their reference phases were set to have a phase difference of 120 degrees from each other. It was confirmed by calibration that the polishing surface 230 vibrated slightly with an amplitude of 10 m in the Z-axis direction at 1,000 Hz. It was also confirmed that the polishing surface 230 turned around the Z-axis at 100 Hz with a radius of 20 m (slightly moved with an amplitude of 40 m in the radial direction R). Using the polishing apparatus 1, the surface to be polished of the workpiece W was scanned by the polishing surface 230, while the polishing material was being supplied and the workpiece W was being rotated at 100 rpm, so that the surface to be polished was polished to a material removal depth of about 10 nm. During polishing, a gap distance between the workpiece W and the polishing surface 230 was controlled to be 50 m to 100 m. The experiments by the inventors have clarified that as long as the gap distance is within the above range, the polishing material becomes locally viscous due to the slight vibration (pressure) of 1,000 Hz with an amplitude of 10 m in the Z-axis direction.

    [0129] The surface state after the completion of polishing is shown in FIG. 16. As shown in the optical micrograph in FIG. 16A and the three-dimensional profile in FIG. 16B, it was confirmed that hairline-like irregularities (grooves or peaks) were mostly removed on the surface to be polished. This has clarified that the surface precision (PV value) of the surface to be polished can be reduced to 100 nm or less. The surface roughness measured using the three-dimensional profile shown in FIG. 16B was 0.37 nmRa, which indicated that an increase in surface roughness in the polishing process could be suppressed. In other words, according to the polishing apparatus 1 of the present embodiment, the hairline-like irregularities can be flattened to a PV value of 100 nm or less while the increase in surface roughness can be suppressed to 0.50 nmRa or less, for example.

    <Comparative Experiment: Verification of Polishing by Polishing Apparatus>

    [0130] Next, the workpiece W was polished under the conditions completely identical to those in the demonstration experiment 2 except that the turning motion around the Z-axis of the polishing surface 230 (the slight vibration in radial direction R) was stopped in the polishing apparatus 1. The surface state after the completion of polishing is shown in FIG. 17. As shown in an optical micrograph in FIG. 17A and a three-dimensional profile in FIG. 17B, it was confirmed that some hairline-like irregularities (grooves or peaks) remained on the surface to be polished. At the same time, it was confirmed that a local pit (dent) was formed on the surface to be polished. The surface roughness measured using the three-dimensional profile shown in FIG. 17B was 0.51 nmRa, which indicated that the surface roughness increased in the polishing process.

    [0131] As described above, according to the polishing apparatus 1 of the present embodiment, displacing a plurality of seat parts 410, 420 and 430 of the single polishing tool 200 makes it possible to slightly vibrate the polishing surface 230 concurrently in the direction of the polishing axis J and in the radial direction R while elastically deforming the plurality of seat parts. In addition, since crosstalk is less likely to occur in the slight vibrations in the direction of the polishing axis J and in the radial direction R, the slight vibration of the polishing surface 230 in the direction of the polishing axis J and the slight vibration in the radial direction R can independently be controlled. Similarly, since the plurality of driving units 510, 520 and 530 of the tool driving mechanism 140 work in cooperation, the slight vibrations of the polishing surface 230 in the direction of the polishing axis J and in the radial direction R can concurrently be implemented, and therefore the structure of the polishing head 100 can be simplified.

    [0132] For the polishing apparatus 1, a case has been illustrated where the polishing tool 200 includes total three elastic parts including the first elastic part 310, the second elastic part 320, and the third elastic part 330 along the first to third radial directions R1 to R3 with a phase difference of 120 degrees. However, the present invention is not limited to this, and total two elastic parts may be provided with a phase difference of 180 degrees. Total four or more elastic parts may be provided with an equal phase difference in the circumferential direction. In order to achieve the turning motions of the polishing surface 230, at least three elastic parts are preferably provided.

    [0133] For the polishing tool 200, a case has been illustrated where an inclination angle between the first arm axis 310J of the first elastic part 310 and the polishing axis J is an acute angle as illustrated in FIG. 5B. However, the inclination angle may be an obtuse angle. When the inclination angle is an obtuse angle, it is possible to displace the polishing surface 230 in the direction separated from the workpiece W by displacing the first seat part 410 toward the inside in the first radial direction R1.

    [0134] Furthermore, for the tool driving mechanism 140, a case has been illustrated where the first to third seat parts 410, 420, and 430 are displaced toward the polishing axis J radially inward as illustrated in FIG. 2. However, the present invention is not limited to this. For example, while the first to third seat parts 410, 420, and 430 are displaced radially inward, they may be displaced in the direction where their displacement vectors are offset from the polishing axis J. The tool driving mechanism 140 may also displace the first to third seat parts 410, 420, and 430 radially outward.

    [0135] Moreover, for the tool control device 50, a case has been illustrated where the amplitude of the first phase difference frequency signal QA, the second phase difference frequency signal QB and the third phase difference frequency signal QC is larger than the synchronization frequency signal D. However, the present invention is not limited to this. For example, as illustrated in FIG. 18, the amplitude of the first to third phase difference frequency signals QA, QB, and QC may be set to become smaller than the first to third synchronization frequency signals DA, DB, and DC to generate the first to third driving signals KA, KB, and KC.

    [0136] Furthermore, in the present embodiment, a case has been described where the first to third synchronization frequency signals DA, DB, and DC, the first to third phase difference frequency signals QA, QB, and QC, and the first to third bias signals EA, EB, and EC are each generated as an independent waveform for the convenience of explanation. However, the present invention is not limited to this. For example, when an average voltage value of the first synchronization frequency signal DA is set higher than an average voltage value of the second and third synchronization frequency signals DB and DC, it is substantially synonymous with the state of superimposing the first bias signal EA. Similarly, when an average voltage value of the first phase difference frequency signal QA is set higher than an average voltage value of the second and third phase difference frequency signals QB and QC, it is substantially synonymous with the state of superimposing the first bias signal EA.

    [0137] Furthermore, in the present embodiment, a case has been illustrated where the polishing tool is displaced concurrently in the axial direction and the radial direction by separately generating and superimposing the first to third synchronization frequency signals DA, DB, and DC and the first to third phase difference frequency signals QA, QB, and QC. However, the present invention is not limited to this. The same signal source may be used in a time division mode, so that during a predetermined first period, the first to third synchronization frequency signals DA, DB, and DC are generated to displace the polishing tool in the axial direction, and during a predetermined second period, the first to third phase difference frequency signal QA, QB, and QC are generated to displace the polishing tool in the radial direction. In other words, the period of axial displacement and the period of radial displacement may be switched by switching the plurality of first frequency signals.

    [0138] The present invention is not limited to the above-described embodiments, and it goes without saying that various modifications can be made without departing from the spirit and scope of the present invention.

    REFERENCE SIGNS LIST

    [0139] 1 polishing apparatus [0140] 10 base [0141] 20 polishing head holding mechanism [0142] 30 workpiece holding mechanism [0143] 33 relative rotation mechanism [0144] 35 polishing material supplying device [0145] 40 relative movement mechanism [0146] 50 tool control device [0147] 60 movement control device [0148] 62 movement control part [0149] 64 scanning path setting unit [0150] 66 polishing head setting holding unit [0151] 100 polishing head [0152] 110 tool base [0153] 140 tool driving mechanism [0154] 200 polishing tool [0155] 210 main shaft part [0156] 210A central shaft [0157] 211 first rib [0158] 212 second rib [0159] 213 third rib [0160] 230 polishing surface [0161] 310 first elastic part [0162] 320 second elastic part [0163] 330 third elastic part [0164] 410 first seat part [0165] 420 second seat part [0166] 430 third seat part [0167] 510 first driving unit [0168] 520 second driving unit [0169] 530 third driving unit [0170] B base metal [0171] C central axis [0172] DA first synchronization frequency signal [0173] DB second synchronization frequency signal [0174] DC third synchronization frequency signal [0175] J polishing axis [0176] KA first driving signal [0177] KB second driving signal [0178] KC third driving signal [0179] QA first phase difference frequency signal [0180] QB second phase difference frequency signal [0181] QC third phase difference frequency signal [0182] R radial direction [0183] S circumferential direction with reference to polishing axis [0184] U1 first displacement amount [0185] U2 second displacement amount [0186] U3 third displacement amount [0187] W workpiece