POLISHING TOOL, POLISHING METHOD AND POLISHING APPARATUS

Abstract

A polishing tool includes a polishing surface having a spherical zone shape and having a plurality of non-contact portions provided from an inner edge to an outer edge of the polishing surface so as not to contact with a workpiece. The plurality of non-contact portions is a plurality of grooves whose widths in a circumferential direction increase from the inner edge toward the outer edge. A polishing method using the polishing tool includes: rotating the polishing tool about the central axis of rotation; and simultaneously with rotating the polishing tool, swinging relatively at least one of the workpiece and the polishing tool with a predetermined swing width, around a position where a line passing through a center of the workpiece and intersecting with the central axis of rotation passes through a center in a width direction of a spherical zone of the polishing surface, thereby polishing the workpiece.

Description

BACKGROUND

1. Technical Field

The disclosure relates to a polishing tool, a polishing method, and a polishing apparatus for surface finishing of optical elements such as lenses.

2. Related Art

Typically, for surface finishing of optical elements such as lenses, prisms, and mirrors, a polishing tool and a workpiece are made to slide along each other so that the object is polished by abrasive grains for polishing present at the interface. A polishing tool is fabricated by making pellets of fixed abrasive grains adhere to a base plate to make a desired curved surface with the fixed abrasive grains or adhering polishing sheets made of polyurethane formed in a desired curved surface onto a base plate.

In recent years, the have been demands for optical elements with high shape accuracy and with no surface irregularity. For example, JP 2006-136959 A discloses a polishing tool in which the distances from the rotary axis of the polishing tool to the outer circumferential shape of the work surface on which a workpiece is polished are not equal along the rotational direction, which is a polishing tool that achieves high shape accuracy by using an existing polishing apparatus without any change.

SUMMARY

In some embodiments, a polishing tool includes a polishing surface having a spherical zone shape and having a plurality of non-contact portions provided from an inner edge to an outer edge of the polishing surface so as not to contact with a workpiece. The plurality of non-contact portions is a plurality of grooves whose widths in a circumferential direction increase from the inner edge toward the outer edge.

In some embodiments, a polishing method using the polishing tool includes: rotating the polishing tool about the central axis of rotation; and simultaneously with rotating the polishing tool, swinging relatively at least one of the workpiece and the polishing tool with a predetermined swing width, around a position where a line passing through a center of the workpiece and intersecting with the central axis of rotation passes through a center in a width direction of a spherical zone of the polishing surface, thereby polishing the workpiece.

In some embodiments, a polishing apparatus includes: the polishing tool; a pressure applying unit configured to bring the workpiece into contact with the polishing surface of the polishing tool, thereby to apply pressure to the workpiece; a rotating unit configured to rotate the polishing tool about the central axis of rotation; and a swinging unit configured to swing relatively at least one of the workpiece and the polishing tool with a predetermined swing width, around a position where a line passing through a center of the workpiece and intersecting with the central axis of rotation passes through a center in a width direction of a spherical zone of the polishing surface, thereby to polish the workpiece.

In some embodiments, a polishing tool includes a polishing surface having a spherical zone shape and having a plurality of non-contact portions provided from an inner edge to an outer edge of the polishing surface so as not to contact with a workpiece. The plurality of non-contact portions is formed by a plurality of holes, and a density per unit area of the plurality of holes increases from the inner edge toward the outer edge.

In some embodiments, a polishing method using the polishing tool includes: rotating the polishing tool about the central axis of rotation; and simultaneously with rotating the polishing tool, swinging relatively at least one of the workpiece and the polishing tool with a predetermined swing width, around a position where a line passing through a center of the workpiece and intersecting with the central axis of rotation passes through a center in a width direction of a spherical zone of the polishing surface, thereby polishing the workpiece.

In some embodiments, a polishing apparatus includes: the polishing tool; a pressure applying unit configured to bring the workpiece into contact with the polishing surface of the polishing tool, thereby to apply pressure to the workpiece; a rotating unit configured to rotate the polishing tool about the central axis of rotation; and a swinging unit configured to swing relatively at least one of the workpiece and the polishing tool with a predetermined swing width, around a position where a line passing through a center of the workpiece and intersecting with the central axis of rotation passes through a center in a width direction of a spherical zone of the polishing surface, thereby to polish the workpiece.

The above and other features, advantages and technical and industrial significance of this invention will be better understood by reading the following detailed description of presently preferred embodiments of the invention, when considered in connection with the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic view illustrating a configuration of a polishing apparatus according to a first embodiment of the present invention;

FIG. 2 is a cross-sectional view of a polishing tool used in FIG. 1;

FIG. 3 is a top view of the polishing tool of FIG. 2;

FIG. 4 is a schematic view for explaining a method for polishing a lens using the polishing apparatus illustrated in FIG. 1;

FIG. 5 is a schematic view for explaining the method for polishing a lens using the polishing apparatus illustrated in FIG. 1;

FIG. 6 is a top view of a polishing tool according to a first modification of the present invention;

FIG. 7 is a top view of a polishing tool according to a second modification of the present invention;

FIG. 8 is a top view of a polishing tool according to a third modification of the present invention;

FIG. 9 is a top view of a polishing tool according to a fourth modification of the present invention;

FIG. 10 is a top view of a polishing tool according to a fifth modification of the present invention;

FIG. 11 is a top view of a polishing tool according to a sixth modification of the present invention; and

FIG. 12 is a diagram explaining a structure of a polishing surface formed on a polishing tool according to a second embodiment.

DETAILED DESCRIPTION

Embodiments of the present invention will now be described with reference to the drawings. The present invention is not limited to the embodiments. The same reference signs are used to designate the same elements throughout the drawings. The drawings are schematic, and the relative sizes and ratios of elements may be different from the actual sizes and ratios. The relative sizes and ratios of the elements may be different between the drawings.

First Embodiment

FIG. 1 is a schematic view illustrating a configuration of a polishing apparatus according to a first embodiment of the present invention. FIG. 2 is a cross-sectional view of a polishing tool used in FIG. 1, and FIG. 3 is a top view of the polishing tool of FIG. 2. A polishing apparatus 100 according to the first embodiment includes a polishing tool 3, a holder 2 for bringing a lens 1 as a workpiece, into contact with a polishing surface 30b of the polishing tool 3, a rotary motor 7 for rotating the polishing tool 3, and a swing motor 6 for swinging the polishing tool 3.

As illustrated in FIGS. 2 and 3, the polishing tool 3 has a base plate 30a, and the polishing surface 30b of a spherical zone shape. The spherical zone shape refers to a shape of a surface of a spherical segment remaining between two parallel planes when a sphere is cut by the two parallel planes. An opening 30c is formed on a projection plane on which the polishing surface 30b is projected and which is perpendicular to a central axis of rotation O of the polishing surface, on the inner edge side of the polishing surface 30b, where the opening 30c and the outer edge of the polishing surface 30b are concentric about the central axis of rotation O. The base plate 30a is formed to have a predetermined radius of curvature, which is substantially an inverse of the shape of the lens 1 as a workpiece.

As illustrated in FIG. 3, the polishing surface 30b includes effective polishing portions 30d that come into contact with the lens 1 and practically polish the lens 1, and non-contact portions 30e that do not come into contact with the lens 1 and do not directly contribute to polishing the lens 1. In the first embodiment, 12 polishing sheets having a substantially rectangular shape are attached to part of the surface of the base plate 30a to form the effective polishing portions 30d and the non-contact portions 30e. The effective polishing portions 30d are regions of the polishing surface 30b to which the polishing sheets are attached. The effective polishing portions 30d are shaded in FIG. 3.

The non-contact portions 30e are regions of the polishing surface 30b where the polishing sheets are not attached so as to expose the surface of the base plate 30a, and form grooves recessed from the effective polishing portions 30d. Hereinafter, the non-contact portions 30e will also be referred to as grooves 30e. In the first embodiment, the grooves 30e are substantially fan-shaped on the projection plane on which the polishing surface 30b is projected and which is perpendicular to the central axis of rotation O. FIG. 2 is a cross-section of the polishing tool 3 along the groove 30e.

As illustrated in FIG. 1, the polishing tool 3 is connected to an upper end of a tool shaft 4, and the tool shaft 4 is integrally attached to a spindle 5. The spindle 5 is connected to the rotary motor 7, and the rotary motor 7 is fixed to a lower shaft base plate 14 that rotatably supports the spindle 5. The rotary motor 7 is a rotating unit for rotating the polishing tool 3 about the axis of the rotary shaft under the control of a controller for controlling the polishing apparatus 100. The lower shaft base plate 14 has an upper portion extending through a swing member 9, and is mounted in such a manner that the outer surface of the upper portion is integrated with the swing member 9. The swing motor 6 is fixed to the lower shaft base plate 14 in such a manner that the rotary axis of the swing motor 6 is perpendicular to that of the rotary motor 7. The swing motor 6 swings the swing member 9 under the control of the controller. The rotating speed and the number or rotations of the swing motor 6 can be freely controlled. The swing motor 6 and the swing member 9 constitute a swinging unit.

The swing member 9 has a boat shape with a lower surface supported by a swing member receiving portion 10 fixed to a main body of the polishing apparatus 100. The swing member receiving portion 10 has a surface facing the swing member 9 having a concave shape corresponding to the bottom surface of the boat shape to swingably support the swing member 9, and forms an opening portion for eliminating interference with the lower shaft base plate 14 while the swing member 9 swings.

A gear 6a is attached to a drive shaft of the swing motor 6, and meshes with an arc-shaped guide 8. The guide 8 is fixed to a polishing apparatus main body 20, so that the gear 6a is rotated by the swing motor 6 while moving along the guide 8, which makes the lower shaft base plate 14 swing and makes the swing member 9, the polishing tool 3, and so on swing in a reciprocating manner.

The lens 1 held by attachment to an attachment plate 12 is placed above the polishing tool 3. The lens 1 has a lens surface 1a to be processed having a convex spherical shape and facing the polishing tool 3, and the attachment plate 12 is held in the inside of the holder 2, which is a holding tool, so that the lens 1 is rotatably supported relative to the holder 2. Although the attachment plate 12 and the holder 2 are illustrated in a separated state in FIG. 1, the attachment plate 12 and the holder 2 are assembled with the polishing apparatus main body 20 therebetween. The holder 2 is coupled to a lower end side of a work shaft 11, and the work shaft 11 is moved vertically by a rod of a pressure applying air cylinder 16 coupled to an upper end of the work shaft 11. In addition, a polishing solution supplying part 13 for supplying polishing solution to the polishing surface 30b is provided near the polishing tool 3.

The pressure applying air cylinder 16 is attached to a first attachment plate 19a fixed to a top surface of a back plate 19, and makes the lens surface 1a to be processed in contact with the polishing surface 30b of the polishing tool 3 to apply pressure thereto during processing of the lens 1 after the lens 1 is moved downward toward the polishing tool 3 under the control of the controller for controlling the polishing apparatus 100. The first attachment plate 19a and the back plate 19 do not move vertically during processing of the lens 1.

The central axis of the work shaft 11 is positioned on an axis passing through the center of curvature of the polishing surface 30b of the polishing tool 3. A coarse adjustment air cylinder 18 is fixed to the polishing apparatus main body 20, and has a rod coupled to a second attachment plate 19b fixed to a front surface of the back plate 19. The coarse adjustment air cylinder 18 vertically moves the back plate 19, the pressure applying air cylinder 16, and the like. When the back plate 19, the pressure applying air cylinder 16, and the like are moved downward, the work shaft 11 and the holder 2 pass through a hole 20a formed in the polishing apparatus main body 20 to make the lens 1 face the polishing tool 3. In FIG. 1, a state in which the work shaft 11 and holder 2 have not passed through the hole 20a is illustrated. The pressure applying air cylinder 16 applies pressure in a direction in which the holder 2 and the like supporting the lens 1 are moved downward, that is, vertically downward.

Linear scales 17, which are measuring devices or position detectors used as a pair on a movable side and a fixed side, are disposed on the work shaft 11 and the back plate 19 below the pressure applying air cylinder 16. The linear scale 17 detects the amount by which the work shaft 11 is moved by the pressure applying air cylinder 16, and displays the movement amount on a display or the like. In addition, a stopper 15 capable of adjusting vertical position is fixed to the back plate 19. The stopper 15 is disposed so that, when the back plate 19, that is, the entire upper part of the holder 2 and the like supporting the lens 1 via the back plate 19 is moved downward by the coarse adjustment air cylinder 18, the stopper 15 on the back plate 19 side abuts a stopper 21 on the main body side fixed to the polishing apparatus main body 20.

Next, a method for polishing the lens 1 using the polishing apparatus 100 according to the first embodiment will be explained. FIGS. 4 and 5 are schematic views for explaining the method for polishing the lens 1 using the polishing apparatus 100 according to the first embodiment.

In the first embodiment, polishing of the lens 1 with the polishing apparatus 100 is performed by swinging the polishing tool 3 around a swing center position illustrated in FIG. 4 with a certain amplitude while rotating the polishing tool 3 about a central axis of rotation O by the rotary motor 7. The swing center position is a position where a line L passing through the center C of the lens 1 and intersecting with the central axis of rotation O passes through the center B in the width direction of the spherical zone of the polishing surface 30b as illustrated in FIG. 4. The lens 1 is rotated with the polishing tool 3 in the same direction as the rotating direction by a frictional force caused by the rotation. The lens 1 is polished by the polishing surface 30b having the spherical zone shape where the circumferential speed at the inner diameter D_in, which is an inner edge side of the polishing surface 30b, is different from the circumferential speed at an outer diameter D_out, which is an outer edge side thereof. The applicant has found that, when the difference in the circumferential speed between the inner edge side and the outer edge side of the polishing surface 30b is large, a surface irregularity such as a central rise where the central portion of the processed lens surface 1a of the lens 1 is higher than that of a reference lens as a reference, or a central drop where the central portion is lower than that of the reference lens occurs, which lowers the surface accuracy.

Thus, in the first embodiment, as illustrated in FIGS. 4 and 5, the polishing surface 30b has a spherical zone shape so that a circumferential speed ratio Vo/Vi of the circumferential speed Vo on the outer edge side to the circumferential speed Vi on the inner edge side is smaller than that of a conventional polishing tool, that is, a polishing tool having a spherical surface without the opening 30c. Furthermore, as illustrated in FIG. 3, the polishing surface 30b has the grooves 30e such that an effective circumferential speed ratio is approximately constant regardless of the diameter, at an arbitrary diameter on the projection plane on which the polishing surface 30b is projected and which is perpendicular to the central axis of rotation O. The effective circumferential speed ratio refers to a ratio between a length per unit time where the lens 1 is in contact with the effective polishing portions 30d at an arbitrary diameter of the polishing surface 30b (hereinafter referred to as an effective circumferential speed) and the effective circumferential speed at the inner edge of the polishing surface 30b. The effective circumferential speed ratio corresponds to a ratio of an effective circumferential length at an arbitrary diameter of the polishing surface 30b to an effective circumferential length at the inner edge of the polishing surface 30b. The effective circumferential length refers to a total of the circumferential lengths of the effective polishing portions 30d of the polishing surface 30b.

Specifically, the effective circumferential speed ratio α at the outer edge of the polishing surface 30b is 6.0 or smaller, preferably 4.0 or smaller, and more preferably 3.0 or smaller. The effective circumferential speed ratio α is most preferably 1.0, and may be smaller than 1.0. Preferably, the effective circumferential speed ratio α may be 0.7 or higher. Furthermore, a tolerance range of the effective circumferential speed ratio α is preferably within ±30%, and more preferably ±10%, in view of the accuracy of the finishing shape of the polishing surface 30b, the posture stability of the lens 1 during processing of the lens 1, the surface accuracy after processing, and the like.

If the effective circumferential speed ratio α between the inner edge and the outer edge of the polishing surface 30b is α≠1.0, the effective circumferential speed ratio β at an arbitrary diameter preferably changes as linearly as possible from the inner edge toward the outer edge. If the effective circumferential speed ratio α is α=1, it is preferable that the effective circumferential speed ratio β be also 1, and in this case, the tolerance range of the effective circumferential speed ratio β is also preferably within ±30%, and more preferably within ±10%.

The effective circumferential speed ratio α at the outer edge of the polishing surface 30b is given by the following expression (1) using the effective circumferential length L_in at the inner edge and the effective circumferential length L_out at the outer edge of the polishing surface 30b.

α=L_out/L_in  (1)

In addition, the effective circumferential length L_in at the inner edge is given by the following expression (2) using the groove width g of the grooves 30e and the number m of the grooves 30e.

$\begin{array}{cc}{\mathrm{Li}}_n=\pi \times D_{in}-\frac{D_{in}\times m}{2}\times \arcsin \left(\frac{g}{D^{in}}\right)& \left(2\right)\end{array}$

When the effective circumferential length L_out at the outer edge and the effective circumferential length L_in at the inner edge are different from each other, that is, when the effective circumferential speed ratio α is α≠1.0, the effective circumferential speed ratio β is changed linearly from the inner edge toward the outer edge in the radial direction of the polishing surface 30b as described above. In this case, the effective circumferential speed ratio β(D) at an arbitrary diameter D (D_in<D<D_out) is given by the following expression (3) using the inner diameter D_in and the outer diameter D_out of polishing surface 30b.

$\begin{array}{cc}\beta \left(D\right)=\frac{\left(\alpha -1\right)\times \left(D-D_{in}\right)}{D_{\mathrm{out}}-D_{in}}+1& \left(3\right)\end{array}$

Here, a line passing through the center in the circumferential direction of an arbitrary groove 30e at the inner edge is referred to as a reference line L1, and a line or a curve passing through the center in the circumferential direction of another groove 30e other than the arbitrary groove 30e is referred to as a center line L2. In addition, an angle between the reference line L1 and a line for connecting a point P1 where the center line L2 passes through a circumference at the arbitrary diameter D and the central axis of rotation O of the polishing surface 30b, is denoted by θ. The line connecting the point P1 and the central axis of rotation O corresponds to the center line L2 itself in FIG. 3.

The angle θ is given by the following expression (4).

$\begin{array}{cc}\theta =n\times \frac{2\pi }{m}+f\left(D\right)\left(n=1,2,\dots ,m\right)& \left(4\right)\end{array}$

In the expression (4), a function f(D) is a function expressing the angle between the center line L2 and a radius passing through the P1. In the case of FIG. 3, f(D)=0, and the center line L2 is a line passing through the central axis of rotation O. When the function f(D) is varied with the diameter D, the center line L2 is an arbitrary curve.

In the groove 30e including the center line L2, an angle φ between a radius passing through each of end points P2 and P3 on the circumference with the diameter D and the reference line L1 is given by the following expression (5).

φ=θ±ω  (5)

The angle ω in the expression (5) is a half-angle of the central angle of a sector with an arc of the groove 30e on the circumference with the diameter D, that is, the central angle of an arc connecting the points P1 and P2 or an arc connecting the points P1 and P3, and is given by the following expression (6).

$\begin{array}{cc}\omega =\frac{\pi }{m}-\frac{\beta \times L_{in}}{m\times D}& \left(6\right)\end{array}$

With the expressions (1) to (6), the shape of the grooves 30e on the polishing surface 30b can be designed in such a manner that the parameters including the inner diameter D_in and the outer diameter D_out of the polishing surface 30b, the number m of the grooves 30e, the groove width g at the inner edge, the effective circumferential speed ratio α at the outer edge, and the function f(D) are set, and coordinates of the end points P2 and P3 are sequentially calculated. The polishing surface 30b illustrated in FIG. 3 is an example of a design with the inner diameter D_in=18 cm, the outer diameter D_out=36 cm, the number m of the grooves m=12, the groove width g at the inner edge g=1 cm, the effective circumferential speed ratio α=1, and the function f(D)=0.

As described above, in the polishing tool according to the first embodiment, the shape of the polishing surface is a spherical zone shape so that the difference in the circumferential length between the inner edge and the outer is made small, and grooves that are not brought into contact with a workpiece are formed on the polishing surface. As a result, the effective circumferential length ratio at the outer edge of the polishing surface can be made smaller, and variation in the effective circumferential length ratio can be reduced regardless of the diameter. Consequently, occurrence of a surface irregularity on the polishing surface can be reduced, and the surface accuracy of a workpiece can be increased.

Although the effective polishing portions 30d and the grooves 30e are formed by attaching polishing sheets shaped into a predetermined shape onto the surface of the base plate 30a in the first embodiment, the grooves 30e may alternatively be formed by fixing abrasive grains for polishing on the base plate with resin or the like, forming the polishing surface 30b of a spherical zone shape having a desired radius of curvature by cutting, and then cutting out regions of the polishing surface 30b other than the effective polishing portions 30d.

Furthermore, although the holder 2 is not particularly moved but only the lens 1 is pressed against the polishing tool 3 and the polishing tool 3 side is rotated and swung during polishing of the lens 1 in the first embodiment, either side may be moved as long as the lens 1 and the polishing tool 3 can be relatively moved. For example, the polishing tool 3 may be rotated and the lens 1 and the holder 2 side may be swung. Alternatively, the polishing tool 3 may be rotated and both the lens 1, the holder 2 and the polishing tool 3 may be swung relatively.

First Modification

Next, a first modification of the first embodiment will be described. FIG. 6 is a top view of a polishing tool according to the first modification. A polishing surface 31 illustrated in FIG. 6 is an example of a design of effective polishing portions 31a and grooves 31b with the parameters in the expressions (1) to (6) being: the inner diameter D_in=18 cm, the outer diameter D_out=36 cm, the number m of grooves m=6, the groove width g at the inner edge g=0 cm, the effective circumferential speed ratio α=1, and the function f(D)=0. The grooves 31b are substantially fan-shaped on the projection plane obtained by projecting the polishing surface 31 having the spherical zone shape onto the plane perpendicular to the central axis of rotation O of the polishing surface 31. The effective polishing portions 31a are shaded in FIG. 6.

Although the number of grooves 31b formed on the polishing surface 31 is not limited, the lens 1 needs to be prevented from falling into the groove 31b during processing of the lens 1 in the polishing apparatus 100 illustrated in FIG. 1. Thus, when the center axis C of the lens 1 is at a position at an end of the groove 31b or on the groove 31b, a required condition is that part of a sphere (the hatched part, for example) of the lens 1 defined by an arbitrary line passing through the center axis C of the lens 1 remains on an effective polishing portion 31a. To meet the condition, for making ends of the grooves 31b on a projection plane of the polishing surface 31 linear (that is, f(D)=0), the number of grooves may be at least six.

Even if the groove width g at the inner edge is zero, a gap for a processing tool may actually be present between adjacent grooves 31b at the inner edge of the polishing surface 31.

Second Modification

Next, a second modification of the first embodiment will be described. FIG. 7 is a top view of a polishing tool according to the second modification. A polishing surface 32 illustrated in FIG. 7 is an example of a design of effective polishing portions 32a and grooves 32b with the parameters in the expressions (1) to (6) being: the inner diameter D_in=18 cm, the outer diameter D_out=36 cm, the number m of grooves m=12, the groove width g at the inner edge g=0 cm, the effective circumferential speed ratio α=1, and the function f(D)=0. The grooves 32b are substantially fan-shaped on the projection plane on which the polishing surface 32 having the spherical zone shape is projected and which is perpendicular to the central axis of rotation O of the polishing surface 32. The effective polishing portions 32a are shaded in FIG. 7.

Third Modification

Next, a third modification of the first embodiment will be described. FIG. 8 is a top view of a polishing tool according to the third modification. A polishing surface 33 illustrated in FIG. 8 includes effective polishing portions 33a, grooves 33b extending in the circumferential direction, and grooves 33c formed in the radial direction. The polishing surface 33 is obtained by forming the grooves 33c using the same parameters as those of the second modification, and forming the grooves 33b in the circumferential direction so that the effective polishing portions 33a forming an alternate strip pattern in adjacent regions other than the grooves 33c are left. The effective polishing portions 33a are shaded in FIG. 8.

Formation of such grooves 33b facilitates flow out of slurry during processing of the lens 1. Furthermore, since the grooves 33b are formed to have an alternative strip pattern in adjacent regions on the same circumference, the effective polishing portions 33a remaining on the circumference at an arbitrary diameter, that is, the effective circumferential length, can be made uniform regardless of the diameter. Furthermore, as a result of formation of the grooves 33b, the lens 1 is prevented from falling into the groove 33b or 33c during processing of the lens 1 while increasing the total area of the grooves 33b and 33c on the polishing surface 33.

Fourth Modification

Next, a fourth modification of the first embodiment will be described. FIG. 9 is a top view of a polishing tool according to the fourth modification. A polishing surface 34 illustrated in FIG. 9 is designed to have effective polishing portions 34a and grooves 34b with the parameters in the expressions (1) to (6) being as follows: the inner diameter D_in=18 cm; the outer diameter D_out=36 cm; the number m of the grooves m=12; the groove width g at the inner edge g=0 cm; the effective circumferential speed ratio α=1; and the function f(D)=arccos(k×D). The coefficient k is designed to be constant such that f(D)=0 when D=18 cm and f(D)=60° when D=36 cm. With such a function f(D), spiral grooves 34b each having a straight center line L2 in the circumferential direction are formed. The effective polishing portions 34a are shaded in FIG. 9.

Similarly to the third modification, grooves extending in the circumferential direction may be provided in the effective polishing portions 34a of the fourth modification.

Fifth Modification

Next, a fifth modification of the first embodiment will be described. FIG. 10 is a top view of a polishing tool according to the fifth modification. A polishing surface 35 illustrated in FIG. 10 is designed to have effective polishing portions 35a and grooves 35b with the parameters in the expressions (1) to (6) being as follows: the inner diameter D_in=18 cm; the outer diameter D_out=36 cm; the number m of the grooves m=12; the groove width g at the inner edge g=0 cm; the effective circumferential speed ratio α=1; and the function f(D)=k×(D−18). The coefficient k is designed to be constant such that f(D)=0 when D=18 cm and f(D)=36° when D=36 cm. With such a function f(D), spiral grooves 35b each having an arc-like center line L2 in the circumferential direction are formed. The effective polishing portions 35a are shaded in FIG. 10.

Similarly to the third modification, grooves extending in the circumferential direction may also be provided in the effective polishing portions 35a of the fifth modification.

Sixth Modification

Next, a sixth modification of the first embodiment will be described. FIG. 11 is a top view of a polishing tool according to the sixth modification. A polishing surface 36 illustrated in FIG. 11 is designed to have effective polishing portions 36a and grooves 36b with the parameters in the (1) to (6) being as follows: the inner diameter D_in=18 cm; the outer diameter D_out=36 cm; the number m of the grooves m=12; the groove width g at the inner edge g=0 cm; the effective circumferential speed ratio α=1; and the function f(D)=j×sin(k×D). The coefficient k is designed to be constant such that f(D)=0 when D=18 cm and 36 cm, and a single inflection point is present in a range of 18 cm<D<36 cm. In addition, the coefficient j is designed to be constant such that f(D) 14.3 at the inflection point. As in the sixth modification, the center line L2 in the circumferential direction of the groove 36b is not limited to a straight line or an arc-like line, but may be any curve having an inflection point. The effective polishing portions 36a are shaded in FIG. 11.

Similarly to the third modification, grooves extending in the circumferential direction may also be provided in the effective polishing portions 36a of the sixth modification.

Second Embodiment

Next, a second embodiment of the present invention will be described. FIG. 12 is a diagram explaining a structure of a polishing surface formed on a polishing tool according to the second embodiment. The polishing tool according to the second embodiment has a polishing surface 37 illustrated in (a) of FIG. 12. The polishing surface 37 has a spherical zone shape, and an opening 38 is formed on a projection plane on which the polishing surface 37 is projected and which is perpendicular to a central axis of rotation O of the polishing surface 37 on the inner side of the polishing surface 37, where the opening 38 and the outer edge of the polishing surface 37 are concentric about the central axis of rotation O. The structure of the polishing tool and the structure of the whole polishing apparatus according to the second embodiment other than the polishing surface 37 are the same as those of the first embodiment illustrated in FIGS. 1 and 2.

The polishing surface 37 includes effective polishing portions 37a that come into contact with the lens 1 and practically polish the lens 1, and non-contact portions 37b that do not come into contact with the lens 1 and do not directly contribute to polishing the lens 1. The effective polishing portions 37a are formed by attaching polishing sheets, which are obtained by fixing abrasive grains onto the surfaces of viscoelastic sheets made of polyurethane or the like, onto the base plate 30a illustrated in FIG. 2. The effective polishing portions 37a are shaded in FIG. 12.

In contrast, the respective non-contact portions 37b are hole portions formed in the polishing sheets where the surface of the base plate 30a is exposed. The non-contact portions 37b have a predetermined shape such as a circular shape, a rectangular shape, a polygonal shape, or a star-like shape. One non-contact portion 37b may be continuous with another adjacent non-contact portion 37b or may be separate from an adjacent non-contact portion 37b.

The non-contact portions 37b are formed so that the hole density is increased from the inner edge side toward the outer edge side of the polishing surface 37. (b) in FIG. 12 is a graph showing a distribution of the hole density in the non-contact portions 37b in the radial direction (x direction) of the polishing surface 37. In the second embodiment, the non-contact portions 37b are arranged so that the hole density increases approximately linearly from the inner edge side toward the outer edge side.

As a result of forming the non-contact portions 37b to achieve the above-described hole density, the effective circumferential speed ratio at the outer edge of the polishing surface 37 is reduced, and variation in the effective circumferential speed ratio at an arbitrary diameter is reduced. Consequently, occurrence of a surface irregularity on the polishing surface is reduced and the surface accuracy of a workpiece increased.

In the second embodiment, instead of adhering polishing sheets having holes formed therein onto the base plate, the non-contact portions 37b may alternatively be formed by fixing abrasive grains for polishing on the base plate with resin or the like, forming the polishing surface 37 of a spherical zone shape having a desired radius of curvature by cutting, and then performing cutting out on the polishing surface 37.

According to some embodiments, it is possible to improve a surface accuracy of a workpiece while utilizing an existing apparatus without introducing a new control device or the like.

The first and second embodiments and the modifications described above are only examples for carrying out the present invention, and the present invention is not limited to these embodiments and modification. Furthermore, in the present invention, more than one element disclosed in the first and second embodiments and the modifications may be combined where appropriate to constitute various aspects of the present invention. The present invention can be modified in various manners depending on specifications or the like, and various other embodiments can be present within the scope of the present invention.

Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and representative embodiments shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.

Claims

1. A polishing tool comprising: a polishing surface having a spherical zone shape and having a plurality of non-contact portions provided from an inner edge to an outer edge of the polishing surface so as not to contact with a workpiece, whereinthe plurality of non-contact portions is a plurality of grooves whose widths in a circumferential direction increase from the inner edge toward the outer edge.

2. The polishing tool according to claim 1, wherein the plurality of grooves is provided radially from the inner edge toward the outer edge.

3. The polishing tool according to claim 1, wherein the plurality of grooves forms a spiral pattern from the inner edge toward the outer edge.

4. The polishing tool according to claim 2, wherein the polishing surface further has a plurality of second grooves extending in the circumferential direction of the polishing surface in regions of the polishing surface excluding the plurality of grooves.

5. The polishing tool according to claim 3, wherein the polishing surface further has a plurality of second grooves extending in the circumferential direction of the polishing surface in regions of the polishing surface excluding the plurality of grooves.

6. The polishing tool according to claim 4, wherein the plurality of second grooves is provided in every other region in the circumferential direction.

7. The polishing tool according to claim 5, wherein the plurality of second grooves is provided in every other region in the circumferential direction.

8. The polishing tool according to claim 1, wherein on a projection plane on which the polishing surface is projected and which is perpendicular to a central axis of rotation of the polishing surface:an effective circumferential length of the polishing surface is defined as a circumferential length at an arbitrary diameter by removing the plurality of non-contact portions; andif the effective circumferential length at the outer edge is different from the effective circumferential length at the inner edge, the effective circumferential length at the arbitrary diameter linearly changes from the inner edge toward the outer edge.

9. A polishing method using the polishing tool according to claim 1, the method comprising: rotating the polishing tool about the central axis of rotation; andsimultaneously with rotating the polishing tool, swinging relatively at least one of the workpiece and the polishing tool with a predetermined swing width, around a position where a line passing through a center of the workpiece and intersecting with the central axis of rotation passes through a center in a width direction of a spherical zone of the polishing surface, thereby polishing the workpiece.

10. A polishing apparatus comprising: the polishing tool according to claim 1;a pressure applying unit configured to bring the workpiece into contact with the polishing surface of the polishing tool, thereby to apply pressure to the workpiece;a rotating unit configured to rotate the polishing tool about the central axis of rotation; anda swinging unit configured to swing relatively at least one of the workpiece and the polishing tool with a predetermined swing width, around a position where a line passing through a center of the workpiece and intersecting with the central axis of rotation passes through a center in a width direction of a spherical zone of the polishing surface, thereby to polish the workpiece.

11. A polishing tool comprising: a polishing surface having a spherical zone shape and having a plurality of non-contact portions provided from an inner edge to an outer edge of the polishing surface so as not to contact with a workpiece, whereinthe plurality of non-contact portions is formed by a plurality of holes, anda density per unit area of the plurality of holes increases from the inner edge toward the outer edge.

12. The polishing tool according to claim 11, wherein on a projection plane on which the polishing surface is projected and which is perpendicular to a central axis of rotation of the polishing surface:an effective circumferential length of the polishing surface is defined as a circumferential length at an arbitrary diameter by removing the plurality of non-contact portions; andif the effective circumferential length at the outer edge is different from the effective circumferential length at the inner edge, the effective circumferential length at the arbitrary diameter linearly changes from the inner edge toward the outer edge.

13. A polishing method using the polishing tool according to claim 11, the method comprising: rotating the polishing tool about the central axis of rotation; andsimultaneously with rotating the polishing tool, swinging relatively at least one of the workpiece and the polishing tool with a predetermined swing width, around a position where a line passing through a center of the workpiece and intersecting with the central axis of rotation passes through a center in a width direction of a spherical zone of the polishing surface, thereby polishing the workpiece.

14. A polishing apparatus comprising: the polishing tool according to claim 11;a pressure applying unit configured to bring the workpiece into contact with the polishing surface of the polishing tool, thereby to apply pressure to the workpiece;a rotating unit configured to rotate the polishing tool about the central axis of rotation; anda swinging unit configured to swing relatively at least one of the workpiece and the polishing tool with a predetermined swing width, around a position where a line passing through a center of the workpiece and intersecting with the central axis of rotation passes through a center in a width direction of a spherical zone of the polishing surface, thereby to polish the workpiece.