U.S. patent application number 15/367315 was filed with the patent office on 2017-03-23 for polishing tool, polishing method and polishing apparatus.
This patent application is currently assigned to OLYMPUS CORPORATION. The applicant listed for this patent is OLYMPUS CORPORATION. Invention is credited to Takashi HORIKOSHI.
Application Number | 20170080542 15/367315 |
Document ID | / |
Family ID | 54833294 |
Filed Date | 2017-03-23 |
United States Patent
Application |
20170080542 |
Kind Code |
A1 |
HORIKOSHI; Takashi |
March 23, 2017 |
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.
Inventors: |
HORIKOSHI; Takashi;
(Atsugi-shi, JP) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
OLYMPUS CORPORATION |
Tokyo |
|
JP |
|
|
Assignee: |
OLYMPUS CORPORATION
Tokyo
JP
|
Family ID: |
54833294 |
Appl. No.: |
15/367315 |
Filed: |
December 2, 2016 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
PCT/JP2015/063206 |
May 7, 2015 |
|
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15367315 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
B24D 11/04 20130101;
B24B 13/01 20130101; B24B 13/02 20130101; B24D 7/14 20130101; B24D
7/00 20130101; B24B 37/26 20130101 |
International
Class: |
B24B 13/01 20060101
B24B013/01; B24D 7/00 20060101 B24D007/00; B24B 13/02 20060101
B24B013/02 |
Foreign Application Data
Date |
Code |
Application Number |
Jun 10, 2014 |
JP |
2014-119901 |
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, wherein 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.
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; and if
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; 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.
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; 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.
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, wherein 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.
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; and if 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; 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.
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; 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.
Description
CROSS REFERENCES TO RELATED APPLICATIONS
[0001] This application is a continuation of PCT international
application Ser. No. PCT/JP2015/063206, filed on May 7, 2015 which
designates the United States, incorporated herein by reference, and
which claims the benefit of priority from Japanese Patent
Application No. 2014-119901, filed on Jun. 10, 2014, incorporated
herein by reference.
BACKGROUND
[0002] 1. Technical Field
[0003] The disclosure relates to a polishing tool, a polishing
method, and a polishing apparatus for surface finishing of optical
elements such as lenses.
[0004] 2. Related Art
[0005] 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.
[0006] 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
[0007] 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.
[0008] 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.
[0009] 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.
[0010] 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.
[0011] 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.
[0012] 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.
[0013] 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
[0014] FIG. 1 is a schematic view illustrating a configuration of a
polishing apparatus according to a first embodiment of the present
invention;
[0015] FIG. 2 is a cross-sectional view of a polishing tool used in
FIG. 1;
[0016] FIG. 3 is a top view of the polishing tool of FIG. 2;
[0017] FIG. 4 is a schematic view for explaining a method for
polishing a lens using the polishing apparatus illustrated in FIG.
1;
[0018] FIG. 5 is a schematic view for explaining the method for
polishing a lens using the polishing apparatus illustrated in FIG.
1;
[0019] FIG. 6 is a top view of a polishing tool according to a
first modification of the present invention;
[0020] FIG. 7 is a top view of a polishing tool according to a
second modification of the present invention;
[0021] FIG. 8 is a top view of a polishing tool according to a
third modification of the present invention;
[0022] FIG. 9 is a top view of a polishing tool according to a
fourth modification of the present invention;
[0023] FIG. 10 is a top view of a polishing tool according to a
fifth modification of the present invention;
[0024] FIG. 11 is a top view of a polishing tool according to a
sixth modification of the present invention; and
[0025] FIG. 12 is a diagram explaining a structure of a polishing
surface formed on a polishing tool according to a second
embodiment.
DETAILED DESCRIPTION
[0026] 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
[0027] 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.
[0028] 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.
[0029] 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.
[0030] 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.
[0031] 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.
[0032] 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.
[0033] 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.
[0034] 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.
[0035] 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.
[0036] 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.
[0037] 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.
[0038] 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.
[0039] 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.sub.in, which is an inner edge side of the
polishing surface 30b, is different from the circumferential speed
at an outer diameter D.sub.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.
[0040] 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.
[0041] Specifically, the effective circumferential speed ratio
.alpha. 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 .alpha. is most
preferably 1.0, and may be smaller than 1.0. Preferably, the
effective circumferential speed ratio .alpha. may be 0.7 or higher.
Furthermore, a tolerance range of the effective circumferential
speed ratio .alpha. 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.
[0042] If the effective circumferential speed ratio .alpha. between
the inner edge and the outer edge of the polishing surface 30b is
.alpha..noteq.1.0, the effective circumferential speed ratio .beta.
at an arbitrary diameter preferably changes as linearly as possible
from the inner edge toward the outer edge. If the effective
circumferential speed ratio .alpha. is .alpha.=1, it is preferable
that the effective circumferential speed ratio .beta. be also 1,
and in this case, the tolerance range of the effective
circumferential speed ratio .beta. is also preferably within
.+-.30%, and more preferably within .+-.10%.
[0043] The effective circumferential speed ratio .alpha. at the
outer edge of the polishing surface 30b is given by the following
expression (1) using the effective circumferential length L.sub.in
at the inner edge and the effective circumferential length
L.sub.out at the outer edge of the polishing surface 30b.
.alpha.=L.sub.out/L.sub.in (1)
[0044] In addition, the effective circumferential length L.sub.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.
Li n = .pi. .times. D i n - D i n .times. m 2 .times. arcsin ( g D
i n ) ( 2 ) ##EQU00001##
[0045] When the effective circumferential length L.sub.out at the
outer edge and the effective circumferential length L.sub.in at the
inner edge are different from each other, that is, when the
effective circumferential speed ratio .alpha. is .alpha..noteq.1.0,
the effective circumferential speed ratio .beta. 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 .beta.(D) at an
arbitrary diameter D (D.sub.in<D<D.sub.out) is given by the
following expression (3) using the inner diameter D.sub.in and the
outer diameter D.sub.out of polishing surface 30b.
.beta. ( D ) = ( .alpha. - 1 ) .times. ( D - D i n ) D out - D i n
+ 1 ( 3 ) ##EQU00002##
[0046] 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 .theta.. The line connecting the point P1 and the
central axis of rotation O corresponds to the center line L2 itself
in FIG. 3.
[0047] The angle .theta. is given by the following expression
(4).
.theta. = n .times. 2 .pi. m + f ( D ) ( n = 1 , 2 , , m ) ( 4 )
##EQU00003##
[0048] 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.
[0049] In the groove 30e including the center line L2, an angle
.phi. 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).
.phi.=.theta..+-..omega. (5)
[0050] The angle .omega. 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).
.omega. = .pi. m - .beta. .times. L i n m .times. D ( 6 )
##EQU00004##
[0051] 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.sub.in and the
outer diameter D.sub.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 .alpha. 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.sub.in=18 cm, the outer diameter D.sub.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 .alpha.=1, and
the function f(D)=0.
[0052] 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.
[0053] 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.
[0054] 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.
[0055] First Modification
[0056] 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.sub.in=18 cm, the outer diameter
D.sub.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
.alpha.=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.
[0057] 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.
[0058] 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.
[0059] Second Modification
[0060] 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.sub.in=18 cm, the outer diameter
D.sub.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
.alpha.=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.
[0061] Third Modification
[0062] 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.
[0063] 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.
[0064] Fourth Modification
[0065] 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.sub.in=18 cm; the outer diameter
D.sub.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 .alpha.=1; and the function f(D)=arccos(k.times.D). The
coefficient k is designed to be constant such that f(D)=0 when D=18
cm and f(D)=60.degree. 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.
[0066] Similarly to the third modification, grooves extending in
the circumferential direction may be provided in the effective
polishing portions 34a of the fourth modification.
[0067] Fifth Modification
[0068] 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.sub.in=18 cm; the outer diameter
D.sub.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 .alpha.=1; and the function f(D)=k.times.(D-18). The
coefficient k is designed to be constant such that f(D)=0 when D=18
cm and f(D)=36.degree. 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.
[0069] 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.
[0070] Sixth Modification
[0071] 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.sub.in=18 cm; the outer diameter D.sub.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 .alpha.=1;
and the function f(D)=j.times.sin(k.times.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.
[0072] 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
[0073] 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.
[0074] 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.
[0075] 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.
[0076] 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.
[0077] 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.
[0078] 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.
[0079] 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.
[0080] 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.
[0081] 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.
* * * * *