Abstract:
A polishing tool that includes: an arbor with a shank having a first cylindrical axis; an offset cylinder extending from the shank, the offset cylinder having a second cylindrical axis, the first cylindrical axis being offset from the second cylindrical axis and parallel thereto, the offset cylinder terminating at a distal end thereof with a support surface that is angled in a range of from about 1° to about 20° from perpendicular to the first and second cylindrical axes; and a toroidal polishing head supported on the support surface, rotation of the shank causing an oscillating rotational movement of the toroidal polishing head.

Description:
FIELD OF THE INVENTION 
   The invention relates generally to the field of optical manufacturing processes, and in particular to polishing of optical surfaces. More specifically, the invention relates to a high-precision polishing tool for polishing an optical quality surface onto a substrate. 
   BACKGROUND OF THE INVENTION 
   In manufacturing of optical components, lenses, molds, and the like, preliminary operations, such as grinding or diamond turning, are performed to generate an optical surface on a raw blank of material. The preliminary operations provide the general form of the component, but leave surface defects that include turning grooves, cutter marks, and sub-surface damage. A final polishing step is required to remove these surface and sub-surface defects. Polishing is accomplished in a variety of ways depending upon the material and the surface&#39;s form (i.e.: a surface can have plano, spherical, or aspherical form). 
   Plano and spherical surfaces are typically polished using “full-aperture” or “full-surface” tools. Full aperture tools tend to cover over 80% of the work piece surface during polishing. Full-aperture tools may be constructed in a variety of ways, including traditional “pitch” and more recent pad-type. “Pitch” polishing tools are comprised of a soft flow-able material, such as pitch or bees wax, which is used to create a mold of the optical surface. Referring to  FIG. 1 , this mold is a mirror replica of the work piece surface and becomes a polishing tool  300  once the mold is modified with grooves  305 . Polishing tool  300  has a support surface  310  and is fixedly attached to a shank  315  that forms an arbor  320  that is used to hold the polishing tool  300  in application. During polishing, polishing tool  300  is held against the work piece (not shown, but conventionally, made of optical glass) with an applied force and the two components are moved relative to one another in the presence of a free abrasive polishing compound, such as cerium oxide, to achieve polishing. 
   A pad-type full-aperture polishing tool depicted in  FIG. 2  consists of a polishing tool  300  incorporated with polishing pad  325  resting or adhered to support surface  310 . The polishing pad  325  is typically attached to the support surface  310  via adhesive or via friction grip as disclosed in U.S. Pat. No. 4,274,232 issued to Wylde, on Jun. 23, 1981. 
   Polishing of aspheric surfaces using full-aperture tools involves much iteration to rebuild or reshape the polishing tool slowing the polishing process considerably. Therefore, polishing of aspheric surfaces is commonly restricted to sub-aperture methods using ring-tools or small-area tools. Sub-aperture methods using ring-tools or small-area tools rely on a polishing tool that contacts less than 50% of the work piece surface at one time. Ring tools, as disclosed in U.S. Pat. No. 4,768,308 issued to Atkinson, III et al. on Sep. 6, 1988, have a diameter that is comparable to or larger than the radius of the work piece and contact the work piece surface over an area that is much larger than that for a small-area tool. Small-area tools contact only a small area of the work surface at a time and create an interfacial contact area that is on the order of 99% smaller than the area of the work piece surface. 
   Traditionally, manufacturers made polishing tools rotationally symmetric, with minimal radial and axial run-out, such as the full-aperture and sub-aperture polishing tools depicted in U.S. Pat. No. 6,033,449, issued to Cooper et al., on Mar. 7, 2000. Sub-aperture small-area tools may be outfitted with a variety of polishing head shapes, including spherical (as shown in  FIG. 3 ), but may also include conical, cylindrical, and flat along with a polishing pad. In  FIG. 3 , a sub-aperture polishing tool  330  includes an arbor  335  fixedly attached to a spherical polishing head  340 . It should be noted that the spherical polishing head  340  may be substituted with one of the aforementioned polishing heads of a different geometrical shape. Sub-aperture ring-tools may be considered a variation on the small-area tool with the polishing head being of ring-shaped configuration with surface contact during polishing being from 3% to 50% of the work piece surface. 
   Such rotationally symmetric polishing tools, as described above, require a driving device to impart various motions, for example, rotational and oscillatory motions. However, where the work piece surface has a consistent rotational motion relevant to the rotational polishing tool, unwanted grooves can occur. These unwanted grooves negatively affect the optical properties of the work piece surface, because they prevent the work piece surface from being perfectly smooth. 
   Driving devices, as noted in U.S. Pat. No. 1,422,505 issued to Weaver on Jul. 11, 1922, and U.S. Pat. No. 3,156,073 issued to Strasbaugh on Nov. 10, 1964, are limited in velocity and subsequent oscillation frequency due to the mass and complexity required to impart such motions. Moreover, these prior art solutions are only applicable to full aperture polishing found in spheres and plano type surfaces and not aspheric surfaces. Consequently, there is a need for a polishing tool that will effectively polish aspheric surfaces. 
   SUMMARY OF THE INVENTION 
   The need is met according to the present invention by providing a polishing tool that includes: a) an arbor with a shank having a first cylindrical axis; an offset cylinder extending from the shank, the offset cylinder having a second cylindrical axis, the first cylindrical axis being offset from the second cylindrical axis and parallel thereto, the offset cylinder terminating at a distal end thereof with a support surface that is angled in a range of from about 1° to about 20° from perpendicular to the first and second cylindrical axes; and a toroidal polishing head supported on the support surface, rotation of the shank causing an oscillating rotational movement of the toroidal polishing head. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above and other objects, features, and advantages of the present invention will become more apparent when taken in conjunction with the following description and drawings wherein identical reference numerals have been used, where possible, to designate identical features that are common to the figures, and wherein: 
       FIG. 1  is an isometric view of a prior art polishing tool; 
       FIG. 2  is an isometric view of a prior art polishing tool with a polishing pad; 
       FIG. 3  is an isometric view of a prior art sub-aperture polishing tool with a spherical polishing head; 
       FIG. 4  is an isometric view of one embodiment of the invention, e.g., a dual motion polishing tool assembly with toroidal polishing tip; 
       FIG. 5  is an isometric view of the dual motion polishing tool arbor; 
       FIG. 6  is a plane view of the dual motion polishing tool arbor; 
       FIG. 7  is a close up view of the distal end of the dual motion polishing tool arbor showing the tilt angle; 
       FIG. 8  is a plane view of the dual motion polishing tool in contact with a contact plane showing the contact angle; 
       FIG. 9  is a close up view of the distal end of the dual motion polishing tool showing a toroidal polishing tip with a single transparent wedge representing a 30-degree contact plane; 
       FIG. 10  is a close up view of the toroidal polishing tip; 
       FIG. 11  is a series of eight front views of a conventional sub-aperture polishing tool with an applied eccentric showing a toroidal polishing tip engagement (represented by an oval contact area) with contact plane (represented by a transparent wedge) throughout eight 45-degree rotations of the polishing tool; and 
       FIG. 12  is a series of eight front views of the dual motion polishing tool showing a toroidal polishing tip engagement (represented by an oval contact area) with contact plane (represented by a transparent wedge) throughout eight 45-degree rotations of the polishing tool. 
   

   To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the figures. Herein, an applied eccentric motion is equivalent to a cylindrical offset and the two phrases may be used interchangeably. 
   DETAILED DESCRIPTION OF THE INVENTION 
   The disclosed invention provides motion in two separate directions within a polishing tool, thereby allowing greater velocity and subsequent oscillation frequency. The present invention incorporates radial and axial offset components within the polishing tool itself, thereby creating simultaneous motion in two perpendicular planes at the point of contact during pure rotation of the polishing tool. The present invention is exceptionally well-suited to sub-aperture polishing. 
   As illustrated in  FIG. 4 , one embodiment of a dual motion polishing tool  100  includes two parts, (i) an arbor  102  and (ii) a toroidal polishing tip  104 . Polishing tool  100  provides an advantageous dual motion polishing, i.e., simultaneous motion in two perpendicular planes at the point of contact during pure rotation of the polishing tool  100 . The arbor  102  fixedly attached to polishing tool  100  facilitates the dual motion polishing. 
   Referring to  FIG. 5 , the arbor  102  is constructed as a shank  106  that is inserted into a drive unit (not shown). Arbor  102  also includes an offset cylinder  108  that encompasses a portion of shank  106  and has a distal end  114 . Upon distal end  114  a centering boss  125  may be added which aids in providing concentric alignment of toroidal polishing tip  104  during attachment. Arbor  102  may be manufactured as a single piece, wherein offset cylinder  108  extends from shank  106 . The construction of the arbor  102  is most efficiently done by a turning process upon a solid piece of metal to form the shank  106  and the offset cylinder  108 . A four jaw chuck may be employed in the turning process. Consequently, the eccentric motion is built into the arbor  102 . In one embodiment of the invention, as illustrated in  FIG. 6 , an axis  110  of shank  106  is offset from an axis  112  of offset cylinder  108 . The two offset axes  110  and  112  provide an eccentric motion to the polishing tool  100  as it rotates. The distal end  114  of offset cylinder  108  is machined to provide a tilt that is in-line with the direction of offset as shown in  FIGS. 6 and 7 . The tilt angle can be about 1° to about 20°. If provided, centering boss  125  projects normally from the tilted support surface. A toroidal polishing tip  104  of toroidal geometry is then attached centrally to tilted distal end  114 , whereby the toroidal polishing tip  104  itself is concentric with the tilted diameter of the distal end  114 . The toroidal polishing tip  104  may have an alignment port  126  (shown in  FIG. 10 ) concentric with its outside diameter, intended to mate with centering boss  125  if provided on arbor  102  to provide concentric alignment and to aid in attachment. Attachment of the toroidal polishing tip  104  to the arbor  102  may be accomplished in a variety of ways including adhesive, chemical, thermal, or mechanical bonding. 
   The amount of tilt and offset required is determined by two factors. One being the angle of inclination, herein, referred to as the contact angle, (typically about 15° to about 45°) of the polishing tool  100  with respect to the work piece surface  115 , as shown in  FIG. 8 . The second factor is the desired amount of oscillation in the plane of contact. The first factor, contact angle, is chosen to provide productive surface speeds for material removal during polishing while allowing the greatest range of tool movement. The second factor, oscillation in the contact plane, is dependent on the size and configuration of the toroidal polishing tip  104  and the amount of eccentric required to provide uniform contact during rotation for the given tilt angle. 
   In yet another embodiment, the dual motion polishing tool  100 , as described, would be mounted in a device (not shown) intended to provide purely rotary motion, such as a standard drill motor, high speed spindle, and the like. The high speed spindle can have speeds that range from 2,000–40,000 rpm. These speeds may be controlled to go as high as 80,000 rpm with an air-driven turbine. Activation of the drill motor would cause dual motion polishing tool  100  to spin, which due to the dual motion polishing tool&#39;s unique geometry, would cause the toroidal polishing tip  104  to oscillate in an eccentric fashion about the axial centerline of the arbor  102 . The dual motion polishing tool  100  would then be brought close to a work piece surface to be polished, while tilted at a predetermined contact angle that deviates from surface normal, thereby allowing increased productive material removal. As the dual motion polishing tool  100  makes contact with the work piece surface  115  (shown in  FIG. 8 ), due to the eccentric offset and tilt provided, the contact area created will be uniform and moves laterally back and forth along the work piece surface  115  in the contact plane. The magnitude of oscillation is dependent upon the magnitudes of eccentric offset and tilt angle. 
     FIG. 9  illustrates a contact patch  124  formed by the intersection of toroidal polishing tip  104  and the work piece surface  115 , as represented by a transparent wedge  123 . The contact patch  124  is shown inside the transparent wedge  123  that represents the contact plane described above. One skilled in the art should note that motion may be described relevant to the contact plane. For example, an in-plane motion is within the contact plane; whereas an out-of-plane motion occurs perpendicular to the contact plane. The toroidal polishing tip&#39;s  104  magnitude of oscillation in-plane and out-of-plane may be approximated using the following equations: 
                 In   ⁢     -     ⁢     plane   :                                   X   =       ⁢     [         (         D   CS     2     +       D   ID     2       )     /     cos   ⁡     (   β   )         +                       ⁢         (         D   CS     2     ⁢     sin   ⁡     (     α   -     β   ⁢           ⁢     cos   ⁡     (   θ   )           )         )     /     cos   ⁡     (   β   )         +                     ⁢     (             D   CS     2     [     1   +       cos   (     α   -     β   ⁢           ⁢     cos   ⁡     (   θ   )           ]     ⁢     tan   ⁡     (   θ   )           )     ⁢     cos   ⁡     (   β   )       ⁢     cos   ⁡     (   θ   )         +                         ⁢       (   Ecc   )     ⁢     cos   ⁡     (   θ   )         ]     /     cos   ⁡     (   α   )                     (     Equation   ⁢           ⁢   1     )               Out   ⁢     -     ⁢   of   ⁢     -     ⁢     plane   :                                   Y   =       ⁢         D   CS     2     +     [       {       Ecc     cos   ⁡     (   β   )         ⁢     sin   (     α   -     β   ⁢           ⁢     cos   ⁡     (   θ   )           }     ⁢     cos   ⁡     (   θ   )         ]     +                         ⁢     [         {         D   CS     2     +       D   ID     2       }     ⁢     sin   (     α   -     β   ⁢           ⁢     cos   ⁡     (   θ   )           ]       +     [         D   CS     2     ⁢     cos   (     α   -     β   ⁢           ⁢     cos   ⁡     (   θ   )           ]                           (     Equation   ⁢           ⁢   2     )               
Where, D CS  and D ID  are the cross-sectional diameter and internal diameter of the toroidal polishing tip  104 , respectively. Alpha, α, is the contact angle, Beta, β, is the tilt angle, and Theta, θ, is the rotation angle. Ecc is the value of the eccentric.  FIG. 10  shows a close isometric view of the toroidal polishing tip  104  with the alignment port  126 . The toroidal polishing tip  104  is about 1–3 mm in diameter and can be constructed of Buna-N Nitrile, Ethylene Propylene, Silicone, Neoprene, or Polyurethane for greater material removal efficiency.
 
     FIG. 11  discloses a front view of a conventional sub-aperture polishing tool  330  with an applied eccentric and the contact plane represented by a transparent wedge  123 . The use of a transparent wedge  123  in the representation allows one to actually see the contact patch  124  created by the area of interface between toroidal polishing tip  104  and work piece surface  115  (shown here as the contact plane represented by a transparent wedge  123 ). Indexes A through H, in  FIG. 11  provide a representation of contact for a given rotation of the sub-aperture polishing tool  330 . For all indexes, the leftmost corner of the transparent wedge  123  is coincident with a point at the intersection of the shank axis  110  and a 30-degree contact plane. For clarification, a bold vertical axis is created at this intersection. Index A represents the initial start point (0 degrees) as the sub-aperture polishing tool  330  is engaged with the work piece surface  115  creating a contact patch  124 . The in-plane distance, X, between the bold vertical axis and the center of the contact patch  124  is at its maximum at this index. Due to the cylindrical-axis offset, maximum compression of the toroidal polishing tip  104  is also observed at this index. The compression of the toroidal polishing tip  104  is represented by the contact patch size. Variation in contact patch size provides a graphical representation of the out-of-plane motion. As the sub-aperture polishing tool  330  rotates 45 degrees, represented by index B, the toroidal polishing tip  104  translates to the left and compression of the toroidal polishing tip  104  is reduced, showing a reduction in contact patch size. Index C shows an additional 45 degrees of rotation of the sub-aperture polishing tool  330 , where a further reduction of the contact patch size is observed as the toroidal polishing tip  104  translates further left. Another 45 degrees of rotation (Index D) shows no contact patch, indicating the toroidal polishing tip  104  is no longer in contact with the work piece surface  115 . Translation of the toroidal polishing tip  104  continues to the left until  180  degrees rotation of the sub-aperture tool  330  has been made (Index E). At index E, the in-plane distance, X, is at its minimum. Due to the cylindrical-axis offset, minimum compression of the toroidal polishing tip  104  is also observed at this index (for this case, the toroidal polishing tip  104  is at its peak distance off the work piece surface  115 ). Beyond this index, continued rotation begins to mirror observations made during the previous rotational steps. An additional 45 degree rotation of the sub-aperture polishing tool  330  begins to translate the toroidal polishing tip  104  to the right (Index F at 225 degrees). No observation of the contact patch is made, indicating the toroidal polishing tip  104  is still off the work piece surface  115 . Observations for Index F and index D are the same. Observations of the contact patch size for index G at 270 degrees and index H at 315 degrees are the same for index C at 90 degrees and index B at 45 degrees, respectively. The only difference being that the contact patch moves from right-to-left during indexes A to E and from left-to-right during indexes E to H.  FIG. 11  shows that in one embodiment, if no support surface tilt is applied, intermittent contact is observed (i.e., using a polishing tool with toroidal polishing tip  104  with a cylindrical axis offset only). 
     FIG. 12  discloses a front view of the dual motion polishing tool  100  with the contact plane represented by the transparent wedge  123 . The use of the transparent wedge  123  in the representation allows one to actually see the contact patch  124  created by the area of interface between toroidal polishing tip  104  and work piece surface  115  (shown here as the contact plane represented by a transparent wedge  123 ). Indexes A through H, in  FIG. 12  provide a representation of contact for a given rotation of the dual motion polishing tool  100 . For all indexes, the leftmost corner of the transparent wedge  123  is coincident with a point at the intersection of the shank axis  110  and a 30-degree contact plane. For clarification, a bold vertical axis is created at this intersection. Index A represents the initial start point (0 degrees) as the dual motion polishing tool  100  is engaged with the work piece surface creating a contact patch  124 . The in-plane distance, X, between the bold vertical axis and the center of the contact patch  124  is at its maximum at this index. The compression of the toroidal polishing tip  104  at this index is at a minimum value. The compression of the toroidal polishing tip  104  is represented by the contact patch size. Variation in contact patch size provides a graphical representation of the out-of-plane motion. As the tool rotates 45 degrees, represented by index B, the toroidal polishing tip  104  translates to the left and compression of the toroidal polishing tip  104  is increased, showing an enlargement in contact patch size. Index C shows an additional 45 degrees of rotation of the dual motion polishing tool  100 , where a further enlargement of the contact patch size is observed as the toroidal polishing tip  104  translates further left. At this index (index C at 90 degrees) compression of the toroidal polishing tip  104  reaches a maximum, due to the unique combination of the cylindrical-axis offset and support surface tilt. Another 45 degrees of rotation (Index D) continues contact patch translation to the left while the size of the contact patch begins to reduce, indicating a reduction in compression. Translation of the toroidal polishing tip  104  continues to the left until 180 degrees rotation of the tool has been made (Index E). At index E, the in-plane distance, X, is at its minimum. Also, the compression of the toroidal polishing tip  104  at this index is again at a minimum value. Beyond this index, continued rotation begins to mirror observations made during the previous rotational steps. An additional 45 degree rotation of the dual motion polishing tool  100  begins to translate the toroidal polishing tip  104  to the right (Index F at 225 degrees). Observations of the contact patch size for index F at 225 degrees, G at 270 degrees, and index H at 315 degrees are the same for index D at 135 degrees, index C at 90 degrees, and index B at 45 degrees, respectively. The only difference being that the contact patch moves from right-to-left during indexes A to E and from left-to-right during indexes E to H, creating the in-plane distance, X, oscillation. In this embodiment,  FIG. 12  shows that with the addition of a slight support surface tilt in the direction of cylindrical axis offset (provided by the dual motion polishing tool  100 ) continuous contact is observed and a slight oscillation of the contact area is achieved. In order to increase oscillation magnitude while maintaining continuous contact with the surface being polished, support surface tilt angle and cylindrical axis offset should, preferably, be increased together. For small oscillation magnitudes (shallow tilt angles), surface oscillation occurs primarily in the contact plane or zone. As the magnitude of surface oscillation is increased, larger surface support tilt angles and cylindrical axis offsets are required and result in a component of oscillation that moves in and out of the contact plane. One revolution of the rotating dual motion polishing tool  100  provides a single back-and-forth oscillation of the contact patch  124 . The distance in the contact plane covered in this motion by the contact patch  124  is equivalent to approximately twice the magnitude of the cylindrical axis offset. 
   The dual motion polishing tool  100  disclosed is preferably used in the presence of a free-abrasive liquid lap such as cerium oxide, chromium oxide, colloidal silica, diamond suspension, and the like. Free-abrasive liquid is chosen based on the material being polished, the desired level of surface smoothness, and on the mechanism of removal being pursued and corresponding efficiency. For glasses, chemical-mechanical polishing is the most efficient mechanism for polishing and an oxidant such as cerium oxide is typically used. Presently, diamond suspension is chosen for ceramics. As the dual motion polishing tool  100  rotates, the liquid lap is carried on the toroidal polishing tip  104  via laminar boundary layer flow. The polishing fluid travels along the outside of the toroidal polishing tip  104  and is carried into the contact region between the toroidal polishing tip  104  and the work piece surface  115 . The motion that is provided by the dual motion polishing tool  100  allows advantageous bi-directional polishing. 
   Bi-directional polishing, is defined by the motions created as the tool oscillates during rotation, thus allowing the polishing fluid to deviate from straight-line motion reducing potential grooving of the work piece surface. 
   The invention has been described with reference to a preferred embodiment; However, it will be appreciated that variations and modifications can be effected by a person of ordinary skill in the art without departing from the scope of the invention. 
   PARTS LIST 
   
       
         100  dual motion polishing tool 
         102  arbor 
         104  toroidal polishing tip 
         106  shank 
         108  offset cylinder 
         110  shank axis 
         112  offset cylinder axis 
         114  distal end of offset cylinder  108   
         115  work piece surface 
         123  transparent wedge 
         124  contact patch 
         125  centering boss 
         126  alignment port 
         300  polishing tool 
         305  grooves 
         310  support surface 
         315  shank 
         320  arbor 
         325  polishing pad 
         330  sub-aperture polishing tool 
         335  sub-aperture arbor 
         340  sub-aperture polishing head