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Title:
HIGH REMOVAL RATE MAGNETORHEOLOGICAL FINISHING HEAD
Document Type and Number:
WIPO Patent Application WO/2021/046119
Kind Code:
A1
Abstract:
A magnetorheological finishing head comprising magnetic pole pieces, nozzle shape, and wheel shape tailored to maximize volumetric removal rate. The carrier wheel for a ribbon of magnetorheological fluid is aspherical, preferably a toroid having a short radius perpendicular to, and the long radius parallel to, the axis of rotation, although the shape of the wheel may be any aspherical or free form parallel to the wheel's axis of rotation, e.g., toroidal or cylindrical. A magnetic field is generated by shaping the pole pieces to create a substantially uniform magnetic field over a defined gap therebetween such that the field strength in the area of the fluid ribbon is uniform. The nozzle has a non-circular opening to provide a fluid stream having a width that covers the width range of the magnetic field. It is the combination of these three features that allows for a novel MRF removal function.

Inventors:
MESSNER WILLIAM (US)
DAVIS JOHNATHAN (US)
MALONEY CHRISTOPHER (US)
Application Number:
PCT/US2020/049053
Publication Date:
March 11, 2021
Filing Date:
September 02, 2020
Export Citation:
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Assignee:
QED TECH INTERNATIONAL INC (US)
International Classes:
B24B31/112; B24B1/00
Foreign References:
US5951369A1999-09-14
US20030087585A12003-05-08
US20020177392A12002-11-28
US5616066A1997-04-01
KR20110138005A2011-12-26
Attorney, Agent or Firm:
OMHOLT, Thomas (US)
Download PDF:
Claims:
CLAIMS

What is claimed is:

1. A magnetorheological finishing head, comprising, a) a rotatable finishing wheel having a non-spherical finishing surface; b) first and second magnetic pole pieces of opposing polarity having comers disposed within said finishing wheel and having opposing faces, wherein the comers of said opposing faces closest to said finishing surface have a shape selected from the group consisting of conical, beveled, toroidal, radial, and freeform; and, c) a nozzle assembly terminating in a non-circular exit.

2. A magnetorheological finishing head, comprising any one of the following three elements: a) a rotatable finishing wheel having a non-spherical finishing surface; b) first and second magnetic pole pieces of opposing polarity disposed within said finishing wheel and having opposing faces, wherein the comers of said opposing faces closest to said finishing surface have a shape selected from the group consisting of conical, beveled, toroidal, radial, and freeform; and c) a nozzle assembly terminating in a non-circular exit.

3. A magnetorheological finishing head, comprising any two of the following three elements: a) a rotatable finishing wheel having a non-spherical finishing surface; b) first and second magnetic pole pieces of opposing polarity having comers disposed within said finishing wheel and having opposing faces, wherein the comers of said opposing faces closest to said finishing surface have a shape selected from the group consisting of conical, beveled, toroidal, radial, and freeform; and, c) a nozzle assembly terminating in a non-circular exit.

4. A magnetorheological finishing head in accordance with any one of Claims 1-3 wherein the shape of said non-spherical finishing surface is selected from the group consisting of toroidal, cylindrical, and free-form.

5. A magnetorheological finishing head in accordance with any one of Claims 1-3 wherein said magnetic pole pieces are components of a magnetic system selected from the group consisting of electromagnet and permanent magnet.

6. A magnetorheological finishing head in accordance with any one of Claims 1-3 wherein a magnetic field formed above said finishing surface is substantially uniform from edge to edge of said magnetic field.

7. A magnetorheological finishing head in accordance with any one of Claims 1-3 wherein said non-circular exit is a slot.

8. A magnetorheological finishing head in accordance with any one of Claims 1 wherein said rotatable finishing wheel is formed in accordance with the formula

Z = f(x,y) = Ry ±V[(Ry-g(x))2-y2], where g(x) is the generating curve and Z is the algebraic definition of said rotatable finishing wheel.

9. A magnetorheological finishing head in accordance with any one of Claims 1-3 wherein said first and second magnetic pole pieces are formed such that when they are energized a uniform magnetic fringing field is formed over a desired width on said rotatable finishing wheel.

10. A magnetorheological finishing head in accordance with any one of Claims 1-3 wherein said nozzle assembly is formed such that a ribbon of magnetorheological fluid extruded therefrom is of uniform thickness from edge to edge of said ribbon.

11. A magnetorheological finishing head in accordance with any one of Claims 1-3 wherein said non-circular exit of said nozzle assembly is selected from the group consisting of a slot, a slot with rounded ends, and a plurality of holes.

Description:
HIGH REMOVAL RATE MAGNETORHEOLOGICAL FINISHING HEAD FIELD OF THE APPLICATION

The present invention is directed to systems for magnetorheological finishing of substrate surfaces; more particularly, to a magnetorheological finishing head comprising a rotatable work surface (the outer surface of an equatorial section of a “wheel”) disposed between opposing magnetic pole pieces and capable of carrying magnetorheological fluid (MR fluid) on the surface of the wheel into and through a work zone (the “spot”) between the wheel and the work surface of the substrate (“workpiece”) being finished, wherein the MR fluid is “stiffened” by being subjected to a magnetic field exerted by the magnetic pole pieces which may be electromagnets or permanent magnets, and material is removed from the substrate surface through abrasion by the stiffened MR fluid; and most particularly, to such a magnetorheological finishing head wherein the rotatable work surface is non- spherical, the magnetic pole pieces generate a substantially uniform magnetic field, and the MR fluid is presented to the work zone on the rotatable work surface as a wide ribbon of fluid material.

BACKGROUND OF THE INVENTION

Use of magnetically-stiffened magnetorheological fluids for abrasive finishing and polishing of substrates is well known. Such fluids, containing magnetically-soft abrasive particles dispersed in a liquid carrier, exhibit magnetically-induced plastic behavior in the presence of a magnetic field. The apparent viscosity of the MR fluid can be magnetically increased by many orders of magnitude, such that the consistency of the MR fluid changes from being nearly watery to being a very stiff abrasive paste. When such an abrasive paste is directed appropriately against a substrate surface to be shaped or polished, e.g., an optical element, a very high level of finishing quality, accuracy, and control can be achieved.

US Patent No. 5,795,212, “Deterministic magnetorheological finishing”, issued August 18, 1998 to Jacobs et al, discloses a method and apparatus for finishing a workpiece surface using MR fluid wherein the workpiece is positioned near a carrier surface such that a converging gap is defined between a portion of the workpiece surface and the carrier surface. A magnetic field is applied substantially at the gap, and a flow of stiffened MR fluid is introduced into the gap such that a work zone is created in the MR fluid, thereby forming a sub-aperture transient finishing tool for engaging and causing material removal at the portion of the workpiece surface. The workpiece or the work zone is moved relative to the other to expose different portions of the workpiece surface to the work zone for predetermined time periods to selectively finish portions of the workpiece surface to predetermined degrees.

US Patent No. 5,839,944, “Apparatus for deterministic finishing of workpieces”, issued November 24, 1998 to Jacobs et al., discloses a method and apparatus for finishing a workpiece surface using MR fluid wherein the workpiece is positioned near a carrier surface such that a converging gap is defined between a portion of the workpiece surface and the carrier surface. A magnetic field is applied substantially at the gap, and a flow of stiffened MR fluid is introduced into the converging gap such that a work zone is created in the MR fluid, thereby forming a sub-aperture transient finishing tool for engaging and causing material removal at the portion of the workpiece surface. The workpiece or the work zone is moved relative to the other to expose different portions of the workpiece surface to the work zone for predetermined time periods to selectively finish portions of the workpiece surface to predetermined degrees.

US Patent No. 5,951,369, “System for magnetorheological finishing of substrates”, issued September 14, 1999 to Kordonski et al, discloses an improved system for increasing the effectiveness of magnetorheological finishing of a substrate. An inline flowmeter is close-loop linked to the rotational speed of a pressurizing pump to assure that the flow of magnetorheological fluid to the work zone is constant. A simplified capillary viscometer is disposed in the fluid delivery system at the exit thereof onto the wheel surface. Output signals from the flowmeter and the viscometer pressure sensor are sent to a computer which calculates the viscosity of MRF being delivered to the work zone and causes replenishment of carrier fluid to the work-concentrated MR fluid to return the viscosity to aim to assure that a constant concentration of magnetic solids is being provided to the work zone. Asymmetric pole pieces for the field magnet at the work zone extend the magnetic field along the wheel surface upstream of the work zone to permit full magnetic stiffening of the MRF before it engages the work piece, while minimizing fringing field in the vicinity of the viscometer, and to shorten the magnetic field along the wheel surface downstream of the work zone.

US Patent No. 6,106,380, “Deterministic magnetorheological finishing”, issued August 22, 2000 to Jacobs et al, discloses method and apparatus for finishing a workpiece surface using MR fluid wherein the workpiece is positioned near a carrier surface such that a converging gap is defined between a portion of the workpiece surface and the carrier surface. A magnetic field is applied substantially at the gap, and a flow of stiffened MR fluid is introduced into the converging gap such that a work zone is created in the MR fluid, thereby forming a sub aperture transient finishing tool for engaging and causing material removal at the portion of the workpiece surface. The workpiece or the work zone is moved relative to the other to expose different portions of the workpiece surface to the work zone for predetermined time periods to selectively finish the portions of the workpiece surface to predetermined degrees.

US Patent No. 6,506,102, “System for magnetorheological finishing of substrates”, issued January 14, 2003 to Kordonski et al, discloses an improved system for magnetorheological finishing of a substrate comprising a vertically oriented bowl-shaped carrier wheel having a horizontal axis. The carrier wheel is preferably an equatorial section of a sphere, such that the carrier surface is spherical. The wheel includes a radial circular plate connected to rotary drive means and supporting the spherical surface which extends laterally from the plate. An electromagnet having planar north and south pole pieces is disposed within the wheel, within the envelope of the sphere, and preferably within the envelope of the spherical section defined by the wheel. The magnets extend over a central wheel angle of about 120 degrees, such that magnetorheological fluid is maintained in a partially stiffened state ahead of and beyond the work zone. A magnetic scraper removes the MR fluid from the wheel as the stiffening is relaxed and returns it to a conventional fluid delivery system for conditioning and re-extrusion onto the wheel. The system is useful in finishing large concave substrates, which must extend beyond the edges of the wheel, as well as for finishing very large substrates in a work zone at the bottom dead center position of the wheel.

US Patent No. 8,944,883, “System for magnetorheological finishing of a substrate”, issued February 3, 2015 to Kordonski, discloses a spherical wheel meant for carrying a magnetorheological finishing fluid and housing a variable-field permanent magnet system having north and south iron pole pieces separated by primary and secondary gaps with a cylindrical cavity bored through the center. A cylindrical permanent magnet magnetized normal to the cylinder axis is rotatably disposed in the cavity. An actuator allows rotation of the permanent magnet to any angle, which rotation changes the distribution of flux in the magnetic circuit through the pole pieces. Thus, one can control field intensity in the gaps by positioning the permanent magnet at whatever angle provides the required field strength. Because the field also passes above the pole pieces, defining a fringing field outside the wheel surface, the variable field extends through a layer of MR fluid on the wheel, thus varying the stiffness of the MR fluid as may be desired for finishing control.

In all of these prior art references, the disclosed wheel is an equatorial spherical section; a method to tailor the shape of the magnetic field by shaping the tips of the pole pieces is not disclosed; and method and apparatus for shaping the cross-sectional area of the magnetorheological fluid ribbon on the wheel with a non-circular nozzle exit is not disclosed.

Prior art magnetorheological finishing heads have a limit in material removal rate that is driven by two primary factors. The first factor is the fluid being used in the process, which drives the peak removal rate. The second factor is the apparatus that makes up the finishing head, which drives both the peak and the volumetric removal rate.

The geometry of the apparatus limits the physical size of the removal tool and in many cases limits the deterministic magnetorheological finishing process. In particular, prior art processes that focus on finishing large optics and/or inducing an aspheric shape to a spherical surface can take hours or even days of finishing to reach the desired final figure. In such cases, having a larger removal function provides the opportunity to significantly reduce the cycle time of the polishing run.

In the prior art, larger removal functions have been created simply by increasing the diameter of the spherical magnetorheological finishing wheel, but in many cases a larger wheel is not possible or practical and also is very costly to fabricate with the required precision. As the wheel gets larger, the same precision is still required for wheel runout, and achieving the desired tolerances becomes significantly harder and more expensive.

Considering the factors controlling removal rate, the work zone must be enlarged both in the direction of wheel travel and transverse to the direction of wheel travel to increase the removal rate. It is known that the spot can be lengthened by increasing the wheel radius, and that the peak removal rate can be increased by making the spot deeper between the wheel and the substrate workpiece. What is not known in the prior art is how to increase the volumetric removal rate by making the spot wider, preferably without increasing substantially the radius or other geometry of the wheel.

What is needed in the art is a magnetorheological finishing head having a tailored magnetic field, nozzle shape, and wheel shape that maximizes the volumetric removal rate of substrate material.

SUMMARY OF THE INVENTION

A magnetorheological finishing head comprises magnetic pole pieces having specifically shaped opposing tips; a non-circular nozzle shape; and anon-spherical wheel shape and surface to maximize volumetric removal rate. The carrier wheel for a ribbon of MR fluid is non-spherical and is preferably an equatorial section of a toroid having a short radius about an axis parallel to, and a long radius about an axis perpendicular to, the axis of rotation of the wheel, although the shape of the wheel may be any aspherical or free form shape having an axis of rotation parallel to the wheel’s axis of rotation, e.g., toroidal or cylindrical. A tailored magnetic field is generated by shaping the tips of the pole pieces to create a magnetic fringing field over a defined gap therebetween greater than a prior art gap such that the field strength is maintained at a useful intensity over the width of the ribbon. The magnets may be either electromagnets or permanent magnets, although typically electromagnets are employed as in the prior art. The nozzle has a non-circular opening to provide a fluid stream in a width that covers the range of the magnetic field. It is the combination of these three features that allows for a maximum increase in MRF removal function, although these features taken singly or in pairs can provide a significant increase in MRF removal function over that of the prior art.

The present invention creates an opportunity for material removal rates at least four times greater than do prior art systems.

The system is especially useful for conducting low order figure corrections on large substrates and introducing shape change to an optical surface such as aspheric generation.

Further features and advantages of the present invention will become apparent to those of ordinary skill in the art in view of the drawings and detailed description of preferred embodiments below.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will now be described, by way of example, with reference to the accompanying drawings, in which: FIG. 1 is an elevational cross-sectional view of a portion of a prior art magnetorheological finishing head;

FIG. 2a is an elevational cross-sectional view of a portion of a magnetorheological finishing head in accordance with the present invention;

FIG. 2b is an elevational view of the portion of a magnetorheological finishing head shown in FIG. 2a showing in addition an MR fluid ribbon on the wheel surface, a workpiece in position for material removal, and work zone or “spot” therebetween;

FIG. 3 is a perspective view from above of the magnetorheological finishing head shown in FIGS. 2a and 2b;

FIG. 4 is an elevational view of a first embodiment of a nozzle in accordance with the present invention;

FIG. 5 is a cross-sectional pan view of the nozzle shown in FIG. 4;

FIG. 6 is an elevational cross-sectional view of the elements of a magnetorheological work zone;

FIG. 7 is an elevational cross-sectional view of a portion of an MR finishing head showing dimensions of a ribbon of MR fluid in accordance with the present invention;

FIG. 8a is a diagram showing the relationship of a toroid formed in accordance with the present invention to a finishing wheel taken as an equatorial section of the toroid; FIG. 8b is a diagram like that shown in FIG. 8a showing orthogonally intersecting arcs on the surface of a toroid formed in accordance with the present invention, the arcs having respective radii Ri and R2, wherein Ri ¹ R2;

FIG. 9 is an isometeric view of a first embodiment of magnetic pole pieces in accordance with the present invention;

FIG. 10 is an isometric view of a second and preferred embodiment of magnetic pole pieces in accordance with the present invention;

FIG. 11 is a cross-sectional view of the magnetic field resulting from simply moving prior art parallel pole planes apart in an effort to widen the magnetic field and hence the width of the work zone;

FIG. 12 is a cross-sectional view of the magnetic field resulting from forming the opposing pole surfaces as conic sections in an effort to widen the magnetic field and hence the width of the work zone;

FIG. 13 is a cross-sectional view of the magnetic field resulting from forming the opposing pole surfaces as toroidal sections in an effort to widen the magnetic field and hence the width of the work zone;

FIG. 14 is a graph showing idealized magnetic field lines from FIGS. 11-13;

FIG. 15 is a plan view of material removal rate in a typical prior art work zone; and FIG. 16 is a plan view of typical material removal rate in a work zone produced by a magnetorheological finishing head formed in accordance with the present invention.

DETAILED DESCRIPTION OF THE INVENTION

Referring to FIGS. 1 and 6, a portion of a prior art magnetorheological finishing head 10 comprises a finishing wheel 12 having a disc-shaped central portion 14 supporting an equatorial spherical finishing portion 16 having a finishing surface 18. Wheel 12 is mounted for rotation on axle 20 carried in precision bearings 22a, 22b. Axle 20 is driven about axis of rotation 30 by an electric motor system (not shown). Below and adjacent to finishing portion 16 and on opposite sides of disc-shaped central portion 14 are first and second magnet pole pieces 24a, 24b, preferably identical but of opposite polarities, i.e., north and south. These pole pieces typically have planar opposing faces 26a, 26b set at a predetermined first spacing from each other. Polepieces 24a, 24b may be electromagnets or permanent magnets.

When the electromagnets are energized, a magnetic fringing field (not shown) is formed through and above finishing portion 16 wherein a ribbon of MR fluid 17 being carried on surface 18 is stiffened to a paste consistency. A substrate 21 to be finished, e.g., a lens as shown in FIG. 6, is positioned, typically for rotation about its own axis 23, above the wheel surface at a distance from the wheel less than the thickness of the incoming MR fluid ribbon, thus creating a converging gap and forming a work zone or “spot” 19 wherein abrasive finishing of substrate 21 disposed in work zone 19 is carried out. The dimensions of the converging gap may be varied according to the requirements of a specific finishing application. In FIG.

6, the height of the ribbon entering the work zone is RH, the plunge depth of the work piece into the ribbon is D, and the resulting gap G between the work piece and the wheel surface is the thickness of the work zone 19.

Referring now to FIGS. 2a, 2b, 6,8, and 9-13, an improved magnetorhological finishing head 110 for forming a wider and longer work zone is substantially identical with the prior art magnetorheological finishing head 10 shown in FIG. 1 except that the upper comers of the magnetic pole pieces 124a, 124b are modified as shown. Preferably, the upper comers are rounded 128a, 128b as shown in FIGS. 2a, 10, and 13 or beveled 126a, 126b and 226a, 226b as shown in FIGS. 9 and 12 and may be of any desired shape, e.g., conical, curved with a radius, or freeform. The actual values of radius and spacing between pole pieces 124a, 124b may be selected as required to form a specific size work zone for any particular application. It has been found that providing a rounded or beveled shape can result in a fringing field 40,240 having lateral uniformity over a substantially greater width than that formed by the prior art pole piece arrangement shown in FIG. 1.

Preferably, the curved shapes 128a, 128b are formed as portions of a torus in accordance with the equations shown hereinbelow regarding the shape of the finishing wheel surface, in particular a ring toms wherein the distance from the center of the tube to the center of the torus is larger than the radius of the tube. Referring still to improved magnetorheological finishing head 110, as described hereinabove, finishing portion 116 having finishing surface 118 is formed as a non-sphere, preferably a toroid having a short radius 119 perpendicular to, and a long radius coincident with, the axis of rotation 130, although the shape of the wheel may be any aspherical or free form parallel to the wheel’s axis of rotation 130, e.g., toroidal or cylindrical (toroid with infinite long radius). An advantage of this geometry is that it allows for larger removal functions without a significant increase in the size of the overall tool, i.e., the diameter of the wheel. Another advantage is that the toroidal wheel allows the removal function to get wider without requiring an increase in the volume of the fluid that a prior art spherical wheel requires. This feature helps reduce the need for higher flow rates and larger pumping systems to achieve an equivalent result.

Referring to FIGS. 2a, 8a, and 8b, a finishing wheel 116 having surface 118 may be more generally defined as a surface of revolution other than spherical.

FIGS. 8a, 8b show an idealized shape 142 having a first radius Ri being rotated about a second radius R2 to form a three-dimensional shape 144 wherein Ri and R2 create respective orthogally-intersecting arcs Ai and A2 on wheel surface 118. (Note that when Ri = R2, the wheel surface is spherical as in the prior art.) In simplest form, shape 142 is a circle and shape 144 is atoms, but it is possible that a higher-order polynomial or other equation can be used to define a surface that can be revolved around R2. For higher removal rates Ri should be much larger than R2. These values can be chosen based on two factors: 1) the shape of the optic to avoid the geometry of the wheel interfering with the geometry of the workpiece (concave optics in particular), and 2) the larger the radius R2 the wider (and thus larger) the removal function will be for a given MRF flowrate.

In explicit form, the wheel geometry may be expressed by:

Z = f(x,y) = R ±V[(Ryg(x)) 2 -y 2 ], where g(x) is the generating curve and Z is the algebraic shape of the wheel.

For atoms: g(x) = R x {l-V[l-(x/R x 2 ]}, where g(x) is a circle with radius R x . Referring to FIGS. 3 through 5, the present invention requires a shape change to the MRF ribbon formed on finishing surface 118. Prior art MRF ribbons are created using a round nozzle exit of a specified inner diameter. A typical ribbon shape is round when extruded from a prior art exit port having a diameter of 3 mm and a cross-sectional area of 7.3 mm 2 .

To increase the size of the removal function (work zone) the need is to increase its width. A wider removal function requires an MRF stream that is spread out laterally and injected on the wheel across the area that covers the width of the removal function before the MRF ribbon 150 reaches the work zone, typically at the top-dead-center position of the wheel. Thus, if the nozzle exit is non-circular, and preferably is shaped as a slot, the MR fluid is spread out prior to landing on the wheel, allowing for wider removal functions.

Nozzle assembly 132 comprises a feed tube 134 entered into a housing block 136 and terminating in a distributor 138 within housing block 136 that discharges into an internal slot formed at the desired width of the MRF ribbon to be generated and terminating at an exit slot 140. In a presently preferred embodiment, exit slot 140 is about 19 mm wide and about 0.9 mm high, resulting in an aspect ratio greater than 20. The cross-sectional area of this design is 17.8 mm 2 , allowing nearly two and a half times the flow rate of the prior art nozzle when operated at the same delivery pressure. Increased flow is required to generate a wider removal function by filling a larger area between the wheel and substrate. Preferably, the ends of the slot are rounded to avoid stagnant zones in the comers and unwanted buildup of fluid.

Obviously, other slot shapes and dimensions may be selected as may be required for specific finishing applications, e.g., the “slot” may be formed by a line of discharge holes rather than a continuous slot, or the slot may be non-uniform in height.

The height and width of the ribbon may be manipulated on the wheel after extrusion. The angle of incidence of the fluid jet onto the wheel can influence the ribbon width: as the nozzle extrusion angle increases from tangential toward perpendicular, the ribbon tends to spread laterally on the wheel. Increasing the wheel velocity to beyond the “flow matching” value at which the fluid jet velocity matches the wheel’s tangential velocity causes the fluid to be stretched out, resulting in a lower cross-sectional area of the ribbon. The benefit of spreading the ribbon out allows the operator to manage the overall height of the ribbon and the dimensions shown in FIG. 6 to achieve a wide removal function. Once the fluid ribbon is energized by the magnetic field, the abrasive boundary layer 19 (work zone) is generated across the width of the ribbon.

Preferably, the height of a ribbon of magnetorheological fluid on a finishing wheel when entering a work zone is between 1.20 mm and 1.56 mm, the plunge depth into said ribbon of magnetorheological fluid by a workpiece being finished by the magnetorheological finishing head is between 0.60 mm and 0.81 mm, and a gap between the work piece and the finishing wheel is between 0.60 mm and 0.75 mm.

FIGS. 3 and 7 show a ribbon 150 of width W and thickness RH disposed on wheel surface 118.

Referring now to FIG. 1 l,it is seen that simply moving the prior art planar- facing pole pieces 26a, 26b farther apart than the standard spacing shown in FIG. 1 creates a magnetic field 140 in the work zone that is laterally non-uniform and somewhat weaker in the center, resulting in an undesirable bimodal removal function. Alternatively (FIGS. 9, 12 and 14), beveling the pole pieces as with conical faces 226a,226b results in a fairly uniform field 240 overall with a slightly lower field intensity. Referring now to FIGS. 10,13 and 14 with a radius on the pole pieces 124a, 124b results in a fairly uniform field 40 overall with a higher field intensity.

Referring now to FIG. 14, idealized magnetic fields just above the wheel surface are shown for the conditions disclosed hereinabove in FIGS. 11-13.

Referring now to FIGS. 15 and 16, a prior art work zone spot 55 (FIG. 15) is shown in comparison to a work zone spot 155 achievable by a magnetorheological finishing apparatus in accordance with the invention as shown in FIG. 2a. A typical prior art spot 55, from a spherical 150mm diameter wheel, has a width 60 of about 4.0 mm and a length 70 of about 10.0 mm, thus having a working area of about 40.0 mm 2 , whereas an improved spot 155 may have a width 160 of about 18.0 mm and a length 170 of about 21.0 mm, thus having a working area of about 378.0 mm 2 , providing a removal rate many times larger than a prior art spot. Thus, the present invention comprises three novel elements: a) magnet pole pieces having rounded upper comers, b) a non-spherical wheel finishing surface, preferably toroidal, and c) an MRF application nozzle having a non-circular exit. It is the combination of these three features that allows for a maximum increase in MRF removal function, although these features taken singly or in pairs can provide a significant increase in MRF removal function over that of the prior art.

Various changes may be made to the structure and method embodying the principles of the invention. The foregoing embodiments are set forth in an illustrative and not in a limiting sense. The scope of the invention is defined by the claims.