HIGH REMOVAL RATE MAGNETORHEOLOGICAL FINISHING HEAD

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.

Claims

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 corners disposed within said finishing wheel and having opposing faces, wherein the corners 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 corners 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 corners disposed within said finishing wheel and having opposing faces, wherein the corners 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. The magnetorheological finishing head in accordance with claim 1 wherein the shape of said non-spherical finishing surface is selected from the group consisting of toroidal, cylindrical, and free-form.

5. The magnetorheological finishing head in accordance with claim 1 wherein said magnetic pole pieces are components of a magnetic system selected from the group consisting of electromagnet and permanent magnet.

6. The magnetorheological finishing head in accordance with claim 1 wherein a magnetic field above said finishing surface is substantially uniform from edge to edge of said magnetic field.

7. The magnetorheological finishing head in with claim 1 wherein said non-circular exit is a slot.

8. The magnetorheological finishing head in accordance with claim 1 wherein said rotatable finishing wheel is formed in accordance with the formula
Z=f(x,y)=R.sub.y±√[(R.sub.y−g(x)).sup.2-y.sup.2], where g(x) is the generating curve and Z is the algebraic definition of said rotatable finishing wheel.

9. The magnetorheological finishing head in accordance with claim 1 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. The magnetorheological finishing head in accordance with claim 1 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. The magnetorheological finishing head in accordance with claim 1 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.

12. The magnetorheological finishing head in accordance with claim 2 wherein the shape of said non-spherical finishing surface is selected from the group consisting of toroidal, cylindrical, and free-form.

13. The magnetorheological finishing head in accordance with claim 2 wherein said magnetic pole pieces are components of a magnetic system selected from the group consisting of electromagnet and permanent magnet.

14. The magnetorheological finishing head in accordance with claim 2 wherein a magnetic field formed above said finishing surface is substantially uniform from edge to edge of said magnetic field.

15. The magnetorheological finishing head in accordance with claim 2 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.

16. The magnetorheological finishing head in accordance with claim 2 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.

17. The magnetorheological finishing head in accordance with claim 3 wherein the shape of said non-spherical finishing surface is selected from the group consisting of toroidal, cylindrical, and free-form.

18. The magnetorheological finishing head in accordance with claim 3 wherein said magnetic pole pieces are components of a magnetic system selected from the group consisting of electromagnet and permanent magnet.

19. The magnetorheological finishing head in accordance with claim 3 wherein a magnetic field formed above said finishing surface is substantially uniform from edge to edge of said magnetic field.

20. The magnetorheological finishing head in accordance with claim 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.

21. The magnetorheological finishing head in accordance with claim 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.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0019] The present invention will now be described, by way of example, with reference to the accompanying drawings, in which:

[0020] FIG. 1 is an elevational cross-sectional view of a portion of a prior art magnetorheological finishing head;

[0021] FIG. 2a is an elevational cross-sectional view of a portion of a magnetorheological finishing head in accordance with the present invention;

[0022] 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;

[0023] FIG. 3 is a perspective view from above of the magnetorheological finishing head shown in FIGS. 2a and 2b;

[0024] FIG. 4 is an elevational view of a first embodiment of a nozzle in accordance with the present invention;

[0025] FIG. 5 is a cross-sectional pan view of the nozzle shown in FIG. 4;

[0026] FIG. 6 is an elevational cross-sectional view of the elements of a magnetorheological work zone;

[0027] 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;

[0028] 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;

[0029] 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 R.sub.1 and R.sub.2, wherein R.sub.1≠R.sub.2;

[0030] FIG. 9 is an isometric view of a first embodiment of magnetic pole pieces in accordance with the present invention;

[0031] FIG. 10 is an isometric view of a second and preferred embodiment of magnetic pole pieces in accordance with the present invention;

[0032] 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;

[0033] 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;

[0034] 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;

[0035] FIG. 14 is a graph showing idealized magnetic field lines from FIGS. 11-13;

[0036] FIG. 15 is a plan view of material removal rate in a typical prior art work zone; and

[0037] 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

[0038] 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.

[0039] 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.

[0040] Referring now to FIGS. 2a, 2b, 6,8, and 9-13, an improved magnetorheological 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 corners of the magnetic pole pieces 124a,124b are modified as shown. Preferably, the upper corners 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 torus wherein the distance from the center of the tube to the center of the torus is larger than the radius of the tube.

[0041] 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.

[0042] 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 R.sub.1 being rotated about a second radius R.sub.2 to form a three-dimensional shape 144 wherein R.sub.1 and R.sub.2 create respective orthogally-intersecting arcs A.sub.1 and A.sub.2 on wheel surface 118. (Note that when R.sub.1=R.sub.2, the wheel surface is spherical as in the prior art.) In simplest form, shape 142 is a circle and shape 144 is a torus, but it is possible that a higher-order polynomial or other equation can be used to define a surface that can be revolved around R.sub.2. For higher removal rates R.sub.1 should be much larger than R.sub.2. 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 R.sub.2 the wider (and thus larger) the removal function will be for a given MRF flowrate.

[0043] In explicit form, the wheel geometry may be expressed by:

[0044] Z=f(x,y)=R.sub.y±√[R.sub.y−g(x)).sup.2−y.sup.2], where g(x) is the generating curve and Z is the algebraic shape of the wheel.

[0045] For a torus:

[0046] g(x)=R.sub.x{1−√[1−(x/R.sub.x.sup.2]}, where g(x) is a circle with radius R.sub.x.

[0047] 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.sup.2.

[0048] 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.

[0049] 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.sup.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 corners and unwanted buildup of fluid.

[0050] 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.

[0051] 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.

[0052] 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.

[0053] FIGS. 3 and 7 show a ribbon 150 of width W and thickness RH disposed on wheel surface 118.

[0054] Referring now to FIG. 11, 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.

[0055] Referring now to FIG. 14, idealized magnetic fields just above the wheel surface are shown for the conditions disclosed hereinabove in FIGS. 11-13.

[0056] 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 150 mm 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.sup.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.sup.2, providing a removal rate many times larger than a prior art spot.

[0057] Thus, the present invention comprises three novel elements: a) magnet pole pieces having rounded upper corners, 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.

[0058] 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.