ELASTIC EMISSIONS MACHINING SYSTEMS AND METHODS THEREOF

Abstract

An elastic emission machining apparatus includes a machining element having a non-spherical shape that is configured to spin about an axis of rotation, a tank, and a driving system. The tank has a chamber positioned to receive the machining element and a slurry comprising a mixture of a liquid and chemically reactive fine particles. The driving system is coupled to and configured to engage the machining element to spin about the axis of rotation adjacent to a surface of the workpiece to accelerate the chemically reactive fine particles through a gap between the machining element and the surface of the workpiece.

Description

This application claims the benefit of U.S. Provisional Patent Application No. 63/411,434, filed Sep. 29, 2022, which is hereby incorporated by reference in its entirety.

FIELD

The technology generally relates to systems and methods for precisely machining the surface of an article of manufacture, and, more particularly, for the fine figuring of an optical element using an elastic emission machining process.

BACKGROUND

Traditionally optical surfaces have been polished with so-called chemical-mechanical polishing (CMP) processes, such as that shown in FIGS. 1A and 1B. As shown in the diagrams of FIGS. 1A and 1B, a prior art CMP machine 10 has a workpiece 20 having a surface 30 to be polished is mounted onto spindle 32 that rotates 22 about its axis. At the same time a polishing pad 24 attached to a second spindle 34 is caused to spin 26 about its axis while also being rotated about the surface of the workpiece 20 in a planetary motion. Furthermore, polishing slurry 18 is directed onto the surface 30 of workpiece 20 through hose 14 and nozzle 16 such that polishing slurry 18 fills the gap between polishing pad 24 and workpiece surface 30, and effects a polishing process on surface 30 when the workpiece 20 and pad 24 are in motion with respect to one another as described above.

However, this particular CMP example is limited to spherical-shaped workpiece surfaces as only spherical-shaped workpiece and pad surfaces have full contact across their operative surfaces (assuming they both have the same radius of curvature). Nonetheless CMP figuring and polishing can produce optical surfaces having a roughness of less than 10 nm RMS and peak-to-valley figure error of less than 20 nm.

Elastic Emission Machining, or EEM, is a process for finishing (i.e., polishing and figuring) the surface of an optical element, including spherical, aspherical, cylindrical, acylindrical, free-form, etc., such as a mirror or the surface of a lens, with great precision. A typical prior art EEM system 50, as shown in FIG. 2, can remove material from a surface 72 of a workpiece 70 at the atomic level, and do so in a deterministic machining process. Workpieces fabricated with EEM typically have surface roughness less than 1 nm RMS and a peak-to-valley error of less than 10 nm.

Continuing with reference to FIG. 2, a prior art EEM system 50 includes a workpiece 70 having a surface 72 wherein the workpiece is coupled to a workpiece mount 68. A spherical machining element 64 is coupled to a spindle 62 which in turn is coupled to a motor 60 which causes the spherical machining element 64 and the spindle 62 to rotate about their common axis. The spherical machining element 64 and the workpiece 70 are submerged within a tank 76 of slurry 78 which also fills the small gap between the spherical machining element 64 and the surface 72 of the workpiece 70. A slurry temperature control unit 80 is also provided to maintain the slurry 78 at a constant temperature so that, accordingly, the removal rate of the material from the surface 72 of the workpiece 70 does not vary during the EEM process. A circulating pump 90 causes slurry 78 to flow through source hose 88 and return hose 92, as well as through tank 76 so that the slurry 78 within tank 76 stays substantially homogeneous in terms of temperature, particle concentration within the vehicle of the slurry, and so on. A numerically-controlled positioning table 82 is also provided, on which the tank 76 is placed, so that workpiece 70 and its surface 72 being EEM'ed can be translated in space with respect to the spherical machining element 64 so that the surface 72 can be EEM'ed in its entirety by the spherical machining element 64.

In operation the surface 66 of the spinning spherical machining element 64 does not come into actual physical contact with the surface 72, but instead is placed within a few microns of surface 72 at its closest point of contact. As the spherical machining element 64 spins, particulates within the slurry 78 are drawn through the gap between surface 72 and the spinning spherical machining element 64 by the rotational action of the spinning spherical machining element 64, and these particulates subsequently come into contact with the surface 72 and, accordingly, cause material to be removed from the surface 72 of the workpiece 70. Indeed, to a first order approximation, the amount of material removed from the surface 72 is proportional to the distance or space between the surface 72 and the spherical machining element 64. Since the machining element 64 in the prior art is spherical, the machining element 64 will impart a spherical-shaped divot, such as the spherical machining mark 94 illustrated in FIG. 3, into the surface 72 of workpiece 70 (assuming the NC table 82 is not activated).

As shown in FIG. 3, an example of a spherical machining mark 94 resulting from elastic emission machining with a spherical machining element 64, has a width in the X-direction of W_X that is equal to the width in the Y-direction, W_Y, that are both substantially equal to twice the radius, R, of the machining mark 94. As a numerical example, if the radius of the spherical machining element 66 is 25 mm and the width of the spherical machining mark 94 is 1 mm, then the depth of the fully-developed (i.e., after material removal has substantially completed) spherical machining mark 94 into the surface 72 of workpiece 70 is approximately 5 microns. Note that machining mark 94 also has equal-depth contour lines 96A, 96B, 96C whose cross-section profile in the X-Z or Y-Z planes, for example, are circular owing to the spherical shape of spherical machining element 64. Note also that the equal-depth contour lines 96A, 96B, 96C are themselves circular, again due to the spherical shape of spherical machining element 64. While circular cross-sectional profiles and equal-depth contours of machining mark 94 are certainly useful, other profiles which are not circular are needed.

SUMMARY

An elastic emission machining apparatus includes a machining element having a non-spherical shape that is configured to spin about an axis of rotation, a tank, and a driving system. The tank has a chamber positioned to receive the machining element and a slurry comprising a mixture of a liquid and chemically reactive fine particles. The driving system is coupled to and configured to engage the machining element to spin about the axis of rotation adjacent to a surface of the workpiece to accelerate the chemically reactive fine particles through a gap between the machining element and the surface of the workpiece.

A method of making an elastic emission machining apparatus includes providing a machining element having a non-spherical shape and that is configured to spin about an axis of rotation. A chamber of a tank is positioned to receive the machining element and a slurry comprising a mixture of a liquid and chemically reactive fine particles. A driving system is coupled to and is configured to engage the machining element to spin about the axis of rotation adjacent to a surface of the workpiece to accelerate the chemically reactive fine particles through a gap between the machining element and the surface of the workpiece.

An elastic emission machining system for polishing, smoothing, and/or figuring the surface of an article of manufacture, such as an optical device including mirrors and lenses, in which a spinning elastic emission machining element in close proximity to the surface and submerged in a slurry causes particulates in the slurry to remove material from the surface in accordance with the shape of the elastic emission machining element. The elastic emission machining element have a non-spherical shape, including toroidal, atoroidal, ellipsoidal, acylindrical, aspherical, and polynomial shapes, and have an axis of rotation about which the machining element spins during the elastic emission machining process. Examples of this technology retain the beneficial features of elastic emission machining systems found in the prior art, including but not limited to sub-nanometer RMS surface roughness and deterministic material removal at the atomic mono-layer level. Additionally, examples of this technology have the added benefits of non-circular machining marks, methods for precision machining element manufacturing, machine control over the gap distance, and polishing slurry compound control, which can improve the precision of the machining elements, reduce machining time, improve the quality of the machined surface figure, and increase the utility of the EEM system.

Accordingly, examples of the claimed technology provide a number of advantages including providing an EEM system that employs a non-spherical machining element, several methods for manufacturing the precision machining elements, machine control over the gap, and polishing slurry compound control. Non-spherical machining elements impart a non-spherical machining mark onto the surface being EEM'ed. Non-spherical machining marks can have large aspect ratios in which a first width of the machining mark is significantly smaller than a second width of the mark, for example, which can be advantageously employed by an EEM machine to improve the efficacy of the EEM process. The roughness and precision of the machining element impacts the removal stability as well as the texture of the surface left behind by the machining element. To achieve the desired roughness and precision of the machining element, special manufacturing of the machining element had to take place. Controlling the EEM gap dictates the removal rate as well as the surface roughness of the workpiece. The polishing slurry compound and fluid can be controlled as well to include differing polishing compounds, different polishing compound particle sizes, and changing the fluid medium will also dictate the removal rate and surface roughness of the workpiece.

Applications of examples of this technology include, but are not limited, to silicon mirror manufacturing for X-ray synchrotrons, silicon wafer polishing for high accuracy flat silicon wafers, high energy laser optical elements, X-ray telescope optical elements, and other high accuracy optical element applications.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGS. 1A and 1B are plan-view and side-view diagrams, respectively, of a prior art system for figuring the surface of an optical device;

FIG. 2 is a diagram of a prior art elastic emission machining system for figuring the surface of a workpiece in which the elastic emission machining head is substantially spherical;

FIG. 3 is an exemplary diagram of a machining mark on the surface of a planar workpiece produced by a prior art elastic emission machining system shown in FIG. 2;

FIG. 4 is a side view of a system for figuring the surface of an optical device with an elastic emission machining system with a machining element in accordance with examples of this technology with the optical device polishing surface being in the XY plane and the machining element driven by a belt that is driven by a motor;

FIG. 5 is a block diagram of a system for figuring the surface of an optical device with elastic emission machining system with a machining element in accordance with examples of this technology with the optical device polishing surface being in the XZ plane and the machining element driven directly by a motor;

FIG. 6 is an electrical interconnect diagram of a system for figuring the surface of an optical device with an elastic emission machining system in accordance with examples of this technology;

FIG. 7 is a side view of the elastic emission machining head in the belt driven orientation and workpiece of an elastic emission machining system for figuring the surface of the workpiece in accordance with examples of this technology;

FIG. 8 is an enlarged side view of an example of the tooling shown in the block diagram in FIG. 7, specifically looking at the forces acting upon the machining elements.

FIG. 9 is a side view of the elastic emission machining head in the straight spindle orientation and workpiece of an elastic emission machining system for figuring the surface of the workpiece in accordance with other examples of this technology;

FIG. 10 is an enlarged view of an example of the tooling shown in FIG. 9, specifically looking at the forces acting upon the machining elements.

FIG. 11 is a close-up, side-view of the elastic emission machining element and workpiece of an elastic emission machining system for figuring the surface of the workpiece in accordance with examples of this technology;

FIGS. 12A and 12D are drawings of the side view of the machining element for figuring the surface of a workpiece in accordance with examples of this technology;

FIGS. 12B, 12C, and 12E are drawings of the cross section of machining elements for figuring the surface of a workpiece in accordance with examples of this technology;

FIGS. 13A, 13B, 13C and 13D are diagrams of different grooves that can be cut into the machining elements for adjusting the removal profile when figuring the surface of a workpiece in accordance with examples of this technology;

FIG. 14 is a diagram of a cross-section of a toroidal elastic emission machining element of an elastic emission machining system for figuring the surface of a workpiece in accordance with examples of this technology;

FIG. 15 is a diagram of an ellipsoidal elastic emission machining element of an elastic emission machining system for figuring the surface of a workpiece in accordance with examples of this technology;

FIG. 16 is a diagram of an elastic emission machining element of an elastic emission machining system for figuring the surface of a workpiece in accordance with examples of this technology in which the cross-section of the element can be mathematically expressed as a polynomial;

FIG. 17 is an exemplary diagram of an eccentric machining mark on the surface of a planar workpiece produced by an elastic emission machining system in accordance with examples of this technology;

FIGS. 18A and 18B are illustrative diagrams of an elastic emission machining element and its associated eccentric machining mark, respectively, on the surface of a planar workpiece produced by an elastic emission machining system in accordance with examples of this technology;

FIGS. 19A through 19E are a series of cross-sectional diagrams of elastic emission machining elements spanning a range of surface eccentricities and convex/concave shapes in accordance with examples of this technology;

FIG. 20 is a diagram of a system for figuring the surface of an optical device with an elastic emission machining system with a directly driven machining element in accordance with examples of this technology;

FIGS. 21A and 21B are side and plan-views, respectively, of an alternate configuration of an elastic emission machining system for figuring the surface of an optical device in accordance with examples of this technology;

FIG. 22A is a front view of a highly elastic machining element with illustrated internal forces present at the start of an EEM process in accordance with examples of this technology;

FIG. 22B is a plan view of a machining mark resulting from a highly elastic machining element in accordance with examples of this technology;

FIG. 23A is a front view of a highly inelastic machining element with illustrated internal forces present at the start of an EEM process in accordance with examples of this technology; and

FIG. 23B is a plan view of a machining mark resulting from a highly inelastic machining element in accordance with examples of this technology.

DETAILED DESCRIPTION

The following detailed description of examples of this technology utilize a right-hand Cartesian coordinate system in which the Z-direction is the Up direction and the EEM machining element rotates about an axis parallel to the X-axis in the belt orientation (FIG. 7) or rotates about an axis parallel to the Z-axis in the straight spindle orientation (FIG. 9) for simplicity and brevity of explanation, although other coordinate systems, such as spherical or cylindrical coordinate systems could be used, or a left handed Cartesian system or even a right handed Cartesian system in which the axes are swapped or in which the axes of the described examples of this technology are not parallel to any one or more axis or axes of the coordinate system.

Examples of this technology will now be described with reference to FIGS. 4-23. As seen in these figures an elastic emission machining system 100 can include a drive head 102 which further includes a motor 104 mechanically coupled to drive pulley 144 which together rotate or spin about motor axis 148. A drive belt 106 is coupled to and caused to move by the drive pulley 144. A drive arm 108 is coupled to drive head 102 and also to an axle 114 in a manner that allows the axle 114 to freely rotate or spin about axis 151. A driven pulley 146 is coupled to the axle 114 and to drive belt 106. A machining element 110 is coupled to the axle 114 so that when motor 104 rotates, that rotation is coupled as explained above to the machine element 110 which is caused to rotate accordingly.

Continuing with reference to FIGS. 4 and 5, elastic emission machining systems 100 or 150 can also include a tanks 128 or 178 filled with a slurry 126 mixture in which a temperature control unit 130 is at least partially submerged and in which the machining element 110, the axle 114, driven pulley 146, drive belt 106, and drive arm 108 or the machining element 160 and axle 164, respectively, are all at least partially submerged or fully submerged. Within the tanks 128 or 178, and also at least partially submerged within slurry 126 is a workpiece 122 having a surface 120 to be machined and a workpiece holder 124 or 174, respectively, to which the workpiece 122 is fixedly attached. Elastic emission machining systems 100 or 150 can additionally include a circulation system 137 comprising a circulating pump 140 which is coupled to a source hose 138 and a return hose 142, both of which are coupled to ports or holes in tanks 128 or 178 so that slurry 126 can flow circuitously from the tanks 128 or 178 through source hose 138, pump 140, return hose 142, and back into the tanks 128 or 178 as the slurry is pumped by pump 140.

Elastic emission machining systems 100 or 150 can also include an X-Y workpiece stage 132 which can be integrated into one mechanism or implemented as two separate stages, such as X-stage 170 and Y-stage 172 as shown in FIG. 6, mechanically coupled to one another. In any event, X-Y stage 132 shown in FIG. 4 is mechanically coupled to workpiece holder 124 either directly or indirectly through the bottom wall of tank 128 so that as the X-Y stage 132 is caused to move or translate in the X and/or Y directions the workpiece holder 124 will also translate in the X and/or Y direction accordingly. In FIG. 5, the X-Y stage 132 is not shown mechanically coupled to workpiece holder 174 which in this example is secured to a sidewall of the tank 178.

Elastic emission machining systems 100 or 150 can additionally include a force gauge 116 shown in FIG. 6 which can be coupled to any of several components comprising elastic emission machining systems 100 or 150 including drive arm 108 and drive head 102 or drive head 152, and which is configured to measure the amount of force being indirectly exerted on the surface 120 by machining element 110. An example of the mechanism of this force will be described later herein in connection with FIGS. 8 and 10.

Elastic emission machining systems 100 or 150 can additionally include a Z and ⊖_Y stage 134, as shown in the example in FIGS. 4 and 5, which can be integrated into one mechanism or implemented as two separate stages, such as Z-stage 174 and ⊖_Y stage 176 shown in FIG. 6, mechanically coupled to one another. In any event Z and ⊖_Y stage 134 is mechanically coupled to drive head 102 or 152, respectively, and can cause drive head 102 or 152—and any downstream components attached thereto—to translate up and down vertically in a direction substantially parallel to the Z-axis as well as to rotate about an axis that is substantially parallel to the Y-axis. It should be noted, however, that exemplary elastic emission machining systems 100 or 150 can also comprise other components and systems not described above, or some described components and sub-systems can be excluded from the described elastic emission machining systems 100 or 150.

As seen in FIG. 6, elastic emission machining systems 100 or 150 can also include a digital processor 180 which is electrically coupled to an operator interface 182 as well as to digital memory 183 and also to digital input port 186. Further, an output of digital processor 180 can also be electrically coupled to: an input of motor 104 or 154, respectively, so that the rotational speed of motor 104 or 154 can be controlled by the digital processor 180; an input of temperature control unit 130 so that the temperature of slurry 126 can be controlled by the digital processor 180 through the temperature control unit 130; an input of circulating pump 140 so that the circulating pump 140 can be controlled by the digital processor 180; to the inputs of X-Stage 170 and Y-stage 172 of X-Y stage 132 so the X and Y translational positions of X-Stage 170 and Y-stage 172, respectively, can be controlled; to an input of Z-stage 174 and θ_Y Stage 176 of Z-θ_Y stage 168 so that the translational position of Z-stage 174 and the angular position of θ_Y Stage 176, respectively, can be controlled by digital processor 180, although the digital processor 180 can be coupled to control other systems, devices, components, and/or other elements as necessary to manage control and other operations for the examples illustrated and described herein. Further, inputs of digital processor 180 are electrically coupled to: outputs of tachometer 112 (which in turn is coupled to motor 104 or 154) so that the rotational speed of motor 104 or 154, respectively, can be measured and processed by digital processor 180; outputs of Z force gauge 116 so the amount of pressure borne by gap 200 (shown for example in FIGS. 7-9) can be measured and processed; pH gauge 118 so the acidity or alkalinity of slurry 126 can be measured and processed; thermometer 136 so the temperature of slurry 126 can be measured and processed; O₂ gauge 178 so the oxygen content of the slurry 126 can be measured and processed; dissolved solids gauge 190 so the proportion of (fine) particles 226 within slurry 126 can be measured and processed; and turbidity gauge 192 so the homogeneity of slurry 126 as well as so the proportion of (larger) particles 226 within slurry 126 can be measured and processed by digital processor 180.

Referring more specifically to the example shown in FIGS. 4, 7, and 8, the drive head 102 includes an assembly comprising a motor 104 having an axle 148 onto which is coupled drive pulley 144 which is coupled to and drives belt 106, and also includes drive arm 108. Drive head 102 in turn is coupled to the Z force gauge 116. Although other arrangements and couplings of these components is possible as well, the purpose of drive head 102 is to provide an attachment mechanism to attach motor 104 and drive arm 108 to force gauge 116.

Referring more specifically to the example shown in FIGS. 5 and 9, the drive head 152 is an assembly comprising motor 154 having an axle 164 onto which is machining element 160. Drive head 152 in turn is coupled to force gauge 166. Although other arrangements and couplings of these components is possible as well, the purpose of drive head 152 is to provide a simple means of attaching motor 154 and axle 164 to force gauge 166.

Referring to FIGS. 4-9, drive motor 104 or 154 can for example be a brushless DC motor or even an AC motor that operates with standard 60 Hz grid power, although other types of driving systems may be used. Drive motor 104 or 154 can be controlled by digital processor 180 based on executed programmed instructions stored in memory 183 to, for example, enable control over the rotational speed of drive motor 104 or 154 or to activate or de-activate motor 104 or 154 as needed, although other types of controls can be executed. Speed control of drive motor 104 or 154 by digital processor 180 is needed so that the rotational speed of machining element 110 or 160 can be controlled to accommodate EEM process variations, such as, for example, variations in gap 200 width or changes in slurry 126 temperature, although controlled changes in rotational speed of machining element 110 can accommodate other changes in process variables as well. Drive motor 104 can range in power from 1.0 Watts up to 250 Watts.

Referring to FIGS. 4, 7, and 8, the belt 106 is coupled to drive pulley 144 at an end proximal to motor 104 and also coupled to driven pulley 146 at an end distal to motor 104, such that driven pulley 146 rotates about axis 151 in accordance with the rotation of motor 104. Belt 106 can be a V-belt, or in other examples can have teeth or grooves on its innermost surface for improved gripping of drive pulley 144 and driven pulley 146. However, since belt 106 is at least partially submerged in slurry 126, belt 106 preferably has smooth surfaces so slurry is not drawn or splashed out of tanks 128 or 178 when the motor 104 is activated. Belt 106 can have a width of less than 20 mm and a circumference of less than one meter and preferentially in some examples includes a material that is not reactive with any of the constituents of slurry 126.

Drive arm 108 is coupled to drive head 102 at one end and is coupled to axle 114 at the other end and, in this example, provides rigid spacing of driven pulley 146 from drive pulley 144 so that the belt 106 remains taut. Drive arm 108 is also shaped to enclose belt 106 and drive arm 108 at least partially to contain any splashes of slurry 126 that may occur as belt 106 moves through the slurry 126. Drive arm 108 can be made of a material, or coated with a material, which is not reactive with any of the constituents of slurry 126.

Tachometer 112 shown in FIG. 6 is a device used for transducing the mechanical rotational speed of motor 104 into a corresponding electrical signal that is output to an input of digital processor 180. Since the rotational speed of motor 104 or 154 is proportional to the rotational speed of machining element 110 or 160, respectively, the tachometer 112 indirectly provides an electrical measurement to digital processor 180 of the rotational speed of machining element 110 or 160. Tachometer 112 can be either mechanically coupled to motor 104 or 154, electrically coupled, or even optically coupled to motor 104 or 154 in order to transduce the rotational speed of motor 104 or 154. Alternately, tachometer 112 can be mechanically coupled to machining element 110 or 160, electrically coupled, or even optically coupled to machining element 110 or 160 in order to directly transduce the rotational speed of machining element 110 or 160.

Force gauge 116 or 166 shown in the examples in FIGS. 4-6 measures the net forces acting on the machining element 110 or 160, respectively. These forces can be due to gravity of the devices directly and indirectly coupled to it, including device head 102, motor 104, belt 106, drive arm 108, axle 114 and machining element 110 as shown in FIGS. 4 and 6-8 or device head 152, motor 154, axle 164, and machining element 160 as shown in FIGS. 5, 6, and 9. Note that if any of these directly or indirectly coupled components have a density less than that of slurry 126 and are at least partially immersed in slurry 126 then these components can be buoyant and impart a negative weight to the sum of the weights of the components measured by force gauge 116 or 166. More importantly, as, for example, if the Z-stage, such as the Z-⊖_Y stage 134 shown in FIG. 4, is activated in a manner that lowers machining element 110, and if, for example, machining element 110 is also spinning about its axis on axle 114, then as the apex of machining element 110 approaches surface 120 and the gap 200 (as seen in FIG. 7-10) becomes small, but non-zero, the slurry 126 in gap 200 (gap 200 is also known in the art as the elastohydrodynamic lubrication zone) will begin to impart a force normal to the surface 120 is applied on the machining element 110, and this normal force will also be detectable and measurable by force gauge 116. Obviously if the Z-stage of the Z-⊖_Y stage 134 is activated in a manner that further lowers machining element 110 so that machining element 110 contacts surface 120 (in which case the elastohydrodynamic lubrication zone has been eliminated), then an abrupt change in force will be detectable and measured by force gauge 116 which indicates that the width of gap 200 has reached zero. Since a zero-thickness gap 200 is undesirable for optimal performance of elastic emission machining, a reading of force gauge 116 of zero gap thickness can be used by the operator or digital processor 180 to indicate that the Z-stage of the Z-⊖_Y stage 134 is to be activated in a manner that raises the machining element 110. Additionally, once calibrated, the force gauge 116 can provide an output that is indicative of the width of gap 200 (the width of gap 200 is the shortest distance between surface 120 and machining element 110). Since gap 200 is a key determinant of the material removal rate from surface 120, knowing the width of the gap from the force gauge 116 reading provides an important feedback mechanism that can be used by the operator or digital processor 180 to maintain an optimum EEM process by the elastic emission machining system 100 in this example.

Force gauge 116 can have a Z-force measurement range of from 0 to 500 Newtons, and accuracy of better than 0.1 Newton, and precision better than 0.01 Newton. The temporal response of force gauge 116 can be such that less than 10 ms of time can elapse from when a change in gap 200 width occurs until digital processor 180 receives data from Z-force gauge 116 that the gap change has occurred. Force gauge 116 can also be such that forces can be measured as vectors and the X, Y, and Z components of the force can be calculated.

The free body force diagram 202 in FIGS. 8 and 205 in FIG. 10 show the considered forces that force gauge 116 may feel. FIG. 8 shows that the positive Z forces 203 can be attributed to the buoyancy force as well as the normal force acting on the machining element 110 from the gap 200. This normal force is caused by physical phenomena of the elastohydrodynamic lubrication zone in the gap 200. It can also be seen that negative Z forces 204 acting on the machining element 110 can be attributed to the force of gravity and pressure from the machining element 110 on the worksurface 120. FIG. 10 shows the positive Z force 206 to be the buoyancy force, shows the normal force acting on machining element 110 from the gap 200 as the positive Y force 207, the force due to gravity as the negative Z force 208, and the force of machining element 110 on the worksurface 120 as the negative Y force 209. Note that in both FIG. 8 and FIG. 10 all forces acting upon the machining element 110 are not listed.

The pH gauge 118, which is at least partially submerged in slurry 126 within tanks 128 or 178, is an electronic device for measuring the acidity or alkalinity of the slurry during the EEM process. The pH of the slurry 126, as known in the art, becomes more basic during the EEM process as material is machined or otherwise removed from surface 120 of workpiece 122 and accumulates in slurry 126. As such, monitoring the slurry can be used as an indicator to the operator of the elastic emission systems 100 or 150 that the slurry 126 needs replacement. The pH of the slurry is also correlated to the concentration of the particles that are dissolved or suspended in a fluid. This value is calibrated with the initial pure particulate in the fluid, and as the machining action is taking place is monitored for changes. Changes in pH value, as stated previously, can be used as in indicator to the operator of the lifetime status of the slurry. pH gauge 118 can have an accuracy of 0.1 on the pH scale, or preferably have an accuracy of better than 0.01 on the pH scale. Note that pH gauge 118 can alternately be in circulation system 137, such as downstream from pump 140, so that circulating slurry 126 can flow through pH gauge 118 after being pumped by pump 140.

Workpiece 122 is an article of manufacture whose surface 120 is being machined by any one of the examples of this technology. Workpiece 122 is coupled to workpiece holder 124 during the EEM process so that workpiece 122, and its surface 120, can be positioned in a known location, especially in relation to machining element 110, so that only the certain desired location(s) of surface 120 is processed. Workpiece 122 can have rotational symmetry, or its periphery can be polygonal, elliptical, or otherwise be asymmetric, and the edges can be square to the coordinate system of elastic emission systems 100 or 150 (i.e., not tilted with respect to the Z-axis as defined in FIG. 4) or not square. Workpiece 122 can include a glass material such as BK7, Fused Silica, Zerodur or Ultra-low Expansion Glasses, for example, or be metallic such as Aluminum, Nickel or Invar, for example, a semiconductor such as Silicon or Germanium, for example, or a ceramic such as Clearceram, or hygroscopic materials such as Potassium Dihydrogen Phosphate (KDP) or Potassium Bromide, for example, or a non-linear crystalline material such as Lithium Triborate (LBO) and ideally in some examples includes a material that particles 226 do not react with. Workpiece 122 can have a thickness (along the Z-direction in FIG. 8 or Y-direction in FIG. 10) between 1 mm and 500 mm and a width (in the X-Y plane in FIG. 8 or in the X-Z Plane in FIG. 10) of between 1 mm and 20 meters. Workpiece 122 can be an optical device such as a mirror substrate or a lens, for example, or a mechanical device such as a gear, valve or valve seat, turbine blade, or a mold insert for example. Note that one, two, or three or more surfaces of workpiece 122 be EEM'ed by one or more of the various examples of this technology.

Surface 120 of workpiece 122 is a surface being processed by any one of the examples of this technology. Surface 120 can include a clear aperture that does not extend to the edge of workpiece 122 and within which the EEM processing takes place. Surface 120 can have rotational symmetry and be spherical or aspherical in form for example, have left-right symmetry and be cylindrical or acylindrical in form for example, be substantially planar, or have a free-form shape without any symmetry. The peak-to-valley range of departure of surface 120 from a best-fit plane can be from 10 nm to 200 mm. The roughness of surface 120 before being processed with the elastic emission machining systems 100 or 150 can be between 100 microns RMS and 0.1 nm RMS, while the roughness of surface 120 after being processed with the elastic emission machining system 100 or 150 can be between 100 nm RMS and 0.05 nm RMS although other pre- and post-processing roughness ranges are possible as well.

Workpiece holder 124 is a mechanical device that detachably secures workpiece 122 to X-Y stage 132 either directly or indirectly through the floor of tanks 128 or 178. Workpiece holder 124 therefore must have a mechanism to capture, clamp, bond, or fasten workpiece 122, and, importantly, do so without stressing workpiece 122 or imparting a change in shape to surface 120. Workpiece holder 124 can also support workpiece 122 so that workpiece 122 is not deformed in a manner that changes the shape of surface 120 during the EEM process when machining element 110 is in close proximity to, and imparting a force onto, surface 120.

Slurry 126 is a mixture of water or oil and small particles 226 that are uniformly dispersed within the fluid. The fluid can be ultrapure and de-ionized and de-oxygenated water for best control and/or performance of the EEM process. The fluid can also be a pure oil-based fluid for EEM processes where water is unacceptable as in materials which are hygroscopic in nature. Particles 226 can have a width less than 10 microns, or more preferably less than 1 micron, and in any event must have widths less than the width of gap 200 as shown in FIGS. 7-10. Particles 226 can include an oxide such as, for example, silicon dioxide, zirconium dioxide, cerium oxide, or aluminum oxide, as is well-known in the art. The concentration of particles 226 within the fluid can be between 1% and 20% by weight, such as approximately 10% by weight. With different fluid types and concentrations of particles in those fluids, differences in viscosity well occur and can change the substrate material removal rates. Water has a standard viscosity of about 0.00065 Pascal seconds at 40° C. and oils, such as mineral oil, can have standard viscosities of 0.02 to 0.05 Pascal seconds at 40° C. With the addition of particles 226 in suspension and dissolved into the fluids, these viscosities will increase by up to 20% based on Einstein's equation for the viscosity of a dispersion or suspension:

E=E₀(1+2.5*V)  (Equation 1)

Where in the above equation, E₀ is the viscosity of the dispersion medium, V is the volume being occupied by the assumed spherical particulate, and E is the viscosity of the mixture.

In each of the examples, tanks 128 or 178 are used to contain the slurry 126 and ensure that a stable volume of slurry 126 always surrounds machining element 110, workpiece 122 and workpiece surface 120. Tanks 128 or 178 can have transparent sidewalls for ease of visual inspection of the EEM process as it occurs, or tanks 128 or 178 can have opaque sidewalls. Tanks 128 or 178 can be substantially filled with slurry 126 and outfitted with an air-tight cover such that air is kept out of tanks 128 or 178 so that, for example, the slurry 126 never comes into contact with air thereby preventing ambient O₂ from dissolving into the slurry 126 from the atmosphere. Alternately tanks 128 or 178 can be mostly filled with slurry 126 while also provided with an air-tight cover, and the top-most portion of the tank filled with a non-reactive gas such as nitrogen. Drive head 102 or 154, respectively, can be located within tanks 128 or 178 or located outside of tanks 128 or 178, but if located outside of tanks 128 or 178 and tanks 128 or 178 are provided with an air-tight cover then the cover should also have sealing provisions about drive arm 108 or axle 164, respectively, which prevent ambient air from reaching slurry 126. All components comprising tanks 128 or 178 that encounter slurry 126 can include materials that are non-reactive with the constituents of slurry 126.

Temperature control unit 130, which is at least partially submerged in slurry 126 within tanks 128 or 178 can include a thermometer 136 as well as a device for heating and/or cooling the slurry 126 as needed to maintain a substantially constant temperature of the slurry 126 during the EEM process. To maintain the predictability or repeatability of the removal rate of material from surface 120 of workpiece 122 during the EEM process, the temperature of the slurry should be maintained within a ±1° C. temperature range, or more preferably within a ±0.1° C. temperature range, and the temperature of the slurry should be substantially homogeneous throughout the volume of tanks 128 or 178. The thermometer 136 of temperature control unit 130 measures the temperature of slurry 126, and the measured temperature is provided as an input to the heater or cooler of temperature control unit 130, through digital processor 180 so the heater or cooler of temperature control unit 130 can be activated as necessary by digital processor 180 to heat or cool the slurry 126 as needed so that the temperature of slurry 126 is maintained within a prescribed temperature range. Note that temperature control unit 130 can alternately be located in circulation system 137, such as downstream from pump 140, so that circulating slurry 126 can flow through temperature control unit 130 after being pumped by pump 140.

Referring to FIGS. 4-5, X-Y translation stage 132 or 182, respectively, is a motorized device that can cause an object coupled to it, such as workpiece holder 124 in FIG. 4 or the tank 178 to which the workpiece holder 174 is attached in FIG. 5 by way of example, to move in directions parallel to the X and/or Y axes. As shown in FIGS. 4 and 5, respectively, tanks 128 or 178 are each mechanically coupled to X-Y translation stage so that tanks 128 or 178 and all its contents including slurry 126, can be caused to translate in the X and Y directions in accordance with the X and Y translations of X-Y translation stage 132. In an alternate configuration in FIG. 4, X-Y translation stage 132 can be installed inside tank 128 and workpiece holder 124 can be mechanically coupled to X-Y translation stage 132 so that workpiece holder 124 and workpiece 122 can be caused to translate in the X and Y directions in accordance with the X and Y translations of X-Y translation stage 132.

Referring to FIGS. 4-5, Z-⊖_Y stage 134 or 184, and all devices coupled directly and indirectly thereto including force gauge 116, drive head 102, drive arm 108, axle 114, and machining element 110 in the example in FIG. 4 and including force gauge 116 166, drive head 152, axle, 164, and machining element 160 in the example in FIG. 5, are not coupled to X-Y translation stage 132, and their motions and positions are independent of the motions and positions of X-Y translation stage 132 or 182, respectively. In FIG. 4, the range of motion of X-Y stage 132 in each axis should be at least as long as the width of surface 120 so that machining element 110 in the example in FIG. 4 can reach the entire surface 120 of workpiece 122, and the range of motion can be at least 1000 mm in accordance with the described width of workpiece 122 as described in a preceding paragraph. In FIG. 5, the range of motion of X-Y stage 182 in the Y-axis should be enough to control the gap 200 as described by the examples herein and in the X-axis should be at least as long as the width of surface 120 so that with the Z-⊖_Y stage 184 covering movement along the length of the surface 120 the machining element 160 in the example in FIG. 5 can reach the entire surface 120 of the workpiece 122. The accuracy of the positioning of the X-Y translation stage 132 or 182, as well as the precision of the X-Y translation stage 132 or 182 are both key parameters of X-Y translation stage 132 or 182 as highly accurate and precise X-Y positioning of surface 120 with respect to machining element 120 will ensure that the correct X-Y location of surface 120 will be machined by the machining element 110. The positioning accuracy in X and/or Y of X-Y translation stage 132 or 182 can be less than 0.1 mm, or preferably less than 0.01 mm, and the precision of the positioning in X and/or Y of X-Y translation stage 132 or 182 can be less than 0.01 mm, or preferably less than 0.001 mm.

Referring to FIG. 4, the Z-⊖_Y stage 134 is a motorized device that causes an object coupled to it to move in a direction parallel to the Z axis and/or rotate about an axis parallel to the Y axis. Force gauge 116 is mechanically coupled to Z-⊖_Y stage 134 so that force gauge 116 and all devices coupled directly and indirectly thereto including drive head 102, motor 104, drive arm 108, axle 114, and machining element 110 all translate and/or rotate accordingly. Referring to FIG. 5, the Z-⊖_Y stage 184 is a motorized device that causes an object coupled to it to move in a direction parallel to the Z axis. Force gauge 166 is mechanically coupled to X-Y translation stage 182 and Z-⊖_Y stage 184 so that force gauge 166 and all devices coupled directly and indirectly thereto including drive head 152, motor 154, axle 164, and machining element 160 all translate and/or rotate accordingly. In the example in FIG. 4, the range of motion of Z-⊖_Y stage 134 in the Z-direction should be at least as great as the peak-to-valley depth of surface 120 so that machining element 110 can reach the entire surface 120 of workpiece 122, and the range of motion can be at least 100 mm in accordance with the peak-to-valley depth range of workpiece 122. In the example in FIG. 5, the range of motion of X-Y stage 182 in the Y-axis should be at least as great as the peak-to-valley depth of surface 120 so that machining element 160 can reach the entire surface 120 of workpiece 122, and the range of motion can be at least 100 mm in accordance with the peak-to-valley depth range of workpiece 122. More preferably in some examples, such as in FIG. 4 the range of motion of Z-⊖_Y stage 134 in the Z-direction or in FIG. 5 the range of motion of X-Y stage 182 in the X-direction should be large enough to allow machining element 110 or 160, respectively, to be withdrawn from tanks 128 or 178, respectively, so that machining element 110 or 160 can be inspected, maintained, or replaced as needed, in which case the range of motion of Z-⊖_Y stage 134 in the Z-direction or the range of motion of X-Y stage 182 in the X-direction can be more than 200 mm, or even more than 500 mm. In FIG. 4 the range of motion of Z-⊖_Y stage 134 in the rotational axis or in FIG. 5 the range of motion of X-Y stage 182 in the Y-direction can be at least as great as the maximum angular slope of the surface 120 of workpiece 122. For example, in FIG. 4 the range of motion of Z-⊖_Y stage 134, or more particularly ⊖_Y stage 176, in the rotational axis or in FIG. 5 in the X-Y stage 182 in the Y-direction can be from −20° to +20°, or more preferably from −80° to +80° so that highly sloped areas on surface 120 can be processed by elastic emission machining systems 100 or 150.

In the examples in FIGS. 4, the accuracy of the positioning of the Z-⊖_Y stage 134 as well as the precision of the Z-⊖_Y stage 134 are both key parameters of Z-⊖_Y stage 134 as a highly accurate and precise Z-⊖_Y stage 134 will allow for the accurate and precise positioning of machining element 110 with respect to surface 120 and will ensure that the correct location of surface 120 will be machined by the machining element 110, at the correct angular orientation of machining element 110 and with the correct width of gap 200 between machining element 110 and surface 120. The positioning accuracy in Z of Z-⊖_Y stage 134 can be less than 0.01 mm, or preferably less than 0.001 mm (1.0 micron), and the precision of the positioning in Z of Z-⊖_Y stage 134 can be less than 0.001 mm, or preferably less than 0.1 micron. The rotational positioning accuracy in ⊖_Y of Z-⊖_Y stage 134 can be less than 0.1 degree or preferably less than 0.01 degree, and the precision of the positioning in ⊖_Y of Z-⊖_Y stage 134 can be less than 0.01 degree, or preferably less than 0.001 degree. This is the same with the different orientation positioning elements shown in the example in FIG. 5.

Circulation system 137 includes circulating pump 140, along with source hose 138 and return hose 142 form a circuit through which slurry can flow outside and around tanks 128 or 178 thereby providing a means of agitating, stirring, mixing, or otherwise homogenizing the distribution of particles 226 within the slurry 126. The connections, ports, or interface of the source hose 138 with tanks 128 or 178 can be as simple as a unitary hole in a sidewall of tanks 128 or 178 to which source hose 138 is coupled, or a plurality of holes in one or more sidewalls of tanks 128 or 178 which can provide a broader areal distribution of intake to the circulation system 137. Alternately the entrance port of source hose 138 can be well inside tanks 128 or 178, such as, for example, proximal to machining element 110. Similarly, the connections, ports, or interface of the return hose 142 with tanks 128 or 178 can be as simple as a unitary hole in a sidewall of tanks 128 or 178 to which return hose 142 is coupled, or a plurality of holes in one or more sidewalls of tanks 128 or 178 which can provide a broader areal distribution of return flow to the tanks 128 or 178. Alternately the output port of return hose 142 can be well inside tanks 128 or 178, such as, for example, proximal to machining element 110. The rate of flow of slurry through circulating pump 140 can be between 100 ml/minute and 100 ml/second, or as expressed as a percentage of tanks 128 or 178 volume the rate of flow of slurry through circulating pump 140 can be between 0.1% of the tank volume/minute to 100% of the tank volume/minute. Components of circulating system including circulating pump 140, source hose 138 and return hose 142, whose elements encounter circulating slurry 128 generally have those elements, such as an impeller of circulating pump 140 and the inner walls of source hose 138 and return hose 142, made of a material that do not interact with the particles 226 within the slurry 128, said materials therefore generally being polymeric and non-metallic. The inner diameter of source hose 138 and return hose 142 can be between 1.0 mm and 52 mm.

Circulating system 137 can also include a filter 139 that serves to capture and sequester spurious particles in slurry 128 that have widths that are larger than approximately 50% of the gap 200 so these particles are not wedged into gap 200 or scraped across surface 120 at the gap 200 thereby imparting an undesirable gouge or scratch into surface 120. Filter 139 can capture and sequester spurious particles in slurry 128 that have widths that are larger than 10 microns, or preferably those particles having widths greater than 4 microns.

Circulating system 137 can also include an O₂ gauge 178 which is coupled into circulating system 137 in a manner that O₂ gauge 178 can access and sample slurry 126 as it flows through circulating system 137 for O₂ gauge 178 to measure the oxygen content within slurry 126 and report the oxygen measurement to digital processor 180. Knowing the O₂ content of the slurry 126 is important because it is known to those skilled in the art that oxygen dissolved in slurry 126 degrades the EEM material removal process, and therefore it is necessary that the oxygen content of the slurry is measured and monitored to ensure the oxygen content remains below a minimum threshold during the EEM process. The oxygen content of the slurry 126 preferably remains below 10 PPM, and ideally below 1 PPM. O₂ gauge 178 can have an accuracy of 1% of its O₂ reading, a measurement range of from 0.1 PPM to 100 PPM for example, and a resolution of 0.01 PPM. Note that O₂ gauge 178 can be located elsewhere in elastic emission machining systems 100 or 150, such as within tanks 128 or 178 instead of being part of circulating system 137.

Dissolved solids gauge 190 is a device that measures the proportion or concentration of particles 226 within slurry 126, wherein the size of particles that dissolved solids gauge 190 is responsive to is less than approximately 2 μm in size. Similarly, turbidity gauge 192 is also a device that measures the proportion or concentration of particles 226 within slurry 126, wherein the size of particles that turbidity gauge 190 is responsive to is greater than approximately 0.5 μm in size. Utilizing both dissolved solids gauge 190 and turbidity gauge 192 allows for the measurement and determination of the concentration of particles 226 within slurry 126 in which the size of the particles can span a broad range such as from, for example, 0.1 μm in width up to 10 μm in width.

Digital processor 180 can be or include a conventional microprocessor with an external memory 183 or digital processor 180 can be or include a microcontroller with all memory located onboard. In another example, digital processor 180 can be or include a digital signal processor (DSP) integrated circuit, which is a microcomputer that has been optimized for digital signal processing applications, including mathematical operations needed for control of the EEM process. Digital processor 180 can be as simple as a sixteen-bit integer system, a thirty-two-bit, sixty-four-bit, or higher, and/or a floating-point system for higher performance when cost is not an issue. Also, by way of example only, the digital processor 180 can be an FPGA (Field-programmable gate array) or a CPLD (complex programmable logic device). Note that digital processor 180 can be coupled to, or provided with, ports through which electronic communications can be performed with all the peripheral devices shown in FIG. 6.

Operator interface 182 can include any device peripheral to digital processor 180 through which an operator inputs commands to the digital processor 180 or receives information from digital processor 180. Examples of peripheral devices for inputting commands to digital processor 180 include a keyboard, computer mouse, pen, trackball, or touch-pad. Examples of peripheral devices for outputting information from digital processor 180 to an operator include displays and monitors, printers, as well as audible signaling devices.

Memory 183 stores programmed instructions and data for performing the EEM process or controlling the EEM process by digital processor 180 as illustrated herein for execution by the processing unit, although some or all of these instructions and data may be stored elsewhere. A variety of different types of memory storage devices, such as a random-access memory (RAM), a read only memory (ROM), hard disk, CD ROM, USB thumb-drive, flash memory, or other computer readable medium which is read from and/or written to by a magnetic, optical, or other reading and/or writing system coupled to the processing unit, can be used for the memory.

Digital input port 186 is an electronic interface through which digital data originating in an external electronic device is input to digital processor 180. Typically, the external electronic device, such as an areal interferometer or scanning displacement-measuring probe, is located several meters away from digital processor 180, and a digital serial communication bus is used through which digital data, such as measured surface topography data of surface 120, is communicated, is connected between the external electronic device and digital input port 186. Digital serial communication bus can be a USB, RS-232, RS-422, or preferably an ethernet bus protocol, and digital input port 186 translates or reformats the data arriving over the communication bus into electronic signaling usable by digital processor 180.

Machining element 110 or 160 is a key component of the elastic emission systems 100 or 150, respectively, as machining element 110 or 160 is what causes the particles 226 within slurry 126 to be accelerated to a non-zero velocity and move rapidly past surface 120 of workpiece 122 causing material to be removed form surface 120 during the EEM process. Machining element 110 is coupled to axle 114 and spins or rotates about an axis 151 which is common both to axle 114 and machining element 110 and machining element 160 is coupled to rotate on axle 164. The rotational velocity of machining element 110 or 160 can be at least 100 RPM (revolutions per minute) but less than 15,000 RPM, with an angular velocity of between 100 and 5000 RPM being ideal. Machining element 110 or 160 has rotational symmetry about axis 151, and the outer periphery region of machining element 110 or 160, which is that region about apex 201 and proximal to gap 200 as will be described later, can have a circular cross section, an elliptical cross section, parabolic or polynomial cross section, a trapezoidal or piece-wise linear cross-section, or any combination of these. The outer diameter of machining element 110 or 160 can be between 4 mm and 400 mm, and the width of machining element at its maximum extent can be between 4 mm and 100 mm. Machining element 110 or 160 can include an elastic material such as an elastomer such as silicone, polyisoprene, polybutadiene, rubber, or any organic material such as a polymer such as polycarbonate or acrylic. Alternately machining element can include a metal such as aluminum or stainless steel, or a ceramic material. The roughness of the surface of machining element 110 or 160, particularly at the outer periphery region, can be between 2 nm RMS and 10 microns RMS, although a surface roughness that is the same as, or less than, a width of particles 226 within slurry 126 is preferable. Elastomeric machining element 110 or 160 may be stiff and rigid and be substantially inelastic, which would be the case if machining element 110 or 160 were includes a metal, or elastomeric machining element 110 or 160 may be elastic in nature in which, for example, the elasticity of the elastomeric machining element 110 or 160 can be less than 60 on the Shore D scale. By way of example as shown in FIG. 13A-D, elastomeric machining element 110 may have grooves cut into its surface 201 to enhance or effect the removal parameters, although machining element 160 could have similar grooves. These grooves vary in depth from 100 microns to 10 mm dependent on the application and can be oriented to be cut perpendicular to the rotating surface 255, parallel to the rotating surface 256 at any angle between those previous stated 257, as well as be in any sort of pattern not dissimilar to the treads on an automotive tire 258.

With the EEM process, machining element 110 or 160 can be, but is not limited to, being represented by a thick rubber machining element 235 or a thin shrink-wrapped rubber machining element 236. The surface of the machining elements 110 or 160 need to be high precision, because the surface texture of the machining element 110 or 160 is imparted into the workpiece surface 120. With this knowledge, the machining element 110 or 160 needs to be precision manufactured and polished to a surface roughness that is on the order of the particle 226 size, from 50 nm to 10 μm. This roughness can be achieved in a variety of ways. The polished metal body 230 needs to start with this roughness such that any imperfections in the polished metal body 230 will not print through to the rubber 231 that is molded around it or to the heat shrink wrapped rubber 232 that is fitted to the surface as shown in FIGS. 12A and 12D. For the machining element 110, such as shown in FIG. 12A, the polished metal body 230 may have a surface which matches the curvature desired by the rubber 231, as shown in FIG. 12B, such that the thickness of the rubber layer 231 is substantially constant. The machining element 110 shown in FIG. 12A may also have a polished metal body 230 which has a flat surface such that the rubber layer 231 thickness varies based upon the radius desired. For a machining element 236 such as shown in FIG. 12D, the polished metal body 230 be required to have the curvature cut and polished for the surface, such that when the heat shrink wrap 232 is applied to the outer surface, it can be formed uniformly across the surface and still end in the desired shape. The forming of the heat shrink wrap 232 machining element 110 can be done by applying the heat shrink wrap, then utilizing an external heating element 233 (not shown) such as a heat gun for localized heating or through the use of a heating element source such as an oven for global, even heating of the machining element 110 and heat shrink wrap 232. The machining element 110 or other machining elements as illustrated and described by way of the examples herein is not limited to solely elastomer or elastomer covered tools, as fully metallic tools such as stainless steel, brass or aluminum may also be utilized.

Machining element 110 or other machining elements as illustrated and described by way of the examples herein can have the shape of toroidal machining element 210 as illustrated in FIGS. 12A-12E and 14. Toroidal machining element 210 has a major radius 242 of length R and a minor radius 240 of length p which extends from center of circular section 244 and defines the radius of circular section 246. An outer periphery 212 of toroidal machining element 210 is that portion of toroidal machining element 210 that is proximal to and includes the apex of toroidal machining element 210 and engages with gap 200 and performs the machining of surface 120. Toroidal machining element 210 has an inner width W that can be equal to the diameter or width of circular section 246 (as shown implicitly in FIG. 7, for example), or W can be less than the diameter or width of circular section 246 as shown in FIG. 14.

Machining element 110 or other machining elements as illustrated and described by way of the examples herein can alternately have the shape of an asphere as defined by,

$\begin{array}{cc}D\left(x\right)=\frac{C*x^2}{1+\sqrt{1-\left(1+k\right)*C^2*x^2}}+A_2*x^2+A_4*x^4+A_6*x^6+\cdots & \left(\mathrm{Equation}2\right)\end{array}$

where C is the curvature (inverse of the radius), x is the radial distance from the apex of the tool, k is the conic constant, and A_n is the nth order aspheric coefficient.

Machining element 110 or other machining elements as illustrated and described by way of the examples herein can alternately have the shape of an elliptical machining element 250 as illustrated in FIG. 15. Elliptical machining element 250 has a major radius of length RA that extends from the axis of rotation 254 to the major apex of the ellipse and a minor radius of length R_B which together define the mathematical prescription of the cross-section of elliptical machining element 250. An outer periphery 252 of elliptical machining element 250 is that portion of elliptical machining element 250 that is proximal to and includes the apex of elliptical machining element 250 and engages with gap 200 and performs the machining of surface 120.

Machining element 110 or other machining elements as illustrated and described by way of the examples herein can alternately have the shape of polynomial machining element 300 as illustrated in FIG. 16. Polynomial machining element 300 has a major radius of length R that extends from the axis of rotation 304 to the apex of the polynomial and a width W. Note that a distance from the apex D varies with a distance from the central Y-Z plane x in a polynomial relationship, such as for example,

D=R+k₂x²+k₄x⁴+k₆x⁶+ . . . etc.  (Equation 3)

where k₂, k₄, and k₆ are constants. Note that Equation 3 represents an even 6^th order polynomial, although polynomials of other orders such as 2 (representing a parabola), 4, 8, 10, or higher, are possible as well, as is an odd polynomial in which case polynomial machining element 300 does not have left-right symmetry. An outer periphery 302 of polynomial machining element 300 is that portion of polynomial machining element 300 that is proximal to and includes the apex of polynomial machining element 300 and engages with gap 200 and performs the machining of surface 120.

An example of a machining mark 400 installed in a surface 120 by elastic emission machining system 100 having a non-spherical machining element 110 such as toroidal machining element 210 is illustrated in FIG. 17. That is, given a stationary workpiece 122 (i.e., workpiece 122 is not translating in X or in Y directions), toroidal machining element 210 is rotating about its axis while being driven by motor 104 through belt 106 while Z-stage 174 is activated such that toroidal machining element 210 is lowered in Z and the width of gap 200 is slowly yet continually decreased, then toroidal machining element 210 will cause particles 226 in slurry 126 to remove material from workpiece surface 120 in accordance with the shape of toroidal machining element 210 thereby imparting machining mark 400 into the surface 120 of workpiece 122. As shown in FIG. 17, machining mark 400 has a significant amount of eccentricity in which a long width of machining mark 400 such as W_Y is much greater than a short width W_X. Indeed, defining the eccentricity, E, of machining mark 400 to be E=W_Y/W_X, a value of E can be in the range of 1.0<E<1000, where a value of E=1.0 indicates that the perimeter of machining mark 400 is circular.

Note that if the quantity W_Y of eccentric machining mark 400 of FIG. 17 is equal to the quantity W_Y of circular machining mark 94 of FIG. 3 of the prior art, and the depth of machining mark 400 is the same as the depth of machining mark 94, then the radius of the prior art (spherical) machining element 64 must be the same as the radius (ie, R+ρ) of toroidal machining element 210, assuming toroidal machining element 210 was used to produce machining mark 400. This implies that, given equal rotational velocities of toroidal machining element 210 and the prior art (spherical) machining element 64, then the removal rate of material from a workpiece for these two machining elements are substantially equal. However, toroidal machining element 210 has the advantage of being able to remove a narrower portion of material from the surface 120 of a workpiece 122, so that for example, narrower bumps or imperfections in surface 120 can be removed by a toroidal machining element 210 as compared to a spherical machining element of the prior art. That is, a non-spherical machining element in accordance with the examples described herein can remove material just as fast as a spherical machining element of the prior art but can do so more selectively which allows for more efficient machining and figuring of a surface of a workpiece.

An additional benefit of an eccentric machining element as compared to a spherical machining element is that an eccentric machining element has less surface area and therefore has less total areal contact with slurry 126. Since slurry 126 has a non-zero viscosity, then the slurry 126 acts to resist the rotational motion of the machining element when it is submerged in slurry, and this resistance is in accordance with the contact or surface area of the machining element. A machining element, such as exemplary toroidal machining element 210, elliptical machining element 250, polynomial machining element 300 having less surface area than prior art (spherical) machining element 64, will have less rotational resistance and can therefore spin faster for a given motor 104 power, or at an equivalent rotational speed with a lower powered motor 104.

FIG. 18A is an illustration of an elliptical machining element 500 whose defining ellipse has a major axis in the X-direction whose length, W_X,E is greater than the length W_Y,E of the minor axis in the Y-direction. Note that elliptical machining element 500 has an actual width, W_X,ME, that is significantly less than W_X,E, and that elliptical machining element 500 has an axis of rotation 512 about which elliptical machining element 500 has rotational symmetry and about which it spins or rotates while performing an EEM process. Elliptical machining element 500 can have a shape wherein W_X,ME is centered within W_X,E such that elliptical machining element 500 (and its corresponding machining mark 502) has left-right symmetry, or elliptical machining element 500 can have a shape wherein W_X,ME is not centered within W_X,E, but offset in the X-direction such that elliptical machining element 500 (and its corresponding machining mark 502) does not have left-right symmetry wherein said offset can be up to W_X,E/2.0 millimeters in length. W_X,ME can be between 1.0 mm and 200 mm's, and W_Y,E can be between 2.0 mm and 200 mm. The eccentricity of elliptical machining element 500, defined as E=W_X,E/W_Y,E, can be in the range of 1.0<E<10,000. Elliptical machining elements 500 having large eccentricities are especially useful for figuring substantially planar optical surfaces, or optical surfaces that are concave with small curvature.

FIG. 18B is an illustration of the machining mark 502 produced by elliptical machining element 500 in the surface of a workpiece in accordance with the EEM processes and examples described in this disclosure. Note that the machining mark 502 is produced in a manner wherein elliptical machining element 500 is not translated with respect to the workpiece in the X and Y directions during the EEM process, but elliptical machining element 500 does translate in Z and spins about its axis 512 (which is assumed to be parallel to the X-axis in FIG. 18B) while machining mark 502 is being produced. Note that machining mark 502 has equal-elevation contour lines 504A and 504B, and that machining mark 502 has up-down symmetry (i.e., in the Y-direction) as well as left-right symmetry as the offset (described in previous paragraph) is set to 0.0.

FIGS. 19A through 19E illustrate a range of eccentricities and concavities/convexities that are possible for the exemplary machining element 110. FIG. 19A illustrates a strongly convex machining element 550 having a strongly convex outer periphery 552 that produces a highly eccentric concave machining mark in a workpiece surface, wherein strongly convex machining element 550 would be suitable for machining a concave optical surface that has small surface figure anomalies. FIG. 19B illustrates a mildly convex machining element 560 having a convex outer periphery 562 that produces a concave machining mark in a workpiece surface, wherein mildly convex machining element 560 would be suitable for machining a concave optical surface that has large surface figure anomalies. FIG. 19C illustrates a cylindrical machining element 570 having a substantially linear outer periphery 572 cross section that produces a cylindrical machining mark in a workpiece surface, wherein cylindrical machining element 570 would be suitable for machining a planar optical surface that has small and large surface figure anomalies as well as mildly convex workpiece surfaces. FIG. 19D illustrates a mildly concave machining element 580 having a concave outer periphery 582 that produces a convex machining mark in a workpiece surface, wherein mildly concave machining element 580 would be suitable for machining a convex optical surface that has large surface figure anomalies. Finally, FIG. 19E illustrates a strongly concave machining element 590 having a strongly concave outer periphery 592 that produces a strongly convex machining mark in a workpiece surface, wherein strongly concave machining element 590 would be suitable for machining a convex optical surface that has small surface figure anomalies.

The operation of elastic emission system 100 will now be described with reference to FIGS. 4 through 10. At the start of an elastic emission machining process the topography of surface 120 is precisely measured off-line, such as for example, with an areal interferometer or with a scanning non-contact displacement-measuring probe, so that the locations and heights of the figure errors in surface 120 are determined. Based on the surface figure errors and the base form of the surface 120 (e.g., mildly convex, or strongly concave) the operator selects an appropriate machining element 110 or other machining element as illustrated and described by way of the examples herein and installs it onto axle 114 (the Z-stage 174 will have positioned the drive head 102 in the fully UP position prior to machining element installation). The measured surface figure errors, as well as the geometry of the machining element 110 are input, through input port 186, to a tool-path computing algorithm executing on digital processor 180 which then determines the path that machining element 110 must take to improve the surface figure of surface 110 as well as the translational speed of machining element 110 for each small segment of the tool path. This process is known in the art as deterministic polishing, and the ability to incorporate a variety of shapes for machining element 110, as described throughout this disclosure, vastly improves the range of surface 120 types that can be deterministically EEM processed, the speed or efficacy with which surfaces 120 can be EEM processed, and the quality of the results (i.e., the remaining residual surface figure errors present in surface 120) after completion of a deterministic metrology-figure cycle.

Note that tool path calculations will incorporate other factors, variables, and parameters into the calculations to improve the performance of the deterministic EEM process, including, but not limited to, the temperature of the slurry 126, the pH of the slurry 126, the oxygen content of the slurry 126, the type and size of particulates 226 in slurry 126, the concentration of the particles 226 in slurry 126, the nominal gap 200 between machining element 110 and surface 120, and the rotational speed of machining element 110.

Next workpiece 122 is mechanically coupled to workpiece holder 124 in a known position relative to the coordinate system of the elastic emission machining system 100 so the desired toolpath on surface 120 substantially coincides with the path that machining element 110 will actually follow during EEM processing of surface 110 as described below. If not already prepared, the slurry 126 is then prepared in accordance with the parameters assumed by the tool path calculating algorithm, and the tanks 128 or 178 is then filled with the slurry. Circulating pump 140 is then activated by digital processor 180 and accordingly slurry 126 begins to flow through circulation system 137 as well as through tanks 128 or 178, and any oversized particles or contaminants in slurry 126 are removed by filter 139. At this time digital processor 180 receives slurry 126 temperature information from thermometer 136 and activates temperature control unit 130 to cool or heat slurry 126 as necessary so the temperature of slurry 126 becomes substantially the same as the slurry temperature assumed by the tool path calculating algorithm. At this time digital processor 180 receives slurry 126 oxygen content information from O₂ gauge 178, and if the slurry 126 oxygen content is substantially different than that value assumed by the tool path calculating algorithm then the tool path calculating algorithm may be re-executed by digital processor 180 to account for the actual oxygen content of slurry 126. Similarly, at this time digital processor 180 receives slurry 126 pH information from pH gauge 118, and if the slurry 126 pH is substantially different than that value assumed by the tool path calculating algorithm then the tool path calculating algorithm may be re-executed by digital processor 180 to account for the actual pH of slurry 126.

After the temperature of the slurry 126 has stabilized and the properties of slurry 126 are in conformance with those slurry properties assumed by the tool path calculating algorithm, the actual EEM processing of surface 120 can begin. At this juncture the angle of the θ_Y-stage 176 is set by digital processor 180 to that angle prescribed by the tool path calculating algorithm at the start of the tool path, the X-stage 170 is set by digital processor 180 to that position prescribed by the tool path calculating algorithm at the start of the tool path, and the Y-stage 172 is set by digital processor 180 to that position prescribed by the tool path calculating algorithm at the start of the tool path. At this time digital processor 180 activates motor 104 which causes machining element 110 to spin accordingly, and while motor 104 is activated digital processor also receives information from tachometer 112 about the speed of motor 104 and/or machining element 110 whereafter digital processor 180 issues commands to motor 104 that cause the rotational speed of machining element 110 to accelerate or decorate as needed to conform to the rotational speed of machining element 110 assumed by the tool path computing algorithm. Next digital processor 180 receives information from Z-force gauge 116 at the same time digital processor 180 activates Z-stage 174 causing drive head 102 and all associated components including machining element 110 to lower thereby causing machining element 110 to approach surface 120. As the drive head 102, etc., is being lowered by Z-stage 174 under the control of digital processor, the width of gap 200 is decreasing accordingly. When the gap 200 narrows sufficiently an opposing force will be generated by the dynamics of the slurry 126 within the gap 200, and this opposing force will be detected by Z-force gauge 116 and input to digital processor 180 which will use the force information as a proxy to the actual width of gap 200 (assuming an a priori relationship has been established between the force and the width of the gap 200). Once the desired gap 200 width has been reached, digital processor 180 issues new commands to Z-stage 174 to maintain this gap width.

At this juncture the spinning machining element 110 is at the nominal starting location (and nominal EEM processing conditions) relative to the surface 120 of workpiece 122. From this juncture it is a straightforward process for the digital processor 180 to execute the toolpath computed by the tool path computing algorithm, which is done by causing the machining element 110 to be translated in the X-direction by X-stage 170, causing the machining element 110 to be translated in the Y-direction by Y-stage 172, causing the machining element 110 to be rotated about the Oy-direction by Oy-stage 176, and causing the machining element 110 to be translated in the Z-direction by Z-stage 174 under the control of digital processor 180. During this process digital processor 180 receives information from Z-force gauge 116 about the width of gap 200 and accordingly digital processor 180 issues positioning commands to Z-stage 174 to maintain a nominal width of gap 200. Similarly, digital processor 180 continues to receive information from tachometer 112 and there-after issues commands to motor 104 in real-time to maintain a substantially constant rate of rotation of machining element 110. This process continues until the machining element 110 runs the entire length of the computed toolpath over surface 120, which may take between one second for small surfaces requiring minimal surface figuring to ten days for bigger surfaces requiring large amounts of surface figuring. The removal rate of material from the surface 120 of workpiece 122 by the machining element 100 of the described EEM process can be between ten seconds per atomic monolayer to ten atomic monolayers per second.

After the machining element 110 has run the entire length of the computed toolpath, the EEM figuring process of surface 120 is complete and the digital processor 180 issues commands to Z-stage 174 to retract and cause machining element 110 to be raised upward, away from surface 120, to its home position. Similarly, there-after digital processor 180 issues commands to X-stage 170, Y-stage 172, and θ_Y-stage 176, so that each of these stages are also returned to their home positions. At this juncture machining element 110 can be removed from axle 114 and workpiece 122 can be removed from workpiece holder 124. Circulation pump 140 may remain ON so that slurry 126 remains in circulation and stays in a state of homogeneity for the next EEM process. Similarly, digital processor 180 may continue to receive information from thermometer 136 and accordingly issue commands to temperature control unit 130 to heat or cool the slurry 126 as needed to maintain the temperature of the slurry 126 at a prescribed temperature in anticipation of the next EEM process.

After removal from tanks 128 or 178 surface 120 is carefully cleaned of slurry 126 and then inspected with an areal interferometer or scanning displacement-measuring probe wherein its post-EEM-process surface figure is measured. If the remaining surface errors exceed a prescribed limit, then the new surface figure data from the metrology process are input to digital processor 180 through digital input port 186 and the above EEM process is repeated. This deterministic metrology—toolpath determination—EEM process can be executed multiple times until the surface figure error of surface 120 is less than a specified threshold.

Note that elastic emission system 100 is a four-axis system, utilizing motion control in the X, Y, Z, and θ_Y axes. Alternate configurations having different numbers of axes such as three (in which one axis of motion is removed, such as the θ_Y axis for example), five (in which one axis of motion is added, such as the θ_Z axis in which the workpiece 124 is rotated about an axis parallel to the Z-axis for example), or even six (in which two axes of motion are added, such as the θ_Z described above as well as a θ_X axis in which force gage 116 and all components coupled thereto rotate about an axis parallel to the X-axis for example). Note that adding axes of motion improves the versatility of the elastic emission system while removing one or more axes significantly diminishes the versatility of the elastic emission system while also reducing its cost and complexity. Additionally, the configuration of the axes relative to the workpiece 120 and machining element 110 can be re-arranged, such that, for example, the X and Y translation stages (170 and 172, respectively) cause the machining element 110 to move in X and Y instead of the workpiece 120, and the Z translation stage 174 can be configured to make the workpiece 120 move in the Z-direction instead of the machining element 110. Numerous other configurations of the motion stages and their respective translational and rotational actions are possible as well. Further, the same exemplary process can be used with the other examples illustrated and described herein, such as shown in FIGS. 5 and 9 by way of example, with the X, Y, and Z axes controlled by different stages and the workpiece coupled to the drive head in a different manner.

Elastic emission system 150 as illustrated in FIG. 20 is an example similar to elastic emission system 100 as described in the preceding paragraphs with one difference being that the motor that drives the machining element is not located above the slurry 126 but is instead immersed in slurry 126. That is, as seen in FIG. 20, motor 154 is directly coupled to machining element 160, eliminating the need for drive pully 144, driven pulley 146, and drive belt 106. A drive arm 158 is still required to mechanically couple motor 154 and machining element 160 to force gauge 166, although drive arm 158 is simpler in design and construction than drive arm 108 as drive arm 158 does not need to contain slurry splashes arising from drive belt motions through the slurry 126. Note that in this configuration the tachometer (not shown in FIG. 20) that is used to measure the rotational velocity of motor 154 must be collocated with the motor 154 and machining element 160, meaning that both the motor 154 and tachometer must be capable of being reliably operated while submersed in slurry 126. Note further that electrical wiring associated with motor 154 and tachometer must also pass-through slurry 126, preferably coupled to support arm 158. One undesirable aspect of this configuration is that drive motor 154 constitutes a heating element within slurry 126 which can cause slurry 126 to increase in temperature. This heating can be mitigated by the activation of the cooling element within temperature control unit 130, although this increases the temperature control burden placed on the temperature control unit 130.

Drive motor 154 can be a brushless DC motor or, less preferably, an AC motor that operates with standard 60 Hz grid power. Drive motor 154 can be controlled by digital processor 180 such that digital processor 180 can control the rotational speed of drive motor 154, or even activate or de-activate motor 154 as needed. Drive motor 154 speed control is needed so that the rotational speed of machining element 160 can be controlled by digital processor 180, which is needed to accommodate EEM process variations such as, for example, variations in gap 200 width or changes in slurry 126 temperature. Drive motor 154 can range in power from 1.0 Watts up to 250 Watts.

Yet another example utilizing a novel non-spherically shaped machining element is illustrated in FIGS. 21A and 21B. As shown in FIGS. 21A and 21B an alternate elastic machining head 600 comprises a broad machining element 604 having a broad machining element surface 610 that rotates or spins about an axis 602 driven by a motor as described in connection to previous examples. Broad machining element surface 610 has a length along its axis 602 that spans a significant portion of surface 620 of workpiece 622, said spanning can be at least 10% of the width of surface 620, preferably 50% or more than a width of surface 620, or even 100% or more of the width of surface 620. Workpiece 622 is coupled to workpiece mount 634 having a spindle 632 which in turn is coupled to and attached to a second motor (not shown) which causes the spindle 632, workpiece mount 634, and workpiece 622 to rotate in a workpiece direction of rotation 630, which occurs concurrently with the rotation of broad machining element 604 about its axis 602. The rotational speed along the workpiece direction of rotation 630 can be between 1.0 RPM and 3600 RPM, although slower rotational velocities such as 2 to 10 RPM are preferred. Note the presence of gap 606 between surface 620 and broad machining element 604 in which slurry 626 is present and effects an EEM processing operation while the broad machining element 604 is spinning as described earlier in connection to previous examples. Importantly, the geometric shape of broad machining element surface 610 is imparted onto surface 620 of workpiece 622, therefore the surface figure of broad machining element surface 610 itself must be highly accurate, without significant form errors, as it is the shape or form of broad machining element surface 610 that is imparted onto surface 620 during the EEM process. Note also that surface 620 must have rotational symmetry, about workpiece axis 628, so elastic machining head 626 is incapable of machining free-form optical surfaces, although surface 620 may have other shapes imparted, such as spheres and aspheres.

As with machining element 110, broad machining element 610 is a key component of an elastic emission system as machining element 610 is what causes the particles 226 within slurry 126 to be accelerated to a non-zero velocity and move rapidly past surface 620 of workpiece 622 causing material to be removed form surface 620 during the EEM process. The rotational velocity of broad machining element 610 can be at least 3600 RPM (revolutions per minute) but less than 14,400 RPM, with an angular velocity of between 8,000 and 12,000 RPM being ideal. Broad machining element 610 has rotational symmetry about axis 602, and a cross section of broad machining element surface 610 can have a circular cross section, an elliptical cross section, parabolic or polynomial cross section, a trapezoidal or piece-wise linear cross-section, or any combination of these. The outer diameter of broad machining element 610 can be between 4 mm and 400 mm, and the diameter of broad machining element at its maximum extent can be between 4 mm and 100 mm. Broad machining element 610 can include an elastic material such as an elastomer such as silicone, polyisoprene, polybutadiene, rubber, or any organic material such as a polymer such as polycarbonate or acrylic. Alternately broad machining element 610 can include a ceramic material, or a metal such as aluminum or stainless steel although metals are not preferred because particles 226 in slurry 626 can often react with a metal. The roughness of the surface of broad machining element 610 can be between 2 nm RMS and 10 microns RMS, although a surface roughness that is the same as, or less than, a width of particles 226 within slurry 626 is preferable. Elastomeric broad machining element 610 may be stiff and rigid and be substantially inelastic, which would be the case if machining element were includes a metal, or elastomeric broad machining element 610 may be elastic in nature in which, for example, the elasticity of the elastomeric machining element 610 can be less than 60 on the Shore D scale.

The elasticity of the elastic machining elements described heretofore has been noted as being a key parameter in the control and, indeed, the capabilities, of the EEM process, which is even more pronounced when the machining element is eccentric (i.e., non-spherical). FIG. 21A illustrates an eccentric machining element 700 (eccentric meaning toroidal, ellipsoidal, polynomial, etc.) that is includes a material that is highly elastic. In an EEM process, when elastic machining element 700 is brought into close proximity with workpiece 120 the outer periphery 702 of machining element 700 proximal to surface 120 flattens at gap 200 as the outer periphery 702 conforms to the topography of surface 120. When the nominal gap 200 width is first reached, and before significant amounts of material have been removed from surface 120, the internal forces 710 within machining element 700 proximal to surface 120 are substantial uniform in magnitude across the machining area 708. Under these conditions a machining mark 720 begins to form (as shown in FIG. 21B) within surface 120 wherein the periphery of the machining mark 720 is at machining area 730 and the depth of the developing machining mark 720 is substantially uniform throughout machining area 730. If the spinning machining element 700 is allowed to stay in place (i.e., none of the motion stages are activated) with respect to surface 120, then after a time Δt the outer portion of machining mark 720 will be fully machined and only that portion of machining mark 720 within machining area 732 will be in the process of being actively EEM'ed as an area closer to mid-plane 706 of outer periphery 702 of elastic machining element 700 gradually expands due to the internal forces 710 and effects the machining process within machining area 732. If the spinning machining element 700 is allowed to stay in place even longer (i.e., none of the motion stages are activated), then after a time 2Δt the outer portions of machining mark 720 will be fully machined and only that portion of machining mark 720 within machining area 734 will be in the process of being actively EEM'ed as an area proximal to mid-plane 706 of outer periphery 702 of elastic machining element 700 fully expands due to the internal forces 710 and effects the machining process within machining area 732. This process is noteworthy because with an elastic machining element 700 the machining of machining mark 720 proceeds from the outer bounds of machining mark 720 inward.

Alternately, FIG. 22A illustrates an eccentric machining element 800 (eccentric meaning toroidal, ellipsoidal, polynomial, etc.) that is includes a material that is highly inelastic. In an EEM process, when inelastic machining element 800 is brought into close proximity with workpiece 120 the outer periphery 802 of machining element 800 proximal to surface 120 flattens at gap 200 as the outer periphery 802 conforms to the topography of surface 120. (Note that the width of flat machining area 808 is narrower than the width of flat machining area 708 although they are drawn as being the same in FIGS. 22A and 21A for clarity). When the nominal gap 200 width is first reached, and before significant amounts of material have been removed from surface 120, the internal forces 810 within machining element 800 proximal to surface 120 are substantially non-uniform in magnitude across the machining area 808, being greater at positions closer to mid-plane 806. Under theses condition a machining mark 820 begins to form (as shown in FIG. 22B) within surface 120 wherein the initial periphery of the machining mark 820 is at machining area 834 and the depth of the developing machining mark 820 is deeper at the center of machining area 834. If the spinning machining element 800 is allowed to stay in place (i.e., none of the motion stages are activated) with respect to surface 120, then after a time Δt the portion of machining mark 820 that is being actively EEM'ed will have expanded to middle machining area 832, and then after a time 2Δt the portion of machining mark 820 that is being actively EEM'ed will have expanded to the final perimeter 830 of machining mark 820. This process is noteworthy because with an inelastic machining element 800 the machining of machining mark 820 proceeds from the innermost portion of machining mark 820 outwards, which is in sharp contrast to how the generation of machining mark 720 proceeds with an elastic machining element 700. Since a machine toolpath is that path of a machining element that must be followed in order to produce a desired change in the figure of a surface and is simply a sequence of a large number of machining marks, the elasticity of the machining element not only greatly affects the characteristics of the machining mark but the characteristics and results of the EEM machining along the tool path and the final results of the EEM process on the surface being processed.

Note further that the width and depth of a machining mark is proportional to the dwell time (i.e., the length of time that a machining element is EEM'ing a particular location on surface 120) when an inelastic machining element 800 is utilized, while only the depth of a machining mark is proportional to the dwell time when an elastic machining element 700 is utilized. Finally, it should be noted that with an elastic machining element 700, the centrifugal forces within elastic machining element 700 arising from its rotation about axis 704 may modify the magnitude of the forces 710. That is, the rotational speed of elastic machining element 700 may be used to control the generation of machining mark 720 which provides another means for controlling the EEM material removal process from a surface 120 along a toolpath.

Having thus described the basic concept of invention, it will be rather apparent to those skilled in the art that the foregoing detailed disclosure is intended to be presented by way of example only and is not limiting. Various alterations, improvements, and modifications will occur and are intended to those skilled in the art, though not expressly stated herein. These alterations, improvements, and modifications are intended to be suggested hereby, and are within the spirit and scope of the invention. Additionally, the recited order of processing elements or sequences, or the use of numbers, letters, or other designations, such as arrows in the diagrams, therefore, is not intended to limit the claimed processes to any order or direction of travel of signals or other data and/or information except as may be specified in the claims. Accordingly, the invention is limited only by the following claims and equivalents thereto.

Claims

1. An elastic emission machining apparatus comprising:

a machining element having a non-spherical shape that is configured to spin about an axis of rotation;

a tank with a chamber positioned to receive the machining element and a slurry comprising a mixture of a liquid and chemically reactive fine particles; and

a driving system coupled to and configured to engage the machining element to spin about the axis of rotation adjacent to a surface of the workpiece to accelerate the chemically reactive fine particles through a gap between the machining element and the surface of the workpiece.

2. The apparatus as set forth in claim 1 wherein the machining element is configured to spin about the axis of rotation that extends in a direction substantially parallel to at least a portion of a surface of the workpiece.

3. The apparatus as set forth in claim 1 wherein the shape of the machining element is acylindrical.

4. The apparatus as set forth in claim 1 wherein the shape of the machining element is an ellipsoid.

5. The apparatus as set forth in claim 1 wherein the shape of the outer perimeter of the machining element is polynomial.

6. The apparatus as set forth in claim 1 wherein the shape of the machining element is aspherical.

7. The apparatus as set forth in claim 1 wherein the shape of the machining element is toroidal.

8. The apparatus as set forth in claim 1 wherein the shape of the machining element is cylindrical.

9. The apparatus as set forth in claim 1 wherein the machining element is coupled to an axle and further comprising motion control devices coupled to effect at least one axis of linear motion and at least one axis of angular motion of the machining element.

10. The apparatus as set forth in claim 1 wherein the thickness of the gap is greater than the width of the chemically reactive fine particles.

11. A method of making an elastic emission machining apparatus, the method comprising:

providing a machining element having a non-spherical shape and that is configured to spin about an axis of rotation;

positioning a chamber of a tank to receive the machining element and a slurry comprising a mixture of a liquid and chemically reactive fine particles; and

coupling a driving system to and that is configured to engage the machining element to spin about the axis of rotation adjacent to a surface of the workpiece to accelerate the chemically reactive fine particles through a gap between the machining element and the surface of the workpiece.

12. The method as set forth in claim 11 wherein the machining element is configured to spin about the axis of rotation that extends in a direction substantially parallel to at least a portion of a surface of the workpiece.

13. The method as set forth in claim 11 wherein the shape of the machining element is acylindrical.

14. The method as set forth in claim 11 wherein the shape of the machining element is an ellipsoid.

15. The method as set forth in claim 11 wherein the shape of the outer perimeter of the machining element is polynomial.

16. The system as set forth in claim 11 wherein the shape of the machining element is aspherical.

17. The method as set forth in claim 11 wherein the shape of the machining element is toroidal.

18. The method as set forth in claim 11 wherein the shape of the machining element is cylindrical.

19. The method as set forth in claim 11 wherein the machining element is coupled to an axle and further comprising motion control devices coupled to effect at least one axis of linear motion and at least one axis of angular motion of the machining element.

20. The method as set forth in claim 11 wherein the thickness of the gap is greater than the width of the chemically reactive fine particles.