Abrasive tools, abrasive machines and methods for abrading workpieces

Abstract

The present invention relates to a sub-aperture polishing tool comprising a support member including a connection mechanism for connection to a sub-aperture polishing machine. An end of the support member has an abrasive head, the abrasive head being connected to or integral with the support member and including a base structure configured to define a non-planar surface. The abrasive head also has an outer shell, at least a portion of an outer surface of which defines a working surface of the polishing tool, the outer shell being secured to the base structure and enclosing a cavity between the outer shell and the non-planar surface. The cavity located between the outer shell and the base structure is filled with a viscoelastic material.

Description

[Technical field]

[0001] The present invention relates to an abrasive tool and a polishing machine incorporating said abrasive tool. A method for polishing a workpiece is also provided. Both full-aperture and sub-aperture apparatus and techniques are disclosed. [Background technology]

[0002] Many processes for manufacturing objects in various technical fields require polishing of each part of the workpiece being manufactured. For example, medical surfaces such as lenses, mirrors and other optical components, surfaces of ophthalmic devices and prosthetics, and engineered parts such as jet engine turbine blades are generally all polished to produce a finished product with a smooth surface with few defects and aberrations. Similarly, molding tools for manufacturing molded parts that require a very smooth surface finish, for example, for molding curved glass screens for wearable technology such as mobile phones and watches, and consumer products such as tablets and computer screens, must be highly polished. The polishing process may be a "full aperture" polishing process, where the polishing tool contacts the entire surface being polished simultaneously, or a "sub-aperture" polishing process, where the polishing tool is smaller than the surface being polished. In the latter case, each part of the surface is polished sequentially by moving the polishing tool across the entire workpiece surface (along with rotating, oscillating or vibrating the tool that performs the polishing action).

[0003] Before being polished, the workpiece from which the product is to be formed is generally ground into the desired shape by moving the surface with an abrasive surface or substance capable of removing material from the workpiece while pressing against it. The material used to subsequently polish the surface is finer than the abrasive used in grinding and does not remove a significant proportion of material from the workpiece. Thus, in theory, the overall surface shape of the workpiece surface is determined during the grinding stage of the process, and subsequent polishing removes defects and smoothes the surface without significantly altering its shape as seen by the naked eye.

[0004] However, it is often difficult to obtain the desired results because the polishing action cannot distinguish between the various features of the work surface, i.e., to treat the unwanted surface roughness while not removing the desired geometric features. For example, the macroscopic shape of the workpiece may be distorted and / or desired small features may be lost. These problems are particularly evident (but not limited to) in sub-aperture polishing processes where the dimensions of the working surface of the polishing tool (i.e., the portion or portions of the surface of the tool that can polish the workpiece surface) are smaller than the dimensions of the surface being polished. Although sub-aperture polishing techniques are useful because they allow a limited set of tools to be used to polish surfaces of virtually any shape (sometimes called "free-form" in contrast to symmetrical or otherwise regular surfaces), the types of surfaces to which the sub-aperture technique is applied (e.g., surfaces that are irregular, have sharp features, are strongly curved, or are asymmetric) can be particularly difficult to polish accurately. Thus, there is a need to provide a polishing tool that allows for improved control of the polishing process. Summary of the Invention

[0005] A first aspect of the present invention provides a sub-aperture polishing tool, comprising: a support member including a connection mechanism for connection to a sub-aperture polisher; and The support member has an end portion provided with a polishing head, the polishing head comprising: a base structure connected to or integral with the support member, the base structure being configured to form a non-planar surface; an outer shell at least a portion of which defines a working surface of the abrasive tool and which is secured to the base structure so as to enclose a cavity between the outer shell and the non-planar surface; and a viscoelastic material filling the cavity located between the outer shell and the base structure; A sub-aperture polishing tool is provided.

[0006] Viscoelastic materials are non-Newtonian, which means that they do not have a constant viscosity (if the material is a fluid) or a constant stiffness (if the material is a solid). Rather, their parameters change depending on the applied shear or strain rate, or the amount of applied stress. As a result, the polishing tool responds differently to the various features it encounters as it moves over the workpiece surface. Relatively small or closely spaced features (such as sharp edges) impact the tool's work surface with relatively high shear or strain rates, while the opposite is true for relatively low curvature features. Thus, the viscoelastic material supporting the work surface changes its apparent viscosity or stiffness, which results in different polishing pressures for different types of features on the workpiece surface. This results in better control of the process.

[0007] As described above, the outer shell and the non-flat surface surround the cavity. As a result, the cavity is sealed. Thus, the viscoelastic material in the cavity cannot escape the cavity, and the amount of viscoelastic material in the cavity remains constant even if the outer shell is subjected to pressure changes and deforms during use. This is in contrast to some known abrasive tools in which a bladder or similar structure is filled with a fluid introduced through a conduit, allowing the amount and / or pressure of the fluid inside the tool to be changed during use.

[0008] Depending on the nature of the workpiece, the viscoelastic material sealed inside the cavity may be one whose viscosity / stiffness increases with increasing shear / strain rate (or applied stress) or vice versa. Some viscoelastic materials can exhibit either behavior depending on the range of shear / strain rates (or applied stress) they are subjected to. An example of an application where each behavior is useful is described below.

[0009] The non-planar surface of the base structure plays an important role in the effectiveness of the tool, as it allows for better control over the viscoelastic material and its behavior. For example, the non-planar surface can be configured to bring the viscoelastic material into greater contact with the outer shell during use. Furthermore, the amount of viscoelastic material located between the non-planar surface and the outer shell at any given location on the machining surface (i.e., the thickness of the layer measured there in a direction perpendicular to the machining surface) affects the tool's response to shear caused by contact with the workpiece surface. In general, the thinner the layer of viscoelastic material, the greater the absolute thickness and / or stiffness of said material that causes shear when each portion of the machining surface contacts the feature. As the viscoelastic material fills the cavity surrounded by the outer shell and the non-planar surface, it forms a layer whose thickness at each location on the machining surface depends on the distance separating the outer shell and the non-planar surface. Thus, in some embodiments, the non-planar surface can be configured to define a macrostructure that allows the thickness of the viscoelastic material at each location on the workpiece surface to be controlled, without restricting the shape of the outer shell when designing the tool. Examples are provided below. Alternatively or additionally, the non-flat surface can be used to define a microstructure (which exists on a smaller scale than any macrostructure) that "grabs" the viscoelastic material in a surface texture and more efficiently transfers rotation from the support member to the material during use.

[0010] The non-planar surfaces as part of the base structure are intended to be relatively rigid (i.e., not deformable) compared to the outer shell, at least during any grinding procedure. However, as will be described below, the non-planar surfaces may be formed in a number of alternative ways to include portions that are not rigid until configured for use. The outer shell is generally relatively flexible compared to the non-planar surfaces, allowing the tool working surface to conform to the overall shape of the workpiece surface during use. It is understood that the non-planar surfaces may include one or more areas that are locally flat, although not entirely flat (planar) from one periphery to the other. In general, the non-planar surfaces of embodiments of the invention deviate from (i.e., are non-parallel to) a notional minimal surface at the points at which the outer shell is affixed to the base structure. By "minimal surface" is meant the smallest area surface bounded by the points at which the outer shell is affixed to the base structure. For example, in some embodiments, the base structure has the overall shape of a disk and the outer shell is fixed around the circumference of said disk. The minimal surface in this case is a perfectly flat surface that is bounded by the circumference of the disk, and non-flat surfaces actually present on the tool deviate from this conceptual minimal surface, for example, due to microstructures (e.g., textures) present on the non-flat surfaces or macrostructures (e.g., protruding cores) on the non-flat surfaces. In some embodiments, the conceptual minimal surface is perpendicular to the axis about which the sub-aperture abrasive tool rotates during use. In some other embodiments, the conceptual minimal surface can be parallel to the axis of rotation.

[0011] As mentioned above, the term "subaperture" means that the working surface of the abrasive tool has dimensions smaller than the surface of the workpiece that the tool is used to polish. A "subaperture abrasive tool" is therefore suitable for polishing workpieces having surfaces with dimensions larger than the dimensions of the working surface of the abrasive tool. Typically, the working surface of the abrasive tool is much smaller than the surface to be polished, e.g. less than half its surface area (and can be much smaller). The tool moves across the workpiece surface, typically rotating around the tool axis at high speed, so that all points of the workpiece surface that require polishing are treated sequentially (rather than simultaneously).

[0012] It has been found by the inventors that abrasive tools of the above type, in which the viscoelastic material is a shear-thickening and / or stress-stiffening material (i.e., its viscosity / stiffness increases with increasing shear / strain rate (or applied stress)), are particularly useful for removing so-called "mid-spatial defects" on the workpiece surface.

[0013] Although techniques have been developed that allow the surfaces of workpieces to be ground and polished to a high level of precision, the grinding stage of these manufacturing processes is highly susceptible to the formation of these "meso-space defects" on the surfaces being machined. Meso-space defects (or simply "meso-spaces") are defects that appear as waves or undulations on the surface of a workpiece, typically with a spatial period in the range of 0.1 to 10 millimeters (mm). Meso-spaces can be detrimental for a variety of reasons. In the case of optical components (whether formed by the workpiece itself or subsequently shaped from it), for example, the defects can degrade the quality of the image formed by the component. In the case of prosthetic devices, they can gradually undermine the adhesion of the component to human tissue. Typical abrasive tools are ineffective at removing features the size of meso-spaces, and therefore tend to simply smooth out the surface with this defect while retaining its wavy profile.

[0014] Traditional methods of removing interspaces involve intensive grinding of the workpiece with an abrasive tool. Although this can ultimately result in a reduction in the amplitude of the interspaces, the macroscopic shape of the surface can be distorted because the rate difference at which material is removed from the "peaks" of the interspaces is typically smaller than that at the "valleys." Therefore, to suppress interspace defects, a large amount of unwanted material must be removed during the grinding step.

[0015] Thus, in a particularly preferred embodiment, the cavity surrounded by the outer shell and the non-planar surface is filled with a shear-thickening and / or stress-hardening viscoelastic material. "Shear-thickening" means that the viscosity of a (fluid) material increases with the shear rate experienced by the material. Similarly, "stress-hardening" means that the stiffness of a (solid) material increases with the stress experienced by the material. A material may be both shear-thickening and stress-hardening, but it is not essential that a material have both of these properties. Shear-thickening materials may also be referred to as "dilatants". Examples of suitable materials are provided below.

[0016] It has been found that this type of abrasive tool is capable of efficiently removing meso-spatial defects during normal polishing without the need for intensive application leading to distortion of the workpiece surface as described above. Since a shear-thickening and / or stress-hardening viscoelastic material is more resistant to deformation where it is subjected to higher shear rates, each part of the machined surface that repeatedly comes into contact with the peaks of meso-spatial defects on the surface (where the surface protuberances vary over a much smaller distance than they do in the overall surface profile, resulting in a high frequency of impacts between the material and each succeeding peak) thickens and / or stiffens in the vicinity of this feature, but the machined surface still generally conforms to the overall shape of the area where the tool is applied. This selective thickening and / or stiffening of the machined surface allows the peaks of meso-spatial defects to be preferentially removed by polishing compared to the valleys between them and any non-defective parts around the surface.

[0017] In a preferred embodiment, the outer shell comprises a layer of abrasive material forming an outer surface and suitable for sub-aperture polishing of a workpiece. This is commonly referred to in the art as a "polishing pad" and may carry abrasive particles by itself or may be designed for use with an abrasive slurry. In a preferred embodiment, the abrasive material comprises at least one of polyurethane, breathable cloth, tar-based viscoelastic polymer and / or other compatible material. By "compatible material" is meant a material that can conform to the surface of the workpiece when in contact therewith. Polyurethane, breathable cloth and tar-based viscoelastic polymer are examples of compatible materials. The abrasive material may optionally be porous. An additional layer of pitch or similar may be provided outside the layer of abrasive material if desired.

[0018] In some preferred embodiments, the abrasive material is in direct contact with the viscoelastic material in the cavity. The outer shell may, for example, consist of only the abrasive material. This may be the case, for example, when the viscoelastic material is a highly viscous material that does not end up leaking through the abrasive material during abrasion. Pitch is an example of such a viscoelastic material. It may also be the case that the abrasive material is a non-porous material that can retain the viscoelastic material. In most other preferred embodiments, the outer shell may further comprise an elastic layer located between the layer of abrasive material and the viscoelastic material, preferably the elastic layer being in direct contact with the viscoelastic material. The elastic layer may, for example, increase the strength of the outer shell, for example, to prevent tearing, and serve as a barrier to prevent leakage of the viscoelastic material. The elastic layer also helps the shell to return to its intended shape if it is deformed during use. In preferred embodiments, the elastic layer comprises at least one of rubber, silicone, neoprene, and a polymeric elastomer. The elastic layer preferably has a thickness in the range of 0.1 to 5 mm. It should be noted that if the outer shell includes a resilient layer, the abrasive need not have the same lateral extent as the resilient layer. For example, the abrasive can be disposed on all or only a portion of the outer surface of the resilient layer to form the desired working surface, as desired.

[0019] As mentioned above, the structure of the tool is such that the viscoelastic material forms a layer between the non-flat surface of the base structure and the outer shell. In some preferred embodiments, the non-flat surface defines a macrostructure that is rigid during use and has a surface texture (profile) that varies on the same scale as that of the outer shell, the macrostructure being shaped to determine the thickness of the viscoelastic material between the outer shell and the non-flat surface at each location on the outer surface. The surface texture of the macrostructure varies on the same scale as that of the shape of the outer shell, e.g. with similar lateral spatial frequency (i.e. following a path that deviates (vary) by various distances from a certain flat reference plane). The deviation may, for example, be monotonic in one direction over about half of the lateral dimension of the tool and then monotonic in the opposite direction over the remaining half. The amount of deviation (e.g. maximum height of the macrostructure) may be at least one tenth of the height of the outer shell relative to a notional flat reference plane depicted by the base structure. Advantageously, the macrostructure is rotationally symmetric about an axis about which the outer shell is also rotationally symmetric. This helps to avoid introducing any eccentricity into the tool. The presence of macrostructures can promote good contact between the viscoelastic and the outer shell to improve the performance of the tool through controlling the thickness of the viscoelastic and / or by controlling the direction in which the viscoelastic flows / deforms during use.

[0020] In some preferred embodiments, the macrostructure and outer shell are configured such that the viscoelastic material forms a layer having a substantially constant thickness between the non-planar surface and the outer shell, and the surface texture of the macrostructure preferably includes regions that follow the shape of the outer shell. By "constant thickness" it is meant that the thickness of the viscoelastic material between the outer shell and the non-planar surface is substantially the same at all positions on the machining surface (measured perpendicular to the machining surface). This ensures that the behavior (response) of the tool when applied to the workpiece being processed (which depends on the thickness of the viscoelastic material as described above) is the same regardless of which part of the tool is in contact with the workpiece and at what angle.

[0021] However, in other preferred embodiments, the macrostructure and the outer shell are shaped differently from each other such that the thickness of the viscoelastic material varies at different locations on the work surface. For example, the outer shell may include a part-spherical cross section, whereas the macrostructure may be aspherical. This allows the behavior of the tool to be controlled by placing different parts of the work surface in contact with the workpiece (and / or changing the orientation of the tool relative to the workpiece), and the thickness variation may be designed such that different parts of the tool are optimized, for example, to remove mid-spatial defects of different wavelengths as described above, or to help protect intentional sharp edges. By controlling the basic thickness of the semi-compatible material, the grinding pressure can be actively adjusted to produce machining conditions that are best suited to the particular spatial content found on the workpiece surface. Preferably, the maximum thickness of the viscoelastic material is in the range of 2-200 mm.

[0022] It is particularly advantageous if the macrostructure has an at least partially convex or concave curved shape, preferably part-spherical, part-elliptical, part-parabolic, part-annular. It has been found that the behavior of the viscoelastic material as it deforms at portions of the work surface near where the outer shell meets the base structure can be influenced by the presence of the underlying base structure. This effect can be reduced by forming the macrostructure with a concave shape (so that at least a portion of the non-flat surface has a concave shape in a direction away from the outer shell), as this causes the non-flat surface to curve (or slope) away from the outer shell, thus reducing the extent to which the non-flat surface interferes with the properties of the work surface. The concave shape can also be used to counter the natural tendency of a tool with a part-spherical contour to push the fluid towards the equator. As the tool rotates about its axis, the non-Newtonian material will try to climb the slope of the concave macrostructure to balance the similar and opposite effect of the part-spherical outer work surface. In other embodiments, it has been found that convex cores having, for example, a partially spherical, elliptical or parabolic shape are particularly suitable for controlling the thickness of the layer formed by the viscoelastic material, since these shapes can be configured to protrude into the space surrounded by the outer shell, thus causing the cavity to form a well-defined layer between the outer shell and the non-flat surface.

[0023] The non-planar surface can be configured in a variety of different ways. In a preferred embodiment, the macrostructure is at least partially formed by a core that extends towards the outer shell and is configurable to be rigid during use. As described below, this core can be formed by a variety of structures and may or may not be integral with the remainder of the non-planar surface. In the simplest case, the core may simply be a solid body, e.g. a metal hemisphere, that can be machined into the surface of the base structure. However, other more complex structures may be employed, examples of which are described below. Thus, in a preferred embodiment, the core comprises one or more of a solid body, an inflatable structure, and an adjustable piston. The inflatable structure may be a non-porous bladder, e.g. it may be configured to be filled with a fluid, such as air, oil or water, during use using a hydraulic system to give the structure the required rigidity. In the case of an inflatable structure, the support member may advantageously comprise a conduit for supplying a fluid to the inflatable structure during use. By providing an adjustable piston as part of the core, the shape of the machined surface and / or the thickness of the layer of viscoelastic material between the outer shell and the non-planar surface can be altered.

[0024] In most cases, the macrostructure will not be in direct contact with the outer shell (other than around the non-flat surface where it extends to the point where it connects with the base structure). However, in some embodiments, the core can extend continuously from the base structure to a part of the outer shell (which part may or may not coincide with a part of the work surface). This may be the case for a particular shape of the tool, for example if the tool has the shape of a truncated cone intended to rotate around its axis of symmetry during use, the core may extend continuously from the base structure to the end of the truncated cone. It goes without saying that the cavity may for example be in the shape of an annulus located around the core. A macrostructure thus in contact with the outer shell at at least one point is also useful since it allows the tool to be used to probe the workpiece before, during or after the grinding operation. That is, this part of the outer shell (which will be robust due to its direct contact with the base structure) can be used to measure the position and / or shape of the workpiece surface.

[0025] When a core of the above type is provided as part of a macrostructure, the non-planar surface may further include a peripheral region adjacent the core, in which case the peripheral region is preferably relatively flat (relative to the core). For example, the macrostructure may include a hemispherical core surrounded by a relatively flat disc-shaped peripheral region. In that case, the outer shell may meet the base structure at the outer edge of the disc-shaped peripheral region.

[0026] In many embodiments, it is desirable to use the non-planar surface of the base structure to control the thickness of the viscoelastic layer (i.e., the amount of viscoelastic at any point between the base structure and the outer shell), but as noted above, the non-planar surface can be utilized for other purposes. In some preferred embodiments, the non-planar surface defines a microstructure in the form of a surface texture configured to grip the viscoelastic as the sub-aperture polishing tool rotates during use. By "microstructure" is meant a surface relief profile (shape) that is on a much smaller scale than that of the outer shell (and compared to any macrostructure that may also be present). It should be noted that "micro" in this specification refers to points that should not be held in order to impose any particular size limit (e.g., having a spatial frequency of less than 1 millimeter) and / or that the structure is so small that it is not visible to the naked eye, although either of these features may in fact be the case. Thus, the presence of this surface relief on the base structure results in only slight (if any) variations in the thickness of the viscoelastic layer at various points on the work surface. However, the microstructure engages with the viscoelastic layer, thereby improving the transmission of torque from the support member to the material and ensuring rotation of the material and the tool during use. Any shape of surface relief can be utilized for this purpose, including regular or irregular patterns such as a grid of grooves or lines. In a preferred embodiment, the surface texture comprises a plurality of protruding and / or recessed features on the non-flat surface, the protruding and / or recessed features preferably forming a stud and / or pit texture. If the non-flat surface also defines a macrostructure, the surface texture can be present on all or part of the macrostructure. For example, if the macrostructure comprises a core and a peripheral region, the microstructure can be provided on the surface of only the core and not the peripheral region, or vice versa.

[0027] Preferably, the microstructure is partially defined by a plurality of protrusions integrally defined in the base structure and / or fixed to the base structure. The microstructure can therefore be formed by suitable shaping of the base structure itself, e.g. machining of a solid material or moulding of a material to form the desired undulations. Alternatively, the microstructure can be formed by locally fixing one or more materials to the base structure to form protrusions of the desired undulations. The material forming such protrusions may be a conforming or non-conforming material, but is preferably as rigid in use (compared to the outer shell) as the remaining non-planar surface. For example, the protrusions can be formed from a viscoelastic material, provided that they remain in place and do not significantly change their shape or frictional properties in use. The protrusions can also be formed from an elastic material such as rubber and bonded to the remaining base structure by means of an adhesive. In the preferred case, the protrusions are at least as rigid as the remaining material forming the non-planar surface (e.g. steel). For example, the protrusions (also indentations) can be machined directly into the base structure material. Therefore, the microstructures can be formed by additive and / or subtractive manufacturing techniques.

[0028] In a preferred embodiment, the microstructure features may have an amplitude (i.e., peak to trough height) in the range of 0.1 mm to 10 mm, or larger for larger tools. The amplitude is smaller in relation to the thickness of the viscoelastic material filling the cavity. The protrusions may have any shape, e.g., cylindrical protrusions or elongated grooves, and may be arranged in a one- or two-dimensional regular pattern, e.g., pseudo-random, or in a line grid, hexagonal arrangement, concentric circles, etc. The lateral size (e.g., line width or diameter) of each protrusion is preferably in the range of 0.1 mm to 10 mm, and again may be larger for larger tools. The average center-to-center spacing (or periodicity, if arranged in a regular array) may be between 0.1 mm to 10 mm, or larger for larger tools. In the case where the surface texture consists of indentations formed in the base structure, all of these dimensional requirements apply equally to the indentations.

[0029] The working surface may be flat or nearly flat when not pressed against a workpiece surface. However, preferably, the working surface of the tool is non-flat when not pressed against a surface. In other words, the outer shell, the viscoelastic material and the base structure are arranged such that the working surface is non-flat when the tool is at rest and the material is free to relax to an equilibrium state. Typically, the outer shell is manufactured to conform to the workpiece during use, but retain a desired shape when at rest. For example, the working surface of the tool may be shaped as a cross section of a sphere. Curved (whether convex, concave or otherwise non-flat) working surfaces are particularly suited to sub-aperture polishing, as they can be applied to surfaces with a larger range of shapes and curvatures than typically flat working surfaces. For example, a working surface in the shape of a cross section of a sphere can in principle polish any concave surface whose radius of curvature is greater than that of the working surface.

[0030] In a preferred embodiment, at least a portion of the work surface is part-spherical, part-elliptical, part-cylindrical, part-conical or toroidal. These shapes have been found to be suitable for polishing surfaces having a range of topologies and are therefore particularly suitable for polishing free-form surfaces. Work surfaces including multiple laterally offset regions, each of a different shape (such as any one of the shapes mentioned above), are also possible.

[0031] Preferably, the work surface has a lateral width in the range of 0.5 millimeters (mm) to 1 meter (m), preferably 0.5 mm to 0.5 m, more preferably 0.5 mm to 200 mm, most preferably 0.5 to 5 mm. A range of such abrasive tools with different dimensions and / or shapes can be made available to suit different workpieces or for polishing different parts of one workpiece.

[0032] It should be noted that while preferred embodiments of viscoelastic materials have been described as either (i) "shear thickening" and / or "stress hardening" and (ii) "shear thinning" and / or "stress thinning", the two are not mutually exclusive. That is, as noted above, some viscoelastic materials can exhibit both types of behavior at various ranges of applied shear / strain rates (or applied stresses). Therefore, each of the above terms includes any viscoelastic material that exhibits the respective properties under at least one range of shear / strain rates (or applied stresses), even if it exhibits opposite properties in other ranges. As an example, some mixtures of cornstarch and water may exhibit a shear thickening response in one range of shear rates and a shear thinning response in a different range of shear rates, and thus may be considered to satisfy both definitions (i) and (ii). Of course, in practice, the polishing tool will be controlled such that the shear / strain rate (or applied stress) applied to the material is within the range required to induce the desired viscoelastic behavior (response) (i.e., either (i) or (ii)). In some preferred embodiments, the viscoelastic material is selected to exhibit only either behavior (i) or (ii), i.e., its response type is the same at all shear / strain rates (or applied stress levels). In preferred examples, the viscoelastic material comprises at least one of pitch, non-Newtonian fluid, polymer, silicon polymer, starch, clay, metamaterial, suspension of particles in a solvent, or any combination thereof (e.g., in a homogeneous mixture). A preferred example of a shear-thickening and / or stress-stiffening viscoelastic material comprises at least polydimethylsiloxane (PDMS). For example, the material may be a suspension of dimethylsiloxane, silicon dioxide, castor oil, and polydimethylsiloxane. Suitable examples of shear-thinning and / or stress-weakening viscoelastic materials include soaps, shampoo compositions, mixtures of cornstarch and water, and mixtures of particulates (e.g., talc) and solvents. For example, some paints exhibit shear-thinning behavior if the constituent particles are small enough (e.g., 5 micron particles).An example of a suitable commercially available product is Carbopol 940 gel (available from Lubrizol, Ohio, USA), which contains carbomer and carboxypolymethylene.

[0033] The first aspect of the present invention is The sub-aperture polishing tool as described above, a workpiece holder for holding a workpiece during use; and There is further provided a sub-aperture polishing machine comprising a drive mechanism mechanically connected to the connecting mechanism, the drive mechanism configured to, in use, rotate the sub-aperture polishing tool about a first rotational axis passing through the tool while at least a portion of the working surface is in contact with a surface of the workpiece such that the working surface moves relative to the surface of the workpiece.

[0034] This provides all the advantages already explained above for abrasive tools.

[0035] Preferably, the drive mechanism is further controllable to change the position and / or orientation of the sub-aperture polishing tool relative to the workpiece during use. Desirably, the drive mechanism is controllable to move the polishing tool along three orthogonal spatial directions. The drive mechanism may be controllable to change the orientation of the polishing tool with respect to a first axis of rotation and a second and / or a third axis of rotation, each orthogonal to the other. For example, a 3-axis, 4-axis or 5-axis CNC machine may be utilized. Alternatively, the polishing machine may be a multi-task machine (e.g., FANUC Robodrill), an industrial robot (e.g., FANUC LR Mate) or a belt drive (i.e., a system of gears and pulleys used to move a tool across a surface in some repeating pattern).

[0036] Advantageously, the drive mechanism is further controllable to drive the movement of the tool relative to the surface of the workpiece such that the viscoelastic material exhibits either (i) shear thickening and / or stress hardening behaviour, or (ii) shear thinning and / or stress weakening behaviour. If the viscoelastic material of the tool is capable of exhibiting both types of behaviour, it is also possible to configure the machine such that the movement of the tool is driven differently (e.g. driven at different speeds) in different areas of the workpiece to sequentially produce each type of behaviour (i) and (ii) from the same tool.

[0037] The first aspect of the present invention is (a) Prepare the sub-aperture polishing tool described above; (b) placing a working surface of the sub-aperture abrasive tool in contact with a surface of a workpiece; (c) polishing the workpiece surface by moving the workpiece surface relative to the workpiece surface; A method for polishing a workpiece is further provided.

[0038] Preferably, the movement of the machining surface relative to the workpiece surface includes a rotation of the sub-aperture polishing tool about a first axis of rotation passing through the sub-aperture polishing tool. This will typically be an axis about which the outer shell (and machining surface) has 360 degrees of rotational symmetry. In an advantageous embodiment, steps (b) and (c) are performed multiple times at various positions on the workpiece surface, with the orientation of the sub-aperture tool relative to the workpiece surface being different at at least some positions. This can be used to obtain different polishing behaviors at different positions on the workpiece surface in order to construct different types of surface features.

[0039] In some preferred embodiments, the viscoelastic material is a shear-thickening and / or stress-hardening viscoelastic material, and the work surface is moved relative to the work piece surface to reduce and / or remove mesospheric defects from the work piece surface. Movement of the tool relative to the work surface is preferably controlled (e.g., with respect to its speed) such that the viscoelastic material exhibits shear-thickening and / or stress-hardening behavior.

[0040] The tool may be moved across the workpiece surface such that the polishing conditions are constant at all points (e.g., constant relative orientation of the tool and workpiece surface, constant pressure, etc.). This may be desirable when the surface defects are similar across the entire surface. However, in other preferred embodiments, steps (b) and (c) may be repeated sequentially at two or more different locations on the workpiece surface, each of the plurality of locations containing mid-spatial defects each having a wavelength different from that of at least some of the other locations, and in which case step (b) is carried out at each location under polishing conditions selected depending on the wavelength of the respective mid-spatial defects. That is, the nature of the polishing may be varied across the workpiece surface such that the polishing is "tuned" to remove the particular type of defect present at each location. Advantageously, the polishing conditions that vary depending on the wavelength of the mid-spatial defects include at least one of the rotational speed of the sub-aperture polishing tool, the pressure between the working surface of the sub-aperture polishing tool and the workpiece surface, and the orientation of the sub-aperture polishing tool relative to the workpiece surface.

[0041] It has been found to be particularly useful if the orientation of the subaperture tool relative to the workpiece surface is different at least in some locations. Preferably, the orientation of the subaperture polishing tool relative to the workpiece surface in each location is selected depending on the wavelength of the respective mid-spatial defect. This is particularly effective when using a tool in which the viscoelastic material is arranged such that the thickness of said material between the surface and the core of the workpiece varies between two or more different orientations. In this way, the contact between the two will involve different points of the working surface of the tool, so that the properties of the polishing head will be different when applied to the workpiece in different orientations.

[0042] In other preferred embodiments, the viscoelastic material is a shear thinning and / or stress weakening viscoelastic material, and the work surface is moved relative to the work surface in a manner that preserves sharp features (e.g., edges) of the work surface while preferentially smoothing relatively flat areas. Movement of the tool relative to the work surface is preferably controlled (e.g., with respect to its speed) such that the viscoelastic material exhibits shear thinning and / or stress weakening behavior. Exemplary applications of such processes include polishing Fresnel lenses, diffractive optical elements, or semiconductor wafers.

[0043] Preferably, the surface of the workpiece has a shape and / or surface profile different from that of the working surface of the sub-aperture abrasive tool, at least when the sub-aperture abrasive tool is not in contact with the surface of the workpiece. Advantageously, the working surface of the sub-aperture abrasive tool has a surface area that is smaller, preferably less than half, more preferably less than 10% of the surface area of ​​the surface of the workpiece. In a preferred embodiment, the working surface of the sub-aperture abrasive tool has a maximum lateral dimension that is smaller, preferably less than half, more preferably less than 10% of the maximum lateral dimension of the surface of the workpiece. Desirably, at least a portion of the working surface of the sub-aperture abrasive tool has a radius of curvature that is less than the minimum radius of curvature of the surface of the workpiece. This allows the entire surface of the workpiece to be polished with the same tool, if required. The disclosed polishing tools and methods are particularly well suited when the workpiece is not rotationally symmetric and / or when the surface of the workpiece includes at least one convex region and at least one concave region, or when both convex and concave curves are present in the same region (e.g., a "saddle" surface).

[0044] In a further preferred embodiment, the movement of the machining surface relative to the surface of the workpiece includes rotating the sub-aperture abrasive tool at a first rotational speed when in contact with a first location on the surface of the workpiece and rotating the sub-aperture abrasive tool at a second rotational speed when in contact with a second location on the surface of the workpiece, such that the shape of the machining surface is different when in the first position than when in the second position. Due to the flexible nature of the outer shell and the conforming nature of the viscoelastic material, when the tool is rotating at high speed, centrifugal forces can change the shape of the machining surface, which can be utilized to change the abrasive characteristics of the tool.

[0045] The invention further provides products polished by the above method, which are preferably either optical elements such as lenses or prisms, semiconductor wafers, screens for electronic devices, medical prosthetics, or molds. For example, the devices and methods disclosed herein can be used for ultra-precision polishing in the mass consumer market, including precision optical components (lenses and mirrors for imaging, microscopy, spectroscopy), precision molds (for replication by plastic injection or glass pressing), medical surfaces (ophthalmic devices, prosthetics), and precision polishing surfaces such as smartphones, smartwatches, eyeglasses, etc.

[0046] As mentioned above, certain workpieces have high spatial frequency features that need to be preserved during the polishing process. These include Fresnel lenses, diffractive optical elements and semiconductor wafers. Traditional polishing tools run the risk of polishing away sharp edges in these cases, which is detrimental to the finished product. This problem is faced in both sub-aperture and full aperture settings.

[0047] Thus, a second aspect of the invention provides an abrasive tool comprising a support member including a connection mechanism for connection to a grinding machine, and an abrasive head at an end of the support member, the abrasive head comprising a base structure connected or integral with the support member, an outer shell at least a portion of which defines a working surface of the abrasive tool, the outer shell being fixed to the base structure and enclosing a cavity between the outer shell and the base structure, and a shear-thinning and / or stress-weakening viscoelastic material filling the cavity located between the outer shell and the base structure.

[0048] "Shear thinning and / or stress weakening" means that the viscoelastic material sealed in the cavity exhibits this type of behavior, as described above, at least over a range of shear / strain rates (or applied stresses), and preferably at all shear / strain rates (or applied stress levels). As already explained, this type of viscoelastic material thins or weakens with increasing shear / strain rates (or increasing stresses). This results in preserving sharp edges and other high frequency features of the workpiece surface during grinding. The grinding tool may be a sub-aperture grinding tool or a full-aperture grinding tool designed to grind the entire surface of the workpiece (or one or more workpieces) at the same time.

[0049] It should be noted that unlike the first aspect of the invention, it is not essential to provide a non-flat surface of the base structure. However, this may be included as an option, providing all of the same attendant advantages as described above, particularly in the case of sub-aperture tools. Such a non-flat surface may define a macro- and / or micro-structure having any of the preferred features already mentioned with respect to the first aspect. Alternatively, the non-flat surface may be configured to match the contour of the workpiece surface to be polished, particularly in the case of full-aperture polishing tools.

[0050] As in the first embodiment of the invention, the cavity enclosed by the outer shell and base structure is sealed, so that the shear thinning and / or stress weakening material that fills the cavity cannot leak out of the cavity and the volume inside the cavity remains constant during use.

[0051] The outer shell may be constructed in any of the ways already described with respect to the first aspect of this invention. Similarly, the working surface may have any of the shapes described with respect to the first aspect of this invention. The working surface may be flat or nearly flat when not pressed against the workpiece surface.

[0052] A second aspect of the invention further provides a polishing machine comprising the polishing tool of said second aspect, a workpiece holder for holding a workpiece in use, and a drive mechanism in mechanical communication with said connection mechanism, said drive mechanism configured to move the polishing tool relative to the workpiece in use while at least a portion of the working surface is in contact with a surface of the workpiece. The nature of said drive mechanism may depend on whether the machine is configured to perform sub-aperture polishing or full-aperture polishing. In a preferred embodiment, the drive mechanism is configured to rotate the polishing tool about a first axis of rotation passing through the tool.

[0053] Advantageously, the drive mechanism is further controllable to drive the movement of the tool relative to the surface of the workpiece such that said viscoelastic material exhibits shear thinning and / or stress weakening behavior. This may be necessary where a viscoelastic material is selected that exhibits shear thinning and / or stress weakening behavior at one range of shear / strain rates (or applied stresses) and not at another. This may for example involve controlling the rotational speed of the tool.

[0054] A second aspect of the invention further provides a method of polishing a workpiece, comprising: (a) providing an abrasive tool according to the second aspect; (b) positioning a working surface of the abrasive tool in contact with a surface of the workpiece; and (c) moving the working surface relative to the surface of the workpiece to polish the workpiece surface. In a preferred embodiment, the working surface is moved relative to the surface of the workpiece so as to preserve sharp edges of the workpiece surface, e.g., sharp peaks of a Fresnel lens or diffractive optical element, or sharp edges of a semiconductor wafer, while preferentially smoothing relatively flat areas. Movement of the tool relative to the working surface is preferably controlled (e.g., with respect to its speed) such that the viscoelastic material exhibits (if not always) shear thinning and / or stress weakening behavior.

[0055] In some preferred embodiments, the abrasive tool is a sub-aperture abrasive tool and the surface of the workpiece has a shape and / or surface texture that differs from that of the working surface of the sub-aperture abrasive tool, at least when the sub-aperture abrasive tool is not in contact with the surface of the workpiece.

[0056] Alternatively, the abrasive tool may be a full aperture abrasive tool, where the surface of the workpiece being abraded is substantially the same size as or smaller than the working surface of the abrasive tool. Full aperture tools can be used to abrade the entire workpiece surface simultaneously, or even multiple workpieces simultaneously.

[0057] A second aspect of the invention further provides an article polished by the above-mentioned method, said article being preferably any one of an optical element such as a lens or a prism, a diffractive optical element, a semiconductor wafer, a screen for an electronic device, a medical prosthetic device, or a mould.

[0058] Examples of abrasive tools, machines and methods according to the invention are described below with reference to the accompanying drawings and compared with the known art. [Brief description of the drawings]

[0059] [Figure 1] 1 illustrates an example of a sub-aperture polisher according to one embodiment of the present invention. [Diagram 2] 1 illustrates an example of a sub-aperture polisher according to one embodiment of the present invention. [Diagram 3] 1 illustrates an example of a sub-aperture polisher according to one embodiment of the present invention. [Figure 4] 1 illustrates an example of a sub-aperture polisher according to one embodiment of the present invention. [Figure 5(a)] 1A-1C show examples of sub-aperture polishing tools of various geometries according to embodiments of the present invention. [Figure 5(b)] 1A-1C show examples of sub-aperture polishing tools of various geometries according to embodiments of the present invention. [Figure 5(c)] 1A-1C show examples of sub-aperture polishing tools of various geometries according to embodiments of the present invention. [Figure 5(d)] 1A-1C show examples of sub-aperture polishing tools of various geometries according to embodiments of the present invention. [Figure 5(e)] 1A-1C show examples of sub-aperture polishing tools of various geometries according to embodiments of the present invention. [Figure 5(f)] 1A-1C show examples of sub-aperture polishing tools of various geometries according to embodiments of the present invention. [Figure 5(g)] 1A-1C show examples of sub-aperture polishing tools of various geometries according to embodiments of the present invention. [Figure 6(a)] 1 illustrates a further example of a sub-aperture polishing tool according to an embodiment of the present invention. [Figure 6(b)] 1 illustrates a further example of a sub-aperture polishing tool according to an embodiment of the present invention. [Figure 6(c)] 1 illustrates a further example of a sub-aperture polishing tool according to an embodiment of the present invention. [Figure 6(d)] 1 illustrates a further example of a sub-aperture polishing tool according to an embodiment of the present invention. [Figure 6(e)] 1 illustrates a further example of a sub-aperture polishing tool according to an embodiment of the present invention. [Figure 6(f)] 1 illustrates a further example of a sub-aperture polishing tool according to an embodiment of the present invention. [Figure 6(g)] 1 illustrates a further example of a sub-aperture polishing tool according to an embodiment of the present invention. [Figure 6(h)] 1 illustrates a further example of a sub-aperture polishing tool according to an embodiment of the present invention. [Figure 6(i)] 1 illustrates a further example of a sub-aperture polishing tool according to an embodiment of the present invention. [Figure 6(j)] 1 shows an example of a base structure suitable for use in some sub-aperture polishing tools according to an embodiment of the present invention. [Figure 7(a)] 1 shows an example of a sub-aperture abrasive tool according to the present invention in use to abrade a workpiece. [Figure 7(b)] 1 shows an example of a sub-aperture abrasive tool according to the present invention in use to abrade a workpiece. [Figure 7(c)] 1 shows an example of a sub-aperture abrasive tool according to the present invention in use to abrade a workpiece. [Figure 8(a)] 1 is a photograph showing a first exemplary sub-aperture abrasive tool according to the present invention. [Figure 8(b)] 8(b) is a photograph showing the internal structure of the sub-aperture polishing tool of FIG. 8(a). [Figure 9] 4(a), (b) and (c) are photographs showing a second exemplary abrasive tool according to the present invention. [Figure 10(a)] 1 illustrates a further example of a sub-aperture polishing tool according to an embodiment of the present invention. [Figure 10(b)] 1 illustrates a further example of a sub-aperture polishing tool according to an embodiment of the present invention. [Figure 11(a)] 1 illustrates generally the behavior of a shear-thickening and / or stress-stiffening viscoelastic material suitable for use in an embodiment of the present invention. [Figure 11(b)] 1 shows measured properties of an exemplary shear-thickening and / or stress-hardening viscoelastic material suitable for use in embodiments of this invention. [Figure 11(c)] 1 shows measured properties of an exemplary shear-thickening and / or stress-hardening viscoelastic material suitable for use in embodiments of this invention. [Figure 12(a)] 1 is a graph illustrating the behavior of three exemplary material compositions, one of which exhibits shear thickening and / or stress stiffening behavior. [Figure 12(b)]1 is a graph illustrating the behavior of an exemplary viscoelastic material suitable for use in embodiments of the present invention, which exhibits a shear thickening and / or stress hardening response under some conditions and a shear thinning and / or stress weakening response under other conditions. [Figure 13] (a) shows an example of sub-aperture polishing according to an embodiment of the present invention during polishing of an exemplary workpiece, (b) shows an enlarged detailed view of a workpiece that was over-polished using a conventional polishing tool, and (c) shows an enlarged detailed view of a workpiece polished using the polishing tool of Figure 13(a). [Figure 14] FIG. 1A shows a portion of one embodiment of a full aperture polishing device according to the present invention in use, and FIG. 1B shows a schematic cross-sectional view of the polishing head. [Figure 15] 15 is a graph showing material removal rate versus distance from the center of the workpiece for an exemplary polishing process of the type shown in FIG. 14 for two different polishing heads (a) and (b), where polishing head (a) is conventional and polishing head (b) is according to one embodiment of the present invention. EXAMPLES

[0060] 1-4 show an example of a sub-aperture grinding machine according to an embodiment of the present invention. The sub-aperture grinding machine includes a sturdy table 1 that is resistant to vibration. An X-slide mechanism 2 that moves in the x-direction is mounted on the table 1. A Y-slide mechanism 3 that moves in the y-direction is mounted on the X-slide mechanism 2. A turntable 4 that rotates around an axis indicated by the symbol C is mounted on the Y-slide mechanism 3. The turntable 4 is mounted on the Y-slide mechanism 3 via a Z-movement mechanism (not shown) that moves the turntable 4 in the z-direction. The turntable 4 has a workpiece holder on which a workpiece can be placed for polishing. This configuration provides four axial movements of the workpiece, namely linear movements in the x-, y- and z-directions, as well as rotation about the C-axis. Needless to say, in the illustrated configuration, the rotation axis C is parallel to the movement axis Z.

[0061] Also attached to the table 1 is a generally "L" shaped arm 6 having a generally horizontal base 6a and a generally vertical upright 6b. The arm 6 is attached to the table 1 at the end of the base 6a remote from the upright 6b and rotates about a vertical axis A. At the upper end of the upright 6b a tool holder 7 is attached to the upright such that it is rotatable about a horizontal axis B relative to the upright. A sub-aperture polishing tool 8 is attached to the tool holder 7 by its support member and rotates relative to the tool holder 7 about an axis of rotation H which is set at an angle to the axis B about which the tool holder 7 rotates relative to the upright 6b.

[0062] The sub-aperture polishing tool 8 of this example has a part-spherical working surface and is arranged such that the axes of rotation A, B and H coincide at the centre of the part-spherical surface. However, as noted above, sub-aperture polishing tools according to the invention may have a range of geometric shapes, some of which are not spherical or part-spherical, and some examples of sub-aperture polishing tools having such geometric shapes are provided below. The sub-aperture polishing tool 8 of this example could be substituted for any of the embodiments of sub-aperture polishing tools described in the examples below.

[0063] In this embodiment the sub-aperture grinding machine is configured such that rotation of the tool arm 6 about axis A rotates the part-spherical surface without translating the sub-aperture grinding tool and similarly rotation of the tool holder 7 about axis H does not translate the sub-aperture grinding tool but simply changes the plane of the precession angle between the tool rotation axis B and the tool holder axis H.

[0064] The movement of the workpiece in the x, y and z directions and the control of the rotation about the c-axis, as well as the control of the rotation of the tool arm 6, the tool holder 7 and the sub-aperture polishing tool 8 are affected by a drive mechanism including actuators and drives controlled by a processor unit 9 shown diagrammatically in Figure 4. The processor unit 9 may include input means 10 such as a keyboard and a port or disk drive for external input signals to receive process parameters and control commands for controlling the movements of the workpiece and the tool. A display means 11, e.g. a screen, can provide display information to the machine operator.

[0065] By controlling the movements of the workpiece and the tool, the sub-aperture polishing tool 8 can be positioned in contact with any part of the workpiece, and by controlling the rotation of the tool holder 7 about axis H, the direction of relative movement of the tool with respect to the workpiece in the area of ​​contact between the tool and the workpiece can be selected. Movement of the working surface of the sub-aperture polishing tool 8 across the workpiece surface within the area of ​​contact is controlled by varying the precession angle, which is the angle between the normal to the workpiece surface at the area of ​​contact and the axis about which the tool rotates. As described below, some sub-aperture polishing tools are constructed so that the thickness of the viscoelastic material at the point of the working surface in contact with the workpiece varies depending on the precession angle.

[0066] The sub-aperture polishing tool 8 has a deformable outer shell so that the contact area between the working surface of the sub-aperture polishing tool and the workpiece to be polished can be increased by pressing the sub-aperture polishing tool against the workpiece.

[0067] In a method according to an embodiment of the invention, a workpiece can be mounted in a workpiece holder of the polishing machine described above. The sub-aperture polishing tool 8 is rotated by the aperture and its working surface is brought into contact with the surface of the workpiece so as to move relative to the workpiece surface, thereby polishing the workpiece. Other machines that can be used with the polishing tools disclosed herein to perform polishing operations are disclosed in International Publication WO 00 / 32353 (Figures 1-3).

[0068] Examples of sub-aperture polishing tools according to embodiments of the present invention are described with reference to Figures 5(a)-6(j). The examples of Figures 5(a)-5(f) show a (non-exhaustive) selection of exemplary geometries in which sub-aperture polishing tools according to the present invention may be constructed, and Figures 6(a)-6(j) show various other features that may be present in tools according to preferred embodiments of the present invention.

[0069] It goes without saying that all of the exemplary tools are shown and described in their "rest" state, i.e., stationary and not in contact with anything else. In use, the shape of the tool will be different from the shape when the tool is at rest. In particular, when the tool is in contact with the workpiece surface, it will deform and locally adapt to the shape of the workpiece surface. The stretching of (for example) a spherical tool into an elliptical or annular shape can maximize the contact area between the tool and the workpiece in folded areas such as rounded edges, rolled edges of the workpiece surface, which is advantageous in smoothing the surface (indeed, contact area is a key factor in removing mid-to-high spatial frequencies, and increasing contact area results in faster smoothing). Furthermore, when the tool rotates at high speed, centrifugal forces can also change its shape. In many cases, the tool will generate forces that force the surface of the tool into the correct shape depending on its rotation speed. The viscoelastic material is preferably soft enough to shape the sack of the tool into a conformal shape. As described below, the tool is moved across features of the workpiece surface (e.g., gaps or sharp edges) to harden or soften the work surface (depending on the type of viscoelastic material used) and either remove or preserve those features.

[0070] FIG. 5(a) is a cross-sectional view of an exemplary sub-aperture polishing tool 501a according to one embodiment of the present invention. The tool 501a has a support member 503 suitable for connection to a polishing machine as shown in FIGS. 1-4 and a base structure comprising a cylindrical substrate 505 whose axis of rotation is aligned and oriented along the axis of rotation H and connected to (or integral with) an end of the support member 503. The support member 503 and base structure may generally be formed from a metal or alloy, such as stainless steel. In this example, the substrate 505 has a generally flat surface 505' opposite the support member 503. A hemispherical core 511a is fixed to the substrate 505 on the same side as the flat surface 505', the flat surface 505' and a surface of the solid core 511a together defining a non-flat surface. Alternatively, the core 511a may be formed integrally with the substrate 505, for example by machining its shape into the surface 505' or by casting the substrate 505 accordingly. The central portion of this non-planar surface is therefore hemispherical (due to the presence of hemispherical core 511a) and is surrounded by a flat ring-shaped peripheral region.

[0071] In combination, the surface of the hemispherical core 511a and the shape of the periphery of the flat surface 505' define a non-flat macro-structure, i.e. a variation over a distance of the same or similar order of magnitude relative to the dimensions of the sub-aperture polishing tool 501a as a whole. In particular, said macro-structure has a surface shape that varies in height in a similar order of magnitude as the surface shape of the outer shell 507'. The macro-structure in this example also has perfect rotational symmetry (like the outer shell 507) with respect to the axis of rotation H of the sub-aperture polishing tool. In some embodiments, the non-flat surface can also define a micro-structure, for example as a result of a texture formed on the surface of the flat surface 505' and / or the core 511a. The core 511a in this example is configured to be rigid during use and does not deform when subjected to stresses induced during use when the tool 501a is applied to a workpiece. In the simplest case, said core 511a can be a solid structure formed from a hard material such as a metal, a hard polymer or a ceramic. However, more complex structures may be used to form a core with the required stiffness, examples of which are given below.

[0072] The outer shell 507 is fixed to the substrate 505 at its periphery (preferably only at the periphery and along the entire periphery). In this example, the outer shell 507 is hemispherical in shape and is concentrically disposed about the hemispherical core 511a. The outer shell 507 comprises at least one layer of abrasive material (often referred to in the industry as a "polishing pad"), e.g., polyurethane, breathable fabric, tar-based viscoelastic polymer, or any other suitable compatible material, which forms a working surface 507' of the outer shell 507 suitable for polishing a workpiece during use. The abrasive material may or may not be porous. In some embodiments, the abrasive material may include abrasive particles or may be designed for use with an abrasive slurry.

[0073] As mentioned above, the "non-planar" surfaces of embodiments of the invention deviate from (i.e. are non-parallel to) the notional minimal surface bounded by the points where the outer shell is fixed to the base structure. In the example of Fig. 5(a), the points where the outer shell 507 is fixed to the substrate 505 (and in this example the notional minimal surface itself, since the periphery of the substrate 505 has the form of a ring that lies in this plane) lie in a planar plane parallel to the line A-A' and perpendicular to the axis of rotation H. The non-planar surface of the base structure deviates from this minimal surface due to the presence of the core 511a.

[0074] The outer shell 507 and the non-flat surfaces formed by the core 511a and the substrate 505 together enclose a sealed cavity which is filled with a (non-Newtonian) viscoelastic material 509. In this example, the cavity is shaped such that the viscoelastic material forms a layer having the same thickness between the core 511a and the outer shell 507 at all positions on the working surface 507' (as a result of the shape and configuration of the core 511a, the substrate 505 and the outer shell 507). Here, the "thickness" of the layer means the distance between the surface of the outer shell 507 and the core 511a along a direction perpendicular to the working surface 507' at that position. As a result of this configuration, when the tool 501a rotates about the rotation axis H during use and is applied to a workpiece, its behavior (response) is substantially the same regardless of which part of the working surface 507' is in contact with the workpiece surface. Viscoelastic materials 509 suitable for use in this tool 501a exhibit behaviors that fall into two general categories: (i) shear-thickening and / or stress-stiffening, (ii) shear-thinning and / or stress-weakening. Viscoelastic materials exhibiting the first category of response would be selected for applications where the workpiece contains relatively high frequency features that need to be polished, and viscoelastic materials exhibiting the second category of response would be selected where relatively high frequency features on the workpiece (e.g., sharp edges) need to be retained. As noted above, some viscoelastic materials can exhibit behaviors in both categories at different ranges of applied shear / strain rates (or applied stresses), an example of which is described below. When this type of material is selected, the type of behavior it exhibits can be controlled through changes in the motion parameters of the tool relative to the workpiece (e.g., its rotational speed).

[0075] As described above, the cavity enclosed by the outer shell 507 and base structure is sealed. To produce the tool, the viscoelastic material 509 can be introduced through a conduit in the base structure (e.g., through the substrate 505) that is substantially closed, for example, by the insertion of a pin or screw, after which the cavity is sealed.

[0076] Exemplary viscoelastic materials include pitch, non-Newtonian fluids, polymers, silicon polymers, starches, clays, metamaterials, suspensions of particles in a solvent, or any combination thereof (e.g., in a homogeneous mixture). A preferred example of a shear-thickening and / or stress-stiffening viscoelastic material includes at least polydimethylsiloxane (PDMS). For example, the material may be a suspension of dimethylsiloxane, silicon dioxide, castor oil, and polydimethylsiloxane. Preferred examples of shear-thinning and / or stress-weakening viscoelastic materials include soap, toothpaste, shampoo compositions, mixtures of cornstarch and water, and mixtures of particulates (e.g., talc) and solvents. For example, some paints exhibit a shear-thinning response if their constituent particles are small enough (e.g., 5 micron particles). One example of a suitable commercial product is Carbopol 940 Gel (available from Lubrizol Corporation, Ohio, USA), which contains carbomer and carboxypolymethylene. Further details of suitable viscoelastic materials 509 are provided below.

[0077] Optionally, the outer shell 507 may include a layer of elastic material such as rubber, silicone, neoprene or another polymeric elastomer, in which case the layer of abrasive material is disposed on the outside of this elastic layer. The provision of an elastic layer may provide several advantages. Firstly, the elastic layer may help restore the shape of the outer shell 507 after it has been deformed in the course of abrading the workpiece. The elastic layer may also help retain the viscoelastic material 509 and prevent leakage, which is advantageous when the abrasive material forming the working surface 507' is porous. The outer shell may optionally have an additional layer of material such as pitch applied to its outer surface as required.

[0078] The outer shell 507 can be secured to the base structure in a variety of ways. For example, the outer shell can be adhered or clamped around the periphery of the substrate 505. Alternatively, the outer shell 507 can fit around a portion of the substrate 505 and be held by its own elasticity and / or can be heat shrunk onto the base structure.

[0079] The tools can be manufactured in any size to suit the workpiece to be polished. For example, the diameter of the outer shell may range from 0.5 mm to 1 m, preferably 0.5 mm to 0.5 m, more preferably 0.5 mm to 200 mm, most preferably 0.5 to 5 mm. A range of polishing tools with different dimensions and / or shapes can make them available for polishing different workpieces, or different parts of one workpiece. Preferably, the minimum curvature of the tool is selected to allow free contact with all possible positions on the workpiece surface (e.g., convex and concave surfaces of curved smartphone or smartwatch screens, sunglasses, etc.). The same dimensional requirements apply to all embodiments disclosed herein.

[0080] FIG. 5(b) shows a second example of a sub-aperture polishing tool 501b according to the invention. This tool 501b has a support member 503, a substrate 505 and a hemispherical outer shell 507 similar to the tool 501a of FIG. 5(a). However, in this example, the tool 501b has a core 511b that is aspherical, e.g., has the shape of a portion of a prolate spheroid (i.e., a sphere elongated along the direction of the rotation axis H) and has an elliptical cross section. Since the shape of this core 511b does not match the shape of the hemispherical outer shell 507, the cavity between the non-flat surface of the base structure (formed by the flat surface 505' of the substrate 505 and the surface of the core 511b) and the outer shell is shaped such that the thickness of the viscoelastic material varies between positions on the working surface 507'. For example, said thickness is smallest at a point L1 on the working surface 507' corresponding to the "tip" of the tool 501b. The thinner the viscoelastic layer, the more resistant the machined surface tends to be to deformation at a given shear rate. This is useful because it allows the abrasive behavior (response) of the tool to be altered depending on the orientation in which the tool is applied to the workpiece.

[0081] Thus, for example, in a tool designed to remove mid-space defects (wherein the viscoelastic material 509 would be selected to exhibit shear-thickening and / or stress-hardening viscoelastic properties), the portion of the machining surface 507' where the viscoelastic material layer is thinner is suitable for removing mid-space defects of smaller spatial frequencies. For the same reason, the portion where the viscoelastic material layer is thinner (e.g., point L2) is optimal for removing mid-space defects of relatively larger spatial frequencies. In this example, since the core 511b and the outer shell 507 have perfect rotational symmetry about the rotation axis H, the thickness of the viscoelastic material layer at the point where the machining surface 507' contacts the workpiece surface can be controlled by simply changing the angle between the rotation axis H and the portion of the workpiece surface to which the tool 501b is applied, as will be demonstrated below. Thus, the tool 501b in this example is suitable for polishing workpieces known or believed to contain mid-space defects of different spatial frequencies. In contrast, the sub-aperture polishing tool 501a of FIG. 5(a) behaves similarly regardless of which portion of its machining surface 507' is in contact with the workpiece surface, and is therefore suitable for polishing workpieces (or portions of workpieces) having complex geometries, including intermediate spatial defects whose spatial frequencies do not change significantly (even if they also contain shear-thickening and / or stress-hardening viscoelastic materials 509).

[0082] To illustrate the difference in functionality between the sub-aperture polishing tools of Figures 5(a) and 5(b), Figure 7(a) shows the sub-aperture polishing tool 501a of Figure 5(a) in use at two different locations on a curved surface of a workpiece 701. The workpiece surface 701' has a "wavy" shape due to the presence of meso-spatial defects thereon (it should be understood that the drawings are not to scale and the meso-spatial defects are generally shown much larger than they are in reality for clarity). In both the first location C1 and the second location C2, the thickness of the viscoelastic material layer between the part of the processing surface 507' in contact with the workpiece 701 and the core 511a is the same. Figure 7(b) shows the sub-aperture polishing tool 501b of Figure 5(b) applied at two different locations on a different workpiece surface 703'. At a first location C3 on this surface 703', meso-spatial defects with a first spatial period P1 are present. The tool 501b is applied to the surface in a first position C3 at an oblique angle to the plane of the surface 703', since the parts of the tool 501b with a thicker viscoelastic layer are optimal for removing mid-spatial defects with a larger spatial period (and therefore a smaller spatial frequency). At a second position C4 on the same surface 703', the mid-spatial defects present have a smaller spatial period P2 less than P1, and the tool 501b is applied with its axis of rotation H substantially perpendicular to the surface 703'. Thus, at the second position C4, the thickness of the viscoelastic layer between the tool 501b and the parts of the work surface 701' in contact with the workpiece surface 703' of the workpiece is reduced compared to the first position C3, removing the high frequency mid-spatial defects in the most efficient possible way.

[0083] Returning to the example of tool geometry, FIG. 5(c) illustrates a third exemplary sub-aperture polishing tool 501c according to an embodiment of the present invention. Again, this tool 501c has the same support member 503 and outer shell 507 as the previous example, but in this case, the tool 501c has a base structure 513 shaped to define a concave surface 513' (herein the shape of an inverted cone). Whereas in the previous example, the non-flat surface of the base structure is non-flat due to the presence of a core, in this case, the non-flat surface is provided solely by the concave surface 513', and the macrostructure of the non-flat surface is correspondingly concave. Due to the concave shape of the non-flat surface 513', the thickness of the viscoelastic material between the working surface 507' and the base structure varies less between positions on the working surface 507' than if the same surface were flat. This ensures that the behavior of the tool 501c is relatively uniform regardless of the angle at which the tool is applied to the workpiece being polished. However, as discussed above, some variation in behavior may be desirable for dealing with mid-spatial imperfections (or other features) of different frequencies, and the exact shape of convex surface 513' may be selected to allow for some variation.

[0084] Figure 5(d) shows a fourth exemplary sub-aperture polishing tool 501d according to an embodiment of the present invention. This tool 501d is similar to that of Figure 5(a), but in this case the core 515 is shaped with a cylindrical portion 515a extending from the substrate 517 along the direction of the rotation axis H and a hemispherical portion 515b forming the end of the core 515 distal to the substrate 517. The core 519 is fixed to a flat substrate 521, which together with the core 519 defines a non-flat surface formed by a surface of the core 519 and a ring-shaped portion around a surface 521' of the substrate 521.

[0085] The shape of the outer shell 519 matches the shape of the core 515, so that the thickness of the viscoelastic material 509 between the outer shell 519 and the core 515 is constant, and the working surface 519' has a cylindrical region 519'a adjacent to the substrate 517 and a domed region 519'b forming the tip of the tool 501d. This type of tool (whose working surface 519' has differently shaped regions) is suitable for polishing differently shaped portions of the surface of a workpiece. For example, the cylindrical region 519'a is suitable for polishing convex features, while the domed region 519'b can reach concave regions with a larger radius of curvature than the domed region 519'b.

[0086] FIG. 5(e) illustrates a fifth exemplary sub-aperture polishing tool 501e according to an embodiment of the present invention. The tool 501e has a support member 503 and a substrate 527 connected to each other. A core 523 is connected to the substrate 527 on the opposite side from the support member 503, the core 523 having the form of a truncated cone whose axis of rotation is aligned with the axis of rotation H of the tool. An outer shell 525 (which may be formed from the same material used to form the outer shell described above) is secured to the substrate 527 about its periphery and extends circumferentially around the core 523. As in the previous example, the portion of the outer shell 525 extending circumferentially around the core 523 forms a working surface 525' suitable for polishing a workpiece during use as the tool 501e rotates about the axis of rotation H. End 525" of the outer shell is not part of the machining surface in this embodiment, but also extends across the tip of tool 501e and contacts the narrower end of core 523 (i.e. the end distal to substrate 527). Core 523 thus extends continuously from substrate 527 to end 525" of outer shell 525. Where core 523 contacts the outer shell, the outer shell remains rigid and can be used to probe the workpiece if desired, as will be further explained in relation to FIG. 10(b) below. In this embodiment, outer shell 525 is shaped such that the thickness of the viscoelastic material in the cavity (measured along a direction perpendicular to machining surface 525' at that location) is greatest where outer shell 525 contacts substrate 527 and decreases with distance from substrate 527.

[0087] FIG. 5(f) is a cross-sectional view of a sixth exemplary sub-aperture polishing tool 501f according to an embodiment of the present invention. As in the previous examples, the tool has a support member 503 for connection to a polishing machine and is configured to rotate about a rotation axis H in use. A base structure 531 is attached to the support member 503. The base structure 531 is perfectly rotationally symmetric about the rotation axis H. By means of its central portion 533, the base structure 531 is attached to the support member 503. The central portion 533 has the shape of a disk of approximately constant thickness. Surrounding the central portion 533 is an intermediate portion 535, which tapers along a radial direction perpendicular to the rotation axis H. An outer portion 537 of the base structure 531 is curved relative to a circumferential direction extending around the rotation axis H and has a semi-elliptical cross section.

[0088] The outer shell 541 is fixed to the tapered surface of the intermediate portion 535 and extends completely around the circumference of the base structure 531. As a result, the outer shell 541 defines an annular machined surface 541' with perfect rotational symmetry about the axis of rotation H. In this case, the outer portion 537 and the part of the intermediate portion 535 surrounded by the cavity formed by the outer shell 541 form a non-flat surface, the macrostructure of which is defined by the tapered surface of the intermediate portion 535 and the curved surface of the outer portion 537.

[0089] As noted above, the "non-planar" surfaces of embodiments of the invention deviate from (i.e., are non-parallel to) the notional minimal surface bounded by the points where the outer shell is secured to the base structure. In the example of Fig. 5(f), the outer shell is secured to the base structure along two annular lines, each extending circumferentially around the axis of rotation H. The notional minimal surface is the cylindrical surface connecting these two lines (line B-B' lies in the notional minimal surface), and the actual non-planar surface formed by outer portion 537 and middle portion 535 deviates from this notional minimal surface since it protrudes radially from this surface.

[0090] As with all polishing tool embodiments described herein, the non-planar surface of the tool of FIG. 5(f) may have a microstructure defining a surface texture configured to grip the viscoelastic material in the cavity as the sub-aperture polishing tool rotates during use. Examples of surface microstructures are described below with reference to FIGS. 6(a)-6(c). FIG. 5(g) shows a seventh example sub-aperture polishing tool 501g according to an embodiment of the invention. The tool 501g includes a support member 503, a substrate 505, an outer shell 507 and a viscoelastic material similar to the example shown in FIG. 5(a). However, in this case there is no core on the generally planar surface 505' of the substrate. Instead, the base structure includes an array of protruding surface elements 551 disposed on the planar surface 505' of the substrate 505. The surface elements 551 may be integral with the substrate 505 or may be formed separately and glued or otherwise secured to the planar surface 505'. The surface elements 551 together with the planar surface 505 ′ of the substrate define a non-planar surface (non-planar due to the protruding surface elements 551 ) having a microstructure corresponding to the texture formed by the surface elements 551 .

[0091] This texture defines a "microstructure" in the sense defined above, which renders the surface of the base structure in contact with the viscoelastic material uneven, but does not cause a significant change in the thickness of the viscoelastic material layer between the outer shell and the uneven surface of the base structure. The surface elements protrude towards the viscoelastic material in the cavity enclosed by the outer shell 507 and have the effect of engaging the viscoelastic material as the tool 501g rotates about the axis of rotation H, thus aiding in the transmission of torque from the rotating tool to the viscoelastic material in the cavity. Here, the surface elements 551 are shown as protruding relative to the flat surface 505', however, alternatively or in addition, there may be indentations in the flat surface 505' which contribute to the uneven character of the surface in contact with the viscoelastic material. The microstructure may be integrally formed with the base structure 505 (e.g. machined or molded into the surface 505') or may comprise a material fixed to the surface 505'. Such a material may be a compliant or non-compliant material. For example, separate portions of material may be locally adhered to surface 505' and separated from one another as needed to form the desired surface texture.

[0092] The protrusions 551 may themselves be formed from a viscoelastic material, if desired, provided that they remain in place and do not significantly change their shape or frictional properties during use. The protrusions 551 may alternatively be formed from an elastic material such as rubber and bonded onto the base structure using an adhesive. In the preferred case, the protrusions 551 are at least as strong as the remaining material (e.g. steel) that forms the non-planar surface. For example, the protrusions (or recesses) may be machined directly into the surface 505' of the base structure 505. Thus, the microstructure may be formed by additive and / or subtractive manufacturing techniques.

[0093] The microstructure features may have an amplitude (i.e., peak-valley height) in the range of 0.1 mm to 10 mm, or larger for larger tools. The amplitude may be smaller in relation to the thickness of the viscoelastic material filling the cavity. The protrusions may have any shape, e.g., cylindrical protrusions or elongated grooves, and may be arranged in one or two dimensional pseudorandom or regular patterns, e.g., line grids, hexagonal arrangements, concentric circles, etc. The lateral size (e.g., line width or diameter) of each protrusion is preferably in the range of 0.1 mm to 10 mm, although again it may be larger for larger tools. The average center-to-center spacing (or periodicity, if arranged in a regular array) may be between 0.1 mm to 10 mm, or larger for larger tools. If the surface texture consists of indentations formed in the base structure, all of these dimensional requirements apply equally to the indentations.

[0094] FIG. 7(c) shows cross-sectional views of the sub-aperture polishing tools of FIG. 5(d), FIG. 5(e) and FIG. 5(f) being used to polish various features on the surface of a free-form workpiece 711. In general terms, the sub-aperture polishing tools disclosed herein are particularly well suited to polishing complex free-form surfaces that can suddenly change curvature and / or reverse themselves (saddle points), such as knee prostheses or molded inserts for eyeglasses. For example, the part-spherical machining surface of tool 501d of FIG. 5(d) is well suited to polish features with relatively low curvature, while annular tool 501f of FIG. 5(f) is well suited to polish highly curved and hard-to-reach areas. For straight inclined surfaces, conical tool 501e of FIG. 5(e) is particularly suited to polish features that are flat or curved in a single direction (e.g., ridges with a topology of a part of a cylinder).

[0095] Having described a range of examples of geometries suitable for constructing subaperture abrasive tools according to the present invention, examples of possible variations and specific implementations of features of subaperture abrasive tools according to preferred embodiments of the present invention are now provided below with reference to Figures 6(a)-6(j). It should be understood that any of these preferred features apply to tools of any shape (and / or having any form of macrostructure), including all of the options shown in Figures 5(a)-5(g), but for simplicity will be described with reference to hemispherical tools only.

[0096] As mentioned above, the non-flat surface formed by the base structure can define one or both of the macrostructures and the microstructures. Now, in Figures 6(a), 6(b) and 6(c) there is shown a modification of the sub-aperture polishing tool of Figures 5(a), 5(b) and 5(c) respectively, in each case with surface elements 651 of the kind described above, configured to form a microstructure on the macrostructure of the respective base structure. These have the same advantage as the embodiment of Figure 5(g), namely that they engage with the viscoelastic material, thereby aiding in the transmission of torque to the viscoelastic material as the tool rotates. In the illustrated example, the microstructures extend over the entire macrostructure, but this is not necessary and the microstructures may be provided on only a part of it.

[0097] Figures 6(d) and 6(e) show an example of a sub-aperture polishing tool 601d with a core of preferred shape. In this example, the tool 601d includes a piston 611 that is movable along the direction of the rotation axis H. The piston 611 has a shaft 612 that extends through a hole in the support member 613 and has a head 611' that occupies a correspondingly shaped recess in the substrate 605. The head 611' and the peripheral surface 605' of the substrate together define a non-planar surface (stepped in this example), and the outer shell 507 is fixed to the periphery of the substrate 605. As the piston moves towards the outer shell 507, the shape of the non-planar surface and the shape of the cavity between the non-planar surface and the outer shell 507 change. This causes the working surface 507' to also change shape, modifying the behavior of the tool in response to shear when applied to the workpiece in use. Thus, the position of the piston 611 can be selected during use to modify the behavior of the tool, for example to better accommodate differently shaped areas of the workpiece and / or to optimally remove mid-spatial defects of different spatial frequencies. Movement of the piston 611 can be actuated, for example, by a hydraulic mechanism configured to transmit a force to the piston shaft 612.

[0098] 6(f) and 6(g) show a further exemplary sub-aperture polishing tool 601f having a core whose rigidity during use is provided by a fluid. The tool 601f has a support member 625 attached to a substrate 621, which is similar in construction to those previously described. However, in this example, a conduit 625 extends through the support member 625 and the substrate 621 and connects to the interior of an expanding bladder 627 which is fixed to a flat surface 621' of the substrate 621. During use, as shown in FIG. 6(g), the bladder can be filled with a fluid 629, which causes the bladder to expand and become rigid. The bladder will then act as a rigid core in the same manner as the core previously described, for example, shown in FIG. 5(a). The fluid is introduced through the conduit 625 from, for example, a tank constituting the polishing machine in which the tool 601f is used. The expansion of the bladder 627 causes it to expand or change shape, which causes a corresponding change in shape of the viscoelastic layer 509 and the outer shell 507. Suitable fluids for this purpose include liquids, such as water or oil, and gases, such as air.

[0099] As explained above, the outer shell of the polishing tool in some embodiments can be simply formed by a layer of abrasive material, e.g., polyurethane, breathable cloth, tar-based viscoelastic polymer, or any combination thereof ("polishing pad"). Figure 6(h) shows a sub-aperture polishing tool 601h according to an embodiment of the invention, whose structure corresponds to that of Figure 5(a), where the outer shell 647 is formed only by a layer of abrasive material fixed to the substrate 505 at its periphery. It has been found that this type of embodiment, where the layer of abrasive material is in direct contact with the viscoelastic material, gives good results, since the material behavior is transferred to the workpiece surface with little or no modification. This works particularly well for tools of relatively small size (e.g., radius of 5 mm or less) and / or where the viscoelastic material is hard or very viscous and cannot leak through the abrasive material.

[0100] FIG. 6(i) shows another sub-aperture polishing tool 601i based on that of FIG. 5(a), also according to an embodiment of the invention, but with an outer shell 657 including an elastic layer 659, which gives the outer shell 657 its hemispherical shape and is fixed around the periphery of the substrate 505. The area of ​​the outer shell opposite the substrate 505 is covered by a layer of abrasive material 671, which does not extend over the entire area of ​​the outer shell 657. In this embodiment, the abrasive material defines a working surface 671' of the tool 601i, where the working surface 671' has an overall smaller area than the outer shell 657. The provision of the elastic layer 659 has been found to be particularly beneficial in medium to large polishing tools, for example polishing tools having a radius larger than 5 mm. The elastic layer helps the tool to retain the desired shape and helps to prevent leakage of the viscoelastic material. The elastic layer preferably has a thickness in the range of 0.1 to 5 mm, depending on the size of the tool. The elastic layer 659 may be formed, for example, from nitrile rubber, silicone rubber, polyethylene, or any other impermeable sheet material.

[0101] Figure 6(j) shows an example of a base structure 564 suitable for incorporation into a sub-aperture tool according to some embodiments of the invention. The base structure 564 is fixed to a support member 563 of the type previously described. In a tool incorporating this base structure 564, an outer shell (not shown) in the shape of a ring would be fixed to edges 567, 568 of the base structure 564 such that the surface 564' of the base structure and the outer shell together extend circumferentially around the base structure 564 and enclose an annular cavity which is filled with a viscoelastic material.

[0102] In use, a tool incorporating this base structure rotates about a rotation axis H. The geometry of this base structure 564 is similar to that of the tool shown in FIG. 5(f) in that the base structure 564 has the general shape of a disk that is rotationally symmetric about the axis H, but in this case the surface 564' surrounding the cavity generally corresponds to a minimal surface bounded by the edges 567, 568 of this surface. However, in this example there are fins 565 periodically arranged around the periphery of the surface 564', which becomes internal to the cavity when the outer shell is fixed to the base structure 564. Due to the presence of the fins 565, the surface of the base structure surrounding the cavity is non-flat (as these fins 565 deviate from the minimal surface bounded by the edges 567, 568 of the base structure). As the tool rotates in use, the fins 565 engage with the viscoelastic material inside the cavity and aid in the rotation of the viscoelastic material inside the cavity. Of course, such fins, or other protrusions, may also be provided on a macrostructure, such as that formed by surfaces 535 and 537 in the embodiment of Figure 5(f), to further enhance the interaction between the underlying structure and the viscoelastic material.

[0103] FIG. 8(a) is a photograph of a first sample sub-aperture polishing tool 801 manufactured in accordance with one embodiment of the present invention. FIG. 8(b) shows the same tool 801 in a partially disassembled state, with a portion of its outer shell 807 cut away to reveal the internal structure. The tool 801 has an elongated support member 803 configured for attachment to a polishing machine, for example one of the types shown in FIGS. 1-4. A base structure 805 is attached to (and in this example is integral with) the support member 803. The base structure has a generally cylindrical shape, with the support member 803 and the distal end being a generally planar surface 805' on which are disposed a plurality of protruding surface elements (not visible) of the type previously described. Due to the presence of said surface elements, this end of the support structure forms a non-planar surface in which a microstructure is defined by the arrangement of the surface elements. As with the example shown in FIG. 5(g), there is no macrostructure in this embodiment.

[0104] The outer shell 807 is arranged to enclose a hemispherical cavity bounded by the non-flat surface of the base structure 805 and filled with a viscoelastic material 809, which in this embodiment is pitch. The outer shell 807 includes an elastic layer 815 which extends along the length of the base structure 805 and is held in place by its own elasticity (optionally a clamp may be provided, not shown). At the end of the elastic layer 815 is a part-spherical cap 813 of an abrasive material, here polyurethane, which forms part of the outer shell 807 distal to the support member 803. The abrasive material 813 defines a working surface of the tool 801 which is arranged to rotate about a rotation axis H in use.

[0105] Figures 9(a)-9(c) are photographs illustrating a second sample sub-aperture polishing tool 901 manufactured in accordance with one embodiment of the present invention. Figure 9(a) shows the tool 901 in an assembled state, while Figures 9(b) and 9(c) show the tool components disassembled to reveal features of its construction.

[0106] The tool 901 has a support member 903 to which a base structure 905 is attached. The base structure in this embodiment is shaped to define a stepped profile non-flat surface 905' and is perfectly rotationally symmetrical about the axis of rotation H of the tool 901. The stepped profile defines a protruding annular region 905'a and a higher circular central mesa 905'b. The tool 901 also includes an outer shell 907 which is disposed at the end of the base structure 905 and which, when the tool 901 is assembled, encloses a cavity on one side of which the non-flat surface 905' is disposed. The outer shell has a rigid ring 917 at its base which, when the tool 901 is assembled, is disposed in contact with the non-flat surface 905'. Attached to the ring 917 is an elastic layer 915 which encloses a cavity which is filled with a shear thickening putty 909 (a viscoelastic material in this embodiment). The resilient layer has a domed end on which a polishing pad 913 made of an abrasive material (polyurethane in this example) is disposed to form the working surface 907' of the tool 901. The base structure 905 has a threaded end 921 (visible in FIG. 9(c)) on which a collar 919 having a correspondingly threaded inner surface is screwed to complete the assembly of the tool 901. The collar 919 is shaped with an opening through which emerges a portion of the outer shell 907 carrying the polishing pad 913 which makes the working surface available for polishing. The diameter of the opening is smaller than the diameter of the ring 917 and holds the outer shell 907 in place when the tool is in the assembled state, as shown in FIG. 9(a).

[0107] When assembled, the annular region 905'a and the circular mesa 905'b are in contact with the shear thickening putty 909. The circular mesa 905'b defines a substantially cylindrical core and thus a non-planar macrostructure with the attendant advantages discussed above.

[0108] Figures 10(a) and 10(b) show two further embodiments of an abrasive tool. In both cases only the abrasive head is shown, which is in fact fixed at the end of a support member as described above. The embodiment of Figure 10(a) shows an abrasive tool 941, in which a base structure 945 is in the form of an annular ring 945a, in which a core 945b is fixed, for example by a screw fastening. Both the ring 945a and the core 945b may be made of a hard material such as steel (or another metal or alloy). The core 945b comprises a curved convex surface 945', which defines the macrostructure described above. Said curved surface 945' may for example be a part-spherical surface, which is rotationally symmetrical with respect to the axis of the tool 941. An outer shell 947 is fixed to the ring 945a around the base structure 945. The outer shell 947 defines the working surface of the tool and may comprise an abrasive material or may include an elastic layer as described above. In the latter case, the textured surface should not extend over the entirety of the outer shell 947. Between the outer shell 947 and the non-flat surface 945' of the base structure defined by the core 945b there is a cavity which is filled with a viscoelastic material 949. In this embodiment, the shape of the macrostructure 945' substantially matches the shape of the outer shell 947, and the thickness (amount) of material 949 between the two components is substantially the same at all points on the textured surface. This has the advantages described for Figure 7(a) above.

[0109] The structure of the polishing tool 961 shown in Fig. 10(b) is similar to that of Fig. 10(a), i.e. the viscoelastic material 969 is located in a cavity formed between the outer shell 967 and the non-flat macrostructure 965' defined by the core 965b of the base structure 965. However, in this embodiment the non-flat surface 965' is more complex and includes an extension 965" in the centre of the tool that contacts the outer shell 967. The cavity containing the material 969 is therefore annular and there is no viscoelastic material 969 between the outer shell 967 and the extension 965". This configuration is advantageous as it allows the tool 961 to be additionally utilized as a probe, i.e. it can be used to measure the shape of the workpiece either before, during or after the polishing operation. This is achieved by positioning the portion of the outer shell that aligns with extension 965" into contact with the workpiece, sensing when contact occurs and using a CNC machine (or equivalent) carrying tool 961 to verify the exact location of the contact point. The stiffness of the tool at this point imparted by extension 965" in contact with the outer shell ensures accuracy of the measurement. Typically, the grinding operation is performed with the tool in an orientation selected so that contact between the workpiece and tool is away from extension 965".

[0110] FIG. 11(a) shows diagrammatically the behavior of the viscoelastic material of the abrasive tool for a point on the machining surface traversing the surface of the workpiece 1001 in a direction M substantially parallel to the plane of the machining surface. In reality, this relative motion is due to the rotation of the tool, so that each point on the surface follows a straight or curved path depending on the inclination of the tool. However, for simplicity of illustration, a straight path is considered here. As can be seen in FIG. 10, the surface of the workpiece 1001 has a "wavy" profile due to the presence of a mesospace defect, which can be captured by the grinding process as described above. The outer shell 1007 of the tool can simply be formed by a layer of abrasive material or some other more complex structure as described above, which fits and matches the shape of the defect on the surface of the workpiece 1001. As the working surface 1007' of the tool moves along the movement direction M, each portion of the viscoelastic material close to the inner surface 1007" of the outer shell periodically compresses (when located at a "peak" of the surface profile, e.g. at position M1) and expands (when located at a "valley" of the surface profile, e.g. at position M2), as shown diagrammatically by a spring in the drawing. That is to say, each position on the surface of the viscoelastic material 1009 periodically deforms with a frequency f corresponding to the speed VM at which the working surface 1007' moves relative to the surface of the workpiece 1001, as distinguished by the spatial periodicity P of the defects. Importantly, this frequency is directly dependent on the rotational speed of the sub-aperture polishing tool.

[0111] The response of the viscoelastic material 1009 to the frequency of deformation depends on the nature of the viscoelastic material, and whether it exhibits shear thickening or shear thinning behavior, particularly in the frequency range of interest. If the viscoelastic material 1009 is a shear thickening and / or stress hardening material under operating conditions in use, it will harden as the frequency increases, meaning that small features on the workpiece surface (such as mesospace defects) will be preferentially polished away. In contrast, if the viscoelastic material 1009 is a shear thinning and / or stress weakening material under operating conditions in use, it will soften as the frequency increases, meaning that small features (such as sharp edges) will be preferentially retained.

[0112] Viscoelastic materials simultaneously exhibit both viscous and elastic behaviours. Due to the elastic component of the material's behaviour, energy is stored in the material when it is deformed cyclically (for example as shown in Figure 11(a)), and is represented by a parameter called the shear storage modulus G', measured in units of Pascals (Pa). Similarly, due to the viscous side of its behaviour, the material dissipates energy when it is deformed, and this is represented by the shear loss modulus G'', also measured in units of Pa. Each of G' and G'' can vary according to the frequency of the cyclic deformation the material undergoes. When the value of G' is greater than the value of G'', the elastic component of the material's behaviour dominates (similarly, when G'' exceeds G', the viscous behaviour dominates). The frequency at which G' and G" are equal for a given material is called the viscoelastic transition. (It is noted that some materials have more than one viscoelastic transition point.) The frequency at which the viscoelastic transition occurs is relevant to this discussion because the behavior of a material can be characterized as hardening where elastic behavior dominates, and therefore the rotational speed of a sub-aperture polishing tool can be controlled to ensure that a shear-thickening and / or stress-hardening viscoelastic material behaves stiffly enough to remove mid-spatial defects of a given spatial frequency, or conversely, in a tool containing a shear-thinning and / or stress-weakening viscoelastic material, it can be made thin enough to ensure that features of a given spatial frequency are preserved.

[0113] Measured values ​​of G' and G" over a range of deformation frequencies for two samples of shear-thickening and / or stress-hardening viscoelastic materials are shown in Figure 11(b). The horizontal axis represents deformation frequency in Hertz (Hz) and the vertical axis represents the shear storage and shear loss moduli in Pa. For the first sample, designated "Sample C," the measured shear storage modulus G' is plotted as diamonds with line 1101a and the measured shear loss modulus G" is plotted as crosses with line 1101b. It can be seen that at lower frequencies (left hand side of the graph), G" is significantly greater than G'. As the frequency approaches approximately 2 Hz, both G' and G" increase, but the rate of increase of G" begins to slow down. At 2.516 Hz the elastic moduli become equal and at higher frequencies G' exceeds G". Thus, Sample C has its viscoelastic transition point at approximately 2.516 Hz. Figure 11(b) also shows the measured G' and G" for a second sample, "Sample D". The measured G' for Sample D is plotted as a diamond with line 1103a and the measured G" is plotted as a cross with line 1103b. It can be seen that Sample D has a viscoelastic transition point 1005b at a slightly higher frequency than that of the orange sample.

[0114] FIG. 11(c) shows the measured shear loss and shear storage moduli for two further samples, "Sample A" and "Sample B". For Sample A, G' is plotted by diamonds with line 1111a and G" is plotted by crosses with line 1111b. For Sample B, G' is plotted by diamonds with line 1113a and G" is depicted by crosses with line 1113b. Sample B has a viscoelastic transition point 1115a at a frequency of about 3.981 Hz, while Sample A has a viscoelastic transition point at a similar but slightly higher frequency.

[0115] All of the aforementioned sample materials are suitable for use as shear-thickening and / or stress-stiffening viscoelastic materials in embodiments of the present invention. Each material is comprised of a suspension of primarily dimethylsiloxane, silicon dioxide, castor oil, and / or polydimethylsiloxane. The proportions can be varied to modify the properties as shown in the graph of FIG. 11. One exemplary composition is 65% dimethylsiloxane (a hydroxy-terminated polymer with boric acid), 17% silica (crystalline quartz), 9% Thixatrol ST (a castor oil derivative), 4% polydimethylsiloxane, 1% decamethylcyclopentasiloxane, 1% glycerin, and 1% titanium dioxide. Another suitable exemplary material is comprised of cornstarch (corn flour) mixed with water in various proportions.

[0116] More generally, suitable shear-thickening and / or stress-stiffening viscoelastic materials for use in embodiments of the present invention include dilatants (shear-thickening fluids) and pentamodal metamaterials (metafluids). Dilatant (also called shear-thickening) materials are materials whose viscosity increases with shear strain rate. Such shear-thickening fluids are an example of non-Newtonian fluids. This behavior is not normally observed in pure substances but can occur in suspensions. Dilatants are non-Newtonian fluids whose shear viscosity increases with applied shear stress. This behavior is the only one type of deviation from Newton's laws and is controlled by factors such as particle size, shape, and distribution. The properties of these suspensions are determined by Hamaker theory and van der Waals forces and can be electrostatically or sterically stabilized. Shear-thickening behavior occurs when colloidal suspensions transition from a stable state to a flocculated state. Most of the properties of this system are due to the surface chemistry of particles in dispersion, known as colloids. This is easily seen in cornstarch and water mixtures, which behave counter to common sense when struck or thrown against a surface. Sand that is completely soaked with water also behaves as a dilatant material.

[0117] Examples of suitable shear-thinning and / or stress-weakening viscoelastic materials for use in embodiments of this invention include soaps, toothpastes, shampoo compositions, mixtures of cornstarch and water, and mixtures of particulates (e.g., talc) and solvents. For example, some paints exhibit shear-thinning behavior if their constituent particles are small enough (e.g., 5 micron particles). One example of a suitable commercial product is Carbopol 940 Gel (available from Lubrizol Corporation, Ohio, USA), which contains carbomer and carboxypolymethylene.

[0118] FIG. 12(a) is a graph showing the apparent viscosity of three different materials (i), (ii) and (iii) over a range of applied stress levels. Material (i) is a pure solvent with no dispersed particles. Materials (ii) and (iii) are coating compositions based on the same dissolved but carrying a suspension of talc particles. Material (ii) coating contains 29% coarse talc (D50=19 microns) while material (iii) coating contains 29% fine talc (D50=5 microns). It can be seen that materials (i) and (ii) exhibit a substantially constant viscosity (i.e. no viscoelastic properties) over the range of stress levels examined. However, material (iii) has a decreasing apparent viscosity with increasing applied stress and is an example of a shear thinning and / or stress weakening viscoelastic material suitable for use in embodiments of the invention.

[0119] As noted above, some materials exhibit shear-thickening behavior over one range of applied shear / strain rates (or applied stresses) and shear-thinning behavior over a different range. Figure 12(b) shows the behavior of an exemplary material of this type, a mixture of cornstarch and water. -3 From 0.1s -1 In the first region i, where the shear rate is about 0.1 to 1 s, the apparent viscosity of the material decreases as the shear rate increases, and so the material here can be characterized as shear thinning. -1(second region ii), the apparent viscosity increases as the shear rate increases and the material is now characterized as shear thickening. As the shear rate increases above about 1 s-1 (third region iii), the material again exhibits shear thinning behavior. Such materials are considered to be both "shear thickening and / or stress hardening" and "shear thinning and / or stress weakening" for the purposes of this disclosure. The material is controlled to exhibit the desired type of behavior through control of the movement between the tool and workpiece surface, for example through control of the rotational speed, to ensure that it operates within the correct shear rate regime.

[0120] Pentamode metamaterials are artificial three-dimensional structures that, despite being solids, ideally behave like fluids; that is, they have finite bulk but vanishing shear modules; in other words, they are hard to compress but easy to deform. More mathematically, pentamode metamaterials have an elasticity tensor with only one non-zero eigenvalue and five (penta) vanishing eigenvalues. According to theory, pentamode metamaterials can be used as the building blocks for materials with completely arbitrary elastic properties and can therefore be designed to be "shear thickening and / or stress stiffening" or "shear thinning and / or stress weakening" as required. Anisotropic versions of the pentamode structure are candidates for transformation elastodynamics and elastodynamic cloaking.

[0121] 13(a), (b) and (c) show further embodiments of the invention utilizing shear thinning and / or stress weakening viscoelastic materials. Here, a polishing tool 1201 is shown in use in a subaperture process polishing a workpiece 1210 in the form of an optical structure such as a Fresnel lens or diffractive optical element. The workpiece 1210 may also be a mold for such an optical structure. The workpiece 1210 contains sharp features 1211 corresponding to peaks of the optical structure, which need to be accurately retained in the finished product. FIG. 13(b) shows such a polished workpiece processed using a typical conventional polishing tool. It is shown that the sharp edge features have been removed and rounded (curved), which would interfere with the performance of the optical structure.

[0122] However, the polishing tool 1201 preferentially polishes the flanks of the optical structure and not the peaks 1211, leaving sharp edges as shown in FIG. 13(b). This is because the tool 1201 contains a shear thinning and / or stress weakening viscoelastic material 1209, which will soften as the shear rate experienced increases as described above. The structure of the sub-aperture polishing tool 1201 is similar to that already described, and includes a support member 1203 for connection to a polishing machine (not shown, but the one in FIGS. 1-4 is suitable) and a base structure 1205 of a hard material (e.g. steel). A cavity is formed between the base structure 1205 and an outer shell 1207 which defines the working surface of the tool. In this embodiment, the working surface is substantially flat when the tool is not in contact with the workpiece and conforms to the general contour of the workpiece during use as shown in FIG. 13(a). The outer shell 1207 in this embodiment includes both an elastic layer 1207a and an abrasive pad 1207b, although as before, the elastic layer 1207a is optional. Enclosed within the cavity is a shear thinning and / or stress weakening viscoelastic material 1209, which may be any of the exemplary compositions described above.

[0123] In this embodiment, the base structure 1205 presents a flat surface to the viscoelastic material 1209. However, in variants, the base structure may have a non-flat surface as described above that defines macrostructures and / or microstructures of any of the types described above, to better control the movement of the viscoelastic material 1209, as described above.

[0124] In use, the tool 1201 is rotated by the grinder about its axis H to grind the area of ​​the workpiece it contacts. The tool 1201 also traverses laterally (arrow D) across the workpiece surface to grind different areas.

[0125] Figures 14(a) and (b) show a further embodiment, showing a polishing tool 1301 in use in a full aperture polishing process. Figure 14(a) shows a perspective view of the tool in use to polish a workpiece 1310, together with selected other parts of the polishing apparatus. The workpiece 1310, for example a lens or semiconductor wafer, is placed on a workpiece holder 1311. The polishing tool 1301 here takes the form of a disk having a diameter larger than that of the workpiece. This allows the tool to polish the entire workpiece surface simultaneously, and it can also be used to polish multiple workpieces (not shown) simultaneously. In a variant, the tool can be substantially the same diameter as the workpiece surface to be polished.

[0126] The polishing tool 1301 comprises a rigid base structure (or "substrate") 1305, for example made of steel, which is fixed to or integral with a support member 1303 which, in use, is coupled to an actuator for rotating the polishing tool about its central axis. As shown in FIG. 14(b), the periphery of the base structure 1305 is bonded to an outer shell 1307, which defines an internal cavity which is filled with a shear-thinning and / or stress-weakening viscoelastic material 1309. Any of the exemplary shear-thinning and / or stress-weakening viscoelastic materials described above may be used for this purpose. As described above, the outer shell 1307 may be a single layer comprising only the abrasive layer 1307b, but in this example it is shown as being formed from two layers, an elastic layer (or "membrane") 1307a and an abrasive pad 1307b. The outer shell 1307 may be flange-threaded, or in some other manner coupled to the base structure 1305, where the shear thinning material is sealed inside. In this embodiment, the working surface extends across the entire surface of the outer shell 1307 and is frusto-conical. However, in other cases, if desired, the abrasive 1307b may be limited to a flat upper region of the outer shell, in which case the working surface will be similarly flat.

[0127] In use, a workpiece 1310 is held against the tool's polishing pad 1307b by a workpiece holder 1311, which may or may not rotate about the axis of the workpiece holder itself. The polishing pad 1307b may or may not itself be abrasive and in the version shown an abrasive slurry 1314 is supplied to the work surface by a conduit 1312 to perform the polishing.

[0128] As in the embodiment described above, here the surface of the base structure opposite the work surface is flat. However, in a variant, a base structure can be provided with a non-flat surface as described above. This allows the movement of the viscoelastic material 1309 to be controlled and / or to conform to the shape of the workpiece, which is particularly useful in the case of full aperture polishing tools that are substantially the same size as the workpiece surface to be polished. For example, if the workpiece to be polished is a curved surface of a lens (or other object), a base structure may be provided that has substantially the same curved shape, e.g. part-spherical or aspherical.

[0129] The use of a shear thinning and / or stress weakening viscoelastic material 1309 in this situation provides the advantage that flatter features of the workpiece are polished in preference to sharper features such as edges. FIG. 15 illustrates an example of this effect, where a semiconductor wafer is polished by the type of process shown in FIG. 14 using (a) a conventional polishing tool and (b) a polishing tool according to an embodiment of the invention, including a shear thinning and / or stress stiffening viscoelastic material 1309 as described above. It can be seen that with the conventional tool (a), the material removal rate (rate) increases sharply towards the edge of the wafer, peaking at the edge and causing the edge to become rounded and lose its desired shape. In contrast, the material removal rate with the tool disclosed herein (b) is relatively constant over the entire radius of the wafer and does not exhibit a significant peak at the edge, thereby preserving the sharp edge.

[0130] Certain preferred aspects of the present invention are described in the following clauses.

[0131] Clause 1 a support member including an attachment feature for connection to a subaperture polisher; The support member has an end portion provided with a polishing head, the polishing head comprising: a base structure connected to or integral with the support member and configured to form a non-flat surface; an outer shell, at least a portion of its exterior surface defining a working surface of the abrasive tool, the outer shell being secured to the base structure so as to enclose a cavity between the outer shell and the non-planar surface; and a viscoelastic material filling the cavity located between the outer shell and the base structure; Sub-aperture polishing tool.

[0132] Clause 2 2. The sub-aperture polishing tool of claim 1, wherein the outer shell forms the outer surface and is provided with a layer of abrasive material suitable for sub-aperture polishing of a workpiece.

[0133] Clause 3 The sub-aperture abrasive tool of clause 2, wherein the abrasive material comprises at least one of polyurethane, breathable fabric, tar-based viscoelastic polymer, and / or another suitable material.

[0134] Clause 4 4. The sub-aperture abrasive tool of claim 2 or 3, wherein the abrasive is in direct contact with the viscoelastic material.

[0135] Clause 5 4. The sub-aperture abrasive tool of claim 2 or 3, wherein the outer shell further comprises a resilient layer positioned between the layer of abrasive and the viscoelastic material, preferably the resilient layer being in direct contact with the viscoelastic material.

[0136] Clause 6 6. The sub-aperture polishing tool of claim 5, wherein the elastic layer comprises at least one of rubber, silicone, neoprene, and a polymeric elastomer.

[0137] Clause 7 7. The sub-aperture polishing tool of claim 5 or 6, wherein the elastic layer has a thickness in the range of 0.1 to 5 millimeters (mm).

[0138] Clause 8 13. A sub-aperture abrasive tool as claimed in any preceding clause, wherein the non-planar surface defines a macro-structure which is rigid in use, the macro-structure having a surface profile which varies on a scale of the same order of magnitude as that of the outer shell, the macro-structure being shaped to determine a thickness of the viscoelastic material between the outer shell and the non-planar surface at each location on the outer surface.

[0139] Clause 9 9. The sub-aperture abrasive tool of claim 8, wherein the macrostructure is rotationally symmetric about an axis about which the outer shell is also rotationally symmetric.

[0140] Clause 10 10. A sub-aperture abrasive tool as described in clause 8 or clause 9, wherein the macrostructure and the outer shell are configured such that the viscoelastic material forms a layer having a substantially constant thickness between the non-planar surface and the outer shell, and the surface texture of the macrostructure preferably includes a region which follows the shape of the outer shell, and most preferably the layer has a thickness in the range of 2 to 200 mm.

[0141] Clause 11 A sub-aperture abrasive tool as described in any of clauses 8 to 10, wherein the macrostructure and the outer shell are shaped differently relative to one another such that the thickness of the viscoelastic material varies between various locations on the working surface.

[0142] Clause 12 12. The sub-aperture polishing tool of claim 11, wherein the maximum thickness of the viscoelastic material is in the range of 2 to 200 mm.

[0143] Clause 13 13. A sub-aperture polishing tool as described in any of clauses 8 to 12, wherein the macrostructure has an at least partially convex or concave curved shape, preferably partially spherical, partially elliptical, partially parabolic or partially annular.

[0144] Clause 14 A sub-aperture abrasive tool as described in any of the preceding clauses, wherein the macrostructure is at least partially formed by a core extending toward the outer shell and configurable to be rigid during use.

[0145] Clause 15 15. The sub-aperture abrasive tool of claim 14, wherein the core comprises one or more of a solid body, an inflatable structure, and an adjustable piston.

[0146] Clause 16 A sub-aperture abrasive tool as described in clause 15, wherein the support member is provided with a conduit for supplying fluid to the expansion structure during use.

[0147] Clause 17 17. A sub-aperture abrasive tool as described in any one of clauses 14 to 16, wherein the core extends continuously from the base structure to a portion of the outer shell.

[0148] Clause 18 18. A sub-aperture abrasive tool as described in any one of clauses 14 to 17, wherein the core is movable relative to the support member.

[0149] Clause 19 19. The sub-aperture abrasive tool of any of clauses 14 to 18, wherein the macrostructure of the non-planar surface further comprises a peripheral region adjacent the core, preferably the peripheral region being relatively flat.

[0150] Clause 20 A sub-aperture abrasive tool as described in any of the above clauses, wherein the non-flat surface defines a microstructure in the form of a surface texture configured to grip shear-hardening and / or shear-thickening material as the sub-aperture abrasive tool rotates during use, preferably the microstructure being integrally defined in the base structure and / or partially defined by a plurality of protrusions fixed to the base structure.

[0151] Clause 21 21. A sub-aperture abrasive tool as described in clause 20, wherein the surface texture includes a plurality of protruding and / or recessed features on the non-planar surface, the protruding and / or recessed features preferably forming a stud and / or pit structure.

[0152] Clause 22 A sub-aperture polishing tool as described in clause 20 or clause 21, when subject to any of clauses 8 to 19, wherein said surface texture is present in all or part of said macrostructure.

[0153] Clause 23 11. A sub-aperture abrasive tool according to any of the preceding clauses, wherein the working surface is non-flat when not pressed against a surface.

[0154] Clause 24 24. A sub-aperture abrasive tool as described in clause 23, wherein at least a portion of the working surface is curved in at least one direction, preferably in two directions.

[0155] Clause 25 25. A sub-aperture abrasive tool as described in clause 23 or clause 24, wherein at least a portion of the working surface is part-spherical, part-elliptical, part-cylindrical, part-conical or annular.

[0156] Clause 26 A sub-aperture polishing tool according to any of the preceding clauses, wherein the machining surface has a lateral width in the range of 0.5 millimeters (mm) to 1 meter (m), preferably 0.5 mm to 0.5 m, more preferably 0.5 mm to 200 mm, and most preferably 0.5 to 5 mm.

[0157] Clause 27 13. A sub-aperture abrasive tool according to any of the preceding clauses, wherein the viscoelastic material is a shear-thickening and / or stress-stiffening viscoelastic material.

[0158] Clause 28 27. A sub-aperture abrasive tool as described in any of clauses 1 to 26, wherein the viscoelastic material is a shear-thinning and / or stress-softening material.

[0159] Clause 29 The sub-aperture abrasive tool of any of the preceding clauses, wherein the viscoelastic material comprises at least one of pitch, a non-Newtonian fluid, a polymer, a silicone polymer, a starch, a clay, a meta-material, a suspension of particles in a solvent, or any combination thereof.

[0160] Clause 30 A sub-aperture polishing tool according to any of the preceding clauses, a workpiece holder for holding the workpiece during use; and an actuating mechanism in mechanical communication with a connecting mechanism, the actuating mechanism configured to, during use, rotate the sub-aperture polishing tool about a first rotational axis passing through the tool such that the working surface moves relative to the surface of the workpiece while at least a portion of the working surface is in contact with the surface of the workpiece; Sub-aperture polisher.

[0161] Clause 31 A polishing machine as described in clause 30, wherein the drive mechanism is further controllable to change the position and / or orientation of the sub-aperture polishing tool relative to the workpiece during use.

[0162] Clause 32 32. The polishing machine of claim 31, wherein the drive mechanism is controllable to move the polishing tool along three orthogonal spatial directions.

[0163] Clause 33 A grinding machine as described in clause 30 or clause 31, wherein the drive mechanism is controllable to change the orientation of the grinding tool with respect to a second rotational axis and / or a third rotational axis, each perpendicular to the first rotational axis and perpendicular to each other.

[0164] Clause 34 (a) preparing a sub-aperture polishing tool as described in any one of clauses 1 to 29; (b) placing a working surface of the sub-aperture abrasive tool in contact with a surface of a workpiece; (c) moving the work surface relative to the work surface to polish the work surface; A method for grinding a workpiece.

[0165] Clause 35 The method of claim 34, wherein moving the machining surface relative to the surface of the workpiece includes rotating the sub-aperture polishing tool about a first rotational axis passing through the sub-aperture polishing tool.

[0166] Clause 36 36. The method of claim 34 or 35, wherein steps (b) and (c) are performed a plurality of times at different locations on the workpiece surface, and an orientation of the sub-aperture tool relative to the workpiece surface is different at at least some of the plurality of locations.

[0167] Clause 37 37. The method of any of clauses 34 to 36, wherein the viscoelastic material is a shear-thickening and / or stress-hardening viscoelastic material and the workpiece surface is moved relative to the workpiece surface to reduce and / or remove mid-spatial defects from the workpiece surface.

[0168] Clause 38 38. The method of claim 37, wherein steps (b) and (c) are repeated sequentially at two or more different locations on the workpiece surface, each of the plurality of locations including a mid-spatial defect having a respective wavelength different from at least some of the other locations, and step (b) is performed at each location under polishing conditions selected depending on the wavelength of the respective mid-spatial defect.

[0169] Clause 39 The method of claim 38, wherein the polishing conditions, which vary depending on the wavelength of the mid-space defect, include at least one of the rotational speed of the sub-aperture polishing tool, the pressure between the machining surface of the sub-aperture polishing tool and the workpiece surface, and the orientation of the sub-aperture polishing tool relative to the workpiece surface.

[0170] Clause 40 40. A method according to any of clauses 37 to 39, wherein the sub-aperture polishing tool is moved to a plurality of locations on the workpiece surface, at least some of the locations containing mid-spatial defects of different wavelengths than those present at other locations, and an orientation of the sub-aperture polishing tool relative to the workpiece surface at each location is selected depending on the wavelength of each mid-spatial defect.

[0171] Clause 41 The method of claim 40, wherein the viscoelastic material is arranged such that a thickness of the viscoelastic material between the surface and core of the workpiece varies between the two or more different orientations.

[0172] Clause 42 37. A method according to any of clauses 34 to 36, wherein the viscoelastic material is a shear thinning and / or stress weakening viscoelastic material and the work surface is moved relative to the workpiece surface in a manner that preferentially smooths relatively flat areas whilst retaining sharp edges of the workpiece surface.

[0173] Clause 43 A method according to any of clauses 34 to 42, wherein the surface of the workpiece has a shape and / or profile different from that of the working surface of the sub-aperture abrasive tool, at least when the sub-aperture abrasive tool is not in contact with the surface of the workpiece.

[0174] Clause 44 44. A method according to any of clauses 34 to 43, wherein the working surface of the sub-aperture abrasive tool has an area which is smaller than the area of ​​the surface of the workpiece, preferably less than half, more preferably less than 10%.

[0175] Clause 45 45. A method according to any of clauses 34 to 44, wherein the working surface of the sub-aperture abrasive tool has a greatest lateral dimension which is smaller, preferably less than half, more preferably less than 10% of the greatest lateral dimension of the surface of the workpiece.

[0176] Clause 46 46. ​​A method according to any of clauses 34 to 45, wherein at least a portion of the working surface of the sub-aperture abrasive tool has a radius of curvature that is less than the minimum radius of curvature of the surface of the workpiece.

[0177] Clause 47 A method as described in any of clauses 34 to 46, wherein the movement of the machining surface relative to the surface of the workpiece comprises rotating the sub-aperture polishing tool at a first rotational speed when in contact with a first position on the surface of the workpiece and rotating the sub-aperture polishing tool at a second rotational speed when in contact with a second position on the surface of the workpiece, such that the shape of the machining surface is different when in the first position and when in the second position.

[0178] Clause 48 48. A method according to any of clauses 34 to 47, wherein the workpiece is not rotationally symmetric and / or the surface of the workpiece comprises at least one convex region and at least one concave region.

[0179] Article 49 A product polished by the method according to any one of clauses 34 to 48, said product being preferably any one of an optical element such as a lens or a prism, a diffractive optical element, a semiconductor wafer, a screen for an electronic device, a medical prosthetic device, or a mould.

[0180] Article 50 a support member including a connection mechanism for connection to a grinding machine; and a grinding head at an end of the support member; The polishing head is A base structure connected to or integral with the support member, an outer shell, at least a portion of its exterior surface defining a working surface of the abrasive tool, the outer shell being secured to the base structure so as to enclose a cavity between the outer shell and the base structure; and a shear thinning and / or stress weakening viscoelastic material filling the cavity located between the outer shell and the base structure; Polishing tools.

[0181] Article 51 51. An abrasive tool as described in clause 50, wherein the outer shell forms the outer surface and comprises a layer of abrasive material suitable for abrading a workpiece, the abrasive material preferably comprising at least one of polyurethane, breathable fabric, tar-based viscoelastic polymer and / or another suitable material.

[0182] Clause 52 52. The abrasive tool of claim 51, wherein the abrasive is in direct contact with the shear thinning and / or stress weakening viscoelastic material.

[0183] Clause 53 52. The abrasive tool of clause 50 or 51, wherein the outer shell further comprises an elastic layer positioned between the layer of abrasive and the shear thinning and / or stress weakening viscoelastic material, preferably the elastic layer being in direct contact with the viscoelastic material.

[0184] Clause 54 54. The abrasive tool of claim 53, wherein the elastic layer comprises at least one of rubber, silicone, neoprene, and a polymeric elastomer.

[0185] Clause 55 55. An abrasive tool as described in clause 53 or clause 54, wherein the elastic layer has a thickness in the range of 0.1 to 5 millimeters (mm).

[0186] Article 56 56. An abrasive tool according to any one of clauses 50 to 55, wherein said abrasive tool is a sub-aperture abrasive tool or a full-aperture abrasive tool.

[0187] Clause 57 57. An abrasive tool as described in any of clauses 50-56, wherein the base structure is configured to form a non-planar surface, and the cavity is enclosed between the outer shell and the non-planar surface.

[0188] Article 58 An abrasive tool as described in any of clauses 50 to 57, wherein the machined surface is non-flat when not pressed against a surface, and preferably at least a portion of the machined surface is curved in at least one direction, most preferably in two directions.

[0189] Article 59 59. The abrasive tool of claim 58, wherein at least a portion of the working surface is frustoconical, partially spherical, partially elliptical, partially cylindrical, partially conical or annular.

[0190] Clause 60 An abrasive tool according to any one of clauses 50 to 59, a workpiece holder for holding the workpiece during use; and a drive mechanism in mechanical communication with a connecting mechanism, the drive mechanism configured to, during use, move the abrasive tool relative to the workpiece while at least a portion of a working surface is in contact with a surface of the workpiece; polishing machine.

[0191] Article 61 A grinding machine as described in clause 60, wherein the drive mechanism is configured to rotate the grinding tool about a first rotational axis passing through the tool.

[0192] Article 62 A polishing machine as described in clause 60 or 61, wherein the polishing machine is configured for sub-aperture polishing or full-aperture polishing of the workpiece.

[0193] Article 63 A method for grinding a workpiece, comprising: (a) preparing an abrasive tool according to any one of clauses 50 to 62; (b) placing a working surface of the abrasive tool in contact with a surface of the workpiece; (c) moving the work surface relative to the work surface to polish the work surface; A method for grinding a workpiece.

[0194] Article 64 64. A method of polishing a workpiece as described in clause 63, wherein the machining surface is moved relative to the surface of the workpiece in a manner that preferentially smooths relatively flat areas while retaining sharp edges of the workpiece surface.

[0195] Clause 65 65. A method of polishing a workpiece as described in clause 63 or 64, wherein the polishing tool is a sub-aperture polishing tool and the surface of the workpiece has a shape and / or surface texture different from that of the working surface of the sub-aperture polishing tool, at least when the sub-aperture polishing tool is not in contact with the surface of the workpiece.

[0196] Article 66 65. A method of polishing a workpiece according to clause 63 or 64, wherein the polishing tool is a full aperture polishing tool and the surface of the workpiece to be polished is substantially the same size as the working surface of the polishing tool or smaller than the working surface of the polishing tool.

[0197] Article 67 67. A product polished by the method according to any one of clauses 63 to 66, said product being preferably any one of an optical element such as a lens or a prism, a diffractive optical element, a semiconductor wafer, a screen for an electronic device, a medical prosthetic device, or a mould.

Claims

1. a support member including a connection mechanism for connection to a sub-aperture polisher; and The support member has an end portion provided with a polishing head, the polishing head comprising: a base structure connected to or integral with the support member and configured to define a non-planar surface; an outer shell, at least a portion of its exterior surface defining a working surface of the abrasive tool, the outer shell secured to the base structure so as to enclose a cavity between the outer shell and the non-planar surface; and a viscoelastic material filling the cavity located between the outer shell and the base structure; Sub-aperture polishing tool.

2. 10. The sub-aperture abrasive tool of claim 1, wherein the outer shell defines an exterior surface and comprises a layer of abrasive material suitable for sub-aperture abrasion of a workpiece.

3. 3. The sub-aperture abrasive tool of claim 2, wherein the abrasive is in direct contact with the viscoelastic material.

4. 3. The sub-aperture abrasive tool of claim 2, wherein the outer shell further comprises a resilient layer positioned between the layer of abrasive and the viscoelastic material, preferably in direct contact with the viscoelastic material.

5. 2. The sub-aperture abrasive tool of claim 1, wherein the non-planar surface defines a macrostructure that is rigid during use and has surface texture that varies on the same magnitude scale as that of the outer shell, the macrostructure shaped to determine a thickness of the viscoelastic material between the outer shell and the non-planar surface at each location on the exterior surface.

6. 6. The sub-aperture abrasive tool of claim 5, wherein the macrostructure and the outer shell are configured such that the viscoelastic material forms a layer having a substantially constant thickness between the non-planar surface and the outer shell, the surface profile of the macrostructure preferably including regions that follow the profile of the outer shell, and most preferably the layer has a thickness in the range of 2-200 mm.

7. 7. The sub-aperture abrasive tool of claim 5 or 6, wherein the macrostructure and the outer shell are shaped differently relative to one another such that a thickness of the viscoelastic material varies among various locations on the work surface.

8. 7. The sub-aperture abrasive tool of claim 5 or 6, wherein the macrostructure has an at least partially convex or concave curved shape, preferably part-spherical, part-elliptical, part-parabolic or part-annular.

9. 7. The sub-aperture abrasive tool of claim 5 or 6, wherein the macrostructure extends toward the outer shell and is at least partially formed by a core that is configurable to be rigid during use.

10. 2. The sub-aperture abrasive tool of claim 1, wherein the non-planar surface defines a microstructure in the form of a surface texture configured to grip shear hardening and / or shear thickening material as the sub-aperture abrasive tool rotates during use, and preferably the microstructure is integrally defined in the base structure and / or is partially defined by a plurality of protrusions secured to the base structure.

11. 10. The sub-aperture abrasive tool of claim 1, wherein the work surface is non-planar when not pressed against a surface.

12. 10. The sub-aperture abrasive tool of claim 1, wherein the viscoelastic material is a shear thickening and / or stress hardening viscoelastic material.

13. 10. The sub-aperture abrasive tool of claim 1, wherein the viscoelastic material is a shear thinning and / or stress weakening viscoelastic material.

14. 2. The sub-aperture abrasive tool of claim 1 , a workpiece holder for holding a workpiece during use; and a drive mechanism in mechanical communication with a connecting mechanism, the drive mechanism configured to rotate the sub-aperture polishing tool about a first rotational axis passing through the tool such that, during use, the working surface moves relative to the surface of the workpiece while at least a portion of the working surface is in contact with the surface of the workpiece; Sub-aperture polisher.

15. 15. The polishing machine of claim 14, wherein the drive mechanism is further controllable to change the position and / or orientation of the sub-aperture polishing tool relative to the workpiece during use.

16. (a) providing a sub-aperture polishing tool according to claim 1; (b) placing a working surface of the sub-aperture abrasive tool in contact with a surface of a workpiece; (c) moving the work surface relative to the surface of the work piece to polish the surface of the work piece; A method for grinding a workpiece.

17. 17. The method of claim 16, wherein steps (b) and (c) are performed a plurality of times at different locations on the workpiece surface, and an orientation of the sub-aperture tool relative to the workpiece surface is different at at least some of the plurality of locations.

18. 18. The method of any of claims 16 to 17, wherein the viscoelastic material is a shear-thickening and / or stress-hardening viscoelastic material and the work surface is moved relative to the work piece surface to reduce and / or remove mesospace defects from the work piece surface.

19. 20. The method of claim 18, wherein steps (b) and (c) are repeated sequentially at two or more different locations on the workpiece surface, each of the plurality of locations including a mid-spatial defect having a respective wavelength different from that of at least some of the other locations, and step (b) is performed at each location under polishing conditions selected depending on the wavelength of the respective mid-spatial defect.

20. 18. The method of claim 16 or 17, wherein the viscoelastic material is a shear thinning and / or stress weakening viscoelastic material, and the working surface is moved relative to the workpiece surface in a manner that preserves sharp edges of the workpiece surface while preferentially smoothing relatively flat areas.

21. 17. A product polished by the method of claim 16, comprising: Preferably, the object is any one of an optical element such as a lens or prism, a diffractive optical element, a semiconductor wafer, a screen for an electronic device, a medical prosthetic device, or a mold. product.

22. a support member including a connection mechanism for connection to a grinding machine; and The support member has an end portion provided with a polishing head, the polishing head comprising: a base structure connected to or integral with the support member; an outer shell, at least a portion of its exterior surface defining a working surface of the abrasive tool, the outer shell being secured to the base structure so as to enclose a cavity between the outer shell and the base structure; and a shear thinning and / or stress weakening viscoelastic material filling the cavity located between the outer shell and the base structure; Polishing tools.

23. 23. The abrasive tool of claim 22, wherein the outer shell forms the exterior surface and comprises a layer of an abrasive material suitable for abrading a workpiece, the abrasive material preferably comprising at least one of polyurethane, breathable fabric, a tar-based viscoelastic polymer, and / or another suitable material.

24. 24. The abrasive tool of claim 23, wherein the abrasive is in direct contact with the shear thinning and / or stress weakening viscoelastic material.

25. 25. The abrasive tool of claims 23 or 24, wherein the outer shell further comprises a resilient layer located between the layer of abrasive and the shear thinning and / or stress weakening viscoelastic material, preferably in direct contact with the viscoelastic material.

26. A polishing machine comprising:

23. The abrasive tool of claim 22, a workpiece holder for holding a workpiece during use; and a drive mechanism in mechanical communication with the connecting mechanism, the drive mechanism configured to, during use, move the polishing tool relative to the workpiece while at least a portion of a working surface is in contact with a surface of the workpiece; Polishing machine.

27. 27. The polishing machine of claim 26, wherein the drive mechanism is configured to rotate the polishing tool about a first axis of rotation passing through the tool.

28. A method for polishing a workpiece, comprising the steps of: (a) providing an abrasive tool according to claim 22; (b) placing a working surface of the abrasive tool in contact with a surface of the workpiece; (c) moving the work surface relative to the surface of the work piece to polish the surface of the work piece; A method for grinding a workpiece.

29. 30. A method of polishing a workpiece as recited in claim 28, wherein the working surface is moved relative to the surface of the workpiece in a manner that preferentially smoothes relatively flat areas while preserving sharp edges of the workpiece surface.

30. 30. A method of polishing a workpiece according to claim 28 or 29, wherein the polishing tool is a sub-aperture polishing tool and the surface of the workpiece has a shape and / or surface texture different from that of the working surface of the sub-aperture polishing tool, at least when the sub-aperture polishing tool is not in contact with the surface of the workpiece.

31. 30. A method of polishing a workpiece according to claim 28 or 29, wherein the polishing tool is a full aperture polishing tool and the surface of the workpiece to be polished is substantially the same size as or smaller than the working surface of the polishing tool.

32. 29. A product polished by the method of claim 28, comprising: Preferably, the object is any one of an optical element such as a lens or prism, a diffractive optical element, a semiconductor wafer, a screen for an electronic device, a medical prosthetic device, or a mold. product.

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