WO2025126044A1 - Structured abrasive article with a scalloped edge - Google Patents

Abstract

Aspects of the present disclosure relate to a structured abrasive article having a backing. Scalloped abrasive composites can be secured to the backing. The scalloped abrasive composites can include abrasive grit dispersed in a binder matrix. At least some of the scalloped abrasive composites independently include a bottom surface configured to attach to the backing, and an apex opposite the bottom surface. The apex can form a cutting surface of the scalloped abrasive composite. In at least one embodiment, the scalloped abrasive composite includes at least a sidewall. The sidewall abuts the bottom surface, and abuts another sidewall at a lateral edge. The sidewall slopes inwardly towards the apex. A portion of the sidewall and edge is concave and forms a curved surface.

Description

STRUCTURED ABRASIVE ARTICLE WITH A SCALLOPED EDGE

BACKGROUND

[0001] Structured abrasive articles are a specific type of coated abrasive article that has a plurality of shaped abrasive composites secured to a major surface of a backing. Each shaped abrasive composite has a bottom surface in contact with the backing and a distal end that extends outwardly from the backing. The shaped abrasive composites comprise abrasive grit dispersed in a binder matrix, typically including a crosslinked organic polymer. The shaped abrasive composites are usually arranged in an array. In one common configuration of a structured abrasive article, the shaped abrasive composites are pyramidal (e.g., tetrahedral or square pyramidal).

[0002] Traditionally, structured abrasive products such as, for example, those available as TRIZACT STRUCTURED ABRASIVE from 3M Company of St. Paul, Minn., have utilized pyramidal abrasive composites. Pyramids are typically used for a variety of reasons, not all of them based on abrading performance. For example, pyramids are an easy shape to produce in the tooling used in the manufacture of the structured abrasive products. Further, during manufacture, the tooling is typically relatively easy to fill with curable slurry and separate from the structured abrasive article after curing when pyramids are used.

[0003] A characteristic of pyramidal abrasive composites is a change in load-bearing area from the tops of the shaped composites to their bottom surfaces as they erode during use. Initially, the erosion is rather rapid. With continued use the load-bearing area increases until it reaches a point beyond which it no longer breaks down and stops efficiently abrading. This usually occurs when the load-bearing area is in a range of from fifty to seventy percent of the area of the working abrasive surface. In practice, this has limited the useful life of structured abrasive articles incorporating pyramidal shaped features.

BRIEF SUMMARY

[0004] Use of inwardly sloping sidewalls is described in U.S. Pat. No. 10,293,466 (Haas et al.). However, even if having a curved surface, the curved surfaces may have issues with consistent cut and finish as well as difficulty in removing from tools.

[0005] The use of concave curved surfaces has been shown to improve the consistency of performance by reducing the change in bearing area as the abrasive wears.

[0006] Aspects of the present disclosure relate to a structured abrasive article having a backing. Scalloped abrasive composites can be secured to the backing. The scalloped abrasive composites can include abrasive grit dispersed in a binder matrix. At least some of the scalloped abrasive composites independently include a bottom surface configured to attach to the backing, and an apex opposite the bottom surface. The apex can form a cutting surface of the scalloped abrasive composite. In at least one embodiment, the scalloped abrasive composite includes a sidewall that abuts the bottom surface and slopes inwardly towards the apex. A portion of the sidewall is concave and forms a curved surface.

[0007] In one embodiment, the structured abrasive article further comprises at least three sidewalls, wherein each sidewall abuts another surface at a lateral edge. The bottom surface of the scalloped abrasive composite can be a regular n-gon, where n is an integer of at least 3, and the composite comprises at least n sidewalls. Alternatively, the bottom surface can be an ellipsoidal shape. In another embodiment, a first sidewall in the at least three sidewalls is a hyperbolic polygon having n-1 edges, and a second sidewall adjacent to the first sidewall is a hyperbolic n-gon having n edges.

[0008] The bottom surface of the scalloped abrasive composite can also be an irregular n-gon, where n is an integer of at least 4. The bottom surface may feature a curved perimeter section with a curved vertex. The apex of the scalloped abrasive composite can be an elongate apex extending along the length of the composite, forming an elongate cutting edge. In one embodiment, the scalloped abrasive composite is a truncated triangular prism, with the bottom surface being a triangular prism lateral face that is rectangular, and two sidewalls being triangular prism lateral faces that are trapezoidal and congruent.

[0009] In another embodiment, the triangular prism bases are non-truncated, extending continuously along the length of the abrasive composite to form infinitely long scribes. The crosssection of the scalloped abrasive composite in a width dimension can be a hyperbolic triangle, while in a length dimension it can be a hyperbolic trapezoid. The dimensions of the scalloped abrasive composite can vary, with the width dimension at a bottom edge being no greater than 90 microns, the length dimension at the bottom edge being no greater than 300 microns, and the height dimension from the bottom surface to the elongate apex being no greater than 100 microns. In another embodiment, the width dimension at a bottom edge is no greater than 50 microns, the length dimension at the bottom edge is no greater than 300 microns, and the height dimension from the bottom surface to the elongate apex is no greater than 55 microns.

[0010] The shape of the scalloped abrasive composite can also be a concave cone, resembling a hyperbolic inwardly-curving cone, or a cone having concave curved surfaces. The sidewall of the scalloped abrasive composite can comprise at least two lateral edges, with each lateral edge connecting the bottom surface to a portion of the apex. The lateral edges can be concave toward the geometric center of the scalloped abrasive composite. In one embodiment, the scalloped abrasive composite can be a hyperbolic tetrahedron, or a tetrahedron with concave curved surfaces, with the curved surface established by a sphere having a radius of curvature of 25% to 75% of the height. The geometric center of one scalloped abrasive composite can be between 125 to 250 microns (or between 50% to 100% of the length of the scalloped abrasive composite) from an adjacent scalloped abrasive composite in the cross direction or the machine direction. The angle between a bottom plane and the sidewall can be between 40 and 90 degrees. [0011] In one embodiment, the curved surface of a sidewall is formed from a curved vertical segment and a linear vertical segment. A cap section is formed by the linear vertical segments, excluding the curved vertical segments, with the cap section having a width and height dimension. The width and height dimension of the cap section are each at least the D5 of the abrasive grit used in the abrasive composite. For example, such that at least 5% of the abrasive grit fits within the cap section. As referred to herein, the D5 can refer to a particle size distribution for diameter of a plurality of abrasive particles where no greater than 5% of particles have a smaller diameter. Alternatively, the cap section can be formed by the linear vertical segments, the curved vertical segments, or a combination of both.

[0012] The structured abrasive article can further comprise an array of scalloped abrasive composites, with each array comprising a series of parallelograms arranged in a parallelogram strip. At least three arrays can be positioned adjacent to each other, forming a larger hexagonal shape, with each array sharing a common edge with the adjacent array. The angle between the sides of each parallelogram array can be at least 60 degrees. The scalloped abrasive composites can also be arranged in a non-regular array, with the non-regular array including variations in the dimensions, orientations, and spacing of the scalloped abrasive composites to create a random pattern.

[0013] The inclusion of the cap section with dimensions at least the D5 of the abrasive grit ensures that a significant portion of the abrasive grit are effectively utilized, enhancing the cutting efficiency and longevity of the abrasive article.

[0014] The arrangement of the scalloped abrasive composites in both regular and non-regular arrays allows for flexibility in design and application. The regular arrays, such as those forming parallelogram strips and hexagonal shapes, provide a uniform and predictable abrasive surface, ideal for applications requiring consistent performance. The non-regular arrays, with their variations in dimensions, orientations, and spacing, create a random pattern that can be beneficial in applications where a more aggressive or varied abrasive action is desired.

[0015] The structured abrasive article can be manufactured using various techniques to ensure precise alignment and secure attachment of the scalloped abrasive composites to the backing. The use of advanced manufacturing methods, such as high-resolution additive manufacturing or diamond-turning, allows for the creation of intricate geometric shapes and ensures the consistent quality of the abrasive composites. The ability to form non-truncated triangular prism bases that extend continuously along the length of the abrasive composite to form infinitely long scribes further enhances the versatility and effectiveness of the abrasive article.

[0016] In one embodiment, the structured abrasive article includes scalloped abrasive composites arranged in a non-regular array. This non-regular array comprises a combination of elements and shapes with an overall randomness, including variations in the dimensions, orientations, and spacing of the scalloped abrasive composites. This random pattern can enhance the abrasive action and provide a more aggressive cutting performance, making it suitable for a variety of applications. [0017] The structured abrasive article also features a curved surface formed from a curved vertical segment and a linear vertical segment. This design ensures that the abrasive composites maintain their structural integrity and cutting efficiency throughout their use. The cap section, formed by the linear vertical segments, has a width and height dimension that is greater than or equal to the D5 of the abrasive grit. This can ensure that at least 5% of the abrasive particles in the abrasive grit fit within the cap section. This design optimizes the abrasive action and enhances the overall performance of the article.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0018] To easily identify the discussion of any particular element or act, the most significant digit or digits in a reference number refer to the figure number in which that element is first introduced.

[0019] FIG. 1 illustrates a perspective view of a structured abrasive article in accordance with one embodiment.

[0020] FIG. 2 illustrates a perspective view of a close-up view of a pattern of FIG. 1 in accordance with one embodiment.

[0021] FIG. 3A illustrates a side cross-sectional view of a scalloped abrasive composite from FIG. 2 along its width dimension in accordance with one embodiment.

[0022] FIG. 3B illustrates a top elevational view of the scalloped abrasive composite from FIG. 3A in accordance with one embodiment.

[0023] FIG. 3C illustrates a side cross-sectional view of the scalloped abrasive composite along the length dimension in accordance with one embodiment.

[0024] FIG. 4 illustrates a side cross-sectional view of an embodiment of a scalloped abrasive composite along its width dimension in accordance with one embodiment.

[0025] FIG. 5 illustrates a side cross-sectional view of an embodiment of a scalloped abrasive composite along its width dimension in accordance with one embodiment.

[0026] FIG. 6 illustrates a side cross-sectional view of an embodiment of a scalloped abrasive composite along its width dimension in accordance with one embodiment.

[0027] FIG. 7A illustrates a top elevational view of a structured abrasive article in accordance with one embodiment.

[0028] FIG. 7B illustrates a bottom elevational view of a scalloped abrasive composite from the structured abrasive article of FIG. 7A in accordance with one embodiment.

[0029] FIG. 8A illustrates a perspective view of an embodiment of a scalloped abrasive composite in accordance with one embodiment.

[0030] FIG. 8B illustrates a top elevational view of the embodiment of the scalloped abrasive composite from FIG. 8A in accordance with one embodiment. [0031] FIG. 8C illustrates another perspective view of the embodiment of the scalloped abrasive composite from FIG. 8A in accordance with one embodiment.

[0032] FIG. 9A illustrates elevational view of a portion of the tiling pattern in accordance with one embodiment.

[0033] FIG. 9B illustrates a perspective view of a portion of the tiling pattern in accordance with one embodiment.

[0034] FIG. 9C illustrates a bottom view of a scalloped abrasive composite in accordance with one embodiment.

[0035] FIG. 9D illustrates a side cross-sectional view of the scalloped abrasive composite in accordance with one embodiment.

[0036] FIG. 9E illustrates a top elevational view of a parallelogram strip in accordance with one embodiment.

[0037] FIG. 9F illustrates a top elevational view of a parallelogram cell in accordance with one embodiment.

[0038] FIG. 9G illustrates a top elevational view of a portion of a triangular pattern in accordance with one embodiment.

[0039] FIG. 9H illustrates a top elevational view of a plurality of triangular patterns in accordance with one embodiment.

[0040] FIG. 91 illustrates a top elevational view of a portion of the pattern in FIG. 9H in accordance with one embodiment.

[0041] FIG. 10 illustrates a scalloped abrasive composite in accordance with one embodiment.

[0042] FIG. 11 illustrates a side cross-sectional view of a convex abrasive composite in accordance with one embodiment.

[0043] FIG. 12 illustrates a side cross-sectional view of an abrasive composite having straight sidewalls in accordance with one embodiment.

DETAILED DESCRIPTION

[0044] FIG. 1 illustrates an exemplary structured abrasive article 100 comprising backing 106, which has respective (top) major surface 108 and (bottom) major surface 110.

[0045] Examples of useful backings include films, foams (open-cell or closed-cell), papers (wet or dry), foils, and fabrics (e.g., wovens, nonwovens, and knitted fabrics). The backing may be, for example, a thermoplastic film that includes a thermoplastic polymer, which may contain various additive(s). Examples of suitable additives include colorants, processing aids, reinforcing fibers, heat stabilizers, UV stabilizers, and antioxidants. Examples of useful fillers include clays, calcium carbonate, glass beads, talc, clays, mica, wood flour, and carbon black. The backing may be a composite film, for example a coextruded film having two or more discrete layers.

[0046] Suitable thermoplastic polymers include, for example, polyolefins (e.g., polyethylene and polypropylene), polyurethanes, polyesters (e.g., polyethylene terephthalate), polyamides (e.g., nylon-6 and nylon-6, 6), polyimides, polycarbonates, and combinations and blends thereof. The average thickness of the backing can range from at least about 1 mil (25 micrometers) to about 250 mils (6350 micrometers), although thicknesses outside of this range may also be used. In one embodiment, the thickness of the thermoplastic polymers can be from 1 to 5 mils. The thermoplastic polymers can be coated with various release coatings which may provide a smooth surface to facilitate release of the abrasive material during use.

[0047] In one embodiment, the backing 106 may include one or more intermediate layers positioned between the abrasive layer 102 and the backing 106. These intermediate layers can facilitate the attachment of the abrasive layer 102 and/or the scalloped abrasive composites 104 to the backing 106. Examples of intermediate layers include adhesive layers, primer coatings, or tie layers made from materials such as thermoplastic polymers, thermosetting resins, or elastomeric compounds. These layers can be designed to interface with both the abrasive layer 102 and the backing 106, providing a structured configuration that supports the overall assembly.

[0048] In one embodiment, the abrasive layer 102 can be directly adhered to the backing. For example, abrasive layer 102 can contact and may be secured to major surface 108. Abrasive layer 102 comprises a plurality of scalloped abrasive composites 104. Optional attachment interface layer 112 is secured to second major surface 110 by optional adhesive layer 114.

[0049] Individual precisely-shaped scalloped abrasive composites 104 can include abrasive grit dispersed in binder matrix. The scalloped abrasive composites 104 can be arranged in a pattern 120 which are described further herein in FIG. 2.

[0050] Abrasive grit

[0051] Any abrasive grit may be included in the abrasive composites. The abrasive grit can have a Mohs hardness of at least 8, or even 9. Examples of such abrasive grit include aluminum oxide, fused aluminum oxide, ceramic aluminum oxide, white fused aluminum oxide, platey white aluminum oxide, heat-treated aluminum oxide, silica, silicon carbide, green silicon carbide, alumina-zirconia, diamond, iron oxide, ceria, cubic boron nitride, garnet, tripoli, sol-gel-derived abrasive grit, and combinations thereof.

[0052] The abrasive grit can have an average particle size of less than or equal to 1500 micrometers, although average particle sizes outside of this range may also be used. For repair and finishing applications, useful abrasive grit sizes can include an average particle size in a range of from at least 0.01, 1, 3 or even 5 micrometers up to and including 35, 100, 250, 500, or even as much as 1500 micrometers.

[0053] Binder Matrix [0054] The abrasive grit are dispersed in a polymeric binder, which may be thermoplastic and/or crosslinked. This is generally accomplished by dispersing the abrasive grit in a binder precursor, usually in the presence of an appropriate curative (e.g., photoinitiator, thermal curative, and/or catalyst). Examples of suitable polymeric binders that are useful in abrasive composites include phenolics, aminoplasts, urethanes, epoxies, acrylics, cyanates, isocyanurates, glue, and combinations thereof.

[0055] The polymeric binder can be prepared by crosslinking (e.g., at least partially curing and/or polymerizing) a binder precursor. During the manufacture of the structured abrasive article, the polymeric binder precursor is exposed to an energy source which aids in the initiation of polymerization (which can include crosslinking) of the binder precursor. Examples of energy sources include thermal energy and radiation energy, which includes electron beam energy, ultraviolet light, and visible light. In the case of an electron beam energy source, curative is not necessarily needed because the electron beam itself generates free radicals.

[0056] After this polymerization process, the binder precursor is converted into a solidified binder. Alternatively for a thermoplastic binder precursor, during the manufacture of the abrasive article the thermoplastic binder precursor is cooled to a degree that results in solidification of the binder precursor. Upon solidification of the binder precursor, the abrasive composite is formed.

[0057] There are two main classes of polymerizable resins that may be included in the binder precursor: condensation-polymerizable resins and addition-polymerizable resins. Addition polymerizable resins are advantageous because they are readily cured by exposure to radiation energy. Addition polymerized resins can polymerize, for example, through a cationic mechanism or a free-radical mechanism. Depending upon the energy source that is utilized and the binder precursor chemistry, a curing agent, initiator, or catalyst may be useful to help initiate the polymerization.

[0058] Examples of suitable binder precursors include phenolic resins, urea-formaldehyde resins, aminoplast resins, urethane resins, melamine formaldehyde resins, cyanate resins, isocyanurate resins, (meth)acrylate resins (e.g., (meth)acrylated urethanes, (meth)acrylated epoxies, ethylenically-unsaturated free-radically polymerizable compounds, aminoplast derivatives having pendant alpha, beta-unsaturated carbonyl groups, isocyanurate derivatives having at least one pendant acrylate group, and isocyanate derivatives having at least one pendant acrylate group), vinyl ethers, epoxy resins, and mixtures and combinations thereof.

[0059] Phenolic resins have good thermal properties and availability, and relatively low cost and ease of handling. Phenolic resins can include resole and novolac. Resole phenolic resins have a molar ratio of formaldehyde to phenol of greater than or equal to one to one, or in a range of from 1.5: 1.0 to 3.0: 1.0. Novolac resins have a molar ratio of formaldehyde to phenol of less than one to one. Examples of commercially available phenolic resins include those known by the trade designations DUREZ and VARCUM from Occidental Chemicals Corp, of Dallas, Tex.; RESINOX from Monsanto Co. of Saint Louis, Mo.; and AEROFENE and AROTAP from Ashland Specialty Chemical Co. of Dublin, Ohio. (Meth)acrylated urethanes include di(meth)acrylate esters of hydroxyl-terminated NCO extended polyesters or polyethers. Examples of commercially available acrylated urethanes include those available as CMD 6600, CMD 8400, and CMD 8805 from Cytec Industries of West Paterson, N.J. (Meth)acrylated epoxies include di(meth)acrylate esters of epoxy resins such as the diacrylate esters of bisphenol A epoxy resin. Examples of commercially available acrylated epoxies include those available as CMD 3500, CMD 3600, and CMD 3700 from Cytec Industries.

[0060] Ethylenically-unsaturated free-radically polymerizable compounds include both monomeric and polymeric compounds that contain atoms of carbon, hydrogen, and oxygen, and optionally, nitrogen and the halogens. Oxygen or nitrogen atoms or both are generally present in ether, ester, urethane, amide, and urea groups. Ethylenically-unsaturated free-radically polymerizable compounds can have a molecular weight of less than about 4,000 g/mole and can be esters made from the reaction of compounds containing a single aliphatic hydroxyl group or multiple aliphatic hydroxyl groups and unsaturated carboxylic acids, such as acrylic acid, methacrylic acid, itaconic acid, crotonic acid, isocrotonic acid, maleic acid, and the like. Representative examples of (meth)acrylate resins include methyl methacrylate, ethyl methacrylate styrene, divinylbenzene, vinyl toluene, ethylene glycol diacrylate, ethylene glycol methacrylate, hexanediol diacrylate, triethylene glycol diacrylate, trimethylolpropane triacrylate, glycerol triacrylate, pentaerythritol triacrylate, pentaerythritol methacrylate, pentaerythritol tetraacrylate and pentaerythritol tetraacrylate. Other ethylenically unsaturated resins include monoallyl, polyallyl, and polymethallyl esters and amides of carboxylic acids, such as diallyl phthalate, diallyl adipate, and N,N-diallyladipamide. Still other nitrogen containing compounds include tris(2-acryloyl- oxyethyl) isocyanurate, I,3,5-tris(2-methyacryloxyethyl)-s-triazine, acrylamide, N- methylacrylamide, N,N-dimethylacrylamide, N-vinylpyrrolidone, and N-vinylpiperidone.

[0061] Useful aminoplast resins have at least one pendant alpha, beta-unsaturated carbonyl group per molecule or oligomer. These unsaturated carbonyl groups can be acrylate, methacrylate, or acrylamide type groups. Examples of such materials include N-(hydroxymethyl)acrylamide, N,N'- oxydimethylenebisacrylamide, ortho- and para-acrylamidomethylated phenol, acrylamidomethylated phenolic novolac, and combinations thereof.

[0062] Epoxy resins have one or more epoxy groups that may be polymerized by ring opening of the epoxy group(s). Such epoxy resins include monomeric epoxy resins and oligomeric epoxy resins. Examples of useful epoxy resins include 2,2-bis[4-(2,3-epoxypropoxy)-phenyl propane] (diglycidyl ether of bisphenol) and materials available as EPON 828, EPON 1004, and EPON 1001F from Shell Chemical Co. of Houston, Tex.; and DER-331, DER-332, and DER-334 from Dow Chemical Co. of Midland, Mich. Other suitable epoxy resins include glycidyl ethers of phenol formaldehyde novolac commercially available as DEN-431 and DEN-428 from Dow Chemical Co. [0063] The epoxy resins can polymerize via a cationic mechanism with the addition of an appropriate cationic curing agent. Cationic curing agents generate an acid source to initiate the polymerization of an epoxy resin. These cationic curing agents can include a salt having an onium cation and a halogen containing a complex anion of a metal or metalloid. Other curing agents (e.g., amine hardeners and guanidines) for epoxy resins and phenolic resins may also be used.

[0064] To promote an association bridge between the above-mentioned binder and the abrasive grit, a silane coupling agent may be included in the slurry of abrasive grit and binder precursor, in an amount of from about 0.01 to 5 percent by weight, or in an amount of from about 0.01 to 3 percent by weight, or in an amount of from about 0.01 to 1 percent by weight, although other amounts may also be used, for example depending on the size of the abrasive grit. Suitable silane coupling agents include, for example, methacryloxypropylsilane, vinyltriethoxysilane, vinyltris(2- methoxyethoxy) silane, 3,4-epoxycyclohexylmethyltrimethoxysilane, gamma- glycidoxypropyltrimethoxysilane, and gamma-mercaptopropyltrimethoxysilane (e.g., as available under the respective trade designations A-174, A-151, A-172, A-186, A-187, and A-189 from Witco Corp, of Greenwich, Conn.), allyltriethoxysilane, diallyldichlorosilane, divinyldiethoxy silane, and meta, para-styrylethyltrimethoxysilane (e.g., as commercially available under the respective trade designations A0564, D4050, D6205, and S 1588 from United Chemical Industries of Bristol, Pa.), dimethyldiethoxysilane, dihydroxydiphenylsilane, triethoxysilane, trimethoxy silane, triethoxysilanol, 3 -(2-aminoethylamino)propyltrimethoxysilane, methyltrimethoxy silane, vinyltriacetoxysilane, methyltriethoxysilane, tetraethyl orthosilicate, tetramethyl orthosilicate, ethyltriethoxysilane, amyltriethoxysilane, ethyltrichlorosilane, amyltrichlorosilane, phenyltrichlorosilane, phenyltri ethoxy silane, methyltrichlorosilane, methyldichlorosilane, dimethyldichlorosilane, dimethyldiethoxysilane, and mixtures thereof.

[0065] The binder precursor may optionally contain additives such as, for example, colorants, grinding aids, fillers, wetting agents, dispersing agents, light stabilizers, and antioxidants.

[0066] Structured abrasive article 100 can be made in a process similar to that used in US patent application number publication 2013/0280994.

[0067] In one embodiment, the method of making a scalloped abrasive composite involves several key steps to ensure the creation of a high-quality abrasive article. First, a backing material with first and second opposed major surfaces may be prepared, and the first major surface may optionally be coated with an adhesive layer to enhance the attachment of abrasive composites. Next, an abrasive slurry may be prepared by mixing abrasive grit with a binder matrix, which may include curable resins such as phenolic, epoxy, or urethane resins. Additives like fillers, colorants, or coupling agents can be added to the slurry to improve performance. The abrasive slurry may then be applied onto a production tool with cavities that correspond to the desired shape of the scalloped abrasive composites. These cavities may have sidewalls that are curved, straight, or a combination thereof, forming a hyperbolic profile or other geometric profile. The slurry is ensured to fill the cavities completely to form the scalloped abrasive composites. [0068] The filled production tool may be brought into contact with the first major surface of the backing material, and pressure may be applied to ensure the abrasive slurry adheres to the backing. The abrasive slurry may then be exposed to an energy source, such as ultraviolet (UV) light, electron beam, or thermal energy, to cure the binder matrix and solidify the abrasive composites. This curing process should be sufficient to fully harden the binder matrix and secure the abrasive grit within the composites. After curing, the production tool may be separated from the backing material to reveal the formed scalloped abrasive composites attached to the first major surface of the backing. Additional curing or post-processing steps may be performed to enhance the durability and performance of the abrasive composites.

[0069] The present disclosure relates to the production tool, e.g., a mold for making a structured abrasive article. The structured abrasive article may comprise a backing having first and second opposed major surfaces, with scalloped abrasive composites secured to the first major surface. The scalloped abrasive composites may comprise abrasive grit dispersed in a binder matrix, and at least some of the scalloped abrasive composites may independently include a bottom surface configured to attach to the backing, an apex opposite the bottom surface forming a cutting surface, and a sidewall that abuts the bottom surface and slopes inwardly towards the apex, with a portion of the sidewall being concave and forming a curved surface. The mold may comprise a mold body having a surface with a plurality of cavities, each cavity corresponding to the desired shape of the scalloped abrasive composites. Each cavity may have sidewalls that are curved, straight, or a combination thereof, forming a hyperbolic profile or other geometric profile. The cavities may be configured to receive an abrasive slurry and form scalloped abrasive composites with the specified features. The mold body may be made from a material that allows for the easy release of the cured abrasive composites, ensuring efficient production of the structured abrasive articles.

[0070] FIG. 2 illustrates a closer view of the pattern 120 of the structured abrasive article 100. The pattern 120 can be a plurality of scalloped abrasive composites that are arranged along axis 206, axis 212, axis 214, and axis 216. For example, set of scalloped abrasive composites 202 can be arranged along axis 216 and set of scalloped abrasive composites 204 can be arranged along axis 206. The axis 214 and axis 216 (and axis 206 and axis 212) can be parallel to each other. The axis 214 and axis 206 (and axis 216 and axis 212) can intersect each other and form angle 208. The angle 208 can range from 1-179 degrees but is shown as perpendicular (e.g., 90 degrees).

[0071] The pattern 120 of the structured abrasive article is depicted as a basketweave pattern; however, any pattern is feasible, including those described in PCT publication WO 2015/179335. In one embodiment, a perpendicularly aligned scalloped abrasive composite may be positioned between two of the set of scalloped abrasive composites 204 aligned along axis 206. In another embodiment, the pattern may encompass more than two axes, such as a pattern including three axes, and could theoretically include a plurality of additional axes. In at least one embodiment, the distance 220 from an adjacent scalloped abrasive composite oriented in the same direction along the same axis may be no greater than 150 microns or at least twice the width of the scalloped abrasive composite. In one embodiment, the distance 220 from an adjacent scalloped abrasive composite oriented in the same direction along the same axis may be at least one-third the width dimension of a scalloped abrasive composite.

[0072] In one embodiment, the set of scalloped abrasive composites 204 parallel to another set of scalloped abrasive composites can be offset in the perpendicular axis. In at least one embodiment, the distance 210 between the geometric center of the closest of two parallel scalloped abrasive composites can be at least one length of a scalloped abrasive composite. In one embodiment, the distance 210 can be at least 200 micrometers, or at least 250 micrometers, or between 100 microns and 400 microns.

[0073] For fine finishing applications, the areal density of shaped abrasive composites in the abrasive layer is typically in a range of from at least 1,000, 10,000, or even at least 20,000 shaped abrasive composites per square inch (e.g., at least 150, 1,500, or even 7,800 shaped abrasive composites per square centimeter) up to and including 50,000, 70,000, or even as many as 100,000 shaped abrasive composites per square inch (7,800, 11,000, or even as many as 15,000 shaped abrasive composites per square centimeter), although greater or lesser densities of shaped abrasive composites may also be used.

[0074] FIG. 3A, FIG. 3B and FIG. 3C illustrate a scalloped abrasive composite 104 having a truncated triangular prism shape with scalloped sidewalls. As used herein, discussion of the sidewalls can refer to one or more of the sidewalls unless specifically addressed.

[0075] The scalloped abrasive composite 104 can have a bottom surface 318 that is oriented towards the major surface 108. The bottom surface 318 of the scalloped abrasive composite 104 is configured to attach to the major surface 108 of the backing 106. In one embodiment, the bottom surface 318 is n-polygon where n is at least 3. As shown, the bottom surface 318 is rectangular in shape (where n is 4). The bottom surface 318 can have n-sidewalls extending therefrom (where n is 4 in FIG. 3A- FIG. 3C).

[0076] In one embodiment, the scalloped abrasive composite 104 can have a cross-sectional shape taken along the frontal plane 368 (which is parallel to the bottom plane 346) that is a regular or irregular n-gon. As shown, the scalloped abrasive composite 104 is shown as a regular n-gon (i.e., rectangle). This shape is maintained in the cross-section as the frontal plane 368 is moved towards the apex 320 and culminate at the elongate cutting edge.

[0077] As shown, two of the sidewalls are triangular prism bases, and two of the sidewalls are triangular prism lateral faces.

[0078] The sidewalls can have a tapered profile meaning that a sidewall axis connected between a top vertex and a bottom vertex is less than 90 degrees. For example, the sidewalls can be tapered at any suitable angle 358 or angle 338 relative to the bottom surface 318 of the scalloped abrasive composite 104. For example, the sidewalls can be tapered at an angle 338 relative to the bottom surface 318 ranging from 1 degree to less than 90 degrees, between 40 and 80 degrees, or between 50 and 70 degrees as measured about side axis 344 and bottom plane 346. In another example, the angle 358 can be between 40 and 90 degrees, 40 and 89 degrees, or between 50 and 70 degrees as measured about the side axis 344 and the bottom plane 346. In one embodiment, the angle 358 can be established by the curved surface of the sidewall. For example, angle 358 could be less than 60 degrees or even less than 50 degrees.

[0079] In at least one embodiment, the bottom plane 346 can align with a plane of the bottom surface 318 and the side axis 344 can align with the curved surface 314 (or along an edge). For example, the side axis 344 can connect a bottom vertex (bottom surface/sidewall) with a top vertex (elongate cutting edge/sidewall).

[0080] The curved surface 314 can curve inwardly (towards the geometric center of the scalloped abrasive composite 104) from the side axis 344. The term "geometric center" refers to the central point of the scalloped abrasive composite 104, which is equidistant from all the outer edges of the composite. This central point can serve as a reference for the overall shape and symmetry of the composite.

[0081] The inward curvature of the curved surface 314 is designed to enhance the structural integrity and performance of the scalloped abrasive composite 104. By curving inwardly towards the geometric center, the curved surface 314 creates a concave profile that helps to distribute abrasive forces more consistently as the abrasive composite wears. This inward curvature also reduces the rate of change of contact between the abrasive composite and the material being abraded, thereby improving the cutting efficiency and effectiveness of the composite.

[0082] The side axis 344, which extends from the bottom surface 318 to the apex 320, serves as a reference line for the curvature of the curved surface 314. As the curved surface 314 curves inwardly from the side axis 344, it forms a smooth, continuous curve that converges towards the geometric center of the scalloped abrasive composite 104.

[0083] In one embodiment, the radius of curvature of the curved surface 314 can be precisely controlled to achieve the desired inward curvature. The radius of curvature can range from 25 microns to 350 microns, depending on the specific design requirements and intended application of the abrasive composite. For example, the radius of curvature can be no greater than 300 microns, no greater than 275 microns, no greater than 250 microns, no greater than 225 microns, no greater than 200 microns, no greater than 175 microns, or no greater than 150 microns. By carefully selecting the radius of curvature, the inward curvature of the curved surface 314 can be optimized to provide the best balance between structural integrity and cutting performance.

[0084] In one embodiment, the radius of curvature can range from 100 microns to 175 microns (inclusive). In one embodiment, the radius of curvature can be from 70 to 200 microns, 70 to 150 microns, or 70 to 100 microns. In at least one embodiment, a portion of the sidewall can have the radius of curvature. The side wall can have more than one radius of curvature. In one embodiment, the overall curvature (from apex to the bottom edge) can follow the radius of curvature (even if there are variations with smaller segments) .

[0085] The angle 338 can be different than angle 340 (formed from bottom plane 346 and side axis 348) and angle 358. For example, there may be at least a 5 degree difference between angle 338 and angle 340.

[0086] The sidewalls may have curved surfaces. For example, curved surface 310, curved surface 312, curved surface 314, curved surface 316 can all be concave and inwardly curved towards the geometric center of the scalloped abrasive composite 104.

[0087] Each of the sidewalls can have a different shape profile. For example, the curved surface 316 and curved surface 314 can be a hyperbolic triangular shape and/or have a hyperbolic triangular cross-section in the width dimension 304 (e.g., having a (n-l)-gon shape, where n is the number of bottom edges in bottom surface 318). In at least one embodiment, the width dimension 304 can be no greater than 300 microns, no greater than 200 microns, no greater than 100 microns, or no greater than 50 microns.

[0088] In one embodiment, the curved surface 310 and curved surface 312 can have a hyperbolic trapezoidal shape and/or have a hyperbolic trapezoidal cross-section (n-gon shape) in the length dimension 324. In one embodiment, the length dimension 324 can be no greater than 500 microns, no greater than 400 microns, no greater than 300 microns, or no greater than 250 microns.

[0089] In at least one embodiment, the bottom edge 352 of the sidewalls can abut the perimeter 350 of the bottom surface 318 and the top edges 354 of the sidewalls can abut each other thereby forming an apex. As shown, the apex 320 can form an elongate cutting edge having a length dimension 356 along the length of the scalloped abrasive composite 104.

[0090] In one embodiment, adjacent sidewalls (e.g., the sidewall 362 having curved surface 312 and the sidewall 360 having curved surface 314) can form a lateral edge 364. As shown, there are n- lateral edges (where n is the number of verticies on the bottom surface 318 shape). In one embodiment, the lateral edges are also hyperbolic or concave and curved.

[0091] The length dimension 356 can be less than the length dimension 324. In one embodiment, the length dimension 356 is less than the length dimension 324. In one embodiment, the ratio of the length dimension 356 to the length dimension 324 is no greater than 1: 1, no greater than 1: 1.25, no greater than 1: 1.5. In one embodiment, the ratio of the length dimension 356 to length dimension 324 is at least 1:2.

[0092] In one embodiment, the width dimension 304 can be the same, or have a 5% variance with the height dimension 302. In one embodiment, the ratio of the height dimension 302 to width dimension 304 is at least 1: 1, or at least 4:3.

[0093] In one embodiment, the height dimension 302 of the shaped abrasive composites is generally greater than or equal to 0.039 mil (1 micrometer) and less than or equal to 20 mils (510 micrometers); for example, less than 15 mils (380 micrometers), 10 mils (200 micrometers), 5 mils (200 micrometers), 2 mils (5 micrometers), or even less than 1 mil, although greater and lesser heights may also be used.

[0094] FIG. 4 illustrates a different cross-section of a scalloped abrasive composite 400 taken along the width dimension 404. The proportion of height dimension 402 to width dimension 404 can be greater than found in scalloped abrasive composite 104. As shown the height dimension 402 can be no greater than 100 microns and the width dimension 404 can be no greater than 75 microns. As shown, the scalloped abrasive composite 400 can have a radius of curvature 406 that is greater than shown in scalloped abrasive composite 104. For example, the radius of curvature 406 can be at least 150 microns, or at least 200 microns. In one embodiment, the ratio of the height dimension 402 to the radius of curvature 406, can be from 1:2 to 2: 1.

[0095] FIG. 5 illustrates a scalloped abrasive composite 500 having ratio of a height dimension 504 and a width dimension 502 that is similar to the scalloped abrasive composite 104 (i.e., about 1 : 1). The scalloped abrasive composite 500 can have a parabolic sidewall 510 established by a parabola where the angle of the slope changes from the base 514 to the apex 512. As shown, the angle of the slope increases from the base 514 to the apex 512.

[0096] FIG. 6 illustrate a scalloped abrasive composite 600 having a ratio of height dimension 606 to a width dimension 608 that is similar to the scalloped abrasive composite 104 (i.e., about 1: 1). The scalloped abrasive composite 600 can have a curved vertical segment 610 where the curvature is established by a radius of curvature 614 (shown to be about half of the height dimension 606) and a linear segment 612 where there is no curved surface. Overall, the sidewall 618 can have at least one curved vertical segment 610 resulting in a curved surface. If a series of linear segments, then the overall shape can follow a radius of curvature from the base 620 to the apex 616.

[0097] FIG. 7A and FIG. 7B illustrate a portion of a structured abrasive article 700 having a tetrahedral array 710 of scalloped abrasive composites 704. The bottom surface 702 can be a regular triangle (e.g., an equilateral triangle) (i.e., n-gon where n is an integer of 3) with sidewalls also being hyperbolic triangles (n-gon having an integer of 3). In one embodiment, the sidewall 712 can have the same cross-section as shown in curved surface 314 in FIG. 3A and FIG. 3C.

[0098] FIG. 8A, FIG. 8B, and FIG. 8C illustrate a scalloped abrasive composite 800 having an overall L-shape. The scalloped abrasive composite 800 can be similar to the scalloped abrasive composite 104 except that scalloped abrasive composite 800 has curved perimeter sections in the middle of the shape to form an overall L-shape. The scalloped abrasive composite 800 can have sidewall 802, sidewall 804, sidewall 806, and sidewall 808, each of which can have curved surfaces similar to those of scalloped abrasive composite 104.

[0099] The scalloped abrasive composite 800 is an irregular n-gon (hexagon) having curved perimeter section 812 and curved perimeter section 830 in place of vertices. In one embodiment, the curved perimeter section 812 and curved perimeter section 830 can be referred to as curved vertices. These curved vertices replace the traditional sharp vertices found in regular polygons, providing a unique geometric configuration that enhances the structural integrity and performance of the abrasive composite.

[0100] The term "curved perimeter section" used herein refers to a portion of the perimeter of the scalloped abrasive composite that is smoothly curved rather than angular. This curvature in the backing plane can be concave or convex and is designed to replace the sharp angles typically found at the vertices of regular polygons. The curved perimeter sections 812 and 830 in the scalloped abrasive composite 800 create a more fluid and continuous boundary, which can help in distributing stress more evenly and reducing the likelihood of fracture or wear at specific points.

[0101] The L-shape of the scalloped abrasive composite 800 is defined by the arrangement of its sidewalls and curved perimeter sections. The sidewalls 802, 804, 806, and 808 are arranged in such a way that they form two distinct arms of the L-shape, with the curved perimeter sections 812 and 830 located at the junctions where the arms meet. This configuration allows for a more complex and versatile design, which can be beneficial in various abrasive applications.

[0102] The curved surfaces of the sidewalls contribute to the overall effectiveness of the scalloped abrasive composite 800. These surfaces are characterized by their inward curvature, which helps to distribute abrasive forces more evenly across the composite. The curved surfaces also enhance the cutting efficiency of the composite by providing multiple points of contact with the material being abraded.

[0103] In addition to the unique L-shape and curved surfaces, the scalloped abrasive composite 800 also features a bottom surface that is configured to attach securely to a backing. The bottom surface can be designed to ensure stable attachment and optimal performance during use. The combination of the L-shape, curved perimeter sections, and curved surfaces makes the scalloped abrasive composite 800 a highly effective and versatile component of the structured abrasive article. [0104] FIG. 9A - FIG. 9F illustrate an exemplary tiling pattern 906 featuring an embodiment of a scalloped abrasive composite discussed herein.

[0105] FIG. 9B illustrates a perspective view of the tiling pattern 906. The tiling pattern 906 can include a plurality of parallelogram cells 904, each comprising one or more parallelogram strips 902. Each parallelogram strip 902 can include at least two scalloped abrasive composites as described herein. As shown in FIG. 9A, each parallelogram strip 902 includes three scalloped abrasive composites 940, and each parallelogram cell 904 includes three parallelogram strips 902.

[0106] The scalloped abrasive composites within each strip are aligned with their adjacent composites, providing a continuous and uniform abrasive surface. The parallelogram strips are positioned adjacent to each other, creating a repeating pattern across the surface. The arrangement of the strips forms a hexagonal tiling pattern, characterized by the interlocking nature of the parallelogram shapes. This configuration allows for efficient packing of the abrasive composites, potentially maximizing the abrasive surface coverage and enhancing the overall performance of the abrasive article. [0107] Each scalloped abrasive composite within the tiling pattern 906 may feature concave curved sidewalls that converge towards an apex, optimizing the cutting efficiency and material removal capabilities. The alignment and packing of the composites minimize gaps between the strips, potentially ensuring consistent performance during use.

[0108] The tessellated pattern of parallelogram strips is designed to provide a stable and durable abrasive surface, capable of conforming to various contours while maintaining its structural integrity. The geometric arrangement of the strips contributes to the uniform distribution of abrasive forces, potentially enhancing the longevity and effectiveness of the abrasive article.

[0109] FIG. 9C illustrates the bottom surface 908 of the scalloped abrasive composite 940. The bottom surface 908 is defined by a parallelogram geometric shape. In one embodiment, the parallelogram has a base dimension that does not exceed 300 microns and a height dimension that does not exceed 100 microns. The parallelogram shape ensures a stable attachment to the backing material and contributes to the overall structural integrity of the abrasive composite.

[0110] The bottom surface 908 is designed to provide optimal contact with the backing, ensuring secure adhesion and uniform distribution of abrasive forces during use. The parallelogram shape allows for efficient packing of multiple scalloped abrasive composites within a given area, maximizing the abrasive surface coverage. Additionally, the specific dimensions of the base and height are chosen to balance the need for durability and flexibility, allowing the abrasive composite to conform to various surface contours while maintaining its cutting efficiency.

[0111] The edges of the bottom surface 908 are precisely defined to ensure a tight fit with adjacent scalloped abrasive composites, minimizing gaps and enhancing the overall performance of the abrasive article. The parallelogram shape can also facilitate the alignment of the scalloped abrasive composites in a tessellated pattern, contributing to the uniformity and consistency of the abrasive surface.

[0112] FIG. 9D illustrates a side cross-sectional view of the scalloped abrasive composite 940. The scalloped abrasive composite 940 can have a similar arrangement to FIG. 6. For example, the scalloped abrasive composite 940 can have at least two sidewalls, sidewall 912 and sidewall 930. The sidewalls can have a curved vertical segment 914 and a linear vertical segment 916 with mirrored symmetry along each sidewall, as shown in FIG. 9D. The two sidewalls culminate at apex 918.

[0113] In one embodiment, the radius of curvature of the curved vertical segment 914 can be no greater than 250 microns, no greater than 225 microns, no greater than 200 microns, no greater than 175 microns, or no greater than 150 microns.

[0114] The cap section 944, formed by the linear vertical segments 916, has a base portion denoted by the intersection of the curved vertical segment 914 and the linear vertical segment 916. This base portion is less than the dimension formed by the bottom surface 908. The cap section 944 can have a cross-sectional area no greater than 50 square microns, or no greater than 100 square microns. In one embodiment, the cap section 944 can have a height and width of no greater than 20 microns, no greater than 15 microns, no greater than 10 microns, no greater than 9 microns, or no greater than 8 microns. These dimensions can accommodate abrasive grit of 1200 grit.

[0115] In at least one embodiment, the cap section could be designed to have a higher or lower density of abrasive grit of a particular particle size compared to that of the base section. For example, the density of abrasive grit having a particular size (e.g., 1200 grit abrasive grit) in the cap section can be up to 50% greater than that in the base section.

[0116] The cap section 944 of a scalloped abrasive composite is a region that influences the performance and efficiency of the abrasive article. The cap section 944 can be defined by the linear vertical segments (e.g., linear vertical segment 916) of the sidewalls and culminates at the apex of the scalloped abrasive composite. The cap section 944 is identified as the uppermost portion of the composite, formed by the intersection of the linear vertical segments 916 with the curved vertical segments 914. The width 976 of the cap section 944 is measured at the base of the linear vertical segments, perpendicular to the height 978 of the cap section 944, while the height 978 is measured from the base to the apex 918 along the vertical axis 980.

[0117] The D5 of the abrasive grit is a statistical measure representing the diameter at which 5% of the grits in a given sample are smaller. This value is determined using particle size analysis techniques such as laser diffraction or sieving. To ensure that the cap section 944 can accommodate at least 5% of the abrasive grit, the width and/or height dimensions of the cap section can be at least the D5 value of the abrasive grit. For example, if the D5 value of the abrasive grit is 10 microns, both the width and/or height of the cap section should be at least 10 microns.

[0118] In one embodiment, the cap section 944 can represent no greater than 40 percent, no greater than 30 percent, no greater than 20 percent, or no greater than 10 percent of the volume of the scalloped abrasive composite.

[0119] In another embodiment, the cap section 944 can be defined by the size of abrasive grit. The dimensions of the cap section 944, including its width and/or height, are designed to accommodate the abrasive grit used in the composite. Specifically, the cap section 944 is configured to ensure that a significant portion of the abrasive grit, such as those with a D5 value, fit within the cap section. Thus, if the abrasive grit have a D5 value of 25 microns, then the boundary of the cap section can be selected such that the opening defined by the width of the scalloped abrasive composite along the sidewalls is also about 25 microns, even if such boundary includes some portions of curved vertical segments.

[0120] FIG. 9E illustrates a perspective view of the parallelogram strip 902. As depicted, the parallelogram strip 902 comprises a series of scalloped abrasive composites arranged in a parallel configuration. Each scalloped abrasive composite within the strip is precisely aligned with its adjacent composites, ensuring a continuous abrasive surface. There are no gaps between each scalloped abrasive composite within the parallelogram strip 902, resulting in a seamless arrangement.

[0121] In one embodiment, there may be an overlap between the bases or bottom surfaces of adjacent scalloped abrasive composites within the same parallelogram strip 902. This overlap can be no greater than 5 microns, no greater than 4 microns, or no greater than 3 microns. The defined overlap ensures that the scalloped abrasive composites are tightly packed, enhancing the structural integrity and performance of the abrasive article.

[0122] The scalloped abrasive composites are characterized by their geometric shape, which includes concave sidewalls that converge towards an apex (e.g., apex 918). This design allows for efficient material removal and consistent abrasive action. The parallelogram strip 902 is designed to be part of a larger tessellated pattern, where multiple strips are arranged adjacent to each other to form a continuous and repeating pattern across the surface.

[0123] The precise alignment and defined overlap between the scalloped abrasive composites within the parallelogram strip 902 contribute to the overall effectiveness of the abrasive article. The seamless arrangement ensures that the abrasive surface remains uniform, providing consistent performance during use. The design also allows for efficient manufacturing, as the tight packing of the composites minimizes material waste and maximizes the use of the abrasive material.

[0124] FIG. 9F illustrates a tiling pattern comprising multiple repeated parallelogram arrays, referred to as parallelogram cell 904. Each array consists of a series of parallelograms aligned in parallel rows, with the angles between the sides of the parallelograms being about 60 degrees. The parallelogram arrays are arranged in a tessellated manner, forming a continuous and repeating pattern across the surface, resulting in a hexagonal shape.

[0125] In one embodiment, the apexes of each scalloped abrasive composite are configured to intersect with those of another scalloped abrasive composite from a different parallelogram strip. This intersection forms an angle 948, which can be no greater than 90 degrees, no greater than 80 degrees, no greater than 70 degrees, or no greater than 60 degrees. A gap 936 can be formed between adjacent parallelogram strips. In one embodiment, the gap 936 can be no greater than 30 microns, no greater than 20 microns, or no greater than 10 microns. Additionally, the gap can be no greater than 4 percent, no greater than 3 percent, no greater than 2 percent, or no greater than 1 percent of the dimension 952 of the parallelogram cell 904.

[0126] The parallelogram arrays are positioned adjacent to each other, creating a nearly seamless pattern. Minor gaps are present between the hexagonal formations of the parallelogram arrays, while major gaps are present between the larger triangular formations created by the tessellated pattern. The tessellated pattern of parallelogram arrays is arranged to form a larger triangular shape, which is equilateral, with each side of the triangle being of equal length. The pattern extends uniformly to the edges of the triangle, maintaining the integrity of the triangular shape despite the presence of gaps. [0127] The term "tessellated pattern" as used herein refers to an arrangement of shapes closely fitted together in a repeated pattern without overlapping, but allowing for intentional gaps between the shapes. These gaps can be minor, occurring between individual shapes within the pattern, or major, occurring between larger formations created by the tessellated arrangement.

[0128] In at least one embodiment, the parallelograms within each array are congruent, and the angles between the sides of the parallelograms are about 60 degrees, creating an equilateral configuration within each array. The arrays are arranged in such a manner that the overall structure exhibits symmetry and uniformity, with intentional gaps. The tiling pattern exhibits hexagonal symmetry due to the 60-degree angles of the parallelograms. The repeating nature of the pattern allows it to cover large surfaces with minor and major gaps. The triangular arrangement adds a unique geometric dimension to the overall design.

[0129] FIG. 9G illustrates the triangular pattern 954 featuring the tiling pattern 906 as described in FIG. 9A. The triangular pattern 954 is formed as an equilateral triangle, comprising a plurality of parallelogram cells 904. Each parallelogram cell 904 includes one or more parallelogram strips 902, which are arranged in a tessellated configuration to create a continuous and repeating pattern across the surface of the triangle.

[0130] The equilateral triangular shape of the pattern 954 ensures uniform distribution of the parallelogram cells 904, providing a stable and consistent abrasive surface. The precise arrangement of the parallelogram strips 902 within each cell 904 contributes to the overall structural integrity and performance of the abrasive article. The interlocking nature of the parallelogram shapes within the cells 904 allows for efficient packing of the scalloped abrasive composites, maximizing the abrasive surface coverage.

[0131] The triangular pattern 954 is designed to provide abrasive action, with the scalloped abrasive composites within each parallelogram strip 902 featuring concave sidewalls that converge towards an apex. This design enhances the cutting efficiency and material removal capabilities of the abrasive article. The tessellated arrangement of the parallelogram cells 904 ensures that the abrasive surface remains uniform and consistent, even when applied to various contours.

[0132] FIG. 9H illustrates a pattern 960 having a plurality of the triangular patterns (e.g., triangular pattern 954 described in FIG. 9G, and triangular pattern 966 which is substantially the same as triangular pattern 954). The pattern 960 shows an overall hexagonal shape. A gap 964 can be formed between the triangular pattern 966 and triangular pattern 954. This gap 964 is further illustrated in FIG. 91.

[0133] In one embodiment, the structured abrasive article can have a pattern 960 comprising a plurality of triangular patterns with each triangular pattern 954 comprising a tiling pattern 906. The tiling pattern 906 can include a plurality of parallelogram cells 904. Each parallelogram cell 904 can include a plurality of parallelogram strips 902 (shown as three askew parallelogram strips 902 per parallelogram cell 904). Each parallelogram strip 902 can include a plurality of scalloped abrasive composites.

[0134] In one embodiment, the gap 964 can have a dimension 974 of no greater than 100 percent, no greater than 90 percent, no greater than 80 percent, no greater than 71 percent, no greater than 70 percent of dimension 952 across the midpoint of the parallelogram cell 904. In one embodiment, the dimension 974 can be measured from vertex of one edge from triangular pattern 966 to the vertex of another edge from triangular pattern 954.

[0135] FIG. 10 illustrates an embodiment of a conical scalloped abrasive composite 1010. The conical scalloped abrasive composite 1010 comprises a bottom surface 1006, which is generally circular in shape, providing a stable base for attachment to a backing material. Extending upwardly from the perimeter of the bottom surface 1006 is a single continuous sidewall 1002 (thus n=l).

[0136] FIG. 10 illustrates an embodiment of a scalloped abrasive composite where the bottom surface 1006 is ellipsoidal in shape. In one embodiment, the bottom surface 1006 can take the form of an ellipse, which is a type of conic section resulting from the intersection of a plane with a cone. An ellipse is defined by its two focal points, with the sum of the distances from any point on the ellipse to the two foci being constant. This geometric property gives the ellipse its characteristic elongated shape. Ellipses are commonly found in various natural and man-made structures, such as planetary orbits, architectural arches, and certain types of lenses.

[0137] In addition, the bottom surface 1006 can be circular, which is a special case of an ellipse where the two focal points coincide at the center, resulting in a shape with a constant radius from the center to any point on the circumference. Circles are ubiquitous in both nature and human constructions, appearing in objects such as wheels, coins, and various mechanical components.

[0138] In addition to ellipses and circles, other ellipsoidal shapes include oblate and prolate spheroids. An oblate spheroid is formed by rotating an ellipse about its minor axis, resulting in a flattened sphere-like shape, similar to the shape of the Earth. A prolate spheroid, on the other hand, is formed by rotating an ellipse about its major axis, creating an elongated sphere-like shape, similar to a rugby ball or an American football.

[0139] In one embodiment, the ellipsoidal shape for the bottom surface 1006 can be taken along the plane of the base, ensuring a stable and secure attachment to the backing. This flat configuration along the plane of the base allows for consistent contact with the backing material, providing a uniform surface for the abrasive composite to adhere to. The selection of a specific ellipsoidal shape, whether elliptical, circular, oblate, or prolate, can be tailored to meet the requirements of different applications, offering versatility in the construction of the structured abrasive article.

[0140] The sidewall 1002 is characterized by its smooth, concave curvature, which gradually narrows as it extends towards the apex 1008. The apex 1008 is the uppermost point of the conical scalloped abrasive composite 1010 and serves as the primary cutting surface. The concave nature of the sidewall 1002 ensures that the load-bearing area of the abrasive composite changes minimally as the abrasive material wears down during use, thereby maintaining consistent performance. In at least one embodiment, the conical scalloped abrasive composite 1010 is designed in the shape of a concave cone, optimizing the distribution of abrasive grit and enhancing the overall efficiency of the abrasive process. The unique geometry of the conical scalloped abrasive composite 1010 allows for improved cutting action and longevity compared to traditional abrasive composites.

[0141] FIG. 11 illustrates an example convex abrasive composite 1102 having sidewall 1108 and sidewall 1110 that protrude beyond the side axis 1104 and side axis 1106 respectively to form a convex shape.

[0142] EXAMPLES:

[0143] The construction of the abrasive article is prepared in a similar manner to the commercially available Trizact™ Hookit™ Foam Sheets from 3M (Saint Paul, MN).

[0144] Unless otherwise noted, all parts, percentages, ratios, etc. in the examples and the rest of the specification are by weight, and all reagents used in the examples were obtained, or are available, from general chemical suppliers such as, for example, Sigma-Aldrich Company, Saint Louis, Mo., USA or may be synthesized by conventional methods.

[0145] The following abbreviations are used throughout the Examples:

degrees Centigrade

grams per square foot g/m²: grams per square meter rpm: revolutions per minute mil: 10’³ inches p-inch: 10’⁶ inches pm micrometers ft/min: feet per minute m/min: meters per minute mm: millimeters cm: centimeters kPa: 10³ Pascals psi: pounds per square inch kg: kilogram lb: pound

UV: ultraviolet weight percent

W/in: Watts per inch

W/cm: Watts per centimeter

A-174: gamma-methacryloxypropyltrimethoxysilane, available under the trade designation “SIUQUEST A174” from Momentive, Columbus, Ohio, USA

D-6019: a hot melt pressure sensitive adhesive obtained under the trade designation

“DYNAHM 6019” from Dyna-Tech Adhesives, Inc., Grafton, West Virginia, USA

F800-8000 a silicon carbide abrasive mineral having a grade ranging from JIS 800-8000 (15 microns-1 micron) under the trade designation “GC Green Silicon Carbide” from Fujimi Corp. Tualatin, Oregon

H-2679: a latex dispersion, obtained under the trade designation “HYCAR 2679” from

Lubrizol Advanced Materials, Inc., Cleveland, Ohio, USA a silicon carbide abrasive mineral having a grade ranging from JIS 2500 800-

N800-8000 8000 (15 microns-1 micron) under the trade designation “GC Green Silicon Carbide” from Nanko Abrasives Industry Co., Ltd., Tokyo, Japan

S24000: a 100% active polymeric dispersant, obtained under the trade designation

“SOLSPERSE S24000 SC/GR” from Lubrizol Advanced Materials, Inc., Cleveland, Ohio, USA

SG-1582: a reactive polyurethane adhesive, obtained under the trade designation

“SG1582-082” from Bostik, Inc., Wauwatosa, Wisconsin, USA

SR339: 2 -phenoxy ethyl acrylate monomer available under the trade designation

“SR339” from Sartomer Company, Exton, Pennsylvania, USA

SR351 : trimethylolpropane triacrylate available under the trade designation "SR351H" from Sartomer Company, Exton, Pennsylvania, USA.

TPO-L: acylphosphine oxide, commercially available under the trade designation

“LUCERIN TPO-L” from BASF Corp, of Florham Park, New Jersey, USA

[0146] Preparation of Foam Backed Substrate

[0147] A 90 mil (2.29 mm) layer of polyurethane foam, available under the trade designation “HYPUR-CEL S0601”, from Rubberlite, Inc., Huntington, West Virginia, USA, was coated with 3- 7 g/ft² (32.29 g/m²) dry weight of “H-2679”. A 3.0 mil (76.2 pm) polyester film, obtained under the trade designation “HOSTAPHAN 2262”, from Mitsubishi Polyester Film, Inc., Greer, South Carolina, USA, was then laminated to the opposite side of the foam using D-6019. A 52 g/m² brushed nylon loop fabric, available under the trade designation “ART. TROPICAL L”, from Sitip SpA, Cene, Italy, was then laminated to the exposed face of the polyester film using SG-1582.

[0148] Preparation of Abrasive Slurries: AS-1 & AS-2

[0149] AS-I

[0150] A resin pre-mix was made as follows: 218.4 grams SR339, 328.9 grams SR351 and 52.0 grams S24000 were mixed together, heated to 60° C. and intermittently stirred until the S24000 was dissolved, about one hour. The solution was then cooled to 21° C. and 32.5 grams A-174 plus 18.2 grams TPO-L were added and the resin pre-mix stirred until homogenously dispersed.

[0151] 160 grams F2500 was homogeneously dispersed into 100 grams of the resin pre-mix for 15 minutes at 21° C. using a high speed shear mixer, after which the slurry was heated to 60° C., held for 2 hours, then cooled back to 21° C.

[0152] AS-2

[0153] A resin pre-mix was made as follows: 296.3 grams SR339, 444.5 grams SR351 and 32.8 grams S24000 were mixed together, heated to 60° C. and intermittently stirred until the S24000 was dissolved, about one hour. The solution was then cooled to 21° C. and 23.5 grams A-174 plus 23 grams TPO-L were added and the resin pre-mix stirred until homogenously dispersed.

[0154] 272 grams of N2500 was homogeneously dispersed into 150 grams of the resin pre-mix for 15 minutes at 21° C. using a high speed shear mixer, after which the slurry was heated to 60° C., held for 2 hours, then cooled back to 21° C.

[0155] Preparation of Micro-replicated Toolings MRT-1 & MRT-2

[0156] MRT-1

[0157] Examples of detailed fabrication of useful tooling can be found in US-A-5152917 (Pieper et al.); US-A-5435816 (Spurgeon et al.); US-A-5672097 (Hoopman et al.); US-A-5946991 (Hoopman et al.); US-A-5975987 (Hoopman et al.); and US-6129540 (Hoopman et al. and US- 5851247 (Stoetzel et al.).

[0158] Indentations, corresponding to the micro-replicated abrasive pattern shown in FIG. 1, FIG. 2, FIG. 3A, FIG. 3B, and FIG. 3C can be fabricated by any conventional technique known to those of skill in the art, including but not limited to: photolithography, knurling, engraving, hobbing, additive manufacturing, electroforming, and diamond turning. Polypropylene resin was pressed onto the master plate and then cooled, resulting in a sheet of flexible polymeric production tool. The array of cavities formed on the surface of the polymeric production tool corresponded to the inverse pattern of the microreplicated abrasive pattern. The production tool can result in a shape having base dimensions of 250 pm by 55 pm and height of 55 pm. The resulting scalloped abrasive composite had sidewalls having a radius of curvature of 100 microns.

[0159] MRT-2/Comyarative A [0160] The fabrication procedure generally described for MRT-1 above was repeated with similar dimensions, wherein the micro-replicated abrasive pattern corresponded to the pattern shown with convex edges as described and illustrated in the side cross-sectional view in FIG. 11. The dimensions of the shapes are similar to that provided in MRT-1.

[0161] MRT-3/Comparative B

[0162] The fabrication procedure generally described for MRT-1 above was repeated with similar dimensions, wherein the micro-replicated abrasive pattern corresponded to the triangular abrasive composite 1202 shown in the side cross-sectional view in FIG. 12 without any modification to the edges. The dimensions of the shapes are similar to that provided in MRT-1.

[0163] MRT-4

[0164] Examples of detailed fabrication of useful tooling can be found in US-A-5152917 (Pieper et al.); US-A-5435816 (Spurgeon et al.); US-A-5672097 (Hoopman et al.); US-A-5946991 (Hoopman et al.); US-A-5975987 (Hoopman et al.); and US-6129540 (Hoopman et al. and US- 5851247 (Stoetzel et al.).

[0165] Indentations, corresponding to the micro-replicated abrasive pattern shown in FIG. 9A - FIG. 91 can be fabricated by any conventional technique known to those of skill in the art, including but not limited to: photolithography, knurling, engraving, hobbing, electroforming, and diamond turning. Polypropylene resin was cast onto the master roll and extruded between a nip roll then cooled, resulting in a sheet of flexible polymeric production tool. The array of cavities formed on the surface of the polymeric production tool corresponded to the inverse pattern of the microreplicated abrasive pattern. The production tool can result in a shape having base dimensions of 300 pm by 88.03 pm and height of 100 pm grouped in sets of three with an overlap of 2.13 pm of the widths of the features. The 300-micron rectangle is then skewed by 30 degrees in the longitudinal axis with replicating units at 120 degrees offsets rotating about a central point. The scalloped abrasive composite had sidewalls having a radius of curvature of 175 microns.

[0166] Example 1

[0167] Abrasive slurry AS-1 was applied by drop bar coating in the micro-replicated polypropylene tooling MRT-1 at a coating weight of about 5.5 mg/cm². The slurry filled polypropylene tooling was then contacted onto the latex coated surface of the foam, pressed between two quartz plates, and UV cured using a UV processor having two “D” type bulbs, from Fusion Systems Inc., Gaithersburg, Maryland, USA, at 600 W/in. (236 W/cm), a line speed of 50 ft/min (15.24 m/min). The tooling was subsequently removed to expose a micro-replicated abrasive coating having base dimensions of 250 pm by 55 pm and height of 55 pm, on the polyurethane foam. The scalloped abrasive composite had sidewalls having a radius of curvature of 100 microns.

[0168] 3 -inch (7.6 cm) diameter abrasive discs were die-cut from this material for cut and finish test 1.

[0169] Example 2 [0170] Abrasive slurry AS-2 was applied by knife coating to the micro-replicated polypropylene tooling MRT-4 at a coating weight of about 13.2 mg/cm². The slurry filled polypropylene tooling was then contacted in a nip roll onto the latex coated surface of the foam and UV cured using a UV processor having two “D” type bulbs, from Fusion Systems Inc., Gaithersburg, Maryland, USA, at 600 W/in. (236 W/cm), a line speed of 90 ft/min (27.43 m/min), and a nip pressure of 80 psi (413.7 kPa). The tooling was subsequently removed to expose a scalloped micro-replicated abrasive coating having base dimensions of 300 pm by 88.03 pm and height of 100 pm grouped in sets of three with an overlap of 2.13 pm of the widths of the features. The 300-micron rectangle is then skewed by 30 degrees in the longitudinal axis with replicating units at 120 degrees offsets rotating about a central point, on the polyurethane foam. The scalloped abrasive composite had sidewalls having a radius of curvature of 175 microns.

[0171] 6-inch (15.2 cm) diameter abrasive discs were die-cut from this material for cut and finish tests 1.

[0172] Comparative A

[0173] The procedure generally described in Example 1 was repeated, wherein the microreplicated tooling MRT-1 was replaced with MRT-2.

[0174] Comparative B

[0175] The procedure generally described in Example 1 was repeated, wherein the microreplicated tooling MRT-1 was replaced with MRT-3.

[0176] Comparative C

[0177] Comparative Example C was a 3 inch diameter (7.6 cm) abrasive finishing disc available under the trade designation Trizact™ 3000 from 3M Company, St Paul, Minnesota, USA.

[0178] Comparative D

[0179] Comparative Example D was an average of 4 different 6 inch diameter (15.2 cm) abrasive finishing discs available under the trade designation Trizact™ 3000 from 3M Company, St Paul, Minnesota, USA.

[0180] Evaluations

[0181] Unless otherwise stated, all tools and materials identified by their trade designations in the following evaluations were obtained from 3M Company, St Paul, Minnesota, USA.

[0182] Cut and Finish Test 1

[0183] Abrasive performance testing was performed on an 18 inches by 24 inches (45.7 cm by 61 cm) black painted, clear coated, cold roll steel test panels, part no. “64464”, obtained from ACT Laboratories Inc., Hillsdale, Michigan, USA. A 6 inch (152 mm) diameter sanding disc, trade designation “260L P1200 HOOKIT FINISHING FILM” was attached to an equally sized “HOOKIT SOFT INTERFACE PAD, PART No. 05777”, which in turn was attached to a “HOOKIT BACKUP PAD, PART No. 05551”. The pad assembly was then secured to a model number “28500” random orbital sander. Using a line pressure of 40 psi (275.8 kPa) and a down force of about 10 lbs (4.54 kg), the panel was pre-scuffed by sweeping the sander horizontally across the panel 7 times, then vertically 9 times, with about a 50% overlap between sweeps. The scuffed panel was wiped with a microfiber cloth and weighed.

[0184] A 3 inch (76 mm) sample disc was attached to an equally sized “HOOKIT SOFT INTERFACE PAD, PART No. 05771”, which in turn was attached to a “HOOKIT BACKUP PAD, PART No. 20427”. The pad assembly was then secured to a model number “28494” random orbital sander. Using a line pressure of 40 psi (275.8 kPa) and a down force of about 10 lbs (4.54 kg), the panel sprayed lightly with water and the sanding repeated, in horizontal and vertical sweeps with

50% overlap, for one minute. The panel was then wiped dry, re-weighed in order to measure the amount of cut, and the average surface finish (Rz) measured at five positions using a model “SURTRONIC 3+ PROFILOMETER” from Taylor Hobson, Inc., Leicester, England. The average surface finish (Rz) for all measurements ranged from 17.4 to 28.2 and were all visually comparable. The sanding process was then repeated three times, with the cumulative cut and average finish listed in Table 1.

[0185] TABLE 1

[0186] Cut and Finish Test 2

[0187] Abrasive performance testing was performed on an 18 inches by 24 inches (45.7 cm by 61 cm) black painted, clear coated, cold roll steel test panels, part no. “64464”, obtained from ACT Laboratories Inc., Hillsdale, Michigan, USA. A 6 inch (152 mm) diameter sanding disc, trade designation “260L P1200 HOOKIT FINISHING FILM” was attached to an equally sized “HOOKIT SOFT INTERFACE PAD, PART No. 05777”, which in turn was attached to a “HOOKIT BACKUP PAD, PART No. 05551”. The pad assembly was then secured to a model number “28500” random orbital sander. Using a line pressure of 40 psi (275.8 kPa) and a down force of about 10 lbs (4.54 kg), the panel was pre-scuffed by sweeping the sander horizontally across the panel 7 times, then vertically 9 times, with about a 50% overlap between sweeps. The scuffed panel was wiped with a microfiber cloth and weighed. The 260L finishing film was replaced with a sample disc, the panel sprayed lightly with water and the sanding repeated, in horizontal and vertical sweeps with 50% overlap, for one minute. The panel was then wiped dry, re-weighed in order to measure the amount of cut, and the average surface finish (Rz) measured at five positions using a model “SURTRONIC 3+ PROFILOMETER” from Taylor Hobson, Inc., Leicester, England. The resulting Rz measurements ranged from 20.28 to 39.2 and were all visually comparable. The sanding process was then repeated three times, with the cumulative cut and average finish listed in TABLE 2.

[0188] TABLE 2

[0189] The embodiments described in this disclosure are provided for illustrative purposes only and are not intended to be exhaustive or to limit the to the precise forms disclosed.

[0190] The term "about" as used herein refers to a range of values that are approximately equal to the specified value. This range can account for minor variations or deviations that are generally accepted in the relevant field of art. The exact range may depend on the context in which the term is used, but typically it encompasses variations of up to 10% above or below the specified value. For example, if a dimension is described as "about 100 microns," it can include values from 90 microns to 110 microns.

[0191] DEFINITIONS

[0192] Abrasive grit" refers to small, hard particles used in abrasive materials to wear away the surface of a workpiece through friction. These particles can be composed of various materials, including aluminum oxide, silicon carbide, diamond, and cubic boron nitride. The size of the abrasive grit can be measured in micrometers or mesh sizes, with smaller grit sizes indicating finer particles and larger grit sizes indicating coarser particles. As used herein, abrasive particles can be referred to as abrasive grit. Abrasive grit in the singular form can refer to a plurality of abrasive particles depending on the context.

[0193] " Bottom surface" refers to the bottommost surface of the scalloped abrasive composite facing the backing. The bottom surface may be notional and the cross-section taken along the plane of the backing if the scalloped abrasive composite is integrally formed with the backing.

[0194] " Bounded" refers to the exposed surfaces and edges of each composite that delimit and define the actual three-dimensional shape of each shaped abrasive composite. These boundaries are readily visible and discernible when a cross-section of an abrasive article is viewed under a scanning electron microscope. These boundaries separate and distinguish one precisely shaped abrasive composite from another even if the composites abut each other along a common border at their bases. By comparison, in a shaped abrasive composite that does not have a precise shape, the boundaries and edges are not well defined (e.g., where the abrasive composite sags before completion of its curing).

[0195] " Concave" refers to a shape or surface that curves inward, resembling the interior of a bowl or a cave. In a concave structure, any line segment drawn between two points on the surface will lie entirely within or on the boundary of the shape. This inward curvature means that the surface or shape bends away from the viewer, creating a hollowed-out appearance. Concave shapes are the opposite of convex shapes, which curve outward. In mathematical terms, a concave function or curve is one where the line segment between any two points on the graph of the function lies below or on the graph. [0196] " Curved perimeter section" refers to a curve along the perimeter of a cross-sectional shape taken along a frontal plane.

[0197] " Curved surface" refers to a surface that deviates from being flat or planar, exhibiting a continuous and smooth curvature. This curvature can be concave, convex, or a combination of both, and may follow various geometric profiles such as circular, elliptical, parabolic, or hyperbolic curves. A curved surface can be characterized by its radius of curvature, which measures the degree of bending at any given point.

[0198] " Curved vertex" refers to the point where a curved line intersects with either a straight line or another curved line, forming a vertex. This point of intersection creates a distinct angle or junction, which can be part of various geometric shapes and structures.

[0199] " Curved vertical segment" refers to a curve in the sidewall in the longitudinal or transverse plane.

[0200] "Cutting surface" refers to the part of an abrasive structure in contact with an abrasive element during abrasion.

[0201] " Distance" refers to the distance between the geometric center (centroid of a volume) of scalloped abrasive composites unless otherwise noted.

[0202] "Elongate cutting edge" refers to an edge of an abrasive element which imparts the cut. The cutting edge defines a contact area for a substrate to be abraded in accordance with their orientation with respect to the direction of cut.

[0203] "Hyperbolic" refers to a shape characterized by an inward curvature similar to that of a hyperbola. This can include surfaces that are smoothly curved in a continuous manner, as well as those composed of multiple curved sections or a series of straight sections that together form a general hyperbolic shape. In the case of multiple curved sections, each segment contributes to the overall hyperbolic appearance, creating a composite curvature. When composed of straight sections, the surface approximates the hyperbolic curve through piecewise linear segments, maintaining the general inward curvature from the base to the apex. This definition encompasses both precise mathematical hyperbolic curves, such as those described by parabolic, cubic, or quintic equations, as well as practical approximations of a hyperbola used in design and manufacturing.

[0204] " Lateral" refers to from the side of the scalloped abrasive composite.

[0205] " Linear vertical segment" refers to a linear segment on the sidewall taken in the longitudinal or transverse plane.

[0206] "N-gon" refers to a polygon having n number of segments(edges). The n-gon can have two edges that meet in a vertex.

[0207] " Radius of curvature" refers to a measure of the curve's bending or sharpness at a given point, which may be defined as the radius of the osculating circle that best approximates the curve near that point by having the same tangent and curvature, for complex curves not easily expressed with a simple mathematical formula, the radius of curvature can be determined using a be st- fit circle approach. This may involve identifying a small segment of the curve around the point of interest, determining the circle that best fits this local segment by minimizing deviation (using techniques such as least squares fitting), and taking the radius of this best-fit circle as the radius of curvature. For curves in multidimensional spaces, the best-fit circle may be considered within the plane that best approximates the curve's local behavior, determined by analyzing the principal directions of curvature. This method provides a practical and intuitive measure of curvature for both simple and complex curves.

[0208] "Scalloped" refers to having an inwardly-curving or concave curved surface.

[0209] "Scalloped abrasive composite" refers to shaped abrasive composites defined by relatively smooth surfaced sides that are bounded and joined by a well-defined edge having a distinct edge length with distinct endpoints defined by the intersections of the various major surfaces. In one embodiment, the term scalloped abrasive composite can include one or more surfaces characterized by curvatures of constant radii (where the radius is not changing), curvatures of multiple radii or curvatures of continuously changing radii (for example a parabolic surface).

[0210] " Sidewall" refers to the vertical or inclined surface that forms the boundary or edge of an object, structure, or geometric shape. It can consist of either curved or straight segments, or a combination of both. In the context of a three-dimensional object, the sidewall extends from the base or bottom surface to the top or apex, defining the lateral limits of the object. For example, in a cone, the sidewall is the single continuous surface that extends from the circular base to the apex. Curved sidewalls may follow various geometric profiles, such as circular, parabolic, or hyperbolic curves, while straight sidewalls are linear and form sharp angles at their intersections with other surfaces.

[0211] " Truncated triangular prism" refers to a shape generally having a triangular prism base on each side that connects triangular prism lateral faces. Truncated can mean that the angle between a triangular prism lateral face and a triangular prism base is different from the opposing angle between the triangular prism lateral face and triangular prism base .

Claims

CLAIMS What is claimed is:

1. A structured abrasive article comprising: a backing; scalloped abrasive composites secured to the backing, wherein the scalloped abrasive composites comprise abrasive grit dispersed in a binder matrix, and wherein at least some of the scalloped abrasive composites independently comprise: a bottom surface configured to attach to the backing; an apex opposite the bottom surface, wherein the apex forms a cutting surface; a sidewall, wherein the sidewall abuts the bottom surface and the sidewall slopes inwardly towards the apex, a portion of the sidewall is concave and forms a curved surface.

2. The structured abrasive article of claim 1 wherein the backing has first and second opposed major surfaces; wherein the scalloped abrasive composites are secured to the first major surface.

3. The structured abrasive article of claim 1 or 2 further comprising at least three sidewalls, wherein the sidewall abuts another surface at a lateral edge.

4. The structured abrasive article of claim 3 wherein the bottom surface is a regular n-gon, wherein n is an integer of at least 3, and the scalloped abrasive composite comprises at least n sidewalls.

5. The structured abrasive article of claim 4, wherein a first sidewall in the at least three sidewalls is a hyperbolic polygon having n-1 edges.

6. The structured abrasive article of claim 4 or 5, wherein a second sidewall in the at least three sidewalls adjacent to a first sidewall is a hyperbolic n-gon having n edges.

7. The structured abrasive article of any of claims 1 to 3, wherein the bottom surface is an irregular n-gon, where n is an integer of at least 4.

8. The structured abrasive article of any of claims 1 to 7 wherein the apex is an elongate apex extending along a length of the scalloped abrasive composite which forms an elongate cutting edge.

9. The structured abrasive article of claim 1 or 2 wherein a shape of the scalloped abrasive composite is a concave cone.

10. The structured abrasive article of any of claims 1 to 8 wherein the sidewall comprises at least two lateral edges, wherein a lateral edge connects the bottom surface to a portion of the apex.

11. The structured abrasive article of claim 10 wherein the at least two lateral edges are concave toward a geometric center of the scalloped abrasive composite.

12. The structured abrasive article of any of claims 1 to 11 wherein the curved surface has at least one portion having a radius of curvature from 100 to 175 microns, inclusive.

13. The structured abrasive article of any of claims 1 to 12 wherein the curved surface of the sidewall is formed from a curved vertical segment and a linear vertical segment.

14. The structured abrasive article of claim 13, wherein a cap section is formed by the linear vertical segments, excluding the curved vertical segments, wherein the cap section has a width and height dimension.

15. The structured of claim 14, wherein the width dimension, height dimension, or combinations thereof of the cap section are at least a D5 diameter of the abrasive grit used in the abrasive composite.

16. The structured abrasive article of any of claims 1 to 6, further comprising an array of scalloped abrasive composite comprises, wherein each array comprises a series of parallelograms arranged in a parallelogram strip.

17. The structured abrasive article of claim 16, wherein at least three arrays are positioned adjacent to each other forming a larger hexagonal shape.

18. The structured abrasive article of claim 17, wherein each array shares a common edge with an adjacent array, wherein an angle between sides of adjacent parallelogram array is at least 60 degrees.

19. A method of making the structured abrasive article of any of claims 1 to 18, comprising: providing a backing material having first and second opposed major surfaces; optionally coating the first major surface with an adhesive layer; preparing an abrasive slurry by mixing abrasive grit with the binder matrix, wherein the binder matrix includes a curable resin; applying the abrasive slurry onto a production tool having cavities corresponding to the scalloped abrasive composites; curing the binder matrix to solidify the abrasive composites; separating the production tool from the backing material to reveal the formed scalloped abrasive composites attached to the first major surface of the backing.

20. A mold for making the structured abrasive article of any of the claims 1 to 19, the mold comprising: a mold body having a surface with a plurality of cavities, each cavity corresponding to a desired shape of the scalloped abrasive composites; wherein each cavity has sidewalls that are curved, straight, or a combination thereof; wherein the cavities are configured to receive an abrasive slurry and form scalloped abrasive composites with the bottom surface configured to attach to the backing, an apex opposite the bottom surface, and a sidewall that slopes inwardly towards the apex, with a portion of the side wall being concave and forming the curved surface; wherein the mold body is made from a material that allows for the release of the cured abrasive composites.