Abrasive article and method of forming the same

Abstract

A method for forming an abrasive article via an additive manufacturing technique, the method comprising forming a layer of a powder material comprising a precursor bond material and abrasive particles; compacting at least a portion of the layer to form a compacted layer; bonding at least a portion of the compacted layer; and repeating the steps of forming, compacting, and bonding to form a green abrasive article.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to aspects of forming abrasive articles and one or more green bodies and / or final formed abrasive articles. BACKGROUND

[0002] Abrasive articles are used in material removal operations, such as cutting, grinding, or shaping various materials. An abrasive article or a green body of an abrasive article can be formed via additive manufacturing. There is a need to develop improved abrasive articles. BRIEF DESCRIPTION OF DRAWINGS

[0003] The embodiments are illustrated by way of example and not limited to the figures.

[0004] Figures 1A-1E includes a perspective view of an abrasive article according to an embodiment.

[0005] Figure 2A and Figure 2B includes a perspective view of an abrasive article according to an embodiment.

[0006] Figure 3 includes a diagram of the measurement principle of the developed interface area ratio Sdr.

[0007] Figures 4A-4E includes a cross-sectional image of an abrasive article according to an embodiment.

[0008] Figure 5A and Figure 5B includes an image from a bonded abrasive formed by conventional hot-pressing processing techniques.

[0009] Figure 6A includes a diagram of a build box with loose or unbound powder.

[0010] Figure 6B includes a diagram of a process for capturing loose powder after a forming operation is complete.

[0011] Figure 6C is a diagram of a process for recycling unused and loose powder material.

[0012] Figure 7A is a perspective view of a body of an abrasive article.

[0013] Figure 7B to D includes Figure 7A a cross-sectional image of an abrasive article.

[0014] Figure 8A includes a perspective view of an intended shape of an abrasive article.

[0015] Figure 8B includes a perspective view of a formed abrasive article.

[0016] Figure 8C Perspective view including a comparison of the formed abrasive article to an intended shape.

[0017] Figure 9A and Figure 9B Illustration including a scan of an abrasive article.

[0018] Figure 10 Method for forming an abrasive article according to an embodiment.

[0019] Figure 11 Perspective view including a first body, a second body, a third body, and a fourth body contained in a build cassette.

[0020] Figure 12A Top view of a build bed including a plurality of bodies according to an embodiment.

[0021] Figure 12B Top view of a build bed including a plurality of bodies according to an embodiment.

[0022] Figure 12C Cross-sectional view of a build bed including a plurality of bodies according to an embodiment.

[0023] Figure 12D Top view of a build bed including a plurality of bodies according to an embodiment.

[0024] Figure 12E Cross-sectional view of a build bed including a plurality of bodies according to an embodiment.

[0025] Figure 12F and Figure 12G Top view of a green abrasive article body and a support element according to an embodiment.

[0026] Figure 13A Top view image of a build bed including a plurality of bodies according to an embodiment.

[0027] Figure 13B Perspective view of a body within a build bed according to an embodiment.

[0028] Figure 14A and Figure 14B Image of an abrasive article having a layer shift.

[0029] Figure 15 Image of an abrasive article from a comparative sample.

[0030] Figure 16A Top view image of a build cassette including a green abrasive article body and a support element.

[0031] Figure 16BA plot of the spread and print direction difference percentage for samples CS2 and S5. DETAILED DESCRIPTION

[0032] The present disclosure can be better understood, and its numerous features and advantages can become more apparent to one skilled in the art by reference to the following drawings.

[0033] As used herein, the terms "comprises," "comprising," "includes," "including," "has," "having," or any other variation thereof, are intended to cover a non-exclusive inclusion. For example, a process, method, article, or apparatus that comprises a list of features is not necessarily limited only to those features but can include other features not expressly listed or inherent to such process, method, article, or apparatus.

[0034] As used herein, unless expressly stated to the contrary, "or" means an inclusive or and not an exclusive or. For example, a condition A or B is satisfied by any one of the following: A is true (or present) and B is false (or not present), A is false (or not present) and B is true (or present), and both A and B are true (or present).

[0035] Also, use of "a" or "an" are employed to describe elements and components described herein. This is done merely for convenience and to give a general sense of the scope of the application. This description should be read to include one, at least one, an, or singular as well as the plural unless it is clear from the context that it is meant otherwise.

[0036] The present disclosure relates to methods for forming abrasive articles and features of the resulting abrasive articles. While previous disclosures have provided some limited examples of forming abrasive articles via additive manufacturing, such abrasive articles have been limited in their size, quantity, and quality. In fact, the Applicant of the present disclosure has conducted significant empirical research and has discovered that the knowledge necessary to produce high quality abrasive articles according to conventional additive manufacturing techniques is notable, particularly in the context of dry powder layering and binding techniques. To date, disclosures in the prior art have been limited to micro abrasive bodies. This is because forming large scale, high quality abrasive articles via dry powder layering and binding techniques is not easily scalable. Many obstacles limit the development of the technology, including but not limited to the ability to manufacture dense parts, dimensional stability during and after formation, and the empirical research necessary to fully understand and appreciate the complexity of process variables. Such process variables include but are not limited to the composition of the powder material, the flowability of the powder material, the force applied to the powder layer or layers by the compaction object, the traverse speed of the compaction object, the average thickness of the layer prior to compaction, the particle size distribution of the powder, the number of previously formed layers underneath the powder layer, the number of compacted layers underneath the powder layer, the density of any layers underneath the powder layer, the amount of binder in any layers underneath the powder layer, the relative size of the layer relative to the layer or layers underneath it, the average thickness of the layer prior to compaction, the print head deposition resolution, the saturation limit of the binder, the composition of the binder material, and the like.

[0037] In one aspect, the additive manufacturing techniques of the embodiments herein can be part of a binder jetting manufacturing process.

[0038] Figure 1A An illustration of a portion of the process is included, the process including forming one or more layers of a powder material, the powder material can include abrasive particles and can include a mixture of abrasive particles and a precursor binder material. The powder layer can have an average thickness (t). The powder material layer can be dispensed as described in the embodiments herein.

[0039] In embodiments, the layer of powder material can have an average thickness (t) that can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the layer of powder material can have an average thickness (t) of at least 1 micron, such as at least 5 microns or at least 10 microns or at least 15 microns or at least 20 microns or at least 25 microns. In still other embodiments, the layer of powder material can have an average thickness (t) of not greater than 500 microns, such as not greater than 400 microns or not greater than 300 microns or not greater than 200 microns or not greater than 100 microns or not greater than 90 microns or not greater than 80 microns or not greater than 70 microns or not greater than 60 microns or not greater than 50 microns or not greater than 40 microns or not greater than 30 microns or not greater than 20 microns. The average thickness (t) of the layer of powder material can be a value between any of the minimum and maximum values described above, including, for example, but not limited to, in a range of at least 1 micron to not greater than 500 microns or in a range of at least 10 microns to not greater than 300 microns or in a range of at least 25 microns to not greater than 100 microns.

[0040] In particular embodiments, forming one or more layers of powder material can include depositing powder material from a container via agitation of the powder material in the container, then the powder material flows through a screen in the container, and wherein the powder material falls from the container via gravity into the build box or a previously deposited layer of powder material. In still other embodiments, the agitation method and screen size can be selected based on the particle size distribution of the powder.

[0041] In an aspect, the powder material can include a precursor bond material that can facilitate improved manufacturing and / or performance of the abrasive article. For example, in an embodiment, the bond material can include one or any combination of an organic material, an inorganic material, a metal, a metal alloy, a ceramic, an oxide, a carbide, a nitride, a boride, an amorphous material, a crystalline material. In particular embodiments, the precursor bond material can be chemically transformed or undergo a phase change during processing from the precursor bond material to the bond material of the final formed abrasive article. In still other embodiments, the precursor bond material need not undergo any physical or chemical change during processing and is present as the bond material in the final formed abrasive article.

[0042] In an aspect, the powder material can include an abrasive particle that can facilitate improved manufacturing and / or performance of the abrasive article. For example, in an embodiment, the abrasive particle can include an oxide, a carbide, a nitride, a boride, a superabrasive, or any combination thereof. In embodiments, the abrasive particle can include diamond, silicon dioxide, cubic boron nitride, silicon carbide, boron carbide, aluminum oxide, silicon nitride, tungsten carbide, zirconium oxide, or any combination thereof.

[0043] In embodiments, the abrasive particles can include a particle size distribution having an average particle size (D50a) that can facilitate improved manufacturing and / or performance of the abrasive article. As used herein, a D50 value represents a size value in a distribution within which 50% of the total count of abrasive particles defining the distribution are "contained" (up to and including the size value). For example, in a non-limiting example, if the D50 is 25 microns, then 50% of the abrasive particles have a size of 25 microns or less. It will be appreciated that the D50 value can also be referred to as the median of the sample. In one embodiment, the average particle size (D50a) of the abrasive particles can be at least 0.025 microns, such as at least 0.05 microns or at least 0.1 microns or at least 0.3 microns or at least 0.4 microns or at least 0.5 microns or at least 0.8 microns or at least 1 micron or at least 1.5 microns or at least 2 microns or at least 3 microns or at least 5 microns or at least 10 microns or at least 50 microns or at least 100 microns or at least 200 microns or at least 300 microns. In yet other non-limiting embodiments, the average particle size (D50a) of the abrasive particles can be not greater than 500 microns, such as not greater than 400 microns or not greater than 300 microns or not greater than 200 microns or not greater than 100 microns or not greater than 50 microns or not greater than 10 microns or not greater than 5 microns or not greater than 4 microns or not greater than 3 microns or not greater than 3 microns or not greater than 1 micron. The average particle size (D50a) of the abrasive particles can be a value between any of the minimum and maximum values described above, including, for example, but not limited to, in a range of at least 0.25 microns to not greater than 500 microns or in a range of at least 0.5 microns to not greater than 300 microns or in a range of at least 1 micron to not greater than 10 microns.

[0044] In yet other embodiments, the abrasive particles include abrasive particles having a Mohs hardness of at least 6, such as at least 7 or at least 8 or at least 9. In yet other embodiments, the abrasive particles include abrasive particles having a Mohs hardness of not greater than 30, such as not greater than 25 or not greater than 20 or not greater than 15 or not greater than 10. It will be appreciated that the Mohs hardness of the abrasive particles can be a value between any of the minimum and maximum values described above, including, for example, but not limited to, in a range of at least 6 to not greater than 30 or at least 8 to not greater than 20.

[0045] Figure 1BAn illustration of a process including compacting at least a portion of the layer with a compacting object (120). The compacting object 120 can traverse the layer and compact the layer to form a compacted layer having an average thickness (tc). The compacted layer thickness (tc) can be less than the layer thickness (t) prior to compaction, as described in accordance with embodiments herein. It will be appreciated that in some cases multiple layers of powder material can be formed and compaction can be completed on more than one layer of powder material at the same time. In some optional embodiments, a smoothing roller can traverse the surface of a layer of powder, but the smoothing roller does not exert enough force to cause compaction, rather they scrape the surface of the layer to remove and smooth any large undulations. In yet another embodiment, the smoothing roller is configured to make sufficient contact with the upper surface of the layer after the layer is formed to spread the powder material and smooth the upper surface.

[0046] In an implementation, the compacted layer may include an average compacted layer thickness that may facilitate improved manufacturing and / or performance of the abrasive article. In one embodiment, the average compacted layer thickness may be at least 0.1 micrometers, such as at least 0.5 micrometers, at least 0.8 micrometers, at least 1 micrometer, at least 2 micrometers, at least 3 micrometers, at least 4 micrometers, at least 5 micrometers, at least 6 micrometers, at least 7 micrometers, at least 8 micrometers, at least 9 micrometers, at least 10 micrometers, at least 11 micrometers, at least 12 micrometers, at least 13 micrometers, at least 14 micrometers, at least 15 micrometers, at least 16 micrometers, at least 17 micrometers, at least 18 micrometers, at least 19 micrometers, at least 20 micrometers, at least 21 micrometers, at least 22 micrometers, at least 23 micrometers, at least 24 micrometers, at least 25 micrometers, at least 26 micrometers, at least 27 micrometers, at least 28 micrometers, at least 29 micrometers, at least 30 micrometers, at least 31 micrometers, at least 32 micrometers, at least 33 micrometers, at least 34 micrometers, at least 35 micrometers, at least 36 micrometers, at least 37 micrometers, at least 38 micrometers, at least 39 micrometers, or at least 40 micrometers or more. At least 41 micrometers or at least 42 micrometers or at least 43 micrometers or at least 44 micrometers or at least 45 micrometers or at least 46 micrometers or at least 47 micrometers or at least 48 micrometers or at least 49 micrometers or at least 50 micrometers or at least 51 micrometers or at least 52 micrometers or at least 53 micrometers or at least 54 micrometers or at least 55 micrometers or at least 56 micrometers or at least 57 micrometers or at least 58 micrometers or at least 59 micrometers or at least 60 micrometers or at least 65 micrometers or at least 70 micrometers or at least 75 micrometers or at least 80 micrometers or at least 85 micrometers or at least 90 micrometers or at least 95 micrometers or at least 100 micrometers or at least 110 micrometers or at least 120 micrometers or at least 130 micrometers or at least 140 micrometers or at least 150 micrometers or at least 160 micrometers or at least 170 micrometers or at least 180 micrometers or at least 190 micrometers or at least 200 micrometers or at least 210 micrometers or at least 220 micrometers or at least 230 micrometers or at least 240 micrometers or at least 250 micrometers. In yet another non-limiting embodiment, the average compacted layer thickness may be no greater than 400 micrometers, such as no greater than 300 micrometers, no greater than 200 micrometers, no greater than 100 micrometers, no greater than 90 micrometers, no greater than 80 micrometers, no greater than 70 micrometers, no greater than 60 micrometers, no greater than 50 micrometers, no greater than 40 micrometers, no greater than 30 micrometers, no greater than 20 micrometers, no greater than 15 micrometers, no greater than 10 micrometers, no greater than 8 micrometers, no greater than 5 micrometers, no greater than 3 micrometers, no greater than 1 micrometer, or no greater than 0.8 micrometers. The average compacted layer thickness may be a value between any of the above minimum and maximum values, including, for example, but not limited to, a range of at least 0.1 micrometers to no greater than 400 micrometers, or a range of at least 1 micrometer to no greater than 200 micrometers, or a range of at least 5 micrometers to no greater than 90 micrometers.

[0047] In embodiments, the compacting can include increasing the density of the compacted layer by at least 2%, such as at least 3% or at least 4% or at least 5% or at least 6% or at least 7% or at least 8% or at least 9% or at least 10% or at least 11% or at least 12% or at least 13% or at least 14% or at least 15% or at least 18% or at least 20% or at least 22% or at least 25% or at least 28% or at least 30% or at least 32% or at least 35% or at least 38% or at least 40% or at least 42% or at least 45% or at least 48% or at least 50% or at least 52% or at least 55% or at least 58% or at least 60% or at least 62% or at least 65% or at least 67% or at least 68% or at least 70% or at least 72% or at least 75% or at least 78% or at least 80% or at least 82% or at least 85% or at least 88% or at least 90% or at least 92% or at least 95% or at least 98% or at least 100% or at least 102% or at least 105% or at least 108% or at least 110% or at least 115% or at least 120% or at least 125% or at least 130% or at least 140% or at least 150% compared to the layer prior to compaction. In yet another non-limiting embodiment, the compacting can include increasing the density of the compacted layer by not more than 2000%, such as not more than 1500% or not more than 1000% or not more than 900% or not more than 800% or not more than 700% or not more than 600% or not more than 500% compared to the layer prior to compaction. The compacting can include increasing the density of the compacted layer by any of the minimum and maximum percentages described above, including for example but not limited to in a range of at least 2% to not more than 2000% or in a range of at least 13% to not more than 1000%.

[0048] In embodiments, compacting can include compacting a layer of powder material by at least 1% to no more than 95% of an initial layer thickness of the layer, such as compacting the layer by at least 2% or at least 3% or at least 4% or at least 5% or at least 6% or at least 7% or at least 8% or at least 9% or at least 10% or at least 11% or at least 12% or at least 13% or at least 14% or at least 15% or at least 16% or at least 17% or at least 18% or at least 19% or at least 20% or at least 21% or at least 22% or at least 23% or at least 24% or at least 25% or at least 26% or at least 27% or at least 28% or at least 29% or at least 30% or at least 31% or at least 32% or at least 33% or at least 34% or at least 35% or at least 36% or at least 37% or at least 38% or at least 39% or at least 40% or at least 41% or at least 42% or at least 43% or at least 44% or at least 45% or at least 46% or at least 47% or at least 48% or at least 49% or at least 50% or at least 51% or at least 52% or at least 53% or at least 54% or at least 55% or at least 56% or at least 57% or at least 58% or at least 59% or at least 60% or at least 61% or at least 62% or at least 63% or at least 64% or at least 65% or at least 66% or at least 67% or at least 68% or at least 69% or at least 70% or at least 71% or at least 72% or at least 73% or at least 74% or at least 75% or at least 76% or at least 77% or at least 78% or at least 79% or at least 80% or at least 81% or at least 82% or at least 83% or at least 84% or at least 85% or at least 86% or at least 87% or at least 88% or at least 89% or at least 90% or at least 91% or at least 92% or at least 93% or at least 94% of an initial layer thickness of the layer prior to compacting.In yet another non-limiting embodiment, compacting can include compacting a layer of powder material by at least 1% to no more than 95% of an initial layer thickness of the layer, such as compacting the layer by no more than 94% or no more than 93% or no more than 92% or no more than 91% or no more than 90% or no more than 89% or no more than 88% or no more than 87% or no more than 86% or no more than 85% or no more than 84% or no more than 83% or no more than 82% or no more than 81% or no more than 80% or no more than 79% or no more than 78% or no more than 77% or no more than 76% or no more than 75% or no more than 74% or no more than 73% or no more than 72% or no more than 71% or no more than 70% or no more than 69% or no more than 68% or no more than 67% or no more than 66% or no more than 65% or no more than 64% or no more than 63% or no more than 62% or no more than 61% or no more than 60% or no more than 59% or no more than 58% or no more than 57% or no more than 56% or no more than 55% or no more than 54% or no more than 53% or no more than 52% or no more than 51% or no more than 50% or no more than 49% or no more than 48% or no more than 47% or no more than 46% or no more than 45% or no more than 44% or no more than 43% or no more than 42% or no more than 41% or no more than 40% or no more than 39% or no more than 38% or no more than 37% or no more than 36% or no more than 35% or no more than 34% or no more than 33% or no more than 32% or no more than 31% or no more than 30% or no more than 29% or no more than 28% or no more than 27% or no more than 26% or no more than 25% or no more than 24% or no more than 23% or no more than 22% or no more than 21% or no more than 20% or no more than 19% or no more than 18% or no more than 17% or no more than 16% or no more than 15% or no more than 14% or no more than 13% or no more than 12% or no more than 11% or no more than 10% or no more than 9% or no more than 8% or no more than 7% or no more than 6% or no more than 5% or no more than 4% or no more than 3% or no more than 2% of the initial layer thickness of the layer prior to compacting. Compacting can include compacting a layer of powder material by any of the above minimum and maximum percentages.

[0049] Figure 1C includes bonding at least a portion of the compacted layer of powder material with a binder material. In embodiments, bonding at least a portion of the compacted layer can include using a print head 132, where the print head deposition resolution influences the amount of binder material 131 selectively deposited. As further depicted, the layer can include a region 102 that includes loose or unbound powder material without binder material and a region 103 that includes a region of powder material and binder.

[0050] In embodiments, the binder material can include a liquid vehicle and a polymeric material, where the polymeric material can be soluble in the liquid vehicle. In particular embodiments, the liquid vehicle can include one or more organic solvents, water, or a combination thereof. In further embodiments, the organic solvent can include at least one of an alcohol (e.g., butanol, ethylene glycol monomethyl ether), a ketone, an ether, or any combination thereof. In further embodiments, the alcohol can include methanol, ethanol, n-propanol, isopropanol, n-butanol, sec-butanol, t-butanol, and isobutanol; ketones or ketone alcohols such as acetone, methyl ethyl ketone, and diacetone alcohol; esters such as ethyl acetate and ethyl lactate; polyols such as ethylene glycol, diethylene glycol, triethylene glycol, propylene glycol, butylene glycol, 1,4-butanediol, 1,2,4-butanetriol, 1,5-pentanediol, 1,2,6-hexanetriol, hexylene glycol, glycerol, glycerol ethoxylate, trimethylolpropane ethoxylate; lower alkyl ethers such as ethylene glycol methyl ether or ethyl ether, diethylene glycol ethyl ether, triethylene glycol methyl ether or ethyl ether, ethylene glycol n-butyl ether, diethylene glycol n-butyl ether, diethylene glycol methyl ether, ethylene glycol phenyl ether, propylene glycol methyl ether, dipropylene glycol methyl ether, tripropylene glycol methyl ether, propylene glycol methyl ether acetate, dipropylene glycol methyl ether acetate, propylene glycol n-propyl ether, dipropylene glycol n-propyl ether, tripropylene glycol n-propyl ether, propylene glycol n-butyl ether, dipropylene glycol n-butyl ether, tripropylene glycol n-butyl ether, propylene glycol phenyl ether, and dipropylene glycol dimethyl ether; nitrogen-containing compounds such as 2-pyrrolidone and N-methyl-2-pyrrolidone; sulfur-containing compounds such as dimethyl sulfoxide, tetramethylene sulfone, and thioethylene glycol; and combinations of any of the foregoing. In further embodiments, the polymer can include at least one of polyvinylpyrrolidone, polyvinylcaprolactam, polyvinyl alcohol, polyacrylamide, poly(2-ethyl-2-oxazoline) (PEOX), copolymers of polyvinyl butyrate, methyl vinyl ether, and maleic anhydride, certain copolymers of acrylic acid and / or hydroxyethyl acrylate, methyl cellulose, natural polymers (e.g., dextrin, guar gum, xanthan gum). In embodiments, the binder material can include one or more free-radically polymerizable or otherwise radiation-curable materials, including at least one of an acrylic monomer and / or oligomer and / or an epoxy resin, a photoinitiator and / or photocatalyst for curing the free-radically polymerizable or otherwise radiation-curable material. In particular embodiments, the organic solvent can have a flash point higher than 100 °C. In one aspect, the one or more organic solvents can be configured to control the drying speed of the liquid vehicle, control the surface tension of the liquid vehicle, or allow dissolution of ingredients (e.g., of a surfactant).

[0051] The amount of binder material is sufficient to bind the powder material. The areas that do not include binder material can be loose or unbound powder, which can be removed and captured after the process is complete and used as recycled powder. Notably, at the edges of the areas between bound powder material and unbound powder material, binder material can be present in some loose powder. Thus, the recycled powder can include some content of organic material, such as binder material included in the captured loose or unbound powder material, particularly at the interface areas of bound and unbound powder. Methods can be used to treat the loose powder material containing organic material to first remove a certain content of organic material, then recycle the powder material and use in one or more subsequent additive manufacturing processes to form an abrasive article.

[0052] Figure 1D The process includes binding the powder material by treating the layer to convert the binder from a liquid material to a solid material to bind the powder material. The process can include curing at least a portion of the binder material. In particular embodiments, the binding can include evaporation, thermal curing, chemical curing, radiation curing, or any combination thereof.

[0053] In embodiments, forming the green abrasive article can be conducted at a formation rate that can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, forming the green abrasive article can be conducted at a formation rate of at least 120 cc / hr, such as at least 130 cc / hr or at least 150 cc / hr or at least 180 cc / hr or at least 200 cc / hr or at least 300 cc / hr or at least 400 cc / hr or at least 500 cc / hr or at least 600 cc / hr or at least 700 cc / hr or at least 800 cc / hr or at least 900 cc / hr or at least 1000 cc / hr or at least 1200 cc / hr or at least 1400 cc / hr or at least 1600 cc / hr or at least 1800 cc / hr or at least 2000 cc / hr or at least 2200 cc / hr or at least 2400 cc / hr or at least 2600 cc / hr or at least 2800 cc / hr or at least 3000 cc / hr. In yet other embodiments, the formation rate can be no greater than 7000 cc / hr, such as no greater than 6000 cc / hr or no greater than 5000 cc / hr or no greater than 4000 cc / hr. It will be appreciated that the formation rate can be between any of the minimum and maximum values described above, including, for example, but not limited to, in the range of at least 120 cc / hr to no greater than 7000 cc / hr, such as in the range of at least 200 cc / hr to no greater than 5000 cc / hr or at least 800 cc / hr to no greater than 3000 cc / hr.

[0054] Figure 1Eis a depiction of an abrasive article, which can represent a green or a final formed abrasive article. It should be understood that the abrasive articles of the embodiments herein can have any three-dimensional shape, and Figure 1E only one possible shape is illustrated. The length (L) defines the longest dimension of the body, and the width (W) defines a dimension of the body that is substantially perpendicular to the length and can be a value that is less than the length and greater than the thickness (T). The thickness (T) of the body can extend in a direction that is perpendicular to the plane defined by the length and the width. The dimensions of any body of the embodiments herein can have a relationship of the length, width, and thickness defined as L > W > T. In those cases where the body is in the form of a cylindrical body with the axial axis longest, the length is the longest dimension in the axial direction, the width can be a first diameter of an end face, and the thickness can be another diameter. In the case of an abrasive article in the form of a disc, where the diameter is the largest dimension, the diameter defines the length of the body, the width defines a diameter that is perpendicular to the length (and can be the same as the length), and the thickness defines the dimension of the body in an axial direction that is perpendicular to the plane of the circular end face. It should be understood that reference to the length can be a reference to the diameter of a circular shape or surface or to the major axis of an elliptical shape or surface. It should also be understood that reference to the width can be a reference to the diameter of a circular shape or surface that is substantially perpendicular to the diameter defining the length or to the transverse (minor) axis of an elliptical shape or surface that extends substantially perpendicular to the major axis.

[0055] In embodiments, the green body can include an amount of abrasive particles that can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the green body can include at least 1 volume percent, such as at least 2 volume percent or at least 3 volume percent or at least 4 volume percent or at least 5 volume percent or at least 6 volume percent or at least 7 volume percent or at least 8 volume percent or at least 9 volume percent or at least 10 volume percent or at least 11 volume percent or at least 12 volume percent or at least 13 volume percent or at least 14 volume percent or at least 15 volume percent or at least 16 volume percent or at least 17 volume percent or at least 18 volume percent or at least 19 volume percent or at least 20 volume percent or at least 21 volume percent or at least 22 volume percent or at least 23 volume percent or at least 24 volume percent or at least 25 volume percent or at least 26 volume percent or at least 27 volume percent or at least 28 volume percent or at least 29 volume percent or at least 30 volume percent or at least 31 volume percent or at least 32 volume percent or at least 33 volume percent or at least 34 volume percent or at least 35 volume percent or at least 36 volume percent or at least 37 volume percent or at least 38 volume percent or at least 39 volume percent or at least 40 volume percent or at least 41 volume percent or at least 42 volume percent or at least 43 volume percent or at least 44 volume percent or at least 45 volume percent or at least 46 volume percent or at least 47 volume percent or at least 48 volume percent or at least 49 volume percent or at least 50 volume percent or at least 51 volume percent or at least 52 volume percent or at least 53 volume percent or at least 54 volume percent or at least 55 volume percent or at least 56 volume percent or at least 57 volume percent or at least 58 volume percent or at least 59 volume percent or at least 60 volume percent or at least 61 volume percent or at least 62 volume percent or at least 63 volume percent or at least 64 volume percent or at least 65 volume percent or at least 66 volume percent or at least 67 volume percent or at least 68 volume percent or at least 69 volume percent or at least 70 volume percent or at least 71 volume percent or at least 72 volume percent or at least 73 volume percent or at least 74 volume percent or at least 75 volume percent or at least 76 volume percent or at least 77 volume percent or at least 78 volume percent or at least 79 volume percent or at least 80 volume percent of abrasive particles, based on the total volume of the green body.In yet other embodiments, the green body can include not greater than 90 vol.%, such as not greater than 85 vol.% or not greater than 80 vol.% or not greater than 75 vol.% or not greater than 70 vol.% or not greater than 69 vol.% or not greater than 68 vol.% or not greater than 67 vol.% or not greater than 66 vol.% or not greater than 65 vol.% or not greater than 64 vol.% or not greater than 63 vol.% or not greater than 62 vol.% or not greater than 61 vol.% or not greater than 60 vol.% or not greater than 59 vol.% or not greater than 58 vol.% or not greater than 57 vol.% or not greater than 56 vol.% or not greater than 55 vol.% or not greater than 54 vol.% or not greater than 53 vol.% or not greater than 52 vol.% or not greater than 51 vol.% or not greater than 50 vol.% or not greater than 49 vol.% or not greater than 48 vol.% or not greater than 47 vol.% or not greater than 46 vol.% or not greater than 45 vol.% or not greater than 44 vol.% or not greater than 43 vol.% or not greater than 42 vol.% or not greater than 41 vol.% or not greater than 40 vol.% or not greater than 39 vol.% or not greater than 38 vol.% or not greater than 37 vol.% or not greater than 36 vol.% or not greater than 35 vol.% or not greater than 34 vol.% or not greater than 33 vol.% or not greater than 32 vol.% or not greater than 31 vol.% or not greater than 30 vol.% or not greater than 29 vol.% or not greater than 28 vol.% or not greater than 27 vol.% or not greater than 26 vol.% or not greater than 25 vol.% or not greater than 24 vol.% or not greater than 23 vol.% or not greater than 22 vol.% or not greater than 21 vol.% or not greater than 20 vol.% or not greater than 19 vol.% or not greater than 18 vol.% or not greater than 17 vol.% or not greater than 16 vol.% or not greater than 15 vol.% or not greater than 14 vol.% or not greater than 13 vol.% or not greater than 12 vol.% or not greater than 11 vol.% or not greater than 10 vol.% or not greater than 9 vol.% or not greater than 8 vol.% or not greater than 7 vol.% or not greater than 6 vol.% or not greater than 5 vol.% of abrasive particles. It will be appreciated that the green body can include abrasive particles in a percentage of the total volume of the green body between any of the minimum and maximum values described above, including, for example, but not limited to, a range of at least 1 vol.% to not greater than 99 vol.% of abrasive particles, such as at least 2 vol.% to not greater than 80 vol.% or at least 10 vol.% to not greater than 75 vol.% of abrasive particles.

[0056] In embodiments, the green body can include a certain amount of precursor bond material that can facilitate improved manufacture and / or performance of the abrasive article. In embodiments, the green body can include at least 1 vol% of the total volume of the green body, such as at least 2 vol% or at least 3 vol% or at least 4 vol% or at least 5 vol% or at least 6 vol% or at least 7 vol% or at least 8 vol% or at least 9 vol% or at least 10 vol% or at least 11 vol% or at least 12 vol% or at least 13 vol% or at least 14 vol% or at least 15 vol% or at least 16 vol% or at least 17 vol% or at least 18 vol% or at least 19 vol% or at least 20 vol% or at least 21 vol% or at least 22 vol% or at least 23 vol% or at least 24 vol% or at least 25 vol% or at least 26 vol% or at least 27 vol% or at least 28 vol% or at least 29 vol% or at least 30 vol% or at least 31 vol% or at least 32 vol% or at least 33 vol% or at least 34 vol% or at least 35 vol% or at least 36 vol% or at least 37 vol% or at least 38 vol% or at least 39 vol% or at least 40 vol% or at least 41 vol% or at least 42 vol% or at least 43 vol% or at least 44 vol% or at least 45 vol% or at least 46 vol% or at least 47 vol% or at least 48 vol% or at least 49 vol% or at least 50 vol% or at least 51 vol% or at least 52 vol% or at least 53 vol% or at least 54 vol% or at least 55 vol% or at least 56 vol% or at least 57 vol% or at least 58 vol% or at least 59 vol% or at least 60 vol% or at least 61 vol% or at least 62 vol% or at least 63 vol% or at least 64 vol% or at least 65 vol% or at least 66 vol% or at least 67 vol% or at least 68 vol% or at least 69 vol% or at least 70 vol% or at least 71 vol% or at least 72 vol% or at least 73 vol% or at least 74 vol% or at least 75 vol% or at least 76 vol% or at least 77 vol% or at least 78 vol% or at least 79 vol% or at least 80 vol% of precursor bond material.In yet other embodiments, the green body can include not greater than 90 vol%, such as not greater than 85 vol% or not greater than 80 vol% or not greater than 75 vol% or not greater than 70 vol% or not greater than 69 vol% or not greater than 68 vol% or not greater than 67 vol% or not greater than 66 vol% or not greater than 65 vol% or not greater than 64 vol% or not greater than 63 vol% or not greater than 62 vol% or not greater than 61 vol% or not greater than 60 vol% or not greater than 59 vol% or not greater than 58 vol% or not greater than 57 vol% or not greater than 56 vol% or not greater than 55 vol% or not greater than 54 vol% or not greater than 53 vol% or not greater than 52 vol% or not greater than 51 vol% or not greater than 50 vol% or not greater than 49 vol% or not greater than 48 vol% or not greater than 47 vol% or not greater than 46 vol% or not greater than 45 vol% or not greater than 44 vol% or not greater than 43 vol% or not greater than 42 vol% or not greater than 41 vol% or not greater than 40 vol% or not greater than 39 vol% or not greater than 38 vol% or not greater than 37 vol% or not greater than 36 vol% or not greater than 35 vol% or not greater than 34 vol% or not greater than 33 vol% or not greater than 32 vol% or not greater than 31 vol% or not greater than 30 vol% or not greater than 29 vol% or not greater than 28 vol% or not greater than 27 vol% or not greater than 26 vol% or not greater than 25 vol% or not greater than 24 vol% or not greater than 23 vol% or not greater than 22 vol% or not greater than 21 vol% or not greater than 20 vol% or not greater than 19 vol% or not greater than 18 vol% or not greater than 17 vol% or not greater than 16 vol% or not greater than 15 vol% or not greater than 14 vol% or not greater than 13 vol% or not greater than 12 vol% or not greater than 11 vol% or not greater than 10 vol% or not greater than 9 vol% or not greater than 8 vol% or not greater than 7 vol% or not greater than 6 vol% or not greater than 5 vol% of precursor bond material, based on the total volume of the green body. It will be appreciated that the green body can include a percentage of precursor bond material, based on the total volume of the green body, between any of the minimum and maximum values described above, including, for example, but not limited to, a range of at least 1 vol% to not greater than 99 vol% of precursor bond material, such as at least 2 vol% to not greater than 80 vol% or at least 10 vol% to not greater than 75 vol% of precursor bond material.

[0057] Figure 2A and Figure 2B including a perspective view of an abrasive article, which can be a green body, a final formed abrasive article, a green body from a batch of green bodies, or an abrasive article body from a batch of abrasive article bodies, in accordance with embodiments herein. Figure 2A and Figure 2BThe body of 201 can be formed by any of the methods of the embodiments herein and formed in a build direction 251. The body 201 can have surfaces 201, 203, 204, and 205 that are transverse to the build direction 251 and surfaces 202 and 207 that are not transverse to the build direction 251. The body 211 can be a cylindrical shape having a surface 213 that is transverse to the build direction and surfaces 212 and 214 that are not transverse to the build direction 251. It should be appreciated that these abrasive articles can be any number of shapes and are not limited to those explicitly shown herein. It should be appreciated that a variety of build directions can be used to form the body. In certain embodiments, the build direction can affect certain characteristics of the abrasive article as a green abrasive article and / or a final formed abrasive article. In certain instances, transverse surfaces can have a different Sdr (developed interface area ratio) than other surfaces. In one embodiment, a transverse surface can have a higher Sdr than a surface having a different orientation than the transverse surface, and more specifically, a surface having a different orientation relative to the build direction 251. It should be appreciated that the build direction can be manipulated to control which surfaces have a relatively higher or lower Sdr. For example, the abrasive can be configured such that the smallest surface is not transverse to the build direction, thereby minimizing the amount of surface area having a low Sdr. Different Sdr values can be valuable for different applications. For example, a high Sdr surface can be useful as an abrasive working surface in low pressure grinding applications. High or low Sdr surfaces can also be more easily bonded or adhered to a substrate or another surface using a bond, adhesive, or other coupling means, depending on the composition of the coupling means. In one embodiment, a transverse surface can be an abrasive working surface of the body. In another embodiment, a surface that is not transverse can be an abrasive working surface of the body. In embodiments, a transverse surface or a surface that is not transverse can be coupled to another surface via a bond or adhesive. In one embodiment, a transverse surface can have visible layering or roughness that is not present on other surfaces.

[0058] Figure 3 An illustration of the measurement principle of the developed interface area ratio Sdr. The developed interface area ratio Sdr represents the percentage increase of the surface area 301 (provided by the surface texture) relative to the corresponding underlying projected area 302 (ideal plane) and is measured according to ISO standard method ISO 25178-2:2012.

[0059] The developed interface area ratio Sdr represents the percentage increase of the surface area Al 301 related to the surface texture compared to the projected area A0 702, where A0 302 corresponds to the ideal plane underlying the measured surface texture. Figure 3A plot showing the relationship of surface area A1301 to projected area A0302 is shown in FIG. 13. Sdr measurements were made with an Olympus LEXT OLS5000 laser confocal microscope. At 50x magnification, using a filter cartridge, the surface area analyzed was 257 x 257 pm.

[0060] Sdr can also be expressed by the following formula: Sdr = [(Al / AO) - 1] x 100 (%).

[0061] In one embodiment, the additive manufacturing process can be conducted at a particular print head deposition resolution, which can result in improved manufacture or performance of the abrasive body. It will be appreciated that the print head deposition resolution can be between any minimum value and any maximum value claimed herein. Without wishing to be bound by theory, some data suggest that the manipulation resolution can change the Sdr on the surface of the body. A small resolution can result in a smaller Sdr on the surface transverse to the build direction, as well as a smaller difference in Sdr between the transverse surface and the surface not transverse to the build direction. The same can be true for the layer thickness before and / or after compaction.

[0062] In one aspect, the additive manufacturing process can include using a powder material having a multimodal particle distribution as a starting material. The multimodal particle size distribution of the powder material can be related to different sizes of a single phase material or a mixture formed from different powder components, including, for example, but not limited to, a mixture including a first particulate material (e.g., an abrasive particle having a first particle size distribution) and a second particulate material (e.g., a particulate bond material or a bond material precursor having a second particle size distribution different from the first particle size distribution).

[0063] In one particular aspect, the powder material for the additive manufacturing process can be a bimodal particle distribution, where a first plurality of particles can have an average particle size (D50) of at least 1 pm and not greater than 10 pm, and a second plurality of particles can have an average particle size (D50) of at least 20 pm and not greater than 50 pm.

[0064] In another aspect, the weight % ratio of the first plurality of particles to the second plurality of particles can be 1 :0.1 to 1 :10. In certain aspects, the weight % ratio can be not greater than 1 :0.3, such as not greater than 1 :0.5 or not greater than 1 : 1 or not greater than 1 :2 or not greater than 1 :3 or not greater than 1 :4 or not greater than 1 :5 or not greater than 1 :6 or not greater than 1 :7 or not greater than 1 :8 or not greater than 1 :9 or not greater than 1 : 10.

[0065] In embodiments, the final formed abrasive body resulting from further processing of the green abrasive article body can have the same amount (volume %) of abrasive particles as the embodiments describing the amount of abrasive particles in the green abrasive article body.

[0066] In an embodiment, the body can include a bond material or a bond material precursor comprising an organic material or an inorganic material or any combination thereof. In an embodiment, the bond material can comprise a thermoplastic, a thermoset, a resin, or any combination thereof. In an embodiment, the bond material can comprise a phenolic resin, a polyimide, a polyamide, a polyester, an aromatic polyamide, an epoxy resin, or any combination thereof. In an embodiment, the bond material can comprise a transition metal element. In another embodiment, the bond material can include an amorphous phase, a polycrystalline phase, or any combination thereof. In an embodiment, the bond material can comprise a ceramic material, a vitreous material, or any combination thereof, or wherein the ceramic material is polycrystalline, or wherein the vitreous material is amorphous. In an embodiment, the bond material can comprise an oxide. In an embodiment, the bond material can comprise an alumina-containing vitreous material. In an embodiment, the bond material can comprise a silica-containing vitreous material. In an embodiment, the bond material can comprise at least one of alumina, silica, boron oxide, bismuth oxide, zinc oxide, barium oxide, magnesium oxide, calcium oxide, lithium oxide, sodium oxide, potassium oxide, cesium oxide, strontium oxide, zirconium oxide, manganese oxide, or any combination thereof.

[0067] In an embodiment, the abrasive body can include a first surface having a first developed interfacial area ratio (Sdr1) and a second surface having a second developed interfacial area ratio (Sdr2). In an embodiment, Sdr1 can be greater than Sdr2. In another embodiment, Sdr1 can be less than Sdr2. In an embodiment, the first surface can be a transverse surface with respect to a build direction of the abrasive article.

[0068] In an embodiment, a certain percentage of the surface area of the body can be surfaces of relatively higher Sdr. It will be appreciated that a surface having a relatively higher Sdr has an Sdr that is greater than the average Sdr of the entire body. In embodiments, at least 5% or at least 7% or at least 10% or at least 12% or at least 14% or at least 16% or at least 20% or at least 22% or at least 24% or at least 26% or at least 28% or at least 30% or at least 32% or at least 34% or at least 36% or at least 38% or at least 40% or at least 42% or at least 44% or at least 46% or at least 48% or at least 50% or at least 52% or at least 54% or at least 56% or at least 58% or at least 60% or at least 62% or at least 64% or at least 66% or at least 68% or at least 70% or at least 72% or at least 74% or at least 76% or at least 78% or at least 80% or at least 82% or at least 84% or at least 86% or at least 88% or at least 90% or at least 93% or at least 95% of the outer surface area of the body can be surfaces of relatively higher Sdr. In embodiments, no more than 95% or no more than 93% or no more than 90% or no more than 88% or no more than 86% or no more than 84% or no more than 82% or no more than 80% or no more than 78% or no more than 76% or no more than 74% or no more than 72% or no more than 70% or no more than 68% or no more than 66% or no more than 64% or no more than 62% or no more than 60% or no more than 58% or no more than 56% or no more than 54% or no more than 52% or no more than 50% or no more than 48% or no more than 46% or no more than 44% or no more than 42% or no more than 40% or no more than 38% or no more than 36% or no more than 34% or no more than 32% or no more than 30% or no more than 28% or at least 26% or no more than 24% or no more than 22% or no more than 20% or no more than 18% or no more than 16% or no more than 14% or no more than 10% or no more than 7% or no more than 5% of the outer surface area of the body can be surfaces of relatively higher Sdr. It will be appreciated that the percentage of surface area having a relatively higher Sdr can be between any of the minimum values and any of the maximum values described above.

[0069] In an embodiment, the first surface can have a particular Sdr1, which can facilitate improved performance and / or manufacturing of the abrasive article. In embodiments, the Sdr1 can be at least 40% or at least 42% or at least 44% or at least 46% or at least 48% or at least 50% or at least 52% or at least 54% or at least 56% or at least 58% or at least 60% or at least 62% or at least 64% or at least 66% or at least 68% or at least 70%. In another embodiment, the Sdr1 is not greater than 140% or not greater than 135% or not greater than 130% or not greater than 125% or not greater than 120% or not greater than 115% or not greater than 110% or not greater than 105% or not greater than 100% or not greater than 95% or not greater than 90% or not greater than 85% or not greater than 80%. It will be appreciated that the Sdr1 will be between any of the minimum values and any of the maximum values described above.

[0070] In an embodiment, the abrasive body can include a second surface having a particular Sdr2, which can facilitate improved performance of the abrasive article. In embodiments, the Sdr2 can be not greater than 110% or not greater than 105% or not greater than 100% or not greater than 95% or not greater than 90% or not greater than 85% or not greater than 80% or not greater than 75%. In another embodiment, the Sdr2 is at least 5% or at least 10% or at least 15% or at least 20% or at least 25% or at least 30% or at least 35% or at least 40% or at least 45%. It will be appreciated that the Sdr2 will be between any of the minimum values and any of the maximum values described above.

[0071] In an embodiment, the first surface can have an Sdr1 that differs from the Sdr2 of the second surface by a particular amount, which can facilitate improved manufacturing or performance of the abrasive article. In a non-limiting embodiment, the Sdr1 can have a greater value relative to the Sdr2. In embodiments, the first surface can have an Sdr1 that differs from the Sdr2 of the second surface by at least 1% or differs from the Sdr2 by at least 2% or at least 3% or at least 4% or at least 5% or at least 6% or at least 7% or at least 8% or at least 9% or at least 10%. In another embodiment, the first surface can have an Sdr1 that differs from the Sdr2 by not greater than 25% or differs from the Sdr2 by not greater than 24% or not greater than 23% or not greater than 22% or not greater than 21% or not greater than 20% or not greater than 19% or not greater than 18% or not greater than 17% or not greater than 16% or not greater than 15%. It will be appreciated that the percentage difference between the Sdr1 and the Sdr2 can be between any of the minimum values and any of the maximum values described above. It will be appreciated that there can be more than two surfaces having different Sdr values, and the above-described difference in Sdr1 and Sdr2 can apply equally between two or more surfaces (e.g., outer surfaces) of the body.

[0072] In embodiments, the ratio of Sdr1 :Sdr2 can be no greater than 1 :2 or no greater than 1 :1.9 or no greater than 1 :1.8 or no greater than 1 :1.7 or no greater than 1 :1.6 or no greater than 1 :1.5 or no greater than 1 :1.4 or no greater than 1 :1.3. In embodiments, the ratio of Sdr1 :Sdr2 can be at least 1 :1.01 or at least 1 :1.03 or at least 1 :1.05.

[0073] In embodiments, the first surface (optionally the working surface) can be at a particular angular orientation relative to the second surface. The angle can be at least 2°, at least 5°, at least 8°, at least 10°, at least 12°, at least 15°, at least 18°, at least 19°, at least 20°, at least 22°, at least 25°, at least 27°, at least 30°, at least 33°, at least 35°, at least 37°, at least 40°, at least 41°, at least 43°, at least 45°, at least 47°, at least 48°, at least 50°, at least 52°, at least 55°, at least 58°, at least 60°, at least 62°, at least 64°, at least 66°, at least 68°, at least 70°, at least 72°, at least 74°, at least 76°, at least 78°, at least 80°, at least 82°, at least 85°, at least 88°, or at least 90°. In another embodiment, the angle can be at most 180°, at most 178°, at most 176°, at most 174°, at most 172°, at most 170°, at most 168°, at most 166°, at most 164°, at most 162°, at most 160°, at most 158°, at most 156°, at most 154°, at most 152°, at most 150°, at most 147°, at most 145°, at most 143°, at most 140°, at most 138°, at most 135°, at most 133°, at most 130°, at most 127°, at most 124°, at most 121°, at most 118°, at most 115°, at most 112°, at most 109°, at most 105°, at most 102°, at most 99°, at most 96°, at most 93°, at most 90°, such as at most 88°, at most 86°, at most 84°, at most 82°, at most 80°, at most 78°, at most 75°, at most 74°, at most 72°, at most 70°, at most 68°, at most 66°, at most 64°, at most 62°, at most 60°, at most 58°, at most 66°, at most 64°, at most 62°, at most 60°, at most 58°, at most 55°, at most 54°, at most 52°, at most 50°, at most 48°, at most 46°, at most 44°, at most 42°, at most 40°, at most 38°, at most 36°, at most 34°, at most 32°, or at most 30°. It will be appreciated that the angle between the first surface and the second surface can be between any of the minimum and maximum values described above. In one non-limiting embodiment, the first surface and the second surface can be orthogonal to one another.

[0074] In an embodiment, the first surface can have a particular surface roughness (Sai), which can facilitate improved performance and / or manufacturing of the abrasive body. In embodiments, Sai can be at least 1 micron or at least 1.5 microns or at least 2 microns or at least 2.5 microns or at least 3 microns or at least 3.5 microns or at least 4 microns or at least 4.5 microns or at least 5 microns. In another embodiment, Sai can be no greater than 30 microns, such as no greater than 28 microns or no greater than 25 microns or no greater than 22 microns or no greater than 18 microns or no greater than 15 microns. It will be appreciated that Sai can be between any of the minimum values and any of the maximum values described above.

[0075] In an embodiment, the second surface can have a particular surface roughness (Sa2), which can facilitate improved performance and / or manufacturing of the abrasive body. In embodiments, Sa2 can be at least 1 micron, such as at least 2 microns or at least 3 microns or at least 4 microns or at least 5 microns. In another embodiment, Sa2 can be no greater than 25 microns, such as no greater than 23 microns or no greater than 21 microns or no greater than 19 microns or no greater than 17 microns or no greater than 15 microns or no greater than 14 microns or no greater than 13 microns. It will be appreciated that Sa2 can be between any of the minimum values and any of the maximum values described above.

[0076] In an embodiment, the first surface can have a Sai that differs from the Sa2 of the second surface by a particular amount, which can facilitate improved manufacturing or performance of the abrasive article. In embodiments, the first surface can have a Sai that differs from the Sdr2 of the second surface by at least 0.2 microns, such as at least 0.4 microns or at least 0.6 microns or at least 0.8 microns or at least 1 micron. In another embodiment, the first surface can have a Sai that differs from Sa2 by no greater than 6 microns or differs from Sa2 by no greater than 5.5 microns or no greater than 5 microns or no greater than 4.5 microns or no greater than 4 microns or no greater than 3.5 microns or no greater than 3 microns. It will be appreciated that the percentage difference between Sai and Sa2 can be between any of the minimum values and any of the maximum values described above.

[0077] Frequency domain images were obtained by processing SEM images via a Fourier transform in Python. Three SEM images were taken of three cross-sections of a bonded abrasive body. Figures 4A to 4E An image including a cross-section of a body of a final formed abrasive article formed according to an additive manufacturing technique. Figure 4A A scanning electron microscope image including a cross-section of a body. As shown, the abrasive body can include abrasive particles 401 bonded by a bond matrix including a bond material 402 and an infiltrant material 403 and a filler material 404. The image can be processed by adjusting the threshold so that only the bond material remains Figure 4A Figure 4B ​of the image. Figure 4C including images further processed by focusing on Figure 4B the center (brightest region) of the image. Figure 4D is Figure 4C is an image of the magnified region within box 407 in Figure 4D As shown, the noise 408 is gray and the frequency signals 410 and 412 have a higher brightness than the noise. From Figure 4D the noise is removed, a frequency domain image is generated and shown in Figure 4E The bright spot in the center is the zero frequency component indicative of the average brightness of the image in Figure 4B and the other two symmetrically distributed bright spots represent the frequencies of the bond material 402. The fast Fourier transform value is the average number of points shown in the frequency domain image other than the zero frequency component shown in at least three cross-sectional images from the same body. For example, the microstructure feature value can be determined by dividing the sum of the number of points that are not the center point of each frequency domain image by the total number of frequency domain images.

[0078] In embodiments, the body of the abrasive article can include a microstructure feature value that can facilitate improved performance of the abrasive article. In embodiments, the microstructure feature can be at least 1, such as at least 2 or at least 3 or at least 4 or at least 5 or at least 6 or at least 7. In yet other embodiments, the microstructure feature can be not greater than 10 or not greater than 9 or not greater than 8 or not greater than 7 or not greater than 6 or not greater than 5 or not greater than 4 or not greater than 3. It will be appreciated that the microstructure feature can be a value between and including the minimum and maximum values described above, such as in a range of at least 1 to not greater than 10 or in a range of at least 2 to not greater than 10.

[0079] In another embodiment, the microstructure feature can include a pitch value. The abrasive body can include an average distance determined based on frequency domain images (i.e., images of Figure 4E the body of the abrasive article). As used herein, the pitch value can be determined using the average distance. The average distance is the average of the distances between the zero frequency component (i.e., the center point) of the frequency domain images of the at least three cross sections of the abrasive body and another point. For example, the average distance can be calculated by dividing the sum of the distances between the center point of each frequency domain image and another point by the number of distances that make up the sum. The pitch value of the abrasive body can be a relative value that can be obtained by dividing the average distance of the abrasive body by the average distance of an abrasive body having layers printed with a thickness of 120 micrometers.

[0080] More specifically, the pitch value can be determined as follows. The bonded abrasive body includes layers printed with a thickness of 120 micrometers. All SEM images are processed to obtain Figure 4E images as shown. As Figure 4EThe average distance was then divided by itself, which resulted in the pitch value of the body.

[0081] In yet another embodiment, the body of the abrasive article can include a microstructure feature that includes a pitch value that can facilitate improved performance of the abrasive article. In embodiments, the pitch value can be at least 0.01 or at least 0.03 or at least 0.04 or at least 0.06 or at least 0.08 or at least 0.1 or at least 0.2, at least 0.3 or at least 0.4 or at least 0.5 or at least 0.6 or at least 0.7 or at least 0.8 or at least 0.9 or at least 1, at least 1.1 or at least 1.3 or at least 1.4 or at least 1.5 or at least 1.6 or at least 1.8 or at least 1.9 or at least 2 or at least 2.1 or at least 2.3 or at least 2.5 or at least 2.6 or at least 2.8 or at least 3 or at least 3.1 or at least 3.3 or at least 3.5 or at least 3.6 or at least 3.8 or at least 4, at least 4.2 or at least 4.5 or at least 4.7 or at least 5 or at least 6 or at least 7 or at least 8 or at least 9 or at least 10 or at least 11 or at least 12 or at least 15 or at least 20 or at least 30 or at least 80 or at least 100 or at least 200 or at least 300 or at least 400 or at least 500. In yet another embodiment, the pitch value can be no greater than 2000 or no greater than 1000 or no greater than 500 or no greater than 400 or no greater than 300 or no greater than 200 or no greater than 100 or no greater than 80 or no greater than 50 or no greater than 40 or no greater than 30 or no greater than 20 or no greater than 10 or no greater than 9.8, no greater than 9.6, no greater than 9.5, no greater than 9.3 or no greater than 9 or no greater than 8.8, no greater than 8.6, no greater than 8.4, no greater than 8.2 or no greater than 8 or no greater than 7.8, no greater than 7.6, no greater than 7.4, no greater than 7.2 or no greater than 7 or no greater than 6.8, no greater than 6.6, no greater than 6.4, no greater than 6.2 or no greater than 6 or no greater than 5.8, no greater than 5.6, no greater than 5.5, no greater than 5.2 or no greater than 5 or no greater than 4.8, no greater than 4.6, no greater than 4.4, no greater than 4.2 or no greater than 4 or no greater than 3.8, no greater than 3.6, no greater than 3.4, no greater than 3.2 or no greater than 3 or no greater than 2.8, no greater than 2.6, no greater than 2.4, no greater than 2.2 or no greater than 2 or no greater than 1.8 or no greater than 1.6 or no greater than 1.5 or no greater than 1.4 or no greater than 1.3 or no greater than 1.2 or no greater than 1 or no greater than 0.8, no greater than 0.6, no greater than 0.4, no greater than 0.2 or no greater than 0.1. It will be appreciated that the pitch value can be between and including the values of the minimum and maximum values described above, for example, in the range of at least 1 to no greater than 1000.

[0082] Figure 5A and Figure 5B represents an image from a bonded abrasive formed by a conventional hot-pressing processing technique. Figure 5A is a cross-sectional SEM image, which is processed in the same manner as described above according to a fast Fourier transform to obtain an image of Figure 5B The microstructure feature value of the sample is 1.

[0083] Figure 6A includes an illustration of a build box for forming an abrasive article according to an embodiment. The build box 600 is configured to contain powder material as it is deposited. As shown in Figure 6A the build box 600 can include a portion comprising loose or unbound powder 601. The build box 600 can also include a portion representing a region of bound powder, which portion defines a green abrasive article 603 surrounded by the portion of loose or unbound powder 601.

[0084] Figure 6B includes an illustration of a process for capturing loose powder after a forming operation to form a green abrasive article is completed. The loose powder 605 can be captured via a capture mechanism 607, which can include suction or any other suitable means to remove the loose powder 605 and separate the green abrasive article 603 from the portion of loose or unbound powder 601. The captured loose powder 605 can be stored in a container. Additionally or alternatively, the loose powder 605, which can include some content of organic material from the forming process (e.g., binder material), can be processed to remove a content of organic material. Thus, the loose powder 605 can be a recycled powder material that is suitable for use in subsequent forming operations to form one or more green abrasive articles.

[0085] Figure 6C is an illustration of a process for recycling unused and loose powder material.

[0086] Figure 7A is a perspective view of a body of an abrasive article. As shown, the body has a length, a width, and a thickness, and can be evaluated along any of these axes by destructive or non-destructive methods to evaluate one or more properties associated with the body or a batch of bodies. Such properties can include, but are not limited to, density variation-L, density variation-W, density variation-T, size variation-L, size variation-W, size variation-T, hardness variation-L, hardness variation-W, hardness variation-T, MOR variation-L, MOR variation-W, MOR variation-T, MOE variation-L, MOE variation-W, and MOE variation-T. Figure 7BThree cross-sectional images including cross-sections "a", "b", and "c" along the length of the body. Such cross-sections can be generated by cutting the sample for evaluation of one or more properties claimed herein. Alternatively, these cross-sections can be generated from a 3D scan of the body to evaluate certain dimensional features and to evaluate the quality and consistency of the geometry of the body. Figure 7C Three cross-sectional images including cross-sections "d", "e", and "f" along the width of the body. Figure 7D Three cross-sectional images including cross-sections "g", "h", and "i" along the thickness of the body. In certain cases, the difference in cross-sectional area of each cross-section can be used to quantify the geometric quality of the body.

[0087] In embodiments, the body of the abrasive article can have a density variation -L that can facilitate improved performance of the abrasive article. In embodiments, the density variation -L can be no greater than 20%, such as no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1%. The density variation -L is calculated by taking multiple measurements of the density spaced apart from each other along the length of the body. The density measurements can be evaluated by cross-sectional images taken in a plane substantially perpendicular to the length of the body. Alternatively, ultrasonic or other non-destructive techniques can be used to create a map of the density variation in the body and to measure the density values and the variation of the density values of the body along the length of the body. The density variation -L can be the percent difference between the average density value of the body and the density value of the body having the greatest positive or negative density difference from the average density value. The number of density values of the body or batch should have a suitable statistically relevant sample size.

[0088] In embodiments, the body of the abrasive article can have a density variation-W that can facilitate improved performance of the abrasive article. In embodiments, the density variation-W can be no greater than 20%, such as no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1%. The density variation-W is calculated by taking multiple measurements of density spaced apart from one another along the width of the body. The density measurements can be assessed by cross-sectional images taken in a plane substantially perpendicular to the width of the body at different locations spaced apart from one another along the width dimension. Alternatively, ultrasound or other non-destructive techniques can be used to create a map of the density variation in the body and to measure the density values and the variation in the density values of the body along the width of the body. The density variation-W can be the percent difference between the average density value of the body and the density value of the body having the greatest positive or negative density difference from the average density value. The number of density values of the body or batch should have a suitable statistically relevant sample size.

[0089] In embodiments, the body of the abrasive article can have a density variation-T that can facilitate improved performance of the abrasive article. In embodiments, the density variation-T can be no greater than 20%, such as no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1%. The density variation-T is calculated by taking multiple measurements of density spaced apart from one another along the thickness of the body. The density measurements can be assessed by cross-sectional images taken in a plane substantially perpendicular to the thickness of the body at different locations spaced apart from one another along the thickness dimension. Alternatively, ultrasound or other non-destructive techniques can be used to create a map of the density variation in the body and to measure the density values and the variation in the density values of the body along the thickness of the body. The density variation-T can be the percent difference between the average density value of the body and the density value of the body having the greatest positive or negative density difference from the average density value. The number of density values of the body or batch should have a suitable statistically relevant sample size.

[0090] In embodiments, the body of the abrasive article can have a hardness variation-L that can facilitate improved performance of the abrasive article. In embodiments, the body of the abrasive article can have a hardness variation-L of not greater than 20%, such as not greater than 19% or not greater than 18% or not greater than 17% or not greater than 16% or not greater than 15% or not greater than 14% or not greater than 13% or not greater than 12% or not greater than 11% or not greater than 10% or not greater than 9% or not greater than 8% or not greater than 7% or not greater than 6% or not greater than 5% or not greater than 4% or not greater than 3% or not greater than 2% or not greater than 1% or not greater than 0.5% or not greater than 0.3% or not greater than 0.1% of the average hardness value of the body, where the hardness variation-L is measured along the length of the body. In yet other embodiments, the hardness variation-L can be at least 0.00001% or at least 0.0001%. It will be appreciated that the hardness variation-L can be within a range including any of the minimum and maximum values noted above, including, for example, but not limited to, at least 0.0001% and not greater than 20%, or within a range of at least 0.001% and not greater than 10%.

[0091] In embodiments, the body of the abrasive article can have a hardness variation-W that can facilitate improved performance of the abrasive article. In embodiments, the body of the abrasive article can have a hardness variation-W of not greater than 20%, such as not greater than 19% or not greater than 18% or not greater than 17% or not greater than 16% or not greater than 15% or not greater than 14% or not greater than 13% or not greater than 12% or not greater than 11% or not greater than 10% or not greater than 9% or not greater than 8% or not greater than 7% or not greater than 6% or not greater than 5% or not greater than 4% or not greater than 3% or not greater than 2% or not greater than 1% or not greater than 0.5% or not greater than 0.3% or not greater than 0.1% of the average hardness value of the body, where the hardness variation-W is measured along the width of the body. In yet other embodiments, the hardness variation-W can be at least 0.00001% or at least 0.0001%. It will be appreciated that the hardness variation-W can be within a range including any of the minimum and maximum values noted above, including, for example, but not limited to, at least 0.0001% and not greater than 20%, or within a range of at least 0.001% and not greater than 10%.

[0092] In embodiments, the body of the abrasive article can have a hardness variation-T that can facilitate improved performance of the abrasive article. In embodiments, the body of the abrasive article can have a hardness variation-T of not greater than 20%, such as not greater than 19% or not greater than 18% or not greater than 17% or not greater than 16% or not greater than 15% or not greater than 14% or not greater than 13% or not greater than 12% or not greater than 11% or not greater than 10% or not greater than 9% or not greater than 8% or not greater than 7% or not greater than 6% or not greater than 5% or not greater than 4% or not greater than 3% or not greater than 2% or not greater than 1% or not greater than 0.5% or not greater than 0.3% or not greater than 0.1% of the average hardness value of the body, where the hardness variation-T is measured along the thickness of the body. In still further embodiments, the hardness variation-T can be at least 0.00001% or at least 0.0001%. It will be appreciated that the hardness variation-T can be within a range including any of the minimum and maximum values noted above, including, for example, but not limited to, at least 0.0001% and not greater than 20%, or within a range of at least 0.001% and not greater than 10%.

[0093] In embodiments, a batch of abrasive articles can have a batch hardness variation that can facilitate improved performance of the abrasive articles. In embodiments, the batch of abrasive articles can have a batch hardness variation of not greater than 20%, such as not greater than 19% or not greater than 18% or not greater than 17% or not greater than 16% or not greater than 15% or not greater than 14% or not greater than 13% or not greater than 12% or not greater than 11% or not greater than 10% or not greater than 9% or not greater than 8% or not greater than 7% or not greater than 6% or not greater than 5% or not greater than 4% or not greater than 3% or not greater than 2% or not greater than 1% or not greater than 0.5% or not greater than 0.3% or not greater than 0.1% of the average hardness value of the batch. In still further embodiments, the batch hardness variation can be at least 0.00001% or at least 0.0001%. It will be appreciated that the batch hardness variation can be within a range including any of the minimum and maximum values noted above, including, for example, but not limited to, at least 0.0001% and not greater than 20%, or within a range of at least 0.001% and not greater than 10%. The batch hardness variation is calculated by measuring the hardness of each body of the plurality of bodies produced via a single operation, where the batch hardness variation is a measure of the percent difference between the average hardness value of the batch and the hardness value of the body having the greatest positive or negative hardness difference from the average hardness value of the batch. It is noted that a plurality of hardness values can be obtained for each of the plurality of bodies in the batch, and any hardness value obtained from a body is relevant for comparison and calculation of the batch hardness variation. Each hardness value of the body can be averaged to produce an average body hardness value for each discrete body in the batch. The average batch hardness value can be calculated by averaging the average hardness value of each body of the batch. The number of hardness values of a body or batch should have a suitable statistically relevant sample size.

[0094] In embodiments, the body of the abrasive article can have a dimensional variation-L that can facilitate improved performance of the abrasive article. In embodiments, the dimensional variation-L can be no greater than 90% of an average dimension value of the body, such as no greater than 89% or no greater than 88% or no greater than 87% or no greater than 86% or no greater than 85% or no greater than 84% or no greater than 83% or no greater than 82% or no greater than 81% or no greater than 80% or no greater than 79% or no greater than 78% or no greater than 77% or no greater than 76% or no greater than 75% or no greater than 74% or no greater than 73% or no greater than 72% or no greater than 71% or no greater than 70% or no greater than 69% or no greater than 68% or no greater than 67% or no greater than 66% or no greater than 65% or no greater than 64% or no greater than 63% or no greater than 62% or no greater than 61% or no greater than 60% or no greater than 59% or no greater than 58% or no greater than 57% or no greater than 56% or no greater than 55% or no greater than 54% or no greater than 53% or no greater than 52% or no greater than 51% or no greater than 50% or no greater than 49% or no greater than 48% or no greater than 47% or no greater than 46% or no greater than 45% or no greater than 44% or no greater than 43% or no greater than 42% or no greater than 41% or no greater than 40% or no greater than 39% or no greater than 38% or no greater than 37% or no greater than 36% or no greater than 35% or no greater than 34% or no greater than 33% or no greater than 32% or no greater than 31% or no greater than 30% or no greater than 29% or no greater than 28% or no greater than 27% or no greater than 26% or no greater than 25% or no greater than 24% or no greater than 23% or no greater than 22% or no greater than 21% or no greater than 20% or no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1%, wherein the dimensional variation-L is measured along the length of the body. In yet another embodiment, the dimensional variation-L is at least 0.0001% or at least 0.001% or at least 0.01% or at least 0.1%. It will be appreciated that the dimensional variation-L can be within a range including any of the minimum and maximum values noted above, including, for example, but not limited to, at least 0.0001% and no greater than 90%, or within a range of at least 0.001% and no greater than 80%.

[0095] It should be understood that a batch of abrasive articles can have a batch size variation - L having a value of any of the values described above, including a range between any of the minimum and maximum values described above with respect to size variation - L, where the batch size variation - L is calculated by measuring the length of each of the plurality of bodies produced via a single operation, where the batch size variation - L is the percent difference between the average length of the same shape bodies of a batch and the length value of the body having the greatest positive or negative length difference from the average length value of the batch. Note that multiple length values can be obtained for each of the plurality of bodies in the batch, and any length value obtained from a body is relevant for comparison and calculation of the batch size variation - L. More than one length measurement can be made on a separate body and averaged to produce an average length value for each discrete body in the batch. An average length value for the batch can be calculated by averaging the average length values for each same shape body of the batch. The number of length values for a body or the batch should have a suitably statistically relevant sample size.

[0096] In embodiments, the body of the abrasive article can have a dimensional variation -W that can facilitate improved performance of the abrasive article. In embodiments, the dimensional variation -W can be no greater than 90% of the average dimension value of the body, such as no greater than 89% or no greater than 88% or no greater than 87% or no greater than 86% or no greater than 85% or no greater than 84% or no greater than 83% or no greater than 82% or no greater than 81% or no greater than 80% or no greater than 79% or no greater than 78% or no greater than 77% or no greater than 76% or no greater than 75% or no greater than 74% or no greater than 73% or no greater than 72% or no greater than 71% or no greater than 70% or no greater than 69% or no greater than 68% or no greater than 67% or no greater than 66% or no greater than 65% or no greater than 64% or no greater than 63% or no greater than 62% or no greater than 61% or no greater than 60% or no greater than 59% or no greater than 58% or no greater than 57% or no greater than 56% or no greater than 55% or no greater than 54% or no greater than 53% or no greater than 52% or no greater than 51% or no greater than 50% or no greater than 49% or no greater than 48% or no greater than 47% or no greater than 46% or no greater than 45% or no greater than 44% or no greater than 43% or no greater than 42% or no greater than 41% or no greater than 40% or no greater than 39% or no greater than 38% or no greater than 37% or no greater than 36% or no greater than 35% or no greater than 34% or no greater than 33% or no greater than 32% or no greater than 31% or no greater than 30% or no greater than 29% or no greater than 28% or no greater than 27% or no greater than 26% or no greater than 25% or no greater than 24% or no greater than 23% or no greater than 22% or no greater than 21% or no greater than 20% or no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1%, wherein the dimensional variation -W is measured along the width of the body. In yet another embodiment, the dimensional variation -W is at least 0.0001% or at least 0.001% or at least 0.01% or at least 0.1%. It will be appreciated that the dimensional variation -W can be within a range including any of the minimum and maximum values noted above, including, for example, but not limited to, at least 0.0001% and no greater than 90%, or within a range of at least 0.001% and no greater than 80%.

[0097] It should be understood that a batch of abrasive articles can have a batch size variation - W having a value of any of the values described above, including a range between any of the minimum and maximum values described above with respect to size variation - W, where the batch size variation - W is calculated by measuring the width of each of the plurality of bodies produced via a single operation, where the batch size variation - W is the percent difference between the average width of the same shape bodies of a batch and the width value of the body having the greatest positive or negative width difference from the average width value of the batch. Note that a plurality of width values can be obtained for each of the plurality of bodies in the batch, and any width value obtained from a body is relevant for comparison and calculation of the batch size variation - W. More than one width measurement can be made on a single body, and averaged to produce an average width value for each discrete body in the batch. An average width value for the batch can be calculated by averaging the average width values for each same shape body of the batch. The number of width values for a body or the batch should have a suitably statistically relevant sample size.

[0098] In embodiments, the body of the abrasive article can have a dimensional variation-T that can facilitate improved performance of the abrasive article. In embodiments, the dimensional variation-T can be no greater than 90% of the average dimension value of the body, such as no greater than 89% or no greater than 88% or no greater than 87% or no greater than 86% or no greater than 85% or no greater than 84% or no greater than 83% or no greater than 82% or no greater than 81% or no greater than 80% or no greater than 79% or no greater than 78% or no greater than 77% or no greater than 76% or no greater than 75% or no greater than 74% or no greater than 73% or no greater than 72% or no greater than 71% or no greater than 70% or no greater than 69% or no greater than 68% or no greater than 67% or no greater than 66% or no greater than 65% or no greater than 64% or no greater than 63% or no greater than 62% or no greater than 61% or no greater than 60% or no greater than 59% or no greater than 58% or no greater than 57% or no greater than 56% or no greater than 55% or no greater than 54% or no greater than 53% or no greater than 52% or no greater than 51% or no greater than 50% or no greater than 49% or no greater than 48% or no greater than 47% or no greater than 46% or no greater than 45% or no greater than 44% or no greater than 43% or no greater than 42% or no greater than 41% or no greater than 40% or no greater than 39% or no greater than 38% or no greater than 37% or no greater than 36% or no greater than 35% or no greater than 34% or no greater than 33% or no greater than 32% or no greater than 31% or no greater than 30% or no greater than 29% or no greater than 28% or no greater than 27% or no greater than 26% or no greater than 25% or no greater than 24% or no greater than 23% or no greater than 22% or no greater than 21% or no greater than 20% or no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1%, wherein the dimensional variation-T is measured along the thickness of the body. In yet another embodiment, the dimensional variation-T is at least 0.0001% or at least 0.001% or at least 0.01% or at least 0.1%. It will be appreciated that the dimensional variation-T can be within a range including any of the minimum and maximum values noted above, including, for example, but not limited to, at least 0.0001% and no greater than 90%, or within a range of at least 0.001% and no greater than 80%.

[0099] It should be appreciated that a batch of abrasive articles can have a batch size variation-T having a value of any of the values described above, including a range between any of the minimum and maximum values described above with respect to size variation-T, where the batch size variation-T is calculated by measuring the thickness of each of the plurality of bodies produced via a single operation, where the batch size variation-T is the percent difference between the average thickness of the same shaped bodies of a batch and the thickness value of the body having the greatest positive or negative thickness difference from the average thickness value of the batch. Note that multiple thickness values can be obtained for each of the plurality of bodies in the batch, and any thickness value obtained from a body is relevant for comparison and calculation of the batch size variation-T. More than one thickness measurement can be made on a separate body and averaged to produce an average thickness value for each discrete body in the batch. The average thickness value for the batch can be calculated by averaging the average thickness value of each same shaped body of the batch. The number of thickness values of a body or the batch should have a suitably statistically relevant sample size.

[0100] In embodiments, the bodies of the abrasive article can have a theoretical density that can facilitate improved performance of the abrasive article. In embodiments, the theoretical density can be no greater than 99.9% or no greater than 99.5% or no greater than 99%. Further, in non-limiting embodiments, the theoretical density can be at least 50% or at least 51% or at least 53% or at least 54% or at least 55% or at least 56% or at least 57% or at least 58% or at least 59% or at least 60% or at least 61% or at least 62% or at least 63% or at least 64% or at least 65% or at least 66% or at least 67% or at least 68% or at least 69% or at least 70% or at least 71% or at least 72% or at least 73% or at least 74% or at least 75% or at least 76% or at least 77% or at least 78% or at least 79% or at least 80% or at least 81% or at least 82% or at least 83% or at least 84% or at least 85% or at least 86% or at least 87% or at least 88% or at least 89% or at least 90% or at least 91% or at least 92% or at least 93% or at least 94% or at least 95% or at least 96% or at least 97% or at least 98% or at least 99%. It should be appreciated that the theoretical density can be within a range including any of the minimum and maximum values described above, including, for example, but not limited to, within a range of at least 50% to no greater than 99.9%, or within a range of at least 62% to no greater than 98%. It should be appreciated that the theoretical density of each body of the plurality of bodies of a batch of abrasive articles can be any of the values described above with respect to the theoretical density of a body.

[0101] In embodiments, the body of the abrasive article can have a MOR variation-L that can facilitate improved performance of the abrasive article. In embodiments, the MOR variation-L can be no greater than 20%, such as no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1% than the average MOR value of the body, where the MOR variation-L is measured along the length of the body.

[0102] In embodiments, the body of the abrasive article can have a MOR variation-W that can facilitate improved performance of the abrasive article. In embodiments, the MOR variation-W can be no greater than 20%, such as no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1% than the average MOR value of the body, where the MOR variation-W is measured along the width of the body.

[0103] In embodiments, the body of the abrasive article can have a MOR variation-T that can facilitate improved performance of the abrasive article. In embodiments, the MOR variation-T can be no greater than 20%, such as no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1% than the average MOR value of the body, where the MOR variation-T is measured along the thickness of the body.

[0104] In embodiments, a batch of abrasive articles can have a batch MOR variation that can facilitate improved performance of the abrasive articles. In embodiments, the batch MOR variation can be no greater than 20%, such as no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1% of the average MOR value of the batch. In yet other embodiments, the batch MOR variation is at least 0.00001% or at least 0.0001%. It will be appreciated that the batch MOR variation can be within a range including any of the minimum and maximum values described above, including, for example, but not limited to, at least 0.0001% and no greater than 90%, or within a range of at least 0.001% and no greater than 80%. The batch MOR variation is calculated by measuring the MOR of each of the plurality of bodies produced via a single operation, where the batch MOR variation is a measure of the percent difference between the average MOR value of the batch and the MOR value of the body having the greatest positive or negative MOR difference from the average MOR value of the batch. The number of MOR values for a batch should have a suitable statistically relevant sample size.

[0105] In embodiments, a body of an abrasive article can have a MOE variation-L that can facilitate improved performance of the abrasive article. In embodiments, the MOE variation-L can be no greater than 20%, such as no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1% of the average MOE value of the body, where the MOE variation-L is measured along the length of the body.

[0106] In embodiments, the body of the abrasive article can have a MOE variation-W that can facilitate improved performance of the abrasive article. In embodiments, the MOE variation-W can be no greater than 20%, such as no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1% of the average MOE value of the body, where the MOE variation-W is measured along the width of the body.

[0107] In embodiments, the body of the abrasive article can have a MOE variation-T that can facilitate improved performance of the abrasive article. In embodiments, the MOE variation-T can be no greater than 20%, such as no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1% of the average MOE value of the body, where the MOE variation-T is measured along the thickness of the body.

[0108] In embodiments, a batch of abrasive articles can have a batch MOE variation that can facilitate improved performance of the abrasive articles. In embodiments, the batch MOE variation can be no greater than 20%, such as no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1% of the average MOE value of the batch. In yet another embodiment, the batch MOE variation is at least 0.00001% or at least 0.0001%. It will be appreciated that the batch MOE variation can be within a range including any of the minimum and maximum values noted above, including, for example and without limitation, at least 0.0001% and no greater than 90%, or within a range of at least 0.001% and no greater than 80%. The batch MOR variation is calculated by measuring the MOE of each of the plurality of bodies produced via a single operation, where the batch MOE variation is a measure of the percent difference between the average MOE value of the batch and the MOE value of the body having the greatest positive or negative MOE difference from the average MOE value of the batch. The number of MOE values for a batch should have a suitable statistically relevant sample size.

[0109] In embodiments, the abrasive article can include a particular porosity that can facilitate improved manufacturing of the abrasive article. In embodiments, the porosity of the abrasive article can be at least 1 vol% or at least 2 vol%, such as at least 3 vol% or at least 4 vol% or at least 5 vol% or at least 10 vol% or at least 15 vol% or at least 20 vol% or at least 25 vol% or at least 30 vol% or at least 35 vol% based on the total volume of the abrasive article. In another embodiment, the porosity of the abrasive article can be no greater than 90 vol%, such as no greater than 80 vol% or no greater than 70 vol% or no greater than 60 vol% or no greater than 50 vol% or no greater than 45 vol% or no greater than 40 vol% or no greater than 30 vol% or no greater than 20 vol% or no greater than 10 vol% or no greater than 8 vol% or no greater than 7 vol% or no greater than 6 vol% or no greater than 5 vol% or no greater than 4 vol% or no greater than 3 vol% or no greater than 2 vol% or no greater than 1 vol%. The porosity of the abrasive article can be a value between any of the minimum and maximum values noted above, including, for example and without limitation, within a range of at least 1 vol% to no greater than 90 vol% based on the total volume of the abrasive article, such as within a range of at least 10 vol% to no greater than 60 vol% based on the total volume of the abrasive article body.

[0110] Additionally, as shown, the body has four major flat surfaces and two end faces. Any of the four major flat surfaces extending between the two smaller end faces can be used to assess certain properties as claimed herein, including, for example, but not limited to, normalized warp (nWarp), normalized flatness (nFlatness), normalized bow (nBow). In the case of the property normalized dimensional variation (nDimensional variation), multiple measurements can be taken at random locations between two opposing major flat surfaces to assess the normalized dimensional variation. Such measurements can be taken in the thickness dimension, which is approximately perpendicular to the plane defined by the length and width of the body. A plurality of randomly selected points on a first major surface are selected and the shortest distance through the body to a second major surface is recorded as a dimension. These dimensions are averaged to define an average dimensional variation. This average is then normalized relative to the surface area of the first major surface. If one of the major surfaces is smaller than the other major surface, the smaller surface is used. The normalized dimensional variation is the average of the dimensional variations normalized (divided by) by the area of the smaller of the major flat surfaces.

[0111] In embodiments, the major flat surface of the body can have an nWarp that can facilitate improved performance of the abrasive article. In embodiments, the major flat surface of the body can have an nWarp of no greater than 50 pm / cm 2 , such as no greater than 40 pm / cm 2 or no greater than 30 pm / cm 2 or no greater than 20 pm / cm 2 or no greater than 10 pm / cm 2 or no greater than 9 pm / cm 2 or no greater than 8 pm / cm 2 or no greater than 7 pm / cm 2 or no greater than 6 pm / cm 2 or no greater than 5 pm / cm 2 or no greater than 4 pm / cm 2 or no greater than 3 pm / cm 2 or no greater than 2 pm / cm 2 or no greater than 1 pm / cm 2 or no greater than 0.9 pm / cm 2 or no greater than 0.8 pm / cm 2 or no greater than 0.7 pm / cm 2 or no greater than 0.6 pm / cm 2 or no greater than 0.5 pm / cm 2 or no greater than 0.4 pm / cm 2 or no greater than 0.3 pm / cm 2 or no greater than 0.2 pm / cm 2 or no greater than 0.1 pm / cm2 or not greater than 0.09 pm / cm 2 or not greater than 0.08 pm / cm 2 or not greater than 0.07 pm / cm 2 or not greater than 0.06 pm / cm 2 or not greater than 0.05 pm / cm 2 or not greater than 0.04 pm / cm 2 or not greater than 0.03 pm / cm 2 or not greater than 0.02 pm / cm 2 or not greater than 0.01 pm / cm 2 nWarp, where nWarp is the warp of the major planar surface normalized to the surface area of the major planar surface. In yet another embodiment, nWarp can be at least 0.0001 pm / cm 2 or at least 0.0005 pm / cm 2 or at least 0.001 pm / cm 2 or at least 0.005 pm / cm 2 or at least 0.01 pm / cm 2 or at least 0.1 pm / cm 2 It should be appreciated that nWarp can be within a range including any of the minimum and maximum values described above, including, for example, but not limited to, within a range of at least 0.0001 pm / cm 2 to not greater than 50 pm / cm 2 or within a range of at least 0.001 pm / cm 2 to not greater than 10 pm / cm 2

[0112] ​In embodiments, a batch of abrasive articles can have a batch nWarp standard deviation that can facilitate improved performance of the abrasive article, where the batch nWarp variation is a standard deviation of nWarp for all bodies of the same shape in a batch. In embodiments, the batch nWarp standard deviation can be no greater than 10, such as no greater than 9 or no greater than 8 or no greater than 7 or no greater than 6 or no greater than 5 or no greater than 4 or no greater than 3 or no greater than 2 or no greater than 1 or no greater than 0.9 or no greater than 0.8 or no greater than 0.7 or no greater than 0.6 or no greater than 0.5 or no greater than 0.4 or no greater than 0.3 or no greater than 0.2 or no greater than 0.1 or no greater than 0.09 or no greater than 0.08 or no greater than 0.07 or no greater than 0.06 or no greater than 0.05 or no greater than 0.04 or no greater than 0.03 or no greater than 0.02 or no greater than 0.01. In yet other embodiments, the batch nWarp standard deviation can be at least 0.0005 or at least 0.001 or at least 0.005 or at least 0.01 or at least 0.1. It will be appreciated that the batch nWarp standard deviation can be within a range including any of the minimum and maximum values noted above, including, for example, but not limited to, within a range of at least 0.01 to no greater than 10, or within a range of at least 0.1 to no greater than 5.

[0113] In embodiments, the major planar surface of the body can have an nFlatness that can facilitate improved performance of the abrasive article. In embodiments, the major planar surface of the body can have an nFlatness of no greater than 50 pm / cm 2 , such as no greater than 40 pm / cm 2 or no greater than 30 pm / cm 2 or no greater than 20 pm / cm 2 or no greater than 10 pm / cm 2 or no greater than 9 pm / cm 2 or no greater than 8 pm / cm 2 or no greater than 7 pm / cm 2 or no greater than 6 pm / cm 2 or no greater than 5 pm / cm 2 or no greater than 4 pm / cm 2 or no greater than 3 pm / cm 2 or no greater than 2 pm / cm 2 or no greater than 1 pm / cm 2 or no greater than 0.9 pm / cm 2 or no greater than 0.8 pm / cm 2 or no greater than 0.7 pm / cm 2 or no greater than 0.6 pm / cm 2 or no greater than 0.5 pm / cm 2 or no greater than 0.4 pm / cm 2or not greater than 0.3 pm / cm 2 or not greater than 0.2 pm / cm 2 or not greater than 0.1 pm / cm 2 or not greater than 0.09 pm / cm 2 or not greater than 0.08 pm / cm 2 or not greater than 0.07 pm / cm 2 or not greater than 0.06 pm / cm 2 or not greater than 0.05 pm / cm 2 or not greater than 0.04 pm / cm 2 or not greater than 0.03 pm / cm 2 or not greater than 0.02 pm / cm 2 or not greater than 0.01 pm / cm 2 nFlatness, where nFlatness is the flatness of the major planar surface normalized to the surface area of the major planar surface. In yet another embodiment, nFlatness can be at least 0.0001 pm / cm 2 or at least 0.0005 pm / cm 2 or at least 0.001 pm / cm 2 or at least 0.005 pm / cm 2 or at least 0.01 pm / cm 2 or at least 0.1 pm / cm 2 It will be appreciated that nFlatness can be within a range including any of the minimum and maximum values described above, including, for example, but not limited to, within a range of at least 0.0001 pm / cm 2 to not greater than 50 pm / cm 2 or within a range of at least 0.001 pm / cm 2 to not greater than 10 pm / cm 2

[0114] ​In embodiments, a batch of abrasive articles can have a batch nFlatness standard deviation that can facilitate improved performance of the abrasive article, where the batch nFlatness variation is a standard deviation of the nFlatness for all bodies of the same shape in a batch. In embodiments, the batch nFlatness standard deviation can be no greater than 10, such as no greater than 9 or no greater than 8 or no greater than 7 or no greater than 6 or no greater than 5 or no greater than 4 or no greater than 3 or no greater than 2 or no greater than 1 or no greater than 0.9 or no greater than 0.8 or no greater than 0.7 or no greater than 0.6 or no greater than 0.5 or no greater than 0.4 or no greater than 0.3 or no greater than 0.2 or no greater than 0.1 or no greater than 0.09 or no greater than 0.08 or no greater than 0.07 or no greater than 0.06 or no greater than 0.05 or no greater than 0.04 or no greater than 0.03 or no greater than 0.02 or no greater than 0.01. In yet other embodiments, the batch nFlatness standard deviation can be at least 0.0005 or at least 0.001 or at least 0.005 or at least 0.01 or at least 0.1. It will be appreciated that the batch nFlatness standard deviation can be within a range including any of the minimum and maximum values noted above, including, for example, but not limited to, within a range of at least 0.01 to no greater than 10, or within a range of at least 0.1 to no greater than 5.

[0115] In embodiments, the major planar surface of the body can have an nBow that can facilitate improved performance of the abrasive article. In embodiments, the major planar surface of the body can have an nBow of no greater than 50 pm / cm 2 , such as no greater than 40 pm / cm 2 or no greater than 30 pm / cm 2 or no greater than 20 pm / cm 2 or no greater than 10 pm / cm 2 or no greater than 9 pm / cm 2 or no greater than 8 pm / cm 2 or no greater than 7 pm / cm 2 or no greater than 6 pm / cm 2 or no greater than 5 pm / cm 2 or no greater than 4 pm / cm 2 or no greater than 3 pm / cm 2 or no greater than 2 pm / cm 2 or no greater than 1 pm / cm 2 or no greater than 0.9 pm / cm 2 or no greater than 0.8 pm / cm 2 or no greater than 0.7 pm / cm 2 or no greater than 0.6 pm / cm 2 or no greater than 0.5 pm / cm 2 or no greater than 0.4 pm / cm2 or not greater than 0.3 pm / cm 2 or not greater than 0.2 pm / cm 2 or not greater than 0.1 pm / cm 2 or not greater than 0.09 pm / cm 2 or not greater than 0.08 pm / cm 2 or not greater than 0.07 pm / cm 2 or not greater than 0.06 pm / cm 2 or not greater than 0.05 pm / cm 2 or not greater than 0.04 pm / cm 2 or not greater than 0.03 pm / cm 2 or not greater than 0.02 pm / cm 2 or not greater than 0.01 pm / cm 2 nBow, where nBow is the bow of the major planar surface normalized to the surface area of the major planar surface. In yet another embodiment, nBow can be at least 0.0001 pm / cm 2 or at least 0.0005 pm / cm 2 or at least 0.001 pm / cm 2 or at least 0.005 pm / cm 2 or at least 0.01 pm / cm 2 or at least 0.1 pm / cm 2 It should be appreciated that nBow can be within a range including any of the minimum and maximum values described above, including, for example, but not limited to, within a range of at least 0.0001 pm / cm 2 to not greater than 50 pm / cm 2 or within a range of at least 0.001 pm / cm 2 to not greater than 10 pm / cm 2

[0116] ​In embodiments, a batch of abrasive articles can have a batch nBow standard deviation that can facilitate improved performance of the abrasive article, where the batch nBow variation is a standard deviation of nBow for all bodies of the same shape in one batch. In embodiments, the batch nBow standard deviation can be no greater than 10, such as no greater than 9 or no greater than 8 or no greater than 7 or no greater than 6 or no greater than 5 or no greater than 4 or no greater than 3 or no greater than 2 or no greater than 1 or no greater than 0.9 or no greater than 0.8 or no greater than 0.7 or no greater than 0.6 or no greater than 0.5 or no greater than 0.4 or no greater than 0.3 or no greater than 0.2 or no greater than 0.1 or no greater than 0.09 or no greater than 0.08 or no greater than 0.07 or no greater than 0.06 or no greater than 0.05 or no greater than 0.04 or no greater than 0.03 or no greater than 0.02 or no greater than 0.01. In yet other embodiments, the batch nBow standard deviation can be at least 0.0005 or at least 0.001 or at least 0.005 or at least 0.01 or at least 0.1. It will be appreciated that the batch nBow standard deviation can be within a range including any of the minimum and maximum values noted above, including, for example, but not limited to, within a range of at least 0.01 to no greater than 10, or within a range of at least 0.1 to no greater than 5.

[0117] In embodiments, the distance between the first major planar surface and the second major planar surface of the body can have an nDimensional Variation that can facilitate improved performance of the abrasive article. In embodiments, the distance between the first major planar surface and the second major planar surface can have no greater than 100 pm / cm 2 , such as no greater than 90 pm / cm 2 or no greater than 80 pm / cm 2 or no greater than 70 pm / cm 2 or no greater than 60 pm / cm 2 or no greater than 50 pm / cm 2 or no greater than 40 pm / cm 2 or no greater than 30 pm / cm 2 or no greater than 20 pm / cm 2 or no greater than 10 pm / cm 2 or no greater than 9 pm / cm 2 or no greater than 8 pm / cm 2 or no greater than 7 pm / cm 2 or no greater than 6 pm / cm 2 or no greater than 5 pm / cm 2 or no greater than 4 pm / cm 2 or no greater than 3 pm / cm 2 or no greater than 2 pm / cm 2 or no greater than 1 pm / cm 2or not greater than 0.9 pm / cm 2 or not greater than 0.8 pm / cm 2 or not greater than 0.7 pm / cm 2 or not greater than 0.6 pm / cm 2 or not greater than 0.5 pm / cm 2 or not greater than 0.4 pm / cm 2 or not greater than 0.3 pm / cm 2 or not greater than 0.2 pm / cm 2 or not greater than 0.1 pm / cm 2 or not greater than 0.09 pm / cm 2 or not greater than 0.08 pm / cm 2 or not greater than 0.07 pm / cm 2 or not greater than 0.06 pm / cm 2 or not greater than 0.05 pm / cm 2 or not greater than 0.04 pm / cm 2 or not greater than 0.03 pm / cm 2 or not greater than 0.02 pm / cm 2 or not greater than 0.01 pm / cm 2 or at least 0.0001 pm / cm 2 or at least 0.0005 pm / cm 2 or at least 0.001 pm / cm 2 or at least 0.005 pm / cm 2 or at least 0.01 pm / cm 2 or at least 0.1 pm / cm 2 or at least 1 pm / cm 2 or at least 5 pm / cm 2 It will be appreciated that the nDimensional Variation can be within a range including any of the minimum and maximum values described above, including, for example, but not limited to, within a range of at least 0.0001 pm / cm 2 to not greater than 50 pm / cm 2 or at least 0.001 pm / cm 2 to not greater than 10 pm / cm 2

[0118] ​In embodiments, a batch of abrasive articles can have a batch nDimensional standard deviation that can facilitate improved performance of the abrasive article, where the batch nDimensional standard deviation is a standard deviation of the nDimension variation for all bodies of the same shape in a batch. In embodiments, the batch nDimensional standard deviation can be no greater than 10, such as no greater than 9 or no greater than 8 or no greater than 7 or no greater than 6 or no greater than 5 or no greater than 4 or no greater than 3 or no greater than 2 or no greater than 1 or no greater than 0.9 or no greater than 0.8 or no greater than 0.7 or no greater than 0.6 or no greater than 0.5 or no greater than 0.4 or no greater than 0.3 or no greater than 0.2 or no greater than 0.1 or no greater than 0.09 or no greater than 0.08 or no greater than 0.07 or no greater than 0.06 or no greater than 0.05 or no greater than 0.04 or no greater than 0.03 or no greater than 0.02 or no greater than 0.01. In yet other embodiments, the batch nDimensional standard deviation can be at least 0.0005 or at least 0.001 or at least 0.005 or at least 0.01 or at least 0.1. It will be appreciated that the batch nDimensional standard deviation can be within a range including any of the minimum and maximum values noted above, including, for example, but not limited to, within a range of at least 0.01 to no greater than 10, or within a range of at least 0.1 to no greater than 5.

[0119] In embodiments, the volume of the plurality of bodies of the batch can include a batch volume that can facilitate improved performance of the abrasive article. In embodiments, the batch volume can be at least 10 cm3 3 or at least 11 cm3 3 or at least 12 cm3 3 or at least 13 cm3 3 or at least 14 cm3 3 or at least 15 cm3 3 or at least 16 cm3 3 or at least 17 cm3 3 or at least 18 cm3 3 or at least 19 cm3 3 or at least 20 cm3 3 or at least 21 cm3 3 or at least 22 cm3 3 or at least 23 cm3 3 or at least 24 cm3 3 or at least 25 cm3 3 or at least 26 cm3 3 or at least 27 cm3 3 or at least 28 cm3 3 or at least 29 cm3 3 or at least 30 cm3 3 or at least 31 cm3 3or at least 32 cm 3 or at least 33 cm 3 or at least 34 cm 3 or at least 35 cm 3 or at least 36 cm 3 or at least 37 cm 3 or at least 38 cm 3 or at least 39 cm 3 or at least 40 cm 3 or at least 42 cm 3 or at least 44 cm 3 or at least 46 cm 3 or at least 48 cm 3 or at least 50 cm 3 In yet another embodiment, the batch volume can be no more than 5000 cm 3 or no more than 4000 cm 3 or no more than 3000 cm 3 or no more than 2000 cm 3 or no more than 1000 cm 3 or no more than 800 cm 3 or no more than 600 cm 3 or no more than 500 cm 3 It will be appreciated that the batch volume can be within a range including any of the minimum and maximum values described above, including, for example, but not limited to, within a range of at least 10 cm 3 to no more than 100 cm 3 or within a range of at least 100 cm 3 to no more than 5000 cm 3 .

[0120] According to another embodiment, the body of the abrasive article (which can be in the form of a green abrasive article or a final formed abrasive article) can have a specific volumetric shape factor that can be achieved by one or more of the forming processes of the embodiments herein and that facilitates improved grinding operations. In one embodiment, for a single abrasive article (green or final formed body), the volumetric shape factor can be a comparison between the three-dimensional shape of the body and an intended shape. In certain aspects, the abrasive article is intended to conform to tight dimensional tolerances, and deviations from the intended dimensional tolerances must be addressed by one or more methods, typically post-forming subtractive methods. In some cases, depending on the severity of the deviation of the body from the intended shape, the body can be scrapped.

[0121] Figure 8A A perspective view including an intended shape of the abrasive article. The intended shape can be a well-known standard, which can be stored as electronic data, such as on a computer readable medium in the form of a three-dimensional model. Figure 8BA perspective view of the abrasive article formed. The volume form factor of the individual abrasive article can be compared to how well the abrasive article formed (e.g., Figure 8B ) matches the intended shape (e.g., Figure 8A ). Such a comparison is shown as Figure 8C .

[0122] According to one aspect, a detailed three-dimensional scan of the body can be performed via 3D tomography using X-ray radiation to create a representative three-dimensional model of the abrasive article. The model of the abrasive article can be compared to the model of the intended shape. The model of the abrasive article can be compared to the model of the intended shape using slices of the body and measuring the deviation in one or more selected planes in the model of the abrasive article. Additionally or alternatively, the deviation between the two models can be assessed for the entire volume.

[0123] In one particular embodiment, as Figure 9A illustrated, at least three scans are completed in three different planes on the model of the abrasive article. Figure 9A A total of nine planes are shown that are spaced apart from each other and cut through the model of the abrasive article 900 for the planes X-Y, X-Z, and Y-Z. The scan images can be extracted as 2D images of the body and can be compared to corresponding 2D data from the model of the intended shape (e.g., 903). Image analysis software can compare the 2D images of the abrasive article to the intended shape for differences and assess the area differences between the images for each of the nine planes. As Figure 9B illustrated, additional area outside of the intended surface 901 can be assigned a positive value. Negative area 902 on the model of the abrasive article relative to the model of the intended shape can be assigned a negative value. The sum of the positive and negative areas is added for each scan. The values for each of the nine scans are averaged and recorded as the average volume form value for the model of the abrasive article. The volume form factor is calculated as the absolute value of the ratio of the average volume form value divided by the volume form value of the model of the intended shape. That is, Vff = | Vav / Vmi |, where Vff represents the volume form factor, Vav represents the average volume form value, and Vmi represents the volume form value of the model of the intended shape.

[0124] According to one embodiment, Vffmay be at least 0.1, such as at least 0.2 or at least 0.25 or at least 0.3 or at least 0.35 or at least 0.4 or at least 0.45 or at least 0.5 or at least 0.55 or at least 0.6 or at least 0.65 or at least 0.7 or at least 0.71 or at least 0.72 or at least 0.73 or at least 0.74 or at least 0.75 or at least 0.76 or at least 0.77 or at least 0.78 or at least 0.79 or at least 0.80 or at least 0.81 or at least 0.72 or at least 0.73 or at least 0.74 or at least 0.75 or at least 0.76 or at least 0.77 or at least 0.78 or at least 0.79 or at least 0.80 or at least 0.81 or at least 0.82 or at least 0.83 or at least 0.84 or at least 0.85 or at least 0.86 or at least 0.87 or at least 0.88 or at least 0.89 or at least 0.90 or at least 0.91 or at least 0.92 or at least 0.93 or at least 0.94 or at least 0.95 or at least 0.96 or at least 0.97 or at least 0.98 or at least 0.99 or at least 1.0 or at least 1.01 or at least 1.02 or at least 1.03 or at least 1.04 or at least 1.05 or at least 1.06 or at least 1.07 or at least 1.08 or at least 1.09 or at least 1.10 or at least 1.11 or at least 1.12 or at least 1.13 or at least 1.14 or at least 1.15 or at least 1.16 or at least 1.17 or at least 1.18 or at least 1.19 or at least 1.20 or at least 1.21 or at least 1.22 or at least 1.23 or at least 1.24 or at least 1.25 or at least 1.26 or at least 1.27 or at least 1.28 or at least 1.29 or at least 1.30 or at least 1.31 or at least 1.32 or at least 1.33 or at least 1.34 or at least 1.35 or at least 1.36 or at least 1.37 or at least 1.38 or at least 1.39 or at least 1.40 or at least 1.45 or at least 1.50 or at least 1.55 or at least 1.60 or at least 1.65 or at least 1.70 or at least 1.75 or at least 1.80 or at least 1.85 or at least 1.90 or at least 1.95 or at least 2.00.Further, in non-limiting embodiments, Vffmay be no greater than 10, such as no greater than 9.5 or no greater than 9 or no greater than 8.5 or no greater than 8 or no greater than 7.5 or no greater than 7 or no greater than 6.5 or no greater than 6 or no greater than 5.5 or no greater than 5 or no greater than 4.5 or no greater than 4 or no greater than 3.5 or no greater than 3 or no greater than 2.5 or no greater than 2 or no greater than 1.5 or no greater than 1.45 or no greater than 1.40 or no greater than 1.39 or no greater than 1.38 or no greater than 1.37 or no greater than 1.36 or no greater than 1.35 or no greater than 1.34 or no greater than 1.33 or no greater than 1.32 or no greater than 1.31 or no greater than 1.30 or no greater than 1.29 or no greater than 1.28 or no greater than 1.27 or no greater than 1.26 or no greater than 1.25 or no greater than 1.24 or no greater than 1.23 or no greater than 1.22 or no greater than 1.21 or no greater than 1.20 or no greater than 1.19 or no greater than 1.18 or no greater than 1.17 or no greater than 1.16 or no greater than 1.15 or no greater than 1.14 or no greater than 1.13 or no greater than 1.12 or no greater than 1.11 or no greater than 1.10 or no greater than 1.09 or no greater than 1.08 or no greater than 1.07 or no greater than 1.06 or no greater than 1.05 or no greater than 1.04 or no greater than 1.03 or no greater than 1.02 or no greater than 1.01 or no greater than 1.00 or no greater than 0.99 or no greater than 0.98 or no greater than 0.97 or no greater than 0.96 or no greater than 0.95 or no greater than 0.94 or no greater than 0.93 or no greater than 0.92 or no greater than 0.91 or no greater than 0.90 or no greater than 0.89 or no greater than 0.88 or no greater than 0.87 or no greater than 0.86 or no greater than 0.85 or no greater than 0.84 or no greater than 0.83 or no greater than 0.82 or no greater than 0.81 or no greater than 0.80 or no greater than 0.79 or no greater than 0.78 or no greater than 0.77 or no greater than 0.76 or no greater than 0.75 or no greater than 0.74 or no greater than 0.73 or no greater than 0.72 or no greater than 0.71 or no greater than 0.70. It will be appreciated that Vffmay be within a range including any of the minimum values and any of the maximum values described above, including, for example, but not limited to, at least 0.10 and no greater than 10, or within a range of at least 0.50 and no greater than 1.50, or within a range of at least 0.80 and no greater than 1.2, or within a range including at least 0.90 and no greater than 1.10, or even within a range including at least 0.95 and no greater than 1.05.

[0125] The methods for forming a batch of abrasive articles according to embodiments herein can be adapted to reduce size variation in a batch of abrasive articles and thus improve batch volume form factor. Some data suggests that batch volume form factor of abrasive articles can be affected by the position and / or orientation of the abrasive articles relative to one or more support elements. According to one embodiment, a batch of abrasive articles, which can be green abrasive articles, or final formed abrasive articles, can have a particular batch volume form factor variation. The batch volume form factor variation (batch Vff) can be the standard deviation of the volume form factor of a batch of abrasive articles. According to one embodiment, the batch Vff can be no greater than 0.30, such as no greater than 0.25 or no greater than 0.20 or no greater than 0.18 or no greater than 0.16 or no greater than 0.14 or no greater than 0.12 or no greater than 0.10 or no greater than 0.09 or no greater than 0.08 or no greater than 0.07 or no greater than 0.06 or no greater than 0.05 or no greater than 0.04 or no greater than 0.03 or no greater than 0.02 or no greater than 0.01 or no greater than 0.009 or no greater than 0.008 or no greater than 0.007 or no greater than 0.006 or no greater than 0.005. Further, in one non-limiting embodiment, the batch Vff can be at least 0.00001 or at least 0.0001 or at least 0.0005 or at least 0.001 or at least 0.01 or at least 0.1 or at least 0.2 or at least 0.4 or at least 0.6. It will be appreciated that the batch Vff can be within a range including any of the minimum and maximum values described above, including, for example, but not limited to, within a range of at least 0.00001 and no greater than 0.3, such as within a range of at least 0.00001 and no greater than 0.2, or within a range of at least 0.00001 and no greater than 0.05, or even within a range of at least 0.00001 and no greater than 0.01.

[0126] It will be appreciated that a single forming operation can form a plurality of discrete green abrasive articles, which can be formed into a plurality of final formed abrasive articles. The plurality of abrasive articles can be referred to as a batch of abrasive articles, and can be green or final formed abrasive articles. In one embodiment, a batch of abrasive articles can be formed within the same build box during a single forming process. The foregoing and claimed properties herein can be used to evaluate abrasive articles on a batch basis. That is, the evaluation of one or more geometric features and / or properties of each body within a batch can be compared to evaluate the quality of the entire batch. According to one embodiment, a batch can include a certain minimum size or volume of material, such as described in any embodiment herein. In another non-limiting embodiment, a batch can include a plurality of abrasive articles formed in a single additive manufacturing build cycle, which can include a plurality of abrasive articles (green or final formed) formed in the same build box during the same build cycle.

[0127] According to one embodiment, a method for forming an abrasive article can include quantifying a distortion of a green abrasive article body and / or a final formed abrasive article using data and modifying a model used to control formation of the green abrasive article body using an additive manufacturing process. According to one embodiment, one or more distortion properties can include any measure of distortion between the model and the actual body formed via additive manufacturing. For example, one distortion property can include a volumetric shape factor. It should be appreciated that other methods can be used to characterize the distortion of one or a batch of abrasive articles. In one embodiment, the process for modifying the model can include changing the dimensions of the model based on the quantified and expected distortion that can occur for a particular additive manufacturing process. In one non-limiting embodiment, the process of modifying the model can include comparing one or more dimensions (e.g., length, width, thickness, diameter, etc.) of the model to corresponding dimensions of a batch of abrasive article greens and / or a batch of final formed abrasive articles and changing one or more dimensions of the model to account for the resulting measured distortion of the batch of abrasive article greens and / or the batch of final formed abrasive articles.

[0128] Figure 10 Methods for forming abrasive articles according to embodiments are included. In one aspect, the process can begin at step 1001, which includes forming a first body and a second body via additive manufacturing. The process can continue at step 1003, which includes forming the first body and the second body in controlled positions and / or orientations relative to one another. In one embodiment, the process for forming the first body and the second body can be accomplished using any of the processes of the embodiments herein, including, for example, but not limited to, a binder jetting operation, which can include deposition of a powder material and selective binding of the loose powder material to form one or more green abrasive articles in a bed of loose powder material. The embodiments herein are based on empirical research. There are significant challenges when forming abrasive articles on a commercial scale using certain additive manufacturing processes, including, for example, binder jetting. While previous disclosures have disclosed forming abrasive articles via additive manufacturing, such products are not widely available due to significant difficulties in scaling up the process. The embodiments herein are specifically developed on the basis of empirical research with the goal of advancing additive manufacturing technology to be a commercially viable option.

[0129] According to an aspect, a plurality of abrasive articles (i.e., green abrasive articles or final formed abrasive articles) can be formed via additive manufacturing, where the position and / or orientation of at least the first body and the second body are controlled relative to one another to reduce deformation of the first body or the second body during formation. The plurality of abrasive articles can include a batch of abrasive articles having any one of the batch characteristics described in the embodiments herein. Certain studies conducted by the present applicant have shown that unexpected deformation can occur in large build beds and / or when forming large size batches of abrasive articles. While not wishing to be bound by any particular theory, some data can suggest that layer shifting can occur in large size build beds, which can result in part deformation and poor shape quality.

[0130] Figure 11 A perspective view including a first body 1103, a second body 1104, a third body 1105, and a fourth body 1106 (bodies 1103-1106) contained in a build box 1101. As used herein, the bodies 1103-1106 can be abrasive articles or support elements.

[0131] Figure 12A A top view including a build bed including a plurality of bodies according to an embodiment. Figure 12B A top view including a build bed including a plurality of bodies according to an embodiment. Figure 12C A cross-sectional view including a build bed including a plurality of bodies according to an embodiment.

[0132] According to an aspect, the apparatus 1200 includes a build box 1201 including a bed of loose powder 1202 and bodies 1203, 1204, 1205, and 1206 (i.e., bodies 1203-1206) contained in the bed of loose powder 1202. The bodies 1203-1206 can be portions of the bed of loose powder 1202 that have been bound via a binder that is selectively deposited in areas of the bed of loose powder 1202 that define the bodies 1203-1206. The build box 1201, the loose powder 1202, and the bodies 1203-1206 can have any one or more features from any embodiment herein. In one embodiment, one or more of the bodies 1203-1206 can represent a green abrasive article body. In another embodiment, one or more of the bodies 1203-1206 can be a support element.

[0133] For another aspect, a plurality of abrasive articles (such as green abrasive articles) can include a first body (e.g., body 1203) comprising an abrasive article and a second body (e.g., body 1205) in the form of a support element. According to one embodiment, the support element can be configured to limit significant deformation of the abrasive article during additive manufacturing. In one non-limiting embodiment, the support element can be configured to distribute force and / or pressure applied to an upper surface of a layer of material (e.g., loose powder 1202 and / or green abrasive article body) during additive manufacturing. In another embodiment, the support element can be configured to distribute force and / or pressure applied to an upper surface of a green abrasive article (e.g., bodies 1203-1206) during additive manufacturing. In yet another non-limiting embodiment, the support element can be a sacrificial element. The sacrificial element can be a product produced with the abrasive article, but not used for any other purpose other than the manufacturing process. In one embodiment, the sacrificial element can be configured to be removed and discarded or recycled after formation of the one or more green abrasive article bodies is complete via additive manufacturing.

[0134] In one aspect, the one or more support elements can have a particular relationship with the one or more green abrasive article bodies, which can facilitate improved manufacturing and / or properties of the resulting abrasive article. For example, in one non-limiting embodiment, the support element can differ from the abrasive article based on at least one of: two-dimensional shape in any plane (e.g., top view of the build box or cross-sectional view of the build box), three-dimensional shape, composition, binder content, raw material particle size (e.g., particle size of the powder material of the abrasive article body versus the powder material in the support element), position of the support element body relative to the length, width, and / or thickness of the support element relative to the spreading direction, position of the support element body relative to the length, width, and / or thickness of the support element relative to the compacting direction, or any combination of the foregoing.

[0135] In yet another optional embodiment, the green abrasive article body can be formed at a controlled spacing distance and / or a controlled orientation relative to the support elements to limit significant deformation of the green abrasive article body during additive manufacturing. For example, in one non-limiting embodiment, the body 1203 can be laterally spaced apart from the support elements 1204 by a particular lateral spacing distance 1241. The lateral spacing distance 1241 is the minimum distance between the first body 1203 and the support elements 1204 that are immediately adjacent to each other in a lateral direction parallel to the width of the build box 1201. According to one embodiment, the lateral spacing distance 1241 can be at least 0.01% of the length of the first body 1203 or the length of the second body 1204 (whichever is greater). In still another non-limiting embodiment, the lateral spacing distance 1241 can be at least 0.1%, such as at least 1% or at least 5% or at least 10% or at least 15% or at least 20% or at least 25% or at least 30% or at least 35% or at least 40% or at least 45% or at least 50% or at least 60% or at least 65% or at least 70% or at least 75% or at least 80% or at least 85% or at least 90% or at least 95% or at least 100% or at least 125% or at least 150% or at least 175% or at least 200% of the length of the longer of the green abrasive article body 1203 or the support elements 1204. In another non-limiting embodiment, the lateral spacing distance 1241 can be no greater than 2000% or no greater than 1500% or no greater than 1000% or no greater than 800% or no greater than 500% or no greater than 200% or no greater than 100% or no greater than 90% or no greater than 80% or no greater than 70% or no greater than 60% or no greater than 50% or no greater than 40% or no greater than 30% or no greater than 20% of the length of the first body or the second body. It will be appreciated that the lateral spacing distance 1241 can be within a range including any of the minimum and maximum values described above. It will also be appreciated that the lateral spacing distance 1241 can apply to any two immediately adjacent bodies that intersect along a line parallel to the width of the build box.

[0136] In another aspect, a controlled spacing between two bodies can be expressed as a particular longitudinal spacing distance that can facilitate improved manufacturing and part quality. In one instance, body 1203 can be longitudinally spaced apart from body (e.g., support element) 1205 by a particular longitudinal spacing distance 1242. Longitudinal spacing distance 1242 is the minimum distance between two bodies 1203 and 1205 that are immediately adjacent to one another and that both intersect a longitudinal line drawn parallel to the length of build box 1201. According to one embodiment, longitudinal spacing distance 1242 can be at least 0.01% of the length of first body 1203 or the length of third body 1205 (whichever is greater). In yet another non-limiting embodiment, longitudinal spacing distance 1242 can be at least 0.1%, such as at least 1% or at least 5% or at least 10% or at least 15% or at least 20% or at least 25% or at least 30% or at least 35% or at least 40% or at least 45% or at least 50% or at least 60% or at least 65% or at least 70% or at least 75% or at least 80% or at least 85% or at least 90% or at least 95% or at least 100% or at least 125% or at least 150% or at least 175% or at least 200%. In another non-limiting embodiment, longitudinal spacing distance 1242 can be no greater than 2000% or no greater than 1500% or no greater than 1000% or no greater than 800% or no greater than 500% or no greater than 200% or no greater than 100% or no greater than 90% or no greater than 80% or no greater than 70% or no greater than 60% or no greater than 50% or no greater than 40% or no greater than 30% or no greater than 20% of the length of the first body or the second body. It will be appreciated that longitudinal spacing distance 1242 can be within a range including any of the minimum and maximum values described above.

[0137] In another aspect, a controlled spacing between two bodies (e.g., a green abrasive article body and a support element) can be expressed as a particular vertical spacing distance that can facilitate improved manufacturing and / or part quality. In one instance, body (e.g., a green abrasive article body) 1203 can be vertically spaced apart from body (e.g., a support element) 1205 by a particular vertical spacing distance 1244. Vertical spacing distance 1244 is the minimum distance between two bodies 1203 and 1205 that are immediately adjacent to one another and that both intersect a vertical line drawn parallel to the width of build box 1201. According to one embodiment, vertical spacing distance 1244 can be at least 0.01% of the width of first body 1203 or the width of third body 1205 (whichever is greater). In yet another non-limiting embodiment, vertical spacing distance 1244 can be at least 0.1%, such as at least 1% or at least 5% or at least 10% or at least 15% or at least 20% or at least 25% or at least 30% or at least 35% or at least 40% or at least 45% or at least 50% or at least 60% or at least 65% or at least 70% or at least 75% or at least 80% or at least 85% or at least 90% or at least 95% or at least 100% or at least 125% or at least 150% or at least 175% or at least 200%. In another non-limiting embodiment, vertical spacing distance 1244 can be no greater than 2000% or no greater than 1500% or no greater than 1000% or no greater than 800% or no greater than 500% or no greater than 200% or no greater than 100% or no greater than 90% or no greater than 80% or no greater than 70% or no greater than 60% or no greater than 50% or no greater than 40% or no greater than 30% or no greater than 20% of the width of the first body or the second body. It will be appreciated that vertical spacing distance 1244 can be within a range including any of the minimum and maximum values described above. Figure 12CThe body 1221) can be vertically spaced apart from another body (e.g., the support element 1225) by a particular vertical spacing distance 1243. The vertical spacing distance 1243 is the minimum distance between two bodies (e.g., the body 1221 and the body 1225) that are immediately adjacent to each other and that both intersect along a vertical line drawn parallel to the depth of the build box 1201. According to one embodiment, the vertical spacing distance 1243 can be at least 0.01% of the longer of the length of the body 1221 or the length of the body 1225. In yet another non-limiting embodiment, the vertical spacing distance 1243 can be at least 0.1% or at least 1% or at least 5% or at least 10% or at least 15% or at least 20% or at least 25% or at least 30% or at least 35% or at least 40% or at least 45% or at least 50% or at least 60% or at least 65% or at least 70% or at least 75% or at least 80% or at least 85% or at least 90% or at least 95% or at least 100% or at least 125% or at least 150% or at least 175% or at least 200% of the longer of the length of the body 1221 or the length of the body 1225. In another non-limiting embodiment, the vertical spacing distance 1243 can be no greater than 2000% or no greater than 1500% or no greater than 1000% or no greater than 800% or no greater than 500% or no greater than 200% or no greater than 100% or no greater than 90% or no greater than 80% or no greater than 70% or no greater than 60% or no greater than 50% or no greater than 40% or no greater than 30% or no greater than 20% of the length of the first body or the second body. It will be appreciated that the vertical spacing distance 1243 can have a value within a range including any of the minimum and maximum values noted above.

[0138] According to one non-limiting embodiment, the bodies 1221, 1222, 1223, and 1224 can represent green abrasive article bodies, and the bodies 1225 and 1226 can represent support elements.

[0139] According to one embodiment, any spacing distance (e.g., longitudinal spacing distance, lateral spacing distance, and / or vertical spacing distance) can be at least 0.1 mm, such as at least 0.3 mm or at least 0.5 mm or at least 0.8 mm or at least 1 mm or at least 1.5 mm or at least 2 mm or at least 3 mm or at least 4 mm or at least 5 mm. Further, in another non-limiting embodiment, any spacing distance described in any embodiment herein can be no greater than 500 mm or no greater than 300 mm or no greater than 200 mm or no greater than 100 mm or no greater than 80 mm or no greater than 60 mm or no greater than 40 mm or no greater than 20 mm or no greater than 15 mm or no greater than 10 mm or no greater than 8 mm or no greater than 5 mm. It will be appreciated that any spacing distance of the embodiments herein can have a value within a range including any of the minimum and maximum values noted above.

[0140] Figure 12F A top view including a green abrasive article body 1291 and a support element 1292 spaced apart from one another by a pitch distance 1293. Figure 12G A top view including a green abrasive article body 1295 and a support element 1296 spaced apart from one another by a pitch distance 1297.

[0141] In one embodiment, such as Figure 12A As shown, each of the bodies 1203-1206 has substantially the same two-dimensional shape when viewed from above. And in one non-limiting embodiment, each of the bodies 1203-1206 can have substantially the same length, width, and / or thickness dimensions.

[0142] Further, in another optional aspect, the first and second bodies can differ from one another in at least one of the length, width, and / or thickness dimensions. For example, as shown, the bodies 1203 and 1204 have different lengths and widths relative to the bodies 1205 and 1206 when viewed from above. Figure 12B As shown, each of the bodies 1203-1206 has substantially the same two-dimensional shape when viewed from above. And in one non-limiting embodiment, each of the bodies 1203-1206 can have substantially the same length, width, and / or thickness dimensions.

[0143] According to another non-limiting embodiment, the size of the one or more support elements can be preferably minimized relative to the size of the green abrasive article body. In those particular cases where the one or more support elements are intended to assist in the manufacture of the green abrasive article body, it can be desirable to minimize the size (two-dimensional size in any plane and / or three-dimensional size) of the support elements to minimize the time and cost of the manufacturing operation and to reduce waste. According to one non-limiting embodiment, the size of the support elements can be no greater than the size of at least one green abrasive article body. Reference herein to size can include a two-dimensional area viewed looking down in the plane of the length and width of the build box or a two-dimensional area viewed in cross-section in the plane of the length and depth or the width and depth of the build box. Size can also refer to the three-dimensional volume of the support elements as compared to the one or more green abrasive article bodies. In one non-limiting embodiment, the size (area or volume) of at least one support element can be no greater than 95% of the size of at least one of the green abrasive article bodies, such as no greater than 90% or no greater than 80% or no greater than 70% or no greater than 60% or no greater than 50% or no greater than 40% or no greater than 30% or no greater than 20%. Further, in another non-limiting embodiment, the size (area or volume) of at least one support element can be at least 0.1% of the size of at least one of the green abrasive article bodies, such as at least 1% or at least 3% or at least 5% or at least 8% or at least 10% or at least 20% or at least 30% or at least 40% or at least 50%. The size of the at least one support element relative to the size of the at least one green abrasive article body can be within a range including any of the minimum and maximum percentages described above, including, for example, but not limited to, within a range of at least 0.1% and no greater than 95% or within a range of at least 1% and no greater than 95% or within a range of at least 10% and no greater than 90%.

[0144] According to another aspect, the orientation of the one or more support elements relative to the one or more green abrasive article bodies can assist in reducing unintended deformation of the bodies during manufacture. For example, in one embodiment, at least two bodies (e.g., green abrasive article bodies and support elements) can each have a longitudinal axis that is substantially parallel to one another. For example, with reference to FIG. 1, the longitudinal axis of the green abrasive article body 100 and the longitudinal axis of the support element 102 are substantially parallel to one another. In another embodiment, the longitudinal axis of the green abrasive article body 100 and the longitudinal axis of the support element 102 are substantially perpendicular to one another. In another embodiment, the longitudinal axis of the green abrasive article body 100 and the longitudinal axis of the support element 102 are substantially parallel to one another and the longitudinal axis of the green abrasive article body 200 and the longitudinal axis of the support element 202 are substantially perpendicular to one another. In another embodiment, the longitudinal axis of the green abrasive article body 100 and the longitudinal axis of the support element 102 are substantially perpendicular to one another and the longitudinal axis of the green abrasive article body 200 and the longitudinal axis of the support element 202 are substantially parallel to one another. Figure 12A, the bodies 1203 and 1204 have longitudinal axes 1253 and 1254, respectively. Further, the longitudinal axes 1253 and 1254 are substantially parallel to each other, where substantially parallel is no more than ±5 degrees. The longitudinal axis of a body is the longest dimension of the body that extends along a major surface, if present, and perpendicular to at least one surface. The longest dimension can also extend perpendicular to a width dimension. As used herein, references to the relative relationship of axes between two bodies can be assessed from a top planar view of the build box defined by the length and width of the build box, a cross-sectional planar view of the build box defined by the length and depth of the build box, or a cross-sectional planar view of the build box defined by the width and depth of the build box.

[0145] In another non-limiting embodiment, the at least two bodies (e.g., green abrasive article body and support element) can each have longitudinal axes that are substantially perpendicular to each other, where substantially perpendicular is no more than ±5 degrees.

[0146] Further, in another alternative embodiment, two or more bodies (e.g., green abrasive article body and support element) can be angled relative to each other based on their longitudinal axes. For example, as shown in FIG. 12, the bodies 1263 and 1264 each have longitudinal axes 1273 and 1274, respectively. The smallest angle 1275 formed between the intersecting longitudinal axes 1273 and 1274 can be in a range of at least 6 degrees and no greater than 84 degrees. Figure 12D

[0147] In another embodiment, the at least two bodies (e.g., green abrasive article body and support element) can each have transverse axes that are substantially parallel to each other. For example, referring to FIG. 12, Figure 12A , the bodies 1203 and 1204 have transverse axes 1255 and 1256, respectively. Further, the transverse axes 1255 and 1256 are substantially parallel to each other, where substantially parallel is no more than ±5 degrees. The transverse axis of a body is the second longest dimension (i.e., width) of the body that extends along a major surface, if present, and perpendicular to at least one surface. The second longest dimension can also extend perpendicular to the longitudinal axis.

[0148] In another non-limiting embodiment, the at least two bodies (e.g., green abrasive article body and support element) can each have transverse axes that are substantially perpendicular to each other, where substantially perpendicular is no more than ±5 degrees.

[0149] Further, in another alternative embodiment, two or more bodies (e.g., green abrasive article body and support element) can be angled relative to each other based on their transverse axes. For example, as shown in FIG. 12, Figure 12D ​As shown, the bodies 1263 and 1264 each have a transverse axis 1276 and 1277, respectively. The smallest angle 1278 formed between the intersecting transverse axes 1276 and 1277 can be in a range of at least 6 degrees and no more than 84 degrees.

[0150] In another embodiment, the at least two bodies (e.g., green abrasive article bodies and support elements) can each have a vertical axis that is substantially parallel to one another. For example, referring to Figure 12C , the bodies 1221 and 1222 have a vertical axis 1228 and 1229, respectively. Further, the vertical axes 1228 and 1229 can be substantially parallel to one another, where substantially parallel is no more than ±5 degrees. The vertical axis of a body is the longest dimension of the body that extends perpendicularly and out of the plane defined by the longitudinal and transverse axes.

[0151] In another non-limiting embodiment, the at least two bodies (e.g., green abrasive article bodies and support elements) can each have a vertical axis that is substantially perpendicular to one another, where substantially perpendicular is no more than ±5 degrees.

[0152] Further, in another alternative embodiment, two or more bodies (e.g., green abrasive article bodies and support elements) can be angled relative to one another based on their vertical axes. For example, as Figure 12E shown, the bodies 1281 and 1282 each have a vertical axis 1283 and 1284, respectively. The smallest angle 1285 formed between the intersecting vertical axes 1283 and 1284 can be in a range of at least 6 degrees and no more than 84 degrees.

[0153] In one non-limiting embodiment, the process can include orienting a particular dimension of the one or more bodies (e.g., green abrasive article bodies and support elements) relative to a direction of translation of the compacting object. It will be appreciated that for any of the embodiments herein, the compacting object can be configured to traverse one or more layers of powder material and apply a force sufficient to compact the one or more layers and reduce a thickness of the one or more layers. As used herein, the direction of translation of the compacting object is generally in a direction parallel to a length of the build box or in a direction parallel to a width of the build box.

[0154] According to one embodiment, the process can include forming one or more bodies (e.g., green abrasive article bodies and support elements), each body having a longitudinal axis that is substantially parallel to a direction of translation of the compacting object. For example, referring to Figure 12A, the longitudinal axes 1253 and 1254 are substantially parallel to the length direction of the build box 1201, where the length dimension can also define the direction of translation of the compacted object. Further, in alternative embodiments, one or more of the bodies (e.g., the green abrasive article body and the support element) can each have a longitudinal axis that is substantially perpendicular to the direction of translation of the compacted object. Substantially perpendicular is used to mean the same as described in other embodiments herein. For example, with reference again to Figure 12A , if the direction of translation of the compacted object is parallel to the width, then the longitudinal axes 1253 and 1254 are substantially perpendicular to the direction of translation of the compacted object. In yet another non-limiting embodiment, one or more of the bodies (e.g., the green abrasive article body and the support element) can be formed such that their longitudinal axes are angled within a range of at least 6 degrees and no greater than 84 degrees relative to the direction of translation of the compacted object.

[0155] According to one embodiment, the process can include forming one or more bodies (e.g., the green abrasive article body and the support element) each having a lateral axis that is substantially parallel to the direction of translation of the compacted object. For example, with reference again to Figure 12A , if the width direction of the build box 1201 is parallel to the direction of translation of the compacted object, then the lateral axes 1255 and 1256 are substantially parallel to the direction of translation of the compacted object. Further, in alternative embodiments, one or more of the bodies (e.g., the green abrasive article body and the support element) can each have a lateral axis that is substantially perpendicular to the direction of translation of the compacted object. Substantially perpendicular is used to mean the same as described in other embodiments herein. For example, with reference again to Figure 12A , if the direction of translation is parallel to the length, then the lateral axes 1255 and 1256 are substantially perpendicular to the direction of translation of the compacted object. In yet another non-limiting embodiment, one or more of the bodies (e.g., the green abrasive article body and the support element) can be formed such that their lateral axes are angled within a range of at least 6 degrees and no greater than 84 degrees relative to the direction of translation of the compacted object.

[0156] According to one embodiment, the process can include forming one or more bodies (e.g., the green abrasive article body and the support element) each having a vertical axis that is substantially parallel to the direction of translation of the compacted object. For example, with reference again to Figure 12C , and Figure 12EIf the length of the build box 1201 is parallel to the direction of translation of the compacted object, the vertical axes 1228 and 1229 are angled away from the plane of translation of the compacted object (i.e., the plane defined by the length and width of the build bed). However, in alternative embodiments, one or more bodies (e.g., the green abrasive article body and the support element) can each have a vertical axis that is substantially perpendicular to the direction of translation or the plane of translation of the compacted object. Substantially perpendicular is used to mean the same as described in other embodiments herein. For example, again with reference to Figure 12C If the direction of translation is parallel to the length, the vertical axes 1228 and 1229 are substantially perpendicular to the direction of translation of the compacted object. In yet another non-limiting embodiment, one or more bodies (e.g., the green abrasive article body and the support element) can be formed such that their vertical axes are angled away from the plane of translation of the compacted object, and wherein the angle can be in a range of at least 6 degrees and no greater than 84 degrees.

[0157] As described in embodiments herein, it should be understood that the method can include forming a green abrasive article including a precursor bond material and abrasive particles, wherein the forming is by a process of: a) producing one or more layers of powder material; b) selectively bonding portions of the one or more layers with a binder material, and c) transforming the binder material to at least partially solidify the binder material and bond portions of the powder material from the one or more layers. In one particular embodiment, the process of selectively bonding portions of the one or more layers can include: selectively bonding a first portion of the powder layers defining a portion of a first green abrasive article body; selectively bonding a second portion of the powder layers defining a portion of a second abrasive article body; and selectively bonding a portion of a support element.

[0158] According to one embodiment, the method can further include moving the compacting object over the one or more layers of powder material to apply a force sufficient to compact the layer to a compacted layer thickness that is less than a thickness of the layer prior to compaction. In another non-limiting aspect, the method can further include controlling at least one of: a) the force applied by the compacting object to the layer or layers of powder; b) the traverse speed of the compacting object; c) the average thickness of the layer prior to compaction; d) the particle size distribution of the powder; e) the number of previously formed layers beneath the layer of powder; f) the number of compacted layers beneath the layer of powder; g) the density of any layers beneath the layer of powder; h) the amount of binder in any layers beneath the layer of powder; i) the relative size of the layer relative to one or more layers beneath the layer; or any combination of a) - i). In certain instances, the method can include selecting the placement, orientation, and / or size of the green abrasive article body and / or support element based on any one or more of a) - i) above. In another embodiment, the abrasive article is a green abrasive article or a final formed abrasive article including any one or combination of the features from the claims or embodiments herein.

[0159] The Applicant's experience research has shown that certain compaction operations can result in certain unintended deformations of the green abrasive article body. In some instances, it can not be desirable to change parameters of the compaction operation, such as during the formation of large scale and / or high density abrasive products. The use of a support element can provide a solution to facilitate the formation of the green abrasive article body that would otherwise be infeasible.

[0160] According to another embodiment, the process for moving the compacting object over the one or more layers of powder material can be adjusted based on one or more aspects of the green abrasive article body and the support element. In one embodiment, moving the compacting object over the one or more layers of powder material can be adjusted based on the relative spacing between one of the green abrasive article bodies and the support element. For example, the translation speed of the compacting object, the downward force applied by the compacting object, or any other parameter of the compaction process can be adjusted based on the relative spacing between one of the green abrasive article bodies and the support element. Alternatively, in one non-limiting embodiment, the relative spacing between one of the green abrasive article bodies and the support element can be determined based on one or more parameters of the compaction process including, for example and without limitation, the translation speed of the compacting object, the downward force applied by the compacting object, or any other parameter of the compaction process.

[0161] In another non-limiting aspect, the process of moving the compacting object over the one or more layers of powder material can be adjusted based on a two-dimensional shape of at least one of the green abrasive article bodies as viewed in a top view of the build box or a two-dimensional shape of the green abrasive article bodies as viewed in a cross-section of the build box. For example, the translation speed of the compacting object, the downward force exerted by the compacting object, or any other parameter of the compacting process can be adjusted based on the two-dimensional shape of the at least one green abrasive article body. Alternatively, in one non-limiting embodiment, the two-dimensional shape of the at least one green abrasive article body can be determined based on one or more parameters of the compacting process including, for example and without limitation, the translation speed of the compacting object, the downward force exerted by the compacting object, or any other parameter of the compacting process.

[0162] In still another non-limiting embodiment, the process of moving the compacting object over the one or more layers of powder material can be adjusted based on a three-dimensional shape of the at least one green abrasive article body. For example, the translation speed of the compacting object, the downward force exerted by the compacting object, or any other parameter of the compacting process can be adjusted based on the three-dimensional shape of the at least one green abrasive article body. Alternatively, in one non-limiting embodiment, the three-dimensional shape of the at least one green abrasive article body can be determined based on one or more parameters of the compacting process including, for example and without limitation, the translation speed of the compacting object, the downward force exerted by the compacting object, or any other parameter of the compacting process.

[0163] In another non-limiting aspect, the process of moving the compacting object over the one or more layers of powder material can be adjusted based on a two-dimensional shape of at least one of the support elements as viewed in a top view of the build box or a two-dimensional shape of at least one of the support elements as viewed in a cross-section of the build box. For example, the translation speed of the compacting object, the downward force exerted by the compacting object, or any other parameter of the compacting process can be adjusted based on the two-dimensional shape of the at least one support element. Alternatively, in one non-limiting embodiment, the two-dimensional shape of the at least one support element can be determined based on one or more parameters of the compacting process including, for example and without limitation, the translation speed of the compacting object, the downward force exerted by the compacting object, or any other parameter of the compacting process.

[0164] In still another non-limiting embodiment, the process of moving the compacting object over the one or more layers of powder material can be adjusted based on a three-dimensional shape of the at least one support element. For example, the translation speed of the compacting object, the downward force exerted by the compacting object, or any other parameter of the compacting process can be adjusted based on the three-dimensional shape of the at least one support element. Alternatively, in one non-limiting embodiment, the three-dimensional shape of the at least one support element can be determined based on one or more parameters of the compacting process including, for example and without limitation, the translation speed of the compacting object, the downward force exerted by the compacting object, or any other parameter of the compacting process.

[0165] According to one non-limiting embodiment, the process of moving the compacting object over the one or more layers of powder material can be adjusted based on at least one of: i) a relative spacing between one of the green abrasive article bodies and the support element; ii) a two-dimensional shape of one of the green abrasive article bodies when viewed from above in the build box or in cross-section; iii) a three-dimensional shape of at least one of the green abrasive article bodies; iv) a two-dimensional shape of the support element when viewed from above in the build box or in cross-section; v) a three-dimensional shape of the support element; vi) or any combination of i) - v). Alternatively, in one non-limiting embodiment, any one or more of the parameters of i) - v) above can be determined based on one or more parameters of the compacting process, including for example but not limited to a translation speed of the compacting object, a downward force exerted by the compacting object, or any other parameter of the compacting process.

[0166] In embodiments, the thickness of the green body can facilitate improved manufacture and / or performance of the abrasive article. In embodiments, the thickness of the green body can be at least 0.1 microns, such as at least 0.5 microns or at least 1 micron or at least 2 microns or at least 5 microns or at least 10 microns or at least 20 microns or at least 30 microns or at least 40 microns or at least 50 microns or at least 100 microns or at least 200 microns or at least 300 microns or at least 500 microns or at least 1000 microns or at least 3000 microns or at least 5000 microns or at least 1 cm or at least 5 cm or at least 10 cm or at least 15 cm or at least 25 cm or at least 30 cm or at least 40 cm or at least 50 cm. In yet other embodiments, the length of the green body can be no greater than 100 cm or no greater than 90 cm or no greater than 80 cm or no greater than 70 cm. It will be appreciated that the green body can have a thickness between any of the minimum and maximum values described above, including for example but not limited to a thickness ranging from at least 0.1 microns to no greater than 100 cm or ranging from at least 0.5 microns to no greater than 70 cm. It will be appreciated that each of the plurality of abrasive bodies in a batch of abrasive articles can have a thickness of any of the values described above with respect to the thickness of the green body.

[0167] In embodiments, the length of the green body can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the length of the green body can be at least 1 cm or at least 3 cm or at least 4 cm or at least 7 cm or at least 7.5 cm or at least 8 cm or at least 8.5 cm or at least 9 cm or at least 9.5 cm or at least 10 cm or at least 10.5 cm or at least 11 cm or at least 12 cm or at least 13 cm or at least 14 cm or at least 15 cm or at least 18 cm or at least 20 cm. In yet other embodiments, the length of the green body can be no greater than 100 cm, such as no greater than 90 cm or no greater than 80 cm or no greater than 70 cm or no greater than 60 cm or no greater than 50 cm or no greater than 40 cm or no greater than 30 cm or no greater than 25 cm. It will be appreciated that the green body can have a length between any of the minimum and maximum values described above, including, for example, but not limited to, a length ranging from at least 1 cm to no greater than 100 cm or ranging from at least 8 cm to no greater than 50 cm. It will be appreciated that each of the plurality of abrasive bodies in a batch of abrasive articles can have a length of any of the values described above with respect to the length of the green body.

[0168] In embodiments, the width of the green body can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the width of the green body can be at least 3 cm or at least 3.5 cm or at least 4 cm or at least 4.5 cm or at least 5 cm or at least 5.5 cm or at least 6 cm or at least 6.5 cm or at least 7 cm or at least 7.5 cm or at least 8 cm or at least 8.5 cm or at least 9 cm or at least 9.5 cm or at least 10 cm or at least 10.5 cm or at least 11 cm or at least 12 cm or at least 13 cm or at least 14 cm or at least 15 cm. In yet other embodiments, the length of the green body can be no greater than 500 cm, such as no greater than 450 cm or no greater than 400 cm or no greater than 350 cm or no greater than 300 cm or no greater than 250 cm or no greater than 200 cm or no greater than 150 cm or no greater than 100 cm. It will be appreciated that the green body can have a width between any of the minimum and maximum values described above, including, for example, but not limited to, a width ranging from at least 1 cm to no greater than 100 cm or ranging from at least 8 cm to no greater than 50 cm. It will be appreciated that each of the plurality of abrasive bodies in a batch of abrasive articles can have a width of any of the values described above with respect to the width of the green body.

[0169] In embodiments, the green body can have a primary aspect ratio (length:width) that can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the green body can have a primary aspect ratio (length:width) of at least 1 : 1, such as at least 1.1 : 1 or at least 1.2: 1 or at least 1.3: 1 or at least 1.4: 1 or at least 1.5: 1 or at least 1.8: 1 or at least 2: 1 or at least 3: 1 or at least 4: 1 or at least 5: 1 or at least 6: 1 or at least 7: 1 or at least 8: 1 or at least 9: 1 or at least 10: 1. In still other embodiments, the green body can have a primary aspect ratio (length:width) of not greater than 10000: 1 or not greater than 5000: 1 or not greater than 1000: 1 or not greater than 500: 1 or not greater than 200: 1 or not greater than 100: 1 or not greater than 50: 1. It will be appreciated that the green body can have a primary aspect ratio (length:width) between any of the minimum and maximum values described above, including for example but not limited to a primary aspect ratio in a range of at least 1 : 1 to not greater than 10000: 1 cm or in a range of at least 6: 1 to not greater than 200: 1. It will be appreciated that each of the plurality of abrasive bodies in a batch of abrasive articles can have a primary aspect ratio (length:width) of any of the values described above with respect to the green body.

[0170] In embodiments, the green body can have a secondary aspect ratio (length:thickness) that can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the green body can have a secondary aspect ratio (length:thickness) of at least 1 : 1, such as at least 1.1 : 1 or at least 1.2: 1 or at least 1.3: 1 or at least 1.4: 1 or at least 1.5: 1 or at least 1.8: 1 or at least 2: 1 or at least 3: 1 or at least 4: 1 or at least 5: 1 or at least 6: 1 or at least 7: 1 or at least 8: 1 or at least 9: 1 or at least 10: 1. In still other embodiments, the green body can have a secondary aspect ratio (length:thickness) of not greater than 10000: 1 or not greater than 5000: 1 or not greater than 1000: 1 or not greater than 500: 1 or not greater than 200: 1 or not greater than 100: 1 or not greater than 50: 1. It will be appreciated that the green body can have a secondary aspect ratio (length:thickness) between any of the minimum and maximum values described above, including for example but not limited to a secondary aspect ratio in a range of at least 1 : 1 to not greater than 10000: 1 cm or in a range of at least 6: 1 to not greater than 200: 1. It will be appreciated that each of the plurality of abrasive bodies in a batch of abrasive articles can have a secondary aspect ratio (length:thickness) of any of the values described above with respect to the green body.

[0171] In embodiments, the green body can have a tertiary aspect ratio (width:thickness) that can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the green body can have a tertiary aspect ratio (width:thickness) of at least 1 : 1, such as at least 1.1 : 1 or at least 1.2: 1 or at least 1.3: 1 or at least 1.4: 1 or at least 1.5: 1 or at least 1.8: 1 or at least 2: 1 or at least 3: 1 or at least 4: 1 or at least 5: 1 or at least 6: 1 or at least 7: 1 or at least 8: 1 or at least 9: 1 or at least 10: 1. In yet other embodiments, the green body can have a tertiary aspect ratio (width:thickness) of not greater than 10000: 1 or not greater than 5000: 1 or not greater than 1000: 1 or not greater than 500: 1 or not greater than 200: 1 or not greater than 100: 1 or not greater than 50: 1. It will be appreciated that the green body can have a tertiary aspect ratio (width:thickness) between any of the minimum and maximum values described above, including, for example, but not limited to, a tertiary aspect ratio in a range of at least 1 : 1 to not greater than 10000: 1 or in a range of at least 6: 1 to not greater than 200: 1. It will be appreciated that each of the plurality of abrasive bodies in a batch of abrasive articles can have a tertiary aspect ratio (width:thickness) of any of the values described above with respect to the tertiary aspect ratio (width:thickness) of the green body.

[0172] In yet another embodiment, the green body has a length, a width, and a thickness, and wherein the length > width > thickness. In yet another embodiment, each of the plurality of bodies has a length, a width, and a thickness, and wherein the length > the width > the thickness.

[0173] In embodiments, the green body can have a solid volume that can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the green body can have a solid volume of at least 9 cm 3 , such as at least 10 cm 3 or at least 11 cm 3 or at least 12 cm 3 or at least 13 cm 3 or at least 14 cm 3 or at least 15 cm 3 or at least 16 cm 3 or at least 17 cm 3 or at least 18 cm 3 or at least 19 cm 3 or at least 20 cm 3 or at least 21 cm 3 or at least 22 cm 3 or at least 23 cm 3 or at least 24 cm 3 or at least 25 cm 3 or at least 26 cm 3or at least 27 cm 3 or at least 28 cm 3 or at least 29 cm 3 or at least 30 cm 3 or at least 31 cm 3 or at least 32 cm 3 or at least 33 cm 3 or at least 34 cm 3 or at least 35 cm 3 or at least 36 cm 3 or at least 37 cm 3 or at least 38 cm 3 or at least 39 cm 3 or at least 40 cm 3 or at least 42 cm 3 or at least 44 cm 3 or at least 46 cm 3 or at least 48 cm 3 or at least 50 cm 3 or not greater than 5000 cm 3 or not greater than 4000 cm 3 or not greater than 3000 cm 3 or not greater than 2000 cm 3 or not greater than 1000 cm 3 or not greater than 800 cm 3 or not greater than 600 cm 3 or not greater than 500 cm 3 It will be appreciated that the green body can have a solid volume between any of the minimum and maximum values described above, including, for example, but not limited to, a solid volume in the range of at least 9 cm 3 to not greater than 5000 cm 3 or in the range of at least 25 cm 3 to not greater than 1000 cm 3

[0174] ​In embodiments, the length of the build box can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the length of the build box can be at least 160 mm, such as at least 170 mm or at least 180 mm or at least 190 mm or at least 200 mm or at least 210 mm or at least 220 mm or at least 230 mm or at least 240 mm or at least 250 mm or at least 260 mm or at least 270 mm or at least 280 mm or at least 290 mm or at least 300 mm or at least 310 mm or at least 320 mm or at least 330 mm or at least 340 mm or at least 350 mm or at least 360 mm or at least 370 mm or at least 380 mm or at least 390 mm or at least 400 mm. In yet other embodiments, the length of the build box can be no greater than 3000 mm, such as no greater than 2000 mm or no greater than 1000 mm. It will be appreciated that the build box can have a length between any of the minimum and maximum values described above, including for example but not limited to a length in a range from at least 160 mm to no greater than 3000 mm or in a range from at least 200 mm to no greater than 1000 mm.

[0175] In embodiments, the width of the build box can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the width of the build box can be at least 65 mm or at least 70 mm or at least 80 mm or at least 90 mm or at least 100 mm or at least 110 mm or at least 120 mm or at least 130 mm or at least 140 mm or at least 150 mm or at least 160 mm or at least 170 mm or at least 180 mm or at least 190 mm or at least 200 mm or at least 210 mm or at least 220 mm or at least 230 mm or at least 240 mm or at least 250 mm. In yet other embodiments, the length of the build box can be no greater than 2000 mm, such as no greater than 1500 mm or no greater than 1000 mm. It will be appreciated that the build box can have a width between any of the minimum and maximum values described above, including for example but not limited to a width in a range from at least 65 mm to no greater than 2000 mm or in a range from at least 200 mm to no greater than 1000 mm.

[0176] In embodiments, the depth of the build box can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the depth of the build box can be at least 65 mm or at least 70 mm or at least 80 mm or at least 90 mm or at least 100 mm or at least 110 mm or at least 120 mm or at least 130 mm or at least 140 mm or at least 150 mm or at least 160 mm or at least 170 mm or at least 180 mm or at least 190 mm or at least 200 mm or at least 210 mm or at least 220 mm or at least 230 mm or at least 240 mm or at least 250 mm. In yet other embodiments, the length of the build box can be no greater than 2000 mm, such as no greater than 1500 mm or no greater than 1000 mm. It will be appreciated that the build box can have a depth between any of the minimum and maximum values described above, including for example but not limited to a depth in a range of at least 65 mm to no greater than 2000 mm or in a range of at least 200 mm to no greater than 1000 mm. In embodiments, the depth of the build box can facilitate improved manufacturing and / or performance of the abrasive article. In embodiments, the depth of the build box can be at least 65 mm or at least 70 mm or at least 80 mm or at least 90 mm or at least 100 mm or at least 110 mm or at least 120 mm or at least 130 mm or at least 140 mm or at least 150 mm or at least 160 mm or at least 170 mm or at least 180 mm or at least 190 mm or at least 200 mm or at least 210 mm or at least 220 mm or at least 230 mm or at least 240 mm or at least 250 mm. In yet other embodiments, the length of the build box can be no greater than 2000 mm, such as no greater than 1500 mm or no greater than 1000 mm. It will be appreciated that the build box can have a depth between any of the minimum and maximum values described above, including for example but not limited to a depth in a range of at least 65 mm to no greater than 2000 mm or in a range of at least 200 mm to no greater than 1000 mm.

[0177] In embodiments, the green body or plurality of green bodies of a defined batch can have a volume that is at least 1% of the volume of the build box, such as at least 2% or at least 3% or at least 4% or at least 5% or at least 6% or at least 7% or at least 8% or at least 9% or at least 10% or at least 11% or at least 12% or at least 13% or at least 14% or at least 15% or at least 18% or at least 20% or at least 22% or at least 25% or at least 28% or at least 30% or at least 32% or at least 35% or at least 38% or at least 40% or at least 42% or at least 45% or at least 48% or at least 50% or at least 52% or at least 55% or at least 58% or at least 60% or at least 62% or at least 65% or at least 67% or at least 68% or at least 70% or at least 72% or at least 75% or at least 78% or at least 80% or at least 82% or at least 85% or at least 88% or at least 90% or at least 92% or at least 95% or at least 98% of the volume of the build box. In yet other embodiments, the green body or plurality of green bodies of a defined batch can have a volume that is not greater than 99% of the volume of the build box, such as not greater than 90% or not greater than 85% or not greater than 80% or not greater than 75% or not greater than 70% or not greater than 65% or not greater than 60% of the volume of the build box. In embodiments, the green body or plurality of green bodies of a defined batch can have a volume that is in a range of at least 1% of the volume of the build box to not greater than 99% of the volume of the build box or in a range of at least 10% of the volume of the build box to not greater than 60% of the volume of the build box.

[0178] The processes of the embodiments herein were developed through empirical research that has identified certain elements that improve abrasive articles. One non-limiting example of a property of an abrasive article (green or final formation) that can be improved includes batch density variation. According to one embodiment, the processes can facilitate the formation of a batch of abrasive articles having a batch density variation that is no greater than 20% or no greater than 19% or no greater than 18% or no greater than 17% or no greater than 16% or no greater than 15% or no greater than 14% or no greater than 13% or no greater than 12% or no greater than 11% or no greater than 10% or no greater than 9% or no greater than 8% or no greater than 7% or no greater than 6% or no greater than 5% or no greater than 4% or no greater than 3% or no greater than 2% or no greater than 1% or no greater than 0.5% or no greater than 0.3% or no greater than 0.1% of the average density value of the batch. In yet another embodiment, the batch density variation can be at least 0.00001% or at least 0.0001%. It will be appreciated that the batch density variation can be between any of the minimum and maximum values described above, including, for example, but not limited to, in a range of at least 0.00001% to no greater than 20% of the average density value of the batch or in a range of at least 0.0001% to no greater than 10% of the average density value of the batch. The batch density variation is calculated by measuring the density of each of the plurality of bodies produced via a single operation, where the batch density variation is a measure of the percent difference between the average density value of the batch and the density value of the body having the greatest positive or negative density difference from the average density value of the batch. It is noted that a plurality of density values can be obtained for each of the plurality of bodies in the batch, and any density value obtained from a body is relevant for comparison and calculation of the batch density variation. Each density value of the body can be averaged to produce an average body density value for each discrete body in the batch. The average batch density value can be calculated by averaging the average density value of each body of the batch. The number of density values of a body or batch should have a suitable statistically relevant sample size.

[0179] The methods of the embodiments herein facilitate improved formation of abrasive articles. Notably, empirical research conducted by the present applicant facilitated methods having superior formation ratios (Add / Sub), which can be defined as the ratio of material added to form a body to material subtracted in any post-formation finishing technique. The methods of the embodiments herein facilitate advantageous formation ratios compared to conventional formation techniques and / or less sophisticated additive manufacturing techniques.

[0180] In particular embodiments, the body or the method for forming the body defines a shaping ratio (Add / Sub) of at least 10, where "Add" defines the volume of solid material (cm3) formed via an additive process used to form the body and "Sub" defines the volume of solid material (cm3) formed via a subtractive process to finish the body ultimately formed, the shaping ratio being such as at least 20 or at least 50 or at least 80 or at least 100 or at least 200 or at least 300 or at least 400 or at least 500 or at least 600 or at least 700 or at least 800 or at least 1000 or at least 5000 or at least 10000.

[0181] In embodiments, the final formed abrasive article of the batch can have a residual stress in the outer surface from the post-forming operation that is at least 1% less than the residual stress in a conventionally formed abrasive article, such as at least 2% less or at least 3% less or at least 4% less or at least 5% less or at least 6% less or at least 7% less or at least 8% less or at least 9% less or at least 10% less or at least 11% less or at least 12% less or at least 13% less or at least 14% less or at least 15% less or at least 16% less or at least 17% less or at least 18% less or at least 19% less or at least 20% less or at least 25% less or at least 30% less or at least 35% less or at least 40% less or at least 45% less or at least 50% less or at least 55% less or at least 60% less or at least 65% less or at least 70% less or at least 75% less or at least 80% less or at least 85% less or at least 90% less or at least 95% less or at least 100% less. In further embodiments, the final formed abrasive article of the batch can have a residual stress in the outer surface from the post-forming operation that is no more than 500% less than the residual stress in a conventionally formed abrasive article, such as no more than 400% less or no more than 300% less or no more than 200% less or no more than 100% less or no more than 90% less.

[0182] In embodiments, the final formed abrasive article of a batch can have a subsurface damage or residual stress that extends at least 0.01% and no greater than 200% of the average particle size (D50) of the abrasive particles, such as at least 0.05% of the D50 of the abrasive particles or at least 0.08% or at least 0.1% or at least 0.5% or at least 1% or at least 2% or at least 3% or at least 4% or at least 5% or at least 6% or at least 7% or at least 8% or at least 9% or at least 10% or at least 11% or at least 12% or at least 13% or at least 14% or at least 15% or at least 18% or at least 20% or at least 22% or at least 25% or at least 28% or at least 30% or at least 32% or at least 35% or at least 38% or at least 40% or at least 42% or at least 45% or at least 48% or at least 50% or at least 52% or at least 55% or at least 58% or at least 60% or at least 62% or at least 65% or at least 67% or at least 68% or at least 70% or at least 72% or at least 75% or at least 78% or at least 80% or at least 82% or at least 85% or at least 88% or at least 90% or at least 92% or at least 95% or at least 98% or at least 100% or at least 102% or at least 105% or at least 108% or at least 110% or at least 115% or at least 120% or at least 125% or at least 130% or at least 140% or at least 150% or at least 160% or at least 170% or at least 180% of the D50 of the abrasive particles. In yet embodiments, the subsurface damage or residual stress extends no greater than 190% or no greater than 180% or no greater than 170% or no greater than 160% or no greater than 150% or no greater than 140% or no greater than 130% or no greater than 120% or no greater than 110% or no greater than 100% or no greater than 90% or no greater than 80% or no greater than 70% or no greater than 60% or no greater than 50% or no greater than 40% or no greater than 30% or no greater than 20% or no greater than 10% of the D50 of the abrasive particles within a distance below the outer surface of the body.

[0183] In embodiments, the abrasive articles prepared herein can include fixed abrasives, such as bonded abrasive articles, having abrasive particles contained in a three-dimensional volume of bond material, where the bond material substantially surrounds a majority of the abrasive particles. In yet embodiments, the abrasive articles prepared herein can include fixed abrasives, such as single layer abrasive articles, where substantially a single layer of abrasive particles is contained in a layer of bond material.

[0184] In another non-limiting embodiment, empirical studies conducted by the present applicant have shown that, in some cases, the deposition technique used to dispense the powder material into the build box can require adjustment from standard procedures. In some procedures, a significant portion, a majority, or even in some cases all of the powder material can be deposited in a non-uniform manner across the surface, such as by depositing a greater amount at the starting position relative to the ending position of the deposition system. In some cases, the process can include a leveling or smoothing step in which a roller or blade is pulled across the surface of the deposited powder in an attempt to level the surface. However, it has been noted that, in some cases, such deposition processes can still provide unsatisfactory products that have significant variation in product properties and quality within the same batch.

[0185] In another non-limiting embodiment, the distribution of any one or more features of the abrasive article can be evaluated. The shape of the distribution of such measured features, particularly size features, can be evaluated via kurtosis.

[0186] The improvement in the forming ratio is also evident in terms of limited residual stresses and / or subsurface damage on one or more outer surfaces of the final formed abrasive article. Given the improvements in the forming process, even less effort, if needed, is required to finish the abrasive article into a shape and / or tolerance suitable for its intended application. Thus, the amount of residual stresses and / or subsurface damage in the final formed abrasive article is less compared to conventional products or other less sophisticated additive manufacturing techniques.

[0187] The foregoing properties of the abrasive articles of the embodiments herein provide various methods to define the quality and size of the abrasive articles that can be formed using the methods of the embodiments herein.

[0188] Embodiment

[0189] Embodiment 1. A method for forming an additive manufactured body in a powder bed, the method comprising:

[0190] forming at least a portion of a first green abrasive article body;

[0191] forming at least a portion of a second green abrasive article body; and

[0192] forming a support element between the portion of the first green abrasive article body and the portion of the second green abrasive article body, wherein the support element has a predetermined position between the first green abrasive article body and the portion of the second green abrasive article body.

[0193] Embodiment 2. The method of embodiment 1, wherein the support element is configured to limit significant deformation of the first green abrasive article body during additive manufacturing.

[0194] Embodiment 3. The method of embodiment 1, wherein the support element is configured to distribute forces applied to the upper surface of the first green abrasive article body and the upper surface of the second green abrasive article body during additive manufacturing.

[0195] Embodiment 4. The method of embodiment 1, wherein the support element is configured to reduce pressure applied to the upper surface of the first green abrasive article body and the upper surface of the second green abrasive article body during additive manufacturing.

[0196] Embodiment 5. The method of embodiment 1, wherein the support element is a sacrificial element intended to be discarded after the formation of the first green abrasive article body and the second green abrasive article body is complete.

[0197] Embodiment 6. The method of embodiment 1, wherein the support element is a sacrificial element intended to be recycled after the formation of the first green abrasive article body and the second green abrasive article body is complete.

[0198] Embodiment 7. The method of embodiment 1, wherein the support element differs from the portion of the first green abrasive article body or the portion of the second green abrasive article body based on at least one of:

[0199] i) a two-dimensional shape in any plane;

[0200] ii) a three-dimensional shape;

[0201] iii) composition;

[0202] iv) binder content;

[0203] v) raw material particle size;

[0204] vi) position of the support element body relative to length, width, and / or thickness of the spread direction;

[0205] vii) position of the support element body relative to length, width, and / or thickness of the compaction direction;

[0206] viii) or any combination of i) - vii).

[0207] Embodiment 8. The method of embodiment 1, wherein the support elements are displaced from the portion of the first green abrasive article body or the portion of the second green abrasive article body by a controlled pitch distance configured to reduce significant distortion of the first green abrasive article body or the second green abrasive article body during additive manufacturing.

[0208] Embodiment 9. The method of embodiment 1, wherein the support elements are displaced from the portion of the first green abrasive article body or the portion of the second green abrasive article body by a lateral pitch distance, wherein the lateral pitch distance is a minimum distance between the first body and the second body in a lateral direction parallel to a width of a build box, and wherein the lateral pitch distance is at least 0.01% of a length of a longer of the first green abrasive article body or the second green abrasive article body, and further wherein the lateral pitch distance is at least 0.1% or at least 1% or at least 5% or at least 10% or at least 15% or at least 20% or at least 25% or at least 30% or at least 35% or at least 40% or at least 45% or at least 50% or at least 60% or at least 65% or at least 70% or at least 75% or at least 80% or at least 85% or at least 90% or at least 95% or at least 100% or at least 125% or at least 150% or at least 175% or at least 200%.

[0209] Embodiment 10. The method of embodiment 9, wherein the lateral pitch distance is no greater than 2000% or no greater than 1500% or no greater than 1000% or no greater than 800% or no greater than 500% or no greater than 200% or no greater than 100% or no greater than 90% or no greater than 80% or no greater than 70% or no greater than 60% or no greater than 50% or no greater than 40% or no greater than 30% or no greater than 20% of the length of the first green abrasive article body or second green abrasive article body.

[0210] Embodiment 11. The method of embodiment 1, wherein the support element is displaced from the portion of the first green abrasive article body or the portion of the second green abrasive article body by a longitudinal spacing distance, wherein the longitudinal spacing distance is a minimum distance between the support element and the first green abrasive article body or second green abrasive article body in a longitudinal direction parallel to a length of the build box, and wherein the longitudinal spacing distance is at least 0.01% or at least 0.1% or at least 1% or at least 5% or at least 10% or at least 15% or at least 20% or at least 25% or at least 30% or at least 35% or at least 40% or at least 45% or at least 50% or at least 60% or at least 65% or at least 70% or at least 75% or at least 80% or at least 85% or at least 90% or at least 95% or at least 100% or at least 125% or at least 150% or at least 175% or at least 200% of the longer of the lengths of the first green abrasive article body or second green abrasive article body.

[0211] Embodiment 12. The method of embodiment 11, wherein the longitudinal spacing distance is no greater than 2000% or no greater than 1500% or no greater than 1000% or no greater than 800% or no greater than 500% or no greater than 200% or no greater than 100% or no greater than 90% or no greater than 80% or no greater than 70% or no greater than 60% or no greater than 50% or no greater than 40% or no greater than 30% or no greater than 20% of the lengths of the first body or second body.

[0212] Embodiment 13. The method of embodiment 1, wherein the support element is displaced from the portion of the first green abrasive article body or the portion of the second green abrasive article body by a vertical spacing distance, wherein the vertical spacing distance is a minimum distance between the support element and the first green abrasive article body or second green abrasive article body in a vertical direction parallel to a depth of the build box, and wherein the vertical spacing distance is at least 0.01% or at least 0.1% or at least 1% or at least 5% or at least 10% or at least 15% or at least 20% or at least 25% or at least 30% or at least 35% or at least 40% or at least 45% or at least 50% or at least 60% or at least 65% or at least 70% or at least 75% or at least 80% or at least 85% or at least 90% or at least 95% or at least 100% or at least 125% or at least 150% or at least 175% or at least 200% of the longer of the lengths of the first green abrasive article body or second green abrasive article body.

[0213] Embodiment 14. The method of embodiment 13, wherein the vertical spacing distance is no greater than 2000% or no greater than 1500% or no greater than 1000% or no greater than 800% or no greater than 500% or no greater than 200% or no greater than 100% or no greater than 90% or no greater than 80% or no greater than 70% or no greater than 60% or no greater than 50% or no greater than 40% or no greater than 30% or no greater than 20% of the length of the first or second body.

[0214] Embodiment 15. The method of embodiment 1, wherein the first and second green abrasive article bodies differ from each other in at least one of length, width, and / or thickness.

[0215] Embodiment 16. The method of embodiment 1, wherein the first and second green abrasive bodies have substantially the same length, width, and thickness dimensions.

[0216] Embodiment 17. The method of embodiment 1, wherein the first green abrasive article body comprises a first longitudinal axis and the support element comprises a longitudinal axis, and wherein the first longitudinal axis and the longitudinal axis of the support element are substantially parallel to each other.

[0217] Embodiment 18. The method of embodiment 1, wherein the first green abrasive article body comprises a first longitudinal axis and the support element comprises a longitudinal axis, and wherein the first longitudinal axis and the longitudinal axis of the support element are substantially perpendicular to each other.

[0218] Embodiment 19. The method of embodiment 1, wherein the first green abrasive article body comprises a first longitudinal axis and the support element comprises a longitudinal axis, and wherein the first longitudinal axis and the longitudinal axis of the support element are angled relative to each other in a range of at least 6 degrees and no greater than 84 degrees.

[0219] Embodiment 20. The method of embodiment 1, wherein the first green abrasive article body comprises a first transverse axis and the support element comprises a transverse axis, and wherein the first transverse axis and the transverse axis of the support element are substantially parallel to each other.

[0220] Embodiment 21. The method of embodiment 1, wherein the first green abrasive article body comprises a first transverse axis and the support element comprises a transverse axis, and wherein the first transverse axis and the transverse axis of the support element are substantially perpendicular to each other.

[0221] Embodiment 22. The method of embodiment 1, wherein the first green abrasive article body comprises a first lateral axis and the support element comprises a lateral axis, and wherein the first lateral axis and the lateral axis of the support element are angled relative to one another within a range of at least 6 degrees and no more than 84 degrees.

[0222] Embodiment 23. The method of embodiment 1, wherein the first green abrasive article body comprises a first vertical axis and the support element comprises a vertical axis, and wherein the first vertical axis and the vertical axis of the support element are substantially parallel to one another.

[0223] Embodiment 24. The method of embodiment 1, wherein the first green abrasive article body comprises a first vertical axis and the support element comprises a vertical axis, and wherein the first vertical axis and the vertical axis of the support element are substantially perpendicular to one another.

[0224] Embodiment 25. The method of embodiment 1, wherein the first green abrasive article body comprises a first vertical axis and the support element comprises a vertical axis, and wherein the first vertical axis and the vertical axis of the support element are angled relative to one another within a range of at least 6 degrees and no more than 84 degrees.

[0225] Embodiment 26. The method of embodiment 1, wherein the first green abrasive article body comprises at least one of:

[0226] a first longitudinal axis that is substantially parallel to a direction of translation of the compacted object;

[0227] a first longitudinal axis that is substantially perpendicular to a direction of translation of the compacted object; or

[0228] a first longitudinal axis that is angled relative to a direction of translation of the compacted object within a range of at least 6 degrees and no more than 84 degrees.

[0229] Embodiment 27. The method of embodiment 1, wherein the support element comprises at least one of:

[0230] a longitudinal axis that is substantially parallel to a direction of translation of the compacted object;

[0231] a longitudinal axis that is substantially perpendicular to a direction of translation of the compacted object; or

[0232] a longitudinal axis that is angled relative to a direction of translation of the compacted object within a range of at least 6 degrees and no more than 84 degrees.

[0233] Embodiment 28. The method of embodiment 1, wherein the first green abrasive article body comprises at least one of:

[0234] a first lateral axis that is substantially parallel to a direction of translation of the compacted object;

[0235] a first lateral axis that is substantially perpendicular to a direction of translation of the compacted object; or

[0236] a first lateral axis that is angled within a range of at least 6 degrees and no more than 84 degrees relative to a direction of translation of the compacted object.

[0237] Embodiment 29. The method of embodiment 1, wherein the support element comprises at least one of:

[0238] a lateral axis that is substantially parallel to a direction of translation of the compacted object;

[0239] a lateral axis that is substantially perpendicular to a direction of translation of the compacted object; or

[0240] a lateral axis that is angled within a range of at least 6 degrees and no more than 84 degrees relative to a direction of translation of the compacted object.

[0241] Embodiment 30. The method of embodiment 1, wherein the first green abrasive article body comprises at least one of:

[0242] a first vertical axis that is angled away from a plane of translation of the compacted object;

[0243] a first vertical axis that is substantially perpendicular to a direction of translation or a plane of translation of the compacted object; or

[0244] a first vertical axis that is angled away from a plane of translation of the compacted object within a range of at least 6 degrees and no more than 84 degrees relative to the plane of translation.

[0245] Embodiment 31. The method of embodiment 1, wherein the support element comprises at least one of:

[0246] a vertical axis that is angled away from a plane of translation of the compacted object;

[0247] a vertical axis that is substantially perpendicular to a direction of translation or a plane of translation of the compacted object; or

[0248] a vertical axis that is angled away from the plane of translation of the compacted object in a range of at least 6 degrees and no more than 84 degrees from the plane.

[0249] Embodiment 32. The method of embodiment 1, wherein forming a green abrasive article comprising a precursor bond material and abrasive particles is carried out by:

[0250] a) generating one or more layers of a powder material;

[0251] b) selectively bonding portions of the one or more layers with a binder material; and

[0252] c) transforming the binder material to at least partially solidify the binder material and bond portions of the powder material from the one or more layers.

[0253] Embodiment 33. The method of embodiment 32, wherein selectively bonding portions of one or more layers comprises: selectively bonding a first portion of the powder layers defining a portion of the first green abrasive article body; selectively bonding a second portion of the powder layers defining a portion of the second abrasive article body; and selectively bonding a portion of the support element.

[0254] Embodiment 34. The method of embodiment 32, further comprising moving a compacting object over the one or more layers of powder material to apply a force sufficient to compact the layers to a compacted layer thickness that is less than a thickness of the layers prior to compaction.

[0255] Embodiment 35. The method of embodiment 34, wherein moving the compacting object over the one or more layers of powder material is adjusted based on at least one of:

[0256] i) a relative spacing between one of the green abrasive article bodies and a support element;

[0257] ii) a two-dimensional shape of one of the green abrasive article bodies when viewed looking down in the build box or in cross-section;

[0258] iii) a three-dimensional shape of at least one green abrasive article body;

[0259] iv) a two-dimensional shape of the support element when viewed looking down in the build box or in cross-section;

[0260] v) a three-dimensional shape of the support element;

[0261] vi) or any combination of i) - v).

[0262] Implementation 36. The method of implementation 34, further comprising controlling at least one of:

[0263] a) the force applied to the powder layer or layers by the compacting object;

[0264] b) the traverse speed of the compacting object;

[0265] c) the average thickness of the layer prior to compaction;

[0266] d) the particle size distribution of the powder;

[0267] e) the number of previously formed layers underneath the powder layer;

[0268] f) the number of compacted layers underneath the powder layer;

[0269] g) the density of any layers underneath the powder layer;

[0270] h) the amount of binder in any layers underneath the powder layer;

[0271] i) the relative size of the layer relative to one or more layers underneath the layer; and

[0272] j) any combination of a) - i).

[0273] Implementation 37. The method of implementation 36, further comprising selecting the placement, orientation, and / or size of the first green abrasive article and / or support element based on any one or more of a) - i).

[0274] Implementation 38. The method of implementation 1, wherein the support element has at least one surface that is complementary to at least one surface of the first green abrasive article body or at least one surface of the second green abrasive article body.

[0275] Implementation 39. The method of implementation 38, wherein the first green abrasive article body comprises a first curved surface and the support element comprises a support curved surface that substantially corresponds to the curvature of the first curved surface.

[0276] Implementation 40. The method of implementation 32, wherein the support surface substantially surrounds the first green abrasive article body when viewed from above in the build box and / or when viewed in cross-section.

[0277] Implementation 41. A method for forming an abrasive article, the method comprising:

[0278] quantifying a deformation of the green abrasive article body or the final formed abrasive article as compared to a model used to form the green abrasive article body or the final formed abrasive article; and

[0279] modifying the model used to control the formation of the green abrasive article body or the final formed abrasive article.

[0280] Embodiment 42. The method of embodiment 41, further comprising using any one or more of the methods of the embodiments herein, and further wherein the green abrasive article body can have any one or more of the features of the embodiments herein.

[0281] Example

[0282] The following non-limiting examples illustrate the application.

[0283] Example 1

[0284] A mixture is prepared by combining two separate dry powder materials: a precursor bond material and abrasive particles. The precursor bond material is an oxide-containing material that forms a glassy phase material upon further processing.

[0285] An additive manufacturing process is performed according to the embodiments described herein. The additive manufacturing process can be characterized as a binder jetting operation in which layers of powder material are deposited into a build box, the layers are leveled, compacted, and selectively bound with a binder material to form a batch of green abrasive articles comprising an unbound or loose powder bed. Each green abrasive article has any one or more of the features claimed in the embodiments herein. The batch of green abrasive articles has any one or more of the features claimed in the embodiments herein. The green abrasive articles are converted to final formed abrasive articles via heating as provided below. Example 1 was formed using an ExOne (now Desktop Metal) Innovent+.

[0286] Table 1 :

[0287]

[0288]

[0289] The build box has dimensions of at least 150 mm in length, at least 60 mm in width, and at least 60 mm in depth. The forming process produces green abrasive article bodies having a length of at least 6 cm and / or a width of at least 2.8 cm and / or a height of at least 9 cm 3a green abrasive article having a size of at least 150 mm in length, at least 60 mm in width, and at least 60 mm in depth. The forming process produces a green abrasive article having a size of a solid volume of at least 6 cm in length and / or at least 2.8 cm in width and / or at least 9 cm

[0290] After forming, the green body was heated in air at a rate of 5 °C / min to a temperature of 375 °C and held at 375 °C for 1 hour to remove the binder. The air was then replaced with argon and the body was heated to a maximum temperature of 1000 °C at a ramp rate of 5 °C / min. The temperature was held at 1000 °C for four hours and then cooled at a rate of 5 °C / min.

[0291] Example 2

[0292] A mixture was prepared by combining two separate dry powder materials: a precursor bond material and abrasive particles. The precursor bond material was a metal-containing material.

[0293] The process for forming the green abrasive article of Example 2 was performed using an ExOne 25 Pro (now Desktop Metal). The printing conditions are provided in Table 2 below.

[0294] Table 2 :

[0295]

[0296] The build box had a size of at least 150 mm in length, at least 60 mm in width, and at least 60 mm in depth. The forming process produced a green abrasive article having a size of a solid volume of at least 6 cm in length and / or at least 2.8 cm in width and / or at least 9 cm 3 in length and / or at least 2.8 cm in width and / or at least 9 cm

[0297] Comparative Example 1

[0298] A sample was prepared using a binder jetting operation as generally described in Example 1. However, the powder material was 20 wt% SP1086 glass powder from Specialty Glass Inc. (Oldsmar, Florida) and 80 wt% 200 / 230 mesh D76 diamond powder from Pinnacle Abrasives (Santa Rosa, CA). The binder used was PM-B-SR1-04 from ExOne. The forming conditions are detailed in Table 3 below and formed using an Innovent ExOne (now Desktop Metal) printer. Figure 15 An image of the CS1 sample is included.

[0299] Table 3 :

[0300] Parameter Sample CS1 Saturation (%) 70 Layer thickness [pm] 100 Base layer count 5 Oscillator on delay (seconds) 2 Binder set (seconds) 1 Drying time (seconds) 45 Target temperature (°C) 60 Spreading speed (rpm) 10 Oscillator speed (rpm) 2800 Roller speed (rpm) 60 Roller speed (mm / s) 1

[0301] The body was then cured in an ambient atmosphere oven at 195 °C for 2 hours. After curing and cooling to 23 °C, the cured body was placed in a furnace and burned out at 400 °C for 2 hours, followed by sintering at 700 °C for 4 hours to produce comparative sample CS1.

[0302] SDR and surface roughness

[0303] The transverse surfaces and other surfaces of representative sample (“Sample S1”) and sample CS1 were measured for Sdr and surface roughness (Sa) and are detailed in Table 4 below.

[0304] Table 4 :

[0305]

[0306] Notably, Sample S1 has a much smaller transverse Sdr and Sdr difference than CS1.

[0307] Example 3

[0308] A mixture was prepared by combining two separate dry powder materials: a precursor bond material and abrasive particles. The precursor bond material is an oxide-containing material that forms a glassy phase material upon further processing.

[0309] An additive manufacturing process was performed in accordance with the embodiments described herein. The additive manufacturing process can be characterized as a binder jetting operation in which layers of powder material are deposited into a build box, the layers are leveled, compacted, and selectively bound with a binder material to form a batch of green abrasive articles that include an unbound or loose powder bed. Each green abrasive article has any one or more of the features claimed in the embodiments herein. The batch of green abrasive articles has any one or more of the features claimed in the embodiments herein. The green abrasive articles are converted to a final formed abrasive article via heating as provided below. Example 3 was formed using an ExOne (now Desktop Metal) Innovent+. The printing conditions are summarized in Table 5.

[0310] Table 5 :

[0311]

[0312]

[0313] The build box has dimensions of at least 150 mm in length, at least 60 mm in width, and at least 60 mm in depth. The forming process results in a green abrasive article having dimensions of a solid volume of at least 6 cm in length and / or at least 2.8 cm in width and / or at least 9 cm 3 The green abrasive article has a thickness of at least 1 mm.

[0314] After forming, the green body was heated in air at a rate of 5 °C / min to a temperature of 375 °C and held at 375 °C for 1 hour to remove the binder. The air was then replaced with argon and the body was heated to a maximum temperature of 1000 °C at a ramp rate of 5 °C / min. The temperature was held at 1000 °C for four hours and then cooled at a rate of 5 °C / min.

[0315] Figure 14A and Figure 14B An image including an abrasive article, where the end of the body 1401 of the abrasive article exhibits layer displacement 1402, which results in undesirable shape defects of the green abrasive article bodies of the batch and greater variation in shape fidelity. The lay direction is also indicated and the relationship between the lay direction and the layer displacement is observed.

[0316] Example 4

[0317] A batch of abrasive articles was prepared according to the process of Example 3, except that support elements were added in the build box as depicted in Figure 13A and Figure 13B The Example 4 was formed using an ExOne (now Desktop Metal) Innovent+. The print conditions are summarized in Table 6.

[0318] Table 6 :

[0319]

[0320]

[0321] Figure 13A An overhead view image including bodies 1303, 1304, 1305, and 1306 in a bed of powder material 1301. Figure 13B An image including a perspective view of a model for producing a body, including in Figure 13Aview of the body 1307 that is not visible from above. According to one embodiment, the bodies 1303, 1304, 1305, and 1307 are support elements and the body 1306 is a green abrasive article body. All of the bodies 1303-1307 include a combination of powder materials including abrasive particles, precursor bond material, and a content of binder configured to bind regions of the bodies 1303-1307 to form a suitable green abrasive article. It is apparent that the support elements 1303, 1304, 1305, and 1307 have different shapes compared to the abrasive article 1306 and are formed in a manner that reduces or eliminates unintended defects such as layer displacement.

[0322] Example 5

[0323] A first batch of abrasive articles (sample S5) was prepared from a powder mixture having 70 wt% of iron powder and 30 wt% of diamond by total weight of the mixture. The iron powder had a D50 of about 38 microns. The diamond had a D50 of about 250 microns. The density of the powder was about 3.00 g / cc. The forming parameters are listed in Table 7.

[0324] Figure 16A A top down image of a build box including a plurality of green abrasive article bodies 1601, a plurality of support elements 1603, and a reference of the direction of laydown, which is also the direction of movement of the compacting object during the compaction process. The print direction is in the same plane but perpendicular to the laydown direction. The plurality of green abrasive article bodies 1601 have a circular two-dimensional shape and have a cylindrical three-dimensional shape when viewed from above in the plane of the length and width of the build box.

[0325] A second batch of abrasive articles (sample CS2) was prepared similarly to sample S5 but without the use of support elements. Sample CS2 and S5 were formed using an ExOne (now Desktop Metal) Innovent+. The print conditions for both samples (S5 and CS2) are summarized in Table 7.

[0326] Table 7 :

[0327]

[0328]

[0329] Figure 16BA plot including the difference percentage of the diameter (equivalent to the width) of a green abrasive article body measured in the spread direction compared to the diameter measured in a direction perpendicular to the spread direction diameter and in the same plane as the spread direction diameter. The difference is calculated according to the following formula: Difference 1 = Ds - Dp, where "Ds" is the diameter partially in the spread direction and "Dp" is the diameter partially in the print direction, which is perpendicular to the spread direction. The difference percentage is calculated according to the following formula: Difference Percentage = (Difference 1 / Dp) x 100%.

[0330] Certain dimensional properties of samples S1-S5 and comparative samples CS1 and CS2 were measured. Such dimensional properties include, but are not limited to, bulk shape factor, batch bulk shape factor, and the like. Data is forthcoming and is expected to demonstrate that one or more dimensional properties of samples formed according to embodiments herein have superior dimensional properties over samples formed using conventional knowledge.

[0331] According to embodiments herein, abrasive articles having controlled differences in surface features (e.g., Sdr, etc.) between two surfaces (particularly two different outer surfaces of an abrasive article) can be produced. Research into process variables that can be used to control such differences in surface features is complex and unpredictable. Certain surface features, such as differences in Sdr, are understood to be related to the build direction and orientation of the body during the formation process. As such, the empirical data generated indicates that abrasive articles having selective surface features on various surfaces can be designed by controlling the build direction and build parameters. Such surface features are believed to be technologically advantageous for improving abrasive performance and / or anchoring the abrasive article with a bond system or other component to form a fixed abrasive article.

[0332] Benefits, other advantages, and solutions to problems have been described above with regard to specific embodiments. However, the benefits, advantages, solutions to problems, and any feature(s) that can cause any benefit, advantage, or solution to occur or become more pronounced are not to be construed as a critical, required, or essential feature of any or all the claims. The materials referred to herein including one or more components can be interpreted to include at least one embodiment wherein the material consists essentially of the identified one or more components. The term consisting essentially of is to be interpreted as including a composition that comprises those identified materials and excludes any other materials not specifically identified that would alter the basic and novel properties of the composition. Additionally, or in the alternative, in certain non-limiting embodiments, any of the compositions identified herein can be essentially free of materials not expressly disclosed. Embodiments herein include ranges of content of certain components within a material, and it should be understood that the content of each component within a given material totals 100%. The description and drawings of embodiments described herein are intended to provide a general understanding of the structure of various embodiments. The description and drawings are not intended to serve as an exhaustive and comprehensive description of all the elements and features of apparatuses and systems that use the structures or methods described herein. Separate embodiments can also be provided in combination in a single embodiment, and conversely, various features described in the context of a single embodiment can also be provided separately or in any sub-combination. Furthermore, references to values stated in a range include each and every value within that range. Many other embodiments will be apparent to skilled practitioners in the art after review of this application. Other embodiments can be used and obtained from the disclosure without departing from the scope of the disclosure. Thus, the disclosure should be considered as illustrative and not restrictive.

Claims

1. A method for forming an additively manufactured body in a powder bed, the method comprising: forming at least a portion of a first green abrasive article body; forming at least a portion of a second green abrasive article body; and forming a support element between the portion of the first green abrasive article body and the portion of the second green abrasive article body, wherein the support element has a predetermined position between the portions of the first and second green abrasive article bodies, wherein the support element is displaced from the portion of the first green abrasive article body or the portion of the second green abrasive article body by a controlled spacing distance configured to reduce significant distortion of the first or second green abrasive article body during additive manufacturing.

2. The method of claim 1, wherein the support element is configured to limit significant distortion of the first green abrasive article body during additive manufacturing.

3. The method of claim 1, wherein the support element is configured to distribute forces and / or pressures applied to an upper surface of the first green abrasive article body during additive manufacturing.

4. The method of claim 1, wherein the support element is a sacrificial element intended to be discarded or recycled after the forming of the first and second green abrasive article bodies is complete.

5. The method of claim 1, wherein the support element differs from the portion of the first green abrasive article body or the portion of the second green abrasive article body based on at least one of: i) a two-dimensional shape in any plane; ii) a three-dimensional shape; iii) composition; iv) binder content; v) raw material particle size; vi) position of the support element body relative to length, width, and / or thickness of the spread direction; vii) position of the support element body relative to length, width, and / or thickness of the compaction direction; viii) or any combination of i) - vii).

6. The method of claim 1, wherein the support element is configured to reduce pressure applied to an upper surface of the first green abrasive article body and an upper surface of the second green abrasive article body during additive manufacturing.

7. The method of claim 1, wherein the support element is displaced from the portion of the first green abrasive article body or the portion of the second green abrasive article body by a lateral spacing distance, wherein the lateral spacing distance is a minimum distance between the first and second bodies in a lateral direction parallel to a width of a build box, and wherein the lateral spacing distance is at least 0.01% and no greater than 2000% of a length of the longer of the first or second green abrasive article body.

8. The method of claim 1, wherein the support element is displaced from the portion of the first green abrasive article body or the portion of the second green abrasive article body by a longitudinal spacing distance, wherein the longitudinal spacing distance is a minimum distance between the support element and the first green abrasive article body or second green abrasive article body in a longitudinal direction parallel to a length of the build cartridge, and wherein the longitudinal spacing distance is at least 0.01% and no greater than 2000% of the longer of the lengths of the first green abrasive article body or second green abrasive article body.

9. The method of claim 1, wherein the support element is displaced from the portion of the first green abrasive article body or the portion of the second green abrasive article body by a vertical spacing distance, wherein the vertical spacing distance is a minimum distance between the support element and the first green abrasive article body or second green abrasive article body in a vertical direction parallel to a depth of the build cartridge, and wherein the vertical spacing distance is at least 0.01% and no greater than 2000% of the longer of the lengths of the first green abrasive article body or second green abrasive article body.

10. The method of claim 1, wherein the support element comprises at least one of: a longitudinal axis that is substantially parallel to a direction of translation of a compacted object; a longitudinal axis that is substantially perpendicular to a direction of translation of a compacted object; a longitudinal axis that is angled relative to a direction of translation of a compacted object in a range of at least 6 degrees and no greater than 84 degrees; wherein the support element comprises at least one of: a transverse axis that is substantially parallel to a direction of translation of a compacted object; a transverse axis that is substantially perpendicular to a direction of translation of a compacted object; or a transverse axis that is angled relative to a direction of translation of a compacted object in a range of at least 6 degrees and no greater than 84 degrees; a vertical axis that is angled away from a plane of translation of a compacted object; a vertical axis that is substantially perpendicular to a direction of translation or a plane of translation of a compacted object; or a vertical axis that is angled away from a plane of translation of a compacted object in a range of at least 6 degrees and no greater than 84 degrees relative to the plane of translation.

11. The method of claim 1, wherein forming the first green abrasive article body, the second green abrasive article body, and the support element comprises: a) generating one or more layers of a powder material; b) selectively binding portions of the one or more layers with a binder material; and c) transforming the binder material to at least partially solidify the binder material and bind portions of the powder material from the one or more layers.

12. The method of claim 11, wherein selectively bonding portions of one or more layers comprises: a first portion of the powder layers that are selectively bound that define a portion of the first green abrasive article body; a second portion of the powder layers that are selectively bound that define a portion of the second abrasive article body; and selectively bonding a portion of the support element.

13. The method of claim 11, further comprising moving a compaction object over the one or more layers of powder material to apply a force sufficient to compact the layers to a compacted layer thickness that is less than a thickness of the layers prior to compaction.

14. The method of claim 13, wherein moving the compaction object over the one or more layers of powder material is adjusted based on at least one of: i) a relative spacing between one of the green abrasive article bodies and a support element; ii) a two-dimensional shape of one of the green abrasive article bodies when viewed planarly or in cross-section in the build box; iii) a three-dimensional shape of at least one green abrasive article body; iv) a two-dimensional shape of the support element when viewed planarly or in cross-section in the build box; v) a three-dimensional shape of the support element; vi) or any combination of i) - v).

15. The method of claim 13, further comprising controlling at least one of: a) a force applied by a compaction object to the powder layer or layers; b) a traverse speed of a compaction object; c) an average thickness of the layers prior to compaction; d) a particle size distribution of the powder; e) a number of previously formed layers underlying the powder layer; f) a number of compacted layers underlying the powder layer; g) a density of any layers underlying the powder layer; h) an amount of binder in any layers underlying the powder layer; i) a relative size of the layer relative to one or more layers underlying the layer; and j) any combination of a) - i).

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