Abrasive grain with main surfaces and subsidiary surfaces

Abstract

An abrasive grain includes a surface having at least a first face with a first outline, and at least one second face with a second outline. The first outline does not contain any vertices, but the second outline contains at least one vertex. The abrasive grain may include a ceramic material, especially polycrystalline -Al.sub.2O.sub.3.

Claims

1. An abrasive grain comprising: at least two main surfaces; and at least one subsidiary surface, which is connected by way of a first edge to a first main surface of the at least two main surfaces and is connected by way of a second edge to a second main surface of the at least two main surfaces, wherein the second main surface does not have any edge in common with the first main surface, wherein the at least one subsidiary surface includes a first obtuse angle with the first main surface in a region of the first edge and a second obtuse angle with the second main surface in a region of the second edge, wherein the at least two main surfaces of the abrasive grain are substantially planar and lie on faces of one of an imaginary pyramid, an imaginary frustopyramid, and a tetrahedron, and the at least one subsidiary surface truncates the one of the imaginary pyramid, the imaginary frustopyramid, and the tetrahedron, and wherein each of the at least two main surfaces has a triangular shape.

2. The abrasive grain as claimed in claim 1, wherein each of the at least two main surfaces is connected to at least one other main surface of the at least two main surfaces by way of a subsidiary surface of the at least one subsidiary surface.

3. The abrasive grain as claimed in claim 1, wherein the abrasive grain includes a ceramic material.

4. The abrasive grain as claimed in claim 3, wherein the ceramic material is a polycrystalline ceramic material.

5. The abrasive grain as claimed in claim 4, wherein the polycrystalline ceramic material includes aluminum oxide.

6. The abrasive grain as claimed in claim 5, wherein the aluminum oxide includes Al.sub.2O.sub.3.

7. A casting mold for producing the abrasive grain of claim 1, the casting mold comprising: at least one depression, each depression of the at least one depression including a respective surface that is complementary to a form of at least part of at least one of (i) at least one of the at least two main surfaces and (ii) the subsidiary surface of the abrasive grain.

8. A collective of abrasive grains, comprising: a plurality of first abrasive grains, each first abrasive grain of the plurality of first abrasive grains comprising: at least two main surfaces; and at least one subsidiary surface, which is connected by way of a first edge to a first main surface of the at least two main surfaces and is connected by way of a second edge to a second main surface of the at least two main surfaces, wherein the second main surface does not have any edge in common with the first main surface, wherein the at least one subsidiary surface includes a first obtuse angle with the first main surface in a region of the first edge and a second obtuse angle with the second main surface in a region of the second edge, wherein the abrasive grain has a defined form, wherein the abrasive grain has an abrasive grain body which includes the at least two main surfaces, the at least two main surfaces being substantially planar and lying on faces of one of an imaginary pyramid, an imaginary frustopyramid, and a tetrahedron, wherein the abrasive grain body includes the at least one subsidiary surface, which is formed as a flat surface truncating one of the imaginary pyramid, the imaginary frustopyramid, and the tetrahedron, wherein each of the at least two main surfaces has a triangular shape, and wherein the collective includes at least 20% by weight of the first abrasive grains.

9. The collective of abrasive grains as claimed in claim 8, wherein the collective includes at least 50% by weight of the first abrasive grain.

10. The collective of abrasive grains as claimed in claim 8, wherein the collective includes at least 90% by weight of the first abrasive grain.

11. An abrasive article comprising: the collective of abrasive grains as claimed in claim 8.

12. A method for producing the abrasive article as claimed in claim 11, comprising: fixing the collective of abrasive grains on and/or in a substrate with a binder.

13. A method for grinding a surface or a painted surface, comprising: grinding the surface or the painted surface with the abrasive article of claim 11.

14. A method for producing at least one abrasive grain or a collective of abrasive grains, each grain of the at least one abrasive grain including at least two main surfaces and at least one subsidiary surface, which is connected by way of a first edge to a first main surface of the at least two main surfaces and is connected by way of a second edge to a second main surface of the at least two main surfaces, wherein the second main surface does not have any edge in common with the first main surface, wherein the at least one subsidiary surface includes a first obtuse angle with the first main surface in a region of the first edge and a second obtuse angle with the second main surface in a region of the second edge, wherein the abrasive grain has a defined form, wherein the abrasive grain has an abrasive grain body which includes the at least two main surfaces, the at least two main surfaces being substantially planar and lying on faces of one of an imaginary pyramid, an imaginary frustopyramid, and a tetrahedron, wherein each of the at least two main surfaces has a triangular shape, and wherein the abrasive grain body includes the at least one subsidiary surface, which is formed as a flat surface truncating the imaginary three-dimensional shape, the method comprising: preparing or providing a dispersion containing (i) at least one of -alumina particles and particles that can be converted into -alumina, and (ii) at least one volatile dispersion medium; introducing the dispersion into at least one depression in a casting mold; removing part of the volatile dispersion medium of the dispersion, so as to form at least one abrasive grain precursor; removing the at least one abrasive grain precursor from the casting mold; sintering the at least one abrasive grain precursor in order to obtain the at least one abrasive grain.

15. The method as claimed in claim 14, wherein the at least one volatile dispersion medium includes water.

16. The method as claimed in claim 14, further comprising: wiping an upper side of the casting mold in order to remove at least part of the dispersion that stands above the upper side of the casting mold.

17. The method as claimed in claim 14, further comprising: calcining the at least one abrasive grain precursor.

18. The abrasive grain as claimed in claim 1, wherein: the abrasive grain has an abrasive grain body that includes the at least two main surfaces and the at least one subsidiary surface, and the abrasive grain further comprises a base portion shaped as a prism extending from the abrasive grain body and having a base area corresponding to the truncated one of the imaginary pyramid, the imaginary frustopyramid, and the tetrahedron.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The disclosure is explained in more detail below with the aid of a number of exemplary embodiments and drawings, in which:

(2) FIGS. 1A and 1B show a first embodiment of an abrasive grain according to the disclosure in two views;

(3) FIGS. 2A and 2B show a second embodiment of an abrasive grain according to the disclosure in two views;

(4) FIG. 3 shows a third embodiment of an abrasive grain according to the disclosure; and

(5) FIG. 4 shows a fourth embodiment of an abrasive grain according to the disclosure.

(6) FIGS. 5A and 5B show two views of a further embodiment of an abrasive grain according to the disclosure in the form of a pyramid with a seven-cornered base area; and

(7) FIGS. 6A and 6B show two views of a further embodiment of an abrasive grain according to the disclosure in the form of a frustopyramid with a non-convex base area.

(8) FIG. 7A shows a further embodiment of an abrasive grain according to the disclosure in a perspective view;

(9) FIG. 7B shows the embodiment of an abrasive grain according to the disclosure in a first side view;

(10) FIG. 7C shows the embodiment of an abrasive grain according to the disclosure in a second side view; and

(11) FIG. 7D shows the embodiment of an abrasive grain according to the disclosure in a plan view.

(12) FIG. 8A shows a further embodiment of an abrasive grain according to the disclosure in a perspective view;

(13) FIG. 8B shows the embodiment of an abrasive grain according to the disclosure according to FIG. 8A in a plan view;

(14) FIG. 9A shows a further embodiment of an abrasive grain according to the disclosure in a perspective view;

(15) FIG. 9B shows the embodiment of an abrasive grain according to the disclosure according to FIG. 9A in a plan view of the base area;

(16) FIG. 10A shows a further embodiment of an abrasive grain according to the disclosure in a perspective view;

(17) FIG. 10B shows the embodiment of an abrasive grain according to the disclosure according to FIG. 10A in a plan view; and

(18) FIG. 10C shows the embodiment of an abrasive grain according to the disclosure according to FIG. 10A in a side view.

DETAILED DESCRIPTION

(19) The abrasive grain 110 represented in a perspective view in FIG. 1A includes a planar, circular first face 120 with a first outer contour 121 and a square, that is to say polygonal, second face 125 with a second outer contour 126, parallel to the first face. Between the first face 120 and the second face 125 there is formed a curved lateral face 130. The lines drawn on the lateral face 130 indicate the curved shape of the lateral area 130; however, they do not represent actual edges of the abrasive grain 110. The abrasive grain 110 extends completely between the two planes that are defined by the first face 120 and the second face 125.

(20) The first outer contour 121 has no corner, since the direction of the tangent to the points of the first outer contour 121 runs continuously. The absence of corners in the first outer contour 121 contributes to the secure anchorage of the abrasive grain 110 in a make coat. By contrast with the first outer contour 121, the second outer contour 126 has four corners 127. Both these corners 127 and the four edges 128 extending between them provide an abrasive effect.

(21) The perpendicular projection of the second face 125 onto the first face 120 extends completely within the first face 120, as can also be seen well in FIG. 1B. As a result, the abrasive grain 110 is particularly stable with respect to the tilting forces occurring during grinding if it lies with the first face 120 on an abrasive material backing that is not represented here.

(22) FIG. 1B shows a lateral sectional view through the sectional plane S represented in FIG. 1A. This sectional plane S extends perpendicularly to the first face 120 and the second face 125 and through the center points of these two faces 120, 125. The abrasive grain 110 tapers along the direction R, which runs from the first face 120 perpendicularly to the second face 125. As a result, particularly good anchorage in a make coat applied to a backing can be achieved. Moreover, even with the aid of mechanical scattering, the abrasive grain 110 can with great probability be placed with the first face 120 on the backing. In this orientation, the corners 127 and the edges 128 also face away from the backing, and can consequently cause an abrasive effect. The sectional line of the lateral area 130 with this sectional plane S extends in a straight line.

(23) A further embodiment according to the disclosure is represented in FIGS. 2A and 2B. This abrasive grain 210 also has a planar circular first face 220 with a first outer contour 221 and a square second face 225 with a second outer contour 226, parallel to the first face. By contrast with the abrasive grain 110 according to FIGS. 1A and 1B, the sectional line of the lateral area 230 of the abrasive grain 210 with a sectional plane S is convex, as can be seen in FIG. 2B. This convexity has the effect of producing in the region of the first face 220 a kind of standing foot, with which the abrasive grain 210 can be anchored particularly stably in a make coat.

(24) The abrasive grain 310 shown in FIG. 3 has a planar first face 320 with a first outer contour 321, which though not circular, similarly has no corners. The opposite second face 325, extending parallel to the first face, has the form of an irregular pentagon with five corners 327 and five edges 328 extending in between. This abrasive grain 310 does not taper in the direction R running perpendicularly from the first face 320.

(25) Finally, the abrasive grain 410 according to FIG. 4 also has a planar first face 420 with a first outer contour 421 and a second face 425 with a second outer contour 426, extending parallel to the first face. The second outer contour 426 has four edges 428, 428, 428. Of these edges, the edge 428 is straight; the edges 428 are convexly curved; the edge 428 is concavely curved. At the point where two edges 428, 428, 428 touch, a corner 427 is respectively formed; this is so because at these points the direction of the tangent to the second outer contour 426 runs discontinuously.

(26) The abrasive grains according to the disclosure may be produced for example by a method described hereinafter: firstly, a dispersion of 200 g of -Al.sub.2O.sub.3, 0.4 g of MgO, 90 g of water as a dispersion medium and 0.5 g of dispersant is prepared. The MgO functions here as a nucleating agent. The product Dolapix CE64, obtainable from Zschimmer & Schwarz, 56108 Lahnstein, Germany, may be used for example as the dispersant. The dispersion thus obtained is ground for 30 minutes at 200 revolutions per minute in a planetary ball mill, for example a planetary ball mill PM400, obtainable from Retsch GmbH, 42781 Haan, Germany. Subsequently, the ground dispersion is introduced into a silicone casting mold containing depressions in the form of the desired abrasive grains. After that, the volatile component, that is the water, is removed from the dispersion. This produces an abrasive grain precursor, which is removed from the casting mold. The first face of the abrasive grain can then be produced from the upper free surface of the dispersion, which is not in contact with the casting mold. In a final step, the precursor is sintered as bulk material at 1550 C. for 5 minutes. The dispersant is burnt out in the course of sintering.

(27) An abrasive article according to the disclosure may for example be produced as follows: on a backing of vulcanized fiber with a thickness of 0.8 mm, a phenolic resin dispersion is applied in an amount of 120 g/m.sup.2 as a make coat precursor. Subsequently, 600 g/m.sup.2 of the abrasive grains according to the disclosure are applied by means of electrostatic scattering. After that, the make coat precursor is cured to give a make coat. On top of the make coat and the abrasive grains, a phenolic resin dispersion is applied in an amount of 800 g/m.sup.2 as a size coat precursor, which is likewise cured.

(28) The abrasive grain 110 shown in FIGS. 5A and 5B is formed as a pyramid with a planar base area 111 in the form of a regular heptagon. It is therefore a special cone, in the sense of the definition used here, with a convex polygonal base area. The outer contour 112 of the base area 113 includes seven corners 113 and seven edges 114, which respectively connect two of the corners 113 to one another. Each of the corners 113 of the outer contour 112 of the base area 111 is connected by way of a respective edge 116 to a vertex 115 of the pyramid, which likewise forms a corner of the abrasive grain 110. Altogether, the abrasive grain 110 therefore includes eight corners 113, 115 and fourteen edges 114, 116.

(29) The ratio of the height h and the area diameter (not represented here) of the base area 111 may lie in the range from 0.8 to 1.4. As explained above, it is advantageous for mechanical scattering if the ratio mentioned tends to be small, since, with mechanical scattering, the abrasive grain is then preferably oriented with its base area on an abrasive material backing such that the vertex 115 faces away from this backing. In terms of advantageous chip-forming behavior, on the other hand, greater ratios tend to be expedient.

(30) The abrasive grain 210 according to FIGS. 6A and 6B is formed as a frustopyramid with a base area 211. According to FIG. 6B, the base area 211 has altogether 20 corners 213, 213, which are connected to one another by 20 edges 214. Of the 20 corners, the twelve corners 213 have an internal angle of 90, while the eight corners 213 have an internal angle of 270. The base area 211 is therefore not a convex polygon. The top area 217 of the pyramid is similar to the base area 211; the two areas can therefore be transformed one into the other by a combination of displacement and homothety. The top area 217 consequently also includes 20 corners 218, 218 and 20 edges 219. Between the base area 211 and the top area 217 there extend 20 further edges 216, which respectively connect a corner 213, 213 of the base area 211 to a corresponding corner 218, 218 of the top area 217. The high numbers of edges 216, 219 and of corners 218, 218 provide a high cutting effect.

(31) The abrasive grains according to the disclosure may be produced for example by a method described hereinafter: firstly, a dispersion of 200 g of -Al.sub.2O.sub.3, 0.4 g of MgO, 90 g of water as a dispersion medium and 0.5 g of dispersant is prepared. The MgO functions here as a nucleating agent. The product Dolapix CE64, obtainable from Zschimmer & Schwarz, 56108 Lahnstein, Germany, may be used for example as the dispersant. The dispersion thus obtained is ground for 30 minutes at 200 revolutions per minute in a planetary ball mill, for example a planetary ball mill PM400, obtainable from Retsch GmbH, 42781 Haan, Germany. Subsequently, the ground dispersion is introduced into a silicone casting mold containing depressions in the form of the desired abrasive grains. After that, the volatile component, that is the water, is removed from the dispersion. This produces an abrasive grain precursor, which is removed from the casting mold. In a final step, the precursor is sintered as bulk material at 1550 C. for 5 minutes. The dispersant is burnt out in the course of sintering.

(32) An abrasive article according to the disclosure may for example be produced as follows: on a backing of vulcanized fiber with a thickness of 0.8 mm, a phenolic resin dispersion is applied in an amount of 120 g/m.sup.2 as a make coat precursor. Subsequently, 600 g/m.sup.2 of the abrasive grains according to the disclosure are applied by means of electrostatic scattering. After that, the make coat precursor is cured to give a make coat. On top of the make coat and the abrasive grains, a phenolic resin dispersion is applied in an amount of 800 g/m.sup.2 as a size coat precursor, which is likewise cured.

(33) FIG. 7A shows an embodiment of an abrasive grain 10 according to the disclosure in a perspective view. FIG. 7B shows the first embodiment of the abrasive grain 10 according to the disclosure in a first side view, FIG. 7C in a second side view. FIG. 7D shows the abrasive grain 10 in a plan view.

(34) The abrasive grain 10 has three main surfaces 11, 11, 11 and three subsidiary surfaces 12, 12, 12. The subsidiary surface 12 is connected by way of a first edge 13 to a first main surface 11 and is connected by way of a second edge 13 to a second main surface 11, which does not form any edge in common with the first main surface 11.

(35) The subsidiary surface 12 includes an obtuse angle (not explicitly represented in the figures) with a first main surface 11 in the region of the first edge 13 and an obtuse angle with a second main surface 11 in the region of the second edge 13.

(36) By analogy, the subsidiary surface 12 is connected by way of a first edge to the main surface 11 and is connected by way of a second edge to the main surface 11, and the subsidiary surface 12 is connected by way of a first edge to the main surface 11 and is connected by way of a second edge to the main surface 11.

(37) The abrasive grain 10 has an abrasive grain body 14 of which the surface 15 has three planar main surfaces 11, 11 and 11 that lie on the faces of an imaginary convex polyhedron, here a tetrahedron, the likewise imaginary side edges of which are flatly truncated.

(38) The abrasive grain body 14 is theoretically made up of component bodies, on the one hand the tetrahedron with truncated edges 15, on the other hand a base 16, which has the form of a prism of which the base area corresponds to that of the tetrahedron with the truncated edges 15.

(39) It is of course also conceivable and within the scope of the disclosure that, by contrast with FIGS. 7A to 7D, the abrasive grain body only consists of a tetrahedron with truncated edges 15, but does not include a base.

(40) With mechanical scattering onto a backing, the abrasive grain 10 preferably falls on the base 16, and so the edges 13, 13 and corners 17 face away from the backing.

(41) The abrasive grains according to the disclosure may be produced for example by a method described hereinafter: firstly, a dispersion of 200 g of -Al.sub.2O.sub.3, 0.4 g of MgO, 90 g of water as a dispersion medium and 0.5 g of dispersant is prepared. The MgO functions here as a nucleating agent. The product Dolapix CE64, obtainable from Zschimmer & Schwarz, 56108 Lahnstein, Germany, may be used for example as the dispersant. The dispersion thus obtained is ground for 30 minutes at 200 revolutions per minute in a planetary ball mill, for example a planetary ball mill PM400, obtainable from Retsch GmbH, 42781 Haan, Germany. Subsequently, the ground dispersion is introduced into a silicone casting mold containing depressions in the form of the desired abrasive grains. For some embodiments of the abrasive grain, an additional molding element as described above may be used, for example a further casting mold, with which, in addition to the surface molded in the first casting mold, at least part of the remaining surface of the abrasive grain can be molded. After that, the volatile component, that is the water, is removed from the dispersion. This produces an abrasive grain precursor, which is removed from the casting mold. In a final step, the precursor is sintered as bulk material at 1550 C. for 5 minutes. The dispersant is burnt out in the course of sintering.

(42) An abrasive article according to the disclosure may for example be produced as follows: on a backing of vulcanized fiber with a thickness of 0.8 mm, a phenolic resin dispersion is applied in an amount of 120 g/m.sup.2 as a make coat precursor. Subsequently, 600 g/m.sup.2 of the abrasive grains according to the disclosure are applied by means of electrostatic scattering. After that, the make coat precursor is cured to give a make coat. On top of the make coat and the abrasive grains, a phenolic resin dispersion is applied in an amount of 800 g/m.sup.2 as a size coat precursor, which is likewise cured.

(43) FIG. 8A shows a perspective view of a first exemplary embodiment of an abrasive grain 10 according to the disclosure, FIG. 8B a plan view of the same exemplary embodiment.

(44) The abrasive grain 10 has the form of a cone in the sense of the general definition used here and has a surface 11 with two faces 12, 12, one face 13 being formed as the base area 13. The contour 14 of the base area 13 has a reflex angle 15.

(45) FIG. 9A shows a perspective view of a second exemplary embodiment of an abrasive grain 20 according to the disclosure, FIG. 9B a plan view of the same exemplary embodiment toward the base area 23.

(46) The abrasive grain 20 has a surface 21 with seven faces, one face being formed as the base area 23. The contour 24 of the base area 23 has three reflex angles 25.

(47) Conversely, the contour 24 also has three acute angles 28, which are in each case starting points for sharp cutting edges 27.

(48) The basic form of the abrasive body 20 is a pyramid 29, the base area 30 of which is formed by a star-shaped polygon 31. On account of the concave contour of the base area 23, the faces 22 however include at the edges 27 angles that are smaller than in the case of a tetrahedron. This leads to an increased cutting force of the abrasive grain.

(49) FIG. 10A shows a perspective view of a third exemplary embodiment of an abrasive grain 130 according to the disclosure. FIG. 10B shows a plan view and FIG. 10C shows a side view of the same exemplary embodiment.

(50) The contour 134 of the base area 133 comprises two segments of a circle 141, which are arranged symmetrically in relation to one another. The base area 133 corresponds to the sectional image of a double-T anchor 142, which is known as the logo of the company Robert Bosch GmbH.

(51) The base area 133 has a contour 134 with four reflex angles 135.

(52) The abrasive grain 130 has a body that is theoretically made up of a cylinder 143 in the sense of the general definition used here, the base area of which corresponds to the sectional image of a double-T anchor 142, and a saddleback roof-shaped cap 144. In fact, this abrasive grain 130 is of course likewise formed as one piece and can also be produced as one piecefor example with the aid of a casting mold with depressions that are complementary to the abrasive grain 130.

(53) The sectional image of the saddleback roof, an equilateral triangle, is known as the logo of the company sia Abrasives Industries AG.

(54) The design of the abrasive grain 130 combines functionality and recognizability.

(55) The abrasive grains according to the disclosure may be produced for example by a method described hereinafter: firstly, a dispersion of 200 g of -Al.sub.2O.sub.3, 0.4 g of MgO, 90 g of water as a dispersion medium and 0.5 g of dispersant is prepared. The MgO functions here as a nucleating agent. The product Dolapix CE64, obtainable from Zschimmer & Schwarz, 56108 Lahnstein, Germany, may be used for example as the dispersant. The dispersion thus obtained is ground for 30 minutes at 200 revolutions per minute in a planetary ball mill, for example a planetary ball mill PM400, obtainable from Retsch GmbH, 42781 Haan, Germany. Subsequently, the ground dispersion is introduced into a silicone casting mold containing depressions in the form of the desired abrasive grains. After that, the volatile component, that is the water, is removed from the dispersion. This produces an abrasive grain precursor, which is removed from the casting mold. In a final step, the precursor is sintered as bulk material at 1550 C. for 5 minutes. The dispersant is burnt out in the course of sintering.

(56) An abrasive article according to the disclosure may for example be produced as follows: on a backing of vulcanized fiber with a thickness of 0.8 mm, a phenolic resin dispersion is applied in an amount of 120 g/m.sup.2 as a make coat precursor. Subsequently, 600 g/m.sup.2 of the abrasive grains according to the disclosure are applied by means of electrostatic scattering. After that, the make coat precursor is cured to give a make coat. On top of the make coat and the abrasive grains, a phenolic resin dispersion is applied in an amount of 800 g/m.sup.2 as a size coat precursor, which is likewise cured.

(57) The disclosure includes the following concepts:

(58) Concept 1. An abrasive grain (110; 210; 310; 410), having a surface with at least a first face (120; 220; 320; 420) with a first outer contour (121; 221; 321; 421) and at least a second face (125; 225; 325; 425) with a second outer contour (126; 226; 326; 426), characterized in that

(59) a. the first outer contour (121; 221; 321; 421) does not include a corner and the second outer contour (126; 226; 326; 426) includes at least one corner (127; 227; 327; 427).

(60) Concept 2. The abrasive grain (110; 210; 310; 410) of concept 1, characterized in that the first face (120; 220; 320; 420) is substantially planar.

(61) Concept 3. The abrasive grain (110; 210; 310; 410) of either of the preceding concepts, characterized in that the first face (120; 220; 320; 420) and the second face (125; 225; 325; 425) lie opposite one another and are arranged in relation to one another at an angle that is less than 30, preferably less than 20, more preferably less than 10, and is particularly preferably 0.

(62) Concept 4. The abrasive grain (110; 210; 310; 410) of one of the preceding concepts, characterized in that the abrasive grain (110; 210; 310; 410) extends completely between the two planes that are defined by the first face (120; 220; 320; 420) and the second face (125; 225; 325; 425).

(63) Concept 5. The abrasive grain (110; 210; 310) of one of the preceding concepts, characterized in that the second face (125; 225; 325) is formed by a polygon.

(64) Concept 6. The abrasive grain (110; 210) of one of the preceding concepts, characterized in that the perpendicular projection of the second face (125; 225) onto the first face (120; 220) lies completely within the convex envelope of the first face (120; 220), in particular within the first face (120; 220).

(65) Concept 7. The abrasive grain (110; 210) of concept 6, characterized in that the abrasive grain (110; 210) tapers along a direction (R) running perpendicularly from the first face (120; 220).

(66) Concept 8. The abrasive grain (210) of one of the preceding concepts, characterized in that between the first face (220) and the second face (225), a lateral area (230) is formed, the lines of intersection of the lateral area (230) with at least one sectional plane (S) that extends perpendicularly to the first face (220) and perpendicularly to the second face (225), in particular with each such sectional plane (5), being at least partially, preferably completely, concave, in particular strictly concave.

(67) Concept 9. The abrasive grain (110; 210; 310; 410) of one of the preceding concepts, characterized in that it contains or consists of a ceramic material, in particular a polycrystalline ceramic material, preferably aluminum oxide, particularly preferably -Al.sub.2O.sub.3.

(68) Concept 10. A collective of abrasive grains (110; 210; 310; 410), characterized in that it includes at least 20% by weight, preferably at least 50% by weight, particularly preferably at least 90% by weight, of abrasive grains (110; 210; 310; 410) of one of the preceding concepts.

(69) Concept 11. A method for producing at least one abrasive grain (110; 210; 310; 410) or a collective of abrasive grains (110; 210; 310; 410) of one of the preceding concepts, characterized by the following steps: a. preparing or providing a dispersion, containing -alumina particles and/or particles that can be converted into -alumina, and also at least one volatile dispersion medium, preferably water; b. introducing the dispersion into at least one depression in a casting mold; c. optionally wiping an upper side of the casting mold in order to remove at least part of the dispersion that stands above the upper side of the casting mold; d. removing part of the volatile components of the dispersion, so as to form at least one abrasive grain precursor; e. removing the abrasive grain precursor from the casting mold; f. optionally calcining the abrasive grain precursor; g. sintering the abrasive grain precursor in order to obtain at least one abrasive grain (110; 210; 310; 410).

(70) Concept 12. A casting tool for producing at least one abrasive grain (110; 210; 310; 410) of one of concepts 1 to 9, the casting tool comprising at least one casting mold, which has at least one depression, preferably a multiplicity of depressions, with a respective surface, the surface being complementary to the form of at least part of the surface of the abrasive grain (110; 210; 310; 410).

(71) Concept 13. An abrasive article, containing a collective of abrasive grains (110; 210; 310; 410) of concept 10.

(72) Concept 14. A method for producing an abrasive article of concept 13, including a step in which a collective of abrasive grains (110; 210; 310; 410) of concept 10 is fixed on and/or in a substrate, in particular by means of a binder.

(73) Concept 15. A method for grinding a surface, in particular a painted surface, with a grinding article of concept 13.

(74) Concept 16. An abrasive grain (110; 210) with a surface that includes at least one main face (111; 211) with an outer contour (112; 212) that has at least seven corners (113; 213; 213).

(75) Concept 17. The abrasive grain (110) of concept 16, characterized in that the abrasive grain (110) is formed as a cone, in particular as a pyramid, with a base area (111) of which the outer contour (112) has at least seven corners (113).

(76) Concept 18. The abrasive grain (210) of concept 16, characterized in that the abrasive grain (210) is formed as a frustocone, in particular as a frustopyramid, with a base area (211) of which the outer contour (212) has at least seven corners (213; 213).

(77) Concept 19. The abrasive grain (110; 210) of one of the preceding concepts, characterized in that the ratio of the height (h) of the abrasive grain (110; 210) and the area diameter of the main face (111; 211) lies in the range from 0.8 to 1.4, preferably from 0.9 to 1.2, particularly preferably from 0.95 to 1.05.

(78) Concept 20. The abrasive grain (110; 210) of one of the preceding concepts, characterized in that the base area (111; 211) is a polygon with at least seven corners.

(79) Concept 21. The abrasive grain (110) of concept 20, characterized in that the polygon is convex.

(80) Concept 22. The abrasive grain (110) of concept 21, characterized in that the polygon is regular.

(81) Concept 23. The abrasive grain (110; 210) of one of the preceding concepts, characterized in that the main face (111; 211) is substantially planar.

(82) Concept 24. The abrasive grain (110; 210) of one of the preceding concepts, characterized in that it contains or consists of a ceramic material, in particular a polycrystalline ceramic material, preferably aluminum oxide, particularly preferably -Al.sub.2O.sub.3.

(83) Concept 25. A collective of abrasive grains (110; 210), characterized in that it includes at least 20% by weight, preferably at least 50% by weight, particularly preferably at least 90% by weight, of abrasive grains (110; 210) of one of the preceding concepts.

(84) Concept 26. A method for producing at least one abrasive grain (110; 210) or a collective of abrasive grains (110; 210) of one of the preceding concepts, characterized by the following steps: a. preparing or providing a dispersion, containing -alumina particles and/or particles that can be converted into -alumina, and also at least one volatile dispersion medium, preferably water; b. introducing the dispersion into at least one depression in a casting mold; c. optionally wiping an upper side of the casting mold in order to remove at least part of the dispersion that stands above the upper side of the casting mold; d. removing part of the volatile components of the dispersion, so as to form at least one abrasive grain precursor; e. removing the abrasive grain precursor from the casting mold; f. optionally calcining the abrasive grain precursor; g. sintering the abrasive grain precursor in order to obtain at least one abrasive grain (110; 210).

(85) Concept 27. A casting mold for producing at least one abrasive grain (110; 210) of one of concepts 16-24, the casting mold having at least one depression, preferably a multiplicity of depressions, with a respective surface, the surface being complementary to the form of at least part of the surface of the abrasive grain (110; 210).

(86) Concept 28. An abrasive article, containing a collective of abrasive grains (110; 210) of concept 25.

(87) Concept 29. A method for producing an abrasive article of concept 26, including a step in which a collective of abrasive grains (110; 210) of concept 25 is fixed on and/or in a substrate, in particular by means of a binder.

(88) Concept 30. A method for grinding a surface, in particular a painted surface, with an abrasive article of concept 28.

(89) Concept 31. An abrasive grain (10) with at least two main surfaces (11, 11, 11) and at least one subsidiary surface (12, 12, 12), which is connected by way of a first edge (13) to a first main surface (11) and is connected by way of a second edge (13) to a second main surface (11), which does not have any edge in common with the first main surface (11), characterized in that the subsidiary surface (12) includes an obtuse angle with a first main surface (11) in the region of the first edge (13) and an obtuse angle with a second main surface (11) in the region of the second edge (13).

(90) Concept 32. An abrasive grain (10) with a defined form, in particular an abrasive grain (10) of concept 31, characterized in that the abrasive grain (10) has an abrasive grain body (14) of which the surface (15) has at least two substantially planar main surfaces (11, 11, 11) that lie on the faces of an imaginary convex polyhedron, in particular a Platonic solid, an Archimedean solid, a Catalan solid, a prism or antiprism, on the faces of a linearly distorted Platonic solid, Archimedean solid, Catalan solid, prism or antiprism or on the faces of an imaginary combination of the solids mentioned, the abrasive grain body having at least one flatly truncated edge.

(91) Concept 33. The abrasive grain (10) of concept 31 or 32, characterized in that some of the faces (11, 11, 11) of the abrasive grain (10), in particular main surfaces, lie on the faces of an imaginary pyramid or an imaginary frustopyramid, in particular on the faces of a tetrahedron.

(92) Concept 34. The abrasive grain (10) of one of the preceding concepts, characterized in that each main surface (11, 11; 11) is connected to at least one other main surface (11, 11, 11) by way of a subsidiary surface (12, 12, 12).

(93) Concept 35. The abrasive grain (10) of one of the preceding concepts, characterized in that it contains or consists of a ceramic material, in particular a polycrystalline ceramic material, preferably aluminum oxide, particularly preferably -Al.sub.2O.sub.3.

(94) Concept 36. A collective of abrasive grains (10), characterized in that it includes at least 20% by weight, preferably at least 50% by weight, particularly preferably at least 90% by weight, of abrasive grains (10) of one of the preceding concepts.

(95) Concept 37. A method for producing at least one abrasive grain (10) or a collective of abrasive grains (10) of one of the preceding concepts, characterized by the following steps: a. preparing or providing a dispersion, containing -alumina particles and/or particles that can be converted into -alumina, and also at least one volatile dispersion medium, preferably water; b. introducing the dispersion into at least one depression in a casting mold; c. optionally wiping an upper side of the casting mold in order to remove at least part of the dispersion that stands above the upper side of the casting mold; d. removing part of the volatile components of the dispersion, so as to form at least one abrasive grain precursor; e. removing the abrasive grain precursor from the casting mold; f. optionally calcining the abrasive grain precursor; g. sintering the abrasive grain precursor in order to obtain at least one abrasive grain (10).

(96) Concept 38. A casting mold for producing at least one abrasive grain (10) of one of concepts 31 to 35, the casting mold having at least one depression, preferably a multiplicity of depressions, with a respective surface, the surface being complementary to the form of at least part of the surface of the abrasive grain (10).

(97) Concept 39. An abrasive article, containing a collective of abrasive grains (10) of concept 36.

(98) Concept 40. A method for producing an abrasive article of concept 39, including a step in which a collective of abrasive grains (10) of concept 36 is fixed on and/or in a substrate, in particular by means of a binder.

(99) Concept 41. A method for grinding a surface, in particular a painted surface, with an abrasive article of concept 39.

(100) Concept 42. An abrasive grain (10; 20; 130) with a defined form, the abrasive grain (10; 20; 130) having a body which is simply connected and has a surface (11; 21) with at least two faces, in particular at least five faces (12, 12; 22, 22), preferably at least seven faces, one face being formed as a base area (13; 23; 133), characterized in that the contour (14; 24; 134) of the base area (13; 23; 133) has at least one reflex angle (14; 25; 135).

(101) Concept 43. The abrasive grain (10; 20) of concept 42, characterized in that the abrasive grain (10; 20) or a component body of the abrasive grain (10; 20) has the form of a cone (10; 29), in particular of a pyramid (29), or a frustocone, in particular a frustopyramid, the base area (23) being formed in particular by a star-shaped base area (13; 30) of the cone (10; 29), in particular of the pyramid (29), or the frustocone, in particular the frustopyramid.

(102) Concept 44. The abrasive grain (130) of concept 42 or 43, characterized in that the abrasive grain (130) or a component body of the abrasive grain (130) has the form of a cylinder (143), in particular of a prism, or of an antiprism, the base area (23) being formed in particular by a star-shaped polygon.

(103) Concept 45. The abrasive grain (130) of concept 42 or 44, characterized in that the contour (134) of the base area (133) comprises at least one segment of a circle, preferably at least two and particularly preferably precisely two segments of a circle (141), and in particular corresponds to the sectional image of a double-T anchor (142).

(104) Concept 46. The abrasive grain (10; 20; 130) of one of the preceding concepts, characterized in that it contains or consists of a ceramic material, in particular a polycrystalline ceramic material, preferably aluminum oxide, particularly preferably -Al.sub.2O.sub.3.

(105) Concept 47. A collective of abrasive grains (10; 20; 130), characterized in that it includes at least 20% by weight, preferably at least 50% by weight, particularly preferably at least 90% by weight, of abrasive grains (10; 20; 130) of one of the preceding concepts.

(106) Concept 48. A method for producing at least one abrasive grain (10; 20; 130) or a collective of abrasive grains (10; 20; 130) of one of the preceding concepts, characterized by the following steps: a. preparing or providing a dispersion, containing -alumina particles and/or particles that can be converted into -alumina, and also at least one volatile dispersion medium, preferably water; b. introducing the dispersion into at least one depression in a casting mold; c. optionally wiping an upper side of the casting mold in order to remove at least part of the dispersion that stands above the upper side of the casting mold; d. removing part of the volatile components of the dispersion, so as to form at least one abrasive grain precursor; e. removing the abrasive grain precursor from the casting mold; f. optionally calcining the abrasive grain precursor; g. sintering the abrasive grain precursor in order to obtain at least one abrasive grain (10; 20; 130).

(107) Concept 49. A casting tool for producing at least one abrasive grain (10; 20; 130) of one of concepts 42 to 46, the casting tool comprising at least one casting mold, which has at least one depression, preferably a multiplicity of depressions, with a respective surface, the surface being complementary to the form of at least part of the surface of the abrasive grain (10; 20; 130).

(108) Concept 50. An abrasive article, containing a collective of abrasive grains (10; 20; 130) of concept 47.

(109) Concept 51. A method for producing an abrasive article of concept 50, including a step in which a collective of abrasive grains (10; 20; 130) of concept 47 is fixed on and/or in a substrate, in particular by means of a binder.

(110) Concept 52. A method for grinding a surface, in particular a painted surface, with a grinding article of concept 50.