Multi-abrasive tool

09895790 ยท 2018-02-20

Assignee

Inventors

Cpc classification

International classification

Abstract

A multi-abrasive tool is constituted by a support on which abrasive elements are present. Such abrasive elements are arranged in a manner so as to form one or more paths along which the successive abrasive elements have grain size sequentially increasing or decreasing by an arbitrary quantity when passing from on element to the next. Such principle gives rise to abrasive tools with different conformation both for polishing machines and for grindstones. For roto-orbital and planetary polishing machines, and optionally orbital, such support is circular and the grain sequence is circumferential, or radial, or in both directions. A first tool is constituted by contiguous (or non-contiguous) circular rings, that are differently abrasive. A second tool comprises differently abrasive elements arranged along the circular peripheral edge. A third tool comprises differently abrasive elements arranged along a spiral path of 360 starting from the edge. A fourth tool comprises two 180 spiral paths with reversed roughness sequences. A fourth tool comprises pairs of differently abrasive small cylinders fixed to a plate on concentric circumferences. A fifth tool is obtained directly on the plate of the polishing machine by means of reliefs and spacers for fixing differently abrasive sectors. For linear polishing machines, the abrasive support is a belt along which differently abrasive rectangular or oblique zones follow each other. For alternative polishing machines, the abrasive support is a plate shaped like the aforesaid belt. For tools to use with grindstones, the multi-abrasive element has a cylindrical rotation symmetry, or conical with rounded tip, or spherical symmetry.

Claims

1. An abrasive tool, comprising: a work face; and at least a first abrasive element, a second abrasive element adjacent to the first abrasive element, and a next abrasive element adjacent to the second abrasive element, the first, second, and next abrasive elements being located on the work face, wherein the first abrasive element has a first roughness value, the second abrasive element has a second roughness value different from the first roughness value, and the next abrasive element has a next roughness value different from the first and second roughness values, the first, second, and next roughness values being homogeneous across the first, second, and next abrasive elements, respectively, and the first, second, and next abrasive elements being arranged in a manner so as to form, along at least one path between the first, second, and next abrasive elements, a sequence that is ordered by increasing or decreasing roughness values, wherein the abrasive tool has a circular shape or any one regular polygonal shape, the arrangement of said abrasive tool involving a distribution of abrasive mass with respect to the center of the tool such that abrasive elements whose center of mass are aligned on opposite sides with respect to the center of the tool, at respective equal distances from the center of the tool, generate equivalent contributions to the moment of inertia of the tool, and wherein the first, second, and next abrasive elements are disposed substantially in a spiral pattern relative to the center of the tool, such that the distance of the second abrasive element from the center of the tool is different from the distance of the first abrasive element from the center of the tool, and the distance of the next abrasive element from the center of the tool is different from the distances of the first and second abrasive elements from the center of the tool, such that distance from the center of the tool increases or decreases from one abrasive element to the adjacent one, depending on whether the sequence follows a clockwise or a counter-clockwise direction.

2. The abrasive tool of claim 1, wherein the grain size of the abrasive elements varies nearly continuously in a radial direction.

3. The abrasive tool of claim 1, wherein said abrasive elements are arranged along a spiral path of about 360 starting from the peripheral edge of the tool.

4. The abrasive tool of claim 1, wherein abrasive elements belonging to groups of equal number are spaced along two or more spiral paths with equivalent angular opening, submultiple of 360, and starting from the peripheral edge of the tool.

5. The abrasive tool of claim 1, wherein the abrasive tool is obtained directly on the plate of a polishing machine by means of reliefs arranged in a circle in order to anchor the abrasive elements under pressure against the projecting peripheral edge, both directly and by means of spacers.

Description

BRIEF DESCRIPTION OF THE FIGURES

(1) Further objects and advantages of the present invention will be clearer from the detailed description that follows of an embodiment of the same and from the enclosed drawings given as a merely non-limiting example, in which:

(2) FIG. 1 is a perspective view of a typical portable polishing machine of planetary type;

(3) FIG. 2 is a bottom perspective view of the head of the planet comprised in the polishing machine of FIG. 1;

(4) FIGS. 3-8 show a subset of abrasive tools belonging to the prior art used in the planetary head shown in FIG. 2;

(5) FIGS. 9 and 10 show the two faces of a backing pad fixable to the rotary plate of a single-disc polishing machine as intermediate support for abrasive elements of various shape;

(6) FIGS. 11, 12, 13 show three flexible abrasive discs each one having an its own grain size, and the three grains with decreasing size, fixable to the backing plate of FIG. 9;

(7) FIGS. 14, 15, 16 are perspective views of abrasive tools of the prior art comprising abrasive elements mounted on the rotary plate of a single-disc polishing machine;

(8) FIGS. 17-24 show the same number of discoid tools according to the present invention;

(9) FIG. 25 shows a perspective view of a backing pad on which cylindrical abrasive tools are mounted, arranged according to the invention;

(10) FIG. 26 is a bottom view of the rotary plate of a single-disc polishing machine on which the cylindrical abrasive tools are mounted, arranged according to the invention;

(11) FIGS. 27, 28, 29 show a perspective views of other configurations of abrasive tools according to the invention that can be mounted on the plate of FIG. 26;

(12) FIG. 30 shows an elevation view of a linear polishing machine which mounts an abrasive belt made according to the present invention;

(13) FIG. 31 shows a bottom view of a section of the abrasive belt mounted on the polishing machine of FIG. 30;

(14) FIG. 32 is an elevation view of an orbital polishing machine or alternative which mounts an abrasive plate made according to the present invention;

(15) FIG. 33 shows a bottom view of the abrasive plate mounted on the polishing machine of FIG. 32;

(16) FIG. 34 is a perspective view of a bench grinding tool with cylindrical shape made according to the present invention;

(17) FIG. 35 is a perspective view of a bench grinding tool with cylindrical shape according to the present invention, including a bottom view of the rounded tip;

(18) FIG. 36 is a front view of a bench grinding tool of spherical shape obtained according to the present invention.

DETAILED DESCRIPTION OF SEVERAL PREFERRED EMBODIMENTS OF THE INVENTION

(19) In the following description, equivalent elements which appear in different figures can be indicated with the same symbols. In the illustration of one figure, it is possible to make reference to elements not expressly indicated in that figure but in preceding figures. The scale and the proportions of the various depicted elements do not necessarily correspond with the actual scale and proportions.

(20) FIG. 17 shows an abrasive tool 50 constituted by a centrally-perforated discoid support 51, made of material suitable for the type of abrasive material employed and for the technique used for fixing the abrasive powder. If the tool 50 is a diamond tool, the support 51 could be, for example: brass, aluminum, resinoid material, vegetable or artificial fiber, etc. On the support 51, the abrasive powder, starting from the external edge, forms ten concentric circular rings 52-61 of equal width, contiguous to each other, made of different size grains. The finest grain is present on the outermost circular ring 52, the largest grain is present on the innermost circular grain 61, while on the other circular rings 53-60 the grain increases size, passing from a more external to a more internal circular ring. The number of circular rings, their width, as well as the size of the increase in abrasive grain size from one ring to the next, are all parameters which can be freely selected based on the materials to be polished and on the best experimental results. The abrasive tool 50 is dynamically balanced and is indicated for polishing flat or curved surfaces not surrounded by walls.

(21) FIG. 18 shows a discoid abrasive tool 64 which differs from the tool 50 only for the fact that on the discoid support 65, the finest grain is present on the innermost circular ring 66, the largest grain is present on the outermost circular ring 75, while on the other circular rings 74-67 the grain decreases size, passing from a more external circular ring to a more internal one. The tools of the FIGS. 17 and 18 can be made with a minimum of two circular rings and a maximum which allows continuously varying the grain sizes.

(22) FIG. 19 shows a bottom view of an abrasive tool 78 constituted by a discoid support 79 perforated at the center, on whose work face four abrasive elements 80, 81, 82, 83 are present. Such elements are arranged along the external edge, and have the same geometric form, the same size, and different grain size ordered in sequence. The plan form is that of a circular ring sector 70 wide, the four sectors are mutually separated by a gap of 20 wide without abrasive. The form in the space of each abrasive element is obtained by extruding the flat form along a line orthogonal to the surface of the plate 79, in such a manner generating a thickness which is the same for all the abrasive elements. The depth in radial direction is arbitrary but equal for all the sectors, such to render the tool dynamically balanced. Starting from the abrasive element 80 with larger grain, the grain of the other abrasive elements decreases by an arbitrary quantity in passing from element to the next in counterclockwise direction. Starting instead from the abrasive element 83 with finest grain, the grain of the other abrasive elements increases by the same arbitrary quantity, passing from one element to the next in clockwise direction. The selection of clockwise or counterclockwise direction is arbitrary. The circular ring sector form is that capable of occupying most of the peripheral surface of the plate 97 with separate abrasive elements; it is not, however, binding in the obtainment of the tool and other formsfor example: circular sector, circle polygon, trapezoid, rectangle or other formcan utilize the same principle of sequential nature in the size of the various abrasive grains.

(23) FIG. 20 shows an abrasive tool 86 which differs from the tool 78 due to the fact that on the external edge of the work surface of the discoid support 87, six abrasive elements are present in circular ring sector form 88, 89, 90, 91, 92, 93 with different grain size ordered in sequence, 48 wide and mutually separated by a space of 12 without abrasive. Starting from the abrasive element 88 with largest grain, the grain of the other abrasive elements decreases by an arbitrary quantity, passing from one element to the next in counterclockwise direction. The selection of the clockwise or counterclockwise selection is arbitrary. The grain of the abrasive element 88 with largest grain belonging to the tool 86 is of lower size than the grain of the abrasive element 83 with finest grain belonging to the tool 78 of FIG. 19. Considering the two tools 78 and 86 together, they provide an array of ten abrasive elements ordered in grain size sequence. With only two multi-abrasive tools, it is therefore possible to execute the entire polishing process of Table 1 which according to the prior art would require some ten single-abrasive tools. The following Table 2 summarizes the new process.

(24) In the present description, the term multi-abrasive is referred to the plurality of abrasive grains of different size.

(25) TABLE-US-00002 TABLE 2 Multi-abrasive tools for single-disc polishing machine Corre- spondence Grain with the classifica- Step steps of Step de- Type of Type of tion, Mesh No. Table 1 scription tool Abrasive ASTM - No 1 1-2-3-4 Rough- * Tool Diamond: 16-30-46-60 shaping of two grains FIGS. plus internal 19 or 21 nickel binder; two grains plus ex- ternal brass binder 2 5-6-7-8- Refining ** Tool Diamond with 120-220-400- 9-10 of resinoid 800-1200-3500 FIGS. binder 20 or 22

(26) In addition, having considered the arrangement of the abrasive elements, all adjoining the peripheral edge of the respective tools, the supplementary polishing in the perimeter strips surrounded by walls is reduced to a minimum if not actually non-existent. The tools of FIGS. 19 and 20 can be achieved with a minimum of two circular ring sectors, wide up to 180.

(27) FIGS. 21 and 22 show, in bottom view, a variant which adds a radial component in the abrasive grain size sequence to the tools of FIGS. 19 and 20. The grain size sequence of a circular tool according to the variant will thus have two geometric components: one angular and one radial. The abrasive elements of any preselected form will therefore have to be arranged along a spiral path, limited to the first turn or to a fraction thereof. By operating in such sense, in the presence of identical abrasive elements having circular ring shape, the diameter symmetry in the distribution of abrasive mass would necessarily be altered. It will then be necessary to suitably vary the size of the abrasive elements in order to restore the dynamic balance of the circular tool during rotation. With the lack of balance, the tool would trigger oscillations tending to alternately lift and lower a tool portion from the surface to be polished with respect to the diametrically opposed portion, comprising the process efficiency. The balancing requires the cancellation of the forces acting on the rotation axis; this can be obtained by equalizing the moments of inertia m.sub.i r.sub.i.sup.2 of the single abrasive elements aligned along a diameter on opposite sides with respect to the center. Since the circular ring sector form of the abrasive elements remains in the new tool, in order to avoid overlaps the angular opening must decrease, passing from a more external abrasive element to a more internal one, this due to the progressive diminution of the curvature radius of the spiral. Thus, it will be necessary to vary the size in radial direction as well, in order to compensate both for the decrease of the angular opening, which reduces the mass, and the smaller distance from the center of the disc 97 which reduces the moment of inertia given the same mass. The abrasive elements will thus become less angularly extended and radially wider, in other words lower and broader as one moves away from the peripheral edge.

(28) With reference to the bottom view of FIG. 21, an abrasive tool 96 is observed that is constituted by a discoid support 97 perforated at the center, on whose work face four abrasive elements 98, 99, 100, 101 are present; such elements are arranged in proximity to the external edge along a spiral path slightly less than a 360 spiral that starts on the edge. The abrasive elements have the same geometric form with circular ring sector, different size in radial and angular direction, and abrasive grains of different size arranged in size sequence. The form in the space is obtained by extruding the flat form along a line orthogonal to the surface of the plate 97, generating a thickness that is the same for all the abrasive elements so that they can simultaneous lie on the surface to be polished, at least in the initial working step. The pitch of the spiral is less than the width in radial direction (depth) of the abrasive element of lower depth 101, which borders on the edge of the plate 97. In such a manner, the area lacking abrasive contiguous to the circular edge is minimized, reducing therewith the width of the perimeter strip which requires a supplementary polishing. Starting from the abrasive element with larger grain 98, the grain of the other abrasive elements decreases by an arbitrary quantity in passing from one element to the next in counterclockwise direction. Starting instead from the abrasive element with finest grain 101, the grain of the other abrasive elements increases by the same arbitrary quantity in passing from one element to the next in clockwise direction. The selection of the clockwise or counterclockwise direction is arbitrary. With regard to the dynamic balancing, one considers for example the two abrasive elements 98 and 100 and one assumes to concentrate the mass of each of these in the respective barycenter, the barycentric masses and the respective distances from the center of the plate 97 are such that the following equation is verified: m.sub.98 r.sub.98.sup.2=m.sub.100 r.sub.100.sup.2, and this is valid for all the pairs of abrasive elements, obtaining the balancing of the tool 96 therewith. The spaces lacking abrasive between one abrasive element and the adjacent element vary their width along the spiral path following the variation of the angular width of the same.

(29) The addition of the radial component in the size sequence of the abrasive grains increases the efficiency of the multi-abrasive tool by decreasing the times required for polishing and improving the quality of the polished surfaces. Maximum efficiency was experimentally detected in the sequences where the larger grain abrasives are the more internal ones. With regard to the polishing in the perimeter strip against the wall, the configuration that arranges abrasive sectors of small area along the edge, in grain size succession, prevents the formation of an edge slightly raised towards the building wall. Such edge elevation would otherwise occur since the larger grain abrasive is the more internal one; in fact it results as close as possible to the edge of the plate, taking under consideration the fact that the part that works most in the abrasive sector is the external edge, the remaining part acting more as a support and only subsequently becoming relevant.

(30) FIG. 22 shows an abrasive tool 104 which differs from the tool 96 for the fact that on the outer edge of the work face of the discoid support 105, six abrasive elements are present with circular ring sector form 106, 107, 108, 109, 110, 111 with different grain, size. Starting from the innermost abrasive element with largest grain 106, in the spiral path the grain of the other abrasive elements decreases by an arbitrary quantity, passing from one element to the next in counterclockwise direction. The selection of the clockwise or counterclockwise direction is arbitrary. The grain of the abrasive element with largest grain 106 of the tool 104 has lower size than the grain of the abrasive element with finest grain 101 of the tool 96 of FIG. 21. The arrangement and the size of the abrasive elements are such to make the tool 104 dynamically balanced. Considering the two tools 96 and 104 together, they provide a deployment of ten abrasive elements ordered in grain sequence like the tools 78 and 86 of FIGS. 19 and 20; therefore Table 2 is applicable without any modification to the pair of tools 96 and 104. The tools of FIGS. 21 and 22 can be made with a minimum of two circular ring sectors wide up to nearly 180 and sized in a manner so as to maintain the equality of the angular moment, according to the two following alternative modes: a) the sector furthest from the peripheral edge, slightly less wide than the first and slightly deeper; b) the sector furthest from the peripheral edge, slightly wider than the first and with equivalent depth.

(31) The subsequent FIGS. 23 and 24 show two abrasive tools which synthesize, and double, in a single tool the two abrasive tools 96 and 104 of the FIGS. 21 and 22, allowing the completion of the rough-shaping and the refining in Table 2 in a single step.

(32) The bottom view of FIG. 23 shows an abrasive tool 114 constituted by a discoid support 115 perforated at the center, on whose work face 20 abrasive elements are present. Such elements are subdivided into two groups of ten, each occupying one half of the work face of the discoid support 115. The abrasive elements of a first group, indicated with 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, are arranged in proximity to the external edge along a spiral path of 180, corresponding with a half spiral with start on the edge. The abrasive elements of the second group, indicated with 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, are also arranged in proximity to the external edge along another spiral path with half spiral length, which however does not continue from the preceding half spiral but restarts on the external edge from the end of the preceding half spiral.

(33) The abrasive elements have the same geometric form with circular ring section, angular openings slightly different, the same depth in radial direction, and abrasive grains with different size arranged in sequence. Starting from the first group of ten abrasive elements, the element 125 with finest grain is that in contact with the peripheral edge of the plate 115, the grain of the other abrasive elements of the sequence increases by an arbitrary quantity, passing from one element to the next in clockwise direction until the innermost element 116 with largest grain is reached. Continuing in clockwise direction, the second group of ten abrasive elements continues, in which the element 135 with largest grain is that in contact with the peripheral edge of the plate 115, the grain of the other abrasive elements of the sequence decreases by an arbitrary quantity, passing from one element to the next in clockwise direction until the innermost element 116 with finest grain is reached. It can be appreciated in the figure that by varying the direction in the arrangement of all the abrasive grains, the configuration of the tool 114 does not vary, such variation in fact equates to a rigid half-turn rotation. It can also be appreciated that whatever the preselected rotation direction, the transition between the grains of the two groups occurs continuously. For an improved polishing, it is advantageous to maintain the same grain size values of the elements which occupy the same position in the respective sequence. The observation of the figure reveals two other interesting aspects. A first aspect regards an achievement simplification in attaining the dynamic balancing. The second aspect regards an advantage in polishing the perimeter strips. With regard to the first aspect, by observing the dashed-line diameters, one can observe that the elements of the same order in the two sequences are aligned along a common diameter at the same distance from the center of the plate 115 from opposite sides. This signifies that they have the same angular opening and thus must have the same size in radial direction. This holds true for all the corresponding element pairs, which suggests maintaining the radial size of all the abrasive elements unchanged. With regard to the second aspect, one can observe that, even for maintaining the sequential size variation of the ten grains in radial direction, it is necessary to more greatly space the abrasive elements from the edge of the plate 115 with respect to the tool 104 of FIG. 22; it is also true that the lack of polishing due to the gradual absence of abrasive along each sequence, is mainly recovered during a complete turn due to the radially offset arrangement of the abrasive elements with the same grain size. Indeed, the offset arrangement allows abrasives of the same grain to complete two parallel circumferences in the perimeter strip.

(34) The bottom view of FIG. 24 shows an abrasive tool 140 constituted by a discoid support 141 perforated at the center, on whose work face twenty abrasive elements are presented, subdivided into four groups of five that are contiguous to each other. The abrasive elements of each group of five elements are arranged along a 90 spiral path corresponding to a quarter of spire, each time beginning from the external edge of the plate 141. The four groups are in turn grouped two-by-two to form two super-groups, each composed of ten abrasive elements ordered by sequential size of the grains. Each super-group occupies half of the work face of the discoid support 141. The abrasive elements of a first super-group are indicated with: 142, 143, 144, 145, 146, 147, 148, 149, 150, 151. The abrasive elements of the second super-group are indicated with: 152, 153, 154, 155, 156, 157, 158, 159, 160, 161. The abrasive elements have the same geometric shape with circular ring sector, the same angular opening, the same depth in radial direction and, as said, abrasive grains of different size that are sequentially ordered. Unlike the tool 114, the external margin of each abrasive element is placed on a circumference of radius lower or equal to that of the circumference on which the innermost edge lies of the more external adjacent abrasive element. With such arrangement, the abrasive elements are radially as well as angularly separated. Of course, the elements must have a width in radial direction that is less than that of the elements of the tool 114 in order to avoid an excessive enlargement of the peripheral zone lacking abrasive; it is for this reason that the super-group of ten was subdivided into two groups of five, each starting from the peripheral edge of the plate 141. In the first super-group of ten abrasive elements, the element 142 with finest grain is in contact with the peripheral edge of the plate 141, like the sixth element 147 with intermediate grain; starting from the element 141, the grain of the subsequent abrasive elements of the sequence of ten increases by an arbitrary quantity in passing from one element to the next in clockwise direction, until the largest grain element 151 is reached. Continuing in clockwise direction, the second super-group of ten abrasive elements continues, in which the element 152 with largest grain and the sixth element 157 with intermediate grain are in contact with the peripheral edge of the plate 115, the grain of the other abrasive elements of the sequence decreases in passing from one element to the next in clockwise direction until the finest grain element 161 is reached. The clockwise or counterclockwise direction in the arrangement of the abrasive elements is entirely arbitrary. The considerations on the balancing and the advantages obtainable with the tool 140 coincide with that stated regarding the tool 114 of FIG. 23. The smaller width in radial direction of the abrasive elements does not appear to negatively affect the operating duration of the tool 140 in a significant manner, since (as stated) the abrasive elements mainly work on the external edge.

(35) The subsequent FIGS. 25, 26, 27, 28, 29 are aimed to illustrate the abrasive tools achieved according to the dictates of the present invention, obtained by adapting in an artisanal manner the plates of the polishing machines and the abrasive components easily found on the market. Structurally, such new tools are simpler to obtain than those described in the preceding FIGS. 17 to 24, since they do not require an ad-hoc design of the abrasive elements; on the other hand, the polishing process which uses ten decreasing sizes of abrasive grains requires more than the two abrasive tools indicated in Table 2, but in any case less than the ten tools listed in Table 1. The considerations made on the balancing are also hold true for the plates of the polishing machines which mount the tools of the configurations shown in FIGS. 25 to 29, provided that said tools are anchored in a symmetric manner with respect to the center of the plate that hosts them.

(36) The perspective view of FIG. 25 shows a tool 170 comprising a circular plate 171 on which six abrasive elements 172, 173, 174, 175, 176, 177 are fixed, having the form of small cylinders, spaced 60 from each other and arranged two-by-two on concentric circles. The fixing to the plate 171 can be one of the following types: Velcro, glue, or fitting in suitable grooves or cavities. The six small cylinders form three groups of three different grain sizes; each group includes two elements of the same abrasive grain size. The abrasive small cylinders of each group are aligned along a common diameter on opposite sides with respect to the center of the plate 171 at the same distance therefrom. The distances from the center vary from one group to the other, such that it is possible to identify a first group whose two small cylinders are at greater distance from the center; a second group in which they are at intermediate distance; and a third group in which they are at the smallest distance. The difference in the distances from the center of adjacent group elements is greater than or equal to the diameter of the base of the abrasive small cylinders, which thus result radially separated. The three groups are ordered in abrasive grain size sequence. More specifically, a first group comprises the outermost small cylinders 172, 173 with finest grain, placed in proximity to the external edge of the plate 171; a second adjacent group comprises the small cylinders 174, 175 with intermediate grain size; and finally a third adjacent group comprises the cylinders 176, 177 with largest grain size. The following design parameters can be arbitrarily changed without limiting the invention: the number of abrasive small cylinder groups; the number of small cylinders per group; the distance in radial direction between the elements of adjacent groups; the increasing or decreasing grain size sequence in radial direction; the size of the initial grain and the extent of the single grain variation steps. The polishing process of Table 1 can be made quicker and more efficient by using abrasive tools of type 170. It is possible, for example, to complete the rough-shaping with two tools of type 170, equipped with only two small cylinder groups, and the subsequent refining with two tools 170 like that shown in the figure. The tool 170 can be mounted on any type of polishing machine which includes a rotation in its movement.

(37) The bottom view of FIG. 26 shows a polishing configuration 180 constructed on the circular plate 181 of a single-disc polishing machine. The plate 181 has a peripheral edge 182 projecting orthogonally beyond the surface of the face on which six trapezoidal reliefs 183, 184, 185, 186, 187, 188 are anchored. Such reliefs are arranged in a circle around a central hole in order to lock six respective abrasive sectors against the edge 182, as stated for the Cassani abrasive sectors of FIG. 15. In the bottom view, each abrasive sector has the form of a mixtilinear trapezoid or more suitably of a circular ring sector. In spatial view, each sector is composed of a non-abrasive support, e.g. magnesic, from which the actual diamond abrasive element extends upward, occupying the portion comprised between the outermost edge of the second up to over half the width in radial direction. With reference to FIG. 26, one can observe three abrasive sectors 190, 192, 194, of equivalent grain size, spaced from each other by 120, and maintained against edge 182 by the pressure exerted by the respective trapezoidal reliefs 183, 185, 187 against the magnesic supports 191, 193, 195 belonging to the respective abrasive sectors. Another three abrasive sectors 196, 199, 202 mutually spaced by 120, with equivalent grain size, greater than the grain size of the preceding abrasive elements, are interposed with the three abrasive sectors 190, 192, 194, in receded position with respect to the circular edge 182. The three receded abrasive sectors are arranged along a circumference and maintained fixed on the plate 182 by the pressure jointly exercised by the respective trapezoidal reliefs 188, 186, 184 against the supports 197, 200, 203 belonging to respective sectors, and by pairs of spacers 198, 201, 204 placed between the external edge of the abrasive sectors 196, 199, 202 and the peripheral circular edge with relief 182 of the plate 181. In conclusion, the abrasive elements project from the edge 182 by a section of equivalent height. The spacers 198, 201, 204 maintain the abrasive sectors at an arbitrary distance from the edge 182, in particular greater than or equal to the width of the adjacent abrasive sectors so to be radially in addition to angularly separated with grain succession. The polishing process of Table 1 can be made quicker and more efficient by using the configuration of the plate 180; indeed, it is possible to halve the number of steps and tools. Based on the diameter of the plate 181 and the size of the used abrasive sectors, it is possible (according to the same scheme) to mount sectors having more than two abrasive grains.

(38) The abrasive configuration of FIG. 26 can be achieved with a minimum of two abrasive sectors wider than those shown in the figure, sized so as to maintain the equality of the angular moment.

(39) FIG. 27 shows a perspective view of an abrasive tool 210 constituted by a support 211 with circular ring sector form from which two parallel rows of parallelepiped abrasive blocks project; such blocks have the same thickness and different grain size. The outermost row comprises three diamond abrasive blocks 212, 213, 214, arranged along the external edge; the innermost row comprises two diamond abrasive blocks 215, 216 arranged along the inner edge. The abrasive grain of the blocks 215, 216 has greater grain size than the grain of the blocks 212, 213, 214. The tool 210 can be considered a variant according to the invention of an abrasive sector of Cassani type of FIG. 15, or a variant according to the invention of a fraction of the diamond resinoid disc of FIG. 8.

(40) FIG. 28 shows a perspective view of an abrasive tool 218 constituted by a support 219 with circular ring sector form, on which two abrasive sectors 220 and 221 are glued, having circular ring sector form of equivalent size. The abrasive sector 220 is flush with the external edge of the support 219 astride one side, while the sector 221 is more receded with respect to the 220 and is extended on the support 219 beyond the other side and beyond the lower edge. The abrasive sector 220 is constituted by a support on which four abrasive elements 222, 223, 224, 225 are glued; such elements are pseudo-parallelepiped, with reduced thickness and different size, and are arranged on two parallel rows. The abrasive elements 222 and 223 border the external edge of their own sector while the elements 224 and 225 border the internal edge. The abrasive sector 221 is constituted by a support on which four abrasive elements 226, 227, 228, 229 are glued, arranged on two parallel rows. The latter elements are pseudo-parallelepiped, with reduced thickness, with different size and with greater grain size than that of the preceding abrasive elements. The abrasive tool 218 can be advantageously mounted on a plate of a single-disc polishing machine by utilizing the suitable reliefs. In the structure of the abrasive configuration, for example on plate 181 of FIG. 26, each abrasive sector 220 and 221 must be considered as a unique abrasive element, such that the sequential nature of the grain size has two values, both in radial and circumferential direction. The set of the two sectors comes to resemble two adjacent sectors of the configuration 180 of FIG. 26 brought close to each other to the point of being contiguous.

(41) FIG. 29 shows a perspective view of an abrasive tool 230 constituted by three contiguous abrasive supports 231, 232, 233, having a shape which resembles a long/broad circular ring sector or a mixtilinear trapezoid. The three adjacent supports gradually recede from a subsequent support. The supports 231 and 232 are glued along one side; the support 233 is rotated 90 and has the inner edge glued to the other side of the support 232. The abrasive support 231 includes two abrasive elements 234, 235 that are pseudo-parallelepiped and have reduced thickness. The abrasive support 232 includes three abrasive elements 236, 237, 238, pseudo-parallelepiped and with reduced thickness, whose grain is greater than that of the preceding abrasive elements. The abrasive support 233 includes two abrasive elements 239 and 240, pseudo-parallelepiped and with reduced thickness, whose grain is greater than that of the preceding abrasive elements. All the parallelepiped abrasive elements have a short side bordering a curvilinear edge of its own support. The element 234 borders the external edge of their own support, while the element 235 borders the internal edge. The two elements are not aligned. The elements 236 and 237 border the external edge of their own support, while the element 238 borders the internal edge and is not aligned with the two preceding elements. The elements 239 and 240 border both the edges of their own sector. The abrasive tool 230 can be advantageously mounted on the plate of a single-disc polishing machine by utilizing the suitable reliefs. Also in this case, each abrasive sector can be considered as a single abrasive element, such that the sequential nature of the grain size has three values, both in radial and circumferential direction.

(42) FIG. 30 shows a belt polishing machine 250 whose electric motors rotates an abrasive belt 254 wound on an assembly of three parallel rollers 251, 252, 253, maintained by the weight of the polishing machine against a sheet 255 to be polished. An abrasive belt section 254 is shown in FIG. 31, where one can observe that the abrasive surface is constituted by a repetitive sequence in longitudinal direction of four rectangular abrasive zones: 258, 259, 260, 261, having abrasive grain size decreasing by an arbitrary quantity in passing from one zone to the next. So as to avoid sudden discontinuities in the grain size when passing from one sequence to the next, or to the preceding, the grain size order is reversed in the adjacent sequences to the right and left, in a manner such that the zone with finest grain 261 has to its left a zone 263 with the same size as the preceding zone 260, and similarly the zone with largest grain 258 has to its right a zone 262 whose grain has the same size as the subsequent zone 259. Compatibly with the length of the belt 254, the number of abrasive zones, with a minimum of two, and their length are arbitrary parameters. The abrasive zone could also be oblique.

(43) FIG. 32 shows an orbital polishing machine 270 of manual type, or of alternative rectilinear type on which an abrasive plate 271 is mounted, such plate moved by a mechanism 272 driven by an electric motor 273. A handle 274 is gripped by the operator in order to maneuver the plate 271 on a sheet 275 to be polished. With reference to FIG. 33, it can be observed that the rectangular plate 271 comprises in longitudinal direction a sequence of four rectangular abrasive zones: 278, 279, 280, 281, having abrasive grain size decreasing by an arbitrary amount in passing from one zone to the next. Compatibly with the length of the plate 271, the number of abrasive zones, with a minimum of two, and their width are arbitrary parameters. The abrasive zones can also be oblique.

(44) The subsequent FIGS. 34, 35, 36 show the multi-grain abrasive tools particularly suitable for use in grindstones.

(45) FIG. 34 shows a cylindrical abrasive tool 290 perforated at its center, whose lateral surface supports four abrasive annular zones contiguous with each other, respectively 291, 292, 293, 294, in a grain size sequence starting from the largest grain of zone 291 adjacent to the base. The order of the sequence can be overturned and the number of the annular bands changed as required. The tool 290 is particularly suitable for use in bench grindstones.

(46) FIG. 35 shows a cylindrical abrasive tool 298 with rounded tip, equipped with a shank 299 for fixing to the flexible grinding wheel of a grindstone. The tip seen from below is shown in the figure. The cylindrical surface supports an alternation of contiguous bands of helical form having abrasive grains with three different sizes indicated with the letters F (fine), M (medium), and G (large). Each helical band is wound along the entire lateral surface. The tip supports three sequential abrasive spherical zones with grains F, M, G. One can appreciate in the figure that the transition from one grain size to the next occurs with the smallest allowed variation.

(47) FIG. 36 shows an abrasive tool 302 of spherical form, equipped with a shank 303 for fixing to the flexible grinding wheel of a grindstone. The spherical surface supports an alternation of contiguous bands, of which the part opposite the shank is a spherical cap and the other parts are spherical zones. The bands have the three grains G, M, F starting from the cap and they continue with a soft transition.

(48) On the basis of the description provided for a preferred embodiment, it is obvious that some changes can be introduced by the man skilled in the art, without departing from the scope of the invention as results from the following claims.