METHOD FOR MAKING A SEAMLESS APERTURED METAL BELT

Abstract: The present invention provides a method for making a seamless apertured belt comprising the steps of: (a) providing a strip of material having two opposing ends and having a length at least equal to a finished belt length; (b) providing an aperture pattern having a length substantially equal to the finished belt length, the pattern including a plurality of two-dimensional geometrical shapes, the pattern having opposing end edges which can be tiled together; (c) removing a pre-determined portion of each end of the pattern and joining the pre-determined portions to one another along the opposing end edges to form a re-etch pattern; (d) forming apertures in the strip corresponding to the two-dimensional geometrical shapes in the pattern, the strip remaining free of apertures in regions near each end comprising fusion zones; (e) fusing the ends of the strip to one another such that the fusion zones form a common fusion zones; and (f) forming apertures in the common fusion zone corresponding to the re-etch pattern. In a preferred embodiment, the two-dimensional pattern is an amorphous two-dimensional pattern of interlocking two-dimensional geometrical shapes. The strip of material may comprise a material selected from the group consisting of metal, plastic, fabric, rubber, and combinations thereof.

Description: METHOD FOR MAKING A SEAMLESS APERTURED METAL BELT FIELD OF THE INVENTION The present invention relates to methods for forming seams in endless apertured belts of mateπal. The present invention further relates to a method of creating such seams without accompanying disruptions in the aperture pattern. BACKGROUND OF THE INVENTION The use of amoφhous patterns for the prevention of nesting in wound rolls of three dimensional sheet products has been disclosed in commonly-assigned, co-pending (allowed) U.S. Patent Application Seπal No. 08/745,339, filed November 8, 1996 m the names of McGuire, Tweddell, and Hamilton, entitled "Three-Dimensional, Nestmg-Resistant Sheet Materials and Method and Apparatus for Making Same", the disclosure of which is hereby incorporated herein by reference. In this application, a method of generating amorphous patterns with remarkably uniform properties based on a constrained Voronoi tesselation of 2-space was outlined. Using this method, amoφhous patterns consisting of an interlocking networks of irregular polygons are created using a computer. The patterns created using the method descπbed m the above mentioned application work quite well for flat, small mateπals. However, when one tries to use these patterns m the creation of production tooling (such as embossing rolls or belts), there is an obvious seam where the pattern "meets" as it is wrapped around the roll or belt due to the diverse edges of the pattern. Further, for very large rolls or belts, the computing time required to generate the pattern to cover these rolls or belts becomes overwhelming. What is needed then, is a method of creating these amoφhous patterns that allows "tiling." As utilized herein, the terms "tile", "tiling", and "tiled" refer to a pattern or pattern element compπsing a bounded region filled with a pattern design which can be joined edge-wise to other identical patterns or pattern elements having complementary but non-identical edge geometries to form a larger pattern having no visually- apparent seam. If such a "tiled" pattern were used in the creation of an embossing roll, there would be no appearance of a seam where flat the pattern "meets" as it is wrapped around the roll. Further, a very large pattern (such as the surface of a large embossing roll) could be made by "tiling" a small pattern, and there would be no appearance of a seam at the edges of the small pattern tiles. Notwithstanding the development of vaπous patterns, there remains the difficult task of forming an endless apertured belt of mateπal to serve as a forming structure for forming three- dimensional webs with patterns of protrusions corresponding to apertures m the belt. Pπor art belt forming techniques generally rely upon welding or fusing non-apertured ends of the belt mateπal together and drilling holes therethrough to approximate the appearance of the patterned apertures However, particularly with amoφhous patterns, the regular nature of dπlled holes creates a readily visibly discernible seam m the belt, and hence a corresponding interruption m the pattern of protrusions in the finished product. Forming patterned apertures all the way to the ends of the belt mateπal likewise creates a difficult challenge in terms of satisfactory fusing discontinuous end edges of the mateπal together. For example, a commonly used method of converting a thin metal stπp into a cyhndπcal belt is by butt-welding the ship into a cylinder using a high energy beam (electron beam or laser beam) as the energy source. One requirement of this welding step is that the welding be earned out across a continuous stπp of metal. Interruptions in the metal cause the welding to be inaccurate and discontinuous as holes are left by the beam at the entrance and exit of a weld line. Accordingly, it would be desirable to provide a method of creating continuous apertured belts with no readily discernible seam or interruption in amoφhous patterns of apertures. SUMMARY OF THE INVENTION The present invention provides a method for making a seamless apertured belt compπsing the steps of: (a) providing a stπp of mateπal having two opposing ends and having a length at least equal to a finished belt length; (b) providing an aperture pattern having a length substantially equal to the finished belt length, the pattern including a plurality of two-dimensional geometπcal shapes, the pattern having opposing end edges which can be tiled together; (c) removing a pre-determined portion of each end of the pattern and joining the pre-determined portions to one another along the opposing end edges to form a re-etch pattern; (d) forming apertures m the strip corresponding to the two-dimensional geometπcal shapes in the pattern, the stπp remaining free of apertures in regions near each end compπsmg fusion zones; (e) fusing the ends of the stπp to one another such that the fusion zones form a common fusion zone; and (0 forming apertures in the common fusion zone corresponding to the re-etch pattern. In a preferred embodiment, the two-dimensional pattern is an amoφhous two- dimensional pattern of interlocking two-dimensional geometπcal shapes. The stπp of mateπal may comprise a mateπal selected from the group consisting of metal, plastic, fabπc, rubber, and combinations thereof. BRIEF DESCRIPTION OF THE DRAWINGS While the specification concludes with claims which particularly point out and distinctly claim the present invention, it is believed that the present invention will be better understood from the following description of preferred embodiments, taken m conjunction with the accompanying drawings, m which like reference numerals identify identical elements and wherein: Figure 1 is a plan view of a stπp of mateπal suitable for making belt with a pattern supeπmposed thereon to illustrate vaπous dimensions relevant to the present invention; Figure 2 is an enlarged partial plan view of the stπp of Figure 1 with the end edges fused together to illustrate additional dimensions relevant to the present invention; Figure 3 is a plan view of four identical "tiles" of a representative embodiment of an amoφhous pattern useful with the present invention; Figure 4 is a plan view of the four "tiles" of Figure 3 moved into closer proximity to illustrate the matching of the pattern edges; Figure 5 is a schematic illustration of dimensions referenced in the pattern generation equations useful with the present invention; and Figure 6 is a schematic illustration of dimensions referenced m the pattern generation equations useful with the present invention. DETAILED DESCRIPTION OF THE INVENTION Belt Fabrication; Figure 1 illustrates a stπp of mateπal suitable for making belt 10 m accordance with the method of the present invention. The stπp of mateπal has a pattern P supeπmposed thereon to illustrate vaπous dimensions relevant to the present invention. The pattern P may take vaπous forms, but by way of example may compπse a photographic negative of a pattern of apertures to be photoetched into a metal belt such as descπbed m the aforementioned McGuire et al. application. The stπp has an initial length SL and an initial width SW. The stπp length is measured parallel to the longitudinal axis of the stπp, which will become the machine direction of the finished belt. Dimensions and markings are preferably, though not necessaπly, made sym-metncally with respect to a midpoint of the stπp along the longitudinal centerhne. The desired finished length of the belt (i.e., the circumference when formed into a closed loop) is designated BL, and the finished belt width m this example is equal to the stπp width. The difference in length between SL and BL will be tπmmed in preparation for joining the end edges SE, as descπbed hereafter. If final tnmming is not desired, SL and BL could be equal. The pattern has a pattern length equal to the finished belt length BL and a pattern width PW which may be equal to the stπp width SW but is preferably slightly less than SW to leave a uniform border for belt tracking puφoses. It is important that the pattern length be equal to the finished belt length BL so that there is no break or seam m the pattern when the ends of the belt are fused together It is likewise preferred that the opposing ends of the pattern have complementary shapes so that they "tile" or mate together to avoid creation of a visibly discernible seam when the ends of the pattern are joined together. A suitable technique for generating such a pattern of an amoφhous vaπety is descπbed hereafter. To manufacture a belt 10 in accordance with the present invention, a stπp of suitable belt-making mateπal is provided having dimensions SL and SW. A wide vaπety of mateπals may be suitable for belt manufacture, depending upon the desired manufactuπng operation. A sheet of 0.005 inch thick seπes 304 stainless steel has been found suitable for belt manufacture. For puφoses of an illustrative example, a belt having a finished width of 12.5 inches and finished circumference/length of 72 inches will be assumed. The stπp length SL is therefore slightly greater than 72 inches to allow for final tπmmmg (i.e., stπp edges SE will be removed), while the stπp width SW is therefore 12.5 inches. A suitable pattern P is generated and a photographic negative thereof is prepared having a pattern width PW of 12 inches and a pattern length equal to the finished belt length BL, which is 72 inches. Four measurement marks M are placed on the stπp outside of the space to be occupied by the pattern to aid in alignment of the negative duπng subsequent operations. Marks M may be of any shape, though 0.010 inch diameter circles have been found satisfactory Marks M are placed symmetπcally with respect to the longitudinal axis of the stπp and define a measurement length ML, which is less than the finished belt length BL. The difference between BL and ML should be sufficient to provide clearance for fusion equipment and operations without disturbing an etched aperture pattern corresponding to pattern P. A difference of 2 inches at each end of the stπp has been found satisfactory, such that for BL equal to 72 inches ML should equal 68 inches. The pattern P is then marked and the ends of the pattern beyond the measurement marks M are removed, joined to one another via their oπgmal marginal ends by computer or other techniques to form what is hereafter referred to as the "re- etch pattern", and saved for a subsequent step. The resulting tπmmed pattem P is then etched into the strip, making sure that the trimmed ends of the pattern remain aligned with the measurement marks M. After the pattern has been etched into the strip, the two opposing ends of the stπp are then brought into overlapping relationship until the measurement marks M are separated from one another by a distance X (see Figure 2), which represents the difference between BL and ML and which corresponds to the total length of pattern removed earlier (the "re-etch pattern"). For the present example, the distance X would be 4 inches. The strip ends SE are then simultaneously removed along a common line to ensure that their profiles are identical, and the cut ends are then fused along a line W by butt-welding via a high energy beam (electron beam or laser beam) or other suitable technique depending upon the stπp mateπal. Since the stπp mateπal is uninterrupted by apertures or other geometπes, the fusion produces a high quality, high strength seam. After fusing the stπp ends together to form the belt 10, the dimension X is re-measured to ensure that no deviations occurred duπng the fusion operation. Any minor deviations can be accommodated by "tnmming" the saved portion of the pattern, if generated via computer, or other suitable technique for blending m the pattern edges. The re-etch pattern is then supeπmposed upon the "blank" area of the belt between the measurement marks M (onented with the end edges facing the pattern edges from which they were severed) and the re-etch pattem is then photoetched into the belt. While much of the foregoing discussion has focused upon the fabncation of a belt, i.e., a flexible structure which may conform to supporting rolls and assume a vaπety of pathway profiles when run on an apparatus, it should be understood that the present invention may also find applicability to the fabncation of seamless drums when the belt is in fact secured to a supporting structure and formed into a cylinder of circular cross-section and rotatably secured for operation m an apparatus. It should also be understood that, while the preferred embodiments utilize a metal belt mateπal, such as stainless steel, the method of the present invention may also be utilized in conjunction with other matenals as well, such as polymeric mateπals, fabπc, rubber, etc. so long as suitable apertunng and fusion techniques are employed. Pattern Generation: Figures 3 and 4 show a pattern 20 created using an algoπthm descπbed in greater detail in commonly-assigned, concurrently-filed, co-pending U.S. Patent Application Seπal No [ ], in the name of Kenneth S McGuire, entitled "Method of Seaming and Expanding Amoφhous Patterns", the disclosure of which is hereby mcoφorated herein by reference. It is obvious from Figures 3 and 4 that there is no appearance of a seam at the borders of the tiles 20 when they are brought into close proximity Likewise, if opposite edges of a single pattern or tile were brought together, such as by wrapping the pattern around a belt or roll, the seam would likewise not be readily visually discernible. As utilized herein, the term "amoφhous" refers to a pattern which exhibits no readily perceptible organization, regulaπty, or oπentation of constituent elements. This definition of the term "amoφhous" is generally in accordance with the ordinary meaning of the term as evidenced by the corresponding definition in Webster's Ninth New Collegiate Dictionary. In such a pattern, the onentation and arrangement of one element with regard to a neighboπng element bear no predictable relationship to that of the next succeeding element(s) beyond. By way of contrast, the term "array" is utilized herein to refer to patterns of constituent elements which exhibit a regular, ordered grouping or arrangement. This definition of the term "array" is likewise generally m accordance with the ordinary meaning of the term as evidenced by the corresponding definition m Webster's Ninth New Collegiate Dictionary. In such an array pattern, the oπentation and arrangement of one element with regard to a neighboπng element bear a predictable relationship to that of the next succeeding element(s) beyond. The degree to which order is present in an array pattem of three-dimensional protrusions bears a direct relationship to the degree of nestability exhibited by the web. For example, in a highly-ordered array pattern of uniformly-sized and shaped hollow protrusions m a close-packed hexagonal array, each protrusion is literally a repeat of any other protrusion. Nesting of regions of such a web, if not in fact the entire web, can be achieved with a web alignment shift between supeπmposed webs or web portions of no more than one protrusion-spacing m any given direction. Lesser degrees of order may demonstrate less nesting tendency, although any degree of order is believed to provide some degree of nestability. Accordingly, an amoφhous, non-ordered pattern of protrusions would therefore exhibit the greatest possible degree of nesting-resistance. Three-dimensional sheet mateπals having a two-dimensional pattern of three-dimensional protrusions which is substantially amoφhous in nature are also believed to exhibit "isomoφhism" . As utilized herein, the terms "isomoφhism" and its root "isomoφhic" are utilized to refer to substantial uniformity m geometrical and structural properties for a given circumscπbed area wherever such an area is delineated within the pattern. This definition of the term "isomoφhic" is generally in accordance with the ordinary meaning of the term as evidenced by the corresponding definition in Webster's Ninth New Collegiate Dictionary By way of example, a prescπbed area compπsing a statistically-significant number of protrusions with regard to the entire amoφhous pattern would yield statistically substantially equivalent values for such web properties as protrusion area, number density of protrusions, total protrusion wall length, etc. Such a correlation is believed desirable with respect to physical, structural web properties when uniformity is desired across the web surface, and particularly so with regard to web properties measured normal to the plane of the web such as crush-resistance of protrusions, etc. Utilization of an amoφhous pattern of three-dimensional protrusions has other advantages as well. For example, it has been observed that three-dimensional sheet mateπals formed from a matenal which is initially lsotropic within the plane of the mateπal remain generally isotropic with respect to physical web properties in directions within the plane of the matenal. As utilized herein, the term "isotropic" is utilized to refer to web properties which are exhibited to substantially equal degrees m all directions within the plane of the matenal. This definition of the term "isotropic" is likewise generally m accordance with the ordinary meaning of the term as evidenced by the corresponding definition in Webster's Ninth New Collegiate Dictionary. Without wishing to be bound by theory, this is presently believed to be due to the non-ordered, non-onented arrangement of the three-dimensional protrusions within the amoφhous pattem. Conversely, directional web mateπals exhibiting web properties which vary by web direction will typically exhibit such properties in similar fashion following the introduction of the amoφhous pattern upon the mateπal. By way of example, such a sheet of mateπal could exhibit substantially uniform tensile properties in any direction withm the plane of the mateπal if the starting mateπal was isotropic in tensile properties. Such an amoφhous pattern in the physical sense translates into a statistically equivalent number of protrusions per unit length measure encountered by a line drawn m any given direction outwardly as a ray from any given point withm the pattern. Other statistically equivalent parameters could include number of protrusion walls, average protrusion area, average total space between protrusions, etc. Statistical equivalence m terms of structural geometπcal features with regard to directions m the plane of the web is believed to translate into statistical equivalence in terms of directional web properties. Revisiting the array concept to highlight the distinction between arrays and amoφhous patterns, since an array is by definition "ordered" in the physical sense it would exhibit some regularity in the size, shape, spacing, and/or onentation of protrusions. Accordingly, a line or ray drawn from a given point in the pattern would yield statistically different values depending upon the direction m which the ray extends for such parameters as number of protrusion walls, average protrusion area, average total space between protrusions, etc. with a corresponding vaπation in directional web properties Within the preferred amoφhous pattern, protmsions will preferably be non-uniform with regard to their size, shape, oπentation with respect to the web, and spacing between adjacent protrusion centers. Without wishing to be bound by theory, differences m center-to-center spacing of adjacent protmsions are believed to play an important role m reducing the likelihood of nesting occurπng the face-to-back nesting scenaπo. Differences in center-to-center spacing of protmsions m the pattern result in the physical sense in the spaces between protmsions being located m different spatial locations with respect to the overall web. Accordingly, the likelihood of a "match" occurnng between supenmposed portions of one or more webs m terms of protrusions/space locations is quite low Further, the likelihood of a "match" occurπng between a plurality of adjacent protrusions/spaces on supeπmposed webs or web portions is even lower due to the amoφhous nature of the protrusion pattern. In a completely amoφhous pattern, as would be presently preferred, the center-to-center spacing is random, at least within a designer-specified bounded range, such that there is an equal likelihood of the nearest neighbor to a given protrusion occurπng at any given angular position withm the plane of the web. Other physical geometπcal characteπstics of the web are also preferably random, or at least non-uniform, withm the boundary conditions of the pattem, such as the number of sides of the protmsions, angles included within each protrusion, size of the protrusions, etc. However, while it is possible and in some circumstances desirable to have the spacing between adjacent protmsions be non-uniform and/or random, the selection of polygon shapes which are capable of interlocking together makes a uniform spacing between adjacent protmsions possible. This is particularly useful for some applications of the three-dimensional, nestmg-resistant sheet mateπals of the present invention, as will be discussed hereafter. As used herein, the term "polygon" (and the adjective form "polygonal") is utilized to refer to a two-dimensional geometπcal figure with three or more sides, since a polygon with one or two sides would define a line. Accordingly, tπangles, quadπlaterals, pentagons, hexagons, etc. are included within the term "polygon", as would curvilinear shapes such as circles, ellipses, etc. which would have an infinite number of sides. When descnbmg properties of two-dimensional structures of non-uniform, particularly non-circular, shapes and non-uniform spacing, it is often useful to utilize "average" quantities and/or "equivalent" quantities. For example, in terms of charactenzmg linear distance relationships between objects in a two-dimensional pattern, where spacmgs on a center-to-center basis or on an individual spacing basis, an "average" spacing term may be useful to characteπze the resulting stmcture Other quantities that could be descπbed in terms of averages would include the proportion of surface area occupied by objects, object area, object circumference, object diameter, etc For other dimensions such as object circumference and object diameter, an approximation can be made for objects which are non-circular by constructing a hypothetical equivalent diameter as is often done m hydraulic contexts. A totally random pattern of three-dimensional hollow protmsions m a web would, in theory, never exhibit face-to-back nesting since the shape and alignment of each frustum would be unique. However, the design of such a totally random pattern would be very time-consuming and complex proposition, as would be the method of manufactunng a suitable forming stmcture. In accordance with the present invention, the non-nesting attnbutes may be obtained by designing patterns or structures where the relationship of adjacent cells or structures to one another is specified, as is the overall geometπcal character of the cells or structures, but wherein the precise size, shape, and oπentation of the cells or structures is non-uniform and non-repeating. The term "non-repeating", as utilized herein, is intended to refer to patterns or structures where an identical stmcture or shape is not present at any two locations within a defined area of interest. While there may be more than one protrusion of a given size and shape within the pattern or area of interest, the presence of other protmsions around them of non-uniform size and shape virtually eliminates the possibility of an identical grouping of protrusions being present at multiple locations. Said differently, the pattern of protmsions is non-uniform throughout the area of interest such that no grouping of protrusions within the overall pattern will be the same as any other like grouping of protmsions The beam strength of the three-dimensional sheet mateπal will prevent significant nesting of any region of matenal surrounding a given protrusion even in the event that that protrusion finds itself supeπmposed over a single matching depression since the protrusions surrounding the single protrusion of interest will differ in size, shape, and resultant center-to-center spacing from those surrounding the other protrusion/depression. Professor Davies of the University of Manchester has been studying porous cellular ceramic membranes and, more particularly, has been generating analytical models of such membranes to permit mathematical modeling to simulate real-world performance. This work was descπbed in greater detail in a publication entitled "Porous cellular ceramic membranes: a stochastic model to descnbe the stmcture of an anodic oxide membrane", authored by J Broughton and G. A. Davies, which appeared m the Journal of Membrane Science., Vol. 106 (1995), at pp. 89-101, the disclosure of which is hereby mcoφorated herein by reference. Other related mathematical modeling techniques are descπbed in greater detail in "Computing the n- dimensional Delaunay tessellation with application to Voronoi polytopes", authored by D F Watson, which appeared in The Computer Journal. Vol. 24, No. 2 (1981), at pp. 167-172, and "Statistical Models to Descπbe the Stmcture of Porous Ceramic Membranes", authored by J. F. F. Lim, X. Jia, R. Jafferah, and G. A. Davies, which appeared in Separation Science and Technology. 28(1-3) (1993) at pp. 821-854, the disclosures of both of which are hereby mcoφorated herein by reference. As part of this work, Professor Davies developed a two-dimensional polygonal pattern based upon a constrained Voronoi tessellation of 2-space. In such a method, again with reference to the above-identified publication, nucleation points are placed in random positions in a bounded (pre-determined) plane which are equal m number to the number of polygons desired in the finished pattern. A computer program "grows" each point as a circle simultaneously and radially from each nucleation point at equal rates. As growth fronts from neighboπng nucleation points meet, growth stops and a boundary line is formed. These boundary lines each form the edge of a polygon, with vertices formed by intersections of boundary lines. While this theoretical background is useful in understanding how such patterns may be generated and the properties of such patterns, there remains the issue of performing the above numencal repetitions step-wise to propagate the nucleation points outwardly throughout the desired field of interest to completion. Accordingly, to expeditiously carry out this process a computer program is preferably wπtten to perform these calculations given the appropnate boundary conditions and input parameters and deliver the desired output. The first step in generating a pattern useful in accordance with the present invention is to establish the dimensions of the desired pattem. For example, if it is desired to construct a pattern 10 inches wide and 10 inches long, for optionally forming into a dram or belt as well as a plate, then an X-Y coordinate system is established with the maximum X dimension (x ma χ) being 10 inches and the maximum Y dimension (y m aχ) being 10 inches (or vice-versa). After the coordinate system and maximum dimensions are specified, the next step is to determine the number of "nucleation points" which will become polygons desired withm the defined boundanes of the pattern. This number is an integer between 0 and infinity, and should be selected with regard to the average size and spacing of the polygons desired in the finished pattem. Larger numbers correspond to smaller polygons, and vice-versa. A useful approach to determining the appropnate number of nucleation points or polygons is to compute the number of polygons of an artificial, hypothetical, uniform size and shape that would be required to fill the desired forming structure. If this artificial pattern is an array of regular hexagons 30 (see Figure 5), with D being the edge-to-edge dimension and M being the spacing between the hexagons, then the number density of hexagons, N, is: It has been found that using this equation to calculate a nucleation density for the amoφhous patterns generated as descπbed herein will give polygons with average size closely approximating the size of the hypothetical hexagons (D). Once the nucleation density is known, the total number of nucleation points to be used in the pattern can be calculated by multiplying by the area of the pattem (80 in 2 in the case of this example). A random number generator is required for the next step. Any suitable random number generator known to those skilled in the art may be utilized, including those requinng a "seed number" or utilizing an objectively determined starting value such as chronological time. Many random number generators operate to provide a number between zero and one ( 0 - 1 ), and the discussion hereafter assumes the use of such a generator. A generator with diffeπng output may also be utilized if the result is converted to some number between zero and one or if appropnate conversion factors are utilized. A computer program is wntten to mn the random number generator the desired number of iterations to generate as many random numbers as is required to equal twice the desired number of "nucleation points" calculated above. As the numbers are generated, alternate numbers are multiplied by either the maximum X dimension or the maximum Y dimension to generate random pairs of X and Y coordinates all having X values between zero and the maximum X dimension and Y values between zero and the maximum Y dimension. These values are then stored as pairs of (X,Y) coordinates equal in number to the number of "nucleation points". It is at this point, that the invention descπbed herein differs from the pattern generation algoπthm descπbed in the previous McGuire et al. application. Assuming that it is desired to have the left and πght edge of the pattern "mesh", i.e., be capable of being "tiled" together, a border of width B is added to the nght side of the 10" square (see Figure 6). The size of the required border is dependent upon the nucleation density; the higher the nucleation density, the smaller is the required border size. A convenient method of computing the border width, B, is to refer again to the hypothetical regular hexagon array descπbed above and shown in Figure 5 In general, at least three columns of hypothetical hexagons should be mcoφorated into the border, so the border width can be calculated as. R = 3(- + H) Now, any nucleation point P with coordinates (x,y) where x<B will be copied into the border as another nucleation point, P',wιth a new coordinate (x^, * + χ,y). If the method descπbed in the preceding paragraphs is utilized to generate a resulting pattern, the pattern will be truly random. This truly random pattem will, by its nature, have a large distribution of polygon sizes and shapes which may be undesirable m some instances. In order to provide some degree of control over the degree of randomness associated with the generation of "nucleation point" locations, a control factor or "constraint" is chosen and referred to hereafter as β (beta). The constraint limits the proximity of neighbonng nucleation point locations through the introduction of an exclusion distance, E, which represents the minimum distance between any two adjacent nucleation points. The exclusion distance E is computed as follows: ■ fλπ where λ (lambda) is the number density of points (points per unit area) and β ranges from 0 to 1. To implement the control of the "degree of randomness", the first nucleation point is placed as descπbed above, β is then selected, and E is calculated from the above equation. Note that β, and thus E, will remain constant throughout the placement of nucleation points. For every subsequent nucleation point (x,y) coordinate that is generated, the distance from this point is computed to every other nucleation point that has already been placed. If this distance is less than E for any point, the newly-generated (x,y) coordinates are deleted and a new set is generated. This process is repeated until all N points have been successfully placed. Note that in the tiling algoπthm useful in accordance with the present invention, for all points (x,y) where x<B, both the oπgmal point P and the copied point P' must be checked against all other points. If either P or P' is closer to any other point than E, then both P and P' are deleted, and a new set of random (x,y) coordinates is generated. If β=0, then the exclusion distance is zero, and the pattern will be truly random. If β=l , the exclusion distance is equal to the nearest neighbor distance for a hexagonally close-packed array Selecting β between 0 and 1 allows control over the "degree of randomness" between these two extremes. In order to make the pattern a tile in which both the left and nght edges tile properly and the top and bottom edges tile properly, borders will have to be used in both the X and Y directions. Once the complete set of nucleation points are computed and stored, a Delaunay tπangulation is performed as the precursor step to generating the finished polygonal pattern. The use of a Delaunay tπangulation in this process constitutes a simpler but mathematically equivalent alternative to iteratively "growing" the polygons from the nucleation points simultaneously as circles, as descπbed in the theoretical model above. The theme behind performing the tnangulation is to generate sets of three nucleation points forming tnangles, such that a circle constmcted to pass through those three points will not include any other nucleation points withm the circle. To perform the Delaunay tnangulation, a computer program is wntten to assemble every possible combination of three nucleation points, with each nucleation point being assigned a unique number (integer) merely for identification puφoses. The radius and center point coordinates are then calculated for a circle passing through each set of three tπangularly- arranged points. The coordinate locations of each nucleation point not used to define the particular tπangle are then compared with the coordinates of the circle (radius and center point) to determine whether any of the other nucleation points fall within the circle of the three points of interest. If the constmcted circle for those three points passes the test (no other nucleation points falling withm the circle), then the three point numbers, their X and Y coordinates, the radius of the circle, and the X and Y coordinates of the circle center are stored. If the constmcted circle for those three points fails the test, no results are saved and the calculation progresses to the next set of three points. Once the Delaunay tnangulation has been completed, a Voronoi tessellation of 2-space is then performed to generate the finished polygons. To accomplish the tessellation, each nucleation point saved as being a vertex of a Delaunay tnangle forms the center of a polygon. The outline of the polygon is then constmcted by sequentially connecting the center points of the circumscnbed circles of each of the Delaunay tnangles, which include that vertex, sequentially in clockwise fashion. Saving these circle center points in a repetitive order such as clockwise enables the coordinates of the vertices of each polygon to be stored sequentially throughout the field of nucleation points. In generating the polygons, a companson is made such that any tnangle vertices at the boundanes of the pattern are omitted from the calculation since they will not define a complete polygon. If it is desired for ease of tiling multiple copies of the same pattern together to form a larger pattern, the polygons generated as a result of nucleation points copied into the computational border may be retained as part of the pattern and overlapped with identical polygons in an adjacent pattern to aid in matching polygon spacing and registry. Alternatively, as shown in Figures 3 and 4, the polygons generated as a result of nucleation points copied into the computational border may be deleted after the tnangulation and tessellation are performed such that adjacent patterns may be abutted with suitable polygon spacing. Once a finished pattern of interlocking polygonal two-dimensional shapes is generated, in accordance with the present invention such a network of interlocking shapes is utilized as the design for one web surface of a web of matenal with the pattern defining the shapes of the bases of the three-dimensional, hollow protmsions formed from the initially planar web of starting mateπal. In order to accomplish this formation of protmsions from an initially planar web of starting mateπal, a suitable forming stmcture compπsing a negative of the desired finished three- dimensional stmcture is created which the starting mateπal is caused to conform to by exerting suitable forces sufficient to permanently deform the starting mateπal. From the completed data file of polygon vertex coordinates, a physical output such as a line drawing may be made of the finished pattem of polygons. This pattern may be utilized in conventional fashion as the input pattern for a metal screen etching process to form a three- dimensional forming stmcture. If a greater spacing between the polygons is desired, a computer program can be wπtten to add one or more parallel lines to each polygon side to increase their width (and hence decrease the size of the polygons a corresponding amount). While particular embodiments of the present invention have been illustrated and descπbed, it will be obvious to those skilled in the art that vaπous changes and modifications may be made without departing from the spiπt and scope of the invention, and it is intended to cover in the appended claims all such modifications that are withm the scope of the invention.

Claims: WHAT IS CLAIMED IS: 1. A method for making a seamless apertured belt, said method comprising the steps of: (a) providing a strip of material having two opposing ends and having a length at least equal to a finished belt length; (b) providing an aperture pattern having a length substantially equal to said finished belt length, said pattern including a plurality of two-dimensional geometrical shapes, said pattern having opposing end edges which can be tiled together; (c) removing a pre-determined portion of each end of said pattern and joining said pre-determined portions to one another along said opposing end edges to form a re-etch pattern; (d) forming apertures in said strip corresponding to said two-dimensional geometrical shapes in said pattern, said strip remaining free of apertures in regions near each end comprising fusion zones; (e) fusing said ends of said strip to one another such that said fusion zones form a common fusion zone; and (f) forming apertures in said common fusion zone corresponding to said re-etch pattern. 2. The method of Claim 1, wherein said two-dimensional pattern is an amoφhous two- dimensional pattern of interlocking two-dimensional geometrical shapes. 3. The method of Claim 1, wherein said strip comprises a material selected from the group consisting of metal, plastic, fabric, rubber, and combinations thereof. 4. The method of Claim 1, wherein said strip has an initial length which is longer than said finished belt length, and wherein said ends of said strip are trimmed to attain said finished belt length prior to said step of fusing said ends together. 5. The method of Claim 4, wherein said ends of said strip are overlapped with one another and trimmed along a common line to said finished belt length. 6. The method of Claim 1, wherein stnp of mateπal is metal and said ends are fused via a welding operation. 7. The method of Claim 1, wherein said pattern compnses a photographic negative and said apertures are formed by a photoetchmg process. 8. The method of Claim 1, further including the step of marking said stnp with measurement marks a predetermined distance from each of said ends to define a fusion zone at each end pnor to removing pre-determmed portions of said pattern, said predetermined portions corresponding to said fusion zones. 9. The method of Claim 1 , wherein said method results m a finished belt having no readily discernible seam or interruption in the pattern of apertures. 10. The method of Claim 1, wherein said belt is secured to a supporting structure and formed into a cylinder of circular cross-section to form a drum.

Inventors: HAMILTON PETER WORTHINGTON, MCGUIRE KENNETH STEPHEN, HAMILTON, PETER, WORTHINGTON, MCGUIRE, KENNETH, STEPHEN
Applicants: PROCTER & GAMBLE, THE PROCTER & GAMBLE COMPANY
Application year: 2000
Main classification: B29D29
IPC codes: B26F1, B29D28, B29D29, B44B5, F16G1