WO2000061357A2 - Method for making a seamless apertured belt - Google Patents
Method for making a seamless apertured belt Download PDFInfo
- Publication number
- WO2000061357A2 WO2000061357A2 PCT/US2000/009100 US0009100W WO0061357A2 WO 2000061357 A2 WO2000061357 A2 WO 2000061357A2 US 0009100 W US0009100 W US 0009100W WO 0061357 A2 WO0061357 A2 WO 0061357A2
- Authority
- WO
- WIPO (PCT)
- Prior art keywords
- pattern
- strip
- dimensional
- length
- belt
- Prior art date
Links
- 238000000034 method Methods 0.000 title claims abstract description 44
- 230000004927 fusion Effects 0.000 claims abstract description 18
- 239000002184 metal Substances 0.000 claims abstract description 10
- 239000000463 material Substances 0.000 claims abstract description 6
- 238000005304 joining Methods 0.000 claims abstract description 4
- 239000005060 rubber Substances 0.000 claims abstract description 4
- 239000004033 plastic Substances 0.000 claims abstract description 3
- 239000004744 fabric Substances 0.000 claims abstract 2
- 238000005259 measurement Methods 0.000 claims description 7
- 238000003466 welding Methods 0.000 claims description 7
- 230000008569 process Effects 0.000 claims description 5
- 230000006911 nucleation Effects 0.000 description 35
- 238000010899 nucleation Methods 0.000 description 35
- 239000012528 membrane Substances 0.000 description 6
- 238000004590 computer program Methods 0.000 description 5
- 238000004519 manufacturing process Methods 0.000 description 5
- 230000007717 exclusion Effects 0.000 description 4
- 238000004364 calculation method Methods 0.000 description 3
- 239000000919 ceramic Substances 0.000 description 3
- 238000013461 design Methods 0.000 description 3
- 238000004049 embossing Methods 0.000 description 3
- 230000001413 cellular effect Effects 0.000 description 2
- 230000000295 complement effect Effects 0.000 description 2
- 239000000470 constituent Substances 0.000 description 2
- 238000010894 electron beam technology Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000012360 testing method Methods 0.000 description 2
- 239000010963 304 stainless steel Substances 0.000 description 1
- 229910000589 SAE 304 stainless steel Inorganic materials 0.000 description 1
- 239000010407 anodic oxide Substances 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000003491 array Methods 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 238000005553 drilling Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 238000005530 etching Methods 0.000 description 1
- 230000001747 exhibiting effect Effects 0.000 description 1
- -1 fabπc Substances 0.000 description 1
- 230000001788 irregular Effects 0.000 description 1
- 238000002156 mixing Methods 0.000 description 1
- 230000008520 organization Effects 0.000 description 1
- 230000037361 pathway Effects 0.000 description 1
- 239000002243 precursor Substances 0.000 description 1
- 238000002360 preparation method Methods 0.000 description 1
- 230000002265 prevention Effects 0.000 description 1
- 230000003252 repetitive effect Effects 0.000 description 1
- 230000000717 retained effect Effects 0.000 description 1
- 238000004826 seaming Methods 0.000 description 1
- 238000000926 separation method Methods 0.000 description 1
- 229910001220 stainless steel Inorganic materials 0.000 description 1
- 239000010935 stainless steel Substances 0.000 description 1
- 238000013179 statistical model Methods 0.000 description 1
Classifications
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- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29D—PRODUCING PARTICULAR ARTICLES FROM PLASTICS OR FROM SUBSTANCES IN A PLASTIC STATE
- B29D29/00—Producing belts or bands
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B44—DECORATIVE ARTS
- B44B—MACHINES, APPARATUS OR TOOLS FOR ARTISTIC WORK, e.g. FOR SCULPTURING, GUILLOCHING, CARVING, BRANDING, INLAYING
- B44B5/00—Machines or apparatus for embossing decorations or marks, e.g. embossing coins
- B44B5/02—Dies; Accessories
- B44B5/026—Dies
-
- B—PERFORMING OPERATIONS; TRANSPORTING
- B29—WORKING OF PLASTICS; WORKING OF SUBSTANCES IN A PLASTIC STATE IN GENERAL
- B29L—INDEXING SCHEME ASSOCIATED WITH SUBCLASS B29C, RELATING TO PARTICULAR ARTICLES
- B29L2031/00—Other particular articles
- B29L2031/709—Articles shaped in a closed loop, e.g. conveyor belts
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
- Y10T29/00—Metal working
- Y10T29/49—Method of mechanical manufacture
- Y10T29/49826—Assembling or joining
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y10—TECHNICAL SUBJECTS COVERED BY FORMER USPC
- Y10T—TECHNICAL SUBJECTS COVERED BY FORMER US CLASSIFICATION
- Y10T29/00—Metal working
- Y10T29/49—Method of mechanical manufacture
- Y10T29/49826—Assembling or joining
- Y10T29/49861—Sizing mating parts during final positional association
Definitions
- the present invention relates to methods for forming seams in endless apertured belts of mate ⁇ al.
- the present invention further relates to a method of creating such seams without accompanying disruptions in the aperture pattern.
- amo ⁇ hous 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 Se ⁇ al 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.
- a method of generating amorphous patterns with remarkably uniform properties based on a constrained Voronoi tesselation of 2-space was outlined. Using this method, amo ⁇ hous patterns consisting of an interlocking networks of irregular polygons are created using a computer.
- the terms "tile”, “tiling”, and “tiled” refer to a pattern or pattern element comp ⁇ sing 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.
- va ⁇ ous patterns there remains the difficult task of forming an endless apertured belt of mate ⁇ al to serve as a forming structure for forming three- dimensional webs with patterns of protrusions corresponding to apertures m the belt.
- P ⁇ or art belt forming techniques generally rely upon welding or fusing non-apertured ends of the belt mate ⁇ al together and drilling holes therethrough to approximate the appearance of the patterned apertures
- the regular nature of d ⁇ lled 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 mate ⁇ al likewise creates a difficult challenge in terms of satisfactory fusing discontinuous end edges of the mate ⁇ al together.
- a commonly used method of converting a thin metal st ⁇ p into a cyhnd ⁇ cal belt is by butt-welding the ship into a cylinder using a high energy beam (electron beam or laser beam) as the energy source.
- a high energy beam electron beam or laser beam
- One requirement of this welding step is that the welding be earned out across a continuous st ⁇ p 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.
- the present invention provides a method for making a seamless apertured belt comp ⁇ sing the steps of: (a) providing a st ⁇ p of mate ⁇ al 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 geomet ⁇ cal 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 geomet ⁇ cal shapes in the pattern, the st ⁇ p remaining free of apertures in regions near each end comp ⁇ smg fusion zones; (e) fusing the ends of the st ⁇ p 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
- the two-dimensional pattern is an amo ⁇ hous two- dimensional pattern of interlocking two-dimensional geomet ⁇ cal shapes.
- the st ⁇ p of mate ⁇ al may comprise a mate ⁇ al selected from the group consisting of metal, plastic, fab ⁇ c, rubber, and combinations thereof.
- Figure 1 is a plan view of a st ⁇ p of mate ⁇ al suitable for making belt with a pattern supe ⁇ mposed thereon to illustrate va ⁇ ous dimensions relevant to the present invention
- Figure 2 is an enlarged partial plan view of the st ⁇ p 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 amo ⁇ hous 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.
- Figure 6 is a schematic illustration of dimensions referenced m the pattern generation equations useful with the present invention.
- Figure 1 illustrates a st ⁇ p of mate ⁇ al suitable for making belt 10 m accordance with the method of the present invention.
- the st ⁇ p of mate ⁇ al has a pattern P supe ⁇ mposed thereon to illustrate va ⁇ ous dimensions relevant to the present invention.
- the pattern P may take va ⁇ ous forms, but by way of example may comp ⁇ se a photographic negative of a pattern of apertures to be photoetched into a metal belt such as desc ⁇ bed m the aforementioned McGuire et al. application.
- the st ⁇ p has an initial length SL and an initial width SW.
- the st ⁇ p length is measured parallel to the longitudinal axis of the st ⁇ p, which will become the machine direction of the finished belt. Dimensions and markings are preferably, though not necessa ⁇ ly, made sym-metncally with respect to a midpoint of the st ⁇ p along the longitudinal centerhne.
- the desired finished length of the belt i.e., the circumference when formed into a closed loop
- BL the finished belt width m this example is equal to the st ⁇ p width.
- the difference in length between SL and BL will be t ⁇ mmed in preparation for joining the end edges SE, as desc ⁇ bed 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 st ⁇ p width SW but is preferably slightly less than SW to leave a uniform border for belt tracking pu ⁇ oses. 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 amo ⁇ hous va ⁇ ety is desc ⁇ bed hereafter.
- a st ⁇ p of suitable belt-making mate ⁇ al having dimensions SL and SW.
- a wide va ⁇ ety of mate ⁇ als may be suitable for belt manufacture, depending upon the desired manufactu ⁇ ng operation.
- a sheet of 0.005 inch thick se ⁇ es 304 stainless steel has been found suitable for belt manufacture.
- a belt having a finished width of 12.5 inches and finished circumference/length of 72 inches will be assumed.
- the st ⁇ p length SL is therefore slightly greater than 72 inches to allow for final t ⁇ mmmg (i.e., st ⁇ p edges SE will be removed), while the st ⁇ p 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 st ⁇ p outside of the space to be occupied by the pattern to aid in alignment of the negative du ⁇ ng subsequent operations. Marks M may be of any shape, though 0.010 inch diameter circles have been found satisfactory Marks M are placed symmet ⁇ cally with respect to the longitudinal axis of the st ⁇ p 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.
- the resulting t ⁇ mmed pattem P is then etched into the strip, making sure that the trimmed ends of the pattern remain aligned with the measurement marks M.
- the two opposing ends of the st ⁇ p 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").
- 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 st ⁇ p mate ⁇ al. Since the st ⁇ p mate ⁇ al is uninterrupted by apertures or other geomet ⁇ es, the fusion produces a high quality, high strength seam.
- a high energy beam electron beam or laser beam
- the dimension X is re-measured to ensure that no deviations occurred du ⁇ ng 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 supe ⁇ mposed 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.
- Figures 3 and 4 show a pattern 20 created using an algo ⁇ thm desc ⁇ bed in greater detail in commonly-assigned, concurrently-filed, co-pending U.S. Patent Application Se ⁇ al No [ ], in the name of Kenneth S McGuire, entitled “Method of Seaming and Expanding Amo ⁇ hous Patterns", the disclosure of which is hereby mco ⁇ orated 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.
- amo ⁇ hous refers to a pattern which exhibits no readily perceptible organization, regula ⁇ ty, or o ⁇ entation of constituent elements. This definition of the term “amo ⁇ hous” 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 neighbo ⁇ ng element bear no predictable relationship to that of the next succeeding element(s) beyond.
- 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.
- the o ⁇ entation and arrangement of one element with regard to a neighbo ⁇ ng element bear a predictable relationship to that of the next succeeding element(s) beyond.
- 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 supe ⁇ mposed 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 amo ⁇ hous, non-ordered pattern of protrusions would therefore exhibit the greatest possible degree of nesting-resistance.
- Three-dimensional sheet mate ⁇ als having a two-dimensional pattern of three-dimensional protrusions which is substantially amo ⁇ hous in nature are also believed to exhibit "isomo ⁇ hism” .
- the terms “isomo ⁇ hism” and its root “isomo ⁇ hic” are utilized to refer to substantial uniformity m geometrical and structural properties for a given circumsc ⁇ bed area wherever such an area is delineated within the pattern.
- Utilization of an amo ⁇ hous pattern of three-dimensional protrusions has other advantages as well. For example, it has been observed that three-dimensional sheet mate ⁇ als formed from a matenal which is initially lsotropic within the plane of the mate ⁇ al 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.
- Such an amo ⁇ hous 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 geomet ⁇ cal features with regard to directions m the plane of the web is believed to translate into statistical equivalence in terms of directional web properties.
- protmsions will preferably be non-uniform with regard to their size, shape, o ⁇ entation with respect to the web, and spacing between adjacent protrusion centers.
- differences m center-to-center spacing of adjacent protmsions are believed to play an important role m reducing the likelihood of nesting occur ⁇ ng the face-to-back nesting strig ⁇ o.
- 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.
- 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” occur ⁇ ng between a plurality of adjacent protrusions/spaces on supe ⁇ mposed webs or web portions is even lower due to the amo ⁇ hous nature of the protrusion pattern.
- 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 occur ⁇ ng at any given angular position withm the plane of the web.
- Other physical geomet ⁇ cal characte ⁇ stics 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.
- polygon (and the adjective form "polygonal") is utilized to refer to a two-dimensional geomet ⁇ cal figure with three or more sides, since a polygon with one or two sides would define a line. Accordingly, t ⁇ angles, quad ⁇ laterals, pentagons, hexagons, etc.
- an "average" spacing term may be useful to characte ⁇ ze the resulting stmcture
- Other quantities that could be desc ⁇ bed in terms of averages would include the proportion of surface area occupied by objects, object area, object circumference, object diameter, etc
- 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.
- 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 geomet ⁇ cal character of the cells or structures, but wherein the precise size, shape, and o ⁇ entation of the cells or structures is non-uniform and non-repeating.
- non-repeating 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.
- 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 mate ⁇ al will prevent significant nesting of any region of matenal surrounding a given protrusion even in the event that that protrusion finds itself supe ⁇ mposed 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.
- a computer program is preferably w ⁇ tten 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.
- an X-Y coordinate system is established with the maximum X dimension (x ma ⁇ ) being 10 inches and the maximum Y dimension (y m a ⁇ ) being 10 inches (or vice-versa).
- 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:
- nucleation density for the amo ⁇ hous patterns generated as desc ⁇ bed herein will give polygons with average size closely approximating the size of the hypothetical hexagons (D).
- 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 diffe ⁇ ng 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.
- 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".
- the invention desc ⁇ bed herein differs from the pattern generation algo ⁇ thm desc ⁇ bed in the previous McGuire et al. application.
- 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 desc ⁇ bed above and shown in Figure 5 In general, at least three columns of hypothetical hexagons should be mco ⁇ orated into the border, so the border width can be calculated as.
- R 3(- + H)
- any nucleation point P with coordinates (x,y) where x ⁇ B will be copied into the border as another nucleation point, P',w ⁇ th a new coordinate (x ⁇ , * + ⁇ ,y).
- ⁇ (lambda) is the number density of points (points per unit area) and ⁇ ranges from 0 to 1.
- ⁇ is the number density of points (points per unit area) and ⁇ ranges from 0 to 1.
- the first nucleation point is placed as desc ⁇ bed above, ⁇ is then selected, and E is calculated from the above equation. Note that ⁇ , and thus E, will remain constant throughout the placement of nucleation points.
- 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.
- a Delaunay t ⁇ angulation is performed as the precursor step to generating the finished polygonal pattern.
- the use of a Delaunay t ⁇ angulation in this process constitutes a simpler but mathematically equivalent alternative to iteratively "growing" the polygons from the nucleation points simultaneously as circles, as desc ⁇ bed 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.
- 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 pu ⁇ oses.
- the radius and center point coordinates are then calculated for a circle passing through each set of three t ⁇ angularly- arranged points.
- the coordinate locations of each nucleation point not used to define the particular t ⁇ angle 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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 mate ⁇ al.
- a suitable forming stmcture comp ⁇ sing a negative of the desired finished three- dimensional stmcture is created which the starting mate ⁇ al is caused to conform to by exerting suitable forces sufficient to permanently deform the starting mate ⁇ al.
- 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 w ⁇ tten 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).
Abstract
Description
Claims
Priority Applications (10)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
NZ514494A NZ514494A (en) | 1999-04-09 | 2000-04-06 | Method for making a seamless apertured metal belt |
BR0009661-0A BR0009661A (en) | 1999-04-09 | 2000-04-06 | Features a process for manufacturing a belt with holes and seamless |
EP00921752A EP1169172B1 (en) | 1999-04-09 | 2000-04-06 | Method for making a seamless apertured belt |
AU42028/00A AU762524B2 (en) | 1999-04-09 | 2000-04-06 | Method for making a seamless apertured metal belt |
MXPA01010205A MXPA01010205A (en) | 1999-04-09 | 2000-04-06 | Method for making a seamless apertured metal belt. |
CA002367576A CA2367576C (en) | 1999-04-09 | 2000-04-06 | Method for making a seamless apertured metal belt |
DE60013419T DE60013419T2 (en) | 1999-04-09 | 2000-04-06 | METHOD FOR HOLDING A SEAMLESS BELT WITH OPENINGS |
KR10-2001-7012801A KR100478799B1 (en) | 1999-04-09 | 2000-04-06 | Method for making a seamless apertured metal belt |
AT00921752T ATE275033T1 (en) | 1999-04-09 | 2000-04-06 | METHOD FOR PRODUCING A SEAMLESS BAND WITH OPENINGS |
JP2000610666A JP4583606B2 (en) | 1999-04-09 | 2000-04-06 | Manufacturing method of seamless opening metal belt |
Applications Claiming Priority (2)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
US09/289,223 | 1999-04-09 | ||
US09/289,223 US6148496A (en) | 1999-04-09 | 1999-04-09 | Method for making a seamless apertured metal belt |
Publications (2)
Publication Number | Publication Date |
---|---|
WO2000061357A2 true WO2000061357A2 (en) | 2000-10-19 |
WO2000061357A3 WO2000061357A3 (en) | 2001-01-11 |
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PCT/US2000/009100 WO2000061357A2 (en) | 1999-04-09 | 2000-04-06 | Method for making a seamless apertured belt |
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EP (1) | EP1169172B1 (en) |
JP (1) | JP4583606B2 (en) |
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CN (1) | CN1123438C (en) |
AT (1) | ATE275033T1 (en) |
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CA (1) | CA2367576C (en) |
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ES (1) | ES2223501T3 (en) |
MX (1) | MXPA01010205A (en) |
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WO (1) | WO2000061357A2 (en) |
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WO2018078012A1 (en) * | 2016-10-28 | 2018-05-03 | Ardagh Mp Group Netherlands B.V. | Method for manufacturing an endless belt, of the flat type made of metal material |
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- 2000-04-06 DE DE60013419T patent/DE60013419T2/en not_active Expired - Lifetime
- 2000-04-06 AT AT00921752T patent/ATE275033T1/en not_active IP Right Cessation
- 2000-04-06 JP JP2000610666A patent/JP4583606B2/en not_active Expired - Fee Related
- 2000-04-06 CA CA002367576A patent/CA2367576C/en not_active Expired - Lifetime
- 2000-04-06 EP EP00921752A patent/EP1169172B1/en not_active Expired - Lifetime
- 2000-04-06 AU AU42028/00A patent/AU762524B2/en not_active Ceased
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Also Published As
Publication number | Publication date |
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CN1123438C (en) | 2003-10-08 |
NZ514494A (en) | 2003-03-28 |
BR0009661A (en) | 2002-01-15 |
DE60013419D1 (en) | 2004-10-07 |
AU4202800A (en) | 2000-11-14 |
MXPA01010205A (en) | 2002-03-27 |
DE60013419T2 (en) | 2005-09-08 |
KR20020004994A (en) | 2002-01-16 |
KR100478799B1 (en) | 2005-03-24 |
CN1354712A (en) | 2002-06-19 |
ES2223501T3 (en) | 2005-03-01 |
AU762524B2 (en) | 2003-06-26 |
CA2367576C (en) | 2006-01-24 |
US6148496A (en) | 2000-11-21 |
JP2002540996A (en) | 2002-12-03 |
TW523462B (en) | 2003-03-11 |
WO2000061357A3 (en) | 2001-01-11 |
CA2367576A1 (en) | 2000-10-19 |
EP1169172B1 (en) | 2004-09-01 |
ATE275033T1 (en) | 2004-09-15 |
JP4583606B2 (en) | 2010-11-17 |
EP1169172A2 (en) | 2002-01-09 |
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