|Publication number||USRE40455 E1|
|Application number||US 11/515,509|
|Publication date||Aug 12, 2008|
|Filing date||Aug 31, 2006|
|Priority date||May 30, 1996|
|Also published as||CA2256315A1, CA2256315C, CN1226853A, EP0951383A1, EP0951383A4, EP2246182A2, EP2246182A3, US6015214, US6767102, USRE40700, WO1997045255A1|
|Publication number||11515509, 515509, US RE40455 E1, US RE40455E1, US-E1-RE40455, USRE40455 E1, USRE40455E1|
|Inventors||Sidney A. Heenan, Liviu A. Coman, Dennis I. Couzin|
|Original Assignee||Avery Dennison Corporation|
|Export Citation||BiBTeX, EndNote, RefMan|
|Patent Citations (84), Non-Patent Citations (2), Referenced by (4), Classifications (26), Legal Events (3)|
|External Links: USPTO, USPTO Assignment, Espacenet|
This is a divisional of copending application(s) U.S. Ser. No. 08/655,595 filed on May 30, 1996 now U.S. Pat. No. 6,015,214.
This invention relates to tools for making microcube retroreflective elements for use in manufacturing retroreflective articles, and in particular, retroreflective sheeting; to articles and sheeting having microcubes; and to methods of making such tools and articles; This invention further relates to tools, articles, and methods wherein said microcubes may have boundary shapes other than triangular.
Microcube retroreflective sheeting is now well-known as a material for making reflective highway signs, safety reflectors, reflective vests and other garments, and other safety-related items. Such retroreflective sheeting typically comprises a layer of a clear resin, such as for example, an acrylic or polycarbonate or vinyl, having a smooth front surface and a plurality of retroreflective microcube elements on the reverse surface. Light incident on the smooth front surface passes through the sheeting, impinges on the retroreflective elements, and is reflected back out through the smooth front surface in a direction nominally 180° to the direction of incidence.
The reverse surface of the resin layer bearing the microcubes may be further provided with additional layers, such as metallization, which enhances the entrance angularity of the sheeting, or hydrophobic silica, adhesives, release liners, or other layers which otherwise contribute to the functionality of the sheeting.
Cube corner retroreflectors have been used on automobiles and for highway markings since the early 1900's. These prior art devices were based on macrocube corner elements made by the pin making art. From the use of macrocubes, a number of optical principles involving cube corner technology have been published, and some have been patented. Generally, these principles have involved changes in the size, shape or tilt of the cube faces, or of the included dihedral angles between faces, to achieve desired retroreflector performance. These known optical principles have included:
While these retroreflective optic design principles are well-known in the cube corner art, in more recent years some have attempted to patent them again in microcube sheeting technology, apparently because those persons either did not know what was done in prior macrocube technology, or chose either to ignore or to limit the applicability of the prior art teachings when applied to microcube retroreflective sheeting.
Prior to applicants' present invention, virtually all microcube sheeting has been limited to the use of microcubes made by ruling along parallel planes. This limitation is a result of the microcube dimensions being smaller than the dimensions obtainable by the cutting, polishing and lapping techniques used in the pin making art. The need to use traditional ruling techniques has inhibited the application of known optical principles to microcubes, and has, with one exception, further generally limited percent active aperture to less than 100%.
The present invention is a major advance in microcube sheeting technology. It enhances both the applicability to microcubes of prior known retroreflective optic principles and the manufacturability of microcubes of different base configurations. Before detailing these advances, further background information is provided.
Retroreflective sheeting and methods of forming the microcube retroreflective elements in such sheeting are disclosed, for example in U.S. Pricone et al. Pat. No. 4,486,363, assigned to the common assignee herein, and incorporated herein by reference in its entirety. As disclosed in such patent, the resinous layer of the sheeting may be on the order of 0.01 inch (0.25 mm) thick or less, and the retroreflective elements formed in the reverse face of the resinous layer comprise triangular microcubes such as are known in the manufacture of flexible retroreflective sheeting.
To manufacture such microcube sheeting, generally a master plate of retroreflective triangular microcubes is made by ruling a pattern of retroreflective cube corners into a planar surface of the plate. This is taught generally by Stamm U.S. Pat. No. 3,712,706; is mentioned in U.S. Pat. No. 5,122,902; and is also taught in detail in U.S. Pat. No. 4,478,769, assigned to the applicants' assignee and incorporated herein by reference in its entirety.
As shown in
The ruled master may then be used to make a series of duplicates, such as by electroforming, and the duplicates are assembled together to form a single “mother” tool. The assembled “mother” tool is used to electroform molds, which are then assembled and ultimately used to form a tool capable of providing the microcube retroreflective elements on the sheeting, such as by embossing, casting, or other means known in the art. A continuous embossing method is disclosed in the aforementioned U.S. Pat. No. 4,478,769; a casting technique for forming microcubes is disclosed, for example, in Rowland U.S. Pat. Nos. 3,684,348 and 3,689,346.
As will be described hereafter, triangular microcubes having bases other than equilateral triangles have been used in an effort to achieve enhanced entrance angularity by use of the well known optical principles taught in macrocube technology. Thus, as taught in applicants' assignee's commonly assigned patent Montalbano U.S. Pat. No. 4,633,567, variations of the triangular microcube may be achieved by changing the tool ruling angles (thus, canting the cube axis), thereby adopting and applying some of the prior optical principles to microcube technology. For example, it is possible to achieve arrays having different entrance angularity or orientation angularity (c.f. Rowland U.S. Pat. No. 3,684,348, col. 10, 11, 1-18 and Montalbano U.S. Pat. No. 4,633,567, col. 6, 11, 4-36).
As previously noted, U.S. Pat. No. 3,833,285, discloses that the observation angularity of cube corner retroreflection can be increased in one plane by increasing (or decreasing) one of the three dihedral angles of the cubes; U.S. Pat. Nos. 3,873,184 and 3,923,378, disclose an array of retroreflective elements wherein the cube axes of neighboring cubes are inclined with respect to each other and oppositely oriented such that the entrance angularity is increased; U.S. Pat. No. 3,541,606 discloses that if one cube face of each of the oppositely oriented cubes is “more parallel” to the front surface, entrance angularity is increased in two planes at right angles to each other. Each of the foregoing patents is incorporated herein by reference.
The identical optical principles used in macrocubes for enhancing retroreflectivity have also been applied to the triangular microsized cubes such as are used in retroreflective sheeting. Thus, U.S. Pat. No. 4,588,258 to Hoopman discloses a retroreflective article with purportedly novel wide angularity wherein an array of triangular microcube elements comprises sets of matched pairs with the cube axes of the cubes in each pair being tilted toward one another; but this simply duplicates the face-more-parallel structure disclosed, for example, in applicants' assignee's prior U.S. Pat. No. 3,541,606, U.S. Pat. No. 3,923,378 or U.S. Pat. No. 3,873,184 patents. Moreover, the Hoopman matched pairs of triangles are inherent when ruling triangles, which at the time of Hoopman's application was the only technique used for manufacturing microcubes.
Similarly, U.S. Pat. No. 4,775,219 to Appeldorn, et al., discloses a retroreflective article of modified observation angularity having an array of microcube retroreflective elements formed by three intersecting sets of parallel V-shaped grooves, wherein at least one of the sets includes, in a repeating pattern, at least two groove side angles that differ from one another. The Appeldorn article merely achieves, in an obvious manner, the identical principle taught years ago in applicants' commonly assigned U.S. Pat. No. 3,833,285.
However, all triangular cubes, while providing adequate retroreflectance, suffer the known disadvantage that inherently by their geometry no more than 66% of their area can be retroreflective for any particular incidence angle. In an attempt to overcome this deficiency of triangular cubes, the Minnesota Mining and Manufacturing Company, in a series of published PCT applications (WO 95/11463; WO 95/11465; WO 95/11467; WO 95/11470), has disclosed arrays of microcubes including some non-triangular cubes, and techniques for ruling such arrays. However, the disclosed arrays have cubes of greatly different heights (which may pose manufacturing problems) and greatly varying aperture size (affecting diffraction and impacting on retroreflectivity). At best, the disclosed arrays provide calculated percent effective aperture (at 0° incidence) of 91%, which appears to fall to about 87% when manufacturing draft is considered (see, e.g., WO 95/11470, FIG. 12). If the cubes are canted by the disclosed ruling technique, the efficiency drops even further. The very nature of forming these cubes by intersecting ruled grooves parallel to a single plane inherently limits the results which can be obtained.
The advantages of the techniques and articles of the present invention, as compared to those obtained by the earlier, triangular microcubes or even by the more recent ruled mixtures of triangular and non-triangular cubes, are shown in the drawings of this application and are more specifically described hereinafter.
Unlike triangular cube corners, hexagonal and rectangular cube corners have the advantage that 100% of their area can be retroreflective even at large incidence angles. Also unlike triangular microcubes, however, hexagonal and rectangular microcubes are not defined by continuous straight lines that extend along a planar surface, and therefore cannot be ruled with intersecting sets of parallel lines all parallel to a common plane. Thus, with the sole exception of the rectangular cubes disclosed in U.S. Pat. Nos. 4,349,598 and 4,895,428 (wherein one of the active cube faces is perpendicular to the reflector front surface) it is not possible to cut or rule a master containing all hexagonal or all rectangular microcubes by ruling straight lines in a single flat surface. Moreover, because of the geometric limitations inherent in ruling the cubes for the U.S. Pat. No. 4,349,598 and U.S. Pat. No. 4,895,428 patents, the cube structures disclosed therein are not useful where the primary light source will generally be at a near-zero incidence angle, such as in highway sign sheeting.
Processes for making tools having macrocubes are known in the prior art. Such tools are typically made by assembling a cluster of metal pins, each pin having a single cube corner machined and polished on one end. Hexagonal pins typically may have a dimension across parallel flats on the order of about 0.10 inch (2.5 mm). Rectangular pins have a short dimension of about 0.070 inch (1.8 mm) and a long dimension of about 0.120 inch (3.0 mm). A cluster of such pins is then used as a master to electroform a mold. These larger cubes, because of their height, are too large for use in the manufacture of thin flexible retroreflective sheeting requiring microcubes, but do find utility where larger (and thus taller) retroreflective elements are acceptable, such as in molded plastic reflectors for roadway markers, automobile taillights, and the like.
Because of manufacturing limitations, the smallest pin known to applicants has a cube shape about 0.040″ square. Microcubes as used in flexible retroreflective sheeting generally are no greater than about 0.016 inch (0.4 mm) on a side, and in applicants' assignee's commercial sheeting products, the longest edge of the cube shape is about 0.010 inches (0.25 mm).
The term microcube (or a cube of small dimensions), has been used in patents of others to describe or claim sheeting products produced from tools made directly or indirectly from ruled masters, as opposed to retroreflector articles comprising macrocubes typically formed by grouping pins (or by other techniques used to form the larger cubes).
For tooling hexagonal cubes, as alternative to the “pin cluster” manufacturing technique is shown in Applied Optics, vol. 20, no. 8, Apr. 15, 1981, pages 296-298. It is there stated that one way to achieve hexagonal cube corners is to accurately machine and polish grooves in the edge surfaces of a stack of flat plates and to assemble the plates at a desired angle. The reference shows a photograph of several flat plates with grooves cut in one edge, stacked one atop the other and with adjacent plates shifted with respect to one another so that the grooves are offset. The tilted stack of plates so assembled results in a set of hexagonal cubes which may be used as a master for electroforming molds. However, this technique was disclosed decades earlier by applicants' assignee's founder and was stated to be an unsatisfactory technique for tooling retroreflectors, see U.S. Pat. No. 1,591,572 (FIG. 16, p. 5, 11, 85-99).
Heretoforer, the above-described “stacked plates” method of forming macrocubes was not of practical interest for producing molds for retroreflective products on a commercial scale. First, the molds for macrocubes could be made satisfactorily by the aforementioned clustering of hexagonal pins. Secondly, as observed in U.S. Pat. No. 1,591,572, by using conventional machining and polishing techniques, it was not possible to cut and polish inside-intersecting faces with the precise angular tolerances and sharp edges achievable with the pin technique. In particular, any irregularities in the cube surfaces as might be caused by either the cutting operation or the polishing operation could disadvantageously increase the divergence of the retroreflected light and thus diminish the effective retroreflectivity of the cubes so formed. This recognized difficulty in polishing grooved internal angles is highly exacerbated with microcubes because the area that cannot be polished flat is a relatively greater percentage of the resulting cube face area.
As part of the present application, applicants disclose a technique for making and using thin plates that can be ruled without the need of polishing and that can be assembled in various ways to achieve microcube elements not previously available.
It is an object of the present invention to provide an array of microcubes which cannot be produced by ruling in one plane.
It is a further object of the invention to provide an array of microcubes in which the non-dihedral face-edges are not all parallel to a common plane.
It is still another object of the invention to provide means for interrelating three constructional parameters defining a hexagonal microcube (i.e., slippage, groove depth, and plate thickness, explained infra), by which the desired optical characteristics of the microcube can be optimized.
It is still another object of the invention to provide a retroreflective article and, in particular, retroreflective sheeting, having a pattern of hexagonal retroreflective microcubes having desired retroreflective characteristics.
It is another object of the instant invention to provide a method of making a tool including two or more contiguous hexagonal microcubes, which tool can be used for making a retroreflective article and, in particular, retroreflective sheeting.
It is still another object of the invention to provide a method of making a tool having a pattern of all hexagonal microcubes, which tool is made in part by ruling a set of grooves into the ends of a set of plates and then assembling the plates so as to define an array of hexagonal microcubes having desired retroreflective characteristics.
It is yet another object of the invention to provide an article having hexagonal microcubes wherein all of the cube faces are pentagonal; to provide a tool for making such an article; and to provide methods for making such an article and such a tool.
It is yet another object of the invention to provide a retroreflective article and, in particular, retroreflective sheeting, having rectangular retroreflective microcubes in which no dihedral face-edges of one cube are collinear with those of another cube, and in particular, such an article in which the microcubes provide desired retroreflective characteristics.
It is another object of the invention provide a tool having a unique pattern of rectangular microcubes in which cube axis cant is not constrained by the need for collinearity of dihedral face-edges of adjacent cubes, which tool can be used for making a retroreflective article and, in particular, retroreflective sheeting.
It is another object of the instant invention to provide a method of making a tool having a pattern of rectangular microcubes in which dihedral face-edges are not collinear, which tool can be used for making a retroreflective article having rectangular microcubes, such as sheeting.
It is still another object of the invention to provide a method of making a tool having a pattern of rectangular microcubes, which tool is made in part by ruling grooves and bevels into plate ends to provide a desired rectangular cube shape and pattern.
It is also an object of the invention to provide a method of making rectangular microcube tools by means of assembling flat plates, on one end of which the rectangular microcubes have been formed.
It is still another object of the invention to provide an article having a pattern of retroreflective square microcubes, wherein the microcubes in a square set of four cubes have cube axes canted in four different directions.
It is yet another object of the invention to provide an article having a pattern of retroreflective pentagonal microcubes; to provide a tool for making such an article; and to provide methods for making such an article and such a tool.
It is still another object of the invention to provide an article having a pattern of pentagonal microcubes with canted cube axes, and such an article having pentagonal microcubes with differently canted cube axes, and tools for making such articles and methods for making such tools and articles.
Still a further object of the invention is to provide a retroreflective article having one or more triangular microcubes in which the cube shape and the position of the projection of the cube apex within the cube shape are independent of the cube axis cant.
Yet a further object is to provide such a retroreflective article in which adjacent triangular microcubes may have different degrees of inclination of the cube axes and are not necessarily matched pairs.
Other objects, advantages, and novel features of the instant invention will be understood by those skilled in the art from the following specification and the drawings appended hereto.
In accordance with the invention, methods are disclosed for making a tool having a pattern of microcubes for use in making a retroreflective article. A plurality of plates is provided, each plate having two substantially parallel planar surfaces and at least one end made of a material that can be cut by a cutting tool that will produce an optical surface, as cut. The plate has a micro-sized thickness “t”, i.e., on the order of about one or two microcube widths, depending upon the type of microcube-corner to be tooled. The thickness need not be the same for all plates.
Many shapes of microcubes are manufacturable using the plate process disclosed herein. Two shapes, hexagonal and rectangular, are discussed in detail; other shapes are described more generally to illustrate the versatility of the process.
To produce a pattern of hexagonal microcubes, the plates are stacked one against another so that the set of ends of cuttable material lies substantially in a single plane, which, in a preferred form, is substantially perpendicular to the parallel planar surfaces of each plate. A series of parallel V-shaped grooves is ruled with a cutting tool into the set of cuttable ends. The ruled grooves preferably have polished surfaces as cut and therefore do not require subsequent lapping and polishing as do pins used in making macrocubes.
In one embodiment of the invention, the direction of cutting the grooves is nominally perpendicular to the planar surfaces of the plates, the length “L” of each inclined surface of the groove perpendicular to the direction of cutting is chosen to be equal to the thickness “t” of the plate, and the included angle between the inclined surfaces is about 90°, the included angle may be varied from 90° by tilting the cutting face of the cutting tool with respect to the surface being cut.
The grooved plates are then offset from one another by half a groove width horizontally and possibly, but not necessarily, by the depth “d” of one groove vertically, so that the top edge of a groove in one plate coincides with the bottom edge of a ruled groove in the adjacent plate, thus creating two superimposed arrays of hexagonal cube corners. One array consists of female (concave) hexagonal cube corners, each comprised of the exposed planar surface of one plate plus the two surfaces of one groove of the next adjacent plate. The other array consists of male (convex) hexagonal cube corners, each comprised of the exposed planar surface of one plate plus two adjacent surfaces from adjacent grooves in that same plate. For greater accuracy in the eventual retroreflective article, the male cube corners are preferred, because they avoid any plate-to-plate angular errors.
To produce a pattern of rectangular microcubes, in one embodiment, plates of a chosen thickness “t” are stacked alternately with slightly shorter spacers. The assembly of plates and spacers is tilted at a predetermined preferred angle, with one set of edges of the cuttable ends lying in a plane parallel to the bed of the ruling machine. The cuttable end of each plate is then bevel cut by means of a cutting tool so that the beveled face is perpendicular to the bed of the ruling machine. A series of grooves of desired included angle is then cut by the cutting tool in a direction substantially perpendicular to the beveled face. To crease an electroforming master comprising rectangular microcubes, the spacers are removed and the plates are then stacked together with adjoining plates rotated 180° with respect to each other with the apices of the rectangular cube-corners all lying in the same plane perpendicular to the plane of the sides of the plates and with the apices of cubes in adjoining plates aligned parallel to the grooves.
Manufacture of Article
The stack of grooved plates (for hexagonal cubes) or grooved and beveled plates (for rectangular cubes) may then be used as a master for electroforming a mold insert or for initiating a mothering process to electroform a larger mold insert or an embossing belt, as shown in patent U.S. Pat. No. 4,478,769 for the manufacture of retroreflective articles and, in particular, retroreflective sheeting, but now having a pattern of hexagonal or rectangular microcubes. The use of hexagonal or rectangular microcubes instead of triangular microcubes advantageously increases the active aperture of the article as projected parallel to the principal refracted ray from 66% or less to essentially 100%.
For purposes of this application, Applicants are using certain terms in a particular sense, as defined herein, and other terms in accordance with industry accepted practice, such as current ASTM definitions. Note that many of these definitions distinguish between a cube and a cube shape, each of which is defined herein.
Adjacent—for microcubes, having a portion of an edge of the shape of one cube essentially coincident with a portion of an edge of the shape of another cube.
Angle of incidence—the angle between the illumination axis and the normal to the front surface of a retroreflector. See also “entrance angle.”
Array active aperture—the sum of the active apertures of the individual microcube elements making up the array. (See also “percent active aperture”)
Contiguous microcubes—microcubes, a non-dihedral face-edge of one of which is coincident with a non-dihedral face-edge of another microcube. Compare, “adjacent cubes.” Note that non-contiguous microcubes may be adjacent. An array of contiguous microcubes is one in which the non-dihedral face edges of each microcube (except those at the perimeter of the array) are coincident with non-dihedral face edges of another microcube.
Cube (also “cube corner”)—an element consisting of three nominally perpendicular faces, regardless of the size or shape of the faces; often referred to in industry and literature as “corner cubes”, “trihedrals” or “tetrahedrons”.
Cube area—the area enclosed by the cube shape.
Cube axis—a central axis that is the trisector of the internal space defined by the three intersecting faces of a microcube. In the art, sometimes called the “symmetry axis.”
Cube axis cant—the angle between the cube axis and the principal refracted ray. The sign of the cant is negative for face-more-parallel and positive for edge-more parallel. A cube is considered canted when the cube axis cant is not zero.
Cube diagonal—for certain cube corners, an imaginary line passing through the apex of the cube corner at an angle such that in a projection of the outline of the cube corner parallel to the cube diagonal, every line through the apex terminating on both ends at the cube shape will be bisected by the apex.
Cube perimeter—closed spatial curve comprising the non-dihedral edges of the faces of a cube. In instances where there is an uninterrupted surface shared by two or more microcubes, the dividing lines between microcubes shall be considered to be the shortest lines that can be drawn to complete the polygon (see e.g. FIG. 27B).
Cube shape—the two-dimensional geometrical figure defined by the projection of the cube perimeter in the direction of the principal refracted ray. Thus, a triangular cube has a cube shape that is a triangle, a hexagonal cube has a cube shape that is a hexagon, and so forth.
Cube symmetry plane—a plane that divides a cube corner into mirror images. Not all cube corners have a plane of symmetry.
Design ray—an imaginary line through the cube apex in a tool, which ray is coincident with the principal refracted ray in the article.
Dihedral face-edge—intersection of two faces of a single cube.
Entrance angle—the angle between the illumination axis and the optical axis (retroreflector axis). Note the distinction between entrance angle and angle of incidence. The angle of incidence is always measured between the incident ray and the normal to the surface (which may or may not be the retroreflector axis), whereas the entrance angle is measured between the incident ray and the retroreflector axis (which may or may not be the normal to the surface). Entrance angle is a measure only of the amount by which an incident ray is angled to the retroreflector axis, and is not concerned with the normal; angle of incidence is a measure only of the amount by which an incident ray is angled to the normal, and is not concerned with the retroreflector axis. For example, a pavement marker may be designed for the normal to the marker surface to be angled 60° to the optical axis; if light from an approaching vehicle is incident upon that marker along the retroreflector axis, the entrance angle is 0° and the angle of incidence is 60°, if light from an approaching vehicle is incident on the marker at a horizontal angle of 20° with respect to the retroreflector axis, the entrance angle is 20° and the angle of incidence is 61.98°=[cos−1(cos 60)(cos 20)].
“Face-more parallel” and “edge-more parallel” refer to the positioning of the cube relative to the principal refracted ray. When the angles between the cube faces and the principal refracted ray are not all equal to 35.26°, the cube is “face-more-parallel” or “edge-more-parallel” depending upon whether the face angle with respect to the principal refracted ray that is most different from 35.26° is respectively greater or less than 35.26°. In the case of sheeting or other retroreflectors for which the principal refracted ray is nominally perpendicular to the front surface of the retroreflector, then for face-more-parallel microcubes the selected cube face will also be more parallel to the reflector front surface than will any face of an uncanted microcube.
Horizontal entrance angle—for pavement markers, the angle in the horizontal plane between the direction of incident light and the retroreflector axis.
Incidence angle—see, “angle of incidence.”
Microcube (also “microcube corner”)—a cube corner having a maximum area of about 0.0016 square inches (1 mm2).
Non-dihedral face-edge—edge of a microcube face that is not a dihedral face-edge, i.e., an edge that is a segment of the cube perimeter.
Optical axis—a designated line segment from the retroreflector center that is chosen centrally among the intended directions of illumination, such as the direction of the road on which or with respect to which the retroreflector is intended to be mounted.
Paired—oppositely oriented. Paired cubes, as used herein, refers to oppositely oriented adjacent cubes. Paired arrays, as used herein, refers to two arrays, the cube in one array being oppositely oriented to the cubes of the other.
Percent active aperture—that portion of the projected area of an array that is retroreflectively functional for a particular selected direction of projection. (This definition assumes that the rear surfaces of the cube are 100% reflective. This definition is equivalent to that used in WO 95/11470, page 6, lines 23-25).
Principal incident ray—a light ray parallel to the optical axis, chosen so that after refraction at the article's front surface, the ray passes through the apex of the cube corner.
Principal refracted ray—the continuation of the principal incident ray after refraction at the retroreflector front surface.
Retroreflectance—the product of percent active aperture times each cube face's reflectivity times the square of the transmission (to account for Fresnel transmission loss) of the front surface. (This term differs from “total light return” as defined in WO95/11467, page 17, lines 26 and 27, by inclusion in “retroreflectance” of the Fresnel loss of the front surface.) Photometrically, retroreflectance is the measure of the total retroreflection accumulated over all appropriately small observation angles and all rotation angles.
Retroreflector axis—same as “optical axis.”
Rulable—capable of being generated by the repeated straight-line motion of a shaped tool along paths parallel to a common plane.
Zone of reflectorization—the range of entrance angles in a given entrance plane throughout which the retroreflector maintains a given minimum retroreflectance.
These various figures, which are not to scale, are intended to be merely illustrative and not limiting. The various graphs are similarly not limiting but are for demonstrative and comparative purposes. Other graphs and examples will be apparent from the detailed descriptions which follow.
The inventive method of making microcubes uses the principle of ruling the ends of certain plates in a particular fashion and then assembling these plates in a particular combination to form an array of microcubes. An “array” as used in this patent application shall mean a repeating pattern of geometrical elements, including microcubes. Those skilled in the art will recognize that a retroreflective article having desired performance characteristics could be made from a component of different arrays. For example, such an article could include different arrays each made by one or more techniques of the instant invention, or such an article could include a combination of arrays of the instant invention and arrays made by prior art machining methods. Means for combining different arrays in a single article are known to those skilled in the art, and retroreflective articles having a plurality of arrays, one or more of which is made in accordance with the instant invention, are considered to be within the scope of the instant application. In every instance where different arrays are combined, it shall be understood that the specification and claims are relevant to that array, or that portion of the array, that is made by the technique of the instant invention.
The various examples discussed hereinafter demonstrate the advances in this technology in their simplest form and also disclose specific embodiments in which improved retroreflector performance can be achieved in microcubes using the same optical principles as have been employed in macrocubes.
All embodiments of the invention require the use of plates, which differ somewhat for different types of microcubes. The plates are of micro-sized thickness, on the order of about b 0.004-0.040 inches (0.1-1.00 mm). There are four basic types of plates. Plates 10, suitable for the tooling of hexagonal microcubes, with rectangular cube faces, have flat and parallel faces and, uniquely, one face of the plate becomes a face of the microcube, and therefore, must have a polished surface. Plates 10 and 210, suitable for tooling rectangular and triangular microcubes, have flat and parallel faces and in a preferred form, neither face of the plate becomes a face of the microcube. Plates 710 and 810, suitable for tooling the pentagonal microcubes of
Method of Making Plates
The plates must be of a material that cuts cleanly when ruled, such as with a diamond cutting tool as is known in the art. Electroless nickel is a particularly suitable material for the rulable plates used in the method of the instant invention.
Although the above-described plates may differ, the method of their manufacture can be generally illustrated by the method of making plates 10 used in the manufacture of hexagonal microcubes. For purposes of illustration, plate 10 can have dimensions of about 1.0″×4.0″ and a thickness “t” of about 0.010″.
Machine the 1.0″ by 4.0″ surface 609 of the electroless nickel 604 with a diamond tool to the desired thickness, in this example to 0.010″. Machine the sides of the block with diamond to cut away electroless nickel at 605 (
In the tooling of hexagonal microcubes, a portion of the surface 608
Method of Making Hexagonal Microcubes
As shown in
e=cos−1[(tan 0.5C)/tan 0.5(C+ΔC)] Equation A:
In order to define a pattern of hexagonal retro-reflective microcubes the grooved plates 10 may be offset one from another as shown in FIG. 5. Adjacent plates are offset from one another in the horizontal direction by a distance “a”, which as shown in
With the plates offset in this manner, “male” microcubes are defined by the inclined walls of adjacent grooves which meet at a top edge 20 to form two faces 17 and 18 of the microcube, and the front surface of the same plate which forms the third face 19 of the microcube. It can be seen in
The hexagonal outline of the cube corners produced by the method described above, and the quadrilateral outline of the cube faces, are both readily apparent in
In the embodiment of
While in the foregoing example all the cube dihedral angles are equal and all the cube faces are identical, it is recognized in the art of cube corner retroreflectors that for some applications it may be desirable to alter various optical properties of the retroreflective article by making predetermined modifications to the cube angles and the relative sizes and shapes of the respective cube faces. Those modifications can be achieved using the methods of the instant invention. Thus, for example, the thickness of the plate “t” need not necessarily be equal to the length of the side of the groove “L”, the crest of one groove need not be coincident with the root of a groove in an adjacent plate, and the direction of ruling is not necessarily perpendicular to the face of the plate 10.
The inventive method as described allows the cube designer to control certain retroreflective properties of the resulting array of microcubes. For example, various angles of the principal incident ray can be accommodated by varying the depth of the groove relative to the thickness of the plates (FIG. 10), and/or by tilting the bisector of the groove so that the lengths of the two sides of a single groove are not the same (not illustrated) and/or by changing the offset of adjacent plates (FIG. 12). In another embodiment, the entrance angularity can be increased either in a plane perpendicular to the cube symmetry plane by canting the cube axis to face-more-parallel (
Those skilled in the art will recognize that the above variations of the inventive method allowing for control of incidence angularity, entrance angularity, and observation angularity, are not necessarily mutually exclusive, and can be combined by one skilled in the art to produce an array having a desired combination of retroreflector performance characteristics.
Three constructional parameters determine the geometry and thus the entrance angularity of a regular assembly of identical grooved plates that produces an array of hexagon cube corners: plate thickness t; groove depth d; and plate slip s. (See FIGS. 12C and 12D). Slip is the distance between the crests of one grooved plate and the roots of the next adjacent plate. For the assembly of
Light incident on the front surface of an article at incidence angle I will be retroreflected with 100% geometric efficiency (i.e., percent active aperture equals 100%) if and only if the following relation holds:
I′ is the incidence angle after refraction by the article's front surface. I′=sin−1(sinI/n), where n is the refractive index of the material. I″=I for hollow retroreflectors. I and I′ are either negative or positive; negative and positive values of I and I′ are illustrated in
For every value of I, from −90° to +90°, there are solutions to Equation E for t, d, and s. For small values of slip s/t, Equation E assures a unique ratio of groove depth to plate thickness, the quantity d/t, for each incidence angle. For example, Table B shows solutions when there is no slip, i.e., s/t=0, and when the refractive index is 1.49.
Tailoring of Plates to Incidence Angles,
Assuming s/t = 0, n = 1.49
Ratio of Depth to
For large values of slip s/t, there are solutions to Equation E only for the larger value of I. For example, Table C shows examples when s/t=0.75, and when the refractive index is 1.49.
Tailoring of Plates to Incidence Angles,
Assuming s/t = .75, n = 1.49
Ratio of Depth to
less than −40°
If the radio d/t is fixed, such as would be the case for a set of fabricated plates, then there will be a range of incidence angles for which it is possible to solve equation E with positive values of s/f. For example, Table D was developed for d/t=0.707 and refractive index 1.49.
Slip for Utilization of Plates with
d/t = .707, n = 1.49
Ratio of Slip to
less than 0°
The solution with d/t=0.707 and s/t=0 appearing both in Tables B and D corresponds to the embodiment previously discussed, for which L equals t and adjacent plates are offset in the vertical direction by the groove depth d as in
The solution with d/t=1.423 and s/t=0 appearing in Table B corresponds to the embodiment of
The solution with d/t=0.707 and s/t=0.932 appearing in Table D corresponds to the embodiment illustrated in
The solution with d/t=0.352 and s/t=0.75 appearing in Table C corresponds closely to the embodiment whose performance is shown in the uppermost curve of FIG. 45. Table C shows that this cube is 100% effective at an incidence angle I of 20°. If these cubes are in paired arrays, as they were for the example of
When d/t and s/t solve Equation E for a certain value of r the hexagon cube achieves 100% active aperture for just that one internal incidence angle. Depending on the refractive index this corresponds to one external incidence angle I. The percent active aperture, and more generally the retroreflectance, of this hexagon cube for all other incidence angles requires addition calculation. Graphs of retroreflectance and percent active aperture versus incidence angle from −90° to +90° are shown in
Graphs of retroreflectance versus incidence angle from −90° to +90° are shown in
When slip is non-zero the cube corners are no longer, strictly speaking, hexagons. In instances where there is an uninterrupted face shared by two or more adjacent cube elements, the dividing lines between elements shall be considered to be the shortest imaginary lines (15 in
Slip is a useful parameter for the optical designer. For example, while the solutions in Tables C and D assure 100% geometric efficiency at the chosen incidence angles, they entail different shapes of hexagonal cubes, with different volumes, different diffraction apertures; different spot “weights”, and a different cube axis cant.
Cube axis cant, measured with respect to the front face of the array, depends simply on (s+d)/t according to this equation:
It follows from equation E that for an array of hexagonal cubes assembled from grooved plates to have 100% active aperture at 0° incidence angle, d, s and t must satisfy the equation:
(2d+s).(d+s).=t2. Equation G:
From this it follows that:
This corresponds, according to Equation F, to a range of cants from 0° to −9.74°. While all cants are obtainable with grooved plate constructions, only those in the range from 0° to −9.74° can be chosen also to have 100% active aperture at 0° incidence angle.
To further increase entrance angularity, however, the designer may choose to accept less than 100% efficiency at 0° incidence angle. As illustrated by the series of retroreflectance graphs in
Each of the five families of curves in
Method of Making Rectangular Microcubes
The method of making a tool with rectangular microcubes in accordance with the instant invention begins with a stack of plates 110 (shown in partial top plan view in FIG. 14A), the thickness t of the plate 110 being equal to the desired dimension H (
Each plate 110 or a stack of plates 115 is positioned on a ruling machine with the cuttable end 112 up and with the front faces 124 of the plates angled by a desired amount X, for example 35.26°, with respect to a perpendicular to the cutting plane of the ruling machine, FIG. 15. If a stack of plates is used, the upper edges 125 of the ends 112 all lie within a single plane and, to provide clearance for the cutting tool between the plates to be machined, spacers of cuttable material or spacers 111 retracted from the plane of the edges 125 are provided between plates,
To prevent the formation of burrs, after the bevel faces 113 have been cut, the spaces between plates may be filled with a plastic compound 114,
Note that the microcubes could be machined in one plate at a time, but the plates are preferably grouped for machining in order to minimize cost.
A variation of the process which may be useful to make very small microcubes is to machine two rows of microcubes on a single plate, thereby permitting doubling the thickness of the plate and increasing its rigidity. As shown in
With one cutting edge 219A of the cutting tool 219,
The cut may be filled with a plastic compound 114,
Inclined faces 216 of adjacent grooves, which meet at a top edge 220, form two faces 200B and 200C of microcube 200, and the first bevel face 213 forms the third face 200A,
The plates 210 are then tilted so that front faces 224 are at an angle X with respect to the perpendicular to the plane of the machine bed, FIG. 24. It will be understood that the symbol “X” is used herein generally to designate the angle between the front face of a plate and the perpendicular to the plane of the machine bed, so that the angle “X” in
Inclined faces 316 of adjacent grooves which meet at a top edge 320 form two faces 300B and 300C of microcube 300 and the second beveled surface 313 forms the third face 300A, FIG. 25B. Thus a second row of microcubes is formed on the other side of the same end of the plate where the first row of microcubes was formed. As is evident from the dotted lines in
Method of Positioning Plates for Ruling
Methods of fixturing to obtain the cube corner configurations described herein will be apparent to those skilled in the art. However, because of the exacting tolerances required for microcubes, further detail is provided regarding means of positioning the plates for machining operations. For all shapes of microcubes, two dowel holes R,
To machine rectangular microcubes one plate at a time, the plates will be positioned on the ruling machine by means of dowels through the reference dowel holes R and matching dowel holes provided in a fixture, the surface of which is angled by an amount X from a perpendicular to the bed of the ruling machine. After the bevel face and grooves have been machined, the reference dowel holes R will be used to position the plates of electroforming. The maximum error in positioning the apex for the microcube with respect to the center of the plate is anticipated to be less than 0.0001″ (2.5μ). If a number of plates are to be ruled at one time, secondary dowel holes can be provided on each plate in a manner somewhat similar to the procedure described for hexagonal microcubes; however, for a stack of 10 plates, the error in positioning the apex of the microcube is expected to increase possibly to 0.0005″ (12.5μ) in a direction perpendicular to the side of the plate.
Preferred methods of tooling, microcubes have been described in great detail; however, it should be understood that alternative methods of tooling based upon the plate concept will be readily apparent to a skilled toolmaker, and the descriptions above should not be considered as limiting.
Rectangular microcubes of the present invention differ from hexagonal microcubes of the present invention in two main ways. First, the rectangular microcubes can be arranged as paired (mirror image) elements, whereas the hexagonal microcubes produced from single cut plates are all alike in orientation; pairing of hexagonal microcubes to produce symmetrical performance requires pairing small mirror image arrays of hexagonal microcubes into a larger array. Second, rectangular microcubes offer generally greater design freedom than hexagonal microcubes produced from single cut plates; for rectangles, the axis cant, the apex centration, and the rectangular proportions are each independently variable (see FIG. 28), whereas for hexagons a change in one of the variables also requires a change in one of the other two. Rectangular cubes can have 100% active aperture at 0° incidence by centering the apex; the cant is then fully adjustable from −54.74° to +35.26°, and the proportions are still variable. By contrast, prior art direct ruled triangles have no independent variables; cant, apex centrations and proportions are inextricably interrelated.
For directly ruled triangular microcubes, cube axis cant is determined by the shape of the triangle according to the equation:
where A and B are the tangents of the triangle's two acute angles. For triangular microcubes tooled by the plate assembly technique of the instant invention (see FIG. 31), cube axis cant becomes a combination of the angle calculated above and the angle between the triangle base and the front surface.
In the recent PCT publications Nos. WO 95/11463, WO 95/11465 and WO 95/11470 of the Minnesota Mining and Manufacturing Co., various graphs depict comparisons of retroreflectivity according to percent active aperture, but do not consider total internal reflection (TIR) limits, regarding the cube faces as if metallized to have 100% reflectance; nor do they consider the front surface specular losses, which become substantial at high incidence angles.
In the graphs depicted in the present application, unless noted otherwise, the following parameters were chosen for the determination of retroreflectance:
The various depicted curves of possible designs are not necessarily representative of commercially practical articles, but do ably demonstrate the wide variety of results that can be achieved by producing tools and microcube retroreflectors in accordance with various aspects of the present invention.
Most of the graphs are for unmetallized cubes and include the effect of total internal reflection (TIR).
To increase the entrance angularity of the cubes as described in patents U.S. Pat. Nos. 3,541,606, 3,873,184 and U.S. Pat. No. 3,923,378 issued to the same assignee and incorporated herein by reference, the s/t=0, d/t=0.707 solution shown in
Intimately paired rectangles can be ruled with 1:2 (width:height) proportions of
Since the advantages of cube axis canting are realized primarily with cubes relying on TIR, it is more appropriate to base these efficiency considerations on retroreflectance rather than on percent active aperture. In both the rectangle and hexagon examples, when the incidence angle is 19.6° TIR is preserved for that cube (or array) of the pair which gains in effective aperture and lost for the cube (or array) which loses in effective aperture. The net result is total retroreflectance of 0.898×50.2% for the paired rectangles and 0.898×52.3% for the paired arrays of hexagons. (The 0.898 factor is due to the front surface losses.)
Percent active aperture and retroreflectance for paired pentagons (see
For a discussion of the advantages of the “face-more-parallel” construction with sets of cubes oppositely oriented, see patent U.S. Pat. No. 3,541,606, at col. 15, line 62 through col. 16 line 47, and FIGS. 18, 19 and 20.
Note that the method outlined in Example 1 is intended to maximize the range of entrance angles in one or more planes through which a predetermined minimum retroreflectance can be maintained; the concept requires cubes (or cube arrays) with canted cube axes oppositely oriented as previously described in commonly assigned patents and as used in 3M's “Diamond Grade” sheeting (see also Hoopman U.S. Pat. No. 4,588,258).
Example 2 is quite different. The method of Example 2 is intended to maximize the retroreflectance through a relatively smaller range of entrance angles about an axis (the principal incident ray) which is not normal to the face of the retroreflector. For example, a raised retroreflective lane marker mounted on a road may have its front surface tilted back 60° from a plane perpendicular to the plane of the pavement. A light ray from the headlight of an approaching vehicle, being substantially parallel to the pavement, becomes incident on the face of the retroreflector at an angle to the normal of 60° and is refracted (in acrylic) to an angle to the normal of 35.5°. For purposes of discussion, the ray parallel to the pavement surface and to the centerline of the road will be called the principal incident ray of optical axis and the ray within the marker after reflection at the front surface will be called the principal refracted ray.
A retroreflector for which L=t, the plates for which are illustrated in
As stated in equation E, for hexagonal microcubes the relationship between I′, d, s, and t is:
For an acrylic pavement marker with front surface tilt of 30° to the road, I′=35.54°. If slippage is chosen to be zero (s/t=0), then
from which d/t=1.42.
To produce a tool comprising hexagonal microcubes for the above pavement marker, the plates will be ruled so that d/t=1.42 and will be offset from one another by an amount d=1.42t in both the horizontal and vertical directions as in FIG. 10.
Alternatively, the plates of
Pavement markers comprising rectangular microcubes tooled by the plate method can be made with improved horizontal entrance angularity compared with the direct-ruled cubes of Nelson U.S. Pat. No. 4,895,428. To tool 9 9° face-more-parallel rectangular cubes for use in an acrylic pavement marker with a front surface tilt of 55°, the plate thickness is chosen to be equal to H, which is the dimension of the side of the cube that is parallel to the symmetry plane as projected parallel to the principal refracted ray as in
The divergence of the retroreflected beam (i.e., the observation angularity) can be varied in one plane or in multiple planes by changing the dihedral angles between either two or three faces as taught in U.S. Pat. No. 3,833,285 also to the same assignee and incorporated herein by reference and/or by changing the size of the cube, which affects diffraction.
The dihedral angle can be changed by making the groove angle greater or less than 90° and/or by tilting the stack of plates 10 slightly off the perpendicular to the cutting plane, as illustrated by angle “b” in
The tilt angle “e” of the cutting tool can be held constant for all grooves. Alternatively, the tilt angle “e” of the cutting tool can be adjusted continuously as each groove is cut as a function of the distance traveled by the cutting tool along the ruled surface, or the cutting tool can be held at a constant angle “e” for the entire length of each groove, but changed for each successive groove cut into the surface. It is also possible to use a combination of these techniques; i.e., change the angle “e” of the cutting tool with respect to the surface both along the length of each groove, and from groove to groove.
Diffraction is the spreading of a light beam caused by restriction of the beam size. Diffraction is the main optical difference between macrocubes and microcubes. For the observation angles associated with such commercial applications as highway markings, approximately 0.1° to 1.5°, the diffraction effects for microcubes may be significant while those for macrocubes are insignificant. For macrocubes observation angularity is completely determined by the dihedral angles, the flatness of the faces, and the cube shape, but for microcubes size is an additional determinant.
By making the groove angle 90.103° in the plates of
The plates used in the ruling method of the instant invention may be formed of any material that is sufficiently strong and rigid to be ruled when formed into flat plates of the thinness required. The material must also be capable of being cut and polished with a high degree of precision. Certain plastics, such as polymethylmethacrylate, may be suitable if metallized after machining to provide electrical conductivity for electroforming. Suitable metals include hardened sterling silver 925 fine, hardened aluminum 7075T6, and electroless nickel. Electroless nickel is known to be very hard yet readily cut with a diamond cutting tool. An electroless nickel overlay on a stainless steel substrate may be sliced into plates with the electroless nickel on one end, which plates may be particularly suited for use in the instant invention. Alternatively, the electroless nickel may be formed as non-adherent plates on a passivated stainless steel block (or a block of another material such as aluminum or metallized plastic) to a thickness of about 0.012 inch and separated from the block to serve as plates 10.
In one form of the invention, the assembly of microcubes defined by the plates when ruled, assembled, and oriented as described herein may be used as a master to electroform copies. The copies are then assembled into a cluster of contiguous elements; the cluster is replicated to provide a number of copies; and the process is repeated, eventually to produce flexible strips having an uninterrupted pattern; the strips are assembled on a cylindrical mandrel to provide cylindrical segments; the cylindrical segments are assembled to provide a cylinder of the desired dimensions corresponding to the width of the web intended to be provided with retroreflective elements; and the assembled cylinder is replicated to provide a flexible endless master cylinder having the pattern of microcubes thereon. The master cylinder may then be replicated to form a relatively thick mother cylinder, which may in turn be replicated to form a generally cylindrical metal embossing tool.
The embossing tool so made may then be used to emboss the microcubes on a surface of a continuous resinous sheeting material to manufacture a retroreflective sheeting article, as disclosed in U.S. Pat. No. 4,486,363. In accordance with the method disclosed therein, the embossing tool described above is moved along a closed course through a heating station where it is heated to a predetermined temperature and then to a cooling station where it is cooled below that temperature; a resinous sheeting material is continuously fed onto the embossing tool through a part of the heating station so that the sheeting is in direct contact with the pattern of hollow microcubes; the sheeting is pressed against the embossing tool at one or more points in the heating station until one surface of the sheeting conforms to the pattern of hexagonal or rectangular microcubes; the embossing tool and sheeting are passed to the cooling station such that the sheeting is cooled below its glass transition temperature; and the embossed sheeting is stripped from the embossing tool.
Those skilled in the art will recognize that, in addition to the embossing tools and techniques described above, the hexagonal or rectangular microcube embossing tool made as described above may also be used to manufacture retroreflective sheeting by other methods such as molding, pressing, or casting. For example, the electroformed strip as described above having the pattern of hollow hexagonal or rectangular microcubes can be provided with a proper support and used directly as an embossing or compression molding tool but in a non-continuous manner, as described in Rowland U.S. Pat. No. 4,244,683.
The retroreflective sheeting made in accordance with the instant invention and having a precise optical pattern of microcubes of various cube shapes is advantageous over sheeting currently being made with triangular microcubes. For the small entrance angles of 0° to 5°, which are of particular interest for retroreflective highway markers and signs, substantially the entire area of the hexagonal or rectangular microcubes is effective for retroreflectance, but only 66 percent of the area of triangular microcubes is retroreflective. Thus, at these small entrance angles, the hexagonal or rectangular microcube retroreflective sheeting represents a 50 percent increase in retroreflective area compared with prior art triangular microcubes.
Retroreflective articles other than sheeting that are currently manufactured with macrocubes may also benefit from a change to hexagonal or rectangular, microcubes. For example, pavement markers incorporating microcubes of the instant invention will be less costly because of reduced material cost, may be deteriorated less by abrasion because the exiting rays are closer to the incident rays so that the effect of surface irregularities is reduced, and, for recessed pavement markers or low profile plowable pavement markers, the loss due to shadowing is minimized.
It is well-known in the reflective sheeting art that different sheeting materials such as acrylic, polycarbonate, and vinyl, have different indices of refraction, “n”, and will yield different retroreflective results, even for identical cube shapes (see FIG. 37).
Many variations of cubes are possible by modifications of the tooling procedure of the instant invention. For example:
(1) Square cubes, as in
(2) The angle of the cube axis with respect to the normal to the plane of the cube apices can be varied by selection of the angle X (
(3) For rectangular or pentagonal microcubes, the dihedral angles between cube faces can be varied from 90° by setting the cutting edge 119A of tool 119,
(4) The cube aperture size can be varied by changing the plate thicknesses and groove depth or by machining one row of microcubes on a double thickness plate larger than the row of microcubes with which it is paired; combining microcubes of different cube aperture size minimizes the potential diffraction loss at any one observation angle.
(5) Because one edge of the rectangular cube is rectilinear, sets of opposed pairs of rectangular cubes with different characteristics can be assembled without area loss or slippage walls between the sets; therefore adjoining sets can have different cube axes or different divergence, or different cube height with no inactive surfaces or sharp edges between the sets. For the transition between plates with different cube heights, the cube apices of one or both adjoining rows of cubes of different size may be moved off center; moving the apices of the last row of cubes in a set of large cubes towards a set of smaller cubes will tend to equalize the volume of material in the two sets of cubes. Similarly, sets of opposed pairs of rectangular cubes can be assembled with plates bearing optic detail other than microcubes, such as a flat surface, a cylindrical surface, or lenticular elements. Such sheeting comprising retroreflective portions and other optical portions is known in the art as transilluminated sheeting. The rectilinear edge of a flat or cylindrical optic surface may be set at the same height as the rectilinear edges of the rectangular microcubes, thereby avoiding any slippage walls between the two types of plates.
(6) For large angles of incidence, in macrocube technology the rectangular cubes in a bundle of pins may be assembled oriented all in one direction as exemplified by the use of hex cubes for pavement markers, in which use there will be a slippage wall paralleling the cube axis and corresponding to one exposed side of the pin. Similarly, for microcube technology, plates on which rectangular microcubes have been machined can be assembled with adjacent plates oppositely oriented (or for large incidence angles optionally oriented in the same direction) and with the cube apices contacting a reference surface set at an angle of (90°-R) to the side of the plates, where R is the angle between the principal refracted ray and the normal.
(7) Square cubes such as illustrated in
The above noted values of the cube axis cant are for illustrative purposes only, and are not intended to limit the scope of the invention or the range of cube axis cants obtainable by the method of the instant invention.
(8) To produce pentagonal microcubes such as illustrated in
where g is the included angle of the grooves and u and v are the angles of cant of the cubes formed on plates 710 and 810, respectively (See FIG. 36A). Plates 710 and 810 are not necessarily the same thickness. Bevel faces 813 and groove faces 716 are cut into the smooth side and the grooved side respectively of plate 810 following a procedure similar to that described in detail for rectangular cubes. Bevel faces 713 and groove faces 816 are cut into the grooved side and the smooth side respectively of plate 710. The plates are then assembled as illustrated in
(9) To produce triangular microcubes such as illustrated in
(10) A retroreflective array comprising hexagonal cubes with pentagonal faces,
The plate is positioned with the grooves perpendicular to the bed of the ruling machine. Faces A are machined by a cutting tool having an included angle of 70.52° (as projected in the direction of cutting), the bisector of the included angle being perpendicular to the bed of the machine. The plates then are tilted so that a grooved side makes an angle X equal to 50.77° with respect to a perpendicular to the bed of the machine and faces B1 are cut with a cutting tool having an included angle of 131.81° with bisector of the included angle perpendicular to the bed of the machine. The process is repeated for faces B2.
The finished plates are stacked for electroforming with grooves interlocking, which results in adjacent plates being displaced half a cube width laterally. One plate in the assembly is shown in bold outline.
For each microcube there will be left exposed in the assembly of plates one small triangular vertical wall where the cube dihedral edge in one plate abuts the face of a cube in an adjacent plate as indicated by the circles labeled C in FIG. 35. This exposed wall is not expected to be a problem in either electroforming or in assignee's embossing process, but, if necessary, the exposed wall can be drafted.
Those skilled in the art will recognize alternative methods for making arrays of hexagonal cubes with pentagonal faces, based on the invention herein, but the method shown is preferred for ease of tooling plates.
It will be understood that while machining using diamond tools to form grooves and edges is the disclosed embodiment, other linear forming techniques, such as laser cutting, EDM, or ion machining, or the like may be used. It will further be understood that known variations of ruling techniques may be employed without departing from the scope and spirit of the invention. For example, grooves may be cut wherein the faces are not planar, but have a slight and known curvature.
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|U.S. Classification||359/530, 359/529, 428/172|
|International Classification||B29C33/38, B29C33/30, G02B5/122, B29C33/42, G02B5/124, B29D11/00, B29C39/00, B29C43/00, B32B3/00|
|Cooperative Classification||Y10T428/249921, B29C33/301, B29C43/00, B29C2059/023, B29C33/42, B29C39/00, Y10T428/24612, B29L2011/0091, G02B5/124, B29C33/3842, B29D11/00605|
|European Classification||B29C33/42, G02B5/124, B29D11/00E|
|Sep 29, 2009||CC||Certificate of correction|
|Jan 27, 2012||FPAY||Fee payment|
Year of fee payment: 8
|Jan 15, 2016||FPAY||Fee payment|
Year of fee payment: 12