U.S. patent application number 09/965389 was filed with the patent office on 2002-03-07 for cube corner sheetiing mold and of making the same.
This patent application is currently assigned to 3M Innovative Properties Company. Invention is credited to Benson, Gerald M., Erwin, Robert L., Luttrell, Dan E., Smith, Kenneth L..
Application Number | 20020028263 09/965389 |
Document ID | / |
Family ID | 25388319 |
Filed Date | 2002-03-07 |
United States Patent
Application |
20020028263 |
Kind Code |
A1 |
Luttrell, Dan E. ; et
al. |
March 7, 2002 |
Cube corner sheetiing mold and of making the same
Abstract
Laminae suitable for use in molds for forming retroreflective
cube corner elements and methods for making such laminae are
disclosed. A representative lamina includes a first row of cube
corner elements disposed in a first orientation and a second row of
optically opposing cube corner elements disposed. The working
surface of a lamina is provided with a plurality of cube corner
elements formed by the optical surfaces defined by three groove
sets. Opposing first and second groove sets are formed in the
working surface of a lamina. The first groove set forms a plurality
of structures having first and second optical surfaces disposed in
mutually perpendicular planes that intersect along a reference
edge. The second groove set forms a corresponding plurality of
structures on the opposite side of the lamina. A third groove is
formed in the working surface of the lamina along an axis
substantially perpendicular to the axes of the grooves of the first
and second groove sets. The surfaces of the third groove intersect
the surfaces of the plurality of structures in substantially
mutually perpendicular planes to define a plurality of cube corner
elements. A plurality of such laminae can be assembled to form a
mold useful in the manufacture of retroreflective products such as
cube corner sheeting.
Inventors: |
Luttrell, Dan E.; (Corning,
NY) ; Erwin, Robert L.; (Rohnert Park, CA) ;
Smith, Kenneth L.; (White Bear Lake, MN) ; Benson,
Gerald M.; (Woodbury, MN) |
Correspondence
Address: |
Office of Intellectual Property Counsel
3M Innovative Properties Company
PO Box 33427
St. Paul
MN
55133-3427
US
|
Assignee: |
3M Innovative Properties
Company
|
Family ID: |
25388319 |
Appl. No.: |
09/965389 |
Filed: |
September 27, 2001 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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09965389 |
Sep 27, 2001 |
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09636520 |
Aug 9, 2000 |
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6318987 |
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09636520 |
Aug 9, 2000 |
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08886074 |
Jul 2, 1997 |
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Current U.S.
Class: |
425/193 ;
264/2.5 |
Current CPC
Class: |
B29D 11/00625 20130101;
Y10S 425/03 20130101 |
Class at
Publication: |
425/193 ;
264/2.5 |
International
Class: |
B29D 011/00 |
Claims
What is claimed is:
1. A lamina suitable for use in a mold for use in forming
retroreflective cube corner articles, the lamina having opposing
first and second major surfaces defining therebetween a first
reference plane, the lamina further including a working surface
connecting the first and second major surfaces, the lamina
comprising: two rows of cube corner elements in the working
surface, at least one such row comprising a plurality of
nonidentical cube corner elements.
2. The lamina of claim 1, wherein the two rows of cube corner
elements define therebetween a groove extending along the working
surface of the lamina.
3. The lamina of claim 2, wherein at least one of the two rows of
cube corner elements further define a set of parallel grooves.
4. The lamina of claim 3, wherein the set of parallel grooves
comprises grooves of differing included angles.
5. The lamina of claim 3, wherein the set of parallel grooves
comprises grooves having a nonuniform groove spacing.
6. A mold comprising the lamina of claim 1.
7. A cube corner article formed as a replica of the mold of claim
6.
8. A method of making a lamina suitable for use in a mold for use
in forming retroreflective cube corner articles, the method
comprising: providing a lamina having opposing first and second
major surfaces; and forming a first, second, and third groove set
in the lamina to define two rows of cube corner elements extending
therealong; wherein the forming step is performed with the lamina
registered in one position.
9. The method of claim 8, wherein the first groove set comprises a
first plurality of parallel grooves, and wherein the second groove
set comprises a second plurality of parallel grooves.
10. The method of claim 9, wherein the third groove set consists
essentially of a single groove.
11. A method of making a mold for use in forming retroreflective
cube corner articles, comprising making laminae according to the
method of claim 8 and assembling the laminae together.
12. A method of making a retroreflective article, comprising making
a mold according to claim 11 and forming the retroreflective
article from the mold by at least one replication step.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This is a continuation application of prior U.S. patent
application Ser. No. 09/636,520, filed Aug. 9, 2000, now allowed,
which is a continuation of prior U.S. patent application Ser. No.
08/886,074, filed Jul. 2, 1997, now abandoned.
FIELD OF THE INVENTION
[0002] The present invention relates generally to molds suitable
for use in forming cube corner retroreflective sheeting and to
methods for making the same. In particular, the present invention
relates to molds formed from a plurality of thin laminae and to
methods for making the same.
BACKGROUND OF THE INVENTION
[0003] Retroreflective materials are characterized by the ability
to redirect light incident on the material back toward the
originating light source. This property has led to the wide-spread
use of retroreflective sheeting in a variety of conspicuity
applications. Retroreflective sheeting is frequently used on flat,
rigid articles such as, for example, road signs and barricades;
however, it is also used on irregular or flexible surfaces. For
example, retroreflective sheeting can be adhered to the side of a
truck trailer, which requires the sheeting to pass over
corrugations and protruding rivets, or the sheeting can be adhered
to a flexible body portion such as a road worker's safety vest or
other such safety garment. In situations where the underlying
surface is irregular or flexible, the retroreflective sheeting
desirably possesses the ability to conform to the underlying
surface without sacrificing retroreflective performance.
Additionally, retroreflective sheeting is frequently packaged and
shipped in roll form, thus requiring the sheeting to be
sufficiently flexible to be rolled around a core.
[0004] Two known types of retroreflective sheeting are
microsphere-based sheeting and cube corner sheeting.
Microsphere-based sheeting, sometimes referred to as "beaded"
sheeting, employs a multitude of microspheres typically at least
partially embedded in a binder layer and having associated specular
or diffuse reflecting materials (e.g., pigment particles, metal
flakes or vapor coats, etc.) to retroreflect incident light.
Illustrative examples are disclosed in U.S. Pat. No. 3,190,178
(McKenzie), U.S. Pat. No. 4,025,159 (McGrath), and U.S. Pat. No.
5,066,098 (Kult). Advantageously, microsphere-based sheeting can
generally be adhered to corrugated or flexible surfaces. Also, due
to the symmetrical geometry of beaded retroreflectors, microsphere
based sheeting exhibits a relatively orientationally uniform total
light return when rotated about an axis normal to the surface of
the sheeting. Thus, such microsphere-based sheeting has a
relatively low sensitivity to the orientation at which the sheeting
is placed on a surface. In general, however, such sheeting has a
lower retroreflective efficiency than cube corner sheeting.
[0005] Cube corner retroreflective sheeting comprises a body
portion typically having a substantially planar base surface and a
structured surface comprising a plurality of cube corner elements
opposite the base surface. Each cube-corner element comprises three
mutually substantially perpendicular optical faces that intersect
at a single reference point, or apex. The base of the cube corner
element acts as an aperture through which light is transmitted into
the cube corner element. In use, light incident on the base surface
of the sheeting is refracted at the base surface of the sheeting,
transmitted through the bases of the cube corner elements disposed
on the sheeting, reflected from each of the three perpendicular
cube-corner optical faces, and redirected toward the light source.
The symmetry axis, also called the optical axis, of a cube corner
element is the axis that extends through the cube corner apex and
forms an equal angle with the three optical faces of the cube
corner element. Cube corner elements typically exhibit the highest
optical efficiency in response to light incident on the base of the
element roughly along the optical axis. The amount of light
retroreflected by a cube corner retroreflector drops as the
incidence angle deviates from the optical axis.
[0006] The maximum retroreflective efficiency of cube corner
retroreflective sheeting is a function of the geometry of the cube
corner elements on the structured surface of the sheeting. The
terms `active area` and `effective aperture` are used in the cube
corner arts to characterize the portion of a cube corner element
that retroreflects light incident on the base of the element. A
detailed teaching regarding the determination of the active
aperture for a cube corner element design is beyond the scope of
the present disclosure. One procedure for determining the effective
aperture of a cube corner geometry is presented in Eckhardt,
Applied Optics, v. 10, n. 7, July, 1971, pp. 1559-1566. U.S. Pat.
No. 835,648 to Straubel also discusses the concept of effective
aperture. At a given incidence angle, the active area can be
determined by the topological intersection of the projection of the
three cube corner faces onto a plane normal to the refracted
incident light with the projection of the image surfaces for the
third reflections onto the same plane. The term `percent active
area` is then defined as the active area divided by the total area
of the projection of the cube corner faces. The retroreflective
efficiency of retroreflective sheeting correlates directly to the
percentage active area of the cube corner elements on the
sheeting.
[0007] Additionally, the optical characteristics of the
retroreflection pattern of retroreflective sheeting are, in part, a
function of the geometry of the cube corner elements. Thus,
distortions in the geometry of the cube corner elements can cause
corresponding distortions in the optical characteristics of the
sheeting. To inhibit undesirable physical deformation, cube corner
elements of retroreflective sheeting are typically made from a
material having a relatively high elastic modulus sufficient to
inhibit the physical distortion of the cube corner elements during
flexing or elastomeric stretching of the sheeting. As discussed
above, it is frequently desirable that retroreflective sheeting be
sufficiently flexible to allow the sheeting to be adhered to a
substrate that is corrugated or that is itself flexible, or to
allow the retroreflective sheeting to be wound into a roll to
facilitate storage and shipping.
[0008] Cube corner retroreflective sheeting is manufactured by
first manufacturing a master mold that includes an image, either
negative or positive, of a desired cube corner element geometry.
The mold can be replicated using nickel electroplating, chemical
vapor deposition or physical vapor deposition to produce tooling
for forming cube corner retroreflective sheeting. U.S. Pat. No.
5,156,863 to Pricone, et al. provides an illustrative overview of a
process for forming tooling used in the manufacture of cube corner
retroreflective sheeting. Known methods for manufacturing the
master mold include pin-bundling techniques, direct machining
techniques, and laminate techniques. Each of these techniques has
benefits and limitations.
[0009] In pin bundling techniques, a plurality of pins, each having
a geometric shape on one end, are assembled together to form a
cube-corner retroreflective surface. U.S. Pat. No. 1,591,572
(Stimson), U.S. Pat. No. 3,926,402 (Heenan), U.S. Pat. No.
3,541,606 (Heenan et al.) and U.S. Pat. No. 3,632,695 (Howell)
provide illustrative examples. Pin bundling techniques offer the
ability to manufacture a wide variety of cube corner geometries in
a single mold. However, pin bundling techniques are economically
and technically impractical for making small cube corner elements
(e.g. less than about 1.0 millimeters).
[0010] In direct machining techniques, a series of grooves is
formed in a unitary substrate to form a cube-corner retroreflective
surface. U.S. Pat. No. 3,712,706 (Stamm) and U.S. Pat. No.
4,588,258 (Hoopman) provide illustrative examples. Direct machining
techniques offer the ability to accurately machine very small cube
corner elements which are compatible with flexible retroreflective
sheeting. However, it is not presently possible to produce certain
cube corner geometries that have very high effective apertures at
low entrance angles using direct machining techniques. By way of
example, the maximum theoretical total light return of the cube
corner element geometry depicted in U.S. Pat. No. 3,712,706 is
approximately 67%.
[0011] In laminate techniques, a plurality of laminae, each lamina
having geometric shapes on one end, are assembled to form a
cube-corner retroreflective surface. German Provisional Publication
(OS) 19 17 292, International Publication Nos. WO 94/18581 (Bohn,
et al.), WO 97/04939 (Mimura et al.), and WO 97/04940 (Mimura et
al.), disclose a molded reflector wherein a grooved surface is
formed on a plurality of plates. The plates are then tilted by a
certain angle and each second plate is shifted crosswise. This
process results in a plurality of cube corner elements, each
element formed by two machined surfaces on a first plate and one
side surface on a second plate. German Patent DE 42 36 799 to
Gubela discloses a method for producing a molding tool with a
cubical surface for the production of cube corners. An oblique
surface is ground or cut in a first direction over the entire
length of one edge of a band. A plurality of notches are then
formed in a second direction to form cube corner reflectors on the
band. Finally, a plurality of notches are formed vertically in the
sides of the band. German Provisional Patent 44 10 994 C2 to Gubela
is a related patent. The reflectors disclosed in Patent 44 10 994
C2 are characterized by the reflecting surfaces having concave
curvature.
BRIEF SUMMARY OF THE INVENTION
[0012] The present invention relates to providing a master mold
suitable for use in forming retroreflective sheeting from a
plurality of laminae and methods of making the same.
Advantageously, master molds manufactured according to methods
disclosed herein enable the manufacture of retroreflective cube
corner sheeting that exhibits retroreflective efficiency levels
approaching 100%. To facilitate the manufacture of flexible
retroreflective sheeting, the disclosed methods enable the
manufacture of cube corner retroreflective elements having a width
of 0.010 millimeters or less. Additionally, the present application
enables the manufacture of a cube corner retroreflective sheeting
that exhibits symmetrical retroreflective performance in at least
two different orientations.
[0013] Efficient, cost-effective methods of making molds formed
from a plurality of laminae are also disclosed. In particular, a
reduction of the number of laminae necessary to produce a given
density of cube corner elements in a sheeting is disclosed, thereby
reducing the time and expense associated with manufacturing such
molds.
[0014] In one embodiment, a lamina suitable for use in a mold for
use in forming retroreflective cube corner articles is provided,
the lamina having opposing first and second major surfaces defining
therebetween a first reference plane, the lamina further including
a working surface connecting the first and second major surfaces,
the working surface defining a second reference plane substantially
parallel to the working surface and perpendicular to the first
reference plane and a third reference plane perpendicular to the
first reference plane and the second reference plane. The lamina
includes: (a) a first groove set including at least two parallel
adjacent V-shaped grooves in the working surface of the lamina,
each of the adjacent grooves defining a first groove surface and a
second groove surface that intersect substantially orthogonally to
form a first reference edge; (b) a second groove set including at
least two parallel adjacent V-shaped grooves in the working surface
of the lamina, each of the adjacent grooves defining a third groove
surface and a fourth groove surface that intersect substantially
orthogonally to form a second reference edge; and (c) a third
groove set including at least one groove in the working surface of
the lamina, the groove defining a fifth groove surface and a sixth
groove surface, the fifth groove surface intersecting substantially
orthogonally with the first and second groove surfaces to form at
least one first cube corner disposed in a first orientation and the
sixth groove surface intersecting substantially orthogonally with
the third and fourth groove surfaces to form at least one second
cube corner disposed in a second orientation different than the
first orientation.
[0015] In one embodiment, the first and second groove sets are
formed such that their respective reference edges extend along axes
that, in a top plan view, are perpendicular to the first reference
plane. The third groove set includes a single groove having a
vertex that extends along an axis contained by the third reference
plane. In this embodiment, the lamina comprises a first row of cube
corner elements defined by the grooves of the first groove set and
the third groove and a second row of cube corner elements defined
by the grooves of the second groove set and the third groove.
[0016] The three mutually perpendicular optical faces of each cube
corner element are preferably formed on a single lamina. All three
optical faces are preferably formed by the machining process to
ensure optical quality surfaces. A planar interface is preferably
maintained between adjacent first and second major surfaces during
the machining phase and subsequent thereto so as to minimize
alignment problems and damage due to handling of the laminae.
[0017] Also disclosed is a method of manufacturing a lamina for use
in a mold suitable for use in forming retroreflective cube corner
articles, the lamina having opposing first and second major
surfaces defining therebetween a first reference plane, the lamina
further including a working surface connecting the first and second
major surfaces, the working surface defining a second reference
plane substantially parallel to the working surface and
perpendicular to the first reference plane and a third reference
plane perpendicular to the first reference plane and the second
reference plane. The method includes: (a) forming a first groove
set including at least two parallel adjacent V-shaped grooves in
the working surface of the lamina, each of the adjacent grooves
defining a first groove surface and a second groove surface that
intersect substantially orthogonally to form a first reference
edge; (b) forming a second groove set including at least two
parallel adjacent V-shaped grooves in the working surface of the
lamina, each of the adjacent grooves defining a third groove
surface and a fourth groove surface that intersect substantially
orthogonally to form a second reference edge; and (c) forming a
third groove set including at least one groove in the working
surface of the lamina, the groove defining a fifth groove surface
and a sixth groove surface, the fifth groove surface intersecting
substantially orthogonally with the first and second groove
surfaces to form at least one first cube corner disposed in a first
orientation and the sixth groove surface intersecting substantially
orthogonally with the third and fourth groove surfaces to form at
least one second cube corner disposed in a second orientation
different than the first orientation.
[0018] Further disclosed is a mold assembly comprising a plurality
of laminae, the laminae including opposed parallel first and second
major surfaces defining therebetween a first reference plane, each
lamina further including a working surface connecting the first and
second major surfaces, the working surface defining a second
reference plane substantially parallel to the working surface and
perpendicular to the first reference plane and a third reference
plane perpendicular to the first reference plane and the second
reference plane. The working surface of a plurality of the laminae
includes: (a) a first groove set including at least two parallel
adjacent V-shaped grooves in the working surface of each of the
laminae, each of the adjacent grooves defining a first groove
surface and a second groove surface that intersect substantially
orthogonally to form a first reference edge on each of the
respective laminae; (b) a second groove set including at least two
parallel adjacent V-shaped grooves in the working surface of each
of the laminae, each of the adjacent grooves defining a third
groove surface and a fourth groove surface that intersect
substantially orthogonally to form a second reference edge on each
of the respective laminae; and (c) a third groove set including at
least one groove in the working surface of a plurality of the
laminae, each groove defining a fifth groove surface and a sixth
groove surface, the fifth groove surface intersecting substantially
orthogonally with the first and second groove surfaces to form at
least one first cube corner disposed in a first orientation and the
sixth groove surface intersecting substantially orthogonally with
the third and fourth groove surfaces to form at least one second
cube corner disposed in a second orientation different than the
first orientation.
[0019] In one embodiment of such mold assembly, the first groove
set extends substantially entirely across the respective first
major surfaces of the plurality of laminae and the second groove
set extends substantially entirely across the respective second
major surfaces of the plurality of laminae. Additionally, the first
and second groove sets are formed such that their respective
reference edges extend along axes that, in a top plan view, are
perpendicular to the respective first reference planes. Finally,
the third groove set comprises a single groove in each respective
lamina having a vertex that extends along an axis parallel to the
respective lamina's third reference plane. According to this
embodiment, each respective lamina comprises a first row of cube
corner elements defined by the grooves of the first groove set and
the third groove and a second row of cube corner elements defined
by the grooves of the second groove set and the third groove.
[0020] Also disclosed is a method of manufacturing a plurality of
laminae for use in a mold suitable for use in forming
retroreflective cube corner articles, each lamina having opposing
first and second major surfaces defining therebetween a first
reference plane, each lamina further including a working surface
connecting the first and second major surfaces, the working surface
defining a second reference plane substantially parallel to the
working surface and perpendicular to the first reference plane and
a third reference plane perpendicular to the first reference plane
and the second reference plane. The method includes: (a) orienting
a plurality of laminae to have their respective first reference
planes parallel to each other and disposed at a first angle
relative to a fixed reference axis; (b) forming a first groove set
including at least two parallel adjacent V-shaped grooves in the
working surface of each of the laminae, each of the adjacent
grooves defining a first groove surface and a second groove surface
that intersect substantially orthogonally to form a first reference
edge on each of the respective laminae; (c) orienting the plurality
of laminae to have their respective first reference planes parallel
to each other and disposed at a second angle relative to the fixed
reference axis; (d) forming a second groove set including at least
two parallel adjacent V-shaped grooves in the working surface of
each of the laminae, each of the adjacent grooves defining a third
groove surface and a fourth groove surface that intersect
substantially orthogonally to form a second reference edge on each
of the respective laminae; and (e) forming a third groove set
including at least one groove in the working surface of a plurality
of the laminae, each groove defining a fifth groove surface and a
sixth groove surface, the fifth groove surface intersecting
substantially orthogonally with the first and second groove
surfaces to form at least one first cube corner disposed in a first
orientation and the sixth groove surface intersecting substantially
orthogonally with the third and fourth groove surfaces to form at
least one second cube corner disposed in a second orientation
different than the first orientation.
[0021] In one disclosed method, the plurality of laminae are
assembled in a suitable fixture that defines a base plane. The
fixture secures the laminae such that their respective first
reference planes are substantially parallel and are disposed at a
first angle that preferably measures between about 1.degree. and
about 85.degree., and more preferably measures between about
10.degree. and about 60.degree. relative to a fixed reference axis
that is a normal vector to the base plane. The first groove set is
then formed by removing portions of each of the plurality of lamina
proximate the working surface of the plurality of laminae by using
a suitable material removal technique such as, for example, ruling,
fly-cutting, grinding, or milling. The plurality of laminae are
then reassembled in the fixture and secured such that their
respective first reference planes are substantially parallel and
are disposed at a second angle that preferably measures between
about 1.degree. and about 85.degree., and more preferably measures
between about 10.degree. and about 60.degree. relative to a fixed
reference axis that is a normal vector to the base plane. The
second groove set is then formed using suitable material removal
techniques as describe above. The plurality of laminae are then
reassembled in the fixture and secured such that their respective
first reference planes are substantially parallel to the reference
axis. The third groove set is then formed using suitable material
removal techniques as describe above. Preferably, the third groove
set defines a single groove in each respective lamina.
BRIEF DESCRIPTION OF THE DRAWINGS
[0022] FIG. 1 is a perspective view of a single lamina suitable for
use in the disclosed methods.
[0023] FIG. 2 is an end view of a single lamina following a first
machining step.
[0024] FIG. 3 is a side view of a single lamina following a first
machining step.
[0025] FIG. 4 is a top view of a single lamina following a first
machining step.
[0026] FIG. 5 is an end view of a single lamina following a second
machining step.
[0027] FIG. 6 is a side view of a single lamina following a second
machining step.
[0028] FIG. 7 is a top view of a single lamina following a second
machining step.
[0029] FIG. 8 is a perspective view of a single lamina following a
second machining step.
[0030] FIG. 9 is an end view of a single lamina following a third
machining step.
[0031] FIG. 10 is a side view of a single lamina following a third
machining step.
[0032] FIG. 11 is a top view of a single lamina following a third
machining step.
[0033] FIG. 12 is a perspective view of a single lamina following a
third machining step.
[0034] FIG. 13 is a top view of an alternate embodiment of a single
lamina following a third machining step.
[0035] FIG. 14 is an end view of an alternate embodiment of a
single lamina following a third machining step.
[0036] FIG. 15 is a side view of an alternate embodiment of a
single lamina following a third machining step.
[0037] FIG. 16 is a perspective view of a plurality of laminae.
[0038] FIG. 17 is an end view of the plurality of laminae oriented
in a first orientation.
[0039] FIG. 18 is an end view of the plurality of laminae following
a first machining operation.
[0040] FIG. 19 is a side view of the plurality of laminae following
a first machining operation.
[0041] FIG. 20 is an end view of the plurality of laminae oriented
in a second orientation.
[0042] FIG. 21 is an end view of the plurality of laminae following
a second machining operation.
[0043] FIG. 22 is a side view of the plurality of laminae following
a second machining operation.
[0044] FIG. 23 is an end view of the plurality of laminae following
a third machining operation.
[0045] FIG. 24 is a top view of the plurality of laminae following
a third machining operation.
[0046] FIG. 25 is a top plan view of a portion of the working
surface of a single lamina.
[0047] FIG. 26 is a side elevation view of the working surface
depicted in FIG. 25.
[0048] FIG. 27 is a side elevation view of the working surface
depicted in FIG. 25.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0049] In describing various embodiments, specific terminology will
be used for the sake of clarity. Such terminology is not, however,
intended to be limiting and it is to be understood that each term
so selected includes all technical equivalents that function
similarly. Related applications filed on the same date herewith
include: Retroreflective Cube Corner Sheeting Mold and Sheeting
Formed Therefrom (U.S. Ser. No. 08/886,998 filed Jul. 2, 1997 now
U.S. Pat. No. 5,981,032); Retroreflective Cube Corner Sheeting,
Molds Therefore, and Methods of Making the Same (U.S. Ser. No.
08/887,390 filed Jul. 2, 1997); Tiled Retroreflective Sheeting
Composed of Highly Canted Cube Corner Elements (U.S. Ser. No.
08/887,389 filed Jul. 2, 1997 now U.S. Pat. No. 5,989,523);
Retroreflective Cube Corner Sheeting Mold and Method of Making the
Same (U.S. Ser. No. 08/887,084 filed Jul. 2, 1997); and Dual
Orientation Retroreflective Sheeting (U.S. Ser. No. 08/887,006
filed Jul. 2, 1997 now U.S. Pat. No. 5,936,770).
[0050] The disclosed embodiments can utilize full cube corner
elements of a variety of sizes and shapes. The base edges of
adjacent full cube corner elements in an array are not all in the
same plane. By contrast, the base edges of adjacent truncated cube
corner elements in an array are typically coplanar. Full cube
corner elements have a higher total light return than truncated
cube corner elements for a given amount of cant, but the full cubes
lose total light return more rapidly at higher entrance angles. One
benefit of full cube corner elements is higher total light return
at low entrance angles, without too large of a loss in performance
at higher entrance angles.
[0051] Predicted total light return (TLR) for a cube corner matched
pair array can be calculated from a knowledge of percent active
area and ray intensity. Ray intensity may be reduced by front
surface losses and by reflection from each of the three cube corner
surfaces for a retroreflected ray. Total light return is defined as
the product of percent active area and ray intensity, or a
percentage of the total incident light which is retroreflected. A
discussion of total light return for directly machined cube corner
arrays is presented in U.S. Pat. No. 3,712,706 (Stamm).
[0052] One embodiment of a lamina, as well as a method of making
the same, will now be described with reference to FIGS. 1-12. FIGS.
1-2 depict a representative lamina 10 useful in the manufacture of
a mold suitable for forming retroreflective sheeting. Lamina 10
includes a first major surface 12 and an opposing second major
surface 14. Lamina 10 further includes a working surface 16 and an
opposing bottom surface 18 extending between first major surface 12
and second major surface 14. Lamina 10 further includes a first end
surface 20 and an opposing second end surface 22. In a preferred
embodiment, lamina 10 is a right rectangular polyhedron wherein
opposing surfaces are substantially parallel. However, it will be
appreciated that opposing surfaces of lamina 10 need not be
parallel.
[0053] For purposes of description, lamina 10 can be characterized
in three dimensional space by superimposing a Cartesian coordinate
system onto its structure. A first reference plane 24 is centered
between major surfaces 12 and 14. First reference plane 24,
referred to as the x-z plane, has the y-axis as its normal vector.
A second reference plane 26, referred to as the x-y plane, extends
substantially coplanar with working surface 16 of lamina 10 and has
the z-axis as its normal vector. A third reference plane 28,
referred to as the y-z plane, is centered between first end surface
20 and second end surface 22 and has the x-axis as its normal
vector. For the sake of clarity, various geometric attributes of
the present embodiments will be described with reference to the
Cartesian reference planes as set forth herein. However, it will be
appreciated that such geometric attributes can be described using
other coordinate systems or with reference to the structure of the
lamina.
[0054] FIGS. 2-12 illustrate the formation of a structured surface
comprising a plurality of optically opposing cube corner elements
in the working surface 16 of lamina 10. In brief, according to a
preferred embodiment a first groove set comprising at least two
parallel, adjacent grooves 30a, 30b, 30c, etc. (collectively
referred to as 30) is formed in the working surface 16 of lamina 10
(FIGS. 2-4). A second groove set comprising at least two parallel,
adjacent grooves 38a, 38b, 38c, etc. (collectively referred to as
38) is also formed in the working surface 16 of lamina 10 (FIGS.
5-7). Preferably, the first and second groove sets intersect
approximately along a first reference plane 24 to form a structured
surface including a plurality of alternating peaks and v-shaped
valleys (FIG. 8). It is not necessary for the groove sets 30, 38 to
be aligned, as illustrated in FIG. 8. Alternatively, the peaks and
v-shaped valleys can be off-set with respect to each other, such as
illustrated in FIG. 13.
[0055] A third groove 46 is then formed in the working surface 16
of lamina 10 (FIGS. 9-11). Preferably, third groove 46 extends
along an axis approximately perpendicular to the direction in which
the first and second groove sets were formed. Formation of third
groove 46 results in a structured surface that includes a plurality
of cube corner elements having three mutually perpendicular optical
faces on the lamina (FIG. 12). As used herein, the term `groove
set` refers to all parallel grooves formed in working surface 16 of
the lamina 10.
[0056] The embodiments will now be explained in greater detail.
Referring to FIGS. 2-4, a first groove set comprising at least two
parallel, adjacent grooves 30a, 30b, 30c, etc. (collectively
referred to by the reference numeral 30) is formed in the working
surface 16 of lamina 10. The grooves define first groove surfaces
32a, 32b, 32c, etc. (collectively referred to as 32) and second
groove surfaces 34b, 34c, 34d, etc. (collectively referred to as
34) that intersect at groove vertices 33b, 33c, 33d, etc.
(collectively referred to as 33). At the edge of the lamina, the
groove forming operation may form a single groove surface 32a.
Groove surfaces 32a and 34b of adjacent grooves intersect
approximately orthogonally along a reference edge 36a. As used
herein, the terms `substantially orthogonally` or `approximately
orthogonally` shall mean that the dihedral angle between the
respective surfaces measures approximately 90.degree.; slight
variations in orthogonality as disclosed and claimed in U.S. Pat.
No. 4,775,219 to Appeldorn are contemplated. Similarly, adjacent
groove surfaces 32b and 34c intersect approximately orthogonally
along first reference edge 36b. Preferably this pattern is repeated
across the entire working surface 16 of lamina 10 as illustrated in
FIGS. 3-4. The respective groove vertices 33 are preferably
separated by a distance that measures between about 0.01
millimeters and about 1.0 millimeters.
[0057] In the embodiment of FIG. 2, the grooves 30 are formed such
that the respective groove vertices 33 and the respective first
reference edges 36 extend along an axis that intersects the first
major surface 12 and the working surface 16 of lamina 10. In this
embodiment, the working surface 16 of the lamina 10 includes a
portion which remains unaltered by the formation of the plurality
of grooves 30. It will be appreciated that the grooves can also be
formed such that the respective groove vertices 33 and first
reference edges 36 extend along an axis that intersects the first
major surface 12 and the second major surface 14 of lamina 10 by
forming the grooves deeper into the working surface 16.
Additionally, in the embodiment of FIGS. 2-4 the grooves 30 are
formed such that each of the first reference edges 36 are disposed
in planes that intersect the first reference plane 24 and the
second reference plane 26 at orthogonal angles such that, in the
top view of FIG. 4, the reference edges 36 appear perpendicular to
reference plane 24.
[0058] In the embodiment of FIGS. 2-4, the grooves 30 are formed
such that the first reference edges 36 are all disposed in a common
plane that intersects the second reference plane 26 at an acute
angle .theta..sub.1 of approximately 27.8.degree.. Grooves 30 can
alternately be formed such that the reference edges 36 intersect
reference plane 26 at angles different than 27.8.degree.. In
general, it is feasible to form grooves such that the respective
reference edges 36 intersect reference planes 26 at any angle
between about 1.degree. and about 85.degree., and more preferably
between about 10.degree. and about 60.degree..
[0059] Referring now to FIGS. 5-8, a second groove set comprising
at least two parallel, adjacent grooves 38a, 38b, 38c, etc.
(collectively referred to as 38) is formed in the working surface
16 of lamina 10. Grooves 38 define third groove surfaces 40a, 40b,
40c, etc. (collectively referred to as 40) and fourth groove
surfaces 42b, 42c, 42d, etc. (collectively referred to as 42) that
intersect at groove vertices 41b, 41c, 41d, etc. (collectively
referred to as 41) as shown. At the edge of the lamina, the groove
forming operation may form a single groove surface 40a. Groove
surfaces 40a and 42b of adjacent grooves intersect approximately
orthogonally along a reference edge 44a, which, for the purposes of
the present disclosure, means that the dihedral angle between
surfaces 40a and 42b is approximately 90.degree.. Similarly,
adjacent groove surfaces 40b and 42c intersect approximately
orthogonally along a second reference edge 44b. Preferably this
pattern is repeated across the entire working surface 16 of lamina
10. Groove vertices 41 are preferably spaced apart by between about
0.01 millimeters and 0.10 millimeters.
[0060] Referring particularly to FIG. 5 it can be seen that the
grooves 38 are formed such that the reference edges 44 extend along
an axis that intersects the second major surface 14 and the working
surface 16 of lamina 10. In this embodiment, the reference edges 44
(and groove vertices 41) intersect the second reference plane 26 of
lamina 10 at an acute angle .theta..sub.2 that measures
approximately 27.8.degree.. As discussed above, it is feasible to
form grooves that intersect reference plane 26 at any angle between
about 1.degree. and 85.degree..
[0061] In the embodiment of FIGS. 5-8, grooves 38 are formed such
that the respective reference edges 44 are disposed in planes that
intersect the first reference plane 24 and second reference plane
26 at orthogonal angles such that, in the top view of FIG. 7,
reference edges 44 appear perpendicular to first reference plane
24. Additionally, referring particularly to FIG. 7, grooves 38 are
preferably formed such that the groove vertices 41 are
substantially coplanar with groove vertices 33, and the reference
edges 44 are substantially coplanar with reference edges 36.
Alternatively, groove vertices 33, 41 and reference edges 36, 44
can be shifted with respect to each other. In another alternate
embodiment, the depth of the groove vertices 33, 41 can vary with
respect to one another.
[0062] FIG. 8 presents a perspective view of a representative
lamina 10 upon completion of forming the grooves 38. Lamina 10
includes a series of grooves 30, 38 formed in the working surface
16 thereof as described above. The reference edges 36, 44 intersect
approximately along the first reference plane 24 to define a
plurality of peaks. Similarly, groove vertices 33, 41 intersect
approximately along the first reference plane to define a plurality
of valleys between the peaks.
[0063] FIGS. 9-12 illustrate an embodiment of lamina 10 following
formation of a third groove 46 in lamina 10. In this embodiment
third groove 46 defines a fifth groove surface 48 and a sixth
groove surface 50 that intersect at a groove vertex 52 along an
axis that is contained by the first reference plane 24.
Importantly, third groove 46 is formed such that fifth groove
surface 48 is disposed in a plane that is substantially orthogonal
to the first groove surfaces 32 and the second groove surfaces 34.
This can be accomplished by forming third groove 46 such that fifth
groove surface 48 forms an angle equal to angle .theta..sub.1 with
first reference plane 24; sixth groove surface likewise preferably
forms an angle equal to angle .theta..sub.2 with first reference
plane 24, where .theta..sub.1 and .theta..sub.2 are the same
.theta..sub.1 and .theta..sub.2 illustrated in FIG. 5. Formation of
the fifth groove surface 48 yields a plurality of cube corner
elements 60a, 60b, etc. (collectively referred to as 60) in working
surface 16 of lamina 10. Each cube corner element 60 is defined by
a first groove surface 32, a second groove surface 34, and a
portion of fifth groove surface 48 that mutually intersect at a
point to define a cube corner peak, or apex 62. Similarly, sixth
groove surface 50 is disposed in a plane that is substantially
orthogonal to the third groove surfaces 40 and the fourth groove
surfaces 42 that mutually intersect at a point to define a cube
corner peak, or apex 72. Formation of the sixth groove surface 50
also yields a plurality of cube corner elements 70a, 70b, etc.
(collectively referred to as 70) in working surface 16 of lamina
10. Each cube corner element 70 is defined by a third groove
surface 40, a fourth groove surface 42 and a portion of sixth
groove surface 50. Preferably, both fifth groove surface 48 and
sixth groove surface 50 form a plurality of cube corner elements on
the working surface 16 of lamina 10. However, it will be
appreciated that third groove 46 can be formed such that only the
fifth groove surface 48 or the sixth groove surface 50 forms cube
corner elements.
[0064] Referring particularly to FIGS. 11 and 12, various features
of lamina 10 will be discussed. In the disclosed embodiment, the
dihedral angle defined by opposing surfaces of grooves 30 and 38
measures 90.degree.. The first and second reference edges 36, 44
are disposed in planes that intersect the first reference plane 24
at an orthogonal angle and that intersect the second reference
plane 26 at an orthogonal angle. Thus, in the plan view of FIG. 11,
the reference edges 36 and 44 extend along axes that are
substantially perpendicular to first reference plane 24. Reference
edges 36 extend along axes that intersect the first major surface
12 of lamina 10 and that intersect the second reference plane 26 at
an acute angle of approximately 27.8.degree.. Reference edges 44
likewise extend along axes that intersect the second major surface
14 of lamina 10 and that intersect the second reference plane 26 at
an acute angle of approximately 27.8.degree.. The vertex of third
groove 46 extends along an axis that is substantially parallel to
first reference plane 24 and the dihedral angle between fifth
groove surface 48 and sixth groove surface 50 is approximately
55.6.degree..
[0065] Preferably, working surface 16 is formed using conventional
precision machining tooling and techniques such as, for example,
ruling, milling, grooving, and fly-cutting. In one embodiment
second major surface 14 of lamina 10 can be registered to a
substantially planar surface such as the surface of a precision
machining tool and each groove 30a, 30b, etc. of the first groove
set can be formed in working surface 16 by moving a V-shaped
cutting tool having an included angle of 90.degree. along an axis
that intersects the first working surface 12 and the second
reference plane 26 at an angle .theta..sub.1 of 27.8.degree.. In
the disclosed embodiment each groove 30 is formed at the same depth
in the working surface and the cutting tool is moved laterally by
the same distance between adjacent grooves such that grooves are
substantially identical. Next, first major surface 12 of lamina 10
can be registered to the planar surface and each groove 38a, 38b,
etc. can be formed in working surface 16 by moving a V-shaped
cutting tool having an included angle of 90.degree. along an axis
that intersects the second working surface 14 and the second
reference plane 26 at an angle .theta..sub.2 of 27.8.degree..
Finally, bottom surface 18 of lamina 10 can be registered to the
planar surface and third groove 46 may be formed in working surface
16 by moving a V-shaped cutting tool having an included angle of
55.6.degree. along an axis substantially parallel with base surface
18 and contained by first reference plane 24. While the three
groove forming steps have been recited in a particular order, one
of ordinary skill in the art will recognize that the order of the
steps is not critical; the steps can be practiced in any order.
Additionally, one of ordinary skill in the art will recognize that
the three groove sets can be formed with the lamina registered in
one position; the present disclosure contemplates such a method.
Furthermore, the particular mechanism for securing the lamina,
whether physical, chemical, or electromagnetic, is not
critical.
[0066] To form a mold suitable for use in forming retroreflective
articles, a plurality of laminae 10 having a working surface 16
that includes cube corner elements 60, 70 formed as described above
can be assembled together in a suitable fixture. Working surface 16
is then replicated using precision replication techniques such as,
for example, nickel electroplating to form a negative copy of
working surface 16. Electroplating techniques are known to one of
ordinary skill in the retroreflective arts. See e.g. U.S. Pat. Nos.
4,478,769 and 5,156,863 to Pricone et al. The negative copy of
working surface 16 can then be used as a mold for forming
retroreflective articles having a positive copy of working surface
16. More commonly, additional generations of electroformed replicas
are formed and assembled together into a larger mold. It will be
noted that the original working surfaces 16 of the lamina 10, or
positive copies thereof, can also be used as an embossing tool to
form retroreflective articles. See, JP 8-309851 and U.S. Pat. No.
4,601,861 (Pricone). Those of ordinary skill will recognize that
the working surface 16 of each lamina 10 functions independently as
a retroreflector. Thus, adjacent lamina in the mold need not be
positioned at precise angles or distances relative to one
another.
[0067] FIGS. 16-24 present another method for forming a plurality
of laminae suitable for use in a mold suitable for forming
retroreflective articles. In the embodiment of FIGS. 16-24, a
plurality of cube corner elements are formed in the working
surfaces of a plurality of laminae while the laminae are held
together in an assembly, rather than individually, as described
above. The plurality of laminae 10 are preferably assembled such
that their working surfaces 16 are substantially co-planar. In
brief, the laminae 10 are oriented such that their respective first
reference planes are disposed at a first angle, .beta..sub.1,
relative to a fixed reference axis 82 (FIG. 17). A first groove set
including at least two V-shaped grooves is formed in the working
surface 16 of the plurality of laminae 10 (FIGS. 18-19). The
laminae are then oriented such that their respective first
reference planes are disposed at a second angle, .beta..sub.2,
relative to the reference axis 82 (FIG. 20). A second groove set
including at least two V-shaped grooves is formed in the working
surface 16 of the plurality of laminae 10 (FIGS. 21-22). A third
groove set that preferably includes at least one V-shaped groove in
the working surface 16 of each lamina 10 is also formed (FIG. 23).
Formation of the third groove set results in a structured surface
that includes a plurality of cube corner elements on the working
surface of the plurality of laminae 10 (FIG. 24).
[0068] FIGS. 16-24 will now be described in greater detail. In FIG.
16, a plurality of thin laminae 10 are assembled together such that
the first major surface 12 of one lamina 10 is adjacent the second
major surface 14 of an adjacent lamina 10. Preferably, the laminae
10 are assembled in a conventional fixture capable of securing the
plurality of laminae adjacent one another. Details of the fixture
are not critical. However, the fixture defines a base plane 80
which is preferably substantially parallel to the bottom surfaces
18 of the laminae 10 when the laminae 10 are positioned as depicted
in FIG. 16. The plurality of laminae 10 can be characterized by a
Cartesian coordinate system as described above. Preferably, the
working surfaces 16 of the plurality of laminae 10 are
substantially coplanar when the laminae are positioned with their
respective first reference planes 24 perpendicular to base plane
80.
[0069] In FIG. 17, the laminae 10 are oriented to have their
respective first reference planes 24 disposed at a first angle
.beta..sub.1, from a fixed reference axis 82 normal to base plane
80. In one embodiment, .beta..sub.1 is approximately 27.8.degree..
However, .beta..sub.1 can alternately be between about 1.degree.
and about 85.degree., but more preferably is between about
10.degree. and about 60.degree..
[0070] Referring to FIGS. 18-19, a first groove set comprising a
plurality of parallel adjacent V-shaped grooves 30a, 30b, 30c, etc.
(collectively referred to as 30) is formed in the working surfaces
16 of the plurality of laminae 10 with the lamina disposed at angle
.beta..sub.1. At least two adjacent grooves 30 are formed in
working surface 16 of the plurality of laminae 10. The grooves 30
define first groove surfaces 32a, 32b, 32c, etc. (collectively
referred to as 32) and second groove surfaces 34b, 34c, 34d, etc.
(collectively referred to as 34) that intersect at groove vertices
33b, 33c, 33d, etc. (collectively referred to as 33) as shown. At
the edge of the lamina, the groove forming operation may form a
single groove surface 32a. Significantly, groove surfaces 32a and
34b of adjacent grooves intersect approximately orthogonally along
a reference edge 36a. Similarly, adjacent groove surfaces 32b and
34c intersect approximately orthogonally along reference edge 36b.
Preferably this pattern is repeated across the entire working
surfaces 16 of the laminae 10.
[0071] The grooves 30 can be formed by removing portions of working
surface 16 of the plurality of laminae using a wide variety of
material removal techniques including precision machining
techniques such as milling, ruling, grooving and fly-cutting, as
well as chemical etching or laser ablation techniques. In one
embodiment, the grooves 30 are formed in a high-precision machining
operation in which a diamond cutting tool having a 90.degree.
included angle repeatedly moves transversely across the working
surfaces 16 of the plurality of laminae 10 along an axis that is
substantially parallel to base plane 80. The diamond cutting tool
can alternately move along an axis that is non-parallel to base
plane 80 such that the tool cuts at a varying depth across the
plurality of laminae 10. It will also be appreciated that the
machining tool can be held stationary while the plurality of
laminae are placed in motion; any relative motion between the
laminae 10 and the machining tool is contemplated.
[0072] In the embodiment of FIGS. 18-19, the grooves 30 are formed
at a depth such that the respective first reference edges 36
intersect the first major surface 12 and the second major surface
14 of each lamina. Thus, in the end view depicted in FIG. 18, the
reference edges 36 and groove vertices 33 form substantially
continuous lines that extend along an axis parallel to base plane
80. Further, grooves 30 are formed such that the reference edges 36
are disposed in a plane that intersects the respective first
reference planes 24 and the second reference plane 26 at orthogonal
angles. Thus, in a top plan view analogous to FIG. 4, the first
reference edges 36 would appear perpendicular to the respective
first reference planes 24. However, the grooves 30 can also be
formed at lesser depths, as depicted in FIGS. 2-4, or along
different axes.
[0073] In FIG. 20, the laminae 10 are next oriented to have their
respective first reference planes 24 disposed at a second angle
.beta..sub.2, from fixed reference axis 82 normal to base plane 80.
In one embodiment, .beta..sub.2 is approximately 27.8.degree..
However, .beta..sub.2 can alternately be between about 1.degree.
and about 85.degree., and preferably between about 10.degree. and
about 60.degree.. The angle .beta..sub.2 is independent of angle PI
and need not be equal to PI. To orient the plurality of laminae 10
at angle .beta..sub.2, the laminae 10 are preferably removed from
the fixture and reassembled with their respective first reference
planes disposed at angle .beta..sub.2.
[0074] In FIGS. 21-22, a second groove set comprising a plurality
of parallel adjacent V-shaped grooves 38b, 38c, etc. (collectively
referred to as 38) is formed in the working surfaces 16 of the
laminae 10 with the laminae disposed at angle .beta..sub.2. At
least two adjacent grooves 38 are formed in working surface 16 of
the plurality of laminae 10. The grooves 38 define third groove
surfaces 40a, 40b, 40c, etc. (collectively referred to as 40) and
fourth groove surfaces 42b, 42c, 42d, etc. (collectively referred
to as 42) that intersect at groove vertices 41b, 41c, 41d, etc.
(collectively referred to as 41) as shown. At the edge of the
lamina, the groove forming operation may form a single groove
surface 40a. Significantly, the groove surfaces 40a and 42b of
adjacent grooves intersect approximately orthogonally along a
reference edge 44a. Groove surfaces 40b and 42c likewise intersect
approximately orthogonally along reference edge 44b. Preferably
this pattern is repeated across the entire working surfaces 16 of
the plurality of laminae 10.
[0075] Grooves 38 are also preferably formed by a high-precision
machining operation in which a diamond cutting tool having a
90.degree. included angle is repeatedly moved transversely across
the working surfaces 16 of the plurality of laminae 10 along a
cutting axis that is substantially parallel to base plane 80. It is
important that the surfaces of adjacent grooves 38 intersect along
the reference edges 44 to form orthogonal dihedral angles. The
included angle of each groove can measure other than 90.degree., as
will be discussed in connection with FIG. 15. Grooves 38 are
preferably formed at approximately the same depth in working
surface 16 of the plurality of laminae 10 as grooves 30 in first
groove set. Additionally, the grooves 38 are preferably formed such
that the groove vertices 41 are substantially coplanar with groove
vertices 33, and the reference edges 44 are substantially coplanar
with reference edges 36. After forming the grooves 38, each lamina
10 preferably appears as shown in FIG. 8.
[0076] In FIGS. 23-24, a third groove set that preferably includes
at least one groove 46 in each lamina 10 is formed in the working
surface 16 of the plurality of laminae 10. In the disclosed
embodiment the third grooves 46a, 46b, 46c, etc. (collectively
referred to as 46) define fifth groove surfaces 48a, 48b, 48c, etc.
(collectively referred to as 48) and sixth groove surfaces 50a,
50b, 50c, etc. (collectively referred to as 50) that intersect at
groove vertices 52a, 52b, 52c, etc. (collectively referred to as
52) along axes that are parallel to the respective first reference
planes 24. Significantly, the third grooves 46 are formed such that
respective fifth groove surfaces 48 are disposed in a plane that is
substantially orthogonal to the respective first groove surfaces 32
and the respective second groove surfaces 34. Formation of the
fifth groove surfaces 48 yields a plurality of cube corner elements
60a, 60b, etc. (collectively referred to as 60) in working surface
16 of the respective laminae 10.
[0077] Each cube corner element 60 is defined by a first groove
surface 32, a second groove surface 34 and a portion of a fifth
groove surface 48 that mutually intersect at a point to define a
cube corner peak, or apex 62. Similarly, sixth groove surface 50 is
disposed in a plane that is substantially orthogonal to the third
groove surfaces 40 and the fourth groove surfaces 42. Formation of
the sixth groove surface 50 also yields a plurality of cube corner
elements 70a, 70b, etc. (collectively referred to as 70) in working
surface 16 of laminae 10. Each cube corner element 70 is defined by
a third groove surface 40, a fourth groove surface 42 and a portion
of sixth groove surface 50 that mutually intersect at a point to
define a cube corner peak, or apex 72. Preferably, both fifth
groove surface 48 and sixth groove surface 50 form a plurality of
cube corner elements on the working surface 16 of lamina 10.
However, third groove 46 could alternately be formed such that only
fifth groove surface 48 or sixth groove surface 50 forms cube
corner elements.
[0078] The three mutually perpendicular optical faces 32, 40, 48
and 34, 42, 50 of each cube corner element 60, 70, respectively,
are preferably formed on a single lamina. All three optical faces
are preferably formed by the machining process to ensure optical
quality surfaces. A planar interface 12, 14 is preferably
maintained between adjacent laminae during the machining phase and
subsequent thereto so as to minimize alignment problems and damage
due to handling of the laminae.
[0079] In a preferred method the plurality of laminae 10 are
re-oriented to have their respective first reference planes 24
disposed approximately parallel to reference axis 82 before forming
the plurality of grooves 46. However, the grooves 46 can be formed
with the lamina oriented such that their respective first reference
planes are angled relative to reference axis 82. In particular, in
some embodiments it may be advantageous to form the respective
third grooves 46 with the respective lamina 10 disposed at angle
.beta..sub.2 to avoid an additional orientation step in the
manufacturing process. Preferably, grooves 46 are also formed by a
high precision machining operation. In the disclosed embodiment a
diamond cutting tool having an included angle of 55.6.degree. is
moved across the working surface 16 of each lamina 10 along an axis
that is substantially contained by the first reference plane 24 of
the lamina 10 and that is parallel to base plane 80. Grooves 46 are
preferably formed such that the respective groove vertices 52 are
slightly deeper than the vertices of the grooves in the first and
second groove sets. Formation of grooves 46 result in a plurality
of laminae 10 having a structured surface substantially as depicted
in FIG. 12.
[0080] Working surface 16 exhibits several desirable
characteristics as a retroreflector. The cube corner element
geometry formed in working surface 16 of lamina 10 can be
characterized as a `full` or `high efficiency` cube corner element
geometry because the geometry exhibits a maximum effective aperture
that approaches 100%. Thus, a retroreflector formed as a replica of
working surface 16 will exhibit high optical efficiency in response
to light incident on the retroreflector approximately along the
symmetry axes of the cube corner elements. Additionally, cube
corner elements 60 and 70 are disposed in opposing orientations and
are symmetrical with respect to first reference plane 24 and will
exhibit symmetric retroreflective performance in response to light
incident on the retroreflector at high entrance angles. It is not
required, however, that the cube corner elements be symmetrical
about the reference planes.
[0081] In the embodiments presented in FIGS. 1-12 and 16-24 the
laminae were formed using consistent groove spacing, depths and
tool angles to produce a working surface wherein the cube corner
elements are substantially identical. However, these factors can be
varied to produce a working surface having cube corner elements of
different sizes, shapes and orientations. FIGS. 13-15 illustrate
exemplary alternate embodiments lamina manufactured within the
scope of the present disclosure.
[0082] FIG. 13 shows a lamina 110 that includes an array of cube
corner elements 160a, 160b, 160c, etc. (collectively referred to as
160) disposed in a first orientation and an array of cube corner
elements 170a, 170b, 170c, etc. (collectively referred to as 170)
disposed in a second orientation. The lamina 110 of FIG. 13 is
characterized by the various groove sets being formed at angles
that are not, in plan view, perpendicular to the reference plane
24. Lamina 110 can be formed either individually or as part of an
assembly, as described above, by forming the first and second
groove sets such that the respective reference edges are disposed
in planes that intersect the third reference plane 28 at an oblique
angle, .phi..sub.1, and that intersect the second reference plane
26 at an orthogonal angle. Similarly, the third groove is formed
along an axis that intersects first reference plane 24 at an
oblique angle, .phi..sub.1. Indeed, in this instance each groove in
the third groove set is formed along an axis intersecting the first
reference plane 24 at oblique angle .phi..sub.1. Additionally, the
cube corner elements 160 are not aligned with the cube corner
elements 170 on the lamina 110. Lamina 110 includes a plurality of
cube corner elements having apertures of varying sizes and shapes.
This variation in aperture size and shape may be desirable to
accomplish certain optical objectives such as, for example, to
enhance the uniformity of the retroreflection pattern of a
retroreflective article formed as a replica of lamina 110.
[0083] FIG. 14 shows a lamina 210 in which the third groove 246 is
formed along an axis 216 that is parallel to but displaced from
first reference plane 24. Additionally, the angles .theta..sub.1
and .theta..sub.2 differ from one another such that the symmetry
axes of the respective opposing cube corner elements 214, 216 are
canted at different angles relative to second reference plane
26.
[0084] FIG. 15 shows a lamina 310 wherein the grooves A.sub.1,
A.sub.2, A.sub.3, A.sub.4, A.sub.5 in the first and/or second
groove sets are formed with tools of varying included angles to
yield a structured surface having a plurality of cube corner
elements 312a, 312b, 312c, 312d, 312e and 312f of varying sizes and
having varying included angles. By way of example, the first and
second groove sets can have grooves whose included angle measures
between about 10.degree. and about 170.degree.. For example, the
grooves A.sub.1, A.sub.4, A.sub.5 can measure 90.degree., while
groove A.sub.2 measures 105.degree. and the groove A.sub.3 measures
75.degree.. Additionally, the respective peaks and vertices of the
cube corner elements 312 are disposed at varying distances from the
bottom surface 318 of the lamina 310. By way of example, the
distance between adjacent reference edges in the first and second
groove sets can measure between about 10 and about 1000
microns.
[0085] Methods described above enable the manufacture of a wide
range of cube corner geometries. The size, orientation, and degree
of canting of the cube corner elements formed on the surface of the
plurality of laminae can be varied. Articles can be manufactured as
replicas of the laminae. The preceding discussion disclosed several
embodiments of cube corner geometries. The following paragraphs
provide a generic description of the angular relationships between
the faces of the cube corner elements such that one of ordinary
skill in the art could produce a wide variety of cube corner
element geometries.
[0086] FIGS. 25-27 present a top plan view and side elevation views
of the working surface of a lamina 410 that has an opposing pair of
cube corner elements 460, 470 formed therein. Lamina 410 can be
characterized in 3-dimensional space by reference planes 424, 426
and 428, as discussed above. For purposes of illustration, cube
corner element 460 can be defined as a unit cube having three
substantially mutually perpendicular optical faces 432, 434, 448.
Optical faces 432 and 434 are formed by opposing surfaces of
parallel grooves 430a and 430b that intersect along a reference
edge 436. Optical face 448 is formed by one surface of groove 446.
Grooves 430a and 430b have respective vertices 433a and 433b that
extend along axes that intersect third reference plane at an
arbitrary angle .phi.. Similarly, groove 446 extends along an axis
that intersects first reference plane at an arbitrary angle .phi..
The angle .phi. corresponds to the degree of angular rotation of
the cube corner element on the surface of the lamina. Subject to
machining limitations, the angle .phi. can range from 0.degree.,
such that the groove sets are formed along axes substantially
coincident with reference planes 424 and 428, to nearly 90.degree..
Preferably, however .phi. is between 0.degree. and 45.degree..
[0087] FIG. 26 presents a side elevation view of unit cube 460
taken along lines 26-26. A reference plane 456 is coincident with
the vertex of groove 446 and is normal to second reference plane
426. Angle .alpha..sub.1 defines the acute angle between cube face
448 and reference plane 456. Groove vertices 433a and 433b are
disposed at an acute angle .theta. relative to second reference
plane 426. FIG. 27 presents a side elevation view of unit cube 460
taken along lines 27-27. Planes 450a and 450b are coincident with
the vertices 433a and 433b, respectively. The angle .alpha..sub.2
defines the acute angle between cube face 432 and reference plane
450a. Similarly, the angle .alpha..sub.3 defines the acute angle
between cube face 434 and reference plane 450b.
[0088] A second Cartesian coordinate system can be established
using the groove vertices that form unit cube 460 as reference
axes. In particular, the x-axis can be established parallel to the
intersection of plane 456 and second reference plane 426, the
y-axis can be established parallel to the intersection of plane
450b and second reference plane 426, and the z-axis extends
perpendicular to second reference plane 426. Adopting this
coordinate system, unit normal vectors N.sub.1, N.sub.2 and N.sub.3
can be defined for the unit cube surfaces 448, 432, and 434,
respectively as follows:
N.sub.1=cos(.alpha..sub.1)j+sin(.alpha..sub.1)k
N.sub.2=cos(.alpha..sub.2)i-sin(.theta.)sin(.alpha..sub.2)j+cos(.theta.)si-
n(.alpha..sub.2)k
N.sub.3=-cos(.alpha..sub.3)i-sin(.theta.)sin(.alpha..sub.3)j+cos(.theta.)s-
in(.alpha..sub.3)k
[0089] Surfaces 432, 434 and 448 must be substantially mutually
perpendicular. Thus, the dot products of the normal vectors equal
zero.
N.sub.1.multidot.N.sub.2=N.sub.2.multidot.N.sub.3=N.sub.1.multidot.N.sub.3-
=0.
[0090] Therefore, the following conditions hold:
.alpha..sub.1=74 ; and
tan(.alpha..sub.2)tan(.alpha..sub.3)=1.
[0091] Any set of angles (.alpha..sub.1, .alpha..sub.2,
.alpha..sub.3 and .theta. meeting this criteria will form
retroreflective cube corner elements. In practice, a manufacturer
of retroreflective cube corner sheeting can select a value for
angle .alpha..sub.1 to orient the optical axis of the cube corner
element at a desired angle relative to the base plane of the
retroreflective sheeting formed as a replica of the mold. As stated
above, the present disclosure contemplates minor deviations from
perfect orthogonality designed to alter the characteristics of the
pattern of retroreflected light.
[0092] The laminae are preferably formed from a dimensionally
stable material capable of holding precision tolerances, such as
machinable plastics (for example, polyethylene teraphthalate,
polymethyl methacrylate, and polycarbonate) or metals (for example,
brass, nickel, copper, or aluminum). The physical dimensions of the
laminae are constrained primarily by machining limitations. The
laminae preferably measure at least 0.1 millimeters in thickness,
between 5.0 and 100.0 millimeters in height, and between 10 and 500
millimeters in width. These measurements are provided for
illustrative purposes only and are not intended to be limiting. By
way of example, the thickness of each lamina can measure between
about 0.025 and about 5.00 millimeters, between about 0.025 and
about 1.00 millimeters, between about 0.1 and about 1.00
millimeters, or between about 0.1 to about 0.6 millimeters.
[0093] In the manufacture of retroreflective articles such as
retroreflective sheeting, the structured surface of the plurality
of laminae is used as a master mold which can be replicated using
electroforming techniques or other conventional replicating
technology. The plurality of laminae can include substantially
identical cube corner elements or may include cube corner elements
of varying sizes, geometries, or orientations. The structured
surface of the replica, referred to in the art as a `stamper`
contains a negative image of the cube corner elements. This replica
can be used as a mold for forming a retroreflector. More commonly,
however, a large number of positive or negative replicas are
assembled to form a mold large enough to be useful in forming
retroreflective sheeting. Retroreflective sheeting can then be
manufactured as an integral material, e.g. by embossing a preformed
sheet with an array of cube corner elements as described above or
by casting a fluid material into a mold. Alternatively, the
retroreflective sheeting can be manufactured as a layered product
by casting the cube corner elements against a preformed film as
taught in PCT application No. WO 95/11464 and U.S. Pat. No.
3,648,348 or by laminating a preformed film to preformed cube
corner elements. By way of example, such sheeting can be made using
a nickel mold formed by electrolytic deposition of nickel onto a
master mold. The electroformed mold can be used as a stamper to
emboss the pattern of the mold onto a polycarbonate film
approximately 500 .mu.m thick having an index of refraction of
about 1.59. The mold can be used in a press with the pressing
performed at a temperature of approximately 175.degree. to
200.degree. C.
[0094] Useful materials for making such reflective sheeting are
preferably materials that are dimensionally stable, durable,
weatherable and readily formable into the desired configuration.
Examples of suitable materials include acrylics, which generally
have an index of refraction of about 1.5, such as Plexiglas resin
from Rohm and Haas; thermoset acrylates and epoxy acrylates,
preferably radiation cured, polycarbonates, which have an index of
refraction of about 1.6; polyethylene-based ionomers (marketed
under the name `SURLYN`); polyesters; and cellulose acetate
butyrates. Generally any optically transmissive material that is
formable, typically under heat and pressure, can be used. Other
suitable materials for forming retroreflective sheeting are
disclosed in U.S. Pat. No. 5,450,235 to Smith et al. The sheeting
can also include colorants, dyes, UV absorbers, or other additives
as needed.
[0095] It is desirable in some circumstances to provide
retroreflective sheeting with a backing layer. A backing layer is
particularly useful for retroreflective sheeting that reflects
light according to the principles of total internal reflection. A
suitable backing layer can be made of any transparent or opaque
material, including colored materials, that can be effectively
engaged with the disclosed retroreflective sheeting. Suitable
backing materials include aluminum sheeting, galvanized steel,
polymeric materials such as polymethyl methacrylates, polyesters,
polyamids, polyvinyl fluorides, polycarbonates, polyvinyl
chlorides, polyurethanes, and a wide variety of laminates made from
these and other materials.
[0096] The backing layer or sheet can be sealed in a grid pattern
or any other configuration suitable to the reflecting elements.
Sealing can be affected by use of a number of methods including
ultrasonic welding, adhesives, or by heat sealing at discrete
locations on the arrays of reflecting elements (see, e.g. U.S. Pat.
No. 3,924,928). Sealing is desirable to inhibit the entry of
contaminants such as soil and/or moisture and to preserve air
spaces adjacent the reflecting surfaces of the cube corner
elements.
[0097] If added strength or toughness is required in the composite,
backing sheets of polycarbonate, polybutryate or fiber-reinforced
plastic can be used. Depending upon the degree of flexibility of
the resulting retroreflective material, the material may be rolled
or cut into strips or other suitable designs. The retroreflective
material can also be backed with an adhesive and a release sheet to
render it useful for application to any substrate without the added
step of applying an adhesive or using other fastening means.
[0098] The cube corner elements disclosed herein can be
individually tailored so as to distribute light retroreflected by
the articles into a desired pattern or divergence profile, as
taught by U.S. Pat. No. 4,775,219. Typically the groove half-angle
error introduced will be less than .+-.20 arc minutes and often
less than .+-.5 arc minutes.
EXAMPLE
[0099] An assembly of approximately 25 laminae measuring 127.0
millimeters in length by 25.4 millimeters in height by 0.508
millimeters in thickness were assembled in a fixture substantially
as depicted in FIG. 16. The laminae were formed from 70/30 brass
and the first and second major surfaces of the plurality of lamina
were polished to a surface roughness of approximately 0.005 to
0.025 microns. Wedge blocks having precisely formed inclined
surfaces disposed at an angle of 27.8.degree. from a reference axis
normal to the base plane of the fixture retain the assembly in a
fixed position such that the respective plurality of laminae have
their first reference planes disposed at an angle of 27.8.degree.
from the reference axis. A first groove set was formed by moving a
diamond machining tool transversely across the plurality of laminae
along axes substantially perpendicular to the major surfaces of the
laminae. The grooves were uniformly formed to a depth of
approximately 0.154 millimeters and the groove vertices were
separated by a distance of approximately 0.308 millimeters.
[0100] The plurality of laminae were then removed from the fixture
and repositioned such that the first reference planes of the
plurality of laminae were disposed at an angle of 27.8.degree. from
the reference axis. A second groove set was formed by moving a
diamond machining tool transversely across the plurality of laminae
along axes substantially perpendicular to the major surfaces of the
laminae. The grooves were uniformly formed to a depth of
approximately 0.154 millimeters and the groove vertices were
separated by a distance of approximately 0.308 millimeters.
Additionally, the grooves were formed along axes substantially
coplanar with the axes of corresponding grooves in the first groove
set.
[0101] The plurality of laminae were again removed from the fixture
and were repositioned such that their respective first reference
planes were substantially perpendicular to the base plane of the
fixture. A third groove set was then formed by moving a diamond
machining tool having a 55.6.degree. included angle along an axis
substantially coincident with the first reference plane of each
lamina in the assembly. These machining steps resulted in a working
surface including the positive image of an array of optically
opposing cube corner elements substantially as depicted in FIG.
24.
[0102] The laminae were then removed from the assembly, cleaned,
and reassembled in a fixture to form a master tooling. A nickel
stamper tool was formed from the surface of the master tooling
using chemical vapor deposition of nickel. The reflection
coefficient of a specular nickel surface for incandescent light is
about 0.62 to about 0.64. The percentage light return was measured
for the nickel stamper arranged at an orientation angle of about
zero and an entrance angle of about -4.degree.. The percentage
light return data was adjusted to correspond to a circular area
with a diameter of about 26.99 millimeters (1.0625 inches). The
incremental and cumulative percentage light return for various
observation angles is set forth in Table 1 below:
1TABLE 1 Incremental Observation Incremental Cumulative Angle
Percentage Percentage 0-0.1 4.764 4.76 0.1-0.2 8.438 13.20 0.2-0.3
3.500 16.70 0.3-0.4 0.639 17.34 0.4-0.5 0.592 17.93 0.5-0.6 0.359
18.29 0.6-0.7 0.259 18.55 0.7-0.8 0.209 18.76 0.8-0.9 0.181 18.9
0.9-1.0 0.167 19.1
[0103] For comparison, the percentage light return was measured for
a nickel stamper tool used to make retroflective sheeting with
truncated cube corner elements according to U.S. Pat. No. 4,588,258
(Hoopman) having a base triangle of about
70.degree.-55.degree.-55.degree.. The stamper tool was arranged at
an orientation angle of about 180.degree. and at an entrance angle
of about -4.degree.. The percentage light return data was for a
circular area with a diameter of about 26.99 millimeters (1.0625
inches). The incremental and cumulative percentage light return for
various observation angles is set forth in Table 2 below:
2TABLE 2 Incremental Observation Incremental Cumulative Angle
Percentage Percentage 0-0.1 1.369 1.369 0.1-0.2 3.115 4.484 0.2-0.3
3.197 7.681 0.3-0.4 0.938 8.618 0.4-0.5 0.911 9.530 0.5-0.6 0.434
9.964 0.6-0.7 0.229 10.193 0.7-0.8 0.143 10.335 0.8-0.9 0.103
10.439 0.9-1.0 0.078 10.517
[0104] All patents and patent applications referred to, including
those disclosed in the background of the invention, are hereby
incorporated by reference. The present invention has now been
described with reference to several embodiments thereof. It will be
apparent to those skilled in the art that many changes can be made
in the embodiments described without departing from the scope of
the invention. Thus, the scope of the present invention should not
be limited to the preferred structures and methods described
herein, but rather by the broad scope of the claims which
follow.
* * * * *