U.S. patent application number 14/317632 was filed with the patent office on 2015-01-01 for coated abrasive article based on a sunflower pattern.
The applicant listed for this patent is Saint-Gobain Abrasifs, Saint-Gobain Abrasives, Inc.. Invention is credited to Anuj SETH.
Application Number | 20150004889 14/317632 |
Document ID | / |
Family ID | 52116043 |
Filed Date | 2015-01-01 |
United States Patent
Application |
20150004889 |
Kind Code |
A1 |
SETH; Anuj |
January 1, 2015 |
COATED ABRASIVE ARTICLE BASED ON A SUNFLOWER PATTERN
Abstract
An abrasive article having a plurality of abrasive areas
arranged in a non-uniform distribution pattern, wherein the pattern
is spiral or phyllotactic, such as a spiral lattice, and in
particular those patterns described by the Vogel model, such as a
sunflower pattern.
Inventors: |
SETH; Anuj; (Northborough,
MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Saint-Gobain Abrasives, Inc.
Saint-Gobain Abrasifs |
Worcester
Conflans-Sainte-Honorine |
MA |
US
FR |
|
|
Family ID: |
52116043 |
Appl. No.: |
14/317632 |
Filed: |
June 27, 2014 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
61840854 |
Jun 28, 2013 |
|
|
|
Current U.S.
Class: |
451/529 ;
451/540; 51/298 |
Current CPC
Class: |
B24D 11/04 20130101;
B24D 11/001 20130101; B24D 7/14 20130101; B24D 2203/00
20130101 |
Class at
Publication: |
451/529 ;
451/540; 51/298 |
International
Class: |
B24D 11/04 20060101
B24D011/04; B24D 18/00 20060101 B24D018/00; B24D 5/14 20060101
B24D005/14 |
Claims
1. An abrasive article comprising: a coated abrasive having a
plurality of abrasive areas arranged in a pattern, wherein the
pattern has a controlled non-uniform distribution, and wherein the
pattern is at least one of a radial pattern, a spiral pattern, a
phyllotactic pattern, an asymmetric pattern, or combinations
thereof.
2. The abrasive article of claim 1, wherein the pattern is a spiral
pattern.
3. The abrasive article of claim 2, wherein the spiral pattern is
one of an Archimedean spiral, a Euler spiral, a Fermat's spiral, a
hyperbolic spiral, a lituus, a logarithmic spiral, a Fibonacci
spiral, a golden spiral, or combinations thereof.
4. The abrasive article of claim 3, wherein the pattern has a
controlled asymmetry.
5. The abrasive article of claim 4, wherein the controlled
asymmetry is an at least partial rotational asymmetry about the
center of the pattern.
6. The abrasive article of claim 5, wherein the rotational
asymmetry extends to at least 51% of the abrasive areas of the
pattern.
7. (canceled)
8. (canceled)
9. The abrasive article of claim 1, wherein the pattern is a
phyllotactic pattern.
10. The abrasive article of claim 9, wherein the pattern is a
spiral phyllotactic pattern.
11. The abrasive article of claim 10, wherein the pattern has a
number of clockwise spirals and a number of counter-clock wise
spirals, wherein the number of clockwise spirals and the number of
counterclockwise spirals are Fibonacci numbers or multiples of
Fibonacci numbers.
12. (canceled)
13. The abrasive article of claim 11, wherein the number of
clockwise spirals and the number of counterclockwise spirals are in
a ratio that converges on the golden ratio.
14. The abrasive article of claim 10, wherein the spiral
phyllotactic pattern has a controlled asymmetry.
15. The abrasive article of claim 10, wherein the spiral
phyllotactic pattern is a sunflower pattern.
16. The abrasive article of claim 11, wherein the pattern is
described in polar co-ordinates by the following equation:
.phi.=n*.alpha.,r=c n (Eq. 1) where: n is the ordering number of an
abrasive area, counting outward from the center of the pattern;
.phi. is the angle between a reference direction and a position
vector of the n.sup.th abrasive area in a polar coordinate system
originating at the center of the pattern, such that the divergence
angle between the position vectors of any two successive abrasive
areas is a constant angle .alpha.; r is the distance from the
center of the pattern to the center of the n.sup.th abrasive area;
and c is a constant scaling factor.
17. The abrasive article of claim 16, wherein at least about 51% of
the abrasive areas conform to Eq.1.
18. The abrasive article of claim 16, wherein the pattern has a
divergence angle in polar co-ordinates that ranges from about
100.degree. to about 170.degree..
19. The abrasive article of claim 16, wherein the pattern has a
divergence angle that is 137.508.degree..
20. (canceled)
21. (canceled)
22. (canceled)
23. (canceled)
24. (canceled)
25. (canceled)
26. (canceled)
27. The abrasive article of claim 16, wherein the pattern has a
total open area of about 15% to about 99.5% of the surface
potential surface area of the abrasive article.
28. The abrasive article of claim 16, having a total abrasive
surface area that ranges from about 4.5% to about 85% of the total
potential surface area.
29. (canceled)
30. (canceled)
31. A coated abrasive article comprising: a backing layer having a
first major side and a second major side; and an abrasive layer
disposed on the first major side of the backing layer, wherein the
abrasive layer comprises a plurality of abrasive areas arranged in
a pattern having a controlled non-uniform distribution, and the
pattern is a phyllotactic pattern.
32. A method of making an abrasive article comprising: disposing an
abrasive layer on a backing; wherein the abrasive layer comprises a
plurality of abrasive areas arranged in a pattern having a
controlled non-uniform distribution that is at least one of a
radial pattern, a spiral pattern, a phyllotactic pattern, an
asymmetric pattern, or combinations thereof.
33. (canceled)
34. (canceled)
35. (canceled)
36. (canceled)
37. (canceled)
38. (canceled)
39. (canceled)
40. (canceled)
41. (canceled)
42. (canceled)
43. (canceled)
44. (canceled)
45. (canceled)
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This application claims priority under 35 U.S.C.
.sctn.119(e) to U.S. Provisional App. No. 61/840,854, entitled
"Coated Abrasive Article Based on a Sunflower Pattern", by Anuj
Seth, filed Jun. 28, 2013, which is assigned to the current
assignee hereof and incorporated herein by reference in its
entirety.
FIELD OF THE DISCLOSURE
[0002] The present disclosure relates generally to abrasives, and
more particularly to coated abrasive articles, having abrasive
portions, whether discrete, continuous, semi-continuous, and
combinations thereof that are based on the pattern of a
sunflower.
BACKGROUND
[0003] Abrasive articles, such as coated abrasive articles, are
used in various industries to abrade work pieces by hand or by
machine processes, such as by lapping, grinding, or polishing.
Machining utilizing abrasive articles spans a wide industrial and
consumer scope from optics industries, automotive paint repair
industries, and metal fabrication industries to construction and
carpentry. Machining, such as by hand or with use of commonly
available tools such as orbital polishers (both random and fixed
axis), and belt and vibratory sanders, is also commonly done by
consumers in household applications. In each of these examples,
abrasives are used to remove surface material and affect the
surface characteristics (e.g., planarity, surface roughness, gloss)
of the abraded surface. Additionally, various types of automated
processing systems have been developed to abrasively process
articles of various compositions and configurations.
[0004] Surface characteristics include, among others, shine,
texture, gloss, surface roughness, and uniformity. In particular,
surface characteristics, such as roughness and gloss, are measured
to determine quality. For example, when coating or painting a
surface certain imperfections or surface defects may occur during
the application or curing process. Such surface imperfections or
surface defects might include pock marks, "orange peel" texture,
"fish eyes", or encapsulated bubble and dust defects. Typically,
such defects in a painted surface are removed by first sanding with
a coarse grain abrasive, followed by subsequently sanding with
progressively finer grain abrasives, and even buffing with wool or
foam pads until a desired smoothness is achieved. Hence, the
properties of the abrasive article used will generally influence
the surface quality.
[0005] In addition to surface characteristics, industries are
sensitive to cost related to abrasive operations. Factors
influencing operational costs include the speed at which a surface
can be prepared and the cost of the materials used to prepare that
surface. Typically, the industry seeks cost effective materials
having high material removal rates.
[0006] However, abrasives that exhibit high removal rates often
exhibit poor performance in achieving desirable surface
characteristics. Conversely, abrasives that produce desirable
surface characteristics often have low material removal rates. For
this reason, preparation of a surface is often a multi-step process
using various grades of abrasive sheets. Typically, surface flaws
(e.g., scratches) introduced by one step are repaired (e.g.,
removed) using progressively finer grain abrasives in one or more
subsequent steps. Therefore, abrasives that introduce scratches and
surface flaws result in increased time, effort, and expenditure of
materials in subsequent processing steps and an overall increase in
total processing costs.
[0007] An additional factor affecting material removal rate and
surface quality is the "loading" of the abrasive with "swarf",
i.e., the material that is abraded from the workpiece surface,
which tends to accumulate on the surface of, and between, the
abrasive particles. Loading is undesirable because it typically
reduces the effectiveness of the abrasive product and can also
negatively affect surface characteristics by increasing the
likelihood of scratching defects.
[0008] Although various efforts have been made to reduce the
accumulation of swarf, such as the introduction of fluids onto the
workpiece surface to wash away swarf, as well as the application of
vacuum systems to carry away swarf as it is generated, there
continues to be a demand for improved, cost effective, abrasive
articles, processes, and systems that promote efficient abrasion
and improved surface characteristics.
BRIEF DESCRIPTION OF THE DRAWINGS
[0009] The present disclosure may be better understood, and its
numerous features and advantages made apparent to those skilled in
the art by referencing the accompanying drawings.
[0010] FIG. 1 is an embodiment of a coated abrasive disc without
any apertures and having a pattern with a controlled non-uniform
distribution of abrasive areas (a.k.a., spots) according to the
present invention.
[0011] FIG. 2 is an illustration of an embodiment of a coated
abrasive having abrasive areas in the form of multiple spiral arms,
the spiral arms passing through points conforming to the Vogel
model.
[0012] FIG. 3 is an illustration of an embodiment of a coated
abrasive disc without any apertures and having abrasive areas
corresponding to a phyllotactic spiral pattern, specifically a type
of spiral lattice, having clockwise and counterclockwise parastichy
according to the present invention.
[0013] FIG. 4 is another illustration of an embodiment of a coated
abrasive disc without any apertures having abrasive areas in the
form of a phyllotactic spiral pattern of clockwise and
counterclockwise parastichy according to the present invention.
[0014] FIG. 5 is an illustration of another embodiment of a coated
abrasive disc having abrasive areas corresponding to a phyllotactic
spiral pattern, specifically a type of spiral lattice, having
clockwise and counterclockwise parastichy in combination with
circular abrasive areas where the parastichy intersect according to
the present invention.
[0015] FIG. 6 is an illustration of the Vogel model for placement
of abrasive areas in accordance with the present invention.
[0016] FIG. 7 is another illustration of the Vogel model in
accordance with the present invention showing a numerical
progression of the placement of the abrasive areas.
[0017] FIG. 8A-8C are illustrations of phyllotactic spiral patterns
for the placement of abrasive areas on a coated abrasive, the
patterns conforming to the Vogel model and that have differing
divergence angles according to the present invention.
[0018] FIG. 9 is an illustration of another embodiment of a coated
abrasive disc having abrasive areas corresponding to a phyllotactic
spiral pattern, specifically a type of spiral lattice, having
clockwise and counterclockwise parastichy in combination with
circular abrasive areas of varying size where the parastichy
intersect according to the present invention.
[0019] FIG. 10 is an illustration of another embodiment of a coated
abrasive disc having abrasive areas corresponding to a phyllotactic
spiral pattern having branched parastichy in combination with
circular abrasive areas of varying size where the parastichy branch
according to the present invention.
[0020] FIG. 11 is an illustration of another embodiment of a coated
abrasive disc having abrasive areas corresponding to a phyllotactic
spiral pattern having branched clock-wise parastichy in combination
with circular abrasive areas of varying size where the parastichy
branch according to the present invention.
[0021] FIG. 12 is an illustration of another embodiment of a coated
abrasive disc having abrasive areas corresponding to a phyllotactic
spiral pattern having branched clock-wise and counter clock-wise
parastichy in combination with circular abrasive areas of varying
size where the parastichy branch according to the present
invention.
[0022] FIG. 13 is an illustration of another embodiment of a coated
abrasive disc having abrasive areas corresponding to a phyllotactic
spiral pattern having branched parastichy in combination with
circular abrasive areas of varying size where the parastichy branch
according to the present invention.
[0023] FIG. 14 is an illustration of another embodiment of a coated
abrasive disc having abrasive areas corresponding to a phyllotactic
spiral pattern having branched parastichy in combination with
circular abrasive areas of varying size where the parastichy branch
according to the present invention.
[0024] FIG. 15 is a graphical image of an embodiment of an abrasive
area pattern having 148 abrasive areas according to the present
invention
[0025] FIG. 16 is an illustration of an embodiment according to the
present invention of an alternate abrasive pattern that is a
transpose of abrasive pattern of FIG. 15
[0026] FIG. 17 is an illustration of an embodiment of abrasive
areas in the form of spirals and arcs based on the pattern of FIG.
16
[0027] FIG. 18 is a graphical image of an exemplary embodiment of
an abrasive area pattern having 344 abrasive areas according to the
present invention
[0028] FIG. 19 is an illustration of an exemplary embodiment
according to the present invention of a transpose of the abrasive
area pattern of FIG. 18
[0029] FIG. 20 is an illustration of an exemplary embodiment
according to the present invention of a back-up pad that is
co-operative with the aperture pattern of FIG. 19
[0030] FIG. 21 is a cross-sectional view of an embodiment of a
coated abrasive according to the present invention.
[0031] The use of the same reference symbols in different drawings
indicates similar or identical items.
DETAILED DESCRIPTION
[0032] In an embodiment, an abrasive article comprises a coated
abrasive having a plurality of abrasive areas arranged in a pattern
having a controlled non-uniform distribution. The pattern can be
any pattern having a controlled non-uniform distribution, including
a radial pattern, a spiral pattern, a phyllotactic pattern, an
asymmetric pattern, or combinations thereof. An example of a
combination pattern is a spiral lattice pattern. The pattern can be
partially, substantially, or fully asymmetric. The pattern can
cover (i.e., be distributed over) the entire abrasive article, can
cover substantially the entire abrasive article (i.e. greater than
50% but less than 100%), can cover multiple portions of the
abrasive article, or can cover only a portion of the abrasive
article.
[0033] A controlled "non-uniform distribution" means that the
pattern has a controlled asymmetry (i.e., a controlled randomness),
such that although the distribution of abrasive areas can be
described by or predicted by, for example, a radial, spiral, or
phyllotactic equation, the pattern still exhibits at least a
partial to complete asymmetry.
[0034] The controlled asymmetry can be a controlled reflection
asymmetry (also called mirror symmetry, line symmetry, and
bilateral symmetry), a controlled rotational asymmetry, a
controlled translational symmetry, controlled glide reflection
symmetry, or combinations of thereof. An example of a non-uniform
distribution can be demonstrated for a radial, spiral, or
phyllotactic pattern having a rotational symmetry of an order of
one, meaning that such a pattern has no rotational symmetry because
the pattern repeats itself only once during a rotation of
360.degree. about its center. In other words, if two copies of the
same exact pattern are placed directly over each other and one copy
is held constant while the second copy is rotated 360.degree. about
its center, all of the abrasive areas of both copies will come into
alignment only once during the 360.degree. rotation.
[0035] Typically, all abrasive areas of a pattern (i.e., the entire
pattern) will possess a controlled asymmetry. However, it is
contemplated that patterns according to the present embodiments
also include patterns where only a portion of the total number of
abrasive areas of the pattern (i.e., a portion of the pattern)
possesses a controlled asymmetry. Such can occur for instance by
combining, or substituting, a portion of a uniformly distributed
pattern, or a completely random pattern, with a pattern having
controlled a controlled non-uniform distribution such that only a
portion of the abrasive areas of the resulting pattern have a
controlled non-uniform distribution. The portion of the total
abrasive areas that have a controlled non-uniform can be quantified
as a discrete number, or as a fraction, percentage, or ratio of the
total number of abrasive areas of the pattern. In an embodiment, at
least 50%, at least 55%, at least 60%, at least 65%, at least 70%,
at least 80%, at least 85%, at least 90%, at least 95%, at least
96%, at least 97%, at least 98%, at least 99%, at least 99.5%, at
least 99.9% of the abrasive areas of the pattern possess a
controlled asymmetry. The portion of abrasive areas of the pattern
possessing a controlled asymmetry can be within a range comprising
any pair of the previous upper and lower limits. In a particular
embodiment, from about 50% to about 99.9%, from about 60% to about
99.5%, from about 75% to about 99%% of the pattern possesses a
controlled non-uniform distribution.
[0036] In another embodiment, the pattern possesses controlled
asymmetry over at least approximately 5 abrasive areas, at least
approximately 10 abrasive areas, at least approximately 15 abrasive
areas, at least approximately 20 abrasive areas, at least
approximately 25 abrasive areas, or at least approximately 50
abrasive areas. In another embodiment, the pattern possesses
controlled asymmetry over not greater than approximately 100,000
abrasive areas, not greater than approximately 10,000 abrasive
areas, not greater than approximately 5,000 abrasive areas, not
greater than approximately 2,500 abrasive areas, not greater than
approximately 1,000 abrasive areas, not greater than approximately
750 abrasive areas, or not greater than approximately 500 abrasive
areas. The number of abrasive areas possessing controlled asymmetry
can be within a range comprising any pair of the previous upper and
lower limits.
[0037] As stated above, a pattern of the present embodiments can be
any pattern having a controlled non-uniform distribution, including
a radial pattern, a spiral pattern, a phyllotactic pattern, an
asymmetric pattern, or combinations thereof. An example of a
combination pattern is a spiral lattice pattern. It will be
recognized that a spiral lattice pattern can be classified as a can
be a radial pattern, a spiral pattern, a phyllotactic pattern, and
an asymmetric pattern. A radial pattern can be any pattern that
appears to radiate from a central point, such as spokes from the
hub of a wheel.
[0038] In an embodiment, a spiral pattern can be any curve, or set
of curves, that emanates from a central point on the abrasive
article and extends progressively farther away as it revolves
around the central point. The central point can be located at or
near the center of the abrasive article, or alternatively, away
from the center of the abrasive article. There can be a single
spiral or multiple spirals (i.e., a plurality of spirals). The
spirals can be discreet or continuous, separate or joined. Separate
spirals can emanate from different central points (i.e., each
spiral has its own central point), can emanate from a common
central point (i.e., each spiral shares a central point), or
combinations thereof. Spiral patterns can include: an Archimedean
spiral; a Euler spiral, Cornu spiral, or clothoid; a Fermat's
spiral; a hyperbolic spiral; a lituus; a logarithmic spiral; a
Fibonacci spiral; a golden spiral; or combinations thereof.
[0039] In an embodiment, the pattern can be a phyllotactic pattern.
As used herein, "a phyllotactic pattern" means a pattern related to
phyllotaxis. Phyllotaxis is the arrangement of lateral organs such
as leaves, flowers, scales, florets, and seeds in many kinds of
plants. Many phyllotactic patterns are marked by the naturally
occurring phenomenon of conspicuous patterns having arcs, spirals,
and whorls. The pattern of seeds in the head of a sunflower is an
example of this phenomenon. As shown in FIG. 3 and FIG. 4, multiple
arcs or spirals, also called parastichy, can have their origin at a
center point (C) and travel outward, while other spirals originate
to fill in the gaps left by the inner spirals. See Jean's
Phyllotaxis A Systemic Study in Plant Morphogenesis at p. 17.
Frequently, the spiral-patterned arrangements can be viewed as
radiating outward in both the clockwise and counterclockwise
directions. As shown in FIG. 4, these types of patterns have
visibly opposed parastichy pairs that can be denoted by (m, n)
where the number of spirals or arcs at a distance from the center
point radiating in a clockwise direction is "m" and the number of
spirals or arcs radiating counterclockwise is "n." Further, the
angle between two consecutive spirals or arcs at their center is
called the divergence angle "d." It has been surprisingly
discovered by the inventors that phyllotactic patterns are useful
in creating new patterns for abrasive articles, in particular
coated abrasive articles.
[0040] In an embodiment, the pattern has a number of clockwise
spirals and a number of counter-clock wise spirals, wherein the
number of clockwise spirals and the number of counterclockwise
spirals are Fibonacci numbers or multiples of Fibonacci numbers. In
a particular embodiment, the number of clockwise spirals and the
number of counterclockwise spirals is, as a pair (m, n): (3, 5),
(5, 8), (8, 13), (13, 21), (21, 34), (34, 55), (55, 89), (89, 144)
or a multiple of such pairs. In another embodiment, the number of
clockwise spirals and the number of counterclockwise spirals are
Lucas numbers or multiples of Lucas numbers. In a particular
embodiment, the number of clockwise spirals and the number of
counterclockwise spirals is, as a pair (m, n): (3, 4), (4, 7), (7,
11), (11, 18), (18, 29), (29, 47), (47, 76), or (76, 123), or a
multiple of such pairs. In another embodiment, the number of
clockwise spirals and the number of counterclockwise spirals are
any numbers in a ratio that converges on the golden ratio, wherein
the golden ratio is equal to the sum of one plus the square root of
five, divided by two (1+ 5)/2, which is approximately equal to
1.6180339887. In a particular embodiment, the ratio of the
clockwise spirals to the counterclockwise spirals is approximately
equal to the golden ratio.
[0041] As already mentioned above, it has been observed in nature
that the seeds of the sunflower plant are arranged in a spiral
phyllotactic pattern. In an embodiment, the pattern is a sunflower
pattern.
[0042] The sunflower pattern has been described by Vogel's model,
which is a type of "Fibonacci spiral", or a spiral in which the
divergence angle between successive points is a fixed Fibonacci
angle that approaches the golden angle, which is equal to
137.508.degree..
[0043] FIG. 6 and FIG. 7 illustrate the Vogel model, which is:
.phi.=n*.alpha.,r=c n (Eq. 1) [0044] where: n is the ordering
number of a floret, counting outward from the center; .phi. is the
angle between a reference direction and the position vector of the
nth floret in a polar coordinate system originating at the center
of the capitulum, such that the divergence angle, .alpha., between
the position vectors of any two successive florets is constant, and
with regard to the sunflower pattern, at 137.508.degree.; r is the
distance from the center of the capitulum and the center of the nth
floret; and c is a constant scaling factor.
[0045] In an embodiment, the pattern is described by the Vogel
model or a variation of the Vogel model. In a particular
embodiment, the pattern is described by the Vogel model where:
n is the ordering number of an abrasive area, counting outward from
the center of the pattern; .phi. is the angle between a reference
direction and a position vector of the nth abrasive area in a polar
coordinate system originating at the center of the pattern, such
that the divergence angle between the position vectors of any two
successive abrasive areas is a constant angle .alpha.; r is the
distance from the center of the pattern to the center of the nth
abrasive area; and c is a constant scaling factor.
[0046] As stated above, all, substantially all, or a portion of the
abrasive areas of the pattern will be described by (i.e., conform
to) the Vogel model. In an embodiment, all the abrasive areas of
the pattern are described by the Vogel model. In another embodiment
at least 50%, at least 60%, at least 70%, at least 80%, at least
90%, at least 95%, at least 99% of the abrasive areas are described
by the Vogel model.
[0047] In another embodiment, a suitable spiral or phyllotactic
pattern can be generated from the x and y co-ordinates of any
phyllotactic pattern, such as the Vogel model, or other suitable
pattern having a controlled non-uniform distribution, including a
radial pattern, a spiral pattern, a phyllotactic pattern, an
asymmetric pattern, or combinations thereof. In an embodiment, the
x and y co-ordinates of a spiral or phyllotactic pattern are
transposed and rotated to determine the x' and y' co-ordinates of
the spiral or phyllotactic pattern, wherein .theta. is equal to
.pi./n in radians and n is any integer according to the following
equation:
x ' y ' = cos .theta. - sin .theta. sin .theta. cos .theta. x y (
Eq . 2 ) ##EQU00001##
The transposed and rotated co-ordinates produced (x' and y') can be
plotted, such as by the use of computer aided drafting (CAD)
software, to generate a spiral or phyllotactic pattern. Particular
embodiments of transposed phyllotactic patterns are shown in FIG.
16, which is a transpose of the phyllotactic pattern of FIG. 15;
and FIG. 19, which is a transpose of the phyllotactic pattern of
FIG. 18.
[0048] The inventors have surprisingly found that phyllotactic
patterns are useful in creating new patterns that improve the
performance of abrasive articles, including fixed abrasive
articles, such as bonded abrasive articles and coated abrasive
articles. In particular, phyllotactic patterns are useful in
creating new abrasive area patterns for coated abrasive articles.
Phyllotactic patterns help solve the competing problems of
achieving a high removal rate of surface material while still
achieving an acceptable surface quality, reducing the amount of
swarf loading on the abrasive surface, and maintaining a high
durability and long useful life of the abrasive. This is
surprising, in part, in at least the following respects. First, the
phyllotactic patterns of the present embodiments unexpectedly
provide improved to superior swarf removal coverage and have a more
complete intermingled distribution of swarf extraction sites (e.g.,
open areas, pathways, and/or channels) and abrasive areas (for
instance, in the form of individual abrasive spots, elongated
nodes, semi-continuous arcs, whorls, spirals, and combinations
thereof as described and shown herein) over the face of the
abrasive compared to state-of-the-art abrasive patterns, even when
having a total abrasive area that is less than the total abrasive
area of a state-of-the-art pattern. Second, phyllotactic patterns
of the present embodiments unexpectedly provide at least comparable
to superior abrasive performance (e.g., cumulative material cut)
compared to state-of-the-art patterns, with and without the
application of vacuum, even when the total abrasive area is less
than that of state-of-the-art patterns. Third, as discussed in more
detail later in the application, the effectiveness and performance
of the present embodiments can be even further enhanced when paired
with a co-operative back-up pad and vacuum system.
[0049] It will be appreciated that important aspects of pattern
design for coated abrasive articles include the percentage of total
abrasive surface area, the ratio of total abrasive surface area to
open area, the predicted locations and extensiveness of abrasive
area coverage while the abrasive article is in use (e.g.,
rotational movement in an orbital sander, oscillation movement in a
sheet sander, continuous lateral movement in a belt sander), the
scaling factor, the number of abrasive areas, the divergence angle
between the abrasive areas, the size and shape of the abrasive
areas, the distance between adjacent abrasive areas, and the
distance between the outermost abrasive areas and the edge, or
edges, of the coated abrasive article.
Sizes of Abrasive Discs
[0050] There are various sizes of abrasives that are commonly used
in industry and by commercial consumers that typically range from
about fractions of an inch in diameter up to feet in diameter. The
present patterns are suitable for use on abrasives of most any
size, including various standard sizes of abrasive discs (e.g., 3
inch to 20 inch). In an embodiment, the abrasive article is a
circular disc having a diameter of at least about 0.25 inches, at
least about 0.5 inches, at least about 1.0 inches, at least about
1.5 inches, at least about 2.0 inches, at least about 2.5 inches,
or at least about 3.0 inches. In another embodiment, the abrasive
article is a circular disc having a diameter of not greater than
about 72 inches, not greater than about 60 inches, not greater than
about 48 inches, not greater than about 36 inches, not greater than
about 24 inches, not greater than about 20 inches, not greater than
about 18 inches, not greater than about 12 inches, not greater than
about 10 inches, not greater than about 9 inches, not greater than
about 8 inches, not greater than about 7 inches, or not greater
than about 6 inches. In another embodiment, the abrasive article
has a size in the range from about 0.5 inches in diameter to about
48 inches in diameter, about 1.0 inch in diameter to about 20
inches in diameter, about 1.5 inches in diameter to about 12 inches
in diameter.
Total Potential Surface Area
[0051] The size and shape of the abrasive article determines the
total potential surface area of the abrasive article. For instance,
an abrasive disc having a 1 inch diameter has a total potential
surface area of 0.7854 in.sup.2. As another example, a rectangular
abrasive sheet measuring 2 inches by 3 inches would have a total
potential surface area of 6 in.sup.2.
Total Open Area
[0052] The total open area affects the amount of swarf extraction.
Typically, as the amount of open area increases, the amount of
swarf extraction increases, which tends to maintain, or sometimes
improve the abrasive article's material removal rate (i.e. "cut"
rate) during usage. However, increasing the amount of open area
also directly reduces the amount of available abrasive area, which
at a certain point will reduce the material removal rate. In an
embodiment, the total open area is equal to the sum of the area of
all the open areas on the face of the abrasive article. In other
words, the total open area is equal to the total potential surface
of the abrasive article minus the total abrasive area (i.e., the
sum of all the abrasive areas). Thus, the amount of the total open
area can range from about 15% to about 95.5% of the total potential
surface area, depending on the amount of desired abrasive area. In
an embodiment, the total open area is at least about 15% of the
total potential surface area for the abrasive article, at least
about 20%, at least about 25%, at least about 30%, at least about
35%, at least about 40%, at least about 45%, at least about 50%, at
least about 55%, at least about 60%, at least about 65%, at least
about 70%, at least about 75%, or at least about 80%. In another
embodiment, the total open area is not greater than about 95.5%,
not greater than about 95%, not greater than about 94.5%, not
greater than about 94%, not greater than about 93.5%, not greater
than about 93%, not greater than about 92.5%, not greater than
about 92%, not greater than about 91.5%, not greater than about
91%, not greater than about 90.5%, or not greater than about 90%.
The amount of the total open area can be within a range comprising
any pair of the previous upper and lower limits. In another
embodiment, the total open area ranges from about 65% to about 93%,
about 70% to about 92%, about 75% to about 91%, or about 80% to
about 90%. The total open area may be considered as a discreet
amount instead of a percentage. For example, an abrasive five inch
disc can have a total open area ranging from about 2.95 in.sup.2 to
about 18.75 in.sup.2.
Total Abrasive Surface Area
[0053] The total abrasive surface area affects the amount surface
material removed. Typically, as the amount of total abrasive
surface area is increased, the amount of surface material removed
is increased. Also typically, as the amount of surface material
removed is increased, both the tendency for swarf to build-up is
increased and the surface roughness tends to increase. In an
embodiment, the total abrasive surface area of the coated abrasive
is equal to the total potential surface of the abrasive article
(i.e., the abrasive surface area if there were no apertures) minus
the total open area (i.e., the sum of all the open areas). Thus,
the amount of the total abrasive surface area can range from about
4.5% to about 85% of the total potential surface area, depending on
the amount of desired open area. In an embodiment, the total
abrasive area is at least about 4% of the total potential surface
area for the abrasive article, at least about 4.5%, at least about
5%, at least about 5.5%, at least about 6%, at least about 7.5%, at
least about 8%, at least about 8.5%, at least about 9%, at least
about 9.5%, or at least about 10%. In another embodiment, the total
abrasive area is not greater than about 85%, not greater than about
80%, not greater than about 75%, not greater than about 70%, not
greater than about 65%, not greater than about 60%, not greater
than about 55%, not greater than about 50%, not greater than about
45%, not greater than about 40%, not greater than about 35%, not
greater than about 30%, not greater than about 25%, or not greater
than about 20%. The amount of the total abrasive area can be within
a range comprising any pair of the previous upper and lower limits.
In another embodiment, the total abrasive area ranges from about 7%
to about 35%, about 8% to about 30%, about 9% to about 25%, or
about 10% to about 20%. The total abrasive area may be considered
as a discreet amount instead of a percentage. For example, a 5-inch
disc can have a total abrasive surface area ranging from about 0.88
in.sup.2 to about 16.69 in.sup.2.
Ratio of Total Abrasive Surface Area to Total Open Area
[0054] In an embodiment, the ratio of total abrasive surface area
to total open area is at least about 1:199, at least about 1:99, at
least about 1:65.7; at least about 1:49, at least about 1:39, at
least about 1:29, at least about 1:19, or at least about 1:9. In
another embodiment, the ratio of total abrasive surface area to
total open area is not greater than about 1:0.05, not greater than
about 1:0.1, not greater than about 1:0.2, not greater than about
1:0.3, not greater than about 1:0.4, not greater than about 1:0.5,
not greater than about 1:0.6, not greater than about 1:0.7, not
greater than about 1:0.8, not greater than about 1:0.9, or not
greater than about 1:1. The ratio of total abrasive surface area to
total open area can be within a range comprising any pair of the
previous upper and lower limits.
Number of Abrasive Areas
[0055] The number of abrasive areas influences the total amount of
open area and the amount of total abrasive area. Additionally, the
number of abrasive areas affects the density and distribution of
abrasive coverage on the surface of the abrasive article, which in
turn directly affects the surface material removal rate and swarf
extraction efficiency of the abrasive article. In an embodiment,
the number of abrasive areas is at least about 5, at least about
10, at least about 15; at least about 18, or at least about 21. In
another embodiment, the number of abrasive areas is not greater
than about 100,000; not greater than about 50,000; not greater than
about 10,000; not greater than about 1,000; not greater than about
800; not greater than about 750; not greater than about 600; or not
greater than about 550. The number of abrasive areas can be within
a range comprising any pair of the previous upper and lower limits.
In another embodiment, the number of abrasive areas ranges from
about 21 to about 10,000; about 25 to about 1,000; about 30 to
about 750; or about 35 to about 550. In a particular embodiment,
the number of abrasive areas is in the range of about 21 to about
550.
Divergence Angle
[0056] Increasing or decreasing the divergence angle .alpha.
affects how the abrasive areas are placed within the pattern and
the shape of the clockwise and counter clockwise spirals. The
divergence angle is equal to 360.degree. divided by a constant or
variable value, thus the divergence angle can be a constant value
or it can vary. It has been observed that small changes in
divergence angle can significantly alter the pattern. FIG. 8a, FIG.
8b, and FIG. 8c show phyllotactic patterns that differ only in the
value of the divergence angle. The divergence angle for FIG. 8a is
137.3.degree.. The divergence angle for FIG. 8b is 137.5.degree..
The divergence angle for FIG. 8c is 137.6.degree.. In an
embodiment, the divergence angle is at least about 30.degree., at
least about 45.degree., at least about 60.degree.; at least about
90.degree., or at least about 120.degree.. In another embodiment,
the divergence angle is less than 180.degree., such as not greater
than about 150.degree.. The divergence angle can be within a range
comprising any pair of the previous upper and lower limits. In
another embodiment, the divergence angle ranges from about
90.degree. to about 179.degree., about 120.degree. to about
150.degree., about 130.degree. to about 140.degree., or about
135.degree. to about 139.degree.. In an embodiment, the divergence
angle is determined by dividing 360.degree. by an irrational
number. In a particular embodiment, the divergence angle is
determined by dividing 360.degree. by the golden ratio. In a
particular embodiment, the divergence angle is in the range of
about 137.degree. to about 138.degree., such as about 137.5.degree.
to about 137.6.degree., such as about 137.50.degree. to about
137.51.degree.. In a particular embodiment, the divergence angle is
137.508.degree..
Distance to the Edge of the Abrasive
[0057] Depending on the geometry of the abrasive article and its
intended usage, the overall dimensions of the pattern can be
determined. The distance from the center of the pattern to the
outermost abrasive areas can extend to a distance coterminous with
the edge of the abrasive article. Thus, the edges of the outermost
abrasive areas can extend to or intersect with the edge of the
abrasive article. Alternatively, the distance from the center of
the pattern to the outermost abrasive areas can extend to a
distance that allows a certain amount of space between the edges of
the outermost abrasive areas and the edge of the abrasive article
to be free of abrasive areas. The minimum distance from the edges
of the outermost abrasive areas can be specified as desired. In an
embodiment, the minimum distance from the edges of the outermost
abrasive areas to the outer edge of the abrasive article is a
specific distance, identified as a discreet length or as a
percentage of the length of the face of the abrasive article upon
which the pattern appears. In an embodiment, the minimum distance
from the edges of the outermost abrasive areas to the outer edge of
the abrasive article can be at least about zero (i.e., the edge of
the outermost abrasive areas intersect or are co-terminus with the
edge of the abrasive article) ranging to about 15% of the length of
the face of the abrasive article.
Size of Abrasive Areas
[0058] The size of the abrasive areas is determined, at least in
part, by the desired total amount of abrasive area for the abrasive
article. The size of the abrasive areas can be constant throughout
the pattern or it can vary within the pattern. In an embodiment,
the size of the abrasive areas is constant. In another embodiment,
the size of the abrasive areas varies with the distance of the
abrasive areas from the center of the pattern.
Scaling Factor
[0059] The scaling factor influences the overall size and
dimensions of the pattern. The scaling factor can be adjusted so
that the edges of the outermost abrasive areas are within a desired
distance of the outer edge of the abrasive article.
Distance Between Nearest Adjacent Abrasive Areas
[0060] Along with consideration of the number and size of the
abrasive areas, the distance between the centers of the nearest
adjacent abrasive areas can be determined. The distance between the
centers of any two abrasive areas is a function of the other design
considerations. In an embodiment, the shortest distance between the
center of any two abrasive areas is never repeated (i.e., the
center-to-center spacing is never the same exact distance). This
type of spacing is also an example of controlled asymmetry.
Pattern Coverage--Acceptable Amounts of Anomalies
[0061] It will be apparent that a pattern need not be applied to an
abrasive article in its entirety or in a continuous manner.
Portions of a pattern may be applied or skipped such that various
divisions or sectors of the face of the abrasive article do not
bear the complete pattern. In an embodiment, a half, a third, a
quarter, a fifth, a sixth, a seventh, an eighth, a ninth, or a
tenth of the pattern may be skipped. In another embodiment, the
pattern may be applied to only one or more concentric annular
regions of the abrasive article. In another embodiment, it is
possible to skip one or more of the abrasive areas that would
normally appear in the series of abrasive areas along the
individual arcs or spiral arms of the pattern. In an embodiment,
every n.sup.th, or multiple of every n.sup.th could be skipped. In
another embodiment, individual abrasive areas, groups of abrasive
areas, or abrasive areas according to a specific numerical series
can be skipped. Conversely, it is also possible to include a
certain amount of additional abrasive areas to the pattern. The
addition or subtraction of abrasive areas can be considered as
anomalies to the pattern, and a certain amount of anomalies to the
pattern, plus or minus, can be acceptable. In an embodiment, an
acceptable amount of anomalies to the pattern can range from 0.1%
to 10% of the total abrasive areas of the abrasive article.
Shape of the Abrasive Areas
[0062] The amount of coverage can be influenced by the shape of the
abrasive areas. The shape of the abrasive areas can be regular or
irregular. In an embodiment, the shape of the abrasive areas can be
in the form of short lines, regular polygons, irregular polygons,
ellipsoids, circles, arcs, spirals, whorls, lattices, or
combinations thereof. In a particular embodiment, the abrasive
areas have the shape of a circle. In another embodiment, the shape
of the abrasive areas may be in the form of one or more lines,
arcs, spirals, or whirls having a controlled non-uniform
distribution as described herein. The one or more lines, arcs,
spirals, or whirls can have multiple lines intersect.
[0063] The abrasive areas can be configured so that sufficient
swarf removal can occur with or without the attachment of a vacuum
to the back of the abrasive article. In an embodiment, the abrasive
areas are in form of spirals or parastichy that extend radially
outward from the center of the abrasive article, The spirals or
parastichy can be configured to create air-flow channels in the
open areas between the abrasive areas. In another embodiment, the
abrasive areas are formed to resemble a spiral lattice. Apertures
can be located within the open areas enclosed by the lattice. It is
believed that swarf removal will be promoted by the presence of
open areas that are in fluid connection with the outer edge of the
abrasive article, or that are in fluid connection with apertures in
the abrasive article that open to a vacuum source, or both. Such
abrasive areas and open areas configured to create air-flow paths
will guide swarf so that it is ejected out from the abrasive areas
by centrifugal force or directly into the apertures of a vacuum
system, thus preventing entrainment of the swarf in the abrasive
areas on the face of the abrasive article, as well as any open
fibrous layers, such as hook and loop material layers, that might
be attached to the backside of the abrasive article.
[0064] In an embodiment, the pattern of abrasive areas can comprise
regular polygons, irregular polygons, ellipsoids, arcs, spirals,
phyllotactic patterns, or combinations thereof. The pattern of
abrasive areas can comprise radiating arcs, radiating spirals, or
combinations thereof. The pattern of abrasive areas can comprise a
combination of inner radiating spirals and outer radiating spirals.
The pattern of abrasive areas can comprise a combination of
clock-wise radiating spirals and counter clock-wise radiating
spirals. The abrasive areas can be discrete, or discontinuous, from
each other. Alternatively, one or more of the abrasive areas can be
fluidly connected.
[0065] The number of radiating arcs, radiating spirals, or
combinations thereof can vary. In an embodiment, the number of
radiating arcs, radiating spirals, or combinations thereof can be
not greater than 1000, such as not greater than 750, not greater
than 500, not greater than 250, not greater than 100, not greater
than 90, not greater than 80, or not greater than 75. In an
embodiment, the number of radiating arcs, radiating spirals, or
combinations thereof can be not less than 2, such as not less than
3, not less than 5, not less than 7, not less than 9, not less than
11, not less than 15, or not less than 20. In an embodiment, the
number of radiating arcs, radiating spirals, or combinations
thereof can be from 2 to 500, such as 2 to 100.
[0066] The abrasive areas can vary in width. The width of the
abrasive areas can be constant or varying, or combinations thereof.
In an embodiment, the width of the abrasive areas can be within a
range of fixed lengths. In an embodiment, the width of the abrasive
areas can vary from 0.1 mm to 10 cm. In another embodiment, the
width of the abrasive areas will be related to the desired size of
the adjacent open areas of the abrasive article. In an embodiment,
the width of the abrasive areas is not less than 1/10 the size of
the open areas of the abrasive article, such as not less than 1/8,
1/6, 1/5, 1/4, 1/3, or 1/2 the size of the open areas of the coated
abrasive. In an embodiment, the width of the abrasive areas is not
greater than 10 times the size of the open areas of the coated
abrasive, such as not greater than 8 times, not greater than 6
times, not greater than 5 times, not greater than 4 times, not
greater than 3 times, not greater than 2 times the size of the open
areas of the coated abrasive. In an embodiment, the width of the
abrasive areas is about equal to the size of the open areas of the
coated abrasive.
[0067] In another embodiment, the abrasive areas can be shaped and
configured to form a plurality of air flow paths disposed in a
pattern. The pattern of air flow paths can comprise regular
polygons, irregular polygons, ellipsoids, arcs, spirals,
phyllotactic patterns, or combinations thereof. The pattern of air
flow paths can comprise radiating arcurate paths, radiating spiral
paths, or combinations thereof. The pattern of air flow paths can
comprise a combination of inner radiating spiral paths and outer
radiating spiral paths. The pattern of air flow paths can comprise
a combination of clock-wise radiating spiral paths and counter
clock-wise radiating spiral paths. The air flow paths can be
discrete, or discontinuous, from each other. Alternatively, one or
more of the air flow paths can be can be fluidly connected.
[0068] The number of radiating arcurate paths ("arcs"), radiating
spiral paths, or combinations thereof can vary. In an embodiment,
the number of radiating arcurate paths, radiating spiral paths, or
combinations thereof can be not greater than 1000, such as not
greater than 750, not greater than 500, not greater than 250, not
greater than 100, not greater than 90, not greater than 80, or not
greater than 75. In an embodiment, the number of radiating arcurate
paths, radiating spiral paths, or combinations thereof can be not
less than 2, such as not less than 3, not less than 5, not less
than 7, not less than 9, not less than 11, not less than 15, or not
less than 20. In an embodiment, the number of radiating arcurate
paths, radiating spiral paths, or combinations thereof can be from
2 to 500, such as 2 to 100.
[0069] The air flow paths can vary in width. The width of the air
flow paths can be constant or varying, or combinations thereof. In
an embodiment, the width of the air flow paths can be within a
range of fixed lengths. In an embodiment, the width of the air flow
paths can vary from 0.1 mm to 10 cm. In another embodiment, the
width of the air flow paths will be related to the size of the
abrasive areas of the coated. In an embodiment, the width of the
air flow paths is not less than 1/10 the size of the abrasive areas
of the coated abrasive, such as not less than 1/8, 1/6, 1/5, 1/4,
1/3, or 1/2 the size of the abrasive areas of the coated abrasive.
In an embodiment, the width of the air flow paths is not greater
than 10 times the size of the abrasive areas of the coated
abrasive, such as not greater than 8 times, not greater than 6
times, not greater than 5 times, not greater than 4 times, not
greater than 3 times, not greater than 2 times the size of the
abrasive areas of the coated abrasive. In an embodiment, the width
of the air-flow paths is about equal to the size of the abrasive
areas of the coated abrasive.
[0070] The air flow paths can have one or more cavities, orifices,
passages, holes, openings, or combinations thereof disposed along
or within air flow paths that extend through the through the body
of the abrasive article. In an embodiment, each air flow path will
have at least one hole disposed within the air flow path that that
extends through the through the body of the abrasive article.
Shape and Structure of the Abrasive Article
[0071] The shape of the abrasive article can be any shape that will
accommodate the desired abrasive area pattern and will be dictated
by the intended abrasive process and materials of construction. In
an embodiment, the abrasive article is a bonded abrasive article.
In another embodiment, the abrasive article is a coated abrasive
article. In a particular embodiment, the abrasive article is one of
a sheet, belt, or circular disc.
[0072] FIG. 1 shows a top view of an embodiment of a coated
abrasive article 100 having a plurality of abrasive areas 101
arranged in a pattern having a non-uniform distribution, wherein
the pattern is a phyllotactic spiral pattern that conforms to the
Vogel model (commonly called a "sunflower" pattern). Open areas 103
surround the abrasive areas. The coated abrasive is in the shape of
a substantially planar (i.e., generally flat) circular disc.
[0073] FIG. 21 shows a side view of a coated abrasive article 2100
including a backing 2101 having a first major surface 2103 and a
second major surface 2105. An abrasive layer 2107 is disposed on
the first major surface of the backing. The abrasive layer can
comprise multiple layers, including a binder layer 2109, also
called a make coat. A plurality of abrasive grains 2111 can be
dispersed within, penetrating into, or resting upon the binder
layer, or combinations thereof. A pattern of abrasive areas 2113
are present on the surface of the backing. One or more open areas
2115 will be adjacent to the abrasive areas. A size coat 2117 can
optionally be disposed on the binder layer. A supersize coat 2119
can optionally be disposed over the size coat. A back coat 2121 can
be disposed on the second major surface (i.e., the non-abrasive
side) of the backing layer. A fastener layer 2123 can be disposed
over the back coat, or alternatively can be directly disposed onto
the second major side of the backing. In a particular embodiment,
the coated abrasive article 2100 can optionally be attached to a
back-up pad (not shown) or a vacuum system (not shown).
Backing
[0074] The backing can be flexible or rigid. The backing can be
made of any number of various materials including those
conventionally used as backings in the manufacture of coated
abrasives. An exemplary flexible backing includes a polymeric film
(for example, a primed film), such as polyolefin film (e.g.,
polypropylene including biaxially oriented polypropylene),
polyester film (e.g., polyethylene terephthalate), polyamide film,
or cellulose ester film; metal foil; mesh; foam (e.g., natural
sponge material or polyurethane foam); cloth (e.g., cloth made from
fibers or yarns comprising polyester, nylon, silk, cotton,
poly-cotton or rayon); paper; vulcanized paper; vulcanized rubber;
vulcanized fiber; nonwoven materials; a combination thereof; or a
treated version thereof. Cloth backings may be woven or stitch
bonded. In particular examples, the backing is selected from the
group consisting of paper, polymer film, cloth, cotton,
poly-cotton, rayon, polyester, poly-nylon, vulcanized rubber,
vulcanized fiber, metal foil and a combination thereof. In other
examples, the backing includes polypropylene film or polyethylene
terephthalate (PET) film.
[0075] The backing may optionally have at least one of a saturant,
a presize layer or a backsize layer. The purpose of these layers is
typically to seal the backing or to protect yarn or fibers in the
backing. If the backing is a cloth material, at least one of these
layers is typically used. The addition of the presize layer or
backsize layer may additionally result in a "smoother" surface on
either the front or the back side of the backing. Other optional
layers known in the art can also be used (for example, a tie layer;
see U.S. Pat. No. 5,700,302 (Stoetzel et al.), the disclosure of
which is incorporated by reference).
[0076] An antistatic material may be included in a cloth treatment
material. The addition of an antistatic material can reduce the
tendency of the coated abrasive article to accumulate static
electricity when sanding wood or wood-like materials. Additional
details regarding antistatic backings and backing treatments can be
found in, for example, U.S. Pat. No. 5,108,463 (Buchanan et al.);
U.S. Pat. No. 5,137,542 (Buchanan et al.); U.S. Pat. No. 5,328,716
(Buchanan); and U.S. Pat. No. 5,560,753 (Buchanan et al.), the
disclosures of which are incorporated herein by reference.
[0077] The backing may be a fibrous reinforced thermoplastic such
as described, for example, in U.S. Pat. No. 5,417,726 (Stout et
al.), or an endless spliceless belt, as described, for example, in
U.S. Pat. No. 5,573,619 (Benedict et al.), the disclosures of which
are incorporated herein by reference. Likewise, the backing may be
a polymeric substrate having hooking stems projecting therefrom
such as that described, for example, in U.S. Pat. No. 5,505,747
(Chesley et al.), the disclosure of which is incorporated herein by
reference. Similarly, the backing may be a loop fabric such as that
described, for example, in U.S. Pat. No. 5,565,011 (Follett et
al.), the disclosure of which is incorporated herein by
reference.
Abrasive Layer
[0078] The abrasive layer may be formed from one or more coats and
a plurality of abrasive grains. For example, the abrasive layer
includes a make coat.sub.--09 and can optionally include a size
coat or a supersize coat. Abrasive layers generally include
abrasive grains disposed on, embedded within, dispersed within, or
combinations thereof, in a binder.
Abrasive Grains
[0079] The abrasive grains can include essentially single phase
inorganic materials, such as alumina, silicon carbide, silica,
ceria, and harder, high performance superabrasive grains such as
cubic boron nitride and diamond. Additionally, the abrasive grains
can include composite particulate materials. Such materials can
include aggregates, which can be formed through slurry processing
pathways that include removal of the liquid carrier through
volatilization or evaporation, leaving behind green aggregates,
optionally followed by high temperature treatment (i.e., firing) to
form usable, fired aggregates. Further, the abrasive regions can
include engineered abrasives including macrostructures and
particular three-dimensional structures.
[0080] In an exemplary embodiment, the abrasive grains are blended
with the binder formulation to form abrasive slurry. Alternatively,
the abrasive grains are applied over the binder formulation after
the binder formulation is coated on the backing. Optionally, a
functional powder may be applied over the abrasive regions to
prevent the abrasive regions from sticking to a patterning tooling.
Alternatively, patterns may be formed in the abrasive regions
absent the functional powder.
[0081] The abrasive grains may be formed of any one of or a
combination of abrasive grains, including silica, alumina (fused or
sintered), zirconia, zirconia/alumina oxides, silicon carbide,
garnet, diamond, cubic boron nitride, silicon nitride, ceria,
titanium dioxide, titanium diboride, boron carbide, tin oxide,
tungsten carbide, titanium carbide, iron oxide, chromia, flint,
emery. For example, the abrasive grains may be selected from a
group consisting of silica, alumina, zirconia, silicon carbide,
silicon nitride, boron nitride, garnet, diamond, co-fused alumina
zirconia, ceria, titanium diboride, boron carbide, flint, emery,
alumina nitride, and a blend thereof. Particular embodiments have
been created by use of dense abrasive grains comprised principally
of alpha-alumina.
[0082] The abrasive grain may also have a particular shape. An
example of such a shape includes a rod, a triangle, a pyramid, a
cone, a solid sphere, a hollow sphere, or the like. Alternatively,
the abrasive grain may be randomly shaped.
[0083] In an embodiment, the abrasive grains can have an average
grain size not greater than 800 microns, such as not greater than
about 700 microns, not greater than 500 microns, not greater than
200 microns, or not greater than 100 microns. In another
embodiment, the abrasive grain size is at least 0.1 microns, at
least 0.25 microns, or at least 0.5 microns. In another embodiment,
the abrasive grains size is from about 0.1 microns to about 200
microns and more typically from about 0.1 microns to about 150
microns or from about 1 micron to about 100 microns. The grain size
of the abrasive grains is typically specified to be the longest
dimension of the abrasive grain. Generally, there is a range
distribution of grain sizes. In some instances, the grain size
distribution is tightly controlled.
Make Coat--Binder
[0084] The binder of the make coat or the size coat may be formed
of a single polymer or a blend of polymers. For example, the binder
may be formed from epoxy, acrylic polymer, or a combination
thereof. In addition, the binder may include filler, such as
nano-sized filler or a combination of nano-sized filler and
micron-sized filler. In a particular embodiment, the binder is a
colloidal binder, wherein the formulation that is cured to form the
binder is a colloidal suspension including particulate filler.
Alternatively, or in addition, the binder may be a nanocomposite
binder including sub-micron particulate filler.
[0085] The binder generally includes a polymer matrix, which binds
abrasive grains to the backing or compliant coat, if present.
Typically, the binder is formed of cured binder formulation. In one
exemplary embodiment, the binder formulation includes a polymer
component and a dispersed phase.
[0086] The binder formulation may include one or more reaction
constituents or polymer constituents for the preparation of a
polymer. A polymer constituent may include a monomeric molecule, a
polymeric molecule, or a combination thereof. The binder
formulation may further comprise components selected from the group
consisting of solvents, plasticizers, chain transfer agents,
catalysts, stabilizers, dispersants, curing agents, reaction
mediators and agents for influencing the fluidity of the
dispersion.
[0087] The polymer constituents can form thermoplastics or
thermosets. By way of example, the polymer constituents may include
monomers and resins for the formation of polyurethane, polyurea,
polymerized epoxy, polyester, polyimide, polysiloxanes (silicones),
polymerized alkyd, styrene-butadiene rubber,
acrylonitrile-butadiene rubber, polybutadiene, or, in general,
reactive resins for the production of thermoset polymers. Another
example includes an acrylate or a methacrylate polymer constituent.
The precursor polymer constituents are typically curable organic
material (i.e., a polymer monomer or material capable of
polymerizing or crosslinking upon exposure to heat or other sources
of energy, such as electron beam, ultraviolet light, visible light,
etc., or with time upon the addition of a chemical catalyst,
moisture, or other agent which cause the polymer to cure or
polymerize). A precursor polymer constituent example includes a
reactive constituent for the formation of an amino polymer or an
aminoplast polymer, such as alkylated urea-formaldehyde polymer,
melamine-formaldehyde polymer, and alkylated
benzoguanamine-formaldehyde polymer; acrylate polymer including
acrylate and methacrylate polymer, alkyl acrylate, acrylated epoxy,
acrylated urethane, acrylated polyester, acrylated polyether, vinyl
ether, acrylated oil, or acrylated silicone; alkyd polymer such as
urethane alkyd polymer; polyester polymer; reactive urethane
polymer; phenolic polymer such as resole and novolac polymer;
phenolic/latex polymer; epoxy polymer such as bisphenol epoxy
polymer; isocyanate; isocyanurate; polysiloxane polymer including
alkylalkoxysilane polymer; or reactive vinyl polymer. The binder
formulation may include a monomer, an oligomer, a polymer, or a
combination thereof. In a particular embodiment, the binder
formulation includes monomers of at least two types of polymers
that when cured may crosslink. For example, the binder formulation
may include epoxy constituents and acrylic constituents that when
cured form an epoxy/acrylic polymer.
Additives--Grinding Aid
[0088] The abrasive layer may further include a grinding aid to
increase the grinding efficiency and cut rate. A useful grinding
aid can be inorganic based, such as a halide salt, for example,
sodium cryolite, and potassium tetrafluoroborate; or organic based,
such as a chlorinated wax, for example, polyvinyl chloride. A
particular embodiment includes cryolite and potassium
tetrafluoroborate with particle size ranging from 1 micron to 80
microns, and most typically from 5 microns to 30 microns. The
supersize coat can be a polymer layer applied over the abrasive
grains to provide anti-glazing and anti-loading properties.
Back Coat--Compliant Coat
[0089] The coated abrasive article may optionally include compliant
and back coats (not shown). These coats may function as described
above and may be formed of binder compositions.
Method of Making--Coated Abrasive Article
[0090] Turning to a method of making a coated abrasive article
having an abrasive area pattern, a backing can be distributed from
a roll, the backing can be coated with a binder formulation
dispensed from a coating apparatus. An exemplary coating apparatus
includes a drop die coater, a knife coater, a curtain coater, a
vacuum die coater or a die coater. Coating methodologies can
include either contact or non-contact methods. Such methods include
two roll, three roll reverse, knife over roll, slot die, gravure,
rotary printing, extrusion, spray coating applications, or
combinations thereof.
[0091] In an embodiment, the binder formulation can be provided in
a slurry including the formulation and abrasive grains. In an
alternative embodiment, the binder formulation can be dispensed
separate from the abrasive grains. The abrasive grains may be
provided following coating of the backing with the binder, after
partial curing of the binder formulation, after patterning of the
binder formulation, if any, or after fully curing the binder
formulation. The abrasive grains may, for example, be applied by a
technique, such as electrostatic coating, drop coating, or
mechanical projection.
[0092] In another embodiment, the backing, coated with the binder
and abrasive grains, can be stamped, die-cut, laser cut, or
combinations thereof to form the shape of the coated abrasive
(e.g., round disc) or a pattern of apertures, if any, that are cut
through the coated abrasive.
[0093] In another embodiment, the backing can be selectively coated
with the binder to leave uncoated regions that are then coated with
abrasive grains to form the abrasive areas. For example, the binder
can be printed onto the backing, such as by screen printing, offset
printing, rotary printing, or flexographic printing. In another
example, the binder can be selectively coated using gravure
coating, slot die coating, masked spray coating, or the like.
Alternatively, a photoresist or UV curable mask can be applied to
the backing and developed, such as by photolithography, to mask
portions of the backing. In another example, a dewetting compound
can be applied to the backing prior to applying the binder.
Method of Use--Abrading a Workpiece
[0094] Turning to a method of abrading a work piece, the work piece
can be contacted with a coated abrasive. The coated abrasive can be
rotated relative to the work piece. For example, the coated
abrasive can be mounted on an orbital sander and contacted to the
work piece. While abrading the work piece, material abraded from
the work piece can accumulate in the open areas between, or
adjacent to, the abrasive areas. The accumulated material can be
ejected from the face of the coated abrasive by the movement of the
coated abrasive during use. Alternately, a vacuum system can be
equipped to the abrasive article. The vacuum system can include a
back-up pad that is configured to cooperatively function with the
abrasive article.
Back-Up Pad
[0095] It will be appreciated that back-up pads designed to
correspond to coated abrasives having controlled non-uniform
distributions of abrasive areas can be successfully used in
conjunction with conventional coated abrasives as well as
particular coated abrasives having controlled non-uniform
distributions of abrasive areas. The inventors have surprisingly
discovered that back-up pad embodiments can provide superior swarf
removal and promote improved abrasive performance for conventional
abrasives.
[0096] In an embodiment, the back-up pad can have a pattern of air
flow paths that is cooperatively adapted to operate with coated
abrasives having a controlled non-uniform distribution pattern. As
stated previously, such a back-up can be used in conjunction with a
conventional perforated coated abrasive to promote swarf removal
and abrasive performance.
[0097] In an embodiment, a back-up pad can comprise a pattern of
air flow paths, wherein the pattern of air flow paths is generated
from x and y co-ordinates of a controlled non-uniform distribution
pattern. The controlled non-uniform distribution pattern used to
generate the back-up pad air flow pattern can be the same or
different than the pattern of the coated abrasive being used with
the back-up pad. In an embodiment, the controlled non-uniform
distribution pattern is the same as the pattern of the coated
abrasive being used with the back-up pad. In another embodiment,
the controlled non-uniform distribution pattern is different than
the pattern of the coated abrasive being used with the back-up
pad.
[0098] In an embodiment, a back-up pad can be cooperatively adapted
to operate with coated abrasives having phyllotactic patterns
according to the coated abrasive embodiments described herein. A
back-up pad is co-operative with a coated abrasive having
phyllotactic patterns when the back-up pad includes a plurality of
openings, a plurality of cavities, a plurality of channels,
plurality of passages, or combinations thereof, that are configured
in a pattern designed to promote suction and swarf removal away
from the work surface during the abrasion process through the
apertures of a coated abrasive having a phyllotactic pattern. The
openings, cavities, channels, passages, or combinations thereof can
define air-flow paths that are located along, within, or though the
back-up pad, or combinations thereof. The air-flow paths promote
improved suction and swarf removal through the apertures of a
coated abrasive and away from the work surface during the abrasion
process. In an embodiment, the pattern of openings, cavities,
channels, passages or combinations thereof can be in the form of a
regular polygons, irregular polygons, ellipsoids, arcs, spirals,
phyllotactic patterns, or combinations thereof. In another
embodiment, the air-flow paths can be in the form of a regular
polygons, irregular polygons, ellipsoids, arcs, spirals,
phyllotactic patterns, or combinations thereof.
[0099] The patterns can then be used to define radiating accurate
and spiral channels, as well as, annular channels that can
intersect the arcurate and spiral channels, or combinations
thereof. The annular, arcurate, spiral, or combination channels can
then be cut into a suitable material, such as in the form of
grooves, cavities, orifices, passages, or other pathways to form a
co-operative back-up pad.
[0100] In certain embodiments, the air-flow paths of the back-up
pad will partially, to fully, match-up with the apertures of the
coated abrasive. It will be understood that an air-flow path
matches-up with an aperture when at least a portion of the area of
an aperture coincides with, or is aligned with, a portion of the
air-flow path. In an embodiment, the air-flow paths of the
corresponding back-up pad will match-up with at least 5%, at least
10%, at least 15%, at least 20%, at least 25% of the apertures. In
an embodiment, the air-flow paths of the corresponding back-up pad
can match-up with at least 5%, at least 10%, at least 15%, at least
20%, at least 25%, at least 30%, at least 35%, at least 40%, at
least 55%, at least 50%, at least 55%, at least 60%, at least 65%,
at least 70%, at least 75%, at least 80%, at least 85%, at least
90%, at least 95%, or at least 100% of the apertures of the coated
abrasive.
[0101] It will be appreciated that certain of the back-up pad
spiral and phyllotactic air-flow patterns will exhibit a certain
quality of alignment with an aperture pattern of a coated abrasive,
particularly when the air-flow pattern is based on a transpose and
rotation of the co-ordinates of the abrasive areas of the coated
abrasive. In an embodiment, the air-flow pattern of the back-up pad
will match up with a majority, to nearly all, of the coated
abrasive apertures when the back-up pad is in a particular phase,
or degrees of rotation, with respect to the coated abrasive. A
back-up pad is said to be a single-alignment (also called a 2-fold
alignment) back-up pad when the air-flow paths of the back-up pad
match up with the apertures of the coated abrasive when the back-up
is rotated 90.degree. or 180.degree. compared to the coated
abrasive and a majority to nearly all of the apertures of the
coated abrasive match-up with at least one of the air-flow paths of
the back-up pad.
[0102] In an embodiment, the back-up pad can include or be adapted
to include an alignment indicator. An alignment indicator can be a
marking, device, notch, attachment, collar, protrusion, or
combination thereof to indicate the degree of alignment of the
back-up pad with the coated abrasive. In a specific embodiment, the
alignment indicator can be marking.
[0103] Although described as co-operative with the embodiments of
the abrasive articles described herein, such back-up pads can also
be used with standard state-of-the art perforated coated abrasives.
It has been unexpectedly found that back-up pads having a plurality
of openings, a plurality of cavities, a plurality of channels, or
combinations thereof that form suitable spiral or phyllotactic
pattern air-flow paths have improved swarf removal, can promote
abrasive cutting performance, and abrasive lifespan for both
standard state-of-the art perforated coated abrasives and coated
abrasives having phyllotactic patterns of perforations.
[0104] A back-up pad can be flexible or rigid. The back-up pad can
be made of any number of various materials, or combinations of
materials, including those conventionally used in the manufacture
of back-up pads. The back-up pad can be made of single piece,
unitary construction, or multi-piece construction, such as
multi-layer construction or concentric layer construction. The
back-up pad is preferably a resilient material such as a flexible
foam. Suitable foams can be polyurethane, polyester,
polyester-urethane, polyetherurethane; a natural or artificial
rubber such as a polybutadiene, polyisoprene, EPDM polymer,
polyvinylchloride (PVC), polychroloprene, or styrene/butadiene
copolymer; or combinations thereof. The foam can be open or closed
cell. Additives, such as coupling agents, toughening agents, curing
agents, antioxidants, reinforcing materials, and the like can be
added to the foam formulation to achieve desired characteristics.
Dyes, pigments, fillers, anti-static agents, fire retardants, and
scrim can also be added to the foam or other resilient material
used to make the back-up pad.
[0105] Particularly useful foams include TDI (toluene
diisocyanate)/polyester and MDI (methylene diphenyl
diisocyanate)/polyester foams. In an embodiment, the back-up pad is
made of resilient, open cell polyurethane foam formed as the
reaction product of a polyether polyol and an aromatic
polyisocyanate. In another embodiment, the back-up pad can be a
foam, a vulcanized rubber, or any combination thereof.
[0106] Note that not all of the activities described above in the
general description or the examples are required, that a portion of
a specific activity may not be required, and that one or more
further activities may be performed in addition to those described.
Still further, the order in which activities are listed are not
necessarily the order in which they are performed.
[0107] In the foregoing specification, the concepts have been
described with reference to specific embodiments. However, one of
ordinary skill in the art appreciates that various modifications
and changes can be made without departing from the scope of the
invention as set forth in the claims below. Accordingly, the
specification and figures are to be regarded in an illustrative
rather than a restrictive sense, and all such modifications are
intended to be included within the scope of invention.
[0108] As used herein, the terms "comprises," "comprising,"
"includes," "including," "has," "having" or any other variation
thereof, are intended to cover a non-exclusive inclusion. For
example, a process, method, article, or apparatus that comprises a
list of features is not necessarily limited only to those features
but may include other features not expressly listed or inherent to
such process, method, article, or apparatus. Further, unless
expressly stated to the contrary, "or" refers to an inclusive-or
and not to an exclusive-or. For example, a condition A or B is
satisfied by any one of the following: A is true (or present) and B
is false (or not present), A is false (or not present) and B is
true (or present), and both A and B are true (or present).
[0109] Also, the use of "a" or "an" are employed to describe
elements and components described herein. This is done merely for
convenience and to give a general sense of the scope of the
invention. This description should be read to include one or at
least one and the singular also includes the plural unless it is
obvious that it is meant otherwise.
[0110] Benefits, other advantages, and solutions to problems have
been described above with regard to specific embodiments. However,
the benefits, advantages, solutions to problems, and any feature(s)
that may cause any benefit, advantage, or solution to occur or
become more pronounced are not to be construed as a critical,
required, or essential feature of any or all the claims.
[0111] After reading the specification, skilled artisans will
appreciate that certain features are, for clarity, described herein
in the context of separate embodiments, may also be provided in
combination in a single embodiment. Conversely, various features
that are, for brevity, described in the context of a single
embodiment, may also be provided separately or in any
subcombination.
[0112] Further, references to values stated in ranges include each
and every value within that range. When the terms "about" or
"approximately" precede a numerical value, such as when describing
a numerical range, it is intended that the exact numerical value is
also included. For example, a numerical range beginning at "about
25" is intended to also include a range that begins at exactly
25.
[0113] Item 1. An abrasive article comprising:
a coated abrasive having a plurality of abrasive areas arranged in
a pattern, wherein the pattern has a controlled non-uniform
distribution, and wherein the pattern is at least one of a radial
pattern, a spiral pattern, a phyllotactic pattern, an asymmetric
pattern, or combinations thereof.
[0114] Item 2. The abrasive article of item 1, wherein the pattern
is a spiral pattern.
[0115] Item 3. The abrasive article of item 2, wherein the spiral
pattern is one of an Archimedean spiral, a Euler spiral, a Fermat's
spiral, a hyperbolic spiral, a lituus, a logarithmic spiral, a
Fibonacci spiral, a golden spiral, or combinations thereof.
[0116] Item 4. The abrasive article of item 3, wherein the pattern
has a controlled asymmetry.
[0117] Item 5. The abrasive article of item 4, wherein the
controlled asymmetry is an at least partial rotational asymmetry
about the center of the pattern.
[0118] Item 6. The abrasive article of item 5, wherein the
rotational asymmetry extends to at least 51%, at least 70%, or at
least 85% of the abrasive areas of the pattern.
[0119] Item 7. The abrasive article of item 5, wherein the
rotational asymmetry extends to at least 20 abrasive areas, at
least 50 abrasive areas, or at least 100 abrasive areas of the
pattern.
[0120] Item 8. The abrasive article of item 5, wherein the pattern
is rotationally asymmetric about the center of the pattern.
[0121] Item 9. The abrasive article of item 1, wherein the pattern
is a phyllotactic pattern.
[0122] Item 10. The abrasive article of item 9, wherein the pattern
is a spiral phyllotactic pattern.
[0123] Item 11. The abrasive article of item 10, wherein the
pattern has a number of clockwise spirals and a number of
counter-clock wise spirals, wherein the number of clockwise spirals
and the number of counterclockwise spirals are Fibonacci numbers or
multiples of Fibonacci numbers.
[0124] Item 12. The abrasive article of item 11, wherein the number
of clockwise spirals and the number of counterclockwise spirals are
Lucas numbers or multiples of Lucas numbers.
[0125] Item 13. The abrasive article of item 11, wherein the number
of clockwise spirals and the number of counterclockwise spirals are
in a ratio that converges on the golden ratio.
[0126] Item 14. The abrasive article of item 10, wherein the spiral
phyllotactic pattern has a controlled asymmetry.
[0127] Item 15. The abrasive article of item 10, wherein the spiral
phyllotactic pattern is a sunflower pattern.
[0128] Item 16. The abrasive article of item 11, wherein the
pattern is described in polar co-ordinates by the following
equation:
.phi.=n*.alpha.,r=c n (Eq. 1)
[0129] where:
n is the ordering number of an abrasive area, counting outward from
the center of the pattern; .phi. is the angle between a reference
direction and a position vector of the n.sup.th abrasive area in a
polar coordinate system originating at the center of the pattern,
such that the divergence angle between the position vectors of any
two successive abrasive areas is a constant angle .alpha.; r is the
distance from the center of the pattern to the center of the
n.sup.th abrasive area; and c is a constant scaling factor.
[0130] Item 17. The abrasive article of item 16, wherein at least
about 51%, at least about 70%, at least about 85% of the abrasive
areas conform to Eq.1.
[0131] Item 18. The abrasive article of item 16, wherein the
pattern has a divergence angle in polar co-ordinates that ranges
from about 100.degree. to about 170.degree..
[0132] Item 19. The abrasive article of item 16, wherein the
pattern has a divergence angle that is 137.508.degree..
[0133] Item 20. The abrasive article of item 16, wherein at least
about 80%, at least about 85%, at least about 90% of the total
abrasive area conforms to Eq.1.
[0134] Item 21. The abrasive article of item 16, wherein the
plurality of abrasive areas ranges from about 5/10/20 abrasive
areas to about 500/1000/10,000 abrasive areas.
[0135] Item 22. The abrasive article of item 16, wherein the
pattern covers substantially the entire face of the abrasive
article.
[0136] Item 23. The abrasive article of item 16, wherein an edge of
an outermost abrasive area of the pattern intersects the edge of
the abrasive article.
[0137] Item 24. The abrasive article of item 16, wherein an edge of
an outermost abrasive area of the pattern is at least a specific
distance from the edge of the abrasive article.
[0138] Item 25. The abrasive article of item 16, wherein the
pattern covers only a portion of the face of the abrasive
article.
[0139] Item 26. The abrasive article of item 16, wherein the
pattern covers periodic portions of the face of the abrasive
article.
[0140] Item 27. The abrasive article of item 16, wherein the
pattern has a total open area of about 15% to about 99.5% of the
surface potential surface area of the abrasive article.
[0141] Item 28. The abrasive article of item 16, having a total
abrasive surface area that ranges from about 4.5% to about 85% of
the total potential surface area.
[0142] Item 29. The abrasive article of item 16, having the shape
of a disc.
[0143] Item 30. The abrasive article of item 16, wherein the
abrasive areas have a shape selected from one of short line
segments, polygons, ellipsoids, circles, arcs, spirals, whorls, a
spiral lattice, or combinations thereof.
[0144] Item 31. A coated abrasive article comprising:
a backing layer having a first major side and a second major side;
and an abrasive layer disposed on the first major side of the
backing layer, wherein the abrasive layer comprises a plurality of
abrasive areas arranged in a pattern having a controlled
non-uniform distribution, and is at least one of a radial pattern,
a spiral pattern, a phyllotactic pattern, an asymmetric pattern, or
combinations thereof.
[0145] Item 32. A method of making an abrasive article
comprising:
disposing an abrasive layer on a backing; wherein the abrasive
layer comprises a plurality of abrasive areas arranged in a pattern
having a controlled non-uniform distribution that is at least one
of a radial pattern, a spiral pattern, a phyllotactic pattern, an
asymmetric pattern, or combinations thereof.
[0146] Item 33. A coated abrasive article comprising:
a plurality of abrasive areas disposed on a major surface of the
coated abrasive article, wherein the abrasive areas are configured
to form a plurality of air flow paths comprising arcs, spirals,
whorls, phyllotactic patterns, or combinations thereof.
[0147] Item 34. The coated abrasive of item 34, wherein the pattern
of air flow paths comprises radiating arcurate paths, radiating
spiral paths, or combinations thereof.
[0148] Item 35. The coated abrasive of item 34, wherein the pattern
of air flow paths comprises a combination of inner radiating spiral
paths and outer radiating spiral paths.
[0149] Item 36. The coated abrasive of item 34, wherein the pattern
of air flow paths comprises a combination of clock-wise radiating
spiral paths and counter clock-wise radiating spiral paths.
[0150] Item 37. The coated abrasive of item 34, wherein the pattern
of air flow paths further comprises an annular airflow path that
intersects the radiating arcurate paths or radiating spiral paths,
or combinations thereof.
[0151] Item 38. The coated abrasive comprising a pattern of air
flow paths, wherein the pattern of air flow paths is generated from
x and y co-ordinates of a controlled non-uniform distribution
pattern.
[0152] Item 39. The coated abrasive of item 38, wherein the x and y
co-ordinates of the controlled non-uniform distribution pattern are
transposed and rotated according to the equation (Eq. 2) below, to
determine x' and y' co-ordinates of the pattern of air flow paths,
wherein 8 is equal to .pi./n in radians and n is any integer:
x ' y ' = cos .theta. - sin .theta. sin .theta. cos .theta. x y (
Eq . 2 ) ##EQU00002##
[0153] Item 40. The coated abrasive of item 39, wherein the
controlled non-uniform distribution pattern is a phyllotactic
pattern.
[0154] Item 41. The coated abrasive of item 40, wherein the
controlled non-uniform distribution pattern is the Vogel
equation.
[0155] Item 42. The coated abrasive of item 41, wherein n is any
integer from 1 to 10.
[0156] Item 43. The coated abrasive of item 42, wherein n is 1, 2,
3, 4, 5, or 6.
[0157] Item 44. The coated abrasive of item 39, wherein the pattern
of air flow paths comprises a plurality of openings, cavities,
channels, passages, or combinations thereof.
[0158] Item 45. An abrasive system comprising:
a coated abrasive; and a back-up pad, wherein the coated abrasive
comprises a controlled non-uniform distribution pattern of abrasive
areas, and wherein the back-up pad comprises a plurality of air
flow paths disposed in a pattern adapted to correspond with the
abrasive areas of the coated abrasive.
* * * * *