U.S. patent application number 16/635427 was filed with the patent office on 2020-05-21 for placement of abrasive particles for achieving orientation independent scratches and minimizing observable manufacturing defects.
The applicant listed for this patent is 3M INNOVATIVE PROPERTIES COMPANY. Invention is credited to James P. Endle, Vincent Jusuf, Richard L. Rylander, Michael J. Wald.
Application Number | 20200156215 16/635427 |
Document ID | / |
Family ID | 63013069 |
Filed Date | 2020-05-21 |
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United States Patent
Application |
20200156215 |
Kind Code |
A1 |
Jusuf; Vincent ; et
al. |
May 21, 2020 |
PLACEMENT OF ABRASIVE PARTICLES FOR ACHIEVING ORIENTATION
INDEPENDENT SCRATCHES AND MINIMIZING OBSERVABLE MANUFACTURING
DEFECTS
Abstract
The present invention includes an abrasive tool comprising a
substrate and plurality of abrasive grains arranged in a
pseudo-random pattern on the substrate. The abrasive grains cover
in the range of 10% to 30% of the substrate surface, and in some
instances, the arrangement of abrasive grains demonstrate improved
orientation independence and homogeneity in distribution of
abrasive grains.
Inventors: |
Jusuf; Vincent;
(Minneapolis, MN) ; Wald; Michael J.; (Woodbury,
MN) ; Endle; James P.; (New Richmond, WI) ;
Rylander; Richard L.; (Stillwater, MN) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
3M INNOVATIVE PROPERTIES COMPANY |
St. Paul |
MN |
US |
|
|
Family ID: |
63013069 |
Appl. No.: |
16/635427 |
Filed: |
July 3, 2018 |
PCT Filed: |
July 3, 2018 |
PCT NO: |
PCT/IB2018/054924 |
371 Date: |
January 30, 2020 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
62538895 |
Jul 31, 2017 |
|
|
|
Current U.S.
Class: |
1/1 |
Current CPC
Class: |
B24D 11/001 20130101;
B24D 3/00 20130101; B24D 3/28 20130101; B24D 11/00 20130101 |
International
Class: |
B24D 11/00 20060101
B24D011/00; B24D 3/28 20060101 B24D003/28 |
Claims
1. An abrasive tool comprising a substrate and plurality of
abrasive grains arranged in a pseudo-random pattern on the
substrate, wherein the abrasive grains cover in the range of 10% to
30% of the substrate surface and wherein the arrangement of
abrasive grains has a score of 20% or less on the Orientation
Independence Test and has a score in the range of 0.7 to 0.9 in the
Local Homogeneity Index Test.
2. The abrasive tool of claim 1, wherein the arrangement of
abrasive grains has a score of 10% or less on the Orientation
Independence Test.
3. The abrasive tool of claim 1, wherein the abrasive grains cover
10% to 15% of the surface substrate.
4. The abrasive tool of claim 1, wherein the substrate comprises a
lofty non-woven material.
5. The abrasive tool of claim 4, wherein the lofty non-woven
material comprises a densified surface.
6. The abrasive tool of claim 1, wherein the abrasive grains are at
least one of: single abrasive grits, cutting points, and composites
comprising a plurality of abrasive grits, and combinations
thereof.
7. The abrasive tool of claim 6 wherein the composites comprise a
plurality of abrasive grits in a resin.
8. The abrasive tool of claim 1, wherein the abrasive grains are
printed onto the substrate.
9. The abrasive tool of claim 1, wherein the average abrasive grain
height from the surface of the substrate is in the range of 0.25 mm
to 1.5 mm.
10. The abrasive tool of claim 1, wherein the pseudo-random pattern
comprises clusters of abrasive grains.
11. The abrasive tool of claim 1, wherein the substrate is selected
from the group consisting of paper, woven fabrics, nonwoven
fabrics, calendared nonwoven fabrics, polymeric films, stitchbonded
fabrics, open cell foams, closed cell foams, and combinations
thereof.
12. The abrasive tool of claim 1, wherein the substrate comprises
an open cell foam or a closed cell foam laminated to a substrate
selected from the group consisting of paper, woven fabrics,
nonwoven fabrics, calendared nonwoven fabrics, polymeric films,
stitchbonded fabrics, open cell foams, closed cell foams, and
combinations thereof.
13. The abrasive tool of claim 1, wherein the pseudo-random pattern
is a pseudo-poisson pattern.
14-24. (canceled)
Description
FIELD OF THE INVENTION
[0001] The present invention relates to the placement of abrasive
features on an abrasive work tool.
BACKGROUND
[0002] Tools with abrasive features can be used for a variety of
applications, including grinding, polishing, abrading, finishing,
scouring and scrubbing. Abrasive tools can be made with a variety
of substrates including paper, woven fabrics, nonwoven fabrics,
calendared nonwoven fabrics, polymeric films, stitch-bonded
fabrics, open cell foams, closed cell foams, and combinations
thereof. Abrasive tools can also include a variety of types of
abrasive features or abrasive grains, including single abrasive
grits, cutting points, and composites comprising a plurality of
abrasive grits, and combinations thereof.
[0003] Abrasive features or grains can be arranged on a variety of
surfaces in a variety of methods and arrangements. For example,
some abrasive features are randomly distributed on a surface of a
work tool and placed using coating, spraying, printing and solvent
methods. Some abrasive features can be arranged in a pattern on a
surface of a work tool.
[0004] The arrangement or placement of abrasive features can impact
many aspects of the abrasive tool including the efficiency of
cutting, the orientation in which the abrasive tool should be used,
the scratch pattern left behind by the tool, and the manufacturing
requirements for the abrasive tool. Improvements in abrasive tools
to allow orientation independence, reduced visibility of scratch
patterns, and ease of manufacturing are desired.
SUMMARY
[0005] The present disclosure provides several advantages over the
state of the art. For example, the present disclosure provides for
an abrasive tool that can perform more consistently in any mode of
use, or when held at any orientation relative to a cut direction.
The present disclosure also provides for an abrasive tool with
abrasive grains arranged in a manner to reduce visibility of
scratch patterns left on a work piece. The present disclosure
further provides for placement of abrasive grains on an abrasive
tool in a pseudo-random pattern such that slight manufacturing
defects, such as missing or extra abrasive grains, are not
noticeable to a user of the abrasive tool. The present disclosure
also provides for an arrangement of abrasive features that provides
for more even distribution of mass removal from a work piece. In
some instances, the present disclosure allows for an arrangement of
abrasive particles on a substrate in a way that can be visually
pleasing independent of the orientation or shape of the
substrate.
[0006] In one aspect, the present invention includes an abrasive
tool comprising a substrate and plurality of abrasive grains
arranged in a pseudo-random pattern on the substrate. The abrasive
grains cover in the range of 10% to 30% of the substrate surface,
and the arrangement of abrasive grains has a score of 20% or less
on the Orientation Independence Test.
[0007] In another aspect, the present invention includes an
abrasive tool comprising a substrate and a plurality of abrasive
grains arranged in a pseudo-random pattern on the substrate,
wherein the abrasive grains cover in the range of 10% to 30% of the
substrate surface and wherein the arrangement of abrasive grains
has a score in the range of 0.7 to 0.9 in the Local Homogeneity
Index Test.
[0008] In some instances, the arrangement of abrasive grains has a
score of 10% or less on the Orientation Independent Test.
[0009] In some instances, the abrasive grains cover 10% to 15% of
the surface substrate.
[0010] In some instances, the substrate comprises a lofty non-woven
material.
[0011] In some instances, the lofty non-woven material comprises a
densified surface.
[0012] In some instances, the abrasive grains are at least one of:
single abrasive grits, cutting points, and composites comprising a
plurality of abrasive grits, and combinations thereof.
[0013] In some instances, the composites comprise a plurality of
abrasive grits in a resin.
[0014] In some instances, the abrasive grains are printed onto the
substrate.
[0015] In some instances, the average abrasive grain height from
the surface of the substrate is in the range of 0.25 mm to 1.5
mm.
[0016] In some instances, the pseudo-random pattern comprises
clusters of abrasive grains.
[0017] In some instances, the substrate is selected from the group
consisting of paper, woven fabrics, nonwoven fabrics, calendared
nonwoven fabrics, polymeric films, stitchbonded fabrics, open cell
foams, closed cell foams, and combinations thereof.
[0018] In some instances, the substrate comprises an open cell foam
or a closed cell foam laminated to a substrate selected from the
group consisting of paper, woven fabrics, nonwoven fabrics,
calendared nonwoven fabrics, polymeric films, stitchbonded fabrics,
open cell foams, closed cell foams, and combinations thereof.
[0019] In some instances, the pseudo-random pattern is a
pseudo-poisson pattern.
BRIEF DESCRIPTION OF THE DRAWINGS
[0020] The invention may be more completely understood in
consideration of the following detailed description of various
aspects of the invention in connection with the accompanying
drawings, in which:
[0021] FIG. 1 shows an example of an abrasive tool with a regular
hexagonal pattern of abrasive grains.
[0022] FIG. 2 shows an image of a scratch pattern formed by the
prior art abrasive tool of FIG. 1 in two different cutting
directions.
[0023] FIG. 3 shows an example of a pseudo random pattern of
abrasive grains, wherein the pseudo random pattern is a
pseudo-poisson pattern with a 14% abrasive grain coverage.
[0024] FIG. 4 shows an example of five circular active areas on an
abrasive tool with a regular hexagonal pattern of abrasive
grains.
[0025] FIG. 5 shows cutting direction for an abrasive tool.
[0026] FIG. 6 shows a flow chart illustrating how to convert an
abrasive pattern into data that can be used for the Orientation
Independence Test and the Local Homogeneity Test.
[0027] FIG. 7 shows the results of the Orientation Independence
Test for abrasive grain pattern in FIG. 4.
[0028] FIG. 8 shows the output of the Local Homogeneity Test for
the abrasive grain pattern in FIG. 4.
[0029] FIG. 9 shows the schematic for the regular hexagonal
abrasive patterns used for Comparative Examples 1 and 2.
[0030] FIGS. 10a-10h show images of the patterns used for the
Examples.
[0031] It is understood that the aspects of the invention may be
utilized and structural changes may be made without departing from
the scope of the invention. The figures are not necessarily to
scale. Like numbers used in the figures refer to like components.
However, it is understood that the use of a number to refer to a
component in a given figure is not intended to limit the component
in another figure labeled with the same number.
DETAILED DESCRIPTION
[0032] FIG. 1 shows a perspective view of example of an abrasive
tool 10 with a regular hexagonal pattern of abrasive grains 12.
Abrasive grains 12 comprise abrasive particles suspended in a resin
and printed on a densified surface 16 of nonwoven web 14.
[0033] FIG. 2 shows an image of scratch patterns formed by the
abrasive tool of FIG. 1. When the abrasive tool 20 is held at the
orientation shown in FIG. 2, and the tool is moved in a lateral
direction as shown by arrow 28, the cut patterns 22 created on a
stainless steel surface. In general, a cutting surface or a work
piece can be any surface less hardness than the abrasive
features.
[0034] The cut patterns 22 on surface 21 are approximately evenly
spaced apart and quite distinct and visible. In this scenario, the
patterns are particularly visible because each of abrasive grains
23a, 23b, 23c, and so on are all cutting along the same line, thus
resulting in a very noticeable cut or scratch pattern. When
abrasive tool 24 is held at a slightly angled orientation, and the
tool is moved in a lateral direction as indicated by arrow 28, the
resulting cut or scratch lines 26 are more randomly spaced apart,
but are still quite visible
[0035] Further, if a single abrasive grain was missed during the
manufacturing process of abrasive tools 20 and 24, or if an extra
abrasive grain was added to one of the pads, it would be visually
apparent to even a casual observer. This results in a more
challenging manufacturing quality standard and greater waste from
the manufacturing process.
[0036] FIG. 3 shows an example of a pseudo random pattern of
abrasive grains consistent with the present invention. A pseudo
random pattern is an arrangement of abrasive grains that does not
include a visually identifiable pattern to a human observer.
However, in a pseudo-random pattern, the same seed in an algorithm
that determines placement of the abrasive grains will result in the
same distribution or placement of abrasive grains on an abrasive
tool every time the algorithm is executed. While a pseudo-poisson
arrangement of abrasive grains is used as an example in the present
application, other specific pseudo-random abrasive arrangements
will be apparent to one of skill in the art upon reading the
present disclosure and are within the scope of the present
invention.
[0037] Unlike a purely random pattern, a pseudo random pattern can
provide the advantage of a relatively even distribution of abrasive
grains on an abrasive tool without the manufacturing constraints
created by a regular pattern of abrasive grains. Further, random
patterns can have relatively large working surface areas without
abrasive grain coverage, resulting in inferior performance in that
particular area, while other areas may have a high concentration of
abrasive grains, resulting in excessive or visual scratching
resulting from use of that portion of the abrasive tool.
[0038] Unlike a regular pattern (as shown in FIG. 1), a pseudo
random pattern can provide greater orientation independence, as
defined according to the Orientation Independence Test, so that it
can be used to abrade or scour at any orientation with comparable
results. Additionally, relatively minor manufacturing defects in
abrasive grain placement are visually apparent in the instance of a
regular or patterned arrangement of abrasive grains. But a
pseudo-random pattern consistent with the present application
provides for more manufacturing flexibility.
[0039] In some instances, a pseudo-random pattern can comprise
clusters of abrasives grains, where each cluster includes a
plurality of abrasive grains arranged in a pseudo-random pattern,
and where the clusters of abrasive grains form an array on a
substrate in a regular or pseudo-random arrangement.
[0040] Generally, a cluster is a subsection of the hand-pad
containing at least 3 features such that the percent of local area
coverage of abrasive grains in the cluster is greater than the
percent total area coverage of the abrasive grains in the hand
pad.
[0041] As shown in FIG. 3, the pseudo random pattern is a
pseudo-poisson pattern with a 14% abrasive grain coverage. A
pseudo-poisson pattern is a variation on a traditional poisson
distribution and is described in more detail in the Examples
section. While 14% abrasive grain coverage is shown in FIG. 3, an
abrasive tool consistent with the present disclosure may have a
range of abrasive grain coverage, for example, abrasive grains may
cover 10% to 30% of the working surface of an abrasive tool.
Alternatively, an abrasive tool may have abrasive grain coverage in
the range of 10% to 20% or 10% to 15%. While more abrasive grain
coverage on a tool may lead to faster or more efficient cutting,
other factors such as freer cutting to allow debris to fall away
easily from the tool, cooler grinding or abrading, and
manufacturing efficiency can result from lower abrasive grain
coverage.
[0042] Abrasive tool 30 includes a substrate 32 and abrasive grains
33. In FIG. 3, the abrasive tool 30 is a hand pad that can be used
for scouring or scrubbing; however, an abrasive tool consistent
with the present disclosure can be any type of substrate with
abrasive grains present. Examples of abrasive tools include tools
for grinding, scouring, polishing, cutting, cleaning, finishing and
sanding.
[0043] A substrate consistent with the present disclosure can
include any substrate, such as paper, cloth, woven fabrics,
nonwoven fabrics, calendared nonwoven fabrics, polymeric films,
stitch-bonded fabrics, open cell foams, closed cell foams,
vulcanized fiber materials, scrims, films, foils, screens,
perforated sheets, other web-like substrates and combinations
thereof. A substrate can include a single material with different
types of treatments on different parts of the material. For
example, a substrate made from a non-woven web may include a
semi-densified layer as described by U.S. Patent Publication
2017/0051442 to Endle et al., incorporated herein by reference.
[0044] An abrasive grain may refer to single abrasive grits,
engineered, structured or shaped cutting points, abrasive
agglomerates, or abrasive particles, composites comprising a
plurality of abrasive grits or composites thereof. Examples of
abrasive grits include diamond, cubic boron nitride, boron,
suboxide, various alumina grains, such as fused alumina, sintered
alumina, seeded or unseeded sintered sol gel alumina, alumina
zirconia grits, oxy-nitride alumina grits, silicon carbide,
tungsten carbide, titanium carbide, garnet, iron oxide, tin oxide,
feldspar, flint, emery, and modifications and combinations thereof.
Such abrasive grits may exhibit a Mohs hardness in the range of
8-10 Mohs. Other materials that exhibit sufficient hardness to
provide a scouring function may include, for example, particles of
melamine-formaldehyde resin, phenolic resin, polymethl
methacrylate, polystyrene, polycarbonate, certain polyesters and
polyamides, and the like. Such materials may have a hardness in the
range of at least 3 Mohs.
[0045] An abrasive grain may be any size consistent with the
desired application for the abrasive tool. A composite having a
plurality of abrasive grits in a resin may have a diameter in the
range of 0.10 mm to 5 mm. Or may diameter in a range defined by any
of 0.10 mm, 0.50 mm, 1 mm, 1.5 mm, 2 mm, 2.5 mm, 3 mm, 4 mm or 5
mm. A composite may have a height in the range of 0.05 mm to 2 mm.
Or may have a height in a range defined by any of 0.10 mm, 0.25 mm,
0.50 mm, 0.75 mm, 1.0 mm, 1.5 mm or 2 mm.
[0046] Examples of shaped abrasive particles can be found in U.S.
Pat. No. 5,201,916 (Berg); U.S. Pat. No. 5,366,523 (Rowenhorst RE
35,570); and U.S. Pat. No. 5,984,988 (Berg). U.S. Pat. No.
8,034,137 (Erickson et al.) describes alumina crushed abrasive
particles that have been formed in a specific shape, then crushed
to form shards that retain a portion of their original shape
features. In some instances, shaped alpha alumina particles are
precisely-shaped (i.e., the particles have shapes that are at least
partially determined by the shapes of cavities in a production tool
used to make them.)
[0047] Structured or shaped abrasive particles may be desirable for
more efficient or higher precision grinding, polishing or abrading
applications. In these types of tools, small shaped composite
structures, such as three dimensional pyramids, diamonds, lines,
and hexagonal ridges are replicated in a regular pattern on a
surface of a tool.
[0048] Abrasive agglomerates can include single abrasive particles
bonded together with, for example, a polymer, a ceramic, a metal or
a glass to form an abrasive agglomerate.
[0049] Composites comprising a plurality of abrasive grits can
include any type of abrasive grit discussed herein, or another type
of abrasive grit that would be apparent to use to one skilled in
the art upon reading the present disclosure. Abrasive grits can be
combined with a range of resins, such as thermosetting resins, UV
curable resins, solvent-based resins, including, in a non-limiting
fashion, resins such as phenolic resins, aminoplast resins, curable
acrylic resins, cyanate resins, urethanes, latex resins, nitrile
resin, ethylene vinyl acetate resin, polyurethane resin, polyurea
or urea-formaldehyde resin, isocyanate resin, styrene-butadiene
resin, styrene-acrylic resin, vinyl acrylic resin, melamine resin,
polyisoprene resin, epoxy resin, ethylenically unsaturated resin,
and combinations thereof.
[0050] Abrasive grains may be aligned and placed on a substrate
using an alignment tool as described in U.S. Patent Publication No.
2016/037250. In another instance, direct transfer of abrasive
grains onto the substrate may be carried out by placing a droplet
of bonding material on the substrate at the proper location and
using a robotic arm to place each abrasive grain on the substrate.
A robotic arm may also be used to place a suspended array of
abrasive on a substrate that is pre-coated with a bonding material.
In some instances, a bonding material may be a resin as discussed
herein. In some instances, a bonding material may be an
adhesive.
[0051] In some instances, abrasive grains (and particularly grits
in resin) may be printed on an abrasive substrate using a screen
printing or other printing method as will be apparent to one of
skill in the art upon reading the present disclosure.
[0052] Abrasive grains may be bonded to a substrate using an
adhesive make coat, or they may be affixed directly to a substrate.
Adhesives or bonding materials used to secure an abrasive grain to
a substrate will depend on the particular abrasive grain and
substrate. Examples of bonding materials include adhesives, brazing
materials, electroplating materials, electromagnetic materials,
electrostatic materials, vitrified materials, metal powder bond
materials, polymeric materials and resin materials and combinations
thereof.
[0053] While the abrasive tool shown in FIG. 3 has a rectangular
substrate and is designed for lateral movement, an abrasive tool
may be a variety of geometric shapes and may be designed for
rotation instead of lateral movement. For example, an abrasive tool
may have a shape such as a rectangle, disk, rim, ring, cylinder,
belt, conical, irregular shapes (such as in dental drills) or any
combination of these shapes.
[0054] Variations on the present invention will be apparent to one
of skill in the art upon reading the present disclosure, and are
within the scope of the invention set forth herein.
Examples
[0055] Example patterns for abrasive hand-pad articles were
generated. The scratch patterns on a simulated surface were
analyzed. And the results are shown below.
[0056] Test Methods
[0057] Orientation Independence Test (OIT)
[0058] OIT Test Overview
[0059] The OIT analyzed the number of unique scratches made by
Active Areas (AAs) chosen on a hand-pad (a type of abrasive tool).
The active areas were defined as sections of the hand-pad
encompassing a subset of the features used to abrade a substrate.
The analysis consisted of randomly chosen (AAs) on the hand-pad
surface that were of equal size and encompassed 10 to 50 abrasive
features or abrasive grains. FIG. 4 shows an example of five
circular AAs 41, 42, 43, 44, 45 chosen on a hand-pad 40 with a
hexagonally close-packed (Hex) abrasive pattern.
[0060] To conduct the OIT, linear scratches made or simulated with
the chosen AAs 41, 42, 43, 44, 45 covering cutting directions
ranging from 0 to 90 degrees in one degree increments, where 0
degree cutting direction is defined to be in the X direction were
evaluated. FIG. 5 illustrates cutting direction. Axis 51 shows the
alignment of the abrasive grains with X and Y coordinates. Diagram
52 shows a cut direction at a 0 degree angle. Diagram 53 shows a
cut direction at a 90 degree angle.
[0061] The OIT linear scratch test can be simulated or performed on
a physical abrasive tool. The simulated test assumes that both the
2D coordinates of the centers of the abrasive features, and the
average feature diameter on the hand-pad are known. Also note that
the simulated test can be performed from a physical hand-pad or
other type of abrasive tool providing these inputs are made
available. For a step-by-step procedure on how the inputs can be
obtained from a physical hand-pad, refer to the section titled `OIT
Test Input` below.
[0062] OIT Test Input
[0063] For the simulated OIT test described, the tests take as
input: 1) the 2D coordinate of the centers of the abrasive
features, and 2) the average diameter of the envelope that
surrounds each abrasive feature. The method to obtain these two
inputs for a physical hand pad or other abrasive tool can be done
through image analysis and is illustrated in the steps shown in
FIG. 6 and described below:
[0064] Step 1: Image Capture 61 of Abrasive Tool
[0065] Place abrasive tool onto a flat surface so that the abrasive
grains (or abrasive features) are clearly visible. Arrange a camera
so that the lens points in the direction approximately
perpendicular to the hand-pad. Place the camera sufficiently far to
capture the entire surface of the abrasive tool in the camera's
field of view and capture the image. Abrasive tool 64 in FIG. 6 is
an example of an image capture of a hand-pad with a hexagonal
abrasive grain pattern. Also shown in image 64 is the definition of
the XY plane (that is, the XY plane is defined as the plane spanned
by the flat abrasive tool surface). For abrasive tools that are not
flat, a rectangular representative surface area of the abrasive
tool can be extracted, flattened, and used for the following
analysis.
[0066] Step 2: Acquire Coordinates 62 of Abrasive Grain Centers
[0067] Define one corner of the hand-pad as (0, 0) and generate
list of the coordinates of the centers of the abrasive features.
Image 65 in FIG. 6 shows an example of acquiring the coordinates of
three abrasive grains 65a (coordinates (84, 2.5)), 65b (coordinates
(72, 2.5)), and 65c (coordinates (60, 2.5)) on the hand-pad.
[0068] Step 3: Acquire Average Diameter 63 of the Abrasive
Grains
[0069] Define the average diameter of the abrasive grains or
abrasive features as:
D Ave = 1 N pad i = 1 N pad D i ##EQU00001##
[0070] where D.sub.i is the diameter of each abrasive grain. When
an abrasive grain is non-circular, D.sub.i is measured as the
diameter of the smallest circle that can fit around the abrasive
grain. N.sub.pad is the number of grains on the abrasive pad or in
the sampled section. Image 66 in FIG. 6 shows an example of
acquiring the abrasive grain diameter three of the abrasive grains
66a, 66b, 66c on the abrasive tool. Each of the abrasive grains
66a, 66b, 66c had a diameter of 2.5 mm as shown in Image 66.
[0071] Performing the OIT Test
[0072] The OIT method uses a scratch profile made by N.sub.OIT
cutting points for analysis. N.sub.OIT should be in the range of 10
to 50 cutting points. N.sub.OIT represents the number of abrasive
grains in an AA.
[0073] For each cutting direction the number of unique scratches
found on the abraded substrate were counted. Multiple cutting
points may result in scratches that are very close or even
overlapping. Scratches that were closer to each other than 10% of
the average abrasive grain diameter (D.sub.AVE) were counted as a
single scratch. The analysis was repeated for the 90 cutting
directions considered and normalize by the maximum number of unique
scratches found. The OIT score is the difference between the
maximum and minimum number of unique scratches found in the 90
cutting directions considered. The pass/fail criteria is defined to
be patterns that exhibit OIT scores of less than 0.20 (i.e.,
OIT<0.20=pass). FIG. 7 shows an example of the output 70 of a
simulated OIT for the abrasive tool shown in FIG. 4. Points 73, 74
and 75 are all areas where multiple abrasive features scratched
along the same line. Orientation Independence is measured by the
difference between the highest and lowest point on the output 70.
Difference 72 is approximately 0.20 for the abrasive tool shown in
FIG. 4, and thus not a passing score on the OIT.
[0074] Local Homogeneity Test (LHT)
[0075] The LHT evaluates the homogeneity of the entire abrasive
tool by calculating the Homogeneity Index (HI) each of multiple
sections located on the abrasive tool. Each section considered was
chosen such N.sub.LHT of the nearest abrasive grains were included,
and N.sub.LHT was in the range of 40 to 70. When performing the LHT
on the abrasive tool shown in FIG. 4, the abrasive tool was divided
up into sections that were evenly spaced 1 mm apart. Each section
comprised a region containing 50 of the nearest abrasive grains.
Each section was analyzed according to equation below. The LHT
analyzes each section and creates a heat map based on the HI score
of each section. The HI score for a section on the abrasive tool is
given by:
HI = 1 - 1 N LHT i = 1 N LHT ( d i - d theory ) 2 d theory , d
theory = 2 A N LHT 3 ##EQU00002##
[0076] Where:
[0077] N.sub.LHT is the number of features in the bounding box;
[0078] A is the area of the bounding section; and
[0079] d.sub.i is the nearest neighbor distance of the i-th feature
in the bounding section.
[0080] The resulting HI is associated with the abrasive grain at
the center of a given section
[0081] The pass criteria for the LHT is defined as all sections on
an abrasive tool having an HI score between 0.7 and 0.9 (i.e.,
(0.7<HI<0.90)=pass).
[0082] FIG. 8 shows a heat map of the output of a LHT for the
abrasive grain pattern shown in FIG. 5. In the heat map shown in
FIG. 8, the LHI score is: (min, max)=(0.9395, 0.9956) (a failing
score).
[0083] Empirical observations of LHT results of several abrasive
tool examples indicated that abrasive tools with regions having
HI<0.70 was found to exhibit poor average feature spacing
control. On the other hand, regions with HI>0.90 are regions of
high symmetry which would manifest itself in poor OIT performance
implying sensitivity of the hand-pad to varying cutting directions.
Passing both tests (OIT and LHT) according to the passing criteria
described herein ensures that the patterns exhibit 1) consistent
feature to feature spacing across the hand-pad, and 2) an
insensitivity to cutting direction, regardless of which section of
the abrasive tool is used.
[0084] Simulated Abrasive Grain Examples
[0085] A total of eight different simulated abrasive grain
arrangements were tested under the OIT and the LHT. The eight
abrasive grain arrangements included four different "patterns",
with each pattern being tested at two different levels of abrasive
grain coverage, 14% and 26%, respectively.
[0086] Hex Pattern:
[0087] Two of the patterns were abrasive grains arranged in a
regular hex pattern. The 14% coverage hex pattern is shown in FIG.
10a (referred to as Comparative Example 1 or CE 1), and the 26%
coverage hex pattern is shown in FIG. 10b (referred to as
Comparative Example 2 or CE 2). FIG. 9 shows the basic arrangement
of abrasive grains use to create the hex pattern in FIGS. 10a and
10b. The hex pattern shown in FIG. 9 was two interpenetrating
rectangular grids where the second grid was offset by c and d in
the horizontal and vertical directions respectively. Distances a,
b, c, and d as labeled in FIG. 9 are shown in the table below for
CE1 and CE2.
TABLE-US-00001 TABLE 1 Quantities to generate the hex comparative
example patterns Hex at 14% (CE1) Hex at 26% (CE2) a 11.0 mm 8.5 mm
b 6.5 mm 4.5 mm c 5.5 mm 4.25 mm d 3.25 mm 2.25 mm
[0088] Vogel Pattern:
[0089] Two of the patterns were abrasive grains arranged in a Vogel
pattern. The 14% coverage Vogel pattern is shown in FIG. 10c
(referred to as Comparative Example 3 or CE 3), and the 26%
coverage Vogel pattern is shown in FIG. 10d (referred to as
Comparative Example 4 or CE 4). The Vogel pattern was defined by
the following equation:
r=c {square root over (n)},.theta.=ng
[0090] Where n represents a positive integer and indexes the number
of abrasive grains generated, c represents a positive real number,
and g represents an irrational number approximately equal to
2.39996 radians (an approximation of the golden angle). In the
present work, c=1 mm and so the (x,y) coordinate of the n-th
feature in the pattern was given by:
(X,Y).sub.n= {square root over (n)}(cos(ng), sin(ng))
[0091] Pseudo-Random Pattern:
[0092] Two of the patterns were abrasive grains arranged in a
Pseudo-Random (Pseudo-Poisson). The 14% coverage pseudo-random
pattern is shown in FIG. 10e (referred to as Example 1 or E1). The
26% coverage pseudo-random pattern is shown in FIG. 10f (referred
to as Example 2 or E2). The pseudo code below explains how the
locations for each point in the pseudo-random pattern of Example 1
and Example 2 were generated.
TABLE-US-00002 CODE FOR PSEUDO-POISSON PATTERN GENERATION Inputs:
PadX; Width of abrasive pad PadY; Height of abrasive pad x.sub.0;
Initial position of 1.sup.st dot. Bold quantities denote 2D
vectors. R.sub.ave; Average radius of dots Coverage; Area coverage
of dots .alpha.; User-prescribed to control spacing variance
(.DELTA.x, .DELTA.y); Vector of maximum allowable deviation from
minimum. Prescribed to control randomness Start of pseudo-code
PadArea = PadX * PadY; area of rectangular abrasive pad DotArea =
3.14159 * Rave{circumflex over ( )}2; area of each dot N.sub.pts =
Floor[(Coverage * Pad Area)/(DotArea)]; Number of points for
desired coverage X.sub.0 = x.sub.0; 1st point (taken as input) d =
Sqrt[ PadX{circumflex over ( )}2 + PadY{circumflex over ( )}2];
distance from periodic images of 1.sup.st point Energy = .alpha. /
d{circumflex over ( )}2 Energy increase due to insertion of
1.sup.st point For i=1 to N.sub.pts Loop to fill abrasive pad area
with points X = Minimize[Energy + alpha / (X.sub.i-1 - X) Find X
that minimizes energy. (X.sub.i-1 - X)]; Minimize[ ] is a standard
technique in numerical methods. The function here searches for X in
the abrasive pad that minimizes the value in the parenthesis
[Energy0 + alpha / (X.sub.i-1 - X) (X.sub.i-1 - X). `` denotes dot
product between two vectors Xi = X + [Rand([-1, 1]) * .DELTA.x;
Perturbed position to insert Rand[-1, 1]) * .DELTA.y]; randomness.
Rand[(-1, 1)] returns random number between -1 to 1. Energy =
Energy + alpha / (X.sub.i-1 - X.sub.i) (X.sub.i-1 - X.sub.i);
endfor end of pseudo-code Outputs: X.sub.0, X.sub.1, .... ,
X.sub.Npts Positions of all the points in the pattern
[0093] Random Pattern:
[0094] Two of the patterns were abrasive grains arranged in a
random manner. The 14% coverage random pattern is shown in FIG. 10g
(referred to as Comparative Example 5 or CE5). The 26% coverage
random pattern is shown in FIG. 10h (referred to as Comparative
Example 5 or CE5). The random arrangement of particles was
generated using Mathematica version 10.3 (a commercial mathematical
analysis tool available form Wolfram, Champaign, Ill.) random
number generator, a random hand-pad pattern was generated by
prescribing the minimum distance between each feature, and
generating enough points so as to cover the entire hand-pad at the
prescribed coverage.
[0095] In each of the Examples/Comparative Examples, the feature
diameters are all 2.5 mm, and the XY coordinates are can be derived
as described herein. The OIT and LHT described above were performed
on each of the Examples/Comparative Examples described. The results
from these tests are summarized in Table 2.
Results
TABLE-US-00003 [0096] TABLE 2 Results from the OIT and LHT of the 8
different abrasive feature patterns % Area LHI: Cover- OIT OIT: LHI
LHI Pass/ Example age Score Pass/Fail Min Max Fail E1 14 0.0571
Pass 0.7528 0.8801 Pass E2 26 0.0554 Pass 0.7410 0.8780 Pass CE1 14
0.2000 Fail 0.9395 0.9956 Fail CE2 26 0.1510 Pass 0.8751 0.9673
Fail CE3 14 0.0667 Pass 0.7799 0.9166 Fail CE4 26 0.0585 Pass
0.7722 0.9398 Fail CE5 14 0.0476 Pass 0.5461 0.7039 Fail CE6 26
0.0037 Pass 0.6419 0.7891 Fail
[0097] Of the various patterns tested, only E1 and E2 exhibited
passing scores for both the Orientation Independent Test and the
Local Homogeneity Test.
* * * * *