A
FRACTAL VIEW OF TOOL-CHIP INTERFACIAL FRICTION IN MACHINING
INTRODUCTION
The friction and wear in machining have been researched for
the last fifty years. However, accurate descriptions/interpretations
of the contact geometry are still largely unavailable. Prior
prediction of frictional boundary conditions is even more
difficult. Friction directly impacts the power consumed in
a cutting process and is inseparable from the wear of cut-ting
tools.
An accurate predictive model of the friction boundary conditions
(extent and geometry of sticking and sliding friction) in
machining is critical in tool design as well as in the development
of coatings. Frictional contact in the rake face also influences
the selection of cutting conditions and tool/work materials
for different machining applications. Further, accurate modeling
of the frictional boundary conditions is mandatory for the
development of accurate models for stress and temperature
determination, strain-rate and velocity field description,
shear angle and shear zone determination and tool wear calculations.
The frictional boundary in machining consists of varying extent
and geometry (map area, perimeter, etc) of sticking and sliding
interfaces, that could change over a period of time during
the cut. Statically, these boundaries also vary with different
cutting conditions and different tool and work materials.
For simplicity, past researchers have assumed pure sliding
geometry or a fixed geometry of sticking followed by sliding.
This is a very macroscopic approach that does not account
for the microscopic contacts that actually occur during machining
(Wright et al. 1979). In fact, significant inaccuracies result
due to the improper consideration of these contacts and the
'blanket assumption’ of the extent and geometry of sticking
and sliding friction. One of the reasons researchers have
not tried to model the frictional contacts is due to their
apparent non-Euclidean nature and the unavailability of
mathematical tools to model them. Since 1983, Fractals and
Fractal mathematics have been successfully developed to
model such fragmented patterns in nature. In fact, good
success has been reported in the application of fractals in
modeling surface roughness, cluster-cluster aggregation and
fluid fingering that have resulted in improved understanding
of the appropriate fields.
It is proposed that a reevaluation of the frictional
boundary conditions in machining using fractal geometry can
shed some new light and help create more accurate
descriptions of the cutting process. The perusal of the
literature indicates that there are no applications of
fractals in machining process (specifically friction)
modeling. However, examination of past experimental data
(rake face photographs, etc.) provided in the literature and
preliminary analysis conducted in this work strongly
indicate the fractal nature of seizure areas in machining.
There is significant untapped potential in this area with a
promise of better results that can significantly improve the
practice of machining.
STATE-OF-THE-ART IN FRICTION MODELING DURING MACHINING
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Conventional modeling uses either Merchant's model (pure
sliding-Figure 1a) or Zorev's Model (fixed geometry of sticking
(A) followed by sliding (B) as shown in Figure 2c, Figure
1d). (Notations in figure 1 is standard)
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Currently available techniques cannot accurately model
the situations shown in Figures 1b, 1c, 1e, 1f, 2a and 2b.
Further, photomicrographs in machining provided by Trent (1991)
indicate non-Euclidean boundaries of seizure islands. This
gives rise to more and more cases of frictional contact (than
illustrated in Figures 1 and 2), that occur in real machining,
that do not have any available models to describe them. Certainly
these cannot be modeled as over-enveloping rectangles as is
the majority practice. Making simplifying assumptions (and
force-fitting all cases to Merchant or Zorev models) can result
in poor calculation of variables such as coefficient of friction
and area and length of contact. A poor calculation of these
variables can result in a poor calculation of forces, workrate
(power), heat and temperatures (and consequently, wear).
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To achieve generality, the tool-chip interface friction
must hence be modeled as a networked cluster of microscopic
contacts, each of which could exhibit sticking or sliding,
at any given instant of time, as suggested by Wright et al.'s
(1979) qualitative arguments. In addition, the contacts must
be allowed to have different non-Eulidean shapes and sizes.
Then all of the above scenarios can be modeled and unified
within a single framework. Merchant and Zorev models will
hence only be special cases of the proposed general model.
However, current theory in machining does not have any such
model available.
MATHEMATICAL DESCRIPTION OF SEIZURE ISLANDS
It
is assumed based on a preliminary observation of
photomicrographs of tool rake face that seizure islands may
follow a power law relationship with a larger number of
seizure islands with smaller sizes. The distribution of
islands will have a fractal nature if they satisfy Korcak’s
power law relationship which states that the total number (N)
of islands of areas greater than a particular area a, on the
earth’s surface follow the relation,
 |
(1) |
where
B is Korcaks’ Patchiness exponent.
According to Mandelbrot [1982],
B = D / 2. Thus equation (1)
becomes
 |
(2) |
where
D is the fractal or box dimension for coastlines or
contours of the Aegian islands on the earth’s surface.
According to Majumdar and Bhushan [1990], the hills and
valleys of a machined metal surface on sufficient
magnification look similar to that found on the earth’s
surface, and thus may be represented by the same power law
distribution. Drawing analogies to the flow in porous media,
the seizure islands generated by adhesion of the chip to the
tool in machining can appear similar to the islands found on
the earth’s surface and may also be assumed to follow the
power law relationship. The seizure islands will assume a
fractal nature and follow the power law relationship if the
experimental plot of
 to log a yields a linear slope.
Through a normalization of the distribution in equation (2) by
the area of the largest island
as developed by Majumdar and Bhushan [1990] for contact spots
of a surface.
Kaye (1989) illustrates the size distribution of the Aegian
island system similar to that suggested by Korcak and the
corresponding log-log plot. N represents the number of islands
greater than or equal to a on the earth’s surface, and a is
the projected area of the islands [Kaye, 1989]. If
 be the size
distribution of seizure islands, then the number of seizure
islands
 of area lying between particular areas
a and a + da
can be obtained by differentiating equation (3) and summing
them to obtain the total seizure area as shown by Majumdar and
Bhushan [1990] for contact spots of a surface.
Accordingly,
the total seizure area,
 |
(4) |
This equation
provides for the computation of the total seizure area at
the tool-chip contact interface in terms of the seizure fractal
dimension D and area of largest island
 and
can be determined
experimentally by image analysis of photomicrographs of tool-chip
contact.
The main features as pointed out by Majumdar and Bhushan in
their study of elastic/plastic contacts are adapted here to
describe the power law size distribution of seizure islands
at the tool-chip interface. These are:
1). The
size distribution of seizure islands at the interface may
be fully determined by the knowledge of fractal dimension
D and the area of the largest island . The large number of
very small islands may present marginal effect on Ast.
2). The power law distribution may indicate the multi-scale
nature of seizure islands as the distribution may not limited
by any smallest length scale.
Due to
the large normal loads experienced at the tool-chip interface
in machining, the apparent area of contact approaches the
real area of contact and hence,
 |
(5) |
However, from Mandelbrot’s area (A)-perimeter (P) relation
[1982] for a fractal island , where Da is the fractal dimension of the enveloping profile
and A is the projected or apparent (enveloping) contact area.
The apparent (or real) contact area may be shown as
 |
(6) |
where
P is the enveloping (outermost) perimeter of tool-chip contact
surface.
For
example, the determination of D and for any tool-chip
micrograph can be easily demonstrated using the Box-Counting
Method. Here, plastic grids of different box sizes are used to
count the number of boxes N’ occupied by the tool contact
profile for a particular box-size l. The fractal or box
dimension is given by the slope of the log-log plot of N’
versus 1/lamda (Figure 3). Substituting equations (5) and (6), the
real contact area is given by,
Thus the total sliding area is obtained as
 |
(7) |
The welded
(seized) fraction of real contact area is shown as
 |
(8) |
Equation
8 provides a relationship for the welded fraction k based
on fractal dimensions D and Da , of the seizure and overall
rake face contact profile, respectively. Wright et al (1979)
make qualitative arguments that this ratio is dependent on
the work material purity, tool preparation, cutting speed
time and machine tool stability. The Mean Number (n) of Seizure
islands per unit area may be computed as
 |
(9) |
These
equations provide a static basis for the existence and microscopic
analysis for modeling the sticking/sliding contact geometry
in machining. More rigorous analysis must be conducted to
develop more comprehensive equations for the tool-chip boundary
conditions. Of most importance at this juncture is to experimentally
verify the fractal nature of the contact and show how the
fractal dimension can be determined.
FRACTAL DIMENSION AND OBSERVATIONS WITH VARYING CONDITIONS
The results
of the box counted Fractal Dimension can be found in Table
1, according to the tool edge designation. Figure 4 shows
binarized Micrographs of the rake face for four of the tests.
In Trial I of phase II cuts (T1A, T1B, T1C), three exact replicate
cuts were made. The fractal dimensions for these cuts are
very similar in value, with an average of 1.76 ± 0.017.
This suggests that, indeed, fractal dimension is a characterizing
value for a given set of cutting conditions. Visual analysis
of the images reveals that they share certain adhesion patterns,
particularly the adhesion-free region surrounded by adhesion
islands. The extent of the adhesion area is approximately
the same, with more sporadic sticking occurring on the left
side of the pattern. At the same time, there are some visible
differences, which apparently do not alter the fractal dimension.
While these are encouraging more trials should be run and
the stationarity checked. A stationary fractal is one that
yields the same dimension for the entire surface.
Trial 2 (T2A, T2B, T2C, T2D) was the first of the cutting
condition trials. Cutting times varied from 2 minutes – a
relatively short cut – to 12 minutes, the longest single
pass possible for those feed and speed conditions. For these
trials, some variability with time was anticipated, with
possibly more adhesion (larger fractal dimension) occurring
as time increased. This is because an increase in time can
often lead to the cleaning of interfaces, promoting virgin
contact between surfaces that are reactive. The actual
values do not seem to agree with this expectation. Further
testing must be conducted and stationarity checked in future
research.
In Trial 3 (T3A, T3B, T3C, T3D), the turning speed was varied,
extending over the range of acceptable speeds. As the turning
speed increased, the fractal dimension decreased, by approximately
20% over the full range of the trials (Figure 5). This trend
deserves a more in-depth analysis. Visual inspection of the
images reveals large changes in the adhesion patterns. Initially,
at the lowest speed, the adhesion pattern is extensive with
an area of complete seizure near the tip, and sporadic seizure
closer to the center of the tool. As the next higher speed,
the area of sporadic seizure has contracted dramatically,
with approximately the same area of complete seizure at the
edge. The next tool, at higher speed, shows further contraction
of the seizure area, with an adhesion-free zone in the middle
of that area. At the highest speed, very little adhesion occurs
at the very edge of the tool, followed by a clear area, then
a thin band of seizure.
Trial 4 (T4A, T4B, T4C, T4D) explored the possible variation
of D with change in feed rate and Trial 5 (T5A, T5B, T5C,
T5D) investigated the possible connection between depth of
cut and fractal dimension. No consistent trends of varying
fractal dimensions with these cutting conditions was observed,
although visual patterns of adhesion were different. Testing
the stationarity of fractals may be useful here and will be
investigated further in future research.
In fact, more tests must be conducted to explore the relationship
between cutting conditions, tool geometry, tool/work materials
and the fractal dimension. All the same, it must be realized
that the principal goal of this work was to show that the
seizure islands demonstrate fractal nature and that a fractal
dimension can be computed on the rake face. A factorial experiment
controlling the factors and levels must be conducted and statistical
analysis performed, prior to providing concrete discussions
on the role of cutting variables on the fractal dimension.
The issue of multiple dimensions has again not been addressed
in this work and will be the subject of continuing work.
MECHANISMS OF SEIZURE IN MACHINING
Both mechanical interlocking and welding are non-interactive
adhesion theories. That is, chip and tool will mesh together
or soften without chemically or atomically interacting with
each other. Still to be explored is the physical interaction
of atomic bonding that may occur between atoms and molecules
of the two surfaces (Loomis, 1985). A fundamental exploration
becomes important if the results developed here are to be
extended for multi-scale modeling of friction in machining.
The various categories of atomic bonding - covalent, ionic,
van der Waals, metallic, hydrogen - have been discussed by
Bhushan (1999). There are three types of bonds that may occur
in machining: metal-metal bonds, metal-oxide bonds, and oxide-oxide
bonds (Royer, 1968; Wright et al., 1979). Metal-metal bonds
would occur between two ideally clean surfaces, where neither
the chip nor the tool has any oxide layer. If one or the other
of these does have an oxide layer, but the other surface is
oxide-free, then a metal-oxide bond is possible. Finally,
if both chip and tool have an oxidized surface, then oxide-oxide
bonding is possible. Understanding which type of bond is likely
to form in a given situation may assist in modeling the adhesion
pattern on used tools. Based on the composition of the tool
and work materials, a first attempt is made to explain bond
strengths (bond dissociation energy), to study seizure and
separation.
One consideration in the modeling of adhesion is the likeliness
of oxides on the tool and chip surfaces. For the tool, this
is a fairly easy assessment. Both Trent (1991) and Kubaschewski
and Hopkins (1962) agree that tungsten carbide is highly reactive
in the presence of oxygen. This oxidation sensitivity can
be modulated by the presence of cobalt, titanium carbide,
chromium, and other elements (Kubaschewski and Hopkins, 1962).
However, because the tool is still 94% W-C, it is very likely
to develop an oxide layer unless specially treated. Since
none of the tools in our tests were vacuum packed, and the
cutting was performed in normal atmosphere, an oxide layer
on the tool can be assumed. The depth of the oxide should
range between 10 and 500 Å (Illiuc, 1980; Kubaschewski
and Hopkins, 1962; Rabinowicz, 1984), more likely at the lower
end of the range since the oxidation would mostly occur at
room temperature. This oxide layer is also likely to be tightly
bound, at the least near the tool surface. However, there
are reports to the effect that the strength of natural oxide
layers is quite lower than that of anodized oxide layers.
Certainly, both aluminum and iron are reactive in the
presence of oxygen. The outer layer of the work material is
certain to have an oxide layer. However, the estimate of the
thickness of that layer imply that it is most likely in the
same range as the tool oxide, i.e. no more than 500 Å thick
(Illiuc, 1980; Kubaschewski and Hopkins, 1962; Rabinowicz,
1984) which is very much smaller than the shallow cuts
performed in traditional machining, 0.01 inches deep, or
2,540,000 Å. Oxidation on the interfacial surface of the
chip is another possibility, while cutting in air. Further,
in traditional machining regime, Rowe and Smart reached a
conclusion that “the influence of atmospheric oxygen is
primarily associated with adsorption or reaction on the tool
rather than the chip (Rowe and Smart, 1973).” Vacuum
machining experiments must be pursued and compared against
cutting in air, to test this.
Metal-metal bonding is the bonding of oxide-free surfaces
and not the interaction of the metal atoms within the work
material. As discussed above, the tool surface initially is
almost certain to have an oxide layer, so metal-metal
bonding will not occur. However, if the oxide layer is
removed from the tool, then metal-metal bonding could occur.
The probability of the oxide layer being completely removed
at any spot is probably small, given the strong bond that
W-C, and its constituents, forms with oxygen. If this should
occur, then the resulting chip-tool bond is likely to be
very strong (Loomis, 1985). At the edge of the tool, the
cutting forces are greatest, the temperature close to its
maximum, and the speed of the chip higher. These conditions
may subject this region to oxide removal – this may
account for the nearly universal band of adhesion at the
edge of the tool images. Clear spots along the tool edge
could be areas where oxide was not completely removed, or
where chip material had been completely stripped from the
tool during cutting.
The severe conditions at the tool edge that could allow for
oxide removal tend to decrease, in some cases dramatically,
further back along the rake face. Here, then, a more likely
bonding mechanism is metal-oxide, where the chip bonds to
the tool oxide layer. In the dynamic cutting process, this
bond could be broken in several ways. First, since the
oxygen bond with the tool is likely to be stronger than the
bond with the chip, the adhered chip could be forced off,
leaving the tool’s oxide layer essentially untouched. Both
aluminum and iron bond more weakly to oxygen than tungsten
and carbon. Second, the oxide layer itself may fracture, so
that the chip is removed, with some oxide attached, and a
thinner oxide layer is left on the tool surface. Based upon
published data , this would be more likely to happen to the
steel chip than the aluminum chip. However, if the
relationship of Royer (1968), and Wright et al. (1979) is
true, the metal-oxide break is the more likely event. Both
of these situations would allow for a dynamic adhesion
pattern to the tool – at any one time, a region on the
tool may have adhered material, but that material could be
broken away in the next moment, leaving a visually unchanged
surface to the tool. Most of the rake face of the tool is
probably under this regime, which would account for the
sporadic adhesion patterns, as well as the differences in
pattern of the duplicate tools. This might also explain the
inconsistencies in the adhesion effects of surface oxidation
(Rowe and Smart, 1973). There is one more possible breakage
method for the metal-oxide bond: the chip removes all of the
oxide, exposing the clean surface of the tool, and allowing
for later metal-metal bonding. This is probably the least
likely outcome, but still possible. The final bonding
mechanism, that of oxide-oxide, has a smaller probability of
occurrence, but should not be discounted.
POSSIBLE CONTACT SUMMARIES
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Pure sliding
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Uniform stress on rake
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Full sticking
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Normal stress varying
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Frictional stress uniform over entire zone
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c) |
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d) |
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Non uniform stress (normal and shear)
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Sticking close to tip
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Frictional stress uniform over sticking area
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Frictional Stress
varies as a power function over sliding areas
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Normal stress varying
over entire area
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e) |
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f) |
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Figure 1. Possible contact
scenarios at the tool-chip interface (Orthogonal Cutting
assumption is made for demonstrating these scenarios).
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a. Our first assumption |
b. Trent assumption |
c. Zorev-type assumption. |
Figure 2.
Some assumptions employed regarding the tool-chip frictional
boundary conditions. (dark and shaded areas denote seizure).
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Figure 3. Figure illustrating computation of fractal dimension
using box counting. |
a.
T5B |
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b.
T2C |
c.
T1B
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d. T3D |
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Figure 4. Sample adhesion patterns, binarized (B/W) from
original micrographs (30X). (Adhesion islands indicated in
black. 2024 aluminum with uncoated tools.) |
FRACTAL DIMENSION BY BOX
COUNTING ROUTINE
To find more quantitative
support for a fractal nature, a procedure known as “box
counting” is performed on the SEM images. The general procedure
for box counting is as follows: various square grids, of known
dimensions, are individually overlaid on the image. All boxes
of the grid that contain any part of the feature of interest are
marked, and the number of those marked boxes is counted. After
all grids have been subject to this counting procedure, the data
is tabulated and graphed as a log-log plot. The independent
axis is the “size” of the box, i.e. the length of a single
square in the grid. The number of occupied boxes counted from
above forms the dependent axis. The slope of this log-log plot
is the fractal dimension, D.
After some trial and error,
the most advantageous method for performing box counting on the
SEM images was discovered. Since some of the tool images from
the preliminary trials had been saved directly from the SEM to a
disk as .TIF format files, they could be readily imported to a
computer program. The program Sigma Scan Proä,
was employed in the box counting procedure. This program
allowed the user to define and save grids of specific sizes, to
overlay on the images. It also had a marking and counting
feature; the user “marks” (left clicks) each occupied box on an
image, and the computer counts the marks when instructed. This
had two major advantages over other methods. First, it
eliminated human error in the counting process. Second, it
zoomed in on the image, helping the user define the boundaries
of adhesion islands and allowing for smaller, and more
effective, box sizes.
The preliminary experimental images saved as computer files had
default dimensions of 1024 x 1024 pixels. Using these
dimensions, a series of six different grid sizes were defined,
ranging from 150 pixels to 15 pixels, or 14.6% to 1.46% of the
image. The relative sizes of these boxes can be seen in Figure
A1. As each grid was overlaid on the image, the number of boxes
occupied by adhesion islands was counted, and those values
tabulated. The procedure for box counting is illustrated in
Figure A2. After all sizes had been utilized, the log-log graph
was generated by the MS Excelä
chart command, and the fractal dimension found using the MS
Excelä
data analysis – linear regression tool. A sample of this
process, including a box counting table, graph (Figure 3), and
regression statistics, can be found in Figure A3.
Before starting the counting procedure, various image
enhancement techniques were tried, in an attempt to enhance the
boundaries of the adhesion islands and allow for maximum
accuracy in counting. Techniques such as dilation and erosion,
as well as binarization and other methods were tried.
Ultimately, it was found that these techniques were not very
effective for this study. While some images could be made more
distinct by changing the contrast or brightness of an image, the
other enhancement procedures actually obscured some features.
This is due to the nature of the SEM scans – some island
boundaries appear lighter than the surrounding islands, and with
enhancement these boundaries would disappear.
Loss of detail was deemed
inappropriate for box-counting uses. So, instead of using
enhancement techniques, the decision was made that human
judgment must be used in determining the island boundaries, as
the computer operator could distinguish much more detail than
any program.
In theory, the box counting
routine is independent of the size of the image. Rather than
test this, however, a procedure was established to normalize the
image sizes. As can be seen on the main experimental images,
every image has a scale bar. In sizing the cropped images,
these scale bars were used to compare and change the relative
size of the images, so that all the images analyzed by box
counting were equal in size. Once the images had been sized
appropriately, they were then analyzed by the box counting
procedure.
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150 Pixels
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100 Pixels |
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75 Pixels
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50 Pixels |
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25 Pixels |
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15 Pixels |
Figure A1. Relative sizes of box counting grids used. Values
are size of each box in the grid. Grids were overlaid on
experimental images 1024 pixels wide
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(a) T2A with overlaid grid.
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(b) Occupied boxes are marked, then counted (boxes = 14
here). |
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Figure A2. Box counting
procedure.
Grid is removed, then process repeated with different grid. |
EXPERIMENTAL DESIGN
Preliminary Test
The qualitative results of experiments conducted strongly
support the fractal theory for material adhesion. Both grades
of Aluminum tested showed significant adhesion islands, with
steel and stainless exhibiting less in comparison. Hence, for
brevity only Aluminum testing during phase II of our tests is
detailed here. SEM Micrographs obtained revealed that
apparent sticking and sliding regions are intermingled in a
variety of areas on the rake face with quite irregular
boundaries. Line scans and back-scattered images were used to
confirm adhering profiles of chip material on the tool. This
has lead to the “fractal island” theory (Figure 2b), which is
similar to intermittent sticking (Trent, 1991) but allows for
regions of complete seizure within regions of incomplete
seizure. As first postulated, adhesion islands are seen in
many varying sizes, and the locations of seizure islands, and
free areas, are fairly diverse. Sliding regions – those
without adhesion islands – can be seen in the center of
sticking regions, on the cutting edge, and in other
positions. Figure 4 illustrates some of the regional
characteristics of selected tools. At the very least, these
images illustrate that neither the Merchant nor Zorev models
are sufficient for describing the frictional regimes along the
rake face. The fractal model proposed seems a better fit,
since it can incorporate the many types of adhesion patterns
observed. However, more research into this area is needed
before a definitive answer is reached. The variation of
fractal dimensions with cutting conditions (preliminary
examination) is briefly outlined in the next sections. The
fundamentals of sticking friction and seizure are explained in
the subsequent section.
Effect of Speed
Preliminary
experiments conducted on various Aluminum and Steel grades
with carbide and TiN Coated tools were quite encouraging in
verifying the fractal nature of the seizure islands.
Consequently, detailed experimentation and analysis was
conducted. Cutting conditions were selected to allow the
study of adhesion resulting from the formation of Built-Up
Edge (BUE) as well during the formation of a flow-zone. As
expected, at very low speeds the seizure islands were almost
continuous, while at recommended speeds of machining the
adhesion was more sporadic. Analyses were based on the
post-mortem observations of the rake face. Cutting speed was
varied in experiments while machining two grades of Aluminum.
Other variables varied during the experiments were the rake
geometry, tool coating and feed rate. The effect of varying
the cutting speed was studied on the computed fractal
dimension. The other machining parameters did not exhibit
much variation with the fractal dimensions during the
preliminary experiments.
The 6061- T6511
aluminum alloy chosen was extruded while the 2024- T351
aluminum alloy was cold rolled. The work pieces were obtained
as 6” diameter 36” length solid metal billets and prepared for
turning experiments. All the experiments were carried under
dry conditions without any coolants.
SPEED EFFECTS ON FRACTAL DIMENSION
At first glance,
rake-face micrographs confirmed the limitations of the
Merchant and Zorev-type assumptions. Visual analysis of the
replication tests, with 2024-T351 Aluminum alloy, revealed
similar adhesion patterns, a sliding region surrounded by
seizure islands. Consequently, the computed fractal
dimensions using the Box Counting method, D, for these
cuts were very similar in value. The average value of D for
these cuts was 1.6488
±
0.0089. The extent and distribution of the seizure islands
were seemingly identical for all cuts. Similar consistency
was noted while machining
6061-T6511 Aluminum alloy with a carbide tool and fractal
dimensions were determined to be 1.748
±
0.006. The consistency in the values of D for the replicate
cuts implies that the fractal dimension D could be a
consistent descriptor.
It was found
that the fractal dimension D increased with a decrease in the
cutting speed, in a designed set of cuts (T2). A visual
analysis confirmed that the sticking pattern changed with a
change in cutting speed. Initially, at the lowest speed, the
adhesion pattern is extensive with an area of complete seizure
near the tip, extending all the way to the center of the
tool. At the next higher speed, the area of seizure has
contracted dramatically, with a clear (adhesion-free) area in
the middle. A higher speed, shows further contraction of the
seizure area in the middle, and some seizure closer to the
center of the tool. At the highest speed, very little
adhesion occurs at the very edge of the tool, followed by a
clear area, then a band of seizure.
A second set of
trials (T3) investigated the possible variation in D with a
change in cutting speed at a lower feed rate. This was done to
investigate the possible effect of feed rate on speed versus
D. It was again found that the fractal dimension increased
with a decrease in the cutting speed. Comparing, the range of
D in T2 tests was 1.51-1.75 whereas the range was 1.48-1.73 in
T3 tests. The difference in the range was not noteworthy,
although the feed rate was halved.
In trial set T4,
a
TiN
coated positive rake angle tool insert of type SPG422 grade (Kennametalâ)
K730 was used instead of
an uncoated
negative rake angle tool insert of type
SNG422 grade (Kennametalâ) K68 used in T1-T3 experiments. This was intended
to find any possible influence of coating material on the
fractal dimension D. The cutting speed was varied in all the
four cuts. A similar trend of D with speed as before was
observed. The range of D was 1.40-1.65. It could be envisaged
that the reduction in D compared to those obtained when using
an uncoated tool might be due to the influence of the coating
material in altering the frictional contact and consequently
D. However, more experiments must be conducted before
concrete conclusions are drawn.
Trials T5
were
performed using an uncoated positive rake angle tool insert of
type SPG422 grade K68 to note the effect of the tool rake
angle on the seizure pattern and the fractal dimension D.
Similar to the other trials the cutting speed was the only
variable and the fractal dimension D ranged between
1.54-1.68. To determine the effect of the tool geometry on D,
the values of D, under the same cutting conditions at 1175
fpm, using an uncoated negative rake angle tool and an
uncoated positive rake angle tool were compared. The value of
D was 1.486 for the former while D was 1.538 for the latter.
Thus it was interpreted that the tool geometry could have an
effect on the seizure pattern and D. Similarly, tests were
conducted with 6061-T6511 and similar observations were noted.
Sample observations
for the Al-2024 tests are summarized in figure 2. The fractal
dimension variations with speed, at some parameter
combinations are shown for Al 2024 in Figure 3.
Based on
these observations it could be stated that the speed effect on
the fractal dimension is also visually revealing. As the
speed increases, the seized material band adjacent to the edge
becomes thinner thereby opening up a large sliding island in
the middle. Sporadic seizure follows in the rear of the
contact zone. These observations, at the very least, pose a
challenge to conventional model assumptions regarding seizure
and sliding and their domains of existence.
 |
 |
|
2024 (1175 fpm) |
2024 (851 fpm) |
 |
 |
|
2024 (252 fpm) |
2024 (606 fpm) |
|
Tool Material: Uncoated
Carbide, Negative Rake Angle SNG422-K68
Cutting time (constant):
2.58 MIN
Depth Of Cut (constant):
0.04 INCH
Feed Rate (constant):
0.014 INCH/REV |
|
Figure 2.
Friction patterns observed in the turning of 2024 Al T-351
with an uncoated carbide tool. |
 |
| Figure 3. The variation of the
fractal dimension D with the cutting speed. |
|
