TodPmastersthesis

Surface Characterization and Evolution of Sub-scale Brake Materials
by
Tod Policandriotes
B. S. Physics (1995)
Southern Illinois University
Carbondale, Illinois
A Thesis Submitted in Partial Fulfillment of the
Requirements for the Degree of
Master of Science in Physics
Department of Physics
Southern Illinois University
Carbondale, Illinois
July 1998

ii
Abstract
Tod Policandriotes, for the Master of Science degree in Physics,
Presented on July 27, 1998, at Southern Illinois University at Carbondale.
Title: Surface Characterization and Evolution of Sub-scale Brake Materials
Major Professors: Dr. David T. Marx
Dr. J. Thomas Masden
In order to design materials that reduce wear and maintain a constant friction
coefficient during use, thorough experimental testing, observation, and analysis is
required. This thesis introduces new methods for characterizing the evolution of sub-
scale brake materials and identifies some of the instruments used to characterize these
materials and their properties. Experimentation with Carbon-Carbon (C-C) composites
used in aircraft brakes are presented. The study of brake processes of C-C composites
that were fabricated from pitch- and PAN-based carbon fiber-phenolic carbon char
precursor densified to about 1.80 g/cm3
includes a variety of experimental testing and
analysis. In testing using a dynamometer, the energy absorbed per stop can be changed
by varying either the inertia or the velocity. The dynamometer can be programmed to
control either the torque or the applied normal load.
The use of profilometry and topography allows the measurement, analysis, and
modeling of surfaces. Using a skidless stylus profilometer with a tip radius of 5 µm,
topographies were taken in approximately the same location in which each topography
consists of 50 to 64 traces with a tracelength of 10 mm. The topographies were measured
while the brake discs were mounted on the dynamometer using an xyz positioning
system. These topographies will describe the evolution of the surface of the brake discs
as a result of testing. The xyz positioning system was built to have 13-nanometer

iii
resolution in the x-plane and 19-nanometer resolution in the y- and z-plane. For the
analysis of the measured surface, software has been developed using most of the
published statistical methods for analyzing topographies. The methods incorporated to
date include: arithmetical mean deviation (sRa, sPa), root mean square deviation (sRq,
sPq), least squares approximation of the mean plane of the surface, the kurtosis (sRku), the
skewness (sRsk), separated waviness and roughness surfaces, distribution of peak heights
above any chosen plane, density of summits calculation, fractal parameters D and G,
areal autocorrelation function, FFT, APSD, interfacial area ratio, Abbott-bearing ratio,
and the real area of contact (classical and fractal).
Analysis of the topographies has shown that the average friction coefficient varies
with roughness. The other relationships discussed are: fractal parameters and the average
friction coefficient, the density of summits and the fractal dimension D, the skewness and
the dimension D, and the surface area ratio and friction. A brief analysis of wear is also
discussed.

iv
Acknowledgements
First and foremost, I would like to thank my wife Lisa for her patience,
understanding, and support during the last two years. I would like to thank my advisor,
Dr. David T. Marx, for asking me to be a part of the Center for Advanced Friction
Studies and for all of the help that he has given me. I would like to thank Dr. Maurice
Wright for supporting my ideas and allowing me to build the equipment that I required
for the experiments. I would also like to thank Dr. J. Thomas Masden for his help and
support as my departmental advisor. Finally, I wish to thank all of the staff at CAFS for
their continued support in all areas of research.

v
Table of Contents
Abstract… … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ii
Acknowledgements… … … … … … … … … … … … … … … … … … … … … … … … … .. iv
Table of Contents… … … … … … … … … … … … … … … … … … … … … … … … … … . v
List of Tables and Figures… … … … … … … … … … … … … … … … … … … … … … … viii
Chapter 1
I. Introduction… … … … … … … … … … … … … … … … … … … … … … … … … … … . 1
A. The Coefficient of Friction… … … … … … … … … … … … … … … … … … … ... 4
B. Mechanisms of Sliding Friction… … … … … … … … … … … … … … … … … … 5
C. Adhesion… … … … … … … … … … … … … … … … … … … … … … … … … … … 9
D. Abrasion… … … … … … … … … … … … … … … … … … … … … … … … … … … 11
E. Third-Body Interactions… … … … … … … … … … … … … … … … … … … … … 11
F. Directionality… … … … … … … … … … … … … … … … … … … … … … … … … . 13
G. Temperature Effects on Friction… … … … … … … … … … … … … … … … … ... 14
II. Profile Analysis… … … … … … … … … … … … … … … … … … … … … … … … … .. 16
A. Two Dimensional Analysis… … … … … … … … … … … … … … … … … … … ... 16
B. Roughness and Filtering… … … … … … … … … … … … … … … … … … … … … 17
II. Basic Fractal Theory… … … … … … … … … … … … … … … … … … … … … … … .. 24
A. Self Similarity and Scale… … … … … … … … … … … … … … … … … … … … ... 25
B. The Fractal Dimension… … … … … … … … … … … … … … … … … … … … … .. 27
C. Fractal Roughness and Surface Profiles… … … … … … … … … … … … … … … 29

vi
Chapter 2
I. Topographical Analysis… … … … … … … … … … … … … … … … … … … … … … … 35
A. 3-D Characterization Parameters and Filtering of Height Data… … … … … … . 36
B. Surface Area… … … … … … … … … … … … … … … … … … … … … … … … … ... 41
C. Areal Autocorrelation Function… … … … … … … … … … … … … … … … … … . 42
D. Fractal Surfaces… … … … … … … … … … … … … … … … … … … … … … … … . 44
1. Hurst Analysis… … … … … … … … … … … … … … … … … … … … … … … ... 44
2. Discrete Fourier Transform Method for Fractal Analysis… … … … … … … . 49
II. Experimental Apparatus and Data Collection… … … … … … … … … … … … … … . 54
A. Sub-scale aircraft dynamometer… … … … … … … … … … … … … … … … … … 54
B. The profilometer… … … … … … … … … … … … … … … … … … … … … … … … 55
C. XYZ positioning system… … … … … … … … … … … … … … … … … … … … … 57
D. Brake materials, experimental conditions, and procedures… … … … … … … ... 60
E. The Surface Analysis Program… … … … … … … … … … … … … … … … … … .. 64
III. Results and Discussion of Collected Data… … … … … … … … … … … … … … … . 65
A. Correlations of surface parameters… … … … … … … … … … … … … … … … … 71
1. Roughness sRq and µ… … … … … … … … … … … … … … … … … … … … … 71
2. Hurst D, µ , and the Density of Summits… … … … … … … … … … … … … . 75
3. Hurst G and µ… … … … … … … … … … … … … … … … … … … … … … … … 80
4. The Surface Area Ratio and µ… … … … … … … … … … … … … … … … … ... 82
5. The Hurst D and the skewness… … … … … … … … … … … … … … … … … .. 85
Chapter 2 (cont.)
B. Wear results… … … … … … … … … … … … … … … … … … … … … … … … … ... 88

vii
IV. Conclusion… … … … … … … … … … … … … … … … … … … … … … … … … … … 89
References… … … … … … … … … … … … … … … … … … … … … … … … … … … … … 93
Vita… … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … ... 95

viii
List of Figures and Tables
Figure 1. Picture of dynamometer 2
Figure 2. C-C fiber composite brake pads and their design. 3
Figure 3. Positioner and profilometer in experimental position measuring the stator. 4
Figure 4. A simulated rough surface formed using a random function. 6
Figure 5. Machine surface of a C-C brake disc, lathe turned at 1000 RPM using a
cutting tool of radius 0.381mm. The inner radius is on the left. Length is
10 mm, width 0.171 mm, and the maximum peak to valley height is 40
µm.
7
Figure 6. Various contacts for cone shaped asperities. 7
Figure 7. Atomic adhesion between two contact interfaces. 10
Figure 8. Conical asperity plowing a surface. 11
Figure 9. A simulated interface. 13
Figure 10. Plot of friction coefficient versus temperature during a dynamometer test 15
Figure 11. Profile of a machined surface. 16
Figure 12. Roughness plot for Figure 11. 17
Figure 13. The waviness plot for figure 11. 18
Figure 14. Plots showing the differences in filtering techniques. 22
Figure 15. Pin on disk tribometer made by Micro Photonics. 24
Figure 16. The actual image(mag. 5000×) and an image obtained by stylus
profilometry(5.6 mm × 5.6 mm), the square showing the relative area
between the two images.
26
Figure 17. Example of a real profile and its randomness. 30
Figure 18. Effect of varying D and G on rough profiles. These are simulated from
the W-M function in equation (7).
31
Figure 19. The power spectrum (left) and log(f) vs. log(p(f)) (right). 32
Figure 20. A real surface topography shown in low resolution for easy viewing. 36

ix
Figure 21. Waviness of the surface of Figure (20). 40
Figure 22. Roughness surface of Figure (20). 40
Figure 23. Comparison of different roughness parameters. 41
Figure 24. Surface area measurement triangles. 42
Figure 25. Areal autocorrelation surface showing the directionality of the surface. 43
Figure 26. Examples of the circular areas of increasing diameter used in the Hurst
method.
45
Figure 27. Log (distance) vs. log (difference) of a typical measured area for Hurst
analysis.
46
Figure 28. An example of the possible data variation for the Hurst method. 46
Figure 29. Side view to see the slope of Figure (30). 47
Figure 30. Grid plot showing the surface representation for the Hurst orientation
transform.
47
Figure 31. Log (difference) vs. log (distance) at a given angle using the HOT
method.
48
Figure 32. Typical power spectrum (APSD) for an anisotropic surface. A pie
shaped wedge enclosed for the fractal D calculation.
50
Figure 33. The fast fourier transform of an anisotropic surface. 50
Figure 34. The real surface for the APSD and the FFT above. 50
Figure 35. The change in slope with respect to angle for one quadrant of an
anisotropic surface.
51
Figure 36. The change in slope with respect to angle for one quadrant of an
isotropic surface.
52
Figure 37. The transformed image of an isotropic surface. 53
Figure 38. The profilometer attached to the xyz positioner. 56
Figure 39. An image of a 5 µm radius diamond stylus similar to the one used on the
profilometer. Courtesy of Mahr Corp.
57
Figure 40. Top view of positioner. 59
Figure 41. High resolution stepmotor driver control board. 60
Figure 42. Initial machined surface for pad 15, Test 20. 62
Figure 43. Initial polished surface for pad 15, Test 21. 62

x
Figure 44. Initial machined surface for pad 15, Test 26. 63
Figure 45. Initial polished surface for pad 15, Test 27. 63
Figure 46. Conforming rotor and stator. 63
Figure 47. Example output of the surface analysis program. 64
Figure 48. The standard deviation at various length scales. 71
Figure 49. The dimension D at various length scales. 71
Figure 50. Roughness vs. friction for Test 20. 73
Figure 54. Hurst D against µ for Test 20. 76
Figure 58. Hurst D against DSUM for Test 20. 78
Figure 62. Hurst G against µ for Test 20. 81

xi
Figure 66. The surface area ratio against µ for Test 20. 84
Figure 70. The Hurst D against the skewness of the surface for Test 20. 87
Figure 74. Wear of the outer radius edge for Test 21. 90
Figure 75. Wear across the surface, inner radius to outer radius, for Test 26. 91
Figure 76. Wear across the surface, inner radius to outer radius, for Test 27. 91
Table 1. Relevant experimental information. 61

1
Chapter 1
I. Introduction
The characterization and analysis of worn surfaces has become a very important
topic in scientific and industrial research. This is primarily because industry has sought
ways to reduce costs by minimizing friction and wear. For the braking industry, materials
are needed that have a constant coefficient of friction, low wear, and good thermal
properties. Solid surfaces, irrespective of their method of formation, generally contain
surface irregularities. A surface may be defined as the outermost atomic layer of a solid.
The properties of this layer are in most cases impossible to predict. When two nominally
flat surfaces are placed in contact, surface roughness causes contact to occur at discrete
contact points. Deformation occurs at these points that may be elastic, elasto-plastic, or
plastic depending on the applied stress, surface roughness geometry, and material
properties. The sum of the areas of all contact points constitutes the real contact area.
For most materials at normal loads, the real contact area is a small fraction of the area that
would be in contact if the surfaces were perfectly smooth.1
If the real area of contact is
minimized, adhesion, friction, and wear are also minimized. Research at the micrometric
scale on subscale braking materials for use in aircraft and automobiles provides a way to
expand our understanding of surfaces. By characterizing the evolution of the interfaces of
two rough surfaces after interfacial contact, correlations between parameters and
properties can be revealed. Correlations between the coefficient of friction and surface
roughness geometry are the focus of this research. The basic hypothesis is that surface
roughness has a direct influence on the average friction coefficient of the material.

2
FIG. 1. Picture of dynamometer
Experimental testing was performed on the Link sub-scale aircraft dynamometer
shown in Figure (1). The dynamometer uses two brake rings comprising a rotor and a
stator. The brake rings used are carbon fiber-reinforced carbon composites (C-C) shown
in Figure (2). C-C composites are not metals. Four dynamometer experiments were
performed using two different carbon fiber types. One pair was made out of pitch fibers
and the other of PAN (polyacrylonitrile) fibers. The brake rings were tested using two
different energy conditions. Surface topographies were measured on the rotor and stator
in-situ on the dynamometer using a Mahr profilometer and a custom built high resolution
XYZ positioning system shown in Figure (3). The topographies were measured after each
of the first five brake stops and then every five stops thereafter for 150 or 200 stops. The
topographies were analyzed using a custom windows interface FORTRAN program. The
Inertia
Section
Tailstock

3
output of the program consists of classical and fractal statistical parameters. These
parameters were then used to characterize the surface topographies. The contents of this
first chapter have been chosen so that the reader will be familiar with the material that will
be used to analyze the data. The second chapter consists of a few easily derived and
tested equations currently not found in texts or publications. The second chapter also
contains the development of the XYZ positioner, the surface analysis program, and the
experimental apparatus, procedures, results, and discussion.
Brake Pad Geometry
CAFS
SIUC
FIG. 2. C-C fiber composite brake pads and their design.

4
FIG. 3. Positioner and profilometer in experimental position measuring the stator.
A. The Coefficient of Friction
The study of friction began in the 15 th
century with Leonardo da Vinci’s study of
the motion of a rectangular block sliding on a flat surface. His notes remained
unpublished for hundreds of years. It wasn’t until the 17 th
century that the French
physicist Guillaume Amontons rediscovered the classic laws of friction. Amontons first
law is: The friction force that resists sliding is proportional to the normal load. The
second law is: The amount of friction force does not depend on the nominal or apparent
area of contact. In the 18th
century Charles-Augustin de Coulomb attempted to explain
the friction force in terms of roughness only. The result of Coulombs work led to a third
law: The friction force is independent of velocity once motion is started. 2
The three laws
stated above constitute the classic laws of friction. Since the introduction of atomic force
StatorRotor
Profilometer Positioner

5
microscopy (AFM) by Jacob N. Israelachvili 1
in 1985 and friction force microscopy (FFM)
soon after, these laws have been challenged, as will be discussed in the next section.
To facilitate the understanding of the friction force, let us now consider two
stationary bodies with machined surfaces in contact. When the two contacting bodies are
held together by a normal force N and one of them slides tangentially against the other,
there is a resistive force in the opposite direction. The resistive force is the friction force;
and the resistance is called friction. If the two bodies are initially at rest, then the ratio
between the force needed to start the sliding and the normal force is the static coefficient
of friction, µs. After sliding is initiated, the ratio between the friction force and the normal
force is the kinetic coefficient of friction, µk. Both coefficients are independent of the size
or shape of the contact surfaces. They are, however, very dependent on the materials and
the cleanliness of the contacting surfaces. 3
(Bowden and Tabor) For ordinary metallic
surfaces, the friction coefficient is somewhat less sensitive to surface roughness. 4
When
the surfaces are ultrasmooth or very rough, however, the friction coefficient can be very
large due to the mechanisms of sliding friction discussed in the next section. If two metals
in contact have different hardness characteristics, then the roughness of the harder metal
can greatly influence friction because the harder metal will gouge the softer. 3
Increasing
temperature at the interface of the two contacting materials can also cause a decrease in
the friction coefficient.
B. Mechanisms of Sliding Friction
Solid surfaces, irrespective of their method of formation, are not perfectly flat and
smooth, but have roughness consisting of peaks and valleys produced from the processes

6
which formed them (see Figures (4) and (5)). When the two rough surfaces are forced
together, contact occurs only at discreet points called asperities (see Figure (6)). The sum
of all of the contact areas is the real area of contact.
0
50
1 0 0
1 5 0
200
250 0
50
1 0 0
150
200
250
-0.125
0 .031
0 .188
0 .344
0 .500
-0.125 0 .031 0 .188 0 .344 0 .500
FIG. 4. A simulated rough surface created using a random function .

7
FIG. 5. Machine surface of a C-C brake disc, lathe turned at 1000 RPM using a cutting
tool of radius 0.381mm. The inner radius is on the left. Length is 10 mm, width 0.171
mm, and the maximum peak to valley height is 40 µm.
The real area of contact is generally much smaller than the nominal or apparent
contact area of the surface; and it is within this small area that the friction force acts.
FIG. 6. Various contacts for cone shaped asperities
With the aid of the atomic force microscope (AFM) and the friction force
microscope (FFM), introduced in the previous section, the mechanisms of friction are
being studied. Using the AFM and FFM, Bushan et al .1
and McClelland et al. 4
are re-

8
evaluating the classic laws of friction. Bushan et al . found that the coefficients of friction
at the microscopic scale on thin films are much lower than those at the macroscopic scale.
Indentation hardness and modulus of elasticity of metals are higher at the microscale for
small contact areas and low loads. This results in reduced wear. By using small apparent
areas of contact, the number of particles at the interface is reduced, minimizing the
plowing contribution to friction. When larger loads are used, the coefficient of friction
increases to the macroscale value and surface damage increases. Therefore, Amontons’
law of friction stating that the amount of friction force does not depend on the nominal or
apparent area of contact, does not hold for microscale measurements. 2
Whenever one
considers surface interactions, the physical properties of the surface must be used in the
analysis and not the bulk properties. For example, Marx 5
et al. found that for C-C
composites, the near-surface indentation hardness and modulus of elasticity are reduced at
the microscopic scale compared to the bulk (macroscopic) values. In 1995, Sokoloff et
al.6
proposed that friction arises from phonon generation (when atoms on one surface are
set into motion by the sliding motion of the atoms on the opposing surface). The energy
imparted by the sliding atoms is converted into heat and is carried via phonons. The
amount of energy converted to phonons is dependent on the material and its natural
frequencies. If the vibration frequency of the sliding atoms in one surface resonates with
one of the natural frequencies in the other, then friction results. McClelland et al .4
later
found that at the microscopic scale the friction force has no dependence on normal load.
Thus, Amontons law stating that the friction force is proportional to the normal load is
incorrect for the microscopic scale. Instead, the friction force depends on the adhesion
properties of the material which is essentially a chemical bond between the two surfaces

9
and; it is proportional to the degree of irreversibility of the force that squeezes the two
surfaces together rather than the magnitude of the force. 1,2,4
Experiments using a quartz
microbalance and FFM have shown that friction is dependent on velocity because at high
velocities, high temperatures are generated. 2
At these high temperatures many materials
become fluid at the contact points and a decrease in the coefficient of friction is observed. 1
Coulombs’law stating that friction is independent of velocity is wrong if the contact
surfaces increase in temperature. 1
These temperature effects have also been observed in
our lab, but C-C does not fluidize at its surface so the mechanism is unknown. Therefore,
the three primary contributors to kinetic friction in contacting surfaces are adhesion,
abrasion (plowing), and third-body interactions. 7
Directionality and temperature of the
surface also affect friction at the macroscopic and microscopic scales. 1
The exact
magnitude of each of the contributions from the above mechanisms is not known and is
material dependent.
C. Adhesion
Bowden and Tabor3
found that adhesion occurs when the atoms or molecules of
the two contacting surfaces approach each other close enough for attractive forces to
bond them (see Figure (7)). The relative strength of the bond depends on the size of the
atoms, the distance between them, and the surface structure of the contacting material.

10
FIG. 7. Atomic adhesion between two contact interfaces.
Separation of the contacting areas requires the adhesive bonds to be broken. If a
tangential force is applied, the motion between the surfaces requires the adhesive junctions
at the real area of contact be sheared. This shearing of the adhesive junctions constitutes
one of the primary components of friction and wear. 3
If adhesion was the only
contribution, then the friction force is approximately the product of the real area of
contact times the shear strength of the adhesive junctions within that area.3
However, the
mechanisms which cause friction are many and the exact contribution of adhesion to
friction is variable.

11
D. Abrasion (plowing)
Abrasion, plowing, and deformation occur when asperities gouge the contacting
surface. The contribution to the friction from abrasion depends on the surface roughness
and the compressive strength of the materials. When a surface is very smooth, the
roughness contribution to friction decreases and adhesion increases. A simple model of a
cone penetrating the surface of the opposing material and then moving tangentially across
the surface can be seen in Figure (8).
FIG. 8. Conical asperity Plowing a Surface.
E. Third-Body Interactions
There are three zones shown in Figure (9) that define an interface. The third-body
is zone 3 in the figure. Zones 1 and 2 are the two bulk solids in contact. Particles moving
in Zone 3 are the result of sheared or broken asperities, oxides or other contaminants.
The third-body can act as a lubricant or an abrasive depending on the material, particle
size, and shape. The effects of the third-body somewhat depend on the roughness of the
interface surfaces. Rougher surfaces tend to promote internal shearing of the powder
mass and enable particle flow. 7
A book written by Blau7
summarizes most of the literature
concerning the contribution of the third-body to the friction force. One of the

12
contributions to the third-body is the development of a friction film on the interfacial
surfaces. The friction film is developed by the deposition of debris particles in pores and
crevices on the interfacial surface. This friction film has been studied extensively by K.
Lafdi at the Center for Advanced Friction Studies 8
(CAFS). The following two
paragraphs are a summary of his optical and SEM characterization of the friction film of
six worn C-C brake pads.
Characterization of the surface of a machined sample using optical microscopy
shows that two types of carbon are present: graphitic and non-graphitic. The graphitic
carbon is the result of the high temperature heat treatment (graphitization) process used in
the fabrication of these samples. Phenolic resin was used to bind the fibers in the
composite. The non-graphitic portion is the phenolic char present after graphitization.
During fabrication, the density was increased by depositing carbon from methane at 1000
*
C. This carbon, called CVD carbon, is graphitizable, but considered ordered, non-
graphitic carbon. The initial surface structure is made up of three major phases, with a
gradient of crystallinity, but it is not amorphous. The surface has a high porosity. Visual
inspection of a non-worn brake pad shows a random framework of interlocking fiber
bundles. The surface is dull and rough. Particles are easily removed from the surface of
the brake pad. After testing, the worn surface is generally very shiny, wavy, and smooth.
The pores in the surface become filled with debris as braking progresses. The size of the
embedded debris particles gets smaller and smaller near the wear surface. At the wear
surface itself, a thin friction film forms. This film is mostly isotropic at the microscale and
is made up of layers of material. In Lafdi’s model, upon brake pad separation, unstable
upper layers break free of the surface and are “folded over,”and compacted again

13
elsewhere. The friction film tends to fill in the contour of the rough surface, resulting in a
smooth, but wavy composite surface. The cohesive bonds of the friction film are greater
than the adhesive bonds between the friction film and the bulk material. This suggests a
single continuous phase for the friction film.
SEM characterization has shown that the pores of the worn brake pads are filled
with an aggregate of nanoscale particles. At high magnification, the particles seem to be
loosely compacted. In some regions, debris particles still remain on the surface. There is
intricate layering and cracks on the surface. The cracks within the plane of the friction
film run parallel to the wavy worn surface. This shows that there is anisotropy in the film
surface.
FIG. 9. A simulated interface.
F. Directionality
Most machined or prepared surfaces have directionality associated with them.
Preparation of surfaces leads to the formation of asymmetric surface asperities. Using an

14
FFM, Bushan et al.1
found the effect of directionality on friction is always present at the
microscopic scale. The interaction of the FFM tip is dependent on the direction of the tip
motion. In addition, surface preparation can cause a build up of material on one side of
the asperities causing the asperity to be elongated in one direction. The result is that the
friction coefficient is lower along the orientation direction of the surface. 1
Directionality
can be studied quantitatively using the areal autocorrelation function applied to the
measured surface data as will be discussed later. Looking back at Figure (5), the
directionality of the surface is obvious. The friction coefficient between two surfaces
sliding parallel to the surface direction would be lower than in transverse sliding.
G. Temperature Effects on Friction
A change in the friction coefficient has been observed in our laboratory as a linear
reduction in friction coefficient as surface interface temperature is increased. In a sliding
interface, the temperature of contacting regions increases due to frictional heating. The
increase in temperature changes the properties of the material at the interface, which alters
the friction force. Increasing the temperature of the surroundings increases the bulk
temperature of the material also alters the friction force. The graph in Figure (10) shows
typical behavior of the friction coefficient versus temperature for C-C composites with the
thermocouple placed 2.5 – 3.5 mm from the interface.

15
1 2 3 4 5
0.416
0.418
0.420
0.422
0.424
0.426
0.428
0.430
0.432
µ
Time(sec)
40
60
80
100
120
140
160
Temperature
Friction
Temperature(
0
C)
FIG. 10. Plot of friction coefficient versus temperature during a dynamometer test.
Blau7
lists the following temperature-dependent properties that effect the friction
coefficient:
1. Shear strength of interfacial materials.
2. Viscosity of solid and liquid lubricants.
3. Tendency of the surfaces of materials to react with their surrounding
environment to form films or tarnishes.
4. Tendency of formulated liquid lubricants to change chemically.
5. Material wear process affects surface roughness and tractional characteristics.
6. Tendency of certain materials to transfer to the rubbing partner.
7. Surface to absorption of contaminants from the surrounding environment.
It is obvious that the temperature dependence of friction at a material interface is
complicated. Most materials have more than one of the above factors contributing to

16
temperature-dependent frictional changes. Identifying which factors may be involved
requires careful visual observation, data analysis, and knowledge of the material’s
properties.7
II. Profile Analysis
A. Two Dimensional Analysis
The analysis of surface profiles (two dimensions) began in the 1950’s. Stylus
profilometer (see Figure (3)) traces of nominally smooth surfaces at the macroscopic scale
showed that they are very rough at the microscopic scale. Statistical parameters obtained
from these traces are still used extensively in science and industry to characterize a
surface. An analysis of two-dimensional methods is necessary before considering three –
dimensional analysis and displaying the similarities and differences between them. In two
dimensions a surface is simply a profile line as in Figure (11).
0 2000 4000 6000 8000
-20
-15
-10
-5
0
5
10
15
0 2000 4000 6000 8000
-20
-15
-10
-5
0
5
10
15
Height(µm)
Datapoint
FIG. 11. Profile of a machined surface.

17
B. Roughness and Filtering
ASME B46.1-19959
outlines methods in the analysis of surface roughness,
waviness, and lay. This standard is used in most commercially available software capable
of analyzing two-dimensional surface profile data. Roughness is defined as the finer
irregularities of the surface texture that usually result from the inherent action of some
production process, such as machining or wear. Roughness features are typically in the
submicron to 10-µm range. Waviness can be defined as the more widely spaced
component of the surface texture. Roughness may be considered to be superimposed on
the wavy surface. The roughness and waviness of Figure (11) are shown in Figures (12)
and (13), respectively.
0 2000 4000 6000 8000
-10
-5
0
5
0 2000 4000 6000 8000
-10
-5
0
5
Height(µm)
Datapoint
FIG. 12. Roughness plot for Figure 11.

18
0 2000 4000 6000 8000
-20
-15
-10
-5
0
5
10
15
0 2000 4000 6000 8000
-20
-15
-10
-5
0
5
10
15
Height(µm)
Datapoint
FIG. 13. The waviness plot for figure 11.
Lay is defined as the predominant direction of the surface pattern, ordinarily
determined by the production method used. The basic process for the measurement and
analysis of surface profile data is illustrated schematically as follows:
Data from
Profilometer
Filtering
process
Roughness
component
Waviness
component
Apply
statistics to
generate
desired
parameters

19
Data manipulation begins with a least squares fit to determine the reference mean line
(y = 0). The data is then passed through a filtering process to separate the roughness and
waviness components of the surface profile. After filtering, the roughness and waviness
components should add together and result in the original profile. However, if one uses
the current standard filtering techniques, the components do not always add to give the
raw profile. In the ASME9
standard, two types of filtering processes used are: phase
correct Gaussian filter and 2RC filtering. The method of 2RC filtering models the surface
profile as the analog signal of two RC filters in a series circuit. Capacitor and resistor
values are chosen for a specific or desired transmission characteristic that is consistent
with the traversing speed of the profilometer. When using 2RC filtering, it is important to
consider that the waviness and roughness components cannot be added back together to
form the original profile. For this reason, 2RC filtering is not recommended. 9
This
method can also result in significant errors in calculated surface parameters. In Gaussian
filtering, a series of Gaussian curves is fit to the data at each data point by averaging over
an interval specified by the stylus tip radius, the trace length, the number of data points
collected, and the step size. This produces a mean line through the data set, or waviness
component, which is then subtracted from the original curve to yield the roughness
component. In this method, the waviness and roughness components can be added back
together to recreate the original profile. The Gaussian filter equation used for each point i
is:9
(1) ′=
+
−
−













+
+
−
∑y
k
x x
yi
c
i k i
c
i k
k
k
1
2 1
2
αλ
π
αλ( )
exp

20
where yi is the set of y values or heights associated with each xi along the measured profile
line. The roughness line is the collection of points ( xi, y yi i− ′). The number k is the
number of points averaged around each yi. λc is the roughness long wavelength cut-off
value specified by the ASME for a particular tip radius and sampling interval; and λs is
used in place of λc to determine the roughness at short wavelengths. The value of
α π= =ln / .2 04697 .9
A method of filtering not discussed in the ASME standard is adjacent averaging.
As in Gaussian filtering, adjacent averaging averages a fixed number of adjacent heights
around each specified point xi. The tip radius, the traversing length, and the number of
data points collected determine the number of adjacent points averaged. This method
produces a mean line (the waviness component) that is subtracted from the raw profile to
give the roughness component. The two components yield the original profile when
added together. The equation for adjacent averaging for each point i is
(2) ′=
+
+
−
∑y
k
yi i k
k
k
1
2 1
and the roughness line is comprised of the set of points ( xi, y yi i− ′).
Equations (1) and (2) are essentially the same with the exception that (1) contains
a weighting function. The weighting function is usually constant, but it can vary when the
sample spacing varies (phase variations). The function provides some degree of
smoothing of the real profile and compensates for possible sample spacing variations. The
amount of smoothing is based on the cutoff standards specified by ASME B46.1-1995 [2,
see section 9, table 9-2]. The cutoff standards do not apply when the surface structures to
be assessed are outside of the bandwidths 2.5 µm < λ< 0.8 mm for a 2-µm tip radius and

21
8 µm < λ< 2.5 mm for 5-µm tip radius or if damage occurs to the surface when using a
skidless instrument. The application of adjacent averaging requires the user to determine
the appropriate bandwidth parameter to use. In determining the bandwidth, the user must
know the number of data points taken over the tracelength. A suitable bandwidth
parameter would be 1 % of the number of data points collected over the tracelength.
Without obtaining too much fine structure, a 1 % bandwidth parameter would remove
most of the waviness. Plots comparing Gaussian and adjacent averaging filter techniques
are shown in Figures (14a and b). Adjacent averaging usually results in a better mean line
through the raw data than the Gaussian filter produces.
After the data has gone through some sort of filtering process and has been
separated into roughness and waviness components, a number of statistical equations can
be used to determine roughness parameters.
A few of the more common parameters and equations are shown as equations (3)
below.
(3)
( )[ ]
( )
R
l
Y x
R
l
Y x
R
N
Z Z Z Z
R Y Y
R
n
Y
m
Y
a
x
N
q
x
N
z N
zISO Pk
k
Nk
k
c Pk
k
n
Nk
k
m
=
=






= + + + +
= +
= +
=
=
= =
= =
∑
∑
∑ ∑
∑ ∑
1
1
1
1
5
1
5
1 1
0
2
0
1
2
1 2 3
1
5
1
5
1 1
( )
.....
(arithmetical mean devi ation)
(root - mean - square deviation)
(roughness depth)
where l is the evaluation length, Y(x) is the data set, N is the number of points, and ZN is
the height from the highest to the deepest profile point within regularly spaced intervals.

22
2400 2600 2800 3000 3200 3400
-8
-7
-6
-5
-4
-3
313 points averaged
Original Trace
Gaussian Filter
Adjacent AverHeight(µm)
Length (µm)
800 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 3200
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
Adjacent Ave.
Gaussian
313 averaged points
Length (µm)
Height(µm)
Adjacent aver.
Gaussian
FIG. 14. Plots showing the differences in filtering techniques.

23
Ra values indicate the average of the peak and valley heights in the roughness component.
Rq values indicate the average of the squares of the peak and valley heights in the
roughness component. RzISO is the arithmetical mean value of the amplitudes of the five
highest profile peaks ( YPk) and the five deepest profile valleys ( YNk). Rc is the arithmetical
mean value of the amplitudes of all profile peaks and profile valleys. Equations (3) are
considered standard for determining the “roughness of a surface,”but there are many
other equations and methods used in literature for determining roughness. One should
keep in mind that these parameters are the result of statistical equations with input from a
filtered data set. ASME suggests that in any study at least 5 profiles should be taken and
the resulting values should be averaged and the scan length, tip radius, and sampling
information should be reported.
Experimental studies on profile roughness and its effect on friction have been
performed on bearing surfaces by Yeau-Ren Jeng 10
. Using a pin-on-disk tribometer
system, similar to the one shown in Figure (15), Jeng tested surfaces of varying roughness
under varying applied loads. He found that lower roughness yields lower friction and
confirmed that transverse roughness has lower friction than longitudinal roughness. Under
larger loads, the effects of roughness and lay orientation are increased. Conversely, as
surface roughness decreases, the effect of lay orientation becomes smaller. For thin films,
it was also found that surface roughness has a significant impact on friction. Jeng’s result
shows that surface roughness effects friction in metals, a direct contradiction of the earlier
adhesion model of friction.

24
FIG. 15. Pin on disk tribometer made by Micro Photonics [photo from their website at
www.microphotonics.com].
Experimental studies of roughness using single profilometer traces were
abandoned early in the present study because, statistically, a topographical profile will
yield a better population sample than a trace. This results in values that are more
representative of the surface. Marx et al.5
found that for C-C composite materials single
profile roughness intermittently correlated with the measured average friction coefficient
from dynamometer testing.
III. Basic Fractal Theory
Fractal theory was introduced by Benoit B. Mandelbrot11
at the beginning of the
1970’s. Fractals, however, were discovered by mathematicians over a century ago and
have been used as subtle examples of continuous, non-rectifiable curves (those whose
length cannot be measured) or of continuous, non-differentiable curves (those for which it
is impossible to draw a tangent at any of their points). Mandelbrot realized that many

25
shapes in nature exhibit a fractal structure such as: trees, clouds, mountains, plants,
coastlines, and other natural surfaces. The existence of such structures in nature reveals
the presence of complexity and disorder in the universe. Fractal theory finds the order in
the disorder. The study of surfaces generally involves some sort of statistical or Euclidean
geometrical form, such as random field theory or spectral density theory, which is used by
most researchers to obtain a characterization of rough surfaces in contact. Euclidean
ideals are often held out as approximations, or caricatures, of natural forms that may be
inherently complex and irregular. That is, simplicity is achieved by filtering out the
complexity and uniqueness of natural forms and identifying their essence with the class of
shapes, which can be rendered by protractors, conic sections, and Gaussian curves. To
quote the founder of this field, Benoit Mandelbrot (1989): “Fractals provide a workable
new middle ground between the excessive geometric order of Euclid and the geometric
chaos of roughness and fragmentation.”
A. Self-Similarity and Scale
The key idea in fractal geometry is self-similarity or scale invariance. An object or
surface is self-similar if it can be decomposed into smaller copies of itself. 12
Therefore, the
concept of self-similarity is the property in which the structure of the whole is contained in
its parts. A fractal object has no characteristic length scale. This implies that the essential
features of a fractal exist at all length scales. Therefore, magnifying a small piece of a
fractal surface or object results in a similar surface or object, that is similar to the whole
surface.13
For example, in the study of surfaces, a profilometer can be used to study the

26
surface at the micrometric scale and a scanning electron microscope can be used to study
the surface at the nanometric scale. Upon a comparison of the topography obtained from
the profilometer and an image obtained from an electron microscope (see Figure (16)) the
surfaces are similar. Both images are grayscale, but the electron micrograph is a photo
and the profilometer image is generated from a topographical scan. The small rectangle
on the profilometer image is a similar sized area to that shown in the micrograph. Fractals
may be self-similar or self-affine. 13
Self-affine, or random, fractals may be defined as a
union of rescaled copies of itself, where the rescaling may be anisotropic (dependent on
direction).13
Self-similar, or regular, fractals can then be defined as a union of rescaled
copies of itself, with isotropic rescaling (uniform in all directions). Virtually all naturally
occurring fractals are random. Regular fractals include: line intervals, solid squares, solid
FIG. 16 The actual image(mag. 5000 ×) and an image obtained by stylus profilometry(5.6
mm ×5.6 mm), the square showing the relative area between the two images.

27
cubes, and snowflakes. Simple regular fractals have integral scaling dimensions and
complex regular fractals have non-integral scaling dimensions. Worn surfaces fit into the
class of random fractals and are self-affine, but the scaling dimension has not yet been
determined.
B. The Fractal Dimension and Profile Analysis
The notion of "fractional dimension" 13
provides a way to measure how rough
fractal curves are. We normally consider lines to have a dimension of 1; surfaces have a
dimension of 2; and solids have a dimension of 3. However, a rough curve in the extreme
may be so rough that it effectively fills the surface on which it lies. Very convoluted
surfaces, such as a tree's foliage or the internal surfaces of lungs, may effectively be three-
dimensional structures. We can therefore think of roughness as an increase in dimension: a
rough curve has a dimension between 1 and 2, and a rough surface has a dimension
somewhere between 2 and 3. The dimension of a fractal curve is a number that
characterizes the way in which the measured length between given points increases as
scale decreases. Whilst the topological dimension of a line is always 1 and that of a
perfectly smooth surface always 2, the fractal dimension of a real surface may be any real
number between 2 and 3. Mandelbrat’s study of Earth coastlines showed that a self-
similar curve of fractal dimension D is related to the surface dimension Ds by the relation
Ds=D+1 where11
(4)
( )
( )
D
L L
S S
=
log /
log /
2 1
1 2

28
L1, L2 are the measured lengths of the curves (in units), and S1, S2 are the sizes of the units
(i.e. the scales) used in the measurements. Suppose that we wish to measure fractal
properties of the surface of a brake disc. There are two different sorts of measurements
that we might make. One sort of measurement would consist of measuring distances
between two points on the disc with varied point spacing on several profilometer traces.
Estimates of D for the brake surface would then be made using equation (4). If instead we
moved along the same transect and measured the height of the brake surface above the
mean line, then we could not measure the fractal index in the same way. For the height
data we would have to estimate the fractal dimension from the power spectrum of the data
series11
(5) ( ) ( )
2
1
120 0
∑=
⋅−π⋅−
=
N
k
dkfi
k eZ
N
d
fP
where i = − 1, N is the number of data points, d0 is the distance between data points, the
spatial frequency f is equal to K/L, and K is an integer that ranges from 1 to N/2. If D is
the fractal index, f is a frequency, and P(f) is the spectral value of f, then
(6) ( )P f kf D
= −5 2
where k is a scaling constant that relates G to the magnitude of the surface roughness
discussed later.14
It is important to realize that true fractals are an idealization. No curve
or surface in the real world is a true fractal; real objects are produced by processes that act
over a finite range of scales only. Thus estimates of D may vary with scale. The variation
can serve to characterize the relative importance of different processes at particular scales.

29
Mandelbrot called the breaks between scales dominated by different processes “transition
zones.”11
C. Fractal Roughness and Surface Profiles
Single trace surface profiles like Figure (17), appear random, multiscale, and
disordered. As mentioned above, the properties of such a profile are that it is continuous,
nondifferentiable, and statistically self-affine. The Weierstrass-Mandelbrot function (W-
M) satisfies all of these properties and is given by
(7) ( ) ( ) ( )
( ) 1;21;
2cos
1
2
1
>γ<<
γ
πγ
= ∑
∞
=
−
−
D
x
Gxz
nn
nD
n
D
where G is a characteristic length scale of the surface, n1 is first number in the data set
which is not equal to 0, and γn
determines the frequency spectrum of the surface
roughness. The fractal dimension D is known as the Hausdorff-Besicovitch dimension. 11
The variable γhas been found to be 1.5 for most surface.15
An increase in the dimension
D increases the jaggedness of the surface and a value of D = 3 is space filling. An increase
in the dimension D increases the total area of the surface and increases the spatial
frequency. An increase in G broadens the surface height variations making the surface
wavier. The G parameter also controls the absolute amplitude of the roughness over all
length scales and has units of length. The graphs in Figure (18) show how changes in D
and G change the surface profile. 14

30
-2 0 2 4 6 8 10 12 14 16
-80
-60
-40
-20
0
20
Height
Tracelength
FIG. 17. Example of a real profile and its randomness.
The power spectrum relationship to D and G can be found by using equation (6) and
replacing k by
(8)
( )
( )
γ
= −
−
ln2 252
12
D
D
f
G
k
that yields
(9) ( )
( )
( ) ( )D
D
f
G
fP ⋅−
−⋅
γ
= 25
12
ln2
.
Since a rough surface is a nonstationary random process 16
the lowest frequency is related
to the length L of the sample by
(10)
L
n 11
=γ .

31
0 200 400 600 800 1000
-0.4
-0.2
0.0
0.2
0.4
0 200 400 600 800 1000
-0.4
-0.2
0.0
0.2
0.4
D=1.5
G=1.0
Height(arbitrary)
Length (arbitrary)
0.0 0.2 0.4 0.6 0.8 1.0
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.0 0.2 0.4 0.6 0.8 1.0
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
D=2.0
G=0.15
Height(arbitrary)
Length (arbitrary)
0 200 400 600 800 1000
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0 200 400 600 800 1000
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
D=1.0
G=1.0
Height(arbitrary)
Length (arbitrary)
0 200 400 600 800 1000
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
0 200 400 600 800 1000
-0.03
-0.02
-0.01
0.00
0.01
0.02
0.03
D=2.0
G=0.05
Height(arbitrary)
Length (arbitrary)
FIG. 18. Effect of varying D and G on rough profiles. These are simulated from the W-M
function in equation (7).

32
-0.10 -0.05 0.00 0.05 0.10
0
20000
40000
60000
80000
P(f)
f
1E-3 0.01 0.1
100
1000
10000
log[(P(f)]
log [f]
FIG. 19. The power spectrum (left) and log(f) vs. log(p(f)) (right).
If P(f) is plotted as a function of f on a log-log plot as in Figure (19), then the power law
behavior would result in a straight line. The slope of the line η and the topological
dimension d are related to the dimension D as12
(11)
2
3 η−
+= dD .
The topological dimension d for a profile is 1 and for a surface it is 2. To find the
parameter G, D must be calculated first. The idea behind the fractal approach is that
instead of characterizing the actual disorder of surface roughness as the classical statistical
methods do, it is more logical to identify and characterize the order behind the disorder.
The variance function or structure function (SF) shown as equation (12) 14
, can be
used for the calculation of a measured surface profile with a total of N points. The SF
S(τ) can be calculated by varying the distance τ from a given point z(xi) and then finding
the difference z(xi) –z(xi + τ). The critical value of τ occurs when N = τ/∆x where ∆x is
the sample spacing. The benefit of using the SF is that it prevents aliasing (misplaced

33
harmonics) in the power spectrum. 17
Aliasing arises because the roughness profile is not
bandwidth limited to the Nyquist critical frequency ωH. The aliasing causes the power of
frequencies in the range ω > ωH to be falsely translated into the range ω < ωH. By
avoiding aliasing, the structure function yields more accurate values for D and G.14
(12) ( ) ( )[ ]∑
∆
τ−
=
τ+−








∆
τ−
=τ
x
N
i
ii xzxz
x
N
S
1
21
)(
A trace is said to be fractal if the structure function has a power law form: 1
(13) ( ) ( )DD
GS −−
τ=τ 2212
)(
The fractal parameters G and D are found from the power spectrum as mentioned earlier.
Alternatively, equation (13) has been derived from the power spectrum using the relation 18
(14) ( ) ( )[ ]1
1
−ω=τ τω
=
∑ ii
N
i
i ePS
As in the power spectrum method for finding the D and G parameters, the structure
function S(τ) can be plotted against τ on a log-log plot. The curve will be a straight line if
the profile is fractal. The slope of the line is related to D as in equation (11). The value of
G is obtained from the intercept at a certain value of τ. Using the fractal power law of
equation (6) in equation (14), the structure function is then given by 18
(15) ( ) ( ) ( ) ( )D
D
D
D
C
S −
τ−Γ




 −π






−
=τ 22
32
2
32
sin
2
where Γ is the gamma function, and the constant C of the power spectrum is related to G
of the structure function as
(16)
( )
( ) ( )32
2
32
sin
2 )1(2
−Γ




 −
−
=
−
D
D
GD
C
D
π

34
Berry et al.19
state that a surface profile is a self-affine fractal when
(17) ( ) ( ) ( )
0for2212
→ττ=τ −− DD
GS
For larger scale roughness Berry et al. suggest another expression for S(τ) shown
as equation (18). As τ → 0, S(τ)→ 0; and when ( ) ( )D
GG
−
σ>>τ
21
2 , S(τ)=2σ2
. In the
latter case the standard deviation, σ, which is equal to Rq, is assumed to be independent
of the sample size. It is also assumed that σcan be obtained from the roughness data for a
sample size larger than the correlation length, ( ) ( )D
c GG
−
σ=τ
21
2 . Experimental data has
shown that equation (18) is valid when the above criteria are met. However, Sayles and
Thomas (1978)16
have shown that the expression fails if σis scale dependent.
(18) ( )
( ) ( )












σ
τ
−σ=τ
−−
2
2212
2
2
exp12
DD
G
S
The variance σ2
(equation (19)) or Rq2
can be found using the fractal power law variation
of the power spectrum. If σ2
is found by using Rq2
, then equation (19) can be solved for
the scaling constant G.
(19)
( ) ( )32
2
32
sin2
)2(2
)2(2)1(2
)2(2
1
)25(
2
−Γ




 −π
=
−
=ω
ω
=σ
−−
−
∞
−∫
D
D
LG
L
D
C
d
C DD
D
L
D
Where L the tracelength, σ2
is the variance, and Γis the gamma function. If the parameter
D is found using another fractal method, then equation (19) can also be used to find G.

35
Chapter 2
I. Topographical Analysis
The use of topographies in the analysis of surfaces provides a more accurate
method of defining and characterizing these surfaces than the use of a few traces. Many
of the characterization parameters used in profile analysis cannot be directly extended to
surface topography analysis since one more dimension is involved. These topographical
parameters will, however, be more representative of the entire surface because of the
large quantity of data collected in one topography. It is important to remember that the
surfaces obtained from the various measurement techniques are only digitized
approximations of the actual surface. Therefore, statistical information based on these
surfaces can only be an approximation of the real surface. The information obtained
from these surfaces, although only approximations, can be used to correlate parameters
such as the average friction coefficient, however.
Most statistical parameters remain quite stable when taken at random locations on
an isotropic surface. Anisotropic surfaces such as machined or worn surfaces, usually
have characteristic directionality or lay associated with them. This anisotropy may have
a different power spectrum in different directions. Topographies taken parallel to the lay
of the surface will contain much less power at some wavelengths than will topographies
taken transverse to the lay.20
Thus, it is important to classify the directionality and
periodicity in the surface for a full understanding of its evolution in a wear process. An
example of a topographical surface is shown in Figure (20).

36
0
1250
2500
3750
5000
6250
7500
row
0
13
25
38
50
63
col
-15
-7
2
10
FIG. 20. A real surface topography shown in low resolution for easy viewing.
A. 3-D Characterization Parameters and Filtering of Height Data
When surface heigh t data is obtained by taking multiple parallel traces with a
profilometer, the data is stored as a matrix representing surface heights defined as
Z(N,M). The number of columns M is simply the number of traces; and the number of
rows N is the number of data points taken along the trace. The separation between row
data points is (tracelength) divided by (number of data points − 1). The column
separation is (width of the measured surface) divided by (number of traces − 1). The
position arrays are defined as X(N) and Y(M). A required first step in calculating
parameters is to determine the least squares mean plane (LSM). The least squares mean
plane for the surface represented by the Z(N, M) matrix is
(20) ( ) where, cybxayxf ++=

37
a Z bX cY= − −
( ) ( )[ ]
( ) ( )[ ]
b
X k Z k j Z
X k X k X
j
M
k
N
j
M
k
N
=
−
−
==
==
∑∑
∑∑
,
11
11
( ) ( )[ ]
( ) ( )[ ]
c
Y j Z k j Z
Y j Y j Y
j
M
k
N
j
M
k
N
=
−
−
==
==
∑∑
∑∑
,
11
11
The variables b and c are the slopes in the two orthogonal directions and a is the height
intersecting the Z-axis (or the datum plane). The residual surface R(N,M) can be obtained
by equation (21).
(21) ( ) ( ) ( ) ( )( )R N M Z N M a bX N cY M, ,= − + +
The residual surface R(N, M) can now be used to calculate surface parameters.
Since the separation between rows and columns can be different, a length scale l
must be defined. The length scale at which a surface is measured is important because
some parameters characterizing the surface can change significantly with a change in
scale. This is not true for all parameters though. Let
(22) l l lx y= +
2 2
where lx is the spacing between the rows and ly is the spacing between the columns. The
length scale (hypotenuse) l can be thought of as a magnification of the surface and its
resolution in the surface plane is l units. For fractal calculations l is the asperity base
diameter. The height resolution depends on the measuring instrument. The tip radius of
a stylus used in profilometry is neglected in this study since the length scale is of the
same order of magnitude as the stylus tip radius (2µm - 10µm).

38
In series of papers written by W.P. Dong et al.21
, many generalized three
dimensional characterization parameters were proposed. These parameters were adapted
and used in the current research. Most of the equations in the rest of this section are
standard equations for three dimensions; since they are all used, they will be reviewed.
The surface roughness characterization parameters sPa and sPq are the
arithmetical mean deviation and the root mean square (rms) deviation from the surface
mean plane, respectively. The parameter sPq is also known as the surface standard
deviation. These parameters are defined by
(23) ( )sP
NM
R k ja
j
M
k
N
=
==
∑∑
1
11
,
(24) ( )sP
NM
R k jq
j
M
k
N
=
==
∑∑
1 2
11
,
The roughness characterization parameters in equations (23) and (24) are obtained from
the real surface before any filtering techniques are applied. This parameter has been
shown by W. P. Dong et al.22
to be invariant to a change in scale l.
The kurtosis sRku (given by equation (25) below) relates to the peak height
distribution. A Gaussian surface has a kurtosis of 3. If the kurtosis is less than 3 the
height distribution tends to be more spread out. If the kurtosis is greater than 3 the height
distribution is more centrally distributed. The skewness sRsk relates to the length of the
tail of a Gaussian distribution. A positive value indicates a longer tail at the upper side of
the mean plane and a negative value indicates a longer tail at the lower side of the mean
plane. The skewness (given by equation (26) below) is sensitive to outliers such as large
peaks. A large positive skewness can indicate that the surface has many significantly

39
large peaks while negative values of sRsk can indicate that the surface has relatively few
outlying peaks.23
(25) ( )sR
MNsR
R N Mku
q l
M
k
N
≈
==
∑∑
1
4
4
11
,
(26) ( )sR
MNsR
R N Msk
q l
M
k
N
≈
==
∑∑
1
3
3
11
,
Filtering of data is currently a widely discussed topic, therefore a filtering
technique that can be adjusted for the change in length scale is appropriate. The filtering
method of adjacent averaging for a surface is given in equation (27) that was developed
for this work. It is easily obtained by expanding equation (2) to another dimension. For
each N and M in the surface matrix R(N,M) a waviness surface wave(N,M) can be
extracted and then subtracted from the original surface to obtain a roughness surface.
Examples of the waviness and roughness surfaces are shown in Figures (22) and (23).
The bandwidth parameters k and l can be adjusted to optimize the degree of
smoothing in the two orthogonal directions.
(27) ( ) ( )∑ ∑− −
++





+






+
=
k
k
l
l
lMkNR
lk
MNwave ,
12
1
12
1
,
The absolute surface roughness sRa and sRq can be calculated using equations
similar to (23) and (24) on the roughness surface. When sRa and sRq are plotted together
with sPa and sPq as shown in Figure (23), they are simply different magnitudes of the
roughness. The parameter sRp is the highest peak from the LSM plane of the roughness
surface. The parameter sRt is the distance between the highest peak and the lowest valley
of the roughness surface. All sR values are obtained from the roughness surface and sP
values from the real surface after LSM plane is subtracted.

40
1250
2500
3750
5000
6250
row
0
10
20
30
40
50
col
-12.5
-5.8
0.8
7.5
FIG. 21. Waviness of the surface of Figure (20).
1250
2500
3750
5000
6250
row
0
10
20
30
40
50
col
-5.00
-2.50
0.00
2.50
FIG. 22. Roughness surface of Figure (20).

41
0 20 40 60 80 100 120 140
0
1
2
3
4
5
6
7
sPa
sPq
sRa
sRq
Height(µm)
Stop #
0 20 40 60 80 100 120 140
0
1
2
3
4
5
6
7
FIG. 23. Comparison of different roughness parameters.
B. Surface Area
There are two kinds of surface area, nominal and real. The nominal surface area
is the length times the width of the measured surface. The real surface area can be
estimated by breaking up the surface grid into triangles and summing the surface areas of
these triangles as shown in Figure (24). The real surface area is almost always greater
than the nominal surface area.

42
FIG. 24. Surface area measurement triangles.
Cleaved mica is the only surface that has an equivalent nominal to real surface area since
it is smooth down to the atomic scale. Measurements of the real surface area can be used
to show the development of the surface from machined to worn.24
These measurements
can also be used to observe the effects of various surface treatments on the wear of the
material being tested.
C. Areal Autocorrelation Function
The spatial properties of a surface can be examined through the use of the
autocorrelation function and the power spectral density (PSD). Both functions are well
defined in mathematics. 24
For a 3-D surface, a non-biased estimation of the areal
autocorrelation function (AACF) in digital approximation is

43
(28) ( )
( )( )
( ) ( )jlikRlkR
jNiM
AF
jM
l
iN
k
ji ++
−−
= ∑ ∑
−
=
−
=
,,
1
,
1 1
ττ
where i = 1, … , m < M ; j = 1, … , n < N ; τi = i∆x ; and τj = j∆y. The maximum
autocorrelation lengths are m and n in the x and y directions, respectively. The AACF
describes the general dependence of one data point to another. The directionality of the
surface can be analyzed from a graph of the AACF as shown in Figure (25). The
correlation of the surface lay is observed as a decay in the figure. The decay is in the
direction of the surface lay. Strong decay can be observed in the lay direction which
corresponds to the power of the surface in that direction.
0
1 2 5 0
2 5 0 0
3 7 5 0
5 0 0 0
6 2 5 0
7 5 0 0
r o w
0
5
1 0
1 5
2 0
2 5
3 0
3 5
4 0
4 5
-10
-5
0
5
1 0
1 5
2 0
2 5
FIG. 25. Areal autocorrelation surface showing the directionality of the surface .
Weak correlation
Strong correlation

44
D. Fractal Surfaces
A fractal surface has a dimension D between the values of 2 and 3. Surfaces that
have a standard deviation, σ, that is nearly linear, with a relatively small slope, through
several length scales (scale-independent) have been shown to be fractal surfaces.14
There
are numerous methods to determine the fractal dimension of a surface. Since the surfaces
may be anisotropic it is necessary to use fractal methods that can adequately define them.
There are two main methods presented for calculating the dimension D for anisotropic
surfaces; The Hurst orientation transform13
(Hurst) and the Fourier transform (FT)
method. Both Hurst and FT analysis can be used for isotropic and anisotropic surfaces.
1. Hurst Analysis
Hurst analysis for isotropic surface data consists of creating a log-log plot of the
difference in elevation between the highest and lowest points within a circle of varying
diameter.13
At each chosen central point, all data points within the initial circle are
compared. Differences between data points are calculated, normalized using the standard
deviation of the surface, and, finally, sorted. The largest difference and the diameter of
the circle are stored. The diameter of the circle is then increased and the above process is
executed again for 7 to 10 different circle diameters. The data points are plotted as log
(difference) versus log (diameter). A least squares mean line is calculated and the slope
obtained. This slope is called the Hurst slope, H, and its relationship to the D parameter
is11,12,13,25
(29) HD −= 3

45
The slope H must be between 0 and 1. The method above should be repeated using the
same circle diameters at different locations on the surface as shown in Figure (26) below.
0 1 2 5 0 2 5 0 0 3 7 5 0 5 0 0 0 6 2 5 0 7 5 0 0
0
1 3
2 5
3 8
5 0
6 3
-15-10-5051 0
-15 -10 -5 0 5 1 0
Real
FIG. 26. Examples of the circular areas of increasing diameter used in the Hurst method.
The slopes can then be averaged to obtain an average D value for the surface. The plot of
the data obtained using the Hurst method in Figure (27) shows the data points to be quite
linear.13
Large changes in the surface such as open pores, cracks, gouges, or wear tracks
tend to effect the slope of the plot. The effect of these large dropoffs as seen in Figure
(28) actually bring the slope of the LSM fit into the Hurst slope range. Since the
surfaces that are being analyzed are anisotropic it was necessary to alter the Hurst method
to obtain angular relationships as well.
The Hurst orientation transform (HOT) is a modified Hurst method. The HOT is
calculated by dividing the surface data into circular or rectangular areas. In each area, all
of the data points are compared and the largest difference between the points is stored.
The distance between the data points is calculated and stored along with the difference in
height. The angle from the highest data point in the area is calculated from the center of
the area. By sorting this data with respect to angle and distance and then plotting the log

46
(difference) versus the log (distance) at each angle, the Hurst slope is obtained with
respect to angle. The angular relationship for a whole surface is shown in the side view
5.4 5.6 5.8 6.0 6.2
-1.8
-1.6
-1.4
-1.2
-1.0
5.4 5.6 5.8 6.0 6.2
-1.8
-1.6
-1.4
-1.2
-1.0
SLOPE = 0.9965
D - VALUE = 2.0035
Data
Fit
LogDifference
Log Distance
FIG. 27. Log (distance) vs. log (difference) of a typical measured area for Hurst analysis.
2.45 2.50 2.55 2.60 2.65 2.70
-0.9
-0.8
-0.7
-0.6
-0.5
2.45 2.50 2.55 2.60 2.65 2.70
-0.9
-0.8
-0.7
-0.6
-0.5Data
Fit
SLOPE = 0.86402
D - VALUE = 2.13598
LogDifference
Log Distance
FIG. 28. An example of the possible data variation for the Hurst method.

47
250 300 350 400 450
D istance (microns)
0255075100125150175
A n g le (microns)
0.0000
0.0305
0.0611
0.0916
Difference (microns)
FIG. 29. Side view to see the slope of Figure (30).
2 5 0
3 0 0
3 5 0
4 0 0
4 5 0
D istan ce (microns)
0
25
50
7 5
1 0 0
1 2 5
1 5 0
1 7 5
A n g le (degrees)
0 .0 0 0 0
0.0 2 9 2
0.0 5 8 3
0.0 8 7 5
D ifferen ce (microns)
0.0 0 0 0 0.0 2 1 9 0 .0 4 3 7 0.0 6 5 6 0.0 8 7 5
D ifferen ce (microns)
FIG. 30. Grid plot showing the surface representation for the Hurst orientation transform.
plot in Figure (29). The Hurst transform surface in Figure (30), as viewed from a
perspective angle, shows how the slope of the surface varies as the angle changes. The
slopes do not vary greatly with angle, so the surface must be nearly isotropic. As an
example, Figure (31) shows the typical relationship between of log (difference) versus
log (distance) at an angle of 11°
. The D parameter is then calculated from the slope using
equation (29). Depending on degree of anisotropy in the surface there may be only a few
angles with enough data to obtain a reliable D parameter. These angles can be used to

48
evaluate the change in D with respect to angle.
10 100
0.000
0.001
0.010
0.100
1.000
10 100
1E-4
1E-3
0.01
0.1
1
Data
Fit
SLOPE = 0.95489
D - VALUE = 2.05511
Angle = 11 Degrees
LogDifference
Log Distance
FIG. 31. Log (difference) vs. log (distance) at a given angle using the HOT method.
The equation used to obtain the fractal G dimension of profiles is also modified
for topographical surface data. The modification requires the substitution of 1+= DDs
into equation (19). The resulting equation for G becomes
(30)
( )
( )
( ) ( )52
2
52
sin2
where
22
1
32
2
−Γ




 −π
=ϕ





 ϕσ
=
−
−
s
s
D
D
D
D
L
G
s
s
This variation of equation (19) assumes that the measured area is square. The
corresponding asperity height from equation (31) is
(31) ss DD
lG −−
=δ 32

49
where l is given in equation (22).
2. The Discrete Fourier Transform and Fractals
The discrete Fourier transform (DFT), shown in equation (32), is used to find the
frequency distribution of a surface. For a two dimensional grid of height data the DFT
can be calculated as17
(32) ( )21
21
0
1
0
2
21 ,),( 1
11
2
2
1
1
2
22
kkmeennM N
nikN
k
N
k
N
nik
















≡
π−
=
−
=
π
∑ ∑
where m(k1,k2) is the complex or real surface array to be transformed and M(n1,n2) is the
transformed complex surface array. The variables N1 and N2 are the number of rows and
columns in the array and must be powers of 2. If N1 and N2 are not the result of a power
of 2, then the FFT will have a large number of high frequency terms added. The
variables n1, n2, k1, and k2 are the frequency and position of the height data, in each
direction respectively. If the surface is not evenly sampled, aliasing will always occur
along one or both dimensions.13
After a surface has been Fourier transformed, the fractal
parameter D, the power spectrum (Figure (32)), and the anisotropy can be obtained. The
fractal parameter D can be calculated by taking a pie shaped wedge in the power
spectrum surface and finding its least squares mean plane as shown in Figure (32). It is
necessary to use this method in each of the four quadrants in the APSD surface. Once the
LSM plane is found for each pie shaped wedge, the slope in all directions can be
calculated. The variation in the slope of the LSM plane shows the difference in D with
the direction of the surface.

50
0 1 2 5 0 2 5 0 0 3 7 5 0 5 0 0 0 6 2 5 0 7 5 0 0
0
1 3
2 5
3 8
5 0
6 30 .0 0 x 1 0
+0002 .5 0 x 1 0
+0065 .0 0 x 1 0
+0067 .5 0 x 1 0
+006
0 .0 0 e+000 3 .7 5 e+006 7 .5 0 e+006
APSD
FIG. 32. Typical power spectrum (APSD) for an anisotropic surface. A pie shaped
wedge enclosed for the fractal D calculation.
0 1 2 5 0 2 5 0 0 3 7 5 0 5 0 0 0 6 2 5 0 7 5 0 0
0
1 3
2 5
3 8
5 0
6 32 1 6 79 8 3 31 7 5 0 0
-5000 2 5 0 0 1 0 0 0 0 1 7 5 0 0
FFT
FIG. 33. The fast fourier transform of an anisotropic surface.
0 1 2 5 0 2 5 0 0 3 7 5 0 5 0 0 0 6 2 5 0 7 5 0 0
0
1 3
2 5
3 8
5 0
6 3
-15-10-5051 0
-15 -10 -5 0 5 1 0
Real
FIG. 34. The real surface for the APSD and the FFT above.

51
An isotropic surface would yield nearly equal slopes in the two orthogonal directions.
Figures (35) and (36) show plots of the slope for an anisotropic and an isotropic surface,
respectively. The variation of the slope can be seen as the angle changes from 0 to 90
degrees. In Figure (35), the first quadrant of the APSD for the anisotropic surface in
Figure (34) shows a large slope in the direction of the machined gouges. This means that
the dimension D in the parallel direction of the gouges is closer to 2 and in the transverse
direction D is closer to 3. In Figure (36), the first quadrant of the APSD for the isotropic
surface shows the dimension D varying around the value of 2 with the slopes in the
orthogonal directions nearly equal. Equation (29) was used to obtain the dimension D for
the Figures below.
0 10 20 30 40 50 60 70 80 90
0.0
0.2
0.4
0.6
0.8
1.0
Mean = 0.51115
Dimension D = 2.48885
Slope
Angle (Deg)
0 10 20 30 40 50 60 70 80 90
0.0
0.2
0.4
0.6
0.8
1.0
FIG. 35. The change in slope with respect to angle for one quadrant of an anisotropic
surface.

52
0 10 20 30 40 50 60 70 80 90
0.7
0.8
0.9
1.0
1.1
Mean = 0.96453
Slope
Angle (Deg)
0 10 20 30 40 50 60 70 80 90
0.7
0.8
0.9
1.0
1.1
Dimension D = 2.03547
FIG. 36. The change in slope with respect to angle for one quadrant of an isotropic
surface.
Solving equation (33)14,25,26
gives the D parameter for each slope. The D values obtained
are then averaged to give the average D of the surface.
(33)
2
5 slope
D
−
=
The slope must be between –1 and 1. Equation (29) can also be used as long as the slope
is normalized to vary from 0 to 1.12,25
The power spectrum can be obtained by
multiplying the Fourier transform times its complex conjugate as shown in equation (34).
(34) ),(),(),( 212121 nnMnnMnnAPSD ∗
=
The surface power spectrum is commonly called the areal power spectral density
(APSD). The anisotropy of a surface can be viewed as a directionality in the spectrum.
Although the anisotropy can be seen in the Fourier transform, the APSD is sometimes

53
easier to interpret. Compare the FFT in Figure (33) to the APSD in Figure (32) for the
same anisotropic surface. The general direction of the surface is obvious in both Figures
(32) and (33), but the APSD in Figure (32) shows more detail because there are no
negative values. The real surface in Figure (34) shows a large number of wear tracks
which are transformed into the APSD as a spread of power in the center of the image.
The intensity of the frequency distribution in the APSD is directly related to the strength
of the anisotropy of the surface. For an isotropic surface, the frequency distribution is
even around the center of the APSD as shown in Figure (37). Different filtering
techniques can be applied to the transform to obtain a variation of the original surface
such as a smoothing function. Once a filtering process has been completed on the
transformed surface, applying the inverse FFT can restore the real surface.
FIG. 37. The transformed image of an isotropic surface.

54
The contents of chapter 1 and the preceding sections of this chapter provide
sufficient background material to follow the analysis of the experimental studies
performed in the next section.
II. Experimental Apparatus and Data Collection
A. Sub-Scale Aircraft Dynamometer
Experimental testing was performed on a sub-scale aircraft dynamometer that is
shown in chapter 1 as Figure (1). The dynamometer was designed and constructed by
Link Engineering specifically for the Center for Advanced Friction Studies (CAFS) at
Southern Illinois University at Carbondale. Two test C-C composite brake rings can be
attached to the dynamometer. One brake as a rotor and one as a stator. Figure (3) shows
the rotor and stator locations while Figure (2) shows how the brake is attached. The
tailstock of the dynamometer contains the stator, its fixture, and the force and torque load
cells. The torque-measuring device is a “Z” –style load cell combined with a 15.24-cm
lever arm that is capable of measuring a maximum torque of 677.909 N-m. If the torque
limit is exceeded the overload protection will separate the pads. The maximum applied
load is 13.344 kN; and the load ramp rate is selected by the user. Our experiments used a
ramp rate of 6.672 kN/s.
The tailstock can be moved to separate the pads to a maximum of 33 cm for easy
access to the rotor and stator. Before testing the pads have a separation of approximately
0.5 mm.
The inertia section in Figure (1) contains a rotor shaft with a rotational inertia of
0.2712 kg-m2
. There are two large inertia disks each with a rotational inertia of 1.8642

55
kg-m2
, five medium disks each with 0.339 kg-m 2
of rotational inertia, and one small disk
with 0.1695 kg-m2
rotational inertia. The inertia can be varied between 0.2712 kg-m 2
and 5.8639 kg-m2
.
The dynamometer can control either the torque or the force in a stop. In our
experiments the torque was held constant. Force, torque, and temperature data is
collected at a maximum sampling rate of 500 points per second. The average friction
coefficient is calculated by calculating the coefficient at each point within a stop for times
t1 ≤t ≤t2 where t1 is 0.5 s after the threshold time and t2 is 0.5 s before ts, the stop time,
using
(35)
effFr
τ
=µ
where τ is the measured torque, F is the measured applied load, and reff is the effective
radius which is
2
0 irr +
.
B. The Profilometer
Surface topographies were measured using the Mahr skidless stylus profilometer
shown in Figure (38). The profilometer can measure a maximum tracelength of 17 mm
with 8064 data points. It has a maximum vertical resolution of 7 nm. The stylus tip is
made of diamond and has a radius of curvature of 5 µm. The maximum force the stylus
applies is 0.8 mN. An electron micrograph of the stylus against a surface is shown in
Figure (39). The profilometer can be mounted in any orientation making it possible to
measure the surfaces in-situ between dynamometer stops. In order to measure

56
topographies it was necessary to build an accurate xyz positioning system (also in Figure
(38)), because the profilometer can only measure single traces. The xyz positioner makes
it possible to take multiple traces across the surface of the brake pads without removing
them. Topographies obtained by skidless stylus profilometry can be also used to study the
evolution of a surface in a wear process. Data collected from a stylus profilometer has
been shown to be accurate in describing the real surface as digitized height data. 27
FIG. 38. The profilometer attached to the xyz positioner.
Profilometer
z-axis
x-axis
y-axis

57
FIG. 39. An image of a 5-µm radius diamond stylus similar to the one used on the
profilometer. (Photo Courtesy of Mahr Corp.)
C. XYZ Positioning System
The XYZ positioning system shown in Figures (2) and (38) was designed and
constructed to accurately position an attached measuring device such as the profilometer
in Figures (2) and (38). The three stages of the positioner are constructed out of an
aluminum alloy with a coefficient of linear expansion of 21.0 o
C-1
, modulus of elasticity
of 70 GPa, and a tensile strength of 325 MPa. The base of the positioner can be bolted to
a surface or held in place using a large magnet. The x and y axes each have two ground
linear guide bars (x-axis 6.35 mm bars, y-axis 9.525 mm bars) passing through the central
guiding block with three linear bearings embedded in the block for each guide bar. The z
axis has four 9.525 mm guide bars each with three linear bearings embedded in the
guiding block. The ground guide bars are made of stainless steel with a Rockwell C 60-

58
65 hardness and a linearity of 4.17 µm per meter. Each axis has a reference surface with
a ground finish roughness of Ra ≅.005 microns. The central guiding block for the x and
y axes is made of Delrin, a Teflon based flouropolymer. Delrin was chosen for its low
coefficient of static friction, its high compressibility, and strength. The z-axis guiding
block is made from the same aluminum alloy used for the stages. The block has 0.672-
mm Teflon skids contacting the reference surfaces. All stages and guide bars have
alignment set screws for precision alignment.
The lead screw used to move the x axis stage is made of a 9.525-mm ground
stainless steel bar with 3.15 thread(s)/mm and mates with 57.15 mm of threaded nuts
embedded in the guiding block. The y- and z-axis lead screws have 2.2 thread(s)/mm and
mate with 63.5 mm of threaded nuts embedded in the guiding blocks. The y-axis lead
screw can be exchanged with a 3.15 thread(s)/mm lead screw for greater accuracy. The
large number of threads being in contact assures accurate movement of the stages in the
direction of travel. Each lead screw has precision bearings at the ends for smooth
rotation. The lead screws are driven by high performance stepper motors (see Figure
(40)). These stepper motors are driven by high resolution motor drivers (see Figure (41)).
The motor drivers provide microstepping of 125 steps per motor step. The digital motor
rotates 1.8 degrees per step, but with microstepping the motor rotates .0144 degrees per
step. The total distance the x axis stage travels per step is then 12.7 nm and the y and z
axis is 18.14 nm per step. The total range for each axis is; 43.42 mm for the x-axis, 41.82
mm for the y-axis, and 143.76 mm for the z-axis. The speed of the stepper motors may
be selected from the range of ¼ steps/sec to 500 000 steps/sec, however, for precise
positioning, 1000 steps/sec or less is recommended. The controller provides the step

59
pulse to the drivers the step pulse is calibrated digitally and has no deviation. The
controller also monitors the home and limit switches and provides monitoring of other
inputs. For topographical scanning the positioner was moved along a preset number of
steps after each trace of the profilometer. This movement was triggered using the step
pulse output line for an x-y stage that was purchased with the profilometer.
The starting point for each topography was found on the rotor to within about1
micron from each other using a diode laser and a silicon photodetector with a 2 micron
pinhole mounted on the positioner in a fixture. The laser can be back focused from a
mirror on the side of the rotor fixture to the 2-micron pinhole covering the detector.
Measuring wear during dynamometer testing by removing the discs and weighing
them is impractical and would substantially alter the performance of the brakes. Using
the positioner and profilometer to measure the amount of wear by direct measurement
provides more information. With a reference position located at the inner radius, the
distance from the surface of the brake pad to the rotor mounting fixture can be measured
and the absolute wear across the surface can be assessed.
FIG. 40. Top view of positioner.

60
FIG. 41. High-resolution stepmotor driver control board.
D. Brake Materials, Experimental Conditions, and Procedures
There were two pair of C-C brake pads used in four experiments. Figure (3)
shows the brake pad geometry. The four experiments as displayed in this paper are
labeled as Test 20, 21, 26, and 27. Each experiment required two weeks of dynamometer
time for data collection. Table (1) shows the relevant experimental information for the
four Tests. The R and S labels next to the C-C pad names are the rotor and stator,
respectively.
The first pair of brake pads are labeled KLF013 (13) and KLF014 (14). The
second pair of brake pads are labeled KLF015 (15) and KLF016 (16). Pads 13, 14, 15
and 16 were fabricated at CAFS using chopped pitch (pads 13 and 14) and PAN (pads 15

61
and 16) fibers pre-impregnated with phenolic resin and carbon vapor infiltration (CVI)
densified at Aircraft Braking Systems, Inc to densities between 1.75 and 1.84 g/cm 3
. The
surfaces of the pads were machined on a lathe at 1000 rpm using a cutting tool with a
radius of 0.381 mm. The surfaces for Tests 20 and 26 were machined only whereas Tests
21 and 27 were polished using 1000 grit sandpaper.
E = 18 204 J (13 400 ft-lb)
I = 3.32 kg-m2
(2.45 slug-ft2
)
ω0 = 1000 rpm
Environment: Lab air
T0 = 45 o
C
Torque control
Test
#
C-C
Pads
Fiber
Material
Machining
Process
stop time
(s)
number of
stops
20 KLF013(R)
KLF014(S)
pitch machined
only
12 150
21 KLF013(R)
KLF014(S)
pitch polished to
1000 grit
6 150
26 KLF015(R)
KLF016(S)
PAN machined
only
12 200
27 KLF015(R)
KLF016(S)
PAN polished to
1000 grit
6 200
Table 1. Relevant experimental information.
Initial topographies were measured after the disks were placed in the rotor and
stator fixtures on the dynamometer. Figures (42) through (45) are the initial measured
rotor surface topographies for Tests 20, 21, 26, and 27. The topography trace lengths are
10 mm for all four tests. The topographies were measured from the inner radius to the
outer radius where the inner radius is always on the left side of the image. The number of
traces and widths of the topographies are: 50 traces in 1.15 mm for Test 20, 50 traces in
0.133 mm for Test 21, and 64 traces in 0.171 mm for Tests 26 and 27. The topographies

62
in Figures (42) through (45) have been widened with fewer points plotted for easier
viewing. Before topographies were measured, the surface was cleaned in the area to be
measured with air to remove any loose particles. Topographies of the rotor were
measured after each of the first 5 dynamometer stops. Topographies were then measured
every 5 stops between stops 5 and 150 for Tests 20, 21, 26, and 27, and every 10 stops
after stop 150 for Tests 26 and 27. The stator was measured every 15 stops since the
surfaces are assumed to be conforming as shown in Figure (46). The profilometer is
removed after each inspection stop and then replaced at the next inspection stop. The
surface evolution data presented in this paper is from the rotor only and further studies of
the stator are planned in the future.
There are large differences in roughness and fractal dimension between the
machined and polished surfaces as seen in the figures to follow. These differences can be
characterized using the equations discussed in chapter 1 and at the beginning of this
chapter. The integration of the characterization equations into software is discussed next.
FIG. 42. Initial machined surface for pad 13, Test 20.
FIG. 43. Initial polished surface for pad 13, Test 21.

63
FIG. 44. Initial machined surface for pad 15, Test 26.
FIG. 45. Initial polished surface for pad 15, Test 27.
FIG. 46. The rotor and stator conform to each other during the wear process. Note: the
topography for the stator has been inverted.

64
E. The Surface Analysis Program
Using Microsoft’s FORTRAN Developer Studio, a program was created that
incorporates most of the equations and methods presented in this paper and more. The
Windows-based FORTRAN program used for the calculations has been named “The
Surface Analysis Program.” The program is the culmination of two years of work and
has over 800 kilobytes of code. The program is continually being updated with additions
and is currently capable of handling arrays of height data with dimensions as large as
9000 rows by 1024 columns in double precision.
In addition to the material presented here, the program computes real area of
contact information (classical and fractal methods), bearing area information such as the
core fluid retention, valley fluid retention, surface bearing index, and the output data to
make a plot of the bearing area ratio. The program also allows the user to alter the slope
of the surface in the x or y direction and then save the real and altered surface. There are
the equation of the mean plane is:
f(x,y)= .022272+ .000045x + -.000013y
The total developed surface area is(sA): 1004056.43495
The developed interfacial area ratio is(sAr): 1.19780
The Nominal area is= 992172.241 square microns
The density of summits per unit area(inv. sq. mm) is =
7193.00000
There are 7193 peaks on this surface
sPa= .149261 sPq= .185361
sRa= .122166 sRq= .157691
sRku= 5.258118 sRsk= .045160
The standard deviation M0 is: .18536
The moment M2 is: .06389
The moment M4 is: 2.60298
h at .05= 3.161970406067176E-001
h at .08= 2.700997460628478E-001
h at .25= 1.331249E-01
h at .75= -1.250199214560361E-001
h at .95= -2.883360506971748E-001
A(h) at .05= 4.540495697021533E-002
A(h) at .08= 7.594800064086996E-002
A(h) at .25= 2.408286676025416E-001
A(h) at .95= 9.350856225586037E-001
Surface bearing index Sbi= 3.162584944125992
sRp= 6.599512051267931E-001
sRt= 1.317065612174926
Core fluid retention index Sci= 9.740698948596414E-001
Valley fluid retention index Svi= 5.833080159824159E-002
HURST D= 2.811560007685879
G-VALUE= 4.308270E-02
Average asperity height= 1.076092150741939E-001
FFT fractal parameters!
The equations of the FFT mean planes are:
f(x,y)= 3.058089+ -.030543x + -.030330y
f(x,y)= 3.069368+ .047835x + -.010826y
FFT D using AVE slope= 2.965855935107066
G-VALUE= 2.094039108054365E-001
Average asperity height= 2.298059792303134E-001
Total area of peaks= 3.256337334085845
Percent of peak area to nominal area= 3.282028258864996
The number of roughness peaks is= 6740
The area of the largest contact spot is= 4.831361072659397
The real area of contact using fractals is=
7.208481282431879
Time Start; 0: 3: 46: 0
Time Finish; 0: 16: 2:
FIG. 47. Example output of the surface analysis program.

65
17 output files if all calculations are chosen. The list in Figure (47) shows all of the
output information listed in the info.txt file. The executable program file and some
sample surfaces are included on the CD in the back cover.
In order to use the surface analysis program in Windows NT or 95, the computer
must have at least 64 megabytes of RAM and 400 megabytes of virtual memory. This is
not a DOS based program. The windows interface has been made user friendly, but must
be exited and restarted after the completion of data analysis.
III. Results and Discussion of Collected Topography Data
During dynamometer testing visual observations of the interface surfaces were
recorded. Torque overlimits and rough stops were also recorded to find out if any
correlation exists between these overlimits and roughness. Movies were made using each
topography to observe the evolution of the interface surfaces. The movies for each test
are saved on the CD as avi files and can be viewed in Windows. A qualitative discussion
of the evolution of the interface surfaces for Tests 2028
, 2128
, 26, and 27 follow.
Test 20 rotor evolution observations:
1. The machine surface shown in Figure (42) shows a few shallow cracks near the
middle of the rubbing path. The peak height distribution appears to be near-Gaussian.
2. After the first stop, a concentric wear pattern consisting of four rings was present.
The peak height distribution broadened, but remained somewhat Gaussian.

66
3. Inspection stop 10: three rough stops occurred between stops 5 and 10. Large pieces
of material were removed from the surfaces. In the scanned area, material was
removed (leaving small holes) from the middle and outer portions of the rubbing path.
4. After stop 20, the peak height distribution becomes less Gaussian; and after stop 35, it
isn’t Gaussian.
5. Stop 33 was rough and holes were observed near the inner portion of the rubbing path
for inspection stops 35 and 40.
6. Stops 42, 43, and 44 were rough and by stop 45 only three concetric rings were
visible. Significant surface damage was evident on the inner radius portion.
7. After rough stops 77 through 80, inspection showed new damage to the inner radius
portion. Two concentric rings near the outer portion seemed to merge into one as
most wear occurred in that region.
8. For stops 115 through 150, the surfaces maintained a regular wear process and no
significant changes in the surface peak height distribution were observed.
1. After Test 20, the surfaces of pads 13 and 14 were remachined and finished with 1000
grit sandpaper. The initial surface in Figure (43) is somewhat smoother than Figure
(42). Large cracks were visible near the outer radius of the scanned area. The peak
height distribution was narrow and skewed toward the left.
2. After stop 1, several concentric rings were present, the deepest near the inner radius.
The peak height distribution became somewhat broader and more skewed toward the
left.

67
3. Between stops 5 and 25, the surface becomes smoother and three concentric rings are
present. The peak height distribution was similar to that of the initial surface. The
wear process seemed to be stablizing and the average friction coefficient achieved a
constant value near 0.40.
4. Stop 26 was rough and resulted in a complete reconfiguration of the interface surface
as excessive wear occurred both on the inner and outer portions of the rubbing path.
The new surface went through a new run-in with most wear occuring in the middle of
the rubbing path. A raised area appeared between the middle and outer concentric
rings.
5. There were numerous rough stops and over-torque stops between stops 56 and 67 that
resulted in substantial wear and roughening near the inner radius and near the middle
of the rubbing path. The peak height distribution was similar to that of stop 1.
6. Between stops 70 and 95, the surface undergoes another run-in process; and near stop
90, the average friction coefficient seems to stabilize at 0.44. Rough stops occurred
between stops 95 and 100 that roughened the surface again and began a new run-in
process. By stop 115, the average friction coefficient stabilized again to about 0.44
and the peak height distribution was non-Gaussian until the end of testing.
1. Test 26, shown in Figure (44), begins with a machined surface as in Test 20.
Waviness is noticable in the Figure along with strong anisotropy resulting from the
machining process. The waviness may be due to the underlying fiber orientation

68
which is nearly parallel to the machining direction in the measured area. The peak
height distribution is nearly Gaussian. The surface appears dull.
2. After stop 1, the waviness was reduced and the peak height distribution skewed
toward zero showing a removal of the larger peaks.
3. The peak height distribution became non-Gaussian after stop 10. A large gouge
appears in stop 10 which is the result of fibers being literally “ripped”out of the
surface. This gouge remains until it is worn away around stop 50. A loosely packed
friction film is developing on both stator and rotor surfaces. The very smooth parts of
the topographies correspond to the areas containing a well bonded friction film. After
stop 20, the friction film seems to cover a large portion of the surface. Occasional
rough stops seemed to remove some of the developing friction film.
4. Stop 25 inspection revealed several wear tracks developing at outer radius.
5. The first one or two stops after an inspection stop were generally rough, but no torque
overlimits occurred.
6. After stop 50, the surface shows a clear wear pattern developing which consists of
concentric rings that generally do not move radially from their current position. This
pattern continues to develop for the remainder of the Test. Rough stops continue to
occur after inspection stops.
7. The surfaces appear to be very shiny at stop 75 indicating almost complete coverage
of the surface film. Concentrically-oriented fiber bundles have been ripped from the
surface. Fine particulate debris can be seen on the rotor and stator surfaces during
inspection stops. After stop 75, the surfaces remain smooth and shiny.

69
1. The initial machine surface, shown in Figure (45), was polished using 1000 grit
sandpaper. A few large cracks can be seen near the outer radius. The peak height
distribution is very narrow and nearly Gaussian. The surface appears to be semi-
shiny.
2. After stop 1, the peak height distribution is non-Gaussian and remains this way for
the remainder of the Test. Only a few torque over limits occurred throughout Test
27, with most of them before stop 10.
3. By stop 15 the surface is very shiny, but the surface film is not flaky as in Test 26.
Very little waviness developed through stop 110. Overall, the stops seem to be
much smoother than Test 26. Debris particles are always covering the surfaces
when viewed at each inspection stop. Very small scratches or cracks are visible in
the shiny film with their lengths varying concentrically around the surface. As in
Test 26, these may be the result of fiber bundles being pulled out of the surface.
4. At the end of testing, the surfaces had worn very little. Wear occurred mostly on
the outer radius portion of the rotor surface. The surfaces appeared very shiny and
smooth.
Most real surface have been shown to be non-Gaussian, so the results presented above
confirm previous results.29
To verify that a surface is fractal, the standard deviation, σ, should be fairly linear
over different length scales. 14
The graph in Figure (48) shows the standard deviation
of a typical worn C-C brake surface which is fairly linear, therefore the surface is

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