Tribological behavior and gas-surface interactions of hydrogenated carbon films

MISSING IMAGE

Material Information

Title:
Tribological behavior and gas-surface interactions of hydrogenated carbon films
Physical Description:
xv, 126 leaves : ill. ; 29 cm.
Language:
English
Creator:
Dickrell, Pamela Laurie
Publication Date:

Subjects

Subjects / Keywords:
Mechanical Engineering thesis, Ph. D   ( lcsh )
Dissertations, Academic -- Mechanical Engineering -- UF   ( lcsh )
Genre:
bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

Notes

Thesis:
Thesis (Ph. D.)--University of Florida, 2005.
Bibliography:
Includes bibliographical references.
Statement of Responsibility:
by Pamela Laurie Dickrell.
General Note:
Printout.
General Note:
Vita.

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003397100
sobekcm - AA00004680_00001
System ID:
AA00004680:00001

Full Text












TRIBOLOGICAL BEHAVIOR AND
GAS-SURFACE INTERACTIONS OF
HYDROGENATED CARBON FILMS








By,

PAMELA LAURIE DICKRELL


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


2005































Copyright 2005

by

Pamela Laurie Dickrell































This work is dedicated to Miss Sara Gabrielle Nannis for reminding me what is most
important in life.















ACKNOWLEDGMENTS

This body of work has been completed with as much support and effort from

people in my life as it has by my time with a pen and paper.

The first and foremost acknowledgement goes to my husband Dan. I thank him for

always supporting that, while formally educated in science, 99% of my decisions in life

are made with a blatant disregard to logic and are solely based on my heart. While he

does not always understand why I do things, he has never kept me from being who I am

or reaching for my goals. This girl could never ask for anything more. He may never

know how to make a pie, but he has learned how to duck faster and laugh out loud when

frustrated Sicilian women throw stuff across the house. I could not, would not, have

written this without my best friend Dan. Rock!

My mom deserves all the credit for raising me. She never kept us from being who

we were by both promoting and joining in the silliness of being kids. I have to thank her

for giving so much to me and Monica by not showering us with things but rather by

teaching us how to live. I know I would not have made it in school and life without her

teaching me how to take care of myself. She has always encouraged me to think freely

and argue my points, even when I was wrong. It was better to scrape my knee than to

have my hand held, the scratches and bruises have built character along the way.

My sister Monica deserves thanks for being my voice all those times I was too shy

to speak. I am grateful to have had her as my partner in crime growing up; our









adventures together are the most memorable events of childhood. My experiences with

her have made me who I am today and I am looking forward to watching our families

grow together. She has always been there for me and I will always do the same, no

questions asked.

I thank my grandma for all the prayers and for passing on her happiness and love

for life to the family. She has never hesitated to laugh out loud or do silly things to make

us smile. The wagon wheel tradition will always remain strong.

Miss Sara Gabrielle Nannis deserves thanks for reminding me what is most

important in life.

Katie and Daisy, I thank them for the four ears that have been open twenty-four

hours a day to listen; man's best friends indeed.

There are a few friends whose both personal and professional support has made this

work possible. I am grateful for the help of Jason Action, Dr. Thierry Blanchet (lab

grandpa), Jerry Bourne, Dave (the oil can) Burris, Matthew Hamilton, Alison Rennie

(Dunn), Dr. Irwin Singer, and Jason Steffens.

I appreciate the constructive input and words of wisdom both professionally and

personally from the members of my committee: Dr. David Hahn, Dr. Tony Schmitz, Dr.

John Ziegert, and Dr. Paul Holloway.

Particular thanks go to Dr. Ali Erdemir for all of his help in this work. The scope

of this thesis would not have been possible without his ingenuity and research. The

summer working together and the many conversations along the way have greatly shaped

my professional and personal character.









Finally, recognition and gratitude goes out to my friend (first) and advisor (second),

Wallace Gregory Sawyer. Thoughts: irrational impatience may actually work.

Concerns: never write a book. Gripes: eat something, coffee and diet cokes do not a meal

make. Grievances: do you actually think it would be more fun had I been a "yes" man?

Professionally, I thank him for the fishing lessons, I shouldn't go hungry. Personally, I

thank him for both the adventures and kicks in the ass when I needed each of them the

most.














TABLE OF CONTENTS

page

ACKNOWLEDGMENTS .............................................................................................. iv

LIST OF TABLES ........................................................................................................... x

LIST OF FIGURES ........................................................................................................ xi

A B ST R A C T ..................................................................................................................... xiv

CHAPTER

1 NEAR FRICTIONLESS CARBON (NFC): HYDROGENATED DIAMOND-
LIKE CARBON............................................................................................................ 1

1.1 Introduction.............................................................................................................
1.2 Material Properties...............................................................................................3...
1.3 Investigation Goals..............................................................................................5...

2 GAS-SURFACE MODELING IN TRIBOLOGICAL CONTACTS........................6...

2.1 Tribological Configurations.................................................................................6...
2.2 Pin-on-Disk/Midpoint Reciprocation Modeling..................................................7...
2.3 Positional Reciprocation Model ........................................................................ 13
2.4 Linear Rule of Mixtures.....................................................................................20

3 FRICTION MODELING AND DATA COMPARISON........................................22

3.1 Near Frictionless Carbon Self-Mated Experiments...........................................22
3.2 Pin-on-Disk / Reciprocation Midpoint Model Fit .............................................24
3.3 Positional Reciprocation Model Fit...................................................................28

4 MICRO-TRIBOMETER: EXPERIMENTAL APPARATUS AND
UNCERTAINTY ..................................................................................................... 33

4.1 Reciprocating Pin-on-Disk Microtribometer .....................................................33
4.2 Microtribometer Friction Coefficient Values ....................................................39
4.3 Propagation of Uncertainty in the Friction Coefficient .....................................48
4.3.1 Law of Propagation of Uncertainty .........................................................48
4.3.2 p: Friction Coefficient.............................................................................51








4.3.3 Friction Coefficient Expansion................................................................52
4.3.3.1 5: Pitch misalignment angle..........................................................52
4.3.3.2 tf': Tribometer reported friction coefficient..................... 53
4.3.3.3 0: Roll misalignment angle ...........................................................53
4.3.4 Tribom eter Read Forces .......................................................................... 54
4.3.4.1 Fv: Tribometer read vertical force.................................................54
4.3.4.2 FHf: Tribometer read forward sliding horizontal force..................55
4.3.4.3 FHr: Tribometer read reverse sliding horizontal force...................56
4.3.5 Force Expansion ...................................................................................... 57
4.3.5.1 V : Optical sensor voltage .............................................................. 57
4.3.5.2 C: Displacement Voltage calibration constant...........................57
4.3.5.3 d, G: Mounting offset error and calibration slope constant ...........58
4.3.5.4 K : Flexure stiffness ....................................................................... 61
4.3.6 Stiffness Expansion ................................................................................. 62
4.3.6.1 M g: Calibration force .................................................................... 62
4.3.6.2 8: Calibration displacement...........................................................62

5 INITIAL ENVIRONMENTAL TRIBOLOGY OF NFC FILMS ...........................68

5.1 Near Frictionless Carbon Run-In Testing..........................................................69
5.2 Sample Pair and Humidity Variation Experiments ...........................................72
5.3 W ater V apor Ram p ............................................................................................ 75

6 WATER VAPOR PRESSURE AND SUBSTRATE TEMPERATURE EFFECTS .78

6.1 Water Vapor and Surface Temperature Experiments........................................78
6.2 Gas-Surface Modeling: Adsorption and Desorption Rates ..............................84

7 CONCLUDING REMARKS ...................................................................................91

APPENDIX

A LANGMUIR MODEL DERIVATION...................................................................93

B H EN R Y 'S LA W .................................................................................................... 95

C ELOVICH EQUATION .......................................................................................... 97

D LINEAR APPEARANCE OF CURVES................................................................100

E INFLUENCE OF PITCH ANGLE ON UNCERTAINTY.................................... 102

F RUN-IN BOND ENERGY ..................................................................................... 104

G PRELIMINARY LOW CONTACT PRESSURE EXPERIMENTS........................ 106

H NFC-NFC DRY ARGON ....................................................................................... 108








I GLASS-NFC DRY ARGON .................................................................................. 113

J NFC-NFC HUMID ARGON....................................................................................118

K LANGMUIR ADSORPTION AND DESORPTION INTEGRATION.................122

LIST OF REFERENCES...............................................................................................123

BIOGRAPHICAL SKETCH ......................................................................................... 126














LIST OF TABLES

Table page

2-1 Recursive model parameters ...................................................................................7...

2-2 Fractional coverage expressions............................................................................10

2-3 Difference in coverage expressions.......................................................................10

2-4 Positional fractional coverage expressions ...........................................................16

2-5 Positional difference in coverage expressions ......................................................17

2-6 Positional model variable definitions....................................................................18

4-1 Nomenclature for microtribometer measurement analysis ...................................40

4-2 Measured values used in the calculation of uncertainty........................................50

4-3 Uncertainty in measured values. ............................................................................51

6-1 Gas-surface modeling nomenclature.....................................................................85














LIST OF FIGURES


Figure page

1-1 View into NFC magnetron deposition chamber and TEM cross section view of
deposited N FC coating ............................................................................................3...

1-2 Outline of compositions of bulk NFC films and the interface between self-mated
NFC coatings in a tribological contact....................................................................5...

2-1 Rotating pin-on-disk configuration for tribological testing ....................................8...

2-2 Reciprocating pin-on-flat configuration for tribological testing........................... 14

2-3 Positional reciprocation schematic........................................................................ 15

2-4 Pin-on-disk and reciprocating model comparison.................................................21

3-1 NFC self mated dry nitrogen data ......................................................................... 24

3-2 a) Pin-on-disk/reciprocating midpoint model (eqn 2.11) fit to average Heimberg
et al. data (Figure 3-1). b) Fraction removed (1-A) parameter as a function of
sliding speed for m odel fit..................................................................................... 25

3-3 a) Pin-on-disk/reciprocating midpoint model (eqn 2.11) fit to constant
velocity/dwell data. b) Fraction removed (1-A) parameter as a function of dwell
tim e for m odel fit................................................................................................... 26

3-4 Positional model comparisons to friction coefficient data for a) cycle 19/20 at
multiple sliding speeds. b) data from multiple cycles at a 30 pm/s sliding speed...28

3-5 Removal ratio as a function of friction coefficient................................................31

4-1 Environmental control, contact region and operational parameters of
m icrotribom eter..................................................................................................... 33

4-2 Gaseous environment and counterface surface temperature control.....................35

4-3 Schematic of tribometer test assembly and manufacturer defined axes of motion..36

4-4 Example of positional data collected from CSM nanotribometer for a
reciprocating test on vertically aligned nanotubes showing the loop of friction
coefficient or frictional force versus wear track position......................................38








4-5 Potential misalignment angles in positioning counterface stub into reciprocating
stage ..........................................................................................................................4 1

4-6 The effect of the misalignment angle P on the ratio of the tribometer reported
forward and reverse friction coefficient values.....................................................46

4-7 Equation derived frictional loop for pin and counterface pair with friction
coefficient jp=0.12 and misalignment roll angle P=50.............................................. 47

4-8 Propagation of uncertainty hierarchy ....................................................................50

4-9 Operating ranges and calibration curves for optical sensors.................................58

4-10 Schematic analysis to find the mounting offset error (dv,H) and slope constant
(G v,H) ............................................................................................ ......... ......... 59

4-11 Lines of constant uncertainty in the friction coefficient........................................64

4-12 Lines of constant uncertainty in friction coefficient over the friction coefficient....65

4-13 Relative contributions to the variance in the friction coefficient..........................66

5-1 Surface scans of uncoated pin sample and coated flat sample..............................68

5-2 Initial run-in of two unworn self-mated NFC samples in a dry argon
environm ent........................................................................................................... 69

5-3 Environment exposure dwell experiments ............................................................71

5-4 Test conditions for the three matrix series ............................................................73

5-5 Surface scans of pin samples after a) self mated NFC tests in dry argon, b) glass
pin against a NFC coated counterface in dry argon, and c) self mated NFC tests
in hum id argon. ...................................................................................................... 74

5-6 Variation of friction coefficient of self mated NFC pair to a prescribed change in
relative humidity of an argon environment ...........................................................76

6-1 Experimental matrix for variations of chamber vapor pressure and NFC
tem perature ........................................................ .................................................... 79

6-2 Steady state friction coefficient values as a function of counterface surface
temperature for a) 123 Pa, b) 1233 Pa, c) 2837 Pa and d) 4933 Pa of water vapor
pressure.....................................................................................................................80

6-3 Counterface roll angle P as a function of surface temperature for the experiments
from Figure 6-2. .................................................................................................... 83








6-4 Experimental results of friction coefficient (g) and surface coverage (0) as a
function of counterface surface temperature and water vapor pressure................84

6-5 Model fit ofeqn 6.4 to experimental data with a) a universally fit value for To
and Ea, and b) a universally fit value of To and a variable fit of Ea .......................88

6-6 Model fit of eqn 6.4 to experimental data with a set value of ro=lE-13 sec for a)
a universally fit value of Ea, and b) a variable fit of Ea..........................................89














Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

TRIBOLOGICAL BEHAVIOR AND GAS-SURFACE INTERACTIONS OF
HYDROGENATED CARBON FILMS

By

Pamela Laurie Dickrell

August 2005

Chair: Wallace Gregory Sawyer
Major Department: Mechanical and Aerospace Engineering

Diamond-like carbon films are used as tribological coatings for surfaces of devices

that see relative motion. One class of highly hydrogenated diamond-like carbon coatings,

termed near frictionless carbon (NFC), have experimentally shown extremely low friction

coefficients and wear rates when used in a dry or inert environment. The tribological

properties of NFC films are influenced by the surrounding environment and this is

thought to be due to gaseous species interaction on the NFC coating surfaces.

This body of work develops models of gas-surface interactions in tribological

contacts. Model predictions of friction coefficient are compared to experimental data

from self mated NFC contacts to investigate if frictional trends are due to balancing rates

of surface adsorption and removal of environmental species. An uncertainty analysis is

performed on the low contact pressure tribometer used for environmental testing of the

NFC films. Tribological experiments with variations in normal load, sliding speed, track

length, environmental water vapor concentration and counterface temperature are run on








NFC films using the low contact pressure tribometer. Gas surface adsorption and

desorption modeling is used to examine frictional trends seen with imposed variations in

water vapor pressure and temperature. This modeling is used to confirm surface

adsorption and removal of water vapor as contributing factors to the environmental

performance of NFC films as solid lubricant coatings.













CHAPTER 1
NEAR FRICTIONLESS CARBON (NFC): HYDROGENATED DIAMOND-LIKE
CARBON



1.1. Introduction

Diamond-like carbon (DLC) films are of tribological interest due to their low

friction, low wear rate, high hardness, and chemical inertness [1, 2]. These films can

potentially be used in a wide range of applications, such as bearings, cutting tools,

submersible parts, and biomedical applications [3-6]. One class of diamond-like carbon

coatings termed near frictionless carbon (NFC) that was developed at Argonne National

Laboratory has been shown to sustain superlow coefficients of friction (p <0.003) and

wear rates (K <3-10 mm3/Nm) in self-mated contacts [3]. The tribological behavior of

these films is sensitive to the environment, only realizing their low coefficient of friction

and wear rate in inert, dry, or vacuum environments [3, 7-10]. It would be useful to

understand in what functional environmental regimes the low friction and wear

characteristics of NFC films were realized. In addition, it would be beneficial to

understand why NFC films have different tribological characteristics in various

environments. This information would allow the pool of potential applications for these

coatings to be narrowed and specific useful applications for NFC to be realized.

Because NFC films have different tribological characteristics in various

environments, it has been theorized that gas-surface interactions between the NFC

coating and environmental species are the cause for variation in the friction coefficient








and wear rate of the films [8-10]. Environment/surface interaction models have been

created by other research groups in an attempt to describe friction coefficient variations

in tribological experiments. To the author's knowledge, the first modeling of this in

tribology is the work of Rowe [11 ], who used the Langmuir adsorption model [12] to

describe the wear in boundary lubrication. Gas/surface interactions were reported in

1957 by Bowden and Rowe [13] to describe the lubrication of molybdenum in hydrogen

disulfide gases, but were not modeled. Blanchet and Sawyer [14] included both

deposition and removal rates in a model developed to study transitions from adequate to

inadequate lubrication in vapor phase lubrication; this model was based on balancing the

rates of layer formation and removal but was not fractional (friction was predicted to be

either low or high in the adequate or inadequate regime respectively). A time-dependent

fractional coverage model, without removal, was proposed by Zaidi et al. [15] to describe

gas interactions with carbon surfaces. The interaction kinetics used followed the work of

Elovich [16]. Models that predict steady-state friction coefficients for pin-on-disk

contacts and combined rolling and sliding contacts [17] were developed by applying the

competitive rate model of Blanchet et al. [18] with Langmuir fractional surface

adsorption [12] and fractional removal [19].

Some testing on the gas-surface interactions of NFC films has already been

performed. Heimberg et al. [9] hypothesized that velocity dependence of the friction

coefficients of NFC films was due to a gas-surface interaction that had longer times to

affect the film at slower sliding speeds. This hypothesis was further supported by

experiments that varied exposure time under constant sliding speeds using periods of

dwell at the reversal locations. These tests showed a clear dependence on exposure time








as opposed to velocity. In addition, Heimberg et al. modeled the transient portion of gas-

surface interactions using an Elovich model for adsorption, but did not achieve steady

state modeling for friction coefficient [9].

1.2. Material Properties

Near frictionless carbon films are a thin film, amorphous type of diamond-like-

carbon, composed of a mix of carbon and hydrogen. They are made by a room

temperature plasma-enhanced chemical vapor deposition process, performed in a

magnetron sputtering system [20]. A target substrate material is sputter cleaned in an Ar

plasma for 30 minutes by applying a 1200-1700 V bias [3,20]. Next, a 50-70 nm thick Si

bond layer is applied by sputter coating from a Si target [3,20]. Then mixes of CH4,

C2H2, C2H4, or C2H6, and H2 gases are introduced into the deposition chamber, depending

on the desired ratio of H:C in the film [7]. The specific NFC films investigated in this

study use 25% CH4 and 75% H2 for chamber flow ratios during coating. This results in a

film that is approximately 60% carbon and 40% hydrogen atomically. The final films are

1-1.5 gm thick [8].

magnetron sputtering chamber




Si oxide
bond layer is t

images courtesy of Dr. Ali Erdemir, Argonne National Laboratory

Figure 1-1 View into NFC magnetron deposition chamber and TEM cross section view
of deposited NFC coating.








Indentation tests were performed by other researchers using a Vickers indentation

on a Fisherscope H100 dynamic micro-hardness tester with a maximum load of 4.2 mN

[3]. In over 30 indentation tests the film was found to have a hardness of 7.66 GPa and

elastic modulus of 47.2 GPa. It was also found that as the hydrogen content of the films

increase, both the hardness and modulus decrease [3]. In addition, in self mated pin-on-

disk tests in a dry nitrogen environment it was found as the hydrogen content of the NFC

films increased the steady state friction and wear rate decreased [3]. Raman spectroscopy

has been used to determine these NFC films are approximately 60% sp3 in composition,

with most of the sp3 bonds being hydrogen terminated [21].

It has been proposed that since NFC films are chemically inert they exact very little

adhesive force while sliding against other materials [7]. The films used in this study

have high hydrogen content and it has been theorized that free hydrogen in these films

can terminate carbon bonds at the surface [8]. Hydrogen may attach to and passivate

dangling surface bonds of carbon atoms in such materials and reduce the friction

coefficient; when the hydrogen is removed the dangling carbon bonds are reactivated and

friction coefficient rises [7]. It has also been proposed that in a self mated NFC pair, the

hydrogen terminated surfaces slide freely across one another in an inert environment [8].

When a gaseous species is added to the environment the friction coefficient in NFC self-

mated contacts rises [10], suggesting a gas-surface interaction where environmental

species may disrupt the hydrogen termination of the NFC pair and lead to a rise in

friction coefficient. In contrast, hydrogen-free diamond-like carbon films show lower

friction coefficients in humid air than in inert or vacuum conditions [22], further





5

suggesting this hydrogen at the surface plays a strong role in the frictional performance of

self-mated NFC films.


to carbon
Oxygen .
e hydrogen C ,

A -liding_
p Pane


+ hyroe
tt) terminated
carbon atoms


tttftfttttftttfttftt P


S'courtesy of Dr. Ali Erdemir, Argonne National Laboratory

Figure 1-2 Outline of compositions of bulk NFC films and the interface between self-
mated NFC coatings in a tribological contact.

1.3. Investigation Goals


This body of work aims to:
1) Develop closed form models for surface coverage in tribological contacts based
on competitive rates of gas-surface adsorption and periodic adsorbate removal
through the tribological contact. (Chapter 2)
2) Use developed surface-coverage modeling to make predictive statements of
transient and steady state frictional performance and compare these predictions to
other investigators' experimental friction results on NFC films. (Chapter 3)
3) Perform an uncertainty analysis on a commercially available low contact pressure
tribometer used in this study for NFC frictional testing. (Chapter 4)
4) Execute a series of tribological experiments on NFC films using the low contact
pressure tribometer to look at the environmental dependence of the frictional
performance of NFC coatings, initial surface layers on the coatings, and isolate
which environmental species is controlling the frictional performance of NFC.
(Chapter 5)
5) Based on the results in Chapter 5 execute a series of experiments varying both
concentrations of the isolated influential environmental species and substrate
temperature to investigate frictional trends within combinations of these two
parameters. The frictional trends seen in variations of species concentration and
temperature will be modeled using a first-order gas surface model to further
determine if surface adsorption and desoprtion is controlling friction coefficient
trends in NFC films. (Chapter 6)













CHAPTER 2
GAS-SURFACE MODELING IN TRIBOLOGICAL CONTACTS

2.1. Tribological Configurations

Two common configurations for tribological testing of friction coefficient are the

rotating pin on disk and reciprocating pin on flat contacts. In both of these there is a pin

specimen that can be flat or radiused that is loaded against a (usually) flat counterface.

There is relative motion between the pin and flat sample; in the pin on disk case, the disk

is usually rotated and the pin held stationary to make a circular wear track path, and in the

reciprocating case either the pin or flat is moved in a forward and reverse motion to make

a linear wear track path. This work models the evolution of environmental species

adsorption on a counterface during a tribological contact. The parameters that will be

used in model derivation are listed in Table 2-1.








Table 2-1 Recursive model parameters.
a adsorption fraction
subscript c cycle
subscriptf forward direction
subscript in entrance of pin contact
L track length
x removal ratio (%o., /OJ
9__, friction coefficient of covered surface
go0 friction coefficient of nascent surface
n cycle number
v deposition constant
subscript out exit of of pin contact
P partial pressure
1-0 nascent surface area fraction
0 covered surface area fraction
subscript r reverse direction
t time between pin events
T time since test inception
V velocity


There are a few assumptions being used in the modeling for surface coverage and

friction coefficient predictions. First, there is no surface wear taking place; instead there

is a covering by environmental species and partial removal of this coverage through the

pin contact. The coverage fraction (0) remains between 0 (completely nascent surface)

and 1 (fully covered surface). Modeling also assumes a constant sliding velocity.



2.2. Pin-on-Disk / Midpoint Reciprocation Model

A schematic of the rotating pin-on-disk configuration for surface species modeling


is shown in Figure 2-1.






















\ nascent surfaces
Figure 2-1 Rotating pin-on-disk configuration for tribological testing.

Modeling of the pin-on-disk configuration assumes some initial surface fractional

coverage (0o) of an adsorbed species. At time equals zero, or the initiation of an

experiment, this term is the fractional coverage that enters into the initial pin contact.

The fractional coverage that then leaves the contact (Oout) is assumed to be less than the

entering fractional coverage for two reasons: 1) adsorption of gaseous species is assumed

to be negligible under the pin contact, and 2) removal of adsorbed species is assumed to

occur under the pin contact as a combination of mechanical removal and thermal

desorption as a result of frictional heating. After the surface element leaves contact, it is

exposed to the gaseous environment, and adsorption occurs on the nascent portion on the

surface during the time it takes for the surface element to return to contact. The

subsequent entering fractional coverage Gin varies from cycle to cycle until the system

reaches equilibrium.

The model addressed in the body of this investigation follows the works of

Langmuir [12] and Blanchet and Sawyer [18] for the adsorption and removal of fractional

films, respectively. Model equation derivation of the Langmuir expression is included in








Appendix A. There are other commonly used gas-surface adsorption models in the

literature. The model derivation and fit to experimental data are performed and discussed

in Appendix B and C for two other common gas-surface models: Henry's Law and the

Elovich Model. For the body of this work, following Langmuir, the adsorption of a gas

species occurs on the fraction of the surface that is not covered (1 0out) in the time from

when the surface exits the pin contact to when it enters the pin contact on the next

revolution. The adsorption ratio, a, is the fraction of the uncovered surface coming out of

the pin contact that becomes covered by an adsorbed species between cycles. If the time

between contacts, temperature, and gaseous environment remains constant, the adsorption

ratio a will not change between cycles, although the fractional coverage will. Following

Blanchet and Sawyer [18], the removal ratio (X) is the ratio of the fraction of the surface

covered at the exit of the pin contact to that at the entrance. This fractional removal of

the adsorbed species occurs differentially through the pin contact and is ensured to be

between 0 and 1. An expression for the average fractional coverage under the pin is used

to make friction coefficient predictions. This model is recursive, and application of the

equations gives a fractional coverage sequence for the first few cycles, as shown in table

2-2.








Table 2-2 Fractional coverage expressions.
00,. = 0) =o0o
0o0,. = A00o =Ao

o, = ),,. = A(A0o +a--AaO,)
02l. = O,, +(1-0,,,,)a = ;A20 +Aa -2A2a0o +a-Aa +2a20'a
2o. = t = A ('o + Aa 2;'a o + a Aa2 + A'a2o)
03in = 02o +(1- 02,,)a = A300 + A2a -3A'a0, +Aa-2A'2a' +3A3a20o+a -Aa2 +2a 3 -A3ao3
036, = A036, = A (A;30 + A'a 3A'a00 + Aa -2A'a2 +3A3a2 0 +a -Aa2 + A2a3 -A3a 00)

No pattern quickly emerges from this sequence. However, the pattern emerges if

one looks at the difference between the entering fractional coverage for each cycle and

that of the previous cycle. In table 2-3, N is the cycle number, and the difference in

fractional coverage is defined as AON = 0N -0(N-.)*

Table 2-3 Difference in coverage expressions.
AO, = A0+a-AaOo-00
A02 = A(l-a)(X0, +a-AaO -0o)
A03 = A(1l-a)2(Ao +a -Aa0 -0o)
A04 = 3(1 -a)3 (AO +a -AaOo -0o)
AO, = A4(-a)4 (0o+a -Aa0o -o)
AO = A"-,(1-()I-a) (AO, +a -aLOo -0)
Thus, the equation for the coverage going into the pin contact at any cycle n is the

initial coverage plus the sum of the differences up to cycle n, as shown in eqn. 2.1.


. = 0 + 2(N-')(1-a)(N- (A2o + a- 2a0o -0o) eqn 2.1

Quite fortuitously this series has a closed-form expression, given in eqn 2.2.

(N-(-a)(N- 1- (A(1-a)) eqn 2.2
N-1 1 A + a2

The cycle-dependent entering fractional coverage at any cycle n can then be compactly

written as given in eqn. 2.3.








S 1-An(1-a)"n
o,r = o0 (A(l1-a)) +a eqn 2.3

The steady-state solution for the entering fractional coverage can be determined by taking

the limit of this function as the number of cycles approaches infinity, given by eqn 2.4.

=01.,in a eqn 2.4
1- (1- a),.

This expression agrees with steady-state expressions developed previously by

Sawyer and Blanchet [17]. The adsorption ratio a can be found from the Langmuir

solution for vapor adsorption, which states that the rate of adsorption is a product of the

adsorption coefficient (v), the gas pressure (P), and the nascent surface area fraction

(1-0).

dO
S= vP(l -) eqn 2.5
dt

From this, the change in fractional coverage for any cycle is given by eqn 2.6, where tcis

the time the element is exposed to the environment between exiting the contact and re-

entry. The adsorption fraction is then given by eqn 2.7.

0,,,, = 1 (- O- ,)e-' eqn 2.6

a=1-e (-v''c) eqn 2.7

The derivation of the adsorption fraction from the Langmuir model can be seen in

Appendix A. Substituting this expression fora into eqn 2.3 and simplifying gives eqn

2.8, which is a cycle-dependent solution for the entering fractional coverage.

O,, = o ("n (e-"P' )) + (1- e-' )1-~(eVP) eqn 2.8







The exposure time for one cycle (tc) can be expressed as a track length (L) divided

by the sliding speed (V), tc = L/V, and the number of cycles can be expressed as the

product of the sliding speed (V) and the cumulative run time (T) divided by the track

length (L), n=VT/L. The fractional coverage of the surface entering the contact as a

function of run time, track length and velocity (parameters normally measured during

tribological experiments) is given by eqn 2.9.

SVT( VTvPL)

. = [0 [e JJ + -e 1LA eqn 2.9
1 e 1-A e )


The relationship between the entering fractional coverage (0,,) and the average fractional

coverage (0) under the pin can be derived from the fractional removal equations

developed by Blanchet and Sawyer [18], as shown in eqn 2.10.

0= (-A, ) eqn 2.10
-ln(A)

The average fractional coverage under the pin contact at any cumulative run time is found

by substituting eqn 2.9 into eqn 2.10, which is done in eqn 2.11.
(-A) Lr LVA( (e/ 1VT ( vPL
1-A e-L v}\
1- oA ( )t( e VT vPL PL
0= () +V V e(VL ) eqn 2.11



Two nondimensional groups can be defined: normalized time T* = VT / L, and

normalized deposition D* = vPL / V. Substituting these two nondimensional groups into








eqn 2.11 gives a dimensionless form of average fractional coverage under the contact in

eqn 2.12.


0-= ((1-) ( ( -T'D+ -D( 1 T -TD eqn 2.12


The model derived by examining a rotating pin-on-disk configuration can be used

to predict fractional coverage values for any point around the circular wear path of a pin-

on-disk contact because all the points around the track experience the same amount of

exposure time to the environment between pin contacts. For this reason the model can

also be used to predict coverage values for the midpoint of a reciprocating pin-on-flat

contact because the midpoint of reciprocation sees the same amount of environmental

exposure times between pin contacts.

The correlation of model predicted surface coverage to predicted friction coefficient

is done in section 2.4. This can then be used for comparison to experimental friction

results.



2.3. Positional Reciprocation Model

In a reciprocating configuration the amount of time a given spot will be exposed to

the environment will depend on both the sliding velocity and the location along the track.

The schematic of the reciprocating configuration is shown in Figure 2-2.


















Nascent surfaces
Figure 2-2 Reciprocating pin-on-flat configuration for tribological testing.


In reciprocating tribometry, every location on the wear track comes in and out of

contact with the pin moving either forward subscriptt f) or reverse subscriptt r); it

makes no difference whether the pin or the counterface is moving for the purposes of

modeling, which uses a counterface-attached coordinate system for the derivation. The

amount of time a particular location is exposed to the environment is a function of its

location, the overall path length, and sliding speed of the pin, which is assumed to be

constant along the track length. The increase in coverage at a particular location is a

function of the surface area fraction (0) when the pin last exposed the counterface at that

position and the amount of time (tfr)) that the location was exposed to the environment

before the pin returned. One item to note is the distinction between the forward (tf) and

reverse (t) exposure times. For any given position along the wear track there exists

unique values for tf and t,, only at the midpoint does tf = tr. The total cycle time (tc)

is defined as the sum of the forward and reverse portions of the cycle motion, tc = tf +tr.

Speed dependence of the coefficient of friction is attributed to a change in exposure time

between contacts, the faster the sliding speed the less time between pin contacts (lower








values of t(fr)). Figure 2-3 shows the schematic used for this position and time-

dependent reciprocating modeling.


forward


reverse


a tr



9af(in)= 0 position along track Bar(in)l= 0 +ar(1-0aflout))


21.. .

Saf(in)2= ar(out)1+ r(out)1


Vf

(af(in)N 0ar(out)(N-1)+ 1-0ar(out)(N-1))

Figure 2-3 Positional reciprocation schematic


sites of gas/surface
interaction
Vr /


Oar(in)2=0af(out)2+ar(l Oaf(out)2


Vr


Bar(in)N='af(out)N+r(N)


The modeling initiates with each position along the track having 0 = 0 coverage for

the first forward pass. On the first reverse pass the pin has traveled to the end of the wear

track and back to the position of interest. During this time the reverse adsorption fraction

(a,) acts on the nascent portion of the surface from the previous pass (1- O, ), giving


an entering fractional coverage (0Or, ) of the form 0,.)f = (,) + (1- 0,) )a(r,,f)

Table 2-4 shows the evolution of the coverage equations derived for the position

dependent modeling.









Table 2-4 Positional fractional coverage expressions.
in 9fin = 0 0
South flout =A(Ofl) 0
i Orlin =Oflout + a,.(l-Ofut) -a,
r
roout Orlout = rlmn) Aa r
Of2in rlut f(1 rlou) 2 fr I Aaa(-2r)
f
out 9f2oU, =A(o2.) A(Aa,+a (1 -Aa,))
Ai (a, + af (I A a))+
2 in Or2in =Of2ow,+ a,1-f2,) -
a, (l-A(Aa,+a (1-Aa,)))
r
SA a, + +af (1-Aa,))+
Sout 9r2out = (r2,n) -
a (I A (Ara +af (1 -2a, )))


This process continues, forward-reverse-forward-reverse ..., as illustrated in Figure

2-3. The change in fractional coverage that occurs when the pin rides over a particular

location (O(f,,, O(r,, ) follows a model for the fractional removal of films as in the

rotating section, of the form ,r),,. = O(,.r), where 2 is a removal ratio between A = 0

(complete removal) and A = 1 (no removal).

For consecutive forward and reverse passes the difference in entering fractional

coverage is given in Table 2-5 for the first 4 cycles. The change in entering fractional

coverage is defined as AO, = O+,, 09 for any cycle N, where the subscript N is

understood to mean Nin.










Table 2-5 Positional difference in coverage expressions.
forward reverse
AOI = (aA + af aaA) AOri = A(l-a,)AO,
A0,2 =2 = (l-a)(l-a,)AO, AOr2 =3 (l-a )(l-a,,)2 Af

AO,) = 4 ( a2 Af r3 Al-a )2(-a

AO4 = A6(-a) (-a)AO,= A ,r4 Ao,
AO, = A(2N-2) (-a )(N-1) (1 -ar)(N-1) Af, A = (N-') (1- a )(N-') (1 -a, )N Af


The patterns for the differences in entering fractional coverage for forward and

reverse passes in terms of cycle number, removal ratio A and the forward and reverse

adsorption fractions a, and a, are given in eqns 2.13 and 2.14 respectively:

AOG = A(2N-2) (I-af )(N-) (1-a)(N-1) (ar + a. af a,) eqn 2.13


AO_ = A(2N-') (1- )(N-1) (1- a,)N (ar + f -a ,A) eqn 2.14

The fractional coverage entering the pin contact for forward or reverse travel for

any cycle (n) is the coverage entering the first cycle in that direction plus the sum of the

differences in fractional coverage up to that cycle (n), as given by eqn 2.15.
n
(f,r)n = O(/,r)l + AO(f,r) eqn 2.15
N=1

Fortunately, there are closed-form solutions to the summations in eqn. 2.15, and the

entering coverage for any cycle with the pin moving either forward or reverse is given in

eqns 2.16 and 2.17, respectively.


c(1- = g- )) eqn 2.16
1 -g








b,, =- cdg(n-) eqn 2.17
1-g

The variables (c, g, b, and d) are given in Table 2-6.



Table 2-6 Expressions for the variables (c, g, b, and d ) used in eqns. 2.16 and 2.17.
All variables are expressed in terms of the forward or reverse adsorption coefficient
(a1, a,) and the removal ratio (2).
c 2a,(1-a,)+a, 2(1-e-"P )e -P' +(i -e-vp')
g (1-af)(1-a,)A22 e- ve-P, A2
b af (1- a,)+ a, Al I-e-ve ) e-"Pt +(1- e-P"')
d A(1-a,.) Ae-_1


The adsorption fractions can be expressed in a Langmuir form similar to the previous

model section as given by eqns 2.18 and 2.19 for the forward and reverse cases,

respectively.

a =I e-P' eqn 2.18

a,. = 1 e" eqn 2.19

The adsorption fractions are a function of the deposition constant (v), the partial

pressure of the gas (P), and the exposure time in the forward or reverse directions

(tf,t,). The only difference between the forward and reverse adsorption coefficients

concerns the exposure time in the direction of travel t and t,. Each position along the

track has a unique value for tf and t,r. Only at the midpoint of the track does t, equal t,.

The coefficients v and P are constants for a gaseous environment that is

compositionally and thermally steady. Eqns 2.20 and 2.21 give the closed-form







expressions in a form similar to the position-dependent steady-state equations for

reciprocating motion published in [23], where tc = tf + t,.


, =[1-(1-[A)e -vP]e-'" 1 eqn 2.20


( 2)ePAe-, vp'] [ e-vp( 2 e-vp, )] 2 -vP (-'
A) = 1-(1- -P ] e- L -- i_] eqn 2.21
11 2 e-vPtI

The first check for the validity of eqns 2.20 and 2.21, which are spatially dependent

(through tf and tr values) and time dependent (through the cycle number, n), was to

evaluate the limit of these functions as n -+ oo and compare this with the previously

developed steady-state expressions, which were created by balancing the deposition and

removal rates at steady state. As expected, eqns 2.20 and 2.21 are identical to the steady-

state equations published earlier [23]. The second check was that this model matched the

time-dependent model in eqn 2.8 developed in the pin-on-disk/reciprocation midpoint

section at the midpoint of the track (when t, = t,). The final verification step was to take

the limit of the model as n -> oo when tf = t, and compare this to the steady-state

coverage expression in eqn 2.4, derived using the pin-on-disk model. In all of these

cases, the model was able to be expressed in an equivalent form to the previously

developed models. To predict friction coefficients at specific pin locations, the average

fractional coverage within the contact, 0, is calculated according eqn 2.10










2.4. Linear Rule of Mixtures

In the tribological experiments that are going to be used for comparison to this

modeling the friction coefficient is the only value that can be used as an indication of

surface coverage of environmental species. To correlate model predicted coverage, 0, to

friction coefficient, ji, this work uses a linear rule-of-mixtures. The friction coefficient

pu can be estimated by eqn 2.22, where p/ is the friction coefficient of the nascent

surface, and A/ is the friction coefficient of the surface covered with adsorbed

contaminants.

/ = Ao + (6 Po) eqn 2.22

A linear rule of mixtures is one of multiple approaches for predicting the influence

of surface coverage on friction. There is no clearly defined correct relationship for how

the surface coverage influences friction coefficient in these tribological contacts. While

the influence of species coverage on friction coefficient may not follow a simple linear

relationship, this work is going to use eqn 2.22 as a first approach to correlate read

friction coefficient to surface coverage.

Figure 2-4 examines the comparative progression of the pin-on-disk/midpoint

reciprocation model (Figure 2-4a) and the positional-dependent model (Figure 2-4b) from

transient to steady state friction coefficient predictions. This is performed for a standard

set of experimental conditions that will be examined in Chapter 3 of this work.















average friction coeffi
(sliding speed 30 pn


b) coefficient of friction vs. position
b) (sliding speed 30 gm/s)
contact diameter
-0.15 mm Vr---/ ----V

cient
) s/


., "I


\ / \


f


0.06 cycIE

0.05 -2

E 0.04



t 0.02 reverse (cycle =1.5) 7{

0.01 forward (cycle =1)

0 -* .
0 5 10 15 20 0 i 1 2 3 4 5
cycle position along track (mm) :-
reversal reversal
zone zone
Figure 2-4 Pin-on-disk and reciprocating model comparison.



These model predictions for friction coefficient as a function of tribological testing

conditions and environmental species can now be compared to other investigators'

experimental results on self-mated NFC films in tribological contacts. This should give

some indication if gas-surface interactions are playing a dominant role on the frictional

behavior of these films.













CHAPTER 3
FRICTION MODELING AND DATA COMPARISON



3.1. Near-Frictionless Carbon Self-Mated Experiments

Other investigators, Heimberg et al., investigated the frictional behavior of NFC

coatings [9]. Their samples consisted of a NFC coated 12.7-mm diameter steel sphere

with a constant dead weight load of 9.8 N against a NFC coated H13 steel flat over a

5mm track length. All tests were run in nominally dry nitrogen (relative humidity and

oxygen concentration of less than 1%). Their experimental apparatus was a reciprocating

tribometer from which time dependent friction data was read. Position dependent (along

reciprocating path) data was interpolated from the time dependent data. Details on their

experiments and apparatus are covered in their publication [9].

Two sets of experiments run by Heimberg et al. were of interest to the modeling

derived in this study. The first set of interest was a single series of tests in which sliding

speed was varied from 0.01 to 5mm/s. Time-dependent data was collected over this

series of experiments that varied the sliding speed systematically from high to low (the

exposure time from short to long). At sliding speeds of 1-5 mm/s, this coating had a

friction coefficient of p = 0.007, which is assumed to correspond to the friction

coefficient of the nearly clean or nascent surface po. At sliding speeds of 10 pm/s, this

coating had a friction coefficient near p = 0.12, which was assumed to correspond to the

friction coefficient of a nearly saturated or covered surface The published friction








data from these tests was the average friction coefficient on each pass, which is assumed

to be a reasonable approximation for the pin-on-disk/reciprocating midpoint model. This

set of tests consisted of a single wear track that was run-in at 1mm/s until low friction

(p = 0.007) was realized. Then, in the same track the speed was alternated between

1000 cycles of high speed (1 mm/s) sliding and 20 cycles of a lower speed (0.01-0.513

mm/s), systematically decreasing the lower sliding speed from high to low. During the

portions of high speed sliding the exposure time between pin contacts is minimized and

the amount of pin "wiping" is maximized. It is assumed for modeling the coverage (0)

during high speed sliding goes to zero and the friction coefficient goes to that of a fully

nascent surface. The pin-on-disk/reciprocating midpoint model contains four parameters

that were allowed to vary during the optimization routine that was employed against this

data. These parameters are a deposition term vP, a removal ratio X, and friction

coefficients for the nascent and covered surfaces, po and p, respectively. It was

assumed that vP, po and p, are constant for each data set run in the same continuous

environment. The removal ratio X was allowed to vary as a function of speed. Data from

the sliding speed experiments of Heimberg et al. is shown in Figure 3-1.








0.12- 10 P /s

0.1 E
C:

o 0.06 E
r .-r-4
0 0.06-8 E


0 E o 0

0.02- r

0 i -.. .... I I
0 200 400 600 800
cycle
Figure 3-1 NFC self mated dry nitrogen data from Heimberg et al. [9].

Heimberg et al. also investigated the superlow friction behavior holding the sliding

speed constant at 1 mm/s but varying the time between successive passes of the pin

between 5 s and 162 s. This was to eliminate sliding speed and isolate exposure time

between pin contacts as the variable in the friction coefficient performance. This data is

also used for comparison to the pin-on-disk/reciprocation midpoint model. During these

same experiments, time dependent data was taken along the reciprocation cycle. From

this data, position dependent friction coefficient data was calculated for each cycle that

average data was reported for in Figure 3-1. This position data was used for comparison

with the positional reciprocating model equations (eqns 2.20 and 2.21).



3.2. Pin-on-Disk / Reciprocation Midpoint Model Fit

The pin-on-disk/reciprocating midpoint model fit (eqn 2.11) to the collected data

(Figure 3-1) is shown in Figure 3-2a. This model fit gives a deposition term vP=0.00059

s"', a nascent surface friction coefficient /0 = 0.0075, and a covered surface friction









coefficient A/ = 0.126. The fraction removed (1 -2) systematically increases with


increasing sliding speed and decreasing friction coefficient (Figure 3-2b).

sliding seed


a) (irm/s) b)
0.1 vP=0.0006 1/s m 10
go=0.0075
l =0.1260

C30
50
0 1


10 100 1,000 10,000 10 30 50 75100 303 513 1,000
time (seconds) speed (pm/s)
Figure 3-2 a) Pin-on-disk/reciprocating midpoint model (eqn 2.11) fit to average
Heimberg et al. data (Figure 3-1). b) Fraction removed (1-A) parameter as a function of
sliding speed for model fit.

Model fits to the data in Figure 3-2 are also performed using two additional gas-

surface adsorption models. Model derivation, fits to the data and discussion using both

Henry's Law and the Elovich adsorption model expressions are included in Appendix B

and C.

The fit of the pin-on-disk/reciprocating midpoint model (eqn 2.11) to the constant

speed and dwell tests performed by Heimberg et al. is shown in Figure 3-3a. This model

fit gives a deposition term vP=0.00067 s-1, a nascent surface friction coefficient

/Po = 0.0057, and a covered surface friction coefficient /u = 0.136. The removal fraction

(1 2) systematically increased with decreasing dwell times and decreasing friction

coefficient (Figure 3-3b).


S
0
S
S


......









a) 0.1 dwell time b) 1.0
vP=0.0007 1/s (seconds)
,o=0.0057
1-i=0.1360 162 0.7
C2
W 95 05

.0 45 E
S0.3

0.01 -
0 0.2 .



0.003- 0.1 .1 -
10 100 1,000 10,000 1 5 12 45 95 162 1,000
time (seconds) dwell time (seconds)
Figure 3-3 a) Pin-on-disk/reciprocating midpoint model (eqn 2.11) fit to constant
velocity/dwell data. b) Fraction removed (1-A) parameter as a function of dwell time for
model fit.

The fit of pin-on-disk/reciprocation midpoint model to the average friction and

dwell data is excellent; however, it does raise some interesting questions. Namely, why

would the removal fraction change with sliding speed and dwell time? There is no

suitable hypothesis for increasing removal fraction with increasing sliding speed and

decreasing dwell times. Although, in both cases the fraction removed is increasing with

decreasing exposure time, which suggests that the exposure time dependence of the

removal fraction may be compensating for something missing in the deposition model. A

couple of hypotheses can be offered. One hypothesis is that desorption of the

contaminant species is occurring under the pin contact. As derived by Langmuir [12], the

desorption rate increases monotonically with increasing surface temperature, and to the

first order the dependence is to the square root of temperature. The low Peclet number

suggests that stationary heat transfer analysis is appropriate, and, therefore, the

temperature rise under the contact at any contaminated sites will be proportional to the

sliding speed to the first power. However, fits to the constant speed tests showed








systematic variations that do not support this hypothesis. Another hypothesis is that the

surface topography is changing during these experiments and this change is altering the

removal rate. In both data sets the later experiments were less efficient at removing the

contaminants than the earlier ones. This change in surface topography might also be

enhancing the deposition rates, however, fits holding the removal ratio constant and

allowing the deposition terms to vary did not fit the data well. Finally, since the later

tests were also higher friction it may be that the removal fraction has a dependence on

friction coefficient.

The parameters that were fit for these two data sets all gave remarkably reasonable

results. The friction coefficients Po and p, were close to what were predicted prior to

fitting and were similar for the two tests. The removal fraction (1 A) varied from nearly

zero to 50%, which is also quite reasonable. It is somewhat curious that the time constant

for the adsorption rate found by fitting eqn 2.11 to the data is between 1600 and 1800

seconds. This seems high for an adsorption process although dry nitrogen can have very

little water and it may not be an adsorption process causing the increase in friction;

rather, some other gas surface interaction.








3.3. Positional Reciprocation Model Fit

Time dependent data was taken along the reciprocation cycle for the experiments in

Figures 3-1 and 3-2. Position dependent friction coefficient data was calculated from this

time data and the positional reciprocating model equations (eqns 2.20 and 2.21) were fit

to it. The model curves and data along the reciprocating length for cycle 19/20 under

multiple sliding speeds is shown in Figure 3-4a (this condition was assumed to be nearly

steady state). Figure 3-4b shows the model curves and data for multiple cycles during a

single sliding speed. The model curves in Figure 3-4 use the parameters (vP, A, u/ and

/ ) determined from the midpoint modeling (Figure 3-2), and no further curve fitting

was performed. The data at the first and last 0.5 mm of track length were discarded due

to the reversal zones. The grey dots in Figure 3-4 correspond to the crossing points in the

model, where the coefficient of friction was the same in the forward and reverse motion

directions for a specific cycle; at steady state this is at the midpoint.



a)0.08 cycle 19 b)o.08 30 sm/s
0.07- \.,, 0.07 -; ,iv

0o.06- .30 m/s 0.06- o cycle



20.051 3 0.051 -oward data and model
S0.04 1 2 3 4 5 00.04 2 3 4 5


Figure 3-4 Positional model comparisons to friction coefficient data for a) cycle 19/20 at

multiple sliding speeds. b) data from multiple cycles at a 30 pm/s sliding speed.

The positional reciprocating friction behavior provides a more detailed picture of

the competitive rates of Langmuir adsorption and fractional removal, which can be tested








against NFC vs. NFC data. There are similarities between the model curves and the data.

The first is that the model tracks the midpoint coefficient of friction data well. Secondly,

the crossing point of the coefficient of friction between the forward and reverse directions

of motion for a given cycle occurs in similar locations along the track in both the model

and data. In Figure 3-4a the crossing points are located at approximately the midpoint

track, when the model has reached steady state for multiple sliding speeds. As shown in

Figure 3-4b, the crossing point for a single sliding speed progresses from the extremity of

the wear track toward the midpoint as the coefficient of friction progresses towards

steady state.

In the low friction regime (p < 0.05) both the model and the data show close to

linear variations in friction coefficient versus track position, with higher friction

coefficient being found at the end of a cycle and lower friction coefficient at the

beginning. Additionally, friction coefficients at a position on the track after the crossing

point during forward motion are higher than the values at the same position after the turn

around, during reverse motion. This difference in friction coefficient is due to the fact

that for a specific track position past the midpoint, the exposure time between pin

contacts is longer in the forward than in the reverse direction of travel, and the removal

ratio is less than unity. Longer exposure time to the environment allows more

adsorption/interaction to occur, resulting in a higher fractional coverage and friction

coefficient. The linear variation of the model curves is surprising given that the surface

coverage expressions have exponential dependencies; a description of the linear

appearance of the model curves is included in Appendix D.








The monotonic rise in experimental curves in the low (p/ < 0.05) friction regime

may be due to surface chemical or physical effects, in addition to fractional coverage.

These effects may include defect formation, defect annealing, and film formation, some

of which have been identified in atomic-scale friction studies [24, 25]. There are also

some differences between the model curves and data. A striking difference is the trend in

the data for the friction coefficient to be higher at both the beginning and end of a cycle at

higher friction levels (p > 0.05). For these cases the model fails to describe the

spatially-resolved friction data. The friction coefficient near the turn-around points is

higher than in the middle of the track, independent of direction of travel.

The friction coefficient is not proportional to surface coverage, as it was in the

superlow friction regime. This behavior in the high friction regime may be due to third

bodies. Investigators have reported that transfer films are formed during sliding against

DLC coatings in this friction regime [26, 27] and with NFC coatings against non-NFC

coated counterfaces run in dry N2 [28]. In contrast, transfer films have not been detected

with NFC vs. NFC coatings in the superlow friction regime [3, 9]. The generation of

transfer films at the higher friction coefficients indicates that gas-surface interactions

promote detachment of material at the sliding interface. A gas could disrupt the

passivating bonds at the nascent surface or produce surface films that detach intact. The

likely gas culprit is H20, known to raise the friction coefficient of hydrogenated carbon

coatings [10, 29]. In situ tribometry has recently provided direct evidence that sliding

against DLC coatings in humid air produces thicker transfer films and higher friction

coefficients than in dry air [27]. Thus, moisture likely promotes particle detachment,

which requires extra energy and raises the friction coefficient.








Finally, although the model does not describe the higher friction behavior, one of

the fit parameters in the model suggests why the friction behavior changed. As seen in

Figure 3-2b, the fraction removed for each pass (1 ) approaches 0 for the slower

sliding speeds, when the friction coefficient rises the most. The midpoint model curves

and data for both the multiple sliding speeds (Figure 3-2) and dwell experiments (Figure

3-3) leading to higher friction have been re-examined. Instead of looking at the fraction

removed (1-2) as a function of sliding speed, the removal ratio (2) as a function of

steady-state friction coefficient was examined. No additional model fits were performed.

Figure 3-5 shows that as the friction coefficient climbed toward 0.12, (1-2) approached

a value of 0.



1.0


0.8 0


0.6


0.4 -
not included in experimental conditions
least squares regression o v = 10 tm/s- 513 pm/s
dwell = 0 s
0.2 0 v= 1,000 pm/s
dwell =5-162s
0 lI I I
0 0.02 0.04 0.06 0.08 0.10 0.12
Hpss
Figure 3-5 Removal ratio as a function of friction coefficient.

This suggests that as the friction coefficient increases, it becomes harder to

continuously remove the product of the gas-surface interaction by wiping. One

consequence would be that removal would become discontinuous, for example, by








coating fracture. However, surface analytical studies will be necessary to determine the

actual physical changes that accompany the transition from the superlow to the higher

friction (0.05 and up) regime.

One item of note in the Heimberg et al. experiments is the environment they used

for all tests was nominally dry nitrogen. Their testing did not isolate which

environmental species in the nitrogen may be leading to a rise in friction coefficient with

increasing surface exposure time. Based on other investigators work [22] the two likely

candidates in the chamber are water vapor and oxygen. In an effort to determine the

culpable environmental species it would be beneficial to isolate and control levels of the

potentially influential species in the chamber during tribological testing. This

investigation aims to achieve such environmental experimentation on NFC films using a

controlled environmental chamber and a low contact pressure tribometer. The

experimental apparatus used for environmentally controlled experiments is analyzed in

Chapter 4 of this work.














CHAPTER 4
MICRO-TRIBOMETER: EXPERIMENTAL APPARATUS AND UNCERTAINTY


4.1. Reciprocating Pin-on-Disk Microtribometer

The tribometer shown in Figure 4-1 is a commercially available instrument for

testing the frictional properties of samples in reciprocating motion.

gas outlet
Sgas u chamber gas inlet apparatus parameter range
to vacuum pump sliding speed 0-18 mm/s
track length 0-0.6 mm
sampling rate 0-100 Hz
normal load 0.1 mN-1N
pin size -50 mg











3mm
1. flexure
2. vertical displacement sensor
3. mirrors
LVDT, humidity, pressure vibration 4. horizontal displacement sensor
and temperature gages isolation 5.pin
display table 6. sample
7. reciprocating stage
8. LVDT

Figure 4-1 Environmental control, contact region and operational parameters of
microtribometer.

This apparatus uses stepper motors for gross loading and positioning and piezo-

electric actuators for fine loading, positioning and reciprocating motion. A dual flexure

both applies normal load and reacts frictional forces between the pin and counterface








samples. Mirrors are mounted on this flexure in the horizontal and vertical directions.

Optical light intensity sensors are positioned at a distance from the mirrors to read the

magnitude of deflection of the flexure in the machine defined frictional and normal load

directions. A pin sample is mounted on the end of the flexure using cyanoacrylate. The

counterface is mounted on a microscopy stub which is fixed into the linear reciprocating

stage. The tribometer was user outfitted with a linear variable displacement transducer

(LVDT) to record relative reciprocating track position. Environmental control is

achieved through a user designed acrylic chamber and the whole assembly is located on

an active vibration isolation table. The tribometer operating parameter ranges of interest

include a linear sliding speed up to 18 mm/sec, track length up to 0.6 mm, sampling rate

up to 100 Hz, and a machine applied normal load range from 0.5 mN to IN. This range

of applied normal loads is achieved by having three different types of dual flexures, with

varying stiffness values. Low range normal loading (0.5-100 mN) is achieved with a

glass flexure, middle range loading (50 mN-300 mN) is achieved with a stainless steel

flexure, and high range loading (200 mN-lN) is achieved with a thicker stainless steel

flexure. Chamber gaseous species and counterface surface temperature control is

outlined in Figure 4-2.































bubbler collector


Figure 4-2 Gaseous environment and counterface surface temperature control.

All experiments in this study were run in an argon gas environment with varying

amounts of water vapor added to the chamber. To achieve this laboratory grade argon as

delivered from the manufacturer (<5 ppm 02 and H20) is either delivered to the chamber

as is or is bubbled through water to achieve varying amounts of water vapor while

maintaining <20 ppm 02 during tests. The chamber is outfitted with a 5 ppm resolution

humidity meter and a 2 ppm resolution oxygen analyzer. There is also a rough vacuum

pump attached to the chamber to promote rapid environment changes. For temperature

testing the counterface substrate surface temperature is controlled through an

encapsulated flexible heater mounted to the back side of the substrate and an adhesive

thermocouple attached to the counterface surface. The working regions of the tribometer








can be examined in a schematic of the tribometer with the manufacturer designated axes

of motion as shown in Figure 4-3.


x -


horizontal
optical sensor


Figure 4-3 Schematic of tribometer test assembly and manufacturer defined axes of
motion.

Each flexure comes from the manufacturer pre-mounted on a carrier block. The

first step in using the apparatus is to mount that carrier block and dual flexure assembly

into the flexure housing, using the machined faces of the carrier bock and housing as the

mating surfaces and two screws for attachment. The positions of the optical sensors are


test assembly


ho usin g 0


carrier block -*

dual flexure
counterface --
mounting stub reciprocating
~ stage
set scre


0 g Egg'_M- __ o: 1
*--: 01111
__WQ r(








then adjusted so the unloaded starting distance between each optical sensor and mirror is

in the middle of the operating voltage range of the optical sensor. The pre-mounted

counterface sample and microscopy stub are then inserted into the reciprocating stage

assembly and tightened in place using a set screw. The pin is located relative to the

counterface through a software interface which actuates stepper motors in the X, Y and Z

directions. The entire linear reciprocating stage is located on a platform that moves in the

X and Y directions for sample positioning. Gross flexure housing assembly motion in the

Z direction is achieved with a separate motor. Once the desired X and Y starting position

of the pin is located the user enters test parameters into the software, including the

desired Z direction approach speed and a value of minimum applied vertical load that

defines pin contact on the counterface. The test is started and the software begins by

automating the Z motion of the flexure housing assembly with the Z stepper motor until it

is close to the desired vertical applied load, at which point the final Z motion is achieved

through the Z axis piezo. After the vertical load is applied reciprocating motion is

controlled by the X piezo. The reciprocating motion of the tribometer produces a

frictional loop when the machine forward (tf') and reverse (tr') friction coefficient

values are examined as a function of reciprocation track position. The forward and

reverse reciprocating motion, along with the reversal locations makes a frictional loop for

each cycle of sliding. An example of the positional friction coefficient data from the

tribometer is shown in Figure 4-4.








a) 1.5 b) 20-
f' data from vertically aligned 20 mN
1.0 s---d Z 15 carbon nanotubes
sliding E with a layer thickness
S0.5 cycle 1 10 -50 micrometers
cycle
o 0 5-mN
.2-0.5- .2 0 .mN
-1. sliding

-1.5 o o o-. -10
0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6
wear track position (mm) wear track position (mm)
Figure 4-4 Example of positional data collected from CSM nanotribometer for a
reciprocating test on vertically aligned nanotubes showing the loop of friction coefficient
or frictional force versus wear track position.

Under certain loading and sliding speed conditions the free sliding portion of the

frictional loop can become small (Figure 4-4b) or ever non-existent (20 mN load).

During these portions the pin and base sample are stuck to one another and are moving

together, without relative free sliding between the two samples. Only data during the free

sliding portion of the frictional loop is used to report friction coefficient recorded during

this investigation. The reversal location portion of the frictional loops is discarded. The

frictional loop starts with the pin sample vertically loaded against the counterface at the

beginning of cycle 1. The counterface begins to move in the arbitrarily designated

forward direction. The pin and counterface samples stay in the same point of contact,

experiencing no relative motion, until the counterface has moved far enough to build up

sufficient strain in the flexure to break free. Once this happens there is free relative

sliding between the pin and counterface in the forward direction until the end of the

reciprocation track is reached. At this point the X piezo motion reverses to move in the

opposite direction. Again, during reversal there is no relative motion between the pin and

the counterface until the cantilever bends far enough in the opposite direction to break

free and have free sliding reverse motion. This loop of free sliding and reversal continues








for all the reciprocation cycles of an experiment. A point to note in Figure 4-4a is the

magnitude of the forward and reverse tribometer measured friction coefficient values is

not equal. This discrepancy will be described by examining the method the machine uses

to calculate the friction coefficient.



4.2. Microtribometer Friction Coefficient Values

The coefficient of friction defined by the microtribometer is the ratio of the

measured force in the horizontal (X axis) direction to the applied load in the vertical (Z

axis) direction. Misalignments between these tribometer measurement axes and the

actual directions of the frictional and normal forces will lead to a discrepancy between

the measured and actual friction coefficient values. This discrepancy between the

forward and reverse reported friction coefficient values and the surface friction

coefficient will be investigated by examining the design and method of signal

measurements in the tribometer. Table 4-1 is a list of nomenclature that will be used in

examining the influence of the tribometer design on the measured friction coefficient

value.








Table 4-1 Nomenclature for microtribometer measurement analysis.

symbol units definition
t friction coefficient between pin and counterface
9' friction coefficient reported by tribometer
F mN force
subscript H n/a horizontal (along tribometer X axis)
subscript V n/a vertical (along tribometer Z axis)
subscript f n/a forward direction of sliding
subscript r n/a reverse direction of sliding
f3 radians misalignment roll angle
radians misalignment pitch angle
V V voltage read by optical sensor
C um/V sensor displacement-voltage calibration constant
K mN/um flexure stiffness
d um sensor-mirror offset error
G 1/um flexure slope-displacement constant
Mgiooopm mN stiffness calibration force
VioooPm V stiffness calibration voltage


Since the counterface sample is user aligned and uses a set screw for attachment

there are potential misalignments between the counterface orientation and the tribometer

measured horizontal and vertical axes. The effect of two misalignment angles, P and 4~,


will be examined. Figure 4-5 defines these two misalignment angles and their resulting


coordinate system rotations.





41


Z ? = tribometer defined
horizontal direction
Y
t <^ = tribometer defined
X vertical direction


- - -
^k


T' TI = 'cosp ^'sinp

^k = ^'=cosp +t'sinp

counterface misalignment roll angle (3, rotation about I axis




l ,- T'=tr=oso- ^i'ino

k = 1koso +J"sino

counterface misalignment pitch angle (, rotation about 1'axis

Figure 4-5 Potential misalignment angles in positioning counterface stub into
reciprocating stage.

The counterface sample starts aligned with the tribometer measurements axis. Unit

vectors located on the counterface, 1, j ,and k are respectively parallel to the X

(horizontal), Y, and Z (vertical) measurement axes of the tribometer. In positioning the

counterface stub into the reciprocating stage a first possible rotation error, the roll angle,

3, about the j axis may occur, resulting in new counterface defined coordinates i, j'

and k'. A second possible rotation error, the pitch angle, (, about the ? axis results in


the final counterface orientation coordinate system, i ", )" and k". The equations

relating the actual counterface sample coordinate directions (i", j" and k") and the








tribometer measured coordinate directions (1, j ,and k) are shown in Figure 4-5. The

force vectors tangent to the counterface surface in the forward and reverse directions are

the vectors along the positive and negative i' direction.

Ftgenf = F, 'angentr = -pF7?' eqns 4.1,4.2

The force vectors normal to the counterface surface in the forward and reverse sliding

directions are in the k" direction.

Fn, = Fk", F = Fk" eqns 4.3,4.4

The total force vectors for each direction of sliding are the sums of the vectors acting

tangent and normal and to the misaligned counterface surface.

If= FI" +pFni eqn4.5

Fr= = F,"-/pF' eqn 4.6

Using the relations established in Figure 4-5 the counterface defined force vectors can

then be related back through the pitch angle j to get expressions in the ', 3' and k'


directions.

F = Fn cos Oik'- F, sin k' + pF' eqn 4.7

F, = F, cos /k'- F. sin k'-pFiF' eqn 4.8

The forward and reverse force vectors can then be related back through the roll angle P3 to

get an expression for the surface force vector in the i?, j' and k' (tribometer read)

directions.

Ff = F, cos f cos Ok F, sin f cos fi F, sin







F1 = F, cos f cos k F,/ sin f cos #i F, sin #0 -,uF, cos fi F,, sin fl eqn 4.10

The horizontal force read (FH) and vertical force applied (Fv) by the tribometer can

now be expressed in terms of the coefficient of friction (g), the applied force normal to

the counterface surface (F,), and the two sample misalignment angles (P3, 4).


The horizontal force components read by the tribometer are those in the 1 direction

and the vertical force components are those in the k direction. Forward sliding

expressions are shown in equations 4.11 and 4.12, reverse sliding expressions in

equations 4.13 and 4.14.

FHf = R Ff cos F, sinf cos eqn 4.11

Fvy = pF,, sin f + F,, cos flcos 0 eqn 4.12

Fr, = -/Fr. cos F,, sin l cos # eqn 4.13

Fw, = -pF,, sin + F,, cos f cos # eqn 4.14

The friction coefficients reported by the tribometer when moving in the forward (pf') and

reverse (Pr') directions are defined as the ratio of the horizontal to vertical forces.

F~ F
= Hf =FrHr eqns 4.15,4.16
Vf FVr

This results in expressions for the vertical force applied (Fv) by the tribometer in each

sliding direction.

F F
Fv, =- Fvr, eqns 4.17,4.18


The tribometer has active feedback control of the vertical force it applies, so the applied

force in the forward and reverse sliding directions can be equated (Fvr=Fvr=Fv).







Equating the vertical applied force expressions in the forward (eqn 4.12) and reverse (eqn

4.14) directions results in a relation between the actual surface applied normal forces in

the forward and reverse directions.

(cos # cosf + p sinf) eqn 4.19
(cos # cos f p sin f)

Using expressions from eqns 4.11-4.14, the horizontal force read by the tribometer when

sliding in the forward and reverse directions (FHf, FHr) can be expressed in terms of the

vertical force applied by the tribometer (Fv) the coefficient of friction at the surface (g)

and the misalignment angles (3, 4).


(pcos -cossing)F --F (p/cos + cos#sin /)
(cos#cos + psin p) (cos cos psinlp)


eqns 4.20,4.21


Using relations in eqns 4.15-4.21 the tribometer read friction coefficients in the forward

(pf') and reverse (gr') directions can be expressed in terms of the actual coefficient of

friction (p) and the misalignment angles (3, ().

(p cosfl-cos#singf) (. cosfl+cos#sinf)
/ (cos # cos f +p sin f) = (p sin? coscos) eqns 4.22,4.23

From eqns 4.22 and 4.23 expressions for the actual coefficient of friction (p) in terms of

the tribometer read forward (pif') and reverse (pr') values and the misalignment angles (3,

() can be found.


(,1ucosfl+sinfl) (pr, cosfi+sinfl)
pu = cos# P,/. = -cos# o
(cosi pf sin f) (cos? -u, sinfi)


eqns 4.24,4.25







For a frictionally isotropic material the relations for the friction coefficient (p) in eqns

4.24 and 4.25 can be equated.

C (os cosf +sin) os (Urcosf-+sinf) eqn 4.26
cos- -- ==-cos eqn 4.26
(cos / -, sinp) (cos/J -,u, sinBf)

The pitch angle, 4, is cancelled by the equating of p. This is not a surprising result

since the pitch angle | is in a direction insensitive to the measured horizontal force. This

leaves an expression for the roll angle, P, in terms of the forward and reverse tribometer

reported friction coefficients. It is expected that the misalignment angles of the

counterface samples will be relatively small and for this reason small angle

approximations are used to further simplify eqn 4.26.

(-+'8) (-a'f) eqn 4.27
(I- Pj) (1-,urf)

fl2(u +,u)+2fl(iu,-1)-(pu. +u,)=0 eqn 4.28

The roll angle (3) is expected to very small and the values of pf' and ,r' are usually

fractions. For this reason the higher order terms of p32g are dropped from eqn 4.28.

2pp'fl-2fl p. p =0 eqn 4.29

This results in an expression for the misalignment angle (P) in terms of the tribometer

reported forward and reverse friction coefficients (pf', tr').

S(P,,_) eqn 4.30
2 ( p p 1)

Which can also be expressed in terms of the tribometer applied normal load (Fv) and the

forward and reverse horizontal read forces (FHf, FHr).









=- Fv (FH+FH) eqn 4.31
2(HffFHr Fv2)

The effect of the misalignment angle 0 on the forward and reverse tribometer read

friction coefficients as expressed in eqn 4.31 is shown in Figure 4-6 by examining lines

of constant misalignment angle P.

9'f
-0.2 0.0 0.2 o.1 small 13 range
0.2 Af + .


0.2 -0.,2 ---0 2
0.0- -N N 2--
5 0.2 <1 r <0 .


-0.-0. I



-0.2 0.0 0.2 0.4 0.6 0.8 1.0
I











Figure 4-6 The effect of the misalignment angle P on the ratio of the tribometer reported
forward and reverse friction coefficient values.

The insert in Figure 4-6 shows that for small values of forward and reverse friction

coefficient ( fe', ,' 1 <0.2), the misalignment angle becomes the average of the two

reported friction coefficient values. This analysis allow for the misalignment roll angle,

P, to be solved given the forward and reverse friction coefficients reported from the





47


microtribometer. The bias error in the friction coefficient due to P is corrected for in the

equations developed for the friction coefficient, p.

An equation derived frictional loop can now be examined to see the influence of the

misalignment angle 0 on the relative magnitudes of the forward, uLf', and reverse, gr',

tribometer read friction coefficients. Figure 4-7 is a frictional loop generated from eqns

4.22 and 4.23 with 03=5 and a flexure with a high stiffness value (same flexure as used

for all of the experiments in this study).

0.20
f = forward subscript /u' = tribometer read friction coefficient
r = reverse subscript p = sample realized friction coefficient

0.10 Pik g =0.12
S0.10 0.085
sliding / =.
0 .0 0 -. ............................ ......... .....
5 /,cycle 1 f




-020 I-i -i-i
0.0 0.1 02 0.3 0.4 0.5 0.6
position (mm)

Figure 4-7 Equation derived frictional loop for pin and counterface pair with friction
coefficient jt=0.12 and misalignment roll angle 3=5.

The slopes of the reversal portions of this frictional loop are due to the stiffness of

the flexure used. All else held constant, the stiffer the flexure, the greater the slope and

the smaller the amount of the frictional loop is due to reversal motions. This general

trend makes sense since the stiffer the flexure, the less strain needs to be built up before

there will be free sliding between the pin and counterface sample. The relative

magnitudes of the forward and reverse tribometer reported friction coefficient values are








a function of the misalignment roll angle, (3. The larger the value of 3, the larger the

difference between the magnitudes of If' and Pr'.



4.3. Propagation of Uncertainty in the Friction Coefficient

The friction coefficient (g) as defined in eqn 4.24 is calculated from the tribometer

read forward (rf') and reverse (tr') values and the misalignment angles (3, 4)). Values for


these parameters have to be determined to report a value for the friction coefficient.



4.3.1. Law of Propagation of Uncertainty

When measuring a quantity it should be recognized that there is no exact

measurement. Therefore, when reporting measurement values both the measured value

and the uncertainty in that value should be stated. A method for the evaluation of the

uncertainty in measurements is outlined in [30,31]. This method defines a systematic

procedure to incorporate uncertainties in all the measured values in a function to find the

overall combined standard uncertainty of that function value. The general expression to

determine the variance (combined standard uncertainty squared) of any function

G(x,y,z) is expressed in eqn 4.32 [30,31].


2 (aGG2 (GY 2
u c(xY= (uz)2 () z ) eqn 4.32


This expression assumes no covariance between the measured values in the

function. To use this method, a value for the uncertainty in the measured value of each

parameter (Ux,y,z) in the function of interest has to be determined. There are two

categories of methods for evaluating the uncertainty in a measured value; a Type A








classification includes uncertainties "evaluated by statistical methods and a Type B

includes uncertainty values "evaluated by other means [30,31]. In this microtribometer

analysis a Type B evaluation for the uncertainty in measured values will be performed.

The "other means used to quantify the uncertainty of each measured value is outlined

for each measured parameter in this investigation.

The uncertainties of these measured values will be combined according to eqn 4.32

to find a total combined uncertainty in the friction coefficient based on the

microtribometer measurement design. This approach has been successfully used by other

investigators to evaluate the uncertainty of measurements made in tribological

experiments [32,33].

In this combination of uncertainties the expression for the coefficient of friction at

the surface (g) will be broken down to examine how the measured values of the

tribometer contribute to a quantification of the uncertainty in the friction coefficient.

Figure 4-8 outlines a hierarchy of the contributions to the uncertainty in the coefficient of

friction. A standard uncertainty is evaluated at each level of the hierarchy. Equation

numbers used in relating parameters between levels are indicated in parentheses next to

each corresponding branch. The chapter subsections of the text deriving the standard

uncertainty relations between levels are indicated to the right of the hierarchy level.








hierarchy of parameters in the combined uncertainty of .


chapter
subsection


'voom V VoNPoI CH, *Ooon. Cr V.,0,on. C, VH 000pm CH
\V(4.86) \/(4.82) \V(4.86) (482) V (4.82)
MgVIOOOlPM VOOO1 Mg HOOOPmHWOO,, O MglO1000 m VlOOOm HM0o0S MooHIio0P MgHIOoo mHIOOoim
V(4.78) V(4.74) V(4.78) V(4.74) V(4.74)
Vv C K, d4 Gy VJ CH KQ d11 Gm Vv Cv Kv d4 C% Vf CH KH d Gf, V, CH KH dfj G,

Fv F Fv F FH,

gI (


Figure 4-8 Propagation of uncertainty hierarchy.


Terminating branches on the hierarchy are measured values. Quantities and sources

for those measured values are outlined in Table 4-2. Uncertainty values and sources are

outlined in Table 4-3.



Table 4-2 Measured values used in the calculation of uncertainty.

symbol value units source of value
)0.035 radians user placement misalignment pitch angle
VHf varies V forward horizontal flexure displacement
VHr varies V reverse horizontal flexure displacement
Vv varies V user prescribed applied vertical force
CH 1249.89 um/V distribution on supplied CSM curve
Cv 1282.63 um/V distribution on supplied CSM curve
KH 3.7381 mN/um ST-027 CSM calibration certificate
Kv 2.1235 mN/um ST-027 CSM calibration certificate
dH 0 um machining misalignment
dv 0 um machining misalignment
GH 0 1/um FEA analysis of flexure
Gy -3.71E-5 1/um FEA analysis of flexure
MgHIooovm 3738.1 mN load for 1000 pm displacement
Mgvioootm 2123.5 mN load for 1000m displacement
VHIooopm 0.7756 V 1000ptm displacement sensor voltage
Vviooo_ m 0.7958 V 1000pm displacement sensor voltage








Table 4-3 Uncertainty in the measured values.


symbol value units source of uncertainty value
u(4) 0.035 radians best visual alignment
u(VHf) 0.0005 V 16 bit data acquisition card
u(VHr) 0.0005 V 16 bit data acquisition card
u(Vv) 0.0005 V 16 bit data acquisition card
U(CH) 0.384 um/V standard deviation of distribution
u(Cv) 0.408 um/V standard deviation of distribution
u(KH) 0.0026 mN/um propagation uncertainties on eqn 4.74
u(Kv) 0.0015 mN/um propagation uncertainties on eqn 4.78
u(dH) 50 um machining misalignment
u(dv) 50 um machining misalignment
u(GH) 0 1/um standard deviation of FEA analysis
u(Gv) 1.84E-6 1/um standard deviation of FEA analysis
u(MgHIooopm) 0.001 mN laboratory grade scale
u(MgvioooNm) 0.001 mN laboratory grade scale
u(VHIooOm) 0.0005 V 16 bit data acquisition card
u(Vviooo4m) 0.0005 V 16 bit data acquisition card


The propagation of uncertainties starts at these terminating branch measured values.

At each branching location a standard uncertainty is then determined on the functional

relationships (equations next to each branch in Figure 4-8). These uncertainties are

propagated through each level of the hierarchy resulting in a final combined standard

uncertainty in the friction coefficient. The functional relationships corresponding to each

branch in the uncertainty hierarchy will now be developed based on the measurement

design of the microtribometer.



4.3.2. It: Friction Coefficient

The friction coefficient (p) was defined in eqn 4.24.


= )(p cos fl+sin/)
S= cos( 8/) n
(cosfl-,uy sin/f)


eqn 4.33





52

The variance in ui can be found according to eqn 4.32, using the law of propagation of

uncertainty.


u2 (U)= u2() +u2( ) 2 ( ) eqn 4.34


The partial derivatives with respect to each variable in eqn 4.33 are expressed in eqns

4.35-4.37.


=sin (P cos + sineqn 4.35
o (p, sin fl cos )eqn4.3


-= cos 2 eqn 4.36
a,8 (cosp-_, sinp)

a-- = cos 2, 1inf-- eqn 4.37
apf (cos/ p sin/)

The expression for the coefficient of friction, pt, is a function of the tribometer

reported forward sliding friction coefficient (tf') and the misalignment angles (J3 and 4k).

The uncertainty in each of those values is evaluated using the same application of the law

of propagation of uncertainty to their formulaic expressions.



4.3.3: Friction Coefficient Expansion

4.3.3.1 (: Pitch misalignment angle


The value of the inclination angle 4 is unknown and since it acts perpendicular to

the direction of sliding it cannot be solved for from the tribometer reported forward and

reverse friction coefficient values (pt', r1'). An estimate of the value of the inclination








angle 4 and the uncertainty of the inclination angle, u(4), has to be made. A reasonable

value for potential visual misalignment when placing a one inch disk sample into a set

screw is assumed to be around 0.035 radians. For this reason a value of 0.035 radians is

used for both <4 and u(4)). The influence of varying the value of 4 on the value of the

uncertainty in the friction coefficient is addressed in Appendix E, but for this analysis a

value of 0.035 radians is used for all calculations.


4.3.3.2 (gf'): Tribometer reported friction coefficient

The tribometer reported forward sliding friction coefficient is determined from the

ratio of the horizontal and vertical forces read by the tribometer.

,f = eqn 4.38
Fv

The variance in f' can be found using eqn 4.39.


u2. (.)=u2(FH) P J+u2(Fv)[.] eqn 4.39


The evaluated partial derivatives in eqn 4.39 are expressed in eqns 4.40 and 4.41.

/.I', 1 9/.' F,,
F =F F Fff eqns 4.40,4.41




4.3.3.3 (p): Roll misalignment angle

The sample roll misalignment angle P was established in eqn 4.31 to be a function

of the forward and reverse horizontal forces (FHf, Far) and vertical force (Fv) read by the

tribometer.








F (FH +FH, ) eqn 4.42
2(FHfF, Hr- Fv )

The variance in P can be found using eqn 4.43.


u8 (/)= u2 (FH f )+ +2 v eqn 4.43


The evaluated partial derivatives in eqn 4.43 are expressed in eqns 4.44-4.46.

ap Fp(F +FH eqn 4.44


eqn 4.45
aFHr 2(F FHFHr)2

ap (FHf +FHr,)(F,,H F,, +F )
Fv 2(F FHf FHr)2

Both the expression for the tribometer reported forward sliding friction coefficient

(pf') and the roll misalignment angle (0) are functions of the forward and reverse

horizontal forces (FHf, FHr) and vertical force (Fv) read by the tribometer. The

uncertainty in each of those values is evaluated using the same application of the law of

propagation of uncertainty to their formulaic expressions.



4.3.4. Tribometer Read Forces

4.3.4.1 (Fv): Tribometer read vertical force

The tribometer read vertical force (Fv) is a function of the vertical optical sensor

voltage (Vv), the vertical displacement-voltage sensor constant (Cv), the vertical flexure

stiffness (Kv), the vertical sensor-mirror mounting offset (dv), and the vertical cantilever








slope constant (Gv). The derivation of this functional relationship will be later

established through the definitions of the constants in Figure 4-10 and eqns 4.68-4.73.

Vy C, l,
Fv = vv eqn 4.47
(1-dvGv)

The variance in Fv can be found using eqn 4.48.


u (F)(= u V v ) Y +2 (K, )K )


+u2 (d) v + 2(G) "V2 eqn 4.48

The evaluated partial derivatives in eqn 4.48 are expressed in eqns 4.49-4.53.

v C v v Vv IK 8n VvC eqns449-4.51
OVv (1-dvGv)'aC (1-dvGv)' OKv (1-dvG) 4.49-4.51

OF,_ VvCvKvGv F, VvCKd,
S-=-2 G vCKdv- eqns 4.52,4.53
adv (1-d,G')G1 G, (l-d,G,)2



4.3.4.2 (FHf): Tribometer read forward sliding horizontal force

The tribometer read horizontal force when sliding in the forward direction (FHf) is a

function of the horizontal forward sliding optical sensor voltage (VHf), the horizontal

displacement-voltage sensor constant (CH), the horizontal flexure stiffness (KH), the

horizontal sensor-mirror mounting offset (dH), and the horizontal cantilever slope

constant (GH).

FH f CHKH eqn 4.54
h (1-de GH)

The variance in FHf can be found using eqn 4.55.







+ 2 ,2 2
aF \9F8f f F 2
Uc (F )= u(VHf+U (C ) 2 C) 2 (K aF)
=UV 'HfJ \CH) AH (3UH)


+u2(d) )2 + ( ) IGHf eqn 4.55
+H u2 GH

The evaluated partial derivatives in eqn 4.55 are expressed in eqns 4.56-4.60.
aFM_ CcA. aF., V.K. aQf, V.:C.
F CKH FHf = VHf KH FHf VHfH eqns 4.56-4. 58
a VHf (1- dHG)' CH (1- dG)' 8K, (1- dGH) eqns 4.56-4.58

aFtf = CHKH QGH.F r VH Knd ^
adFH Hf C(IdHGH 8F)2, VH- _CHKHdH eqns 4.59,4.60
dH (1-dHGH )2 '(GH (-dGH)2



4.3.4.3 (FHr): Tribometer read reverse sliding horizontal force

The tribometer read horizontal force when sliding in the reverse direction (FHr) is a

function of the horizontal reverse sliding optical sensor voltage (VHr), the horizontal

displacement-voltage sensor constant (CH), the horizontal flexure stiffness (KH), the

horizontal sensor-mirror mounting offset (dH), and the horizontal cantilever slope

constant (GH).

FHr = VHrHKH eqn 4.61
(1-dHGH)

The variance in FHr can be found using eqn 4.62.

c"(FH)U2(VHr)f 2r+ U(CF2 Ht+u2(K ) (FH,,


2 2
u\ \C ) G (FI QK ^)

+u2 (dH ) H +U2(GH) H eqn 4.62

The evaluated partial derivatives in eqn 4.62 are expressed in eqns 4.63-4.67.








OFH, CKH K FHr = VH.K, aFHr VHrCH
aVH, (1-dHGH)' CH (1-dG)'KH (1-dHGH) eqns 4.63-4.65

8F, VrCHK.G, F5r HrCHK d
aF -= VH-CHKHGH. ) FH. (VHCHKHdH eqns 4.66,4.67
adH (1-dHGH)2 aGH (1-dHGH)2



4.3.5 Force Expansion

4.3.5.1 (V): Optical sensor voltage

The magnitude of the voltage read by the optical sensors in the horizontal (VH) and

vertical (Vv) directions are functions of the applied normal load and reacted frictional

forces. The uncertainty in the values of the optical sensor voltages, U(VH) and u(Vv), is

bounded by the resolution of the tribometer data acquisition card. The tribometer uses a

16 bit data acquisition card (DT322). At a 10 V range this results in a minimum

increment of 0.15 mV on the voltage signal. The uncertainty in the voltage in each

direction is taken as approximately three times this number; u(VH) = u(Vv) ~0.5 mV.



4.3.5.2 (C): Displacement-Voltage calibration constant

The horizontal and vertical optical sensor displacement-voltage calibration

constants, CH, and Cv, are determined from manufacturer supplied voltage-displacement

curves. The optical sensors are designed to be used over two different distance ranges.

The low range (0-100 gm displacement) is used for a higher signal sensitivity in the low

displacement (low force range on each flexure). The high range (0-1000 ILm

displacement) is used to cover the full range of displacement of the flexures (highest

force range on each flexure). All tests in this study were executed with the optical









sensors in the high displacement range. A schematic of the distance operating ranges and

the supplied calibration constant curves is shown in Figure 4-9. The values for the

horizontal and vertical voltage-displacement calibration constants were determined from

the 300 pm to 900 gm portions of the manufacturer supplied calibration curves. Values

for CH and Cv were estimated from a normal distribution of values around this range of

the calibration curves and the uncertainty values, u(CH) and u(Cv), from the standard

deviation of that distribution.



a low b high
range range

optical sensor mirror

12 12
b c b c

C a


.14 vertical |o horizontal
calibration calibration
curve curve
0 500 1000 150 Sl M 0 500 1000 I5M0 21M)
dsplacement(im) displacement (irn)

Figure 4-9 Operating ranges and calibration curves for optical sensors.


4.3.5.3 (d, G): Mounting offset error and calibration slope constant

In addition to the optical sensor voltage (Vv,H) and the displacement-voltage sensor

constant (CV,H), the tribometer read vertical and horizontal forces (Fv,H) are influenced by

the sensor-mirror mounting offset error (dv,H), and the cantilever slope constant (Gv,H).

Figure 4-10 shows a schematic of the influence of the mounting offset error (dv,H) and the

derivation of the slope constant (Gv,H)-










a b

] I 'F1,2,3,4

FoH,v -KHV 0H,V
FmH,V = KH, (80H,V dH, slope)
slope H,V = G 80i d H-
slope 1

0O I slope 2

s FHo slope 3

-FH
slope 4


01


a o b

Figure 4-10 Schematic analysis to find the mounting offset error (dv,H) and slope
constant (Gv,H).

The relations outlined in Figure 4-10 are used to derive eqns 4.47, 4.54, and 4.61.

Following the schematic in Figure 4-10, the force that would be measured by the optical

sensor (Fov,H) if the mounting offset error were zero is the stiffness of the cantilever times

the deflection at that point.

Fv,H = Kv,H6oH,v eqn 4.68

If the mirror and optical sensor are misaligned by dv,H the measured force (Fm) becomes a

function of the zero offset deflection the offset error and the cantilever slope under that

deflection.

FmV,H = KV,H (oH,V dHslope) eqn 4.69

The sensor-mirror mounting offset error, dv,H, value is set to zero. This is done

because the tribometer is designed to try to have the mirror and optical sensors align in


I








the same centralized location each time the carrier block is mounted into the housing.

The uncertainty in the sensor mirror offset uc(dv,H) is given a value of 50 gnm based on

machining tolerances believed to be used in the manufacturing of the carrier block and

housing [34].

Finite element analysis was performed on the flexure used in these experiments to

investigate the influence of applied load on the slope of the flexure at the mirror. In a

similar manner to the schematic in Figure 4-10, the end of each flexure was given a fixed

boundary condition. Four different simulated loads were applied in the vertical and

horizontal directions. The deflection of the flexure was measured at four points along the

mirror location to establish the slope of the flexure under each applied load. The slopes

of the flexures were examined as a function of the zero error point deflection. This

examination showed that for a given direction on a single flexure the value of the slope

defined in Figure 4-10 is a constant multiple (Gv,H) of the zero error point deflection (So).

This value of (Gv,H) is constant for a single direction on a particular flexure.

slope = 8oG,, eqn 4.70

This expression can be substituted into eqn 4.69.

F,,,, = KY,H 8oH, d HySoG, ) eqn 4.71

Substituting eqn 4.68 into eqn 4.71 yields an expression for the measured force.

F. V,H = Fo (1-dy,vG,) eqn 4.72

The force measured by the tribometer in the vertical and horizontal directions is the

product of the optical sensor voltage (VV,H), the displacement-voltage sensor constant

(CV,H), and the flexure stiffness (Kv,H).








F V C K
F = FmVH V, CV,HKV,H eqn 4.73
H = (1- dVHGV ) (1- dVdyHGV )

Eqn 4.73 is the same functional form as the relations used in eqns 4.47, 4.54, and 4.61.



4.3.5.4 (K): Flexure stiffness

A calibration certificate is supplied by the manufacturer with values for horizontal

and vertical cantilever stiffness values (KH, Kv). For this uncertainty analysis the

manufacturer provided values of stiffness are used. These values are also entered into the

software interface any time a new flexure is used. These stiffness values are

manufacturer calculated by mounting each flexure into a similarly designed housing to

that used in the tribometer (Figure 4-3). Known masses are hung from the flexure and the

deflection at the mirror is measured using the same type of optical light intensity sensor

as it in the tribometer. This manufacturer calibration method is examined to determine

the uncertainty in the stiffness values. The maximum measurement displacement for the

optical sensors is 1000 gm. The horizontal stiffness is found by applying the maximum

force (MgmHooom) that would cause the maximum measurable horizontal displacement

(8HlOOOm)-

KHIoooPm Mg mo m eqn 4.74
SHlOOOpm

The variance in the KH expression can be found using eqn 4.74.


2u (KHiooopm) = U2 (M 00pm HIOOpm-- +,2 ( 5H0"0' H0 eqn 4.75
Tuh alt p a d at mgHIOOOum 4 OOOm i 4HlOOO6Im

The evaluated partial derivatives in eqn 4.75 are expressed in eqns 4.76 and 4.77.








8KHIOo,0m 1 aKHOOOIm H g000pm eqns 4.76,4.77
aMgHIOum HHIOOOm 'HI0OOOpm HlOOOpm

The vertical stiffness is similarly found by applying the maximum force (Mgviooopm) that

would cause the maximum measurable vertical displacement (8viooopm).


eqn 4.78


Klooon =Knooo
80vai OOO pm

The variance in the Kv expression can be found using eqn 4.78.


u \ ,U2/( 0M 8KvIOOOpm +. 2 ,0p ,Kvnoo0o"
"c ( ooo,)=uM g (( Mguooo, ).OM + u (, vooo ( a8 ---.


The evaluated partial derivatives in eqn 4.79 are expressed in eqns 4.80 and 4.81.

8Kvlooopm 1 K vioO P MgVooo000 eqns 4
M 0VOOOPm 8VlOOOpm V000vooopm V21000pm


eqn 4.79


.80,4.81


4.3.6 Stiffness Expansion

4.3.6.1. (Mg): Calibration force

The value for the calibration force used in eqns 4.74-4.81 is the force that would

cause a 1000pm displacement based on the stiffness of the flexure. The uncertainty in

this force value u(MgH,V) is taken as 1 tN which is the resolution of a laboratory grade

scale.



4.3.6.2 (5): Calibration displacement

The uncertainty in delta is determined from the displacement-voltage calibration

constant and the sensor voltage at a 1000 im displacement.

SmIOopm CHV ooop. eqn 4.82








The variance in SH can be found using eqn 4.82.

2 2
u m^ooopm)=u (CH ) a m +I2 (VHooo*) V^2ooom
O CH ) aVHIOOOpm


eqn 4.83


The evaluated partial derivatives in eqn 4.83 are expressed in eqns 4.84 and 4.85.

-HI00=m Mooo1m = CH eqns 4.84,4.85
aCH avHIOOOpm

This procedure is repeated for the vertical displacement delta.

VIooopm = CVvnooopm eqn 4.86

The variance in Sv can be found using eqn 4.86.

-( voo,, 2 2 ( a8f o. 2 (

Vc ) VlO00pm

The evaluated partial derivatives in eqn 4.87 are expressed in eqns 4.88 and 4.89.

-v," = Vvlooon', -vC--- = Cv eqns 4.88,4.89
acV VO VIO00Pm

Each one of the uncertainties in the measured values is then propagated through their

relations according to Figure 4-8. This standard procedure is used to find the friction

coefficient, I, and the uncertainty in the friction coefficient u((g) for any reciprocating

test run on the microtribometer.

This analysis allows for the uncertainty in the friction coefficient to be evaluated

over a range of combinations of normal loads and friction coefficient values that may be

realized during testing. This uncertainty space can be displayed graphically using plots

of lines of constant uncertainty in the friction coefficient as a function of friction

coefficient and applied normal load, as shown in Figure 4-11.










Uc(R)
,-'-- .0 0

0.04
SUc(R)




C 0.1






0.01..0. 1. ... ,,

10 100 1000
normal load (mN)

Figure 4-11 Lines of constant uncertainty in the friction coefficient.

The uncertainty in the friction coefficient in Figure 4-11 is a strong function of

applied normal load. Lower applied normal loads lead to more uncertainty in the signal.

This is correlated to the fact that at lighter loads there is a smaller voltage signal being

returned from the optical sensors to the data acquisition card. The uncertainty in the

friction coefficient due to the voltage becomes larger as the overall voltage used to

determine displacements gets smaller.

Another way to examine the uncertainty space over a range of normal load and

friction coefficient values is to look at lines of constant uncertainty in friction coefficient

over the friction coefficient value (uc(g)/u). This is shown in Figure 4-12 over the same








load and friction coefficient range. These lines show the relative magnitude of the

uncertainty in the friction coefficient to the friction coefficient value.






0.1







0.01.3
0 1...... ... .. .. .. ... ..








10 100 1000
normal load (mN)

Figure 4-12 Lines of constant uncertainty inty in friction coefficient over the friction
coefficient.

It can be seen that at low friction coefficient values and low loads the uncertainty in

the friction coefficient can be up to 1000 times the magnitude of the friction coefficient

itself. One thing to note in Figure 4-12 is above approximately 100 mN of normal load

the ratio of uc(t)/t becomes relatively independent of applied normal load. This trend

can be explained if the same load region is examined in Figure 4-11. Above the 100 mN

mark in Figure 4-11 the uncertainty in friction coefficient stays relatively constant at

around uc(g) = 0.04, so the ratio of uc(t)/g only becomes a function of the friction

coefficient value itself and not the applied normal load.








Figure 4-13 explores the contributors to the uncertainty value by examining one set

of data from self-mated NFC films (Chapter 6) and quantifying the relative contributors

to the variance.



Uc2() = 0.009



67.1 % 0.009 % 32.9 %


FHf FV FHf FHr FV
97.7 % 2.3 % 49.9 % 49.8 % 0.3 %


VH VH VH
97.9 % 97.9 % 99.5 %
96.6% of the Uc2(g) are from uncertainty in VH

Figure 4-13 Relative contributions to the variance in the friction coefficient.

The major contributor (96.6%) to the square of the uncertainty in the friction

coefficient is due to the voltage signal and uncertainty in the voltage signal. The

uncertainty in the friction coefficient could be greatly reduced if the quality of this

voltage signal was improved. One way that the voltage signal could be improved would

be to expand the range of the signal from the optical senor by expanding the voltage

range the sensor operates over. Currently for an average test the magnitude of the voltage

signal under a 500 mN load changes by approximately 0.6 V. For a material with a

friction coefficient of 0.01the friction signal will only vary by 0.006 V. It becomes very

difficult to resolve these very small changes in voltage when the uncertainty in the

voltage signal itself is 0.0005 V. The expansion of the operating range of voltages could








be achieved through either amplifying the voltage signal to the data acquisition card or

using a different displacement sensor that has a more expansive voltage operating range.

These potential improvements were not implemented as part of this investigation.

The magnitude of uncertainty in friction coefficient on the low-friction values seen

in self mated NFC testing may be quite significant. Bars signifying one standard

uncertainty based on the formulas developed in this chapter are included on data in

Chapter 6 of this work. In Chapter 6 the significance of this uncertainty interval is

discussed in more detail. The uncertainty analysis and friction coefficient equations

developed in this chapter can now be used to transfer reciprocating forward and reverse

friction coefficient data as it comes from the tribometer into a bias corrected friction

coefficient value, the uncertainty in that value and the misalignment roll angle the

counterface was situated at during testing. Chapter 5 of this work will now examine

some preliminary testing of NFC films on this low contact pressure tribometer. The

uncertainty analysis derived in this chapter is not applied to the preliminary data in

Chapter 5, but is used on the more tailored experiments of Chapter 6.














CHAPTER 5
INITIAL ENVIRONMENTAL TRIBOLOGY OF NFC FILMS



The low contact pressure tribometer was used to investigate the environmental

dependence of friction coefficient of self-mated NFC films. Self-mated is defined as both

the pin and the counterface samples being coated with near frictionless carbon. The pin

sample used in these tests is a borosilicate crown glass with a 7.78 mm radius of

curvature. The counterface sample is a 1 mm thick microscopy slide. Both the pin and

the counterface were coated with NFC. Surface scans (Figure 5-1) of the samples were

performed using a WYKO white light interferometer.



glass lens NFC coated glass slide
300 nm 195 nm


-390 =1 -460 n






Ra = 3.09 nm Ra = 3.17 nm
RMS = 3.88 nm RMS = 5.80 nm
Figure 5-1 Surface scans of uncoated pin sample and coated flat sample.

These surface scans show the NFC coating has an average roughness of approximately

3.2 nm.










5.1 Near Frictionless Carbon Run-In Testing

The first series of experiments run on the low contact pressure tribometer were to

look at the frictional properties of the surface of the NFC films. Other investigators have

used neutron reflectivity to determine that the as-deposited NFC films are composed of

two layers, an approximately 30A thick higher density surface layer with the remainder

or the coating being of lower density [35]. Friction coefficient tests were run with a self-

mated NFC pair in a dry argon gas environment. An initial run-in test was performed in

which the self-mated pair were run against one another at 18 mm/s, under a 100 mN

normal load over a 0.6 mm reciprocating path. This test was run until the surfaces "ran-

in" to a steady state low friction coefficient.



0.60 initial run-in

0.45-
Snormal load: 100 mN
0 L\" sliding speed: 18 mm/sec


.U 0.15

0 1 II
0 2,000 4,000 6,000 8,000 10,000
cycle

Figure 5-2 Initial run-in of two unworn self-mated NFC samples in a dry argon
environment.

It is interesting that the friction coefficient of the as deposited films started at -0.5,

which is a traditionally very high friction coefficient value for self mated NFC films in a

dry environment. Only after 1500-2000 cycles of sliding in dry argon did the self mated

NFC pair run-in to a low friction value. There is a standing hypothesis based on neutron








reflectivity data saying the as-deposited NFC coatings are comprised of two layers (a

thinner high-density surface layer followed by a lower density lower layer) [35]. Initial

calculations for the experiment in Figure 5-2 show that approximately 0.09 J of fictional

energy are put into the contact during the initial 1500 cycles of higher friction sliding.

(Appendix F). The amount of energy required to break the bonds associated with the as-

deposited higher density surface layer is estimated as 8pJ, so the initial higher friction

cycles should have put more than enough energy into the contact to break through the

higher friction layer (Appendix F).

To investigate if this higher friction surface layer re-forms a series of tests was run

in the same wear track as the experiment in Figure 5-2, without breaking the dry argon

environment. A standard test consisting of 1000 cycles at 5 mm/s, under 3 mN of load,

over a 0.6 mm track length was run on the same track. Then periods of dwell were

instituted between this standard test where the pin and flat sample were separated from

one another but remained in the argon environment. The periods of dwell between

standard tests were varied randomly by orders of magnitude from 1 minute to 10,000

minutes. The friction coefficient run-in of each of these standard tests after varying

amount of times of exposure to the inert environment were examined to see if there was

evidence of the surface layer re-forming or environmental species adsorbing on the

surface. Plots of the friction coefficient trends after the periods of dwell for each

standard test are shown in Figure 5-3.








delay series 0.05 1 imin 19sec
10 min
0.15 ,- 100min
S 0.04 1,000 min


6 0.03


S 0 250 500 m
0.05



S0.001




0 200 400 600 800 100O
cycle

Figure 5-3 Environment exposure dwell experiments.

The first item to note for all of the standard experiments, regardless of delay time,

the initial friction coefficient value begins at approximately g=0.13. This value is close

to the longest exposure time steady state friction coefficient seen by Heimberg et al.[9].

Additionally, this value is both lower than the initial friction coefficient of the as

deposited NFC run-in test (g=0.52) and unlike the initial run-in test, quickly dropped

down to reach a steady state low friction coefficient value. It is also observed that over

all dwell times the amount of time to reach a low steady state friction coefficient value

was approximately equal. It appears that even after 10,000 minutes in a dry argon

environment no surface layer like the initial as-deposited layer re-forms on the NFC, and

whatever adsorbents or interactions that do occur on the surface are quickly overcome

regardless of the amount of exposure time they have to form.








5.2 Sample Pair and Humidity Variation Experiments

A preliminary series of experiments is examined and discussed in Appendix G that

consisted of varying the normal load, sliding speed and reciprocating track length to try

to find the range of test conditions under which a self mated NFC pair would realize both

low friction values and free sliding between the pin and flat samples. These preliminary

tests show for self mated NFC samples in dry argon the optimal operating conditions for

a combination of low friction coefficient and free sliding of the samples with the low

pressure tribometer are at speeds above 1.89 mm/s, reciprocating track lengths above

0.3mm, and loads above 300 mN.

After more optimal test conditions were found three additional test matrices were

run. The first was a NFC coated pin against a NFC coated flat in a dry argon

environment (Appendix H), the second was an uncoated pin against a NFC coated flat in

dry argon (Appendix I) and the third was a NFC coated pin against a NFC coated flat in a

humid argon environment (Appendix J). Details and discussions on each of these three

sets of experiments are included in their respective appendices; the results are briefly

described here. The summary of the test conditions for these three series of test is shown

in Figure 5-4.








NFC-NFC dry Ar 7.78 mm radius of curvature normal load [mN] = 100,200,300
borosilicate glass pin coated max Hertzian [MPa] = 70,89, 106
dry argon with NFC6 sliding speed [mm/s] = 1,2,4,5,8,9,10
1mm thick glass microscope track length [mm] = 0.3,0.6
oxygen meter slide coated with NFC6 number of cycles = 400



glass-NFC dry Ar 7.78 mm radius of curvature normal load [mN] = 100, 200, 300
borosilicate glass pin max Hertzian [MPa] = 77, 97, 115
dry(<5 ppm H) argon sliding speed [mm/s] = 1,2,4,5,8,9,10
1 mm thick glass microscope track length [mm] = 0.3,0.6
oxygen meter slide coated with NFC6 number of cycles = 400



NFC-NFC humid Ar 7.78 mm radius of curvature normal load [mN] = 100, 200, 300
borosilicate glass pin coated max Hertzian [MPa] = 70,89,106
argon and H20 with NFC6 sliding speed [mm/s] = 1,2,4,5,8,9,10
(<5 ppm 02) 1mm thick glass microscope track length [mm] = 0.3,0.6
oxygen meter slide coated with NFC6 number of cycles = 400

Figure 5-4 Test conditions for the three matrix series.

The first matrix of tests was a self-mated NFC pair in a dry argon environment. In

examining the steady state friction coefficient data there was no apparent trend in the data

with load, speed or length. In most cases the friction coefficient of the self mated pair in

dry argon averaged =--0.01. This value is fairly low and shows under the range of

experimental conditions in this matrix low friction was sustained and the NFC pair did

not experience any surface adsorption or interaction that interrupted the low friction

regime. The second test matrix in this series consisted of an uncoated borosilicate glass

pin on a NFC coated sample in a dry argon environment. This data also showed no trend

for steady state friction coefficient as a function of load, speed or track length. For the

majority of the tests the steady state friction was slightly higher (g=0.015) than in the self

mated NFC pair in dry argon. It is surprising that for a glass-NFC pair in dry argon the

friction coefficient is similar to the low friction value seen for the NFC-NFC pair in dry

argon. The third matrix of tests in this series consisted of a self-mated pair of NFC films








in an argon environment with water vapor added to achieve 10% relative humidity. This

data also showed no trend for steady state friction coefficient as a function of load, speed

or track length. The average steady state friction coefficient (t=0.35) was higher than

both the self mated NFC pair and glass pin with NFC flat pair in dry argon.

While there were no model correlating trends in friction coefficient, one interesting

aspect of these series of tests were the pin surfaces after the experiments. Interferometer

surface scans (Figure 5-5) of the wear scars on the pin samples were taken after each of

the three test matrices to ensure that the NFC coating was still present and to investigate

whether or not transfer films formed.


(20 X) MMn (41 X)
NFC-NFC P
-2-s dry argon *-5Hm

Ra = 3.64 nm Ra = 2.92 nm
RMS = 9.79 nm RMS = 7.00 nm
u.s (20 X) 126 (41 X)

glass-NFC
b)-.s dry argon -o s. ,
b) p 0.02
Ra = 4.55 nm Ra = 4.90 nm
RMS = 9.33 nm RMS = 9.72 nm


NFC-NFC
-K)sl humid n
c) argon
= n 1- 0.30
Ra = 2.06 nm Ra = 1.80 nm
RMS = 4.13 nm RMS = 3.81 nm

Figure 5-5 Surface scans of pin samples after a) self mated NFC tests in dry argon, b)
glass pin against a NFC coated counterface in dry argon, and c) self mated NFC tests in
humid argon.








For the self mated series of test run in dry argon the surface of the pin showed a

small amount of wear in the sliding direction, but it was not quantifiable (Figure 5-5a).

In the case of the glass pin against the NFC counterface, there seemed to be material

deposited on the glass pin (Figure 5-5b). The composition of material was not analyzed.

It is possible that some of the NFC coating on the counterface was transferred to the glass

pin and the low friction coefficient values realized in this pairing were actually due to a

layer of NFC on the glass pin rubbing against the NFC coated flat. The self-mated NFC

run in humid argon pin sample also showed deposition onto the pin surface (Figure 5-5c).

The nature of this material appears to be a smooth, almost smeared layer in the direction

of pin sliding. It is possible that this deposited material is a transfer layer, but no

chemical composition analysis was performed. These NFC experiments did not show

friction coefficient to be a function of exposure time (through sliding speed and track

length variations) as predicted by modeling in Chapter 2, but they did show a frictional

dependence on the humidity level in the environmental chamber. This result is

investigated further using a humidity ramp in the environmental chamber.



5.3 Water Vapor Ramp

The NFC-NFC humid argon experiments performed isolated water vapor as a

specific species responsible for a rise in the friction coefficient of self mated NFC films.

If gas-surface adsorption and removal of water vapor is occurring the low friction state

should be a recoverable function of chamber humidity. To test this hypothesis an

experiment was run in which the environment starts as dry argon and the friction

coefficient was allowed to run-in to a low value. Then the amount of water vapor was








ramped up and back down to see how the friction coefficient behaved to a prescribed

change in relative humidity of the chamber. Figure 5-6 shows friction coefficient

performance for the prescribed variation of humidity within an argon environment.



35 humidity ramp 0.14

30 0.12

25 ___ o -0.10
0
20 -0.08

S15 99 0.06



5 0.02


0 5,000 10,000 15,000 20,000 25,000 30,000
cycle number
Figure 5-6 Variation of friction coefficient of self mated NFC pair to a prescribed change
in relative humidity of an argon environment.

This test clearly shows that water vapor is a species that affects the friction

coefficient of self mated NFC films. While this data does not indicate the specific role

water plays in the friction coefficient performance, the shape of the curves in Figure 5-6

shows an interesting trend. When humidity is increased there is a slight offset to the

increase in friction coefficient, but the two increasing curves are the same general shape.

However, when the humidity is ramped back down the friction coefficient does drop, but

at a slower rate than the humidity level drops. This could be an indication that a layer has

adsorbed or interacted with the sample surfaces that may take a certain amount of time,

pin interaction, or environmental composition before it can be removed or desorbed.

The tribological testing in this chapter did distinguish an initial higher friction

surface layer on the as-deposited NFC coatings from the lower friction layer established








after run-in. Additionally, the experiments in this chapter isolated water vapor as a

gaseous species that has a detrimental influence on the friction coefficient of self-mated

NFC films in a tribological contact. However, these self-mated NFC experiments did not

show friction coefficient to be a function of exposure time (through sliding speed and

track length variations) as predicted by modeling in Chapter 2. This may be due to the

range of sliding speeds and track lengths chosen for the experiments. An additional

experimental parameter that can be controlled during tribological testing is counterface

temperature. Temperature is a commonly varied parameter to look for trends in gas-

surface interactions. A series of experiments varying chamber water vapor pressure and

counterface surface temperature is investigated in Chapter 6 to see if trends in friction

coefficient can be correlated to activation energies for competitive rates of water

adsorption and desorption on the NFC coating surfaces.













CHAPTER 6
WATER VAPOR PRESSURE AND SUBSTRATE TEMPERATURE EFFECTS



Experiments in the previous chapter isolated water vapor as the environmental

species causing a rise in friction coefficient of self mated NFC tribological pairs. This

chapter will execute a series of experiments varying chamber water vapor pressure and

NFC counterface surface temperature in an attempt to determine if water vapor is

interacting with the NFC by surface adsorption. Frictional trends with prescribed

variations in these two experimental parameters will be compared with modeling using

Langmuir expressions for adsorption and desorption of water vapor on surfaces.



6.1 Water Vapor and Surface Temperature Experiments

The water vapor pressure of the environmental chamber was controlled by mixing

prescribed amounts of dry and humidified argon, while maintaining less than 10 ppm 02

during all tests. Counterface surface temperatures were prescribed through a PID

controller using an encapsulated heater under the counterface and an adhesive

thermocouple on the sample surface. A schematic of this setup was illustrated in Figure

4-2.

A single self-mated NFC coated pin and counterface sample was used for the entire

matrix of experiments in this section. The pin sample consisted of a 7.78 mm radius of

curvature NFC coated borosilicate glass lens and the counterface was a NFC coated

microscopy slide. An initial run-in test, similar to the one in Figure 5-2 was performed to








remove the initial higher friction surface layer and achieve low-friction between the pin

counterface surfaces. The water vapor pressure and temperature experiments were then

all executed in the same wear track as the initial run-in test. The matrix for this series

consisted of four individual experiments. During each experiment the chamber water

vapor pressure was held at a distinct prescribed value, ranging from 123 Pa to 4933 Pa of

vapor pressure. Each vapor pressure experiment consisted of 32,000 cycles of sliding

under a 100 mN normal load, at 18 mm/sec, over a 0.6 mm track length. The

experimental matrix is outlined in Figure 6-1.



surface temperature water vapor test matrix

constant water vapor pressure P1,2,3,4
u 100 C
90 water vapor pressure
(%RH)
S80 C
Pi 123 Pa (1%)
E 70C
40 P2 1233 Pa (10%)

50cC P3 2837 Pa (23%)
40 C 4000 ._ P4 4933 Pa (40 %)
35 C I cycles

0 cycle 32,000

Figure 6-1 Experimental matrix for variations of chamber vapor pressure and NFC
temperature.

The counterface surface temperature was held for 4,000 cycles of sliding at eight

distinct temperatures during each experiment. The friction coefficient values examined

from the four water vapor pressure experiments were average values from cycles 3,500-

4,000 at each temperature step. Steady state friction coefficient values were determined

by averaging over the middle third of the reciprocation length (to discard reversal








locations) for the last 500 cycles of sliding. The results of these experiments are

examined for each water vapor pressure in Figure 6-2.


123 Pa (01% RH)








'I 44 *4 .


340
temperature (KI


0.12


0.08-


0.04-


0.00
300


380


2837 Pa (23% RH)


1233 Pa (10% RH)


a) 0.12
4.,
*-
" 0.08


12 0.04


0.041


300 340 380 300 340 380
temperature (K) temperature (K)

Figure 6-2 Steady state friction coefficient values as a function of counterface surface
temperature for a) 123 Pa, b) 1233 Pa, c) 2837 Pa and d) 4933 Pa of water vapor
pressure.

Using the analysis outlined in Chapter 4, uncertainty intervals representing one

standard uncertainty in friction coefficient are included on each data set. One standard

uncertainty interval signifies a 68% confidence level that the true value of friction

coefficient lays within the interval. As outlined in Chapter 4 and from Figure 6-2 it can

be seen that the uncertainty intervals are significant in magnitude in comparison to the


I i 40

temperature (I


{ 4933 Pa (40% RH)






1 I ,


0.00
300








friction coefficient values. For this reason it would be difficult to say much about the

absolute values of friction coefficient for each experiment. Instead, general trends in

friction coefficient with water vapor pressure and temperature changes will be examined.

Additionally, intervals were calculated for temperature variations that signified the

standard deviation of the temperature readings during the 500 cycles of steady state

sliding for each data point in Figure 6-2. However, the size of these bars was smaller that

the graphic used for each data point in the Figure, so they are not included on the plot.

The average of the standard deviations in temperature was 0.29 K with a maximum

standard deviation of 0.76 K.

In the experiment with the lowest water vapor pressure, 123 Pa (Figure 6-2a), a low

steady state friction coefficient was maintained between the NFC pair over the entire

range of surface temperatures. When the water vapor pressure was increased to 1233 Pa

(Figure 6-2b) the same low steady state friction coefficient was maintained over the

entire range of counterface surface temperatures. When the water vapor pressure in the

chamber was increased further to 2837 Pa (Figure 6-2c), a change in friction coefficient

was realized. At 308 K and 2837 Pa the friction coefficient of the self mated pair started

at g=0.07. As the substrate temperature was increased there was a monotonic drop in

friction coefficient down to the same low friction value as the 123 Pa and 1233 Pa tests

(j-0.009). For the highest water vapor pressure test at 4933 Pa (Figure 6-2d), the friction

coefficient at 308 K started at ~-0. 1, a higher value than all the previous lower humidity

level tests. When the counterface surface temperature was increased the friction

coefficient stayed at approximately the same higher value until it reached 333 K. Then

the friction coefficient monotonically decreased with increasing substrate temperature








down to the same low friction coefficient value of g-0.009. The general trends seen in

the water vapor pressure and substrate temperature data make sense for the hypothesis of

surface adsorption of water on the NFC films interrupting the low friction sliding of the

pairs. As the amount of water vapor in the chamber was increased the initial (lowest

temperature) steady state friction coefficient increased, which may correlate to more

coverage by water vapor leading to a higher friction coefficient. Additionally, if at the

lowest temperature state, there was water on the surface (increased p at T = 308 K), there

was a drop in friction coefficient as the counterface temperature was increased, which

may correlate to more water desorption from the surface as the counterface temperature is

raised.

In addition to putting uncertainty intervals on the data, another useful outcome of

the uncertainty analysis from Chapter 4 is the ability to solve and correct for the

counterface roll angle, 0, for any reciprocating test. It was expected once a counterface

sample and stub was secured into the reciprocating stage the roll angle would not be zero,

but would remain relatively constant during a single experiment. Analyzing the data

from the experiments in Figure 6-2 returned an interesting trend in the roll angle p.

Figure 6-3 examines the counterface roll angle as a function of surface temperature for all

four water vapor pressure experiments.





83

7
o 123 Pa (01% RH)
o 1233 Pa (10% RH)
5 2837 Pa (23% RH) U a
4933 Pa (40% RH)

L.3 0




-13


300 320 340 360 380
temperature (K)

Figure 6-3 Counterface roll angle 3 as a function of surface temperature for the
experiments from Figure 6-2.

In examining the relative positioning of the pin and counterface sample in Figure 4-

3, the temperature effect on the roll angle P is not surprising. The counterface stub is

held in place with a single set screw and in the loop from the counterface surface to the

pin surface there are multiple components made of different materials. Thermal

expansions over the range of temperature tested in these experiments could easily cause

the monotonic change in roll angle seen in Figure 6-3. Using the uncertainty analysis

allowed the temperature dependence of P to been seen and for the bias caused by the

misalignment angle to be accounted for in the data.

Frictional trends in the self mated NFC pairs have been established as a function of

water vapor pressure and counterface surface temperature (Figure 6-2). Gas-surface

modeling for surface coverage will now be used to see if the trends in the friction

coefficient correlate to surface adsorption and desorption of water vapor.








6.2 Gas-Surface Modeling: Adsorption and Desorption Rates

The trends in friction coefficient with water vapor pressure and surface temperature

have been established experimentally. To compare that data to modeling of surface

adsorption and desorption of water vapor, friction coefficient has to be related back to

surface coverage. This is done in the same manner as the modeling in Chapter 2, using a

linear rule of mixtures. The difference in this chapter the friction coefficient data is

transformed into coverage instead transforming the model equations to friction

coefficient. This is just a simple rearrangement of eqn 2.22 to the form in eqn 6.1.


(= _-0) eqn 6.1


Using the same values for nascent and fully covered friction coefficient as in previous

modeling (to = 0.006 and pI = 0.12), the friction coefficient data in Figure 6-2 is

correlated to fraction surface coverage (0) in Figure 6-4.

0.12- 1.0 o 123 Pa (01% RH)
a 1233Pa(10%RH)
0.10- 0.8 2837 Pa (23% RH)
W m 4933 Pa (40% RH)
S0.08
E 0.6
u 0.06 =
"4 0.4
'" 0.04 -
0.2
0.02 -
0.0 8 o B B = B S r'
0.00 0.0
300 320 340 360 380
temperature (K)
Figure 6-4 Experimental results of friction coefficient (g) and surface coverage (0) as a
function of counterface surface temperature and water vapor pressure.

Modeling of the trends in surface coverage with changes in water vapor pressure

and counterface temperature is going to be performed using the Langmuir model for








relative rates of surface adsorption and desorption [36]. Table 6-1 outlines the modeling

parameters that will be used in the derivation.

Table 6-1 Gas-surface modeling nomenclature.
symbol units definition
Ea J/mol energy to dissociate from surface
I #/(cm -sec) molecular impingement rate
k J/K Boltzmann constant
Ka 1/(Pa-sec) adsorption rate coefficient
KI 1/sec desorption rate
m kg molecular mass
no sites/m site density
P Pa pressure
subscript ss n/a steady state
t sec time
T K temperature
Ta sec average stay time
to sec time between attempts
0 covered fraction
1-0 nascent fraction


The Langmuir model for adsorption and desorption says the change in surface

coverage as a function of time is equal to an adsorption rate (KaP) acting on the nascent

portion of the surface (1-0) minus a desorption rate (Kd) acting on the covered fraction of

the surface (0), as expressed in eqn 6.2.

dO
S= K,P(1-0)- Kd eqn 6.2

This expression can be integrated to solve for the fractional coverage (0) as a function of

the adsorption rate (KaP), the desorption rate (Kd) the initial coverage (0o) and time (t).

Details of the integration steps can be found in Appendix K.


0 = KP+ + 0o K iP e-(KP+Kd' eqn 6.3
KaP+Kd KaP +Kd