Davim J.P. Tribology for Engineers: A Practical Guide
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xi
List of fi gures
1.1 Display of surface texture 3
1.2 General typology of surfaces 4
1.3 Typical surface layers 5
1.4 Centre line average of a surface over sampling
length L 8
1.5 Various surface profi les having the same R
a
value 9
1.6 (a) Probability density functions for random
distribution with different skewness;
(b) symmetrical distributions (zero skewness)
with different kurtosis 13
1.7 Schematic illustration for random functions
with various skewness and kurtosis values 14
1.8 Construction of the Abbott bearing area curve
from the topography of a surface 15
1.9 Graphical representation of the autocorrelation
function 16
1.10 Surface textures and their autocorrelation
functions 17
1.11 Qualitative description of statistical self-affi nity
for a surface profi le 18
1.12 Component parts of a typical stylus surface-
measuring instrument 22
1.13 Schematic of working of STM 27
1.14 Schematic operation of AFM/FFM 29
2.1 Scheme of two contacting bodies in relative
motion 34
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Tribology for Engineers
2.2 Variation of the friction coeffi cient with sliding
distance 36
2.3 Friction coeffi cient–sliding distance record
obtained in a pin-on-disc test for a metal–metal
contact under dry conditions 37
2.4 Stick-slip effect 37
2.5 Three-dimensional topography map of a metal
surface obtained by optical profi lometry 38
2.6 Contacts between the surface asperities 39
2.7 A hard conical asperity ploughing through a
softer surface 44
2.8 Model for adhesion, transference of material and
plastic deformation of wear debris 51
2.9 SEM micrograph of an adhesive wear debris
particle showing the fl at rounded morphology 52
2.10 Three-dimensional surface topography profi le
of a dry wear scar 52
2.11 Line-scan of the cross-section of a wear scar 53
2.12 Load-velocity wear map for steel–steel under
pin-on-disc confi guration 54
2.13 Wear map for Al
2
O
3
55
2.14 Abrasive wear mechanisms by a sharp indenter 56
2.15 Abrasive wear by a cone-shaped asperity 56
2.16 Abrasive wear scar profi le obtained by contact
profi lometry 57
2.17 SEM micrograph of an abrasive wear debris
particle produced by a cutting mechanism 58
2.18 Scratch test confi guration for viscoelastic
materials 58
2.19 Variation of erosive wear with impact angle for
ductile and brittle materials 59
3.1 Stribeck curve and lubrication regimes 69
3.2 Derivation scheme for Reynolds’ equation 71
3.3 Slider geometry and coordinates 76
xiii
List of fi gures
3.4 Dimensionless pressure and inlet-to-outlet ratio 77
3.5 Cylindrical journal bearing geometry and
coordinate system 78
3.6 Dimensionless pressure distribution as function
of angle at different eccentricities 80
3.7 Real surface profi le and some roughness parameters 81
3.8 Computer image of surface with randomly
generated asperity heights and roughness step 84
3.9 Surface with sinusoidal (a) and triangular
(b) roughness 84
3.10 Schematic of unequally roughened surfaces
(a) and gap geometry in X,H plane (b) at wave
number k = 5, roughness height ratio
R
a1
/R
a2
= 0.5, and phase displacement Φ = 1/(4k) 86
3.11 Typical pressure distribution in lubricating fi lm
between sinusoidal surfaces with wave number 2,
wave ratio 1, and asperity height of lower surface
0.5 and upper surface 0.25, at time 1/(2k) (a) and
at coordinate y = 1/(2k) (b). 91
3.12 Typical pressure distribution in lubricating fi lm
between rough surfaces with wave number 2 at
wave ratio 0.5 with asperity height of lower
surface 0.5 and of upper surface 0.25 along:
(a) entire rough surface at time 1/(2k); (b) X, T
coordinates at Z = 1/(4k) 92
3.13 Maximal pressures versus asperity height ratio at
different wave ratios with reference wave
number k
x
= 100 94
3.14 Maximal and cavitation pressures at different
numbers of waves and roughness values at
wave ratio 1 (a) and 2 (b) 95
3.15 Schematic of surface (a), surface profi le (b), and
gap geometry (c) at wave numbers k
1x
= 3, k
2x
= 5,
k
1z
= 2, k
2z
= 3, and time and phase displacement of
upper surface Φ = T = 1/(2 k
2x
) 99
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Tribology for Engineers
3.16 Typical pressure distribution in lubricating fi lm
between triangular wave surfaces at asperity height
A
1
= A
2
= 0.15, and inner-surface wave ratio 3/4,
along: (a) entire surface profi le at time 1/(k
2
x
)
and (b) X, T coordinates at Z = 1/(k
2
x
) 108
3.17 Typical pressure distribution in lubricating fi lm
between triangular wave surfaces at asperity
height A
1
= A
2
= 0.15, and inner-surface wave
ratio 4/3 along: (a) entire surface profi le at
time 1/(k
2
x
) and (b) X, T coordinates at
Z = 1/(k
2
x
) 108
3.18 Maximal pressures versus asperity height ratio
A
1
/A
2
at different intra-surface wave numbers
k
1
x
; asperity height of lower surface 0.15;
and intra-surface ratios: (a) 2/3, (b) 1, (c) 2 111
3.19 Maximal and cavitation pressures versus
inter-surface wave ratio at lower surface wave
numbers k
1
x
= 3 and 6, asperity height A
1
= 0.15;
for intra ratios: (a) 2/3, (b) 1, (c) 2 112
3.20 Cavitation threshold and maximal
hydrodynamic pressure versus wave number;
k
1
=
k
2
= 1, A
1
= A
2
= 0.15 for triangular, and
0.25 for sinusoidal roughnesses 114
4.1 Schematic drawing of molecular dynamics
modelling of the sliding processes 131
4.2 The transition of no-wear and wear regimes 134
4.3 Regime transition under specifi c sliding
conditions 135
4.4 Relationship between the frictional force and
contact length 139
4.5 The subsurface microstructure of silicon
monocrystals after a two-body contact sliding 142
4.6 The wear diagram 145
xv
List of fi gures
4.7 Diamond asperity sliding on a monocrystalline
copper surface 149
4.8 Frictional stress vs contact width for indentation
depths of –0.14 nm and 0.46 nm 150
4.9 The mechanics model for multi-asperity contact
sliding 152
4.10 Cross-sectional view of silicon work piece and
asperities A, B and C during sliding 153
4.11 Cross-section of the silicon workpiece
through the centre of asperities (cases II and III) 154
6.1 Anatomy of the human hip joint 247
6.2 Anatomy of the human knee joint 250
6.3 Components of human knee joint 251
6.4 Polyethylene components used in hip and knee
orthopaedics implants 259
6.5 Metallic components used in hip and knee
orthopaedics implants 261
6.6 Ceramic components used in hip and knee
orthopaedics implants 264
6.7 Schematization of osteolysis phenomenon due
to wear and particles debris 266
6.8 Standard wear screening devices used in order
to give information exclusively on the intrinsic
features of the materials studied 270
6.9 Schematic view of a typical hip joint wear
simulator 272
6.10 Schematic view of a typical knee joint wear
simulator 273
xvii
List of tables
1.1 Defi nitions of a few surface roughness
parameters 11
1.2 Summary and comparison of roughness
measurement methods 31
3.1 Reference values applied in calculations 93
3.2 Cavitation wave number at studied values of
viscosity, wave and asperity height ratios 96
3.3 Reference values used in calculations 110
4.1 Comparison of some features of SFA, STM
and AFM 123
4.2 Parameters in the standard Morse potential 133
4.3 Contact lengths by the JKR and MD analyses
for the case of diamond-copper interactions 151
5.1 Equations for calculating elastic (Hertz)
contact stress 163
5.2 Defi nitions of surface roughness parameters 165
5.3 Static friction coeffi cients for clean metals in
helium gas at two temperatures 170
5.4 Static friction coeffi cients for metals and
non-metals (dry or unlubricated conditions) 173
5.5 Reduction of static friction by surface fi lms 176
5.6 Estimates of the maximum plowing contribution
to friction 181
5.7 Critical degree of penetration (D
p
) for
unlubricated friction mode transitions 186
5.8 Effects of material type on friction during
abrasive sliding 186
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Tribology for Engineers
5.9 Measured values for the shear stress dependence
on pressure 189
5.10 Temperature rise during sliding 195
5.11 Effects of deformation type and Peclet number
on fl ash temperature calculation for the circular
contact case 198
5.12 Effects of temperature and pressure on viscosity
of selected lubricants having various viscosity
indexes 203
5.13 Additives to lubricating oils 209
5.14 Effects of oxide scales on boundary-lubricated
friction 213
5.15 Effect of linear undulations on boundary-
lubricated friction of steel on titanium 214
5.16 Friction coeffi cients for steel lubricated by solid
lubricants 219
5.17 Kinetic friction coeffi cients for several oxides
at 704ºC 220
5.18 Properties and friction coeffi cients characteristic
of certain compounds 221
5.19 Effects of moisture on the friction coeffi cients
of various solid lubricants in air of various
relative humidity 222
5.20 Dependence of saturation shear strength and
friction of metals on the applied pressure 223
5.21 Transformations in molybdenum disulfi de as
temperature rises 225
5.22 Steady-state friction coeffi cients for solid
lubricant combinations 226
5.23 Effect of additives on the friction of blended
PTFE 227
5.24 Commonly used lubricants and typical μ
(friction coeffi cient) values in cold and hot
rolling 228
xix
List of tables
5.25 Commonly used lubricants and typical μ
(friction coeffi cient) values in wire and tube
drawing 229
5.26 Commonly used lubricants and typical μ
(friction coeffi cient) values used in extrusion
of metals 230
5.27 Commonly used lubricants and typical μ
(friction coeffi cient) values used in forging
operations 231
5.28 Commonly used lubricants and typical μ
(friction coeffi cient) values used in sheet
metalworking operations 232
6.1 Bearing system proposed and their problems 258