ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 1
Surfaces “If God created Solids, the Devil created Surfaces.” o Impression: surfaces flat & simple o Reality: surfaces extremely complex o Surface properties depend on
topography method & history of surface formation surface & bulk composition environment
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 2
Surface formation example o NaCl, FCC structure Bulk properties depend on crystal’s atoms Surface properties can depend on cleavage Cleavage plane influences surface
properties: Short dashed (plane) exposes white atoms Long dashed (plane) exposes blue atoms Inclined (plane) exposes white & blue atoms
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 3
Surface disrupts crystal structure ⇒ higher energy Unshared electrons Mechanical deformations
o Bulk: large grains (single crystals) consistent
with crystal structure & lower energy levels o Smaller grains @ surface from intense
deformations & higher energy levels (1~100 µm)
o Bielby amorphous layer (~100Å) from machining (work hardened, quenched, alloy mixtures)
o Layer of compounds (~100Å): oxides, sulfides, etc.
o Adsorbed layer via van der Waals forces: hydrocarbons, water, atmospheric impurities, etc.
o Dust particles (~1 µm)
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 4
bulk (larger grains)
smaller grainsnear surface
Bielby amorphous layer
oxide, sulfide, etc. layer
adsorbed, deposited layer
dust particle
inclusions &voids
o Surfaces depend on history: how surface was
made o Layers may/or not be important, depending
on size & phenomena: Can’t measure effect of thin films on
mechanical deformations Same layer can insulate contact & impede
electric conduction.
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 5
Surface Topography
o All surfaces rough: no smooth or flat o Surfaces topography: peaks (asperities) &
valleys (furrows). Size, shape, and distribution determined by surface production (machined, forged, plated, etched, etc.).
o On a typical 1 cm2 surface, very many
asperities. o “Smooth” on large length scale is “rough” on
smaller length scale o Characterization of surface texture Long wavelength (10 µm ~ 10 mm)
undulations o Called “surface waviness” o Man made (scratches, machining marks,
tool & die shapes, etc.) o Fourier series representations
Shorter wavelengths (< 10µm)) o Nature made bumps ⇒ random
structure o Statistically characterized
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 6
SURFACE TOPOGRAPHY
surface height Z ≤ 100 µm, X ≤ 88 cm, Y ≤ 2.54 cm
• All surfaces are rough • Surface features hills (asperities) valleys (furrows) • Surface profile trace
• Surface height descriptions Surface waviness sinusoidal structure Fourier series Surface roughness (random) Gaussian distribution model Fractal models
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 7
SURFACE TOPOGRAPHY DESCRIPTIONS
Sinusoidal models • surface heights Z(x, y) • Z = Zwave + Zrough Z = 300+100 sin[2π x]+120 cos[4πx] + 20 sin[40π x] + 10 sin[100π x] Surface waviness Zwave • long wavelengths • macroscopic features • man-made (often) Zwave = 100 sin[2π x]+120 cos[4πx] Surface roughness Zrough • short wavelength • microscopic features • deterministic or random • very short: random
Zrough=20 sin[40πx]+10 sin[100πx]
x (cm)
z (µm)
x (cm)
z (µm)
x (cm)
z (µm)
8
SURFACE WAVINESS EXAMPLE
Z
Y
X surface height Z(X,Y) ≤ 100 µm, X ≤ Lx = 88 cm, Y ≤ Ly 2.54 cm
Fourier series amplitudes of
waviness profile
Fourier series: waviness profile
Z(X, Y) = ∑Amn sin (m π xLx + φm) sin (n π y
Ly + φn)
Amn: harmonic amplitudes φm, φn: phases of harmonic components
.
0
100
200
300
400
500
600
1 3 5 7 9 11 13 15 17 19 21 23
harmonic number mam
plit
ude A
(µ
m)
m
9
SURFACE ROUGHNESS EXAMPLE
SEM photo: electroplated gold on copper waviness and roughness apparent
10
Measure Surface Topography “Bumps” via
Profilometer, similar to phonograph tone arm.
Stylus “rides” surface ⇒ “trace” signal.
Optical interference techniques that utilize path differences
Electron microscope photographs Atomic force microscope (micro-profilometer
for nano measurements)
11
SURFACE PROFILE MEASUREMENTS
surface
Z(x)
x
stylus
surface
Profilometer • stylus travels surface • motions Z(x) trace profile • stylus = filter big/small bumps stylus cannot sense
www.taylor-hobson.com
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 12
Optical methods: bumps create optical path difference
surface
Z(x)
x
light rays(polarized)
• scan surface ⇒ three dimensional image • profile extracted
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 13
Optical Interferometric Microscope
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 14
Atomic Force Microscope
o Micro-profilometer o Cantilever beam rides surface o Stylus: nano-meter curvature o Laser interferometer detects beam
deflections o Sub-nanometer range
AFM image of graphite atoms AFM image of “contact bump”
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 15
SURFACE TOPOGRAPHY PARAMETERS
Z(x)
x
zi
L
Instrument reference plane
Surface
reference plane
zi
zo
• Locating zero-line:
!
z0
=1
nzi
i=1
n
"
!
=1
Lx
z
0
L
" dx#
$ %
&
' (
!
z i= z
i" z
0 zo: DC component
!
z i : AC component
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 16
Historical Quantities • Centerline Average (CLA)
!
Ra
=1
nz
i
i=1
n
"
!
=1
Lx
z
0
L
" dx#
$ %
&
' (
measures roughness excursion from zero-line • Root Mean Square (RMS)
!
Rq =1
nz i2
i=1
n
" also measures excursion • Not unique: different profiles/same Ra , Rq
• Other measures Maximum peak to valley Rt = max z
heights - min z
heights
Average Rt over segments: Rz = 1n ∑i=1
n Rti
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 17
STATISTICAL QUANTITIES • Surface height distributions
Z(x)
x
zi
L
Z
frequency ofoccurrence
F(z)
• Surface height z treated as random variable • Some surfaces almost Gaussian
F(z) = 1σ 2π e - 12 [z-µ
σ ]2
• Expected values of functions with distributions
E [ g(z) ] = ⌡⌠-∞
∞ g(z) F(z) dz
• Moments: g(z) = zr related to historical & other
quantities
E [ zr] =
!
zrF(z)dz
"#
#
$
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 18
o Ra: 1st moment
Ra = CLA =
!
z F(z)dz"#
#
$ = 2 zF(z)dz0
#
$ o Rq: 2nd moment
Rq = RMS = E [ z2 ] = σ =
!
z2F(z)dz
"#
#
$ o Skewedness s: 3rd moment (r = 3)
s = E [ z3 ]/σ3 =
!
z3F(z)dz
"#
#
$
% 3 o Kurtosis k: 4th moment (r = 4)
k = E [ z4 ]/σ4 =
!
z4F(z)dz
"#
#
$
% 4
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 19
• Autocorrelation function
R(l) =
!
limL"#
1
Lz(x)z(x + l)dx
$L / 2
L / 2
%
R(l) =
!
1
N "1z(x)z(x + l)
x=1
N"1
# • Power spectral density function PSD
PSD(ω) =
!
2
"R(l)cos#ldl
0
$
% = Fourier transform of autocorrelation function o Frequency domain information on profile
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 20
FRACTAL MODELS • Surface roughness characterization • Describes natural "random" processes • Poor model: man-made surfaces • Roughness characterized via spatial frequency ω:
o Surface profile z = z(x)
o Fourier transform
!
Z(") = z(x)e# j"x
#$
$
% dx
o Power spectral density:
!
PSD = Z(")2
o Plot log PSD versus log ω o Similar to Bode plot
• Fractal dimension D characterizes surface roughness
o Valid over several orders of magnitude o Describes bump on bump "random" processes
PSD of Atomic Force Microscope images of polycrystalline Si, with ~3nm RMS roughness. Bora, Plesha, Flater, Street & Carpick, “Multiscale roughness of MEMS surfaces”, 2004 ASME.
Local curve equation:
!
PSD(") =C
" 5#2D
ME 383S-Lubrication, Wear & Bearing Techn. M.D. Bryant January 17, 2006 21
Fractal Dimension & Geometry • Physical geometry described by fractal dimension D
D Object
0 point 1 line 2 area 3 volume
• Fractal geometry describes how object fills a space
• Note repeated structure at different lengthscales
• Repeated structure can capture “bumps on bumps” of nature’s surfaces