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