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Homework 2
Surface Characterization
Answers
1
Find a scholarly recent publication describing the effect of a manufacturing processes on the
nature and features of a metal surface and write a 100 word essay summarizing it.
Answer.- Article by Z. Rimuza, ”Tribology of Polymers”, Archives of Civil and Mechanical Engineering, Vol. VII, No. 4, 2007, 177-184. Rimuza presents and overview of
key issues concerning the tribology of polymers. Many polymers are viscoelastic and exhibit very low values of surface energy, these, together with the long chain nature of their
molecular structures result in peculiar tribological behavior not encountered in metals and
ceramics. As with most frictional systems, adhesion and deformation mechanisms are directly involved in friction and wear. Rimuza first discusses Polymer on Non-polymer contacts
where, with appropriate pairing very low values of friction coefficient can be obtained. Mechanical and adhesive interactions play both important roles on the frictional behavior and
material transfer layers are often associated with wear. In the case of Polymer-on-Polymer
contacts, the phenomenon of stick-slip (brief periods of seizure followed by rapid motion) is
commonly observed and wear is also associated with transfer layers. Lubrication can be used
with polymers but care must be used to avoid weakening the material structure by chemical
modification.
2
Find a scholarly recent publication describing the effect of a surrounding atmosphere on
the nature and features of a freshly exposed metal surface and write a 100 word essay
summarizing it.
1
Answer.- Article by Asay et al. ”Macro to Nanoscale Wear Prevention via Molecular
Adsorption”, Langmuir, Vol. 24, 2008, 155-159. The authors investigated the adsorption of
pentanol molecules on clean single crystal silicon (100) surfaces covered with a thin (20 Å)
native oxide layer, focusing on the effect of the adsorbed alcohol on tribological phenomena in
MEMS devices. The silicon wafers were first exposed to pentanol under carefully controlled
conditions and ≈ 10Å saturated alcohol monolayers formed according to Langmuir-type
adsorption. Next the samples were tested by rubbing a 3 mm quartz sphere on the surface
and significant reductions in friction coefficient were demsontrated to result from alcohol
adsorption. Although various oligomers were identified, it was also noted that denuded,
scratched surfaces were quickly sealed with alcohol promoting continued enhanced lubricating
action. At the microscale, friction was tested using a MEMS sidewall friction device and
the reduction of friction due to friction due to alcohol adsorption was confirmed. Finally,
nanoscale friction tests were conducted using AFM further confirming the friction reducing
effects of adsorbed alcohol layers.
3
Identify a modern profilometer and write a brief 100 word essay describing its features.
Answer.- Nanovea offers a number of non-contact, optical profilometers. For details see
website at http://www.nanovea.com/Profilometers.html?gclid=CPvQgLqOuJ0CFado5Qod6gNMiw.
4
A certain surface is found to have an approximately Gaussian roughness distribution with
mean µ = 4 µm and standard deviation σ = 1 µm. Asperity heigh data has been determined
with a resolution of 1 µm along the direction tangential to the surface. Use the inverse transform method to create 1000 simulated asperity height data points to compute all relevant
statistical functions for the simulated surface and comment on your results.
Answer.- Simulated asperity heights conforming to a Gaussian distribution with mean
µ and standard deviation σ can be readily produced from the formula
z =µ+σ
R0.135 − (1 − R)0.135
0.1975
where R are values of (pseudo) random numbers uniformly distributed between 0 and 1.
Using the Microsoft application Excel, the required values of R are readily produced with the
2
function RAND(). All the statistical function values associated with the resulting sample are
then easily computed using intrisic Excel functions. Alternatively, the FORTRAN subroutine
RANDOM provided in class can be used to produce the required values of R and the program
provided also in class can compute all the necessary statistical functions.
5
The roughness of a certain surface is approximately described by a Weibull distribution with
cumulative distribution function given by
z
F (z) = 1 − exp (−( )4)
4
Obtain and plot the various statistical functions useful in the description of the surface.
Answer.- The following table summarizes the results
Function or Quantity
Expression and/or Value
Probability Density Function (f)
Mean (µ)
Standard Deviation (σ)
Skewness (Sk)
Kurtosis (K)
z3
exp (−( 4z )4 )
R ∞64
0 zfdz = 3.625
2
1
σ3
R∞
(z − µ) fdz = 1.034
R ∞0
(z
− µ)3 fdz = −0.082
0R
∞
1
4
σ4
0
(z − µ) fdz = 2.567
6
The following table summarizes experimental data on the asperity heights of a shot peened
aluminum surface in terms of the cumulative distribution function
z(µm)
1
F (z)(−) 0.005
2
0.05
3
4
5
0.22 0.5 0.8
6
7
0.95 0.99
8
0.9999
Use the data to obtain the various statistical functions useful in the description of the
surface.
Answer.- The cummulative probability distribution function associated with a Normal
distribution of mean m and standard deviation s is given by
1
m
z−m
1
F = erf( √ ) + erf( √ )
2
2
s 2
s 2
3
where
2
erf(x) = √
π
Z
x
exp(−ξ 2 )dξ
0
is the error function fo the argument x.
The data given can be plotted and then compared against a normal distribution of mean
µ = 4 and standard deviation σ = 1.2 to show that it is a good fit for such distribution.
This is to be expected since the roughness of the shot peened surface is the result of a large
number of random events. The calculated values of F from the above formula are
z(µm)
1
F (z)(−) 0.0057
2
0.0473
3
0.2018
4
0.4995
4
5
0.7972
6
0.9517
7
0.9933
8
0.9991