Download HW04 - Beckman.pdf

Friction Wear and Lubrication of Materials
Homework # 4
Bill Beckman
1) The 2007 Nobel prize in chemistry was awarded to Gerhard Ertl for his investigations of fundamental processes
at gas-solid interfaces. Google "chemical processes on solid surfaces Nobel", download the commentary on Ertl's
work produced by the Nobel committee and create a 250 word essay highlighting the main points in the
commentary.
Gerhard Ertl was given the Nobel prize for his studies of chemical processes on solid surfaces. Ertl has been using
high-vacuum tests since the 1960s to observe interactions of atoms on pure bulk materials. Operating in a vacuum, any
miss or contaminated specimen could result in unreliable answers. Ertl developed these experimental processes that
now lead to stable and reliable results of pure surface interactions. Two interactions that he worked on in particular
were enriching fertilizer with nitrogen extracted from air, and carbon monoxide on platinum which is useful to the
automotive industry for developing cleaner exhaust gases.
Ertl’s detailed attention to surface test experiments have rendered reliable results for numerous material and
element combinations. Studying hydrogen’s behavior on various surfaces has led to generation of electricity in a fuel
cell. Understanding and improving the process nitrogen reacting to hydrogen to produce ammonia has benefited crop
growth. The catalyst iron helps in this reaction (Haber-Bosch process) as both elements can attach and more easily react
with one another. Nitrogen being introduced into the vacuum and onto the iron surface first would allow some of the
very strong bonds between nitrogen to break, paving the way for hydrogen to bond. One of Ertl’s biggest
accomplishments was the way he measured nitrogen concentration on the surface by shooting light particles at the
surface, which caused electrons to disperse. These electrons could be measured directly, or visually depicted as light
when returning back to their original position.
2) The attached Excel worksheet contains raw measured asperity elevation data as a function of distance along the
surface for a certain material surface (values in micrometers).
a) Compute the mean asperity height, adopt the computed value as the reference asperity height and create a
new column of transformed data showing the difference between the local asperity height and the reference
value.
zm = 2.959, see Excel sheet for |zi-zm|
b) Use the data to compute the values of Ra, and Rq.
Ra = 0.8196
Rq = 3.116
c) Use the data to construct a histogram. Check that the data is approximately normally distributed and find a
closed form expression for a good fit Gaussian. Compute then the mean µ, variance σ, Skewness Sk and Kurtosis
K. Comment on your results.
Histogram shows the data is isn’t normally distributed. Mean (3) values aren’t that close. 3-Parameter Weibull
fits the data well.
µ = 2.959 σ = 0.976 Sk = -0.195 K = 2.463
d) Compute values of the autocorrelation function and discuss.
The autocorrelation plot shows the data is fairly random, with a few spikes that indicate some correlation.
e) Compute the bearing ratio tp for various preselected asperity heights h* and also the bearing area curve for the
surface. Comment on your results.
The maximum asperity height was found to be 5.5µm. As can be seen in the graph, the bearing area doesn’t
change drastically from a height of 5.5µm to 4.2µm, but then increases steadily.
3) The contact angle of water on platinum has been measured to be ϴ = 40 degrees, while that on paraffin is ϴ =
110 degrees. Estimate the work of adhesion of water on platinum and water on parafin and comment.
Surface tension of water in contact with air at 20°C is 7.28E-2 N/m. From Dupre’s equation the work of adhesion is:
For a contact angle of ϴ = 40° on platinum and ϴ = 110° on paraffin, the work of adhesion is:
platinum, WSL = 0.129 J/m2
paraffin, WSL = 0.048 J/m2
The surface energy contact between water and platinum is much greater than water and paraffin
4) A cylindrical water bridge (radius r = 0.01 m, thickness h = 0.0001 m) forms between two flat platinum surfaces.
Estimate the adhesive force due to the bridge.
Assuming contact angles of 40° for water on platinum and surface tension property for water as above, the force of
adhesion is:
⁄
5) Carry out calculations to simulate the combined effect of a flat punch and a Hertzian pressure distribution.
Compare against the results obtained for the Hertzian pressure alone.
Johnson-Kendall-Roberts and Hertzian model in maple file. Resulting pressure distribution plot
6) The surface of a sample of Al-7075 alloy has been investigated using profilometry. The standard deviation of the
asperity heights was measured as s ≈1.4µm and the average tip radius of curvature was R = 5µm. Compute the
value of the plasticity index ψ and show that the asperities are expected to deform plastically. How small would
the standard deviation of asperity heights would have to be in order for the asperities to deform elastically?
Al-7075 material properties:
E = 72E9 Pa
σY = 500E6 Pa
H=1.5E9 Pa
Plasticity index can be found from:
√
Ψ<0.6, asperities primarily deformed elastically
Ψ>1, asperities primarily deformed plastically
Standard deviation for only elastic deformation must be: