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Homework 1
1
Consider the following function giving the asperity height z of a certain surface with mean
asperity height µ = 2 and standard deviation of asperity heights σ = 0.5 in micrometers, as
a function of the variable R which is a uniformly distributed random number ∈ [0, 1]:
z =µ+σ
R0.135 − (1 − R)0.135
0.1975
Use the Excel function RAND()to create 1000 simulated (pseudo) random numbers R,
substitute in the above equation and assume that the computed values of z represent asperity
heights measured with a profilometer at distances of 1 micrometer along the surface.
a) Plot the surface profile thus obtained
b) Plot the histogram of asperity heights
c) Use numerical integration to estimate the Skewness (S) and Kurtosis (K) of the surface.
2
Do some research on practical methods that are available for the characterization of surface
roughness, select an instrument or method you would like to recommend and write a 200
word long essay describing its features and capabilities.
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