Calculate the standard deviation of the peaks and the roughn

Calculate the standard deviation of the peaks and the roughness average value for a surface texture where he peak ordinates distribution are governed by the following relationship; Z = (2 times 010^4 + L^2/16). where L is the sampling length interval. L = 1 mm. A sinusoidal and triangular profiles with wave length lambda as shown in the figure, calculate the relationships between the maximum amplitudes of the two profiles which give the same values of roughness, R_a and standard deviation, sigma. Expression for the sinusoidal and triangular profiles of wavelength lambda respectively are: Z(k) = A_o sin(2 pi x/lambda) and Z(x) = 4 A_1 x/lambda, where A_o and A_1 are the maximum amplitudes of the sinusoidal and rectangular profiles.

Solution

the standard devalitons of the peaks and the roughness average value for a surface texture where the peak

ordination texcure where the peak ordinates distrubution are governed by the following

the standard devalition of the peaks and the roughness average value for a surface tecture

where the peak ordinstion texcure where