A Fourier series is an expansion of a periodic function f(x) in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions. The computation and study of Fourier series are known as harmonic analysis. It is a useful way to break up an arbitrary periodic function into a set of simple terms that can be plugged in, solved individually, and then recombined to obtain the solution to the original problem or an approximation to it to whatever accuracy is desired or practical. This paper deals with the mathematical basics of Fourier series using trigonometric functions. This is the basic for a discrete Fourier transform. It allows transforming the discrete data to the frequency data or vice versa, i.e. transforming the frequency data to the discrete data. The most important part of the article is the application of the Fourier series and the Fourier transform to metrology, specifically on the roundness profile. The mathematical relationships for the practical use of harmonic analysis and the detailed method of determining the actual phase were described. General relationships do not give accurate results, due to the phase shift quadrant. The results of the harmonic analysis were applied graphically by the authors on a concrete example of a roundness profile. The individual harmonic components are shown in the linear and polar graphs as well as the resulting roundness profile. The Fourier analysis knowledge will contribute to a better analysis of the roundness profiles measured on the drawn tubes that will be investigated in the research project.

In order to increase productivity, machining times and market competitiveness of machining production systems, it is important to continuously develop existing technological solutions. The paper deals with surface roughness and roundness after roller burnishing outer rotary surface. Roller burnishing was applied on turned surfaces with different surface roughness. Each outer rotary surface was roller burnished twice with the same conditions (pressing force, peripheral speed of machine part, feed of tool). The parameters of the surface roughness Ra, Rq and Rt were measured after each single roller burnishing. The results show that the surface roughness is decreasing after the first roller burnishing cycle (additional roller burnishing had only negligible influence on surface roughness) and the original surface roughness has a significant influence on change of surface roughness after roller burnishing.