Application of Fourier Series for Evaluation of Roundness Profiles in Metrology
 
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Slovak University of Technology in Bratislava, Faculty of Materials Science and Technology in Trnava, J. Bottu 25, 917 24 Trnava, Slovakia
CORRESPONDING AUTHOR
Ingrid Görögová   

Slovak University of Technology in Bratislava, Faculty of Materials Science and Technology in Trnava, J. Bottu 25, 917 24 Trnava, Slovakia
Publish date: 2019-12-01
 
Adv. Sci. Technol. Res. J. 2019; 13(4):30–38
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ABSTRACT
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 al-lows transforms discrete data to frequency data or vice versa, transforming frequency data to 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. There are mentioned mathematical relationships for the practical use of harmonic analysis and the detailed method of determining the actual phase. General relationships do not give accurate results, since the phase shift quadrant. The results of the harmonic analysis authors applied graphically 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. 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.