期刊名称：Advances in Science and Technology Research Journal
印刷版ISSN：2080-4075
电子版ISSN：2299-8624
出版年度：2019
卷号：13
期号：4
页码：30-38
DOI：10.12913/22998624/113620
语种：English
出版社：Society of Polish Mechanical Engineers and Technicians
摘要：A Fourier series is an expansion of a periodic function f(x) in terms of an infnite sum of sines and cosines. Fourierseries make use of the orthogonality relationships of the sine and cosine functions. The computation and study ofFourier series are known as harmonic analysis. It is a useful way to break up an arbitrary periodic function intoa set of simple terms that can be plugged in, solved individually, and then recombined to obtain the solution tothe original problem or an approximation to it to whatever accuracy is desired or practical. This paper deals withthe mathematical basics of Fourier series using trigonometric functions. This is the basic for a discrete Fouriertransform. 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 andthe Fourier transform to metrology, specifcally on the roundness profle. The mathematical relationships for thepractical 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 analysiswere applied graphically by the authors on a concrete example of a roundness profle. The individual harmoniccomponents are shown in the linear and polar graphs as well as the resulting roundness profle. The Fourier analysis knowledge will contribute to a better analysis of the roundness profles measured on the drawn tubes that willbe investigated in the research project.
关键词：Fourier series; harmonic analysis; roundness profle; actual phase
