PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Tytuł artykułu

Application of Fourier Series for Evaluation of Roundness Profiles in Metrology

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Twórcy
  • Slovak University of Technology in Bratislava, Faculty of Materials Science and Technology in Trnava, J. Bottu 25, 917 24 Trnava, Slovak Republic
  • Slovak University of Technology in Bratislava, Faculty of Materials Science and Technology in Trnava, J. Bottu 25, 917 24 Trnava, Slovak Republic
Bibliografia
  • 1. Adamczak, S., Makieła, W., Stepien, K. Investigating Advantages and Disadvantages of the Anaysis of a Geometrical Surface Structure with the Use of Fourier and Wavelet Transform. Metrology and Meaurement Systems 17, 2010, DOI 10.2478/ v10178-010-0020-x.
  • 2. Adamczak, S., Makieła, W., Stepien, K. Fourier Transform vs. wavelet transform in analysis of geometrical surface structure. 10th International Scientific Conference - New Ways in Manufacturing Technologies, 77-84, 2010.
  • 3. Bandara, L. Functional calculus and harmonic analysis in geometry. https://arxiv.org/abs/1812.11795, 2018.
  • 4. Clue, V. Harmonic analysis. Proceedings of the 2004 IEEE Electro/Information Technology Conference. Milwaukee USA, 2004, 53–58.
  • 5. Görög, A., Görögová, I. Current concept of geometrical accuracy. Research papers Faculty of Materials Science and Technology Slovak University of Technology in Trnava, 22(34), 2014, 43-50, ISSN 1336-1589.
  • 6. Görögová, I. Technological Heredity in Bearing Production. Plzeň: Aleš Čeněk, ISBN 978-80- 7380-599-9, 2016.
  • 7. Grafakos, L., Oliveira, S.D., Pramanik, M., Seeger, A., Stovall, B. Some Problems in Harmonic Analysis. https://arxiv.org/pdf/1701.06637.pdf, 2017.
  • 8. Karateev, D., Kravchuk, P., Simmons-Duffin, D. Harmonic Analysis and Mean Field Theory. https:// arxiv.org/abs/1809.05111, 2018.
  • 9. Kocsis, P., Balla, P., Antal, Á. Wavelet-based Optimization of Surface Reconstruction. Acta Polytechnica Hungarica, 15 (4), 179-198, ISSN 1785- 8860, DOI: 10.12700/APH.15.4.2018.4.1, 2018.
  • 10. Kowalski, M. Wiśniewska, M. Karolczak, P. Stančeková, D. Applicability of selected groups of roughness parameters for description of surface layer of flat - top “plateau” structures. Advances in science and technology research journal, Vol.: 10 Issue: 32, 2016 Pages: 32-39, ISSN 2299-8624.
  • 11. Krantz, S.G. Harmonic analysis. WIREs Comp Stat 3, 163-167, DOI:10.1002/wics.143, 2011.
  • 12. Li, J. Harmonic analysis of stationary measures. General Mathematics [math.GM]. Université deBordeaux, https://tel.archives-ouvertes.fr/tel- 01975306/document, 2018.
  • 13. Némedi, I., Sekulić, M., Radlovački, V., Hodolič, J., Hadžistević, M., Takács, M. Method for Determining Roundness and Actual Form of Circular Workpiece Cross Sections, Acta Polytechnica Hungarica, 14(6), 2017, 169-184, ISSN 1785-8860 DOI: 10.12700/APH.14.6.2017.6.10.
  • 14. Pérez de Viñaspre, F.P., Pérez Pascual, P.A. Harmonic Analysis: The Aplication of ‘Theoretical Cycles’ to the Economic Analysis. Economic cycles, 2 (1), 2001.
  • 15. Romanovskij, P.I. Fourier series. Field theory. Analytical and special functions. Laplace transform. Praha, SNTL, 1964.
  • 16. Sankararaman, S., Varun, V.S., Balakrishnan, A., Devi, H.V. Harmonic analysis of rectifier and amplifier outputs. 4th International Seminar of Swamy Vivekananda Association of Science and Humanities (SVASH) At: Vyloppilli Samskrithi Bhavan, Trivandrum, Kerala, 2018.
  • 17. Sawano, Y. Elementary Facts on Harmonic Analysis. Theory of Besov Spaces, Developments in Mathematics 56, DOI: 10.1007/978-981-13-0836- 9_1, 2018.
  • 18. Smith, S.W. The Scientist and Engineer’s Guide to Digital Signal Processing, California Technical Publishing, San Diego, California, ISBN 0-9660176-6-8, 1999.
  • 19. Stancekova, D. Mrazik, J. Rybicka, I. Naprstkova, N. Kraus, P. An Impact of Technological Conditions on Surface Burning in Grinding of the Orbit. Advances In Science And Technology, 12 (4), 2018, 19-27, ISSN 2299-8624.
  • 20. Sui, W., Zhang, D. Four Methods for Roundness Evaluation. Physics Procedia, Vol. 24, part C, 2012, 2159–2164. DOI: 10.1016/j.phpro. 2012.02.317.
  • 21. Viitala, R., Widmaier, T., Hemming, B., Tammi, K., Kuosmanen, P. Uncertainty analysis of phase and amplitude of harmonic components of bearing inner ring four-point roundness measurement. Precis. Eng., vol. 54, 2018, 118–130.
  • 22. Walther, E. et al. Technical formulas. Bratislava, Alfa, 1984.
Uwagi
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-6187a6bb-ba9d-4edc-aed9-ede80aad4115
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.