Zastosowanie TKEO w procesie automatycznego wyważania wirnika

Application of TKEO in the process of automatic balancing of the rotor

  • Jędrzej Blaut Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie, Wydział Inżynierii Mechanicznej i Robotyki
  • Rafał Rumin Akademia Górniczo-Hutnicza w Krakowie, Wydział Zarządzania
  • Jacek Cieślik Akademia Górniczo-Hutnicza w Krakowie, Wydział Inżynierii Mechanicznej i Robotyki
  • Paweł Hyla Akademia Górniczo-Hutnicza w Krakowie, Wydział Inżynierii Mechanicznej i Robotyki
  • Janusz Szpytko Akademia Górniczo-Hutnicza w Krakowie, Wydział Inżynierii Mechanicznej i Robotyki
Keywords: TKEO, Teagear-Kaiser, Operator Energetyczny, Teagear-Kaisera, active vibration control, rotating machinery, balancing rotor, controller, rotor dynamics


The article presents an example of application of the Teager-Kaiser Energy Operator in automatic rotor balancing. The Teagear Kaiser Energy Operator is a signal analysis method, which allows for some mechanical objects to estimate energy changes in Newtonian terms by means of a displacement signal.

Rotors are a structural element that rotates around an axis. Traditional balancing of the rotors is based on the introduction of correction masses, the aim of which is to reduce vibrations and noise during machine operation. Traditional balancing of the rotors is also possible. It can be realized by a system of correction masses with variable distance from the axis of rotation. The change of the correction mass distance from the axis of rotation influences the change of inertia of the object and thus reduces the unbalance. Depending on the design of the device, the modernization may assume extension or replacement of individual elements. Improvement of the operation of the device requires selection of elements depending on the overall interference in the operation of the machine and the impact on the operation of the entire device. The presented original method of automatic unbalance control with the use of the Energy Operator with the selection of parameters has been performed on a real laboratory stand.


1. Blaut J., Korbiel T., Batko W. 2016. Application of the Teager-Kaiser energy operator to detect instability of a plain bearing. Dia-gnostyka 17
2. Rumin R., Cieślik J., Mańka M., Szlachetka A., Maliszewski M. 2012. Układ do redukcji drgań urządzeń wirujących. Zgłoszenie patentowe.
3. Rumin R., Cieślik J. 2010. Układ do automatycznego wyważania wirników przy pomocy ciągłej zmiany rozkładu masy korekcyjnej. Drgania w Układach Fizycznych vol. 24: 337–342
4. Maragos P., Kaiser J.F., Quatieri T. F.. 1993. Energy separation in signal modulations with application to speech analysis. IEEE Transactions on Signal Processing, Vol.41, No.10,1993,pp.3024 – 3051
5. Vakman D.. 1996. On the analytic signal, the TeagerKaiser energy algorithm, and other methods for defining amplitude and frequency. IEEE Transactions on Signal Processing, Vol.44, No.4, ,pp.791– 797
6. F. C. Nelson, A Brief History of Early Rotor Dynamics, J. of Sound and Vib., 37 no 6, (2003).
7. S. Zhou and J. Shi , Active Balancing and Vibration Control of Rotating Machinery: A Survey, The Shock and Vibration Digest (2001).
8. R. Rumin and J. Cieślik, System for Automatic Rotor Balancing Using a Continuous Change of the Correction Mass Distribution, Vibrations in Physical Systems, vol. 24, (2010), 337-342.

9. S. V. Pantankar and D. B. Spalding, A calculation processure for heat, mass and momentum transfer in the three-dimensional parabolic flows, International Journal of Heat Mass Transfer, 15, (1972), 1787-1806. 

10. T. C. Papanastasiou, G. C. Georgiou, A. N. Alexandrou, Viscous Fluid Flow: Chapter 6 - Unidirectional Flows, CRC Press, (2000). 

11. J.P. Vanyo, Rotating Fluids in Engineering and Science, Dover Publications, (1993).
12. R. Gryboś, Podstawy mechaniki płynów. Cz. 1, Kinematyka, dynamika cieczy i gazów, hydrostatyka, Cz. 2, Turbulencja, metody numeryczne, zastosowania techniczne, Wyd. Naukowe PWN, Warszawa, (1998).
13. R. Puzyrewski, J. Sawicki, Podstawy mechaniki płynów i hydrauliki, Wydaw. Naukowe PWN, (2000).
14. Gretchen B. Murri, Jeffery R. Schaffb, Fatigue Life Methodology For Tapered Hybrid Composite Flexbeams.
15. Maissan, T.M., The Effects of the Black Blades on Surface Temperatures for Wind Turbines, in W.A.T. J., Editor 2001, Université du Québec à Rimouski: Canada.
16. Alsabagh, Abdel, et al. "A Review of the Effects of Ice Accretion on the Structural Behavior of Wind Turbines." Wind Engineering 37.1 (2013): 59-70.
17. Teager , H. i Teager, S. 1983. A Phenomenological Model for Vowel Production in the Vocal Tract. San Diego: College-Hill Press.
18. Henríquez, P., White, P., Alonso, J., Ferrer, C. i Travieso, C. 2011. Application of Teager-Kaiser Energy Operator to the Analysis of Degradation of a Helicopter Input Pinion Bearing. The International Conference Surveillance 6.
19. Antoniadou, I., Manson, G., Staszewski, W., Barszcz, T. i Wordena, K. 2015, A time–frequency analysis approach for condition monitoring of a wind turbine gearbox under varying load conditions. Mechanical Systems and Signal Processing, strony 188–216.
20. Rumin R., Cieślik J. 2011, Vibration Control of Rotating Machinery. Conference Active Noise and Vibration Control Methods, Krakow-Wojanow, Poland.
Eksploatacja i Testy/Exploitation and Tests