The influence of imbalances on the dynamic characteristics of the laboratory centrifuge HERMLE Z306

Authors

DOI:

https://doi.org/10.20535/2521-1943.2024.8.1(100).294820

Keywords:

rotor, centrifuge, imbalance, modeling, amplitude, frequency

Abstract

Laboratory centrifuges are used in various industries. During operation, vibrations occur that lead to resonant frequencies, which in turn impair functionality. This paper presents an overview of the computational model of the HERMLE Z306 laboratory centrifuge used in medical laboratories to separate mixtures of different fractions to determine the dynamic characteristics. The zones of stable operation of the centrifuge and the influence of the rotation speed on the natural frequencies are analytically determined. Experimental results are presented with the influence of imbalances on the dynamic characteristics of the HERMLE Z306 centrifuge. As a result of the modeling, the amplitude-frequency characteristics are determined and a Campbell diagram is constructed.
Modeling of dynamic processes in laboratory centrifuges by studying the influence of imbalances on the quality of mixture separation. Determination of zones of stable operation of the centrifuge.
Construction of amplitude-frequency characteristics of the centrifuge, determination of zones of stable operation of the laboratory centrifuge during separation and Campbell diagram showing the dependence of natural frequencies on the rotation speed of the HERMLE Z306 centrifuge. This diagram makes it possible to determine the resonance zones.
Based on the use of the Lagrange equation of the second kind, a model is obtained that makes it possible to determine the zones of stable operation of the centrifuge. Using experimental equipment, determine the frequency response of the centrifuge and analyze the Campbell diagram to determine the resonance zones.
The zones of stable operation of a laboratory centrifuge were analytically determined. The amplitude-frequency characteristics of the HERMLE Z306 centrifuge were constructed, the trajectories of the free end of the shaft were built taking into account the corresponding imbalances, and the resonance zones were experimentally determined.
Experimental studies have shown that the free end of a laboratory centrifuge shaft moves along a surface whose shape and, accordingly, the path of movement depend on both the angles of rotation and translational movement that arise as a result of deformations of elastic supports. The analytical and experimental studies made it possible to identify unstable modes and thereby determine the areas of the centrifuge's operating modes. The separation process will be stable if the roots of the equation have a negative real part, and moreover, the motion will be asymptotically stable in the presence of resistance forces. An experimental technique for determining the dynamic parameters of the centrifuge has been developed. On its basis, the effect of the rotation speed on the natural frequencies was determined.

References

  1. J. Fischer and J. Strackeljan, “Stability Analyses of High Speed lab centrifuges considering internal damping in rotor-shaft joints”, Technische Mechanik, vol. 26, no. 2, pp. 131–147, 2006. Available: https://journals.ub.ovgu.de/index.php/techmech/article/view/882.
  2. A. Babenko, Ia. Lavrenko and M. Kurenkov, “Influence of gyroscopic effect on fluctuations of the centrifuge shaft”, Bulletin of the National Technical University of Ukraine "Kyiv Polytechnic Institute", vol. 65, pp. 166–174, 2012.
  3. J. Fischer and J. Strackeljan, “FEM-Simulation and stability analyses of high speed rotor systems”, 7th International Conference on Rotor Dynamics, Vienna, Austria, 2006.
  4. M. Zejtman and M. Kushul, “Izgibnye kolebaniya vertikalnyh rotorov v gravitacionnom pole”, Mashinovedenie, no. 5, 1968.
  5. M. Kushul, “Dvizhenie giroskopa s gibkoj osyu pod dejstviem sily tyazhesti i uprugih svyazej pri malyh uglah nutacii i ustojchivosti ego vertikalnogo vrasheniya”, PMM, vol. 32, no. 4, 1968.
  6. K. Magnus, “Die Schwingungen des Kreisels mit der Massen elastisch gekoppelt ist”, Proc. of the conference on vibration at Göttingen and Kassel, bd. 20, heft 3, 1940.
  7. L. Maunder, “Sobstvennye chastoty kolebanij svobodnogo giroskopa s uprugim valom, ustanovlennogo v kardanovom podvese”, Mehanika, no. 5 (69), 1961.
  8. S. Harsha, “Nonlinear dynamic analysis of a high-speed rotor supported by rolling element bearings”, Journal of Sound and Vibration, vol. 290, no. 1-2, pp. 65–100, 2006. DOI: https://doi.org/10.1016/j.jsv.2005.03.008.
  9. A. Uippel and L. Maunder, “Kolebaniya svobodnogo giroskopa s neodnorodno uprugoj osyu”, Mehanika, no. 6 (88), 1964.
  10. V. Krementulo, “Application of the second method of liapunov in the investigation of the steady motion of a gyroscope when elastic properties of the rotor axis are taken into account”, Journal of Applied Mathematics and Mechanics, vol. 25, no. 3, pp. 859-865, 1961. DOI: 10.1016/0021-8928(61)90057-0.
  11. C.-W. Lee, Evolution of Frequency-Speed Diagram in Rotating Machinery, in IUTAM Symposium on Emerging Trends in Rotor Dynamics, vol. 1011. Dordrecht: Springer Netherlands, 2010, pp. 39-50. DOI: https://doi.org/10.1007/978-94-007-0020-8_4.
  12. S. Harsha, “Nonlinear dynamic analysis of an unbalanced rotor supported by roller bearing”, Chaos, Solitons and Fractals, vol. 26, no. 1, pp. 47–66, 2005. DOI: https://doi.org/10.1016/j.chaos.2004.12.014.
  13. Y. Ishida, T. Inoue, T. Kagawa and M. Ueda, “Nonlinear Analysis and Experiments on Torsional Vibration of a Rotor with a Centrifugal Pendulum Vibration Absorber”, Journal of System Design and Dynamics, vol. 2, no. 3, pp. 715–726, 2008. DOI: https://doi.org/10.1299/jsdd.2.715.
  14. S.-T. Wu, J.-Y. Chen, Y.-C. Yeh and Y.-Y. Chiu, “An active vibration absorber for a flexible plate boundary-controlled by a linear motor”, Journal of Sound and Vibration, vol. 300, no. 1–2, pp. 250–264, 2007. DOI: https://doi.org/10.1016/j.jsv.2006.08.015.
  15. J. Strackeljan, A. Babenko and Ia. Lavrenko, “Necessary conditions of stability moving parts of rotor centrifuge”, Bulletin of the National Technical University of Ukraine "Kyiv Polytechnic Institute". Series: Mechanical engineering, no. 3 (72), pp. 18–23, 2014.
  16. Ia. Lavrenko, T. Sydora and M. Sushchenko, “Determination of dynamic characteristics of the centrifuge shaft”, Scientific Journal of TNTU, vol. 112, no. 4, pp. 32–40, 2023. DOI: https://doi.org/10.33108/visnyk_tntu2023.04.032.
  17. V. Nesterenko, Avtomaticheskaya balansirovka rotorov priborov i mashin so mnogimi stepenyami svobody. Tomsk, TGU, 1985, 84 p.
  18. L. Bakaeva and L. Suevalova, Static and dynamic balancing of rotating parts of machines and mechanisms. Habarovsk, Publisher PNU, 2008.
  19. J. S. Rao, T. N. Shiau, J. R. Chang, “Theoretical analysis of lateral response due to torsional excitation of geared rotors”, Mech. Mach. Theory, vol. 33, no. 6, pp. 761–783, 1998. DOI: https://doi.org/10.1016/S0094-114X(97)00056-6.
  20. Y. Zhang, W. Wang, D. Wei, G. Wang, J. Xu and K. Liu, “Dynamic stability of unbalance-induced vibration in a turbocharger rotor-bearing system with the nonlinear effect of thermal turbulent lubricating fluid film”, Journal of Sound and Vibration, vol. 528, p. 116909, 2022. DOI: https://doi.org/10.1016/j.jsv.2022.116909.
  21. Y. Kang, S. Cao, Y. Hou and N. Chen, “Analysis of backward whirling characteristics of a dual-rotor system caused by unbalance”, Measurement, vol. 203, p. 111982, 2022. DOI: https://doi.org/10.1016/j.measurement.2022.111982.
  22. H. F. de Castro, K. L. Cavalca and R. Nordmann, “Whirl and whip instabilities in rotor-bearing system considering a nonlinear force model”, Journal of Sound and Vibration, vol. 317, no. 1-2, pp. 273–293, 2008. DOI: https://doi.org/10.1016/j.jsv.2008.02.047.
  23. G. Genta, Dynamics of Rotating Systems. New York, NY: Springer US, 2005. DOI: https://doi.org/10.1007/0-387-28687-X.
  24. G. Filimonihin, Zrivnovazhennya i vibrozahist rotoriv avto balansirami z tverdimi koriguvalnimi vantazhami. Kirovohrad: KNTU, 2004, 352 p.
  25. P. Koutsovasilis, “Automotive turbocharger rotordynamics: Interaction of thrust and radial bearings in shaft motion simulation”, Journal of Sound and Vibration, vol. 455, pp. 413–429, 2019. DOI: https://doi.org/10.1016/j.jsv.2019.05.016.
  26. P. Bonello, “The extraction of Campbell diagrams from the dynamical system representation of a foil-air bearing rotor model”, Mechanical Systems and Signal Processing, vol. 129, pp. 502–530, 2019. DOI: https://doi.org/10.1016/j.ymssp.2019.04.018.

Downloads

Published

2024-03-19

How to Cite

[1]
A. Babenko and I. Lavrenko, “The influence of imbalances on the dynamic characteristics of the laboratory centrifuge HERMLE Z306”, Mech. Adv. Technol., vol. 8, no. 1(100), pp. 62–72, Mar. 2024.

Issue

Vol. 8 No. 1(100) (2024)

Section

Mechanics

License

Copyright (c) 2024 Андрій Бабенко, Ярослав Лавренко

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The ownership of copyright remains with the Authors.
 
Authors may use their own material in other publications provided that the Journal is acknowledged as the original place of publication and National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute” as the Publisher.

Authors who publish with this journal agree to the following terms:

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under CC BY 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.

  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.

  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work