On stability of the dual-frequency motion modes of a single-mass vibratory machine with a vibration exciter in the form of a passive auto-balancer

Authors

DOI:

https://doi.org/10.15587/1729-4061.2018.128265

Keywords:

inertial vibration exciter, dual-frequency vibrations, auto-balancer, single-mass vibratory machine, Sommerfeld effect, motion stability

Abstract

By employing computational experiments, we investigated stability of the dual-frequency modes of motion of a single-mass vibratory machine with translational rectilinear motion of the platform and a vibration exciter in the form of a passive auto-balancer.

For the vibratory machines that are actually applied, the forces of external and internal resistance are small, with the mass of loads much less than the mass of the platform. Under these conditions, there are three characteristic rotor speeds. In this case, at the rotor speeds:

– lower than the first characteristic speed, there is only one possible frequency at which loads get stuck; it is a pre-resonance frequency;

– positioned between the first and second characteristic speeds, there are three possible frequencies at which loads get stuck, among which only one is a pre-resonant frequency;

– positioned between the second and third characteristic speeds, there are three possible frequencies at which loads get stuck; all of them are the over-resonant frequencies;

– exceeding the third characteristic speed, there is only one possible frequency at which loads get stuck; it is the over-resonant frequency and it is close to the rotor speed.

Under a stable dual-frequency motion mode, the loads: create the greatest imbalance; rotate synchronously as a whole, at a pre-resonant frequency. The auto-balancer excites almost perfect dual-frequency vibrations. Deviations of the precise solution (derived by integration) from the approximated solution (established previously using the method of the small parameter) are equivalent to the ratio of the mass of loads to the mass of the entire machine. That is why, for actual machines, deviations do not exceed 2 %.

There is the critical speed above which a dual-frequency motion mode loses stability. This speed is less than the second characteristic speed and greatly depends on all dimensionless parameters of the system.

At a decrease in the ratio of the mass of balls to the mass of the entire system, critical speed tends to the second characteristic speed. However, this characteristic speed cannot be used for the approximate computation of critical speed due to an error, rapidly increasing at an increase in the ratio of the mass of balls to the mass of the system. Based on the results of a computational experiment, we have derived a function of dimensionless parameters, which makes it possible to approximately calculate the critical speed.

Author Biographies

Volodymyr Yatsun, Central Ukrainian National Technical University Universytetskyi ave., 8, Kropivnitskiy, Ukraine, 25006

PhD, Associate Professor

Department of Road Cars and Building

Gennadiy Filimonikhin, Central Ukrainian National Technical University Universytetskyi ave., 8, Kropivnitskiy, Ukraine, 25006

Doctor of Technical Sciences, Professor, Head of Department

Department of Machine Parts and Applied Mechanics

Antonina Haleeva, Mykolayiv National Agrarian University Georgiya Gongadze str., 9, Mykolayiv, Ukraine, 54020

PhD, Associate Professor

Department of tractors and agricultural machinery, operating and maintenance

Andrey Nevdakha, Central Ukrainian National Technical University Universytetskyi ave., 8, Kropivnitskiy, Ukraine, 25006

PhD

Department of Machine Parts and Applied Mechanics

References

  1. Bukin, S. L., Maslov, S. G., Ljutyj, A. P., Reznichenko, G. L. (2009). Intensification of technological processes through the implementation of vibrators biharmonic modes. Enrichment of minerals, 36 (77)-37 (78), 81–89.
  2. Kryukov, B. I. (1967). Dinamika vibratsionnyih mashin rezonansnogo tipa [Dynamics of vibratory machines of resonance type]. Kyiv: Naukova dumka, 210.
  3. Lanets, O. S. (2008). Vysokoefektyvni mizhrezonansni vibratsiyni mashyny z elektromahnitnym pryvodom (Teoretychni osnovy ta praktyka stvorennia) [High-Efficiency Inter-Resonances Vibratory Machines with an Electromagnetic Vibration Exciter (Theoretical Bases and Practice of Creation]. Lviv: Publishing house of Lviv Polytechnic National University, 324.
  4. Filimonikhin, G. B., Yatsun, V. V. (2015). Method of excitation of dual frequency vibrations by passive autobalancers. Eastern-European Journal of Enterprise Technologies, 4 (7 (76)), 9–14. doi: 10.15587/1729-4061.2015.47116
  5. Artyunin, A. I. (1993). Research of motion of the rotor with autobalance. Proceedings of the higher educational institutions, 1, 15–19.
  6. Filimonikhin, G. (2004). Zrivnovazhennia i vibrozakhyst rotoriv avtobalansyramy z tverdymy koryhuvalnymy vantazhamy [Balancing and protection from vibrations of rotors by autobalancers with rigid corrective weights]. Kirovohrad: KNTU, 352.
  7. Sommerfeld, A. (1904). Beitrage zum dinamischen Ausbay der Festigkeislehre. Zeitschriff des Vereins Deutsher Jngeniere, 48 (18), 631–636.
  8. Yatsun, V., Filimonikhin, G., Dumenko, K., Nevdakha, A. (2017). Equations of motion of vibration machines with a translational motion of platforms and a vibration exciter in the form of a passive auto-balancer. Eastern-European Journal of Enterprise Technologies, 5 (1 (89)), 19–25. doi: 10.15587/1729-4061.2017.111216
  9. Yatsun, V., Filimonikhin, G., Dumenko, K., Nevdakha, A. (2017). Search for two-frequency motion modes of single-mass vibratory machine with vibration exciter in the form of passive auto-balancer. Eastern-European Journal of Enterprise Technologies, 6 (7 (90)), 58–66. doi: 10.15587/1729-4061.2017.117683
  10. Filimonikhin, G. B., Filimonikhina, I. I., Pirogov, V. V. (2014). Stability of Steady-State Motion of an Isolated System Consisting of a Rotating Body and Two Pendulums. International Applied Mechanics, 50 (4), 459–469. doi: 10.1007/s10778-014-0651-9
  11. Ruelle, D. (1989). Elements of Differentiable Dynamics and Bifurcation Theory. Academic Press Inc., 187.
  12. Nayfeh, A. H. (1993). Introduction to Perturbation Techniques. New York, United States: John Wiley and Sons Ltd., 533.
  13. Blekhman, I. I. (1988). Synchronization in Science and Technology. New York: ASME Press, NY, USA, 255.
  14. Lanets, O. V., Shpak, Ya. V., Lozynskyi, V. I., Leonovych, P. Yu. (2013). Realizatsiya efektu Zommerfelda u vibratsiynomu maidanchyku z inertsiynym pryvodom [Realization of the Sommerfeld effect in a vibration platform with an inertia drive]. Avtomatyzatsiya vyrobnychykh protsesiv u mashynobuduvanni ta pryladobuduvanni, 47, 12–28. Available at: http://nbuv.gov.ua/UJRN/Avtomatyzac_2013_47_4
  15. Hou, Y., Fang, P. (2016). Investigation for Synchronization of a Rotor-Pendulum System considering the Multi-DOF Vibration. Shock and Vibration, 2016, 1–22. doi: 10.1155/2016/8641754
  16. Ryzhik, B., Sperling, L., Duckstein, H. (2004). Non-synchronous Motions Near Critical Speeds in a Single-plane Autobalancing Device. Technische Mechanik, 24 (1), 25–36.
  17. Lu, C.-J., Tien, M.-H. (2012). Pure-rotary periodic motions of a planar two-ball auto-balancer system. Mechanical Systems and Signal Processing, 32, 251–268. doi: 10.1016/j.ymssp.2012.06.001
  18. Artyunin, A. I., Alhunsaev, G. G., Serebrennikov, K. V. (2005). Primenenie metoda razdeleniya dvizheniy dlya issledovaniya dinamiki rotornoy sistemyi s gibkim rotorom i mayatnikovyim avtobalansirom [The application of the method of separation of movements to study the dynamics of a rotor system with a flexible rotor and a pendulum autobalance]. Izvestiya vysshih uchebnyh zavedeniy. Mashinostroenie, 9, 8–14.
  19. Artyunin, A. I., Eliseyev, S. V. (2013). Effect of “Crawling” and Peculiarities of Motion of a Rotor with Pendular Self-Balancers. Applied Mechanics and Materials, 373-375, 38–42. doi: 10.4028/www.scientific.net/amm.373-375.38

Downloads

Published

2018-04-10

How to Cite

Yatsun, V., Filimonikhin, G., Haleeva, A., & Nevdakha, A. (2018). On stability of the dual-frequency motion modes of a single-mass vibratory machine with a vibration exciter in the form of a passive auto-balancer. Eastern-European Journal of Enterprise Technologies, 2(7 (92), 59–67. https://doi.org/10.15587/1729-4061.2018.128265

Issue

Vol. 2 No. 7 (92) (2018): Applied mechanics

Section

Applied mechanics

License

Copyright (c) 2018 Volodymyr Yatsun, Gennadiy Filimonikhin, Antonina Haleeva, Andrey Nevdakha

Creative Commons License

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

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.