Studying the excitation of resonance oscillations in a rotor on isotropic supports by a pendulum, a ball, a roller
DOI:
https://doi.org/10.15587/1729-4061.2019.182995Keywords:
passive auto-balancer, Sommerfeld effect, inertial vibration exciter, resonance vibration machine, bifurcation of motionsAbstract
We have analytically examined the steady motion modes of the system, composed of a balanced rotor on the isotropic elastic-viscous supports, and a load (a ball, a roller, a pendulum), mounted inside the rotor, thus enabling its relative motion. In this case, the pendulum is freely mounted onto the rotor shaft, while the ball or roller rolling without slipping along a ring track centered on the longitudinal axis of the rotor.
The physical-mathematical model of the system has been described. We have recorded differential equations of the system’s motion with respect to a coordinate system rotating at a constant speed of rotation in the dimensionless form.
All steady motion modes of the system have been defined under which a load rotates at a constant angular velocity. In the coordinate system that rotates synchronously to a load, these motions are stationary.
Our theoretical study has shown that under motion steady modes:
– in the absence of resistance forces in the system, a load rotates synchronously with the rotor;
– in the presence of resistance forces in the system, a load is lagging behind the rotor.
The load jamming regimes are the one-parameter families of steady motions. Each jamming mode is characterized by the corresponding jam frequency.
Depending on the system parameters, one, two, or three possible load jam velocities may exist. If, at any rotor speed, there is only a single angular velocity of a load jam, then the corresponding motion mode (a one-parameter family) is globally asymptomatically steady. If the number of jam velocities varies depending on the angular rotor speed, the asymptomatically steady are:
– the only existent mode of jamming (globally asymptomatically steady when there are no others);
– jamming modes with the smallest and greatest velocities.
A load jam mode with the lowest angular velocity (close to resonance) can be used in order to excite resonance oscillations in vibration machines. The highest frequency of a load jam is close to the rotor speed. This mode can be used to excite the non-resonance oscillations in vibration machinesReferences
- Filimonikhin, G., Yatsun, V. (2015). Method of excitation of dual frequency vibrations by passive autobalancers. Eastern-European Journal of Enterprise Technologies, 4 (7 (76)), 9–14. doi: https://doi.org/10.15587/1729-4061.2015.47116
- Filimonikhin, G., Filimonikhina, I., Ienina, I., Rahulin, S. (2019). A procedure of studying stationary motions of a rotor with attached bodies (auto-balancer) using a flat model as an example. Eastern-European Journal of Enterprise Technologies, 3 (7 (99)), 43–52. doi: https://doi.org/10.15587/1729-4061.2019.169181
- Filimonikhin, G., Yatsun, V., Filimonikhina, I., Ienina, I., Munshtukov, I. (2019). Studying the load jam modes within the framework of a flat model of the rotor with an autobalancer. Eastern-European Journal of Enterprise Technologies, 5 (7 (101)), 51–61. doi: https://doi.org/10.15587/1729-4061.2019.177418
- Green, K., Champneys, A. R., Lieven, N. J. (2006). Bifurcation analysis of an automatic dynamic balancing mechanism for eccentric rotors. Journal of Sound and Vibration, 291 (3-5), 861–881. doi: https://doi.org/10.1016/j.jsv.2005.06.042
- Artyunin, A. I. (1993). Issledovanie dvizheniya rotora s avtobalansirom. Izvestiya vysshih uchebnyh zavedeniy. Mashinostroenie, 1, 15–19.
- Artyunin, A. I., Eliseev, S. V., Sumenkov, O. Y. (2018). Experimental Studies on Influence of Natural Frequencies of Oscillations of Mechanical System on Angular Velocity of Pendulum on Rotating Shaft. Lecture Notes in Mechanical Engineering, 159–166. doi: https://doi.org/10.1007/978-3-319-95630-5_17
- 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: https://doi.org/10.4028/www.scientific.net/amm.373-375.38
- Jung, D., DeSmidt, H. (2017). Nonsynchronous Vibration of Planar Autobalancer/Rotor System With Asymmetric Bearing Support. Journal of Vibration and Acoustics, 139 (3). doi: https://doi.org/10.1115/1.4035814
- Jung, D. (2018). Supercritical Coexistence Behavior of Coupled Oscillating Planar Eccentric Rotor/Autobalancer System. Shock and Vibration, 2018, 1–19. doi: https://doi.org/10.1155/2018/4083897
- Ryzhik, B., Sperling, L., Duckstein, H. (2004). Non-synchronous Motions Near Critical Speeds in a Single-plane Auto-Balancing Device. Technische Mechanik, 24, 25–36.
- 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: https://doi.org/10.1016/j.ymssp.2012.06.001
- Jung, D., DeSmidt, H. A. (2016). Limit-Cycle Analysis of Planar Rotor/Autobalancer System Influenced by Alford's Force. Journal of Vibration and Acoustics, 138 (2). doi: https://doi.org/10.1115/1.4032511
- Antipov, V. I., Dentsov, N. N., Koshelev, A. V. (2014). Dynamics of the parametrically excited vibrating machine with isotropic elastic system. Fundamental research, 8, 1037–1042. Available at: http://www.fundamental-research.ru/ru/article/view?id=34713
- Strauch, D. (2009). Classical Mechanics: An Introduction. Springer. doi: https://doi.org/10.1007/978-3-540-73616-5
- Nayfeh, A. H. (1993). Introduction to Perturbation Techniques. Wiley, 536.
- Ruelle, D. (1989). Elements of Differentiable Dynamics and Bifurcation Theory. Academic Press, 196. doi: https://doi.org/10.1016/c2013-0-11426-2
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2019 Volodymyr Yatsun, Gennadiy Filimonikhin, Nataliia Podoprygora, Vladimir Pirogov
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.
