Equations of motion of vibration machines with a translational motion of platforms and a vibration exciter in the form of a passive auto-balancer
DOI:
https://doi.org/10.15587/1729-4061.2017.111216Keywords:
inertial vibration exciter, two-frequency vibrations, resonant vibration machine, auto-balancer, single-mass vibration machine, multi-mass vibration machineAbstract
Generalized models have been built of one-, two-, and three-mass vibration machines with a rectilinear translational motion of platforms and a vibration exciter in the form of a ball, a roller, or a pendulum auto-balancer.
In the generalized model of a single-mass vibration machine, the platform relies on an elastic-viscous support with the guides enabling the platform’s rectilinear translational motion. A passive auto-balancer is installed on the platform.
In the generalized models of two- and three-mass vibration machines, each platform relies on a fixed external elastic-viscous support with the platforms coupled in pairs by elastic-viscous inner supports. The guides allow the platforms to move rectilinearly translationally. A passive auto-balancer is installed on one of the platforms.
We have derived differential equations of the motion of vibration machines. The equations are reduced to the form that is independent of the type of an auto-balancer.
The models of particular one-, two- and three-mass vibration machines can be obtained from the generalized models by selecting a specific type of the auto-balancer.
The models of particular two-mass vibration machines can also be obtained from the corresponding generalized model by rejecting one of the external elastic-viscous supports.
The models of particular three-mass vibration machines can also be derived from the corresponding generalized model by rejecting:
– one or two external elastic-viscous supports;
– one of the three inner elastic-viscous supports;
– one or two external elastic-viscous supports and one of the three inner elastic-viscous supports.
The constructed models are applicable both for analytical studies into dynamics of the relevant vibration machines and for performing computational experiments.
When employed in analytical studies, the models are designed to search for the established modes of a vibration machine motion, to determine conditions for their existence and stabilityReferences
- Bukin, S. L., Maslov, S. G., Lyutiy, A. P., Reznichenko, G. L. (2009). Intensification of technological processes through the implementation of vibrators biharmonic modes. Enrichment of minerals, 36, 81–89.
- Kryukov, B. I. (1967). Dinamika vibratsionnyih mashin rezonansnogo tipa [Dynamics of vibratory machines of resonance type]. Kyiv: nauk. dumka, 210.
- Lanets, O. S. (2008). Vysokoefektyvni mizhrezonansni vibratsiyni mashyny z elektromagnitnym 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.
- Sommerfeld, A. (1904). Beitrage zum dinamischen Ausbay der Festigkeislehre. Zeitschriff des Vereins Deutsher Jngeniere, 48 (18), 631–636.
- Lanets, O. V., Shpak, Ya. V., Lozynskyi, V. I., Leonovych, P. Yu. (2013). Realizatsiya efektu Zommerfelʹda u vibratsiynomu maydanchyku 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
- Kuzo, I. V., Lanets, O. V., Hurskyi, V. M. (2013). Syntez nyzʹkochastotnykh rezonansnykh vibratsiynykh mashyn z aeroinertsiynym zburennyam [Synthesis of low-frequency resonancevibratory machines with an aeroinertia drive]. Naukovyi visnyk Natsionalnoho hirnychoho universytetu, 2, 60–67. Available at: http://nbuv.gov.ua/UJRN/Nvngu_2013_2_11
- Yaroshevich, N. P., Zabrodets, I. P., Yaroshevich, T. S. (2016). Dynamics of Starting of Vibrating Machines with Unbalanced Vibroexciters on Solid Body with Flat Vibrations. Applied Mechanics and Materials, 849, 36–45. doi: 10.4028/www.scientific.net/amm.849.36
- Filimonihin, 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
- Artyunin, A. I. (1993). Research of motion of the rotor with autobalance. Proceedings of the higher educational institutions. Mechanical Engineering, 1, 15–19.
- Filimonihin, G. B. (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.
- Filimonihin, G. B., V. V. Yatsun (2016). Investigation of the process of excitation of dual-frequency vibrations by ball auto-balancer of GIL 42 screen. Eastern-European Journal of Enterprise Technologies, 1 (7 (79)), 17–23. doi: 10.15587/1729-4061.2016.59881
- Yatsun, V., Filimonikhin, G., Dumenko, K., Nevdakha, A. (2017). Experimental research of rectilinear translational vibrations of a screen box excited by a ball balancer. Eastern-European Journal of Enterprise Technologies, 3 (1 (87)), 23–29. doi: 10.15587/1729-4061.2017.101798
- Ryzhik, B., Sperling, L., Duckstein, H. (2004). Non-synchronous Motions Near Critical Speeds in a Single-plane Autobalancing Device. Technische Mechanik, 24, 25–36.
- 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 vyisshih uchebnyih zavedeniy. Mashinostroenie, 9, 8–14.
- 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
- 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
- Strauch, D. (2009). Classical Mechanics: An Introduction. Springer-Verlag Berlin Heidelberg. doi: 10.1007/978-3-540-73616-5
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2017 Volodymyr Yatsun, Gennadiy Filimonikhin, Kostyantyn Dumenko, Andrey Nevdakha
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.
