An increase of the balancing capacity of ball or roller-type auto-balancers with reduction of time of achieving auto-balancing
DOI:
https://doi.org/10.15587/1729-4061.2017.92834Keywords:
auto-balancer, auto-balancing, ball, cylindrical roller, balancing capacity, transition processes, optimizationAbstract
The study has revealed an influence of the parameters of corrective weights (balls and cylindrical rollers) in auto-balancers on the balancing capacity and the duration of the transition processes of auto-balancing in fast-rotating rotors.
A compact analytical function has been obtained to determine the balancing capacity of an auto-balancer (for any quantity of corrective weights – balls or rollers), with a subsequent analysis thereof.
It is shown that the process of approach of the auto-balancing can be accelerated if the auto-balancer contains at least three corrective weights.
It has been proved that at a fixed radius of the corrective weights the highest balancing capacity of an auto-balancer is achieved when the corrective weights occupy nearly half of the racetrack.
The study has revealed that it is technically incorrect to formulate a problem of finding a radius of the corrective weights that would maximize the balancing capacity of the auto-balancer. The statement implies that if it is a ball auto-balancer, the racetrack is a sphere, but if it is a roller-type balancer, the racetrack is a cylinder. This leads to a practically useless result, suggesting that the highest balancing capacity is achieved by auto-balancers with one corrective weight. Besides, with n≥5 for balls and n≥8 for rollers, there happens a false optimization, which consists in several corrective weights being “excess”. Their removal increases the balancing capacity of the auto-balancer.
It is correct (from the engineering point of view) that the mathematical task is to optimize the balancing capacity of an auto-balancer. Herewith, it is taken into account that the racetrack of the auto-balancer is torus-shaped, which restricts the radius of the corrective weights from the top. It is shown that the balancing capacity of an automatic balancer can be maximized if in a fixed volume the corrective weights have the largest possible radius and occupy almost a half of the racetrack.
The research on the duration of the transition processes for the smallest value has produced the following conclusions:
– to accelerate the achieving auto-balancing, the corrective weights should occupy nearly half of the racetrack;
– the shortest time of the auto-balancing is achieved with three balls or five cylindrical rollers.References
- Thearle, E. (1950). Automatic dynamic balancers Part 2 – Ring, pendulum and ball balancers. Machine Design, 22 (10), 103–106.
- Gusarov, A. (2002). Avtobalansirujushhie ustrojstva prjamogo dejstvija [Auto-balancers direct action devices]. Moscow: Nauka, 119.
- Filimonikhin, G. (2004). Zrivnovazhennya i vibrozakhist rotoriv avtobalansiramy z tverdimi koriguvalnimi vantazhami [Balancing and protection from vibrations of rotors by autobalancers with rigid corrective weights]. Kirovograd: KNTU, 352.
- Nesterenko, V. (1985). Avtomaticheskaja balansirovka rotorov priborov i mashin so mnogimi stepenjami svobody [Automatic rotor balancing devices and machines with many degrees of freedom]. Tomsk: Izd-vo Tomsk. un-ta, 84.
- Tadeusz, M. (1988). Position error occurrence in self balancers used on rigid rotors of rotating machinery. Mechanism and Machine Theory, 23 (1), 71–78. doi: 10.1016/0094-114x(88)90011-0
- Yang, Q., Ong, E.-H., Sun, J., Guo, G., Lim, S.-P. (2005). Study on the influence of friction in an automatic ball balancing system. Journal of Sound and Vibration, 285 (1-2), 73–99. doi: 10.1016/j.jsv.2004.08.009
- Chao, P. C.-P., Sung, C.-K., Leu, H.-C. (2005). Effects of Rolling Friction of the Balancing Balls on the Automatic Ball Balancer for Optical Disk Drives. Journal of Tribology, 127 (4), 845. doi: 10.1115/1.2032992
- Ishida, Y., Matsuura, T., Long Zhang, X. (2012). Efficiency Improvement of an Automatic Ball Balancer. Journal of Vibration and Acoustics, 134 (2), 021012. doi: 10.1115/1.4005013
- Sung, C. K., Chan, T. C., Chao, C. P., Lu, C. H. (2013). Influence of external excitations on ball positioning of an automatic balancer. Mechanism and Machine Theory, 69, 115–126. doi: 10.1016/j.mechmachtheory.2013.05.009
- Haidar, A. M., Palacios, J. L. (2016). A general model for passive balancing of supercritical shafts with experimental validation of friction and collision effects. Journal of Sound and Vibration, 384, 273–293. doi: 10.1016/j.jsv.2016.08.023
- Detinko, F. (1956). Ob ustoychivosti raboty avtobalansira dlya dinamicheskoy balansirovki [On the stability of work auto-balancer for dynamic balancing]. Proceedings of the Academy of Sciences of the USSR. Meh. and machine building, 4, 38–45.
- Gorbenko, A. N. (2003). On the Stability of Self-Balancing of a Rotor with the Help of Balls. Strength of Materials, 35 (3), 305–312. doi: 10.1023/a:1024621023821
- Gorbenko, A. (2008). Ismenenie granizy ustoychivosti avtobalansirovki rotora v prozesse ekspluatazii [Change of borders of stability of autobalancing of rotor by balls in process of exploitation]. Aviazionno-kosmicheskaya tekhnika i tekhnologiya [Aerospace Technique and Technology], 8, 156–159. Available at: http://nbuv.gov.ua/UJRN/aktit_2008_8_33
- Gorbenko, A. (2012). Оbobshchnnoe kharakteristicheskoe uravnenie ustoychivosti rotornykh mashin s autobalansirom [The generalized characteristic equation of stability of rotor machines with the autobalancer]. Aviazionno-kosmicheskaya tekhnika i tekhnologiya [Aerospace Technique and Technology], 1, 76–82. Available at: http://nbuv.gov.ua/UJRN/aktit_2012_1_14
- Gorbenko, A. (2015). Mass-Inertial Characteristics and Dimensionless Equations of Two-bearing Rotor Motion with Auto-balancer in Terms of Compensating Body Mass. Science and Education of the Bauman MSTU, 12, 266–294. doi: 10.7463/1215.0827773
- Filimonikhin, G., Goncharov, V. (2014). Uravnoveshivanie avtobalansirom rotora v uprugo-vyazko zakreplennom korpuse s nepodvizhnoy tochkoy [Balancing auto balancer rotor in visco-elastic body fixed to a fixed point]. Bulletin of the Tomsk Polytechnic University, 324 (2), 71–77.
- Filimonikhin, G., Goncharov, V. (2014). Uravnoveshivanie avtobalansirom rotora v uprugo-vyazko zakreplennom korpuse, sovershayushchem prostranstvennoe dvizhenie [Balancing auto balancer rotor in viscoelastic body fixed, making spatial motion]. Bulletin of the Tomsk Polytechnic University, 325 (2), 41–49.
- Goncharov, V. (2015). Doslidzhennya stiykosti rotora v korpysi na podatlyvykh oporakh, yakyy dynamichno srivnovazhuyetssya dvoma avtobalansyramy [Research of stability of rotor that dynamically is counterbalanced by two auto-balancers, in corps on pliable supports]. Vibratsiyi v tekhnitsi ta tekhnologiyakh, 4 (80), 10–18.
- Goncharov, V., Filimonikhin, G., Dumenko, K., Lychuk, M. (2016). Studying the peculiarities of balancing of flexible double-support rotors by two passive automatic balancers placed near supports. Eastern-European Journal of Enterprise Technologies, 4 (7 (82)), 4–9. doi: 10.15587/1729-4061.2016.75115
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Copyright (c) 2017 Valery Goncharov, Gennadiy Filimonikhin, Andrey Nevdakha, Vladimir Pirogov
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