Smart Search 


2_2026_sen_6

Title of the article DETERMINING THE STATIONARY MOTIONS OF A STATICALLY UNBALANCED ROTOR WITH A BALL SELF-BALANCING DEVICE BY A SMALL PARAMETER METHOD
Authors

SIDIKOV Mansur N., Ph. D. in Eng., Associate Professor of the Department “General Technical Disciplines”, Almalyk branch of NUST “MISIS”, Almalyk, Republic of Uzbekistan, This email address is being protected from spambots. You need JavaScript enabled to view it.
In the section MECHANICAL ENGINEERING COMPONENTS
Year 2026
Issue 2(75)
Pages 52–61
Type of article RAR
Index UDK 531.01
DOI https://doi.org/10.46864/1995-0470-2026-2-75-52-61
Abstract The small parameter method was used to analyze the necessary conditions for stationary motions of a rotor mounted on a flexible shaft with a ball self-balancing device, when running tracks of the balancing balls are installed not only by eccentricity, but also have a horizontal axis of rotation. In this case, the parameter inversely proportional to the square of the angular velocity of the rotor is taken as the small parameter. In a particular case, an asymptotic solution is obtained taking into account the second power of the small parameter, as well as an exact solution to one of the cases of unbalanced rotor motion.
Keywords self-balancing device, eccentricity, running track, generalized coordinates
You can access full text version of the article.
Bibliography
  1. Genta G. Dynamics of rotating systems. New York, Springer, 2005. 658 p. 
  2. Yamamoto T., Ishida Y. Linear and nonlinear rotordynamics: a modern treatment with applications. New York, Wiley, 2001. 325 р. 
  3. Nikiforov A.N. Sostoyanie problemy uravnoveshivaniya rotorov [State of rotors balancing problem]. Bulletin of science and technical development, 2013, no. 4(68), pp. 20–28 (in Russ.). 
  4. Bykov V.G., Kovachev A.S. Dinamika rotora s ekstsentricheskim sharovym avtobalansirovochnym ustroystvom [Dynamic of a statically unbalanced rotor with eccentric ball autobalancer]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2014, vol. 1, no. 4, pp. 579–588 (in Russ.). 
  5. Bykov V.G., Kovachev A.S. Prokhozhdenie cherez rezonans staticheski neuravnoveshchannogo rotora s “neidealnym” avtobalansirovochnym mekhanizmom [Passage through the resonance of a statically unbalanced rotor with “imperfect” autobalancing device]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2017, vol. 4, no. 4, pp. 671–680 (in Russ.). 
  6. Bykov V.G., Kovachev A.S. Dinamika staticheski neuravnoveshennogo rotora s ellipticheskim sharovym avtobalansirovochnym ustroystvom [Dynamics of a statically unbalanced rotor with an elliptic automatic ball balancer]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2019, vol. 6, no. 3, pp. 452– 461 (in Russ.). 
  7. Bykov V.G. Nestatsionarnye rezhimy dvizheniya staticheski neuravnoveshennogo rotora s avtobalansirovochnym mekhanizmom [Nonstationary behavior of statically unbalanced rotor with the automatic balancеr]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2010, no. 3, pp. 89–96 (in Russ.). 
  8. Bykov V.G., Melnikov A.E. Matematicheskaya model gibkogo rotora na osnove obobshchennykh lagranzhevykh koordinat [A mathematical model of a flexible rotor using the generalized Lagrangian coordinates]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2010, no. 4, pp. 110– 118 (in Russ.). 
  9. Pasynkova I.A. Sovmestnye nelineynye kolebaniya neuravnoveshennogo rotora i korpusa [Non-linear vibration of the rotor-housing system]. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2014, vol. 1, no. 1, pp. 152–161 (in Russ.).
  10. Gorbenko A.N. Nekotorye netrivialnye svoystva mekhanicheskoy sistemy “rotor – sharikovyy avtobalansir” [Some non– trivial properties of the “rotor – ball auto-balancer” mechanical system]. Vibratsii v tekhnike i tekhnologiyakh, 2002, no. 3(24), pp. 33–36 (in Russ.). 
  11. Kydyrbekuly A.B., Ibrayev G.E. Ob avtokolebaniyakh v vertikalnykh rotornykh sistemakh, ustanovlennykh na uprugikh oporakh [The self-oscillation in the vertical rotor system mounted on elastic supports]. Journal of mathematics, machanics, computer science, 2020, no. 1(105), pp. 160–173. DOI: https://doi. org/10.26577/JMMCS.2020.V105.I1.14 (in Russ.).
  12. Ollson K.-O. Limits for the use of auto-balancing. International journal of rotating machinery, 2004, vol. 10, iss. 3, pp. 221– 226. DOI: https://doi.org/10.1155/S1023621X04000235. 
  13. Zaytsev N.N., Zaytsev D.N., Makarov A.A. Inzhenernyy analiz ustanovivshikhsya rezhimov odnodiskovogo rotora s mnogoryadnym sharovym avtobalansiruyushchim ustroystvom [Engineering analysis of steady-state regimes of the single-disk rotor with multi-row ball self-balancing device]. PNRPU aerospace engineering bulletin, 2017, no. 48, pp. 43–59. DOI: https://doi. org/10.15593/2224-9982/2017.48.05 (in Russ.). 
  14. Dimentberg F.M., Shatalov K.T., Gusarov A.A. Kolebaniya mashin [Machine fluctuations]. Moscow, Mashinostroenie Publ., 1964. 308 p. (in Russ.). 
  15. Kelzon A.S., Malinin L.M. Upravlenie kolebaniyami rotorov [Rotor oscillation control]. Saint Petersburg, Politekhnika Publ., 1992. 118 p. (in Russ.). 
  16. Kelzon A.S., Tsimanskiy Yu.P., Yakovlev V.I. Dinamika rotorov v uprugikh oporakh [Dynamics of rotors in elastic supports]. Moscow, Nauka Publ., 1982. 280 p. (in Russ.). 
  17. Nayfeh A.H. Perturbation methods. Wiley-VCH, 1973. 448 p.