TAKING CONSIDERATION OF RESISTANCE FORCES IN THE PENDULUM SUPPORTS WHEN STUDYING THE PROCESS OF AUTOMATIC BALANCING OF THE ROTORS

Receipt date: 
30.05.2019
Bibliographic description of the article: 

Artyunin A. I., Sumenkov O. Y. Uchet sil soprotivleniya v oporakh mayatnikov pri issledova-nii protsessa avtomaticheskoy balansirovki rotorov [Taking consideration of resistance forces in the pendulum supports when studying the process of automatic balancing of the rotors]. Sovremennye tekhnologii. Sistemnyi analiz. Modelirovanie [Modern Technologies. System Analysis. Modeling], 2019. Vol. 63, No. 3, pp. 53–58. DOI: 10.26731/1813-9108.2019.3(63).53–58.

Year: 
2019
Journal number: 
УДК: 
621.01
DOI: 

10.26731/1813-9108.2019.3(63).53–58

Article File: 
Pages: 
53
58
Abstract: 

When modeling the process of automatic balancing of rotors with the help of pendulum auto-balancers or studying the “sticking” effect of a pendulum on a rotating shaft of a mechanical system, it is important to know the character of the resistance forces in the pendulum supports. In the previously published works on automatic balancing of rotors with the help of pendulum it was accepted that the moment of resistance forces in the pendulum supports proportional to the relative velocity, that is has the character of "viscous" friction. But at velocity increase of rotors revolution it is necessary to consider real load in the pendulum supports, influencing the pendulum motion resistance and so the automatic balancing process. The hypothesis used in the present work is that the moment of resistance forces in the pendulum supports consists of the moment of resistance forces proportional to the relative velocity of the pendulum on rotating shaft ("viscous" friction) and the moment of resistance forces proportional to the radial load on the support ("dry" friction). Both original and simple method of determining the "viscous" friction coefficient with the help of a ruler and a digital camera is described. The model with a pendulum capable of free rotation on the shaft of a rotor permanently attached in a body frame at resilient supports is the closest to really existing constructions. Diagrams and formulas are suggested for the models with the complicated pendulum motion to calculate the radial load in the pendulum support both at acceleration and under stabilized conditions of rotor motion considering Coriolis inertia force.

List of references: 
  1. Machabeli  L.I. O dvizhenii diska s dvumya mayatnikami [On the movement of a disk with two pendula], Izv. AN SSSR, Mekhanika [News of Science Academy of the USSR, Mechanics], 1965. No.2. Pp. 13-18.
  2. Blekhman I.I. Sinchronizatsiya dinamicheskikh system [Dynamic systems synchronization], Moscow, Science Publ., 1971. Pp. 896.
  3. Blekhman I.I. Vibratsionnaya mekhanika [Vibration Mechanics], Moscow, Fizmatgiz Publ., 1994. Pp. 400.
  4. Dubovik V.A., Zamyatin V.M., Ziyakaev G.R. Statsionarnoe vrashenie neuravnoveshennogo avtobalansira na gibkom valu s mayatnirovymi podveskami [Stationary rotation of unbalanced rotor on the flexible shaft with pendulum suspension], Izv. Tomskogo politech. universiteta [News of Tomsk polytechnic university]. 2009, Vol.314. No.3. Pp. 44-48.
  5. Dubovik V.A, Ziyakaev G.R. Osnovnoe dvizhenie dvukhmayatnikovogo avtobalansira na gibrom valu s uprugimi oporami [The basic motion of pendulum auto-balancers on flexible shaft with resilient supports. Izv. Tomskogo politech. universiteta [News of Tomsk polytechnic university]. 2010, Vol.313. No.3. Pp. 37-39.
  6. Artyunin A.I., Alkhunsaev G.G. Ob osobom rezhime dvizheniya zhestkogo rotora s uprugimi oporami i mayatnikovym avtobalansirom [On a special mode of motion of a rigid rotor with elastic supports and a pendulum auto-balancer]. Izvestiya vysshikh uchebnykh zavedenii. Mashinostroenie [News of higher educational institutions. Engineering], 2005. No. 10. Pp. 8–14.
  7. Artyunin A.I., Eliseev S.V., Sumenkov O.Y. Experimental Studies of  Influence of Natural Requncies of  Oscillations of Mechanical System on Angular Velocity of Rendulum on Rotating Shaft. Lecture Notes in Mechanical Engineering ICIE 2018: Proceedings of the 4th International Conference on Industrial Engineering. Pp. 159-166.
  8. Beizel'man R.D., Tsypkin B.V., Perel' L.Ya. Podshipniki kacheniya: Spravochnik [Rolling bearings: a handbook]. Moscow: Mashinostroenie Publ., 1975. Pp. 896.
  9. Opory osei valov mashin i priborov [Bearings of shaft axes of machines and devices]. In Spitsyn N.A., Mashkov I.M. (gen. eds.). Leningrad: Mashinostroenie Publ., 1970. Pp. 896.
  10. Reshetov D.N. Detali mashin [Parts of machines]. Moscow: Mashinostroenie Publ., 1976. P. 655.
  11. Galakhov N.A., Burmistrov A.I. Raschet podshipnikovykh uzlov [Calculation of bearing assemblies]. Moscow: Mashinostroenie Publ., 1988. Pp. 271.
  12. Artyunin A.I. Issledovaniya dvizheniya rotora s avtobalansirom [Studies of the movement of the rotor with auto-balancer]. Izvestiya vysshikh uchebnykh zavedenii. Mashinostroenie [News of higher educational institutions. Mechanical Engineering], 1993. No. 1. Pp. 15-18.
  13. Artyunin A.I. Effekt «zastrevaniya» i osobennosti dvizheniya rotora s mayatnikovymi avtobalansirami [The “sticking” effect and the characteristics of the rotor movement with pendulum auto-balancers]. Nauka i obrazovanie: elektronnoe nauchnoe izdanie NGTU im. N.E. Baumana [Science and education: the electronic scientific publication of the Bauman NSTU], 2013. No. 8. Pp. 443-454. 
  14.  Eliseev S.V., Artyunin A.I. Mekhaniko-matematicheskoe modelirovanie effekta «zastrevaniya» mayatnikov na vrashchayushchemsya valu [Mechanical and mathematical modeling of the "sticking" effect of pendulums on a rotating shaft]. Vestnik Belorusskogo gos. Un-ta transporta: Nauka i transport [Bulletin of the Belarusian State University of Transport: Science and Transport]. Gomel'. 2016. No. 2. Pp. 172-175.