Since 1963
ARTICLE
Spatial synchronization of unbalanced rotors excited with paralleled and counterrotating motors in a far resonance system
| 1 | School of Mechanical Engineering, Southwest Petroleum University, Chengdu, China |
| 2 | Key Laboratory of Oil & Gas Equipment, Ministry of Education, Southwest Petroleum University, Chengdu, China |
| 3 | School of Petroleum Engineering, Southwest Petroleum University, Chengdu, China |
Submission date: 2018-07-23
Acceptance date: 2019-04-03
Online publication date: 2019-07-15
Publication date: 2019-07-15
Journal of Theoretical and Applied Mechanics 2019;57(3):723–738
KEYWORDS
ABSTRACT
Dynamic characteristics of the vibration screening machinery is influenced by synchronization
between induction motors. Therefore, estimating the synchronous state between the
motors is a crucial process for designing the vibration screening machinery. In this paper,
two rotors excited with paralleled and counterrotating motors in a far resonance system are
concerned. To master the synchronization of the system, the dynamic model is firstly established;
then, the synchronous condition of the system is derived with the Poincare method;
subsequently, the synchronous stability of the system is discussed by the Hamilton principle;
finally, some computation simulations are implemented to verify correctness of theoretical
analysis. The research result shows that the system actuated by rotors of the identical mass
is planar motion as the stable phase difference between the rotors is stabilized in the zero
phase. The system actuated by nonequivalent mass rotors exhibits spatial motion as the
stable phase difference stabilizes in a nonzero phase.
REFERENCES (26)
1.
Balthazar J., Felix J., Brasil R., 2004, Short comments on self-synchronization of two non-ideal sources supported by a flexible portal frame structure, Journal of Vibration and Control, JVC, 10, 12, 1739-1748.
2.
Balthazar J., Felix J., Brasil R., 2005, Some comments on the numerical simulation of self-synchronization of four non-ideal exciters, Applied Mathematics and Computation, 164, 2, 615-625.
3.
Banaszewski T., Schollbach A., 1998, Vibration analysis of machines with self-synchronizing unbalance-type exciters, Aufbereitungs-Technik, 39, 8, 383-393.
4.
Blekhman I.I., 1988, Synchronization in Science and Technology, ASME Press, New York.
5.
Chen X.Z., Kong X.X., Zhang X.L., Li L.X., Wen B.C., 2016, On the synchronization of two eccentric rotors with common rotational axis theory and experiment, Shock and Vibration, 2016.
6.
Czolczynski K., Perlikowski P., Stefanski A., Kapitaniak T., 2012, Synchronization of pendula rotating in different directions, Communications in Nonlinear Science and Numerical Simulation, 17, 9, 3658-3672.
7.
Czolczynski K., Perlikowski P., Stefanski A., Kapitaniak T., 2013, Synchronization of the self-excited pendula suspended on the vertically displacing beam, Communications in Nonlinear Science and Numerical Simulation, 18, 2, 386-400.
8.
Djanan A., Nana N., Woafo P., 2013, Electromechanical control of vibration on a plate submitted to a non-ideal excitation, Mechanics Research Communications, 54, 72-82.
9.
Djanan A., Nbendjo B., Woafo P., 2014, Effect of self-synchronization of DC motors on the amplitude of vibration of a rectangular plate, The European Physical Journal Special Topics, 223, 813-825.
10.
Fang P., Hou Y.J., 2018, Synchronization characteristics of a rotor-pendula system in multiple coupling resonant systems, Proceedings of The Institution of Mechanical Engineers Part C – Journal of Mechanical Engineering Science, 232, 10, 1802-1822.
11.
Fang P., Yang Q.M., Hou Y.J., Chen Y., 2014, Theoretical study on self-synchronization of two homodromy rotors coupled with a pendulum rod in a far-resonant vibrating system, Journal of Vibroengineering, 16, 5, 2188-2204.
12.
Hou Y.J., Du M.J., Fang P., Zhang L., 2018, Synchronization and stability of an elastically coupled tri-rotor vibration system, Journal of Theoretical and Applied Mechanics, 55, 1, 227.
13.
Inoue J., Araki Y., Miyaura S., 1951, Self-synchronization of mechanical system (multiple cycle), Proceedings of Japanese Mechanical Engineering Society, 42, 103-110.
14.
Kapitaniak M., Czolczynski K., Perlikowski P., Stefanski A., Kapitaniak T., 2014, Synchronous states of slowly rotating pendula, Physics Reports, 541, 1, 1-44.
15.
Kong X.X., Zhang X.L., Chen X.Z., Wen B.C., Wang B., 2016a, Phase and speed synchronization control of four eccentric rotors driven by induction motors in a linear vibratory feeder with unknown time-varying load torques using adaptive sliding mode control algorithm, Journal of Sound and Vibration, 370, 23-42.
16.
Kong X.X., Zhang X.L., Chen X.Z., Wen B.C., Wang B., 2016b, Synchronization analysis and control of three eccentric rotors in a vibrating system using adaptive sliding mode control algorithm, Mechanical Systems and Signal Processing, 72-73, 432-450.
17.
Paz M., Cole J., 1992, Self-synchronization of two unbalanced rotors, Journal of Vibration and Acoustics, 114, 1, 37-41.
18.
Sperling L., Ryzhik B., Linz C., Duckstein H., 2000, Simulation of two-plane automatic balancing of a rigid rotor, 2nd International Conference on Control of Oscillations and Chaos (COC-2000), St. Petersburg, Russia: Elsevier.
19.
Tang L.P., Zhu X.H., Li J.H., 2019, Effects of the synchronous variation of the static and the kinetic friction coefficients on stick-slip vibration of drillstring, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, 43, 275-283
20.
Wen B.C., Fan J., Zhao C.Y., 2009, Synchronization and Controled Synchronization in Engineering, Science Press, Beijing.
21.
Xiao J.Y., Zhong S.M., Li Y.T., Xu. F., 2017, Finite-time Mittag-Leffler synchronization of fractional-order memristive BAM neural networks with time delays, Neurocomputing, 219, 431-439.
22.
Zhang X.L., Wen B.C., Zhao C.Y., 2014, Vibratory synchronization transmission of two exciters in a super-resonant vibrating system, Journal of Mechanical Science and Technology, 28, 6, 2049-2058.
23.
Zhang X.L., Wen B.C., Zhao C.Y., 2016, Theoretical study on synchronization of two exciters in a nonlinear vibrating system with multiple resonant types, Nonlinear Dynamics, 85, 1, 141-154 .
24.
Zhang X.L., Wen B.C., Zhao C.Y., 2017, Vibratory synchronization transmission of a cylindrical roller in a vibrating mechanical system excited by two exciters, Mechanical Systems and Signal Processing, 96, 88-103.
25.
Zhao C.Y., Zhang Y.M., zhang X.L., 2010a, Synchronisation and general dynamic symmetry of a vibrating system with two exciters rotating in opposite directions, Chinese Physics B, 19, 3.
26.
Zhao C.Y., Zhu H.T., Zhang Y.M., Wen B.C., 2010, Synchronization of two coupled exciters in a vibrating system of spatial motion, Acta Mechanica Sinica, 26, 477-493.
RELATED ARTICLE
We process personal data collected when visiting the website. The function of obtaining information about users and their behavior is carried out by voluntarily entered information in forms and saving cookies in end devices. Data, including cookies, are used to provide services, improve the user experience and to analyze the traffic in accordance with the Privacy policy. Data are also collected and processed by Google Analytics tool (more).
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.
You can change cookies settings in your browser. Restricted use of cookies in the browser configuration may affect some functionalities of the website.