Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Saint Petersburg, Russia

L. I. Blekhman, Cand. Sci. (Eng.), Leading Researcher, liblekhman@yandex.ru

2 Saint Petersburg State University, Saint Petersburg, Russia

P. D. Morozov, Cand. Sci. (Phys.-Math.), Associate Professor, pm-morozovpd@yandex.ru

The dynamics of drives for vibratory machines, in particular vibrating screens, whose working components oscillations are inducted by unbalanced rotors driven by electric motors, is considered. It is shown theoretically and experimentally that the device exhibits a systematic exchange of energy between the rotor and the oscillating body. In this case, the rotational speed of the rotor is not constant, as is commonly assumed, but fluctuates during each revolution at both the initial and multiple frequencies. As a result, the acceleration of the oscillating body also acquires harmonics at multiple frequencies. Estimates of the magnitude of the frequency fluctuations are given for the most common dynamic layouts of such devices. Both the detrimental effects of the observed phenomena and possibilities for their beneficial utilization are discussed.
This research was a part of the state assignment of the Ministry of Science and Higher Education of the Russian Federation for the Institute for Problems in Mechanical Engineering of the Russian Academy of
Sciences (registration number: 124040800009-8).

1. Vibrations in Engineering: A Handbook: In 6 volumes. Vol. 4. Vibrational Processes and Machines. Ed. by E. E. Lavendel. Moscow: Mashinostroenie, 1981. 509 p.
2. Blekhman I. I. Vibrational Mechanics and Vibrational Rheology (Theory and Applications). Moscow: Fizmatlit, 2018. 752 p.
3. Vaisberg L. A. Design and Calculation of Vibrating Screens. Moscow: Nedra, 1986. 144 p.
4. Bykhovskii I. I. Fundamentals of the Theory of Vibrational Equipment. Moscow: Mashinostroenie, 1969. 364 p.
5. Blekhman I. I., Blekhman L. I., Yaroshevich N. P. On the dynamics of the drive of vibrating machines with inertial excitation. Obogashchenie Rud. 2017. No. 4. pp. 49–53.
6. Blekhman I., Blekhman L. I., Vaisberg L. A., Vasilkov V. B. Energy and frequency ripple in devices with inertial excitation of oscillations. Philosophical Transactions of the Royal Society A. 2021. Vol. 379: 20200233.
7. Zhang A., Sorokin V., Li H. Dynamic analysis of a new autoparametric pendulum absorber under the effects of magnetic forces. Journal of Sound and Vibration. 2020. Vol. 485. 115549.
8. Blekhman I. I. Self-synchronization of vibrators in some vibrating machines. Inzhenernyi Sbornik. 1952. Vol. XVI. pp. 49–72.
9. Blekhman I. Synchronization in Science and Technology. New York: ASME Press, 1988.
10. Skubov D., Khodzhaev K. Sh. Non-Linear Electromechanics. Berlin: Springer-Verlag, 2008. XIV, 400 p.
11. Yaroshevich N. P. Complex Cases in the Theory of Self-Synchronization of Mechanical Vibro-Exciters. Lutsk: LDTU (Lutsk National Technical University), 2005. 192 p.
12. Blekhman I., Blekhman L., Vaisberg L., Vasilkov V. Energy Performance of Vibrational Transportation and Process Machines. Proceeding of the 14th International Conference on Vibration Problems. Lecture Notes in Mechanical Engineering. Singapore: Springer, 2021. Vol. 58. pp. 29–46. DOI: 10.1007/978-981-15-8049-9_2
13. Blekhman I. I., Zhgulev A. S. On the calculation of vibrating machines with an eccentrically located unbalanced exciter. Obogashchenie Rud. 1974. No. 2. pp. 36–39.
14. Blekhman I. I., Vaisberg L. A., Vasilkov V. B., Lavrov B. P., Yakimova K. S. Universal vibration stand: experience of use in research, some results. Nauchno-tekhnicheskie vedomosti SPbGTU. 2003. No. 3. pp. 224–227.