Vibrating tool with relay automatic control

O.O. Yanochkina; S.F. Yatsun; D.V. Titov; A.V. Kiselev

Vibrating tool with relay automatic control

O.O. Yanochkina¹, S.F. Yatsun², D.V. Titov³, A.V. Kiselev⁴

research article Pages: 39-45

^1,3 Ph.D. (Eng.), Associate Professor, Department of Information Systems and Technologies, Southwest State University (Kursk)
² Dr.Sc. (Eng.), Professor, Department of Information Systems and Technologies, Southwest State University (Kursk)
⁴ Lecturer, Department of Information Systems and Technologies, Southwest State University (Kursk)

Keywords: hysteretic relay control vibrating tool un-balance exciter

Abstract

The purpose of the present paper is to study the dynamical modes of a vibrating tool with the unbalanced exciter that are controlled by a DC motor. Vibration tools of this type have found a broad range of applications in the industry, for instance, as vibrating technology machine and robots for various purposes.

The considered tool is controlled by a relay system with hysteresis. This type of the switching control provides a smooth start of the DC motor and allows us to exclude the discontinuous conduction sate.

The dynamics of such a system involves two oscillatory modes: a low frequency oscillations of the vibrating tool and a high frequency, relay switching operating regime. This interaction may give birth to a variety of unusual nonlinear dynamic phenomena.

The behavior of such a system is described by a set of five coupled autonomous ordinary differential equations with discontinuous right-hand sides.

We give examples of transient and steady state behaviors, and also illustrate the variation of the oscillation frequency for a vibration tool with the reference signal.

How to cite

Яночкина О.О., Яцун С.Ф., Титов Д.В., Киселёв А.В. Вибрационный инструмент с релейной системой управления // Информационно-измерительные и управляющие системы. 2016. № 10. С. 39–45.

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[1] Panovko G.JA. Dinamika vibracionnykh tekhnologicheskikh processov. Izhevsk: RKHD. 2006. 158 s.

[2] Vejjc V.L., Kolovskijj M.Z., Kochura A.E. Dinamika upravljaemykh mashinnykh agregatov. M.: Nauka. 1984. 352 s.

[3] Panovko G.JA. Lekcii po osnovam teorii vibracionnykh mashin i tekhnologijj: uchebnoe posobie dlja vuzov. M.: Izd-vo MGTU im. N.EH.Baumana. 2008. 192 s.

[4] Volkova L.JU., Lupekhina I.V., Panovko G.JA., JAcun S.F. Issledovanie dinamiki vibracionnogo instrumenta pri ego vzaimodejjstvii s obrabatyvaemojj sredojj // Mashinostroenie i inzhenernoe obrazovanie. 2010. № 4. S. 63-72.

[5] Guskov A.M., Panovko G.JA. Nelinejjnye ehffekty pri kolebanijakh linejjnykh mekhanicheskikh sistem s centrobezhnym vozbuditelem ogranichennojj moshhnosti // Vestnik MGTU im. N.EH.Baumana. Ser. Mashinostroenie. 2012. S. 115-125.

[6] Rudakova E.V., SHevjakin V.N., JAcun S.F. Modelirovanie dinamicheskikh processov vibracionnogo grokhota s uchetom ogranichennojj moshhnosti ehlektroprivoda // Izvestija JUgo-Zapadnogo gos. un-ta. 2011. №6. CH. 2. S. 10-16.

[7] Cypkin JA.Z. Relejjnye avtomaticheskie sistemy. M.: Nauka. 1974. 576 s.

[8] Zhusubaliyev Zh.T., Soukhoterin E.A., Rudakov V.N., Kolokolov Yu.V., Mosekilde E. Bifurcations and chaotic oscillations in an automatic control relay system with hysteresis // Int. J. Bifurcation and Chaos. 2001. V. 11. № 5. P. 1193-1232.

[9] Zhusubaliyev Zh. T., Mosekilde E., Rubanov V.G., Nabokov R.A. Multistability and hidden attractors in a relay system with hysteresis // Physica D: Nonlinear Phenomena. 2015. V. 306. P. 6-15.

[10] Zhusubaliev Zh.T., Titov V.S. Chaotic oscillations in the relay system with hysteresis // Automation and Remote Control. 2001. V. 62. № 1. P. 55-66.