O.O. Yanochkina - Ph.D. (Eng.), Associate Professor, Department of Information Systems and Technologies, Southwest State University (Kursk) E-mail: yanoolga@gmail.com S.F. Yatsun - Dr.Sc. (Eng.), Professor, Department of Information Systems and Technologies, Southwest State University (Kursk) E-mail: teormeh@inbox.ru D.V. Titov - Ph.D. (Eng.), Associate Professor, Department of Information Systems and Technologies, Southwest State University (Kursk) E-mail: amazing2004@inbox.ru A.V. Kiselev - Lecturer, Department of Information Systems and Technologies, Southwest State University (Kursk) E-mail: kiselevalexey1990@gmail.com

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.

 

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