On the effect of vibrational capture of rotation of an unbalanced rotor

Abstract

The dynamics of an unbalanced rotor with a vibrating suspension axis and driven by an asynchronous electric motor of limited power is considered. Stationary (near stationary) modes of rotation of the rotor with a frequency equal to the vibration frequency of the axis are investigated. An explanation of the phenomenon of vibrational capture of rotation of an unbalanced rotor is given. The proposed mechanical interpretation of the effect allows deeper understanding of the classical results and conclusions. The obtained condition for the existence of a stationary mode allows us to estimate the frequency capture interval of the rotor. The case when the mode of vibration capture of rotation is not set is considered. For such a case, an expression for the vibrational moment is obtained, as well as an equation for slow motions. Attention is drawn to the possibility of occurrence in the considered modes of motion of slow (relative to the rotation frequency) rotor oscillations with sufficiently large amplitudes. It is demonstrated that the vibrational capture mode has the property of self-regulation; allows to stabilize the rotation frequency of an unbalanced rotor during load oscillations. Attention is drawn to the fact that in this mode of motion, there is certainly a transfer of energy either from the source of vibration to the rotor, or vice versa. The Sommerfeld effect in an oscillatory system with an inertial vibration exciter is represented by vibration capture of rotation of the vibration exciter by resonant oscillations of the carrier body. The theoretical results are confirmed by numerical modelling.