Entrainment region and energy consumption in vibration quenching device using a Hula-Hoop and assistant motor

Abstract

This paper deals with the vibration quenching problem of the one-degree-of-freedom system with a limited power supply. This system is forced by centrifugal force of rotating unbalance, and the system is quenched using a Hula-Hoop and a motor to assist the rotation of Hula-Hoop. The entrainment region, the amount of vibration quenching, and the energy consumptions of the system are studied from the approximate analysis using the averaging method, the numerical integration analysis, and the experiment. Following was made clear: (1) When the unbalance is large, the entrainment region of the voltage of the assistant motor is large. On the other hand, when the unbalance is small, the entrainment region becomes narrow. (2) When the unbalance is large, by setting the voltage of the assist motor to a value smaller than the optimum value for vibration control, within the range that satisfies the allowable vibration amplitude level, the increase amount of the energy consumption becomes low. (3) The approximate solutions obtained by the averaging method are in good agreement with those obtained by the numerical integration method, and the characteristics of these results coincide with those of the results obtained by experiment.