Parametric spin resonance for a spinner with an orbiting pivot

Abstract

Dynamics are investigated for a rigid spinner with a hole, concentric with its mass center, into which a pivot is loosely fitted. As the spinner is excited by the motion of the contacting pivot, the spinner may sustain a quasi-steady spin angular velocity θ in the pivot's orbiting plane. This spin motion, defined as parametric spin resonance (PSR), is investigated for the case of prescribed, bi-directional, harmonic pivot motion of frequency ω. The ranges of the system's non-dimensional parameters needed to achieve PSR are determined. Experimental data both explain the spinner's direction of rotation and complement the predicted existence of quasi-steady values of θ. The analysis explains the characteristic motions of such toys as the Hula-Hoop and the Indian Windmill (the Gee-Haw Whimmy Diddle), and in general may explain certain unwanted vibrations in machinery with worn or loosely-fitting bearings.