Vibration Behavior of Gravity-Loaded Whirling Micro-Scale Shafts Influenced by an Axial Magnetic Field

Abstract

Some high-speed rotating micro-machines and micro-vibration devices rely on the use of whirling micro-shafts subject to the effect of gravity and magnetic fields. At present, the consequences of the interaction between the elastic deformation of such shafts and the magnetic/gravitational field effects remain unresolved. Focusing on micro-scale whirling shafts with very high torsional rigidity, this study presents a theoretical treatment grounded in the theory of micro-continuum elasticity to examine the ramification of this interaction. The differential transformation method (DTM) is used to obtain extensive numerical results for qualitative assessments of the magnetic-gravitational effects interaction on standing, hanging and horizontally positioned spinning micro-scale shafts. The influence of bearing-support flexibility on the response of the whirling micro-shaft is also considered with rotational and translational springs. The gravitational sag reduces the stability of whirling standing micro-shafts and increases that of the hanging micro-shafts. Further, for all the micro-shafts configurations investigated, the magnetic field is observed to stiffen the response of the shaft and favorably shifts the critical points of vibration of the whirling shafts forward.