Some Stability Considerations in Levitation Melting

Abstract

Two types of instabilities are considered. First a circuit model for a levitation system is used to form linearized equations for the vertical motions of suspended metal samples. The basic inductive-resistive circuit model is dynamically stable, but capacitance in the circuit of the supporting coil can account for the self-oscillations of some practical levitation setups. Next, for an idealized coil arrangement, and in the case of negligible skin depth within a suspended molten samp.le, an upper bound on the mass of the sample is deduced. This result is a simple function of the metal density and surface tension, and of the order of 10g in favorable instances. Since the purely static considerations in this calculation yield an upper mass limit below what some investigators have tried to melt in levitation experiments, this model explains the rupture of such drops without resort to dynamic models of surface oscillations.

Simulation of Motion of an Electromagnetically Levitated Sphere

“…Also, stability criteria can be derived. To investigate the stability of levitated specimens, Bocian and Young [7] developed a circuit model for a levitation system to form the linearized equation for the vertical motion of specimens. Two types of instabilities that often occur in practice were considered, namely, the growing vertical oscillation, leading to the ejection of the specimen through the supporting coil and the rupture of the suspended droplets.…”

“…Bocian [7] derived the levitation force as a function of the velocity of the specimen by using the circuit model of the specimen}coil system. Both damping and sti!ness coe$cients are available in the resulting linearized equation of motion.…”