Gyroscopic magnetic levitation: an original design procedure based on the finite element method

Abstract

To cite this version:Z. De Grève, C. Versèle, J. Lobry. Gyroscopic magnetic levitation: an original design procedure based on the finite element method. European Physical Journal: Applied Physics, EDP Sciences, 2010, 52 (2), <10.1051/epjap/2010080>. <hal-00634371> Abstract. In this work, an original procedure, based on the finite element method, is presented for the design of a Levitron c , a device made of permanent magnets and relying on stable gyroscopic magnetic levitation, using secondhand components. A perturbation force analysis is performed on finite element models of available magnets in order to derive the locus of stable equilibrium, as well as the top mass, for a given configuration of the magnets. We investigate three methods for the estimation of forces from finite element computations, two of them based on the virtual work principle, and one performing numerical integration of the classical expression of forces between magnets. Results are employed to realize a Levitron c in laboratory, and are shown to be in better agreement with experience than those from a simple analytical model available in the literature.

Nonlinear and linearised behaviour of the Levitron®

“…It is emphasized that dissipation is fundamental to the stabilization of the spinning top, but in the present authors opinion this point of view may not be completely shared. In 2008, De Grève et al [14] presents a Levitron Ò made by recycled materials and a finite element model for the analysis of its stability.…”