Translational and rotational dynamic analysis of a superconducting levitation system

Abstract

The rotational dynamics of a disc-shaped permanent magnet rotor levitated over a high temperature superconductor was studied experimentally and theoretically. The interaction between the rotor magnet and the superconductor was modelled by assuming the magnet to be a magnetic dipole and the superconductor a diamagnet. In the magnetomechanical analysis of the superconductor part, the frozen image concept was combined with the diamagnetic image, and the damping in the system was neglected. The interaction potential of the system is the combination of magnetic and gravitational potentials. From the dynamical analysis the equations of motion of the permanent magnet were stated as a function of lateral, vertical, tilt, precision and rotating angles. The vibration behaviour and correlation of the vibration of one direction with that of another were determined with a numerical calculation based on the Runge-Kutta method. The various vibrational frequencies identified were vertical, radial, tilt, precession and rotation. The tests performed for experimental verifications were translational and rotational. The permanent magnet was 'spun up' under vacuum conditions to analyse the dynamics of the free 'spin down' behaviour of the permanent magnet.

Reduced-Order Dynamic Model of Permanent Magnet and HTSC Interaction in an Axisymmetric Frame

“…The derivatives of the elliptical integrals can be found in Smythe [20] and calculated by the formulations in (13) and (14).…”

“…Mirror image and advanced mirror image models have been developed by Kordyuk [12] and by Hull and Cansiz [13], [14]. This methodology modeled the permanent magnet as a dipole with a stationary image on the other side of the bulk HTSC surface, and a diamagnetic image that mirrored the position of the permanent magnet.…”

Foundations of Meissner superconductor magnet mechanismus engineering

“…The total field thus generated for a semi-infinite plane is equivalent to that generated by the method of images (Cansiz & Hull, 2005;Hellman et al 1988;Hull & Cansiz, 1999;Moon, 1994). As the expression (11) has been derived using only local arguments, it may be used for any shape of superconductor.…”

Interpretation of the method of images in estimating superconducting levitation

“…On the other hand some other works [15][16][17] take a different approach. They use the also well-known expression for the potential energy of two real magnetic dipoles m 1 and m 2 at a distance r…”