Dynamics of suspensions with rare-earth permanent magnets

The paper presents a theoretical model of a passive magnetic suspension based on rare-earth permanent magnets: the aim is to minimize the dependence of the natural frequency of a single degree of freedom system on mass. In order to estimate magnetic interactions, the gradient of magnetic induction is evaluated by using a magnetic model based on the analogy of the equivalent currents method in a quasi-static open-circuit-type configuration. Therefore magneto-elastic forces between permanent magnets can be determined and compared with empirical formulas, applied in practical uses. and with experimental static tests. For a single degree of freedom system with variable mass. static configuration and dynamic behavior are evaluated for classic linear elastic systems, for purely magnetic suspensions and for a combination of the two. In particular the dynamics of the magneto-mechanic interaction by use of nonlinear and linearized models are investigated for non-zero initial conditions, in order to underline the influences of nonlinearities on the system response. Finally, the single degree of freedom system frequency response is presented for different values of the Geometrical and inertial properties of the system, thus demonstrating the insensibility of resonance with respect to mass.