Eddy currents damping understood as Zener viscoelastic damping

Abstract

This paper identifies and explains the eddy currents damping originated in a solid that vibrates in a magnetic field as a Zener viscoelastic model damping. For that, a coupled mechanical-electrical model is proposed for the eddy currents damping. The mechanical model is studied as a single degree-of-freedom system, and the electrical model is assumed to be a closed RL circuit. The coupling between them is given by the magnetic force originated by the motional inductance. The motion equation is obtained for the coupled system for two different excitation types: harmonic force and harmonic base motion. These motion equations include derivatives of the displacement with respect to time up to the third order. An equivalence between these motion equations and the ones derived for a viscoelastic system modelled with a Zener model is found. This allows understanding the parameters of the eddy currents model as the ones of a viscoelastic Zener model. The term related with the third order derivative is associated with relaxation, a characteristic property of viscoelastic systems. This equivalence between Zener and eddy currents damping explains forces proportional to the third order derivative that other authors have experimentally found in vibrating systems with eddy currents. The proposed model is validated both from an analytical comparison with another model of the literature and from experimental results previously published. Finally, a parametric study is carried out to show up the influence of the magnetic field and electrical properties of the model on the frequency and time responses of the system.