Eddy current damping due to a linear periodic array of magnetic poles

Eddy currents induced in a conductor moving in a magnetic field produce a retarding force proportional to the heat generated in the material. This principle is utilized in the design of magnetic damping or "braking" systems for various applications. The problem considered here is that of a conducting sheet adjacent to a periodic array of magnetic poles. Quasistatic magnetic field solutions are derived for a sheet of arbitrary permeability and thickness moving uniformly at a fixed distance from the poles. The fields inside and outside the conducting sheet are computed over the complete range of dynamic conditions in terms of a relative magnetic penetration length. The field solutions are then employed to calculate the induced current density in the case where the conductor thickness is large in comparison with the axial pole length. The resulting braking power is computed for the purpose of establishing design principles for effective damping. The derived results are applied to two possible situations: a "high reluctance" magnetic circuit which utilizes a nonpermeable conducting sheet, and a "low reluctance" circuit which requires a highly permeable conductor. Differences in these two approaches are analyzed with respect to braking power and preferred type of permanent magnets for optimum performance.