An Analytic Model for Eddy Current Separation

TL;DR

This paper introduces a simplified 2D analytical model for eddy current separation, using Fourier series to describe magnetic fields and predict particle trajectories, advancing theoretical understanding of ECS.

Contribution

The paper develops a novel analytical model for ECS based on a cylindrical magnet array, providing explicit formulas for magnetic fields and particle dynamics.

Findings

The model accurately predicts particle trajectories in ECS.

Fourier series effectively describes magnetic field profiles.

The approach offers a theoretical basis for optimizing ECS systems.

Abstract

Eddy current separation (ECS) is a process used throughout the scrap recycling industry for separating nonferrous metals from nonmetallic fluff. To date, however, the physical theory of ECS has generally been limited to empirical approximations and numerical simulations. We therefore introduce a simplified, two-dimensional model for ECS based on a cylindrical array of permanent, alternating magnets. The result is a Fourier-series expansion that describes the total magnetic field profile over all space. If the magnets are then rotated with constant angular velocity, the magnetic fields vary as a discrete series of sinusoidal harmonics, thereby inducing electrical eddy currents in nearby conductive particles. Force and torque calculations can then be used to predict the corresponding kinematic trajectories.