Analytical Model Of Eddy Current-Based Device Meant To The Conductive Materials Sorting

The developed analytical model refers to an electromagnetic device intended for sorting conductive materials, as in the waste management domain. The main component of the device is a probe coil with ferrite open core that has to be placed near the piece of conductive material subject to sorting. When the probe coil is supplied by a mean frequency voltage source, eddy currents are induced into the tested conductive media, the measured impedance depends on its physical parameters. The influence of the physical parameters of the coil probe and of the relative position of the probe coil and material are also analyzed. Based on our new analytical model of the system, many numerical results corresponding to a wide range of working parameters have been investigated, in order to identify most proper possible implementations in engineering practice. INTRODUCTION Technical applications of eddy currents are based on revealed changes in the physical properties of materials, e.g. electrical conductivity and magnetic permeability, properties that belong to the object to be controlled. The conductive material is subjected to the alternative magnetic field of a probe coil supplied by mean frequency AC current. The alternative magnetic field induces eddy currents into the conductive material, currents whose magnetic field opposes the inducting magnetic field of the probe coil (Rothwell and Cloud 2001). The resulting magnetic field of the coil depends on the frequency, the material properties, the material's structure or its integrity. From these facts, the eddy currents applications may be applied to measurement of physical properties, material parameters (conductivity, hardness etc.), detection and determination of surface flaws, measurement of covering layers, control of corrosion effects or sorting conductive materials. Eddy currents applications for sorting materials are developed since the management of electrotechnical and electronic waste has become an intense concern for companies in the domain. Therefore, an analytical model of the conductive piece-mean frequency supplied coil ensemble has been developed. The coil impedance modifications due to the induced eddy currents from the conductive material depend on the electrical conductivity and the magnetic permeability of the conductive material, on the frequency domain, on the position of the material relative to the coil and also on the value of the working airgap. Marking the current variations through the probe coil allows separating the metallic conductive materials or separating the ferrous and non-ferrous materials for managing electrotechnical and electronic waste. The analytical model based on the equivalent lumped circuit diagram The probe coil impedance modifications due to the induced eddy currents from the conductive material depend on the electrical conductivity and the magnetic permeability of the conductive material, on the frequency domain, on the position of the material relative to the coil and also on the value of the working airgap. Marking the current variations through the probe coil allows separating the metallic conductive materials or separating the ferrous and non-ferrous materials for managing electrotechnical and electronic waste. PROBE COIL MODELING Our study is focused on the particular case of a probeinductor (fig. 1) manufactured as a coil – 2 wrapped on a half pot-core – 1 of magnetically-soft ferrite. An unavoidable airgap ( δ ) exists between the core and the tested metallic piece – 3. The magnetic field produced by the current flowing the inductor crosses the lowreluctance domain – 1 and the tested piece – 3 (as the shortest path outside the core), assuming, for simplicity, the leakage magnetic flux as negligible; two field lines are shown in fig. 1. The domain of tested piece crossed by the magnetic field can be approximated by the cylindrical crown of radiuses 2 1, r r , with the field lines oriented radially. In order to find an equivalent impedance of the inductor, a proper model of the system is required. Assuming that the ferromagnetic core remains unsaturated, it can be modeled as an electric linear resistance, as well as the airgap. Thus, due to the values of the electric resistivities, the eddy currents flowing the ferrite core (it has the electric resistivity up to m 105Ω ) are negligible compared to those in the tested piece ( m 10 10 6 8 Ω ÷ = ρ − − usually). Proceedings 25th European Conference on Modelling and Simulation ©ECMS Tadeusz Burczynski, Joanna Kolodziej Aleksander Byrski, Marco Carvalho (Editors) ISBN: 978-0-9564944-2-9 / ISBN: 978-0-9564944-3-6 (CD)