Analytical computation of eddy currents and inductances in a conductive rod of finite length wound by a moveable cylindrical coil

This paper presents a complete 2D analytical model for calculating the magnetic field, eddy current and mutual inductance in a conductive rod of finite length wound by a cylindrical coil. The proposed model combines the truncated region eigenfunction expansion (TREEM) method with the separation of variables technique to solve Maxwell’s equations in terms of the magnetic vector potential in the axisymmetric problem. This developed analytical model allows considering the finite length of the cylindrical coil and the conductive rod at the same time, also solves the nonlinear equation that gives the complex eigenvalues. The analytical results are compared to the numerical ones obtained by FEM (COMSOL).

I. Introduction

Electromagnetic devices used in electrical engineering (tubular linear induction motors and actuators, electromagnetic launchers…etc.) require cylindrical coils surrounding a core of conducting material [1]-[3]. Modeling these devices of finite length with electric circuit method requires the computation of self and mutual inductances. The mutual inductance between the coil and the conductive rod depends essentially in the eddy current and the position of the coil.