Eddy currents induced in a conducting rod of finite length by a coaxial encircling coil

Abstract

This paper describes the calculation of eddy currents in a cylindrical conductive rod of finite length due to a coaxial circular coil carrying an alternating current. The coil impedance variation with frequency is determined from the field for an arbitrary coaxial location of the coil. Expressions for electromagnetic field and impedance of a coil encircling an infinite cylindrical rod are well known, the results being expressed as infinite integrals involving Bessel functions. For a finite length rod, additional boundary conditions must be satisfied at the ends. The extra boundary conditions are accommodated here by recasting the problem in a domain of finite extent in the axial direction. The axial length of the truncated domain is arbitrary and can be large compared with the coil length or the length of the rod. Therefore, the truncated domain solution can yield results that are numerically as close to the infinite domain solution as desired. The results provide a simple means of calculating the impedance of an inductor with a lossy core and can be used to investigate the linear properties of the core material.

Electromagnetic methods for measuring material properties of cylindrical rods and array probes for rapid flaw inspection

“…The prescribed coefficients are found from the calculation of the vector potential, A® (p, z), due to a coil in the absence of the rod. The result of this preliminary calculation is that [45] 2 ii 0 nl where cf -i In the steps which follow, the eigenvalues, q^\ and the coefficients ctf* are found by applying interface conditions, at the end of the rod. Then the remaining unknown coeffi cients are determined by applying interface conditions at the cylindrical interfaces where p = ri and p = r 2 .…”

“…In this study, a theory for finite length layered rods is developed accounting for end effects using the truncated region eigenfunction expansion (TREE) method [44][45][46][47]. The work is partly stimulated by the need to evaluate case depths of a case hardened rods taking into account end effects.…”

“…By truncating the problem region to a finite length in the axial direction, one can obtain the solutions in the form of a series. This can be done for a number of similar problems, such as a tube with a bobbin coil inside [44], a finite homogeneous rod encircled by a coil [45], a cylindrical ferrite-cored probe in the presence of a layered conducting half space [46], or a long coil above a conductive plate with a long flaw [47].…”

Inductance and Force Calculation for Axisymmetric Coil Systems Including an Iron Core of Finite Length

“…The solution is given in the form of integrals of firstorder Bessel functions. In [26,27], an analytical approach to compute eddy-currents induced in a conducting/ferromagnetic rod of finite length by a coaxial coil is developed. The authors use the truncated region eigenfunction expansion to compute the magnetic field inside the rod.…”

“…A similar approach to that presented in [16,24,26] is followed to compute the magnetic field. However, compared to [24,26], only the magnetostatic case is studied here (i.e., no-eddy current in the Figure 1. Axisymmetric system: a circular coil of rectangular cross section with an iron cylinder of finite length placed on the same axis at a distance h. ferromagnetic cylinder).…”