Evaluation of Conductivity and Radius of Metallic Rods Based on Magnetic Field Analytical Model

An evaluation of the conductivity and the radius of metallic rods is conducted by utilizing an analytical model of the surface magnetic field. First, an axisymmetric model of a cylindrical coil encircling a metallic rod is established and an analytical solution for the magnetic induction intensity is derived by means of a separation variable technique and a truncated region technique. The results of the analytical model calculation demonstrate that the radial magnetic induction intensity decreases by different degrees at different axial positions as the conductivity and rod radius increase, whereas the axial magnetic induction intensity increases. Moreover, the closer the radial distance is to the rod, the more obvious the change in the magnetic field will be. The radial magnetic field peak (B-r(p)) and the axial magnetic field at zero (B-z(o)) can be used as the characteristic quantities for conductivity and rod radius measurements. Additionally, a butterfly graph is proposed to comprehensively evaluate the effect of conductivity and rod radius on the radial and axial magnetic induction intensities. Most importantly, the calculation results agree well with the numerical simulation, showing that the proposed technique not only illustrates the potential of further development for eddy current testing, but also provides guidance for continued experimental research.