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

Abstract

The case-hardening process modifies the near-surface permeability and conductivity of steel, as can be observed through changes in alternating current potential drop (ACPD) along a rod. In order to evaluate case depth of case hardened steel rods, analytical expressions are derived for the alternating current potential drop on the surface of a homogeneous rod, a two-layered and a three-layered rod. The case-hardened rod is first modeled by a two-layer rod that has a homogeneous substrate with a single, uniformly thick, homogeneous surface layer, in which the conductivity and permeability values differ from those in the substrate. By fitting model results to multi-frequency ACPD experimental data, estimates of conductivity, permeability and case depth are found. Although the estimated case depth by the two-layer model is in reasonable agreement with the effective case depth from the hardness profile, it is consistently higher than the effective case depth. This led to the development of the three-layer model. It is anticipated that the new three-layered model will improve the results and thus makes the ACPD method a novel technique in nondestructive measurement of case depth. Another way to evaluate case depth of a case hardened steel rod is to use induction coils. Integral formmore » solutions for an infinite rod encircled by a coaxial coil are well known, but for a finite length conductor, additional boundary conditions must be satisfied at the ends. In this work, calculations of eddy currents are performed for a two-layer conducting rod of finite length excited by a coaxial circular coil carrying an alternating current. The solution is found using the truncated region eigenfunction expansion (TREE) method. By truncating the solution region to a finite length in the axial direction, the magnetic vector potential can be expressed as a series expansion of orthogonal eigenfunctions instead of as a Fourier integral. Closed-form expressions are derived for the electromagnetic field in the presence of a finite a two-layer rod and a conductive tube. The results are in very good agreement with those obtained by using a 2D finite element code. In the third part, a new probe technology with enhanced flaw detection capability is described. The new probe can reduce inspection time through the use of multiple Hall sensors. A prototype Hall array probe has been built and tested with eight individual Hall sensor ICs and a racetrack coil. Electronic hardware was developed to interface the probes to an oscilloscope or an eddy current instrument. To achieve high spatial resolution and to limit the overall probe size, high-sensitivity Hall sensor arrays were fabricated directly on a wafer using photolithographic techniques and then mounted in their unencapsulated form. The electronic hardware was then updated to interface the new probes to a laptop computer.« less