While open-circuit magnetic measurements are noted to involve distortions related to the image effect and, most significantly, the sample's demagnetizing factor, closed-circuit measurements are generally considered to be free of these distortions. However, it has been reported and observed within this research that for certain sample geometries and materials operating near the magnetic saturation of the electromagnet poles, there are observed distortions of up to 40.7% of the maximum magnetization at a field level of 25 kiloOersteds for a cylindrical sample with an L/D ratio of 0.2. This observed distortion in the magnetic measurement in a closed-circuit has been referred to in the literature as an “apparent image effect” error.
The intent of this research is to apply finite element modeling (FEM) to replicate original experimental and published data for cylindrical samples of both hard and soft magnetic material and to observe the phenomenology of the error within the results of the model. The hard magnetic material of interest is NdFeB and the soft magnetic material used is 1018 steel. Additionally, the sample data base is extended to rectangular prisms with data generated both experimentally and with FEM. Using a validated model it is possible to develop a corrective methodology and equations to address the magnetization measurement errors noted at high field levels within both the first and third quadrants of the hysteresis curve. The methodology developed through this research produced corrective surfaces with two dimensional polynomial fits with average adjusted R-values of 0.97.
As a fault study secondary to the development of the corrective methodology, this project investigated the significance of the sample's surface mating to the poles of the hysteresigraph. It was determined that a 5 ° partial misalignment air gap has only approximately 0.5% variation in magnetization, 4πMmax, from the baseline of an ungapped sample. It is indicated that the sample gap becomes statistically significant at the t-test risk level of α = 0.05 significance level at approximately a 14 ° gap.
The successful use of FEM in determining the closed circuit corrective methodology has led to the identification of the potential for a similar open circuit application. The calculation of the demagnetizing factor, N, required for open circuit measurements is a difficult exercise and, in the past, could only be precisely calculated for an ellipsoidal sample. For other regular geometries N was determined experimentally or calculated using certain assumptions. Either method introduces errors. This application used FEM to calculate the spherical demagnetizing factor of a magnetic sphere within a long solenoid. The FEM results indicated a demagnetizing factor N = 0.333 in all three axis. This result is in agreement with widely published and accepted results for such an arrangement.
The hysteresis distortion complicates identifying and developing new magnetic materials. Only a comprehensive understanding of the phenomenon can help to establish effective correction methods, which is important for infrastructure enhancement in scientific research and for development of advanced modern technology to accurately characterize new magnetic materials.