Global hysteretic properties of electrical steels can be measured using ring or strip samples, while the assessment of the local hysteretic properties is a much more difficult task since the measurement method needs to be very sensitive. This paper presents a new method wherein the intensity and spatial distribution of the magnetic field, arising from large gradients in the local magnetization, are measured. These large gradients are induced by the passage of a test sample through the steep gradient field of a small, proximate permanent magnet. Magnetic field measurements during both directions of motion provide information indicative of the hysteresis properties. We theoretically analyze these measurements and show experimentally that the measurements correlate well with all the significant aspects of conventional hysteresis loops. The results given in this paper are qualitative, and the method is both by its simplicity and its sensitivity to important hysteresis features a powerful means of magnetic nondestructive evaluation.
Hysteresis loss is not only a critical factor in the selection of steels for use in electrical machines but, by its nature, can also provide significant information on the structural condition and/or magnetic anisotropy of ferromagnetic materials generally. With electrical steels, the energy loss itself is the usual parameter of prime interest, whereas one or both of its (typically) key components, namely, coercivity and the remanent induction, or at some other “standard” field intensity, provide the sought for information. There is a need for a technique that can give useful information about relationships between microstructure or internal stress with magnetic performance.
Conventional measurements of hysteretic properties usually employ ring or strip samples, with the latter being necessary when anisotropy is being explored [
A new magnetostatic method for obtaining comparative measurements of hysteresis loss and its components in ferromagnetic sheet materials is described in this paper. The measurements will be shown to provide qualitative information, which correlates directly with all of the significant aspects of conventional hysteresis loops. Essential features of the measurement apparatus are shown in Figure
(a) Side view of basic arrangement. (b) Magnified view of the active elements showing the dimensional factors that contribute to the “Gap”,
The
The inarguable simplicity of the method and apparatus notwithstanding, a detailed understanding of its operation is quite the opposite. Nevertheless, the operational basis and a The The field from the magnet and its spatial distribution are approximated well enough by that of an equal moment dipole located within the magnet body. A solution of the 2D problem is sufficient. The sample is assumed to be thin enough such that the field from the magnet, while varying with longitudinal position, is uniform throughout its thickness. This assumption ignores thus also radial components of the field from the magnet. The instantaneous local magnetization at points within the sample, The
The authors are fully aware that this model is an approximation, but it enables to directly correlate simple hysteresis properties with the
Guided by the previous assumptions, the analysis proceeds as follows. Determine the variation with Determine the sequence of field variation at underlying points in the sample during forward and reverse motion of the magnet, that is, Create families of hysteresis loops with variable loss densities and components, that is, Determine Determine Determine Determine Correlate feature characterizations from (g) with hysteresis loop features from (c).
For the arrangement diagrammed in Figure
Diagram showing the field
The longitudinal component
Variation in (normalized)
Ascending and descending limbs of hypothetical hysteresis loops are, respectively, generated from
A closed loop is formed by shifting
Hypothetical positive and negative
From the above equations, it is possible to determine
To avoid the need to deal with equations having ever growing numbers of ever more complex terms, and to provide means for graphically following the evolving analysis, we assign arbitrary (but as will be seen, arguably reasonable) values to the material-dependent parameters
As the magnet moves forward from
(a) Variation of field and resulting magnetization at the point on the SUT, which is directly over the field sensor during forward motion of the magnet. (b) Same for reverse motion. (
(a) Variation of
Major hysteresis loops created from (
(a) Hysteresis Loops for constant
(a) Hysteresis Loops for constant
An experimental apparatus was set up on a vertical milling machine, thereby conveniently accommodating a variety of experimental conditions, including SUT size (width, thickness, and length), field sensor position relative to the SUT edge, length of Stroke and center position relative to the field sensor, adjustability of both the space between the magnet face and SUT (dimension
Except that the magnet was stationary while the SUT/field sensor combination (being mounted on the milling machine table) were the movable elements, operation of the apparatus followed the description in the Introduction.
For each magnet and gap combination,
Values of
Same as Figure
The versatility of the described method was shown by its use to measure the relative losses in regions near the cut edges of strip samples of the 350 and 800 grades. The SUT was placed with the edge being examined ~1 mm over the center of the field sensor. A magnet, 3.18 mm square by 12.7 mm long (in the direction of
The more compact spacing of the signature features predicted in the analysis than those experimentally observed is attributed to several critical but enormously complicating factors being ignored in the analysis; namely, the interaction between the magnetization and the generated fields and the gradients in these throughout the SUT thickness. Nevertheless, the model correctly shows that the magnetization gradients are different for the two directions of motion, a difference founded on the double-valued
This paper proposes an experimental method for locally assessing hysteresis properties, and a theoretical basis is given for explaining the obtained difference curves. The correlation between the experimentally obtained Figure
A possibility to more quantitative studies is to determine the input model parameters (i.e.,
In this paper, we propose a unique methodology together with its modus operandi and important experimental results. Both analytical and experimental results convincingly show the signature features of the difference measurements