Abstract
We investigated effects of contact gap on magnetic nondestructive evaluation technique using a magnetic single-yoke probe. Firstly, we evaluated hysteresis curves and impedance related to permeability of the material measured by a single-yoke probe, when an air gap length between the probe and specimens changes. The hysteresis curve gradually inclines to the axis of the magneto-motive force and magneto-motive force at which the magnetic flux is 0 decreases with increasing the gap length. The effective permeability also decreases with increasing the gap thickness. The incremental of gap thickness increases the reluctance inside the magnetic circuit composed of the yoke, specimen and gap, which results in the reduction of flux applying to specimen.
Keywords
Introduction
Microstructure changes of ferromagnetic steels affect their mechanical properties and magnetic properties, therefore correlations between mechanical properties, such as hardness, yield strength, and magnetic properties such as coercive field and permeability, exist [1–4]. Based on these correlations, nondestructive evaluation (NDE) using magnetic measurements for mechanical properties of steel has been proposed [5–8]. In a typical case, a magnetic single-yoke is adopted to generate magnetic flux in the material tested, and a pick-up coil wounded around the yoke leg detects the changes in flux passing through the magnetic circuit composed by the yoke and the material tested [9–12]. This method does not directly evaluate the magnetization curve of the material tested itself, however, the obtained hysteresis curves reflect the magnetic property changes generated in the material tested, and the method is quite useful for NDE. On the other hand, the rough surface, some oxidized coating and shot-blasting exist frequently on the surface of steel, which acts as a magnetic gap between the yoke and the specimen; this influences strongly magnetic properties measured. To accomplish highly accurate assessment, we need to deal with measurement results with taking into account effects of contact gap. Therefore, this study investigates the effects of the magnetic gap between the yoke and specimen on evaluation of magnetic properties comprehensively and experimentally, and discusses the obtained results owing to brief FEM simulation and equivalent magnetic circuit analysis.
Experimental procedure
Specimens and set-up
Low carbon steel (S15C) sheets were prepared and one of those steel sheets was undeformed and others were cold-rolled with reduction ratios of 5, 10 and 40%. The composition of the steel is 0.16 wt.% C, 0.2 wt.% Si, 0.44 wt.% Mn, 0.019 wt.% P, 0.018 wt.% S, and 0.01 wt.% Ni and Fe in balance. Then the plates were cut out and the size of the plate is 25 mm × 15 mm × 2 mm. Figure 1 shows the size, configuration of the magnetic yoke and measurement set-up with a gap. The material of the yoke is Fe-Si steel. A magnetizing coil and a pick-up coil have 150 and 50 turns, respectively. The magnetic yoke was located on the specimen with the gap between the yoke and specimen as shown in Fig. 1. The gap length is varied from 0 to 0.5 mm.
Size and configuration of magnetic yoke and set-up of magnetic measurement.
The triangular current of 0.05 Hz is applied to the magnetizing coil of the yoke, which magnetized the specimen. Assume that the magnetic field of the yoke and the specimen is H
y
, H
m
, respectively, and magnetic path length is l
y
, l
m
, the magneto-motive force NI is expressed as the following equation by the Ampere’s law.
It is well known that permeability is also useful parameters on magnetic NDE [13–16] and the parameter can be evaluated by a measurement of impedance of a coil wounded around a magnetic yoke. Thus we also examined permeability changes of the specimen when the gap exists between the yoke and specimen. The impedance (resistance and inductance) of the magnetizing coil was measured by an LCR meter (HIOKI 3522). The measurement frequency varied from 1 Hz to 100 kHz, and ac current of 10 mA was applied to the magnetizing coil.
Experimental results
Hysteresis curves and magnetic parameters
Figure 2(a), (b) shows Φ–NI curves for the undeformed (0% reduction) and the deformed (40% reduction) specimen when the gap thickness between the yoke and the specimen changes. The slope of the curve inclines gradually with increasing gap thickness. This is explained by the increment of the magnetic resistance as mentioned later.
(a), (b) Hysteresis curves (Φ–NI curves) for undeformed and deformed specimen when the gap thickness changes. (c), (d) Dependence of F c on reduction ratio and gap thickness.
Figure 2(c) plots the magneto-motive force where the magnetic flux Φ inside magnetic circuit becomes zero, F c , reflecting changes in the coercive field of the specimen, against the reduction ratio for each gap thickness. When the gap is 0, the value of F c changes from 5. At 0% reduction ratio to 13. At 40% reduction ratio, while the value changes from 3 to 8. At when the gap is 0.5 mm. The changing ratio of F c decreases with increasing gap thickness. Figure 2(d) shows the dependence of F c on the gap thickness at each specimen. The value of F c deceases with an increasing gap thickness for all cases, and the value at 0.5 mm is an almost half value of those at gap = 0.
Figures 3 show the frequency dependence of impedance (inductance L and resistance R) of the magnetizing coil, reflecting the permeability changes of the specimen, at each gap thickness. The inductance is constant at relative lower frequency, and then decreases with rising frequency. When the gap is small, inductance show higher value at low frequency, e.g. 1–100 Hz, whereas the range where inductance constant, extends to higher frequency. The resistance at lower frequency is constant, then increases with increasing frequency. The decreases in inductance and the increases in resistance at a relatively higher frequency are attributed to eddy current loss and skin effect.
Frequency dependence of impedance for the undeformed (0%) and deformed (40%) specimens.
Figure 4(a), (b) shows the gap thickness dependence of the inductance at 1 Hz and resistance at 100 Hz for undeformed and deformed specimen. Basically, the inductance and resistance decrease with increasing the gap thickness for all specimens. The changes in parameters with different reduction ratio is clear at the relatively narrow gap, while the change becomes slight at large gap, which means accurate assessment becomes difficult as the gap thickness becomes large.
(a), (b) Dependence of impedance on gap thickness. (c), (d) Dependence of impedance on reduction ratio at each gap thickness.
Figure 4(c), (d) shows the relation between the inductance at 1 Hz, resistance at 100 Hz and the reduction ratio for each gap thickness. When the gap is small, impedance shows significant dependence on reduction ratio, however, the dependence becomes small with large gap thickness. For example, when the gap is 0.5 mm, both inductance and resistance is almost constant against changes in reduction ratio.
Equivalent magnetic circuit analysis
Figure 5 shows the equivalent magnetic circuit for the measurement system. The parameters of R
y
, R
m
and R
g
, are reluctance (magnetic resistance) of magnetic yoke, specimen and gap, respectively. The value of Φ is the total flux inside the magnetic circuit. The value of NI is a magneto-motive force F and, N is the numbers of turns of the magnetizing coil, I is current applied to the magnetizing coil. Based on the analysis of this circuit, we obtained the total flux is as followed:
Thus inductance L of the magnetizing coils is
If the relative permeability, sectional area and length in each sections, yoke, specimen and gap, are μ
y
, μ
m
, μ
g
, S
y
, S
m
, S
g
, l
y
, l
m
and l
g
respectively, the inductance is expressed:
Equivalent magnetic circuit.
In the present case, only the gap thickness l g changes. From Eq. (4), when the gap thickness increases the inductance L decreases, which means effective permeability inside circuit decreases. The magnetic resistance at the gap is quite large compared with that of the yoke and specimen part. Therefore, when the gap increases, the magnetic resistance of the total magnetic circuit composed by the yoke, specimen and gap, becomes large; this means larger magneto-motive force requires to obtain same magnetic flux level than that of the case which the circuit has a smaller magnetic resistance.
Figure 6 shows the simulation results for the virgin curves of measurement system calculated by FEMM (two dimensional FEM software) [17]. The model for simulation is same as the configuration as shown in Fig. 1. The calculations are done when the specimen is undeformed (0%) and deformed (40%) with different gap thickness. The slope of the curve inclines toward the horizontal axis with increasing gap thickness, which is consistent with the results of measured hysteresis curves. As mentioned in Section 4.1, when the gap increases, the reluctance at gap increases, and large current is required to obtain same flux as that without gap, therefore, the slope becomes smaller.
The virgin curves simulated by FEM.
We also evaluated the field strength near the surface of the specimen by a Gauss meter, and confirm B–H curves of specimens become a minor loop mode with increasing gap thickness as shown in Fig. 7(a), (b). When the gap thickness becomes larger, magnetic flux supplying from the yoke decreases, which means the magnetization field becomes small inside the specimen tested. Thus, since a maximum applied field decreases and then coercive force decreases with increasing gap.
(a), (b) B–H curves of specimens. (c) Relation between L at 1 Hz and gap thickness (experimental and calculation).
Figure 7(c) shows one example of the relation between impedance and gap thickness with comparison of experimental and calculated. The experimental result is inductance at 1 Hz for undeformed an deformed (40%) specimen, while the calculation result was obtained based on the equivalent circuit analysis. The calculation result is well consistent with the experimental results. Therefore, if we can control the gap thickness precisely, an extrapolation of evaluating parameters taking into account effect of the gap can be possible; this makes the method practical usage with high reliability.
We evaluated magnetic properties nondestructively using magnetic yoke with the gap between a yoke and a specimen. The results show the decreases in evaluation parameters with increasing the gap thickness. This can be explained based on the equivalent magnetic circuit analysis and consideration of the minor hysteresis loop mode. On the other hand, if the gap can be controlled quantitatively, NDE using magnetic yoke is possible, even though the gap exists on the surface of the specimen.