Effects of contact gap on nondestructive evaluation using magnetic measurement for ferromagnetic steel

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

Magnetic NDE magnetic yoke probe contact gap coercive field permeability impedance magneto-motive force

1. 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.

2. Experimental procedure

2.1. 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.

Fig. 1.

Size and configuration of magnetic yoke and set-up of magnetic measurement.

2.2. Hysteresis curves

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. $\begin{eqnarray}\displaystyle NI=H_{y}l_{y}+H_{m}l_{m} & & \displaystyle\end{eqnarray}$ (1) where I is the applied current to the magnetizing coil, and N is the number of turns of magnetizing coil. If we assume that the magnetic field is uniform inside magnetic circuit and we can decide the precise magnetic path length, the magnetic field H (= H_y = H_m) can be calculated. However, not easy to decide them practically which means difficult to precise intrinsic magnetization curves of specimen tested, therefore we use Φ − NI (= F: F is a magneto-motive force) curve which includes the information about changes in magnetic properties of specimens. Because the magnetic yoke property does not change, the changes in measurement properties reflect relative changes in magnetic properties of specimen tested. The flux inside magnetic circuit is obtained by the integration of induced voltage at the pickup coil.

2.3. Impedance measurement

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.

3. Experimental results

3.1. 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.

Fig. 2.

(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.

3.2. Inductance and resistance of magnetizing coil

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.

Fig. 3.

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.

Fig. 4.

(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.

4. Discussions

4.1. 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: $\begin{eqnarray}\displaystyle {\Phi}={\displaystyle \frac{NI}{R_{y}+R_{m}+2R_{g}}}. & & \displaystyle\end{eqnarray}$ (2)

Thus inductance L of the magnetizing coils is $\begin{eqnarray}\displaystyle L={\displaystyle \frac{N^{2}}{R_{y}+R_{m}+2R_{g}}}. & & \displaystyle\end{eqnarray}$ (3)

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: $\begin{eqnarray}\displaystyle L={\displaystyle \frac{{\mu}_{0}N^{2}}{{\displaystyle \frac{l_{y}}{{\mu}_{y}S_{y}}}+{\displaystyle \frac{l_{m}}{{\mu}_{m}S_{m}}}+2{\displaystyle \frac{l_{g}}{S_{y}}}}} & & \displaystyle\end{eqnarray}$ (4) where μ₀ is the permeability of vacuum.

Fig. 5.

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.

4.2. FEM simulation

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.

Fig. 6.

The virgin curves simulated by FEM.

4.3. Consideration

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.

Fig. 7.

(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.

5. Conclusions

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.

References

Kronmüller

, Magnetic techniques for the study of dislocations in ferromagnetic materials, International Journal of Nondestructive Testing3 (1972), 315–350.

Swartendruber

L.J.

Hicho

G.E.

Chopra

H.D.

Leigh

S.D.

Adam

and Tsory

, Effect of plastic strain on magnetic and mechanical properties of ultra low carbon sheet steel, Journal of Applied Physics81 (1997), 4263–4265.

Makar

J.M.

and Tanner

B.K.

, The effect of plastic deformation and residual stress on the permeability and magnetostriction of steels, Journal of Magnetism and Magnetic Materials222 (2000), 291–304.

Takahashi

Echigoya

and Motoki

, Magnetization curves of plastically deformed Fe metals and alloys, Journal of Applied Physics87 (2003), 805–813.

Eichmann

Devine

Jiles

and Kaminski

, New procedures for in situ measurement of the magnetic properties of materials: applications of the magnescope, IEEE Transactions on Magnetics28 (1992), 2462–3464.

Panda

Das

Mitra

Jiles

and Lo

, Evaluation of deformation behavior of HSLA-100 steel using magnetic hysteresis technique, IEEE Transactions on Magnetics42 (2006), 3264–3266.

Dobmann

Altpeter

Wolter

and Kern

, Industrial applications of 3MA – micromagnetic multiparameter microstructure and stress analysis, Studies in Applied Electromagnetics and Mechanics, Electromagnetics Nondestructive Evaluation (XI)31 (2008), 18–25.

Stupakov

Tomáš

and Kadlecová

, Optimization of single-yoke magnetic testing by surface fields measurement, Journal of Physics D39 (2006), 248–254.

Kikuchi

Liu

Ara

Kamada

Kobayashi

and Takahashi

, Magnetic yoke probe for in-situ magnetic measruremetns, Transactions of the Institute of Electrical Engineerong of Japan, IEEJ Transactions on Fundamentals and Materials126 (2006), 919–924.

10.

Perevertov

, Influence of the residual stress on the magnetization process in mild steel, Journal of Physics D40 (2007), 949–954.

11.

Kikuchi

Kamada

Kobayashi

and Ara

Magnetic NDE with magnetic yoke-probe for degradation and mechanical properties of steel, in: Nondestructive Testing of Materials and Structures Büyüköztürk

(ed.), RILEM Bookseries, vol. 62013, pp. 505–511.

12.

Vertesy

and Tomas

, Nondestructive magnetic inspection of spot welding, NDT & E International98 (2018), 95–100.

13.

Ryu

K.S.

Nahm

S.H.

Park

J.S.

K.M.

Kim

Y.B.

Kim

Y.B.

and Son

, A new non-destructive method for estimating the remanent life of a turbine rotor steel by reversible magnetic permeability, Journal of Magnetism and Magnetic Materials251 (2002), 196–201.

14.

Kikuchi

Onuki

Ara

Kamada

Kobayashi

and Takahashi

, Initial permeability and Vickers hardness of thermally aged FeCu alloy, Journal of Magnetism and Magnetic Materials310 (2007), 2886–2888.

15.

Kikuchi

Henmi

Liu

Ara

Kamada

Kobayashi

and Takahashi

, The relation between AC permeability and dislocation density and grain size in pure iron, International Journal of Applied Electromagnetics and Mechanics25 (2007), 341–346.

16.

Kikuchi

Ito

and Daimon

, Nondestructive evaluation of hardness using AC permeability and impedance analysis, in: Proceedings of the 2013 Seventh International Conference on Sensing Technology (ICST), 2013, pp. 586–590.

17.

http://www.femm.info/wiki/HomePage.