# Analysis of local magnetic measurements techniques for non destructive testing

Local magnetic measurements are carried out in magnetic circuits with non-uniform electromagnetic field patterns, including excitation windings and/or air gaps, as in the case of rotating electrical machines. The effects of sensor choice, sensor noise sensitivity and electromagnetic field inhomogeneity on the accuracy of the identification of the magnetic material properties are investigated. Moreover, the validity of the local magnetic measurements is confirmed by numerical models, based on the finite element method. We discussed in [1] comprehensively the possibilities, difficulties and limitations of local magnetic measurements in magnetic circuits with non-uniform electromagnetic fields. It is shown that higher accuracy is obtained when the measurements are performed in regions with less stray fields.

### The studied geometries

Figure 1 shows the two studied geometries, made from the same material, i.e. non-oriented electrical steel (M 700/50A). The studied magnetic circuits are magnetic ring cores with Di and Do the inner and outer diameter respectively. Each magnetic circuit consists of ten laminations with a total thickness of 5 mm. The excitation winding is wound over an excitation angle ‘θ’ for both geometries, G1 and G2. In G2, an air gap of 1 mm is introduced. G2 is a simplified magnetic circuit for rotating electrical machines, which have a partially excited stator, and an air gap between the stator and the rotor. Due to the symmetry in the studied geometries, the local magnetic measurements were carried out at the indicated positions in figure 1. Positions 1, 2 and 3 are located at φ = 0, φ/4 and φ/2, respectively, where φ is the unwound angle in degree (φ = 360° − θ).

These positions have been chosen in the unwound area, and not in the wound area, in order to simulate the availability of the local magnetic measurements in rotating electrical machines. It is possible to measure locally magnetic quantities in the unwound area of rotating electrical machines, but not in the wound area because the magnetic material is not accessible.

### Comparison between the state-of-the-art magnetic sensors

Tables 1 and 2 show a brief comparison between the previously mentioned sensors in magnetic field and magnetic induction measurements, respectively. For magnetic field sensors (table 1) each sensor has advantages and disadvantages due to the differences among their characteristics. We can divide the sensors into two groups: self-made sensors (flat H-coil and Rogowski coil) and commercial sensors (fluxgate and Hall-probe sensors). The main advantage of the self-made sensors is their availability. These sensors can be fabricated, easily and cheaply, at any laboratory. Also, these sensors do not require any supply voltage to work. However, the output voltages of these sensors, which are proportional to the time derivative of the measured magnetic field strength, are too weak especially at low frequencies. So, extra components for signal conditioning are needed, such as amplification, filtering and integration units. These extra components complicate the measurement set-up, and hence introduce an error in the measurements. On the other hand, the output voltage of the commercial sensors is directly proportional to the measured magnetic field strength. So, no extra components for signal conditioning are needed, which simplify the measurement set-up. However, these sensors require a separate supply voltage for their excitation. For magnetic induction sensors (table 2) it is clear that the search coil method is much better than the NPM: it needs less measurement set-up components. However, as discussed before, the NPM is preferable for local measurements as it is a ‘non-destructive method’.

*Table 1: Comparison among different sensors for local magnetic field measurements.*

*Table 2: Comparison between two different sensors for local magnetic induction measurements.*

### Modified Needle Probe Method

Research was carried out to increase the accuracy of the low-amplitude magnetic sensors for non-destructive testing. Although the NPM is an efficient technique for measuring the magnetic induction, it encounters numerous errors, such as errors due to vertical field component, and its sensitivity to noise interference. Due to the error introduced by the non-homogeneous air fields, the authors have presented a modified needle probe method [2], based on an anti-series connection of two sets of two needles. The extra two needles are used to compensate for the air flux.

Figure 2 shows the connection of the proposed modified needle probe, which consists of four needles; the output signal of the basic two needles ‘Vx ’ is proportional to the flux through the sample and the air fluxes as well (V12 ~ Bmaterial + Bair). The two extra needles should be located as close as possible to the basic needles, and it should be short-circuited directly above the sample surface. Note that needles 3 and 4 do not make contact with the material. So, the output signal of the extra two needles ‘Vy ’ is approximately proportional to the stray fields only (V12 ~ Bair). Due to the anti-series connection, the air fluxes have been eliminated from the output signal (Vtotal = V12 − V34 ~ Bmaterial).

### Results and discussion

The quasi-static magnetic measurements are performed at 1 Hz for a sinusoidal current excitation, in order to have negligible presence of eddy current effects in the magnetic core. The object under test is demagnetized between two successive measurements. The following aspects were investigated:**The effect of electromagnetic field inhomogeneity**

Figures 3a and 3b show the measured and simulated local magnetic field strength ‘Hlocal’ at positions 1, 2 and 3, using theHall-probe sensors, versus different values of the excitation current, in both geometries (G1 and G2). In figure 3a, we consider the geometry ‘G1’ and we mean by ‘Ampere’s law results’ the magnetic field H obtained by scaling the excitation current I according to H = NI / lm , where N = 550 is the number of turns of the excitation winding and lm = 314 mm is the average material length. However, in figure 3b, we consider the geometry ‘G2’ and we do not compare the measured results with results from Ampere’s law. Indeed, in this case the magnetic field depends on the value of the magnetic relative permeability μr which is a function of the magnetic flux density B. This is already clear from the simplified expression for the magnetic field in a highly ideal magnetic circuit: H = NI / (lm+(δμr(B)) , where δ is the air gap thickness.

Figure 4a shows the comparison among different sensors with respect to the vertical variation of the local field strength. Flat H-coil, Hall-probe and fluxgate sensors use the extrapolation method; however, the Rogowski coil measures the local field value at the sample surface ‘Z = 0’.

*Figure 3: (a) The measured ‘dashed curves’ and
simulated ‘solid curves’ local magnetic field strength at different
positions versus the excitation current in G1. Position 1 (□), position
2 (∆), position 3 (○) (Di = 90 mm, Do = 110 mm, θ = 230◦). (b) The
measured ‘dashed curves’ and simulated ‘solid curves’ local magnetic
field strength at different positions versus the excitation current in
G2. Position 1 (□,■), position 2 (∆,▲), position 3 (○,●) (Di = 90 mm,
Do = 110 mm, θ = 230◦).*

**The effect of sensor positioning**

The accuracy of the magnetic measurements is highly dependent on the position of the measurements, especially at magnetic circuits with high non-uniform fields. Here, we illustrate the effect of the sensor positioning along the radial and the circumference directions on the measurement accuracies.

Figure 4b shows the radial variation of the magnetic field strength at position 3, for different excitation currents in G1. Similar results are obtained for G2 (± 5 mm error in the sensor position along the radial direction results approximately in ±50 A/m error for the magnetic field for the low excitation current 0.5 A, and ±100 A/m error for the magnetic field for the high excitation current 2 A). It is also clear, from figure 4b, that the error between the measured and the simulated field values is high in the proximity of the sample edge, i.e. radius = 50 or 70 mm.

*Figure 4: (a) The magnetic field inhomogeneity above the sample at position 3, G1, using different sensors, compared to the simulated results. (b) The field strength inhomogeneity along the radial direction for different excitation currents, position 3 at G1.*

Figure 5 depicts the magnetic field strength inhomogeneity along the circumference of the unwound area, in both geometries (G1 with 0.5 A and G2 with 2 A). In G1, the field is high near the excitation winding edge, and it decreases with the increase of the unwound angle φ reaching its minimum value at the middle of the unwound area, i.e. φ = 115◦. In G1, the inhomogeneity in the field along the circumference is not so high, i.e. ± 2° error in the sensor position along the circumference results approximately in ±10 A/m error for the magnetic field.

In G2, the field is high near the excitation winding, and it decreases with the increase of the unwound angle φ reaching however its minimum value somewhere in the middle region between the excitation winding edge and the air gap. But due to the presence of an air gap, the field strength is appreciably enhanced toward the air gap. In G2, ±2° error in the sensor position along the circumference may result approximately in ±40 A/m error for the magnetic field.

*Figure 5: The field strength inhomogeneity along the circumference of the unwound area, in both geometries (G1,G2).*

### Magnetic material identification in geometries with non uniform electromagnetic fields using global and local measurements

Using the measurement setup of section 3, we identify magnetic materials using [2]: (A) fully based on the experimental method, (B) a coupled numerical-experimental inverse approach.

**A) Magnetic material identification fully based on the experimental method**

Figure 6 shows the B–H characteristics of both geometries obtained from local (local H and local B at the same position) magnetic measurements. The characteristics are compared with the original normal magnetizing curve B–H curve of the material under test. The magnetizing curve used as the input of the numerical models was obtained by tracing the peak values of both quantities (B and H) for different hysteresis loops. A good correspondence between reconstructed magnetic properties using local measurements and original characteristics in G1 is observed, which reveals the accuracy and validates the local magnetic measurements. However, in G2, the accuracy depends on the position where the measurements were carried out. At the position of less stray fields (position 2), a correspondence is observed, while at the positions of high stray fields (positions 1 and 3), large errors between the recovered characteristic and the original one are observed, especially near the air gap (position 3) due to the double error in the B and H local measurements. The results shown in figure 6 confirm the necessity of a numerical inverse approach in order to reconstruct the material properties accurately. Indeed, the reconstruction of the material properties only based on the local B and H measurements gives inaccurate results if the local measurements are carried out in a region with high inhomogeneity of B and H, due to the duplicated errors in both local measurements B and H. These errors may result from, e.g., not exactly the same position for the H and B sensors. The inverse approach can be based only on one local measurement, e.g. Blocal, which minimizes the error in the reconstructed properties [2].

*Figure 6: B–H characteristic of both geometries G1 ‘solid curves’ and G2 ‘dashed curves’ using the local magnetic measurements compared to the original characteristics. (Di = 90 mm, Do = 110 mm, θ = 230°).*

**B) Magnetic material identification based on a coupled numerical-experimental inverse approach**The identification procedure based on the experimental methods seems to be a valid technique. However, the experimental measurement procedure has to be very accurate, especially at high excitation fields where the stray field has a considerable effect. Small changes in the measured values lead to a substantial error in the identified parameters.

So, in order to reduce the influence of the measurements error, an inverse approach is proposed. The numerical models of both geometries G1 and G2 are constructed using the 3D finite element method (FEM) which solves the nonlinear quasi-static Maxwell’s equation, for the magnetic vector potential with the non-linear permeability. Figure 7a shows the recovered B-H characteristics using geometry G1, while figure 7b depicts the magnetic material characteristics using geometry G2.

*Figure 7: (a) B–H characteristic recovered using inverse approach on geometry G1 (with reference geometry-A being the fully wound ring core) ‘solid curves’. (b) B–H characteristic recovered using inverse approach on geometry G2 (with reference geometry-A being the fully wound ring core) ‘solid curves’.*

## Reference

(1) A. Abdallh, and L. Dupré, "Local magnetic measurements in magnetic circuits with highly non-unifom electromagnetic fields," Measurements Science and Technology, vol. 21, pp. 045109 (10pp), 2010.

(2) A. Abdallh, P. Sergeant, G. Crevecoeur, L. Vandenbossche, L. Dupré, and M. Sablik, "Magnetic material identification in geometries with non uniform electromagnetic fields using global and local magnetic measurements," IEEE Transactions on Magnetics, vol. 45, no. 10, 2009.

## Contact

For more information: Ahmed.Abdallh@ugent.be, luc.dupre@ugent.be