Residual stress evaluation by Barkhausen signals with a magnetic field sensor for high efficiency electrical motors

This paper presents the newly proposed stress evaluation by measuring Barkhausen signals with a magnetic field sensor. It is well known that the magnetic properties of electrical steel sheets, which are used for electrical motor cores, are deteriorated by the residual stress during manufacturing process such as punching, laminating, winding, framing of the electrical motors shown in FIG. 1(a), and then the iron loss of the final laminated electrical steel sheet cores of the electrical motors increases inevitably as shown in FIG. 1(b).^1,2 Conventionally, the residual stress had been removed by the annealing process with a huge-size electric furnace after assembling electrical motors.^3,4 However, a huge-size electric furnace itself is very expensive and the annealing process by it costs a lot and is very time-consuming (normally, it takes about 12 hours), therefore, the annealing process has been eliminated for the cost performance. Especially, the annealing process has never been applied into the “industrial electrical motors” in Japan for these twenty or thirty years. It means that the industrial electrical motors have been used with high iron loss for many years. Meanwhile, the regulations on high efficiency and low loss electrical motors proposed by International Electrotechnical Commission (IEC) have been applied in the world recently to save energy for limited resource on the earth and resolve international global warming.⁵ To overcome these problems, we must reduce the loss of all electrical motors as much as possible.^6,7 Therefore, we have reported the new heating method, whose system expense is not expensive, and which is not time-consuming due to the direct heating by secondary current.⁸ The electromagnetic and heating characteristics of the specimens by proposed method were confirmed, and then it was applied into the laminated cores to reduce iron loss for high efficiency electrical motors.⁸ In this paper, a stress evaluation method by measuring Barkhausen signals with a magnetic field sensor is newly proposed to make clear the local distribution of the residual stress on the electrical motor cores during manufacturing electrical motors to use the heating method effectively.

The Barkhausen signals occur discontinuously with 180-degree magnetic wall movements in magnetic materials. The Barkhausen signals arise from magnetizing moments, and they are affected by the microscopic conditions such as crystal grain, dislocation and impurities. This means that the Barkhausen signal are very sensitive to the stress conditions on magnetic materials including electrical steel sheets. There are a lot of published papers on Barkhausen signals to evaluate stress, fatigue, creep, hardening and so on mainly for mechanical parts.^9–15 In these previous works, Barkhausen signals were measured normally by induced voltage on B-coil type sensors under DC magnetic field or uncontrolled alternating magnetic field because they were enough for evaluating material changes on mechanical parts. Otherwise, we have made clear that the magnetic field strength was much more sensitive to the stress than the magnetic flux density in the case of the controlled magnetic flux condition under alternating and rotating magnetic flux (it means the practical magnetic flux conditions in electrical motors and transformers).^16,17 Therefore, it is supposed that the Barkhausen signals by using a H-sensor can be much effective to evaluate the residual stress on the electrical steel sheets. In this paper, we focused on measuring Barkhausen signals by “H-coil type sensor” and under “controlled magnetic flux conditions” to realize it. We evaluated the tensile stress of the electrical steel sheets by measuring Barkhausen signals by using our developed H-sensor for high efficiency electrical motors in this paper.

A Rogowski-Chattock coil (H-coil) was introduced to measure Barkhausen signals on the specimens (non-oriented electrical steel sheets). The structure of the used Rogowski-Chattock coil is shown in FIG. 2. The magnetic field strength in the air, H_s, and the internal magnetic field strength on the specimen, H_eff, can be written with the following equation by Ampère’s law,

here, l_s, is the length of the Rogowski-Chattock coil and l_eff the length of the specimen that the Rogowski-Chattock coil is attached, respectively, as shown in FIG. 2. The magnetic field strength in the Rogowski-Chattock coil crosses the winding coils perpendicularly, therefore the magnetic field strength can be derived from the induced voltage on the coils (It is named as the Rogowski-Chattock coil). Moreover, there is no electrical current flow in the passes consisted of l_s and l_eff, so the right term of the Ampère’s law becomes zero as shown in Equation (1).¹⁸ The effective magnetic field strength (the internal magnetic field strength on the specimen), H_eff, can be derived from,

The magnetic field strength, H_s, can be calculated from the electromotive force, e_S, which is induced on the Rogowski-Chattock coil by the following equation,

where, N_s and S_S, is the number and the cross section of the Rogowski-Chattock coil as shown in FIG. 2. From (2) and (3), the effective magnetic field strength on the specimens can be calculated, and the Barkhausen signals can be derived from the filtered effective magnetic field strength.

The measurement system for Barkhausen signals is shown in FIG. 3. The specimen is magnetized, after the controlled voltage waveform is generated by D/A converter and amplified by power amplifier. The B-coil wound around the specimen is used to measure the induction voltage at the center of the specimen. The signals are digitized by A/D converter, and the magnetic flux density is calculated on a PC. Controlling the waveform so that the induction voltage waveform corresponds with the required waveform, the feedback control was used. After controlling the waveform of the magnetic flux density, the Barkhausen signals are recorded by the Rogowski-Chattock coil attached on the specimen’s surface as shown in FIG. 3. The specimens were put between double U-shaped magnetizing yokes as shown in FIG. 3. The coil was wound on the yokes with the 1.0-mm diameter copper wire. The tensile stress was calculated from the applied weights and the measured cross-sectional area of the specimen.

Non-oriented magnetic steel sheets, H12, with the 20-mm width × 200-mm length × 0.5-mm thickness were used for the specimens. Each one has two different rolling directions: (a) Sample-0° and (b) Sample-90° to the longitudinal direction of the specimen as shown in FIG 4. Magnetization frequency was selected as f =50 (Hz). The measurement conditions are shown in Table I. In order to evaluate the Barkhausen signals depending on the stress, the magnetic flux density was controlled to be a exact sinusoidal waveform in the amplitudes of 0.4, 1.0 and 1.4 [T] and the tensile stress, 0, 4.9, 9.8, 14.7, 19.6 and 24.5 [MPa], was applied into the specimens as shown in Table I.

To begin with, the B-H loops measured from the Sample-0° and Sample-90° with the tensile stress, 0, 4.9, 9.8, 14.7, 19.6 and 24.5 [MPa], are shown in FIG. 5 and FIG. 6, respectively. FIG. 5(b) and FIG. 6(b) shows the enlarged B-H loops to make clear the difference. Apparently, the B-H loops measured from the Sample-0° have smaller area in comparison with the ones from the Sample-90°, though the variation of the loops on the Sample-90° applying the stress into the samples was larger than the one on the Sample-0°. In the case of the Sample-0°, the slope of the B-H loops increases by the stress, 14.6 [MPa], and then decrease with the stress, 19.6 and 24.5 [MPa]. This is because the magnetic domains can move to the direction of the external magnetic field by 14.6 [MPa] thanks for the tensile stress, and after that larger tensile stress prevent the magnetic domains from moving easily. In the case of the Sample-90°, the slope of the B-H loops increases by the stress, around 19.6 and 24.5 [MPa] because these levels of the tensile stress can help the magnetic domains move easily in the perpendicular direction to the rolling direction.

FIGs.7 show the Barkhausen signals and the controlled magnetic flux density (1.0 [T]) on the Sample-0° measured by the Rogowski-Chattock coil and the conventional sensor without stress. The conventional sensor (B-coil type sensor) had been checked if it could measure the Barkhausen signals properly and was used for the material evaluation.^19–22 By comparing FIG. 7(a) and FIG. 7(b), the Barkhausen signals measure by the conventional sensor looks like the typical Barkhausen signals. However, checking both signals in the frequency domain as shown in FIGs. 8, the FFT waveform transformed from the Barkhausen signals measured by the Rogowski-Chattock coil has much specific feature in comparison with the one by the conventional sensor. As we can see it in FIG. 8(b), the FFT waveform transformed from the Barkhausen signals measured by the conventional sensor is rather flat range.²² FIGs. 7 and FIGs. 8 show the signals and the FFT waveforms without stress. FIGs. 9 show the FFT waveforms transformed from the Barkhausen signals measured by both sensors with 24.5 [MPa] (the maximum tensile stress in this paper). on the Sample-0°. Comparing FIG. 8(b) with FIG. 9(b), it is very difficult to distinguish the difference of the FFT waveforms,²² however, these are some differences around 10 – 30 [kHz] between FIG. 8(a) and FIG. 9(a). The amplitudes in these frequency range by the Rogowski-Chattock coil increased after applying the stress. The Barkhausen signals on the Sample-90° without the stress and with the stress, 24.5 [MPa] are shown in FIGs. 10 and the FFT waveforms of their signals are shown in FIGs. 11. Because the Sample-90° has the transverse direction to the rolling direction, the amplitude in FIG. 10(a) is larger than the one in FIG. 7(a). And on the Sample-90°, the all slopes of the B-H loops increase after applying stress, therefore, the amplitude in FIG. 11(b) is smaller one in the FIG. 11(a). It would be required to check the physical behavior related to the signals in details, the Rogowski-Chattock coil (H-coil type sensor) has higher sensitivity than the conventional B-coil type sensor, therefore, the stress evaluation was done by the Barkhausen signals measured by the Rogowski-Chattock coil in this paper.

As shown in FIGs. 8, FIGs.9 and FIGs. 11, the amplitudes of the FFT waveforms depending on the applied stress, so as to quantitate the applied stress from the measured Barkhausen signals, we focused on the frequency ranges. Here, the total amplitude in the four frequency ranges, 5-10 [kHz], 10-15 [kHz], 15-20[kHz] and 20-25[kHz] were selected to show because the variations of the amplitudes of the FFT waveforms in these frequency ranges were larger than others. The controlled magnetic flux density was also set as the three levels, 0.4, 1.0, 1.4 [T] in this section. FIGs. 12 shows the total voltages in these four frequency ranges on the Sample-0° and FIGs. 13 shows ones on the Sample-90°. From all figures, the tendencies are similar in FIGs. 12 and FIGs. 13. The total voltages on the Sample-0° increased as shown in FIGs. 12 and decreased as shown in FIGs. 13 from the Sample-90°. The tendency in FIGs. 13 could be explained from the results FIGs. 6, it is because the applied stress makes the specimens stronger soft material, therefore, the Barkhausen signals do not occur on the Sample-90° after applying stronger stress. For the Sample-0°, it is supposed that the domain movements and the strength of the magnetic moment are related into the tendency, it should be made clear the mechanism of those to use the results for the practical stress evaluation. FIGs. 14 show the change ratio of the total voltages from the Sample-0° and the Sample-90°. The change ratio of the total voltage in the focused frequency ranges became the largest under the magnetic flux density, 1.0 [T], in both figures.

Therefore, it would be better to select the magnetic flux density under the boundary between linear and nonlinear regions for the stress evaluation.

The results obtained in this paper are summarized as follows.

1. The Barkhausen signals measured by the Rogowski-Chattock coil (H-coil type sensor) had higher sensitivity to the stress than the conventional sensor (B-coil type sensor). The amplitudes of the FFT waveforms transformed by the Barkhausen signals were different from each other depending on the stress and the rolling direction of the specimens.

2. The total amplitudes in the focused frequency ranges increased on the Sample-0° and decreased on the Sample-90° (the rolling direction and transverse direction specimens).

3. The change ratio of the total voltage in the focused frequency ranges became the largest under the magnetic flux density, 1.0 [T]. Therefore, it would be better to select the magnetic flux density under the boundary between linear and nonlinear regions.

It will be made clear some more mechanism of the Barkhausen signals measured by the Rogowski-Chattock coil (H-coil type sensor), those results could be useful for the residual stress evaluation of the electrical steel sheets on the process lines of the electrical motors, moreover in order to develop the high efficiency electrical motors.

Some parts of this work were supported by JSPS KAKENHI Grant Number 17H01259. The authors would like to show our gratitude for this support.