**1. Introduction**

Magnetic Barkhausen noise (MBN) is a phenomenon that occurs when a ferromagnetic material is being magnetized. During that process, when the magnetic field strength increases, the magnetic domain structure is gradually reorganized. This process is associated with the movement of domain walls (DW), followed by the rotation of magnetization vectors inside domains, resulting in discontinuous changes in the magnetic flux inside a material [1–3]. Those changes in the magnetic flux can be observed by a coil located at the surface of the material, in the form of voltage noise induced in its turn as a result of rapid changes in the degree of magnetization [4]. This method is used for various industrial applications for non-destructive condition testing and quality assessment of ferromagnetic materials, e.g., for evaluation of residual stress, active tensile and compressive stress, microstructure and micro hardening [5–19]. In addition to the possible applications mentioned above, the MBN is also used

to evaluate the directional properties of ferromagnetic materials. Within this group of applications, an important aspect is the assessment of magnetic anisotropy of materials and the detection of easy magnetization axes. Recently, the use of MBN to evaluate magnetic anisotropy in steels, which is the result of a number of different factors, has become an equally important issue. The key in this aspect is the possibility of non-destructive and quick assessment of directional magnetic characteristics (introducing the axis of easy/hard magnetization) of steel formulated specially by means of surface engineering methods.

Determining the axis of easy magnetization is particularly important in the process of designing electrical machines, in essence the transformer cores or electric motors. Anisotropic properties allow optimizing their constructions and in consequence increasing effectiveness and reduce the costs of transformation and distribution of energy [20,21]. The resultant easy magnetization axis is influenced by a number of factors, including: residual stress, grain shape and size, etc. [22,23]. Depending on the influence of each factor, the value of anisotropy will change, which changes the magnetization ability in different directions. Within the currently conducted research on the application of the MBN to assess the magnetic anisotropy of materials, two approaches can be distinguished. The first one is related to the analysis of the impact of individual factors and its rate on the scale of anisotropy [24–26]. The second one refers to possible application for the need of rapid assessment of the resultant axis of easy magnetization [27,28]. This paper considers the latter aspect.

In the literature, different approaches to assessing the easy magnetization axis can be distinguished by omnidirectional observation of MBN activity. The following description presents several literature examples of the use of MBN to detect the easy magnetization axis. The first, classic approach is to observe the MBN for various settings of directional magnetic field acting on the examined material. In paper [28], the MBN burst expressed in the time domain was analyzed to obtain information about anisotropic properties. A classical grain-oriented electrical steel sheet was used for the study. The authors observed a higher amplitude value of MBN signal envelope for the rolling direction (RD), which was characterized by the occurrence of two distinct peaks in comparison to the signals obtained for other directions. They explained this phenomenon with much higher MBN activity for RD due to the large number of 180◦ domain walls (DWs), and associated the maximum values with the process of nucleation and annihilation of DWs. Confirmation of these observations was a distribution of the root-mean-square (RMS) value of the measured MBN signal versus the measuring angle, showing the highest value along the RD direction. An attempt to overcome the need for mechanical rotation of the measuring head is to introduce an appropriate modification of the MBN transducer's excitation system. Examples of applications of such original solutions were presented in papers [27,29]. In [29], the authors used two C-shaped cores with coils placed perpendicularly to each other to control the excitation characteristics, a method named rotational Barkhausen noise (RBN). In this way, it is possible to generate a two-dimensional magnetizing field imitating the characteristics occurring during the classical MBN angular measurement, without the need for mechanical rotation of the magnetizing system. A disadvantage of this approach is the problem to obtain full homogeneity of the magnetic field. In paper [27], a rotatable transducer was used, in which the rotating permanent magnets generated a magnetic field, and the centrally located coil measured the MBN signal. The transducer collected data of the generated in the material magnetic induction disturbances, and then the measured MBN signal was analyzed in the time domain using features extracted from the MBN signal's envelope. This method, referred to as continuous rotational Barkhausen noise (CRBN), allows straight observation of directions for which there is a clear increase in magnetic emission. The directional characteristics were related to the anisotropy of the material. The performance of the proposed system was verified based on the comparison with the classical approach. Despite the high correlation between the results obtained and those of the classic angular measurement, the key issue of the proposed CRBN method is the selection of the speed of the transducer motion and the rotation of the magnets. Both factors have a large impact on the sensitivity of the measurement and, as a result, the discrimination between the directional magnetic properties of the material (directions of magnetization). Mindful of the need to increase the effectiveness

of assessing the anisotropic properties of magnetic materials, the idea of sequential analysis of the MBN burst has recently appeared. Its purpose is to divide a single burst into bands (sections) defined in relation to the magnetization period or magnetic field level. An example of such an approach was presented in [25,30,31]. In those works, the area of greatest MBN activity (referred to main MBN peak) was associated by authors with the motion of 180◦ DWs referring to the effect of roll magnetic anisotropy (RMA). The two other sub-periods occurring before and after the major one were associated, respectively, with the process of nucleation of reverse domains influenced by magneto-crystalline anisotropy (MCA) energy and motion of 90◦ DWs. In that work, from each section the energy value of MBN was calculated, and then the angular characteristics of the energy for individual sub-periods were achieved. The results obtained confirmed the possibility of a more accurate analysis of the phenomenon of anisotropy. However, the main problem of the method is the appropriate determination of signal divisions into sub-periods. Additionally subsequent interpretation requires consideration of many factors. Regardless of the approach finally applied, the named factors that define anisotropy are not the only ones that affect the course of angular characteristics of the MBN. The measurement conditions also have a significant impact on the effectiveness of anisotropy detection and measurement sensitivity, as presented and discussed in [31]. Similar observations were made in [23], where the need to maintain a constant value of magnetic flux density was underlined. It was also stated that during the tests it is necessary to observe not only the height of the MBN envelope but also its shape. All of the above factors result in a requirement for a broad analysis of the dynamics of the observed Barkhausen phenomenon, including both time and frequency characteristics. This entails the need for sequential monitoring of time and frequency characteristics in successive short time windows. The synchronous approach creates the opportunity to supplement the acquired information. Therefore, it becomes justified to carry out time-frequency (*TF*) analysis of measured MBN signals. This way of presentation allows more detailed information about the analyzed phenomenon to be obtained, because in addition to the extraction of parameters integrating global information (such as rms, energy or number of pulses) about the signal within the entire MBN period, it is possible to observe detailed relationships between properties in time and in frequency for subsequent time moments. As a result, it is possible to perform additional analysis and provide more detailed data on the nature of the phenomenon, which may be important for carrying out the final assessment. Recently, the authors presented the results of works on the application of the *TF* transformation to quantify the MBN signal information [24,32]. The [32] presents a broad description of the proposed *TF* analysis, *TF* features extraction and their interpretation along with a comparison of the information they carry with respect to the classic features of the MBN signal determined in the time or frequency domain. The influence of measuring conditions on the discrimination level was also discussed. The second paper of the authors [24] proposes a procedure based on *TF* characteristics enabling a clear division of the MBN signal into the aforementioned three sub-bands and determining the corresponding distributions of directional characteristics. However the described procedure did not allow the global anisotropy characteristic to be defined, being an assembly of all factors. Therefore, this paper proposes a procedure for determining the resultant easy magnetization axis based on the *TF* representation as well as a detailed analysis of the factors affecting the results. The successive sections present a setup of the measuring system, a proposed procedure for analyzing and evaluating the resultant easy magnetization axis. Ultimately, the results will be discussed and conclusions will be presented.

## **2. Samples and Measuring System Setup**

In the experiment, the conventional cold-rolled 3%SiFe electrical steel sheet (in reference to EN 10107 and IEC 60404-8-7 Standards) of 0.27 mm thickness, with silicon contents of 3% by mass and iron being almost a complement (over 96%) was used. Additionally, a trace content including carbon or other impurities (not exceeding tenths of a percent in overall) is also expected in this steel. The specific density of steel was 7650 kg/m3. Measurements were made for 16 angles at the location on the sample depicted with the letter A. The Figure 1 shows the view of the sample as well as the visualization of the first 5 measurement steps and rolling direction RD. The axis of first measurement is along to the transverse direction (TD) which corresponds to hard magnetization axis. The transducer was rotated by 22.5◦ after each measurement until reaching a full turn of 360◦. In order to perform the measurement, the MBN system controlled by a personal computer (PC) equipped with a data acquisition board DAQ (NI USB-6251) was used. The system has been described in detail in paper [32]. The scheme of the measuring system setup is shown in Figure 2.

**Figure 1.** Measurement steps and view of conventional electrical steel sheet with marked measurement location.

During the measurements, an MBN transducer having two sections was used (Figure 2c): the magnetizing and measuring ones. The magnetizing section consists of a coil wound on a C-shaped ferrite core. For the need of MBN signal sensing, a setup of coils wound on a rod core placed between the pole pieces of the electromagnetic yoke was utilized. In addition, a coil wound on one of the columns of the electromagnet and a Hall sensor located between its columns were used to control the magnetizing field conditions (magnetic induction and tangential component of magnetic field strength). For the needs of excitation, the sinusoidal waveform was generated using a digital-to-analog D/A converter of a DAQ board and then amplified using Power Amplifier (PA–OPA549) before driving the magnetizing coil. The excitation current frequency was set to 10 Hz, and the amplitude of the current was kept constant during the measurements. The estimated value of the magnetizing filed strength was 1.8 kA/m. The detailed discussion of the measuring conditions and analysis of the influence of the excitation field parameters on the MBN *TF* characteristic, as well as the choice of utilized settings (applied also in this paper) were presented and discussed elsewhere [24]. The MBN signal (*U*BN) induced in measuring coils was fed to the input of the analog processing system (APS) unit [24,32]. First, it was bandpass filtered in 0.6–97.5 kHz range and then amplified. The measurement was made in the angular steps, each time acquiring signals for the successive 10 periods of the magnetization process. The measurement was repeated 10 times, which made it possible to average the obtained results and minimalize the influence of interfering factors. Signal acquisition was carried out using the analog-to-digital A/D converter of DAQ board at sampling frequency of 250 kHz. Then, all measured signals were further processed using digital signal processing procedures.

**Figure 2.** The measurement system and XYZ scanner with mounted transducer: (**a**) schematic view of the configuration, (**b**) photo and (**c**) 3D view of the transducer.
