Extraction of Barkhausen noise from the measured raw signal in high-frequency regimes

Measurement 94 (2016) 456–463

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Extraction of Barkhausen noise from the measured raw signal in high-frequency regimes Dalibor Blazˇek a, Miroslav Neslušan b,⇑, Martin Micˇica a,c, Jaromír Pištora d a

IT4 Innovations National Supercomputing Center, VŠB-TU Ostrava, Studentská 6231/1B, 70833 Ostrava-Poruba, Czech Republic Faculty of Mechanical Engineering, University of Zˇilina, Univerzitná 1, 010 26 Zˇilina, Slovak Republic c Institut d’Electronique, de Microélectronique et de Nanotechnologie, Lille 1 University, France d Nanotechnology Centre, VŠB-TU Ostrava, 17. listopadu 15, 70833 Ostrava-Poruba, Czech Republic b

a r t i c l e

i n f o

Article history: Received 26 June 2016 Received in revised form 16 August 2016 Accepted 19 August 2016 Available online 20 August 2016 Keywords: Magnetic Barkhausen noise Post-processing method Vibrations Thermal noise Frequency spectrum

a b s t r a c t This paper deals with extraction of pure Barkhausen noise from the raw signals received in high-frequency regimes. The raw Barkhausen noise signals measured in high-frequency regimes contain components which cannot be attributed to the interaction of Bloch Walls with pinning sites and stress states such as the thermal noise of the sensor and the mechanical vibrations of the sensor-exciting core. Due to the variable ratios of thermal noise to Barkhausen noise as well as distortion of the signal due to vibrations, the raw signal as received and the pure Barkhausen noise signal can differ remarkably, thus making signal interpretation a debatable issue. For this reason, the post-processing method of the measured signal is presented here. In addition, the properties of lScan 500 device are analysed in detail. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction Barkhausen noise (BN) originates from the irreversible and discontinuous Bloch Walls (BWs) motion in ferromagnetic materials during the cyclic magnetization of an inspected surface. BWs tend to be pinned in their positions and their discontinuous and irreversible motion occurs when the strength of the magnetic field attains the critical value equal to the pinning strength of the structure. BN is a function of both the microstructural features and the stress state, which affect BN in a synergistic manner. However, the microstructure mainly affects the pinning strength and the free path of BWs movement whereas the stress state affects the domain and the corresponding BWs alignment. BN techniques were widely studied and BN signals and extracted BN features (such as rms value, peak position, peak height, noise power spectrum and shape of BN envelopes [1–11]) were correlated to a variety of microstructural features such as dislocations, grain size and grain boundaries, precipitates, and secondary phases as well as the stress state. BN techniques have found a high industrial relevance mainly for monitoring surfaces after grinding of shotpeening. However, BN methods have not yet been standardized ⇑ Corresponding author. E-mail addresses: [email protected] (D. Blazˇek), miroslav.neslusan@fstroj. uniza.sk (M. Neslušan), [email protected] (M. Micˇica), [email protected] (J. Pištora). http://dx.doi.org/10.1016/j.measurement.2016.08.022 0263-2241/Ó 2016 Elsevier Ltd. All rights reserved.

due to the variety of applied devices and the corresponding variability in magnetizing frequencies and voltages as well as detection coils (their shape and frequency responses), which in turn result in the remarkable differences in received BN signals [12]. Aspects of magnetizing frequency were previously studied by Moorthy et al. [13], who adopted low - (0.4 Hz), medium (20 Hz), and high - (125 Hz) frequency techniques mainly to reveal grinding burn (surface over-tempering) and its extent beneath the surface based on the correlation between BN values and BN envelopes (obtained at the different magnetizing frequencies) and the residual stress state assessed by via X-ray diffraction. The detailed investigation of the influence of the amplitude of magnetic field strength and the frequency response of the pick-up coil (4–32 kHz) on the shape of BN profile and frequency has been done by Vashista and Moorthy [12]. Dhar and Atherton [14] also revealed that BN activity, BN pulse – height distribution and flux density are strongly affected by the magnetizing parameters; especially magnetizing frequency. Stupakov et al. [15] discussed influence of the construction of the BN pick-up coil, BN signal sampling and filtering within the variable magnetizing frequencies. Tiitto and Säynäjäkangas [16] reported that the nature of BN changes continuously with increasing magnetizing frequency and explain this phenomenon in terms of the clustering of elementary transitions. Increasing the magnetizing frequency increases the opposition to the rapid change of magnetization due to eddy current generation. As the magnetization frequency increases, the skin

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depth decreases. Eq. (1) indicates that the skin depth d is frequency-dependent

d¼

pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2=xlr

ð1Þ

where x is angular speed (x = 2pf), l is magnetic permeability, and r is electric conductance. Eq. (1) supposes the presence of a medium having constant conductivity and permeability, whereas the real surfaces obtained after, for example, grinding or shot-peening contain stresses and microstructure gradients, which mean in turn that conductivity and permeability are a function of the depth beneath the surface. Calculated skin depths express usually the thickness of the excitation magnetic field penetration. However, calculation based on Eq. (1) indicates that the calculated skin depth is far from the BN-sensitive layer thickness due to the strong attenuation of electromagnetic pulses during their propagation towards the free surface. Although BN pulses are generated in deep regions (beneath the true skin depth) they cannot be detected on the free surfaces. The true skin depth should be considered as a layer from which BN pulses can be received on the free surface. It is worth to mention, that the low frequency components of the received BN signal reach farther than the high components and may originate from deeper regions within skin depth whereas the high frequency components originates from the near surface region. On the other hand, pulse – height distribution is a function of magnetizing frequency [16]. Such behaviour can be employed to link the different frequency components of BN signal with the different layers beneath the surface. For instance, Kypris, Nlebedim and Jiles [11,17] proposed the model by incorporating frequency and depth dependence components to provide a framework for assessment stress variation along depth by the use of BN technique. Moreover, the nonlinear hysteretic response of the material itself is a frequency dependent and the experimental results in dynamic conditions differs from the quasi-static one [18]. The low-frequency techniques are more often employed for material characterizations, where BN pulses are studied as a function of BWs interaction with microstructural features after the different regimes of heat and mechanical treatment, whereas highfrequency systems are mostly adopted for monitoring of the near or subsurface layers of the surfaces after grinding, shot-peening, and so on. Moorthy et al. [13] reported that low- and medium-frequency measurements are more sensitive to deeper extents of thermal softening induced by grinding. However, measurements reported in [19] proved than BN measurements at magnetizing frequencies in the range of 125–225 Hz are also sensitive to the extent of ther-

(a) Brief sketch

457

mal softening after grinding. Saturation of BN values versus thickness of the heat-affected zone occurs when the thickness of the thermally affected zone exceeds 100 lm. Grinding operations can suffer from over-tempering or over-heating of the surface, which in turn cause early crack initiation and premature failure of parts. The thickness of over-tempered (thermally softened) layers can vary in the range of several micrometers up to several hundreds of micrometers depending on the grinding condition, coolant feeding, grinding wheel wear, and so on. For this reason, BN measurements within a quite wide range of magnetizing frequencies (in the range of 0.1 up to 225 Hz) can be successfully suggested for sensitive and reliable monitoring of grinding operations. Nowadays, many grinding operations are replaced by hardturning or hard-milling cycles in a variety of applications [20,21]. The surfaces produced by these operations differ remarkably from the surfaces produced by grinding due to the considerably different mechanism of chip separation and kinematics of the machining cycle compared to the grinding process. Due to the very short period during which the hard-milled surface is exposed to severe plastic deformation at elevated temperatures, hard-turned and-milled surfaces usually exhibit only limited thermally affected zones of only a few micrometers in thickness beneath the white rehardened layer of comparable thickness in the near-surface region [22,23]. Thus, BN signals obtained at the magnetizing frequency of 125 Hz, the frequency usually used for detection of ground surfaces, give only limited information about BWs interaction with pinning sites and stress from the near-surface layer altered by the machining process itself, whereas most of the received BN pulses originate from the untouched structure in the deeper regions within the skin depth (see Fig. 1) [23]. It is well known that for successful application of the BN technique it is essential to achieve the required skin depth of the magnetic field for that specific application. For this reason, higher magnetizing frequencies are needed to reduce the signal of background pulses from deeper regions. It may seem that one could simply use a high-pass filter on the measured Barkhausen signal to receive only emissions near the surface, instead of exciting less volume. However there are situations at which the use of high-pass filter is counterproductive. For example, we have measured the BN on the macroscopic steel samples, where the thin surface layer has been altered by the machining (the altered layer has anisotropic properties while the bulk material remains isotropic) with the goal to find a frequency window at which the BN anisotropy would be strongest. It turned out, that the obtained anisotropy was highest at lower frequencies. StressTech RollScan 300 or lScan 500 are commercially available devices that are widely employed in many industrial applica-

(b) Micrograph

Fig. 1. Hard-milled surface versus skin depth at low magnetizing frequency.

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2. Experimental method BN signals were measured on a hard-milled surface made of bearing steel 100Cr6 (60  43  25 mm; 45 HRC) in two directions by the use of lScan 500. The surface was produced by a cutting tool made of R300-1240E-PMcemented carbides, an R300-050Q2212M 262489 tool holder of diameter Ø 50 mm with four inserts, and dry cutting, with ap = 0.25 mm, vf = 112 mm.min1, vc = 78.5 m.min1, and VB = 0.3 mm (VB – flank wear). Hard milling initiates high temperatures and superimposes hydrostatic pressure ahead of the cutting edge, causing the hard and brittle structure to behave in a malleable manner. The temperature at the tool–workpiece interface exceeds the Curie temperature [22] needed to disturb the domain configuration of ferromagnetic steel. The new domain alignment and the corresponding BWs reorganization are configured during rapid cooling with preferentially oriented domains in the direction of the cutting speed vc at the expense of the transversal direction (represented by the feed speed vf) due to residual stress anisotropy and the magnetostriction effect [24]. For this reason, BN emission in the tangential and transversal (axial) directions differs strongly. In order to investigate the obtained signal as a function of magnetic anisotropy of the surface, BN measurements were carried out in two directions, tangential and transversal, as Fig. 2 illustrates. This figure also illustrates the two perpendicular positions of the sensor (and the corresponding positioning of the exciting magnets) against the cutter path during the data acquisition. The main parameters adjustable on the excitation side which affect measured BN signal [15] as well as extracted BN features are listed in this paragraph. BWs discontinuous motion was excited by a magnetizing frequency in the range of 10–1000 Hz, keeping

excitation voltage constant at 10 V (sine shape); The BN signal was measured by the sensor: S1-18-12-01 with sampling frequency 2.5 MHz without any numerical frequency filter. The BN values reported in this paper represent the rms (effective) values obtained and averaged from six successive magnetizing cycles. The received signals were exported as .txt files and postprocessed in our own software working in a LabView environment. It is well known that BN technique is sensitive to the components geometry. For instance, keeping constant the shape of a sensor (as that illustrated in Fig. 2) an inner cylindrical surface would emit lower BN than that for an outer diameter of the same diameter and state of surface integrity due to the different magnetic flux distribution in the specimen. Moreover, specimen geometry would also remarkably affect the degree of magnetic anisotropy when the surface of a certain magnetic anisotropy is investigated. In order to evaluate the true degree of magnetic anisotropy and keep constant magnetic flux in two perpendicular directions, this study was carried out on the plane samples as that illustrated in Fig. 2. Thus magnetic flux density is the surface is mainly a function of magnetizing frequency [14] as the main parameter along which BN signals are decomposed. Fig. 3 shows the magnetizing current and the raw signal obtained at the magnetizing frequency of 10 Hz measured in the tangential direction. The magnetic field intensity has been measured by the F.W. Bell Gauss/Tesla meter model 7030. An transversal one axis temperature compensated Hall probe have been used. The dimensions of the probe enabled us to measure magnetic flux density between the poles of the sensor exciting magnets.

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tions and laboratory studies in which surface regions are modified in a variety of ways. The main advantages of these systems can be seen as their portability, very fast response, and variety of sensors adopted for variable shapes of products. The magnetizing frequency can be set in the range of several hertz up to 1000 Hz with a supply voltage of up to 16 V. However, magnetizing frequencies in the range of 125–225 Hz dominate in industrial as well as laboratory measurements. The modern trend when grinding operations are replaced with hard-turning or -milling processes is to perform measurements at the much higher magnetizing frequencies needed to achieve skin depths comparable with the thickness of white and thermally softened layers induced by hard-milling or turning. For this reason, this paper discusses specific aspects of such measurements and suggests how to extract the pure BN signal from the raw signals obtained in the high-frequency regimes.

Measured signal [mV]

458

-300 0.20

Time [s] Fig. 3. Raw signal and magnetizing current obtained at a magnetizing frequency of 10 Hz measured in the tangential direction.

Fig. 2. Positioning of BN sensor.

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3.1. Signal post-processing This part of the paper reports on the post-processing of the raw received signals based on the signal decomposition. It is considered that the raw signal contains the following components: – pure BN signal, – thermal noise of the sensor and the captured environmental electromagnetic noise, – vibrations of the sensor excitation core. Due to the typical noisy character of the cumulative BN pulses, BN is a signal with very low autocorrelation time. For this reason, the effective (rms) values are usually calculated to evaluate the intensity of BN emission of an investigated surface. The effective value Urms can be calculated by Eq. (2):

ð2Þ

where N is the number of samples and Un. are the measured values. The raw signal contains three of the abovementioned components. The obtained values of Urms can be written as the sum of partial effective values. This decomposition is possible under the assumption of zero correlation among the components, which is obviously satisfied thanks to the zero autocorrelation of the thermal noise and the negligible correlation time of BN. Therefore, the raw signal can be decomposed, as Eq. (3) indicates.

D

U 2raw

E signal

rms

D E ¼ U 2BN

rms

D E þ U 2vibrations

rms

D þ U 2thermal

E noise

rms

ð3Þ BN is a quasi-random signal of variable intensity within the magnetization cycle. It is well known that the maximum amplitude of BN pulses can be found near the coercive field in the steepest part of the magnetization curve, where BN avalanches occur as a result of the nucleation of reversed domains [25]. From the global point of view, the BN may be considered as an uncorrelated signal with a negligible mean value. Thus, the quasi-periodic component (see Fig. 4b) found in the raw signal (see Fig. 4a) cannot be attributed to the BN in any way. On the other hand, it can be successfully explained by damped vibrations of the exciting magnet’s poles of the sensor. The resonant frequency and damping factor of the vibrations can be determined when the waveform is obtained. The low-frequency periodic component corresponding to the vibrations of the excitation core of the sensor should be extracted 2000

Irreversible BWs motion is a function of the magnetic field strength, which is in turn proportional to the current in the sensor coil. Thus the amplitude and profile of the current strongly affect the energy of BWs and its interaction with pinning sites. BN

(b)

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3.2. Magnetizing current

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U rms

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u N u1 X 2 ¼t U N n¼1 n

and refined afterward from the raw signal. It would be ideal to obtain the time dependence of the signal induced by vibrations by averaging the signal through some consecutive periods and subsequently subtract vibrations from raw signal. A successful application of similar procedure is reported by Palˇa and Bydzˇovsky´ [26]. Unfortunately this technique does not work in the case of vibrations as they are not exactly periodic. The low pass filter must be used. The output form the sinc filter was not satisfactory and we decided to use a combination of two consecutive moving averages, where the number of adjacent samples in the second run is 70% of that in the first run [27]. Afterward, the low-frequency component can be subtracted from the raw signal. The refined signal contains pure BN as well as the background noise of the sensor. The background noise is attributed to thermal noise produced by the random fluctuation of charge carriers, mostly in the Hall sensor, while magnetic dipoles due to thermal vibration of the lattice and/or due to environmental electromagnetic signals can also contribute [25]. It will be shown later (Fig. 12b) that thermal noise is powerfully dominant part of the background noise so the term thermal noise will be used further. Since both components, BN and thermal noise, are broadspectrum, they cannot be refined in the time domain or the frequency domain. However, it is possible to calculate their effective rms values when the signal is squared and afterwards the envelope of this signal is obtained when the squared signal is smoothed by low pass filter (by the use of two consecutive moving averages for example). Fig. 5 shows the envelope of such a signal measured in the air. Fig. 5 clearly shows remarkable peaks as evidence of BN originating from the magnetic core of the sensor. The amplitude of the thermal noise free of BN pulses is given by the value of the envelope curve when saturation of the hysteresis loop during cyclic magnetization is achieved (marked by the purple line in Fig. 5). Without the background noise, the envelope curve in Fig. 5 would drop to zero value during the saturation. Thermal noise does not depend on the magnetizing field, and the pure BN can be found when this offset (corresponding to the value of the thermal noise in Fig. 5) is subtracted from the noisy component of the raw signal, as Eq. (3) indicates. An alternative way to extract thermal noise, based on measurement of the signal at zero magnetic field was suggested by Thomas [28].

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3. The device properties and the post-processing method

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Time [ms]

Fig. 4. The signal measured in the tangential direction at the magnetizing frequency of 525 Hz. The raw signal (a) and the low frequency vibrations extracted from the raw signal (b).

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perature compensated Hall probe the magnetic flux density between sensor poles was measured (with no sample attached). The field strength was proportional to the current bellow 110 mA with the slope 76 mT/A. The magnetic field continues to grow, depending on the current level, well above the core saturation with the slope 12 mT/A. The magnetic properties of measured sample have significant impact on the threshold current. Typically the core saturation occurs at lower current as the maximal magnetic flux is constant and the reluctance of the system is lower.

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BN originating from conditioning circutit

BN envelope Thermal noise

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4. The obtained results Background thermal noise

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0 0.00

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Time [s] Fig. 5. Envelope of the signal obtained at a magnetizing frequency of 10 Hz. The waveform was measured in the air, which means that the sensor measures the BN originating from the exciting magnets.

contains information about the interaction of BWs with weak pinning sites in the low magnetizing fields, whereas higher magnetizing fields causes the BN signal to contain more rich information as a result of BWs interaction with microstructural features of high pinning strength. In the ideal case, the instrument enables direct control of current properties, which is not the case of the presented equipment, which allows us to set only the exciting voltage amplitude and frequency. For this reason, this chapter discusses specific aspects of the magnetizing current. Harrington [29] reports that a significant phase shift between the magnetization current in the coil and magnetic field in the sample occurs at higher magnetizing frequencies. Furthermore, decreasing amplitude of the magnetizing current (see Fig. 6b) with increasing frequency due to an inductance of the coil also contributes to the progressive decline of BN at higher magnetizing frequencies since the magnetizing current corresponds to the strength of the magnetizing field. The amplitude of magnetization current I is frequency-dependent and can be estimated by Eq. (4) [29].

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi I ¼ U=Z ¼ U= R2 þ ðxLÞ2

ð4Þ

where U is the supply voltage amplitude, Z the impedance, R the resistance, and L the inductance of the coil. On the basis of Eq. (4), the frequency dependence of the coil impedance Z can be evaluated from the measured dependence of the amplitude of the magnetizing current on the frequency at constant amplitude of the supply voltage of 10 V. The impedance and the inductance of the coil can be obtained from the measured dependence of the amplitude of the magnetizing current on the frequency. The resistance of the coil impedance at low magnetizing frequencies (R = 50 Ω) dominates over inductance whereas the effect of the coil inductance (L = 76 mH) dominates at high magnetizing frequencies. Moreover, the detailed analysis of the magnetizing current shows that harmonic profiles are distorted (see Fig. 6a) due to the magnetic over saturation of the excitation core. Fig. 6a shows that the magnetizing profile becomes distorted as soon as the magnetizing current exceeds 110 mA, whereas magnetizing profiles at higher magnetizing frequencies of 225 and 1000 Hz remain nearly untouched. The saturating current which provides the maximum magnetic flux transmitted into the investigated surface is indicated by the blue1 horizontal line (see Fig. 6a). Using the transversal tem1 For interpretation of colour in Figs. 6, 9, 11 and 13, the reader is referred to the web version of this article.

The analysis of three important measurements is presented here. Two of them are conducted on the hard-milled surface in the tangential and axial directions (see Fig. 2). The third measurement was made in the air, far enough from any magnetic material. This measurement can serve for calibration. All of the obtained signals were decomposed via the abovementioned post-processing method described in the previous chapter with the goal of distinguishing the core vibrations, thermal noise and Barkhausen noise. Fig. 7 illustrates the effective (rms) values of the signal as received as well as each separated component versus the magnetizing frequency measured in both directions on the hard-milled surface of the sample made of the 100Cr6 steel. It is obvious that BN measured in the tangential direction is many times larger compared to the BN measured in the axial direction. This is due to the strong stress and the corresponding magnetic anisotropy of such a surface [24]. (Note that detailed explanation of such anisotropy is beyond the scope of this paper. The analyzed surface is only employed for the purpose of the study in which different components in the raw BN signal are studied as a function of variable BN emission.) The BN measured in the axial direction is similar in size to the BN measured in the air; hence the BN in the axial direction is much smaller. Fig. 7 shows that BN dominates in the raw signal at lower magnetizing frequencies, whereas the high frequency regimes contain mainly vibration components. Thermal noise does not depend on magnetizing frequency and is nearly constant, with an average value of about 17.5 mV. The most important factor causing the decrease in BN as a function of frequency is the decreasing amplitude of the magnetizing field. On the other hand, the intensity of the core vibrations increases progressively with the magnetizing frequency. The relation discovered between the properties of vibrations and the studied surface is very interesting. Fig. 8 shows the frequency dependence of the measured vibrations in three different positions of sensors compared to the thermal noise. It can be seen that in the case of air or the axial position of the sensor, the vibrations remain small. This may be quite surprising compared to the vibrations measured in the tangential direction. The reason for this effect must be sought in the low amplitude of excitation force acting on the poles in the air, while huge damping eliminates the vibrations in the case of axial orientation of the sensor due to the striated surface. The very strong magnetic anisotropy and the surface pattern of the hardmilled surface play a relevant role. The amplitude of vibrations grows linearly in the air and axial measurements which is very different from the measurement in the tangential direction. It is obvious that after the initial steep increase of the core vibration at very low magnetizing frequencies the intensity of vibration is kept nearly constant within the magnetizing frequency in the range of 75–525 Hz. Further increase of the magnetizing frequency results in a remarkable increase of the core vibrations. The core vibrations at lower magnetizing frequencies contain (in the time scale) attenuated pulses terminating before the subsequent vibration pulse is initiated by the next magnetization cycle. Thus, each vibration pulse can be clearly separated.

D. Blazˇek et al. / Measurement 94 (2016) 456–463

(b)

Amplitude of magnetizing current Core saturation current

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Fig. 6. The measured profiles of the magnetizing currents with respect to the magnetizing frequency (a) frequency-dependent amplitude of current (b).

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Fig. 7. Decomposition of the raw BN signal measured on the hard-milled surface in the tangential direction (a) and the axial direction (b).

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When the magnetizing period becomes shorter than the relaxation time of the attenuation, the mechanical energy starts to accumulate in the core and the amplitude of vibrations grows rapidly. Analysing the data obtained (see Fig. 4b), the resonant frequency of the magnetic core poles can be evaluated to be about 4.1 kHz, so the resonance cannot occur during the measurement. The smallest signal-to-noise ratio occurs at the highest frequencies (sometimes much lower than one). Under these circumstances, decomposition of the measured signal is necessary. The most

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unfavorable raw signals can be obtained at a magnetizing frequency of 1000 Hz measured in the tangential direction (Fig. 9). The decomposition of this raw signal into the vibration and noise components can be found in Figs. 10 and 11. It may be interesting to measure the vibration properties by some direct method, but this is completely beyond our possibilities. Once the resonant frequency is known, the simplest approach is to apply a high pass filter which is completely sufficient in many practical applications. Omission of the vibrations however reduces our knowledge about the experimental technique. As it is shown in the Fig. 4b, the

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Fig. 10. Vibration of the excitation core extracted from the raw signal illustrated in Fig. 9. A tiny part of the BN passed through the filter.

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the magnetization frequency or the medium being measured (Fig. 12a). It is reasonable to assume that the thermal noise of the sensor is white, that is, a random signal with a constant power spectral density. The obtained spectrum shown in Fig. 12b is affected by the transfer characteristic of the lScan 500. So examining the thermal noise spectrum we obtain the actual frequency response of the equipment which is usually an extremely difficult task, as it depends on a number of parameters. This frequency response affects all the measured quantities including the BN. This transfer characteristic may be used to correct the obtained Fourier spectra of the BN. We believe that the spectra repaired with respect to the frequency response of the BN sensor and associated electronics will not be sensitive to the side effects reported by Vashista and Moorthy [12]. The environmental electromagnetic noise manifests itself by discrete part of the spectrum. The effective (rms) value of BN is employed for monitoring surfaces in the majority of industrial applications. However, additional BN features can be used for material characterization. The shape of the BN envelope and BN envelope features such as the peak position, peak height, and full width at half maximum were previously reported as the quantities are directly related to either the stress field or the microstructural features [13,24,30]. Proper interpretation of such features needs extraction of the BN from the raw signal, too. All of the mentioned parameters are very sensitive to the spurious signals. Fig. 13 shows the envelopes of the raw signal

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Time [ms] Fig. 11. BN and thermal noise extracted from the raw signal illustrated in Fig. 9.

vibrations are very anharmonic which imply the presence of very high harmonics in the frequency spectrum. Without prior checking it may happen that even filtered signal will be affected by vibrations. Fig. 11 illustrates the vibration-free signal containing BN and background noise. Pure thermal noise can be analysed during the saturation phase of the magnetization cycle within the period between two subsequent BN bursts. The amplitude of the thermal noise stays nearly constant when taking into consideration either

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Fig. 12. Thermal noise versus magnetizing frequency (a) and the frequency spectrum of thermal noise (b).

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(Fig. 9) and of the extracted BN noise (Fig. 11) versus magnetizing current. The envelope of such a raw signal is attributed to the vibrations with an indistinct contribution of BN. The true BN envelope originating from the investigated surface is indicated in red colour.

5. Conclusions BN measurement techniques are widely used in industry and materials research due to the correlation of BN with many microstructural features. No matter how robust and easily applicable these methods are, there are some aspects which must be considered when a more serious research is conducted. A widely used StressTech instrument with a standard probe was chosen for the detailed analysis. It can be concluded that the raw signal consists of three relevant components: the thermal noise and sensor vibrations among the desired BN. The disturbances are often more powerful than the useful signal as the sensor properties are frequency-dependent. The low-frequency signals can be interpreted as they are received since they mainly contain information about the BN emission of the investigated surface. Thermal noise as well as the vibration of the excitation core contributes only a little to the signal. Although the total current distortion at low frequencies was found to be much more pronounced than that at high frequencies, the profile of the magnetizing current is distorted especially during the saturation phase of the magnetization cycle and does not strongly affect BN emission initiated near the coercive force. On the other hand, the high-frequency regimes require signal post-processing to extract the pure BN signal. Thermal noise stays nearly constant within the possible magnetizing frequencies, whereas vibrations initiated by the excitation core increase remarkably along with magnetizing frequency and must be refined from the raw signal. As the BN signal progressively decreases with rising frequency due to the shrinking current amplitude, the ratio of the signal to the background decreases rapidly, becoming less than one in many cases. It is worth mentioning that, except for the raw BN signal, the standard commercially available postprocessing software also gives the filtered signal in which the low-frequency core vibrations are substantially compensated by the use of frequency band-pass filtration. However, the core vibration patterns can still be easily recognized in the filtered signal and BN envelopes. Despite the systematic and noisy components contributing to the raw signal at high magnetizing frequencies, a BN signal obtained by the use of the abovementioned device can be extracted and consequently interpreted as a pure product of BWs interaction with stress fields and microstructural features. Moreover, the BN originating from the conditioning circuit is measured and may be subtracted from the effective value of measured BN. It was found that the measured thermal noise can be used in two ways: it must be subtracted from the measured signal and it may be used for calibrating the frequency response of the equipment. Thus, the analyzed device represents a powerful tool for BN measurement of thin layers in the high-frequency regimes.

Acknowledgements This work was supported by The Ministry of Education, Youth and Sports of the Czech Republic from the National Programme of Sustainability (NPU II) project ‘‘IT4Innovations excellence in science - LQ1602” and by the SGS project SP2016/167. Partial support from the project 15-08971S Czech Science Foundation is acknowledged.

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