Comprehensive magnetic properties measurement of the laminated silicon steel by 3-D magnetic tester

Abstract

In this paper, a novel three-dimensional (3-D) magnetic tester with symmetrical orthogonal excitation structure and cubic field-metric sensing structure is designed and analyzed. Automatic measurement system, which includes feedback control method, harmonics compensation, and automatic data processing is developed for the 3-D magnetic tester. In order to improve the measurement precision, cross effects of the magnetic fields in three principal directions are concerned, and error mitigation methods which fit for different excitation models are proposed. Magnetic properties of typical grain-oriented (GO) and non-grain-oriented (NGO) laminated silicon steel specimens under alternating and rotating excitations are measured and analyzed by using the designed 3-D magnetic tester.

Keywords

Laminated silicon steel 3-D magnetic tester automatic measurement system dynamic magnetic properties rotating excitation

1. Introduction

Magnetic properties of the silicon steel are key factors in design and performance optimization of the electrical apparatus. Two-dimensional (2-D) measurement methods for single silicon steel sheet have been developed by some researchers [1, 2, 3, 4, 5, 6]. The previous 2-D testing methods were mainly focused on the rolling direction or the rolling plane of silicon steel. However, the silicon steels are laminated and stacked in application, which may arise magnetic interaction between the vicinity layers [7, 8]. The magnetic flux in the complicated working conditions, such as large motor and power transformer, is not completely parallel to the rolling direction or the rolling plane of silicon steel sheet. Note that a part of magnetic flux should penetrate through the laminated silicon steel which causes the error in material modeling and core loss calculation. Magnetic field in laminated direction is confirmed in T-joints of three-phase transformers, which may cause rotating core losses and increase the total core losses enormously [9]. Therefore, comprehensive magnetic properties of the silicon steel including the laminated direction should be taken into account. To guarantee the accuracy and efficiency, feedback control method should be paid much more attention to the magnetic properties measurement. An adaptive digital feedback method for 1-D and 2-D magnetic measurements was designed with multi-variable inputs and outputs [10]. The digital control of the flux loci based on contraction mapping principle showed better performance on the three-phase single sheet tester [11]. For laminated cubic specimen of 3-D magnetic testing, however, the excitation circuit is more complex and the excitation power needs to be increased significantly. Thus, the traditional control method cannot be directly extended to the 3-D condition.

Depending on the first 3-D tester and its improvement, 3-D magnetic properties of soft magnetic composite (SMC) materials have been measured and analyzed [12, 13, 14]. However, joints of the cores and yokes in the first 3-D magnetization structure are not completely uniform, which can cause structural anisotropy and influence the measurement results. In this paper, a novel 3-D magnetic tester with symmetrical orthogonal excitation structure is designed and analyzed. In order to obtain the desired magnetization loci and improve the measurement precision, feedback control method, harmonics compensation, and automatic data processing are developed. Error mitigation methods which fit for different excitation models are proposed according to different error sources. By using this tester, comprehensive magnetic properties of GO and NGO laminated silicon steels are measured and analyzed under various excitation models.

2. 3-D magnetic testing system

As shown in Fig. 1, the 3-D magnetic properties testing system consists of excitation circuit and signal acquisition circuit. The excitation circuit mainly includes excitation signal generation unit of LabVIEW, three high performance power amplifiers and three pairs of excitation coils. And the signal acquisition circuit mainly includes six sets of $B-H$ sensing coils, multi-channel differential amplifier circuits and data acquisition unit of LabVIEW.

Figure 1.

Schematic diagram of 3-D magnetic property testing system.

The excitation signals, which are generated by LabVIEW, are amplified by three channels power amplifier and then are applied to the excitation coils of 3-D magnetic tester. The 3-D magnetic tester is similar to a no-load transformer, which can realize magnetic field coupling between excitation coils and sensing coils by means of orthogonal magnetic circuits. The components of $\bm{B}$ and $\bm{H}$ signals along three directions are obtained by six sets of $B-H$ sensing coils. Due to the weak signals, it is necessary to employ the differential amplifier circuit before signals acquisition and processing. Finally, the closed-loop control and operation of 3-D magnetic measurement can be realized by feedback control and harmonics compensation based on LabVIEW software.

2.1 Structure of 3-D magnetic tester

The excitation structure consists of three orthogonal laminated cores, six multilayer excitation windings, which are wound around the three pairs of orthogonal core-poles, as shown in Fig. 2a and b. Aiming to concentrate magnetic flux density and enhance the excitation field, core poles are shaped in frustum of a square pyramid and the taper angle is about 40 ${}^{\circ}$ . The taper angle is optimized by finite element analysis, in which the uniformity and strength of the magnetic field in test regions are adequately considered. Note that sufficient symmetry should be ensured in the fabrication of laminated cores and core-poles. In addition, the deflection angles of laminated cores should be strictly controlled in assembly of 3-D magnetic tester and specimen.

Figure 2.

3-D magnetic tester. (a) Physical diagrams. (b) Structure model.

The laminated cubic specimen with $B-H$ sensing structure is placed in the center of the 3-D magnetic tester. Between the core and specimen, there placed the thin sensing coils and exists air gaps, which can make the sensing field far away from uniformity. To reduce the influence of non-uniformity, six homogeneous field core shoes with the same material and same lamination direction are fabricated and placed around the cubic specimen, as shown in Fig. 3. It is well known that interlaminar short circuits can cause interlaminar eddy current, which have a negative effect to the measurement accuracy. Thus, necessary insulation should be provided and edge burrs should be prevented in the manufacture of specimen and core shoes. Figure 4 illustrates the magnetic field distribution when only $y$ direction of the 3-D tester is excited. The mesh densifying is performed in air gap between the cores and specimen to improve calculation accuracy. In the figure, a part of the core poles and shoes are hidden for better illustration of the magnetic field distribution on the specimen surface. It shows that relatively uniform magnetic field can be generated in the center of specimen surface.

Figure 3.

Laminated cubic specimen with core shoes.

Figure 4.

Magnetic field distribution of specimen surface.

The phase angle between $\bm{B}$ and $\bm{H}$ cannot be measured by Epstein frame, though this angle is existing and changing under rotating magnetization. So a novel cubic field-metric sensing structure which contains six sets of composite $B$ and $H$ coils is designed to measure the components of $\bm{B}$ and $\bm{H}$ in three directions. Compared with the traditional methods, the cubic field-metric sensing structure overcomes some defects that the measurement of $\bm{H}$ is not based on the Ampere’s law but the electromagnetic induction law. The waveforms of $H$ are accurately measured by field metric method, which avoids the disadvantage that the effective magnetic path length is hard to obtain. To decrease measurement error and improve the accuracy, the $B-H$ sensing coils whose area are smaller than the uniform field regions are attached to the center of specimen surface, as shown in Fig. 5. Also, the cross-bedded winding structure and twisted terminals are adopted to eliminate EMF induced by unwanted stray field. Six sets of combined $B$ and $H$ coils are placed on the six sides of the cubic specimen in a given order and the coils on the opposite sides are connected in series.

Figure 5.

Cubic field-metric sensing structure. (a) Structure model. (b) Physical diagrams.

2.2 Automatic measurement system

The automatic measurement system consists of inner layer waveform compensation, medium layer feedback control and outer layer automatic processing, as shown in Fig. 6. Different excitation models, such as sinusoidal alternating, elliptical and ellipsoidal rotating excitations, are supported by outer layer automatic processing. The desired waveform of magnetic flux density is obtained by feedback control algorithm and harmonics compensation. In addition, the automatic measurement system can realize measurement status monitoring, measurement queue setting, magnetization stability time delay, output recording and online processing.

Figure 6.

Schematic diagram of the automatic measurement system.

In general, the dynamic magnetic properties measurement of soft magnetic materials is performed under steady and periodic magnetization excitation. Therefore, the signal frequency spectrum analysis and frequency domain control can be more effective than that in time domain. As shown in Fig. 7, frequency domain control system is established, in which the digital controller can regulate the PI parameters automatically according to the magnitude and frequency of $B$ .

Figure 7.

Control flow chart of 3-D testing in frequency domain.

The mutual coupling of excitation windings should be taken into account in control of excitation signals. The independent control of excitation signals in three directions is achieved by $G_{1}$ , which is transfer function to decouple the mutual coupling. The function of $\bm{R}^{-1}_{\textit{xyz}}$ is correct the deflections between magnetic filed and sensing coils. Moreover, the measurements of magnitudes and phases are obtained to compare with the reference values which are obtained by FFT of set excitation signals. When the relative error between the measurement and reference (magnitudes and phases) is less than 0.3%, the results are recorded automatically after twenty seconds time-delay and magnetic properties measurement is completed. The proper time-delay is essentials for accurate measurement of magnetic properties, which can ensure the magnetization stability.

To overcome distortion in the $B$ waveform caused by saturation, harmonics compensation method is proposed. In Fig. 8, harmonics are suppressed by adding the corresponding harmonics to compensate the distorted $B$ waveform. Phase and magnitude can be decoupled to control independently during the harmonic suppressing. Phase compensation is applied to the PID output signal to handle the nonlinear phase response at different frequencies. The amount of phase compensation is obtained from a predefined look-up table of lagging phase angles that are caused by the nonlinear power amplifier. The lagging phase angles can be directly measured by the experiment without harmonics compensation. As shown in Fig. 9a and b, the $B_{x}$ harmonics of NGO 35WW270 specimen under rotating magnetic measurement with and without harmonics compensation are compared. It can be seen that the $B_{x}$ harmonics increase gradually with increasing magnetic flux density during the experiment without harmonic compensation, especially the 3 order harmonic is up to 1%. The 3 order harmonic is reduced by introducing the harmonics compensation, however, the 5 order and 7 order harmonics increases slightly due to the highly nonlinear of excitation system. Consequently, The total $B_{x}$ harmonics can be suppressed significantly by the harmonics compensation.

Figure 8.

Control flowchart of harmonic compensation algorithm.

Figure 9.

The ratio of harmonics to fundamental components in the x axis under rotating magnetic measurement (a) without harmonics compensation. (b) With harmonics compensation.

3. Investigation of measurement accuracy

Based on the Faraday Law of Electromagnetic Induction, the $\bm{B}$ and $\bm{H}$ signals can be obtained by corresponding inducted voltage of cubic field-metric sensing coils. Inducted voltages of $B$ and $H$ sensing coils can be expressed as

$\displaystyle V_{Bl}=\mu_{0}\left[{\frac{K_{\textit{Bll}}}{\mu_{0}}\frac{dB_{l% }}{dt}+K_{\textit{Blm}}\frac{dH_{m}}{dt}+K_{\textit{Bln}}\frac{dH_{n}}{dt}}\right]$ (1) $\displaystyle V_{Hl}=\mu_{0}\left[{K_{\textit{Hll}}\frac{dH_{l}}{dt}+K_{% \textit{Hlm}}\frac{dH_{m}}{dt}+\frac{K_{\textit{Hln}}}{\mu_{0}}\frac{dB_{n}}{% dt}}\right]$ (2) $\displaystyle K=NS$ (3)

where $l=x,y,z,m=y,z,x,n=z,x,y,\mu_{0}$ is permeability of air, $K_{B}$ and $K_{H}$ are the coil coefficients of $B$ and $H$ coils, $V_{B}$ and $V_{H}$ are the inducted voltages of the $B$ and $H$ sensing coils, $N$ represents the coil turns, $S$ is equivalent cross-section area of three principal directions.

It is confirmed that the inaccuracy of measured magnetic properties under rotating excitations is due to the cross effects of non-measuring directions and the misalignment of coil, as shown in Fig. 10. For $x$ direction, inducted voltage of $H$ sensing coils can be expressed as

$\displaystyle V_{Hx}=\frac{K_{Hxx}}{\mu_{rx}}\frac{dB_{x}}{dt}+\frac{K_{Hxy}}{% \mu_{ry}}\frac{dB_{y}}{dt}+K_{Hxz}\frac{dB_{z}}{dt}$ (4)

where $\mu_{r}$ is relative permeability of specimen in different directions, the maximum relative permeability of high grain silicon steel is more than 10,000. It shows that the voltage of $H$ sensing coil is not only inducted by magnetic field along $x$ direction but also along $y$ and $z$ directions, especially the inducted voltage of $z$ direction, which may influence the experimental results seriously. Therefore, the comprehensive coefficients of $H$ and $B$ sensing coils must be calibrated and compensated.

The equivalent cross-section area of the minimized coils is difficult to obtain, which leads to the coil coefficient cannot be precisely calculated by Eq. (5). Hence, the tensor coefficient method is proposed and performed in 3-D testing to calibrate the coefficients of $H$ and $B$ sensing coils. In Table 1, the averages of diagonal coefficients for $H$ and $B$ sensing coils are obtained by a long solenoid, which can generate a uniform magnetic field. But the calibration of off-diagonal coefficients must be carried out in the 3-D tester, which are relatively complex and affected by frequency.

Table 1

Averages of diagonal coefficients for $H$ and $B$ sensing coils (m ${}^{2}$ )

$K_{\textit{Hxx}}$	$K_{\textit{Hyy}}$	$K_{\textit{Hzz}}$	$K_{\textit{Bxx}}$	$K_{\textit{Byy}}$	$K_{\textit{Bzz}}$
2.597 $\times$ 10 ${}^{-3}$	2.556 $\times$ 10 ${}^{-3}$	2.663 $\times$ 10 ${}^{-3}$	2.364 $\times$ 10 ${}^{-3}$	2.363 $\times$ 10 ${}^{-3}$	2.359 $\times$ 10 ${}^{-3}$

Figure 10.

Scheme of induction voltages for the $H$ coil.

Figure 11.

CW, CCW and average rotational $\bm{B}$ , $\bm{H}$ loci.

Figure 12.

Hysteresis loops of the NGO 35WW270 in three directions at 50 Hz. (a) Rolling direction. (b) Transverse direction. (c) Laminated direction.

In this paper, the method of averaging clockwise (CW) and anticlockwise (CCW) outcomes is employed under rotating excitations. For circular rotating magnetic field, the components of magnetic field strength $\bm{H}$ can be expressed as

$\displaystyle H_{p}=H_{mp}\cos(2\pi ft)+K_{q}H_{mq}\sin(2\pi ft)$ (5)

where $p$ is the measuring direction of sensing coil, $q$ is non-measuring direction. When the measured $H_{x}$ under CW and CCW have the same magnitude and inverse direction, the desired parts of EMF are identical and the interfering parts are opposite as illustrated in Eq. (5). As shown in Fig. 11, the effect of interfering signals is reduced by averaging CW and CCW outcomes. So, the calibration of off-diagonal coefficient matrix elements for $B$ and $H$ sensing coils can be avoided. Finally, the magnetic properties of alternating and rotating excitations can be measured accurately by cubic field-metric sensing structure.

Figure 13.

Hysteresis loops of the GO 27ZH95 in rolling and transverse directions at 50 Hz. (a) Rolling direction. (b) Transverse direction.

Figure 14.

Alternating core loss in the rolling and transverse directions at 50 Hz.

Figure 15.

$\bm{B}$ loci and corresponding $\bm{H}$ loci of the GO 27ZH95 in rolling plane. (a) Lower exciting current. (b) Higher exciting current.

Figure 16.

$\bm{B}$ loci and corresponding $\bm{H}$ loci of the NGO 35WW270 in rolling plane. (a) Lower exciting current. (b) Higher exciting current.

4. Magnetic properties measurement and analysis

Typical GO 27ZH95 and NGO 35WW270 silicon steels are made into laminated cubic specimen respectively. Meanwhile, the magnetic properties under alternating excitation in three directions, circular and 3-D ellipsoidal excitations are measured systematically. The core losses under different excitation models can be directly calculated by Poynting’s vector theorem.

4.1 Alternating magnetic properties

The alternating magnetic properties measurement of laminated silicon steel specimens is progressed when the $B$ signal is controlled to be sinusoidal alternating waveform by digital feedback method. The magnetic properties of silicon sheets in the laminated direction can be obtained by 3-D tester, which cannot be measured in the 1-D and 2-D tester. There are also some differences of measurement between laminated direction and other two directions. Due to the larger eddy current and skin effect, the experiments should be done in a short time to avoid excessive heat.

For the NGO silicon steel specimen, the hysteresis loops along the rolling, transverse and laminated directions are measured and compared by improved flexible multi-layer windings at 50 Hz, as shown in Fig. 12. It can be seen that saturation magnetic flux density of the NGO silicon steel is approximately up to 1.5 T. In addition, the hysteresis loops of NGO silicon steel represent favorable coherence along the rolling and transverse directions. Due to the leading role of air permeability, the laminated direction is the most difficult magnetization direction and the permeability is approximately linear, which is mainly determined by the stacking coefficient of specimen. Equivalent permeability can be expressed as

$\displaystyle\mu=\frac{\mu_{0}\mu_{r}}{\alpha+(1-\alpha)\mu_{r}}$ (6)

where $\mu_{r}$ is the relative permeability of NGO silicon steel, $\alpha$ is spacing factor.

In Fig. 13, the hysteresis loops are measured along the rolling and transverse directions of GO silicon steel specimen. The rolling direction is the easiest magnetization direction, which saturation magnetic flux density is approximately up to 1.8 T. The permeability of GO 27ZH95 silicon steel along the rolling direction is far higher than that along the transverse direction, which represents strong magnetic anisotropy. In Fig. 14, the alternating core loss are obtained by measured and calculated respectively. It can be observed that the alternating core loss of rolling direction is less than the transverse direction.

4.2 Rotating magnetic properties

To analyze magnetic anisotropy comprehensively and provide reliable data to calculate core loss accurately, the rotating magnetic properties of GO and NGO laminated silicon steel specimens are measured respectively. When the magnetization loci are controlled to be circle, the $\bm{B}$ loci and the corresponding $\bm{H}$ loci are measured and compared in the rolling plane of GO and NGO silicon steel at 50 Hz as shown in Figs 15 and 16.

For the GO 27ZH95, the $x$ direction is rolling direction. When the magnetic flux density is less than 0.9 T, the $\bm{H}$ locus changes to be a saddle-like shape with increasing excitation current. It shows that the rolling direction of the GO silicon steel specimen is easier to be magnetized. When the magnetic flux density is larger than 0.9 T, the loci of $\bm{H}$ appear sharps angle at the direction about 55 ${}^{\circ}$ with $x$ -axis. It is verified that the hard magnetic direction of Goss structure silicon steel is 55 ${}^{\circ}$ with $x$ -axis. The phenomenon is caused by origin of magnetic anisotropy. The rolling stress of GO silicon steel is the primary cause of magnetic anisotropy in lower exciting current. However, the lattice anisotropy takes over from rolling stress by increasing excitation current.

For the NGO 35WW270, the $y$ direction is rolling direction. It can be found that the component $H_{x}$ and $H_{y}$ of $\bm{H}$ have obvious difference in lower exciting current, while the difference is reduced progressively and trend stability with increasing excitation current. It shows that the lattice anisotropy of NGO silicon steel is hardly existence and magnetic anisotropy is mainly caused by rolling stress during whole magnetization processing. In addition, the influence of rolling stress on magnetic anisotropy is determined in material fabrication, however, the contribution of lattice in magnetization is continuously enhanced with increasing excitation current. Compared with the GO 27ZH95, the NGO 35ww270 exhibits outstanding isotropy.

4.3 Core loss analysis

Alternating core losses per cycle along rolling direction of the NGO 35WW270 are calculated and compared at 50 Hz, 100 Hz and 200 Hz, as shown in Fig. 17. It can be found that the total losses are evidently increased with excitation frequency, which is caused by classical eddy loss and excess loss. Figure 18 illustrates the rotating core losses in the rolling plane for the NGO 35WW270 at 50 Hz, 100 Hz and 200 Hz. It can be seen that the rotating core loss increase to peak value when the magnetic flux density is approximately 0.8 T and then gradually decreasing. The magnetic domain walls gradually disappear by the increasing of magnetic flux density, the hysteresis loss decreases while the classical eddy loss increases, so the total rotating core losses may decrease.

Figure 17.

Alternating core losses per cycle along rolling direction of the NGO 35WW270 at 50 Hz, 100 Hz and 200 Hz.

Figure 18.

The rotating core losses in rolling plane of the NGO 35WW270 at 50 Hz, 100 Hz and 200 Hz.

Figure 19.

The hysteresis, classical eddy and excess losses in three directions at $B=$ 0.7 T. (a) Rolling direction. (b) Transverse direction. (c) Laminated direction.

In order to quantitatively study the alternating hysteresis, eddy current and excess losses, total losses separation is performed by Eq. (7).

$\displaystyle P_{t}=P_{h}+P_{c}+P_{e}=k_{h}fB_{m}^{\alpha}+k_{c}(fB_{m})^{2}+k% _{e}(fB_{m})^{1.5}$ (7)

where $P_{t}$ , $P_{h}$ , $P_{c}$ and $P_{e}$ are total losses, hysteresis loss, eddy current loss and excess loss respectively, $k_{h}$ , $k_{c}$ and $k_{e}$ are the alternating hysteresis, eddy current, and excess losses coefficients respectively. Figure 19 shows the frequency dependence of the alternating core losses in three directions when the $B=$ 0.7 T.

The hysteresis loss per cycle $P_{h}$ is constant quantity, which can be obtained by extrapolating the measured the total loss per cycle $P_{t}$ in the condition of $f=$ 0 Hz. In the calculation of classical loss $P_{c}$ and excess loss $P_{e}$ , the parameters are assumed by fitting over a range of $B_{m}$ and $f$ values and found to be a constant, and then eddy current loss and excess loss per cycle are obtained. Note that the eddy current along laminated direction of the NGO 35WW270 is far higher than other directions.

5. Conclusions

In this paper, a novel 3-D magnetic testing structure consists of three orthogonal “C-type” cores with laminated HiB silicon steel is designed and modeled. The concentrated poles can generate relatively uniform and high magnetic field. The enclosed sensing structure with homogeneous field core shoes may ensure uniformity of the sensing field. Desired magnetization loci can be obtained by feedback control algorithm and positive compensation. Meanwhile, measurement precision is guaranteed by combining tensor coefficient and the averaging of CW and CCW outcomes.

By using the novel 3-D magnetic properties tester with feedback control, harmonics compensation, and automatic data processing, the comprehensive magnetic properties of laminated silicon steel are measured and analyzed. Alternating magnetic properties for laminated silicon steel in different directions are obtained, especially in the laminated direction, which is rarely studied but important to practical application. The magnetic anisotropy of GO 27ZH95 and NGO 35WW270 laminated silicon steels are compared and analyzed from origin of magnetic anisotropy. Alternating core loss features of the NGO 35WW270 laminated silicon steel along three directions are calculated and compared at 50 Hz, 100 Hz and 200 Hz. Alternating hysteresis, eddy current and excess losses are obtained by total losses separation. Moreover, the rotating core losses in rolling plane of 35WW270 are measured and analyzed at different excitation frequencies.

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