Comparison and analysis of testing methods for magnetic properties of oriented silicon steel sheets

The magnetic properties of oriented silicon steels with different thickness of 0.18 mm, 0.23 mm, 0.27 mm, and 0.30 mm in rolling direction and transverse direction were studied using the excitation current method and H-coil method. The magnetic field strength deviation and specific total loss of two methods were compared based on the excitation current method. The magnetic field distribution was analyzed using MagNet finite element simulation, and it was found that the measurement deviation of the excitation current method is mainly determined by the effective magnetic circuit length. The higher the magnetic flux density, the smaller the effective magnetic path length. Therefore, under low magnetic flux density conditions, the actual effective magnetic path length is greater than the specified effective magnetic path length, resulting in high measurement results, while under high magnetic flux density conditions, the measurement results are low. Due to the influence of hysteresis loss, the deviation ratio of the two methods on the total loss is generally smaller than the deviation ratio of magnetic field strength, and the 0.18mm oriented silicon steel is smaller than other thickness oriented silicon steel. Due to the difficulty of magnetization in the transverse direction of oriented silicon steel, the variation trend of magnetic field strength deviation and specific total loss along the transverse direction is significantly different from that along the rolling direction. In addition, a measurement correction strategy was proposed by determining the actual effective magnetic circuit length of the excitation current method, which achieved good results. This work has certain significance for the accurate measurement of the magnetic properties of oriented silicon steel, and is expected to provide important reference for the application of 0.18mm oriented silicon steel.


Introduction
Oriented silicon steel is mainly used for manufacturing transformer cores and large generator stator cores, and is an important soft magnetic material in the power industry.The accurate measurement of magnetic properties of oriented silicon steel is the technical basis for performance evaluation, product classification, and standard formulation, providing important references for magnetic core selection and structural design. [1]At present, the mainstream methods for measuring the magnetic properties of oriented silicon steel are the Epstein square ring method and the SST monolithic method [2,3] .The Epstein square ring method has a small sample size, complex sample preparation and measurement processes, and a significant deviation between the measured magnetic properties and the actual magnetic properties of the product [4] .The traditional SST monolithic method uses the excitation current method to test magnetic performance, which requires specifying the effective magnetic circuit length.During the measurement process, the actual effective magnetic circuit length often does not match the agreed effective magnetic circuit length, resulting in significant measurement error [5] .GB/T 39042-2020 "Single Piece Magnetic Properties Test of Electrical Steel H-coil Method" in Chinese specifies a method to measure the magnetic properties of oriented silicon steel using the H-coil method [6] .This method directly measures magnetic performance through induced voltage without specifying the effective magnetic circuit length, eliminating the magnetic property deviation caused by different magnetic circuit lengths, making it closer to the true value [7] .
Although the measurement results of the two methods were compared when formulating the national standard for the H-coil method, these studies only focused on oriented silicon steel with a thickness of 0.23-0.30mmand did not explore the root cause of the difference, nor did they provide a better solution to correct the measurement results.In recent years, in order to further improve the performance of oriented silicon steel and reduce core loss, a high magnetic induction and low loss oriented silicon steel with the thickness of 0.18mm has been developed [8,9] .In order to explore more suitable magnetic testing methods for 0.18mm oriented silicon steel and promote the practical application of 0.18mm oriented high magnetic induction and low loss silicon steel, this article uses the H-coil method and excitation current method to measure the magnetic properties of different thickness oriented silicon steel, and compares the results of the two methods to analyze their changes and reasons.The excitation current method has been improved through finite element analysis.The above results are helpful for accurately measuring the magnetic properties of oriented silicon steel and are expected to provide important references for the application of 0.18mm oriented silicon steel on iron cores.

Experimental procedures
The experimental materials were four kinds of domestic oriented silicon steel with different thicknesses of 0.18mm, 0.23mm, 0.27mm and 0.30mm.According to GB/T 13789-2008 "Method of Measuring Magnetic Properties of Electrical Steel Sheet (Strip) by Single Chip Tester" [10] , magnetic properties of Brockhaus MPG 200D soft magnetic measurement system was tested by excitation current method.According to GB/T 39042-2020 "Single Piece Magnetic Properties Testing of electrical steel H-coil method" [6] , the magnetic properties of H-coil method were tested on TD8520 soft magnetic measurement system (Changsha Tianheng Measurement and Control Company).The specific total loss Ps and magnetic field strength Hm of oriented silicon steel with a magnetic flux density of 0.5T-1.9T(interval 0.1T) were measured using a sinusoidal wave with a frequency of 50 Hz.The principles of the two measurement methods are shown in figure.1.

Figure.1 Schematic diagram of two measurement methods (a) Excitation current method measurement
principle diagram, (b) H-coil method measurement principle diagram The magnetic field generated by the excitation coil in the field current method was simulated using MagNet finite element analysis software, and the magnetic field distribution of 0.18mm oriented silicon steel during the experimental process was simulated.

Analysis of deviation rate of magnetic field intensity measured by different methods
Based on the excitation current method, the formula for calculating the deviation rate of the magnetic field strength measured by the H-coil method and the specific total loss is as follows [11] : s(MC) s(HC) s s(MC) In the formula, ΔHm and ΔPs are the deviation rates of magnetic field strength and specific total loss obtained by the two measurement methods, Hm(MC) and Ps(MC) are the results of magnetic field strength and specific total loss measured by the excitation current method, and Hm(HC) and Ps(HC) are the results of magnetic field strength and specific total loss measured by the H-coil method, respectively.
Figure .2shows the variation curve of Δ Hm with different thickness orientation as a function of magnetic flux density Jmax.It can be found that ΔHm is positive when Jmax is low, and the measurement result of excitation current method is higher than that of H-coil method.With the increase of Jmax, ΔHm gradually decreases and drops to a negative value when Jmax reaches more than 1.7T, that is, the result measured by the H-coil method is higher than that by the excitation current method.

Figure.2 Variation curve of magnetic field intensity deviation rate with magnetic flux density
The variation trend of the deviation rate Δ Hm is similar to the results of previous studies.The difference is that most of the previous studies focused on the magnetic properties of oriented silicon steel with a thickness of 0.23-0.30mmwhen Jmax ≤ 1.7T, and found that Δ Hm is positive under this condition, so it is concluded that the measurement results of the excitation current method are higher than those of the H-coil method.However, as can be seen from figure.2,Δ Hm of 0.18mm oriented silicon steel is in Jmax > 1.7T, the result of H-coil method is lower than that of excitation current method.
The reason is owing to the increase of Jmax, and the effective magnetic circuit length of excitation current method will decrease.When Jmax= 1.7T, the effective magnetic circuit length is only 96.8% of that when Jmax= 1.0T.When Jmax= 1.8T, the effective magnetic circuit length will be further reduced to 95.9% of that when Jmax= 1.0T [12] .The decrease in effective magnetic circuit length may be caused by the increase in permeability caused by the increase in Jmax [13] .The formula for testing magnetic field strength H(t) by excitation current method is as follows [14] : In the formula, N1 is the number of turns of the primary winding coil, I is the size of the incoming current at time t, lm is the length of the effective magnetic circuit, and the conventional effective magnetic circuit length la=450 mm is generally adopted in the test.When the actual effective magnetic circuit length (lr) is greater than la, the actual magnetic field strength Hr will be less than the magnetic field strength Ha calculated according to la, resulting in a larger magnetic field strength measurement value, and vice versa.Because the H-coil method does not need to agree on the effective magnetic circuit length, the corresponding system error is eliminated, so the measurement result is closer to the real value.Therefore, when Δ Hm=0, the magnetic field intensity obtained by the excitation current method is close to the true value, indicating that the lr used is equal to la.Combined with the analysis of the deviation rate of magnetic field strength, it can be seen that the lr of 0.23-0.30mm thicknessoriented silicon steel measured by the excitation current method at 1.7T is greater than 450 mm, while the lr of 0.18 mm oriented silicon steel at 1.7T is very close to 450mm.This conclusion has some reference value for the lr estimation of excitation current method and the amendment of measurement results, and the amendment method will be presented in Section 2.4 of this paper.

Different methods of measuring specific total loss deviation rate analysis
The specific total loss is an important parameter to determine the quality of oriented silicon steel, especially when Jmax is 1.7T, the specific total loss is an important factory index to judge whether the oriented silicon steel meets the requirements of the grade standard. [15]Figure .3shows the variation curve of ΔPs of four groups of silicon steels with different thickness orientations as a function of Jmax.It can be found that the change trend of ΔPs is obviously different from that of ΔHm.Taking 0.18mm oriented silicon steel as an example, its ΔHm is close to 0 at 1.7 T, while its ΔPs drops below 0% after Jmax exceeds 1.5 T. The results show that the measurement of the specific total loss does not depend only on the effective magnetic circuit length and magnetic field strength.

Fig.3 Variation curve of specific total loss deviation rate with flux density
The specific total loss can be divided into eddy current loss, hysteresis loss, and abnormal loss [16] .Due to the reduction of eddy current loss with the thickness of oriented silicon steel, the thinner the thickness of oriented silicon steel, the greater the proportion of hysteresis loss [17] .It can be seen that the hysteresis loss of 0.18mm oriented silicon steel accounts for the largest proportion of the total loss among the four groups of samples.The calculation formula for hysteresis loss is as follows [18] : Where C1 is the coefficient determined by the material properties, J is the magnetic flux density, f is the frequency, and V is the total volume of oriented silicon steel.
Under the same material properties and frequency conditions, magnetic flux density and volume are the decisive factors for the hysteresis loss of oriented silicon steel.However, the magnetization state of the entire silicon steel sheet is uneven, so the effective magnetization volume can be used instead of the total volume to characterize hysteresis loss: (5) Where V1 is the effective magnetization volume of oriented silicon steel under the action of magnetic field, and its value is proportional to the actual effective magnetic circuit length lr: Where, k is the coefficient related to the cross-sectional area of oriented silicon steel.Substituting equation ( 6) into equation ( 5) yields: When the magnetic properties of oriented silicon steel are measured by excitation current method, Pw is affected by both J and lr.Since lr is negatively correlated with J, as J increases, lr decreases, and overall J2 • lr increases.It can be seen that the lr decrease causes the true hysteresis loss to increase, resulting in a decrease in the specific total loss measured by the excitation current method compared with the H-coil method, so that the Δ Ps of 0.18mm oriented silicon steel drops below 0% when J exceeds 1.5T.

Analysis of deviation rate of transverse magnetic properties measured by different methods
In the actual use of iron cores, although most silicon steel sheets are only affected by the rolling magnetic field, some silicon steel sheets located at the corners of formed iron cores (such as U-shaped iron cores) are still affected by magnetic fields from different angles [19] .Due to the serious obstruction of the movement and rotation of magnetic domains during the non-rolling magnetization process of oriented silicon steel, there are significant differences in the magnetic properties of oriented silicon steel under the influence of different angle magnetic fields [20] .Therefore, measuring the magnetic properties of oriented silicon steel at other angles is of great significance for the structural design and selection of devices such as transformers and motors.
Figure .4shows the magnetic field strength deviation rate ΔHp,m measured when the oriented silicon steel is placed laterally in two magnetic properties measurement systems.It can be found that the variation trend of Δ Hp and m of the silicon steel with different thickness orientation increases first, then decreases and then increases.According to the previous section, ΔHp,m are mainly affected by lr in the excitation current method test, and lr is negatively correlated with the magnitude of the permeability.According to previous work, the direction of difficult magnetization under the condition of Jmax= 0.5T is always 90 ° [21] , that is, the transverse direction is the direction with the lowest permeability.This will cause the lr of the excitation current method to increase, making the measured magnetic field strength smaller relative to the true value, resulting in a decrease in ΔHp,m.At the same time, with the increase of Jmax, the direction of difficult magnetization will also change [22] , resulting in changes in the transverse permeability.Therefore, the lr of the excitation current method under different magnetic density is jointly determined by Jmax and the transverse permeability under the magnetic density.The larger the magnetic flux density, the smaller the actual effective magnetic circuit length, and the smaller the permeability, the larger the actual effective magnetic circuit length.

Figure.4
Vertical rolling placement of two methods to measure the magnetic field intensity deviation rate Figure .5 shows the specific total loss deviation ratio ΔPp,s measured when the oriented silicon steel is placed laterally in two magnetic properties measurement systems.It can be seen that the Δ Pp,s of each thickness oriented silicon steel has reached below 0% at 0.5T, indicating that the lr of excitation current method is less than la at lower Jmax.When placed laterally, the magnetization and demagnetization processes of oriented silicon steel require the magnetic domain to rotate at a large angle, resulting in a large hysteresis loss.Based on the conclusion from the previous section, when considering hysteresis loss alone, the actual effective magnetic circuit length is greater than the conventional effective magnetic circuit length, which will result in the measured value being smaller than the actual value.However, in the total loss measurement when placed horizontally, hysteresis loss accounts for a large portion, so the total loss measurement value when placed horizontally is smaller than the actual value, resulting in a deviation rate of less than 0%.At the same time, it can be seen from equation ( 7) that the increase of Jmax will cause the increase of hysteresis loss and further reduce ΔPp,s.

Figure.5
The ratio of the total loss deviation rate between the two methods of vertical rolling placement

The actual effective magnetic circuit length and measurement results are corrected
In order to further explore the determination method of effective magnetic circuit length, taking 0.18mm oriented silicon steel as an example, the magnetic field distribution of oriented silicon steel in the excitation current method test was analyzed using MagNet finite element simulation software.
Figure.6 shows the magnetic field simulation modeling structure of oriented silicon steel.Based on the measurement values of 0.18mm oriented silicon steel, the electromagnetic characteristics of the oriented silicon steel sheet and yoke were determined.The yoke and winding dimensions are set according to the specified values of Method A (current method) [23] in GB/T 13789-2022 "Method for Measuring the Magnetic Properties of Electrical Steel Strip (Sheet) with Single Chip Tester".The yoke height is 125mm, width is 500mm, inner width is 450mm, and the magnetic pole surface width is 25mm.The air gap between the yoke and the silicon steel sheet is 0.004mm, the winding width is 445 mm, the height is 13 mm, and the coil turns are 400.consistent with the set magnetic flux density are concentrated inside the magnetic yoke.This is also the fundamental reason for the difference in measurement results between the excitation current method and the H-coil method, which uses the H-coil method to measure the induced voltage in the middle of oriented silicon steel, effectively avoiding the impact of low magnetic flux density on the measurement results on both sides.Due to the overall measurement of oriented silicon steel, the excitation current method cannot avoid errors caused by low magnetic density on both sides.Meanwhile, due to the fact that the part that reaches the set magnetic flux density is mainly concentrated inside the yoke, the measurement results are relatively closer to the true value when lr is 450mm away from the inside of the yoke.However, due to the uneven measurement of the actual magnetic field inside the yoke, the lr deviation is 450mm, resulting in measurement errors in magnetic properties such as magnetic field strength and specific total loss.In summary, when the average magnetic flux density (Ja) is lower than the set magnetic flux density (Js), the deviation rate decreases.At the same time, the decrease in magnetic flux density leads to an increase in the effective magnetic path length and an increase in the deviation rate.When the two achieve equilibrium at a certain magnetic flux density, accurate measurement results can be obtained, and the corresponding magnetic path length is the actual effective magnetic circuit length.Therefore, in order to correct the effective magnetic circuit length, the magnetic flux density distribution inside the oriented silicon steel should be determined first.Since ΔHm=0 means that the measured value is equal to the actual value, which means that Ja=Js, the Ja values of each group can be calculated by using the distribution coefficient of magnetic flux density at ΔHm=0.The magnetic field intensity (Ha) corresponding to Ja can be obtained by referring to the actual measurement results.Here, Ha is the magnetic field intensity within the range of 450 mm magnetic circuit.Then the actual magnetic field intensity of the oriented silicon steel as a whole can be obtained through calculation.According to Section 2.1, the deviation of magnetic field intensity measurement results is almost entirely caused by the deviation of effective magnetic circuit length.Therefore, it can be considered that the deviation rate of the effective magnetic circuit length equals to the deviation rate of the magnetic field strength measurement results.The actual effective magnetic circuit length can thus be calculated.
Based on the above results, the actual effective magnetic path length can be estimated and the measurement results of excitation current method can be modified.Taking 0.18mm oriented silicon steel used in this experiment as an example, the magnetic field strength of oriented silicon steel measured by excitation current method is shown in Table .1.It can be seen from Section 2.1 that the measured magnetic field strength of 0.18mm oriented silicon steel is closest to the real value when Jmax= 1.7T, so it is agreed that the lr and la (=450 mm) at 1.7T are equal.First, according to the magnetic field strength of 109.9A/m at 1.7T and the actual length of the oriented silicon steel sheet of 500 mm, the average magnetic field strength of the oriented silicon steel can be seen as follows: 450 109.9 98.91A/m 500   Figure. 8 shows the fitting curve of the measured magnetic field strength of oriented silicon steel tested by the excitation current method under different magnetic flux densities.The magnetic induction density corresponding to the magnetic field intensity of 98.91 A/m can be obtained as 1.684T.Setting the magnetic induction density to 1.7T can be further calculated.
Where A is the distribution coefficient of magnetic flux density, J1 is the set magnetic flux density, and J2 is the average magnetic flux density.8 The fitting curve of the relation between magnetic flux density and magnetic field intensity was obtained by excitation current method.From the above analysis of the method for determining the actual effective magnetic length, it can be seen that the actual measurement results are related to the average magnetic flux density, and the change of the average magnetic flux density is positively correlated with the effective magnetic length deviation, so Δ Hm is related to the effective magnetic length deviation rate.Based on the above analysis, the lr under other magnetic density conditions can be estimated using the magnetic flux density distribution coefficient A calculated under the corresponding magnetic density Δ Hm=0.The calculation steps are as follows: 1)Combined with the actual measurement results, the A value was obtained through the fitting curve of the magnetic field intensity and magnetic flux density; 2)Estimate the average magnetic flux density J2 under the magnetic density by setting the magnetic flux density J1 and the magnetic flux density distribution coefficient A, as shown in equation (10); (10) 3)The magnetic field intensity H1 corresponding to the average magnetic flux density was found by using the fitting curve in figure.8combined with Lagrange interpolation method.
4)The magnetic field strength H2 corresponding to the agreed effective magnetic circuit length of 450 mm can be calculated by using the magnetic field strength, as shown in equation (11).
5)The deviation rate of effective magnetic circuit length is obtained by comparing with the actual measured value, and then the actual effective magnetic circuit length is estimated.The resulting deviation of the field strength measured by the excitation current method is mainly determined by the deviation of the actual effective magnetic circuit length from the conventional effective magnetic circuit length, so Δ Hm is almost entirely determined by the effective magnetic circuit length deviation rate (Δl=(lr-la)/la).As shown in figure.9, the variation trend of Δl is similar to that of two different test methods Δ Hm, which also confirms the validity and accuracy of the calculation method and results.

Figure.9
The effective magnetic circuit length deviation rate is compared with the deviation rate of two different test methods The calculated Δl excludes the influence of other factors such as environmental changes and errors of two measurement results.Therefore, the results obtained by using Δl correction are more authentic.According to the data in table.2, the magnetic field strength of oriented silicon steel measured by the excitation current method when the magnetic flux density is 1.0-1.8T is corrected, and the results measured by the excitation current method and the H-coil method are compared with those measured by the excitation current method as shown in figure.10.

Figure.10
The results of correction were compared with those of two measurement methods In figure.10, it can be seen that the measurement results of the improved excitation current method based on the above method are very close to those of the H-coil method, confirming the authenticity and representativeness of the above description of the actual effective magnetic circuit length measurement method.On the other hand, this correction method corrects the measurement results by determining the effective magnetic circuit length of the excitation current method, making the measurement results closer to the true value.In the actual measurement process, accurate effective magnetic circuit length will also play a role in correcting other magnetic properties parameters, and will promote the development of magnetic property testing methods for oriented silicon steel.

Conclusion
(1)The deviation rate between the measurement results of the H-coil method and the excitation current method is mainly determined by the actual effective magnetic circuit length of the excitation current method.The thickness and testing conditions of oriented silicon steel have a significant impact on the deviation rate, indicating that the measurement results of the excitation current method are not always greater than those of the H-coil method.
(2)Under the same total loss, the thinner the oriented silicon steel sheet, the smaller the eddy current loss, and the higher the hysteresis loss in the total loss, resulting in a lower deviation rate between the measurement results of 0.18mm oriented silicon steel sheet and thicker products.The higher the magnetic flux density, the smaller the effective magnetic path length of oriented silicon steel, and the greater the hysteresis loss.Therefore, when the magnetic density of 0.18mm oriented silicon steel is higher than 1.5T, the measurement results of the excitation current method are lower than those of the H-coil method.
(3)The actual effective magnetic circuit length of the transverse excitation current method is determined by the magnetic flux density and the corresponding transverse magnetization ability.The total specific loss of lateral placement is much higher than that of rolling placement, and hysteresis loss accounts for the main part of the total specific loss.
(4)Establish a simulation model for the excitation current method using MagNet finite element analysis software.When the average value of the actual effective magnetic circuit length is lower than the set magnetic flux density, analyze the effective magnetic circuit length, resulting in a decrease in the measured value, while a decrease in the effective magnetic circuit length leads to an increase in the measured value.
(5)This article provides an effective method for correcting the test results of the excitation current method, which not only solves the problem of deviation from the true value of the measurement results of the excitation current method, but also avoids the problem of difficulty in tracing the magnetic properties of the H-coil method, which helps to more accurately measure the magnetic properties of oriented silicon steel.

Figure. 6
Figure.6 Structure illustration of magnetic field simulation of oriented silicon steel driven by excitation coil Jmax of the main part of the oriented silicon steel was made to reach 1.7T by setting the excitation current of the coil, and the magnetic field distribution was obtained using the Static 2D solver (figure.7).Figure.7ashows the magnetic field distribution of the main structure after the air bag is hidden.Figure.7b and c show the magnetic field distribution of the left and right oriented silicon steel and the junction of the yoke amplified in figure.7a.

Figure. 7
Figure.7 Magnetic sensing line and magnetic field distribution when the flux density is 1.7 T(a) Overall magnetic field distribution map, (b) Magnetic field distribution on the left side of oriented silicon steel, (c) Magnetic field distribution on the right side of oriented silicon steel From the magnetic field distribution diagram in figure.7, it can be seen that the overall magnetic field distribution of directional silicon steel under excitation of the excitation coil shows a trend of magnetic flux density closer to both sides, with lower magnetic flux density.Almost all parts

Table . 1
Magnetic field strength of oriented silicon steel measured by excitation current method.

Table . 2
The calculation results are shown in table.2:Estimation results of actual effective magnetic circuit length under different magnetic density conditions