Optimization design of the modified SST based on adaptive genetic algorithm

Abstract

The coupling of magnetic, thermal and structural force fields exists in the design, manufacture and operation of the magnetic core of transformer and motor, which makes the experimental data obtained from the standard magnetic properties measurement inconsistent with the actual problem. In order to obtain the magnetic properties measurement data of soft magnetic materials such as electrical steel sheet under multiple physical factors, the magnetic circuit structure was improved on the basis of the standard single sheet tester. At the same time, anti-bending clips made of polyether ether ketone were installed in order to prevent the bending deformation of the sample sheet during the application of tensile stress which would lead to uneven force. Then0 this basic structure of the tester under the coupling of temperature and stress is designed. In order to further improve the excitation performance of the tester and the magnetization uniformity of the sample, combined with COMSOL and MATLAB co-simulation, adaptive genetic algorithm was used to optimize the size of the yoke and excitation coil, thereby ensuring the uniformity of the magnetic field distribution in the measurement area of the sample. Finally, by combining simulation and specific experiments, the loss measurement results of a single sheet tester under different ambient temperatures and different stresses are studied, which proves that the tester is feasible and accurate, and the variation law of complex magnetic characteristics of electrical steel sheets under multiple physical fields is summarized.

Keywords

Single sheet tester multiple physical factors adaptive genetic algorithm COMSOL MATLAB

1. Introduction

Soft magnetic materials are widely used and have the most types of magnetic materials, covering the fields of power and electronics, etc. As one of the most commonly used soft magnetic materials in the power industry, electrical steel is mainly used to make the core of motors and transformers, and studying the complex magnetic characteristics of electrical steel is a prerequisite for the design of electrical equipment such as transformers and motors [1]. However, electrical steel in the actual operation process is often affected by a variety of physical factors [2], such as motor, transformer in the actual operation due to loss will lead to their temperature rise, thus affecting the magnetic properties of the material; In the manufacturing process of electrical of thermal stress and residual stress.

At present, the conventional methods of measuring magnetic properties of electrical steel include Epstein tester, single sheet tester. At present, Epstein tester and single sheet tester are mainly used to measure electrical soft magnetic materials in China. However, the conventional testing methods do not consider the influence of multiple physical factors on the physical property parameters of materials. If these physical factors are ignored in the design and performance analysis stage, the most accurate performance analysis results will not be obtained. In order to obtain the measurement data of magnetic properties of materials such as electrical steel under conditions of multiple physical factors, the research idea of domestic and foreign teams is to improve the traditional measurement methods and consider how to design the loading methods of factors such as stress and temperature [3–7]. Professor Norio Takahashi [8] improved the single sheet tester and placed the whole measuring device in an incubator to realize loading at different temperatures, with the temperature range from 25 °C to 100 °C. BROCKHAUS, a German company, designed a tester for measuring the magnetic characteristic stress effect of a single piece of material. The tester can measure the magnetic characteristic under the action of stress by applying pressure and pressure to the sample through compressed air. In the above research, only the influence of a single factor on the measurement of magnetic characteristics was considered. Based on the single sheet tester, research team of Shenyang University of Technology designed a vertical orthogonal double-yoke structure measurement device considering the coupling of temperature and stress [9,10], and analyzed the vector magnetic characteristics data of electrical steel sheet under the coupling of temperature and stress. It provides theoretical data support for the design of electrical equipment. In addition to external factors such as temperature and stress, physical factors brought by the tester itself should also be considered. For example, in the standard single sheet tester, the weight of the upper magnetic yoke will produce additional stress on the sample, and in the existing magnetic properties measuring tester, the bending deformation of the thin sample has not been studied by scholars.

To solve the above problems, this paper first improves the magnetic circuit structure on the basis of the standard single sheet tester and designs the anti-bending clamp made of polyether ether ketone material. Considering the influence of multi-physical factors coupling on the measurement of vector magnetic characteristics of electrical steel sheet, the modified SST under the coupling of temperature and stress is designed. Secondly, in order to improve the excitation performance of the modified SST and the magnetization uniformity of the sample, combined with COMSOL and MATLAB co-simulation, adaptive genetic algorithm was used to optimize the design of the magnetic yoke and excitation coil size and reasonable layout, so as to ensure the uniformity of magnetic field distribution in the central area of the sample [11–14]. Finally, on the basis of optimization and comparison with the measurement results of MST500, the measurement results under the power frequency standard excitation and different tension forces are analyzed, and the accuracy and feasibility of the design of the modified SST are verified.

2. Design of the modified SST

According to IEC 60404-3, a standard single sheet tester consists of a yoke, a sample and a coil. The sample is in the middle of two magnetic yoke, which forms a closed loop with the sample, and the coil is divided into a primary winding (excitation coil) and a secondary winding (measurement coil). The sample size is 500 mm × 500 mm. The yoke is made of multiple sheets of insulated nickel-iron alloy or oriented silicon steel. In actual operation, in order to make the flux evenly distributed in the yoke and reduce the influence of eddy current, the two yoke are arranged symmetrically. In order to avoid the influence of excessive stress on the sample due to the weight of the upper yoke itself, a modified magnetic circuit structure with horizontal symmetrical arrangement of the yoke is proposed and designed, which eliminates the use of suspension system and reduces the magnetic effect on the contact surface between the sample and the magnetic pole. In addition to adjusting the yoke arrangement, the winding mode of the excitation coil is also adjusted, and the excitation coil is wound in the middle part of the two yoke respectively, which provides space for the subsequent design of the anti-bending clamp.

In order to improve the measurement accuracy and consider the influence of uniaxial stress on magnetic characteristic parameters, the composite sensor module, stress loading and measurement module and temperature loading and measurement module are designed based on the magnetic circuit structure. The overall structure of the modified SST is shown in Fig. 1. The stress loading and measuring module is mainly composed of linear motor and pressure transduce, and the temperature loading and measuring module is mainly composed of mica heating sheet and temperature sensor. B-H composite sensor module is shown in Fig. 2, and its structure is mainly composed of Hall sensor, B coil, PCB circuit board and backing plate.

In order to study the magnetic properties of soft magnetic materials such as electrical steel caused by uniaxial stress, it is necessary to avoid the negative effects of bending deformation on the magnetic properties of the sample when compressive stress is applied. In view of the above situation, an anti-bending clip made of polyether ether ketone (PEEK) material with high mechanical strength, high geometric stability and low friction is added. The clip avoids bending deformation of the thin sample under compressive stress, and the compressive stress can be applied horizontally on the sample to ensure the uniform force of the sample. Polyether ether ketone material also has the properties of high temperature resistance, long-term use temperature is 260 °C, instantaneous use temperature can reach 300 °C, and long-term operation under high temperature and pressure does not lose any physical properties. In view of this characteristic, slot design is made inside the two splints of the anti-bending clamp, which is used to place the temperature loading module and B-H composite sensor module. The internal structure of the anti-bending clamp is shown in Fig. 3. During measurement, the sample piece is placed between the two cleats and fixed by screws. The internal wire can be connected with the external data acquisition card through the wire slot. In the actual measurement process, considering the temperature resistance of the wire, PCB board and Hall components, the temperature loading range is controlled within 25 °C–120 °C, which can meet the measurement needs. The temperature loading is to set the target temperature value through the temperature controller, generate a control signal to drive the relay, supply power to the mica heating sheet, and then heat the tested sample. In addition, in order to solve the problem that the mica heating sheet may cause uneven temperature distribution on the surface of the sample, a mica heating sheet with a size of 70 mm × 25 mm × 4 mm is selected, and the heating area of the sample can be increased under this size. Because the placement position of the chip thermal resistance is different from that of the B-H sensor, and the temperature distribution after the mica heating sheet is characterized by high temperature in the middle and slightly lower temperature on both sides, simulation analysis shows that the temperature difference between the placement position of the chip thermal resistance and that of the B-H sensor can be up to 4 °C. In order to ensure the uniformity of temperature distribution, the sample can first reach the preset temperature according to the characteristics of fast heating and easy control of the mica heating sheet, and then the whole measuring device is placed in a constant temperature environment, that is, placed in the incubator, to avoid heat exchange resulting in uneven temperature distribution of the sample. In order to detect whether the temperature distribution of the sample is uniform, two chip thermal resistors are used to measure the temperature on the upper surface of the sample to be measured, and the temperature of the two is compared. After the temperature is controlled to reach the constant temperature error range required by the experiment, the magnetic characteristics are tested. The size of the chip type thermal resistance is 20 mm × 7.5 mm × 3 mm.

3. Finite element simulation analysis of excitation performance of the modified SST

The magnetization uniformity of the sample directly affects the measurement accuracy of the tester. Therefore, in order to analyze the excitation performance of the excitation structure, the electromagnetic field simulation calculation is carried out between the improved excitation structure and the single sheet tester, and the distribution of the magnetic flux density of the two samples is compared. Except for the different winding mode of the excitation coil, the other dimensions are the same as the improved excitation structure. Some parameters of the size of the modified magnetic circuit structure designed in this paper are shown in Table 1, and parameter identification is shown in Fig. 4.

Table 1
Partial parameters of the size of modified magnetic circuit structure

Parameter Numerical value/(mm)

Sample size 200 × 50 × 0.30

Magnetic pole surface width a 25

Yoke height h 50

Yoke depth s 100

Width of excitation coil r 120

The height of the excitation coil t 60

Thickness of excitation coil w 5

Parameter	Numerical value/(mm)
Sample size	200 × 50 × 0.30
Magnetic pole surface width a	25
Yoke height h	50
Yoke depth s	100
Width of excitation coil r	120
The height of the excitation coil t	60
Thickness of excitation coil w	5

Modified magnetic circuit structure are set. The material of the sample and magnetic yoke is oriented silicon steel. The conductivity of oriented silicon steel is 2 × 10⁶ S/m, and the relative permeability is 7000. The magnetization curve is shown in Fig. 5. The material of the excitation coil is copper, and the number of turns is set to 400. The sample and the yoke form a closed loop. In order to reduce the influence of the magnetic pole on the edge effect of the sample, the air gap is set to 0 mm.

In the calculation process, the mesh quality determines the accuracy of the calculation. In the process of grid generation, COMSOL is fully used to divide the maximum side lengths of different modules in the model. The grid distribution of the two excitation structures is shown in Fig. 6. The sample to be tested uses a free tetrahedral grid for relatively fine division; The division of yoke, excitation coil and air domain is rough, and the number of grids is reduced as much as possible, which can effectively improve the calculation efficiency.

Because the excitation coil belongs to the uniform multi-turn coil defined by users, the geometric entity shape is more complicated, so it needs to analyze the geometric size and calculate the current direction. In this paper, the current direction is calculated by coil geometry analysis, and then the steady-state step is solved. Finally, the steady-state solution is taken as the initial value of the transient study and the transient simulation is carried out. After solving, you can view the simulation of the model through the drawing group.

In the electromagnetic field simulation calculation, the Maxwell equations are not only the basic theory, but also the constitutive relation of the medium should be considered. In homogeneous isotropic media, the constitutive relationship is as follows: $\begin{eqnarray}\left\{\begin{array}{@{}l@{}}D={\varepsilon}E\quad \\ B={\mu}H\quad \\ J={\sigma}E.\quad \end{array}\right.\end{eqnarray}$ (1)

In formula (1), 𝜀 is the dielectric constant; 𝜇 is the permeability; 𝜎 is the electrical conductivity. Equation (2) can be derived according to the above constitutive relations: B = 𝜇H and the differential form of Ampere’s loop law: 𝛻 × B = 𝜇J. $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle {\nabla}\times {\nabla}\times A={\mu}J\end{eqnarray}$ (2) $\begin{eqnarray}\displaystyle \text{} & \text{} & \displaystyle B={\nabla}\times A.\end{eqnarray}$ (3)

Firstly, the magnetic vector position distribution of the whole region is obtained by solving Eq. (2), and then the magnetic flux density of any position in the domain is solved by Eq. (3). Considering that the model of tester is similar to the transformer model, the magnetic field and circuit coupling theory is introduced for simulation calculation [15], and the equivalent circuit diagram of field-circuit coupling is shown in Fig. 7.

Ignoring the eddy current influence of the excitation coil, the voltage excitation can be derived from Fig. 7 as follows: $\begin{eqnarray}u(t)=Ri(t)+L\frac{di}{dt}-e(t).\end{eqnarray}$ (4)

Where is u (t) voltage excitation; i (t) is the current; R is resistance; L is inductance; e (t) is the electromotive force induced by the excitation coil. The induced electromotive force in the circuit can be obtained by introducing the magnetic potential A without considering the influence of eddy current. $\begin{eqnarray}e(t)=-\frac{n_{c}}{S_{c}}\frac{\partial }{\partial t}\int _{V_{S}}Ahdv.\end{eqnarray}$ (5)

Where S _c is the cross-sectional area of coil; n _c is the number of coil turns; h is the unit vector tangential to the coil. Combining (4) and (5), the equivalent circuit equation is obtained as follows: $\begin{eqnarray}u=Ri+L^{\prime }\frac{di}{dt}+\frac{n_{c}}{S_{c}}\frac{\partial }{\partial t}\int _{V_{S}}Ahdv.\end{eqnarray}$ (6)

Convert the above formula into matrix form as follows: $\begin{eqnarray}U=RI+L^{\prime }\frac{di}{dt}I+C^{T}\frac{\partial }{\partial t}A.\end{eqnarray}$ (7)

Where U is the voltage matrix; I current matrix; L Inductance matrix. Equation (7) can realize the coupling calculation of magnetic field and circuit.

Based on the above theoretical analysis, the excitation size in the excitation coil is adjusted, and the frequency is set to 50 Hz, so that the sample flux density in the two excitation structures reaches the saturation flux density. When solving, a fully coupled solver was selected, the step size was set to 0.0005 s, and the total solution time was 0.05 s. The magnetic induction intensity distribution of the sample was calculated. When t = 0.005 s, the magnetic flux density of the sample reached the maximum value, and the magnetic field distribution of the sample was shown in Fig. 8. It can be seen from the figure that under the improved excitation structure, the magnetic field distribution in the central region of the sample is relatively uniform.

In order to further analyze the uniformity of the magnetic flux density in the central area of the sample, and consider the placement of the B-H composite sensor and the temperature loading module in the actual measurement process, the central area of the sample piece of 100 mm × 50 mm is used as the magnetic field measurement area, that is, the length of the sample piece is within the range of 50 mm–150 mm. The magnetic flux density values of several points along the length direction of the sample were extracted and plotted as Fig. 9. It can be seen from the figure that the magnetic flux density distribution of the sample under the two excitation structures is basically consistent. But in the sample length 50 mm–150 mm range, the sample magnetic field uniformity is excellent under the standard monolithic measuring device, as shown in Fig. 9(a), while the sample magnetic field uniformity is poor under the improved excitation structure, as shown in Fig. 9(b). The reason for the poor uniformity of the magnetic field is mainly related to the size of the excitation structure.

By comparing the magnetic field uniformity of the sample, it can be seen that the improved excitation structure basically meets the feasibility requirements. However, in order to obtain a larger and more uniform magnetic field area, the improved excitation structure needs to be optimized.

4. Adaptive genetic algorithm and example analysis

4.1. Adaptive genetic algorithm

It is very important to select a suitable optimization algorithm for the optimization of magnetic circuit structure. In order to solve the problem of local optimization in current optimization algorithms, this paper proposes an adaptive genetic algorithm which can improve the performance of optimization. Since the crossover probability and mutation probability of genetic algorithm will affect the convergence speed, the adaptive crossover rate model and the adaptive mutation rate model are introduced. If the fitness function of an individual generation is greater than or equal to the average level of fitness function, the individual performance is the best, and the crossover and mutation probabilities should be reduced to retain excellent individuals. On the contrary, the crossover and mutation probabilities should be improved to quickly eliminate the individuals with poor performance. The proposed adaptive process of cross probability and mutation probability is as follows:

Adaptive crossover rate model: $\begin{eqnarray}P_{x}=\left\{\begin{array}{@{}l@{}}\displaystyle P_{x1}-{\displaystyle \frac{(P_{x1}-P_{x2})(f_{a}-f_{av})}{f_{\text{max}}-f_{av}}},\quad f_{a}\geq f_{av}\quad \\ P_{x1},f_{a}<f_{av}.\quad \end{array}\right.\end{eqnarray}$ (8)

Adaptive variation rate model: $\begin{eqnarray}P_{v}=\left\{\begin{array}{@{}l@{}}\displaystyle P_{v1}-\frac{(P_{v1}-P_{v2})(f_{\text{max}}-f_{b})}{f_{\text{max}}-f_{av}},\quad f_{b}\geq f_{av}\quad \\ P_{v1},f_{b}<f_{av}.\quad \end{array}\right.\end{eqnarray}$ (9)

Where, P _x1 and P _x2 are the maximum crossover probability and minimum crossover probability of genetic algorithm, P _v1 and P _v2 are the maximum mutation probability and minimum mutation probability of genetic algorithm, P _max and P _av are the maximum and average value of fitness function, f _a and f _b are the individual fitness value.

On this basis, the steps of protecting the best individual and accelerating the elimination of the bad individual are added. The first N individuals with the fitness of the population were selected for protection, and the last N individuals were replaced and eliminated by the first N, and the popsize-N individuals were roulette selected, crossed, mutated, and then sorted for fitness. The above operations were repeated, which could accelerate the survival of the fittest in the population while maintaining the overall status of the population.

4.2. Function optimization example analysis

In order to verify the feasibility of the optimization algorithm toolbox and adaptive genetic algorithm, and to provide a basis for the subsequent optimization design of the magnetic circuit structure, the minimum value of the following function is solved based on the above two optimization algorithm toolbox and adaptive genetic algorithm. $\begin{eqnarray}f(x,y)=x\cos (2{\pi}y)+y\sin (2{\pi}x)+4.75.\end{eqnarray}$ (10)

In formula (10), the value range of variables x and y are both [−2,2]. This function is a three-dimensional function with multiple peaks in its domain, and the minimum value in the domain is 1. Figure 10 shows the calculated optimal individual fitness value. It can be seen from the figure that the optimal value obtained by genetic algorithm and particle swarm optimization is basically similar to the actual optimal value of the function, but there are errors, while the improved adaptive genetic algorithm is equal to the actual optimal value of the function, and there are no errors. In terms of convergence speed, it takes 34 iterations for PSO to find the optimal value, 31 iterations for GA and 12 iterations for adaptive GA. In summary, the proposed adaptive genetic algorithm has better computational accuracy and convergence speed, which is in line with the research needs of this paper.

5. Optimization design of magnetic circuit structure based on COMSOL and MATLAB co-simulation

5.1. COMSOL and MATLAB co-simulation principle

In the past magnetic field simulation, the parameters generally need to be modified manually, and the steps are more complicated. In order to further improve the calculation efficiency, the advantages of COMSOL5.6 and MATLAB2018b were integrated in this paper to simplify the simulation process, improve the simulation analysis efficiency, and quickly complete the optimization design of the modified SST model size.

In the case of MATLAB, the existing code of its internal toolbox is integrated with COMSOL simulation, and it is even possible to call COMSOL from the user interface created with MATLAB to achieve bidirectional transfer between COMSOL and MATLAB data, as shown in Fig. 11. First, open, write and close the text file (txt) in MATLAB. Secondly, write the design variable to the subfunction para_n.m, where n represents the number of variables, that is, the number of design variables corresponds to the number of subfunction files. Finally, the model.m file is exported by COMSOL, and the model.param.set(‘r_n’, para_n) command is added to read the value of each variable into the variable r_n in turn, and the constant of the corresponding variable in the COMSOL modeling process is replaced by the variable r_n.

5.2. The modified SST size optimization scheme and result analysis

The proper selection of variable parameters plays a key role in improving design efficiency and shortening design cycle. Yoke height h, yoke depth s, excitation coil width r and thickness w are taken as design variables, in which the range of yoke height h and yoke depth s should meet the requirements in IEC 604043. Yoke height h ranges from 50 mm 80 mm, yoke depth s ranges from 90 mm 150 mm, excitation coil width r and thickness w ranges from 120 mm 150 mm and 5 mm to 10 mm, respectively.

COMSOL is used to add current to the excitation coil in the excitation structure model to generate a magnetic field in the center area of the sample to be tested. The magnetic field distribution in the center area of the sample is obtained by adjusting the range of variables corresponding to the adaptive genetic algorithm. In the actual measurement process, considering the position of B-H composite sensor and temperature loading module, the center area of 100 mm × 50 mm sampling sheet is used as the magnetic field measurement area. In order to obtain a more uniform magnetic field in this region, Parts Per Million (PPM) is taken as the objective function to measure the uniformity of magnetic flux density. The smaller the value, the more uniform the magnetic field is. The calculation formula is as follows: $\begin{eqnarray}\mathit{PPM}=2\times \frac{B_{\text{max}}-B_{\text{min}}}{B_{\text{max}}+B_{\text{min}}}\times 10^{6}.\end{eqnarray}$ (11)

B _max and B _min are the maximum and minimum values of the magnetic flux density in the central region of the sample respectively.

The convergence process is shown in Fig. 12, which took 10.8 hours to complete. s = 101.11 mm, h = 52.78 mm, r = 141.11 mm and w = 6.33 mm were obtained respectively. It can be seen from the figure that when convergence is achieved at the 12th time, the PPM before optimization is equal to about 13,000, and the PPM after optimization tends to be stable and converges to the optimal value of 1423.8, which is about one-tenth of the original.

In order to verify the effectiveness of the optimization results, the finite element model was reconstructed with the above dimensions and calculated. The magnetic densification diagram of the excitation structure under the optimal size is shown in Fig. 13. It can be seen that the entire structure has good excitation performance, and the magnetic field uniformity is the best in the 100 mm × 50 mm area of the sample, that is, the length range is 50 mm 150 mm. In addition, the error between the PPM calculation results of the finite element model under the optimal size calculated by formula (11) and that of the standard single sheet tester model is 0.19%, indicating that the optimization results of the above size are valid. The modified SST can produce a magnetic field with high flux density and good uniformity.

6. Accuracy and feasibility verification of the modified SST

Based on the above analysis, a magnetic property measurement platform considering temperature and stress is built. The excitation structure of the measuring device is shown in Fig. 14. In order to verify the accuracy and feasibility of the modified SST, the current more accurate measuring instrument is selected to carry out the loss under different stresses and different temperatures.

In this paper, oriented silicon steel B27R085 is selected as the sample to be tested under different stress loading, and the external stress is applied to the rolling direction of the sample. In order to further verify the feasibility of measuring the single piece magnetic characteristics measurement device under stress, the measurement results of the MST500 testing machine were compared, as shown in Fig. 15.

Figure 16 shows the iron loss under different stresses and magnetic flux densities, with negative sign representing compressive stress and positive sign representing tensile stress. Among them, the difference between the measurement results of the MST500 testing machine and that of the improved monolithic measuring device is not large, the error is less than 6.6%. In addition, as the loss curve changes, the loss of the core also increases with the continuous increase of the magnetic flux density, which is the same as the loss change rule without considering the influence of stress. Under the same magnetic flux density, the tensile stress will reduce the loss of oriented silicon steel sheet slightly, and the compressive stress will increase the loss of oriented silicon steel sheet. Through the above analysis, the accuracy and feasibility of the improved monolithic magnetic characteristic device considering the stress factor can be preliminarily verified.

In order to preliminatively verify the validity of the results, this paper chooses to compare the loss measurement results of a standard Epstein tester, which is made of high temperature resistant material and can withstand a high temperature of up to 120 °C, as shown in Fig. 17. Non-oriented silicon steel with grade B20AT1500 was selected for comparison.

Considering that the variation trend of hysteresis loops at different frequencies is similar, 50 Hz is taken as an example for analysis in this section. Figure 18 shows the loss curve of brand B20AT1500 when the ambient temperature is 50 °C ∼ 120 °C at 50 Hz frequency. In order to facilitate the analysis, the losses at T = 50 °C, 90 °C and 120°C were compared respectively. As can be seen from the figure, there is a small error between the loss value obtained by the Epstein tester and the improved monolithic measuring device. When the magnetic density is low, the total loss error is less than 5.5%, and when the magnetic density is high, the total loss error is less than 8%. And with the increase of temperature, the overall loss shows a decreasing trend. It can be seen that the impact of ambient temperature on the loss performance of silicon steel sheet is more significant. Through the above analysis, the feasibility and accuracy of the improved monolithic measuring device can be preliminarily verified.

7. Conclusion

In order to obtain magnetic characteristics measurement data of soft magnetic materials such as electrical steel under multiple physical factors, this paper designed the modified SST that can meet the temperature and stress coupling under actual operating conditions, which solves the problem of single measurement data in traditional test methods and lays a foundation for subsequent multi-physical field coupling research.

The adaptive genetic algorithm is combined to optimize the size of yoke and excitation coil. After optimization, the PPM is about one-tenth of the original, and the error between the sample magnetic flux density non-uniformity and that of the standard single sheet tester is 0.19% under the optimal size, which effectively improves the magnetic field uniformity of the measuring area in the modified SST.

Through the preliminary verification of the loss measurement results of the single magnetic characteristics measurement device under different ambient temperatures and different stresses, the error values are guaranteed within 7%, which proves that the device is feasible and accurate, and provides conditions for the subsequent construction of multi-physical field coupling measurement platform, which has important reference value.

Footnotes

Acknowledgements

This work was funded by the teaching fund project ZDXM2301 of Tianjin University of Technology and the teaching fund project ZX23-01 of Tianjin University of Technology.

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