## 5 Results and Discussion
### Epstein Square Ring Loss Calculation Results  
#### 5.2.1 Epstein Square Ring Loss Cloud Map  
Similarly, to analyze the distribution of loss in the Epstein frame more intuitively, this paper obtains the loss distribution nephograms of the FBA alloy and the 0.10 mm UTGO  
Figure 10: Cloud images of the magnetic flux density of the 0.10 mm UTGO steel at different frequencies while \(B_{\rm m}\) is 1.2 T. (**a**) 50 Hz; (**b**) 200 Hz; (**c**) 400 Hz. Figure 9: Cloud images of the magnetic flux density of the 0.10 mm UTGO steel at different frequencies while \(B_{\rm m}\) is 1.0 T. (**a**) 50 Hz; (**b**) 200 Hz; (**c**) 400 Hz. silicon steel Epstein frames at different frequencies when the magnetic flux density is 1.0 T and 1.2 T, as shown in Figures 11-14. It can be seen from these diagrams that the loss and magnetic density have the same distribution law. With the increase in the frequency and magnetic flux density, the overall loss of the Epstein frame increases, and the losses at the corners are significantly higher than they are at other positions. The loss at positions other than the corner remains evenly distributed. At the same frequency and magnetic flux density, the loss of the 0.10 mm UTGO silicon steel Epstein frame is higher than that of the FBA alloy Epstein frame. Figure 14: Cloud images of the loss of the 0.10 mm UTGO steel at different frequencies while \(B_{m}\) is 1.2 T: (**a**) 50 Hz; (**b**) 200 Hz; (**c**) 400 Hz. Figure 13: Cloud images of the loss of the 0.10 mm UTGO steel at different frequencies while \(B_{m}\) is 1.0 T: (**a**) 50 Hz; (**b**) 200 Hz; (**c**) 400 Hz. 2.2 Comparison between the Calculated Value of the Epstein Square Ring Loss and the Experimental Value  
The specific gravity loss of the Epstein square ring is calculated as follows:  
\[P_{V}=\sum_{i=1}^{n}p_{i}/m=\frac{\int pdV}{\text{m}} \tag{11}\]  
where \(p_{i}\) is the loss of the Epstein square ring under the \(i\)-th calculation unit and m is the mass of the Epstein square ring. The magnetic properties of the 0.10 mm UTGO silicon steel are measured using the Epstein square ring method; the electromagnetic properties of the 0.10 mm UTGO steel are therefore calculated first. As shown in Figure 15, the calculated values of the Epstein square ring's loss curve using 0.10 mm UTGO steel were compared with the experimental values at 50 Hz, 200 Hz, and 400 Hz frequencies. It can be seen from the figure that the error between the calculated value and the experimental value of the electromagnetic characteristics of the 0.10 mm UTGO steel Epstein square ring is generally large at a frequency of 50 Hz and a range of 0.1-1.5 T, with a maximum error of 9.53%. The maximum error between the calculated value and the experimental value of the electromagnetic characteristics of the 0.10 mm UTGO steel Epstein square ring is 9.87% at a frequency of 200 Hz and a range of 0.1-1.5 T, and the maximum error in the range of 0.7-1.5 T is 3.86%. The error between the calculated value and the experimental value of the electromagnetic characteristics of the Epstein square ring is small at a frequency of 400 Hz and a range of 0.1-1.5 T. In the magnetic flux density range of 0.1-0.4 T, the error is relatively large, with the maximum deviation being 8.87%. In the magnetic flux density range of 0.4-1.5 T, the error is relatively small, with a maximum error of 4.65%. Figure 16 shows a comparison between the calculated and experimental values of the Epstein square ring loss curves using the FBA alloy at 50 Hz, 200 Hz, and 400 Hz. It can be seen from Figure 16 that, when the magnetic induction intensity is in the range of 0.1-0.4 T, the error between the value calculated by the mathematical model and the experimental value of the electromagnetic characteristics of the FBA alloy Epstein square ring is relatively small at 50 Hz, with a maximum error of 3.14%. When the magnetic flux density \(B_{\text{m}}\) is 0.5-1.5 T, the error is larger, with a maximum error of 8.62%.