## 3 Results and Discussion
### Influence of the Mixed Eccentricity on the Air-Gap Magnetic Field
#### 3.2.2 Analysis of the Tangential Air-Gap Flux Density Component  
We define the tangential un-symmetry (_USYt_) of the tangential air-gap flux density component as  
\[USYt=\frac{B_{rm}-B_{tmin}}{B_{tt}}\times 100\% \tag{32}\]  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Mixed Eccentric**} & \multicolumn{8}{c}{**Spatial Harmonic Amplitudes**} & \multicolumn{8}{c}{_USYr_} & **THDr** \\ \cline{2-13} \multicolumn{1}{c}{**Conditions**} & **11** & **13** & **23** & **25** & **35** & **47** & **59** & **71** & **83** & **85** & **(\%)** & **(\%)** \\ \hline Normal & 0.2084 & 0.1309 & 0.114 & 0.0519 & 0.07635 & 0.05658  
where \(B_{t}\) is the spatial distribution of tangential component of air-gap flux density, and \(B_{tmax}\) and \(B_{tmin}\) are the maximum and minimum root mean square values of all periods of \(B_{t}\). \(B_{tn}\) is the root mean square value without eccentricity.  
When mixed eccentricity occurs, the tangential air-gap flux density curve will be distorted and become a non-stationary curve. Thus, spectrum analysis based on Fourier transform cannot accurately describe the frequency and amplitude characteristics of tangential air-gap flux density under different spatial angles. In this paper, the wavelet transform method was used to decompose the original tangential air-gap flux density, and the number of decomposition layers was 7. Among them, the low-frequency components a6 and a7 were closer to the envelope of the original signal. As the eccentricity increases, the distortion becomes serious, that is, the asymmetry tends to be serious. The high-frequency components d1, d2, and d3 are obvious periodic signals, and as the degree of eccentricity increases, the signal energy distributions converge toward the center of the samples, as shown in Figure 8.  
Therefore, the feature of energy proportion is defined to describe the degree of aggregation of signal energy, which is expressed as  
\[E_{oi}=\frac{E_{Mi}}{E_{T}}\times 100\% \tag{33}\]  
where \(i\) = 1,2 are the coefficients of the first layer and the second layer of the high-frequency components of the signal, respectively, signal samples are equally divided into 10 intervals,  
Figure 8: The results of wavelet decomposition of tangential air-gap flux density.  
and \(E_{Mi}\) is the signal energy of the fifth and sixth intervals in the middle. \(E_{T}\) is the total energy of signal samples. The signal energy is calculated by  
\[E=\sum_{m=1}^{N_{d}}s(m)^{2} \tag{34}\]  
where \(N_{d}\) is the calculated sample length and \(s\) is the calculated sample values.  
The samples of low-frequency component a7 were used to calculate the \(USYt\), and the samples of high-frequency components d1, d2, and d3 were used to calculate the \(E_{oi}\). The results are shown in Figure 9. In Figure 9a, \(USYt\) increases significantly with the increase in degree of mixed eccentricity, indicating that mixed eccentricity has a serious impact on the low-frequency component of tangential air-gas flux density. In Figure 9b, \(E_{oi}\) also increases correspondingly. The \(E_{oi}\) of the d1 component is most sensitive to the severity of mixed eccentricity.