## 3 Types of Eccentricities Evaluated and Assessed Performance Indicators  
In this research, both static eccentricity (SE) and dynamic eccentricity (DE) are assessed by means of FEM. When SE is present, and as depicted in Figure 3a, the rotor and stator structures are not coaxial and a non-uniform airgap distribution that does not vary with \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Quantity** & **Value** \\ \hline \(d\) & Effective core length & 70.0 mm \\ \(r_{\text{se}}\) & Stator outer radius & 133.0 mm \\ \(\delta_{\text{g}}\) & Airgap length & 2.0 mm \\ \(b_{\text{s}}\) & Slot width & 24.8 mm * \\ \(h_{\text{s}}\) & Slot height & 27.5 mm \\ \(b_{\text{t}}\) & Tooth width & 10.0 mm * \\ \(h_{\text{ys}}\) & Height of the stator yoke & 10.5 mm \\ \(h_{\text{yr}}\) & Height of the rotor yoke & 10.0 mm \\ \(h_{\text{pm}}\) & PM height & 5.0 mm \\ \(\beta_{\text{r}}\) & PM remanence & 1.1 T \\ \(\mu_{\text{r}}\) & Relative recoil permeability & 1.04 \\ \hline \hline \end{tabular}  
* Reference tooth width and slot width values were considered for the 28-slot, 20-pole machines, as suggested in [17; 18], and they were adjusted for another slot/pole combinations to develop similar saturation levels, based on [17; 21].  
\end{table} 
Table 1: Main data of the machines (MPMSM and PMSM). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Slot Number** & **Pole Number** & \(q\) & **\(\Delta(Q_{\text{s}},2p)\)** & **Winding Layout** \\ \hline
18 & 12 & 1/2 & 6 & \(\ldots\) 1A 1B 1C 1C 1\(\ldots\) \\
18 & 20 & 3/10 & 2 & \(\ldots\) 1C 1A 1A 1B 1B 1B 1C 1C 1C 1\(\ldots\) \\
24 & 20 & 2/5 & 4 & \(\ldots\) 1C 1A 1A 1A 1B 1B 1B 1C 1C 1C 1\(\ldots\) \\
24 & 22 & 4/11 & 2 & \(\ldots\) 1C 1A 1A 1A 1A 1B 1B 1B 1B 1C 1C 1\(\ldots\) \\
24 & 28 & 2/7 & 4 & \(\ldots\) 1C 1A 1A 1A 1A 1B 1B 1B 1B 1C 1C 1\(\ldots\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Selected slot/pole combinations, including their winding layout considering TCW. Figure 2: Schematics of selected PMSMs: (**a**) conventional PMSM with non-segmented stator, (**b**) PMSM with modular stator core. the rotation of the rotor is generated. On the other hand, when DE is present, the rotor and stator are not coaxial and, additionally, the rotational axis and the rotor geometry axis do not match. As shown in Figure 3b, this creates a non-uniform airgap distribution that circulates with the rotor spinning. This work considers the difference between the nominal airgap length and the minimum airgap length generated by the stator/rotor misalignment as the magnitude of eccentricity as suggested in [24,30,33]. In addition, potential axis deflections and axial variations of the eccentricity magnitude are neglected. As a result, five eccentricity magnitudes are studied to cover from very low eccentricity (12.5% of the nominal airgap length) to high eccentricity (half the nominal airgap length), as presented in Table 3.  
The effects of eccentricity on the performance of both PMSMs and MPMSMs are studied by means of: (i) the analysis of the generated radial forces, also called unbalanced magnetic force (UMF), (ii) cogging torque, (iii) back-emf, and (iv) mean torque, as these indicators have proven to be affected in conventional topologies for at least one slot/pole combination. The following sections present the results organized so as to cover the impact of eccentricity on each performance indicator separately. In each case, the results are firstly presented in detail for one slot/pole combinations to show graphics of relevant curves and their harmonic spectrum. From these graphics, the main numerical indicators are extracted and summarized in tables for all the addressed slot/pole combinations, in order to allow  
Figure 3: Representation of eccentricity types depending on its dynamics: **(a)** SE, in which the position of the minimum airgap is fixed, (**b**) DE, in which the position of the minimum airgap changes as the rotor structure rotates. Four arbitrary time instants are represented in the figure.