## 4 Premise for Fair Comparison  
To investigate the validity of the newly proposed SP-PMVM, it is optimized and compared with the conventional PMVM machine proposed in [3], as shown in Figure 3a.  
It is necessary to explain some key design data and coefficients in the following optimization and comparison:  
Figure 5: Magnetic circuit of one section in the rotor of SP-PMVM.  
1. The original parameters of both machines are defined as shown in Figure 4. Other main parameters are listed in Table 1.
2. Some original dimensions and parameters should be defined and explained. \(\psi_{ss\_in}\) and \(\psi_{ss\_out}\) are the pole-arc to pole-pitch ratios of the inner and outer stators, respectively; \(\psi_{st\_in}\) and \(\psi_{st\_out}\) are the stator tooth width of the inner and outer stators, respectively. The \(\psi_{pm}\) is the rotor PM width in degrees, and these parameters are used to define the coefficients: \[k_{st}=\varphi_{st\_in}/\varphi_{s\_np}=\varphi_{st\_out}/\varphi_{s\_np}\] (6) \[k_{rt}=\varphi_{pm}/\left(\varphi_{pm}+\theta_{m}\right)\] (7) where \(\varphi_{s\_np}=\varphi_{st\_in}+\varphi_{ss\_in}=\varphi_{st\_out}+\varphi_{ss\_out}\).
3. The \(\beta_{s}\) is the original rotor module tooth width, which satisfies: \[\beta_{s}=360^{\circ}/P/N_{s}=360^{\circ}/2/24=7.5^{\circ}\] (8) Here, \(\theta\) is twice of the \(\beta_{s}\), so \(\theta=2\times\beta_{s}=15^{\circ}\), and \(\beta_{mcc}\) is defined as the mechanical angle between the outer stator teeth and the inner stator teeth [12], which can be described as: \[\beta_{mcc}=\theta-\theta_{in\_out}\] (9) where \(\theta_{in\_out}\) is the angle between \(d\)-axis and \(q\)-axis (in Figure 4).
4. In addition, to analysis the cogging torque, the rotor speed is set as 1 rpm and all armature winding current are set as zero [13].  
For fair comparison, the following assumption is made. Namely, the two machines are designed with the same: (a) overall dimensions, such as the stator outer diameter and stack length; (b) base speed, and load ratings; (c) phase current and current density [14;15]; and (d) number of PMs.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Items** & **PMVM** & **SP-PMVM** \\ \hline Number of rotor pole pairs \(N_{R}\) & 22 & 22 \\ Number of stator slots \(N_{S}\) & 24 & 24 \\ Winding pole-pairs \(P\) & 2 & 2 \\ Based speed \(n_{0}\) (rpm) & 150 & 150 \\ Stack length, \(l_{a}\) (mm) & 84 & 84 \\ Outer radius of outer rotor (stator), \(R_{so}\) (mm) & 144 & 144 \\ Inner radius of outer rotor (stator), \(R_{sim}\) (mm) & 100.8 & 100.8 \\ Stator yoke length, \(w_{st\_in}\) (mm) & 2.6 & 2.6 \\ Yoke angle, \(\psi_{st\_in}\) (deg) & 8 & 8 \\ Shaft radius, \(R_{half}\) (mm) & 10 & 10 \\ PM thickness, \(R_{m}\) (mm) & 10 & 10 \\ PM width, \(S_{m}\) (mm) & 2.5 & 2.5 \\ Air gap length, \(g\) (mm) & 0.4 & 0.4 \\ Maximum current, \(l_{max}\) (A) & 24.4 & 24.4 \\ Motor power, \(\chi\) (kW) & 5.88 & 14 \\ Stator turns per coil, \(N_{lpc}\) & 15 & 25 \\ Number of slots per pole per phase, \(N_{p}\) & 1 & 1 \\ Wire per conductor, \(N_{w}\) & 1 & 1 \\ Slot space factor \(\beta\) & 0.65 & 0.65 \\ Wires size (AWG) & 19 & 19 \\ Iron type & DW310\_35 & the same \\ PM type & NdFe30 & the same \\ Shaft material & 45 Cr & the same \\ Motor weight (kg) & 38.45 & 34.93 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Design data comparison of PMVM and SP-PMVM.