## 2 General HSPMSM Structure  
In this section, the general concept of HSPMSM, including specifications and topology, is presented. Four 19 kW 160 krpm HSPMSMs were designed for fuel-cell electric-vehicle air compressors; each had 6 stator slots and 2 rotor poles, which resulted in the number of slots per pole per phase being 1 (q = 1) in a three-phase machine. The winding factor of concentrated tooth-coil winding is only half of that of full-pitch winding. The fundamental winding factor of concentrated tooth-coil winding is lower due to its narrow winding step. However, the number of winding turns is so low that halving them does not seriously harm machine performance in HS applications. Iron and rotor losses increase with concentrated tooth-coil windings due to the higher air-gap harmonic content compared to that in distributed windings. The amount of copper can be nearly the same in concentrated tooth-coil and full-pitch windings, as full-pitch winding ends are longer than compact-end windings in the case of tooth-coil windings. To reduce end winding length and improve structure robustness, concentrated tooth-coil windings were adopted for these machines, as shown in Figure 1e. Shorter axial length leads to shorter rotor length, which improves the boundaries of the rotor dynamics with respect to critical speed. The targeted machines' specifications and used material are shown in Table 1. The drawbacks of NdFeB are its bad thermal tolerance and tension weakness. As the ambient environment of the designed machines was not hostile, the maximal operating temperature was below 200 \({}^{\circ}\)C; thus, NdFeB was acceptable [14].  
Four different rotors were designed and are shown in Figure 1 with the same stator configuration. For achieving the performance requirements of the air compressor, the main parameters and used materials of these HSPMSMs are shown in Table 1. In order to balance maximal efficiency and mechanic robustness, a titanium alloy (Ti-6 Al-4V) and CFC were utilized to protect the PM in M1 and M2, respectively. Although the bulk conductivity and flexural modulus of the titanium alloy were higher, they come with greater eddy current losses. As core stator loss is very high under high-speed operation, the high-silicon sheet of 10 JNEX900 was utilized to build the stator core.  
In manufacturing, M1 offers the advantage of high dimensional accuracy, but its assembly process, including that of a PM rotor with its shaft, is complicated and very difficult. Figure 1b shows that the M2 rotor is quite similar to a conventional surface-mounted PM rotor; PM is directly glued on the shaft and is externally protected by CFC. As the strength of shaft is high, the flexural modulus of rotor is high. Figure 1c,d show the interior PM rotors of M3 and M4, which have good flux weakening ability and are sleeve-free. Their sleeve could be removed by utilizing high-strength rotor materials; thus, high-silicon sheets were selected for the rotor core. Moreover, to reduce eddy current loss, the PM needed to be segmented.  
Figure 1: _Cont._  
Figure 1: 19 kW HSPMSM configuration. (**a**) M1, rotor with a solid PM cylinder; (**b**) M2, rotor with segmented magnet; (**c**) M3, rotor with interior magnet; (**d**) M4, rotor with V-shaped interior magnet; (**e**) stator.