# Simplified Design of Magnetic Gear by Considering the Maximum Transmission Torque Line
## 2 Maximum Transmission Torque Line of Magnetic Gear  
### Magnetic Gear Type and Configuration  
The coaxial type magnetic gears are analyzed with different and random parameters. Coaxial magnetic gears have the advantages on the number of pole pairs that engage between high-speed (HS) and low-speed (LS) rotors, which is higher than worm, rack pinion, bevel, spur, and planetary types of magnetic gears. The simple structure of the coaxial magnetic gear also gives an advantage for future work in developing the actual prototype, where the process of assembling the structure of an MG is not complicated. As shown in Figure 1a,b, the pole pieces are mounted directly to the stator part, while both moving parts, which are high-speed and low-speed rotors, have their own shaft that is mounted on the stator part through a pair of bearings.  
A pair of bearings is used instead of single bearing, in order to avoid the misalignment of the shaft that can give adverse effects on the rotation of both rotors and the bearing itself. In this preliminary study, bearing loads were not taken into consideration, since they are not the critical part in a mechanical transmission [18].  
As shown in Figure 1c, the coaxial magnetic gear consists of the pole pieces between the rotors which harmonize all the PMs that are contributed to torque transmission [19]. Surface-type PMs are used at both high-speed and low-speed rotors where the PMs are attached on the arc surface of the iron yoke of the rotors. The surface-type PM has a lower torque ripple compared with the interior-type PM [20]. Thus, the surface of the PMs is curved where the pole directions are outwards and inwards of the arc and are alternately arranged. The material used for the inner yoke, outer yoke, and pole pieces is 50H800, a soft magnetic iron. These cores are laminated in many sheets coated with zinc as  
Figure 1: Structure of surface type permanent magnet (PM) coaxial magnetic gear: (**a**) two-dimensional structure, (**b**) three-dimensional structure, and (**c**) the two-dimensional structure including the bearing and shaft parts.  
the insulating layer, to avoid the eddy current that generates unwanted heat energy. The gear ratio concept for magnetic gears is similar to that of the mechanical gear on the desired speed conversion between the primary rotor and secondary rotor. The number of pole pairs of the PM at high speed or low speed is flexible as long as it is not changing the gear ratio. However, the ratio of pole pieces between high speed and low speed need to be related with the gear ratio, as seen in Equation (1).  
\[G_{\rm r}\ =\ -\frac{p_{\rm ls}}{p_{\rm hs}}=-\frac{n_{\rm hs}}{n_{\rm ls}} \tag{1}\]  
where \(G_{\rm r}\) is the gear ratio, \(p_{\rm hs}\) and \(p_{\rm ls}\) are the number of pole-pairs at high-speed and low-speed rotors respectively, \(n_{\rm hs}\) and \(n_{\rm ls}\) are the speed of high-speed and low-speed rotors respectively, and the negative sign represents the opposite direction of rotation of the high-speed and low-speed rotors.  
Since the pole pieces are stationary, the directions of rotation for high-speed and low-speed rotors are opposite to each other where the pole pieces act as the carriers [21; 22]. The number of iron pole pieces depends on the number of pole pairs of both high-speed and low-speed rotors, as seen in Equation (2).  
\[N_{\rm pp}\ =\ p_{\rm hs}+p_{\rm ls}=\ \frac{N_{\rm hs}+N_{\rm ls}}{2} \tag{2}\]  
where \(N_{\rm pp}\) is the number of iron pole pieces, \(p_{\rm hs}\) is number of pole pairs at high-speed rotor, \(p_{\rm ls}\) is the number of pole pairs at low-speed rotor, \(N_{\rm hs}\) is the number of PMs at the high-speed rotor, and \(N_{\rm ls}\) is the number of PMs at the low-speed rotor.