# Simplified Design of Magnetic Gear by Considering the Maximum Transmission Torque Line
## 3 Maximum Transmission Torque Line and Design Parameters of Magnetic Gear
### Relationship between the Parameter of Permanent Magnets and Irons  
Based on Equation (3), which represents the MTTL, the total volume of PMs can be estimated from any required transmission torque. To obtain the parameters of MG from the estimated total volume of PMs, the relationship between the PMs and irons is identified. As discussed in Section 3.1, the study on the saturation of magnetic flux in the MG must be done to avoid the drop of transmission torque due to the saturation. Therefore, the thickness of irons is optimized through the simulation, to gain the best ratio between the thickness of PMs and irons.  
Figure 4a shows the performance of analyzed MGs, where the size of pole pieces is varied, with different ratios between the thickness of the pole pieces, \(t_{\rm p}\), and the PMs, \(t_{\rm pm}\). Based on the observation, the best performance is achieved when the thickness of pole pieces is 2.5 times of the thickness of PMs, \(t_{\rm pm}\), since, with more than that value, the increment begins to flatten. The thickness of the outer yoke, \(t_{\rm o}\) was also tested from a few analyses of MGs which vary, with different ratios between the thickness of the outer yoke, \(t_{\rm o}\), and the PMs, \(t_{\rm pm}\). By using the 160 cm\({}^{3}\) total volume of PMs, the best ratio of \(t_{\rm o}\) base on Figure 4b is four times the thickness of PMs, \(t_{\rm pm}\), since, with more than  
Figure 3: The characteristic of transmission torque against the total volume of PMs.  
that ratio, the increment of torque is also flattened, causing an increase of load on the MG structure. The same method is used in determining the best ratio between the thickness of inner yoke, \(t_{\rm i}\), and PMs, \(t_{\rm pm}\). The total volume of PM used for the simulation of the MGs is 100 cm\({}^{3}\), where the best ratio for the thickness of inner yoke, \(t_{\rm i}\), is five times the thickness of PMs, \(t_{\rm pm}\). This is because, when the ratio was increased above that value, the increment of torque also started to flatten, reducing the efficiency of the MG, as shown in Figure 4c.  
As a result, the best ratio was observed from the simulation is 1:2.5:4:5, which represents the thickness of PMs, pole pieces, outer yoke, and inner yoke, respectively. It is estimated that the best ratio was achieved due to the better magnetic flux distribution in the MG that increased the transmission torque. Thus, the saturation of magnetic flux can be avoided when the ratio is considered in designing the MG. From the obtained ratio, a few equations are generated, as shown in Equations (4)-(7).  
\[t_{\rm m1} =t_{\rm m2}=t_{\rm pm} \tag{4}\] \[t_{\rm p} =2.5t_{\rm pm}\] (5) \[t_{\rm o} =4t_{\rm pm}\] (6) \[t_{\rm i} =5t_{\rm pm} \tag{7}\]  
where \(t_{\rm m1}\) and \(t_{\rm m2}\) are the thickness of high-speed and low-speed PMs, respectively, which can be replaced with \(t_{\rm pm}\) since both values are same; \(t_{\rm o}\), \(t_{\rm p}\), and \(t_{\rm i}\) are the thickness of outer yoke, pole pieces, and inner yoke iron which are generated from the ratio.