## 4 Optimization of Stator Characteristic Parameters
### Determination of Improved Stator Characteristic Parameters  
In summary, the conditions of the low-speed-high-torque characteristics of TRUM-70 HB can be further parameterized: when the outer diameter and the external drives are certain, ensure that the working modal frequency of the motor is slightly higher than 20 kHz. By analyzing the influence of each parameter on the stator vibration characteristics, the stator base thickness and the tooth height should be reduced first, and then the stator working mode order and tooth spacing should be reduced. Considering the factors of processing technology and cost, the variable design space can be reduced further. Thus, the enumeration method was used to select several sets of suitable parameters for simulation comparison, and finally, a set of parameters was determined. The improved motor was named 70 HB, and its stator characteristic parameters are compared in Table 2 with those of the conventional 70 HA.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Stator Parameters** & **70 HA** & **70 HB** & **Design Space** \\ \hline Outer radius \(r_{c}\) (mm) & 35 & 35 & \{35\} \\ Inner radius \(r_{d}\) (mm) & 24 & 24 & [24] \\ Base thickness \(H_{2}\) (mm) & 2.5 & 1.5 & [1, 5] \\ Tooth height \(H_{1}\) (mm) & 1 & 0.8 & [0.5, 2.5] \\ Tooth spacing \(l\) (mm) & 0.8 & 0.3 & [0.3, 1.5] \\ Working mode order \(n\) & 11 & 9 & [7, 9, 11] \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of the stator characteristic parameters of 70 HA and 70 HB.  
Figure 8: (**a**) Modal frequency affected by the base thickness and tooth height of the stator and (**b**) amplitude affected by the base thickness and tooth height of the stator.  
Figure 7: (**a**) Modal frequency affected by the space width of the stator and (**b**) amplitude affected by the space width of the stator.  
The simulation gave a 70 HB vibration modal frequency of 23.6 kHz, an amplitude of 3.68 \(\upmu\)m, a tangential velocity of 0.1999 m/s, and an amplitude-velocity ratio of 18.41, as shown in Figure 9. Furthermore, using ANSYS for phase response analysis, the motion trajectory of the outer edge of the stator teeth surface in one vibration period could be obtained. When the rotor was not considered, the normal and tangential amplitudes of 70 HA were 1.41 \(\upmu\)m and 0.743 \(\upmu\)m, respectively, and the normal and tangential amplitudes of 70 HB were 3.68 \(\upmu\)m and 0.716 \(\upmu\)m, respectively, as shown in Figure 10a. When considering the rotor preload (550 N), the normal and tangential amplitudes of 70 HA were 0.341 \(\upmu\)m and 0.397 \(\upmu\)m, respectively, and the normal and tangential amplitudes of 70 HB were 0.965 \(\upmu\)m and 0.316 \(\upmu\)m, respectively, as shown in Figure 10b. The simulation results show that the normal and tangential amplitudes of the stator will decrease when the preload exists, and the normal amplitudes will decrease greatly. The elliptical motion trajectory of the stator changes greatly when the stator characteristic parameters are changed: that of 70 HA appears short and fat whereas that of the improved 70 HB appears tall and thin. Due to the existence of the stator teeth, the deformation of the tooth structure at different positions may have a phase difference which is nonzero at the outer edge of the teeth. Therefore, the elliptical trajectory appears to be inclined.