## 6 Conclusions  
In this paper, the intrinsic influencing factors of the low-speed-high-torque characteristics of traveling wave motors were studied without changing the outer diameter or the external drives. It was noted that changing the size and shape of the elliptical motion of the stator is the fundamental way to realize low-speed-high-torque characteristics, whereupon the 70H hollow traveling wave motor was developed. A parameter \(\beta\) for measuring the significance of the low speed and high torque of a traveling wave motor was proposed. The influence of the stator characteristic parameters on the amplitude-velocity ratio was simulated. The larger the value of \(\beta\), the taller and thinner the elliptical motion trajectory of the stator and the more significant the low-speed-high-torque characteristics. Based on this, improved stator characteristic parameters were determined according to the simulation, and the two prototype motors 70 HA and 70 HB were fabricated. On testing the vibration and mechanical \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Performance Parameters** & **70 HB** & **PMR70 ZX** & **USR60-S3** & **PSM60S-A** & **Ref. [26]** & **Ref. [27]** & **Ref. [28]** \\ \hline Outside diameter (mm) & 70 & 70 & 60 & 60 & 30 & 60 & 90 \\ Driving frequency (kHz) & 25-28 & 37-43 & 40-45 & 40-45 & 25-27 & 40-45 & 19-22 \\ Driving voltage (Vrms) & 160 \(\pm\) 20 & 160 \(\pm\) 20 & 130 & 130 & 250 & 140 & 150 \\ Maximum speed (rpm) & 50 & 200 & 150 & 180 & 117.5 & 85 & 146 \\ Stall torque (N-m) & 2.4 & 1.6 & 1.0 & 1.2 & \(9.5\times 10^{-3}\) & 0.5 & 1.0 \\ Mass (g) & 210 & 350 & 258 & 230 & 2.5 & 224.5 & 180 \\ \hline \end{tabular}
\end{table} 
Table 6: Performance comparison between 70 HB and other motors. Figure 16: Effect of different preload levels on the mechanical output characteristics of 70 HA and 70 HB (driving frequency: \(f_{70\text{HA}}=51.3\) kHz, \(f_{70\text{HB}}=25.4\) kHz; excitation voltage: \(U=440\) V\({}_{\text{PP}}\)). characteristics, the measured results were found to be consistent with the simulated ones. Compared with the conventional 70 HA, the improved 70 HB's maximum speed was reduced by 23.1% and its maximum stall torque was increased by 100%. The motor speed changed less with load; that is, 70 HB exhibited a harder mechanical characteristics curve. In addition, 70 HB was lighter at 201 g and had a higher torque density of 11.43 N-m/kg, making it more suitable for aerospace applications. Finally, with a constant outer diameter of the motor, the methods for designing a low-speed-high-torque traveling wave motor stator are summarized as follows: (i) the motor should have a lower working mode order; (ii) the stator base thickness and tooth height should be reduced; (iii) the tooth spacing should be reduced and the contact range between the teeth and the rotor should be increased; and (iv) the actual operating frequency of the motor should be slightly higher than 20 kHz. In the future, this prototype has the potential to be used as an actuator in the aerospace field, such as for satellite Control Moment Gyroscopes (CMGs). In order to control the attitude of a satellite, the motor usually requires very low speed but larger torque and higher positioning accuracy. The 70 HB motor is simple in structure, small in size, and light in weight, and it does not need a deceleration mechanism, which effectively saves space and energy in a system. Conceptualization, J.L. and H.Z. ; Methodology, J.L. ; Software, J.L. ; Validation, J.L., Z.-J.N. ; Writing--original draft preparation, J.L. ; Writing--review and editing, Z.-J.N. and H.Z. ; Supervision, H.Z. ; Project administration, C.-S.Z. The research was funded by the National Basic Research Program of China (973 Program, grant number: 2015 CB057501) and the Priority Academic Program Development of the Jiangsu Higher Education Institutions (PAPD). The authors are very grateful to [PERSON] and [PERSON] from the Shanghai Institute of Ceramics for providing various piezoelectric ceramics for the motors.