## 5 Experiments on Prototype Motors
### Test of Vibration Characteristics  
In this study, vibration tests of the stators were conducted using a scanning Doppler laser vibration measurement system (PSV-300; Polytec Co., Karlsruhe, Germany). The instrument and the software interface are shown in Figure 12. The driving voltage was set to 100 V\({}_{\text{PP}}\). The actual modal frequency of 70 HA-1 was 49.52 kHz and the actual amplitude was 1.4 \(\upmu\)m; the corresponding values for 70 HA-2 were 49.58 kHz and 1.4 \(\upmu\)m, respectively; the corresponding values for 70 HB-1 were 22.07 kHz and 3.5 \(\upmu\)m, respectively; and the corresponding values for 70 HB-2 were 22.12 kHz and 3.6 \(\upmu\)m, respectively. In addition, some of the electrical properties of the stator were also tested using an impedance analyzer (Agilent 4294A; Agilent Technologies Inc., Shanghai, China). The measured results agree well with those from the simulation, as shown in Table 3, thereby verifying the accuracy of the simulation design. The test also showed that the individual differences in the prototypes are very small. Therefore, in the subsequent mechanical characteristics test, comprehensive performance data can be used to reflect the characteristics of the two types of motors.  
Figure 11: Comparison of stators and motors: (**a**) stator of 70 HA; (**b**) stator of 70 HB; and (**c**) two sets of prototype motors.  
Figure 12: _Cont_.  
In order to test the amplitude of the stator with preload, a rotor with an outer diameter 4 mm smaller than that of the stator was made. Thus, the vibration of the stator teeth surface could be measured by laser scanning. When the excitation voltage was 100 V\({}_{\mathrm{PP}}\), the normal amplitudes of 70 HA and 70 HB without preload were 1.4 \(\upmu\)m and 3.5 \(\upmu\)m, respectively; their amplitudes with a preload of 800 N were 0.2 \(\upmu\)m and 0.5 \(\upmu\)m, respectively. When the excitation voltage is 400 V\({}_{\mathrm{PP}}\), the stator deformation will be larger without the compressed rotor, which will lead to ceramic breakage. Therefore, the minimum preload was set to 200 N. At this level, the normal amplitudes of 70 HA and 70 HB were 3.5 \(\upmu\)m and 8.0 \(\upmu\)m, respectively. An accompanying noise indicated that the preload was still too small. The amplitudes with a preload of 800 N were 0.6 \(\upmu\)m and 2 \(\upmu\)m, respectively. As shown in Figure 13, the test results show that the normal amplitude of the stator teeth surface decreases with increasing preload and increases with increasing excitation voltage. The stator amplitude during operation of the motor was maintained above 1 \(\upmu\)m, and the larger the stator amplitude without the rotor, the greater the preload that can be applied.  
Figure 12: (**a**) PSV-300 scanning Doppler laser vibration measurement system; (**b**) measured mode of 70 HA; and (**c**) measured mode of 70 HB.  
Figure 13: Normal amplitude test of the stator teeth surface with preload: (**a**) photograph of the experiment and (**b**) effect of preload and excitation voltage on the normal amplitude.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Motor Type** & **70 HA-1** & **70 HA-2** & **70 HB-1** & **70 HB-2** \\ \hline Modal frequency \(f_{m}\) (kHz), & 51.2/49.52 & 51.2/49.58 & 23.6/22.07 & 23.6/22.12 \\ simulation/measurement & & & & \\ Amplitude \(w_{0}\) (\(\upmu\)m), & 1.41/1.4 & 1.41/1.4 & 3.68/3.5 & 3.68/3.6 \\ simulation/measurement & & & & \\ Error of \(f_{m}\) & 3.39\% & 3.16\% & 6.93\% & 6.27\% \\ Error of \(w_{0}\) & 0.71\% & 0.71\% & 5.14\% & 2.17\% \\ Static capacitance of PZT \(C_{0}\) (nF) & 12.51 & 12.42 & 12.18 & 12.21 \\ Resonant frequency of stator \(f_{r}\) (kHz) & 51.09 & 50.86 & 21.58 & 21.72 \\ Anti-resonant frequency of stator \(f_{a}\) (kHz) & 51.80 & 51.52 & 22.39 & 22.49 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Vibration characteristics measurement of 70 HA and 70 HB.