# A Novel Dual-Rotor Ultrasonic Motor for Underwater Propulsion
## 4 Experimental Results and Discussions  
According to the structure and size parameters mentioned above, a prototype dual-rotor ultrasonic motor was fabricated (see Figure 6). A laser Doppler vibrometer system (PSV-500-3D) was used to measure the vibration characteristics of the stator. Figure 7 depicts the measured average vibration magnitude versus operating frequency when the stator unit was driven by 150 V (peak-to-peak) voltage. It can be seen that the resonance frequency was 62.56 kHz, which was 1.18 kHz higher than the simulation value (61.38 kHz), and may have been caused by the deviation in the fabrication and assembling processes. In addition, the pressure forces and the twisting loads which were neglected during the simulation also contributed to the discrepancy between the calculated and measured  
Figure 5: Simulated vibration of the stator. (**a**) Vibration mode, and (**b**) transient response. frequencies. The vibration pattern shown in the inset agreed well with the calculated working mode shown in Figure 5. With the excitation voltage of 150 V\({}_{\text{P-p}}\) at resonance, the measured amplitude was 1.5 microns. The measured vibration displacements with 300 V\({}_{\text{P-p}}\) and 50 V\({}_{\text{P-p}}\) were 2.8 and 0.4 microns, respectively. In order to measure the speed of the motor, a reflective marker was attached to the rotor and the measurement was carried out by a non-contact laser velocimeter (DT-2234B). In the following experiments, unless otherwise specified, the prototype motor was applied with the driving voltage of 150 V\({}_{\text{P-p}}\) and operated at resonance. The relationship between the no-load speed and the driving frequency with the excitation voltage maintained at 150V\({}_{\text{P-p}}\) is plotted in Figure 8. It was observed that the maximum speed of the motor could reach 144 r/min with the driving frequency of 63.2 kHz. The lower output speed at other driving frequencies indicated that the working behavior of the prototype motor was very sensitive to the operating frequency. Besides, effects of applied voltage at the same operating frequency were measured and results are displayed in Figure 9. It can be seen that with the same driving frequency, the speed of the prototype motor increased as the input voltage was increased. This was because when the motor worked near the resonance frequency, its output speed was determined by the stator's vibration amplitude. It should also be noticed that the increase of the rotating speed appeared non-linearly and reached a maximum value of 150 r/min when the applied  
Figure 6: Image of the prototype motor. Figure 7: Vibration measurement of the stator. voltage increased to 300 V\({}_{\text{P-p}}\), indicating the increase of driving voltage could improve the output performance to a limited extent. In addition, the dependence of the pre-pressure upon the rotating speed of the prototype motor was investigated by dynamic pre-pressure adjustment with an electromagnet modulator [31]. It was mainly composed of a permanent magnet (\(\O 10\) mm \(\times\) 5 mm), a guiding cylinder, an electromagnet (\(\O 20\) mm \(\times\) 15 mm), and a bolt. The permanent magnet was fixed to the bottom face of the base and the electromagnet was fixed to the bracket with a 3 mm gap to the permanent magnet. By adjusting the DC voltage applied to the electromagnet, the changed magnetic force was capable of modulating the pre-pressure between stator and rotor. Figure 10 shows the measured no-load speed versus the pre-pressure. It can be seen that the rotating speed increased from 47 r/min to 57 r/min with the pre-pressure decreasing from 3.25 N to 1.95 N. Dynamic pre-pressure modulation could be used as a rough adjustment strategy when the prototype motor is installed to the underwater robot and the manual positioning of the pre-pressure modulation unit becomes inconvenient. Figure 8: No-load rotating speed versus the driving frequency. Figure 9: No-load rotating speed versus the driving voltage.