# An Eight-Zonal Piezoelectric Tube-Type Thread Ultrasonic Motor Based on Second-Order Bending Mode
## 3 Experiments and Results
### Mechanical Characteristics  
The threaded actuatorwas designed for precise positioning applications with requirement of low driving voltage and high thrust. The performance was evaluated based on measurements including the linear speed (moving velocity), output force with respect to frequency, and driving voltage. The four groups of electric signals with \(\pm 90^{\circ}\) phase shifts were generated by a dual channel DDS signal generator (Model: MHS-2300A, China) and then amplified by a power amplifier (ML3860B, Yangdiaguoxun, China). As shown in Figure 9, the actuator was clamped horizontally at the middle nodal line (as shown in Figure 2) for minimal mechanical interference, and the continuous displacement of the threaded shaft with no load was measured using a laser displacement sensor (optoNCDT 2300, Micro-Epsilon, Germany). Moreover, a digital force gauge (ZP-5N, Imada, Japan) with a resolution of 0.1 N was employed to measure the stall force of the threaded shaft when the velocity was set to zero.  
The relationship between the no-load linear velocity of the actuator and the driving frequency at 40 V\({}_{\mathrm{PP}}\) driving voltage is illustrated in Figure 10. The maximum velocity was 4.9 mm/s when the driving frequency was set to 31.2 KHz. When the frequency was lower than 23.7 KHz or higher than 40.1 KHz, the motor could hardly work normally.  
By comparison with the result of the laser Doppler experiment, these two resonant frequencies measured had a slight difference of 0.7 KHz, which could be ignored. The error might have come from the coupling of nuts and threaded rod when rotating as the motor remained still when it was measured by the laser Doppler vibrometer for only half signals was applied to it.  
It can be concluded that the proposed motor can work smoothly at a fairly low driving voltage in a frequency band with a bandwidth of over 5 KHz, which is wide enough for the design of control circuits and practical applications.  
Figure 11 shows the relationship between the output performance of the motor and the voltage amplitude at frequency 31.2 KHz. As the effective traveling range of the motor was about 20 mm, the examined voltage amplitude ranged from 0 V\({}_{\mathrm{PP}}\) to 60 V\({}_{\mathrm{PP}}\) for fine movement. Both the linear velocity and the stall force increased with elevation of the voltage amplitude, and the maximum stall  
Figure 9: Mechanical characteristics of the testing system.  
force at a voltage of 40 V\({}_{\rm pp}\) was about 5.0 N. Good linearity can be observed from the curves of linear speed and stall force over the voltage amplitude, showing fine output performance controllability.  
The velocity vs. pulling force characteristics are shown in Figure 12, and we applied the pulling force by hanging a weight to the screw rod. Five different amplitudes of the sinusoidal voltage--20, 30, 40, 50, and 60 V\({}_{\rm pp}\)--were adopted and the frequency was set to 31.2 KHz in this experiment. The result shows firstly that the bigger the applied pulling force is, the smaller is the velocity of this motor; secondly, the velocity is bigger when the applied voltage is higher under the same pulling force condition. Through Figure 12, the mechanical power of the motor can be calculated (the mechanical power equals the product of the velocity and the pulling force). From the curve of mechanical power vs. pulling force it can be concluded that the maximum mechanical power at 40 V\({}_{\rm pp}\) was 1.24 mW. The inertia of the rod was ignored in the calculation process of the pulling force. Thus, the mechanical power when there was no pulling force applied to it was zero.  
Figure 11: Linear velocity and stall force vs. driving voltage of the motor.  
Figure 10: Linear velocity versus the driving frequency at 40 V\({}_{\rm pp}\).