## 5 Fabrication and Measurement  
In the proposed piezoelectric motor, three bending transducers are used together to rotate the rotor; three transducers are required to have the same resonance frequency and the same vibration velocity. However, the manufacturing and assembly errors may cause differences. It can be easily understood that these discrepancies must make the three driving tips conflict with each other, which may result in the decrease of the output speed and torque. To solve this problem, six bending transducers were fabricated initially, and the three ones with closest resonance frequencies would be selected for the prototype. In the assembly process of the transducer, the contact surfaces between the PZT plates and the beam were smeared with epoxy adhesive uniformly; then we used precision parallel-jaw vice to clamp the PZT plates on the beam for about 12 h to accomplish the solidification. Figure 7 shows the prototypes of the bending transducers and the final motor. Then, we used a scanning laser Doppler vibrometer (PSV-400-M2, Polytec, Waldbronn, Germany) to obtain the first bending resonance frequencies of the six transducers. During the measurement, the upper surface and the side surface of the transducer were selected separately for the test of the two first bending modes and the transducers were fixed by a clamp. Table 1 and Figure 8 give the tested results. Among the 12 tested frequencies, the minimum and maximum are about 52.646 kHz and 53.218 kHz. Although these tested frequencies are obviously lower than the calculated one, each transducer has very close vertical and horizontal frequencies. Furthermore, the fist bending vibration is the only mode excited in the frequency region from 0 kHz to 80 kHz, as shown by the vibration velocity response spectrums of transducer-1. Finally, transducer-1, transducer-5 and transducer-6 were selected for the motor prototype. It should be noted that the bending resonance frequencies of the transducers listed in Table 1 were obtained under bolt-clamped boundary condition. When the transducers were released from the clampers, their resonance frequencies exhibited decreases of about 0.3 kHz, and the vibration amplitudes of the driving tips also showed minute decreases. These tested results agreed well with the FEM calculation ones. Figure 7: The prototype: (**a**) the bending transducers; (**b**) the final motor. Figure 9a shows the experiment set-up of the rotary piezoelectric motor. Output torque was applied by a weight through a string wound on the rotor, and a tachometer was used to measure the speed. During the experiments, the working frequency was set as 53.2 kHz, this value was a little higher than the tested one as the preload between the rotor and the driving tip increased the resonance frequency. The amplitudes of the sine and cosine voltages were changed to obtain their effects on the output speed and torque. Firstly, the no-load speed and maximum torque were tested by changing the sine and cosine voltages synchronously; the sine and cosine voltages were used to excite the horizontal and vertical bending vibrations respectively, as shown in Figure 1d. Then, cosine voltage was set with amplitude of 160 V\({}_{\text{P-p}}\), and we only changed the amplitude of the sine voltage to obtain the no-load speed and maximum torque. The measured results are plotted in Figure 9.  
The increases of the exciting voltages cause obvious improvements in the output speed and torque. However, the two control methods exhibit different characteristics: the synchronous adjustments of the two voltages bring a quicker and nonlinear change on both speed and torque, while a slower and linear speed control is realized by changing horizontal voltage under constant vertical voltage. For the classic rotary piezoelectric motor driving by bending traveling wave, the amplitude of the two exciting voltages must be changed together to realize the speed and torque control.