## 4 Experimental Investigation of the Traveling Wave Actuator
The lowest velocity in the Z direction was obtained at 25 V, and it was 1.61m/s, while the highest velocity in the Z direction was obtained at 70 V, and it was 2.54 m/s. The difference between velocity amplitudes at the lowest and highest excitation voltages is 0.93 m/s or 36.6%. It can be noticed that the ratio of velocity increment to excitation voltage is 4.13 mm/s/V. Figure 13 also presents velocity amplitudes in the X and Y directions. The lowest velocity amplitude in the X direction was obtained at 25 V and is 1.44 m/s, while the highest velocity amplitude in the X direction was obtained at 70 V and is 2.41 m/s. The difference between the highest and lowest velocity amplitudes is 0.97 m/s or 40.23%. It was found that the ratio of velocity increment to excitation voltage is 4.31 mm/s/V. The lowest velocity amplitude in the Y direction is 1.18 m/s at 25 V, while the highest velocity amplitude is 2.21 m/s at 70 V. The difference between the lowest and highest velocity amplitudes is 1.03 m/s or 46.72%. The ratio of velocity amplitude increment to excitation voltage is 4.57 mm/s/V. Figure 7:1 Schematics of displacement amplitude measurements in different planes; MP, measurement point. Figure 7:2 Velocity amplitude of the contact point in the XYZ directions versus driving voltage. Based on the obtained results it can be concluded that the contact point velocities in the XYZ directions almost linearly depend on the excitation voltage, and differences between the velocity amplitudes in the XYZ directions are small. On the other hand, the actuator exhibits low response to excitation voltage increment due to high stiffness of the waveguide. Dependence of the rotation speed of the rotor on excitation voltage was investigated at a constant preload force of 98.58 mN. The rotation speed was measured by employing the experimental setup (Figure 10). The results are shown in Figure 7:3  
As can be seen in Figure 14, rotation speed varied from 20 RPM at 100 V to 115 RPM at 350 V. The difference between the lowest and highest rotation speeds is 95 RPM or 82.6 %. The ratio between rotation speed and excitation voltage increment is 0.63 RPM/V. Figure 14 shows that the relation of rotation speed to excitation voltage is almost linear. Considering the results of the experimental investigations, it can be concluded that actuator operation is based on the superposition of the first longitudinal and second bending vibration modes. Moreover, the actuator can provide stable and well-predictable displacement and velocity of the contact point, as well as rotation speed of the rotor. On the other hand, the actuator has a relatively low response to excitation voltage amplitude increment, which is influenced by the high structural stiffness of the waveguide. In order to evaluate the performance of the proposed actuator, a comparison between different designs of traveling wave actuators was made. The comparison is given in Figure 7:4  
Table 3 presents a comparison between the proposed actuator and traveling wave actuators reported previously. In order to compare the constructions, the ratio of maximum rotation speed to excitation voltage was calculated. As shown in Table 4, the actuator reported by [PERSON] et al. [13] generates a significantly higher ratio of rotation speed to excitation voltage compared to the proposed actuator--more than 89 times higher. On the other hand, the actuators proposed by [PERSON] and [PERSON] [15] and [PERSON] et al. [16] generate notably lower ratios compared to the proposed actuator--approximately 2 and 16, respectively. Figure 7:5 Rotation speed versus excitation amplitude at constant preload force.