## 4 Experimental Investigation of the Traveling Wave Actuator
A schematic of the measurements is given in Figure 12.  
Analysis of Figure 11a revealed that the contact point has an elliptical displacement trajectory in the XY plane at different amplitudes of excitation voltages. The displacement amplitude in the X direction at 100 V excitation voltage is in the range from \(-42\)\(\upmu\)m to \(41\)\(\upmu\)m, while that in the Y direction is from \(-64\)\(\upmu\)m to \(60\)\(\upmu\)m. On the other hand, alternations in displacements at other excitation voltages are in the range from \(126\)\(\upmu\)m to \(164\)\(\upmu\)m in the X direction, while those in the Y direction are from \(135\)  
Figure 10: Experimental setup: 1, a computer with data acquisition software; 2, four-channel function generator; 3, four-channel power amplifier; 4, oscilloscope; 5, noncontact tachometer; 6, spherical rotor; 7, proximity sensor; 8, traveling wave actuator. Figure 9: Displacement trajectory of the contact point over time; CP is a contact point. \(\upmu\)m to 180 \(\upmu\)m. It can be noted that the ratio between the increment of excitation voltage and generated displacements is low. The low ratio between excitation voltage increment and displacement amplitudes is influenced by geometrical parameters of the waveguide, i.e., displacement amplitudes generated by the second bending mode are suppressed by high stiffness of the waveguide, which is directly related to the diameter of the waveguide and ratio of the conical hole. On the other hand, the characteristics of displacement amplitudes in the XY directions show that the most effective excitation voltage for the actuator is 250 V because it exhibits the best ratio of displacement amplitude to excitation voltage, 0.656 \(\upmu\)m/V. Figure 11b presents contact point trajectories in the XZ plane. The characteristics represent actuator operation in the superposition mode, i.e., the displacement trajectories are generated by the first longitudinal and second bending vibration modes. As can be seen in the graph, the lowest displacement amplitudes were obtained at an excitation voltage of 100 V. The displacements are in the range from \(-42\)\(\upmu\)m to \(41\)\(\upmu\)m in the X direction, while the Z-direction displacement amplitudes are in the range from \(-83\)\(\upmu\)m to \(84\)\(\upmu\)m. As in the case before, it can be seen that the impact of excitation voltage on displacement amplitudes is drastically reduced when the excitation voltage becomes higher than 250 V. Therefore, the ratio of displacement amplitude to excitation voltage is the best at 250 V, i.e., 0.668 \(\upmu\)m/V. Figure 11c presents contact point trajectories in the YZ plane. As in the previous case, the characteristics illustrate actuator operation in the superposition mode. The lowest displacement amplitudes were obtained at 100 V and are in the range from \(-64\)\(\upmu\)m to \(60\)\(\upmu\)m in the Y direction, while Z-direction displacement amplitudes are in the range from \(-86\)\(\upmu\)m to \(87\)\(\upmu\)m. The best ratio of displacement amplitude to excitation voltage was obtained at 250 V as in the previous case, i.e., 0.692 \(\upmu\)m/V. Figure 11: Trajectories of the contact point when different voltages are applied; (**a**) the trajectory of a contact point in the XY plane; (**b**) the trajectory of a contact point in the XZ plane; (**c**) the trajectory of a contact point in the YZ plane. The next step of the experimental study was to measure the contact point velocities in the XYZ directions. The same experimental setup, as shown in Figure 10, was used. The measurements of the contact point velocity were made in the range from 25 V to 70 V. Such a range of the excitation voltage was chosen in order to represent contact point response to low excitation voltage. The results are shown in Figure 7:0  
Analysis of Figure 13 showed that the highest velocity amplitudes of the contact point are in the Z direction.