*3.2. Performance Test*

By utilizing a signal generator and power amplification to apply the sawtooth wave signal with di fferent frequency and voltage on the piezoelectric stack, the relationships between the moving velocity and the driving frequency at di fferent driving voltages were obtained and are shown in Figure 20. The results indicate that the velocity of the actuator has a linear relationship with the frequency of the driving signal under di fferent voltages. The errors come from assembly errors and the uneven contact surface between the mover and the stator.

**Figure 20.** Velocity of the actuator versus the frequency by di fferent voltage.

A driving signal with an input voltage of 100 V and frequency of 100 Hz was sent to the actuator, and the on-o ff characteristic curve of velocity and displacement was obtained, as shown in Figure 21. It illustrates that the velocity of the actuator is 1.2 mm/s in the stable state, and the response time of startup and shutdown is tens of milliseconds.

**Figure 21.** On-off operation characteristics of the actuator.

When the experiment results are compared to the theoretical and FEM results, the motion displacement is slightly smaller than that from the analog results, as shown in Figure 22. Due to manufacture and assembly errors, a difference would exist.

**Figure 22.** The comparison of theoretical, FEM, and the experiment results.

## *3.3. Resolution Test*

To measure the step distance of an actuator with a low voltage signal, a periodic pulse sawtooth wave signal was used. The experiment results are shown in Figure 23 and indicate that when the voltage of the signal is 30 V, 20 V, and 10 V, the step distance of the actuator is about 3.33 μm, 1.75 μm, and 0.875 μm, respectively. When the voltage of the input signal continues to reduce, there is no clear step distance. This is because the smaller step distance is about the same order of magnitude as the background noise. On the other hand, the movement distance of the mover in the driving phase is not much larger than the possible distance of back off in the return phase.

**Figure 23.** The displacement-time curve with a frequency of 20 Hz and a voltage of (**a**) 30 V, (**b**) 20 V, and (**c**) 10 V.
