**4. Characteristic experiments**

The driving voltage is set to 100 Vp-p, and the frequency characteristics of the actuator under different locking forces are tested and shown in **Figure 11**. Under the locking force of 1 N, the maximum velocity is 15.25 mm/s at the frequency of 650 Hz; when the locking forces are 2 N and 3 N, the maximum velocities can be obtained at the frequency values of 700 Hz and 690 Hz, and the velocities are 12.48 mm/s and 9.67 mm/s, respectively.

Thus, there are corresponding different optimal frequencies under the different locking forces conditions. As displayed in **Figure 12**, the voltage characteristics under different locking forces are explored at the corresponding optimal frequency. It can be seen that the minimum starting voltage of the actuator increases with the increases of the locking force, and the minimum starting voltage of the actuator is 21.5 Vp-p under the locking force of 1 N. In addition, the elongation of the piezoelectric stack increases as the voltage raises, the single step displacement of the actuator increases, thereby increasing the velocity. The motion resolution is also an important parameter of the actuator, which reflects the precise positioning characteristics of the actuator. It can

**Figure 11.** *Frequency characteristics under different locking forces.*

**Figure 12.** *Voltage characteristics under different locking forces.*

*Topology Optimization Methods for Flexure Hinge Type Piezoelectric Actuators DOI: http://dx.doi.org/10.5772/intechopen.103983*

**Figure 13.** *The motion resolution under the locking force of 1 N.*

**Figure 14.** *Displacement characteristics under different locking forces.*

be seen from **Figure 13**, the single step motion resolution of the actuator reaches 96 nm under the locking force of 1 N.

Maintaining the voltage is 100 Vp-p, the displacement characteristics under different locking forces are plotted, as shown in **Figure 14**. It is obvious that the velocity is the fastest at the locking force of 1 N, the friction resistance is small at this time, so the backward motion is minimum. The load characteristics of the actuator is emerged in **Figure 15**, as the locking force gradually increases, the maximum load of the actuator increases significantly. Within a certain adjustment range, the greater locking force can increase the friction driving force, which improves the load capacity of the actuator. It can be seen that the velocity decreases almost linearly with the load increases, and the maximum load mass of the actuator exceeds 330 g under 3 N locking force.

The efficiency *η* is usually introduced to evaluate the output capacity of the actuator, which can be calculated by

$$\eta = \frac{P\_{\text{out}}}{P\_{\text{in}}} = \frac{F \times \upsilon}{P\_{\text{in}}} = \frac{\text{mg} \times \upsilon}{P\_{\text{in}}} \times 100\text{\%} \tag{23}$$

**Figure 15.** *Load characteristics under different locking forces.*

**Figure 16.** *Efficiencies under different locking forces.*

where *Pout* represents the output power, *Pin* represents the input power, *F* is the gravity load, and *v* is the output velocity, respectively. The input power can be detected by the power analyzer, and according to the load characteristics of actuator (in **Figure 15**), the output power *Pout* can be calculated.

**Figure 16** shows that the efficiency of the actuator increases first and then decreases with the increases of load. It can be seen that when the locking force is 3 N, the efficiency of the actuator reaches the highest value 0.70% under the load of 240 g.
