# Analysis and Experimental Research of a Multilayer Linear Piezoelectric Actuator
## 4 Results and Discussion
### Mechanical Characteristics  
The testing system of the mechanical characteristic experiments is shown in Figure 9. To form the MLPA, the piezo-vibrator was clamped by leaf springs with a clamping force of 8 N, and pressed by a pre-load spring with a pressing force of 3.5 N. The stage served as a mover, and it was pushed forward by the friction force between the friction trip and the piezo-vibrator. The weight was used to generate and measure the pulling force. The laser interferometer measure system (XL-80, Renishaw plc., Gloucestershire, London, UK) was adopted to measure the velocity of the mover. Figure 8: Fracture form of the piezo-vibrator. Figure 7: Vibration scan results of the stator using Doppler vibrometer. Figure 9: Testing system of velocity vs. tension. When there is no weight, the mover's no-load velocity can be obtained. A sinusoidal voltage with an amplitude of 80 V\({}_{\mathrm{PP}}\) was applied to the piezo-vibrator. The no-load velocity vs. frequency characteristics are shown in Figure 10.  
The impedance-frequency curve, as shown in Figure 10, was measured using the impedance analyzer (E4990A, Agilent Technologies Inc., Santa Clara, CA, USA) to study the velocity-frequency relationship more clearly. The resonant frequencies of the first longitudinal and second bending vibration modes are nearly 54 and 52 kHz, respectively. Both the frequencies are smaller than the vibration scan results shown in Figure 7 because of the influence of the pressing force. The result shows that with the increase of the frequency, the velocity decreases firstly; when the frequency is larger than the resonant frequency of the second bending mode, the velocity gets a rapid rise to the maximum value, and then decreases again with the increase of the frequency. It can be concluded that the frequency range can be from 53 to 59 kHz to get a smooth working status. This range is wide enough to control the velocity through a controller so it is suitable for further use. Velocity vs. frequency characteristics at different loads (hanging different weights), as shown in Figure 11, were measured at 80 V\({}_{\mathrm{PP}}\) to obtain more velocity-frequency characteristics in detail. The results show that the velocity of the stage decreased with the increase of the load, but the regularity was not changed. Figure 12 shows the relationship between no-load velocity of the stage and the applied voltage peak-peak value at frequency of 53 kHz. The velocity increases almost linearly with the voltage peak-peak value, which indicates the relatively well controllability of the actuator compared to some of the single piezoelectric ceramic actuators [6; 14]. The starting voltage is 50 V\({}_{\mathrm{PP}}\), and the starting velocity is 80 mm/s at 53 kHz. To get a smaller starting velocity, the frequency needs to be changed according to the velocity-frequency curve shown in Figure 10, in the frequency range from 53 to 59 kHz. Figure 11: Velocity vs. frequency characteristics at different loads. Figure 10: Impedance and velocity characteristic vs. frequency of the actuator. Figure 13 shows a relationship between velocity of the stage vs. the applied voltage peak-peak value and frequency, the frequency was chosen in the range of 53-56 kHz, and the voltage peak-peak value changed from 50 to 100 V\({}_{\text{PP}}\), the velocity-voltage and the velocity-frequency projections are shown in Figure 13.  
The velocity vs. pulling force characteristics are shown in Figure 14, and the pulling force was obtained through a hanging weight. Three different amplitudes of the sinusoidal voltage, 100, 90, and 80 V\({}_{\text{PP}}\), were adopted and the frequency was fixed to 53 kHz in this study.