# Research on a Piezoelectric Pump with Flexible Valves
## 4 Experimental Results and Discussion
### Amplitude Measurement  
The amplitude measurement of the PZT vibrator was carried out to explore the performance of the actuator. The fluid used in the experiment was room temperature deionized water. The photo of the amplitude test is shown in Figure 5. A signal generator (AFG1062, Tektronix, Beaverton, OR, USA) generated sinusoidal voltage signals of different frequencies, which were amplified by a power amplifier (HVP-300D, Nanjing Foneng, Nanjing, China) and applied to the PZT vibrator. In addition, an oscilloscope (DSO-X2004A, Keysight, Santa Rose, CA, USA) monitored the output signal. When the PZT vibrator was excited, the corresponding action occurred.  
\begin{table}
\begin{tabular}{c c} \hline
**Item** & **Size (mm)** \\ \hline Brass substrate diameter & 41 \\ Brass substrate thickness & 0.23 \\ PZT ceramic diameter & 35 \\ PZT ceramic thickness & 0.30 \\ \hline \end{tabular}
\end{table}
Table 2: The size parameters of the piezoelectric (PZT) vibrator.  
Figure 4: The PPFV: (**a**) Parts and components of the pump; (**b**) the assembled prototype; (**c**) enlarged view of the valve; (**d**) a hinge of the valve.  
A laser displacement sensor (LK-H020, KEYENCE, Japan) with an accuracy of 0.1 \(\upmu\)m was used to collect the vibration displacement of the PZT vibrator center, and the collected data was transmitted to the corresponding software of the computer, and the amplitude could be obtained by data analysis. Last but not least, in order to reduce errors, the results of this and subsequent experiments are the average values obtained after two identical measurements.  
The relation between the amplitude and frequency of the PZT vibrator at 60 V and 100 V is shown in Figure 6. Within the frequency range of 10-40 Hz, the relationship between amplitude and frequency is non-linear. When the frequency of the applied alternating voltage is close to or equal to the natural frequency of the PZT vibrator, the PZT vibrator produces a large vibration, that is, resonance [21]. Therefore, the amplitude of the PZT vibrator increases first and then decreases with the increase in frequency, which is primarily determined by the PZT vibrator's own properties. When the voltage was 60 V, the largest amplitude was 96 \(\upmu\)m and the resonant frequency of the PZT vibrator was about 21 Hz. At 100 V, the largest amplitude was 176 \(\upmu\)m and the resonant frequency was about 19 Hz. The difference in resonance frequency between them is mainly due to the different voltage applied. When other conditions are the same, the amplitude of the PZT vibrator will be different with different voltage because it will affect the quantity of the fluid in the pump chamber. The natural frequency formula of the vibration system is as follows:  
\[f_{0}=\sqrt{\frac{k}{m}} \tag{4}\]  
where \(k\) is the total stiffness of the system, and \(m\) is the total mass of the system. Since the applied voltage and frequency do not affect the total stiffness of the system, only the total mass of the system will be changed. In addition, the vibration velocity of the PZT vibrator will lead to the change of the flow rate, and the change of the flow rate will affect the inertia of the whole system. This is also interpreted as \"additional mass\". The increase of additional mass will reduce the natural frequency of vibration [22]. Therefore, in different voltage conditions, the natural frequency of the PZT vibrator will be different.  
Figure 5: Amplitude detection platform.  
At a voltage of 100 V and a frequency of 19 Hz, the maximum displacements of 17 points in the diameter direction of the PZT vibrator were measured. The experimental results are shown in Figure 7. The maximum displacement of each point was fitted by curve, and the parabolic function was obtained as follows:  
\[\omega(r)=\ -0.0005r^{2}\ +\ 0.0003r\ +\ 0.1747 \tag{5}\]  
According to Equation (1), the volume change quantity in a quarter period can be calculated as follows:  
\[\Delta V=2\pi\int_{0}^{18.5}\omega(r)rdr \tag{6}\]  
The calculated \(\Delta V\) is 0.135 mL.