# Design and Experimental Verification of a PZT Pump with Streamlined Flow Tubes
## 6 Results and Discussion
The low frequency region (1-23 Hz), where the maximum flow rate of different voltages occurred, was exactly the same as the frequency region where the maximum amplitude appeared, indicating that the pumping flow rate of the SLFT PZT pump is closely related to the vibration characteristics of the piezoelectric vibrator. In the high frequency region (\(>\)25 Hz), the pumping flow rate did not show more peak points as the amplitude changed. This is because the amplitude was so small; the pressure difference caused by the volume change cannot noticeably manipulate the liquid in the pump chamber. The local enlarged displacement-frequency relationship and flow-rate-frequency relationship are shown in the dash line rectangle (25-80 Hz) in Figures 11 and 12 respectively. It can be clearly seen that when the working frequency is higher than 25 Hz, the vibration amplitude and the flow rate are rather small (less than 4 \(\upmu\)m and 0.8 mL/min, respectively) and approach zero fast. When  
Figure 11: The amplitude results of the vibrator. Figure 12: The flow rate results of the pump. the working frequency is about 10 Hz, the vibration amplitude and flow rate reach the maximum at different voltages. Thus, we assume that this phenomenon is caused by pump system resonance. According to the literature [45; 46] and the characteristics of the piezoelectric vibrator, another resonance may exist in the high-frequency region (around 1.8 kHz-2.1 kHz). By studying the amplitude of the piezoelectric vibrator, it was found that the amplitude decreases with the frequency increase, as shown in Figure 11, and the amplitude transformation period also decreases. Although there may be another resonance in the high frequency region, the resonance amplitude in the high frequency region will be smaller than the first peak. The working medium of the piezoelectric pump is liquid, and when compared with gas, liquid has the characteristics of high density, high viscosity and incompressibility. The amplitude of the piezoelectric vibrator in the high frequency region is so small that it would cause a small change in the pump chamber volume, and that the pressure difference generated is not enough to make up for the pressure loss caused by the liquid discharged from the pump. Therefore, there is little flow rate output in the high frequency region. According to the theoretical analysis, the resistance coefficients of forward and backward flow were obtained by simulation and substituted into Equations (10)-(12). The amplitudes were measured by laser displacement sensor and input into Equation (13), thereby calculating the theoretical flow rate. The theoretical flow rate was calculated by the amplitude of 100 V and 120 V, whose results were compared with the experiment, as shown in Figure 13.  
It can be seen that the maximum theoretical flow was 16.89 mL/min (100 V, 10 Hz) and 18.75 mL/min (120 V, 9 Hz), respectively, and the maximum experimental flow rate was 16.45 mL/min (100 V, 11 Hz) and 17.01 mL/min (120 V, 10 Hz), respectively. In the low frequency region (1-25 Hz), the theoretical flow rate was consistent with the experimental flow. In the high frequency region (\(>\)25 Hz), the experimental flow was close to zero, and the theoretical flow decreased in fluctuation corresponding to the fluctuation of amplitude, further proving the direct relationship between amplitude and pumping flow rate. By comparison, it was found that the frequency of maximum flow rate in the experiment lagged behind the frequency of maximum flow rate by theory. Several reasons account for the frequency delay, when compared with the theoretical results, and are illustrated as follows:  
1. The vibrator was attached to pump chamber by silica gel bonding, which indirectly increases the volume and reduces the volume change quantity of the pump chamber to some extent. 2. The connection between the flow tube and the pump body is prone to pressure loss, resulting in increased internal pressure loss and decreased pumping efficiency. 3.