# Research on a Piezoelectric Pump with Flexible Valves
## 2 Structure and Working Principle  
The flexible valve is a pair of curved rectangular leaflets made of elastic material, as shown in Figure 1. The leaflets contain a fixed end and a free end, and the free end is divided into three equal parts by two hinges. We marked the initial clearance of the free ends as \(Y_{0}\), the length of the free end as \(L\), the height as \(h\), and the thickness as \(b\).  
Figure 2 displays the three-dimensional model of the PPFV. The PPFV consists of a pump body, a PZT vibrator, two flexible valves, and two valve covers. The flow direction from the fixed end to the free end of the flexible valve is defined as forward, and the flow direction from the free end to the fixed end is defined as reversed. Therefore, the flexible valve installed near the inlet is the inlet valve, and the valve installed near the outlet is the outlet valve.  
Under the action of an alternating current, the PZT vibrator moves up and down reciprocally. When the PZT vibrator moves from the bottom up to the highest point, the  
Figure 1: Structure of the flexible valve.  
Figure 2: Structure diagram of the piezoelectric pump with flexible valves (PPFV).  
pump chamber volume expands, where there is negative pressure. Then, the fluid enters the pump chamber from the inlet valve and the outlet valve at the same time, at which time the clearance of the inlet valve increases and the clearance of the outlet valve reduces, which is called the suction stroke. Similarly, when the PZT vibrator deforms from the top to the lowest point, the pump chamber volume decreases, the pressure in the chamber increases, and the fluid is squeezed out, so the fluid is discharged from the inlet and the outlet simultaneously. At this time, the clearance of the inlet valve reduces, and the clearance of the outlet valve increases, which is called the exhaust stroke. Whether it is the suction stroke or the exhaust stroke, the flowing fluid must be in contact with the valves, generating flow resistance. During the suction stroke, the flow resistance of the outlet valve is greater than that of the inlet valve, so the quantity of fluid inhaled by the inlet valve is more than the amount of fluid inhaled by the outlet valve. Similarly, during the exhaust stroke, the flow resistance of the inlet valve is greater than the flow resistance of the outlet valve, so that the quantity of fluid discharged by the inlet valve is less than the amount of fluid discharged by the outlet valve. Therefore, the PPFV can realize one-way fluid transport macroscopically, suctioning from the inlet and discharging from the outlet.  
When the amplitude of the PZT vibrator is large, the volume of the pump chamber changes greatly and the fluid flows vigorously. The flexible valve can be completely closed, thus appearing as a valved PZT pump. When the amplitude is very small, the fluid flows gently and the flexible valves do not deform. The fastigiate shape of the structure makes it resemble a val valveless PZT pump with cone-shaped tubes. Consequently, the PPFV can realize the free conversion between the valved state and the valveless state.