1 Introduction

The traditional drive pump is subject to large size, electromagnetic interference, energy consumption, complex structure, and other shortcomings that largely restrict the application in microsystems (Azarbadegan et al. 2009; Hwang et al. 2018). In recent years, with the development of smart materials, micro-pumps based on smart materials were extensively studied (Sayar and Farouk 2012)such as electrostatic actuation (Muthu et al. 2022), shape memory (Kotb et al. 2021), magnetostrictive effects (Zhu et al. 2022), piezoelectric actuation (Li et al. 2005), etc. Piezoelectric pumps are already being used in fuel cells (McDonald and Hamdan 2019), chip cooling (Lu et al. 2020), drug delivery, and biochips (Liu et al. 2010). High flow rate and high-pressure transfer pumps are required in fields like hemodialysis machines chips (Salari et al. 2015) cooling systems (Huang et al. 2014), and civil gyroscopes (Leng et al. 2013). Researchers have done a lot of research on how to increase the Output performance of piezoelectric pumps (Guan et al. 2020). Increased output voltage often leads to damage to piezoelectric actuators (Iverson and Garimella 2008). Increasing the pump chamber was commonly used to improve the output performance of the pump (Liu et al. 2022). In 2021, (Yu et al. 2020) proposed a piezoelectric thin-film pump with continuously decreasing pump chambers. The experimental results demonstrated that the flow rate was effectively increased compared to the flow rate of the double-chambers piezoelectric pump. In 2019, Tai Jiang (Peng et al. 2019) proposed a large flow rate, series-parallel hybrid connected four-chamber piezoelectric pump. It shows that the output performance of the piezoelectric pump can be greatly enhanced by using multiple pump cavities and hybrid connections. Dong et al. (2017) proposed a double actuator piezoelectric pump. The experiment proves that changing the driving mode of the piezoelectric actuator can change the output performance of the piezoelectric pump. In 2013, (Jang et al. 2007) proposed a series piezoelectric micropump. The best flow rate reached 3.85 ml/min. Junwu et al. (2005) developed a double-chamber series piezoelectric pump and a double-chamber parallel piezoelectric pump. The experimental results show that the performance of parallel and series piezoelectric pumps in asynchronous driving mode is better than that in synchronous driving. The pump chambers were connected in parallel and the flow rate was higher than in series, but the pressure was higher in series.

From previous studies, it can be seen that increasing the output performance of piezoelectric pumps has generally been achieved by increasing the number of pump chambers and changing the way the chambers are connected. Increasing the number of pump chambers will enlarge the pump body size as well as not being easily miniaturized. In this paper, a cascade type series-parallel hybrid three-chamber piezoelectric pump is proposed. The two upper pump chambers form the first stage and the one lower pump chamber forms the second stage. The pump chambers are arranged in a cascade arrangement with a hybrid of series and parallel connections.

2 Design and principle

2.1 Cascade type three-chamber piezoelectric pump structure design

The structure of the cascade type series-parallel hybrid three-chamber piezoelectric pump is shown in Fig. 1. The pump mainly includes the umbrella valve(c), flow channel plate(d), pump body2(e), back cover(f), front cover(g), piezoelectric actuator(h), pump body1(i), outlet tube(j), inlet tube(k). The two pump chambers are connected in parallel in pump body 1 and then in series with the pump chamber in pump body 2 by a flow channel plate to form a three-chamber hybrid structure. Each pump chamber is equipped with a piezoelectric actuator. Ring seals are used to reduce the vibration of the piezoelectric actuator and seal the pump chambers. Umbrella valves are check valves. Bolts and nuts are used to hold and seal.

Fig. 1
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Exploded view of cascade type series-parallel hybrid three-chamber piezoelectric pump

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2.2 Synchronous and asynchronous driving working principle

Figure 2 shows the wiring diagram of the cascaded series-parallel hybrid three-chamber piezoelectric pump. The two pump chambers form the first stage in pump body (1) The first stage uses a synchronous driving mode. The pump chamber forms a second stage in the pump body (2) As shown in Fig. 2 (a), the first stage is the synchronous driving mode with the second stage. The phase angle of the first and second-stage piezoelectric actuators is 0°. As shown in Fig. 2 (b), the first stage and second stage are in an asynchronous driving mode. The phase angle of the first and second-stage piezoelectric actuators is 180°. When driven asynchronously, the volume change is reversed in the pump chambers in the first and second stages as shown in Fig. 3 (a1-b1). When driven asynchronously, the pump chamber becomes larger in the first stage and the pump chamber becomes smaller in the second stage, the fluid is drawn into the first stage and the fluid in the second stage is discharged as shown in Fig. 3 (a1). As shown in Fig. 3 (b1), fluid flows from the first stage into the second stage as the piezoelectric actuator of the first stage bends downward and the piezoelectric actuator of the second stage bends upward. Where the inlet and outlet tubes and the pump working principles are not in one plane, they are represented by dashed lines in Fig. 3.

Fig. 2
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Diagram of wiring method: (a) synchronous driving, (b) asynchronous driving

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Fig. 3
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Working process of the piezoelectric pump:(a1-b1) asynchronous driving, (a2-b2) synchronous driving

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When driven synchronously, the pump volume changes equally in the first and second stages, the fluid is sucked or discharged at the same time as shown in Fig. 3(a2-b2). The pump chambers in the first stage and the second stage pump chamber in the second stage become larger at the same time as shown in Figure (a2). As shown in Figure (b2), the fluid is discharged from the pump chamber. Since the volume of the pump chambers are simultaneously reduced, the umbrella valve cannot be completely closed in the pump chamber located in the second stage, which may lead to the occurrence of the backflow phenomenon. When the piezoelectric pump is linked in series, the pressure and flow rate are (Kan et al. 2008):

$$ P={\eta }_{1}N{P}_{1}$$
(1)
$$ Q={\eta }_{2}\sqrt{N}{Q}_{1}$$
(2)

where \( {\eta }_{1}\) and \( {\eta }_{2}\) are the efficiency of the umbrella valve, N is the the amount, of pump chambers, P is total output pressure, and Q is total flow rate.

When the piezoelectric pump is linked in parallel with load. The total output pressure and total flow rate are (Yu et al. 2020):

$$ {P}_{p}={P}_{1}$$
(3)
$$ {Q}_{p}=N{Q}_{1}$$
(4)

where from Eqs. (1)–(4), the flow rate and pressure when the pump chamber is connected in a hybrid way are:

$$ {P}_{h}={\eta }_{1}N{P}_{1}$$
(5)
$$ {Q}_{h}={\eta }_{2}{N}^{\frac{3}{2}}{Q}_{1}$$
(6)

According to Eq. (5) and Eq. (6), it can be seen that the multi-chamber piezoelectric pumps are effective in increasing flow rate and pressure, and there is a strong relationship between piezoelectric pump output performance and valve efficiency. The cascade structure is adopted between the pump chambers, which greatly increases the cut-off efficiency between the valves.

Table 1 Parameters of the prototype
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3 Experimental setup and results

3.1 Experimental research

The experimental equipment diagram is shown in Fig. 4. The prototype was created by means of a 3D printer, using a UV-curable resin. The parameters of the prototype are shown in Table 1. The experiments are conducted under constant temperature conditions. The experimental medium is water. The excitation signal (a sine wave signal) is generated by the signal generator (CUH SDVC40-S, Nanjing, China). An electronic balance with a measuring range of 0-2000 g and an accuracy of 0.01. Timer to measure the flow rate. The pressure meter (HT-1895, Manometer) is used to measure the pressure. After several pretests, it has been verified that a drive voltage of 220 V will damage the piezoelectric actuator. To prevent damage to the piezoelectric actuator, voltages of 190 V, 200 and 210 V were selected to measure the relationship between frequency and flow rate and pressure. Fig. 5 shows the experimental prototype as well as the 3D dimensions.

Fig. 4
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Experimental equipment diagram

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Fig. 5
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(a) Experimental prototype. (b) Dimensional

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First, the experiment explores the flow rate at different voltages in asynchronous driving mode.

and synchronous driving mode. Then the flow rate and pressure were studied at different frequencies with driving voltages of 190 V, 200 V, and 210 V, respectively. The relationship between voltage and flow rate is shown in Fig. 6 under different driving modes. The results show that the flow rate increases with increasing voltage and is significantly better in the asynchronous driving mode than in the synchronous driving mode. When asynchronously driving mode with voltage and frequency of 210 V, 50 Hz, the flow rate reaches 466 ml/min. When synchronously driving mode with voltage and frequency of 210 V, 50 Hz, the flow rate reaches 102.07 ml/min. When the piezoelectric actuator of the first and second stages are in asynchronous driving mode, the efficiency of the shut-off valve between the first and second stages can be effectively increased due to the cascade arrangement of the first and second stages.

Fig. 6
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Relationship between voltage and flow rate in different driving modes

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Figure 7 shows the relationship between flow rate and frequency in different voltages in the asynchronous driving mode. The scatter plot distributed over the surface shows that the piezoelectric pump has a better output performance in asynchronous driving mode at low frequency range of 40-70 Hz. In particular, the maximum output flow rate of 466 ml/min is reached at 50 Hz. The flow rate increases with increasing frequency at 40-50 Hz, and decreases with increasing frequency when the frequency is greater than 50 Hz. When the frequency is greater than 50 Hz, the hysteresis of the valve increases with increasing frequency, resulting in a constant reduction in flow rate. The contour plot of the bottom layer shows the increase in the flow rate with increasing voltage.

Fig. 7
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The relationship between flow rate and frequency under different voltages in asynchronous driving

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Figure 8 shows the relationship between pressure and frequency in different voltages in the asynchronous driving mode. The scatter plot of the distribution on the surface shows that the pressure decreases as the frequency increases. When the voltage is 210 V and the frequency is 50 Hz, the pressure reaches 19.38 KPa

Fig. 8
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Relationship between pressure and frequency in different voltage in asynchronous driving modes

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Figure 9 shows flow rate versus frequency in synchronous driving mode. The scatter plot of the distribution over the surface shows that there is a negative correlation between flow rate and frequency The flow rate reaches 100.05 ml/min The projection of the surface plot shows that there can be a higher and more stable flow rate when the frequency is between 40 and 70 Hz.

Fig. 9
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Relationship between flow rate and frequency in different voltage in synchronous driving modes

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Figure 10 shows the relationship between output pressure and frequency in synchronous driving mode. The scatter plot of the distribution on the surface shows that output pressure decreases as the frequency increases. When the voltage is 210 V and the frequency is 40 Hz, the pressure reaches 8.67 KPa. It can be seen in the projection of the surface plot, that there can be a higher pressure when the frequency is in the range of 40-70 Hz.

Fig. 10
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Relationship between pressure and frequency in different volt-age in synchronous driving modes

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3.2 Discussion

The output performance of a cascade three-chamber piezoelectric pump was experimentally investigated in relation to voltage and frequency in different driving modes. And the following conclusions were obtained.

(1) The output flow rate of the piezoelectric pump increases continuously when the voltage increases in asynchronous driving. The optimum flow rate is reached when the voltage is 210 V and the frequency is 50 Hz, and the optimum flow rate reaches 466 ml/min. When the voltage is 210 V, the asynchronous driving pressure reaches 19.38 KPa and the frequency is 50 Hz.

(2) The output flow rate of a synchronously driven cascade three-chamber piezoelectric pump is linearly proportional to the change in voltage, with a much smaller slope than with asynchronous driving. The optimum flow rate is 102.07 ml/min at a voltage of 210 V and a frequency of 40 Hz, and the optimum pressure is 8.67 KPa at 210 V and 40 Hz in synchronous driving mode.

(3) The optimum flow rate in asynchronous driving mode is 356.54% higher than the optimum flow rate in synchronous driving mode. The optimum pressure in the asynchronous driving mode is 123.53% higher than the optimum pressure in the synchronous driving mode.

(4) In both synchronous and asynchronous driving modes, the piezoelectric pump has better output performance in the low frequency range of 40-70 Hz. With increasing frequency, the piezoelectric pump output flow rate is almost zero and the output pressure is extremely low. In addition, asynchronous driving has the best output performance at 50 Hz.

Experiments have shown that the output performance of a cascaded three-chamber piezoelectric pump in asynchronous driving mode is much higher than in synchronous driving mode. When in synchronous driving mode, the first stage piezoelectric pump discharges and absorbs fluid simultaneously with the second stage piezoelectric pump causing the inlet and outlet umbrella valves to fail to close completely. As a result, the fluid discharged or absorbed by the second stage flows into the first stage pump chamber, ultimately leading to a reduction of output flow rate in the synchronous driving mode. The cascaded three-chamber piezoelectric pump does not discharge or absorb fluid simultaneously when driven asynchronously and thus has a better output performance than the synchronous driving mode. Furthermore, as shown in Table 2, the output performance of the cascaded three-chamber series-parallel hybrid piezoelectric pump proposed in this paper is substantially improved compared to previous studies on three-chamber piezoelectric pumps.

Table 2 Performance comparison of the proposed cascaded three-chamber piezoelectric pump with previous studies
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4 Conclusions

In this paper, a cascade type series-parallel hybrid three-chamber piezoelectric pump is proposed. The working process of this piezoelectric pump is described in detail. The reason for a better asynchronous driving mode is initially analyzed. A mathematical model of the hybrid series-parallel connection is developed. Compared with series piezoelectric pumps and parallel piezoelectric pumps, this piezoelectric pump has huge advantages in flow rate and pressure. The flow rate and pressure of this piezoelectric pump are investigated experimentally in asynchronous driving mode and synchronous driving mode. The study’s results show that the optimal flow rate in asynchronous driving mode exceeds the optimal flow rate in synchronous driving mode by 356.54%. The optimal pressure in asynchronous driving mode exceeds the optimal pressure in synchronous driving mode by a percentage (optimal pressure in asynchronous driving mode minus optimal pressure in synchronous driving mode divided by optimal pressure in synchronous driving mode) of 123.53%. The piezoelectric pump provides some reference significance in improving the utilization rate of the multi-chamber piezoelectric pump chambers, thereby improving the flow rate. Because of the cascade structure design, the piezoelectric pump not only improves the output performance of the pump, but also reduces the volume of the pump is expected to be applied in microelectronics integrated heat dissipation.