Theory and Experimental Verification on Cymbal-shaped Slotted Valve Piezoelectric Pump
Huang et al. Chin. J. Mech. Eng.
Theory and Experimental Verification on Cymbal-shaped Slotted Valve Piezoelectric Pump
Jun Huang 2
Yi‑Chao Zhu 2
Wei‑Dong Shi 2
Jian‑Hui Zhang 0 1
0 College of Mechanical and Electrical Engineering, Guangzhou University , Guangzhou 510006 , China
1 College of Mechanical and Electrical Engineering , Guangzhou Univer‐ sity, Guangzhou 510006 , China
2 National Research Center of Pumps, Jiangsu University , Zhenjiang 212013 , China
Valve piezoelectric pumps usually have larger flow rate than that of valveless ones. However, the traditional cantilever valve easily induces stress concentration which impacts the reliability of pumps. Therefore, a cymbal‑ shaped slotted check valve is proposed to be applied in a piezoelectric pump in order to reduce the stress concentration of the valve and thus improve the reliability of the piezoelectric pump. The structure and working principle of the piezoelectric pump are analyzed; the stress analysis of the cymbal‑ shaped slotted valve diaphragm is conducted. In addition, finite element software is employed to analyze the difference of the Von‑ Mises stress between the cymbal‑ shaped slotted diaphragm and the slotted flat diaphragm. The simulation results show that, the Von‑ Mises stress of cymbal‑ shaped slotted diaphragm is smaller than that of the slotted flat one. Furthermore, the cymbal‑ shaped slotted valve piezoelectric pump is also fabricated, and flow rate experiment is performed. The experimental results indicate that the flow rate of piezoelectric pump working in low frequencies (0 Hz < f < 50 Hz) is larger than that working in high frequencies (200 Hz < f < 2000 Hz). When driven at voltage of 160 V and frequency of 5 Hz, the pump reaches its maximum flow rate of 6.6 g/min. The experimental results validate the feasibility of the cymbal‑ shaped slotted check valve. This research can effectively solve the problem of stress concentration of valve piezoelectric pumps and is helpful for improving the reliability of them.
Cymbal‑ shaped slotted; Piezoelectric pump; Valve; Stress
The high requirements of micro-chemical mixing,
biological detection and insulin injection raises new
actuation requirements in the diversity of actuation functions
and types [
], and the conventional actuators cannot
fulfil these requirements efficiently [
]. To meet these
requirements, piezoelectric pumps with the merits of
rapid response, high energy density, perfect integration,
and no electromagnetic interference attracts a large
number of researchers [
Piezoelectric pumps can be sorted by two types,
valveless piezoelectric pumps and valve ones, according to
whether they have an internal moving part (valve) or not.
Zhang et al. [
] proposed a piezoelectric pump with
rotatable unsymmetrical slopes which could be used to
piezoelectric liquid mixing and delivery together or
separately. Yang et al. [
] designed a bidirectional valveless
piezoelectric micropump with double chambers. This
pump has better performance at low Reynolds
number and can change the flow direction by regulating the
Compared with valveless piezoelectric pump, valve
piezoelectric pump has a larger flow rate and a smaller
pulsation, so it has a more extensive application
prospect. Hwang et al. [
] designed a reciprocating
piezoelectric pump which is used for fuel cells. This pump
has the characteristics of compact structure, low energy
consumption and even steady output in low driving
frequencies. Liu et al. [
] proposed a PZT-based valve
piezoelectric pump, and further designed an insulin delivery
system in 2014. This piezoelectric pump, with two pump
chambers and three passive valves, can achieve a precise
supply of drugs by adjusting the voltage and frequency.
Wang et al. [
] proposed a piezoelectric pump having a
compressible chamber and the valve fixed at its two ends
for a fuel cell system in 2014. Due to the fixed passive
valve, this pump has a lower leakage and a good output
performance working in high frequencies. Ma et al. [
put forward a separable piezoelectric pump suitable for
drug delivery. Due to the separable design between the
driving part and the drug delivery unit, this pump can
effectively avoid the secondary pollution in drug delivery.
Cazorla et al. [
] fabricated a functional micro-pump
made of silicon and PZT thin films with standard MEMS
technology. This pump characterizes being driven by low
However, the reciprocating motion in a high frequency
with the check valve as the pump’s core component tends
to make the valve generate fatigue damage. Especially
when the check valve is working in the fluid, it can
generate a large stress which may easily lead to stress
concentration, thus aggravating the fatigue damage and causing
failure of the check valve. As a result of that, the
piezoelectric pump will not work properly.
Ding et al. [
] designed a heart-valve-like check valve
by using a structure simulating the working principle of
human’s heart valve to increase the deformation of the
valve and reduce its stress. Based on this structure, a
bio-inspired cymbal-shaped slotted valve is proposed in
this paper, aiming to largely reduce the stress of the valve
under the same loading conditions.
In this research, the structure design of the
cymbalshaped slotted valve is proposed, and working principle
of the cymbal-shaped slotted valve piezoelectric pump is
analyzed. After theoretically analyzing, the design
parameters of the cymbal-shaped slotted valve are achieved.
And then, through FEM (Finite Element Method)
calculation, the maximum Von-Mises stress on cymbal slotted
diaphragm is just 0.036 kPa, which is much smaller than
that on the flat one. Finally, the performance of the
cymbal-shaped slotted valve piezoelectric pump is tested to
verify the validity of the valve.
2 Structure and Working Principle
As shown in Figure 1, the cymbal-shaped slotted valve is
mainly composed of a cymbal grille and a cymbal
slotted diaphragm. When the fluid flows through the valve
from grille to diaphragm, the valve is open; when the
fluid flows through the valve from diaphragm to grille,
the valve is closed. The displacement of the valve changes
with the fluid pressure, so it makes the flow rate
adjustable. The cymbal-shaped slotted valve piezoelectric pump
is mainly composed of a pump cover, a piezoelectric
vibrator, a pump chamber, two cymbal-shaped
slotted valves, an inlet tube and an outlet tube, as shown in
When an alternating voltage is applied on the
piezoelectric vibrator, the vibrator will do the reciprocating
vibration in normal direction due to the inverse
piezoelectric effect, causing changes in the volume of the pump
chamber. The working principle of cymbal-shaped
slotted valve piezoelectric pump is shown in Figure 3. When
the piezoelectric vibrator moves upward, the volume
of pump chamber increases and the internal pressure
reduces. Under the pressure difference between inside
and outside of the pump chamber, the fluid in the inlet
tube will flow into the pump chamber via grille and
diaphragm. In the meantime, the valve at the outlet tube is
closed. So the piezoelectric pump at this stage is in the
state of suction. Similarly, when the piezoelectric
vibrator moves downward, the volume of pump chamber
decreases and the internal pressure increases. Under the
pressure difference between inside and outside of the
pump chamber, the fluid near the outlet tube will flow
out of the pump chamber via the valve. In the meantime,
the valve at the inlet tube is closed. So the piezoelectric
pump at this stage is in the state of discharge.
3 Theoretical Analysis
As both the valve’s state whether to be open or closed and
its reliability are determined by the movement of cymbal
slotted diaphragm, it is necessary to make stress analysis
of the diaphragm. Mechanics analysis diagram of
cymbalshaped slotted diaphragm is shown in Figure 4 in which a
fan zone with angle of dβ is arbitrarily selected. The stress
deformation of fan-shaped diaphragm is shown in (a) and
equivalent simplified diagram is shown in (b) of Figure 4.
Where the meanings of each parameter in Figure 4 are
expressed as follows: ξ is radial displacement of the
cymbal slotted diaphragm; f is bending displacement;
δ is axial displacement; Δ is tensile deformation; h0 is
the height of the diaphragm; tm is the thickness of the
diaphragm; E is elastic modulus; θ is the cone angle; r1, r2
and r0 are respectively the top, bottom and overall radius
of the diaphragm; b is the arc length at arbitrary position
b = xb1 = ϕ(x).
The inertia moment Ix at x is
Ix = btm3 = tm3 ϕ(x),
where OA = r2, AB = r1, F = qx. To obtain the
deformation of the cantilever at position A, a virtual force Fe is
loaded at arbitrary position on part OB, provided AC = a,
then solve it by using the principle of virtual work:
MAB = qx · 2 x, ,
MBC = qr1 x − 2 r1
= Etm36ϕq(x) 13 r13 − 21
where r2 and r1 can be regarded as constant values. The
range of the angle θ is 0° ≤ θ < 90°. The smaller θ is, the
larger ξ will be, and δ decreases at first then increases.
That is, under the same external conditions, the lower
the cymbal slotted diaphragm is, the larger its radial
displacement will be, and its axial displacement decreases
at first then increases. It can be seen that, when θ is 0°,
the cymbal slotted diaphragm becomes a flat slotted
diaphragm, δ reaches its maximum. This shows that, under
the same external conditions, the axial displacement of
the flat slotted diaphragm is greater than that of the
cymbal-shaped ones. And when θ tends to 90°, the diaphragm
will only move radially.
4 Finite Element Analysis
Three-dimensional modeling via finite element method is
conducted for the cymbal-shaped slotted diaphragm and
the slotted flat diaphragm to compare their Von-Mises
stresses under the same loading conditions. Structure
parameters of cymbal-shaped slotted diaphragm and the
slotted flat diaphragm are shown in Table 1. Their models
are imported into Ansys Workbench, then meshed and
set with the boundary conditions, and applied the
same alternating load to calculate the their Von-Mises
stresses so as to analyze the feasibility of the valve. In
this research, the models of the slotted diaphragms were
divided into more than 3000 tetrahedron elements. The
edges of the diaphragms have ‘zero displacement’
boundary conditions, so the diaphragms could be considered to
be fixed supported.
The curves of pressure vs stress are shown in Figure 5.
It shows that when the frequency of alternating pressure
load applied on them is 10 Hz, with the increase of the
load amplitude, the stress of both diaphragms will
gradually increase; under the same pressure load, the
cymbalshaped slotted diaphragm is obviously smaller than the
slotted flat diaphragm in stress, and with increase of the
pressure load, the difference between their stress will also
When the load amplitude is 10 kPa, the Von-Mises
stress contours of slotted flat diaphragm and cymbal
slotted diaphragm are shown in In Figure 6. It shows that
their maximum stress are both located in the root of the
slot. Under this load, the slotted flat diaphragm has its
maximum Von-Mises stress of 0.249 kPa, and the cymbal
slotted diaphragm 0.036 kPa.
5 Experimental Verification and Discussions
A prototype of the cymbal-shaped slotted valve
piezoelectric pump has been manufactured. Its pump cover,
pump chamber, inlet tube and outlet tube, and the
cymbal grille are shaped by 3D printing photosensitive resin
material. The cymbal slotted diaphragm is made of
beryllium bronze with high elasticity. The geometrical
parameters of piezoelectric vibrator are shown in Table 2,
and the geometrical parameters of pump chamber,
diaphragm and grille are shown in Table 3.
The photos about a physical piezoelectric pump and
its performance test are shown in Figure 7 (Additional
file 1: Experimental video). To eliminate the generation
of bubbles in the test, deionized water was used as the
working fluid. Driving voltage in the test was a peak value
of 160 V, and the pump’s mass output per unit time was
measured by varying the driving frequency of the
piezoelectric vibrator, so that piezoelectric pump’s curve of flow
rate vs frequency can be obtained. In the meantime, laser
displacement sensor (LK-G30, Keyence Inc., Japan) was
used to measure the displacement of the center of the
piezoelectric vibrator to obtain the relationship between
the amplitude of the piezoelectric vibrator and driving
frequency. Flow rate and the amplitude of vibrator in the
test are shown in Figure 8 and Figure 9.
As shown in Figure 8, when the vibrator is working in
low frequencies, with the increase of driving frequency,
both the piezoelectric pump’s flow rate and vibrator
amplitude present to increase at first then decrease.
When the driving frequency is 4 Hz, the piezoelectric
vibrator has its maximum amplitude of 165.8 μm; when
the driving frequency is 5 Hz, the piezoelectric pump has
its maximum flow rate of 6.6 g/min. The reason for the
driving frequency at maximum vibrator amplitude being
different from that at maximum flow rate is that the flow
rate of the piezoelectric pump depends on the volume
change in pump chamber per unit time, that is, the flow
rate is associated with vibrator amplitude and the driving
frequency, therefore, the vibrator amplitude can’t
completely determine the flow rate.
As shown in Figure 9, when the vibrator is working in
high frequencies, with the increase of driving frequency,
the piezoelectric pump’s flow rate presents to increase at
first then decrease, while the vibrator amplitude is
gradually reducing. When the driving frequency is 433 Hz, the
piezoelectric pump has its maximum flow rate of 2.6 g/
min. In addition to the factor of the volume change of
pump chamber, the reason for the driving frequency at
maximum vibrator amplitude being different from that at
maximum flow rate also lies in the pump’s valve
hysteresis characteristics [
(1)To solve the disadvantages of valve piezoelectric
pump, such as valve’s large stress, easy to get
damaged, low reliability of the pump, a cymbal-shaped
slotted check valve is proposed to be applied in a
piezoelectric pump. Based on the theoretical
analysis of cymbal slotted diaphragm, it can be seen that
the displacement of the diaphragm (flow rate of the
piezoelectric pump) has a correlation with the height
of cymbal slotted diaphragm.
(2)The finite element software is employed to calculate
the stresses of the cymbal slotted diaphragm and
the slotted flat diaphragm. When the frequency of
alternating pressure load applied on them is 10 Hz
and the magnitude of the load is 10 kPa, cymbal
slotted diaphragm has its maximum Von-Mises stress
which is 0.036 kPa, and the slotted flat diaphragm is
0.249 kPa. That is, the cymbal slotted diaphragm is
smaller than the slotted flat diaphragm in stress, so
the cymbal slotted diaphragm has a high reliability.
(3)A prototype of the cymbal-shaped slotted valve
piezoelectric pump has been manufactured, and the
pump performance was tested. The results show that:
both the pump’s maximum flow rate and the
maximum vibrator amplitude turn out to be at a low
frequency; when the driving voltage is 160 V and the
driving frequency is 4 Hz, the pump reaches its
maximum flow rate which is 6.6 g/min; when the driving
frequency is 5 Hz, the piezoelectric vibrator has its
maximum amplitude which is 165.8 μm. This test
validates the feasibility of the cymbal-shaped slotted
check valve piezoelectric pump.
J‑HZ proposed the cymbal‑shaped slotted check valve and carried out the
studies in the reviews of the principles of the cymbal‑shaped slotted valve
piezoelectric pump. JH fabricated the cymbal shaped slotted valve piezo‑
electric pump and performed flow rate experiment. He wrote the draft. Y‑ CZ
conducted the stress analysis of the cymbal‑shaped slotted valve diaphragm
and carried out the finite element simulation. W‑DS provided the fabrication
method of the cymbal‑shaped slotted valve. All authors read and approved
the final manuscript.
Jun Huang, born in 1981, is currently an assistant professor at National
Research Center of Pumps, Jiangsu University, China. He received his PhD degree
from Nanjing University of Aeronautics and Astronautics, China, in 2014. His cur‑
rent research focuses on piezoelectric actuators and sensors.
Yi‑ Chao Zhu, born in 1992, is currently a master candidate at Research
Center of Fluid Machinery Engineering and Technology, Jiangsu University, China.
Wei‑Dong Shi, born in 1964, is currently a professor and a PhD candidate
supervisor at Jiangsu University, China. His research area is fluid machinery seal
technology and optimization design of pump devices. E‑mail: .
Jian‑Hui Zhang, born in 1963, is currently a professor and a PhD candidate
supervisor at Guangzhou University, China. His research area is mechanical
design and its theory, piezoelectric driving.
Supported by National Natural Science Foundation of China (Grant No.
51605200), Jiangsu Provincial Natural Science Foundation of China (Grant No.
BK20150518), Jiangsu Provincial Postdoctoral Science Foundation of China
(Grant No. 1501108B), and Senior Talent Start‑up Foundation of Jiangsu Uni‑
versity (Grant No. 14JDG145).
The authors declare that they have no competing interests.
Ethics approval and consent to participate
Springer Nature remains neutral with regard to jurisdictional claims in pub‑
lished maps and institutional affiliations.
Additional file 1 Experimental video of piezoelectric pump.
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