Optimization Study on Expansion Energy Used Air-Powered Vehicle with Pneumatic-Hydraulic Transmission
Fu et al. Chin. J. Mech. Eng.
Optimization Study on Expansion Energy Used Air-Powered Vehicle with Pneumatic-Hydraulic Transmission
Xiang‑Heng Fu 0
Mao‑Lin Cai 0
YiX‑uan Wang 0
Yan Shi 0
0 School of Automation Science and Electrical Engineering, Beihang University , Beijing 100191 , China
Pneumatic‑ hydraulic transmission has been developed for years. However, its dynamic properties are not good enough for application. In this paper, in order to increase the output characteristics, a late‑ model air‑ powered vehicle using expansion energy is proposed which can boost energy through a pneumatic‑ hydraulic transmission. The dynamic characteristics of the air‑ powered vehicle is modeled and verified by conducting experiment. In addition, the influence of the key parameters of the air‑ powered vehicle is researched for the optimization of the system performance. Through the results, the author got the conclusion that, firstly, comparison of the results of model and experiment proves the built model to be effective; secondly, input air pressure should be set according to the request of the practical loads, and range of 0.65 to 0.75 MPa can be chosen; thirdly, as a key structure parameter of the airpowered vehicle, ratio of the areas is considered to be set to approximate 8; what's more, a bigger orifice with a limit will promote the system dynamic characteristic property, and the limit is about 3.5 mm; last but not the least, not too farther position of the rings will increase the quality of output dynamic characteristics. This paper can be a reference for system design of air‑ powered vehicle and dynamic improvement.
Air‑ powered vehicle; Expansion energy; Pneumatic‑ hydraulic transmission; Output dynamic characteristics
1 Introduction
Recently, for advantages of anti-explosion, zero-emission,
and pollution-free, sustainable energy vehicles suitable
for friendly environments have been widely adopted as
a late model green transport. Main part of sustainable
energy vehicles is air-powered engine, and the
pneumatic-hydraulic transmission is broadly applied as the
main heart of the driving system for great advantages
of simple structure, recyclability, low cost, high storage
density of energy and long lifespan [
1–3
]. Though the
advantages are obvious, it also owns disadvantages such
as low efficiency by insufficient of the energy utilization,
which aggravates the waste of energy, especially under
the recent environment of energy shortage and
developing green movements [
4, 5
].
The recent studies on the pneumatic and hydraulic
transmission still mainly focus on method of
optimizing the structure and performance [
6
]. Shen et al. [
7
]
designed and implemented a type of air pump driven
by input gas used in air-powered motorcycle, and its
main process of the pressurizing is piston reciprocating
motion. What is more, Takeuchi et al. [
8
] implemented
the application of expansion energy of compressed air by
designing a kind of expansion-type pump.
About the dynamic characteristics of the hydraulic
model, a serial of works has been published in recent
years. Many kinds of analysis about hydraulic and
pneumatic model have been put forward. Ren et al. and Wang
et al. studied the control method of a pneumatic servo
system by using mathematic modelling and
experimental research [
9, 10
]. Yan et al. and Taleb et al. studied the
pneumatic bi-cylinder transmission system without the
pressurizing function by modelling and parameter
analysis [
11, 12
]. Cai et al. has improved the model based on
a new-type of pneumatic-hydraulic transmission and
analyzed the dynamic characteristics [
13
]. However, the
traditional pneumatic-hydraulic transmission is energy
dissipation because the air expansion energy existing in
the compressed air is wasted. From then on, very little
study on any type of sustainable vehicle driven by
pneumatic-hydraulic transmission has been reported [
14, 15
],
especially that using air expansion energy.
For promoting working efficiency by using the
expansion energy of the compressed air, we proposed a new
type of expansion energy used air-powered vehicle using
pneumatic-hydraulic transmission. However, the
application of air expansion energy used vehicle is still hard to
achieve due to the lack of research on output dynamic
characteristics, which caused trouble for the
performance improvement of air-powered vehicles [
16
].
In this article, an air-powered vehicle using expansion
energy of compressed air has been proposed. In order to
set a foundation on the dynamic performance
optimization of the air-powered vehicle, firstly, a late model
airpowered vehicle with pneumatic-hydraulic transmission
was modeled and experimentally verified. Secondly,
output dynamic characteristics of the new kind of
air-powered vehicle, including the output torque and revolving
speed, were studied through simulation. What’s more,
output dynamic characteristics were studied by analyzing
affection of several key structure parameters for
inspecting the best performance of the air-powered vehicle with
pneumatic-hydraulic transmission.
2 Mathematical Modeling of the Air‑Powered
Vehicle
Structure of the built air-powered vehicle with
pneumatic-hydraulic transmission is shown in Figure 1. As we
can see, the main part of the expansion energy used
airpowered vehicle contains the pneumatic-hydraulic
transmission and the Motor part, including one pneumatic
cylinder and two symmetric hydraulic cylinders. The
magnetic switching valve controls the input way of the
air source. The pneumatic piston is directly driven by the
input air. Through transmission of air pressure, hydraulic
pistons move towards the same direction of pneumatic
piston, then the hydraulic oil drives the hydraulic motor
to work.
In the air-powered vehicle, the structure of magnetic
rings of piston and magnetic inductors ensures the
continuously working of the motor, what is more, the
advantage of expansion energy of compressed air. As shown
from Figure 2, the whole processes of one of the
hydraulic pistons mainly contain four processes. At first, when
1
13
6
the air was put into the pneumatic chamber, the
hydraulic piston moves forward considered the first process.
When the piston gets to the place of magnetic inductor
A, the source of air is stopped inputting by the controller,
which can be considered as the second process. At this
process, the vehicle is completely driven by the expansion
energy of the compressed air in the pneumatic chamber.
When the piston gets to the place of magnetic inductor
B, it works in reverse due to the change of the magnetic
switching valve. The third and fourth processes are the
same as the symmetrical hydraulic piston works in the
same way. The time of third and fourth working processes
of the pistons are completely using expansion energy, and
the energy can be saved to some extent.
In the air-powered vehicle, the structure of magnetic
rings of piston and magnetic inductors ensures the
continuously working of the motor, what is more, the
advantage of expansion energy of compressed air. As shown
from Figure 2, the whole processes of one of the
hydraulic pistons mainly contain four processes. At first, when
the air was put into the pneumatic chamber, the
hydraulic piston moves forward considered the first process.
When the piston gets to the place of magnetic inductor,
the source of air is stopped inputting by the controller,
which can be considered as the second process. At this
process, the vehicle is completely driven by the expansion
energy of the compressed air in the pneumatic chamber.
When the piston gets to the place of magnetic inductor
B, it works in reverse due to the change of the magnetic
switching valve. The third and fourth processes are the
same as the symmetrical hydraulic piston works in the
same way. The time of first and third working processes
of the pistons are completely using expansion energy, and
the energy can be saved to some extent.
Magnetic
Inductor B
Magnetic
Inductor A
Magnetic Ring
of Piston
Hydraulic
Cylinder
the 2nd process
the 1st process
the 3rd process
the 4th process
Hydraulic Piston
According to the working principle of the
expansion energy used air-powered vehicle, the mathematical
model can be obtained as follows.
2.1 Gas Energy Equations
We consider the pneumatic chambers do not charge
and exhaust air at the same time by assuming no leakage
exists in pneumatic chambers. Consequently, gas energy
equations for the inflating and deflating side of each
chamber can be gotten as shown as follows [
17, 18
]:
dT
Cν Wa dt = (St · hc + Cν · q)(Ta − T ) + R0qTa − pAu,
dT
Cν Wa dt = St · hd (Ta − T ) + R0qT − pAu,
where Cv is the specific heat at constant volume of the
air; Wa is the air mess; St is the heat transfer area; Ap is
the area of the pneumatic piston; u is the velocity of the
pistons; T is the temperature of the air; Ta is the
atmospheric temperature; t is the real time; R0 is the gas
constant factor, which is usually 287 J/(kg·K).
2.2 Ideal Pneumatic Continuity Equation
According to the ratio of Pl/Ph, the pneumatic
continuity equation for the flow through a restriction can be
obtained as follows [
19, 20
]:
A√epTphh
q =
A√epTphh
2κ
R0(κ−1)
1
κ−1
2
κ+1
2
pl κ
ph
−
2κ
R0(κ+1)
,
pl
ph
κ+1
κ
, pl > 0.528,
ph
where p, V and q stand for pressure, volume and mass
flow of idea air, respectively.
2.4 Motion Equation of the Pistons
Piston velocity can be calculated by using Newton’s
second law of motion. What is more, the friction force
model is considered as the sum of coulomb friction and
viscous friction in this paper. All the forces on the piston
can be shown from Figure 3.
Motion equation of the pistons can be written [
21
]:
d2x 1
dt2 = M (pdl · Adl − pdr · Adr + phAl · AhAl
− phBl · AhBl + phAr · AhAr − phBr · AhBr − Ff ),
dx
dt = 0, x = 0, L,
Ff =
Fs,
Fc + Cu,
u = 0,
u = 0,
(4)
(5)
(6)
(1)
(2)
where M is the mass of the piston; x is the displacement
of the piston; Adl is the equivalent areas of pneumatic
piston in the left chamber; Adr is the equivalent areas
of pneumatic piston in the right chamber; AhAl is the
equivalent areas of hydraulic piston A in the left
chamber; AhAr is the equivalent areas of hydraulic piston A in
the right chamber; AhBl is the equivalent areas of
hydraulic piston B in the left chamber; AhBr is the equivalent
areas of hydraulic piston B in the right chamber; Pdl is
the air pressure in the left pneumatic chamber; Pdr is the
air pressure in the right pneumatic chamber; PhAl is the
oil pressure of hydraulic cylinder A in the left chamber;
PhAr is the oil pressure of hydraulic cylinder A in the right
chamber; PhBl is the oil pressure of hydraulic cylinder B
where Aep is the effective area of the air ports; ph is the
upstream side pressure; pl is the downstream side
pressure; κ is the specific heat ratio; Th is the upstream side
temperature.
in the left chamber; PhBr is the oil pressure of hydraulic
cylinder B in the right chamber.
What is more, Ff is the force of the friction; Fc and Fs
are force of coulomb friction and maximum static force
of friction, respectively; L stands for the piston stroke,
and C is the viscous friction factor.
2.5 Hydraulic Pressure Equation
The continuous equations of the hydraulic in the left and
right chambers can be written as [
22
]:
dpdl
dt
dpdr
dt
β
= V (QAin − QAout − AhAl u),
β
= V (QBin − QBout + AhAr u),
where QAin is the input flow in hydraulic chamber A;
QAout is the output flow in hydraulic chamber A; QBin is
the input flow in hydraulic chamber B; QBout is the
output flow in hydraulic chamber B; β is the effective bulk
modulus.
2.6 Flow Equation
Volume flow of hydraulic oil through check valve can be
written as follows [
23
]:
Q = Cd Aeh
2(ph − pl ) ,
ρ
where Cd is the flow factor of orifice of check valve, and ρ
is the density of hydraulic oil.
2.7 Hydraulic Motor Equations
As shown from Figure 1, upstream of the hydraulic
motor is directly connected to the output of hydraulic
chambers, and the downstream to oil tank, which the
hydraulic pressure is nearly equal to atmospheric
pressure. The basic equations of the working hydraulic motor
can be written as Eqs. (10) and (11), includes hydraulic
continuity equation and the moment equilibrium
equation described as follows:
qmotor = Cim(p1 − p2) + Cemp1 + Dm ddθtm + Vβ0 · ddpt1 ,
d2θm dθm
Dm(p1 − p2) = Jm dt2 + Bm dt + Gθm + TL, (11)
where qmotor is the hydraulic motor flow; Cim,Cem are
factors of internal and external leakage; pu, pd are motor
upstream and downstream pressures; Jm is the inertia
factor; Bm is the viscous damping factor; G is the spring
stiffness factor; θm is the motor output rotate speed; V0 is the
whole volume of motor chamber; TL is the whole other
external load.
3 Experimental Verification of the Mathematical
Model
As is shown in Figures 4 and 5, an experimental station
of expansion energy used air-powered vehicle was set up.
On the main output road there is a pressure sensor which
tests the output hydraulic pressure, which can also be the
upstream pressure of the motor; downstream pressure of
the motor is the atmospheric pressure as it directly
connects to the oil tank.
On output road of the pneumatic-hydraulic
transmission there still has a flow inductor which can measure the
output flow. The relief valve can make sure that the safety
of the system pressure. We considered that no hydraulic
flow passes through the regulator which means that the
flow sensor measures whole flow into the motor.
However, an over-high hydraulic system pressure will make
the hydraulic flow pass through the regulator more than
the over-loaded motor, which will to some extent affect
the final results of the tests. In addition, a revolving speed
measuring encoder is mounted on the motor shaft for
testing the motor rotating speed.
Considering the system safety and the common
characteristics, in the experiment a little-power hydraulic motor
Accumulator
Mechanical
Load
Source
of Air
Flow Gauge
Pneumatichydraulic
transmission
Oil Tank
Flow Gauge
HP Transformer
Air
Source
Regulator
Pressure
Gauge
Silencer Relief
Tank Valve
Figure 4 Sketch diagram of the air‑powered vehicle
Tank
Hydraulic
Motor
Accumulator
Relief Valve
Speed Encoder
Hydraulic Motor
Figure 5 Experimental station of the air‑powered vehicle
with a relatively low-power load is chosen. The hydraulic
regulator is set up to 2.0 MPa, and the pneumatic
pressure of the input air is 0.67 MPa. Through several groups
of experiments, the experimental curves were obtained
after several collections of the signals. Results of flow and
rotate speed of hydraulic motor from the experiments and
simulations are shown in Figures 6 and 7, respectively.
As shown in Figure 6, the simulation and
experimental results consist well with each other. Both curves from
simulations and experiments are similar to pulse curves.
However, the tops of the experimental curves are not
quite stable comparing to the simulation ones. The
reason for the instability is high stiffness of hydraulic system.
There will be disturbance when the pistons of
pneumatichydraulic transmission sharply shift. In addition, slight
lag happens when the transmission shifts phase, and that
is because in the hydraulic chambers the left hydraulic
fluid left blocks the motion of the pistons.
As shown in Figure 7, motor rotate curves of
simulation and experimental results match with each other, too.
Amplifiers of the simulation curve is higher than that of
4000
3500
)3000
n
i
/m2500
L
/(m2000
w
loF1500
1000
500
0
0
152
150
)
n
i
/m148
r
(
ed146
e
p
se144
t
a
t
o142
R
140
the experimental one, that’s because the regulator will
open when the hydraulic pressure is over-high, and part
of the flow separates from whole road through the motor,
and that will limit the lifting of the motor rotator speed
as the speed is related to the motor flow. What’s more,
the simulation result is much smoother than the
experimental one. In the curve of the experimental result the
sharps are caused by the limit of the encoder sensitivity.
4 Dynamic Characteristics of Expansion Energy
Used Air‑Powered Vehicle
Stability and comfort condition of output dynamic
characteristics of hydraulic system greatly reflect the working
performance and the service life. Researches on
influencing factors of the air-powered vehicle were carried
out for the optimization of sustainable energy vehicle.
Recent studies conclude that parameters such as input
air pressure (pin), pistons area ratio (An) and oil orifice (R)
in pneumatic and hydraulic cylinders will mostly
influence the dynamic characteristics of pneumatic-hydraulic
transmission. While for the expansion energy used
pneumatic-hydraulic transmission compared with the original
air-liquid transformer, structure of magnetic rings is the
main difference and mostly reflects the characteristics.
Dynamic characteristics of rotate speed and output
torque were studied, considering they can affect the
working condition and lifetime of the air-powered vehicle.
Rotate speed is determined by output flow which is mainly
created by extrusion of piston directly during the moving
time, and the flow through hydraulic motor establishes
pressure based on the outside mechanical load which
determines the output pressure of the hydraulic system
and then reflects the output torque. We take the average
rotate speed and torque values during each working
process under difference working condition which can directly
reflect the dynamic capability of the power system. What’s
more, variances of the output rotate speed and torque are
calculated which can reflect the volatility of the dynamic
characteristics and greatly affect the lifetime of the power
system. In order to illustrate the influence, for the
comparison, each parameter changes while other parameters keep
constant. Then we get the final results as follows.
4.1 Influence of Input Pressure on Dynamic Characteristics
As the energy source of power system, input pressure is
usually used to reflect the output characteristics of
pneumatic-hydraulic transmission. In the simulation, when
areas ratio (n) is set to 8, oil orifice (R) is set to 2.5 mm
and input pressure (pin) is set to 0.55 MPa, 0.65 MPa, and
0.75 MPa, the output dynamic characteristics of
air-powered vehicle is analyzed.
As is shown from Figure 8, it’s the torque curves of
power system. All the curves start rising at first, decline
Experimental Curve
Simulation Curve
Experimental Curve
Simulation Curve
0.5 1 1.5 2 2.5 3 3.5
Time / s
Figure 6 Simulation and experimental flow curves
4
4.5
5
0 1 2 3 4
Time (s)
Figure 7 Simulation and experimental rotate speed curves
5
Input Pressure = 0.55MPa
Input Pressure = 0.65MPa
Input Pressure = 0.75MPa
25
20
)
.15
m
N
(
e
u
rq10
o
T
5
01
1.2
1.4 1.6
Time (s)
1.8
2
smoothly for a moment when reach the top valve, and fall
down to the bottom sharply. That’s because the torque
is mainly directly obtained by output pressure which is
directly determined by external load. At first, when
output pressure is under the breakout pressure of hydraulic
motor, the pressure keeps rising when the piston keeps
moving and compressing the chamber space. This process
won’t last too long as the stiffness of hydraulic oil is high
enough. When the piston gets the position of one of the
magnetic ring, input air stops going into the pneumatic
chamber, and the piston moves forward as the pressed air
expands and the expansion energy will reduce, that’s why
the curves will smoothly decrease. As the piston gets the
position of one of the switch rings, the piston changes the
moving direction, and the pressure of the chamber will
release as it is connected to the atmosphere. So the
toquetime curves present statement as shown in Figure 8.
As is shown from Figure 9, curves of rotate speed are
similar to those of the output torque. That’s because
rotate speed is related with the output flow of the motor
which is immediately obtained by orifice throttle formula,
and pressure between output chamber and inlet port of
the motor directly makes up the output flow through the
orifice of the chamber.
From Figures 10 and 11, in the system, higher the input
air pressure is, higher the average torque and rotate
speed are. Variances of torque and rotate speed won’t
apparently change. So the input air pressure should be set
according to the request of the practical loads.
4.2 Influence of Area Ratio on Dynamic Characteristics
Directly piston area ratio determines the pressurizing
level. In the simulation, when input pressure (pin) is set to
0.65 MPa, oil orifice (R) is set to 2.5 mm and areas ratio
(n) is set to 6, 8, and 10, the output dynamic
characteristics are studied as follows.
300
As shown of Figures 12 and 13, comparing with input
air pressure, area ratio of power system will much more
influence the output dynamic characteristics. From the
figures, when area ratio is set to 6, the output torque
and the rotate speed curves won’t have sharp shocks and
the curves are relatively smooth. As the area ratio is set
larger, sharp points appear every working circle time.
From Figures 14 and 15, average torque and rotate
speed curves increase at beginning of the circles and
then reduce a lot. The highest point is at the time when
the area ratio is set to 8. Instead, torque and rotate speed
variances reduce at first and increase then. Similarly, the
lowest point is at the time when the area ratio is 8. So
area ratio of the power system is considered to be set to
approximate 8, which makes the system output capacity
the highest and the dynamic characteristics the best.
4.3 Influence of Orifice on Dynamic Characteristics
In the simulation, when input pressure (pin) is set to fixed
0.65 MPa and areas ratio (n) is set up to 8, we set the oil
orifice (R) of the hydraulic chamber to 2.5 mm, 3.0 mm
and 3.5 mm, and the dynamic characteristics is analyzed.
Figures 16 and 17 show the condition of output
dynamic characteristics influenced by orifice of the
hydraulic chambers. It can be seen that valve of orifice
effects the characteristics of the air-power system greatly.
Based on the principle of oil through orifices throttling,
the larger orifice is, the bigger output flow coefficient
is. When the orifice is larger, the output flow will be
promoted, and then it will obtain a higher rotate speed.
The period of the rotate speed curves will be shorten
when the output flow is relatively higher, too.
As we can see from Figures 18 and 19, a larger orifice
will increase the output capacity of the system, including
higher output torque and system rotate speed, which
will allow the power system to drive a larger mechanical
load. But when the orifice is too big, it will break the
orifices throttling principle, which will disturb the pressure
building of the system in the output chamber. As shown
of all the figures above, under the condition of the
experiment, the orifice is considered to be set about 2.5 mm.
4.4 Influence of Magnetic Ring on Dynamic Characteristics
Position of magnetic switch can be a key parameter of
power system which can increase the system efficiency.
When the piston stroke is set 1100 mm, orifice of output
hydraulic chamber (Rp) is set to 2.5 mm, input pressure of
air source (Pin) to 0.65 MPa, and area ratio of pistons (Ap)
is set to 6, position of the magnetic switch (Lm) is set to
0.015 m, 0.020 m and 0.025 m, then we got the simulation
results as follows.
The position of the magnetic ring is considered to be
the key parameter of the structure of
pneumatic-hydraulic transmission. As shown from Figures 20 and 21, when
the position of the magnetic ring is set farther, the circle
period of the curves will not be changed apparently, but
they will be smoother from a whole view. That’s because a
farther position of the magnetic ring will not be obvious
comparing with the whole piston stroke.
From Figure 22, farther position of the rings will
promote the torque and the speed of the power system.
When it is set lower than 20 mm, it will increase sharply.
When it is set above 20 mm, the speed of the increase
will become slow. Figure 23 shows that the farther the
position is, the smaller the variances of torque and rotate
speed will be. In addition, if the position is set too far, the
piston will hardly get the magnetic switch, and the
piston will stop moving. So for better output dynamic
characteristics of the power system, the position setting of
the magnetic ring can be about 20 mm when the piston
stroke is 1100 mm.
Figure 23 Torque and rotate speed variance trend curves
5 Conclusions
In this paper, for setting the foundation of the
performance optimization of sustainable energy vehicle, a new
type of expansion energy used air-powered vehicle is
proposed, and the mathematical model and output dynamic
characteristics were analyzed by studying influences of
the key parameters. Finally we get conclusions as follows:
(1) Simulation and experimental results are consistent
with each other which demonstrate the mathematic
model to be effective.
(2) For the system of sustainable energy vehicle, input
air pressure won’t influence the dynamic
characteristics and should be set according to the request of
the practical loads.
(3) As a key parameter of the structure of the
pneumatic-hydraulic transmission, area ratio of the
system is considered to be set to 8 approximately
which makes system output capacity highest and
dynamic characteristics best.
(4) A bigger orifice with a limit will promote the
dynamic characteristic property of the power
system, but an oversize orifice will cause instability and
even make the principle of the orifices throttling
invalid. It is considered to be about 20 mm in the
simulation.
(5) Farther position of the rings will increase the
quality of output dynamic characteristics, but piston
will stop working with too far position of the rings.
This paper provides a basis for optimization of
sustainable energy vehicle, especially in the field of compressed
air-driven air-powered vehicle with pneumatic-hydraulic
transmission.
Authors’ contributions
All authors read and approved the final manuscript.
Author details
1 School of Automation Science and Electrical Engineering, Beihang Uni‑
versity, Beijing 100191, China. 2 The State Key Laboratory of Fluid Power &
Mechatronic Systems, Zhejiang University, Hangzhou 310027, China.
Authors’ Information
Xiang‑Heng Fu born in 1983, is currently a PhD candidate at School of
Automation Science and Electrical Engineering, Beihang University, China. He received his
master degree on mechano‑ electronic from Beihang University, China, in 2013.
Mao‑Lin Cai born in 1972, is currently a professor at School of Automation
Science and Electrical Engineering, Beihang University, China. His main research
direction includes pneumatic and hydraulic fluidics, compressed air energy
storage, pneumatic pipe line system.
Yi‑ Xuan Wang born in 1989, is currently a PhD candidate at School of
Automation Science and Electrical Engineering, Beihang University, China. He
received his master degree on mechano‑ electronic from Beihang University,
China, in 2015.
Yan Shi born in 1981, is currently an associate professor at School of
Automation Science and Electrical Engineering, Beihang University, China. He received
his PhD degree on mechanical engineering from Beihang University, China. His
research interests include intelligent mechanical devices and energy‑saving
technologies of pneumatic system.
Acknowledgements
Supported by National Natural Science Foundation of China (Grant No.
51375028).
Competing interests
The authors declare that they have no competing interests.
Ethics approval and consent to participate
Not applicable.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in pub‑
lished maps and institutional affiliations.
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