applied
sciences
Article
Simulation Analysis and Experiment of
Variable-Displacement Asymmetric Axial
Piston Pump
Youshan Gao 1,2 , Jie Cheng 1 , Jiahai Huang 2, * and Long Quan 2
1
2
*
College of Mechanical Engineering, Taiyuan University of Science and Technology, Taiyuan 030024, China;
[email protected] (Y.G.); [email protected] (J.C.)
Institute of Mechatronic Engineering, Taiyuan University of Technology, Taiyuan 030024, China;
[email protected]
Correspondence: [email protected]; Tel.: +86-351-6014-956
Academic Editor: Antonio Ficarella
Received: 1 December 2016; Accepted: 22 March 2017; Published: 27 March 2017
Abstract: The variable displacement pump control system has greater energy-saving advantages
and application prospects than the valve control system. However, the variable displacement pump
control of differential cylinder is not concurrent with the existing technologies. The asymmetric
pump-controlled cylinder is, therefore, used to balance the unequal volume flow through a single
rod cylinder in closed-circuit system. This is considered to be an effective method. Nevertheless,
the asymmetric axial piston pump (AAPP) is a constant displacement pump. In this study,
variable-displacement asymmetric axial piston pump (VAPP) is investigated according to the same
principle used in investigating AAPP. This study, therefore, aims at investigating the characteristics
of VAPP. The variable-displacement output of VAPP is implemented by controlling the swash plate
angle with angle feedback control circuit, which is composed of a servo proportional valve and
an angular displacement sensor. The angular displacement sensor is connected to the swash plate.
The simulation model of VAPP, which is set up through the ITI-SimulationX simulation platform, is
used to predict VAPP’s characteristics. The purpose of implementing the experiment is to verify the
theoretical results. Both the simulation and the experiment results demonstrated that the swash plate
angle is controlled by a variable mechanism; when the swash plate angle increases, the flow of Port B
and Port T increases while the response speed of Port B and Port T also accelerates. When the swash
plate angle is constant, the flow of Port B and Port T increases along with the increase of pump speed,
although the pressure-response speed of Port B is faster than that of Port T. Consequently, the flow
pulsation of Port B and Port T tends to decrease gradually along with the increase of pump speed.
When the pressure loaded on Port B equals to that of Port T, the flow ripple cycle of Port B is longer
than that of Port T, whereas the peak flow of Port B is higher than that of Port T. Since the flow ripple
of Port T is bigger than that of Port B, Port T should be connected to the low pressure sides or the oil
tank so that it does not affect VAPP’s performance. Further, to avoid the backflow of VAPP from Port
T to Port B, Port T cannot be loaded alone, and the loading pressure of Port T also cannot exceed that
of Port B.
Keywords: variable-displacement; asymmetric axial piston pumps; angle feedback control loop; flow
ripple; pressure fluctuation
1. Introduction
Electro-hydraulic system is widely used in a number of factories and mobile machines such as
excavators and cranes. Its hydraulic system has very high power density compared to electricity-
Appl. Sci. 2017, 7, 328; doi:10.3390/app7040328
www.mdpi.com/journal/applsci
Appl. Sci. 2017, 7, 328
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operated systems and machine-drive systems. Electro-hydraulic systems can be divided into two
major categories: valve-controlled systems and pump-controlled (displacement-controlled) systems.
The former mode responds quickly, controls accurately, and its hydraulic system circuit is simple.
Thus, it has widely been used in modern industry, machinery and equipment. The drawbacks of the
valve-controlled system are: (1) a large percentage of power loss in the process of the measure flow
going through the direction control valves; (2) throttling loss causes much heat loss, hence a cooling
device is required, which increases the overall installation power and the cost of the system; (3) the oil
source is easily polluted because of the open loop; and (4) its consumption of oil is high. Moreover,
environmental pollution is anticipated to occur in the process of dealing with waste oil [1].
Compared with the valve-controlled system, the alternative circuit can considerably reduce or
eliminate losses and provide significant energy saving. In 1994, Hewett patented a closed-circuit
displacement control idea, wherein a two-position three-way valve is used to connect the charge line
to the low-pressure side of a single rod cylinder when volumetric flow compensation is required [2].
A similar concept was independently proposed by researchers in British Columbia in 1995 [3]. Further,
in 1998, a closed-circuit displacement-controlled actuation solution was proposed by Ivantysynova,
in which a variable displacement pump controls the motion of a single or double-rod cylinder.
This solution has since been developed by her team [4,5]. An open-circuit configuration may also be
used for displacement control [6]. The pump-controlled system has higher energy efficiency and linear
dynamic characteristics compared with the traditional valve control [7]. In 2012, Wang et al. presented
a new scheme of a closed hydraulic circuit for a single rod cylinder. In this, the unequal flow rate is
balanced through one of the pilot operated check valves to the low-pressure side whose pressure is
close to the charge pump [8].
As mentioned above, the pump control system has great energy-saving advantages and application
prospect, and has been improved in the way of symmetrical cylinder control. Nonetheless, for the
single rod symmetrical cylinder, two hydraulic pump, or hydraulic transformer or hydraulic valve
is used to exchange asymmetric flow. To reduce these inadequacies, Quan presented an asymmetric
pump-controlled asymmetric cylinder strategy for balancing the unequal volumetric flow through
a single rod cylinder in closed-circuit [9]. In 2013, Zhang et al. [10] developed a prototype of fixed
displacement asymmetric axial piston pump (AAPP) with three suction/discharge ports in its rear case.
The pump’s performances such as discharge pressure characteristics were investigated. The test result
demonstrated that the volumetric efficiencies of AAPP were all more than 94.5% within the range of
21 MPa and were also equal to those of existing two-port pumps with the same displacement. Later,
in 2014, the pumping dynamics of the fixed displacement AAPP were studied. The optimization of
valve plate profile was carried out to reduce the amplitude of the pressure fluctuation and flow ripples.
A fixed displacement pump prototype was manufactured and some qualitative tests conducted on
the test rig [11]. Compared with the above methods, the asymmetric pump-controlled system has the
advantage of small size, compact structure, low cost, kinetic, and potential energy recovery.
Accordingly, the displacement of AAPP [9–11] is constant. In this paper, variable-displacement
asymmetric axial piston pump (VAPP) is studied on the same principle with AAPP [8–11].
2. Operation Principle of VAPP
Considering variable control, the variable-displacement mechanism of VAPP includes manual
control, mechanical control, electric control, hydraulic control and electro-hydraulic control for it to achieve
displacement control, pressure control, flow control, power control and some composite control. As
per the AAPP’s control differential cylinder hydraulic system requirements, the variable-displacement
control unit is composed of a servo-proportional valve and symmetric hydraulic control cylinder
(SHCC) (as shown in Figure 1a). The servo proportional valve and the angular displacement sensor,
steadily connected with the swash plate, are used to compose the closed-loop control mode. By
controlling the size and direction of swash plate angle of the asymmetric pump, the control of VAPP
bi-directional variable displacement is attained. Thus, it meets the condition of quick dynamic response
Appl. Sci. 2017, 7, 328
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Appl. Sci. 2017, 7, 328 3 of 16 Appl. Sci. 2017, 7, 328 and optimal energy
3 of 16 cylinder.
In
efficiency. Figure 1b illustrates the loop principle to control differential
the loop principle to Bcontrol differential cylinder. In openings
Figure 1, inPort Port B and Port T are the Figure
1, Port
A, Port
and Port
T are the inlet/outlet
the A, valve
plate.
the loop principle to control differential cylinder. In Figure 1, Port A, Port B and Port T are the inlet/outlet openings in the valve plate. inlet/outlet openings in the valve plate. 8
8
Angle
Senor
Angle
Senor
Controller
B
B
M
3~
M
3~
T
T
A
Controller
(a)
(a)
A
(b)
(b)
Figure 1. (a) The principle of variable mechanism; and (b) the loop principle to control differential Figure 1. (a) The principle of variable mechanism; and (b) the loop principle to control differential
Figure 1. (a) The principle of variable mechanism; and (b) the loop principle to control differential cylinder [10]. cylinder [10].
cylinder [10]. 3. The Mathematical Model of VAPP 3. The Mathematical Model of VAPP
3. The Mathematical Model of VAPP AAPP has 40 cc/rev geometric volume. The design parameters of the AAPP are shown in the AAPP has 40 cc/rev geometric volume. The design parameters of the AAPP are shown in the
AAPP has 40 cc/rev geometric volume. The design parameters of the AAPP are shown in the literature [10]. The principle of variable‐displacement asymmetric pump is indicated in Figure 2. literature [10].
The
ofof variable-displacement
asymmetric
pump
is indicated
in Figure
2. VAPP
literature [10]. The principle
principle variable‐displacement asymmetric pump is indicated in Figure 2. VAPP uses a variable mechanism to adjust the swash plate angle in this way so that it can control the uses
a
variable
mechanism
to
adjust
the
swash
plate
angle
in
this
way
so
that
it
can
control
the
size
VAPP uses a variable mechanism to adjust the swash plate angle in this way so that it can control the size and direction of displacement. By setting unidirectional unloading triangular tank in the and direction
of displacement.
By setting
unloadingunloading triangular triangular tank in the tank distribution
size and direction of displacement. By unidirectional
setting unidirectional in the distribution plate, VAPP can reduce the impact of pressure pulsation. plate,
VAPP
can
reduce
the
impact
of
pressure
pulsation.
distribution plate, VAPP can reduce the impact of pressure pulsation. Figure 2. The schematic diagram representing the variable‐displacement asymmetric pump. Figure 2. The schematic diagram representing the variable‐displacement asymmetric pump. Figure 2. The schematic diagram representing the variable-displacement asymmetric pump.
The angle β of the swash plate type VAPP is one of the key parameters of displacement control. The angle β of the swash plate type VAPP is one of the key parameters of displacement control. In the variable mechanism, x
The angle β of the swashi is the displacement of spool deviated from the zero location. When the plate type VAPP is one of the key parameters of displacement control.
In the variable mechanism, x
i is the displacement of spool deviated from the zero location. When the solenoid receives a control signal, a proportional electromagnetic force acts on the spool and causes In the variable mechanism, xi is the displacement of spool deviated from the zero location. When the
solenoid receives a control signal, a proportional electromagnetic force acts on the spool and causes it to move against the return Valve ports on both sides the valve open; solenoid
receives
a control
signal,spring. a proportional
electromagnetic
forceof acts
onservo the spool
andare causes
it
it to move against the return spring. Valve ports on both sides of the servo valve are open; high‐pressure oil in the hydraulic system flows from the servo valve into the SHCC chamber. In this to move against the return spring. Valve ports on both sides of the servo valve are open; high-pressure
high‐pressure oil in the hydraulic system flows from the servo valve into the SHCC chamber. In this process, the piston rod moves x
0 degrees. At this time, the oil
in the hydraulic system flows0, and makes the swash plate to rotate β
from the servo valve into the SHCC chamber.
In this process, the
process, the piston rod moves x
0
, and makes the swash plate to rotate β
0
degrees. At this time, the servo valve opening size is expressed as x
0 − xi. The hydraulic oil in the other chamber of the piston
rod moves x0 , and makes the swashv = x
plate
to rotate β0 degrees. At this time, the servo valve
servo valve opening size is expressed as x
v = x0 − xi. The hydraulic oil in the other chamber of the SHCC flows back to the tank through the other opening of the servo valve, and vice versa. Figure 3 SHCC flows back to the tank through the other opening of the servo valve, and vice versa. Figure 3 shows the control relation diagram of the asymmetric pump variable mechanism. shows the control relation diagram of the asymmetric pump variable mechanism. Appl. Sci. 2017, 7, 328
4 of 16
opening size is expressed as xv = x0 − xi . The hydraulic oil in the other chamber of the SHCC flows
back to the tank through the other opening of the servo valve, and vice versa. Figure 3 shows the
control
relation diagram of the asymmetric pump variable mechanism.
Appl. Sci. 2017, 7, 328 4 of 16 Figure 3. The control relation diagram of the variable mechanism. Figure 3. The control relation diagram of the variable mechanism.
The connection between the displacement of piston rod xp and the rotated degree of swash plate The connection between the displacement of piston rod xp and the rotated degree of swash plate
β can be expressed as β can be expressed as
xxpp
ββ= arctg
(1)
arctg L (1)
Ld
d
In the equation, Ld is the force arm of the SHCC, which acts on the swash plate. Note VAPP
rotation
speed
is n, and
number
pistons
is SHCC, z. Thus,which the average
theory
flow isplate. givenNote by VAPP In the equation, Ldthe
is the force of
arm of the acts on the swash rotation speed is n, and the number of pistons is z. Thus, the average theory flow is given by πd2k znR tan β
Qpt =
(2)
πdγk2+
znR
tanββsin γ)
2(cos
tan
Qpt =
(2)
（
2 cosγ+tanβ sin γ）
where dk is the plunger diameter and R is the distribution circle radius of the plunger, β is the tilted
degree
the swash plate, z is the number of pistons, and γ is the degree between the piston axis and
where dofk is the plunger diameter and R is the distribution circle radius of the plunger, β is the tilted the
cylinder axis. Therefore, the instantaneous flow Qpi of ith piston is expressed as
degree of the swash plate, z is the number of pistons, and γ is the degree between the piston axis and the cylinder axis. Therefore, the instantaneous flow Qpi of ith piston is expressed as πd2 x p
Rω sin φi
Qpi = πdk 2 x ×
(3)
i φi sin γ)
4 k p cos γ( LdRω
− sin
x p cos
Qpi =

(3)
4
cos γ( Ld  xp cos i sin γ)
where φi is the round angle of the ith cylinder, and ω is the rotational speed of the cylinder block.
For ia is the round angle of the ith cylinder, and ω is the rotational speed of the cylinder block. VAPP with an odd number of pistons, if the conditions 0 ≤ φi ≤ πz , k = z+2 1 and πz ≤ φi ≤
where φ
2π
z −1
= 2 are met, then the instantaneous output flow Qp of VAPP is given by π
z1
z , k For and a VAPP with an odd number of pistons, if the conditions 0  i  , k 
z
2
2
πdk Rωx p ( Ld + x p tan γ) k
sin φ
π
2π
z1
(4)
, k 
Qare met, then the instantaneous output flow Q
 i 
p =
∑ ( Ld − x p cos iφp of VAPP is given by 4 cos γLd
z
z
2
i tan γ )
i =1
πdk Rωx
γ) k
For the instantaneous cylinder
pressure,
the
i angular position of the cylinder
p ( Ld  x pptan
ki with respect tosin
Qp =
(4)
block, φ, with φ = ω ·t and dφ = ω ·dt, is4 cos
given
by
Reference
[12,13]:
γLd
( Ld  xp cos i tan γ)
2

i 1
q
2
For the instantaneous cylinder pressure, p
ki with respect to the angular position of the cylinder E
Q
−
sign
p
−
p
C
A
p
−
p
(
)
|
|
op
pi
ki
di
d
di
ρ ki
dpki
=− (5)
block, φ, with φ = ω∙t and dφ = ω∙dt, is given by Reference [12,13]: 2
dφ
Rπdk tan β
cos φi
1
ω Vo −
−
4
cos γ+tan β sin γ
cos γ−cos φi tan β sin γ


2
E  Qpi  sign  pki  pdi  Cd Aop
pki  pdi 


dpkipump delivery pressure,
where pdi is the
pki is the instantaneousρpressure of ith piston chamber, ρ is


(5)
2
the density ofdφ
oil, Cd is the flow
Aop is the instantaneous
  area of ith
Rπddischarge
tan β  coefficient,
cos φi discharge
1
k

ω  Vvolume


piston, Vo is the nominal
of
chamber whenthe swash plate angle a is zero,
and E is
 o
4 a piston
 cos γ  tan β sin γ cos γ  cos φi tan β sin γ  

the oil bulk modulus which is affected by pressure and temperature [14].
di is the pump delivery pressure, p
ki is the instantaneous pressure of ith piston chamber, ρ is where p
When
swash plate angle β was changed,
the angular acceleration of the slipper relative to the
the density of oil, C
op is the instantaneous discharge area of ith cylinder
is expressedd is the flow discharge coefficient, A
as
piston, Vo is the nominal volume of a piston chamber when the swash plate angle a is zero, and E is the oil bulk modulus which is affected by pressure and temperature [14]. When swash plate angle β was changed, the angular acceleration of the slipper relative to the cylinder is expressed as Appl. Sci. 2017, 7, 328
5 of 16
as = ω 2 Rtg( 2π
z ) cos( φ1 +
R[1 − cos(φ1 +
2ωR sin(φ1 + 2πi
2πi
z ) dx p
z )+
Ld
dt +
d2 x p
( L2d + x2p ) 2 −2x p (
2πi
dt
)]{
z
Ld ( L2 + x2p )
dx p 2
dt )
d
+ 2x p Ld (
dx p 2
dt ) }
(6)
The variable resistance torque, Md , needs to be overwhelmed for the symmetric hydraulic control
cylinder to control the swash plate angle. Variable resistance torque Md -mainly includes torque
Mh -acting on the swash plate by the hydraulic pressure through the piston, Mbf -friction resistance
torque of spherical hinge, Mph -resistance torque (inertia force) of slipper component acting on the
swash plate, Msf -sliding friction resistance torque of the swash plate, and Mif -inertia resistance torque
of the swash plate itself. When Mif is ignored, the variable resistance torque is expressed as
πd2k Rpd
±∑
cos(φ + ia)
4 cos2 β
i =1
z
Md =
!
−
as m ps R z−1
cos(φ + ia)
cos2 β i∑
=1
!
+
πd2k zpd ( R f 1 + r f 2 )
8 cos β
(7)
where pd is the pump delivery pressure, α is the angle between piston hole, mps is the sum of the mass
of piston and shoe, r is the radius of ball head, and f 1 is the sliding friction coefficient between the
swash plate and the shoe. f 2 is the sliding friction coefficient between the ball head and the shoe.
f 2 = 0.08.
The variable resistance FLb controlling the swash plate angle is given by
Md
Ld
FLb =
(8)
The flow continuity equation for the variable cylinder is expressed as
QL = AP
dx p
Vt dp L
+ Ctb p L +
dt
4E dt
(9)
Ctb is the total leakage coefficient of the variable cylinder which is equal to the sum of the internal
and external leakage coefficients of the variable cylinder Ctb = Cib + C2eb .
It is assumed that the oil in the variable system cannot be compressed while ignoring the leakage
of the oil in the system. The dynamic equations of the variable system is, therefore, expressed as
m
d2 x p
dx p
+ Bp
+ Ksb x p + FLb = A p PL
dt
dt2
(10)
where m is the mass of moving parts, Bp is the viscous damping coefficient, Ap is the effective area of
piston, q is the flow in/out of hydraulic cylinder when load is driven, and Ksb is the spring stiffness
loaded on the variable cylinder.
The total hydraulic spring stiffness Kh of the two chambers of the variable cylinder is the
displacement function of the piston position. This can be given by the following equation
Kh = β e A2p
1
1
+
V01
V02
(11)
where V 01 is the initial volume of oil entering the chamber in the variable cylinder, and V 02 is the
initial volume of oil taken back from the chamber in the variable cylinder.
When V 01 = V 02 or the piston locates in the middle position, Kh is the minimum. At this time,
the variable cylinder has the lowest natural frequency and the stability of the system is the worst.
Variable system non-damping hydraulic natural frequency is given by
s
ωh =
4β e A2p
Vt m
(12)
Appl. Sci. 2017, 7, 328 6 of 16 Variable system non‐damping hydraulic natural frequency is given by Appl. Sci. 2017, 7, 328
ωh 
4 βe Ap2
Vt m
The damping ratio of variable system is expressed as
The damping ratio of variable system is expressed as s
s
Bp B p V Vt
KKcece βeβMe M
t
t
t
δδhh =
+
β m
22A
Ap p VtVt 2 A2A
p pβe m e
6 of 16
(12)
(13)
In the equation K
=K
Kcc + +CCtbtb, K
, Kce is the total flow‐pressure coefficient of the system, whereas is
In the equation Kcece = ce is the total flow-pressure coefficient of the system, whereas Kcc is the flow-pressure coefficient which represents the change of flow caused by changed pressure.
the flow‐pressure coefficient which represents the change of flow caused by changed pressure. 4. The Simulation Analysis of VAPP
4. The Simulation Analysis of VAPP The simulation
of variable
mechanism
of asymmetric
pump is
shownis inshown Figure 4.
The simulation model
model of variable mechanism of asymmetric pump in According
Figure 4. to the above mathematical analyses, VAPP simulation model is built by the simulationX. In Figure 4,
According to the above mathematical analyses, VAPP simulation model is built by the simulationX. Port A is the inlet of the pump, while Ports B and T are the outlets. Conversely when Port A is the
In Figure 4, Port A is the inlet of the pump, while Ports B and T are the outlets. Conversely when Port outlet, Ports B and T are the inlets. The flow ratio of A and B is 2:1, In this case, the pump can be used
A is the outlet, Ports B and T are the inlets. The flow ratio of A and B is 2:1, In this case, the pump can for used driving
enforcement
component.
The modelThe is composed
the variable
mechanism
be for asymmetric
driving asymmetric enforcement component. model is of
composed of the variable and
an
asymmetric
pump.
The
variable
mechanism
is
composed
of
variable
piston,
variable
spring,
mechanism and an asymmetric pump. The variable mechanism is composed of variable piston, angle displacement sensor, servo proportional valve and a constant pressure source.
variable spring, angle displacement sensor, servo proportional valve and a constant pressure source. Figure 4. The simulation analysis of VAPP. Figure 4. The simulation analysis of VAPP.
The oil pushed by constant pressure source flows in SHCC through servo‐proportional valves, The oil pushed
constant
pressure
source
flows
in SHCC spring throughforce, servo-proportional
and
and overcomes FLb, by
which is the resultant force of variable inertial force valves,
of variable overcomes FLb , which is the resultant force of variable spring force, inertial force of variable spring force,
spring force, inertial force of the swash plate and piston, and the disturbance torque. The oil pushes inertial
force of
the swash
plate
and piston,
and the disturbance
torque. The
pushes the the variable
the variable piston and the swash plate articulated with it. Further, PID oilcontrols flow of piston
and
the
swash
plate
articulated
with
it.
Further,
PID
controls
the
flow
of
servo-proportional
servo‐proportional valves dependent on the difference valve on the control signal and the angular valves dependent on the difference valve on the control signal and the angular displacement sensors.
displacement sensors. When the angle of swash plate in the simulation model of AAPP is set at 18◦ , and the pump
When the angle of swash plate in the simulation model of AAPP is set at 18°, and the pump speed, nn,, is 600 rpm, the pressure loaded on Ports B and T is 0 MPa while the oil supply pressure of is 600 rpm, the pressure loaded on Ports B and T is 0 MPa while the oil supply pressure
speed, of variable mechanism Psb is 3 MPa and the friction resistance of variable mechanism is 600 N.
Consequently, choosing stiffness of variable spring is 40 N/mm, 50 N/mm and 60 N/mm respectively,
which regulates the PID value to produce overshoot of piston displacement consistent in those cases.
Appl. Sci. 2017, 7, 328 7 of 16 Appl. Sci. 2017, 7, 328 Appl. Sci. 2017,
7, 328
variable mechanism 7 of 16 7 ofN. 16
Psb is 3 MPa and the friction resistance of variable mechanism is 600 Consequently, choosing stiffness of variable spring is 40 N/mm, 50 N/mm and 60 N/mm respectively, variable mechanism Psb is 3 MPa and the friction resistance of variable mechanism is 600 N. which regulates the PID value to produce overshoot of piston displacement consistent in those cases. Consequently, choosing stiffness of variable spring is 40 N/mm, 50 N/mm and 60 N/mm respectively, The displacement and force of variable piston is clearly presented in Figure 5. The variable piston
The displacement and force of variable piston is clearly presented in Figure 5. which regulates the PID value to produce overshoot of piston displacement consistent in those cases. responses are shown to be quick and able to reach the maximum displacement first when the angle
The variable piston responses are shown to be quick and able to reach the maximum displacement The displacement and from
force piston of
is spring
clearly in AtFigure 5. of swash
plate increases
0◦ toof 18◦variable , and the stiffness
Ksb presented is 60 N/mm.
this time,
first when the angle of swash plate increases from 0° to 18°, and the stiffness of spring Ksb is 60 N/mm. The variable piston responses are shown to be quick and able to reach the maximum displacement the variable force FLb is the maximum, at about 1750 N.
At this time, the variable force FLb is the maximum, at about 1750 N. first when the angle of swash plate increases from 0° to 18°, and the stiffness of spring Ksb is 60 N/mm. At this time, the variable force FLb is the maximum, at about 1750 N. (a) (b)
(a) (b)
Figure 5. The
The displacement
displacement and force of the variable piston: (a) the piston X; and (b) the Figure 5.
and
force
of the
variable
piston:
(a) the
piston
stroke,stroke, X; and (b)
the cylinder
cylinder force, F. Figure force, F.5. The displacement and force of the variable piston: (a) the piston stroke, X; and (b) the cylinder force, F. Similarly, when the angle of swash plate in the simulation model of AAPP is 18°, and the speed Similarly, when the angle of swash plate in the simulation model of AAPP is 18◦ , and the speed
of the pump is 600 rpm, then pressure loaded on Ports B and T is 0 MPa, Ksb is 50 N/mm, and friction of theSimilarly, when the angle of swash plate in the simulation model of AAPP is 18°, and the speed pump is 600 rpm, then pressure loaded on Ports B and T is 0 MPa, Ksb is 50 N/mm, and friction
resistance of variable mechanism is 600 N. The supply oil pressures of the variable mechanism Psb are of the pump is 600 rpm, then pressure loaded on Ports B and T is 0 MPa, Ksb is 50 N/mm, and friction resistance of variable mechanism is 600 N. The supply oil pressures of the
variable mechanism Psb
3 MPa, 4 MPa and 5 MPa, respectively, regulating PID value to generate an overshoot of piston resistance of variable mechanism is 600 N. The supply oil pressures of the variable mechanism Psb are are 3 MPa, 4 MPa and 5 MPa, respectively, regulating PID value to generate an overshoot of piston
displacement consistent in those cases. The displacement and force of variable piston is shown in 3 MPa, 4 MPa consistent
and 5 MPa, respectively, regulating PID value to generate an overshoot of piston displacement
in those
cases. The
displacement
and force
of variable
piston is shown
in
Figure 6, in which the angle of swash plate increases from 0° to 18°. The figure also illustrates that displacement consistent in those cases. The displacement and force of variable piston is shown in ◦
◦
Figure 6, in which the angle of swash plate increases from 0 to 18 . The figure also illustrates that
the variable piston responds quickly and reaches the maximum displacement first when oil supply Figure 6, in which the angle of swash plate increases from 0° to 18°. The figure also illustrates that the variable piston responds quickly and reaches the maximum displacement first when oil supply
pressure is 3 MPa. In order to avoid the mechanical impact of variable piston in the extreme position, the variable piston responds quickly and reaches the maximum displacement first when oil supply pressure is 3 MPa. In order to avoid the mechanical impact of variable piston in the extreme position,
it is needed to adjust PID parameter according to the change of parameter of variable mechanism. pressure is 3 MPa. In order to avoid the mechanical impact of variable piston in the extreme position, it is needed to adjust PID parameter according to the change of parameter of variable mechanism.
it is needed to adjust PID parameter according to the change of parameter of variable mechanism. (a) (b)
(a) )
Figure 6. The displacement and force of the variable piston: (a) the piston (bstroke, X; and (b) the cylinder force F. Figure 6. The displacement and force of the variable piston: (a) the piston stroke, X; and (b) the Figure 6. The displacement and force of the variable piston: (a) the piston stroke, X; and (b) the cylinder
cylinder force F. force F.
Equation (3) shows that the oil sucked and discharged by each piston chamber changes with the sine Equation (3) shows that the oil sucked and discharged by each piston chamber changes with the law. Conversely, Equation (5) indicates that the pressure of piston chamber is approximately Equation (3) shows that the oil sucked and discharged by each piston chamber changes with Q
the
equal to the atmospheric pressure during the suction phase, and was affected by the parameters pi, sine law. Conversely, Equation (5) indicates that the pressure of piston chamber is approximately sine
law.
Conversely,
Equation
(5)
indicates
that
the
pressure
of
piston
chamber
is
approximately
equal
ω
, C
d
, ρ and E
during the discharge oil phase. When VAPP speed is set at 1500 r/min and angle as 10°, equal to the atmospheric pressure during the suction phase, and was affected by the parameters Qpi, to the atmospheric pressure during the suction phase, and was affected by the parameters Qpi , ω, Cd , ρ
ω, Cd, ρ and E during the discharge oil phase. When VAPP speed is set at 1500 r/min and angle as 10°, Appl. Sci. 2017, 7, 328
8 of 16
Appl. Sci. 2017, 7, 328 8 of 16 and E during the discharge oil phase. When VAPP speed is set at 1500 r/min and angle as 10◦ , and
the pressure
of Ports
B andB Tand reliefT valve
set are at 0set MPa
the simulation
model, then
the pressure
and the pressure of Ports relief are
valve at in
0 MPa in the simulation model, then the and the flow
of one
of the
piston
chambers
as depicted
indepicted Figure 7.in The
figure
that
pressure and curve
the flow curve of one of the piston is
chambers is as Figure 7. shows
The figure the
pressure
of
piston
chamber
remains
constant
at
around
0
MPa
from
interval
bottom
dead
center
shows that the pressure of piston chamber remains constant at around 0 MPa from interval bottom (BDC)center to top (BDC) dead center
(TDC)
Port A.
The pressure
of Port
suddenly
6 MPa
when
dead to top dead incenter (TDC) in Port A. The A
pressure of rises
Port to
A about
suddenly rises to piston 6 passes
then reduces
about
MPareduces when piston
passes
the non-dead
pointpasses triangular
about MPa TDC.
when Itpiston passes to
TDC. It 4then to about 4 MPa when piston the groove andpoint reaches
Port T. The
pressure
of pistonPort chamber
reduces
to about
0 MPa
periodically
when
non‐dead triangular groove and reaches T. The pressure of piston chamber reduces to piston passes Port B, Port T, BDC and reaches Port A. The reason for the above phenomenon is that
about 0 MPa periodically when piston passes Port B, Port T, BDC and reaches Port A. The reason for the high
pressure
oil in the
discharging
port pours
piston
chamber instantaneously
when
the
the above phenomenon is oil
that the high pressure oil into
in the oil discharging port pours into piston piston
filled
with
low
pressure
oil
move
from
oil
suction
Port
A
to
oil
discharge
port.
Because
the
chamber instantaneously when the piston filled with low pressure oil move from oil suction Port A piston
rotates constantly,
the pressure
in therotates piston chamber
increases
gradually.
The piston piston begins
to
to oil discharge port. Because the piston constantly, the pressure in the chamber discharge
oil
when
the
pressure
in
the
chamber
is
the
same
as
the
pressure
in
the
oil
discharging
port.
increases gradually. The piston begins to discharge oil when the pressure in the chamber is the same At this time, because of the inertia of the fluid and the damping effect of the distribution flow port, the
as the pressure in the oil discharging port. At this time, because of the inertia of the fluid and the resistance of discharged oil is high at the beginning while the pressure in the piston chamber exceeds
damping effect of the distribution flow port, the resistance of discharged oil is high at the beginning the discharging pressure, thus becoming positive pressure overshoot. As the piston moves from the
while the pressure in the piston chamber exceeds the discharging pressure, thus becoming positive oil discharging
port As to the
suction
port,from the high
oildischarging pressure port
is connected
with theport, lowthe oil
pressure overshoot. the oil
piston moves the oil port to the oil suction pressure port in the piston chamber. Therefore, pressure is released, therefore, pressure is released and
high oil pressure port is connected with the low oil pressure port in the piston chamber. Therefore, therefore overshoots. This periodic change of the pressure and flow causes a periodic pulsation of the
pressure is released, therefore, pressure is released and therefore overshoots. This periodic change of oil in the piston chamber.
the pressure and flow causes a periodic pulsation of the oil in the piston chamber. Figure 7. Instantaneous cylinder pressure and flow without load at 1500 rpm. Figure 7. Instantaneous cylinder pressure and flow without load at 1500 rpm.
Piston speed is set at 900 r/min in the VAPP and the angle of the swash plate is 8°, 10° and 12°. Piston speed is set at 900 r/min in the VAPP and the angle of the swash plate is 8◦ , 10◦ and 12◦ .
Port A of the valve plate is for sucking oil, while Port B and Port T of the valve plate are for Port A of the valve plate is for sucking oil, while Port B and Port T of the valve plate are for discharging
discharging oil. The flow of Ports B and T changes over time, as shown in Figure 8. The flow of Ports oil. The flow of Ports B and T changes over time, as shown in Figure 8. The flow of Ports B and T
B and T increases along with the increase in the swash plate angle so that it could realize control of increases along with the increase in the swash plate angle so that it could realize control of variable
variable mechanism, as detailed in Figure 2. The angle of the indexing circle corresponding with Port mechanism, as detailed in Figure 2. The angle of the indexing circle corresponding with Port B and T
B and T of valve plate is 60° and 40°, respectively. When the angle of swash plate is 12°, the flow of of valve plate is 60◦ and 40◦ , respectively. When the angle of swash plate is 12◦ , the flow of Port B is
Port B is about 10.5 L/min while the flow of Port T is about 7.3 L/min. Since the indexing circle angle about 10.5 L/min while the flow of Port T is about 7.3 L/min. Since the indexing circle angle of Port B of Port B is bigger than that of Port T, the flow pulse period of Port B is longer than that of Port T. is bigger than that of Port T, the flow pulse period of Port B is longer than that of Port T. In addition,
In addition, the flow crest of Port B is higher than that of Port T. the flow crest of Port B is higher than that of Port T.
The angle of swash plate is set at 10◦ in the VAPP simulation model, pump speed at 600 rpm,
900 rpm and 1200 rpm, separately, and the pressure loaded on Ports B and T is 0 MPa. The flow of
Port B and Port T changes over time, as shown in Figure 9. As detailed in Figure 9, when the swash
plate angle is constant, the flow of Ports B and T increases along with the increase of pump speed
and the flow pulsation decreasing along with the increase of pump speed. When the pump speed is
1200 r/min, the flow of Port B is about 11 L/min, whereas the flow of Port T is about 7.8 L/min.
Appl. Sci. 2017, 7, 328
Appl. Sci. 2017, 7, 328 9 of 16
9 of 16 (a) (b)
Figure 8. Slots B and T output flow without load at 900 rpm: (a) Slots B output flow; and (b) Slots T output flow. The angle of swash plate is set at 10° in the VAPP simulation model, pump speed at 600 rpm, 900 rpm and 1200 rpm, separately, and the pressure loaded on Ports B and T is 0 MPa. The flow of (a) (b)
Port B and Port T changes over time, as shown in Figure 9. As detailed in Figure 9, when the swash plate angle is constant, the flow of Ports B and T increases along with the increase of pump speed Figure 8. Slots B and T output flow without load at 900 rpm: (a) Slots B output flow; and (b) Slots T Figure 8. Slots B and T output flow without load at 900 rpm: (a) Slots B output flow; and (b) Slots T
and the flow pulsation decreasing along with the increase of pump speed. When the pump speed is output flow. output flow.
1200 r/min, the flow of Port B is about 11 L/min, whereas the flow of Port T is about 7.8 L/min. The angle of swash plate is set at 10° in the VAPP simulation model, pump speed at 600 rpm, 900 rpm and 1200 rpm, separately, and the pressure loaded on Ports B and T is 0 MPa. The flow of Port B and Port T changes over time, as shown in Figure 9. As detailed in Figure 9, when the swash plate angle is constant, the flow of Ports B and T increases along with the increase of pump speed and the flow pulsation decreasing along with the increase of pump speed. When the pump speed is 1200 r/min, the flow of Port B is about 11 L/min, whereas the flow of Port T is about 7.8 L/min. (a) (b)
Figure 9. Slots B and T output flow without load: (a) Slots B output flow; and (b) Slots T output flow. Figure 9. Slots B and T output flow without load: (a) Slots B output flow; and (b) Slots T output flow.
When the pump speed is set at 600 r/min, the angle of swash plate separately at 8°, 10° and 12°, When the pump speed is set at 600 r/min, the angle of swash plate separately at 8◦ , 10◦ and 12◦ ,
and the pressure loaded on Ports B and T are 0 MPa and 10 MPa, separately, the flow of Ports B and and the pressure loaded on Ports B and T are 0 MPa and 10 MPa, separately, the flow of Ports B and
T and the pressure of piston chamber are as indicated in Figure 10. It is observable from Figure 10a T andthe thelarger pressure
of piston
aremake as indicated
in Figure
10. the It is set observable
fromquickly. Figure 10a
(a) chamber
(b)speed more that swash plate angle may the pump to reach In that
the
larger
swash
plate
angle
may
make
the
pump
to
reach
the
set
speed
more
quickly.
In
addition,
addition, it is evident from Figure 10a,c that the flow of Ports B and T increase along with the Figure 9. Slots B and T output flow without load: (a) Slots B output flow; and (b) Slots T output flow. it is evident from Figure 10a,c that the flow of Ports B and T increase along with the increase of swash
increase of swash plate angle. Since the working pressure of Port B was setting at 10 MPa, the flow plate angle. Since the working pressure of Port B was setting at 10 MPa, the flow pulsation decreases
pulsation decreases along with the increase of the swash plate angle, while the flow pulsation of Port When the pump speed is set at 600 r/min, the angle of swash plate separately at 8°, 10° and 12°, along with the increase of the swash plate angle, while the flow pulsation of Port T does not change
T does not change significantly. It is evident from Figure 10d that although the working pressure of and the pressure loaded on Ports B and T are 0 MPa and 10 MPa, separately, the flow of Ports B and significantly.
It is evident
from Figure
10d chamber that although
the working
pressure
of Port in B isthe constant,
Port B is constant, the pressure of piston increases along with the increase swash T and the pressure of piston chamber are as indicated in Figure 10. It is observable from Figure 10a the pressure of piston chamber increases along with the increase in the swash plate angle. When the
plate angle. When the swash plate angle is 8°, the maximum pressure of piston chamber is 11 MPa. that the larger swash ◦plate angle may make the pump to reach the set speed more quickly. In swash plate angle is 8 , the maximum pressure of piston chamber is 11 MPa. However, when the
However, when the swash plate angle is 12°, the maximum pressure of piston chamber is 13 MPa. addition, it is evident from Figure 10a,c that the flow of Ports B and T increase along with the swash plate angle is 12◦ , the maximum pressure of piston chamber is 13 MPa.
increase of swash plate angle. Since the working pressure of Port B was setting at 10 MPa, the flow pulsation decreases along with the increase of the swash plate angle, while the flow pulsation of Port T does not change significantly. It is evident from Figure 10d that although the working pressure of Port B is constant, the pressure of piston chamber increases along with the increase in the swash plate angle. When the swash plate angle is 8°, the maximum pressure of piston chamber is 11 MPa. However, when the swash plate angle is 12°, the maximum pressure of piston chamber is 13 MPa. Appl. Sci. 2017, 7, 328
10 of 16
Appl. Sci. 2017, 7, 328 10 of 16 (a) (b)
(c) (d)
Figure 10. Ten megapascals load in Slots B at 600 rpm: (a) Slots B output pressure; (b) Slots B output Figure 10. Ten megapascals load in Slots B at 600 rpm: (a) Slots B output pressure; (b) Slots B output
flow; (c) Slots T output flow; and (d) instantaneous cylinder pressure. flow; (c) Slots T output flow; and (d) instantaneous cylinder pressure.
In the VAPP model, when the pump speed is set at 600 r/min, the angle of swash plate is 8°, 10° and separately, and the the
pressure loaded ison B r/min,
and Port are of
0 MPa 10 isMPa, In 12°, the VAPP
model,
when
pump speed
setPort at 600
the T angle
swashand plate
8◦ , 10◦
respectively. Under these circumstances, the flow of Ports B and T is as shown in Figure 11. ◦
and 12 , separately, and the pressure loaded on Port B and Port T are 0 MPa and 10 MPa, respectively.
As evident in Figure 11a, the flow of Port B has flow pulsation of about 2 L/min when swash plate Under these circumstances, the flow of Ports B and T is as shown in Figure 11. As evident in Figure 11a,
angle is 8°, 10° and 12°. As Figure 11b details, the flow of Port T changes in the periodic law, the flow of Port B has flow pulsation of about 2 L/min when swash plate angle is 8◦ , 10◦ and 12◦ .
although there is an observed discontinuous flow. The reason for this phenomenon is that the As Figure 11b details, the flow of Port T changes in the periodic law, although there is an observed
pressure is loaded on Port T, thus the internal flow from Port T to Port B is increased. In the actual discontinuous flow. The reason for this phenomenon is that the pressure is loaded on Port T, thus the
work of the pump, the phenomenon is not allowed. Therefore, Port T cannot be loaded alone or the internal
flow
from on Port
T toT Port
B isexceed increased.
In the actual
work
of theon pump,
the
pressure loaded Port cannot the pressure which is loaded Port B in phenomenon
the practical is
notapplications of VAPP. allowed. Therefore, Port T cannot be loaded alone or the pressure loaded on Port T cannot exceed
the pressure which is loaded on Port B in the practical applications of VAPP.
When the pump speed is set at 600 r/min, the angle of swash plate β is 8◦ , 10◦ and 12◦ , separately,
and the pressure loaded on Ports B and T is 10 MPa. The pressure and flow of Port B, Port T and the
piston chamber are as illustrated in Figure 12. As presented in Figure 12a,b, when the swash plate
angle is big, the response of Port B and Port T is quick. Figures 10a and 12c display that when the
pressure loaded on Port T is constant, more pressure is loaded on Port B and the flow becomes less.
By comparing Figures 8 and 11, it can be deduced that when the pressure difference between B and T is
great, the flow pulsation amplitude is large, and vice versa. The reason for this phenomenon is that the
pressure difference between Port B and Port T is large. Therefore, the flow between Port B and Port T
flow from the high-pressure area to the low-pressure area. It means that the flow would be stable if the
pressure is loaded simultaneously on Port B and Port T of the VAPP. As illustrated in Figure 12e, when
◦
the swash plate angle is 12
(a) , the pressure pulsation amplitude in the piston
(b) chamber is about 2 MPa.
However, when the swash plate angle is 8◦ the pressure pulsation amplitude is 1 MPa. In conclusion,
Figure 11. Ten megapascals load in Slots T at 600 rpm: (a) Slots B output flow; and (b) Slots T output flow. When the pump speed is set at 600 r/min, the angle of swash plate β is 8°, 10° and 12°, separately, and 12°, separately, and the pressure loaded on Port B and Port T are 0 MPa and 10 MPa, and the pressure loaded on Ports B and T is 10 MPa. The pressure and flow of Port B, Port T and the respectively. Under these circumstances, the flow of Ports B and T is as shown in Figure 11. piston chamber are as illustrated in Figure 12. As presented in Figure 12a,b, when the swash plate As evident in Figure 11a, the flow of Port B has flow pulsation of about 2 L/min when swash plate angle is big, the response of Port B and Port T is quick. Figures 10a and 12c display that when the angle is 8°, 10° and 12°. As Figure 11b details, the flow of Port T changes in the periodic law, pressure loaded on Port T is constant, more pressure is loaded on Port B and the flow becomes less. Appl. Sci. 2017,
7, 328is an observed discontinuous flow. The reason for this phenomenon is that 11 of
16
although there the By comparing Figures 8 and 11, it can be deduced that when the pressure difference between B and T pressure is loaded on Port T, thus the internal flow from Port T to Port B is increased. In the actual is great, the flow pulsation amplitude is large, and vice versa. The reason for this phenomenon is work of the pump, the phenomenon is not allowed. Therefore, Port T cannot be loaded alone or the for VAPP, when two discharging ports are under the same pressure, the pressure pulsation of the
that the pressure difference between Port B and Port T is large. Therefore, the flow between Port B pressure loaded on Port T cannot exceed the pressure which is loaded on Port B in the practical piston
chamber increases along with the increase in the swash plate angle.
and Port T flow from the high‐pressure area to the low‐pressure area. It means that the flow would applications of VAPP. be stable if the pressure is loaded simultaneously on Port B and Port T of the VAPP. As illustrated in Figure 12e, when the swash plate angle is 12°, the pressure pulsation amplitude in the piston chamber is about 2 MPa. However, when the swash plate angle is 8° the pressure pulsation amplitude is 1 MPa. In conclusion, for VAPP, when two discharging ports are under the same pressure, the pressure pulsation of the piston chamber increases along with the increase in the swash plate angle. In the VAPP model, pump speed is set at 1200 r/min, the angle of swash plate β separately is 8°, 10° and 12°, and the pressure loaded on Ports B and Port T is 10 MPa. Under this working condition, the pressure change overtime of Port B and Port T is as displayed in Figure 13. As shown in Figure 13a, when β = 8°, the pressure gradient stabilization time of Port B and Port T is 140 ms and 170 ms, respectively. When β = 12°, the pressure gradient stabilization time of Port B and Port T is 80 ms and 120 ms, respectively. This indicates that the larger the angle of the swash plate is, the quicker the pressure response speed can reach a stable (a) of the discharging port is. In addition, the system (b)
situation more quickly under the condition of even load. When the swash plate angle is constant, Figure 11. Ten megapascals load in Slots T at 600 rpm: (a) Slots B output flow; and (b) Slots T output flow. Figure 11. Ten megapascals load in Slots T at 600 rpm: (a) Slots B output flow; and (b) Slots T output flow.
the response of Port B is quicker than for Port T. (a) (b)
(c) (d)
Figure 12. Cont.
Appl. Sci. 2017, 7, 328
12 of 16
Appl. Sci. 2017, 7, 328 12 of 16 Appl. Sci. 2017, 7, 328 12 of 16 (e)
Figure 12. Ten megapascals load in Slots B and T, respectively at 600 rpm: (a) Slot B output pressure; Figure 12. Ten megapascals load in Slots B and T, respectively at 600 rpm: (a) Slot B output pressure;
(b) (b) Slot Slot T T output output pressure; pressure; (c) (c) Slots Slots B B output output flow; flow; (d) (d) Slots Slots T T output output flow; flow; and and (e) (e) instantaneous instantaneous
cylinder pressure. cylinder pressure.
In the VAPP model, pump speed is set at 1200 r/min, the angle of swash plate β separately is 8◦ ,
and 12◦ , and the pressure loaded on Ports B and Port T is 10 MPa. Under this working condition,
the pressure change overtime of Port B and Port T is as displayed in Figure 13. As shown in Figure 13a,
when β = 8◦ , the pressure gradient stabilization time of Port B and Port T is 140 ms and 170 ms,
respectively. When β = 12◦ , the pressure gradient stabilization time of Port B and Port T is 80 ms and
(e) the angle of the swash plate is, the quicker the
120 ms, respectively. This indicates that the larger
pressure
response speed of the discharging port is. In addition, the system can reach a stable situation
Figure 12. Ten megapascals load in Slots B and T, respectively at 600 rpm: (a) Slot B output pressure; more(b) quickly
condition
of even
load. flow; When
the
swash
plate flow; angleand is constant,
the response
Slot T under
output the
pressure; (c) Slots B output (d) Slots T output (e) instantaneous of Port
B is quicker than for Port T.
cylinder pressure. 10◦
(a) (b)
Figure 13. Ten megapascals load in Slots B and T, respectively at 1200 rpm: (a) Port B output pressure; and (b) Port T output pressure. 5. The Verification Experiment of VAPP According to the controlling method of variable mechanism in Figure 2, the principle of characteristic test of VAPP variable displacement is shown in Figure 14. The variable displacement system of asymmetric pump controls the angle and direction of the swash plate by controlling the flow direction of oil and the opening area of servo‐proportional valve. Thus, it can achieve accurate control of asymmetric pump displacement through setting the initial state of the swash plate at (a) (b)
meso‐position, or setting the swash plate angle at 0°. Pump 4 supplies oil for the left chamber when Valve 3 is in the left position. The swash plate articulated with the slider in the variable cylinder Figure 13. Ten megapascals load in Slots B and T, respectively at 1200 rpm: (a) Port B output pressure; Figure 13. Ten megapascals load in Slots B and T, respectively at 1200 rpm: (a) Port B output pressure;
rotates clockwise in this process, as chamber sucks the oil but Port B and Port T discharge oil. When and (b) Port T output pressure. and (b) Port T output pressure.
Valve 3 is in a meso‐position, the two chambers of variable cylinders do not suck oil, and when the swash plate is in meso‐position and A, B and T chambers do not discharge oil. When Valve 3 is in the 5. The Verification Experiment of VAPP 5. Theposition, Verification
Experiment
ofoil VAPP
right Pump 4 supplies to the right chamber, but this time, the swash plate rotates According to the controlling method of variable mechanism in Figure 2, the principle of anticlockwise and Chambers B and T suck the oil, while Chamber A discharges the oil. Among them, According to the controlling method of variable mechanism in Figure 2, the principle of
characteristic test of VAPP variable displacement is shown in Figure 14. The variable displacement dSpace
can collect the angle signal displacement
of the swash isplate and to the characteristic
test of
VAPP
variable
shown
in send Figureaccurate 14. The control variablesignals displacement
system of asymmetric pump controls the angle and direction of the swash plate by controlling the servo‐proportion valve. The loading on discharging Port B and Port T is realized by the relief valves. system of asymmetric pump controls the angle and direction of the swash plate by controlling the flow
flow direction of oil and the opening area of servo‐proportional valve. Thus, it can achieve accurate Figure 15 is the image of the VAPP that is used for the experiment, the physical photo of VAPP and direction of oil and the opening area of servo-proportional valve. Thus, it can achieve accurate control
control of asymmetric pump displacement through setting the initial state of the swash plate at test scene of VAPP can be found in Supplementary Materials. The angle displacement sensor, whose of asymmetric pump displacement through setting the initial state of the swash plate at meso-position,
meso‐position, or setting the swash plate angle at 0°. Pump 4 supplies oil for the left chamber when mode is MIDORI PRECISIONS CP‐2UK‐R260, is used for measuring the swash plate angle. Valve 3 is in the left position. The swash plate articulated with the slider in the variable cylinder The maximum input voltage of the sensor is 8 V, and it can detect the angle within ± 30 degrees. rotates clockwise in this process, as chamber sucks the oil but Port B and Port T discharge oil. When Valve 3 is in a meso‐position, the two chambers of variable cylinders do not suck oil, and when the swash plate is in meso‐position and A, B and T chambers do not discharge oil. When Valve 3 is in the right position, Pump 4 supplies oil to the right chamber, but this time, the swash plate rotates Appl. Sci. 2017, 7, 328
13 of 16
or setting the swash plate angle at 0◦ . Pump 4 supplies oil for the left chamber when Valve 3 is in the
left position. The swash plate articulated with the slider in the variable cylinder rotates clockwise
in this process, as chamber sucks the oil but Port B and Port T discharge oil. When Valve 3 is in a
meso-position, the two chambers of variable cylinders do not suck oil, and when the swash plate is in
meso-position and A, B and T chambers do not discharge oil. When Valve 3 is in the right position,
Pump 4 supplies oil to the right chamber, but this time, the swash plate rotates anticlockwise and
Chambers B and T suck the oil, while Chamber A discharges the oil. Among them, dSpace can collect
the angle signal of the swash plate and send accurate control signals to the servo-proportion valve.
The loading on discharging Port B and Port T is realized by the relief valves. Figure 15 is the image
of the VAPP that is used for the experiment, the physical photo of VAPP and test scene of VAPP
can be found in Supplementary Materials. The angle displacement sensor, whose mode is MIDORI
Appl. Sci. 2017, 7, 328 13 of 16 Appl. Sci. 2017, 7, 328 13 of 16 PRECISIONS CP-2UK-R260, is used for measuring the swash plate angle. The maximum input voltage
The model theRexroth 4WRPEH6C4B12L‐20/G24K0/A1M, is used for of theservo sensorproportion is 8 V, and valve, it can detect
angle within
± 30 degrees. The servo proportion
valve,
The servo proportion valve, model Rexroth 4WRPEH6C4B12L‐20/G24K0/A1M, is used for controlling the angle of the swash plate. The maximum input flow of the servo proportion valve is model Rexroth 4WRPEH6C4B12L-20/G24K0/A1M, is used for controlling the angle of the swash plate. controlling the angle of the swash plate. The maximum input flow of the servo proportion valve is 12 L. Further, input
the hydraulic flow meter, whose valve
model isis used for The
maximum
flow of the
servo
proportion
12PARKERSCLV‐PTQ‐300, L. Further, the hydraulic is flow
meter,
12 L. Further, the hydraulic flow meter, whose model is PARKERSCLV‐PTQ‐300, is used for measuring the flow and pressure of Port B and Port T. The maximum flow and pressure which can whose
model is PARKERSCLV-PTQ-300, is used for measuring the flow and pressure of Port B and Port
measuring the flow and pressure of Port B and Port T. The maximum flow and pressure which can be measured by the hydraulic flow meter is 300 L/min and 42 MPa separately. The directly operating T.
The maximum flow and pressure which can be measured by the hydraulic flow meter is 300 L/min
be measured by the hydraulic flow meter is 300 L/min and 42 MPa separately. The directly operating relief valve, model HUADE DBDS6P10B/315, is used for loading on Port B and Port T. The maximum and 42 MPa separately. The directly operating relief valve, model HUADE DBDS6P10B/315, is used
relief valve, model HUADE DBDS6P10B/315, is used for loading on Port B and Port T. The maximum set pressure of directly operating relief is 31.5 MPa. for loading on Port B and Port T. The maximum set pressure of directly operating relief is 31.5 MPa.
set pressure of directly operating relief is 31.5 MPa. M
3~
M
3~
4
4
u
pu
p
3
3
5
5
8
8
dSpace
dSpace
controller
controller
u
au
a qA
qA
u
au
a
2
A 2
A
1 M
1 M
3~
3~
qB
qB
B
B
T
T
7
7qT
6
6
qT
3 3
3 3
u
Au
A
Figure 14. The characteristic test principle of VAPP. Figure 14. The characteristic test principle of VAPP.
Figure 14. The characteristic test principle of VAPP. Figure 15. The VAPP prototype image. Figure 15. The VAPP prototype image. Figure 15. The VAPP prototype image.
Asymmetric pump speed is set at 600 r/min and swash plate angle at 18°. Port B and Port T take Asymmetric pump speed is set at 600 r/min and swash plate angle at 18°. Port B and Port T take 10 MPa and 20 MPa at two levels of pressure to load, respectively. The loading condition of the test Asymmetric pump speed is set at 600 r/min and swash plate angle at 18◦ . Port B and Port T
10 MPa and 20 MPa at two levels of pressure to load, respectively. The loading condition of the test includes two kinds: loading on Port B alone and loading on both Port B and Port T. Collecting the take 10 MPa and 20 MPa at two levels of pressure to load, respectively. The loading condition of the
includes two kinds: loading on Port B alone and loading on both Port B and Port T. Collecting the pressure signals of Ports B and T, respectively, in the experiment. The pressure of Port B under two test includes two kinds: loading on Port B alone and loading on both Port B and Port T. Collecting
pressure signals of Ports B and T, respectively, in the experiment. The pressure of Port B under two different pressure levels is depicted in Figure 16a, when the pressure is loaded on Port B alone. different pressure levels is depicted in Figure 16a, when the pressure is loaded on Port B alone. As shown in the image, the results got from the simulation process are consistent with the results As shown in the image, the results got from the simulation process are consistent with the results obtained from the experiment. The pressure pulsation of Port B increases along with the increase of obtained from the experiment. The pressure pulsation of Port B increases along with the increase of pressure loaded on Port B. The total pulsation amplitude is still small, thus the system performance pressure loaded on Port B. The total pulsation amplitude is still small, thus the system performance is good. The pressure of Ports B and T under four pressure levels is also shown in Figure 16b,c, is good. The pressure of Ports B and T under four pressure levels is also shown in Figure 16b,c, Appl. Sci. 2017, 7, 328
14 of 16
the pressure signals of Ports B and T, respectively, in the experiment. The pressure of Port B under
two different pressure levels is depicted in Figure 16a, when the pressure is loaded on Port B alone.
As shown in the image, the results got from the simulation process are consistent with the results
obtained from the experiment. The pressure pulsation of Port B increases along with the increase of
pressure loaded on Port B. The total pulsation amplitude is still small, thus the system performance
is good. The pressure of Ports B and T under four pressure levels is also shown in Figure 16b,c, in
which the pressure is loaded on Ports B and T at the same time. As detailed in the figure, the results
obtained from the simulation process are consistent with the results attained from the experiment.
The working pressure of Ports B and T fluctuate periodically around the loading pressure, and the
system performance is good. It can also be concluded that the pressure pulsation amplitude of Port T
is slightly bigger than that of Port B. The pulsation amplitude of flow increases synchronously when
loading of Ports B and T is equal. Figure 16d presents the test pressure of Port B when the port is
loaded alone and when Port T and Port B are loaded at the same time. The two sets of curves are
measured
respectively at pressure levels of 10 MPa and 20 MPa. It can be deduced from Figure14 of 16 16d that
Appl. Sci. 2017, 7, 328 pulsation amplitude of pressure when Port B is loaded alone is bigger than the pulsation amplitude of
pulsation amplitude of pressure when at
Ports B and time.
T are The
loaded at the amplitude
same time. ofThe pulsation pressure
when
Ports B and
T are loaded
the same
pulsation
pressure
when
amplitude of pressure when Port B is loaded alone is 1.5 times that of when both Port T and Port B Port B is loaded alone is 1.5 times that of when both Port T and Port B are loaded at the same time
are loaded at the same time and at the pressure level of 10 MPa. The pressure pulsation amplitude and
at the pressure level of 10 MPa. The pressure pulsation amplitude when Port B is loaded alone is
when Port B is loaded alone is 2.3 times that of when Ports T and B are loaded at the same time and 2.3 times that of when Ports T and B are loaded at the same time and pressure levels of 20 MPa.
pressure levels of 20 MPa. (a) (b)
(c) (d)
Figure 16. The comparison of experiment and simulation. (a) Slot B output pressure under Ten and Figure 16. The comparison of experiment and simulation. (a) Slot B output pressure under Ten and
twenty megapascals load alone in Slots B; (b) Slot B output pressure under Ten and twenty twenty megapascals load alone in Slots B; (b) Slot B output pressure under Ten and twenty megapascals
megapascals load in Slots B and T at the same time; (c) Slot T output pressure under Ten and twenty load in Slots B and T at the same time; (c) Slot T output pressure under Ten and twenty megapascals
megapascals load in Slots B and T at the same time; (d) Slot B output pressure under two different load in Slots B and T at the same time; (d) Slot B output pressure under two different operating
operating conditions and two pressure levels. conditions and two pressure levels.
When the pump speed is set at 1500 r/min and swash plate angle is 18°, the flow test result is as illustrated in Figure 17. The no‐load working condition of discharge Port B and Port T is presented in Figure 17a, whereas the working condition is indicated in Figure 17b, when discharging Port B and Port T are loaded at 10 MPa. As shown in the figure, the output flow of Ports B and T is 29 L/min and 20.5 L/min, respectively, when Port B and Port T are no‐load. The output flow of Ports B and T is 24.5 Appl. Sci. 2017, 7, 328
15 of 16
When the pump speed is set at 1500 r/min and swash plate angle is 18◦ , the flow test result is as
illustrated in Figure 17. The no-load working condition of discharge Port B and Port T is presented in
Figure 17a, whereas the working condition is indicated in Figure 17b, when discharging Port B and
Port T are loaded at 10 MPa. As shown in the figure, the output flow of Ports B and T is 29 L/min
and 20.5 L/min, respectively, when Port B and Port T are no-load. The output flow of Ports B and T is
24.5 L/min and 16 L/min, respectively, when Port B and Port T are loaded with pressure of 10 MPa.
The flow pulsation of each discharge oil port is small but the flow pulsation of Port T is bigger than
Appl. Sci. 2017, 7, 328 15 of 16 Port B.
(a) (b)
Figure 17. The volume flow test results of Port B and Port T. (a) Slots B and Slots T output flow under Figure 17. The volume flow test results of Port B and Port T. (a) Slots B and Slots T output flow under
zero megapascals load in Slots B and T; (b) Slots B and Slots T output flow under Ten megapascals zero megapascals load in Slots B and T; (b) Slots B and Slots T output flow under Ten megapascals load
load in Slots B and T. in Slots B and T.
6. Conclusions 6. Conclusions
As compared with the asymmetric axial piston pump (AAPP), the variable‐displacement As compared with the asymmetric axial piston pump (AAPP), the variable-displacement
asymmetric axial piston pump (VAPP) can change the inlet and outlet ports of the flow directly by asymmetric axial piston pump (VAPP) can change the inlet and outlet ports of the flow directly
changing the swash plate angle of the pump. This is important in controlling the speed and position by changing the swash plate angle of the pump. This is important in controlling the speed and position
of the single rod cylinder and balancing the asymmetric flow of the two chambers of the cylinder. of the single rod cylinder and balancing the asymmetric flow of the two chambers of the cylinder.
This method can help in reducing or eliminating the throttling losses and offer significant energy This method can help in reducing or eliminating the throttling losses and offer significant energy
saving, at the same time. VAPP has wide application prospects in the modern engineering machinery. saving, at the same time. VAPP has wide application prospects in the modern engineering machinery.
Experiments and simulation results demonstrate that the operation principles of VAPP are Experiments and simulation results demonstrate that the operation principles of VAPP are
practicable. In implementing the asymmetric pump‐controlled asymmetric cylinder strategy in a practicable. In implementing the asymmetric pump-controlled asymmetric cylinder strategy in a closed
closed circuit, the latest notion is suggested to counterbalance the unequal rate of flow of the circuit, the latest notion is suggested to counterbalance the unequal rate of flow of the asymmetric
asymmetric cylinder in the closed hydraulic circuit. The uniqueness of this new idea is that the cylinder in the closed hydraulic circuit. The uniqueness of this new idea is that the innovativeness of
innovativeness of the design as well as the valve plate’s configuration in the pump is also presented. the design as well as the valve plate’s configuration in the pump is also presented. Therefore, the pump
Therefore, the pump has two ports for intake as well as two delivery systems. has two ports for intake as well as two delivery systems.
In the future, the variable‐displacement control methods and performance would be analyzed In the future, the variable-displacement control methods and performance would be analyzed
to further enhance the dynamics of VAPP’s pumping. Besides, it is recommended that its variable to further enhance the dynamics of VAPP’s pumping. Besides, it is recommended that its variable
displacement components are studied further and designed. displacement components are studied further and designed.
Supplementary Materials: The
The supplementary materials available online at http://www.mdpi.com/ Supplementary Materials:
supplementary
materials
are are available
online
at http://www.mdpi.com/20762076‐3417/7/x/xx/s1, Figure S1: The physical photo of VAPP, Figure S2: The test scene of VAPP. 3417/7/4/328/s1, Figure S1: The physical photo of VAPP, Figure S2: The test scene of VAPP.
Acknowledgments: The
supported
byby National
Natural
Science
Foundation
of Acknowledgments: The research
research work
work reported
reported here
here isis supported National Natural Science Foundation China
(Grant
No.No. 51375324);
National-Shanxi
LowLow Carbon
of coal-based
Foundation
of China
(Grant of China (Grant 51375324); National‐Shanxi Carbon of coal‐based Foundation of (NSFC)
China (NSFC) No. U1510206); and Taiyuan University of Science and Technology Graduate Science and Technology Innovation
(Grant No. U1510206); and Taiyuan University of Science and Technology Graduate Science and Technology Project (Grant No. 20151021).
Innovation Project (Grant No. 20151021). Author Contributions: Youshan Gao and Jie Cheng conceived and designed the experiments; Jie Cheng performed the experiments; Jiahai Huang and Long Quan analyzed the data; Jiahai Huang contributed reagents/materials/analysis tools; and Youshan Gao and Jie Cheng wrote the paper. Conflicts of Interest: The authors declare no conflict of interest. References Appl. Sci. 2017, 7, 328
16 of 16
Author Contributions: Youshan Gao and Jie Cheng conceived and designed the experiments; Jie Cheng
performed the experiments; Jiahai Huang and Long Quan analyzed the data; Jiahai Huang contributed
reagents/materials/analysis tools; and Youshan Gao and Jie Cheng wrote the paper.
Conflicts of Interest: The authors declare no conflict of interest.
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