Abstract and Figures

This paper reviews the state of the art of directly driven proportional directional hydraulic spool valves, which are widely used hydraulic components in the industrial and transportation sectors. First, the construction and performance of commercially available units are discussed, together with simple models of the main characteristics. The review of published research focuses on two key areas: investigations that analyze and optimize valves from a fluid dynamic point of view, and then studies on spool position control systems. Mathematical modeling is a very active area of research, including computational fluid dynamics (CFD) for spool geometry optimization, and dynamic spool actuation and motion modeling to inform controller design. Drawbacks and advantages of new designs and concepts are described in the paper.
Content may be subject to copyright.
Paolo Tamburrano
1
Department of Mechanics,
Mathematics and Management (DMMM),
Polytechnic University of Bari,
Via Orabona 4,
Bari 70125, Italy;
Centre for Power Transmission and
Motion Control (PTMC),
Department of Mechanical Engineering,
University of Bath,
Claverton Down,
Bath BA2 7AY, UK
e-mails: paolo.tamburrano@poliba.it;
P.Tamburrano@bath.ac.uk
Andrew R. Plummer
Centre for Power Transmission and
Motion Control (PTMC),
Department of Mechanical Engineering,
University of Bath,
Claverton Down,
Bath BA2 7AY, UK
e-mail: A.R.Plummer@bath.ac.uk
Elia Distaso
Department of Mechanics,
Mathematics and Management (DMMM),
Polytechnic University of Bari,
Via Orabona 4,
Bari 70125, Italy
e-mail: elia.distaso@poliba.it
Riccardo Amirante
Department of Mechanics,
Mathematics and Management (DMMM),
Polytechnic University of Bari,
Via Orabona 4,
Bari 70125, Italy
e-mail: riccardo.amirante@poliba.it
A Review of Direct Drive
Proportional Electrohydraulic
Spool Valves: Industrial
State-of-the-Art and Research
Advancements
This paper reviews the state of the art of directly driven proportional directional hydrau-
lic spool valves, which are widely used hydraulic components in the industrial and trans-
portation sectors. First, the construction and performance of commercially available
units are discussed, together with simple models of the main characteristics. The review
of published research focuses on two key areas: investigations that analyze and optimize
valves from a fluid dynamic point of view, and then studies on spool position control sys-
tems. Mathematical modeling is a very active area of research, including computational
fluid dynamics (CFD) for spool geometry optimization, and dynamic spool actuation and
motion modeling to inform controller design. Drawbacks and advantages of new designs
and concepts are described in the paper. [DOI: 10.1115/1.4041063]
Keywords: proportional valves, direct-drive, flow forces, discharge coefficient, CFD,
control systems
Introduction
Proportional valves are critical components in many hydraulic
actuation and power transmission systems. They are used where
flow rate, and hence, actuation speed needs to be accurately con-
trolled. Typical applications include mobile hydraulics (excava-
tors, wheel loaders, etc.), machine tools, industrial automation,
and marine hydraulics. However, the terms “proportional valve,”
“servovalve,” and “direct-drive valve” are not well defined and
sometimes used interchangeably. In this paper, we are concerned
with spool valves in which the spool is directly driven by an elec-
trical actuator, specifically a proportional solenoid. Spool position
both determines the direction of flow and modulates the flow rate.
In contrast, a servovalve spool is driven by a faster, more power-
ful and more linear actuator, typically a hydraulic pilot stage, and
is manufactured to finer tolerances. Servovalves often have nomi-
nally zero overlap (dead band), whereas proportional valves are
designed to have appreciable overlap [1].
A review of servovalve technology and research can be found
in Ref. [2]. A servovalve requires more precise manufacturing
tolerances than a proportional valve, and to achieve this, a servo-
valve is usually designed with the spool sliding in a bushing
sleeve made of the same material as that of the spool. Detailed
metering features in a servovalve can be obtained by providing
the sleeve with slots. Instead, the spool in a proportional valve
directly slides in the valve body, and notches and grooves are
machined on the spool to achieve the desired flow rate trend ver-
sus spool position [1]. The smaller overlap of servovalves is also
synonymous with better response speed. This characteristic is fur-
ther enhanced in servovalves by high speed spool actuation in
which the pilot stage serves as a hydraulic amplification system
capable of generating high pressure differences across the end
faces of the main spool, which in consequence is moved by a very
high actuation force. Instead, proportional directional valves are
commonly moved directly by proportional solenoids, whose
actuation forces are lower than those obtained in servovalves [3].
Note, however, that to control higher flow rates, multistage pro-
portional valves may be used, which employ a small pilot spool to
actuate a large main stage spool.
In addition to the lower response speed (which is also due to
the high moving masses of direct actuation systems), direct oper-
ated proportional directional valves are not capable of producing
such a high “chip shear force,” namely, the force necessary to
shear contamination particles that can be caught between the
edges of a metering section. These drawbacks make proportional
1
Corresponding author.
Contributed by the Dynamic Systems Division of ASME for publication in the
JOURNAL OF DYNAMIC SYSTEMS,MEASUREMENT,AND CONTROL. Manuscript received
February 26, 2018; final manuscript received July 28, 2018; published online
October 5, 2018. Assoc. Editor: Heikki Handroos.
Journal of Dynamic Systems, Measurement, and Control FEBRUARY 2019, Vol. 141 / 020801-1
Copyright V
C2019 by ASME
valves unsuitable for critical applications, such as aerospace
(where the additional size and weight is also a problem). How-
ever, by virtue of their robustness and relatively low cost com-
pared to servovalves, proportional valves are extensively used in
many industrial applications. Unlike an on/off valve, a propor-
tional valve can be instrumental in avoiding sudden acceleration
and deceleration of an actuator, in addition to providing more
accurate control of its position and/or velocity [3].
Given their importance in several industrial sectors, this paper
discusses the state of the art of directly driven proportional direc-
tional valves. First, their operating principles and mathematical
models used by researchers and industrial engineers to study and
design these valves will be discussed. Then, an overview of com-
mercially available valves will be given, with the emphasis on
their performance. Finally, a detailed review of the current
research will be provided that is focused on the fluid dynamic
analysis and on spool position control systems.
Operating Principles and Analytical Modeling
Directly driven proportional directional valves have an inner
sliding spool which is directly moved by either one solenoid or
two solenoids placed at the spool extremities. The spool is pro-
vided with notches and grooves designed to achieve a desired
flow rate trend as a function of the spool position [4]. These valves
usually present a dead band given by the spool overlap, which can
be as high as 10% or more of the spool stroke. In addition, usually
the spool moves in a bore directly drilled in the valve body [3].
These valves are used with hydraulic oils, although some attempts
have been made in the scientific literature to effectively adapt
these valves to water [59].
Figure 1shows a typical architecture of the most used valve
typology, namely a four-way three-position (4/3) proportional
valve along with its symbol. The sliding spool is pushed directly
by either the right solenoid or the left solenoid depending on the
required hydraulic connections (P-A and B-T or P-B and A-T)
[10]. The oil enters the valve through the high pressure port P,
then it flows through the metering section P-A or P-B (whose flow
area is determined by both the metering notches in the spool and
the opening degree) and finally exits the valve toward the actuator.
Likewise, the oil discharged from the actuator re-enters the valve
flowing through the metering section A-T
1
or B-T
2
. Ports T
1
and
T
2
are internally connected (not represented in Fig. 1for simplic-
ity) so as to form a single discharge port T [11].
Analytical models were developed in the past [12,13] and are
currently used in scientific literature to easily study these valves
[1418]. The flow rate through a proportional directional valve
depends on the opening area and on the pressure drop through the
valve. If Dpis the pressure drop measured across a metering edge
and A
r
(x) the metering section area (a function of the spool posi-
tion x), the volumetric flow rate Qthrough the metering chamber
can be calculated as
Q¼CdArx
ðÞ ffiffiffiffiffiffiffiffi
2Dp
q
s(1)
where Cdis the discharge coefficient of the metering section. The
desired function A
r
(x) is obtained by properly designing the
notches machined on the spool.
In the case of a 4/3 valve, a discharge coefficient must be
defined for each of the two metering edges in the flow path. In
such a case, the overall discharge coefficient through the valve
can be calculated as proposed in Ref. [10]
Cd;V¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
C2
d;1C2
d;2
C2
d;1þC2
d;2
s¼Q
Arffiffiffiffiffiffiffi
2Dpv
q
q(2)
where Cd;1and Cd;2are the discharge coefficients through the
metering chambers and Cd;Vrepresents the overall flow coefficient
of the valve, with Dpvbeing the overall pressure drop through the
valve. According to Eqs. (1) and (2), it is evident that, for a given
opening degree, the flow rate depends on the pressure drop
through the valve. Figure 2shows qualitatively how the metering
curve changes with the pressure drop through a valve. It refers to
an overlapped valve (namely, a valve having the spool land longer
than the adjacent gap in the valve body), which is the most com-
mon proportional valve typology [19], and the curve is determined
by A
r
(x), given by the notch shape.
For a given opening degree, the change in the flow rate because
of changes in the pressure drop can be calculated through Eq. (3),
with subscripts 1 and 2 denoting two different operating
conditions
Q1
Q2¼ffiffiffiffiffiffiffi
Dp1
Dp2
s(3)
Fig. 1 Proportional valve ATOS-DKZOR-T [28]: 1—valve body, 2—spool, 3—solenoid, 4—LVDT, 5—electronic
control, 6 and 7—connectors)
020801-2 / Vol. 141, FEBRUARY 2019 Transactions of the ASME
It is possible to add pressure compensation by using a combina-
tion of restrictors or additional valves, so that flow fluctuations
due to system pressure changes are reduced. When inlet or work-
ing pressures change, the pressure compensator system keeps the
flow rate constant by maintaining a constant pressure drop across
the spool orifice [3].
Proportional valves can work in an open-loop configuration or
in a closed-loop one, the latter employing a position sensor, typi-
cally a linear variable differential transformer (LVDT), for more
precise control of the spool position [20]. Open loop control sys-
tems are cheaper, but are affected by changes in the operating
conditions, as they rely on fixed parameters tuned for certain
conditions.
In both cases, standard commercial electronic cards (shown in
Fig. 1) provide the solenoids with a pulse width modulation
(PWM) signal having a primary PWM signal frequency usually in
the range 200–20,000 Hz. A dither signal (square or sinusoidal
wave with a frequency lower than the PWM frequency) is also
used to keep the spool vibrating, thus overcoming stiction
between the spool and the valve body bore [21].
The block diagram of a typical control system is shown in
Fig. 3, adapted from Ref. [20]. As discussed in Ref. [20], a
proportional–integral controller can be used for coil current con-
trol, which improves the static and dynamic characteristics of the
valve. Similar to dither, the flutter signal generator has the pur-
pose of reducing both friction and the magnetic hysteresis loop of
the solenoid, improving the performance of the valve in demand-
ing applications [20].
The current iflowing through the solenoids is therefore changed
by varying the PWM duty cycle of voltage Vapplied to the sole-
noid coil, taking advantage of the resistive-inductive behavior of
the coil [22]
V¼iR þLdi
dt (4)
where Rand Lare the resistance and the inductance of the coil,
respectively. The higher the duty cycle of the PWM, the larger the
average intensity of the current flowing through the solenoid, and
hence, the higher the electromagnetic force exerted by the sole-
noid on the spool [23].
The electromagnetic force (F
act
) acts in opposition to the damp-
ing force mainly due to the friction between the spool surface and
the valve body surface (F
fr
¼c_
x), the transient flow forces and
stationary flow forces (F
flow
) due to the fluid motion, and the elas-
tic force (F
el
¼kelx) produced by the centering springs (which are
needed to maintain the spool in a centered position when no signal
is applied to the coils). The resultant force accelerates the spool
mass m
Fact Fflow kelxc_x¼mx(5)
Figure 4provides a representation of a section view of a typical
4/3 valve with the spool being maintained in a fixed spool position
x. The overall stationary flow force acting on the spool surface
along the xaxis is the sum of three contributions, due to the inter-
action between the fluid and the spool within the central chamber
P-B (Fflow;center), the left chamber A-T
1
(Fflow;left ), and the right
chamber in correspondence of the exit T
2
(Fflow;rightÞ. Each com-
ponent is the sum of the pressure forces and viscous forces acting
on the spool surfaces. As analyzed in Refs. [1113] and [2325],
the application of the conservation of momentum to the three con-
trol volumes shown in Fig. 4leads to
Fflow ¼Fflow;left þFflow;center þFflow;right _
m½ðVAÞxðVTÞx
þ_
m½ðVBÞxðVPÞx(6)
where _
mdenotes the overall mass flow rate of the oil entering the
valve; ðVAÞxand ðVTÞxare the average axial velocities at the inlet
and outlet sections of the left control volume, respectively; ðVBÞx
and ðVPÞxare the average axial velocities at the outlet and inlet of
the central control volume, respectively. As the direction of the
Fig. 3 Typical control system of a proportional valve (Adapted
from Ref. [20])
Fig. 4 Section view of a 4/3 proportional valve (a) and enlarge-
ment on the spool surface with velocity and force vectors (b)
Fig. 2 Metering curve as a function of the pressure drop for a
given opening degree
Journal of Dynamic Systems, Measurement, and Control FEBRUARY 2019, Vol. 141 / 020801-3
flow within the right control volume is orthogonal to the xaxis,
Fflow;right can be neglected. In some units, a central conical surface
(to be referred to as the compensation profile) and two lateral con-
ical ones are constructed on the spool surface in order to increase
the axial velocities ðVTÞxand ðVPÞx, thus reducing the overall flow
force acting on the spool [23].
In addition to the stationary flow forces, transient flow forces
are developed during the spool movement from an initial position
to a final one. As demonstrated in Ref. [26], the transient flow
force in a metering chamber can be calculated as
Fflow;trans ¼Ld_
m
dt (7)
where Lis the axial distance between the inlet and outlet ports of
the metering chamber.
Like all spool valves, proportional valves are vulnerable to a
particular problem that is referred to as “hydraulic lock,” caused
by an uneven pressure distribution around the circumference of
the spool which pushes the spool radially against the inner surface
of its bore. Thus, grooves are machined circumferentially around
the spool to avoid an uneven pressure distribution and prevent
hydraulic lock [27].
Commercially Available Proportional Valves
Many manufacturers produce directly driven proportional direc-
tional valves, such as Atos,
2
Parker,
3
Bosch Rexroth,
4
Moog,
5
and
Eaton.
6
Each model is usually provided by their manufacturer as a
unique body which can be equipped with different sliding spools,
according to the operation features required [4].
Commercially available proportional valves have less precise
manufacturing tolerances than servovalves [14]. The larger toler-
ances on the spool geometry and spool overlap result in response
nonlinearities, especially in the vicinity of neutral spool position
[14].
A performance limitation is due to the direct actuation via pro-
portional solenoids: these are relatively heavy and can generally
operate in only one direction. Some solenoids are designed to
operate in push–pull mode, but these are more expensive and gen-
erate lower driving forces than conventional ones [3]. In addition,
for high pressures and/or flow rates required, the actuation force
generated by commercially available solenoids is not high enough
to counteract the opposing forces (flow forces þelastic forces of
the centering springs). This results in a limited operational range
for these valves as far as the maximum achievable flow rate is
concerned [11]. The maximum flow rate is typically 100 l/min,
with some models being capable of over 150 l/min, but only for
low pressure drops. As an example, a large valve produced by
ATOS
2
is the DKZOR-AES model. The solenoids employed in
the DKZOR-AES model are very large and can have a maximum
input power of 50 W. The operational field of the valve is repro-
duced in Fig. 5: it is possible to observe that the maximum flow
rate is about 160 l/min, but the pressure drop must be limited to
70 bar for such a flow rate level in order not to exceed the maxi-
mum power of the solenoids employed (higher pressure drop for
the same flow would require a smaller metering flow area and so a
higher flow velocity and thus a higher flow force). The increase in
the pressure drop causes a decrease in the maximum flow rate
achievable; as shown by the external curve of Fig. 5, at 210 bar,
the maximum flow rate through the valve is lowered to about 90
l/min. This means that, for high pressure drops, it is not possible
to reach the maximum opening degree of the valve, but only a
part of the spool stroke can be used because of the limited power
capability of the solenoids. A similar model, produced by ATOS,
namely the DHZO-AES model,
2
employs smaller solenoids with a
lower maximum power produced, namely up to 30 W. The internal
curve in Fig. 5reports the operational field of the DHZO-AES; in
spite of the similar geometric characteristics, the lower actuation
power reduces the operation field of the valve, with a maximum
flow rate of 64 l/min at 210 bar.
With regard to the dynamic characteristics, they are only
slightly affected by the operating pressure, unlike two stage
valves. Available direct operated proportional directional valves
have 90 deg phase lag frequency ranging from 10 Hz to
70 Hz.
26
The higher values are obtained for small valves and
those using closed-loop controls. As an example, Fig. 6shows a
reproduction of the Bode plot of the proportional valve 4WREE
size 10, produced by Bosch Rexroth.
4
This is a very large model,
capable of achieving 150 l/min at 100 bar pressure drop. The
Bode plot shows that the dynamic performance worsens when the
amplitude of the input signal is increased, with the 90 deg phase
lag frequency varying from 20 Hz to 40 Hz for input signal ampli-
tudes varying from 100% to 10% of the full stroke.
Similarly, the response time to a step demand can vary from
10 ms to 50 ms according to the characteristics of the unit
26
and
to the step amplitude. Figure 7shows the step tests for the valve
4WREE, achieved for 25%, 50%, 75%, and 100% of the full
stroke.
Proportional directional direct operated valves are mainly used
in the industrial and transportation sectors. They are not commonly
used in aerospace, since in such application high response times
and large actuation forces are required. The latter are necessary to
avoid jammed spool conditions because of particle contamination
(chip). A proportional solenoid is not capable of providing large
actuation forces in order to shear a chip if it is jammed between the
metering edges. Such a high force level can only be obtained
through hydraulic amplification systems (e.g., nozzle flapper, jet
pipe, or deflector jet pilot stages) present in servovalves.
Fluid-Dynamic Research
It is common practice to consider, for preliminary calculations, a
constant value of the discharge coefficient for proportional valves,
with assumed values comprised between 0.65 and 0.7. However, as
highlighted in Ref. [28], the discharge coefficient of a proportional
valve is highly dependent on the notch geometry and spool posi-
tion. In addition, the effects of cavitation are expected to affect the
discharge coefficient, as discussed in Ref. [29].
Experimental and theoretical approaches have therefore been
used to investigate the effects of the shapes of the notches upon
the discharge coefficient and exit jet flow angle through a meter-
ing section of a proportional valve. In Ref. [28], three notch
shapes were experimentally analyzed: the first one had a rectangu-
lar shape ended by a semicircle, the second one was obtained by
Fig. 5 Operational field of two commercially available valves:
DKZOR-AES (external line) and DHZO-AES (internal line)
2
2
http://www.atos.com/
3
http://ph.parker.com/us/en/proportional-valves
4
https://www.boschrexroth.com/en/us/products/product-groups/industrial-
hydraulics/proportional-and-servo-valves/index
5
http://www.moog.com/products/servovalves-servo-proportional-valves.html
6
http://www.eaton.com
020801-4 / Vol. 141, FEBRUARY 2019 Transactions of the ASME
connecting three semicircles with very short rectangles, while the
third one had a triangular section (see Fig. 8). The experimental
circuit employed is reported in Fig. 9(a), where a pump, a variable
restrictor, a pressure relief valve, two flowmeters, and two pres-
sure sensors were used to estimate the discharge coefficient. The
experimental results of Ref. [28] showed that, for fully turbulent
flow, the discharge coefficient assumed different values according
to the notch type, number of notches employed, and opening
degree (spanning from 0.45 to 0.75). However, it was shown that,
for a fixed opening degree, number, and typology of notches, the
discharge coefficient first increases rapidly with the Reynolds
number in the laminar flow region, and then gradually achieves
the stable value for a fully turbulent flow. This behavior is qualita-
tively reproduced in Fig. 10 and is similar to the graph reported in
Ref. [13]. According to what was stated by Borghi et al. [28], the
pressure downstream of the restrictor was kept high enough to
avoid cavitation. Instead, the effects of cavitation upon the dis-
charge coefficient of an orifice were experimentally investigated
in Ref. [30], and the preliminary results obtained can be translated
to the metering sections of proportional valves. The experimental
apparatus, shown in Fig. 9(b), was mainly composed of an orifice
interposed between two pressure relief valves which allowed the
pressure drop across the orifice (Dp) to be varied along with
the upstream pressure (p
1
) and the downstream pressure (p
2
).
Figure 11 shows the graph of the flow rate Qthrough the cylindri-
cal orifice (having a fixed diameter of 0.6 mm) as a function of
the square root of the pressure drop across the orifice ( ffiffiffiffiffi
Dp
p); in
addition, different curves are plotted for fixed values of the pres-
sure upstream of the orifice (p
1
). It is noteworthy that, in the first
part of the graph, the flow rate increases linearly with the square
root of the pressure drop, which means that the discharge coeffi-
cient remains constant according to Eq. (1). This confirms the
results achieved in Ref. [28], namely, the discharge coefficient has
a constant value for fully turbulent flows. However, for each
curve, it is noted that, after a linear increase, the flow rate satu-
rates reaching a constant value. This is justified by the occurrence
of cavitation, which tends to reduce the discharge coefficient. In
addition, it is noted that the pressure drop at which the flow rate
saturates increases with the upstream pressure p
1
, because the
higher the upstream pressure, the higher the downstream pressure
for a fixed pressure drop. In other words, the intensity of cavita-
tion is increased by lowering the pressure downstream of an ori-
fice. The graph also shows that the saturated points tend to a
linear boundary (when p
2
!p
1
). The results obtained in Ref.
[30], and, in particular, the flow rate trend shown in Fig. 11, are
confirmed by the work carried out in Ref. [31]. In Ref. [31], it is
also clearly shown that the discharge coefficient of an orifice, after
a constant phase as a function of the Reynolds number, undergoes
a sharp drop when cavitation occurs.
In addition to retrieving the discharge coefficients, experimen-
tal approaches have also been used to measure the flow forces. In
Fig. 6 Reproduction of the Bode plot of the proportional valve 4WREE size 10, produced by
Bosch Rexroth
4
Fig. 7 Reproduction of the step test diagram of the propor-
tional valve 4WREE size 10, produced by Bosch Rexroth
4
Journal of Dynamic Systems, Measurement, and Control FEBRUARY 2019, Vol. 141 / 020801-5
Refs. [20] and [32], the flow forces were calculated as the differ-
ence between the solenoid force (F
act
) and the force of the center-
ing springs (F
el
). The electromagnetic force in a proportional
solenoid is a function of the armature position (coincident with
the spool position x) and current i. In both cases, the force surface
in the x,iplane was experimentally retrieved. In particular, the
armature-solenoid-LVDT assembly was removed from the valve
body and connected with a micrometer screw and a load cell in
order to measure the actuation force as a function of the armature
position and current, as shown in Fig. 12. Figure 13 qualitatively
shows the magnetic force surface as a function of the current and
armature position. The maximum values of the actuation forces
Fig. 8 The three notch typologies analyzed in Ref. [28]
Fig. 9 Experimental circuits employed in [28]: (a), [30]: (b), [46]: (c), [48]: (d), [10]: (e), and [23]: (f)
020801-6 / Vol. 141, FEBRUARY 2019 Transactions of the ASME
were measured to be around 100 N in Ref. [20] and around 140 N
in Ref. [32], evidencing that commercially available solenoids are
not capable of developing high actuation forces compared to ser-
vovalves, whose actuation forces can be as high as 700 N.
5
As an alternative approach, the actuation force was measured in
Refs. [23] and [33] by using a manual actuation system: the arma-
ture inside the coil, which is in contact with the sliding spool, is
moved through a knob; a load cell, interposed between the manual
actuation and the armature, allows the actuation force to be meas-
ured during the operation of the valve (see Fig. 14). A similar
apparatus was used in Ref. [34] to measure the flow forces.
In addition to experimental approaches, a very effective method
for analysis of flow through these valves is computation fluid
dynamics (CFD), available commercially as software tools such
as ANSYS FLUENT [35]. The flow through a valve, supposed to be
incompressible, can be modeled either by setting the values of
pressure at the inlet and outlet or by setting the value of the veloc-
ity at the inlet [36]. The use of CFD modeling has proved its
effectiveness for ON/OFF directional valves, with two-
dimensional (2D) approaches and simplified computational
domains being widely used to study the flow within these valves
[3744]. However, the flow in a proportional valve is not axisym-
metrical due to the presence of notches and grooves on the spool;
for this reason, very detailed three-dimensional (3D) approaches
are commonly used to give more accurate results. Because of the
domain complexity, unstructured grids are used for proportional
valves. In Ref. [4], a partial 3D model (reproducing a circumfer-
ential sector of the entire valve) was used for different spool posi-
tions to study the flow field in a four-way three-position direct
operated proportional directional valve. It was demonstrated in
that paper that the use of small cylindrical notches on a spool with
spherical notches can provide flow rate metering also at very
small valve opening, while not influencing the overall flow forces
acting on the spool. In addition, it was shown that the compensa-
tion profile (i.e., the central conical surface of the spool), if prop-
erly designed, can lead to a significant flow force reduction, with
a negligible flow rate penalization at large openings. The flow
force reduction is due to the increase in the axial component of
the fluid velocity at the inlet section (V
P
)
x
, according to Eq. (6).
In Ref. [36], the high pressure chamber of a 4/3 proportional
valve for load-sensing applications was simulated for five spool
positions by using the open source code OpenFOAM [36]. The
turbulence was modeled by means of the two zonal version of the
kxmodel, known as the shear stress transport model. In particu-
lar, the effect of the direct and inverse flow through the notches of
the metering chamber was investigated, showing that the dis-
charge coefficient changes according to the fluid direction
although a fixed geometry is considered. In addition, transient
simulations were performed, in which the mesh motion was
resolved by using a generalized grid interface approach [45],
Fig. 10 Qualitative trend of the discharge coefficient versus
Reynolds number for a fixed notch geometry [28,46]
Fig. 11 Flow rate through a fixed orifice as a function of the
square root of the pressure drop ( ffiffiffi
D
pp) and upstream pressure
(p
1
)[30]
Fig. 12 Experimental apparatus to evaluate the actuation
forces: 1—coil, 2—LVDT, 3—load cell, 4—micrometer screw,
and 5—armature [32]
Fig. 13 Electromagnetic force as a function of the armature
position and current intensity
Journal of Dynamic Systems, Measurement, and Control FEBRUARY 2019, Vol. 141 / 020801-7
originally developed for turbomachinery applications and modi-
fied to include not only the rotational motion of the moving grid
but also the linear displacement of a valve spool [36].
A partial three-dimensional stationary model was also used in
Ref. [46] to investigate the flow characteristics of three different
groove profiles, namely the triangle shape, the U-shape, and the
spheroid shape, applied to a commercially available valve. The
three groove profiles are shown in Fig. 15, where Xis the spool
opening; A
1
and A
2
are the axial and radial cross section respec-
tively, and A
3
is the cross section which crosses both the throttling
edge and the lowest point of the groove. A
min
is the smallest cross
section across the throttling edge. Each groove has the length of
the throttling grooves in the axial direction equal to 3 mm. The
computational grid is shown in Fig. 16. An experimental circuit
was assembled to validate the results, with the use of a stepper
motor for a fine adjustment of the spool position (see Fig. 9(c)).
The results confirmed those obtained by Ref. [28], showing that
the groove shape has significant effects on the discharge charac-
teristics, the jet flow angle, the steady flow force, and the throt-
tling stiffness of the spool valve [46]. Figure 16 also reports the
pressure contours in the symmetrical surface of the notches at dif-
ferent spool positions. The pressure drop through the spheroid-
Fig. 14 Experimental apparatus for measuring the actuation force that is based on a screw
mechanism coupled with a force sensor
Fig. 15 Geometric characteristics of (a) the spheroid-shape groove, (b) the triangle-shape groove, and (c) the divergent U-
shape groove, analyzed in Ref. [46]
Fig. 16 Left: partial 3D CFD model employed in Ref. [46]; right: pressure contours on the symmetry plane: (a)X50.6 mm, (b)
X51.4 mm, and (c)X52.0 mm [46]
020801-8 / Vol. 141, FEBRUARY 2019 Transactions of the ASME
shape groove is concentrated on cross sections A
2
and A
3
within
the entire range of the spool stroke, and with the increase of the
opening, the proportion of the pressure drop changes gradually
from cross sections A
2
to A
3
. For a triangular notch, the pressure
drop is mainly centralized in cross section A4 [46]. The divergent
U-shape groove has a more complex behavior of the pressure dis-
tribution than the other two types, with the pressure drop distribu-
tion changing remarkably according to the spool position.
The experimental and numerical activity also allowed the con-
stant values of the discharge coefficient to be calculated for fully
turbulent flow (see Fig. 10), and these values are reported in
Table 1. Figure 17 shows the values of the jet flow angles obtained
via CFD for different shapes of the grooves analyzed. It is note-
worthy that very different values are obtained and that the opening
degree also significantly affects the discharge coefficients and
flow angles [46]. This analysis is instrumental in pointing out the
importance of CFD, which can allow a precise evaluation of the
flow characteristics of a proportional valve for a given geometry
of the spool notches.
A 3D CFD model reproducing a part of the spool surface was
used to investigate the effects of other important geometrical fea-
tures [27], such as the circumferential grooves machined on the
spool surface. As only the zone in correspondence of the circum-
ferential grooves was simulated, quadrilateral cells were gener-
ated. Circumferential grooves are fundamental to avoid hydraulic
lock caused by an uneven pressure distribution on the spool sur-
face during its movement. Hong and Kim suggested using spiral
grooves instead of typical circumferential ones. Their work dem-
onstrated that spool valves with spiral grooves could offer better
performance in terms of relieving the asymmetric pressure distri-
bution in the radial clearance because spiral grooves act as one
continuous groove [27].
With the ever-increasing capability of computer hardware
resources, the use of fully 3D approaches has become more com-
mon to study these valves via CFD [32,33,4751]. Full 3D model-
ing was used in Ref. [48] to confirm at first that the use of
constant values for the discharge coefficient may lead to signifi-
cant errors and then to obtain a method for calculating the coeffi-
cient values. Their numerical results were validated through the
experimental circuit shown in Fig. 9(d). In particular, functions
for evaluating the flow coefficient were proposed that depend on
the spool position and on the flow rate. These functions can be
particularly useful at the design stage in order to properly design
the spool surface for a given metering curve.
The full 3D CFD analysis of Ref. [33] was carried out at the
maximum opening of the WE10H valve produced by Bosch
Rexroth to predict the stationary flow force, and this was calcu-
lated as a function of the flow rate. Figure 18 shows the computa-
tional grid, whereas Table 2reports the values of the predicted
flow forces, extrapolated from Ref. [33]. The numerical results
were also in very good agreement with experimental data, thus
confirming the high accuracy reached by current full 3D methods.
A full 3D method was also used in Ref. [51] to develop a pressure
compensation method for multisection proportional directional
control valves which is based on the adjustment of the forces act-
ing on the spool and does not need the use of additional compen-
sating valves or other correcting elements, such as sensors in a
feedback control system [51].
Table 1 Asymptotic value of the discharge coefficient according to different notch profiles
Discharge coefficient (asymptotic value)
Opening (mm) Spheroid shape groove Triangle shape groove Divergent U-shape groove
0.6 0.747 0.720 0.651
1.4 0.682 0.692 0.646
2.2 0.620 0.666 0.652
Adapted from Ref. [46].
Fig. 17 Values of the jet flow angle according to different
notch profiles obtained via CFD [46]
Fig. 18 Full 3D grid developed in Ref. [33]
Journal of Dynamic Systems, Measurement, and Control FEBRUARY 2019, Vol. 141 / 020801-9
A further example of full 3D modeling is reported in Ref. [32].
In that work, the aim was to increase the accuracy in the predic-
tion of the stationary flow rate and flow forces compared to par-
tially 3D models; 11 spool positions covering two-thirds of the
full stroke were simulated for a commercially available valve, and
11 unstructured meshes with about two million cells were gener-
ated. The RNG kemodel coupled with the enhanced wall treat-
ment was implemented to resolve turbulence. The numerical
predictions were compared with experimental results obtained
through an experimental hydraulic circuit. The paper showed that
a full 3D discretization of the entire flow within the valve is
required to properly predict the flow at small openings, where an
axisymmetric approach fails, and in particular at large spool dis-
placements, where also a partially 3D discretization had shown its
limitations in previous papers.
A full 3D model was also employed in Ref. [52] to evaluate the
effects of small cylindrical notches to be machined on the spool
surface of a commercially available valve manufactured by
PONAR Wadowice.
7
Two spool versions with one notch and with
two symmetrical notches were considered. Computational grids,
each composed of about 4.1 million cells, were generated for gap
widths spanning from 0.1 mm to 0.4 mm with a step of 0.1 mm.
The results confirm that the use of small cylindrical notches at the
apex of main grooves can allow a proportional valve to operate
with very low flow at small openings. In addition, it was demon-
strated that the use of two notches arranged symmetrically on both
sides of the spool determines radial force compensation.
A further improvement in the CFD modeling of proportional valves
was given in Ref. [10], where the employed CFD model also
accounted for cavitation, which is a non-negligible effect occurring in
these valves. Among the available cavitation models, the Schnerr and
Sauer model provided by FLUENT was chosen since it is very robust
and converges quickly. The results provided by the cavitation model
were compared with the results obtained by the monophase model (in
which the fluid was treated as incompressible). An experimental
hydraulic circuit, shown in Fig. 9(e), was also assembled in order to
evaluate the effectiveness of the numerical model. A pressure relief
valve was placed downstream of the proportional directional valve
which allowed the pressure to be increased at port T, in order to evalu-
ate the performance of the proportional valve without cavitation (due
to the high discharge pressure). In contrast, cavitation could be gener-
ated by opening a block valve so that the hydraulic oil was able to by-
pass the pressure relief valve, and the pressure at port Twas decreased
nearly to the atmospheric value [10]. Figure 19(a)shows the full 3D
grid employed in the simulations. The “porous jump” boundary con-
dition allowed a fixed pressure variation to be assigned through sec-
tion C (see Fig. 19(a)), so as to simulate the pressure drop registered
through the measuring equipment in the experimental tests. The pres-
sure drop through the porous surface is computed by FLUENT as
Dpporous ¼ l
dþ1
2cq2

Dm(8)
where dis the permeability of the medium, cis the pressure-jump
coefficient, vis the velocity normal to the porous face, qand lare
the density and the molecular viscosity of the fluid, respectively,
and Dmis the thickness of the medium [10].
Figure 19(b)shows the metering curves obtained experimen-
tally and numerically for low discharge pressure and for high dis-
charge pressure maintaining an overall pressure drop of 70 bar. It
can be seen that cavitation affects the flow rate through the valve,
causing a flow rate reduction of about 8% at the maximum open-
ings. The flow rate reduction is due to the reduction of the dis-
charge coefficient in the low pressure chamber (metering section
B-T in Fig. 19(a)), where cavitation occurs. The experimental
results were very close to the numerical predictions, thus demon-
strating that such a CFD model can reliably predict cavitation.
Figure 19(c)provides the contours of the vapor volume fraction
computed on the spool surface and on a section plane in corre-
spondence of metering chamber B-T for the spool displacements
equal to x¼0.8 mm and x¼1.4 mm, highlighting the importance
of the phenomenon, especially at the large openings.
In Ref. [53], a full 3D CFD analysis was performed to study a
new concept of valve. The solution presented in that paper uses an
axial flow valve, where the oil passes through the valve along its
axis, with two rotating surfaces causing a rotational metering. The
result of that new design approach shows several advantages with
respect to the common spool valves, such as the extremely com-
pact size and the device versatility. This particular valve can real-
ize the majority of the functions achievable using a two-way
two-position proportional valve piloted by two pressure signals
(for example, a pressure compensated valve); the axial flow and
the “built-in” metering edges yield the possibility to produce this
valve as a cartridge component [53]. Other examples of new con-
cepts of proportional valves with metering features obtained
through the rotation of the spool and investigated via full 3D CFD
models are present in the literature, such as Refs. [5456].
Such detailed 3D models can also be used at the design stage to
obtain very effective geometries for the spool and for the valve
body of standard valves in order to reduce the flow forces or cavi-
tation intensity. In this regard, the current research studies regard-
ing spool valves are focused on reducing the flow force to extend
their application range [11,2325,34,57]. As pointed out in Ref.
[57], commercially available valves present nonoptimized geome-
tries which restrict their potential, and opportune geometrical
modifications to the valve body and spool are needed to minimize
the stationary flow forces, which play a more important role in the
control of higher hydraulic powers compared to the other resistant
forces. In Ref. [24], effective changes were made both to the slid-
ing spool and to the valve body of an ON/OFF small hydraulic
seat valve, confirming that the nonoptimized profiles of commer-
cially available valves have a great influence on the required
actuation forces. In Ref. [25], some possible methods were also
provided to reduce the static flow forces in sliding-spool valves:
the results of this research are very promising and prove that the
axial component of the flow forces, and therefore, the necessary
actuation force can be reduced significantly just by modifying the
geometry of the valve housing and spool.
In Ref. [11], a genetic algorithm was coupled with a full 3D
model of the flow field of a proportional valve in order to reduce
the flow force at the maximum opening for a commercially avail-
able valve. The geometrical parameters of the valve body were
kept unchanged, whereas four geometrical parameters of the valve
spool were selected as design parameters. The parameters, shown
in Fig. 20, define the central and lateral surfaces of the spool,
allowing the velocities at the inlet and outlet selections of the
valve to be varied according to Eq. (6).
The comparison between the reference values and optimized
ones is shown in Fig. 20. The optimized spool was constructed
and experimentally compared with the reference one in Ref. [23].
A manual actuation system coupled with a load cell was used to
measure the actuation force required by the two spools (see
Figs. 9(f)and 14). An actuation force reduction of about 13% at
the maximum opening was measured for a pressure drop of 70 bar
through the valve.
Table 2 Flow force predicted at the maximum opening for a
commercially available valve as a function of the flow rate
Flow rate (l/min) Flow force (N)
30 10
60 20
90 58
120 80
150 122
Adapted from Ref. [33].
7
http://www.ponar-wadowice.com/directional-control-valves
020801-10 / Vol. 141, FEBRUARY 2019 Transactions of the ASME
Fig. 19 Full 3D grid used in Ref. [10](a), metering curves obtained numerically and experimentally for low and high discharge
pressure with an overall pressure drop 570 bar (b), and contours of volume fraction on the spool surface (c)
Journal of Dynamic Systems, Measurement, and Control FEBRUARY 2019, Vol. 141 / 020801-11
As an alternative approach for the flow force reduction, Lisow-
ski et al. [33] suggested introducing additional channels in the
valve body, without changing the spool geometry, as shown in
Fig. 21. In that paper, it was noted that the reduction of average
velocity around the spool and better pressure compensation in the
valve body are associated with lower flow force acting on the spool
[33]. The numerical and experimental comparison between the ref-
erence valve and the novel one showed that in the latter the pressure
is more balanced around the spool. A very large flow force reduc-
tion, up to 50%, was obtained with the additional channels.
The main settings of some of the 3D simulation studies ana-
lyzed so far that predict the flow field through a proportional
directional valve are summarized in Table 3.
Research on Control Systems
The literature review analyzed so far has been concerned with
the fluid dynamic behavior of proportional valves. In parallel to
this, many studies have considered improving the spool position
control systems for these valves, often with the help of models of
the dynamic characteristics of spool actuation. These models often
take advantage of software packages capable of studying the valve
dynamics, such as MATLAB [58], SIMULINK [59], and AMESIM [60,61].
A nonlinear dynamic model was developed in Ref. [62], in
which the solenoid was modeled as a nonlinear resistor/inductor
combination, with inductance parameters changing according to
the values of displacement and current. Empirical curve fitting
techniques were used to model the magnetic characteristics of the
solenoid, enabling both current and magnetic flux to be simulated.
The spool assembly was modeled as a spring/mass/damper sys-
tem. The inertia and damping effects of the armature were incor-
porated in the spool model. The solenoid model was used to
estimate the spool force in order to obtain a suitable damping
coefficient value. The model accurately predicts both the
dynamic and the steady-state response of the valve to voltage
inputs [62].
Fig. 20 Design parameters adopted for the fluid dynamic optimization performed in Ref. [11] and experimentally validated in
Ref. [23]: comparison between reference geometry and optimized one
Fig. 21 Contours of pressure in the novel valve body geometry presented in Ref. [33]: 2 and 3 denote the
additional channels
020801-12 / Vol. 141, FEBRUARY 2019 Transactions of the ASME
Analysis of a proportional solenoid was performed using finite
element (FE) simulation in Ref. [59], by adopting an axially sym-
metrical two-dimensional (2D) FE model in ANSYS/EMAG. The
electromagnetic force and flux linkage characteristics in all arma-
ture positions and for different currents were analyzed. Also in
Ref. [63], a FE model was used to develop a nonlinear model of
various types of proportional valves, but in this case a full 3D
model was developed and experimentally validated by the
authors. The 3D model allows quantifying the effects of the eddy
currents and retrieving a second-order transfer function which
describes the electromagnet dynamics. The developed nonlinear
model was composed of three submodels based on a lumped
parameter approach: the fluid-dynamic model (for the evaluation of
the main flow features), the mechanical model (which solves the
mobile body motion), and the electromagnetic model (which evalu-
ates the magnetic forces and the electric transient). The comparison
between the nonlinear model and the linear model shows the limits
of the linear approximation to study the real components [63].
In Ref. [64], a discontinuous projection based adaptive robust
controller was developed that is capable of compensating for the
effect of the valve deadband, and certain straight-line approxima-
tions were used to model the nonlinear flow gain coefficient of the
valve. With regard to the analysis of the deadband in these valves,
which is a key factor that limits both static and dynamic perform-
ance in feedback control of fluid power systems, in Refs. [65] and
[66], a new methodology for the identification of the dead zone
was proposed. The proposed method was based on the observation
of the dynamic behavior of the pressure in the valve gaps and was
achieved by using only pressure transducers. Experimental tests
were carried out to demonstrate the efficacy of this methodology.
A novel nonlinear sliding mode controller was developed in
Ref. [67]. The results demonstrated that the sliding mode control-
ler can determine fast response times, with small overshoots and
steady-state errors.
In Ref. [68], a multidomain nonlinear dynamic model of a pro-
portional solenoid valve system was developed in the form of non-
linear state equations and was validated by experimental data.
This model successfully predicts the dynamic characteristics of
the valve and can be used as a powerful computational and simu-
lation tool for valve design and algorithm optimization [68].
In Ref. [21], a control strategy that is based on the peak and
hold (P&H) technique and that requires only a low cost microcon-
troller was proposed. The P&H technique, widely used to control
Diesel fuel injection systems, consists of a particular PWM signal
with a variable duty cycle composed of two constant signal phases
with different voltage and current values. Similarly, the system
proposed in that paper for the control of proportional valves
employs, after the polarization phase, a peak high duty cycle to
approach the target position of the spool followed by a lower duty
cycle (hold) to maintain the position (see Fig. 22). This strategy
gives a very fast valve response, even comparable to that provided
by standard closed-loop control systems, with a cost similar to
available open-loop control systems [21].
In Ref. [69], a digital state observer feedback control system,
which is based on the digital signal processor and dynamic mathe-
matical model of a proportional valve, was designed. Bu and Yao
[70] proposed three different types of controllers to improve the per-
formance of proportional directional valves: (a) an open-loop com-
pensator which requires the accurate valve dynamic model
information; (b) a full state feedback adaptive robust controller, which
effectively takes into account the effect of parametric uncertainties
and uncertain nonlinearities such as friction force and flow force; (c)
an output feedback adaptive robust controller to address the problem
of unmeasurable states which takes into account the effect of both
parametric uncertainties and uncertain nonlinearities [70].
A new method to tune the proportional-integral-derivative
(PID) parameters of controllers for proportional directional valves
without modeling and a priori knowledge of the system was
Table 3 Some partially and fully 3D models presented in the scientific literature that simulate the flow field through a proportional
directional valve
Authors CFD software Simulations Domain Number of cells Fluid model
Turbulence
model Wall treatment
Amirante et al.
[4]
ANSYS FLUENT Full stroke,
pressure
drop ¼40 bar
Partially 3D,
unstructured
800,000 Incompressi-
ble, stationary
RNG-keEnhanced wall
treatment
Milani et al.
[36]
OpenFOAM Five spool
positions
(inverse and
direct flow)
Partially 3D,
unstructured
3,000,000 Incompressi-
ble, stationary
and transient
SST kxNot mentioned
Lisowski et al.
[33]
ANSYS FLUENT Fixed position,
simulation
performed at
30, 60, 90, 120
and 150 l/min
Fully 3D,
unstructured
900,000 Incompressi-
ble, stationary
KeNot mentioned
Amirante et al.
[32]
ANSYS FLUENT 2/3 of the full
stroke,
pressure
drop ¼100 bar
Fully 3D,
unstructured
2,000,000 Incompressi-
ble, stationary
RNG-keEnhanced wall
treatment
Ye et al. [46]ANSYS FLUENT Five positions
of the full
stroke for
different pres-
sure drops
Partially 3D,
unstructured
450,000 Incompressi-
ble, stationary
RNG-keNot mentioned
Amirante et al.
[10]
ANSYS FLUENT Full stroke,
pressure
drop ¼70 bar
Fully 3D,
unstructured
1,500,000–2,000,000
according to the spool
position
Mixture
model,
Schnerr and
Sauer,
stationary
RNG-keEnhanced wall
treatment
Lisowski et al.
[52]
ANSYS FLUENT Gap widths
spanning from
0.1 mm to
0.4 mm with a
step of 0.1 mm
Fully 3D,
unstructured
4,100,000 cells Incompressi-
ble, stationary
KeNot mentioned
Journal of Dynamic Systems, Measurement, and Control FEBRUARY 2019, Vol. 141 / 020801-13
proposed in Ref. [71]. The optimization of the PID parameters was
achieved through statistical analysis by using the proposed method.
The results showed that the optimized controller performs well, con-
firming that the tuning method is effective while also being straight-
forwardtoimplement[71].
Proposals to employ controllers based on Fuzzy logic are also
present in the scientific literature. In Ref. [72], an unconventional
electro-hydraulic proportional flow control valve based on a
switching solenoid and a fuzzy-logic controller was proposed for
application to hydraulic presses. The fuzzy-logic controller was
employed to linearize the force/stroke characteristics. The experi-
mental results showed very good results in terms of the control of
the ram velocity of a press cylinder. A combined fuzzy-PID sys-
tem was designed in Ref. [73] to control a proportional valve,
showing fast response and small overshoot.
In Ref. [20], a control method was proposed that uses the pro-
portional solenoids simultaneously, contrary to the normal control
method that energizes only one solenoid at a time. The perform-
ance of the valve is greatly influenced by the nonlinearity of the
proportional solenoid, such as dead zone and low force gain with
a small current, and this effect cannot be eliminated by a simple
dead-zone current compensation [20]. To avoid this disadvantage,
the authors of that paper proposed a differential control method
(DCM). By employing DCM, the controller outputs differential
signals to simultaneously energize both solenoids of the propor-
tional valve, and the operating point is found by analyzing the
force output of the two solenoids to minimize the variation of the
current-force gain. The comparisons of the valve response charac-
teristics were performed between normal control method and
DCM by nonlinear dynamic simulation and experiments. Simula-
tion and experimental results showed that, by using DCM, the fre-
quency response of the valve is greatly enhanced, especially when
the input is small, which means that the dynamic characteristics of
the proportional valve are improved [20].
In Ref. [74], severe nonlinearities around the spool neutral posi-
tion due to nonlinear spring force, nonlinear solenoid force and
disturbances arising from flow force working on the spool were
overcome through a dead-zone compensation design, a disturb-
ance rejecting control design, and a control design for improving
the reference tracking ability. In particular, an input shaping filter
was applied to optimize the control characteristics in the high fre-
quency range [74]. The results demonstrated that the application
of the proposed control design using input shaping filter can satis-
factorily compensate for the dead-zone and greatly improve the
dynamic response characteristics of the valve [74].
In Ref. [75], relationships of classical electrodynamics were
used to derive a clear and detailed model that describes the influence
of sinusoidal currents on the inductance and eddy current resistance,
dependent on the spool position. In addition, a control theoretic
approach was proposed to determine the spool position, and a
numerically efficient reduced order observer was designed [75].
In Ref. [76], the application of a model-based control structure
called embedded model control was presented. The overall control
consists of two hierarchical loops: the inner loop is the solenoid
current regulator with a closed-loop bandwidth close to 1 kHz.
The outer loop is a position tracking control, in charge of the
accurate positioning of the spool with respect to valve openings
[76].
In Ref. [77], a method for identifying solenoid valve transition
events by analyzing the current through the solenoid coils was
proposed. The method estimates the spool position through identi-
fying slope changes in the solenoid coil current traces. This meth-
odology was able to identify the timing of valve transition events
with less than 7% error compared to the measurement of the posi-
tion of the valve spool obtained through a laser displacement sen-
sor. As the method is based on measuring the current, it requires
no modification to the valve or valve housing [77].
In Ref. [78], an improved nonlinear sliding-mode controller
was developed. Experimental studies were conducted and the
results showed that the controller can achieve a continuous and
stable sliding mode state, realize the time-optimal step response
of a valve, and exhibit strong disturbance rejection abilities [78].
In Ref. [79], the detection of faults in these valves was
addressed. It was shown that faults could be detected with the use
of additional hardware or software. A proposal for low-cost, effi-
cient changes to commercially available valves was also given in
the paper.
A new idea is represented by the “digital hydraulics” approach,
which aims at applying digital principles to hydraulics by using
multiple or high-speed on/off valves controlled through software
rather than using proportional and servovalves [80,81]. With
regard to multiple valves, the idea is to use only one size of valve,
which is optimal in the sense of flow density, response time, and
fault tolerance. However, this concept is very demanding, as a
larger number of valves are needed. The benefits of such systems
are fast and amplitude independent response, redundancy, and
robustness against oil impurities [82]. Drawbacks are large space
requirement, complexity of control, and possibly higher price.
Several papers are present in the scientific literature that study
digital hydraulics systems in detail [49,8289].
Conclusions
This paper has provided an overview on the operating princi-
ples, mathematical modeling, industrial and research state of the
art of directly driven proportional directional hydraulic valves.
These valves contain an inner sliding spool, directly moved by
solenoids inside a valve body, which is provided with notches to
allow flow rate metering as a function of the spool position. Com-
mercially available units present lower dynamic performance but
also lower costs than servovalves. The operational field on the
flow rate-pressure plane is limited because sufficiently compact
solenoids are not capable of counteracting high flow forces.
The flow rate and flow forces can be predicted by means of sim-
ple formulae which can be very useful for preliminary calcula-
tions. The validity of these formulae has been widely
demonstrated; however, they depend on the discharge coefficient
and flow angles, which can assume different values according to
the spool position, notch geometry, and operating conditions. To
investigate how these parameters affect the discharge coefficient
and flow angle, experimental and CFD approaches have been used
in the scientific literature. The role of CFD modeling is notewor-
thy as it can allow a precise evaluation of the flow characteristics
of a proportional valve for a given geometry of the spool notches,
without the necessity of setting up an entire experimental circuit.
At first, authors concentrated their efforts in developing partially
3D CFD models. However, with the ever-increasing capability of
hardware resources, the use of fully 3D approaches has become
more common, and the scientific literature presents several papers
in which the high accuracy of full 3D models is demonstrated by
comparing numerical predictions with experimental data. The
flow is usually treated as incompressible, however some models
also take into account the occurrence of cavitation by means of a
Fig. 22 Peak and hold technique employed in Ref. [21]
020801-14 / Vol. 141, FEBRUARY 2019 Transactions of the ASME
mixture model which simulates the formation of vapor inside the
liquid. The use of CFD to predict the discharge coefficient, flow
angle, and occurrence of cavitation can assist valve design by
studying optimized geometry, in particular to allow the flow
forces to be reduced, thus aiming at enlarging the operation field
of these valves. A few optimized geometries are proposed in the lit-
erature that are more effective than commercial ones in terms of
flow forces. These geometries regard either the optimization of the
spool profile, by acting on the inlet and outlet velocity angles, or
the valve body, by adopting additional channels which can equalize
the circumferential pressure distribution on the spool.
Research has also been focused on improving the control sys-
tems of these valves. Detailed models of the solenoid assembly
are proposed to accomplish this task. Several effective methods
have been proposed, such as a control based on the peak and hold
technique, or a differential control method in which the controller
outputs signals to simultaneously energize both solenoids of a pro-
portional valve to improve linearity, or the employment of shap-
ing filters or hierarchical control loops, or sliding mode
controllers. A new idea is digital hydraulics, which aims at apply-
ing digital principles to hydraulics by using multiple or high-
speed on/off valves controlled through software rather than using
proportional or servovalves.
References
[1] Plummer, A., 2016, “Electrohydraulic Servovalves—Past, Present, and Future,”
Tenth International Fluid Power Conference, pp. 405–424.
[2] Tamburrano, P., Plummer, A. R., Distaso, E., and Amirante, R., 2018, “A
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... The main difference between a servovalve (both two-stage and single-stage) and a proportional valve is that the former employs a bushing sleeve, which allows finer tolerances to be achieved and hence lower overlaps between spool lands and slots [3,7]. [4]; (b) direct drive servovalve [6]. ...
... The main difference between a servovalve (both two-stage and single-stage) and a proportional valve is that the former employs a bushing sleeve, which allows finer tolerances to be achieved and hence lower overlaps between spool lands and slots [3,7]. ...
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This paper is a thorough review of innovative architectures of electro-hydraulic servovalves that exploit actuation systems based on piezo-electric materials. The use of commercially available piezo-electric actuators, namely, piezo stacks, amplified piezo stacks, rectangular benders, and ring benders, is very promising for the actuation of the main stages and of the pilot stages of servovalves given the fast response and low weight of piezoelectric materials. The use of these actuators can also allow novel designs to be developed, thus helping manufacturers to overcome the typical drawbacks of commercial servovalves, such as the high complexity and the high internal leakage of the pilot stages of two-stage servovalves as well as the large size and weight of direct-drive servovalves. First, the piezoelectric actuators that can be used for driving servovalves are presented in the paper, and their characteristics are thoroughly discussed. The main novel architectures present in the literature are then explained and compared with the commercial ones, and their performance parameters are discussed to draw conclusions on the prospect that some of these architectures can be used by manufacturers as future designs.
... Servo valves have functions of both electro-mechanical energy conversion and signal amplification, which, to a great extent, determines overall performance of electrohydraulic control system itself [1][2][3][4]. The electro-hydraulic servo valve can be divided into direct acting type and pilot operated type. ...
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... Для реализации разнообразных схем управления гидроприводом применяются электромагнитные золотниковые распределители [4,5]. На работу подвижных частей золотникового распределителя влияет процесс трения, приводящего к их постепенному разрушению [6], а также существует влияние со стороны эрозионного износа, возникающего при попадании в золотник частиц металла. ...
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Although a two-dimensional (2D) valve has excellent performance, the processing of its spiral groove has a high cost and is time-consuming. This paper proposes a novel torque motor based on an annulus air gap (TMAAG) to replace the negative feedback function of the spiral groove to reduce the machining difficulty. In order to study the torque change law of the TMAAG, the air gap permeance was analyzed, and then a qualitative analytical model was established. Orthogonal tests were carried out to initially select the crucial parameters, which were further optimized through a back propagation (BP) neural network and genetic algorithm. The prototype of TMAAG was machined, and a special experimental platform was built, and experiment results are similar to the simulation values, which verifies the accuracy of the air gap analysis and qualitative model. For torque-angle characteristics, the output torque increases with both current and rotation angle and reaches about 0.754 N·m with 2 A and 1.5°. While for torque-displacement characteristics, due to the negative feedback mechanism, the output torque decreases with increasing armature displacement, which is about 0.084 N·m with 2 A and 1 mm. The research validates the unique negative feedback mechanism of the TMAAG and indicates that it can be potentially used as an electro-mechanical converter of a 2D valve.
... Concerning the discharge coefficient, it was assumed, for simplicity, to be constant and equal to = 0.7. Because of the large pressure drops used in the simulations, this assumption can be considered valid for a large part of the spool stroke, when the flow is turbulent and, for turbulent flows, the discharge coefficient in servovalves is constant, ranging from 0.65 to 0.7 regardless of the spool position [1,33], unlike the discharge coefficient in proportional valves which can have different values even for turbulent flows depending on the notch geometry and on the spool position [34]. The flow in the metering chamber of a servovalve is laminar only for very low values of the Reynolds number, usually for Re < 200 to 400 [1,29]; therefore, an error is introduced only at the very small opening degrees, without affecting the overall simulation. ...
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This paper presents a feasibility study using commercially available amplified piezo-stacks for the direct actuation of four-way three-position (4/3) direct drive servovalves. The prospect of using amplified piezo-stacks in place of linear force motors is very attractive by virtue of their fast response speed and low weight. Piezo-stacks equipped with mechanical amplification systems can give levels of displacement suitable for this application. A very effective amplification system has recently been produced by some manufacturers and is based on a temperature-independent diamond structure. This paper details simulations of a 4/3 servovalve directly actuated by such a piezoelectric actuator with a diamond structure. To this end, well-established equations, implemented in Simulink by means of the libraries of Simscape Fluids, are used. The proposed architecture shows simplicity of construction; in addition, very good step response speed and frequency response are predicted by the simulations.
... The main difference between a servovalve (both two stage and single stage) and a proportional valve is that the former employs a bushing sleeve, which allows finer tolerances to be achieved and hence lower overlaps between spool lands and slots [3,7]. ...
Preprint
Full-text available
This paper is a thorough review of innovative architectures of electro-hydraulic servovalves that exploit actuation systems based on piezo-electric materials. The use of commercially available piezo-electric actuators, namely, piezo-stacks, amplified piezo-stacks, rectangular benders and ring benders, is very promising for the actuation of the main stages and of the pilot stages of servovalves, given the fast response and low weight of piezoelectric materials. The use of these actuators can also allow novel designs to be developed, thus helping manufacturers to overcome the typical drawbacks of commercial servovalves, such as the high complexity and the high internal leakage of the pilot stages of two stage servovalves, as well as the large size and weight of direct drive servovalves. Firstly, the piezoelectric actuators that can be used for driving servovalves are presented in the paper and their characteristics are thoroughly discussed. Then, the main novel architectures present in the literature are explained and compared with the commercial ones, and their performance parameters are discussed to draw conclusions on the prospect that some of these architectures can be used by manufacturers as future designs.
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Flat force–displacement characteristic has crucial influence on the performance of linear electro-mechanical converter of electro-hydraulic servo-proportional valves. The commercial proportional solenoids obtain such features by welding a non-magnetic separator ring, which is complicated and time-consuming. This article presents a novel modulation approach to obtain the flat force–displacement characteristic of linear electro-mechanical converter by constructing a by-pass air gap. Taking an existing linear force motor as an example, the force–displacement characteristic curves of the linear force motor with by-pass air gap and without by-pass air gap are both studied using magnetic circuit analysis and finite element method under different excitation currents. Based on the finite element method simulated data, the response surface method is used to perform the experiment design for structure parameters of linear force motor with by-pass air gap, and the quadratic fitting equations are obtained for further optimization. To balance conflicted design objectives such as linearity, mean value of output force and power-to-weight ratio, the structural parameters of the linear force motor with by-pass air gap are optimized using a multi-objective optimization algorithm based on particle swarm. Prototypes of linear force motor with by-pass air gap and without by-pass air gap are both manufactured, and a special test rig is built. The static and dynamic experimental results are consistent with the theoretical analysis. The former proves that the linear force motor with by-pass air gap can obtain a nearly flat force–displacement curve with reasonable parameter optimization and also improve output force, and the latter reveals that a linear electro-mechanical converter with flat–displacement characteristic has better working stability over common ones. The proposed modulation approach provides a new approach for the design of flat force–displacement characteristic of linear electro-mechanical converter.
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The u-shape notch of spool valve is usually combined with the other typical throttling notches to achieve proportional flowrate adjustments in practical hydraulic control applications. Due to the vacuum-suction nozzle-structural effect, u-shape notch is more likely for cavitation arising. Traditionally, notch throttling is based on the continuity and Bernoulli equation to explain the Harvey nuclei bubble flow from development to collapse, which is not entirely agreed with present proliferated large vapor vortex cavitation researches. In this paper, experimental and numerical analysis discuss the morphological characteristics of u-shape notch vortex cavitation and the choked flow issues caused by vortex cavitation. The large vapor vortex cavitation morphological reproduced by the Large Eddy Simulation (LES) model associated with the multi-phase cavitation model is very close to experimental observations. Further, based on the clear cavity entity obtained by simulation, it could be found that, as notch opening increases, the cavity starting position moves back and the cavity moves upward. And as pressure difference increases, the cavity length increases smoothly until critical pressure value, after which the length increases sharply and maintains in long length level. In addition, it seems that the normalized measurement manner of cavitation length could be proposed, if using local cavitation number dividing incipient cavitation as abscissa to measure the cavity length. Moreover, the cavitating flowrate equation is proposed considering the cavitation-induced serious choked flow problem. The vortex cavitation, especially its length, is assumed to represent intense enough notch vortex flow friction loss. Based on the added flow loss term, the classical flowrate equation is revised, according to which the cavitating flowrate could be predicted within the accuracy of 0.5–2.0%.
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Conference Paper
Full-text available
This paper presents a new concept hydraulic valve that tries to overcome a well-known poser affecting the pilot operated proportional valves, the flow forces. Despite of the traditional compensated profile spool valves, the basic idea is to design a valve that has as few mobile surfaces as possible. This assumption modifies the traditional valve design method and opens to new possibilities for the proportional valves. The solution presented in this paper uses an axial flow valve, where the oil gets through the valve across its axis, with two rotating surfaces causing a rotational metering. The result of this new design approach shows several advantages with respect to the common spool valves, such as the extremely compact size and the device versatility. This particular valve can realize the majority of the functions achievable using a two-way two-position proportional valve piloted by two pressure signals (for example a pressure compensated valve); the axial flow and the "built-in" metering edges yield the possibility to produce this valve as a cartridge component, whit all the advantages incidental to this type of devices. Some Computational Fluid Dynamics Analysis confirm the prediction of a low affection of this valve by flow forces, this attitude makes the axial Flow and Rotational Metering Valve particularly suitable for the local compensation in Flow Sharing Load Sensing distributors.
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This paper provides a review of the state of the art of electro-hydraulic servovalves, which are widely used valves in industrial applications and aerospace, being key components for closed-loop electro-hydraulic motion control systems. The paper discusses their operating principles and the analytical models used to study these valves. Commercially available units are also analysed in detail, reporting the performance levels achieved by current servovalves in addition to discussing their advantages and drawbacks. A detailed analysis of research that investigates these valves via computational fluid-dynamic analysis is also provided. Research studies on novel control systems and novel configurations based on the use of smart materials, which aim to improve performance or reduce cost, are also analysed in detail.
Conference Paper
The energy efficiency of load sensing working hydraulics of mobile machines should be improved. Digital hydraulics is one approach to decrease the losses of cylinder drives and this study concentrates on the design of the control mode selection algorithm for multiactuator system. Measurements are done on a 5-ton wheel loader and the energy consumption of a digital valve system is compared to a traditional load sensing system using simulations.
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This paper aims to analyze the flow characteristics and fluid torques in a direct drive rotary control valve with a novel structure, and based on the computational fluid dynamics method, the advantages of improved structure are verified. With the establishment of the valve structure and the simulation model, the sliding mesh model and moving region grid are applied to simulate the complete opening and closing process of the valve at dynamic conditions. The results present that the fluid torques generate resistance torques during the increasing process of flow area while providing driving torques in the decreasing period of flow area, which is consistent with the theoretical analysis. In addition, the flow regulation of the fluid chamber is conducted with the computational fluid dynamics method and experimental test, which exhibited disagreement due to the oil leakage phenomenon. The simulation results and experimental results both convince the pressure and flow characteristics, and the improved valve model shows decreased fluid torques of around 17% compared with the original one under the system pressure of 6 MPa.
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The main objective of this article was to analyse flow forces acting on a spool of a proportional control valve in the initial phase of the spool gap opening. Accordingly, modification of the spool geometry has been proposed in order to reduce flow force values. The modification consisted in making small circular undercuts at the apex of main triangular grooves, which were made on the spool. The undercuts were made in order to improve flow characteristics, for the gap width less or equal to 0.40 mm. Two arrangements of undercuts were tested. In the first version the undercut was made only on one groove, while in the second version two undercuts were located symmetrically on both sides of the spool. Simulations were carried out by the means of CFD methods and allowed both axial and radial flow forces to be determined. The simulation results showed that the use of a single undercut allowed the valve to operate at a very low flow. However, a significant radial force asymmetry appeared. The use of symmetric undercuts reduced the unevenness of radial forces, with a relatively small increase in flow rate and axial force. The obtained axial force values were next verified experimentally on a test bench.
Conference Paper
A key component of hydraulic fluid power systems - the standard orifice and, consequently, all equivalent components - apparently has, to this day, some mysteries yet to be unveiled. Knowledge on cavitation-induced liquid flow choking or saturation, which is a well founded topic in some areas of the wide field of hydraulics, e.g. water distribution piping systems, is practically neglected when assessing the design of typical mineral-oil-based power generation and control systems, for both mobile and industrial applications. This conclusion holds true at every level of study, from the technical reference literature adopted by designers to the more popular textbooks and journal papers. Moreover, the rare works addressing the phenomenon are focused on the underlying physical mechanics, completely missing any kind of evaluation of the functional consequences, especially the need to "revise" the standard quadratic law of turbulent flow. Prompted by one of these works, a preliminary experimental activity has been carried out, aimed at determining the actual flow characteristic of standard screw-in orifices used in fluid power pilot circuits. The results confirmed the undoubted presence of flow saturation; based on that, a suitable theoretical description was developed, and some practical applications are outlined in the paper. Finally, few open questions are listed, which need to be answered.
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A numerical model of a servoactuator and of a four-port proportional direction control valve has been developed. Mechanical and hydraulic elements have been simulated in the LMS Amesim® environment. The complete model has been validated on the basis of the experimental time histories of the actuator velocity and of the flow-rate controlled by the proportional valve. The validation data have been acquired on a fluid power system used to test electro-hydraulic servovalves according to ISO 10770-1 standard. The measurement of the instantaneous flow-rate through the valve has been performed with an innovative high-dynamics flowmeter, recently developed for high-pressure liquid flows. Furthermore, the model predicted static characteristic of the proportional valve has been compared with a corresponding experimentally derived curve and an analysis of the cause-and-effect relationships has been carried out for the valve static performance. Measured data on valve leakages have also been presented in order to complete the steady-state characterization of the tested valve. The developed model of the hydraulic system has been then applied to realize the Bode diagram of the proportional valve, which is expressed in terms of instantaneous flow-rate as a function of the sinusoidal driving command, as well as the Bode diagram of the subsystem made up of the proportional valve and of the linear actuator. The latter Bode graph is plotted in terms of piston velocity as a function of the sinusoidal driving command provided to the valve. The comparison between the two Bode diagrams has confirmed the accuracy of the ISO procedure, which is based on the assumption of negligible delay introduced by the dynamic response of the servo-actuator and by the oil compressibility. A reliable and cost-saving methodology, which uses the innovative flowmeter instead of the low inertia servo-actuator, is proposed as an alternative to the ISO standard for testing the dynamic response of proportional valves.
Conference Paper
As the force output of an electromagnetic actuator is limited, achieving reliable operation of a direct-acting solenoid valve at high pressures and flow rates can be challenging. The major performance obstacle is the hydrodynamic flow force acting on the spool as it moves between energized and de-energized states. With trends in the fluid power industry requiring valves to operate at higher pressures and volumetric flow rates, while minimizing electrical power consumption, methods to reduce hydrodynamic flow forces become critical in developing functional products. This paper presents CFD simulation and correlating experimental results in using back angles to reduce the hydrodynamic flow forces in a direct-acting, solenoid operated, cartridge-style, directional control valve. Traditional methods of calculating flow forces are discussed and a brief summary of prior research is presented. A commercially available CFD package, Fluent, was used to numerically estimate the flow forces using a realizable k-ε turbulence closure model. A parametric analysis of flow, pressure, and spool stroke showed sensitivity to the metering edge geometry. A special fixture was created to isolate and directly measure the forces acting on the spool. The addition of a +60° back-angle showed the largest flow force reduction of 36% compared to a spool with no back angle.
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Hierarchical control architectures are a common approach when hydraulic systems are under study; provided their multi-domain nature, the control scheme is commonly split into different hierarchical levels each one associated with a particular physical domain. This paper presents the application of a model-based control structure called Embedded Model Control (EMC) when a hierarchical scheme is implemented on an electro-hydraulic proportional valve. The overall control consists of two hierarchical loops: the inner loop is the solenoid current regulator with a closed loop bandwidth close to 1 kHz. The outer loop is a position tracking control, in charge of the accurate positioning of the spool with respect to valve openings. The paper addresses the outer loop, i.e., the tracking of mechanical spool position by using the EMC. Analysis and synthesis are presented as well as experimental results obtained from a test rig provided by an industrial manufacturer.