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The paper presents theoretical and experimental results of studies on the influence of shape and number of spool notches on the discharge characteristics (discharge coefficient, velocity coefficient and flow angle) of a hydraulic distributor metering edge. The flow-rate vs. pressure drop and the steady state axial flow-force vs. pressure drop diagrams are determined for spools with different configurations of multiple notched metering edges. Various combinations of the shape and number of the notches modulating the metering area of the passage between supply and drain ports were investigated and correlated with flow-rate, axial flow-force and pressure drop, in order to get estimates of discharge coefficient and flow angle. The procedure is applied to all the data collected during the experimental activity, and shows the behaviour of the flow characteristics in both the fully turbulent and transitional region of motion. The influence of notch shape and number on the metering edge flow characteristics is evaluated as well. © 2005 TuTech.
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M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 1
INFLUENCE OF NOTCH SHAPE AND NUMBER OF NOTCHES ON THE METERING
CHARACTERISTICS OF HYDRAULIC SPOOL VALVES
1)
M. Borghi,
1)
M. Milani,
2)
R. Paoluzzi
1)
Department of Mechanical and Civil Engineering – University of Modena & Reggio Emilia
Via Vignolese, 905/b – 41100 Modena – Italy
2)
IMAMOTER – CNR
Via Canal Bianco 28 - 44044 Cassana (Ferrara) - Italy
Keywords Hydraulic components, spool valves, metering edge, metering notches, experimental
characterization, discharge coefficient, axial flow-forces
ABSTRACT
The paper presents theoretical and experimental results of studies on the influence of shape and number of spool
notches on the discharge characteristics (discharge coefficient, velocity coefficient and flow angle) of a
hydraulic distributor metering edge.
The flow-rate vs. pressure drop and the steady state axial flow-force vs. pressure drop diagrams are determined
for spools with different configurations of multiple notched metering edges. Various combinations of the shape
and number of the notches modulating the metering area of the passage between supply and drain ports were
investigated and correlated with flow-rate, axial flow-force and pressure drop, in order to get estimates of
discharge coefficient and flow angle.
The procedure is applied to all the data collected during the experimental activity, and shows the behaviour of
the flow characteristics in both the fully turbulent and transitional region of motion. The influence of notch
shape and number on the metering edge flow characteristics is evaluated as well.
1. Introduction
The modulation of fluid power, in modern electro-
hydraulic systems for both industrial and mobile
application, is obtained by proper metering
characteristics of the notches in the metering edge
of the valve spool.
The design of this type of components and the
simulation of their steady state and dynamic
behaviour, is made difficult by the peculiarities of
flow conditions as a function of metering area and
by the complex dependencies on fluid flow. In the
early 60s’ pioneering studies carried out at M.I.T.
focused the attention of researchers on the
fundamental role played by the variability of
discharge coefficient and efflux angle on the
behaviour of a metering edge. This was found to
affect significantly the variation of power
modulation function performed. The effect of
metering edge geometry and of spool-seat coupling
were highlighted by Blackburn et al. (1960) and in
Merritt (1967). Viersma (1980) describes the role
played by stationary and dynamic efflux
characteristics in hydraulic servo-systems, where
the transition from laminar to fully turbulent flow is
handled by a tailored function describing the
variation of the discharge coefficient. The
experimental study presented by Johnston et al.
(1991) details on one hand the effect of the shape
on the metering characteristics of poppet and disk
valves, on the other highlights, in particular for
fully turbulent flows, how the design parameters
could influence these characteristics, mainly in
terms of flow forces acting on the moving element.
The detailed experimental investigation carried out
by Lugowsky (1993), shows that axial flow forces,
and consequently discharge characteristics, are
conditioned not only by opening of the metering
edge, but also by geometries of spool and seat and
by other factors, like the Coanda effect.
The ever increasing demand for numerical tools for
sizing and simulation of fluid power components,
forced many researchers to address the topic of
characterization of static and dynamic flows of
incompressible fluid through geometries
representing the metering edge of hydraulic valves.
Several papers by the Authors were devoted to
Computational Fluid Dynamics (CFD) simulation
and to experimental verification of typical
discharge coefficient values found in industrial
components. They reported results on sharp edged
geometries (Borghi et al., 1996, 1997 and 1998),
conic profile (Borghi et al., 1999) and on typical
‘compensated’ profile for the minimization of axial
flow forces (Borghi et al., 2000). Work by Ellmann
and Piche (1996) and Wu et al. (2002), was
concerned with developing a semi-empirical
expression describing the variability of the
discharge coefficients in fixed-geometry orifices.
Wu et al. (2003) extended this work by considering
the fluid flow at very small openings. All these
approaches can be powerful tools for the modelling
of this kind of simple components but,
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 2
unfortunately, on one hand they are not directly
applicable to complex shapes and, on the other
hand, they need the knowledge of the saturated
flow characteristics in order to give information in
the whole operational envelope of the variable
metering orifice. Other interesting results providing
a better insight into the problem have been obtained
by Elgamil (2001), Gromala et al. (2002) and Del
Vescovo and Lippolis (2002).
The results presented in this paper are concerned
with steady-state analysis of metering edges with
notches. The aim of the paper is to show what
effect the shape and number of notches may have
on the discharge characteristics of orifices under
different operating conditions.
The first part of the paper presents the experimental
set-up used. Eight different spools with different
notches have been tested over a wide range of input
hydraulic power. The shape of the grooves was
derived from typical industrial designs and
metering edges had two, three or four grooves.
Experimental data have been used to estimate the
characteristic of a given metering edge and,
consequently, the discharge coefficient and efflux
angle variations as a function of flow conditions.
The investigation drives to the definition of both
saturation values for discharge characteristics and
variation of coefficients as a function of shape and
number of considered notches.
2. Nomenclature
a, b, c, d, a
1
, b
1
Polynomial coefficient
Dp, ∆p
Pressure drop
A Area Q Flow rate
F Force Re Reynolds number
C
D
Discharge Coefficient R Hydraulic Resistance
C
V
Velocity Coefficient
ρ
Fluid density
*
V
C
Flow Coefficient
ν
Fluid kinematic viscosity
D
H
Hydraulic diameter
θ
Jet Angle
S Wetted Perimeter
Subscript
AX Axial component T Turbulent
EXP Experimental TH Theoretical
Superscript
SAT Saturation
3. Experimental Analysis
The hydraulic components for industrial application
show a wide variety of notch types. The notches are
designed to control hydraulic power supplied to
actuators, by varying the area of the metering edge.
The shape of these notches, as well as their number
and angular position, affect the dynamic behaviour
of the fluid, as they determine the input/output jet
angles and discharge coefficient. The angular
position of the notches determines the symmetry of
the flow through the orifice.
Among the large number of possible edge
configurations, only the three notch shapes shown
in Figure 1 have been considered for the
experimental investigation. The first notch, Figure
1-TYPE A, has a rectangular shape ended by a
semicircle, the second, Figure 1-TYPE B, is
obtained by connecting three semicircles with very
short rectangles (not visible in Figure 1), while the
third notch, Figure 1-TYPE C, has a triangular
section, in both axial and radial direction.
As shown in Figure 1, the three different types of
notches have the same axial length (5.25 mm),
radial depth (2.20 mm), and overlap when the spool
is centered (2.25 mm). All the prototypes were built
with a high control on dimensional tolerances,
maintaining the radial clearance between spool and
sleeve less than 5 µm, and the error in metering
edge opening less than 0.1 mm. This choice of
clearance and positional error permits use of
standard, commercial spools in test rig, and
focusing of the research on the influence of the area
gradient on the orifice flow characteristics.
In order to study the influence of notch number and
their angular positions, three different
configurations were designed and tested: two
notches at 180°, three notches at 120° and four
notches at 90° angular spacing.
The experiments were carried out using the test
bench presented in Figure 2. The circuit schematic
is shown in Figure 2-a. A variable displacement
pump (2) is connected to a volumetric flow-meter
measuring the flow-rate supplied by the pump (3,
range 0-150 l/min, class 0.2 absolute) to a variable
orifice (6) representing the metering edge, and to a
second volumetric flow-meter (10, range 0-150
l/min, class 0.2 absolute). The supply pressure is set
by a relief valve (5), and the pressure drop across
the variable orifice is measured using two piezo-
electric pressure transducers (4 and 5, range 0-600
bar, class 0.2 absolute). A detail of the test bench is
shown in Figure 2-b. A fine pitch worm screw is
used to adjust the axial position of the notched edge
under test and also to measure the axial force
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 3
applied to the spool which is marked (8), (range 0-
150 N, class 0.1 absolute). The equipment which
supports the piezo-electric micrometer (range 0-15
mm, class 0.1 absolute) is marked (9).
NOTCH TYPE A NOTCH TYPE B NOTCH TYPE C
Figure 1: The notch shapes designed to perform the efflux characteristics experimental characterisation.
(a
(b
Figure 2: The test bench used for the experimental activity. (a Circuit sketch. (b A detail of the mechanical
equipments designed to vary and to measure the metering opening, and to measure the axial force acting on the
spool.
The tests were performed in order to determine the
steady-state flow-pressure characteristics of each of
the eight notched edges considered. The opening of
the metering edge were in the range 1 to 4 mm, in
order to reduce the influence of the notch
boundaries on the metering edge discharge
characteristics.
Table 1 shows the openings used in the steady state
characterization, for each one of the cases
considered. Some of the data reported in Table 1
can be reviewed referring to Figure 3, which shows
both the axial location of some of the experimental
openings along the non dimensional spool travel,
and the correspondent non dimensional minimum
value of the geometric area 1 . The spool
displacement was non-dimensioned against
maximum notch length and orifice area against its
maximum value. The total efflux area was
calculated, for each metering edge, as the sum of
the areas geometrically defined by each notch at
given spool axial travel.
As shown in Figure 3, the steady state
characteristics were collected for the metering
1
This is the minimum value of the cross sectional
area of the flow passage across the metering edge,
evaluated at each axial spool position.
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 4
edges designed with the Notches Type A in the
following positions:
an opening representative of the initial area
gradient (in the range 1 to 1.4 mm);
a second opening close to the area
discontinuity (geometrically located 2.25 mm
far from the notch opening);
a third opening placed in the region with
constant metering area.
The Notch TYPE B introduces two discontinuities
into the metering area gradient, and the
experimental activity was carried out in order to
catch the metering edges behaviour in two extreme
conditions:
1. close to the discontinuity;
2. in positions where discontinuity effect can be
neglected.
The area function corresponding to the introduction
of Notches TYPE C is quadratic with the notch
opening. As shown in Figure 3, the measurement
points chosen for this edge configuration were set
far from the notches boundaries, in the range
between 1.60 and 3.60 mm.
The steady-state characteristic curves (namely the
pressure drop vs. flow-rate curve and the axial
flow-force vs. pressure drop curve) were collected
for a large number of points in a range limited by
the available hydraulic power (about 100 kW). The
flow-rate was varied from 0 to 120 l/min and the
relief valve setting from 0 to 300 bar. The steady-
state characterization was performed, for each
metering edge and for each metering opening, with
a step by step increase in the flow-rate. Thanks to
the resistance offered by the volumetric flow-meter
(3), 2-4 bar of backpressure, depending on the
measured flow-rate, no cavitation phenomena were
detected along the discharge line, downstream the
metering section.
For each operating condition, the metering edge
characteristic data (the triple Q – p – F) was
determined using the averaged values obtained
during experiments. The data were collected by the
acquisition system at 250 Hz over a time interval of
0.2 s. All the data collected during the experiments
are summarized in Figures 4 to 6.
Notch Type Configuration X
OP,A
X
OP,B
X
OP,C
2 at 180° 1.05 mm 2.30 mm 3.20 mm
3 at 120° 1.40 mm 2.40 mm 3.40 mm
TYPE A
4 at 90° 1.00 mm 2.15 mm 3.20 mm
2 at 180° 2.10 mm 3.00 mm 4.10 mm
3 at 120° 1.45 mm 2.45 mm 3.45 mm
TYPE B
4 at 90° 1.50 mm 2.50 mm 3.50 mm
2 at 180° 1.60 mm 2.60 mm 3.60 mm
TYPE C
4 at 90° 1.60 mm 2.60 mm 3.60 mm
Table 1: Metering Opening Tested for the Efflux Characteristics Determination.
4. Saturated efflux characteristics of the
notched edges
The steady-state characteristics of a metering edge
as such are not a key-factor for design purposes.
The main reason is that the typical operating
condition of a component is dynamic, or at least
non-stationary. To make the steady-state
investigation effective for design purposes, it is
necessary to extract information and general
guidelines not directly available from the
experimental evidence, such as the discharge (C
D
)
and the flow (C
V
cos θ) coefficients variation with
the metering edge geometry and the fluid flow
characteristics.
Many authors (Merrit, Blackburn et al., Borghi et
al., Vaughan et al., Lugowsky, Johnston et al.),
show that a good design of hydraulic valves is
based on:
fluid flow coefficients characterization for
all active ports;
effect of geometry on the above mentioned
coefficients;
influence of the variation in the operating
conditions on the points above.
In this perspective, the stationary characterization is
a straightforward way to acquire all the information
above, indirectly showing how a specific design
choice might affect the flow conditions through a
specific valve port. The estimated characteristic
curve, in all the cases investigated, is in fairly good
agreement with theoretical predictions. Flow rate
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 5
vs. pressure curves are more or less quadratic with a
vertex in the origin. Axial force versus pressure
curve are interpolated fairly well by a line through
the origin.
In this work, the experimental data have been
interpolated using a third order polynomial in Q-p,
and a first order for F-p.
A least square fitting procedure showed that the
pressure drop can be expressed by a function of
flow rate:
32
EXP EXP EXP EXP
paQbQcQ=⋅ + +
(1)
and the axial force is a function of pressure drop
according to:
EXP EXP
Fdp=⋅ (2)
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
x/x
MAX
A/A
MAX
A
1.05 mm
B
2.3 mm
C
3.2 mm
2 Notches
Type A
at 180°
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
x/x
MAX
A/A
MAX
A
1.45 mm
B
2.45 mm
C
3.45 mm
3 Notches
Type B
at 120°
0.00
0.25
0.50
0.75
1.00
0.00 0.25 0.50 0.75 1.00
x/x
MAX
A/A
MAX
A
1.60 mm
B
2.60 mm
C
3.60 mm
4 Notches
Type C
at 90°
Figure 3: Actual Metering Opening Positions vs. Metering Edges Total Geometric Efflux Area.
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 6
0
100
200
300
0 30 60 90 120
Q [l/min]
Dp
[bar]
2 Notches
Type C
at 180°
B
C
A
0
30
60
90
0 100 200 300
Dp [bar]
F
[N]
B
C
A
2 Notches
Type C
at 180°
0
100
200
300
0 30 60 90 120
Q - l/min
Dp
[bar]
4 Notches
Type C
at 90°
B
C
A
0
50
100
150
0 100 200 300
Dp [bar]
F [N]
B
C
A
4 Notches
Type C
at 90°
Figure 4: Characteristic Curves determined for the Metering Edges having 2 and 4 Notches Type C.
0
100
200
300
0 30 60 90 120
Q - l/min
Dp
[bar]
2 Notches
Type A
at 180°
A
B
C
0
40
80
120
0 100 200 300
Dp [bar]
F [N]
A
B
C
2 Notches
Type A
at 180°
0
100
200
300
0 30 60 90 120
Q - l/min
Dp
[bar]
3 Notches
Type A
at 120°
A
B
C
0
40
80
120
0 100 200 300
Dp [bar]
F [N]
A
B
C
3 Notches
Type A
at 120°
0
100
200
300
0 30 60 90 120
Q - l/min
Dp
[bar]
4 Notches
Type A
at 90°
A
B
C
0
40
80
120
0 100 200 300
Dp [bar]
F [N]
A
B
C
4 Notches
Type A
at 90°
Figure 5: Characteristic Curves determined for the Metering Edges having 2, 3 and 4 Notches Type A.
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 7
0
100
200
300
0 30 60 90 120
Q - l/min
Dp
[bar]
2 Notches
Type B
at 180°
A B
C
0
50
100
150
0 100 200 300
Dp [bar]
F [N]
A
B
C
2 Notches
Type B
at 180°
0
100
200
300
0 30 60 90 120
Q - l/min
Dp
[bar]
3 Notches
Type B
at 120°
A
B
C
0
50
100
150
0 100 200 300
Dp [bar]
F [N]
A
B
C
3 Notches
Type B
at 120°
0
100
200
300
0 30 60 90 120
Q - l/min
Dp
[bar]
4 Notches
Type B
at 90°
B
C
A
0
50
100
150
0 100 200 300
Dp [bar]
F [N]
B
C
4 Notches
Type B
at 90°
A
Figure 6: Characteristic Curves determined for the Metering Edges having 2, 3 and 4 Notches Type B.
Tables from 2 to 4 show the values of the
polynomial coefficients computed for all the
experimental conditions examined. For the sake of
simplicity, the regression coefficient R was not
reported, but it is worth mentioning that its value is
always higher than 0.9997. The fact that the Q-p
experimental characteristic curve is better described
by third order than second order polynomials is at
least partly due to measurement errors intrinsic in
the instrumentation used. However, other
considerations apply. The flow through a restriction
can be classified, according to the amount of the
flow rate, as laminar, for low Reynolds numbers,
transitional and turbulent at higher Reynolds
numbers. The linear relationship between Q and p
used for laminar flows, turns into a second order
curve as the flow rate enters the turbulent range. It
implies that the pressure drop could be described by
the following linear combination:
2
TH1EXP1EXP
p=aQ +bQ⋅⋅ (3)
where linear and quadratic contributes are linearly
combined to describe the overall characteristic of
the restriction. In this paper, the coefficients of the
linear combination are computed using a least
square approximation, in order to give the best
possible approximation of the curve for each notch
type and opening. Tables from 5 to 7 show the
values of
()
11
a,b coefficients thus determined. The
regression values in this case are always higher than
0.97. Equation (3) can be rearranged as:
TH 1
1
2
EXP
EXP
pb
=a +
QQ
(4)
The terms at the second member of Equation (4)
equal the square of the characteristic resistance of a
turbulent orifice for an incompressible fluid, and
include the correction factor fitting the actual data
behaviour to the ideal parabolic correlation. The
resistance is usually expressed as:
ρ
=
2AC
1
R
GEOD
T
(5)
where C
D
is the discharge coefficient, ρ is the fluid
density (850 kg/m
3
) and A
GEO
is the reference cross
sectional area of the orifice.
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 8
TYPE A Opening
a
[bar/(l/min)
3
]
b
[bar/(l/min)
2
]
c
[bar/(l/min)]
d
[N/bar]
A -1.88E-03 3.13E-01 -4.75E-01 0.1557
B 1.41E-04 4.38E-02 5.26E-01 0.3170
2 at 180°
C 7.71E-05 3.65E-02 3.79E-01 0.3669
A 1.80E-04 3.81E-02 5.26E-01 0.3108
B 6.04E-05 1.81E-02 2.77E-01 0.4609
3 at 120°
C 3.38E-05 1.52E-02 1.41E-01 0.4944
A 5.19E-04 2.84E-02 7.37E-01 0.2031
B 2.50E-05 1.30E-02 1.03E-01 0.4310
4 at 90°
C 1.60E-05 8.83E-03 9.97E-02 0.5121
Table 2: Polynomial Coefficients for Experimental Data Interpolation – NOTCHES TYPE A
TYPE B Opening
a
[bar/(l/min)
3
]
b
[bar/(l/min)
2
]
c
[bar/(l/min)]
d
[N/bar]
A 1.67E-04 3.58E-02 5.32E-01 0.3239
B 7.45E-05 1.89E-02 2.64E-01 0.5138
2 at 180°
C 3.58E-05 1.59E-02 1.60E-01 0.6715
A 1.01E-04 3.96E-02 4.64E-01 0.4535
B 5.68E-05 1.21E-02 2.88E-01 0.4940
3 at 120°
C 2.26E-05 9.30E-03 1.34E-01 0.6622
A 2.33E-04 1.17E-02 5.67E-01 0.3830
B 3.40E-05 7.81E-03 2.01E-01 0.4849
4 at 90°
C 1.31E-05 6.43E-03 8.12E-02 0.6949
Table 3: Polynomial Coefficients for Experimental Data Interpolation – NOTCHES TYPE B
TYPE C Opening
a
[bar/(l/min)
3
]
b
[bar/(l/min)
2
]
c
[bar/(l/min)]
d
[N/bar]
A -1.17E-02 2.41E+00 -4.79E+00 0.1167
B -7.01E-03 5.93E-01 -1.52E+00 0.3008
2 at 180°
C -1.21E-03 1.80E-01 -5.13E-02 0.4454
A -1.44E-02 1.07E+00 -2.99E+00 0.2197
B -1.30E-04 1.17E-01 1.98E-01 0.5296
4 at 90°
C 4.29E-05 3.50E-02 2.21E-01 0.8328
Table 4: Polynomial Coefficients for Experimental Data Interpolation – NOTCHES TYPE C
Fitting the polynomials it is possible to derive the
variation of the characteristic resistance as a
function of the flow rate for each and every
metering edge as:
()
12
1
TEXP 1
EXP
b
RQ =a+
Q
⎡⎤
⎢⎥
⎣⎦
(6)
At the same time, the effect of the flow rate on the
discharge coefficients for each metering edge is
derived combining equation 5 and 6
()
()
12
DEXP
1 1 EXP GEO
ρ 1
CQ =
2a+bQ A
⎡⎤
⎢⎥
⎢⎥
⎣⎦
(7)
Recalling equation 4, it can be noted that the
correction term becomes smaller and smaller as the
flow rate increases, allowing the definition of a
limit value for the characteristic resistance of a
given geometry as:
EXP
12
SAT
TH
T1
2
Q
EXP
p
Rlim a
Q
→∞
⎛⎞
==
⎜⎟
⎝⎠
(8)
This definition is obviously valid in the operating
range where the flow can be considered as being
fully turbulent. It can be used to compute the limit
value of the discharge coefficient for a given
geometry, once the flow conditions meet this
turbulence criteria, i.e. Reynolds number above
transitional values, corresponding to values of the
discharge coefficient approximately constant. Using
the definition given in equation 7, this limit is given
by:
EXP
12
SAT
DD
Q
GEO 1
1 ρ
C=limC=
A2a
→∞
(9)
The computation of the saturated discharge
coefficient in all the geometries investigated, lead
to the results presented in Table 8. From a general
point of view, it is noted that the saturated
discharge coefficient in all the cases examined is
bounded between a minimum value of 0.48 and a
maximum of 0.74. For notches TYPE A and B it
presents a minimum value for the three notches
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 9
configuration, while it decreases as the total number
of notches increases for the notches TYPE C.
Notches of TYPE A show a behaviour more or less
independent from their number, but strongly
influenced by their axial position. Starting from
values close to 0.65/0.67, for the smaller openings,
SAT
D
C
drops to 0.54/0.56 at intermediate openings
and rises back to 0.62/0.64 at large openings. This
is a clear effect of the discontinuity in the area
function at intermediate openings, with subsequent
discontinuity in the area gradient. The flow
conditions are significantly affected, and the
discharge coefficients decrease more than 18%. It is
also worth noting that the discharge coefficient at
the minimum opening of the metering edge, where
the area gradient is positive, has a slightly higher
value than at large openings, where the area
gradient is zero.
Notches of TYPE B have a more complex area
function. In this case the discharge coefficient
depends on both opening and notch number.
Comparing configurations having the same number
of notches, the highest value of the discharge
coefficient is always reached at maximum opening.
The lowest value is reached at intermediate
openings in the case of three and four notches, at
minimum opening for the two-notches one. Clear
tendencies are not present in this case, possibly due
to the complexity of the area gradient function, a
piecewise linear function with two discontinuities.
As a consequence, the discharge coefficient for two
notches is an increasing function of opening, from
0.62 to 0.69.
The case of three notches has a minimum value of
discharge coefficient of 0.54 at intermediate
openings and is 0.65 at small and large openings.
The four notches configuration has a maximum
value of the discharge coefficient at large openings
and minimum value at intermediate openings, but
shows values significantly lower (10% to 14%)
than those reached in other configurations. This
kind of behaviour could be the result of errors in
measurements or data handling (at present not
discovered by the authors), however, the absence of
a systematic error only suggests that this
configuration should be better investigated by
means of detailed numerical simulations of the flow
field which are beyond the scope of this work.
Notches of TYPE C have the highest values of the
discharge coefficient at small openings. Two
notches configuration always performs better than
that with four notches. Discharge coefficients
values decrease as the opening increases. It is worth
noting that the value changes significantly during
the spool travel: in the two notches configuration it
drops from 0.74 to 0.57 (-23%), and in the four
notches configuration from 0.70 to 0.53 (-24.3%).
Reconsidering equation 7, the discharge coefficient
as a function of flow rate can be rearranged as:
()
12 -12
1
DEXP
GEO 1 1 EXP
-1 2
SAT
1
D
1EXP
b
1 ρ
CQ = 1+
A2a aQ
b
=C 1+
aQ
⎤⎡
⋅⋅
⎥⎢
⋅⋅
⎦⎣
⎡⎤
⎢⎥
⎣⎦
(10)
TYPE A Opening
a
1
[bar/(l/min)
2
]
b
1
[bar/(l/min)]
A 0.2325 0.0064
B 0.0612 0.0019
2 at 180°
C 0.0473 0.0018
A 0.0520 0.01
B 0.0265 0.0025
3 at 120°
C 0.0200 0.0050
A 0.0718 0.0018
B 0.0167 0.0013
4 at 90°
C 0.0115 0.0013
Table 5: II Order Characteristic Polynomial
Coefficients – NOTCHES TYPE A
TYPE B Opening
a
1
[bar/(l/min)
2
]
b
1
[bar/(l/min)]
A 0.0525 0.1417
B 0.0289 0.0015
2 at 180°
C 0.0210 0.0020
A 0.0510 0.2200
B 0.0200 0.0980
3 at 120°
C 0.0126 0.0400
A 0.0375 0.0350
B 0.0136 0.0150
4 at 90°
C 0.0086 0.0030
Table 6: II Order Characteristic Polynomial
Coefficients – NOTCHES TYPE B
TYPE C Opening a
1
[bar/(l/min)
2
] b
1
[bar/(l/min)]
A 2.1000 0.3000
B 0.3500 0.1500
2 at 180°
C 0.1400 0.1000
A 0.5970 0.5470
B 0.1100 0.2800
4 at 90°
C 0.0400 0.1340
Table 7:
II Order Characteristic Polynomial Coefficients – NOTCHES TYPE C
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 10
The comparison between data on different metering
edges arrangements (experimental or derived
quantities) can be made using either:
1.
comparison of flow characteristic as a function
of spool axial travel;
2.
comparison of flow characteristic as a function
of actual cross sectional area of the equivalent
orifice.
the result is that the curves must be rescaled
according to a non-linear transformation which
needs the definition of the area function of each and
every configuration investigated. This function
varies with the spool position and shows
discontinuities. The only workaround to overcome
these difficulties, is the introduction of a parameter
able to describe the flow conditions and the
geometry. The Reynolds number of a metering
configuration can be defined as:
H EXP GEO
EXP
D(Q A )
4Q
Re =
νν
=
S
(11)
where ν is the kinematic viscosity (32 cSt), D
H
is
the hydraulic diameter of the metering edge, while
S is the wetted perimeter of the reference cross
sectional minimum area of the orifice. It is not
worthy to underline that both the hydraulic
diameter and the wet perimeter vary with the
metering edge opening, introducing the effect of the
notched edge geometry on the Reynolds’ number
definition. In this way, it is possible to consider
equation 10 in the new form:
()
-1 2
SAT
1
DD
1
b
41
CRe= C 1+
aRe
⎡⎤
⋅⋅
⎢⎥
⎣⎦
S
ν
(12)
At the same time, the axial flow force as a function
of the pressure drop across the metering edge can
be expressed using the traditional Von Mises
approximation (Merritt, Blackburn):
()
AX D GEO V
F=2C ReA C cos p
ϑ
⋅⋅ (13)
Equation 13 considers as positive all forces acting
towards a closure of the valve, and drives to a direct
definition of the flow coefficient:
*
VV
CCcos
ϑ
=⋅ (14)
defined as the product of velocity coefficient and
cosine of the jet flow angle. Combining equation 2
with equations 13 and 14, the variation of the efflux
coefficient with flow conditions in the generic
metering edge is given by:
()
*
EXP EXP
DGEOV
EXP TH
FF
=2 C Re A C d
p p
≅⋅= (15)
hence:
()
()
*
V
DGEO
12
1
1
SAT
DGEO
d
CRe
2C Re A
b
41
d1+
aRe
C2A
==
⋅⋅
⎡⎤
⋅⋅
⎢⎥
⎣⎦
=
⋅⋅
S
ν
(16)
The flow coefficient is therefore a function of
geometry and flow conditions, but it is also directly
affected by the saturated value of the discharge
coefficient. Equation 16 shows that the flow
coefficient has a limit of +∞ as Reynolds number
tends to zero, indicating that the approach proposed
here cannot be applied to the analysis of flow at
very low Reynolds numbers. Conversely, Equation
16 holds for the actual metering edges operating
conditions, where flow can be described mainly
with reference to the fully turbulent (or, at least,
high transitional) conditions. In the wide range of
variation of the Reynolds number where Equations
16 holds, the flow coefficient has a saturated value
defined by:
*,SAT *
VV
SAT
Re
DGEO
d
C=limC
C2A
→∞
=
⋅⋅
(17)
Recalling the flow coefficient definition (Equation
14), the variation of the jet angle with the Reynolds
number of the incompressible flow through a given
geometry is described by the function:
()
()
*
V
V
CRe
Re = arccos
C
ϑ
(18)
Which presents a saturated value expressed as:
SAT
SAT
VD GEO
d
= arccos
CC 2A
⎛⎞
⎜⎟
⋅⋅
⎝⎠
ϑ
(19)
Table 9 summarizes the values of the saturated jet
angle computed for all the geometries investigated.
In Equation 19 a velocity coefficient C
V
of 0.98
was used, as an average of the values found in
literature.
Table 9 show that for TYPE A notches the
saturated jet angle has values very close to the
theoretical value found by Von Mises (69°) for an
inviscid, incompressible fluid flowing from a high
pressure confined volume to an unconfined volume
at low pressure.
The configuration with four notches has jet angle
close to 75°, with variations as a function of spool
position lower than 0.4°. Configurations with two
and three notches have values, respectively close to
69° and 70°, with larger variations with spool
position, but in any case lower than 1.5°.
This means that for TYPE A notches it is possible
to define a unique, constant value of the saturated
efflux angle, independent of the axial spool travel.
The behaviour shown by TYPE B notches is
completely different. The two notches configuration
shows values of
SAT
ϑ
significantly decreasing as the
spool travel increases, going from 69.5° at
minimum opening to 63° at maximum opening.
The three notches configuration shows the lowest
SAT
ϑ
value (approximately 61°) at minimum
opening and values close to 70° at intermediate and
large openings. The four notches configuration has
a maximum value of
SAT
ϑ
for intermediate
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 11
openings;
SAT
ϑ
values start from 69.5° at small
openings, increase to 74.5° at intermediate positions
and slightly decreases to 72.5° at large openings.
These results confirm that TYPE B notches have a
much more complex behaviour than all the other
types considered, and these anomalies can be
properly understood only by a deeper investigation
of the flow field inside the metering section of the
valve.
TYPE C notches seem to force the saturated flow in
a direction mainly determined by the radial depth of
the notch, having a nominal angle of 25°, with a
final nozzle effect constraining the efflux angle.
In both configurations tested (two and four
notches),
SAT
ϑ
shows a similar behaviour, varying
from 37.3° at small openings to 38.5 at large
openings. At intermediate openings it reaches its
minimum value, respectively 33.5° and 34.5°.
This configuration show no dependency on the
notches number; it is therefore possible to describe
all of the configuration with a single function
SAT
ϑ
of the spool position.
TYPE A Opening
SAT
D
C
TYPE B Opening
SAT
D
C
TYPE C Opening
SAT
D
C
A 0.67 A 0.62 A 0.74
B 0.55 B 0.64 B 0.69
2 at 180°
C 0.62
2 at 180°
C 0.69
2 at 180°
C 0.57
A 0.67 A 0.65
B 0.56 B 0.54
3 at 120°
C 0.64
3 at 120°
C 0.65
A 0.65 A 0.55 A 0.70
B 0.54 B 0.48 B 0.61
4 at 90°
C 0.63
4 at 90°
C 0.59
4 at 90°
C 0.53
Table 8: Saturated Discharge Coefficient defined adopting the Equation (9)
TYPE A Opening
SAT
ϑ
(°)
TYPE B Opening
SAT
ϑ
(°)
TYPE C Opening
SAT
ϑ
(°)
A 69.4 A 69.6 A 37.4
B 68.4 B 65.8 B 33.3
2 at 180°
C 68
2 at 180°
C 62.8
2 at 180°
C 38.5
A 70.6 A 61.3
B 69.4 B 70.8
3 at 120°
C 70.8
3 at 120°
C 69.6
A 75.2 A 69.6 A 37.2
B 74.8 B 74.6 B 34.4
4 at 90°
C 75.0
4 at 90°
C 72.4
4 at 90°
C 38.6
Table 9: Saturated Jet Angle defined adopting Equation (19) (C
V
= 0.98)
5. Analysing the main features of notched
edges flow characteristics.
As shown by equations 12 and 18, the experimental
data set collect the stationary characterization of all
the metering edges considered in this work. Their
use makes possible the description of discharge
coefficient and jet angle. In figures from 7 to 14 the
values determined for C
D
and θ adopting Equations
(9), (12), (18) and (19) are plotted as a function of
the square root of Reynolds number, as defined in
equation 11.
The curves give a synthetic view of the
characteristics analysed in the previous paragraphs,
and allow a fairly good identification of the
transition Reynolds number, as the limit value
above which a flow can be considered as fully
turbulent with a sufficiently high confidence level.
Figures from 7 to 9 show that TYPE A notches, for
all notch numbers, have a transition Reynolds
number notably low (500÷900). The transition from
the laminar to the transitional and turbulent efflux
conditions is clearly defined, and the saturated
values are stable. Beyond the transition value,
discharge coefficients approach the values given by
equation 9, and it is confirmed that intermediate
openings (close to the area gradient discontinuity
point) show values significantly lower than small
and large openings. It is also worth noting that
discharge coefficients for minimum and maximum
opening tend to get closer and closer as the number
of notches increases. At the same time the jet angle
at Reynolds number beyond the transition,
approaches the value given by equation 19. This
value is practically independent from the valve
opening for each configuration and slightly
increasing with the number of notches.
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 12
0.00
0.20
0.40
0.60
0.80
0 50 100 150 200Re^
0.5
C
D
Opening A
Opening B
Opening C
30
50
70
90
0 50 100 150 200Re^
0.5
θ
Opening A
Opening B
Opening C
Figure 7: Discharge Coefficient and Jet Angle distributions with the Reynolds’ Number variation – 2 notches
TYPE A metering edge.
0.00
0.20
0.40
0.60
0.80
0 50 100 150 200Re^
0.5
C
D
Opening A
Opening B
Opening C
30
50
70
90
0 50 100 150 200Re^
0.5
θ
Opening A
Opening B
Opening C
Figure 8: Discharge Coefficient and Jet Angle distributions with the Reynolds’ Number variation – 3 notches
TYPE A metering edge.
0.00
0.20
0.40
0.60
0.80
0 50 100 150 200Re^
0.5
C
D
Opening A
Opening B
Opening C
30
50
70
90
0 50 100 150 200Re^
0.5
θ
Opening A
Opening B
Opening C
Figure 9: Discharge Coefficient and Jet Angle distributions with the Reynolds’ Number variation – 4 notches
TYPE A metering edge.
0.00
0.20
0.40
0.60
0.80
0 50 100 150 200Re^
0.5
C
D
Opening A
Opening B
Opening C
30
50
70
90
0 50 100 150 200Re^
0.5
θ
Opening A
Opening B
Opening C
Figure 10: Discharge Coefficient and Jet Angle distributions with the Reynolds’ Number variation – 2 notches
TYPE B metering edge.
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 13
0.00
0.20
0.40
0.60
0.80
0 50 100 150 200Re^
0.5
C
D
Opening A
Opening B
Opening C
30
50
70
90
0 50 100 150 200Re^
0.5
θ
Opening A
Opening B
Opening C
Figure 11:
Discharge Coefficient and Jet Angle distributions with the Reynolds’ Number variation – 3 notches
TYPE B metering edge.
0.00
0.20
0.40
0.60
0.80
0 50 100 150 200Re^
0.5
C
D
Opening A
Opening B
Opening C
30
50
70
90
0 50 100 150 200Re^
0.5
θ
Opening A
Opening B
Opening C
Figure 12: Discharge Coefficient and Jet Angle distributions with the Reynolds’ Number variation – 4 notches
TYPE B metering edge.
0.00
0.20
0.40
0.60
0.80
0 50 100 150 200Re^
0.5
C
D
Opening A
Opening B
Opening C
0
20
40
60
0 50 100 150 200Re^
0.5
θ
Opening A
Opening B
Opening C
Figure 13:
Discharge Coefficient and Jet Angle distributions with the Reynolds’ Number variation – 2 notches
TYPE C metering edge.
0.00
0.20
0.40
0.60
0.80
0 50 100 150 200Re^
0.5
C
D
Opening A
Opening B
Opening C
0
20
40
60
0 50 100 150 200Re^
0.5
θ
Opening A
Opening B
Opening C
Figure 14:
Discharge Coefficient and Jet Angle distributions with the Reynolds’ Number variation – 4 notches
TYPE C metering edge.
M. Borghi, M. Milani, R. Paoluzzi
Paper 133-04 14
TYPE B notches give the characteristics plotted in
figures 10 to 12. The observations introduced in the
previous paragraphs on this type of notches apply
also on these curves; however, the graphs seem to
show a transition square root of Reynolds’ number
close to 75÷100, although in some cases it is not
well identified. The differences among the various
jet angles are more significant, when comparing the
same configuration and for different configurations
as well.
TYPE C notches plots are shown in figure 13 and
14. In this case the flow conditions can be
considered saturated only for values of the square
root Reynolds’ number above 100. This limit is
higher the higher is the number of notches. The jet
angle tend to approach its asymptotic value only for
Reynolds numbers particularly high, with the
notable characteristic that, for all configurations,
minimum and maximum opening have asymptotic
values very close to each other and higher than
those typical of intermediate openings.
6. Conclusions
This paper presents a thorough and critical analysis
of stationary flow characteristics in different
configurations of metering edges with timing
notches, which are typically used in industrial
hydraulic valves. The study is developed starting
from experimental data gathered at different valve
openings for eight different configuration of
metering edges. The investigation allow to
highlight trends and overall effects on discharge
coefficient and jet angle of shape, number and
position of timing notches. Among the main results
shown in the paper, the effect of the discontinuities
in area gradient are highlighted, together with the
saturated flow conditions (asymptotic values of
relevant flow parameters), where discharge and
flow coefficients can be considered constant. It has
been shown that the saturated values of the
discharge coefficient are reached at values of the
Reynolds number depending on shape and number
of the notches on the metering edge, giving also
some hints on how these indications can be used to
improve valve design or to increase the
effectiveness of valve metering characteristics.
7. References
1) J.F. Blackburn, G. Reethof, J.L. Shearer - Fluid
Power Control - M.I.T. Technology Press & John
Wiley & Sons - 1960.
2) H. E. Merrit - Hydraulic Control Systems - John
Wiley & Sons – 1967.
3) T.J. Viersma – Analysis, Synthesis and Design of
Hydraulic Servosystems and Pipelines – Elsevier
Scientific Publishing Co. – 1980.
4) Idelchick - Handbook of Hydraulic Resistance -
Springer-Verlag, 1983.
5) D.N. Johnston, K.A. Edge, N.D. Vaughan –
Experimental Investigation of Flow and Force
Characteristics of Hydraulic Poppet and Disk Valves –
Proceedings of the Institution of Mechanical Engineers
– Vol. 205, Part A – Journal of Power and Energy –
pp. 161-171, 1991.
6) J. Lugowsky - Experimental Investigation on the
Origin of Flow Forces in Hydraulic Piston Valves -
10th International Conference on Fluid Power, BHR,
Brugges, B - 5/7 April, 1993.
7) Palumbo, R. Paoluzzi, M. Borghi, M. Milani -
Forces on a Hydraulic Valve Spool - Proceedings of
the Third JHPS International Symposium on Fluid
Power – Pagg. 543-548 - Yokohama, 4-6 November,
1996.
8) A. Ellman, R. Piche – A Modified Orifice Flow
Formula for Numerical Simulation of Fluid Power
Systems – Proceedings of the Fluid Power Systems and
Technology Division Sessions – ASME IMECE ’96 –
Vol. 3, pp. 59-63 – 1996.
9) M. Borghi, G. Cantore, M. Milani, R. Paoluzzi -
Experimental and Numerical Analysis of Forces on a
Hydraulic Distributor - Proceedings of The Fifth
Scandinavian International Conference on Fluid
Power, SICFP ‘97 – Vol. I – Pagg. 83-98 -
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10) M. Borghi, G. Cantore, M. Milani, R. Paoluzzi -
Analysis of Hydraulic Components Using
Computational Fluid Dynamics Models - Paper
C09297 - Proceedings of the Institution of Mechanical
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JHPS ’99 – Ariake, Tokyo, Japan, 15-17 November,
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New Class of Rotary Hydraulic Valves – Proceedings
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June 1, 2001.
14) P. Gromala, M. Domagal, E. Lisowski – Research
on Pressure Drop in Hydraulic Components by means
of CFD Method on Example of Control Valve –
Proceedings of the 2nd International FPNI Ph.D.
Symposium on Fluid Power – ISBN 88-88679-00-6 –
Modena, Italy – 3-5 July, 2002.
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on a Four-Way Valve – Proceedings of the 2nd
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... This can be calculated by measuring the pressure at both ends of the valve ports and the displacement of the valve spool. Das et al. [13] and Borghi et al. [14] used the polynomial equation with the flow rate as an independent variable to fit the pressure drop at both ends of the valve port for different valve openings. Åman et al. [15] also used the pressure difference at both ends of the valve port to fit the flow rate through the valve port on the basis of considering the influence of the flow patterns. ...
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Abstract Electro-hydraulic control valves are key hydraulic components for industrial applications and aerospace, which controls electro-hydraulic motion. With the development of automation, digital technology, and communication technology, electro-hydraulic control valves are becoming more digital, integrated, and intelligent in order to meet the requirements of Industry 4.0. This paper reviews the state of the art development for electro-hydraulic control valves and their related technologies. This review paper considers three aspects of state acquisition through sensors or indirect acquisition technologies, control strategies along with digital controllers and novel valves, and online maintenance through data interaction and fault diagnosis. The main features and development trends of electro-hydraulic control valves oriented to Industry 4.0 are discussed.
... It was found that the divergent u-shape notch had the middle value of throttling stiffness. Borghi et al. [3] conducted the theoretical and experimental research about the influence of notch shape and number on the metering characteristics of hydraulic spool valves. Lisowksi et al. [4] also focused on the influence from different valve opening shapes on the flow characteristics in a proportional valve with a concentric sleeve around the valve spool. ...
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The u-shape notch, one of those representative types of throttling notch, is widely applied in the spools of hydraulic proportional directional valves. Because of its vacuum-suction nozzle-structural effect, the u-shape notch usually possesses relatively large flow capacity, while produces drastic cavitation as well. In this paper, the notch flow characteristics to form the large vapor cavity and its surge instability characteristics are discussed by experimental and numerical analysis. It is found that, instead of the vena contracta flow, but the notch vortex flow creates the more suitable low pressure condition for cavitation inception, with the helical-stream-trend to form the cavity spiral shape with clear vapor-liquid interface. Compared with the RANS turbulent model, the LES turbulent model associated with the multi-phase cavitation model reproduce the cavity volume and the spiral shape better, while the ISO surface of vapor volume fraction number equal to 0.6 is used to approximately represent the two-phase interface. In appropriate notch configurations, the vapor cavity shows surge instability, which couples the fluctuation of flow parameters with the mass transfer process. The notch flow resistance seems to play an important role on the surge behavior, since with the decrease of the notch depth, the harmonic oscillation turns into damped oscillation, while with the increase of the notch opening, the oscillation intensifies, and even gets disturbed from the downstream vapor shedding. The biggish notch flow resistance may suppress the surge instability, but reduce the flow capacity as well. It may be not easy to figure out an optimal notch structure only. However, using more number of larger flow resistance notches to replace few number of smaller flow resistance notches may be a positive suggestion.
Article
The valve spools of hydraulic actuator systems are usually designed into various geometries to achieve different flow characters. Because of the coupling nonlinear flow rate-pressure character and dynamic motion of the valve spool, self-excited vibration can happen in some working conditions of the system, which can lead to unexpected dynamic performance. The object of this paper is to investigate the stability of a hydraulic system with three different spool geometries, a normal sharp edge spool, a spool with chamfer, and a spool with u shape notches. Computational fluid dynamics (CFD) simulations of flow force and flow rate under different pressure difference and valve openings are proposed to obtain the pressure-flow characters of flow field inside the valves with different spool geometries. A nonlinear dynamic model of the actuator system dynamics is established basing on the CFD results of pressure control valve and the system. Numerical Bifurcation analyses are carried out to study the effect of spool geometries on the bifurcation point of the system. Simulation results suggest that the spool geometries can affect the flow characters of the valve and decrease the stable region of the parameter plane.
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Spool clamping is an important source of reliability decline and failure of hydraulic machinery. Aiming at the problem of spool clamping caused by thermal deformation, the viscous heating experiment of V-groove spool was carried out to find out the temperature difference between the two; the thermal deformation diameters of the spool and valve body were measured by constant temperature control method; a measuring device was set up to measure the spool clamping force at different temperatures. The results show that the temperature of the spool under the viscous heating is always higher than that of the valve body, the temperature difference can reach 47.5℃ or even higher. For the spool valve with 20mm diameter and unilateral clearance of 7∼20μm, the thermal deformation of the spool and valve hole can reach 20μm and 41μm respectively after the temperature increases from 25℃ to 120℃. When the temperature of the valve body is constant, the temperature, thermal deformation and clamping force of the spool are positively correlated. Clamping always occurs under a certain temperature and diameter difference between the spool and valve body, which is related to the machining shape error. The greater the temperature difference between the spool and the valve body, the longer the clamping time, the greater the number of pulsations of the clamping force and the greater the peak value of the clamping force. When the valve body temperature is 25℃, the spool can produce a clamping force of 27.41 N at 95℃, and the clamping force can last for 19.1 s, which would obviously affect the working performance of the construction machinery. This study provides a theoretical reference for the design and production of non-clamping spool valves.
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Calculating the flow coefficient of a spool-valve is complicated due to the coupling-throttling effect in the throttling grooves of a proportional-directional valve. In this paper, a methodology for expressing the flow coefficient of coupled throttling grooves is proposed to resolve that difficulty. With this purpose, an approach of a 3D numerical simulation and an experimental bench were introduced based on the prototype of a commercial proportional valve. The results show consistency between the numerical simulation and the bench test. Based on that, the concept of ‘saturation limit’ is introduced to describe the value gap between the current and saturated flows, so that the flow-coefficient saturation limit of the prototype in the process can be deducted. Accordingly, an approximate flow coefficient suitable for coupled throttling grooves within finite variable space, which is based on three typical throttling structures (i.e. O-shape, U-shape, and C-shape) of the coupled throttling grooves, is obtained based on an orthogonal test. The model results are consistent with the numerical and experimental results, with maximum errors of less than 5.29% and 5.34%, respectively. This suggests that the proposed method is effective in approximating the flow coefficient.
Chapter
Proportional control valves are characterized by smooth opening of flow channels by means of the spool control. At the initial stage of opening, the flow gap is of a small cross-section which then gradually expands. This enables smoother start-up of a device as well as more precise control of the working motion compared to conventional control valves. Among the electromagnetically controlled proportional control valves, some complex solutions equipped with spool displacement transducers, compensating valves, advanced electronics, etc. can be distinguished. This allows compensation for the harmful effects of flow-related forces. The article presents the results of flow tests through the USAB10 proportional control valve, designed and manufactured by PONAR Wadowice. The valve can be both used as a single unit or included in the sectional block which supplies multiple actuators. There are many points of fluid flow direction change as well as cross-sectional area change inside the valve block. This leads to the occurrence of forces associated with the flow which are difficult to determine using standard mathematical formulas. Hence, the research process included building of geometrical models, next preparation of discrete models and then carrying out simulation tests using CFD methods. The tests were conducted in Ansys/Fluent environment which allowed velocity distribution, pressure distribution and values of forces acting on the valve spool to be obtained.
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This paper presents a new rotary proportional flow control valve with Cam-Nozzle configuration. The rotating cam against the fixed nozzle changes the flow area and then can meter the fuel flow. This valve equipped with a pressure compensator plunger type valve to retaining constant pressure difference across the flow control or metering valve. The cam shaft directly coupled to an electronic servomotor type rotary actuator and then it is possible to apply digital control techniques such as pulse width modulation (PWM) in this control system. This new valve configuration is developed for an electro hydro mechanical fuel control system in a gas turbine engine. In addition to aero engine application, this type of flow metering valve can widely be used in industrial hydraulic systems. In this unit, the output flow is proportional to the cam's angular position (or throttle command) and it is not sensitive to pressure fluctuations at nozzle inlet and outlet. The aim of this new design is to modify a manual single adjusted hydro-pneumatic fuel control unit to obtain a new electro-hydraulic fuel control system for a gas turbine engine. The main innovations in the presented fuel metering unit include new design of the rotary valve opening shape (Cam-Nozzle) without metal to metal contact, use of a rotary electronic actuating mechanism and also direct coupling between the actuator and the rotating cam. The increased fuel metering precision in the new flow control valve has improved the ultimate control accuracy of system. A computer simulation software based on the proposed model, is performed to predict the steady state and transient performance and to analyze effect of important design parameters on valve outlet fuel flow and obtain the final design parameters. The validity of the proposed valve configuration is assessed experimentally in the steady state and transient modes of operation. The results show good agreement between simulation and experimental in both modes (max. 4% deviation).
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The use of water as a working fluid in hydraulic circuits is being receiving an increasing attention by both manufacturers and users, due to its environmental characteristics. Although the use of water is neither new nor innovative (more than one hundred years ago it was widely used to transfer power, and many pump and valve manufacturers have commercial product lines for water hydraulics) its introduction in the product line of a manufacturers brings many problems to the attention of the designers, from technology adaptation to material compatibility, from erosion to cavitation. The purpose of this paper, based on a joint activity by Cemoter, University of Modena, Aron SpA and Cermet, is to show how the use of a combined approach to valve analysis can provide useful information to shorten the time to market of a valve using tap water as working fluid. Starting from an initial reminder of the basic differences between mineral oil and water in hydraulic circuits, the paper shows the results of some CFD computations on a relief valve, to evaluate the qualitative form of the pressure and velocity field, and to assess the influence of the increased turbulence on the field of motion. In the final part, the results of a comprehensive experimental characterization of the component are presented and considered in view of the indication provided by CFD analysis, both in term of steady state characteristic curves, and dynamic response.
Conference Paper
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The conventional turbulent orifice flow formula has an infinite derivative when the pressure drop is zero. This can cause ODE solvers to crash during numerical simulation of fluid power circuits. A two-regime orifice flow formula is proposed in which an empirical polynomial laminar flow formula is used for small pressure differences. The proposed formula has a smooth transition between laminar and turbulent regimes and does not have a singular derivative, and so is well-suited for accurate and trouble-free simulation.
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The paper deals with an application of a simplified numerical analysis, based on Computational Fluid Dynamics (CFD), of the flow field inside the compensated port connections of a reference spool valve. The aim of the study was to evaluate a proposed analysis procedure, for the major effects related to the presence of steady state flow forces affecting the spool equilibrium. Starting from an initial summary of the dimensional analysis proposed by the authors to approach the application of CFD to hydraulic components, the paper presents the results of three commonly used compensating profiles for two reference spool positions. In order to validate the simulation, the curves obtained for one of the three geometries are compared with the experimental data obtained on an equivalent port connection of a commercial distributor.
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The use of water as a working fluid in hydraulic circuits is being receiving an increasing attention by both manufacturers and users, due to its environmental characteristics. Although the use of water is neither new nor innovative (more than one hundred years ago it was widely used to transfer power, and many pump and valve manufacturers have commercial product lines for water hydraulics) its introduction in the product line of a manufacturers brings many problems to the attention of the designers, from technology adaptation to material compatibility, from erosion to cavitation. The purpose of this paper, based on a joint activity by Cemoter, University of Modena, Aron SpA and Cermet, is to show how the use of a combined approach to valve analysis can provide useful information to shorten the time to market of a valve using tap water as working fluid. Starting from an initial reminder of the basic differences between mineral oil and water in hydraulic circuits, the paper shows the results of some CFD computations on a relief valve, to evaluate the qualitative form of the pressure and velocity field, and to assess the influence of the increased turbulence on the field of motion. In the final part, the results of a comprehensive experimental characterization of the component are presented and considered in view of the indication provided by CFD analysis, both in term of steady state characteristic curves, and dynamic response.
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This paper presents some results obtained during the computational fluid dynamics (CFD) analysis of internal flows inside a hydraulic component, using a scaling technique applied to numerical pre- and post-processing. The main aim of the work is to demonstrate the reduction of computational work needed for a complete analysis of component behaviour over a wide range of operating conditions. This result is achieved through the adoption of a methodology aimed at giving the highest level of generality to a non-dimensional solution, thereby overcoming the two major limitations encountered in the use of CFD in fluid power design: computer resources and time. In the case study, the technique was applied to a hydraulic distributor and computations were performed with a commercial computational fluid dynamics code. The key factor of this technique is the evaluation, for a given distributor opening, of the Reynolds number of the flow in the metering region. Provided that this number is high enough to ensure that the discharge coefficient has reached its asymptotic value, the characterization of the flow by a single non-dimensional numerical run can be shown. The theoretical contents of the analysis of the re-scaling technique, which focuses on the engineering information necessary in component design, are described in detail. The bases for its subsequent application to actual cases are then outlined. Finally, a fairly close correlation between numerical results and experimental data is presented.
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In fluid power systems, flow control is mainly achieved by throttling the flow across valve orifices. Lumped parameter models are generally used to model the flow in these systems. The basic orifice flow equation, derived from Bernoulli's equation of flow, is proportional to the orifice sectional area and the square root of the pressure drop and is used to model the orifice coefficient of proportionality. The discharge coefficient, Cd, is often modeled as being constant in value, independent of Reynolds number.
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Tests have been performed on a range of different poppet and disc valves operating under steady flow, non-cavitating conditions, for Reynolds numbers greater than 2500. The working fluid was water, and the axisymmetric valve housing was constructed from clear perspex to facilitate flow visualization. Measured flow coefficients and force characteristics show marked differences depending on valve geometry and opening. These differences are explained with reference to visualized flow patterns.
Shearer -Fluid Power Control -M.I.T
  • J F Blackburn
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Schoenau – An Empirical Discharge Coefficient Model for Orifice Flow – International Journal of Fluid Power –
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  • R Burton
D. Wu, R. Burton, G. Schoenau – An Empirical Discharge Coefficient Model for Orifice Flow – International Journal of Fluid Power – ISSN 1439- 9776 – Vol. 3, N. 3 – pp. 17/24 – December 2002.
Lippolis – Flow Forces Analysis on a Four-Way Valve – Proceedings of the 2nd International FPNI Ph.D. Symposium on Fluid Power –
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G. Del Vescovo, A. Lippolis – Flow Forces Analysis on a Four-Way Valve – Proceedings of the 2nd International FPNI Ph.D. Symposium on Fluid Power – ISBN 88-88679-00-6 – Modena, Italy – 3-5 July, 2002.