45
Cylinder pressure transients in oil hydraulic pumps
with sliding plate valves
K A Edge, BSc, PhD, CEng, MIMechE and J Darling*, BSc, AMIMechE
School of Engineering, University of Bath
This paper reports an experimental study of the cylinder pressure within an axial piston pump. This study revealed that existing
theoretical models, which are based on the effects of,fiuid compliance within the cylinder, are highly inaccurate a f high speeds or high
loads. Fluid momentum at the point of port opening was found to be of considerable importance and an improved digital computer model
was developed as an aid to pump design. The inclusion offluid momentum efects resulted in a signlJcant improvement in the agreement
between lheory and experiment. Cavitation within the cylinder bore was predicted at both high speed and high load conditions; this was
conjirmed experimentally. The theoretical approach is applicable to any sliding valve plate unit.
NOTATION
silencing groove cross-sectional area
port plate flow area (orifice loss)
oil bulk modulus
port plate coefficient of discharge
port plate flow coefficient
mass of element in silencing groove
pressure
cylinder pressure
differential pressure to accelerate fluid in silencing
groove
port pressure
pressure drop from upstream to vena contracta
steady flow pressure drop
total pressure loss across port plate groove
flowrate through port plate groove
leakage flowrate
port plate flowrate
piston flowrate
time
velocity of oil in port plate groove
velocity of fluid at point X ,
velocity of fluid at point X,
volume of fluid in cylinder
displacement along groove
intersection of cylinder slot and silencing groove
intersection of silencing groove and kidney groove
oil density
1 INTRODUCTION
Axial piston pumps are used extensively in applications
requiring variable displacement machines with high
overall efficiency. However, the operational requirements of users have put an ever increasing demand for
machines capable of operating at greater rotational
speeds and delivery pressures. This often leads to problems of cavitation of the oil within the cylinder bore and
the inlet supply is commonly boosted in an effort to
avoid low transient pressures.
Much research has been carried out to improve pump
design. For example, one of the first theoretical investiThe M S was receioed on 13 M o y 1985 and
was
accrpredfour publiculiun on 23
Sepl emher 1985.
* Present address: Department of Mechanical Engineering, Plymouth Polytechnic.
19/86 @ IMcchE 1986
gations of port plate design was carried out by Zaichenko and Boltyanskii (1). This established useful
design techniques which have since been improved (2)
and used for a number of years. However, little cxperimental evidence has been published as verification of
the theoretical predictions. Furthermore, although
extensive work has been carried out to establish the
suction requirements of pumps (3, 4, 5), a detailed
experimental examination of the cylinder pressure in an
axid piston unit does not appear to have been
published.
In this study, a standard axial piston pump which can
be used in very high power applications, was instrumented to measure, inter alia, the variation of cylinder
pressure with speed, load and swash. Significant discrepancies in the theoretical predictions were highlighted by the experimental programme and an
improved digital computer model was developed.
2 COMPUTER SIMULATION
The simulation package HASP (6) was used to develop
a general model of an axial piston pump. This package
has been developed at Bath University Fluid Power
Centre to simulate complete hydraulic circuits. Each
component is described by a component model subroutine and a FORTRAN program of a complete
hydraulic circuit is formed by linking together the
appropriate models. In this investigation, models of
individual components within the pump are linked
together to form a model of a complete unit. This
approach, modelling on a ‘micro’ scale rather than a
‘macro’ scale, is a departure from the conventional use
of HASP. Because many fluid power systems are represented by differential equations which are numerically
stiff, care must be exercised in the numerical integration
algorithm employed, otherwise very long program run
times are incurred. In HASP, Gear’s algorithm with
modifications for discontinuities, has been found to be
particularly efficient. The simulations reported here will
show that the algorithm is equally suitable for the very
rapid transients occurring in an axial piston pump.
A schematic diagram of an axial piston pump illustrating the basic components is presented in Fig. 1. Initially, a simple single-cylinder model was developed.
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Proc Instn Mech Engrs Vol 200 No BI
46
K A EDGE AND J DARLING
Silencing
grooves
/f-
v ~ o r plate
t
' i
TDC
Cylinder block
Fig. 1 Schematic diagram of axial piston pump
This model takes into account the port plate pressure
loss and the compressible volume of oil within the cylinder. In essence this is the same as the theoretical
approach described by Foster and Hannan (2) and
Kelsey et al. (7). The program is written in a form which
enables a variety of port plate designs to be modelled;
in particular a wide range of port plate silencing groove
configurations can be accommodated. Silencing grooves
produce a progressive increase in the effective flow area
during the earlier stages of port opening. This allows
the port to open early but restricts the initial port plate
flow at the start of the inlet and delivery phases. This is
desirable as it reduces both the rate of change of pressure in the cylinder and the delivery flow ripple produced by the pump. As with many previous workers,
the silencing groove is treated as a variable area orifice
with a constant discharge coefficient of 0.7. The differential pressure across the port plate is used to establish
the flow into or out of the cylinder. The difference
between this flow and the flow due to the motion of the
piston, creates a change in cylinder pressure by virtue of
the oil compressibility. This may be modelled by the
following equations:
occur. At the start of the delivery phase the cylinder
port connects with the delivery kidney port silencing
groove. Since the port plates studied exhibited some
overlap in the dead centre region the cylinder pressure
at the point of port opening was always significantly
less than that in the delivery port. As a result a reverse
flow occurs as shown by the region E C on Fig. 2b. The
severity of the reverse flow depends upon the operating
conditions. As the delivery port flow area increases, the
cylinder pressure rises (B-C, Fig. 2a). The fluid within
1B
Ep
a
0
1
0
Q -Q
-Q
P
O
V dP
--c
F
G
1
10
20
Time
30
40
ms
(a) Cylinder pressure
L - B dt
where positive Q, denotes the delivery phase. The variation of Q , with time will depend, inter aliu, on pump
geometry (swash plate or tilting axis pump for example)
pump speed and fraction of maximum displacement.
A theoretical prediction of the test pump cylinder
pressure and flow over a pumping cycle is shown in
Figs 2a and 2b. The simulation results are very similar
to those achieved by previous workers and demonstrate
the trapping of fluid in the cylinder at dead centres. The
region A-B on Fig. 2a shows the cylinder pressure at
the end of the inlet phase. The reduction in port plate
flow area, associated with the port plate silencing
groove, results in the flow from the inlet port being
throttled. During high-speed conditions this throttling
action may cause an undershoot in cylinder pressure; if
the undershoot is of sufficient magnitude, cavitation will
1
3
c
3.-
01
al
E
z"
-1
(b) Flow into cylinder
Fig. 2 Theoretical cylinder pressure and flow (1500 r/min,
100 bar load, 30 bar boost, full swash)
0 IMechE 1986
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47
CYLINDER PRESSURE TRANSJENTS IN OIL HYDRAULIC PUMPS
the cylinder is compressed by the reverse flow passing
from the delivery port through the port plate orifice
into the cylinder. The piston also provides some compression during this phase. Although the silencing
groove flow area continues to increase with cylinder
barrel rotation, the reduction in port differential pressure leads to a reduction in the magnitude of the reverse
flow. Thus the fluid in the kidney port silencing groove
is initially accelerated into the cylinder and then decelerates as the level of reverse flow reduces. The cylinder
pressure continues to rise and eventually reaches the
level of the delivery port (point C, Fig, 2a). If the
delivery port silencing groove is very restrictive or the
pump rotational speed high, the motion of the piston
may result in the cylinder pressure rising significantly
above the delivery pressure.
The premature reduction of the delivery port flow
area just before the end of the delivery stroke results in
a throttling of the piston flow (region D-E, Fig. 2a).
During high-speed conditions this can lead to an overshoot in cylinder pressure. In a similar manner to that
detailed above, a rapid reverse flow occurs at the start
of the inlet phase (region E-F, Fig. 2b). The initial
direction of flow at the start of the inlet stroke is from
the cylinder into the low-pressure inlet port. As the
cylinder pressure falls (region E-F, Fig. 2a), the level of
reverse flow will reduce and the fluid entering the cylinder will be decelerated. At the pressure equalization
point (where the cylinder pressure equals the inlet pressure, point F, Fig. 2a) the fluid entering the cylinder will
still be decelerating. The flow from the cylinder, due to
the piston movement out of the cylinder bore, results in
an undershoot in cylinder pressure (point G, Fig. 2a).
During high-speed conditions this effect can result in an
undershoot in cylinder pressure sufficient to cause cavitation of the oil within the cylinder bore.
To assess the importance of interaction between
cylinders a multiple-cylinder simulation was also developed. Several of the single-cylinder models detailed
earlier were combined to form a complete pump model.
It was found that the predicted inlet and delivery flow
ripple was of low amplitude and had little effect on the
pressure within the cylinder at dead centres. Since the
computer run times were roughly ten times longer than
the single-cylinder simulations, multiple-cylinder simulations were not used for general cylinder pressure and
flow analysis ; the single-cylinder model was used for all
the simulations discussed below.
In order to examine the accuracy of the computer
simulations, the cylinder of an axial piston pump was
instrumented so that cylinder pressure could be measured.
3 EXPERIMENTAL EQUIPMENT
The accurate measurement of axial piston pump cylinder pressure is a prerequisite for the full understanding
of pump operation. Helgestad (8) instrumented the
cylinder of an axial piston pump and measured the
cylinder pressure at a number of operating conditions.
However, the limited life of the pressure transducer used
to measure cylinder pressure restricted the range of tests
conducted.
The axial piston pump examined in this work was a
conventional nine-cylinder swash plate unit with a con-
tinuous power capability of 373 kW at 3600 r/min. The
unit incorporated a bidirectional port plate with
sloping, semi-circular cross-section silencing grooves at
both the leading and trailing edge of the inlet and
delivery ports. This pump is commonly used with a
swash plate which can reverse the flow direction,
although a unidirectional swash was used for all the
tests reported here. For reasons of commercial confidentiality, detailed dimensions of this unit are not
quoted.
A sub-miniature pressure transducer was used to
measure the cylinder pressure of the test pump. The
transducer was mounted in the cylinder barrel and measured the cylinder pressure in the cylinder ‘run-out’
section near the kidney port. The pressure transducer
was slightly unusual in that the sensing mechanism was
a thin-walled tube rather than a diaphragm. As the
transducer was mounted radially in the cylinder barrel
any forces introduced by the rotation of the instrument
in the pump did not significantly affect the pressure
signal. The transducer wire was led through a machined
hole in the cylinder barrel and out through the centre of
the pump shaft. A slip ring unit was used to carry the
transducer signal from the rotating shaft.
Pressure transducers were also mounted in the pump
inlet and delivery manifolds, as close as possible to the
port plate. This enabled the effect of the manifold pressure ripple on the cylinder pressure to be established.
Pump speed was measured using a magnetic pick-off
and toothed disc whilst an optical sensor identified
bottom dead centre of the instrumented cylinder. A
digital storage scope was used to display the pressure
transducer signals with a transfer to an X-Y recorder
for a permanent record.
A 110 kW variable speed hydrostatic transmission
was used to drive the test pump. Accurate control of the
hydrostatic transmission pump swash setting enabIed
the speed of the test pump to be continuously controlled.
The instrumented pump was tested in a closed circuit
configuration, using a gear pump to make up leakage
flow and boost the inlet line. An accumulator with a
low precharge pressure was used to minimize inlet
pressure fluctuations and so reduce the effect of external
disturbances on cylinder pressure and flow. Loading of
the test pump was achieved with a needle valve
mounted close to the pump delivery manifold. This was
consistent with the computer program which treats the
delivery line as a lumped volume.
4 EXPERIMENTAL INVESTIGATION OF
CYLINDER PRESSURE
A typical set of experimental results is shown in Fig. 3.
Comparison of the simulation results of Fig. 2a with
those measured experimentally (Fig. 3a) shows significant differences. Firstly, it is clear that the inlet and
delivery pressure ripples are not modelled by the computer simulation. This is to be expected: these ripples
are created by the combination of the individual cylinder flows interacting with the circuit; this effect cannot
be readily modelled by a single-cylinder simulation. Secondly, the experimental cylinder pressure at dead
centres is not modelled very accurately. This is shown
more clearly in Figs 3b and 3c. The experimental over-
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K A EDGE AND J DARLING
48
cause cavitation of the oil within the cylinder. This was
not demonstrated by the theoretical analysis. Indeed,
the theoretical results suggest that the pump boost
pressure could be reduced significantly before cavitation
would occur in the cylinder.
1201
O !
0
I
1
10
20
I
I
I
30
40
50
Time
-
ms
(a) Cylinder pressure over one revolution
1204
l2OI
0
1.0
2.0
Time
ms
(b) Cylinder pressure at BDC
Q
1.0
2.0
Time
ms
(c) Cylinder pressure at TDC
Fig. 3 Experimental cylinder pressure (1500 r/min, 100 bar
load, 30 bar boost, full swash)
shoot in cylinder pressure at bottom dead centre (BDC)
and undershoot at top dead centre (TDC) is very much
greater than that simulated and in each case there is a
decaying oscillation in pressure which is not predicted.
The large undershoot at TDC is a most important
finding. If the undershoot is sufficiently large, cavitation
would occur, even when the pump is supplied with a
relatively high boost pressure. Although the oscillation
in cylinder pressure at the beginning of the inlet and
delivery strokes has been measured by Helgestad (8), it
has not been fully explained. Furthermore, the significant anomalies in the theoretical analysis have not been
adequately discussed by previous researchers.
In the light of these results it was decided that further
tests should be performed over a wide range of speeds,
delivery pressures and inlet pressures.
4.2 Variation of cylinder pressure undershoot
and overshoot with delivery pressure
A comparison of the experimental and theoretical variation of cylinder pressure undershoot and overshoot with
load also revealed significant discrepancies in the theoretical model. The experimental results demonstrated a
near linear increase in undershoot at TDC and overshoot at BDC with load, whilst the predicted results
showed a slight decrease with load. In the basic theoretical model the effect of an increased load was to
delay the point of port plate pressure equalization. Thc
resultant increase in silencing groove area at this point
reduced the throttling action of the port plate and hence
reduced the associated cylinder pressure undershoot at
TDC and overshoot at BDC.
The maximum load pressure on the test rig, at full
swash, was limited to 200 bar. If the experimental
results are extrapolated to 300 bar load the undershoot
at TDC would increase to about the same level as the
boost pressure of 30 bar and cavitation of the oil within
the cylinder would occur. In order to investigate operation at high loads a limited number of tests were performed at low swash angles. Cavitation of the oil in the
cylinder at the start of the inlet phase was shown to
occur during these operating conditions.
It is clear that the current approach to the analysis of
axial piston pump cylinder pressure and flow, is inadequate for predicting pump behaviour at high speeds or
high loads.
4.3 Cylinder dynamics during severe cavitation
conditions
At high-speed or hjgh-load conditions, a 20 kHz ripple
was superimposed on the cylinder pressure trace during
decompression. There is experimental evidence to
Cavitation 7
30
undershoot TDC
20
4.1 Variation of cylinder pressure undershoot
and overshoot with speed
The undershoot and overshoot in cylinder pressure
were measured (relative to the mean inlet and delivery
pressures) over a range of speeds. The results are shown
in Fig. 4. The magnitude of cylinder pressure undershoot at TDC and overshoot at BDC both increase
almost linearly with speed. The theoretical results
obtained from the single-cylinder simulation detailed
earlier are also shown in Fig. 4.The agreement with the
experimental results is poor over the complete speed
range and clearly there is a major flaw in the theoretical
analysis.
At high rotational speeds the experimental cylinder
pressure undershoot at TDC was sufficiently large to
overshoot BDC
10
undershoot TDC
0
0
2000
3000
rimin
Fig. 4
Comparison of experimental and theoretical cylinder
pressure undershoot and overshoot with speed (100
bar load, 30 bar boost, full swash)
Proc Instn Mech Engrs Vol 200 No Bl
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CYLINDER PRESSURE TRANSIENTS IN OIL HYDRAULIC PUMPS
0
5.32
TDC
49
lo:@
Time
ms
Fig. 5 Experimental cylinder pressure during low boost pressure conditions
(speed 2820 rimin, 43 bar load, 2.5 bar boost, full swash)
suggest that broad band high-frequency pressure ripples
are created by the collapse of air or vapour bubbles
entrained in the oil (9).In a piston pump, low localized
pressures may occur in the silencing grooves during
high reverse flow conditions and this can result in air
release or even cavitation for brief periods. Dynamic
calibration of the cylinder pressure transducer (using a
very high-frequency response piezo-electric transducer
as a reference) revealed a flat frequency response within
3 dB to 10 kHz, with a strong resonant peak of 25 dB
at 20 kHz. Consequently, the 20 kHz oscillation
observed on the pressure trace is produced by excitation
of the transducer at its natural frequency. Despite the
fact that the amplitude of the oscillation is undoubtedly
in error. the results nevertheless provide a useful indication of the incidence of cavitation.
An example of the cylinder pressure during low
boost, high-speed conditions is shown in Fig. 5. At the
start of the inlet stroke (region A) the pressure was
truncated. This is almost certainly due to a reduction in
oil bulk modulus as a result of air or vapour release
caused by cavitation of the oil within the cylinder bore.
In addition, the high-frequency oscillation associated
with bubble collapse is visible throughout the inlet
stroke. Where cylinder flow interactions cause the inlet
pressure to rise, the high-frequency oscillation is most
evident. The collapse of the entrained air bubbles at the
end of the inlet stroke is marked by a very large pressure oscillation (region B). This continues well into the
delivery stroke and provides an estimate of the rate of
solution of air and vapour bubbles in turbulent flow
conditions. Despite the severity of the cavitation within
the pump, the volumetric efficiency of the unit was only
reduced by a few percent. During the inlet stroke the
cylinder pressure appears to fall significantly below
absolute zero for very short periods. This effect is
almost certainly an instrumentation error produced by
disturbances at the natural frequency of the pressure
transducer.
4.4 Cylinder pressure oscillation at start of stroke
The standard theoretical analysis does not predict any
oscillation in pressure at the start of the inlet and
delivery strokes or provide any explanation of this
behaviour.
There are a number of possible causes for this effect,
and some have been mooted by other workers. Work
carried out at Aston University (lo), for example, suggested that an oscillation of the cylinder barrel longitudinally along the shaft would result in an oscillation in
pressure. Such an oscillation is likely to occur with an
unbalanced port plate. However, this hypothesis is
unlikely to be true as the oscillation in cylinder pressure
occurs only at the start of the inlet and delivery stroke.
Oscillation of the cylinder barrel would result in a
repeating oscillation in cylinder pressure throughout the
inlet and delivery strokes. Such effects have not been
observed. Another possible cause is an oscillating
leakage flow due to a radial oscillation of the piston in
the cylinder. Such oscillations have been investigated by
Etsion and Magen (11). However, such an effect in a
pump would be very small and insufficient to change
the cylinder pressure appreciably. An oscillation of the
piston/slipper assembly was also considered as a possible cause for the oscillation in cylinder pressure.
Normal operating slipper clearances, during the
delivery stroke, are in the region of 5 pm (12). Simulation studies showed that even oscillations of the piston
slipper in excess of 50 pm would be reflected as only
small cylinder pressure oscillations.
Wave propagation within the cylinder of an axial
piston pump was also examined as part of this study,
but the frequency of pressure oscillation was found to
be much too high and the amplitude too low. An initial
investigation of the effect of the inertia of the oil within
the port plate groove, however, was found to produce
very promising results. The theoretical approach
described in the next section was developed to take this
into account in the computer model
5 THEORETICAL ANALYSIS OF FLUID
INERTIA IN SILENCING GROOVE
In order to model fluid inertia effects it is necessary to
examine the behaviour of the fluid in the region of the
silencing groove, as the port opens.
During conditions where flow passes from the cylinder into the diverging groove it is unlikely that the flow
will be laminar; a certain degree of separation from the
groove wall will occur, leading to the formation of a jet
(Fig. Sa). For modelling purposes this introduces a
problem, since it is extremely difficult to estimate the
mass of fluid being accelerated. A similar problem
occurs during conditions where flow passes into the
cylinder; although the fluid is less likely to separate, a
jet will still be created. Clearly, the direction of flow,
flowrate and rate of change of flow will all effect the
shape and volume of the jet. In addition, the shape of
the port plate silencing groove will have a major effect
on whether or not the jet separates from the groove
wall. However, for the purpose of the following analysis,
it has been assumed that the effective mass of the fluid
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K A EDGE AND J DARLING
50
Treating the fluid as incompressible and integrating
gives
AP,
= pQ
['
dx
a
port plate groove
(a) Outflow from cylinder
+ -P (v$ - v:)
2
(3)
where APG is the pressure differential necessary to
accelerate the fluid in the silencing groove. The second
term on the right-hand side of this equation is associated with the change in dynamic pressure over the
length of the groove.
Now, the pressure drop from upstream to the vena
contracta is
A P -~pQ2
- 2C,2A2
hence the total pressure drop is
and under steady flow conditions,
(b) Estimation of mass of fluid to be accelerated
(c) Detail of element of fluid in relief groove
APs =
APs =
Taking the mass m = p a dx, then
PQ'
2C: A 2
~
For computer simulation purposes, it is desirable to
solve the differential equation in terms of Q, thus
This equation is solved simultaneously with the continuity equation (2). It should be noted that the integration
function in the denominator changes with port opening.
To simplify the evaluation of this term, the integral was
expressed in the following form:
s" I*
1dx =
-au- _
at
1
- aQ
so,
_dP_- p - -Q+ dv
pax
a ax
Q
a
(5)
where the flow coefficient C, takes pressure recovery
effects and the change in dynamic pressure into account.
Equation (4) becomes
x1
now,
+ -P2 (vf - u:)
Tests by Helgestad (8) on a port plate of similar
design with a stationary cylinder block indicated that
the steady flow pressure drop changed slightly with the
direction of flow. However, the corresponding changes
in the flow coefficient were found to have only a very
small effect on the theoretical undcrshoots and overshoots in cylinder pressure at dead centres and could bc
neglected. It is convenient therefore to express equation
( 5 ) as follows
Fig. 6 Representation of flow in port plate dencing groove
in the jet will be the same as that contained in the
groove (Fig. 6b).
In the analysis of port plate flow during unsteady
conditions the pressure drop due to the orifice effect
and the rate of change of fluid momentum are analysed
separately and then combined, to find the total differential pressure.
Consider an element of fluid in the port plate groove
(Fig. 6c). A force balance can be carried out by equating
the pressure force to the rate of change of momentum.
Assuming that the rate of change of mass with time due
to the movement of the cylinder block is negligibly
small and the fluid inviscid,
PQ'
2C,2A2
~
a
f dx __
U
1'1
dx
a
The first term on the right-hand side of the equation is
dependent only on the groove geometry and is calculated numerically prior to a transient simulation. The
second term on the right hand side is evaluated numerically and updated at each time step as the groove is
uncovered. When the groove is completely uncovered,
the program reverts to equation (1) for calculation of
the cylinder flow.
Proc Instn Mech Engrs Vol 200 No 61
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51
1.0-
1.0L
a
l.
e
i2
2
F: 0.532 .--
g L 0.5-a
e n
-8 . 5
.*
Oil momentum
effects included
Z L I
-
0”
u”
O , U . U I # . r n #
‘
I
‘
l
n
~
~
l
v
~
~
1
6 IMPROVED COMPUTER SIMULATION
The basic single-cylinder simulation was modified to
include the effects described above. A constant port
plate flow coefficient of 0.7 was assumed throughout. It
was realized that some variation in the flow coefficient
was inevitable during the pumping cycle but a theoretical investigation revealed that cylinder pressure undershoot and overshoot were insensitive to flow coefficient.
The predicted cylinder pressure is shown in Fig. 7.
Comparison between the simple orifice loss prediction
and that including the effect of fluid acceleration shows
significant differences following pressure equalization.
The experimental results of Figs 3b and 3c are more
closely modelled by the simulation which takes account
of fluid momentum within the port plate groove. The
large overshoot in cylinder pressure at BDC and undershoot at TDC is predicted together with the oscillation
in cylinder pressure at the start of both the inlet and
delivery strokes.
0
I
I
,
,
,
”
”
,
‘
,
“
~
fluid in the port plate silencing groove maintains a flow
into the cylinder and, together with the compressibility
flow from the piston raises the cylinder pressure above
that in the delivery port. The reversed pressure differential across the port plate decelerates the fluid in the
silencing groove and causes a reversal of flow. It is
interesting to note that typical decelerations of the fluid
in the port plate silencing grooves are in the region of
5 x lo3 m/s2. It is not surprising, therefore, that the
effect of fluid inertia in the port plate silencing grooves
is a major one. The mass of fluid held in the port plate
silencing groove acts together with the fluid in the cylinder to form a mass/spring/damper system and, as would
be expected, a decaying oscillation of cylinder pressure
and flow occurs at the start of the delivery phase (region
C-D, Fig. 8). In a similar manner to that described
above the momentum of fluid in the port plate silencing
groove accounts for a significantly increased cylinder
pressure undershoot at TDC and cylinder pressure
oscillation following pressure equalization.
6.1 Port plate momentum pressure loss
Figure 8 illustrates how the port plate momentum
pressure loss varies with time. As the port opens to the
cylinder port, the fluid is initially at rest (point A,
Fig. 8). The orifice loss is zero and thus the pressure
differential across the port is accounted for entirely by
fluid acceleration effects. The computational simplifications exaggerate this effect slightly as in practice leakage
effects would allow some flow prior to the port opening.
Once the oil has accelerated into the port groove a
steady velocity is established and the pressure loss
caused by the momentum of the fluid in the port plate
groove falls to a low value. Thus, the orifice loss
becomes the major cause of pressure loss in the port
plate (point B). As the cylinder pressure rises the reverse
flow through the groove reduces and the orifice loss
falls as a result (region B-C). Once pressure equalization occurs and the cylinder pressure rises to the
manifold pressure, the flow through the port is very low
and the orifice loss is negligible. The momentum of the
-20
J
Time
rns
Fig. 8 Computation of momentum pressure loss through
port plate silencing groove during inlet phase ( 1 500
r/min, 100 bar load, 30 bar boost, full swash)
0 IMechE 1986
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K A EDGE AND J DARLING
52
6.2 Variation of cylinder pressure undershoot
and overshoot with speed and load
Figure 9 shows a comparison of the predicted and
experimental cylinder pressure overshoot and undershoot as a function of pump speed. Clearly, there is a
much better agreement between theory and experiment
than was achieved when taking account of the port
plate orifice pressure loss alone. An almost linear
increase in both undershoot at TDC and overshoot ,'
BDC with speed is shown by the simulation results. As
speed increases orifice losses become more significant,
but more importantly, the reverse flow will increase. If
the reverse flow increases, the oil in the port plate
groove will be accelerated at a higher rate and the
pressure drop due to the rate of change of oil momentum will increase. At speeds below 1500 r/min the simulation predicts larger cylinder pressure undershoots and
overshoots than those measured experimentally. At the
higher speeds the reverse is true. This slight discrepancy
between theory and practice is probably caused by
over-simplifications in the analysis of the momentum
effect. For example, the flow through the silencing
groove will almost certainly result in the formation of a
jet. Consequently the mass of fluid to be accelerated will
be larger than that included in the model.
The variation of undershoot and overshoot with load
(Fig. 10) was also modelled with much more success
than had been achieved with the simple orifice loss
analysis. Again at high reverse flow conditions the simulation was less accurate. As the load increases the
reverse flow and associated fluid acceleration at dead
centres will increase. The differential pressure needed to
accelerate the fluid will increase and as a result the
undershoot at TDC and overshoot at BDC will
increase. A levelling off of both undershoot and overshoot is evident from the simulation results at high
loads. Although the rate of change of flow increases
with load, pressure equalization occurs later on the port
plate groove. Thus the mass of fluid in the port plate
groove to be accelerated will decrease and the effect of
increased load is reduced.
0
o x
Theoretical
undershoot TDC
overshoot BDC
o Experimental
undershoot TDC
X Experimental
-
2ol
- Theoretical
o)-"
undershoatTDC
Theoretical
overshoot BDC
0 Experimental
X
undershoot TDC
v'
'
0
I
0
X Experimental
overshoot BDC
100
150
Load pressure
bar
50
200
Fig. 10 Comparison of theoretical and experimental variation of cylinder pressure undershoot and overshoot
with load (1500 r/min, 30 bar boost, full swash)
Tests on other groove designs have been carried out
and similar agreement between theory and experiment
was achieved over a wide range of speeds and pressures.
6.3 Cylinder pressure oscillation
The results from the investigation of cylinder pressurc
oscillation frequency with speed and load predicted the
same trends as those measured experimentally. The predicted frequency was, however, 50 per cent higher than
that measured experimentally. This is thought to be a
result of two factors : over-simplification of the momentum analysis used to model fluid flow in the port plate
groove and too large a value for oil bulk modulus.
At high-speed conditions the point of pressure equalization occurs later o n the groove. The mass of fluid t o
be accelerated within the groove is reduced and thc
oscillation frequency at the start of the inlet and
delivery phases is increased. At high-load conditions the
same is true. However, it would appear from the experimental results that as load increases the reverse flow
increases and the mass of fluid to be accelerated does
not change significantly. Thc influence of the port plate
fluid velocity on the mass of the element to be accelerated is not fully understood and requires further
research.
6.4 Cylinder pressure compression and
decompression at dead centres
overshoot BDC
Figure 11 shows a comparison between the experimental and predicted
cylinder compression and decompress-1 I
O 0- k 560
1000 1500 2000 2500 3000
ion at dead centres. The predicted curves correspond to
bulk moduli of 1.6 x lo4 bar (manufacturer's data) and
Pump speed
rlrnin
1.0 x lo4 bar. The best agreement with experimental
results is obtained with a bulk modulus of around
Fig. 9 Comparison of experimental and theoretical variation
of cylinder pressure undershoot and overshoot with
1.0 x lo4 bar. This also results in an improved predicspeed (100 bar load, 30 bar boost, full swash)
tion of the oscillation in cylinder pressure at the start of
Proc Instn Mech Engrs Vol 200 No B1
0 IMechE
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1986
CYLINDER PRESSURE TRANSIENTS IN OIL HYDRAULIC PUMPS
e!
.B=1.6
-0.1
0
0.1 0.2
0.3
0.4 0.5 0.6 0.7
Time
ms
0.8
0.9
1201
100- B=1.6 x lo4 bar
2olL---,pT----7
-0.1
0
0
0.1 0.2 0.3
0.4 0.5
0.6
0.7
0.8 0.9
Time
ms
Fig. 11 Experimental and theoretical rise and fall in cylinder
pressure at start of delivery and inlet phases (1500
r/min, 100 bar load, 30 bar boost, full swash)
the inlet and delivery phases. The apparent reduction in
oil bulk modulus during the inlet stroke may be a result
of local air release or cavitation in the port plate kidney
groove. The relatively slow adsorption of this free air
may account for the oil bulk modulus remaining at a
reduced level during the delivery stroke.
6.5 Cavitation damage
Despite the incidence of air release/cavitation, no cavitation erosion was evident upon dismantling the pump.
However, the total duration of the test runs was short
(approximately ten hours) and consequently no firm
conclusions can be drawn regarding possible long-term
damage. The authors are aware that cavitation damage
has been noticed by several pump manufacturers even
when the pump in question has been used with relatively high boost pressures.
7 PORT PLATE GROOVE DESIGN
A number of aspects of groove design have been investigated theoretically but only the most general aspects
concerning shape will be discussed here. Sloping and
non-sloping square section grooves were simulated.
These were generally poor, especially those with a large
initial depth and small groove slope. Triangular crosssection grooves were generally found to create low
reverse flows and low cylinder pressure undershoots
and overshoots. If the reverse flow spike is sharp the
0 IMechE
53
fluid in the port plate groove will have a rapid deceleration at the pressure equalization point. The pressure
difference necessary to cause this deceleration will be
large. resulting in a significant undershoot or overshoot
in cylinder pressure. Clearly this is undesirable. A port
plate silencing groove area profile which increases
rapidly at its start but then remains more or less constant, produces a sharp flow spike. A square section
non-sloping groove will have such an area profile.
Experimental and theoretical analysis confirmed that
using such a port plate would not only produce large
pressure fluctuations in the delivery and suction lines
but also large cylinder pressure undershoots and overshoots.
If the groove area is small at its start and increases at
a low rate initially, the peak reverse flow will be limited.
If the groove area then increases rapidly, although the
differential pressure across the port plate will reduce,
the reverse flow will be maintained at a high level. This
results in a rounded reverse flow transient. If the groove
area continues to increase rapidly, the rate of change of
flow at the pressure equalization point will be low. The
associatcd momentum loss will be small and the orifice
loss will be low as the now area is large. A port plate
which exhibits this behaviour is a sharply sloping triangular groove cut with a highly acute milling cutter.
8 COMPUTER SIMULATION OF AN AXIAL
PISTON MOTOR
Axial piston pumps and motors are very similar in construction and often units are designed to operate in
either mode. Computer simulation studies revealed that
the cylinder pressure is similar in nature to that measured in a pump but differences occur around the dead
centres. An undershoot in cylinder pressure at BDC and
overshoot at TDC are caused by the high fluid accelerations in the port plate groove at dead centre. Although
the cylinder pressure undershoots and overshoots are
much lower than in a pump, a motor used in an open
circuit configuration with a low discharge pressure may
experience cavitation in the cylinder and its associated
damage.
9 CONCLUSIONS
An experimental study of thc cylinder pressure within
an axial piston pump has been carried out, and the
results compared with predictions obtained by computer simulations. It was found that the simple orifice
pressure drop used to model flow through the port plate
was highly inaccurate. The expcrimental cylinder pressure undershoot at TDC and overshoot at BDC were
found to be far in excess of those predicted by existing
analysis techniques. Following extensive experimental
and theoretical studies it was established that high fluid
accelerations occur in the port plate silencing groove.
During the change from inlet to delivery port and vice
versa these high fluid accelerations greatly affect cylinder pressure and flow.
An improved digital computer model was developed
to aid in pump design and good agreement between
theory and experiment was achieved. Cavitation within
the cylinder bore of the experimental test pump
occurred at both high-speed and high-load conditions.
1986
Proc Inarn Mrch Engrv Vol 200 N o BI
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K A EDGE AND J DARLING
54
This was predicted by the computer simulation. A
number of aspects of groove design were investigated
theoretically. A sharply sloping triangular groove cut
with a highly acute milling cutter was found to be satisfactory.
ACKNOWLEDGEMENTS
The authors would like to thank the Science and Engineering Research Council and Commercial Hydraulics
(Glos) Limited for financial support in aid of these
studies. They would also like to thank Professor D. E.
Bowns of Bath University for valuable discussions and
Mr J. Flint and Mr D. M. Hannan of Commercial
Hydraulics (Glos) for their help and encouragement.
REFERENCES
1 Zaichenko, I. Z. and Boltyanskii, A. D. Reducing noise levels of
axial piston pumps. Russ. Engng J., 1969, XLIX, 4.
2 Foster, K. and Hannan, D. M. Fundamental fluid borne noise
generation of axial piston pumps. Seminar on Quiet oil hydraulic
sqlstems, 1977, paper C257177 (Institution of Mechanical Engineers,
London).
Proc
lnstn
3 Yamaguchi, A. and Takabe, T. Cavitation in an axial piston pump.
Bull. J.S.M.E., 1983, 26, 211.
4 Hibi, A., Ibuki, T., Ichikawa, T. and Yokote, H. Suction performance of axial piston pumps (1st report, analysis and fundamental experiments). Bull. J.S.M.E., 1Y77,20, 139.
5 Ibuki, T., Hihi, A., Ichikawa, T. and Yokote, H. Suction performance of axial piston pumps (2nd report, experimental results).
Bull. J.S.M.E., 1977,20, 145.
6 Hull, S. R. and Bowns, D. E. The development of an automatic
procedure for the digital simulation of hydraulic systems. Proc.
Instn Mech. Engrs, Part B, 1985, 199 (Bl), 51-65.
7 Kelsey, J., Taylor, R. and Wood, K. The practical benefits of optimising the port plate timing for an axial piston pump. Seminar on
Quieter oil hydraulics, 1980, paper C375/80 (Institution of Mechanical Engineers, London).
8 Helgestad, B. 0. An investigation of noise emission from an axial
piston hydraulic pump. PhD Thesis. Department of Mechanical
Engineering, Birmingham University, 1967.
9 Heron, R. Valve noise. Quieter fluid power handbook, 1980, Ch. 5
(BHRA, Cranfield. Bedford).
10 Second interim report on the DOT MEMTRB project on the
reduction of noise in hydraulic systems, Department of Mechanical Engineering, Ilniversity of Aston in Birmingham, 1978.
11 Etsion, I. and Magen, M. Piston vibration in piston cylinder
systems. Trans. A S M E , J . Fluids Engng, Mar. 1980,102.
12 Hooke, C. J. and Kakoullis, Y. P. On line measurement of film
thickness. Conference on fnstrumenls and computersfor cost efeectiuefluid power teAting, 1979, paper 128/79 (Institution of Mechanical Engineers, London).
Mech Engrs Vol 200 No B1
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