• Sources of vibration
• The pulsation dampener
• Frequency spectrum
• Method of calculation
• Dampening and natural frequency
• Self-induction
• Capacitance
• Resistance
• Hydraulic Muffler
• Expansion Chamber
• Conclusion
In Hydraulics, an accumulator is usually required
for the protection of the system environment:
It reduces disturbances caused by noise within
the acoustic environment, and it increases the reliability of
the system, the stability of the monitoring and measuring instruments
within the structural or physical environment.
Hydraulics devices in pulsation dampening
are designed toeliminate fluctuations in pressure and flow within
the circuit to increase total system efficiency.
There are two possible sources of vibrations
within a hydraulic system :
- the hydraulic source
- the structural source
The hydraulic pulsation dampener filters pressures
and flow pulsation but allows the structural vibrations to be
conveyed to the entire circuit. Hence, before any measures can
be taken to protect a system, there are two problems that must
be addressed:
- mechanical filtration
- hydraulic filtration
The principles of mechanical filtration (flexible
hydraulic hoses, silent bloc, etc.) are already widely known
and will not be discussed here. This study will deal with the
problem of filtering hydraulic pressure fluctuations in a wide
range of frequencies.
There are many potential applications for
pulsation dampening with frequencies ranging from 1Hz to 3000Hz.
Unfortunately, no one device is currently available to filter
fluctuations over this wide frequency range.
There are two specially adapted pulsation
dampeners that can accommodate this problem: the hydro-pneumatic
accumulator and the hydraulic muffler (developed by Nat. Exper.
Lab. Glasgow-Scotland). The hydropneumatic accumulator operates
at low frequencies (1-300 Hz) and the hydraulic muffler at high
frequencies (150-3000Hz).
The theoretical performance of these devices
can be calculated. in order to determine the characteristics
required to meet a particular problem, it is important that
the method of calculation be understood. While the operating
principle is the same for each device, this study will evaluate
their respective possibilities and limitations. The devices
will both be referred to as "Pulsation Dampeners".
The hydraulic pulsation dampener behaves like
a mass spring system excited at a given frequency (f).
Hydraulic excitation can be generated by any
device creating fluctuations in pressure and flow within a hydraulic
circuit.
The pump is an obvious example, but motors,
vibrating valves and even turbulence can generate hydraulic
fluctuations. Piston pumps, for example, are characterised by
flow variations which correspond to pressure variations. If
the changes in flow with respect to time and number of pistons
are known, the amplitudes of these fluctuations and their frequencies
can be derived from the rotation speed.
The excitation is defined by its frequency
and corresponding amplitude or frequency spectrum. This study
will show how a pulsating source is composed of range of elementary
excitations.
The "pulsation dampener" is subject
to excitation caused by pressure variations within the flow
line. It reacts to these pressure variations with a compression-release
motion which absorbs the flow fluctuations.
The role of "pulsation dampener " is to absorb the
motion amplitude or flow fluctuation with minimum resistance
so that the flow downstream is virtually constant. This system
will be most efficient when the excitation frequency (f) is
as close as possible to the natural frequency (f0) of the "pulsation
dampener".
The best performances are actually achieved when the system
is excited at its natural frequency, with minimal energy input
when the device operates in resonance. This resonance is subject
to a damping effect caused by the separator and hydraulic frictions.
In general, the damping effect is sufficient to rule out any
potential divergence.
Moreover, the masses in motion (inertia) are
minimal. A "pulsation dampener" can be used at frequencies
other than its natural frequency.
Hence, it is necessary to calculate the performance
of the pulsation dampener in attenuation as a function of the
exciting frequency caused by the hydraulic system.
The performance can be defined:
-either in dB (see curve below), giving the ratio of incident
pulsations to pulsations transmitted by the pulsation dampener.
Or, as the level of residual pulsations, defined as the ratio
of pulsations transmitted to mean pressure.
The definition, currently in use, requires that flow variations
in the main flow line be known.
Hence, the performance is dependent on the operational conditions
of the system (e.g. type of pumps and rotation speed).
The first definition (used by NEL) relates
to the pulsation dampener. It is not dependent on operational
conditions. A pulsation dampener has a performance curve which
is a function of the operational frequency. The performance
curve is primarily dependent on the geometry of the pulsation
dampener and, in the case of the hydro-pneumatic accumulator,
on the precharge pressure and the working pressure. It can be
used to calculate the level of pulsations of residual pressures
downstream from the pulsation dampener as a function of the
level of fluctuations upstream and the exciting frequency.
Pressure fluctuations within a flow line do
not generally follow a fixed frequency sine wave.
The signal actually comprises a larger number
of elementary sinusoidal signals which correspond to the natural
exciting frequency of the source of the pulsations and its various
harmonics, i.e.
Real signal as displayed on oscilloscope,
using rapid response pressure transducer (e.g. piezoelectric
transducer).
However, the display does not tell us much
about the individual elements (natural frequency, harmonics
and corresponding amplitudes). Any signal can be broken down
into the sum of elementary signals using the Fourier method
of analysis.
This breakdown can be performed in real time
with a spectrum analyzer. This device uses a digital or analog
method of calculation known as the "Fast Fourier Transforms",
or "FFT" and displays the result of the breakdown
as an amplitude spectrum.
If, for example, the FFT is applied to the
above signal, the frequency amplitude spectrum is as follows:
This spectrum displays the frequencies making
up the real signal and their corresponding fluctuation amplitudes.
This kind of analysis is very important when determining the
frequency range to be filtered and, hence, when defining the
most suitable pulsation dampener.
It can also be performed when using a microphone
which detects the loudest device within a system, for example:
Natural frequency 200 Hz, 1st harmonic
400Hz.
This measurement could have the following
spectrum:
Analysis could show, for example, that the
loudest element in the system is the pump, because, in this
spectrum, it generates the greatest amplitudes. Hence, the pump
would have to be fitted with hydraulic and mechanical filtering
equipment.
The amplitude spectra for a signal for pressure
fluctuations within a flow line generally shows a far greater
variety of frequencies.
Pressure amplitude spectrum
The amplitude levels for the fundamental mode
and for the harmonics are clearly visible, but all the intermediate
frequencies may also be included in a spectrum of this kind.
A muffler in the circuit would attenuate the
amplitudes of the frequency spectrum as far as its performance
curve, for example:
Attenuation by the muffler
Giving the following amplitude spectrum, which
is the difference between the two spectra:
Pressure amplitude spectrum
This muffler acts primarily in the frequency
range f' - f", and only filters the low frequencies (<f')
and high frequencies (>f") to a limited extent.
The frequency range in which the muffler operates
satisfactorily can be defined immediately using its performance
curve. Generally, an attenuation level of 20dB is sufficient,
20dB corresponds to a reduction by 99% if the incident pressure
fluctuation energy, 40dB to 99.9%. Hence, the operating frequency
range will be defined fro 20dB (or 25dB to provide a safety
margin), giving the operation range for the muffler must therefore
lie between frequencies f1 and f2 to ensure an attenuation greater
than or equal to 20 dB.
For a given pulsation dampener (with known
geometry and working conditions), the method of calculation
must allow the natural frequency/frequencies of the system and
its/their corresponding dampening coefficient/coefficients to
be determined. After it is possible to calculate the performance
curve fro the muffler and to specify its range of applications.
Electrical analogy allows any system to be
reproduced simply using basic electrical elements: capacitance
- C, self-induction - L, and resistance - R.
For example, a hydro-pneumatic accumulator
may be reproduced simply as follows:
equivalent to:
Pe, Ps : amplitude of fluctuations in input-output
pressure. Me, Ms : amplitude of fluctuations in input-output
flow.
These simple equations allow us to define
the frequency and dampening of a system of this kind giving
The natural frequency of the muffler is dependent
on the self-induction L and the Capacitance C alone.
The dampening meanwhile is dependent on the
dissipation caused by the resistance R, the capacitance C and
the natural frequency f0.
The natural frequency of a muffler can be
increased only by reducing the self-induction L and the capacitance
C. The dampening coefficient has the following effect on the
performance curve:
Therefore to increase the muffler performance
for the same natural frequency f0, its resistance R must be
minimised.
In order to determine the performance curve
for a hydro-pneumatic accumulator, the parameters self-induction,
capacitance and resistance must be defined.
Equations used in fluid mechanics will yield
these parameters. Only the results obtained and the main observations
will be analysed here.
The self-induction L of a hydro-pneumatic
accumulator is defined with respect to the geometry of the connection
to the main flow line.
Where Q is the density of the liquid, the
total self-induction Lt can be obtained by adding to L the self-induction
caused by any additional pipe with a cross section, Sc and a
length Lc. Hence, Lt = L*+Lc.
The self-induction Lt must be reduced if the
natural frequency of the accumulator is to be increased. If
L is kept as low as possible, the accumulator will be suitable
for a wide range of frequencies. Consequently the connection
length Lc must be reduced and the cross section of flow Sc increased.
This is where the pulsation dampener can be of use.
The calculation of the self-induction should
not present any problems. in addition, by reducing L,hydraulic
friction at the connection will be reduced. This length is,
in fact, an equivalent length, part of which can be attributed
to any jet effect produced in the accumulator, and is generally
greater than the geometric length of the connection.
Similarly, the capacitance C of an accumulator
is defined with respect to the geometry and is also dependent
on the operational conditions.
The capacitance is given by:
where:
Vm = Volume of gas
= adiabatic coefficient at pressure Pm
Pm = nominal working pressure
Vm and Pm are a function of Vo and Po (volume
of the accumulator and nitrogen precharge pressure), given that
Pm x Vm/Tm = Po x Vo/To.
If the natural frequency of the accumulator
is to be increased, the capacitance C must be reduced. Hence,
the volume of the accumulator and the precharge pressure under
defined operational conditions must be reduced.
The performance will increase as a logarithm
of C. Hence, when selecting the capacitance C, suitable natural
frequency-performance values must be found.
The resistance of the accumulator is made
up of various forms of energy dissipation, falling into two
categories:
1. Dissipative hydraulic resistance as laminar
pressure drop of type 
in the accumulator main flow line connecting pipe.
2. Mechanical resistance or mechanical dissipation
due to performance of the gas/liquid separator.
The dissipative hydraulic resistance may be
calculated theoretically by applying the laws of fluid mechanics.
The mechanical resistance is more difficult to calculate. However,
results from tests performed at CETIM ( a test lab) proved that
the damping coefficient due to the separator can be determined
as constant. This makes calculation less difficult.
Nevertheless, this value can change, either
as a function of the compression ratio Pm/Po, or when there
is a diaphragm as separator with an elastomer mass/capacitance
ratio very different from that of a bladder as separator.
The laws generally applied by OLAER to define
hydro-pneumatic accumulators take only the compression ability
of the gas into account and not its inertia.
This means that these laws should, strictly
speaking, be applied only if the phase difference between fluctuations
in pressure and flow is negligible. Hence, bearing in mind the
damping of the accumulators (~0,1), this method should only
be used for operational frequencies of less than 1/10th of the
accumulator natural frequency.
In accordance with the above, the range of
hydro-pneumatic accumulators for pulsation dampening are defined
considering high and average pressures.
The self-induction of standard OLAER accumulators
must be reduced.
Methods for reduction are :
adapting a connection on standard accumulators
so that a deflector can be fitted producing the greatest possible
reduction of self-induction. Fitting a button shut-off valve
instead of plug and poppet assembly. The valve guide with its
6 or 8 holes is detrimental to the self-inductionL and is preponderant
in the calculation of L.
Low pressure fluid ports with screens impede
the smooth running of the accumulator in pulsation dampening.
The large number of small holes considerably increases the self-induction
L and the resistance R, leading to low natural frequencies with
very high damping rates (>3).
A standard accumulator with plug and poppet
assembly has a coefficient approx 0.1 which is 30 times weaker.
Manufacturers have developed pulsation dampener
accumulators for stabilisation on the low pressure suction side
of pumps. The volume of the separator is usually identical to
that of the pulsation dampening accumulator on the high pressure
side.
If we assume that:
The pump compression ratio lies between 50
bars (700 psi) and 150 bars (approximately 2000 psi), and the
volume of the accumulator installed on the high pressure side
is 1 litre (1/4 Qt). How should the litre separator low pressure
accumulator be defined, given that both accumulators must have
approximately the same natural frequency ?
Let us calculate the self-induction LLP required
for the low pressure accumulator.
Hence the self-induction LLp does not depend
on the volume of the separator. Moreover, if it is assumed that
the compression ratio P is approximately the same for both types
of accumulator, then:
This accumulator must have a very low self-induction.
For reference, the self-induction of a pulsation dampener with
a deflector is approximately 60m-1.
This self-induction can be obtained with a
geometric set up as follows: giving a liquid volume greater
than 6L (1½GAL). These capacitances have a far greater
volume. This type of accumulator also has the following advantages:
To filter pockets of gas or vapor, and, to buffer volume upstream
from the pump to accommodate variations in pump flow.
The hydraulic mufflers developed by NEL, incorporating
an expansion chamber, are more complex to simulate. However,
they can be described in analog form as below.
Hydraulic diagram:
giving the following electric circuit diagram:
This system comprises several natural frequencies
depending on components 1, 2, and 3. Morerover, the individual
performance curves differ greatly.
The natural frequency of the flow lines can
be calculated using the ratio of the speed of sound over length
of pipe: giving f o ~a/l.
If both flow lines are of the same length,
the natural frequencies will be the same. If the flow lines
are of different lengths, the frequencies will be different,
but in the same ratio.
The performance curve of a flow line section
is expressed as follows:
The value of A is dependent on the inside
surface area of the main flow line in relation to the surface
area of the flow line. Should the natural frequencies be different,
the sum of these curves could have been the next form:
The shorter the flow lines, the greater the
natural frequencies.
Moreover, as the flow lines reduction ratios
increase, the performance becomes greater. However, this geometric
change will cause pressure drops in the fluid flow.
Theoretically, the natural frequency of the
chamber can be calculated, the same way as that of the hydro-pneumatic
accumulator.
The capacitance C is defined by:
The self-induction L is defined in the same way as for the hydro-pneumatic
accumulator, i.e. from the geometric set-up of the flow lines
connecting the main flow line to the expansion chamber, giving
:
As seen above, the natural frequency of this
chamber is :
A muffler adjusted for low frequency use requires
large volume V and vice-versa for high frequency use.
The performance curve of the expansion chamber
is similar to that of the hydro-pneumatic accumulator, giving
:
damping is due to viscous friction in the
holes and to the thermal dissipation of the fluctuations in
pressure into the oil.
The performance of the muffler may be calculated
by combining the two effects (flow line and expansion chamber).
A great number of geometric parameters are
needed to define the natural frequency and the attenuations
obtained for each frequency. With a symmetrical muffler (holes
in the centre of the internal tube), only two natural frequencies
give the following performance curve : addition of the 3 elementary
curves:
A simple computational model has been developed
based on the elements defined in the paragraph above.
The resistances R2, R2 and R3 have been defined
empirically to align the simplified OLAER model with the NEL
results.
For a given application, frequencies and attenuation
level, there are many methods of defining the muffler by the
choice of natural frequencies fo1, fo2, fo3. (fig 31,32,33).
However, the performance obtained at frequencies less than 140
Hz is very poor (<20dB) and, in general, the frequency band
in which the performance is greater than 20-25 dB corresponds
to a decade e.g. 140-1400 Hz or 300-3000 Hz.
As already mentioned, the determination of
the performance curve does not depend on the working pressure
or on the flow. Pressure drops in the muffler are mainly due
to the restriction to the entry and the widening to the exit.
More the pressure drop will be important, therefore more the
ratio of section between supply flow line and the internal pipe
will be great, better performance is observed especially at
high frequencies. In fact, the low frequency and the natural
frequencies of the muffler remain virtually unchanged. Only
the attenuation levels are reduced, particularly those due to
the effect of the internal pipe.
There are many possible ranges of applications
for the system in pulsation dampening. the user must be well
acquainted with the advantages and disadvantages of mufflers
(hydro-pneumatic or NEL) so any encountered problems can be
accommodated.
Provided that the operational conditions remain
unchanged (pressure and working temperature) and the ranges
of frequencies to be filtered remain sufficiently narrow (1
to 300 Hz), this type of pulsation dampener can easily be adapted.
If there are considerable variations in the operational pressure,
two individually adjusted pulsation dampeners can be fitted
(e.g. with different precharge pressures).
Example :
A pump operating between 100 and 200 bars
(1500 and 3000 psi). The choice of an accumulator will be based
on its natural frequency to correspond as closely as possible
to the exciting frequency. This calculation and the performance
as a function of the exciting frequency f0 for a given natural
frequency can be easily performed by a small-size pocket calculator.
Using the standard laws of pulsation dampening,
it is also possible to define the accumulator required and to
check that its natural frequency is not two times less than
the working frequency.
Fewer problems will be encountered with a
hydraulic muffler because it is not affected by the pressure
or flow. However, adapting it to meet individual needs will
prove problematic.
Therefore, it is suggested that a muffler
which will cater to most needs be selected from a predefined
range. But for special problems, it is possible to develop the
muffler to meet specific needs.
These special cases are as follows:
Permitted low pressure drop (<5 bars -
70 psi), and, low filtration frequency ranging between 140 and
170 Hz.
These specific applications will generally
involve mufflers which are more bulky than those offered by
the range, since the first natural frequency is reduced and
the volume increased. Moreover, the performance caused by the
flow line effect is lower, giving more narrow filtered frequency
20 dB bands. Using the simplified model resented above, a number
of specific applications can rapidly be catered to.
Two problem areas may develop when a muffler
is fitted in a flow line:
The first relates to the transmission of vibrations
within the structure of the piping itself. The muffler will
have no effect on this. For this reason it is advisable to fit
a hose assembly upstream and downstream from the device, the
second relates to its position with respect to the pulsation
source. It is best to place the muffler as near as possible
to the source.
The determination on a regular basis of the
pulsation dampener and particularly the accumulators from the
exciting frequencies and natural frequencies may appear difficult.
Using this method of calculation, at least regarding accumulators,
the operational conditions can be checked and certain problems
relating to exciting frequencies for greater than the natural
frequencies of pulsation dampeners can be checked simply by
using a pocket calculator. This study highlights the important
parameters to be observed when designing an accumulator for
pulsation dampening.
There are many possible applications for pulsation
dampening accumulators. The desired result is the reduction
of acoustic noise generated by hydraulic systems.
Hydraulic devices in pulsation dampening are
only one step in the right direction.
The transmission of vibrations by the structure
taken place on a large scale and is difficult to control and,
as a general rule, the energy of the mechanical vibrations is
equivalent to that existing in the liquid. For this reason,
even if all problems with the attenuation of pressure fluctuations
have been solved, this will not necessarily lead to a considerable
reduction of acoustic noise. In general, a study of the reduction
of mechanical vibrations should be carried out.
Francois Brault, OLAER engineer.
