# Engineering Acoustics/Noise in Hydraulic Systems

## Noise in Hydraulic Systems

Hydraulic systems are the most preferred source of power transmission in
most of the industrial and mobile equipments due to their advantages in
power density, compactness, flexibility, fast response and efficiency.
The field hydraulics and pneumatics is also known as \'Fluid Power
Technology\'. Fluid power systems have a wide range of applications
which include industrial, off-road vehicles, automotive system and
aircrafts. In spite of these advantages, there are also some
disadvantages. One of the main drawbacks with the hydraulic fluid power
systems is the vibration and noise generated by them. The health and
safety issues relating to noise, vibration and harshness (NVH) have been
recognized for many years and legislation is now placing clear demands
on manufacturers to reduce noise levels \[1\]. Hence, a lot of attention
has been paid on reducing the noise of hydraulic fluid power systems
both from the industrial and academic researchers. A good understanding
of the noise generation, transmission and propagation is very important
in order to improve the NVH performance of hydraulic fluid power
systems.

## Sound in fluids

The speed of sound in fluids can be determined using the following
relation.

$c = \sqrt {\frac{K}{\rho}}$ where K - fluid bulk modulus, $\rho$- fluid
density, c - velocity of sound

Typical value of bulk modulus range from **2e9 to 2.5e9 N/m2**. For a
particular oil, with a density of **889 kg/m3**,

speed of sound $c = \sqrt {\frac{2e9}{889}}= 1499.9 m/s$

## Source of Noise

The main source of noise in hydraulic systems is the pump which supplies
the flow. Most of the pumps used are positive displacement pumps. Of the
positive displacement pumps, axial piston swash plate type is mostly
preferred due to their controllability and efficiency.

The noise generation in an axial piston pump can be classified under two
categories:

\(i\) fluidborne noise and

\(ii\) Structureborne noise

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Fluidborne Noise (FBN)

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Among the positive displacement pumps, highest levels of FBN are
generated by axial piston pumps and lowest levels by screw pumps and in
between these lie the external gear pump and vane pump \[1\]. The
discussion in this page is mainly focused on **axial piston swash plate
type pumps**. An axial piston pump has a fixed number of displacement
chambers arranged in a circular pattern separated from each other by an
angular pitch equal to $\phi = \frac {360}{n}$ where n is the number of
displacement chambers. As each chamber discharges a specific volume of
fluid, the discharge at the pump outlet is sum of all the discharge from
the individual chambers. The discontinuity in flow between adjacent
chambers results in a kinematic flow ripple. The amplitude of the
kinematic ripple can be theoretically determined given the size of the
pump and the number of displament chambers. The kinematic ripple is the
main cause of the fluidborne noise. The kinematic ripples is a
theoretical value. The actual **flow ripple** at the pump outlet is much
larger than the theoretical value because the **kinematic ripple** is
combined with a **compressibility component** which is due to the fluid
compressibility. These ripples (also referred as flow pulsations)
generated at the pump are transmitted through the pipe or flexible hose
connected to the pump and travel to all parts of the hydraulic circuit.

The pump is considered an ideal flow source. The pressure in the system
will be decided by resistance to the flow or otherwise known as system
load. The flow pulsations result in pressure pulsations. The pressure
pulsations are superimposed on the mean system pressure. Both the **flow
and pressure pulsations** easily travel to all part of the circuit and
affect the performance of the components like control valve and
actuators in the system and make the component vibrate, sometimes even
resonate. This vibration of system components adds to the noise
generated by the flow pulsations. The transmission of FBN in the circuit
is discussed under transmission below.

A typical axial piston pump with 9 pistons running at 1000 rpm can
produce a sound pressure level of more than 70 dBs.

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Structureborne Noise (SBN)

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In swash plate type pumps, the main sources of the structureborne noise
are the fluctuating forces and moments of the swas plate. These
fluctuating forces arise as a result of the varying pressure inside the
displacement chamber. As the displacing elements move from suction
stroke to discharge stroke, the pressure varies accordingly from few
bars to few hundred bars. This pressure changes are reflected on the
displacement elements (in this case, pistons) as forces and these force
are exerted on the swash plate causing the swash plate to vibrate. This
vibration of the swash plate is the main cause of **structureborne
noise**. There are other components in the system which also vibrate and
lead to structureborne noise, but the swash is the major contributor.

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![](Pump_noise.png "Pump_noise.png")

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**Fig. 1 shows an exploded view of axial piston pump. Also the flow
pulsations and the oscillating forces on the swash plate, which cause
FBN and SBN respectively are shown for one revolution of the pump.**

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## Transmission

### FBN

The transmission of FBN is a complex phenomenon. Over the past few
decades, considerable amount of research had gone into mathematical
modeling of pressure and flow transient in the circuit. This involves
the solution of wave equations, with piping treated as a distributed
parameter system known as a transmission line \[1\] & \[3\].

Lets consider a simple pump-pipe-loading valve circuit as shown in Fig.
2. The pressure and flow ripple at ay location in the pipe can be
described by the relations:

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$\frac {}{} P = Ae^{-k x} + Be^{-k x}$ \...\...\...(1)

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$Q = \frac {1}{Z_{0}}(Ae^{-k x} - Be^{-k x})$\.....(2)

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where $\frac {}{} A$ and $\frac {}{} B$ are frequency dependent complex
coefficients which are directly proportional to pump (source) flow
ripple, but also functions of the source impedance $\frac {}{} Z_{s}$,
characteristic impedance of the pipe $\frac {}{} Z_{0}$ and the
termination impedance $\frac {}{} Z_{t}$. These impedances ,usually vary
as the system operating pressure and flow rate changes, can be
determined experimentally.

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**Fig.2 Schematic of a pump connected to a hydraulic line**

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For complex systems with several system components, the pressure and
flow ripples are estimated using the transformation matrix approach. For
this, the system components can be treated as lumped impedances (a
throttle valve or accumulator), or distributed impedances (flexible hose
or silencer). Various software packages are available today to predict
the pressure pulsations.

### SBN

The transmission of SBN follows the classic source-path-noise model. The
vibrations of the swash plate, the main cause of SBN, is transferred to
the pump casing which encloses all the rotating group in the pump
including displacement chambers (also known as cylinder block), pistons
and the swash plate. The pump case, apart from vibrating itself,
transfers the vibration down to the mount on which the pump is mounted.
The mount then passes the vibrations down to the main mounted structure
or the vehicle. Thus the SBN is transferred from the swash plate to the
main strucuture or vehicle via pumpcasing and mount.

Some of the machine structures, along the path of transmission, are good
at transmitting this vribational energy and they even resonate and
reinforce it. By converting only a fraction of 1% of the pump
structureborne noise into sound, a member in the transmission path could
radiate more ABN than the pump itself \[4\].

## Airborne noise (ABN)

Both FBN and SBN , impart high fatigue loads on the system components
and make them vibrate. All of these vibrations are radiated as
**airborne noise** and can be heard by a human operator. Also, the flow
and pressure pulsations make the system components such as a control
valve to resonate. This vibration of the particular component again
radiates airborne noise.

## Noise reduction

The reduction of the noise radiated from the hydraulic system can be
approached in two ways.

\(i\) **Reduction at Source** - which is the reduction of noise at the
pump. A large amount of open literature are availabale on the reduction
techniques with some techniques focusing on reducing FBN at source and
others focusing on SBN. Reduction in FBN and SBN at the source has a
large influence on the ABN that is radiated. Even though, a lot of
progress had been made in reducing the FBN and SBN separately, the
problem of noise in hydraulic systems is not fully solved and lot need
to be done. The reason is that the FBN and SBN are interlated, in a
sense that, if one tried to reduce the FBN at the pump, it tends to
affect the SBN characteristics. Currently, one of the main researches in
noise reduction in pumps, is a systematic approach in understanding the
coupling between FBN and SBN and targeting them simultaneously instead
of treating them as two separte sources. Such an unified approach,
demands not only well trained researchers but also sophisticated
computer based mathematical model of the pump which can accurately
output the necessary results for optimization of pump design. The
amplitude of fluid pulsations can be reduced, at the source, with the
use of an hydraulic attenuator(5).

\(ii\) **Reduction at Component level** - which focuses on the reduction
of noise from individual component like hose, control valve, pump mounts
and fixtures. This can be accomplished by a suitable design modification
of the component so that it radiates least amount of noise. Optimization
using computer based models can be one of the ways.

## Hydraulic System noise

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![](Noise.png "Noise.png")

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**Fig.3 Domain of hydraulic system noise generation and transmission
(Figure recreated from \[1\])**

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## References

1\. *Designing Quieter Hydraulic Systems - Some Recent Developements and
Contributions*, Kevin Edge, 1999, Fluid Power: Forth JHPS International
Symposium.

2\. *Fundamentals of Acoustics*, L.E. Kinsler, A.R. Frey, A.B.Coppens,
J.V. Sanders. Fourth Edition. John Wiley & Sons Inc.

3\. *Reduction of Axial Piston Pump Pressure Ripple*, A.M. Harrison. PhD
thesis, University of Bath. 1997

4\. *Noise Control of Hydraulic Machinery*, Stan Skaistis, 1988. MARCEL
DEKKER , INC.

5\. *Hydraulic Power System Analysis*, A. Akers, M. Gassman, & R. Smith,
Taylor & Francis, New York, 2006, 

6\. *Experimental studies of the vibro-acoustic characteristics of an
axial piston pump under run-up and steady-state operating conditions*,
Shaogan Ye et al., 2018, Measurement, 133.

7\. *Sound quality evaluation and prediction for the emitted noise of
axial piston pumps*, Junhui Zhang, Shiqi Xia, Shaogan Ye et al., 2018,
Applied Acoustics 145:27-40.

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