# 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 $c={\sqrt {\frac {2e9}{889}}}=1499.9m/s$

## 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

## Fluidborne Noise (FBN)

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.

## Structureborne Noise (SBN)

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.

## 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:
${\frac}P=Ae^{-kx}+Be^{-kx}$
$Q={\frac {1}{Z_{0}}}(Ae^{-kx}-Be^{-kx})$
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.
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.

## 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, ISBN 0-8247-9956-9
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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