# Psychoacoustic Evaluation of Hydraulic Pumps

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Motivation and Introduction

#### 1.1. Basics of Acoustics and Psychoacoustics

_{p}according to Equation (1), from the effective sound pressure p in relation to the reference sound pressure p

_{0}. The SPL is expressed in dB. For airborne sound, the reference SPL is p

_{0}= 20 µPa, equivalent to the human hearing threshold [6].

_{TQ}as well as E

_{0}are used in the calculation of the specific loudness. E

_{TQ}is the excitation at threshold in quiet. E

_{0}correspond to the reference intensity I

_{0}[13]. For further information about the calculation of the specific loudness and the derivation of Equation (3) for example [13] can be used.

_{N}using Equations (4) and (5) [15].

_{1kHz}= 3.15 sone, while the axial piston pump (APP) with a loudness of N

_{APP}= 9.50 sone and the internal gear pump (IGP) with a loudness of N

_{IGP}= 9.83 sone are perceived more than three times as loud by humans.

#### 1.2. Noise Generation in Hydraulic Systems

^{−1}. The load pressure is 250 bar. However, the dominant excitation frequencies depend on the rotational speed n and on the number of displacers z. For the axial piston pump, z is equal to the number of pistons. In this case, a pump with nine pistons is used. For the internal gear pump, z

_{1}is the number of teeth of the external gear, which is the driving gear, and z

_{2}the number of teeth of the internal gear, which is the driven gear. For the internal gear pump, the number of teeth of the external gear is z

_{1}= 13 and for the internal gear z

_{2}= 19. Figure 6 shows a good correlation between the number of displacers and the dominant excitation frequencies.

^{−1}. The load pressure is equal to Figure 6. The dominant excitation frequencies still correlate with the number of displacers and the rotational speed. Due to the higher rotational speed, there is a shift to higher frequencies. Both diagrams illustrate the impact of the mechanical kinematic effects inside the pump on the pressure sound level, which are sketched in Figure 5.

## 2. Materials and Methods

#### Instrumental Measurement of an Axial Piston Pump and an Internal Gear Pump

^{−1}and 3500 min

^{−1}in steps of 500 min

^{−1}. The load pressure is set between 50 bar and 250 bar, in steps of 50 bar, via a proportional directional valve. Each operating point is held for at least 60 s before the sound recording is started. The sound was recorded for another 60 s. The measurements are performed with an HLP 46, at temperatures between 50 °C and 64 °C. The temperature of the fluid increases especially at high speed and high load pressure due to the high cooling requirement. Figure 8 shows the simplified schematic hydraulic circuit used for the measurements. The main components of the drive chamber are the electric drive motor and the hydraulic infrastructure, including a proportional directional valve to apply the pressure. The separation between the pump and the drive is achieved by the anechoic chamber.

^{−1}/250 bar, the A-weighted SPL of the internal gear pump is about 10% lower than the A-weighted SPL of the axial piston pump. For both pumps, the SPL increases with increasing speed and pressure. The effect of the rotational speed on the SPL has to be considered higher.

^{−1}/250 bar, the loudness of the internal gear pump is about 30% lower than the loudness of the axial piston pump.

## 3. Analysis of Results

#### 3.1. Listening Tests to Determine the Subjectively Perceived Pleasantness or Annoyance

#### 3.2. Regression Analyses to Predict the Subjectively Perceived Pleasantness or Annoyance

## 4. Conclusions

^{−1}/250 bar. However, the A-weighted SPL of the internal gear pump is only about 10% lower than the A-weighted SPL of the axial piston pump in the same operation point. The interpretation of the sharpness is very difficult, because there is no obvious dependency of the sharpness on pressure or rotational speed in the measured data. In context of electrification and the noise of hydraulic pumps, increasing the pressure level has a lower impact on the emitted sound than increasing the rotational speed of the electro-hydraulic drive. The study also shows that the trend to higher rotational speed has to consider noise emission as well.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

**Note:**This article is a modified and extended version of a conference paper published in the German language: Pietrzyk, Tobias; Georgi, Markus; Schlittmeier, Sabine; Schmitz, Katharina: Psychoakustische Beurteilung drehzahlvariabler hydraulischer Antriebe, 8. Fachtagung Baumaschinentechnik 2020, Dresden, Germany, 1–2 October 2020.

## Appendix A

**Figure A1.**Complete preference matrix for all paired-comparisons (N = 20 participants) of the axial piston pump (APP) and of the internal gear pump (IGP) at the different operation points (rotational speed and pressure).

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**Figure 2.**Distribution of the SPL in the third-octave spectrum, total SPL of 58.5 dB for each sound.

**Figure 3.**Specific loudness for an internal gear pump (IGP), an axial piston pump (APP) and a sound of 1 kHz with a SPL of 58.5 dB.

**Figure 5.**Schematic sketch of internal forces and their mechanical coupling to the housing structure for an axial piston pump (

**top**) and for an internal gear pump (

**bottom**).

**Figure 6.**Normalized FFT of the SPL for an internal gear pump (

**top**) and an axial piston pump (

**bottom**) at 1000 min

^{−1}, 250 bar and a frequency range of 40 Hz to 1 kHz.

**Figure 7.**Normalized FFT of the SPL for an internal gear pump (

**top**) and an axial piston pump (

**bottom**) at 3000 min

^{−1}, 250 bar and a frequency range of 40 Hz to 3 kHz.

**Figure 9.**Set up for the instrumental measurements: (

**a**) electric drive motor and the hydraulic infrastructure; (

**b**) arrangement of the microphones in the anechoic chamber.

**Figure 15.**Preference matrices (N = 20 participants) for sound pairs in which both sounds were derived either from the axial piston pump (

**upper panel**) or from the internal gear pump (

**lower panel**).

**Figure 16.**Priority vectors for the axial piston pump (

**left**) and the internal gear pump (

**right**) representing the subjectively perceived pleasantness.

**Figure 17.**Scatter plot for rotational speed and priority vector with separated regression lines for the axial piston pump and the internal gear pump. Each circle represents the measured values for one of the 18 pump sounds in the present study.

**Figure 18.**Scatter plot for A-weighted SPL and priority vector with regression line. Each circle represents the measured values for one of the 18 pump sounds in the present study.

**Figure 19.**Scatter plot for rotational speed and A-weighted SPL with separated regression lines for axial piston pump and internal gear pump. Each circle represents the measured values for one of the 18 pump sounds in the present study.

**Figure 20.**Scatter plot for rotational speed and A-weighted SPL with regression line without consideration of pump type. Each circle represents the measured values for one of the 18 sounds in the present study.

**Table 1.**Regression table for the regression of subjective pleasantness as indicated by priority vector from pump type, rotational speed, and load pressure, as given in Equation (9). The table displays for each predictor variable the unstandardized regression coefficient B with standard error (SE), the standardized regression coefficient β and the corresponding t-test with p-value.

Variable | B | SE B | β | t | p |
---|---|---|---|---|---|

constant | 0.11 | 0.15 | |||

Pump type | 0.04 | 0.01 | 0.47 | 6.78 | <0.001 |

Speed (rpm) | −0.001 | 0.001 | −0.84 | −12.00 | <0.001 |

Pressure (bar) | −0.001 | 0.001 | −0.09 | −1.29 | 0.22 |

**Table 2.**Regression table for the regression of subjective pleasantness in terms of priority vector from a-weighted SPL and sharpness, as given in Equation (10). The table displays, for each predictor variable, the unstandardized regression coefficient B with standard error (SE), the standardized regression coefficient β, and the corresponding t-test with p-value.

Variable | B | SE B | β | t | p |
---|---|---|---|---|---|

constant | 0.30 | 0.03 | |||

SPL (dB(A)) | −0.004 | 0.001 | −0.99 | −21.11 | <0.001 |

Sharpness (acum) | 0.001 | 0.02 | 0.001 | 0.03 | 0.98 |

**Table 3.**Regression table for the regression of A-weighted SPL from pump type, rotational speed, and load pressure, as given in Equation (11). The table displays, for each predictor variable, the unstandardized regression coefficient B with standard error (SE), the standardized regression coefficient β, and the corresponding t-test with p-value.

Variable | B | SE B | β | t | p |
---|---|---|---|---|---|

constant | 50.82 | 3.60 | |||

Pump type | −10.21 | 1.35 | −0.52 | −7.58 | < 0.001 |

Speed (rpm) | 0.01 | 0.001 | 0.82 | 11.99 | < 0.001 |

Pressure (bar) | 0.01 | 0.02 | 0.03 | 0.50 | 0.63 |

**Table 4.**Regression table for the regression of A-weighted SPL from rotational speed and load pressure, as given in Equation (12). The table displays, for each predictor variable, the unstandardized regression coefficient B with standard error (SE), the standardized regression coefficient β, and the corresponding t-test with p-value.

Variable | B | SE B | β | t | p |
---|---|---|---|---|---|

constant | 45.72 | 7.72 | |||

Speed (rpm) | 0.01 | 0.001 | 0.82 | 5.49 | <0.001 |

Pressure (bar) | 0.01 | 0.04 | 0.03 | 0.23 | 0.82 |

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## Share and Cite

**MDPI and ACS Style**

Pietrzyk, T.; Georgi, M.; Schlittmeier, S.; Schmitz, K.
Psychoacoustic Evaluation of Hydraulic Pumps. *Sustainability* **2021**, *13*, 7320.
https://doi.org/10.3390/su13137320

**AMA Style**

Pietrzyk T, Georgi M, Schlittmeier S, Schmitz K.
Psychoacoustic Evaluation of Hydraulic Pumps. *Sustainability*. 2021; 13(13):7320.
https://doi.org/10.3390/su13137320

**Chicago/Turabian Style**

Pietrzyk, Tobias, Markus Georgi, Sabine Schlittmeier, and Katharina Schmitz.
2021. "Psychoacoustic Evaluation of Hydraulic Pumps" *Sustainability* 13, no. 13: 7320.
https://doi.org/10.3390/su13137320