# Noise Reduction in Spur Gear Systems

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### FEM Static Analysis of a Spur Gear Pair

_{s}, the kinetic friction coefficient μ

_{k}, and the decay coefficient d

_{c}as well. This model was based on the following equation, where ϒ is the slip rate:

## 3. Results

**Condition A**: The first analysis involved a steel spur gear pair and was characterized by frictionless contact. The results are shown in Figure 3 and Figure 4.

**Condition B**: The second analysis involved a steel spur gear pair and was characterized by the mentioned exponential-decay-based friction model. The results are shown in Figure 5 and Figure 6.

**Condition C:**The third analysis involved a ductile iron spur gear pair and was characterized by frictionless contact. The results are shown in Figure 7 and Figure 8.

**Condition D**: The fourth analysis involved a ductile iron spur gear pair and was characterized by the mentioned exponential-decay-based friction model. The results are shown in Figure 9 and Figure 10.

**Condition E**: The fifth analysis involved a steel spur gear pair and was characterized by the mentioned exponential-decay-based lubricated friction model. The results are shown in Figure 11 and Figure 12.

#### 3.1. Comparisons

The second analysis (condition B) showed higher von Mises stress and contact pressure values than the first one, so the presence of friction made the stress increase together with the sound excitation, as previously mentioned for this parameter.

Third Analysis (Condition C) versus Fourth Analysis (Condition D)

As we can see in the third and fourth analyses, the ductile iron spur gears had lower von Mises stress and lower contact pressure values, in agreement with comments regarding gear materials and ductile iron properties. Therefore, the sound excitation was lower as well.

Fifth Analysis (Condition E) versus First Analysis (Condition A)

The fifth analysis showed that lubricated friction made the stress decrease together with the contact pressure, leading to agreement that the oil coating reduced the sound excitation of the gears.

First Two Analyses (Conditions A and B) versus Third and Fourth (Conditions C and D) Analyses

#### 3.2. Difference Static and Dynamic Analyses

#### 3.3. Coupled Eulerian–Lagrangian (CEL) Analysis of a Spur Gear Pair

“EULERIAN BOUNDARY, OUTFLOW = NON REFLECTING”.

_{ref}is the sound pressure level at a distance of about 80 mm; r is a distance of 1 m; r

_{ref}is a distance of about 80 mm.

_{s}, the kinetic friction coefficient μ

_{k}, and the decay coefficient d

_{c}as well. This model was based on Equation (1), in which ϒ is the slip rate (Figure 15).

## 4. Discussion

**Condition 1**: The first analysis involved a steel spur gear pair and was characterized by frictionless contact and a rotational speed of 500 RPM. Figure 16 shows the sound pressure level of the meshing gears at a distance of 1 m.

**Condition 2**: The second analysis involved a steel spur gear pair and was characterized by the mentioned exponential decay friction model and a rotational speed of 500 RPM. Figure 17 shows the sound pressure level of the meshing gears at a distance of 1 m.

**Condition 3**: The third analysis involved a steel spur gear pair and was characterized by the mentioned exponential decay friction model and a rotational speed of 1500 RPM. Figure 18 shows the sound pressure level of the meshing gears at a distance of 1 m.

**Condition 4**: The fourth analysis involved a steel spur gear and was characterized by the mentioned exponential decay friction model and a rotational speed of 3000 RPM. Figure 19 shows the sound pressure level of the meshing gears at a distance of 1 m.

**Condition 5**: The fifth analysis involved a steel spur gear pair and was characterized by the mentioned exponential decay friction model (lubricated friction) and a rotational speed of 500 RPM. Figure 20 shows the sound pressure level of the meshing gears at a distance of 1 m.

#### 4.1. Comparisons

#### 4.1.1. First Analysis (Condition 1) versus Second Analysis (Condition 2)

#### 4.1.2. Third Analysis (Condition 3) versus Fourth Analysis (Condition 4)

#### 4.1.3. Fourth Analysis (Condition 4) versus Fifth Analysis (Condition 5)

#### 4.1.4. Second Analysis (Condition 2) versus Fifth Analysis (Condition 5)

#### 4.1.5. Final Remarks

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

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Parameters | Values |
---|---|

Number of teeth N | 55 |

Module | 2.72 |

Pitch circle | 150 mm |

Dedendum circle | 142.50 mm |

Addendum circle | 156 mm |

Circular pitch | 6.5° |

Pressure angle | 20° |

Condition | Friction | Material Parameters | Lubricated Friction |
---|---|---|---|

A | NO | Steel | NO |

B | μ_{s} = 0.74μ _{k} = 0.57d _{c} = 0.2 | Steel | NO |

C | NO | Ductile Iron | NO |

D | μ_{s} = 1.1μ _{k} = 0.15d _{c} = 0.2 | Ductile Iron | NO |

E | NO | Steel | μ_{s} = 1.1μ _{k} = 0.15d _{c} = 0.2 |

Condition | Parameters | |||
---|---|---|---|---|

Friction | Material | Lubricated Friction | Rotational Speed (RPM) | |

1 | NO | Steel | NO | 500 |

2 | μ_{s} = 0.74μ _{k} = 0.57d _{c} = 0.2 | Steel | NO | 500 |

3 | μ_{s} = 0.74μ _{k} = 0.57d _{c} = 0.2 | Steel | NO | 1500 |

4 | μ_{s} = 0.74μ _{k} = 0.57d _{c} = 0.2 | Steel | NO | 3000 |

5 | NO | Steel | μ_{s} = 0.11μ _{k} = 0.05d _{c} = 0.2 | 500 |

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**MDPI and ACS Style**

Liguori, A.; Armentani, E.; Bertocco, A.; Formato, A.; Pellegrino, A.; Villecco, F.
Noise Reduction in Spur Gear Systems. *Entropy* **2020**, *22*, 1306.
https://doi.org/10.3390/e22111306

**AMA Style**

Liguori A, Armentani E, Bertocco A, Formato A, Pellegrino A, Villecco F.
Noise Reduction in Spur Gear Systems. *Entropy*. 2020; 22(11):1306.
https://doi.org/10.3390/e22111306

**Chicago/Turabian Style**

Liguori, Aurelio, Enrico Armentani, Alcide Bertocco, Andrea Formato, Arcangelo Pellegrino, and Francesco Villecco.
2020. "Noise Reduction in Spur Gear Systems" *Entropy* 22, no. 11: 1306.
https://doi.org/10.3390/e22111306