# Determination of Material and Fracture Properties of a Case-Hardened Planet Gear and Its Homogenisation Method to Obtain the Damage Mechanism Caused by Fragment Ingestion

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Approach

#### 2.1. Experimental Approach to Determine Constitutive Material Model

#### 2.1.1. Compression Test

#### 2.1.2. Vickers Indenter Test

#### 2.1.3. Quasi-Static Ingestion of a Fragment into a Scaled Gearbox

#### 2.2. Numerical Approach to Determine Failure Model

#### 2.2.1. Quasi-Static Pulsator Test

#### 2.2.2. Fragment-Ingestion Test (FIT)

## 3. Numerical Approach to Determine Constitutive Material Model

#### 3.1. Determine Core Material Parameters

#### 3.2. Determine Case Material Parameters

#### 3.3. Determine Homogenised Material Parameters

## 4. Verification and Validation of the Constitutive Material Model

#### 4.1. Verify Homogenised Material Model Based on the Pulsator Test and FIT

#### 4.2. Validate Homogenised Material Model Based on the Quasi-Static Ingestion Tests on the Scaled Gearbox

## 5. Determine the Fracture Locus of the Layered Material Model

#### 5.1. Determination Based on Pulsator Test

#### 5.2. Validation Based on FIT

## 6. Determine and Verify the Fracture Locus for the Homogenised Material Model

## 7. Summary

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Crack Propagation—FIT

## References

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**Figure 8.**Plastic deformation after ingestion of a spherical fragment with a diameter of D = 8 mm—top view.

**Figure 15.**Distribution of the stress triaxiality over the tooth root area for the layered material model.

**Figure 16.**Distribution of the stress triaxiality over the tooth root area for the homogenised material model.

**Figure 17.**Distribution of the plastic strain over the tooth root area for the layered material model.

**Figure 18.**Distribution of the plastic strain over the tooth root area for the homogenised material model.

**Figure 19.**Plastic deformation after ingestion of a sphere (D = 8 mm) within the numerical simulation.

**Figure 21.**Determined shift of the known fracture locus based on pulsator test [35].

**Figure 23.**Plastic strain to stress triaxiality for layered flank elements at a distance of 0.5 mm of the edge at ${d}_{max}$.

**Figure 24.**Plastic strain to stress triaxiality for layered flank elements at a distance of 1.5 mm of the edge at ${d}_{max}$.

**Figure 25.**Comparison of plastic strain-to-stress triaxiality for layered and homogenised flank elements at a distance of 0.5 mm of the edge at ${d}_{max}$.

**Figure 26.**Comparison of plastic strain-to-stress triaxiality for layered and homogenised flank elements at a distance of 1.5 mm of the edge at ${d}_{max}$.

**Figure 27.**Comparison of the plastic strain-to-stress triaxiality of the layered and homogenised material model at the tooth root based on the pulsator test at ${d}_{mean}$.

**Figure 28.**Comparison of the plastic strain-to-stress triaxiality of the layered and homogenised material model at the tooth root based on the pulsator test at ${d}_{max}$.

Parameter | Value |
---|---|

Teeth number (Sun), ${z}_{S}$ | 24 |

Teeth number (Planet), ${z}_{P}$ | 21 |

Teeth number (Ring), ${z}_{R}$ | 66 |

Module, ${m}_{n}$ | 5 mm |

Face width of gear, b | 20 mm |

Pressure angle, $\alpha $ | 20° |

Shifting coefficient, x | 0.101 |

Form | Sphere | Cylinder | ||||
---|---|---|---|---|---|---|

ID | S2 | S3 | C1 | C2 | C3 | C4 |

Size | 6 | 8 | 6 × 6 | 8 × 8 | 8 × 10 | 8 × 20 |

Position/gear width | 25|50|75 | 25|50|75 | 25|50|75 | 25|50|75 | 25|50 | 50 |

Complete over-roll | x|x|x | x|x|x | x|x|x |

Test-ID | max. Force [kN] |
---|---|

H33#02 V01 | 103.23 |

H33#02 V02 | 102.93 |

H33#02 V03 | 98.17 |

H33#02 V04 | 86.88 |

H33#02 V05 | 111.35 |

H34#02 V01 | 103.04 |

Test | Force—Initial Crack | Force—Secondary Crack | Fracture Location |
---|---|---|---|

1 | $128.6\mathrm{k}\mathrm{N}$ | $133.5\mathrm{k}\mathrm{N}$ | root |

2 | $125.9\mathrm{k}\mathrm{N}$ | $131.4\mathrm{k}\mathrm{N}$ | root |

3 | $106.0\mathrm{k}\mathrm{N}$ | $291.1\mathrm{k}\mathrm{N}$ | flank |

4 | $115.6\mathrm{k}\mathrm{N}$ | $123.4\mathrm{k}\mathrm{N}$ | root |

5 | $126.2\mathrm{k}\mathrm{N}$ | $149.2\mathrm{k}\mathrm{N}$ | root |

6 | $115.4\mathrm{k}\mathrm{N}$ | $132.5\mathrm{k}\mathrm{N}$ | root |

Material | A | B | n |
---|---|---|---|

30CrNiMo8 | 322 MPa | 912 MPa | 0.3179 |

34CrAlNi7-10 | 729 MPa | 565 MPa | 0.3800 |

Material | Core | Layer 1 | Layer 2 | Layer 3 | Layer 4 |
---|---|---|---|---|---|

30CrNiMo8 | 1029 MPa | 1160 MPa | 1385 MPa | 1600 MPa | 1803 MPa |

34CrAlNi7-10 | 741 MPa | 960 MPa | 1396 MPa | 2087 MPa | 3126 MPa |

Config | Axial Position/Gear Width | ${\mathit{h}}_{\mathbf{ind}}$—FEM | ${\mathit{h}}_{\mathbf{ind}}$—Experiment |
---|---|---|---|

Sphere ($d=6\mathrm{m}\mathrm{m}$) | 50% | 2.0 | 2.0 |

Sphere ($d=6\mathrm{m}\mathrm{m}$) | 25% | 1.3 | 1.4 |

Sphere ($d=6\mathrm{m}\mathrm{m}$) | 75% | 1.6 | 1.6 |

Sphere ($d=8\mathrm{m}\mathrm{m}$) | 50% | 2.3 | 2.4 |

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**MDPI and ACS Style**

Jeßberger, J.; Fischer, C.; Rinderknecht, S.
Determination of Material and Fracture Properties of a Case-Hardened Planet Gear and Its Homogenisation Method to Obtain the Damage Mechanism Caused by Fragment Ingestion. *Materials* **2024**, *17*, 366.
https://doi.org/10.3390/ma17020366

**AMA Style**

Jeßberger J, Fischer C, Rinderknecht S.
Determination of Material and Fracture Properties of a Case-Hardened Planet Gear and Its Homogenisation Method to Obtain the Damage Mechanism Caused by Fragment Ingestion. *Materials*. 2024; 17(2):366.
https://doi.org/10.3390/ma17020366

**Chicago/Turabian Style**

Jeßberger, Julia, Christian Fischer, and Stephan Rinderknecht.
2024. "Determination of Material and Fracture Properties of a Case-Hardened Planet Gear and Its Homogenisation Method to Obtain the Damage Mechanism Caused by Fragment Ingestion" *Materials* 17, no. 2: 366.
https://doi.org/10.3390/ma17020366