# Simulation and Verification of Involute Spline Tooth Surface Wear before and after Carburizing Based on Energy Dissipation Method

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## Abstract

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## 1. Introduction

## 2. Wear Prediction Model of Floating Spline Couplings

#### 2.1. Wear Mechanism Analysis of Floating Spline in the Working Process

#### 2.2. Calculation Model of Wear Depth of Floating Involute Spline

## 3. Simulation and Analysis of Wear Depth Distribution of Floating Spline Couplings after Different Surface Hardening Treatments

#### 3.1. Establishment of Finite Element Model of Floating Spline Couplings

#### 3.2. Working Conditions

## 4. Wear Analysis of 32Cr3MoVA Involute Spline Tooth Surface without Carburizing Treatment

#### 4.1. Floating Distance Is 0 mm

#### 4.2. Floating Distance Is 0.3 mm

#### 4.3. Floating Distance Is 0.6 mm

#### 4.4. Summary

## 5. Analysis of 32Cr3MoVA Involute Spline Tooth Surface Wear after Carburizing

#### 5.1. Floating Distance 0 mm

#### 5.2. Floating Distance 0.3 mm

#### 5.3. Floating Distance Is 0.6 mm

#### 5.4. Summary

## 6. Test

#### 6.1. Test Principle and Device

#### 6.2. Test Piece Parameters

#### 6.3. Analysis of Test Results

#### 6.3.1. Macro Analysis of Tooth Surface Topography

#### 6.3.2. Microanalysis of Tooth Surface Topography

#### 6.3.3. Analysis of Tooth Surface Wear Depth

#### 6.4. Summary

## 7. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Finite element model of spline couplings. (

**a**) External spline; (

**b**) internal spline; (

**c**) spline coupling engagement diagram.

**Figure 3.**Wear distribution diagram of the tooth surface of the external spline without carburizing treatment when the floating distance is 0 mm. (

**a**) Wear depth distribution curve of the external spline in the axial direction; (

**b**) distribution curve of wear depth of external spline in the radial direction.

**Figure 4.**Distribution curve of wear depth of each tooth surface of external spline without carburizing treatment when the floating distance is 0 mm.

**Figure 5.**Wear distribution diagram of the tooth surface of the external spline without carburizing treatment when the floating distance is 0.3 mm. (

**a**) Wear depth distribution curve of the external spline in the axial direction; (

**b**) distribution curve of wear depth of external spline in the radial direction.

**Figure 6.**Distribution curve of wear depth on tooth surfaces of external spline without carburizing treatment when floating distance is 0.3 mm.

**Figure 7.**Wear distribution diagram of external spline tooth surface without carburizing treatment when the floating distance is 0.6 mm. (

**a**) Curve diagram of the wear depth distribution of external spline in the axial direction; (

**b**) distribution curve of wear depth of external spline in the radial direction.

**Figure 8.**Distribution curve of wear depth on tooth surfaces of external spline without carburizing treatment when floating distance is 0.6 mm.

**Figure 9.**Wear distribution diagram of external spline tooth surface after carburizing when floating distance is 0 mm. (

**a**) Wear depth distribution curve of external spline in the axial direction; (

**b**) distribution curve of wear depth of external spline in the radial direction.

**Figure 10.**Distribution curve of wear depth of each tooth surface of external spline after carburizing when the floating distance is 0 mm.

**Figure 11.**Wear distribution diagram of external spline tooth surface after carburizing when the floating distance is 0.3 mm. (

**a**) Curve diagram of the wear depth distribution of external spline in an axial direction; (

**b**) distribution curve of wear depth of external spline in the radial direction.

**Figure 12.**Distribution curve of wear depth of each tooth surface of the external spline after carburizing when the floating distance is 0.3 mm.

**Figure 13.**Wear distribution diagram of external spline tooth surface after carburizing when the floating distance is 0.6 mm. (

**a**) Wear depth distribution curve of external spline in the axial direction; (

**b**) distribution curve of wear depth of external spline in a radial direction.

**Figure 14.**Distribution curve of wear depth of each tooth surface of the external spline after carburizing when the floating distance is 0.6 mm.

**Figure 18.**Tooth surface of external spline without wear. (

**a**) External spline without carburizing treatment; (

**b**) external spline with carburizing treatment.

**Figure 19.**Typical tooth surface wear of splines without carburizing. (

**a**) Wear of external splines with a floating distance of 0 mm; (

**b**) wear of external spline tooth surface when the floating distance is 0.3 mm.

**Figure 20.**Typical tooth surface wear of spline after carburizing. (

**a**) External spline tooth surface wear when floating distance is 0 mm; (

**b**) wear of external spline tooth surface when the floating distance is 0.3 mm.

**Figure 21.**Partial enlargement of typical tooth surface wear of spline without carburizing treatment. (

**a**) Wear of external spline tooth surface when floating distance is 0 mm; (

**b**) wear of external spline tooth surface when the floating distance is 0.3 mm.

**Figure 22.**Local enlargement of typical tooth wear of spline after carburizing. (

**a**) External spline tooth surface wear when floating distance is 0 mm; (

**b**) wear of external spline tooth surface when the floating distance is 0.3 mm.

**Figure 24.**Measuring the wear depth of tooth surface. (

**a**) Top position of tooth surface; (

**b**) middle position of tooth surface; (

**c**) root position of tooth surface.

**Figure 25.**Comparison of theoretical and actual values of wear depth of each tooth of involute spline before and after carburizing when the floating distance is 0 mm.

**Figure 26.**Comparison of theoretical and actual values of wear depth of each tooth of involute spline before and after carburizing when the floating distance is 0.3 mm.

Item | Parameter | Item | Parameter |
---|---|---|---|

Number of teeth $z$ | 12 | Contact Length/mm | 10 |

Modulus $m$/mm | 1.25 | Torque T/$\mathrm{N}\cdot \mathrm{m}$ | 50 |

Speed $N$/r/min | 900 | Outer spline inner hole diameter ${D}_{b}$/mm | 8 |

Internal spline shaft diameter ${D}_{0}$/mm | 25 |

Item | Poisson’s Ratio | Friction Factor $\mathit{\mu}$ | Elastic Modulus E/GPa |
---|---|---|---|

1 | 0.25 | 0.1 | 196 |

2 | 0.3 | 0.2 | 210 |

Serial No | Tooth Surface Condition | Floating Distance e |
---|---|---|

1 | Unhardened | 0 mm 0.3 mm 0.6 mm |

2 | ||

3 | ||

4 | After hardening | 0 mm 0.3 mm 0.6 mm |

5 | ||

6 |

Equipment Name | Model | Parameter |
---|---|---|

Three-phase asynchronous motor | YE2-132M-41280 | Rated power 7.5 Kw, maximum speed 1500 r/min |

Vector frequency converter | ZK880 | Power 7.5 Kw, frequency 0–600 Hz |

retarder | ZDY-80 | Maximum current 2 A, torque 200 Nm |

Magnetic powder brake | FZ-200J/Y | Reduction ratio 2.8 |

Name | Parameter |
---|---|

Number of teeth $z$ | 12 |

Modulus $m$ | 1.25 |

Pressure angle $\alpha $ (°) | 30 |

Spline countershaft diameter $D$ (mm) | 30 |

Fitted length $l$ (mm) | 10 |

Item | C | Si | Mn | Mo | Cr | Ni | Fe |
---|---|---|---|---|---|---|---|

1 | 0.3 0.5 | 0.25 | 0.35 | 0.5 | 0.7 | 1.45 | Remainder |

2 |

Mechanical Property | Compressive Strength/MPa | Yield Strength/MPa | Hardness |
---|---|---|---|

1 | 880–980 | 835–870 | 269–307 HBS |

2 | 1080–1280 | >880 | 384–433 HBS |

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**MDPI and ACS Style**

Xue, X.; Liu, J.; Jia, J.; Yang, S.; Li, Y.
Simulation and Verification of Involute Spline Tooth Surface Wear before and after Carburizing Based on Energy Dissipation Method. *Machines* **2023**, *11*, 78.
https://doi.org/10.3390/machines11010078

**AMA Style**

Xue X, Liu J, Jia J, Yang S, Li Y.
Simulation and Verification of Involute Spline Tooth Surface Wear before and after Carburizing Based on Energy Dissipation Method. *Machines*. 2023; 11(1):78.
https://doi.org/10.3390/machines11010078

**Chicago/Turabian Style**

Xue, Xiangzhen, Jian Liu, Jipeng Jia, Siwei Yang, and Yifan Li.
2023. "Simulation and Verification of Involute Spline Tooth Surface Wear before and after Carburizing Based on Energy Dissipation Method" *Machines* 11, no. 1: 78.
https://doi.org/10.3390/machines11010078