# 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

- Xiao, L.; Xu, Y.; Chen, Z.; Sun, X.; Xu, H. Prediction of fretting damage and wear fatigue of floating involute splines. J. Northwest Polytech. Univ.
**2022**, 40, 549–559. [Google Scholar] [CrossRef] - Curà, F.; Mura, A. Theoretical and numerical evaluation of tilting moment in crowned teeth splined couplings. MeCcanica
**2018**, 53, 413–424. [Google Scholar] [CrossRef] - Xue, X.Z.; Wang, S.M. Dynamic Characteristics and Load Coefficient Analysis of Involute Spline Couplings. Adv. Mater. Res.
**2014**, 890, 450–454. [Google Scholar] [CrossRef] - Xue, S.; Wang, M.; Yuan, R. Investigation of Load Distribution among Teeth of An Aero-Engine Spline Coupling; Springer: Berlin/Heidelberg, Germany, 2016; Volume 367, pp. 1152–1162. [Google Scholar]
- Tang, Y.; Meng, J.; Xia, F. Analysis of the influence of lubrication and surface treatment on the wear of the spline couplings of the helicopter reducer. Mech. Res. Appl.
**2021**, 34, 60–62. [Google Scholar] - Xu, Y. Strength and Wear Analysis of Involute Spline of Aircraft Flap Transmission System; Chongqing University: Chongqing, China, 2018. [Google Scholar]
- Yu, Y.; Hu, Y.; Dai, X.; He, Z.; Li, M. Fretting wear analysis and parameter optimization of spline couplings. Mech. Sci. Technol.
**2021**, 40, 828–834. [Google Scholar] - Tan, Y.; Jiang, L.; Jiang, S.; Yang, S.; Liu, S.; Hu, Q. Analysis of fretting friction contact of involute spline couplings. J. Mech. Eng.
**2018**, 54, 123–130. [Google Scholar] [CrossRef] - Jiang, L. Research on Fretting Wear of Floating Involute Spline Couplings; Xiangtan University: Xiangtan, China, 2018. [Google Scholar]
- Wei, Y.; Liu, L. Load distribution and stress analysis of tooth direction and tooth profile of shield spline connection. Eng. Mach.
**2017**, 48, 10–15. [Google Scholar] - Wei, Y.; Liu, L.; Xiao, R.; Li, J. Research on tooth modification of shield spline shaft. Mech. Manuf.
**2018**, 56, 90–93. [Google Scholar] - Ratsimba, C.H.H.; McColl, I.R.; Williams, E.J.; Soh, H.P. Measurement, analysis and prediction of fretting wear damage in a representative aeroengine spline coupling. Wear
**2004**, 257, 1193–1206. [Google Scholar] [CrossRef] - Hyde, T.R.; Leen, S.B.; McColl, I.R. A simplified fretting test methodology for complex shaft couplings. Fatigue Fract. Eng. Mater. Struct.
**2005**, 28, 1047–1067. [Google Scholar] [CrossRef] - Baker, D.A. A Finite Element Study of Stresses in Stepped Splined Shafts,and Partially Splined Shafts Under Bending, Torsion, and Combined Loadings. Va. Tech.
**1999**, 6, 41–47. [Google Scholar] - Leen, S.B.; Richardson, I.J.; McColl, I.R.; Williams, E.J.; Hyde, T.R. Macroscopic fretting variables in a splined coupling under combined torque and axial load. J. Strain Anal. Eng. Des.
**2001**, 36, 481–497. [Google Scholar] [CrossRef] - Leen, S.B.; Hyde, T.H.; Ratsimba, C.; Williams, E.J.; McColl, I.R. An investigation of the fatigue and fretting performance of a representative aero-engine spline coupling. J. Strain Anal. Eng. Des.
**2002**, 37, 565–583. [Google Scholar] [CrossRef] - Madge, J.J.; Leen, S.B.; Shipway, P.H. A combined wear and crack nucleation propagation methodology for fretting fatigue prediction. Int. J. Fatigue
**2008**, 30, 1509–1528. [Google Scholar] [CrossRef] - Olver, A.V.; Medina, S. Tribology of spline couplings. Tribol. Ser.
**2003**, 41, 589–602. [Google Scholar] - Medina, S.; Olver, A.V. Regimes of contact in spline couplings. Trans. Am. Soc. Mech. Eng. J. Tribol.
**2002**, 124, 351–357. [Google Scholar] [CrossRef] - Medina, S.; Olver, A.V. An analysis of misaligned spline couplings. J. Eng. Tribol.
**2002**, 216, 269–279. [Google Scholar] [CrossRef] - Hong, J.; Talbot, D.; Kahraman, A. A semi-analytical load distribution model for si-de fit involute splines. Mech. Mach. Theory
**2014**, 76, 39–55. [Google Scholar] [CrossRef] - Hong, J.; Talbot, D.; Kahraman, A. Load distribution analysis of clearance fit spline joints using finite elements. Mech. Mach. Theory
**2014**, 74, 42–57. [Google Scholar] [CrossRef] - Ding, J.; Mccoll, I.; Leen, S. The application of fretting wear modelling to a spline coupling. Wear
**2007**, 262, 1205–1216. [Google Scholar] [CrossRef] - Ding, J.; Madge, J.; Leen, S.B.; Williams, E.J. Towards the modelling of fretting wear and fatigue interaction in spline couplings. Appl. Mech. Mater.
**2006**, 5, 165–172. [Google Scholar] [CrossRef] - Hattori, T.; Watanabe, T. Fretting fatigue strength estimation considering the fretting wear process. Tribol. Int.
**2006**, 39, 1100–1105. [Google Scholar] [CrossRef] - Matveevsky, R.M. The critical temperature of oil with point and line contact machines. Trans. ASME
**1965**, 87, 754. [Google Scholar] [CrossRef] - Sauger, E.; Fouvry, S.; Ponsonnet, L.; Kapsa, P.; Martin, J.M.; Vincent, L. Tribologically transformed structure in fretting. Wear
**2000**, 245, 39–52. [Google Scholar] [CrossRef] - Fouvry, S.; Kapsa, P.; Vincent, L. An elastic–plastic shakedown analysis of fretting wear. Wear
**2001**, 247, 41–54. [Google Scholar] [CrossRef] - Zhang, T.; McHugh, P.E.; Leen, S.B. Computational study on the effect of contact geometry on fretting behaviour. Wear
**2011**, 271, 1462–1480. [Google Scholar] [CrossRef] [Green Version] - Zhang, M.; Pang, D.; Wang, H.; Huang, T.; Ming, M. Energy dissipation characteristics of linear normal vibration contact interface. Mech. Strength
**2022**, 44, 788–794. [Google Scholar] - Yang, W.; Guo, X.; Zhao, Y. Effect of convection and radiation heat transfer on estimation of metal high cycle fatigue energy dissipation. J. Mech. Eng.
**2021**, 57, 187–195. [Google Scholar] - Zheng, W.; Wang, S.; Jie, X.; Li, H. Energy dissipation method for fretting wear analysis of involute spline couplingss. China Mech. Eng.
**2017**, 28, 2171–2176. [Google Scholar] - Xue, X. Research on Fretting Wear Mechanism and Wear Prediction Method of Aviation Involute Spline Couplings; Northwest Polytechnical University: Xi’an, China, 2017. [Google Scholar]

**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