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Bending Fatigue Life Prediction Model of Carburized Gear Based on Microcosmic Fatigue Failure Mechanism

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Abstract

Bending fatigue tests of carburized gear in high cycle fatigue life regime were performed under stress ratio of 0.04. All the crack sources of the broken teeth are originated from the stress concentration on the surface of teeth root. By considering the effects of surface residual stress, notch effect, stress gradient and crack size, the predicted initiation life model of carburized gear is established by dislocation energy method. Meanwhile, based on the Paris Equation, the crack length a corresponding to fracture toughness and real crack propagation path, the predicted growth life model of carburized gear can be established. Finally, based on the behaviors of crack initiation and propagation, the whole life prediction model of carburized gear can be constructed, and the prediction accuracy of the model is within three times of the test life, which can be used to predict the bending fatigue life of carburized gear.

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Abbreviations

σ r :

Residual stress

\(\to _{A}\) :

Regression coefficient vector of \(\sigma_{{\text{r}}} = \to _{A} \cdot \to _{x}\)

\(\to _{x}\) :

Depth vector

\(\to _{B}\) :

Regression coefficient vector of \(C_{x} = \to _{B} \cdot \to _{x}\)

\(\to _{C}\) :

Regression coefficient vector of \(x = \to _{C} \cdot \to _{{C_{x} }}\)

\(\to _{{C_{x} }}\) :

The vector of carbon content at the depth of x

C x :

Carbon content at depth x from the surface

F t :

Nominal tangential force

Y F :

Tooth shape coefficient

Y s :

Stress correction coefficient

b :

Tooth width

m n :

Normal module of the gear

Y ST :

Stress correction coefficient of the gear

Y δ relT :

Sensitivity coefficient of the relative root fillet

Y Rrelt :

Relative tooth root surface condition factor

Y X :

Factor for calculating bending strength

ΔK :

Stress intensity factor range

ΔK inc -S :

Stress intensity factor range for surface inclusion

U 1 :

Single slip band dislocation energy

μ :

Shear modulus of matrix

k :

Frictional stress of dislocations

l :

Half the size of grain

ΔU :

Incremental in dislocation energy

Δτ :

Local shear stress range

τ 1 :

Maximum shear stress

τ 2 :

Minimum shear stress

U i :

Increase of the dislocation energy of a single slip band under the action of the ith cyclic stress

N i :

Predicted initiation life of gear bending fatigue

N p :

Predicted growth life of gear bending fatigue

W s :

Fracture energy for a unit area along the slip band

d :

Grain size of martensite

τ f :

Critical shear stress

h :

Width of the slip band zone

c :

Crack length in crack initiation region

σ a :

Stress amplitude

σ w :

Fatigue limit

\(l^{*}\) :

Maximum crack length

σ rs :

Surface residual stress

N f :

Whole predicted bending fatigue life of carburized gear

L :

Length of the finite element on the crack surface

u b :

Displacements of nodes b in the x-axis

u c :

Displacements of nodes c in the x-axis

u d :

Displacements of nodes d in the x-axis

u e :

Displacements of nodes e in the x-axis

v b :

Displacements of nodes b in the y-axis

v c :

Displacements of nodes c in the y-axis

v d :

Displacements of nodes d in the y-axis

v e :

Displacements of nodes e in the y-axis

K th :

Crack stress intensity factor

K IC :

Fracture toughness

a :

Crack length in crack growth region

References

  1. C. Dengo, G. Meneghetti and M. Dabalà, Experimental Analysis of Bending Fatigue Strength of Plain and Notched Case-Hardened Gear Steels, Int. J. Fatigue, 2015, 80, p 145–161.

    Article  CAS  Google Scholar 

  2. R. Thirumurugan and N. Gnanasekar, Influence of Finite Element Model, Load-Sharing and Load Distribution on Crack Propagation Path in Spur Gear Drive, Eng. Fail. Anal., 2020, 110, p 104383.

    Article  Google Scholar 

  3. J.L. Woods, S.R. Daniewicz and R. Nellums, Increasing the bending Fatigue Strength of Carburized Spur Gear Teeth by Presetting, Int. J. Fatigue, 1999, 21(6), p 549–556.

    Article  Google Scholar 

  4. AGMA Standard 2003-A86, AGMA Standard for Rating the Pitting Resistance and Bending Strength of Spur and Helical Involute Gear Teeth, American Gear Manufacturers Association, USA, 1982.

    Google Scholar 

  5. B.A. Shaw, C. Aylott, P. O’Hara and K. Brimble, The role of residual stress on the fatigue strength of high performance gearing, Int. J. Fatigue, 2003, 25(9), p 1279.

    Article  CAS  Google Scholar 

  6. G. Albertini, G. Bruno, F. Fiori, E. Girardin, A. Giuliani and E. Quadrini, Neutron diffraction measurements for the determination of heat treatment effectiveness in generating compressive residual stress in an automotive crown gear, Phys. B, 2000, 276–278, p 925–926.

    Article  Google Scholar 

  7. S.G. Irizalp, N. Saklakoglu, F. Baris and S. Kayral, Effect of Shot Peening on Residual Stress Distribution and Microstructure Evolution of Artificially Defected 50CrV4 Steel, J. Mater. Eng. Perform., 2020, 29(11), p 7607–7616.

    Article  Google Scholar 

  8. A. Fischer, B. Scholtes and T. Niendorf, On the Influence of Surface Hardening Treatments on Microstructure Evolution and Residual Stress in Microalloyed Medium Carbon Steel, J. Mater. Eng. Perform., 2020, 29(5), p 3040–3054.

    Article  CAS  Google Scholar 

  9. B. Salehnasab and E. Poursaeidi, Mechanism and Modeling of Fatigue Crack Initiation and Propagation in the Directionally Solidified CM186 LC Blade of a Gas Turbine Engine, Eng. Fract. Mech., 2020, 225, p 106842.

    Article  Google Scholar 

  10. K. Vučković, I. Galić, Ž Božić and S. Glodež, Effect of Friction in a Single-Tooth Fatigue Test, Int. J. Fatigue, 2018, 114, p 148–158.

    Article  Google Scholar 

  11. X. Wang, Y.S. Yang, W.J. Wang and W.Q. Chi, Simulating Coupling Behavior of Spur Gear Meshing and Fatigue Crack Propagation in Tooth Root, Int. J. Fatigue, 2020, 134, p 148.

    Article  Google Scholar 

  12. I. Čular, K. Vučković, D. Žeželj and S. Glodež, Analytical Approach for Low and High Cycle Bending Fatigue Life Prediction of Carburized Gear Steel Specimens, Eng. Fail. Anal., 2020, 108, p 104328.

    Article  Google Scholar 

  13. S. Glodez, M. Sraml and J. Kramberger, A Computational Model for Determination of Service Life of Gears, Int. J. Fatigue, 2002, 24(10), p 1013–1020.

    Article  CAS  Google Scholar 

  14. J. Kramberger, M. Šraml, S. Glodez, J. Flašker and I. Potrč, Computational Model for the Analysis of Bending Fatigue in Gears, Comput. Struct, 2004, 82(23), p 2261–2269.

    Article  Google Scholar 

  15. G.J. Wang, M.H. Jiang, S.S. Zhu and A.T. Xu, Using Multiaxial Fatigue Method to Predict Gear Bending Fatigue Life, Key Eng. Mater., 2010, 419, p 201–204.

    Google Scholar 

  16. H. Guechichi and L. Castex, Fatigue Limits Prediction of Surface Treated Materials, J. Mater. Process. Technol., 2007, 172(3), p 381–387.

    Article  Google Scholar 

  17. C. Gu, Y.P. Bao, P. Gan, M. Wang and J.S. He, Effect of Main Inclusions on Crack Initiation in Bearing Steel in the Very High Cycle Fatigue Regime, Int. J. Miner Metall. Mater., 2018, 25(6), p 623–629.

    Article  CAS  Google Scholar 

  18. Y. Wang, S.Q. Zhang, X.J. Tian and H.M. Wang, High-Cycle Fatigue Crack Initiation and Propagation in Laser Melting Deposited TC18 Titanium Alloy, Int. J. Miner. Metall. Mater., 2013, 20(7), p 665–670.

    Article  Google Scholar 

  19. H. Mughrabi, On the Life-Controlling Microstructural Fatigue Mechanisms in Ductile Metals and Alloys in the Gigacycle Regime, Fatigue Fract. Eng. Mater. Struct., 1999, 22(7), p 633–641.

    Article  CAS  Google Scholar 

  20. P. Lukáš and L. Kunz, Specific Features of High-Cycle and Ultra-High-Cycle Fatigue, Fatigue Fract. Eng. Mater. Struct., 2002, 25(8), p 747–753.

    Article  Google Scholar 

  21. C. Bathias, There is No Infinite Fatigue Life in Metallic Materials, Fatigue Fract. Eng. Mater. Struct., 1999, 22(7), p 559.

    Article  CAS  Google Scholar 

  22. S. Nishijima and K. Kanazawa, Stepwise S-N Curve and Fish-Eye Failure in Gigacycle Fatigue, Fatigue Fract. Eng. Mater. Struct., 1999, 22(7), p 601–607.

    Article  CAS  Google Scholar 

  23. Y. Kuroshima, Y. Saito and M. Shimizu, Relationship Between Fatigue Crack Propagation Originating at Inclusion and Fracture-Mode Transition of High-Strength Steel, Trans. JSME Part A, 1994, 60(580), p 2710. (in Japanese)

    Article  CAS  Google Scholar 

  24. T. Nakamura, M. Kaneko and T. Tanabe, Cause of the Second Drop of the S-N Diagram of ADI After Levelling Off, Trans. JSME Part A, 1995, 61(582), p 441. (in Japanese)

    Article  Google Scholar 

  25. Y. Murakami, T. Nomoto and T. Ueda, Factors Influencing the Mechanism of Superlong Fatigue Failure in Steels, Fatigue Fract. Eng. Mater. Struct., 1999, 22(7), p 581–590.

    Article  CAS  Google Scholar 

  26. M. Kato, G. Deng, K. Inoue and N. Takatsu, Evaluation of the Strength of Carburized Spur Gear Teeth Based on Fracture Mechanics, JSME Int. J., 1993, 36(2), p 233–240.

    Google Scholar 

  27. D.G. Lewicki and R. Ballarini, Rim Thickness Effects on Gear Crack Propagation Life, Int. J. Fract., 1997, 87(1), p 59–86.

    Article  CAS  Google Scholar 

  28. M. Guagliano and L. Vergani, Effect of Crack Closure on Gear Crack Propagation, Int. J. Fatigue, 2001, 23(1), p 65–73.

    Article  Google Scholar 

  29. S. Pehan, J. Kramberger, J. Flasker and B. Zafosnik, Investigation of Crack Propagation Scatter in a Gear Tooth’s Root, Eng. Fract. Mech., 2008, 75(5), p 1266–1283.

    Article  Google Scholar 

  30. J.G. Verma, S. Kumar and P.K. Kankar, Crack Growth Modeling in Spur Gear Tooth and Its Effect on Mesh Stiffness Using Extended Finite Element Method, Eng. Fail. Anal., 2018, 94, p 109–120.

    Article  Google Scholar 

  31. X.Q. Zhang, J. Wang, W. Wei, X.T. Ji, B. Chen and G.W. Fang, Simulation of Fatigue Cracks Growth Processes of Two Parallel Cracks in Thin Plate Pulled by the Constant Amplitude Cyclic Loading, J. Braz. Soc. Mech. Sci., 2019, 41(9), p 374.

    Article  Google Scholar 

  32. H.K. Kim and S.B. Lee, Influence of Indenter Geometry on Half-Plane with Edge Crack Subjected to Fretting Condition, Theor. Appl. Fract. Mech., 2001, 36(2), p 125–139.

    Article  Google Scholar 

  33. Y. Sun, X. Li and T. Bell, Structural Characteristics of Low Temperature Plasma Carburised Austenitic Stainless Steel, Mater. Sci. Technol, 1999, 15(10), p 1171–1178.

    Article  CAS  Google Scholar 

  34. Y. Sun and L.Y. Chin, Residual Stress Evolution and Relaxation in Carbon S Phase Layers on AISI 316 Austenitic Stainless Steel, Surf. Eng., 2002, 18(6), p 443–446.

    Article  CAS  Google Scholar 

  35. Z.C. Li, A.M. Freborg, B.D. Hansen and T.S. Srivatsan, Modeling the Effect of Carburization and Quenching on the Development of Residual Stresses and Bending Fatigue Resistance of Steel Gears, J. Mater. Eng. Perform., 2013, 22(4), p 664–672.

    Article  CAS  Google Scholar 

  36. G.J. Yuan, R.Z. Wang, C.Y. Gong, X.C. Zhang and S.T. Tu, Investigations of Micro-notch Effect on Small Fatigue Crack Initiation Behaviour in Nickel-Based Alloy GH4169: Experiments and Simulations, Int. J. Fatigue, 2020, 136, p 105578.

    Article  CAS  Google Scholar 

  37. K. Tanaka and T. Mura, A Theory of Fatigue Crack Initiation at Inclusions, Metall. Mater. Trans. A., 1982, 13(1), p 117–123.

    Article  Google Scholar 

  38. G. Venkataraman, Y.W. Chung and T. Mura, Application of Minimum Energy Formalism in a Multiple Slip Band Model for Fatigue—I. Calculation of Slip Band Spacing, Acta Metall. Mater., 1991, 39(11), p 2621–2629.

    Article  CAS  Google Scholar 

  39. K.S. Chan, A Microstructure-Based Fatigue-Crack-Initiation Model, Metall. Mater. Trans. A, 2003, 34(1), p 43–58.

    Article  Google Scholar 

  40. A.S. Cheng and C. Laird, A Quick and Simple Method for Orienting Cubic Single Crystals from Laue Back-Reflection Photographs, J. Appl. Crystallogr., 1982, 15(1), p 137.

    Article  CAS  Google Scholar 

  41. Q.Y. Wang, C. Bathias, N. Kawagoishi and Q. Chen, Effect of Inclusion on Subsurface Crack Initiation and Gigacycle Fatigue Strength, Int. J. Fatigue, 2002, 24(12), p 1269–1274.

    Article  CAS  Google Scholar 

  42. H. Neuber, Theory of Notch Stresses: Principle for Exact Stress Calculations, Books on Demand, USA, 1945.

    Google Scholar 

  43. Y. Wei and Y. Jiang, Fatigue Fracture Analysis of Gear Teeth Using XFEM, Trans. Nonferrous Met. Soc., 2019, 29(10), p 2099–2108.

    Article  Google Scholar 

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Acknowledgments

The authors gratefully appreciate the financial support granted by Natural Science Foundation of Inner Mongolia (Nos. 2018BS05005, 2018NMKJ11 and 2021LHMS05009), Inner Mongolia Higher Education Research Project (No. NJZY21306), and Foundation Sciences Research Project of Inner Mongolia University of Technology (Nos. ZZ201801 and ZY202005).

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Authors and Affiliations

  1. College of Mechanical Engineering, Inner Mongolia University of Technology, Hohhot, 010051, China

    Hailong Deng, Yang Guo, Hang Liu, Qichen Liu, Yupeng Guo & Huan Yu

  2. Inner Mongolia Key Laboratory of Advanced Manufacturing Technology, Hohhot, 010051, China

    Hailong Deng, Yang Guo, Hang Liu, Qichen Liu, Yupeng Guo & Huan Yu

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  1. Hailong Deng
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Deng, H., Guo, Y., Liu, H. et al. Bending Fatigue Life Prediction Model of Carburized Gear Based on Microcosmic Fatigue Failure Mechanism. J. of Materi Eng and Perform 31, 882–894 (2022). https://doi.org/10.1007/s11665-021-06236-8

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