Journal of Failure Analysis and Prevention

, Volume 18, Issue 1, pp 121–129 | Cite as

Study on Random Fracture and Crack Growth of Gear Tooth Waist

  • Xinxiao BianEmail author
  • Xiaole Li
  • Xiaolu Zhu
Technical Article---Peer-Reviewed


The gear tooth fracture usually occurs at the root, but sometimes also occurs at the waist, or even at the top. The random fracture is defined as the rupture at the waist or top of the tooth. The random fracture at the waist is studied in this paper. In order to simulate a manufacturing defect on the tooth surface, a mic-notch (a minute notch) was cut at the waist of the twelve teeth in the two test gears. A gear-running test was carried out under ladder loading till a gear tooth fractured. The fracture appearance illuminates that the failure is fatigue fracture. The initial crack of the notch grew in the five teeth, and no crack propagation was not found in the other seven teeth. The stress intensity factor and the crack propagation length are comparatively studied by three methods such as linear elastic fracture mechanics theory (LEFMT), FRANC3D simulation and the test. In the early stage of crack propagation, the theory values of LEFMT are close to the simulation, but the difference gets larger and larger with the increase in crack length till the gear tooth is broken. However, the difference of crack propagation length between simulation and the test is less, and the error is in the range of 2.4–13.3%. Therefore, the simulation could truly predict the crack growth length.


Gear Random fracture Initial crack Stress intensity factor Crack propagation length 


  1. 1.
    M.B. Sánchez, M. Pleguezuelos, J.I. Pedrero, Calculation of tooth bending strength and surface durability of internal spur gear drives. Mech. Mach. Theory 95, 102–113 (2016)CrossRefGoogle Scholar
  2. 2.
    N.A. Mohan, S. Senthilvelan, Preliminary bending fatigue performance evaluation of asymmetric composite gears. Mech. Mach. Theory 78, 92–104 (2014)CrossRefGoogle Scholar
  3. 3.
    M.B. Sánchez, J.I. Pedrero, M. Pleguezuelos, Critical stress and load conditions for bending calculations of involute spur. Int. J. Fatigue 48, 28–38 (2013)CrossRefGoogle Scholar
  4. 4.
    X.X. Bian, G. Zhou, Liwei, J.Z. Tan, Investigation of bending fatigue strength limit of alloy steel gear teeth. Proc. Inst. Mech. Eng. C: J. Mech. Eng. Sci. 226, 615–625 (2012)CrossRefGoogle Scholar
  5. 5.
    E. Olsson, A. Olander, M. Öberg, Fatigue of gears in the finite life regime—experiments and probabilistic modeling. Eng. Fail. Anal. 62, 276–286 (2016)CrossRefGoogle Scholar
  6. 6.
    R.L. Mott, Machine Elements in Mechanical Design, 3rd edn. (Pearson Education North Asia Limited and China Machine Press, London, 2002)Google Scholar
  7. 7.
    J.E. Shigley, C.R. Mischke, R.G. Budynas, Mechanical Engineering Design, 7th ed. (Higher Education Press, Beijing, 2003), pp. 284–286Google Scholar
  8. 8.
    Anon, ISO/DIS 6336 Calculation of Load Capacity of Spur and Helical Gears. ISO/TC60/WG6 (1987)Google Scholar
  9. 9.
    Anon, Calculation Methods of Load Capacity for Involute Cylindrical Gears. GB3480-1997 (Standard of China, 1997)Google Scholar
  10. 10.
    R. Guilbault, S. Lalonde, M. Thomas, Modeling and monitoring of tooth fillet crack growth in dynamic simulation of spur gear set. J. Sound Vib. 343, 144–165 (2015)CrossRefGoogle Scholar
  11. 11.
    M.A. Ghaffari, E. Pahl, S. Xiao, Three dimensional fatigue crack initiation and propagation analysis of a gear tooth under various load conditions and fatigue life extension with boron/epoxy patches. Eng. Fract. Mech. 135, 126–146 (2015)CrossRefGoogle Scholar
  12. 12.
    F. Cura, A. Mura, C. Rosso, Crack propagation behavior in planet gears. Procedia Struct. Integr. 2, 3610–3616 (2016)CrossRefGoogle Scholar
  13. 13.
    O.D. Mohammed, M. Rantatalo, Dynamic response and time-frequency analysis for gear tooth crack detection. Mech. Syst. Signal Process. 66–67, 612–624 (2016)CrossRefGoogle Scholar
  14. 14.
    V. Sharma, A. Parey, Gear crack detection using modified TSA and proposed fault indicators for fluctuating speed conditions. Measurement 90, 560–575 (2016)CrossRefGoogle Scholar
  15. 15.
    H. Ma, J. Zeng, R.J. Feng, X. Pang, Q.B. Wang, B.C. Wen, Review on dynamics of cracked gear systems. Eng. Fail. Anal. 55, 224–245 (2015)CrossRefGoogle Scholar
  16. 16.
    Z.G. Chen, W.M. Zhai, Y.M. Shao, K.Y. Wang, G.H. Sun, Analytical model for mesh stiffness calculation of spur gear pair with non-uniformly distributed tooth root crack. Eng. Fail. Anal. 66, 502–514 (2016)CrossRefGoogle Scholar
  17. 17.
    H. Ma, R.Z. Song, X. Pang, B.C. Wen, Time-varying mesh stiffness calculation of cracked spur gears. Eng. Fail. Anal. 44, 179–194 (2014)CrossRefGoogle Scholar
  18. 18.
    A. Saxena, A. Parey, M. Chouksey, Time varying mesh stiffness calculation of spur gear pair considering sliding friction and spalling defects. Eng. Fail. Anal. 70, 200–211 (2016)CrossRefGoogle Scholar
  19. 19.
    Anon, Gear-Tooth Failure Modes, Nomenclature of ANSI/AGMA110.04-1980Google Scholar
  20. 20.
    Anon, Nomenclatures, Characteristics and Causes of Tooth Damage on Gear Transmission, GB3481-1983 (Standard of China, 1983)Google Scholar
  21. 21.
    S. Netpu, P. Srichandr, Failure of a helical gear in a power plant. Eng. Fail. Anal. 32, 81–90 (2013)CrossRefGoogle Scholar
  22. 22.
    O. Asi, Fatigue failure of a helical gear in a gearbox. Eng. Fail. Anal. 13, 1116–1125 (2006)CrossRefGoogle Scholar
  23. 23.
    N.A. Siddiqui, K.M. Deen, M.Z. Khan, R. Ahmad, Investigating the failure of bevel gears in an aircraft engine. Eng. Fail. Anal. 1, 24–31 (2013)Google Scholar
  24. 24.
    P. Liu, X.Y. Wang, Fracture failure analysis of the six-speed gear on heavy-duty gearbox. Heat Treat. Technol. Equip. 4, 58–60 (2013)Google Scholar
  25. 25.
    Y. Feng, Fracture failure analysis of motor gear. Heat Treat. Met. 06, 155–157 (2014)Google Scholar
  26. 26.
    X.M. Yu, L.C. Feng, H. Wang et al., Fracture failure analysis of 12Cr2Ni4 steel gear. Heat Treat. Met. 40(11), 191–194 (2015)Google Scholar
  27. 27.
    X.L. Zhu, T.J. Shi, Random fracture of gear teeth. J. Mech. Transm. 23(1), 29–31 (1999)Google Scholar
  28. 28.
    X.X. Bian, X.Q. Gan, J.C. Zhang et al., Analysis on random fracture of gear tooth, in Proceedings of the International Conference on Mechanical Transmissions (2001), pp. 442–444Google Scholar
  29. 29.
    X.X. Bian, X.Q. Gan, X.L. Zhu, Experimental study on random fracture of gear. J. Mech. Transm. 27(4), 23–25 (2003)Google Scholar
  30. 30.
    X.Q. Gan, Experimental Study on Random Fracture of Gear. Study on Random Fracture of Gear (University of Science and Technology Beijing, Beijing, 1988)Google Scholar
  31. 31.
    Y. Wu, Fraction and Fatigue (China University of Geosciences Press, Beijing, 2008)Google Scholar
  32. 32.
    Z.Q. Wang, Advanced Fracture Mechanics (Science Press, Beijing, 2009)Google Scholar
  33. 33.
    B.Q. Yu, Liwei, J.H. Xue et al., Prediction of bending fatigue life for gears based on dynamic load spectra. J. Univ. Sci. Technol. Beijing 06, 813–817 (2013)Google Scholar

Copyright information

© ASM International 2018

Authors and Affiliations

  1. 1.School of Mechanical EngineeringUniversity of Science and Technology BeijingBeijingChina

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