Abstract
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.
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References
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)
N.A. Mohan, S. Senthilvelan, Preliminary bending fatigue performance evaluation of asymmetric composite gears. Mech. Mach. Theory 78, 92–104 (2014)
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)
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)
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)
R.L. Mott, Machine Elements in Mechanical Design, 3rd edn. (Pearson Education North Asia Limited and China Machine Press, London, 2002)
J.E. Shigley, C.R. Mischke, R.G. Budynas, Mechanical Engineering Design, 7th ed. (Higher Education Press, Bei**g, 2003), pp. 284–286
Anon, ISO/DIS 6336 Calculation of Load Capacity of Spur and Helical Gears. ISO/TC60/WG6 (1987)
Anon, Calculation Methods of Load Capacity for Involute Cylindrical Gears. GB3480-1997 (Standard of China, 1997)
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)
M.A. Ghaffari, E. Pahl, S. **ao, 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)
F. Cura, A. Mura, C. Rosso, Crack propagation behavior in planet gears. Procedia Struct. Integr. 2, 3610–3616 (2016)
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)
V. Sharma, A. Parey, Gear crack detection using modified TSA and proposed fault indicators for fluctuating speed conditions. Measurement 90, 560–575 (2016)
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)
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)
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)
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)
Anon, Gear-Tooth Failure Modes, Nomenclature of ANSI/AGMA110.04-1980
Anon, Nomenclatures, Characteristics and Causes of Tooth Damage on Gear Transmission, GB3481-1983 (Standard of China, 1983)
S. Netpu, P. Srichandr, Failure of a helical gear in a power plant. Eng. Fail. Anal. 32, 81–90 (2013)
O. Asi, Fatigue failure of a helical gear in a gearbox. Eng. Fail. Anal. 13, 1116–1125 (2006)
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)
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)
Y. Feng, Fracture failure analysis of motor gear. Heat Treat. Met. 06, 155–157 (2014)
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)
X.L. Zhu, T.J. Shi, Random fracture of gear teeth. J. Mech. Transm. 23(1), 29–31 (1999)
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. 442–444
X.X. Bian, X.Q. Gan, X.L. Zhu, Experimental study on random fracture of gear. J. Mech. Transm. 27(4), 23–25 (2003)
X.Q. Gan, Experimental Study on Random Fracture of Gear. Study on Random Fracture of Gear (University of Science and Technology Bei**g, Bei**g, 1988)
Y. Wu, Fraction and Fatigue (China University of Geosciences Press, Bei**g, 2008)
Z.Q. Wang, Advanced Fracture Mechanics (Science Press, Bei**g, 2009)
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. Bei**g 06, 813–817 (2013)
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Bian, X., Li, X. & Zhu, X. Study on Random Fracture and Crack Growth of Gear Tooth Waist. J Fail. Anal. and Preven. 18, 121–129 (2018). https://doi.org/10.1007/s11668-018-0388-6
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DOI: https://doi.org/10.1007/s11668-018-0388-6