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Planetary gear set, LEFM, FEM, ABAQUS, Crack growth path, Contact stress, XFEM.


Automotive and aerospace industries are relevant to use planetary gear sets headed for their incomparable features. Planetary gears flexibility in achieving different speed ratio and high-power-density design makes them often suitable to counter-shaft gear reduction systems. The main components are sun, ring and planet gears. Planet gears are engaged with sun and ring gears and subjected to the severe contact stresses. Consequently, gear tooth crack failure may occur when the critical values are reached. Hence assessment of strength due to contact stresses and failure phenomena is vital to avoid catastrophic damage to the system. Basic types of gear teeth damages include: surface deterioration, scuffing, permanent deformation, surface fatigue phenomena, cracks, and gear tooth fracture. Failure may occur by crack growth through the gear teeth or through the gear rim. These types of failures are caused excessive damage to the system and should be prevented. In this paper contact stress distribution between gears are investigated by mean of finite element method and compared to ISO standards. Then planet gear root crack failure analysis is carried out with the principles of linear elastic fracture mechanics. Fracture mechanics deals with the study of how a crack in a structure propagates under applied loads. For this purpose, Multistep analysis is used to determine stress intensity factors for different crack sizes to evaluate the crack propagation path, incrementally. Also, XFEM-LEFM based analysis performed to evaluate the efficiency of this method compared with contour integral method. Rim thickness effect has been studied to assess its influence on the crack growth path.


Acta Mechanica Slovaca. Volume 17, Issue 1, Pages 68 – 74, ISSN 1335-2393


  Stress Analysis and Study the Fracture Mechanics in Planetary Gear Set Using FEM


[1] Master Thesis, O., 2004, “Stresses and deformations in involute spur gears by finite element method”. MS Thesis, University of Saskatchewan.

[2] Chen, Z and Shao, Y, “Dynamic simulation of spur gear with tooth root crack propagation along tooth width and crack depth”. Engineering Failure Analysis, 18(2011) 2149-2164.
[3] Ristic, D, “Numerical model for the critical stress determination in spur gears, 2009.
[4] Manual of ABAQUS finite element analysis software package.
[5] ISO 6336, 1998.
[6] Lewicki, D, G, “Effect of rim thickness on gear crack propagation path”, Army Research Laboratory, 1996.

[9] Rao, SS (1995). Mechanical Vibrations. 3/e. Addison-Wesley. Boston. ISBN: 0201526867.
[10] Young, P (2006). Solving Systems of Differential Equations.

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