A numerical model for total bending fatigue life estimation of carburized spur gears considering the hardness gradient and residual stress

The paper introduces a novel three-dimensional numerical model considering hardness gradient and residual stress to predict carburized gears’ total bending fatigue life. The crack initiation life was forecasted by the strain life method, considering hardness gradient and residual stress. Linear elastic stresses and strains in the tooth root fillet were corrected by Neuber’s rule for elastic–plastic material behavior. The tooth root area of the spur gear is segmented into layers using the thin slice method, and the fatigue properties of each layer are determined using the multilayer method. The crack propagation life was predicted by the extended finite element method (XFEM), considering hardness gradient and residual stress. Fracture surface analysis with electron microscopy determines the exact location where cracks initiate. The high-speed camera records the path and life of crack propagation. Single-tooth bending fatigue life (STBF) tests are conducted to validate the proposed model. The predicted fatigue lifetimes, failure locations, and crack propagation paths agree well with the experimental results.