A geometric-based method for the mesh stiffness evaluation of spur gears with spatial cracks

Bending fatigue is one of the most common failure modes of gear-based transmissions. Bending fatigue often manifests in the form of cracks at the gear tooth root, which propagates over the time, until a part of the tooth or the whole tooth is removed. Many papers have been published to determine the effect of this failure mode on the gear system dynamics, specifically, the gear mesh stiffness. But the majority of them considered uniform propagation paths and distribution of the crack profile. Moreover, as we know, the effect of the crack initiation point on the mesh stiffness deformation has not been investigated previously.

In this study, a geometric-based method is proposed to investigate the effect of non-uniform crack faults on the gear mesh stiffness. This is realized by uncoupling the crack geometry modeling from the stiffness calculation equations, which will enable us to model any crack geometry without any change in the mathematical expressions of the stiffness components. Furthermore, limiting lines of a specific crack shape and initiation point are customized in this study to better consider the effect of random propagated cracks including reascending cracks on the mesh stiffness variation. Simulation results showed that the crack shape, length, and initiation point have a significant effect on the final deformation of the gear mesh stiffness.