The effects of spur gear tooth spatial crack propagation on gear mesh stiffness

Due to the presence of non-uniform load distribution, local non-homogeneity of material quality and potential misalignment of gear shafts and bearings, etc., spatial cracks may occur in the fillet region of spur gear teeth. These cracks will eventually propagate in three distinct directions either individually or simultaneously. These directions are the crack depth direction, the tooth width direction and the tooth profile direction. In this paper, an analytical investigation of the influence of spatial crack propagation on the time-varying Gear Mesh Stiffness (GMS) and also the Load Sharing Ratio (LSR) is presented. In order to quantitatively define the spatial crack propagation scenario, the involute spur gear tooth geometry cut with a typical double rounded rack is first determined using two parametric equations. The effects of some gear design parameters and initial crack locations on GMS and LSR are determined and compared with the results from previous papers that used Finite Element Analysis (FEA) in order to verify the proposed analytical model. Finally, a quasi-parabolic crack propagation scenario is assumed, in which 7 propagation cases and 3 typical crack growth paths on the tooth surface are investigated to determine their effect on the maximum reduction of GMS when compared to normal conditions. The results are important for the dynamic simulation of gear transmission behavior, and consequently helpful for the monitoring of gearbox working condition and detection of early crack damage that may exist in gear sets.