Improved analytical methods for calculation of gear tooth fillet-foundation stiffness with tooth root crack

Two improved analytical calculation models of gear tooth fillet-foundation stiffness are proposed for spur gears with tooth root crack. The proposed two models are capable of taking tooth root crack into account in the calculation of gear tooth fillet-foundation stiffness. For Model-1, the reduction of gear tooth fillet-foundation stiffness is assumed to be the production of the stiffness under healthy condition and the ratio of the crack length to the tooth thickness along the potential crack path. While in Model-2, the stiffness of the gear tooth fillet-foundation is calculated by updating related geometrical parameters in the traditional calculation formulas for the healthy gears according to the variation of the load carrying zone due to tooth root crack. The two calculation models for calculating the tooth fillet-foundation stiffness of cracked gears are verified by the finite element method (FEM). The results show that model-1 has a relatively poor accuracy for large crack cases when the position of applied force is close to the tooth root, while model-2 has a higher accuracy for both small and large crack length. The proposed models can be employed to improve the accuracy of gear mesh stiffness calculation and assist gear faults detection and diagnosis.