A novel analytical model for calculating the time-varying mesh stiffness of helical gears considering pitting propagated along a curve

Pitting is one of the common failure forms of the helical gear. To investigate its effect on time-varying mesh stiffness (TVMS), this work addresses two limitations of existing models: (1) pitting propagation along straight lines deviates from the true pitch curve path; (2) ignorance of pitting growth order and stress concentration. We propose a novel analytical method (AM) featuring a 2D Gaussian pitting model propagating along the pitch curve and a cluster classification mechanism. Firstly, two coordinate systems are established with the intersection direction of the gear tooth and the base circle and the gear axis as the Z axis, respectively. The two coordinate systems are used as the coordinate system of pitting generation and propagation and the coordinate system of calculating the TVMS of helical gears by the ‘slice method’, respectively. Secondly, according to the pitting generation and propagation model, pitting teeth in four degrees are generated. Thirdly, the TVMS of the helical gear in four degrees are calculated by the ‘slice method’ and the ‘potential energy method’. Finally, a finite element model is established to verify the accuracy of the pitting distribution model and TVMS AM. Compared to the finite element method (FEM), the error of the AM of TVMS is less than 2%, and the calculation time is only 1/1000 of the FEM. The pitting generation and propagation model of the helical gear can well characterize all pitting characteristics following a two-dimensional Gaussian distribution. Pitting reduces the TVMS of the helical gear, and the reduction of TVMS increases with the increase of pitting degree. The model provides a theoretical basis for gear health monitoring and design optimization in industries such as new energy vehicles and wind power.