Deformation and meshing stiffness analysis of cracked helical gear pairs

Based on the slice method, a new method is proposed for calculating the time-varying mesh stiffness (TVMS) of helical gears. The proposed method uses the idea of 'offset and superposition' to avoid the repetitive calculation of the TVMS of each sliced gear. Taking the TVMS obtained from the finite element (FE) method as a benchmark, the correction coefficient of the gear foundation stiffness is obtained by the optimization method. Four types of spatial crack are modeled, including addendum non-penetrating crack, addendum penetrating crack, end face non-penetrating crack and end face penetrating crack. The computational efficiency and accuracy are discussed under different crack parameters and crack types. Compared with the FE method and the traditional analytical method, the proposed method agrees well, and its efficiency is higher. For example, the proposed method costs 8 s to calculate the TVMS of helical gears with identical slice profile in one mesh period, while the traditional method and the FE method cost 2 min and 2.5 h, respectively. For the helical gears without identical slice profile, the proposed method is also applicable but the improvement of the calculation efficiency is not evident. The effects of extended tooth contact are ignored in the proposed analytical method, which leads to some errors between the TVMS of the cracked helical gears obtained from the proposed method and the FE method, but the change laws of the TVMS are in consistent.