An improved analytical method for calculating time-varying mesh stiffness of helical gears

A "slice method" is adopted to calculate the time-varying mesh stiffness (TVMS) of helical gear pairs, where the tooth is divided into many individual sliced spur gears along the tooth width, and the TVMS of helical gear pairs is obtained by accumulating the TVMS of the sliced spur gear pairs. Based on the slice method, an improved analytical method (IAM) is proposed to calculate TVMS of the helical gear pairs. The proposed method is also verified by comparing TVMS obtained from IAM with that obtained from references and the finite element method. Based on the proposed IAM, the effects of the helix angle, gear width, modification coefficient and friction coefficient on mesh characteristics are also discussed. The results show that the total contact ratio of helical gear changes under different helix angles and gear tooth widths, and the fluctuation of mesh stiffness will reduce when the overlap contact ratio approaches an integer. Meanwhile, addendum modifications can not only change the total contact ratio but also affect the mean mesh stiffness of gear pairs. Furthermore, not only will the friction coefficients affect the mean mesh stiffness, and it can lead to an abrupt change of TVMS in double-teeth engagement region.