Analytical formulas for gear body-induced tooth deflections of spur gears considering structure coupling effect

Abstract As a result of gear body flexibility, fillet foundation stiffness is defined as the meshing force needed for unit gear body-induced tooth deflections. However, it has long been overestimated in double-tooth engagement region in TAM (traditional analytical model), in which the structure coupling effect is ignored. Based on the elastic circular ring theory of Muskhelishvili, simplified analytical formulas are derived to conveniently calculate the gear body-induced tooth deflections considering structure coupling effect, where cubic and parabolic stress distributions along the junction arc are adopted. To prove the effectiveness of the proposed formulas, the gear body-induced tooth deflections obtained by the proposed formulas are compared with those by FEM (finite element method). The results show that proposed formulas can offer a relatively accurate estimation for gear body-induced tooth deflections.