Bending strength model for internal spur gear teeth

Internal spur gear teeth are normally stronger than pinion teeth of the same pitch and face width since external teeth are smaller at the base. However, ring gears which are narrower have an unequal addendum or are made of a material with a lower strength than that of the meshing pinion may be loaded more critically in bending. In this study, a model for the bending strength of an internal gear tooth as a function of the applied load pressure angle is presented which is based on the inscribed Lewis constant strength parabolic beam. The bending model includes a stress concentration factor and an axial compression term which are extensions of the model for an external gear tooth. The geometry of the Lewis factor determination is presented, the iteration to determine the factor is described, and the bending strength J factor is compared to that of an external gear tooth. This strength model will assist optimal design efforts for unequal addendum gears and gears of mixed materials.