Analysis of the Influence of the Tooth Root Fillet Manufacturing Method on the Bending Strength of Spur Gears

This paper presents the results of a numerical study on the influence of the tooth root fillet manufacturing method on the bending strength of spur gears with straight teeth. A mathematical model describing the gear tooth geometry was developed, in which the transition curve at the tooth root was directly related to the applied machining process—either gear shaping or hobbing. Based on this model, a numerical procedure for calculating the bending stresses at the tooth root was formulated and verified using the finite element method (FEM). The results demonstrated high consistency between the proposed approach and FEM analysis, confirming the accuracy of the developed mathematical model and numerical methodology. The study also examined the effect of the tool fillet radius on the stress distribution in the root region. It was found that increasing the tool radius leads to a reduction in bending stresses, while the differences between the two machining methods gradually diminish. For small-tooth gears, shaping provides a more favorable stress distribution, whereas for higher gear ratios the influence of the machining method becomes negligible. The proposed methodology offers a reliable numerical framework for assessing the strength of spur gears and can be effectively used in the design of lightweight, high-performance gear transmissions for aerospace and automotive applications.