Stress concentrations in undercut spur gear teeth via the finite element method

An analysis of the influence of undercutting on the stress concentration factor for undercut gears using the finite element method is presented. The models used are in the shape of a whole gear with three teeth. The middle tooth is loaded assuming single-tooth contact. Thirty seven finite element models were used to compute stress concentrations in gear teeth. The results for non-undercut gears were compared with the Dolan and Broghamer results, and were not more than 9.5 percent different. The results are expressed in the form of a linear relationship giving the stress concentration factor at the root fillet as a function of the geometry of the tooth. It has been verified that this equation is an accurate formula for both undercut and non-undercut gears with nominal proportions.