Design and Stress Analysis of Gears Using the Boundary Element Method

Basic design and stress analysis of gears can be, for the most part, accomplished through the use of the American Gear Manufacturers’ Association (AGMA) criterion or use of a machine design text book such as Norton[1]. Real life questions as to the effect of undercut, misalignment, notches or grooves, and so on are not answered quite so quickly or with reasonable accuracy. The boundary element method (BEM) provides a relatively quick modeling method for assessing stresses and a means to accurately predict crack propagation in components. Lubricated bodies in contact, such as gears, cams and bearings, provide an application for which BEM can be applied. This paper has been written to provide an assessment of the use of BEM to evaluate the effect of undercut on the stresses in a gear, the propagation of a notch in the root of a gear, with and without undercut. Future work will be expanded to include contact analysis using a second gear and three dimensional analysis, possibly providing a means for assessing misalignment of gears and load distribution effects on gears.