A finite element analysis of pinion shaped spur gear teeth

An analysis of the effects of gear shaping with a pinion cutter upon the geometry and root stresses in external spur gears using the finite element method is given. The models analyzed have the shape of a ring with three teeth. The middle tooth is loaded and load sharing has been assumed. Thirty-five finite element models were used for the computation of stress concentration factors in pinion shaped gear teeth. The results for pinion shaped teeth are compared to those results obtained when shaping with a hob. The Dolan and Broghamer stress concentration factor was also calculated for comparison with the results from finite element analysis. The difference in the two was not more than 8%. The results from finite element analysis have been condensed into an empirical expression which gives the stress concentration factor as a function of the dedendum of the pinion, the numbers of teeth on the pinion and cutter, and the number of teeth on the mating gear. A comparison of the bending stress in the root of a tooth shaped by standard pinion and hob cutters indicated no appreciable differences in strength.