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. / M.S.

A unique multifrequencied transfer matrix method performs three-dimensional harmonic, steady-state response calculations on geared-rotor systems. The full six degrees-of-freedom method includes physical branching to accommodate multiple shafting and frequency branching to simultaneously accommodate multiple frequencies and their interdependence resulting from time-varying mesh stiffness. Areas of emphasis include development of a modified transfer matrix to handle multiple frequencies and shafting; description of the time-varying stiffness tensor representing the involute spur gear mesh based on bending, shear, compression, and local contact deformation; development of the mesh transfer matrix; development of an automatic system solver to allow the engineer to analyze systems of arbitrary construction; and the development of a matrix solver to efficiently handle large systems. A computer analysis demonstrates the significance of terms included in the stiffness evaluation as compared with less rigorous treatment in the literature. An analytical example problem illustrates the automated model generation through complete rotor system dynamic response analysis produced by the current work with special attention to the significance of parametric excitation due to the gear mesh. / Ph. D.