Application of plate and shell models in the loaded tooth contact analysis of bevel and hypoid gears

A numerical procedure based on the Rayleigh-Ritz method is used to investigate the flexural behavior of an annular sector plate and a segment of circular cylindrical shell. The annular sector plate is cantilevered along the radial edge and the shell segment is cantilevered along the circular edge. The static analysis incorporates the effects of variable rigidity, including the effects of shear deformation. The Ritz method used, employs algebraic polynomial trial functions in two dimensions, to obtain the deflections and stresses. Convergence is investigated with attention being given to the number of terms taken for each coordinate direction. Although an increase in number of terms improves the accuracy in the Ritz procedure, the solution times are seen to increase considerably.; Two levels of shear based theories, the Mindlin and the Bhimaraddi theory are used in this study. The Mindlin theory assumes a constant shear strain through the thickness; the Bhimaraddi theory assumes a parabolic variation through the thickness. It is seen that for a choice of identical number of terms in the Ritz expansion, the Bhimaraddi theory is far more computationally intensive. The Ritz solutions for the sector plate and the cylindrical shell compare well with finite element predictions and experimental results and demonstrate numerical efficiency compared to the finite element procedure.; The application of the sector plate and the shell model to predict the deflections and root stresses in bevel gears is demonstrated. The sector plate and the cylindrical shell are shown to be natural representations of straight and spiral bevel teeth. The compliance calculations based on the plate and shell models can be readily incorporated into existing computer codes for bevel gear design to determine the load distribution and transmission error.; This dissertation has led to the development of mesh generators for bevel and hypoid gears to perform a full fledged finite element based loaded tooth contact analysis using CAPP. It is now possible to obtain the load distribution and static transmission error for all types of bevel and hypoid gears if the blank dimensions and machine settings are provided. Sample case studies for straight and spiral bevel gears are performed and discussed. (Abstract shortened by UMI.)...