Analysis of the contact stress of beveloid gears with straight teeth and parallel axes

Beveloid gears are spur or helical gears whose outside radius, root radius and shift coefficient vary linearly along the face width, but with constant module and base radius. Accordingly, the gear outer surface is not a cylinder, but a cone. Beveloid gears mounted with parallel axes and opposite cone angles are interesting because they allow backlash control. In this case, the transverse sections have the profile of a spur gear, but with different outside radii, root radii and shift coefficients in each section. Accordingly, the inner and outer contact points and the transverse contact ratio are different, and an axial contact ratio can be defined. This paper studies the contact stress of beveloid gears with straight teeth and parallel axes, based on the analysis of contact segments along the meshing cycle, and the variation of the tooth-pair mesh stiffness and load-sharing ratio along the instantaneous contact lines. The analysis is based on minimum elastic potential energy and considers teeth undercutting and pointing. Results are validated through finite-element analysis of a sample gear pair. The analytical method presented in this work is computationally efficient and can be used as a calculation step within an optimization algorithm.