A load distribution model for hypoid gears using ease-off topography and shell theory

A computationally efficient load distribution model is proposed for both face-milled and face-hobbed hypoid gears produced by Formate and generate processes. Tooth surfaces are defined directly from the cutter parameters and machine settings. A novel methodology based on the ease-off topography is used to determine the unloaded contact patterns. The proposed ease-off methodology finds the instantaneous contact curve through a surface of roll angles, allowing an accurate unloaded tooth contact analysis in a robust and accurate manner. Rayleigh-Ritz based shell models of teeth of the gear and pinion are developed to define the tooth compliances due to bending and shear effects efficiently in a semi-analytical manner. Base rotation and contact deformation effects are also included in the compliance formulations. With this, loaded contact patterns and transmission error of both face-milled and face-hobbed spiral bevel and hypoid gears are computed by enforcing the compatibility and equilibrium conditions of the gear mesh. The proposed model requires significantly less computational effort than finite elements (FE) based models, making its use possible for extensive parameter sensitivity and design optimization studies. At the end, comparisons to the predictions of a FE hypoid gear contact model are also provided to demonstrate the accuracy of the model under various load and misalignment conditions.