Development of tooth contact and mechanical efficiency models for face-milled and face-hobbed hypoid and spiral bevel gears.

摘要

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 curves 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. 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.;The proposed ease-off formulation is generalized next to include various types of tooth surface deviations in the tooth contact analysis. These deviations are grouped in two categories. The proposed ease-off based method is shown to be capable of modeling both global deviations due to common manufacturing errors and heat treat distortions and local deviations due to surface wear.;The proposed loaded contact model is combined at the end with a friction model based on a mixed elastohydrodynamic lubrication model to predict the load dependent (mechanical) power losses and efficiency of the hypoid gear pairs. The velocity, radius of curvature and load information predicted by the contact model is input to the friction model to determine the distribution of the friction coefficient along the contact surfaces. At the end, the variations of predicted mechanical efficiency with geometry, surface and lubricant parameters are quantified.