An analytical model that allows for a computationally efficient analysis of face-milled spiral bevel gears, is presented. The methodology builds on the consideration that the mating tooth flanks are designed to transmit motion in a nearly conjugate manner. A multibody approach to tooth contact analysis is proposed that assumes contact between rigid surfaces. By taking advantage of the action surfaces for each flank pair, contact is detected in a computationally efficient and accurate way. An analytical load distribution model is used to translate the detected penetration into resulting contact forces, under the assumption that the flank penetration matches the deformation of the teeth if they were flexible. To account for the global tooth deformation Tredgold's approximation in combination with a set of expressions based on beam theory are utilized, while the local contact deformation is modeled based on Hertz theory. The methodology is validated against nonlinear finite element simulations. A comparison in terms of transmission error, contact patterns and contact pressure is provided. Contrary to FE simulations the proposed methodology requires significantly less computational effort, allowing further extension to optimization or system analysis problems.

Presented is Tredgold's Approximation for using an equivalent cylindrical gear with spur teeth to "approximate" a bevel gear with straight teeth. This relation is extended to spiral bevel and hypoid gears by utilizing pitch surface curvature in the direction perpendicular to the gear tooth spiral to establish an equivalent gear. Subsequently, the envelope of a planar gear tooth profile in this perpendicular direction is presented. The envelope of the gear tooth profile is used to determine fully conjugate gear teeth profiles for spatial gear elements. This procedure is valid for any tooth profile along with circular and non-circular gears. To validate the methodology, a virtual model of a bevel gear pair (" ") is created and an unloaded tooth contact presented model analysis is performed. The procedure used to perform the unloaded tooth contact analysis and determine the corresponding unloaded transmission error is based on the concept of ease-off topography. An example of a face-milled bevel gear pair (" ") serves as a reference of correctness in determining the ease-off for unloaded contact. To conclude the pap literature model er, the obtained ease-off topography and unloaded transmission error of the presented model are calculated and displayed, demonstrating the specification of fully conjugate teeth.