Curvature-based framework for contact analysis of complex tooth surfaces

Abstract

Increasing demands for transmission performance have driven the development of more complex tooth surface designs, which present different contact states that may vary with external disturbances. This study integrated a curvature-based framework that simplifies the representation of complex tooth surface geometries, enabling a unified analysis across various gear types. Numerical methods and analytical examples for calculating the curvature attributes were provided to support the methodology. Contact types are categorized into line and point contact states, with cylindrical and elliptical models used depending on the curvature sum. For line contact, the pressure distribution follows the contact line; for point contact, it is modeled as an incomplete ellipse that accommodates the transition between contact states and the constraints imposed by the surface edges. The findings indicate that the contact profile is primarily governed by the curvature sum and the directions of the principal curvatures, regardless of variations in tooth surface geometry across gear types. The study examined contact characteristics in spherical involute tooth surfaces and spiral bevel gears. A comparative analysis was conducted to evaluate the transition between point and line contact states. The analysis showed that contact stiffness increases during the transition, with the change in contact profile becoming more rapid as the curvature difference approaches zero. This study advances contact modeling in practical engineering by introducing a flexible framework for analyzing contact states and their transitions, applicable to a wide range of gear types.