Fractal Contact Mechanics Model for the Rough Surface of a Beveloid Gear with Elliptical Asperities

Understanding the contact mechanics of rough tooth surfaces is critical in order to understand phenomena such as tooth surface flash temperature, tooth surface wear, and gear vibration. In this paper, the contact behavior between the meshing tooth surfaces of beveloid gear pairs with elliptical asperities is the focus. The contact area distribution function of the elliptical asperity was proposed for the point contact of curved surfaces by transforming the elastic contact problem between gear meshing surfaces into the contact between elastic curved surfaces with an arbitrary radius of curvature. In addition, a fractal contact mechanics model for the rough surface of a beveloid gear with elliptical asperities was established. The influence of tooth surface topography on the contact load and contact stiffness under different fractal parameters was investigated, and the results demonstrated that the real contact load and the contact stiffness of curved surfaces increase with the increase in the fractal dimension D and the contact coefficient λ. Conversely, the real contact load and normal contact stiffness decrease with the increase in the fractal roughness G and eccentricity e.