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.

The contact surfaces of beveloid gears have different topography features due to different machining methods, manufacturing accuracies, and surface wear, and they are not always smooth. As a consequence, in this study, a nonlinear dynamic model of a crossed beveloid gear was developed, considering tooth surface topography features and friction. The phase plane diagram, Poincare diagram, time-domain response diagram, bifurcation diagram, and spectrum diagram of the system response were obtained using the Runge–Kutta method to dissolve the differential equations of the system dynamics. The effect of parameters such as tooth roughness and time-varying friction on the dynamic response of a beveloid gear was then investigated, and the results show that the motion of the gear system denotes a simple harmonic with a period of 1 when the tooth surface roughness R _a is <1.6 μm. And with the variation of tooth surface roughness, the motion state of the system presents a variety of response forms, such as single-period, multi-period, quasi-period, bifurcation, and chaos.

Based on the potential energy method (PEM) and elastohydrodynamic lubrication (EHL) theory, this paper proposes an approximate solution for the time-varying meshing stiffness (TVMS) of straight bevel gears that accounts for the actual tooth cross-section and lubrication conditions. By introducing the influence of tooth surface roughness, the tooth surface lubrication status is characterized as full-film, mixed, or boundary lubrication. Additionally, the effects of varying torque, rotational speed, and surface roughness on the TVMS and contact stiffness of straight bevel gears under these three lubrication regimes are examined. The results indicate that the meshing stiffness under the actual cross-section is higher than that under the approximate cross-section, yet the stiffness variation trends for both cross-sections are consistent. During the transition of lubrication regimes, both contact stiffness and time-varying meshing stiffness are highest under full-film lubrication and lowest under boundary lubrication. As surface roughness or rotational speed increases, the contact stiffness and time-varying meshing stiffness decrease across all three lubrication regimes; whereas, with an increase in torque, both stiffness values increase.