Existing studies primarily focus on stiffness and damping under full-film lubrication or dry contact conditions. However, most lubricated transmission components operate in the mixed lubrication region, indicating that both the asperity contact and film lubrication exist on the rubbing surfaces. Herein, a novel method is proposed to evaluate the time-varying contact stiffness and damping of spiral bevel gears under transient mixed lubrication conditions. This method is sufficiently robust for addressing any mixed lubrication state regardless of the severity of the asperity contact. Based on this method, the transient mixed contact stiffness and damping of spiral bevel gears are investigated systematically. The results show a significant difference between the transient mixed contact stiffness and damping and the results from Hertz (dry) contact. In addition, the roughness significantly changes the contact stiffness and damping, indicating the importance of film lubrication and asperity contact. The transient mixed contact stiffness and damping change significantly along the meshing path from an engaging-in to an engaging-out point, and both of them are affected by the applied torque and rotational speed. In addition, the middle contact path is recommended because of its comprehensive high stiffness and damping, which maintained the stability of spiral bevel gear transmission.

To assess the meshing quality of spiral bevel gears, the static meshing characteristics are usually checked under different contact paths to simulate the deviation in the footprint from the design point to the heel or toe of the gear flank caused by the assembly error of two gear axes. However, the effect of the contact path on gear dynamics under lubricated conditions has not been reported. In addition, most studies regarding spiral bevel gears disregard the lubricated condition because of the complicated solutions of mixed elastohydrodynamic lubrication (EHL). Hence, an analytical friction model with a highly efficient solution, whose friction coefficient and film thickness predictions agree well with the results from a well-validated mixed EHL model for spiral bevel gears, is established in the present study to facilitate the study of the dynamics of lubricated spiral bevel gears. The obtained results reveal the significant effect of the contact path on the dynamic response and meshing efficiency of gear systems. Finally, a comparison of the numerical transmission efficiency under different contact paths with experimental measurements indicates good agreement.

Although several empirical wear formulas have been proposed, theoretical approaches for predicting surface topography evolution during sliding wear are limited. In this study, we propose a novel wear-prediction method, wherein the energy-based Arrhenius equation is combined with a mixed elastohydrodynamic lubrication (EHL) model to predict the point-contact wear process in mixed lubrication. The surface flash temperature and contact pressure are considered in the wear model. Simulation results are compared with the experimental results to verify the theory. The surface topography evolutions are observed during the wear process. The influences of load and speed on wear are investigated. The simulation results based on the Arrhenius equation relationship shows good agreement with the results of experiments as well as the Archard wear formula. However, the Arrhenius equation is more accurate than the Archard wear theory in some aspects, such as under high-temperature conditions. The results indicate that combining the wear formulas with the mixed EHL simulation models is an effective method to study the wear behavior over time.

The rolling contact fatigue (RCF) model is commonly used to predict the contact fatigue life when the sliding is insignificant in contact surfaces. However, many studies reveal that the sliding, compared to the rolling state, can lead to a considerable reduction of the fatigue life and an excessive increase of the pitting area, which result from the microscopic stress cycle growth caused by the sliding of the asperity contact. This suggests that fatigue life in the rolling-sliding condition can be overestimated based only on the RCF model. The rubbing surfaces of spiral bevel gears are subject to typical rolling-sliding motion. This paper aims to study the mechanism of the micro stress cycle along the meshing path and provide a reasonable method for predicting the fatigue life in spiral bevel gears. The microscopic stress cycle equation is derived with the consideration of gear meshing parameters. The combination of the RCF model and asperity stress cycle is developed to calculate the fatigue life in spiral bevel gears. We find that the contact fatigue life decreases significantly compared with that obtained from the RCF model. There is strong evidence that the microscopic stress cycle is remarkably increased by the rolling-sliding motion of the asperity contact, which is consistent with the experimental data in previous literature. In addition, the fatigue life under different assembling misalignments are investigated and the results demonstrate the important role of misalignments on fatigue life.