Nonlinear dynamical behaviors of spiral bevel gears in transient mixed lubrication

Herein, a new and actual nonlinear dynamic model of spiral bevel gears (SBG) in transient mixed lubrication was firstly developed, which considered the coupling action of direct contact of asperity and the transient squeezing effect of lubricant along the entire contact trajectory in the form of time-variant contact stiffness and damping. Besides, the nonlinear backlash, actual time-variant rotating contact radii and static transmission error obtained by loaded tooth contact analysis (LTCA) method were all involved in this model. Based on the proposed model, notable deviations were found compared with traditional Hertz contact or full-film lubrication assumptions, which highlight the important role of film lubrication and asperity contact. After that, a series of investigations on nonlinear dynamic of SBG were implemented to reveal the influence of lubrication, roughness, applied torque, especially, the influence of contact trajectory which has not been reported. The results demonstrate that the influence of roughness on dynamic response are complicated, and the excessive roughness tends to arise bilateral impact of gear tooth. The effect of transmission torque is more significant than that of contact stiffness and damping. As for different contact trajectories, the vibration response of heel contact is the strongest, while toe contact leads to the weakest vibration.