Transmission efficiency is a significant index of the transmission system. Even though much research has been carried out to calculate gear transmission efficiency, only a few of them studied spiral bevel gear due to its complexity. Moreover, spiral bevel gear does not have a “standard surface”, which means more complex coupling relations between different parameters and makes efficiency optimal design more difficult. Therefore, an instantaneous transmission efficiency computing model of a spiral bevel gear was set up based on loaded tooth contact analysis and hybrid elasto-hydrodynamic lubrication theory. Then, the particle swarm optimization–gravitational search algorithm (PSOGSA) optimal model was constructed to obtain the best parameters that maximize the average transmission efficiency of spiral bevel gears. Control parameters and machining parameters are optimized in sequence based on the proposed optimal model. The results showed that both optimal designs could help improve transmission efficiency, but the range of machining parameters is limited in a small interval because of the complex coupling relations. Therefore, the machining parameters optimization are conducted after control parameters optimization, which showed good results. Transmission efficiency was finally improved to 98.78%, which increased more than 4% at least. The proposed optimal model could also be applied into other gear design methods or even other fields.

Gear transmission system dynamic responses under high-speed and heavy-duty working conditions were obviously affected by support structures, especially in lightweight design. However, web thicknesses and angles were usually ignored in dynamic modeling process. Therefore, a full mesh model with web structure was built and its dynamic characteristics were analyzed by a modified vector form intrinsic finite element (VFIFE), which is proposed to solve high-speed dynamic problems with good efficiency. For spiral bevel gear pair dynamic characteristics, the impacts of web thicknesses and angles were simulated and discussed. Simulation results showed that web support angles will affect gear meshing performance and dynamic characteristics more remarkable than web thickness did. In addition, the good performance of the proposed modified VFIFE method was proved, which showed good computing efficiency.