## 1 Introduction
[PERSON] et al. [17] studied a pair of circular arc spiral level gears in nutation drive system and analyzed influence of system parameters on transmission efficiency. For the optimal design method of gears, more researchers are using intelligent optimization algorithms in gear design with the development of numerical methods. [PERSON] [18] proposed a multi-objective modification optimal design method for helical gears to reduce vibration and average load. [PERSON] et al. [19] established a hybrid metaheuristic algorithm considering the PSO algorithm to solve a multi-objective non-linear optimization problem for planetary gearbox. Based on the non-dominated sorting genetic algorithm III (NSGA-III), [PERSON] et al. [20] realized macro geometry optimal design of a helical gear pair by scoring the mass, efficiency, and peak-to-peak static transmission error. [PERSON] et al. [21] used a genetic algorithm to conduct a multi-objective optimization of a spur gear pair to reduce both transmission volume and power losses. [PERSON] et al. [22] proposed a simplified reliability Kriging model and optimized the reliability of a planetary gear by genetic algorithm (GA) and the discrete element method (DEM). It could be easily concluded from former studies that gear transmission friction, efficiency, power loss, and so forth are becoming attractive research topics. The friction, mixed lubrication, and power loss of gears have been considered in-depth. While transmission efficiency and its optimization of spur gears and helical gears have been studied, transmission efficiency of spiral level gears are usually neglected. The friction coefficient and windage power loss are the main topics in recent research. There are two main reasons:(1) there is no \"standard\" tooth surface for spiral bevel gears and there are too many machining parameters, which means the interaction mechanism and the influence on efficiency between parameters are hard to determine; (2) due to the complexity of the spiral bevel gear tooth surface, different design methods and settings may conduct different tooth surfaces, which means it is hard to obtain an absolute best design. Due to the low complexity of cylindrical gears, a single optimal algorithm is usually used, which is not suitable for high complexity optimization in a spiral bevel gear design. With the development of a modern optimal design method, there is a new way to solve such multi-objective and complex influence-mechanism questions. It could easily avoid multi-factor coupling analysis to combine particle swarm optimization and the gravitational search algorithm. Therefore, we could find a general approach to maximize the efficiency of SBG for certain design parameters or machining parameters. This paper is organized as follows: The basic theory of the efficiency model and PSOGSA optional theory is established in Section 2. Spiral bevel gear meshing theory and optimization settings are conducted in Section 3. Optimal simulation results considering control parameters and machining parameters are discussed in Section 4. Eventually, in Section 5, we draw the conclusions to summarize rules and characteristics of the research.