# Light-Weighting of Planetary Gearbox Based on Multi-Strategy Optimization Sparrow Search Algorithm
## 1 Introduction  
Planetary gearboxes play an important role in the industry. It is used in wind turbines, aircraft, cars, and electric screwdrivers [1, 2]. Planetary gearboxes are usually composed of multi-stage planetary gear trains. The planetary gear train consists of four parts, including the sun gear, the planetary gear, the inner gear, and the planetary carrier [3]. Planetary gearbox has the following characteristics: (1) compared with fixed shaft transmission, it has less noise, longer life, and more compact structure; (2) compared with other gearboxes of the same volume, it can provide a larger transmission ratio; and (3) its input and output axes are concentric, so there is no bending moment or torque to generate radial force [4]. In the conventional design of the planetary gearbox, certain geometric and kinematic conditions are typically prioritized. The practical requirements of improving efficiency and lifespan, light-weighting, and energy loss of the gearbox are ignored in this design mode. Considering these factors, numerous recent studies have focused on optimizing the design of planetary gearboxes. To improve efficiency, [PERSON] [5] developed the theory of dynamic efficiency calculation and introduced a hybrid algorithm combining particle swarm optimization with differential evolution. [PERSON] [2] established a multi-objective uncertainty optimization design framework for planetary gear trains and designed an improved non-dominated sorting genetic algorithm II (NSGA-II). To improve the lifespan and reduce the size, [PERSON] [6] used the exterior point penalty function method to optimize the design. The results show that this method can get ideal results. [PERSON] [7] proposed a hybrid algorithm combining the genetic algorithm with the three parents cross-transformation of the artificial immune system. This algorithm has been successfully applied to planetary gear trains, yielding results comparable to existing studies. For minimal weight and power loss,Parmar [8] proposed an optimization method for planetary gearboxes based on NSGA-II. The results demonstrate that the enhanced gearbox significantly reduces both weight and power loss. [PERSON] [9] proposed a multi-objective hybrid butterfly optimization and particle swarm optimization algorithm. The application results show that the method is effective. Among these studies, the light-weighting of the gearbox becomes increasingly essential. It can improve dynamic performance and energy efficiency while reducing manufacturing and transportation costs. In addition, the smaller volume saves space and material resources, which is in line with the Sustainable Development Goals. Therefore, the light-weighting of gearboxes has been a subject of interest for many years. [PERSON] and [PERSON] [10] introduced an algorithm for optimizing multi-spindle gear trains, offering various optimization options including minimizing volume. [PERSON] [11] proposed a method to obtain the optimal weight of gear by using an improved genetic algorithm. [PERSON] [12] proposed a design method combining a random search method and the simulated annealing (SA) algorithm to minimize the volume of the gearbox. With the development of optimization algorithms, numerous innovative methods have emerged in recent years. These new methods can address the shortcomings of the past methods, such as tedious steps and poor robustness. For the light-weighting design of the gearbox, [PERSON] [13] proposed a method to generate Pareto fronts using NSGA-II and investigate them using fuzzy decision tools. [PERSON] [14] innovatively applied the particle swarm optimization (PSO) algorithm to this issue. [PERSON] [15] proposed a new method of applying [PERSON]'s method and grey relational analysis (GRA). [PERSON] [16] tests the sensitivity of seven different metaheuristic algorithms to this problem. However, the aforementioned methods still have limitations. The SA has the characteristics of a simple calculation process but a slow convergence speed.