## 1 Introduction  
At the beginning of 2021, Beijing China State Railway Group Co., Ltd. (Beijing, China) put forward the \"CR450 Science and Technology Innovation Project Implementation Plan\", which officially launched the CR450 (maximum speed of 450 km/h, sustained speed of 400 km/h) science and technology innovation project, focusing on high-speed EMU system integration, axle drive, braking control, vibration and noise reduction, and other core technologies [1]. A high-speed EMU stock traction gear is the core component of the train's power drive, but it is also one of the primary sources of noise caused by vehicle noise [2]. Currently, existing EMU stock commonly uses helical gear drive systems. However, with long periods of high-load operation, gearbox bearings can develop severe pitting and blackening, which is mainly caused by high oil temperatures. At the same time, gearboxes suffer from other problems, such as seal failure, reduced lubrication, increased gear noise, and shorter service life. Speed is the eternal goal of transportation, and noise is the primary factor limiting higher operating speeds [3]. At present, many countries and organizations have taken in-vehicle noise as an important indicator for measuring the comfort of high-speed rail. [PERSON] et al. tested the radiation characteristics of the noise in the sightseeing area of the train compartment at a speed of 350-400 km/h, and the results showed that the noise value in the compartment ranged from 93 to 98 dB, and increased roughly linearly with the increase in speed [4]. Hearing impairment studies have shown that the human ear can be impaired by prolonged exposure to noise levels above 80 dB [5]. Therefore, it is necessary to effectively reduce the noise of high-speed train gears. The study of traction gears and their noise reduction and modification programs adapted to the new generation of EMU have become a key issue that needs to be addressed urgently. Gear contact analysis is a commonly used method for gear optimization. [PERSON] et al. established a dynamic finite element model of the gear meshing contact impact with a circular arc-toothed line cylindrical gear as the research object and analyzed the relationship between velocity, position, combined force, and time during the impact process. It was found that the velocity and position during impact have a significant influence on the tooth contact characteristics [6]. [PERSON] et al. established an explicit mathematical model between the design parameters and contact stress of cylindrical gears with arc teeth and used the whale optimization algorithm to change the function parameters to optimize and analyze the effect of design parameters on the contact stress of cylindrical gears with circular arc teeth [7]. [PERSON] et al. used the helical gear of a CRH380A high-speed train as the research object, synthesized Pro/E and ANSYS Workbench, and deeply analyzed its meshing characteristics and performance. The dynamic contact stress state is revealed through modeling and finite element simulation, providing substantial guidance for gear strength calculations [8]. The main causes of vibration in gear structures include gear-tooth interaction, unbalanced loads, material quality, resonance effects, and tooth wear. These factors interact to cause vibration problems. Appropriate design and manufacturing measures are required to minimize vibration. Gear shaping is a method of improving gear transmission performance by adjusting the tooth shape of the gear. Potential benefits of gear reshaping include noise reduction, increased gearing efficiency, improved load distribution in gears, and reduced vibration levels. In terms of the design of gear trimming programs, scholars have used different methods to verify the effectiveness of the trimming design. For example, [PERSON] et al. studied a two-stage star gear transmission system and successfully reduced the system vibration through tooth profile modification and dynamic modeling [9]. [PERSON] et al.