# An Advanced DEM-FEM Method for Herringbone Gear in Shot Peening
## 1 Introduction  
Due to their unique tooth profile design, herringbone gears feature a larger contact surface, enabling them to withstand higher loads [1; 2; 3]. They offer advantages such as high transmission efficiency, smooth operation, and a more continuous and smooth meshing process [4; 5]. Consequently, they are widely employed in various mechanical applications, including industrial reducers, marine propulsion systems, aerospace equipment, large generators, and heavy-duty construction machinery [6; 7]. Operating frequently in high-speed and heavy-load environments, herringbone gears are susceptible to failures such as tooth surface wear, scoring, and tooth root fractures [8; 9]. Therefore, surface modification of herringbone gears is essential to enhance their service life. Numerous studies have demonstrated that shot peening can significantly improve the surface physical state and topography of components [10; 11; 12; 13; 14], thereby enhancing their fatigue, wear, and lubrication properties [15; 16; 17; 18]. The favorable economics and wide applicability of shot peening [19; 20; 21; 22] make it suitable for the complex surface contours of herringbone gears, rendering it a crucial process in anti-fatigue manufacturing for these gears. Although shot peening treatment can improve the surface integrity parametersof herringbone gears, thereby enhancing their service performance, several challenges remain. However, the surface profile of the herringbone gear is a complex curved surface, and the motion law of a large number of high-speed moving shots in the herringbone gear tooth surface and the tooth root part of the gear is not clear during shot peening. Efficiently identifying the appropriate process parameters for herringbone gears from the multitude of shot peening variables is difficult, leading to low processing efficiency and unclear correlations between shot peening parameters and surface integrity parameters. Additionally, the confined space at the gear root exacerbates the risk of shot collisions, resulting in variations in surface integrity parameters across different gear tooth positions under the same shot peening conditions. This non-uniform surface integrity state may lead to diverse failure behaviors during the gears' service life. Shot peening, as a surface-strengthening treatment technology, has been widely applied in the aerospace, automotive, and other industries to improve the fatigue life of components [23; 24]. During shot peening, numerous shots continuously impact the surface of components at a certain speed, inducing residual compressive stress in the surface layer and to a certain depth [14; 25; 26]. Residual compressive stress inhibits the initiation and propagation of cracks, thereby enhancing fatigue life, which is currently the most direct explanation for the effects of shot peening and a primary focus of academic research [27; 28; 29]. When shots impact the component, craters are formed on the surface, increasing surface roughness and consequently reducing the effectiveness of shot peening [30; 31; 32]. To enhance the positive effects of shot peening and mitigate the negative effects caused by increased roughness, it is essential to study the relationship between process parameters and surface integrity. Finite element software simulation has become a mainstream method for studying shot peening. [PERSON] et al. [33] proposed a random multi-particle model that closely approximates actual shot peening and has been widely adopted. Compared to experimental methods, using finite element software for simulation significantly reduces research time and costs. [PERSON] et al. [34] studied the impact of mesh density on finite element results, providing a basis for finite element meshing. [PERSON] et al. [35] investigated the relationship between processing parameters and surface integrity, finding that increasing the shot diameter decreases the residual compressive stress in the surface layer but increases the maximum residual compressive stress. [PERSON] et al.