# An Advanced DEM-FEM Method for Herringbone Gear in Shot Peening
## 4 Results and Discussion
### Impact Information Along the Tooth Profile
#### 4.1.2 The Impact Velocity Along the Tooth Profile  
Based on the observed impact counts of both left-handed and right-handed gears, no significant differences were identified between the two orientations. Given that the primary  
Figure 16: Comparison of experimental and simulated residual stress. Figure 17: Impact times of tooth surfaces of different turning gears. (**a**) Left-hand gear. (**b**) Right-hand gear. objective of this study is to investigate the surface integrity parameters distributed along the tooth profile, subsequent analyses of impact velocity and surface integrity parameters will be conducted using the left-handed gear as a representative example. The study focuses on three distinct characteristic positions along the tooth profile: the tooth tip, the pitch circle, and the tooth root, to analyze the impact velocity of the shots on the tooth profile. Due to the complex curved surface of the herringbone gear, the direction of the impact velocity during the shot peening process often does not align with the local area's normal vector. Therefore, this paper discusses the distribution of the impact velocity components, where \(x\), \(y\), and \(z\) correspond to the \(X\), \(Y\), and \(Z\) axes of the local coordinate system in Figure 10, respectively. Here, \(v_{x}\) represents the velocity in the tooth width direction, \(v_{z}\) denotes the velocity in the tooth height direction, \(v_{z}\) is the velocity in the normal vector direction, and \(v_{m}\) signifies the resultant velocity. Figure 18 shows the distribution of impact velocity prior to shot impact at the pitch circle when the initial velocity \(v_{m}\) is 60 m/s. It is observed that upon being ejected from the nozzle, 18% of the shots have an impact velocity \(v_{m}\) ranging from 60 to 65 m/s upon striking the gear surface, indicating that there is a distance over which the shots continue to accelerate after leaving the nozzle. The velocity component \(v_{x}\) in the tooth width direction is predominantly distributed between \(-\) 5 and 5 m/s, with 88% of the shots falling within this range. The velocity \(v_{y}\) along the tooth height direction is mostly concentrated between 40 and 60 m/s, accounting for 58% of the shots. The velocity component \(v_{z}\), which is perpendicular to the gear surface, significantly influences the shot peening effect. The depth and magnitude of residual stress are primarily associated with \(v_{z}\). It is noted that \(v_{z}\) is evenly distributed within the 0 to 30 m/s range, with only 7% of the shots falling within the 35 to 45 m/s range. The distribution of the resultant velocity \(v_{m}\) is mainly concentrated between 55 and 65 m/s, while the proportion of velocities within the 0 to 55 m/s range is relatively uniform. Figure 19 presents the distribution of impact velocity of shots at the tooth tip. It is observed that the velocity component \(v_{x}\) is primarily concentrated within the \(-\)5 to 5 m/s range, with 75% of the shots falling into this interval. The velocity \(v_{x}\) along the tooth height direction is mostly distributed between 40 and 60 m/s, accounting for 60% of the shots. Figure 18: Impact velocity distribution at the gear pitch circle area. Comparing with the impact velocity at the pitch circle, it is noted that \(v_{x}\) and \(v_{y}\) exhibit similar distribution patterns, with the exception that the proportion of shots with \(v_{x}\) in the \(-5\) to \(5\) m/s range at the tooth tip is slightly lower than that at the pitch circle. The proportion of \(v_{z}\) within the 0 to 20 m/s range is 20%, whereas at the pitch circle, this interval accounts for 67% of the shots. It is evident that near the tooth tip, the velocity component \(v_{z}\) perpendicular to the gear surface is mainly distributed between 20 and 45 m/s, with a proportion of 80%. The resultant velocity \(v_{m}\) at the tooth tip is predominantly distributed within the 55 to 65 m/s range, with a high proportion of 48%, compared to 43% at the pitch circle.