## 4 Analysis of Anti-Friction Characteristics of Textured Raceway of the Ball Screws
### Analysis of EHL Characteristics of Textured Raceway of the Ball Screws  
To investigate the EHL characteristics of the lubricating oil film of the textured raceway of the ball screws under the oil-rich condition. Following the EHL model established and the geometric feature parameters of the textures, the preload force is 1500N, the entrainment speed is 83 mm/s, the texture diameter \(d_{t}=10\) um, the texture depth \(h_{t}=5\) um, the area density \(\rho_{t}=6\%\), and the bearing stress distribution and thickness distribution of the oil film at the contact point of the textured raceway are obtained as shown in Figure 12. It can be observed from Figure 12a that the bearing stress distribution of the oil film in the contact area is no longer a smooth surface but a rough and uneven surface, taking into account the ground surface topography of the raceway and the geometric features of the textures manufactured on the raceway surface. The oil film thickness distribution in the textured area of the screw raceway is significantly increased, reducing the direct contact of the asperities in the contact area, as shown in Figure 12b. The working ball is repeatedly rolling and sliding in the textured raceway of the ball screws under steady-state conditions. It is essential to investigate the impact of varying the positions of the texture within the elliptical contact area of the screw raceway on the EHL characteristics of the oil film. The surface texture is located at the inlet, center, and outlet of the contact area between the ball and screw raceway, and the EHL characteristics of the oil film are solved based on the established EHL model of the textured raceway of the ball screws. The two-dimensional distribution of the bearing stress and oil film thickness and the contour map of the bearing stress of the oil film are presented in Figure 13.  
The ball screw of the textured raceways is in a state of mixed lubrication. The balls are in direct contact with the rough raceway surface in the contact area of the asperity, resulting in the wear of the textured raceway. In addition, it can be seen from Figure 13 that the viscous lubricating oil flows through the texture area of the raceway surface, and the oil film produces a dynamic pressure effect that reduces the friction coefficient of the ball screws, achieving the effect of reducing friction and anti-wear. The friction coefficient is used as the design objective for textured raceways of the ball screws, and the anti-friction characteristics of ball screws are investigated under different axial loads and rotation speeds and geometric features of the manufactured textures. To reduce the calculation error, the friction coefficient of the textured raceway of the ball screws is averaged when the texture is located at the inlet, center, and outlet of the contact area, respectively. Figure 12: The EHL characteristics of the textured raceway of the ball screws; (**a**) Bearing stress distribution; (**b**) Film thickness distribution. Influence of the Axial Loads on the Anti-Friction Characteristics of the Textured Raceway of the Ball Screws  
The friction coefficient is composed of the contact friction coefficient of the asperity and the shear friction coefficient of the oil film between the ball and the textured raceway. The range of the friction coefficient of the ball screws is 0.003-0.01 in the THK product manuals. The normal contact force between the ball and the textured raceway is determined by the axial loads of the ball screws. To investigate the influence of the axial loads of the ball screws on the EHL characteristics of textured raceways with different geometrical features of the textures.