## 4 Analysis of Anti-Friction Characteristics of Textured Raceway of the Ball Screws
### Analysis of EHL Characteristics of Textured Raceway of the Ball Screws
The working conditions of the ball screws are determined as follows: the rotation speed of the ball screws is 100 r/min, that is, the entrainment speed of the oil film  
Figure 13: The EHL characteristics of the textured raceway under different texture positions; (**a**) 2D curve of the EHL characteristic: inlet; (**b**) Contour map of the bearing stress: inlet; (**c**) 2D curve of the EHL characteristic: center; (**d**) Contour map of the bearing stress: center; (**e**) 2D curve of the EHL characteristic: outlet; (**f**) Contour map of the bearing stress: outlet. \(u_{s}=167.5\) m/s; the preload force of the ball screws is 1500N; the axial loads of the ball screws are 1000N, 2000N, and 3000N, and the corresponding normal contact forces are 37.31N, 48.12N, and 60.23N, respectively. The variation trend of the friction coefficient with the texture diameter (workpiece#1) is illustrated in Figure 14 under the action of three different axial loads. Figure 14 demonstrates that the variation trend of the friction coefficient between the ball and the textured raceway is the same under three different axial loads, and the friction coefficient initially decreases and then slowly increases with the change in the texture diameter. The friction coefficient of the textured raceway of the ball screws is lower than that of the non-textured raceway, indicating that the textured raceway of the ball screws has an anti-friction effect. Furthermore, the higher the axial load is subjected to the ball screws, the more obvious the changes in the dynamic pressure effect and the anti-friction effect of the textured raceway of the ball screws with the texture diameter. With the increase in the axial load of the ball screws gradually, the average thickness of the oil film between the ball and the rough surface of the screw raceway gradually decreases, and the bearing area of the asperity gradually increases, resulting in the friction coefficient of the textured raceway of the ball screws increases. The textured raceway of the ball screws provides an anti-friction effect, and the friction coefficient of the contact system of the ball screws is reduced by 15.2% under the axial load of 3000 N, and the texture diameter is 40 \(\upmu\)m.  
Figure 15 displays the variation trend of the friction coefficient with the texture depth under three axial loads (workpiece#2). It can be seen from Figure 15 that the friction coefficient between the ball and the textured raceway of the ball screws is lower than that of the non-textured raceway of the ball screws under the three axial loads, indicating that the textured raceways have the effect of reducing friction. The ball screw is in a mixed lubrication state, and the oil film thickness is very thin under the condition of the entrainment speed \(u_{s}=167.5\) m/s. The shear friction coefficient of the oil film is a small proportion of the total friction coefficient. The friction coefficient under three axial loads does not change significantly with increasing texture depth. The average thickness of the oil film gradually decreases with increasing normal contact force, the bearing contact area of the asperity gradually increases, and then the friction coefficient of the textured raceway gradually increases. When the axial load of the ball screws is 3000 N, and the texture depth is 10 \(\upmu\)m, the textured raceway of the ball screws exhibits optimum friction-reducing effects, and the friction coefficient of the textured raceway is reduced by 7.6%. Figure 14: Trend of friction coefficient with texture diameter (workpiece#1). The variation trend of the friction coefficient with the areal density of the texture (workpiece#3) is shown in Figure 16. Figure 16 illustrates that the friction coefficient between the ball and the textured raceway decreases initially and subsequently increases with the change in the areal density under the three axial loads.