## 4 Analysis of Anti-Friction Characteristics of Textured Raceway of the Ball Screws
### Analysis of EHL Characteristics of Textured Raceway of the Ball Screws
It is interesting to note that the friction coefficient of the textured raceway is lower than that of the non-textured raceway, and the textured raceway of the ball screws provides an anti-friction effect. The higher the axial load of the ball screws, the higher the proportion of the contact area of asperity, and the friction coefficient of the texture raceway of the ball screws is increased. The textured raceway of the ball screws achieves the best friction reduction effect when the axial load of the ball screw is 1000 N, the areal density of the texture is 8%, and the friction coefficient is reduced by 8.3%. Influence of the Rotation Speeds on the Anti-Friction Characteristics of the Textured Raceway of the Ball Screws  
The rotation speed of the ball screws determines the entrainment speeds of the oil film in the contact area. To investigate the influence of the rotation speeds of the ball screws on the EHL characteristics of textured raceways with different geometrical features of the textures, the ball screw is only subject to the preload force. That is, the normal contact force of the ball is 27.6N. The rotation speeds of the ball screws are 100 r/min, 350 r/min, and 600 r/min, and the corresponding entrainment speeds of the oil film between the ball and textured raceway are 167.5 mm/s, 586.4 mm/s, and 1005.3 mm/s. The variation trends of  
Figure 16: Trend of friction coefficient with areal density of the texture (workpiece#3). Figure 15: Trend of friction coefficient with texture depth (workpiece#2). the friction coefficient between the ball and the textured raceway with geometric features of the texture are investigated under three different rotation speeds of the ball screws. The relationship between the friction coefficient and the texture diameter is illustrated in Figure 17 under three different rotation speeds (workpiece#1). Figure 17 indicates that the friction coefficient initially decreases and then increases with increasing texture diameter under three different rotation speeds of the ball screws. The friction coefficient of the textured raceway is smaller than that of the non-textured raceway, indicating that the textured raceway has an anti-friction effect. The ball screw is in a mixed lubrication state, the oil film thickness is thin, and the contact friction coefficient of the asperity accounts for a large proportion of the total friction coefficient. The surface texture reduces the contact area of the asperity in the elliptical contact area, thereby reducing the contact friction coefficient of the asperity. The friction coefficient of the textured raceway of the ball screw is higher than that of the non-textured raceway when the texture diameter is 60 \(\upmu\)m, and the rotation speeds of the screw are 350 r/min, and 600 r/min, suggesting that the inappropriate geometric feature parameters of the texture increase the friction of the ball screws. The lubrication condition of the ball screw is good at medium and high rotation speeds, and the friction force is mainly the shear friction force of the oil film. The ball screw is in the EHL state, the oil film thickness between the ball and the raceway is thick, and the asperity on the rough raceway surface is completely covered. The friction coefficient is mainly composed of the shear friction coefficient of the oil film, and the textured raceway of the ball screws further increases the oil film thickness, resulting in a higher friction coefficient. The friction-reducing effect of the textured raceway is optimum when the rotation speed of the screw is 100r/min, and the textured diameter is 40 \(\upmu\)m, and the friction coefficient is reduced by 13.8%. The variation trend between the friction coefficient of the textured raceway of the ball screws and the texture depth is shown in Figure 18 under three different rotation speeds (workpiece#2). The friction coefficient reaches the minimum when the rotation speed is 100 r/min, the texture depth is 5 \(\upmu\)m, and the friction coefficient increases slightly as the texture depth increases.