Anti-Friction and Anti-Wear Mechanisms of Micro Textures and Optimal Area Proportion in the End Milling of Ti6Al4V Alloy

To solve the problems of low efficiency, poor surface quality, and short tool life in the milling of titanium alloys, this study took the micro-textured ball-end milling tool as a starting point and established a platform for friction and wear tests. Based on a new method of external friction theory, the anti-friction and anti-wear mechanisms of the micro-textured tool were analyzed. According to these mechanisms, the optimal area proportion of the micro textures in the contact area between the chip and tool was theoretically investigated considering the milling force, and the proportion was verified experimentally. This work provides a reference for improving the cutting performance of hard metal tools.


Introduction
Recent studies have demonstrated that micro textures can effectively reduce friction force, so micro textures with a regular arrangement can be prepared on the friction pair surface of tools. This method can significantly reduce the friction of the contact surface of friction pairs [1]. Numerous authors have conducted a substantial amount of related research in recent years.
Wojciechowski S, Chwalczuk T, Twardowski P, et al. [2] concentrated on the modeling of a cutter's displacements during ball-end milling with various surface inclinations. The cutter's displacements (vibrations) model was proposed. Subsequently, this model was validated empirically during the milling tests with various feed per tooth (f z ), depth of cut (a p ) and surface inclination angle (a) values. Experiments were carried out with the application of a laser displacement sensor and force dynamometer. The research revealed that the cutter's displacements are strongly affected by the cutter's run out and surface inclination. This observation is also confirmed by the developed model. A new approach to surface roughness parameters estimation during finish cylindrical end milling was presented by Wojciechowski S, Chwalczuk T, Twardowski P, et al. [3] In the first stage, tool working part instantaneous displacements was estimated. The height of the tool's displacement envelope obtained was then applied in the second stage to the calculation of surface roughness parameters. These calculations assumed that in the cylindrical milling process two different mechanisms of surface profile formation exist. Which mechanism was present was dependent on the feed per tooth and the maximum height of the tool's displacement envelope. The developed model was validated during the cylindrical milling of hardened hot-work tool steel 55NiCrMov6 using a stylus profiler and scanning laser. Vazquez Martinez J, Irene D S I, Iglesias Victoria P, et al. [4] investigated the effect of laser-textured the optimal area proportion on the rake face. Therefore, this study reveals the anti-friction mechanism considering external friction, which simultaneously demonstrates the anti-wear mechanism. On this basis, the contact area between the tool and chip can be determined, and the optimal area proportion of the micro textures in the contact area can be obtained. This research provides a reference for optimizing the cutting performance of micro-textured ball-end milling tools.

Construction of Friction and Wear-Test Platform
The materials used in the experiment were YG8 hard metal and Ti6Al4V titanium alloy. The properties of the above materials are shown in Tables 1 and 2. The hard metal was shaped into a cylinder with a diameter of 16 mm and height of 12 mm, using cutting equipment. Micro textures on cemented carbide surface were fabricated by the fiber laser. In this experiment, the fiber laser produced by the Zhengtian laser company was used. The output center wavelength of the fiber laser is 1064 nm. It has the advantages of good beam quality, strong material adaptability, flexible processing mode and high processing accuracy. It is widely used in the surface micro processing of various materials. The laser parameters of optical fiber laser equipment is shown in Table 3. During the preparation process, the activated discharge produced by the cutting had a certain influence on the material surface, so the surface was firstly lapped and then polished to achieve the goal of no burrs.   A high-speed friction and wear-testing machine (MMG-500) (see Figure 1) was used. Four independent variables were considered in the friction and wear experiments, namely the micro-textured diameter, distance between two adjacent micro textures l 1 , loads, and rotation. Therefore, the experiment was designed as an orthogonal experiment with four factors and five levels. The factor level table of the orthogonal experiment is presented as Table 4. The studies demonstrated that the fabrication accuracy of the micro-pit textures was the highest when the laser power was 35 W, the scanning speed was 1700 mm/s, and the scanning times were 7 [15]. In the process of grinding the micro textures, grinding powder would enter the inner part of the micro textures and influence their effects. The grinding time of different tests is the same, that is 30 s. Therefore, following grinding, the micro textures were soaked in an acetone solution, and the grinding powder was cleaned by an ultrasonic wave. demonstrated that the fabrication accuracy of the micro-pit textures was the highest when the laser power was 35 W, the scanning speed was 1700 mm/s, and the scanning times were 7 [15]. In the process of grinding the micro textures, grinding powder would enter the inner part of the micro textures and influence their effects. The grinding time of different tests is the same, that is 30 s. Therefore, following grinding, the micro textures were soaked in an acetone solution, and the grinding powder was cleaned by an ultrasonic wave.   Based on the friction and wear test results, the wear depths of two specimens from each sample were measured using a three-coordinate measuring instrument, mainly to measure the wear area. Five points were measured in the wear area and the average wear value for the two specimens was obtained. A comparison of the wear values is presented in Table 5.

Analysis of Wear Test Results
Based on the friction and wear test results, the wear depths of two specimens from each sample were measured using a three-coordinate measuring instrument, mainly to measure the wear area. Five points were measured in the wear area and the average wear value for the two specimens was obtained. A comparison of the wear values is presented in Table 5. It can be observed from Figure 2 that the larger part the micro-textured surface exhibited less wear than the smooth surface. However, several groups were close to the amount of wear on the smooth surface, which was caused by the laser machining process and errors in the friction and wear experiments, although the error was within the allowable range. In general, the fatigue performance of the smooth-surfaced hard metal material was inferior to that of the micro-textured surface. The minimum wear rate for sample No. 10 was 12.5 µm, and the maximum surface fatigue resistance for the micro-textured surface was 38.4% higher than the average wear rate for the smooth surface.

Analysis of Friction Test Results
The experimental results are presented in Table 6. The average friction force of the micro-textured surface was 25% lower than that of the smooth surface, while the average friction coefficient was 22% lower than that of the smooth surface. Figure 3 presents a diagram of the comparative analysis of the friction force and coefficient of the micro-textured surface. It can be observed that the micro texture preparation on the material surface could effectively reduce the friction force and friction coefficient.

Analysis of Friction Test Results
The experimental results are presented in Table 6. The average friction force of the micro-textured surface was 25% lower than that of the smooth surface, while the average friction coefficient was 22% lower than that of the smooth surface. Figure 3 presents a diagram of the comparative analysis of the friction force and coefficient of the micro-textured surface. It can be observed that the micro texture preparation on the material surface could effectively reduce the friction force and friction coefficient.

Analysis of Micro-Textured Effects
Under experimental conditions, the friction between the hard metal and titanium alloy was purely sliding friction. Under highly compressive contact stress, small fragments were produced in the local areas of the two contact surfaces, eventually leading to the formation of pits. Moreover, owing the viscous properties of the titanium alloy material, the hard metal surface left a sticky mark. Following a lengthy period, the friction on the hard metal surface resulted in surface fatigue wear. The wear morphology is illustrated in Figure 4. To provide an improved analysis of the impurities on the hard metal surface, which could arise from the titanium alloy or hard metal, energy spectrum analysis of the worn sample surface was performed using a scanning electron microscope (see Figure 5). The analysis results demonstrated that most of the elements in the viscous impurities were titanium. Thus, we can conclude that the adhesive impurities mainly originated from the adhesive wear of the titanium alloy.

Analysis of Micro-Textured Effects
Under experimental conditions, the friction between the hard metal and titanium alloy was purely sliding friction. Under highly compressive contact stress, small fragments were produced in the local areas of the two contact surfaces, eventually leading to the formation of pits. Moreover, owing the viscous properties of the titanium alloy material, the hard metal surface left a sticky mark. Following a lengthy period, the friction on the hard metal surface resulted in surface fatigue wear. The wear morphology is illustrated in Figure 4.

Analysis of Micro-Textured Effects
Under experimental conditions, the friction between the hard metal and titanium alloy was purely sliding friction. Under highly compressive contact stress, small fragments were produced in the local areas of the two contact surfaces, eventually leading to the formation of pits. Moreover, owing the viscous properties of the titanium alloy material, the hard metal surface left a sticky mark. Following a lengthy period, the friction on the hard metal surface resulted in surface fatigue wear. The wear morphology is illustrated in Figure 4. To provide an improved analysis of the impurities on the hard metal surface, which could arise from the titanium alloy or hard metal, energy spectrum analysis of the worn sample surface was performed using a scanning electron microscope (see Figure 5). The analysis results demonstrated that most of the elements in the viscous impurities were titanium. Thus, we can conclude that the adhesive impurities mainly originated from the adhesive wear of the titanium alloy.  To provide an improved analysis of the impurities on the hard metal surface, which could arise from the titanium alloy or hard metal, energy spectrum analysis of the worn sample surface was performed using a scanning electron microscope (see Figure 5). The analysis results demonstrated that most of the elements in the viscous impurities were titanium. Thus, we can conclude that the adhesive impurities mainly originated from the adhesive wear of the titanium alloy.

Analysis of Micro-Textured Effects
Under experimental conditions, the friction between the hard metal and titanium alloy was purely sliding friction. Under highly compressive contact stress, small fragments were produced in the local areas of the two contact surfaces, eventually leading to the formation of pits. Moreover, owing the viscous properties of the titanium alloy material, the hard metal surface left a sticky mark. Following a lengthy period, the friction on the hard metal surface resulted in surface fatigue wear. The wear morphology is illustrated in Figure 4. To provide an improved analysis of the impurities on the hard metal surface, which could arise from the titanium alloy or hard metal, energy spectrum analysis of the worn sample surface was performed using a scanning electron microscope (see Figure 5). The analysis results demonstrated that most of the elements in the viscous impurities were titanium. Thus, we can conclude that the adhesive impurities mainly originated from the adhesive wear of the titanium alloy.

Analysis of Anti-Wear Mechanism of Micro Textures
Based on the scanning electron microscopy observation, the friction and wear mechanisms of the micro-pit textures were analyzed. As illustrated in Figure 6, the friction and wear processes of the micro-textured surface were divided into three stages. In stage I, a small amount of debris was squeezed into the micro-pit textures under the action of surface pressure, and a small number of cracks were produced on the friction pair surface. In stage II, cracks on the friction pair surface were gradually oriented under the action of contact stress. At a certain depth from the surface, when the shear stress reached its maximum, serious plastic deformation occurred on the surface. Under the action of alternating loads, the material around the micro-cracks weakened, and a large number of abrasive particles were produced on the surface. Simultaneously, the abrasive particles and debris produced were extruded under the action of surface pressure, and thus, the micro-pit textures were gradually filled. In stage III, the abrasive debris filled into the micro-pit textures was bonded and separated from them by the debris outside under high pressure and temperature. Based on the scanning electron microscopy observation, the friction and wear mechanisms of the micro-pit textures were analyzed. As illustrated in Figure 6, the friction and wear processes of the micro-textured surface were divided into three stages. In stage I, a small amount of debris was squeezed into the micro-pit textures under the action of surface pressure, and a small number of cracks were produced on the friction pair surface. In stage II, cracks on the friction pair surface were gradually oriented under the action of contact stress. At a certain depth from the surface, when the shear stress reached its maximum, serious plastic deformation occurred on the surface. Under the action of alternating loads, the material around the micro-cracks weakened, and a large number of abrasive particles were produced on the surface. Simultaneously, the abrasive particles and debris produced were extruded under the action of surface pressure, and thus, the micro-pit textures were gradually filled. In stage III, the abrasive debris filled into the micro-pit textures was bonded and separated from them by the debris outside under high pressure and temperature.
The micro-pit textures could store abrasive impurities at different stages of the friction and wear process, and after processing the micro textures with the laser, increased hardness was exhibited in the surroundings of the micro-textured materials owing to the grain refinement under the influence of the laser. Therefore, this played a role in the anti-friction and anti-wear functions, which improved the hard metal strength.

Analysis of Anti-Friction Mechanism of Micro Textures
Relevant research has demonstrated that the use of micro-textured tools can effectively reduce the milling force during the cutting process [16,17]. The milling force has an effect on the contact stress between the tool and chip. The interface between the tool and chip exhibits characteristics of The micro-pit textures could store abrasive impurities at different stages of the friction and wear process, and after processing the micro textures with the laser, increased hardness was exhibited in the surroundings of the micro-textured materials owing to the grain refinement under the influence of the laser. Therefore, this played a role in the anti-friction and anti-wear functions, which improved the hard metal strength.

Analysis of Anti-Friction Mechanism of Micro Textures
Relevant research has demonstrated that the use of micro-textured tools can effectively reduce the milling force during the cutting process [16,17]. The milling force has an effect on the contact stress between the tool and chip. The interface between the tool and chip exhibits characteristics of severe friction, high temperature, high pressure, high chemical activity, and high strain rates, which directly affect the chip formation and workpiece processing quality. To analyze the influence of the micro textures on the friction coefficient of the contact area, a stress characteristic model of the interface was established, as illustrated in Figure 7. The shear stress of the interface can be divided into two regions: the friction force of the interface is equal to the shear yield stress of the material in the bonding area, while the ratio of the interface friction force to the normal stress is constant in the slip area. Moreover, the stress τ generated by the fiction can be expressed as follows: where τ s represents the shear yield limits of the material (MPa); µ denotes the friction coefficient in the slip zone; l p is the bonding area length; l f is the distance between the tool and chip; σ(x) represents the normal stress in the slip area; and x denotes the distance from any point in the slip area to the tool tip.
and 0 at the separation between the tool and chip.
where ξ represents the stress distribution coefficient of the tool, and 2 or 3 is selected according to the processing conditions. To analyze the interface characteristics more accurately, it was assumed that only bonding and slip areas existed at the interface. At the end of the bonding area and beginning of the slip area, the stress generated by the fiction was exactly equal to the material shear yield limit. From Equations (1) and (2), it can be concluded that: Equation (3) indicates that the relationship between the length lp of the bonding area and friction coefficient of the slip area can be determined as follows: The normal stress of the interface is distributed exponentially; it is highest at the cutting edge, and 0 at the separation between the tool and chip.
where ξ represents the stress distribution coefficient of the tool, and 2 or 3 is selected according to the processing conditions. To analyze the interface characteristics more accurately, it was assumed that only bonding and slip areas existed at the interface. At the end of the bonding area and beginning of the slip area, the stress generated by the fiction was exactly equal to the material shear yield limit. From Equations (1) and (2), it can be concluded that: Equation (3) indicates that the relationship between the length l p of the bonding area and friction coefficient of the slip area can be determined as follows: The normal force F N and shear force F ϕ on the tool surface can be obtained by integrating the normal stress and shear stress: where a e represents the cutting width and σ s represents the extrusion yield limit of the two contact materials. According to Equations (5) and (6), the overall friction coefficient of the interface can be obtained as follows: The insertion of the micro textures reduces the contact area between the tool and chip, resulting in the normal stress of the micro-textured tool being greater than that of the non-textured tool. Figure 8 presents a schematic of the micro texture influence on the distribution of the bonding and slipping areas, based on the milling experiment results and the interface stress characteristic model. The micro textures caused the stress to concentrate at the tool edge, so the normal stress σ 0 at the tool edge increased, and the ratio of l p /l f increased obviously compared to that of the non-textured tool [18]. It can be concluded from Equation (7) that the increases in l p /l f and σ 0 decreased the overall friction coefficient µ a of the contact area, which is consistent with the conclusion obtained from the friction and wear experiments. As the friction of the rake face decreased, the tool wear decreased. The normal force FN and shear force Fφ on the tool surface can be obtained by integrating the normal stress and shear stress: where ae represents the cutting width and σs represents the extrusion yield limit of the two contact materials. According to Equations (5) and (6), the overall friction coefficient of the interface can be obtained as follows: The insertion of the micro textures reduces the contact area between the tool and chip, resulting in the normal stress of the micro-textured tool being greater than that of the non-textured tool. Figure 8 presents a schematic of the micro texture influence on the distribution of the bonding and slipping areas, based on the milling experiment results and the interface stress characteristic model. The micro textures caused the stress to concentrate at the tool edge, so the normal stress σ0 at the tool edge increased, and the ratio of lp/lf increased obviously compared to that of the non-textured tool [18]. It can be concluded from Equation (7) that the increases in lp/lf and σ0 decreased the overall friction coefficient μa of the contact area, which is consistent with the conclusion obtained from the friction and wear experiments. As the friction of the rake face decreased, the tool wear decreased.

Analysis of the Contact Area between the Tool and Chip
The friction between the tool and the chip acts on the rake face of the tool when milling titanium alloys. The friction thus affects the formation of the chip, the mechanical-thermal characteristics, tool wear, and the quality of the machined workpiece surface. Therefore, the addition of micro textures to the contact area can play an important role in promoting anti-friction and anti-wear, and can be very important in improving the cutting performance of the tool.

Analysis of the Contact Area between the Tool and Chip
The friction between the tool and the chip acts on the rake face of the tool when milling titanium alloys. The friction thus affects the formation of the chip, the mechanical-thermal characteristics, tool wear, and the quality of the machined workpiece surface. Therefore, the addition of micro textures to the contact area can play an important role in promoting anti-friction and anti-wear, and can be very important in improving the cutting performance of the tool.
In order to determine the contact range between the rake face and the chip, the tool and workpiece coordinate system should first be established. As shown in Figure 9, the workpiece coordinate system was represented by X w Y w Z w , so the position of the workpiece could be determined in accordance with this coordinate system. The tool coordinate system was represented by X c Y c Z c , and the coordinate origin was taken as the tool tip. The transformation relationship between the workpiece coordinate system and the tool coordinate system can be described as follows [19]: In Equation (1), the point (x c , y c , z c ) is any point within the tool coordinate system and the point (x w , y w , z w ) is any point within the workpiece coordinate system. The origin of the tool coordinate system was taken as (x 0 , y 0 , z 0 ) and the diameter of the tool was represented by R. In order to determine the contact range between the rake face and the chip, the tool and workpiece coordinate system should first be established. As shown in Figure 9, the workpiece coordinate system was represented by XwYwZw, so the position of the workpiece could be determined in accordance with this coordinate system. The tool coordinate system was represented by XcYcZc, and the coordinate origin was taken as the tool tip. The transformation relationship between the workpiece coordinate system and the tool coordinate system can be described as follows [19]: In Equation (1), the point (xc, yc, zc) is any point within the tool coordinate system and the point (xw, yw, zw) is any point within the workpiece coordinate system. The origin of the tool coordinate system was taken as (x0, y0, z0) and the diameter of the tool was represented by R. Figure 9. Workpiece and tool coordinate system [20].
In order to simplify the geometrical model, the surface formed by the former tool path should be regarded as part of a cylindrical surface, and the cycloid trajectory of the point on the tool edge should be regarded as a circular trajectory [21]. The angle of inclination of the workpiece was represented by angle a, while the feed rate of each tooth was much smaller than the radius R of the tool. The contact surface between the ball-end milling tool and the workpiece could thus be simplified as part of a spherical surface. Figure 12 shows the contact area between the tool and the workpiece, and each of the related surfaces can be expressed as follows: (1) The surface generated by the former tool path: (2) The surface formed by the pass of the previous tool tooth: (3) The contact area between tool and workpiece: x y z R + + = In order to simplify the geometrical model, the surface formed by the former tool path should be regarded as part of a cylindrical surface, and the cycloid trajectory of the point on the tool edge should be regarded as a circular trajectory [21]. The angle of inclination of the workpiece was represented by angle a, while the feed rate of each tooth was much smaller than the radius R of the tool. The contact surface between the ball-end milling tool and the workpiece could thus be simplified as part of a spherical surface. Figure 12 shows the contact area between the tool and the workpiece, and each of the related surfaces can be expressed as follows: (1) The surface generated by the former tool path: (x − a e cos a) 2 + (z + a e cos a) 2 = R 2 (9) (2) The surface formed by the pass of the previous tool tooth: (3) The contact area between tool and workpiece: (4) The un-machined surface: (5) The surface generated by the current tool path: The contact relationship between the ball-end milling tool and the workpiece during the milling process is shown in Figure 10. The contact area is defined by three arcs: arc AD, arc DB, and arc BA.
These three curves correspond to the intersection of two surfaces. Three simultaneous expressions corresponding to these curves are as follows: (1) Arc AD a e [a e + 2z sin a − 2x cos a] − y 2 = 0 (14) (3) Arc BA Figure 10b shows the contact area in the plane X c -Z. The coordinate system of one of the tool's teeth is described as C'X c 'Y c 'Z c ', and the coordinate system of the other tooth is described as CX c Y c Z c . The projection of any two adjacent tracks onto the plane of X c -Y c is shown in Figure 10c. In the figure, a p represents the cutting depth. According to a geometric analysis of the contact area between the tool and the workpiece, the area enclosed by the functions representing the boundary curves (the simplified cutting area) is area ABD as shown in Figure 10a. (5) The surface generated by the current tool path: 2 2 2 x z R + = (13) The contact relationship between the ball-end milling tool and the workpiece during the milling process is shown in Figure 10. The contact area is defined by three arcs: arc AD, arc DB, and arc BA. These three curves correspond to the intersection of two surfaces. Three simultaneous expressions corresponding to these curves are as follows: (  Figure 10. Milling process of a ball-end milling tool [20]. Figure 10b shows the contact area in the plane Xc-Z. The coordinate system of one of the tool's teeth is described as C'Xc'Yc'Zc', and the coordinate system of the other tooth is described as CXcYcZc. The projection of any two adjacent tracks onto the plane of Xc-Yc is shown in Figure 10c. In the figure, ap represents the cutting depth. According to a geometric analysis of the contact area between the tool and the workpiece, the area enclosed by the functions representing the boundary curves (the simplified cutting area) is area ABD as shown in Figure 10a.
The area of the micro-textured design can be obtained by considering the chip deformation and the spatial relationship between the chip, the cut-in, and the cut-out of the cutting tool. In this study, we needed to determine the farthest distance between the tool edge and the tool tip at the contact area, so that we could more accurately get the position of the contact area between the rake face of the ball-end milling tool and the chip. As shown in Figure 11, the intersection point A between the maximum effective cutting radius AD and the tool edge is the point of interest. When the tool is milling up an incline of a specific angle, the tool edge of the ball-end milling tool in the cutting area Figure 10. Milling process of a ball-end milling tool [20].
The area of the micro-textured design can be obtained by considering the chip deformation and the spatial relationship between the chip, the cut-in, and the cut-out of the cutting tool. In this study, we needed to determine the farthest distance between the tool edge and the tool tip at the contact area, so that we could more accurately get the position of the contact area between the rake face of the ball-end milling tool and the chip. As shown in Figure 11, the intersection point A between the maximum effective cutting radius AD and the tool edge is the point of interest. When the tool is milling up an incline of a specific angle, the tool edge of the ball-end milling tool in the cutting area is the segment AB and the maximum effective cutting radius AD is associated with the angle φ 1 + φ 2 , where φ 2 can be expressed as: The maximum effective cutting radius AD of the ball-end milling tool can be expressed as [22]: We know that in the process of milling titanium alloys with a ball-end milling tool, if contact between the chip and the rake face is incomplete, the chip will curl at a specific angle. If the area of action between the tool and the workpiece is projected onto the rake face, the maximum cutting radius can be approximated as the boundary of the cutting area. The distribution of the micro-textured area designed in this research is roughly fan-shaped, as shown in Figure 12.

Optimal Area Ratio of Micro Textures in Contact Area between Tool and Chip
As can be observed in Figure 13a,b, in the micro-textured tools with blunt and chamfer tool edges, the length and width of the severe abrasion area were approximately 1.7 mm and 0.745 mm. The total abrasion area was a curved sector surrounded by micro textures. To simplify the calculation, the curved sector was equivalent to a parallelogram. Therefore, the ratio of the micro textures in the severe wear area could be determined as follows: (19) where l is the distance between the first row of the micro textures and tool edge, and r is the micro-textured radius. Equation (19) indicates that the area occupancy decreases with an increase in l1, increases with an increase in r, and decreases with an increase in l. Figure 11. Effective cutting radius when milling an inclined plane [20].
We know that in the process of milling titanium alloys with a ball-end milling tool, if contact between the chip and the rake face is incomplete, the chip will curl at a specific angle. If the area of action between the tool and the workpiece is projected onto the rake face, the maximum cutting radius can be approximated as the boundary of the cutting area. The distribution of the micro-textured area designed in this research is roughly fan-shaped, as shown in Figure 12.
is the segment AB and the maximum effective cutting radius AD is associated with the angle 2 1 φ φ + , where 2 φ can be expressed as: The maximum effective cutting radius AD of the ball-end milling tool can be expressed as [22]: We know that in the process of milling titanium alloys with a ball-end milling tool, if contact between the chip and the rake face is incomplete, the chip will curl at a specific angle. If the area of action between the tool and the workpiece is projected onto the rake face, the maximum cutting radius can be approximated as the boundary of the cutting area. The distribution of the micro-textured area designed in this research is roughly fan-shaped, as shown in Figure 12.

Optimal Area Ratio of Micro Textures in Contact Area between Tool and Chip
As can be observed in Figure 13a,b, in the micro-textured tools with blunt and chamfer tool edges, the length and width of the severe abrasion area were approximately 1.7 mm and 0.745 mm. The total abrasion area was a curved sector surrounded by micro textures. To simplify the calculation, the curved sector was equivalent to a parallelogram. Therefore, the ratio of the micro textures in the severe wear area could be determined as follows: From the above, it can be concluded that, under the effects of the micro textures, lp increases, lf decreases, the proportion of lp increases gradually, the proportion of lf decreases gradually, and the cutting force in this region is calculated from Equation (6). Moreover, when r increases and l1 decreases, the length lp increases gradually. Let lp = k × lf (0 < k < 1); then, according to Equation (6) (20) where aw, σs, and τs, ζ are related to the material properties. Therefore, the resultant force is mainly affected by the value of k. From the resultant force of fh, the increase in k causes fjm to decrease and ffd to increase. It is not difficult to observe that, with the increase in k, the decrease in the resultant force of fh is greater than the increase, so the resultant force of fh decreases with the increase in k. Relevant studies have demonstrated that the sizes of micro textures vary from tens to hundreds of microns. Following optimization, the micro-textured diameters ranged from 30 to 70 μm, the distance between two adjacent micro textures ranged from 125 to 225 μm, and the distance between the micro textures and tool edge ranged from 90 to 130 μm [23]. The range of pz could be solved by Equation (19). When l1 and l were the maximum values and r was the minimum value, pz was From the above, it can be concluded that, under the effects of the micro textures, l p increases, l f decreases, the proportion of l p increases gradually, the proportion of l f decreases gradually, and the cutting force in this region is calculated from Equation (6). Moreover, when r increases and l 1 decreases, the length l p increases gradually. Let l p = k × l f (0 < k < 1); then, according to Equation (6), we can obtain: where a w , σ s , and τ s , ζ are related to the material properties. Therefore, the resultant force is mainly affected by the value of k. From the resultant force of f h , the increase in k causes f jm to decrease and f fd to increase. It is not difficult to observe that, with the increase in k, the decrease in the resultant force of f h is greater than the increase, so the resultant force of f h decreases with the increase in k.
Relevant studies have demonstrated that the sizes of micro textures vary from tens to hundreds of microns. Following optimization, the micro-textured diameters ranged from 30 to 70 µm, the distance between two adjacent micro textures ranged from 125 to 225 µm, and the distance between the micro textures and tool edge ranged from 90 to 130 µm [23]. The range of p z could be solved by Equation (19). When l 1 and l were the maximum values and r was the minimum value, p z was minimal, and its value was 1.72%. When l 1 and l were the minimum values and r was the maximum value, p z was maximal and its value was 25.4%.
To study the relationship between p z and one of the parameters l 1 , r, and l, the other two parameters were regarded as fixed values.
where a, b, c, d, e, f, g, and h are constant. When l 1 decreases, r increases and l decreases, while k increases. Because l 1 decreases, r increases, and l decreases, p z also increases. Therefore, suppose that a functional relationship exists between p z and k. Because the influence of p z on k is affected by r, l 1 , and l, the relationship between p z and k is a quadratic function: where a 1 , b 1 , and c 1 are constant. Equation (21) indicates that a 1 is related to l 1 , b 1 is related to r, and c 1 is related to l. When p z increases, k first increases and then decreases; when p z = b 1 , k takes the maximum value of c 1 , which indicates that when p z increases, f h first decreases and then increases, the minimum value of f h exists, and r exhibits the maximum value. The range of p z varies from 8.95% to 21.3% when introducing the variables into Equations (21) and (22).

Construction of Experimental Platform
In this experiment, the VDL-1000E three-axis vertical milling machine was used for processing. A Kistler 9257 dynamometer was used to measure the milling force. The material used was Ti6Al4V titanium alloy. The workpiece dimensions were 160 mm × 22 mm × 85 mm. It has been found that the tool can achieve superior cutting performance when the inclination angle is 15 • and the milling mode is down milling [24], as indicated in Figure 14. The orthogonal test was employed, and the effects of various factors, such as the micro-textured diameters, the distance between the micro textures and tool edge, and the distance between two adjacent micro textures, on the cutting force and cutting temperature of the ball-end milling tool during the processing of the titanium alloys were considered.
The micro texture of YG8 carbide ball-end milling cutter with diameter of 20 mm, rake angle of 0 • and relief angle of 11 • is prepared by using fiber laser. The cutter size is shown in Figure 15. The cutting parameters are shown in Table 7. A total of 25 experimental groups were designed. titanium alloy. The workpiece dimensions were 160 mm × 22 mm × 85 mm. It has been found that the tool can achieve superior cutting performance when the inclination angle is 15° and the milling mode is down milling [24], as indicated in Figure 14. The orthogonal test was employed, and the effects of various factors, such as the micro-textured diameters, the distance between the micro textures and tool edge, and the distance between two adjacent micro textures, on the cutting force and cutting temperature of the ball-end milling tool during the processing of the titanium alloys were considered. The micro texture of YG8 carbide ball-end milling cutter with diameter of 20 mm, rake angle of 0° and relief angle of 11° is prepared by using fiber laser. The cutter size is shown in Figure 15. The cutting parameters are shown in Table 7. A total of 25 experimental groups were designed. Figure 14. Titanium alloy processing method. Figure 14. Titanium alloy processing method.
mode is down milling [24], as indicated in Figure 14. The orthogonal test was employed, and the effects of various factors, such as the micro-textured diameters, the distance between the micro textures and tool edge, and the distance between two adjacent micro textures, on the cutting force and cutting temperature of the ball-end milling tool during the processing of the titanium alloys were considered. The micro texture of YG8 carbide ball-end milling cutter with diameter of 20 mm, rake angle of 0° and relief angle of 11° is prepared by using fiber laser. The cutter size is shown in Figure 15. The cutting parameters are shown in Table 7. A total of 25 experimental groups were designed.

Analysis of Experimental Results
When the diameter and distance between two adjacent micro textures change, the proportion of micro textures in the contact area between the tool and chip differs. Table 8 displays the proportions of the micro-textured area in the contact area. Taking the milling force as an evaluation criterion, the role of the micro textures under different proportions was studied, and the proportion of the micro-textured areas, which can improve the cutting performance of the tools, was obtained. As illustrated in Figure 16, when the proportion of the micro textures under the action of the blunt tool edge was 2% to 7% in the contact area, the milling force was greater than that of the non-textured tool. This is because the micro-textured diameters were excessively small, the anti-friction and anti-wear effects were small, and the surface roughness of the tool was relatively increased, resulting in an increase in the milling force. When the proportion of the micro textures was between 14% and 21%, the secondary cutting phenomenon was serious owing to the dense micro textures, the tool surface roughness was excessive, and the milling force was also greater than that of the non-textured tool. Therefore, the optimal proportion of the micro textures of the blunt edge in the contact area was approximately 7% to 14%. As illustrated in Figure 17, when the proportion of the micro textures under the action of the chamfer tool edge in the contact area was 2% to 9%, the milling force was mostly greater than that of the non-textured tool, and when the proportion of the micro textures was between 11% and 21%, the milling force was greater than that of the non-textured tool. Thus, the optimal proportion of the micro textures under the action of the chamfer tool edge in the contact area was approximately 9% to 11%. The reasons for the above phenomena are the same as those of the micro-textured ball-end milling tool with the blunt tool edge. As the experimental results are basically consistent with the theoretical analysis, it is proven that the area occupancy of the micro textures in the contact area will affect the bonding and slip area lengths, thereby influencing the milling force when micro textures are placed on the rake face of the ball-end milling tool.

Conclusions
(1) A platform was established for friction and wear tests. The anti-wear mechanism of the micro-pit textures was obtained. Abrasive impurities could be stored at different stages of the test, and grain refinement occurred in the surroundings of the micro textures under the influence of laser energy, thereby increasing the hardness of the materials. The anti-friction mechanism of the micro-pit textures was that the insertion of the micro-pit textures increased the normal stress of the tool edge, increased the ratio of the bonding area length to the total length of the contact area, decreased the friction coefficient of the contact area, and decreased the friction of the rake face. This method accurately reveals the anti-wear and anti friction mechanism of micro texture from the view of external friction theory and microcosmic theory.
(2) Based on the milling force, the optimal proportion of the micro textures on tool rake face was determined to be 8.95% to 21.3%. The accuracy of this proportion was verified experimentally, thereby providing a reference for design of micro-textured tool and improving the cutting performance of hard metal tools.
(3) In follow-up work, the optimal proportion of micro textures can also be considered from the perspectives of milling force, workpiece integrity quality and tool wear, in order to make the research more comprehensive.
Milling Force(N) Number 2%-9% Figure 17. Proportion of micro-textured area in contact area of ball-end milling tool with chamfer tool edge.

Conclusions
(1) A platform was established for friction and wear tests. The anti-wear mechanism of the micro-pit textures was obtained. Abrasive impurities could be stored at different stages of the test, and grain refinement occurred in the surroundings of the micro textures under the influence of laser energy, thereby increasing the hardness of the materials. The anti-friction mechanism of the micro-pit textures was that the insertion of the micro-pit textures increased the normal stress of the tool edge, increased the ratio of the bonding area length to the total length of the contact area, decreased the friction coefficient of the contact area, and decreased the friction of the rake face. This method accurately reveals the anti-wear and anti friction mechanism of micro texture from the view of external friction theory and microcosmic theory.
(2) Based on the milling force, the optimal proportion of the micro textures on tool rake face was determined to be 8.95% to 21.3%. The accuracy of this proportion was verified experimentally, thereby providing a reference for design of micro-textured tool and improving the cutting performance of hard metal tools.
(3) In follow-up work, the optimal proportion of micro textures can also be considered from the perspectives of milling force, workpiece integrity quality and tool wear, in order to make the research more comprehensive.