Optimization of Texture Density Distribution of Carbide Alloy Micro-Textured Ball-End Milling Cutter Based on Stress Field

Minli Zheng; Chunsheng He; Shucai Yang

doi:10.3390/app10030818

Optimization of Texture Density Distribution of Carbide Alloy Micro-Textured Ball-End Milling Cutter Based on Stress Field

Zheng, Minli;He, Chunsheng;Yang, Shucai 2020-01-23 00:00:00 applied sciences Article Optimization of Texture Density Distribution of Carbide Alloy Micro-Textured Ball-End Milling Cutter Based on Stress Field Minli Zheng, Chunsheng He and Shucai Yang * Key Laboratory of Advanced Manufacturing and Intelligent Technology, Ministry of Education, Harbin University of Science and Technology, Harbin 150080, China; minli456456@163.com (M.Z.); hechunsheng0118@163.com (C.H.) * Correspondence: yangshucai@hrbust.edu.cn Received: 6 December 2019; Accepted: 20 January 2020; Published: 23 January 2020 Abstract: The insertion of micro-textures plays a role in reducing friction and increasing wear resistance of the cutters, which also has a certain impact on the stress ﬁeld of the cutter during milling. Therefore, in order to study the mechanisms of friction reduction and wear resistance of micro-textured cutters in high speed cutting of titanium alloys, the dynamic characteristics of the instantaneous stress ﬁeld during the machining of titanium alloys with micro-textured cutters were studied by changing the distribution density of the micro-textures on the cutter. First, the micro-texture insertion area of the ball-end milling cutter was theoretically analyzed. Then, variable density micro-textured ball-end milling cutters and non-texture cutters were used to cut titanium alloy, and the mathematical model of milling force and cutter-chip contact area was established. Then, the stress density functions of dierent micro-texture density cutters and non-texture cutters were established to simulate the stress ﬁelds of variable density micro-textured ball-end milling cutters and non-texture cutters. Finally, the genetic algorithm was used to optimize the variable density distribution of micro-textured cutters in which the instantaneous stress ﬁeld of the cutters was taken as the optimization objective. The optimal solution for the variable density distribution of the micro-textured cutter in the cutter-chip tight contact area was obtained as follows: the texture distribution densities in the ﬁrst, second, and third areas are second, and third areas are 0.0905, 0.0712, and 0.0493, respectively. Keywords: variable density; micro-textured ball-end milling cutter; high speed cutting; stress ﬁeld; genetic algorithm 1. Introduction In recent years, titanium alloy materials have been widely used in aerospace, shipbuilding, metallurgy, light industry, chemical industry, biomedical and other industries due to their excellent physical and chemical properties. However, the low thermal conductivity and high chemical activity of titanium alloys lead to severe tool wear and low cutting eciency, which are the main factors limiting the development of titanium alloys. In the ﬁeld of tribology, uneven surfaces have the function of reducing friction, and have received unprecedented attention. Therefore, the basic concept of surface texture is proposed. Preparing regularly arranged micro pits or grooves on smooth and susceptible surfaces can greatly reduce the friction and surface abrasion [1–3]. Micro-textures also play an active role in the ﬁeld of modern cutting tools. Milling titanium alloys is intermittent, and cutting process of the cutter is very complicated. The cutting force on the cutter is unevenly distributed during the milling process, and its size and direction change with time. The distribution of the milling force directly aects the stress distribution inside the Appl. Sci. 2020, 10, 818; doi:10.3390/app10030818 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 818 2 of 20 milling insert. Therefore, it is necessary to study the stress ﬁeld of the cutter during the cutting process in order to obtain the worst conditions of the cutter. Cheng and Li studied the stress density function and stress ﬁeld of the corrugated edge milling cutter and concluded that, during the cutting process of the corrugated edge milling cutters, the stress on the cutter is mainly distributed on the main cutting edge near the tip, and the stress is concentrated near the tip [4,5]. Fan et al. studied the cutting stress ﬁeld of ceramic tools with a gradient function by ﬁnite element analysis and obtained the optimal gradient distribution index by modeling the cutting stress ﬁeld under the same cutting load [6,7]. Li et al. carried out milling force prediction experiments on the titanium alloy TC21. The results show that, in the process of high-speed milling TC21 titanium alloy, the cutting depth and feed per tooth have a greater impact on the cutting force, while the cutting speed and radial cutting depth have no signiﬁcant eect on the cutting force [8,9]. Kim and Ehmann simulated the static and dynamic milling force in the face milling process. Based on the machine tool structure and ﬁxture design, a mathematical model of the scattered force components of the face milling cutter was established. Consistent results were obtained from cutting experiments on dierent milling cutters and workpiece materials [10]. Wertheim et al. studied the performance of spiral and serrated edge milling inserts in the cutting process. They believed that curved-edge milling inserts can improve the stability of machining, reduce milling forces and improve chip ﬂow [11]. Guo et al. numerically modeled and experimentally studied the micro-milling force of titanium alloy based on tool runout. The micro-milling force model was validated by analyzing the width of the steps on the edge of the groove [12,13]. Zhang simulated the stress ﬁeld of a ﬂat-faced milling cutter and a 3D complex groove milling cutter using the density function of the milling force as a boundary condition. It was found that a milling cutter with a rake angle and an edge inclination can fundamentally change the stress at the tool tip [14,15]. Sun et al. fabricated micro-grooves and micro-pits on the rake face of WC/Co tools, and then studied the cutting performance of the tools. The results show that the composite texture with micro-pits and micro-slots can be used as a micro-reservoir to continuously supplement lubricating oil, thus improving the cutting performance of the mixed micro-textured cutter [16–18]. Wei et al. conducted tribological and cutting experiments on aluminum alloy workpieces by sandblasting micro-materials and machining micro-geometric features of the rake face of the sapphire tools. The results show that, compared with traditional tools, the micro-textured tool edge has the lowest interfacial friction and the cutting force is signiﬁcantly reduced. Machining micro-textures on the rake face of the cutter can reduce the adhesion of the workpiece material [19]. Pang et al. prepared symmetric conical micro-grooves and parallel micro-grooves on carbide cutters, and then studied the friction performance of the cutters [20]. Lin et al. modeled the cutting force of the vertical milling cutter under the conditions of oblique cutting and proposed a mechanical model for predicting the cutting force of the vertical milling cutters [21]. Li et al. used a multi-level fuzzy comprehensive evaluation method based on multi-objective decision theory to evaluate the cutting performance of micro-textured cutters in titanium alloy processing [22]. Darshan studied the improvement of tribology and thermal environment of inconel-718 alloy by textured tools. The results reveal that the textured tools perform better, ensuring lower tool wear (VB), reduced cutting forces (Fc), lower surface roughness (Ra) and acceptable chip form [23,24]. In summary, placing micro-textures on the surface of a tool to improve the friction reduction and wear resistance of the tool has become a hot topic. However, in the process of milling titanium alloys, there is still a lack of theoretical research and experimental basis for in-depth study of the anti-wear and friction reduction mechanism of micro-textured cutters. Problems such as “secondary cutting” still exist during the cutting process of micro-textured cutters. Reasonable micro-texture arrangement can make the cutters have good anti-wear and anti-friction performance, and it can also solve the secondary wear problem of the micro-textured cutters, thereby improving the processing eciency. Therefore, in this paper, by changing the single density distribution of the micro-texture in the cutter-chip close contact area, the change of the tool stress ﬁeld during cutting titanium alloys with the variable density micro-textured cutter was studied. Based on the stress ﬁeld, the texture variable density distribution of the micro-textured ball-end milling cutters was optimized. Appl. Sci. 2020, 10, 818 3 of 20 Appl. Sci. 2020, 10, 818 3 of 20 2. Experiment of Milling Titanium Alloy with the Variable Density Micro-Textured Ball-End 2. Experiment of Milling Titanium Alloy with the Variable Density Micro-Textured Ball-End Milling Cutter Milling Cutter 2.1. Design and Fabrication of Variable Density Micro-Textures 2.1. Design and Fabrication of Variable Density Micro-Textures Previo Previous us stud studies ies ofof mic micr ro-t o-textur extureded cutt cutters ers used used a una iform uniform distribut distribution ion method method to prepto are pr micr epar oe - textures in the areas where the cutter-chips are in close contact [25,26]. However, from the tool wear micro-textures in the areas where the cutter-chips are in close contact [25,26]. However, from the tool diagr wearam diagram of the of micro the -micr textured o-textur cutt ed ers cutters after cutt after ing cutting titanium titanium alloy, ialloy t can , be it can seen be th seen at ththat e wear the of wear the tool along the contact length and width of the cutter-chip in the compact contact area of the rake face of the tool along the contact length and width of the cutter-chip in the compact contact area of the is rake irregul facear. is T irr he egular wear. ne The ar th wear e cutt ne ing ar the edge cutting is more edge severe is mor , and e, sever as the e,dis and, tance as fr the om distance the cuttin from g edge the gets longer, the wear on the tool becomes less and less [27]. There is also some wear in the direction cutting edge gets longer, the wear on the tool becomes less and less [27]. There is also some wear in the of dir chip ection outfl of chip ow. Th outﬂow is is bec . This ause is , d because, uring the during outflow the of outﬂow chips, of the chips, cutting thespee cutting d of speed the ball of-en the d ball-end milling cutter along the cutting edge is different, which leads to the transverse curl of the chip. As the cutting milling cutter along the cutting edge is dierent, which leads to the transverse curl of the chip. As the dept cutting h incre depth ases, incr theases, e flow the rate ﬂow at th rate e boat ttom the of bottom the chi of p the is dchip ifferent is di from erent flow from rateﬂow at thrate e top at , an the d top, the chip curls upward. Therefore, in the process of chip deformation, “secondary cutting” occurs at the and the chip curls upward. Therefore, in the process of chip deformation, “secondary cutting” occurs edges of the micro-texture, as shown in Figure 1. This phenomenon will cause secondary wear of at the edges of the micro-texture, as shown in Figure 1. This phenomenon will cause secondary wear micro-textured cutters. of micro-textured cutters. Figure 1. Diagram of “secondary cutting” for the micro-textured cutter. Figure 1. Diagram of “secondary cutting” for the micro-textured cutter. In In order order to to so solve lve th the e “ “secondary secondary cutt cutting” ing” ph phenomenon enomenon of of th the e micr micro o-textur -textured ed c cutter utter, , th the e reg region ion where the cutter-chip is in compact contact is divided into three regions according to the wear condition where the cutter-chip is in compact contact is divided into three regions according to the wear con of the dition cutter of, tnamely he cutter, the nﬁrst amely ar ea the Xfi,rst the are second a X1, th are ea secon X , and d arthe ea X thir 2, and d ar th eae X th,ir as d ar shown ea X3, in as Figur shown e 2 . 1 2 3 Studies have shown that pit texture can eectively reduce friction and wear [28,29]. Therefore, by in Figure 2. Studies have shown that pit texture can effectively reduce friction and wear [28,29]. Th changing erefore, the by density changing of micr the o-textur density e of inm each icro-rtex egion, ture the in dynamic each regievolution on, the dynamic of secondary evolution cutting of between micro-textured cutter and the chip was studied. Experiments have shown that a texture secondary cutting between micro-textured cutter and the chip was studied. Experiments have shown th distribution at a texture density distribution (the ratio density of the (thtotal e ratio area of of the the total pit area textur of eth to e the pit tex total ture area to of the the total micr aro-textur ea of the e preparation is deﬁned as the texture distribution density) between 0.05 and 0.1 can play a better role in micro-texture preparation is defined as the texture distribution density) between 0.05 and 0.1 can pla reducing y a better friction role in and reduc wear ing . The friction refor e, anthe d wea micr r. o-textur Therefore, e densities the micro in-tex theture cutter de-chip nsities contact in the ar cutt eaer of - the cemented carbide tool designed in this paper are 0.05, 0.07 and 0.09, respectively. By arranging chip contact area of the cemented carbide tool designed in this paper are 0.05, 0.07 and 0.09, respect and combining ively. By the arrang three ing textur and ecom densities bining in ththe e th cutter ree tex -chip ture compact densities contact in the ar cutt ea,er thr -chip ee uniformly compact distributed micro-textures and six variable density micro-textures were obtained. The distribution contact area, three uniformly distributed micro-textures and six variable density micro-textures were ob combination tained. Theof dithe stribution texturecom density bination is shown of the intex Table ture1 density . is shown in Table 1. Appl. Sci. 2020, 10, 818 4 of 20 Appl. Sci. 2020, 10, 818 4 of 20 Figure 2. Region segmentation of cutter-chip compact contact area of micro-textured cutter. Figure 2. Region segmentation of cutter-chip compact contact area of micro-textured cutter. Table 1. Distribution and combination of dierent density textures. Table 1. Distribution and combination of different density textures. Distribution of Arrangement and Combination of Micro-Texture Distribution of Micro-Texture Arrangement and Combination of Micro-Texture Micro-Texture Uniform distribution 0.05-0.05-0.05, 0.07-0.07-0.07, 0.09–0.09–0.09 Uniform distribution 0.05-0.05-0.05, 0.07-0.07-0.07, 0.09–0.09–0.09 0.05-0.07-0.09, 0.05-0.09-0.07, 0.07-0.05-0.09, Variable density distribution 0.05-0.07-0.09, 0.05-0.09-0.07, 0.07-0.05-0.09, 0.07-0.09-0.05, 0.09-0.07-0.05, 0.09-0.07-0.05. Variable density distribution 0.07-0.09-0.05, 0.09-0.07-0.05, 0.09-0.07-0.05. According to previous studies, when the diameter, depth and distance from the cutting edge of According to previous studies, when the diameter, depth and distance from the cutting edge of the micro-texture are 50 m, 35 m and 120 m, respectively, the micro-textured cutter can achieve the micro-texture are 50 μm, 35 μm and 120 μm, respectively, the micro-textured cutter can achieve better friction reduction and wear resistance [30]. Therefore, the diameter, depth and distance from the better friction reduction and wear resistance [30]. Therefore, the diameter, depth and distance from cutting edge of the micro-texture designed in this paper are 50 m, 35 m and 120 m, respectively. the cutting edge of the micro-texture designed in this paper are 50 μm, 35 μm and 120 μm, According to the three densities of 0.05, 0.07 and 0.09, the center spacing between the micro-textures are respectively. According to the three densities of 0.05, 0.07 and 0.09, the center spacing between the 190 m, 170 m and 150 m, respectively. The micro-textures were then prepared in three areas of the micro-textures are 190 μm, 170 μm and 150 μm, respectively. The micro-textures were then prepared cutter-chip compact contact by using a ﬁber laser. After processing, the melt around the micro-texture in three areas of the cutter-chip compact contact by using a fiber laser. After processing, the melt was cleaned by sandpaper and an ultrasonic cleaner. around the micro-texture was cleaned by sandpaper and an ultrasonic cleaner. 2.2. Design of Test Scheme and Test Equipment 2.2. Design of Test Scheme and Test Equipment 2.2.1. Design of Test Scheme 2.2.1. Design of Test Scheme In this paper, an orthogonal experiment was used to design the experiment of milling titanium In this paper, an orthogonal experiment was used to design the experiment of milling titanium alloy with a micro-textured ball-end milling cutter. By changing cutting parameters, the change of alloy with a micro-textured ball-end milling cutter. By changing cutting parameters, the change of milling force with time and the change of tool-chip contact length and width with the feed and cutting milling force with time and the change of tool-chip contact length and width with the feed and cutting depth were studied. The orthogonal test was designed to include three factors (cutting speed, cutting depth were studied. The orthogonal test was designed to include three factors (cutting speed, cutting depth and feed rate), which contained four levels, as shown in Table 2. L (4 ) was selected in the depth and feed rate), which contained four levels, as shown in Table 2. L16 (4 ) was selected in the orthogonal table for the milling test. orthogonal table for the milling test. Table 2. Cutting parameters for cutting titanium alloys. Table 2. Cutting parameters for cutting titanium alloys. Factor Cutting Depth Cutting Speed Feed per Tooth Factor Cutting Speed Cutting Depth Feed per Tooth a (mm) Level v (m/min) p f (mm/z) c z Level vc (m/min) ap (mm) fz (mm/z) 1 120 0.3 0.04 1 120 0.3 0.04 2 140 0.5 0.06 2 140 0.5 0.06 3 160 0.7 0.08 3 4 160 180 0.7 0.9 0.10 0.08 4 180 0.9 0.10 Appl. Sci. 2020, 10, 818 5 of 20 Appl. Sci. 2020, 10, 818 5 of 20 According to the arrangement and distribution of textures with different densities, nine combinations were obtained, corresponding to nine micro-texture cutters, and then a non-texture According to the arrangement and distribution of textures with dierent densities, nine cutter was used for comparative analysis. Milling titanium alloy test was carried out for each cutter combinations were obtained, corresponding to nine micro-texture cutters, and then a non-texture cutter according to Table 2. Each cutter was tested in 16 groups, and one layer was milled on the workpiece was used for comparative analysis. Milling titanium alloy test was carried out for each cutter according for each set of cutting parameters. Six points were averaged along the length of the workpiece, and a to Table 2. Each cutter was tested in 16 groups, and one layer was milled on the workpiece for each set set of cutting force values were measured at each point location. Then, by averaging six sets of data of cutting parameters. Six points were averaged along the length of the workpiece, and a set of cutting in each layer, the cutting force values in the X, Y, and Z directions for each set of cutting parameters force values were measured at each point location. Then, by averaging six sets of data in each layer, were calculated. This is the basic data for the next calculation of the cutting force test formula. At the the cutting force values in the X, Y, and Z directions for each set of cutting parameters were calculated. same time, the position of the center point was taken to measure the value of the milling force varying This is the basic data for the next calculation of the cutting force test formula. At the same time, the with time. position of the center point was taken to measure the value of the milling force varying with time. 2.2.2. Test Equipment 2.2.2. Test Equipment In this experiment, a VDL-1000E four-axis CNC milling machine (Dalian Machine Tool, Dalian, In this experiment, a VDL-1000E four-axis CNC milling machine (Dalian Machine Tool, Dalian, China) was used for milling titanium alloy test. The test material was titanium alloy TC4, and the China) was used for milling titanium alloy test. The test material was titanium alloy TC4, and the cutter was a micro-textured ball-end milling cutter. Sinusoidal tongs were used to clamp the cutter was a micro-textured ball-end milling cutter. Sinusoidal tongs were used to clamp the workpiece workpiece at an inclined angle of 15 degrees. In the case of planar milling, the tool bit always at an inclined angle of 15 degrees. In the case of planar milling, the tool bit always participates in participates in cutting, and the linear speed is always zero. This will accelerate the wear of the tool cutting, and the linear speed is always zero. This will accelerate the wear of the tool bit, reduce the bit, reduce the service life of the tool, and affect the quality of the machined surface of the workpiece. service life of the tool, and aect the quality of the machined surface of the workpiece. Some scholars Some scholars have found that when the processing angle of the workpiece is 15 degrees, the ball end have found that when the processing angle of the workpiece is 15 degrees, the ball end milling cutter milling cutter can achieve the best cutting performance [31,32]. The processing method adopted in can achieve the best cutting performance [31,32]. The processing method adopted in this paper was this paper was climb milling, and the established milling test platform is shown in Figure 3. The climb milling, and the established milling test platform is shown in Figure 3. The measurement of measurement of milling force was based on a Kistler 9257B dynamometer (Kistler, Winterthur, milling force was based on a Kistler 9257B dynamometer (Kistler, Winterthur, Switzerland) with a Switzerland) with a response frequency of 5000 Hz. The data acquisition system was the response frequency of 5000 Hz. The data acquisition system was the DH5922_1394 signal test and DH5922_1394 signal test and analysis system of Donghua testing company (Jingjiang, China). analysis system of Donghua testing company (Jingjiang, China). Figure 3. Test platform for milling titanium alloy with micro-textured cutter. Figure 3. Test platform for milling titanium alloy with micro-textured cutter. 2.3. Analysis of Milling Force Test Results 2.3. Analysis of Milling Force Test Results In the process of cutting titanium alloy by an orthogonal test, a dynamometer was used to In the process of cutting titanium alloy by an orthogonal test, a dynamometer was used to measure the change of cutting force of nine kinds of variable density micro-textured cutters and measure the change of cutting force of nine kinds of variable density micro-textured cutters and non- non-texture cutters with time. One of the micro-textured cutters with a texture density combination of texture cutters with time. One of the micro-textured cutters with a texture density combination of 0.09–0.09–0.09 is selected as an example. The cutting parameters are: n = 2729 r/min, a = 0.7 mm, f = p z 0.09–0.09–0.09 is selected as an example. The cutting parameters are: n = 2729 r/min, ap = 0.7 mm, fz = 0.08 mm/z, and the changes of the milling forces in the X, Y and Z directions of a milling cycle were 0.08 mm/z, and the changes of the milling forces in the X, Y and Z directions of a milling cycle were collected, as shown in Table 3. collected, as shown in Table 3. Appl. Sci. 2020, 10, 818 6 of 20 Table 3. Variation of milling force with time for micro-textured cutter. Milling Force in A Milling Cycle (s) the Three 0.0004 0.0008 0.0012 0.0016 0.002 0.0024 0.0028 0.0032 0.0036 Directions X(N) 3.15 50.46 122.33 235.85 305.37 226.94 78.26 9.34 0 Y(N) 14.92 77.98 156.15 220.8 284.28 229.1 156.22 12.44 0 Z(N) 17.87 65.51 103.94 136.53 147.88 126.03 79.28 10.63 0 A three-direction milling force data ﬁtting program was written with MATLAB software, and the equations of the three-direction milling force change over time were ﬁtted. The calculation results are 13 4 11 3 9 2 6 F = 7.106 10 t 5.567 10 t + 1.346 10 t 1.009 10 t + 231.1 13 4 11 3 8 2 5 F = 4.598 10 t + 3.656 10 t 8.69 10 t + 5.752 10 t 134.244 . (1) 13 4 11 3 8 2 5 F = 1.89 10 t 1.439 10 t + 3.075 10 t 1.329 10 t + 33.4 2.4. Analysis of Test Results of Cutter-Chip Contact Area Theoretically, the calculation of the contact area between the cutter and the chip is very complicated for the micro-textured ball-end milling cutter. Therefore, in the milling process, the contact diagram method was used to ﬁt the contact area between the ball-end milling cutter and the chip. After the milling, the titanium alloy, nine texture density combinations and non-texture cutters were observed through an ultra-depth microscopy, and the cutter-chip contact area on the front of the cutter was measured. The contact length and width of the cutter-chip contact were approximated by the contact diagram method. Taking a micro-textured cutter with a texture density combination of 0.09–0.09–0.09 as an example, the experimental data of the tool-chip contact length and width obtained by measuring and ﬁtting are shown in Table 4. Table 4. 0.09–0.09–0.09 contact length and width of micro-textured cutter. Cutting Parameters Cutting Depth Feed per Tooth Cutter-Chip Contact Cutter-Chip Contact a (mm) f (mm) Length l (mm) Number p Width l (mm) f z w 1 0.3 0.04 0.768 0.5302 2 0.3 0.06 0.775 0.5613 3 0.3 0.08 0.784 0.5888 4 0.3 0.1 0.788 0.6031 5 0.5 0.06 1.017 0.5691 6 0.5 0.04 1.008 0.5405 7 0.5 0.1 1.029 0.6124 8 0.5 0.08 1.021 0.5911 9 0.7 0.08 1.318 0.5928 10 0.7 0.1 1.327 0.6103 11 0.7 0.04 1.326 0.5445 12 0.7 0.06 1.315 0.5968 13 0.9 0.1 1.658 0.6179 14 0.9 0.08 1.651 0.5946 15 0.9 0.06 1.636 0.5675 16 0.9 0.04 1.628 0.5494 3. Force Density Function of Variable Density Micro-Texture Ball-End Milling Cutter 3.1. Milling Force Model of Micro-Textured Ball-End Milling Cutter The high-speed milling of titanium alloy by micro-textured ball-end milling cutter is intermittent cutting. With the change of the micro-textured cutter from cutting in to cutting out the workpiece, the magnitude and direction of the instantaneous milling force also change, which aects the stress ﬁeld distribution on the front of the cutter. Therefore, it is necessary to solve the milling cycle T, the angle Appl. Sci. 2020, 10, 818 7 of 20 of cutting into workpiece , the time of cutting into the workpiece t and the cutting time t of the in i 0 micro-textured ball-end milling cutter, respectively. The solution process is as follows: T = , (2) n z R a = 180 arccos , (3) in in t = T , (4) t = T t , (5) 0 i where n is the spindle speed (r/min), z is the number of teeth on the tool edge, and R is the tool edge radius. The main factors of cutting parameters aecting milling force are the cutting depth and feed per tooth. Therefore, an empirical formula model of milling force was established by using multiple linear regression method. The empirical formula model of the milling force is as follows: x x 1 2 F = C a f . (6) p z Taking the logarithm of both sides is lgF = lgC + x lga + x lg f . (7) p 2 z j 1 Let f = lgF , a = lgC, a = lga , a = lga , the linearization of Equation (7) is j 0 1 p 2 f f = a + a x + a x . (8) 0 1 1 2 2 The calculation and ﬁtting were performed using MATLAB software, and the milling force test data collected from the X, Y and Z directions of nine variable density combination cutters and non-textured cutters were substituted into the calculation. Taking a micro-textured cutter with a texture density combination of 0.09–0.09–0.09 as an example, the milling forces in the X, Y and Z directions measured by orthogonal tests are shown in Table 5. The experimental data in the table were substituted into MATLAB for calculation and solution, and the coecients and exponentials of the empirical formula for milling forces were obtained. The empirical formulae for the milling forces in three directions obtained by ﬁtting are 0.4685 0.4301 F = 1129.5 a f x p z 0.6881 0.3336 F = 866.99 a f . (9) y p z 0.6825 0.1807 F = 309.99 a f z p z Table 5. Test data and calculation results of milling force of micro-textured cutter. a f F F F p z x y z Number Lg(F ) lg(F ) lg(F ) lg(a ) lg(f ) x y z p z (mm) (mm/z) (N) (N) (N) 1 0.3 0.04 146.61 121.23 73.22 2.17 2.08 1.86 0.52 1.4 2 0.3 0.06 208.35 134.99 96.28 2.32 2.13 1.98 0.52 1.22 3 0.3 0.08 205.80 143.05 80.48 2.31 2.16 1.91 0.52 1.1 4 0.3 0.1 226.13 177.86 88.71 2.35 2.25 1.95 0.52 1 5 0.5 0.06 214.47 197.65 102.15 2.33 2.30 2.01 0.3 1.22 Appl. Sci. 2020, 10, 818 8 of 20 Table 5. Cont. a f F F F p z x y z Number Lg(F ) lg(F ) lg(F ) lg(a ) lg(f ) x y z p z (mm) (mm/z) (N) (N) (N) 6 0.5 0.04 230.43 227.16 139.25 2.36 2.36 2.14 0.3 1.4 7 0.5 0.1 416.26 389.46 135.73 2.62 2.59 2.13 0.3 1 8 0.5 0.08 222.35 216.19 99.25 2.35 2.33 2.00 0.3 1.1 9 0.7 0.08 305.37 284.28 147.88 2.48 2.45 2.17 0.15 1.1 10 0.7 0.1 408.36 296.41 162.39 2.61 2.47 2.21 0.15 1 11 0.7 0.04 238.45 208.29 110.56 2.38 2.32 2.04 0.15 1.4 12 0.7 0.06 348.95 315.82 164.58 2.54 2.50 2.22 0.15 1.22 13 0.9 0.1 355.73 333.41 196.27 2.55 2.52 2.29 0.05 1 14 0.9 0.08 328.63 304.18 200.08 2.52 2.48 2.30 0.05 1.1 15 0.9 0.06 293.05 302.13 178.88 2.47 2.48 2.25 0.05 1.22 16 0.9 0.04 280.62 293.06 152.83 2.45 2.47 2.18 0.05 1.4 3.2. Test Formula for Cutter-Chip Contact Area In the process of cutting titanium alloy with a micro-textured ball-end milling cutter, the milling force is distributed unevenly along the length and width of the cutter-chip contact, and the cutter-chip contact area directly aects the stress density function of the cutter surface. With the change of cutting parameters and texture density in the cutter-chip compact contact area, the cutter-chip contact area also changes. Therefore, it is necessary to solve the experimental formula of the cutter-chip contact area to determine the force density function of the variable density micro-textured ball-end milling cutter when milling titanium alloy. The experimental data of tool-chip contact length l and width l were ﬁtted and calculated by using MATLAB software. The relationships between l and feed per tooth f , as well as l and cutting depth a were linear functions. Taking a micro-textured cutter with a z w p texture density of 0.09–0.09–0.09 as an example, the obtained linear functions are f = 0.7808l 0.3824 z f . (10) a = 0.6872l 0.2181 p w Substituting Equation (10) into Equation (9), the milling forces for milling a titanium alloy using a micro-textured ball-end milling cutter with a texture density of 0.09–0.09–0.09 are 0.4301 0.4685 ( ) F = 1129.5 0.6872l 0.2181 0.7808l 0.3824 x w 0.3336 0.6881 . (11) F = 866.99 (0.6872l 0.2181) 0.7808l 0.3824 y w f 0.1807 0.6825 F = 309.99 (0.6872l 0.2181) 0.7808l 0.3824 z w 3.3. Establishment of Force Density Function for Variable Density Micro-Textured Cutter When micro-textured ball-end milling cutter cuts titanium alloy, the instantaneous milling forces in the three directions vary with time in the cutter-chip contact area, and the distributions along the cutter-chip contact length and width are uneven. Therefore, the second-order mixed partial derivative of the instantaneous milling force model was used to solve the force density function of the micro-textured ball-end milling cutter, and the instantaneous cutting force variation at a point on the cutter can be obtained by solving the force density function. By calculating the second-order mixed partial derivative of Equation (11), the force density functions of a micro-textured cutter with a texture density combination of 0.09–0.09–0.09 in the coordinate system of the machine tool can be obtained as follows: 0.5699 @F 0.5315 f = = 171.634(l 0.3174) l 0.4898 x w @l @l w f 0.6664 @F y 0.3119 f = = 141.565(l 0.3174) l 0.4898 , (12) y w @l @l w f 0.8193 @F 0.3175 f = = 28.301(l 0.3174) l 0.4898 z w @l @l w f Appl. Sci. 2020, 10, 818 9 of 20 l  1.072,1.929 l  0.5905, 0.6680     w f Appl. where Sci. 2020, 10, 818 , and . 9 of 20 The force density functions above of the micro-textured ball-end milling cutter are solved in the coordinate system of the machine tool. However, the magnitude and direction of the instantaneous where l 2 (1.072, 1.929), and l 2 (0.5905, 0.6680). w f cutting force of the micro-textured ball-end milling cutter change with the rotation of the cutter from The force density functions above of the micro-textured ball-end milling cutter are solved in the cutting in to cutting out the workpiece. The schematic diagram of the cutter from cutting in to cutting coordinate system of the machine tool. However, the magnitude and direction of the instantaneous out the workpiece is shown in Figure 4. Setting XYZ as the workpiece coordinate system and XcYcZc cutting force of the micro-textured ball-end milling cutter change with the rotation of the cutter as the tool coordinate system, Figure 4a shows the process from cutting in to cutting out of the micro- from tex cutting tured ba inll to -end cutting milliout ng cutt theer, workpiece. and Figure The 4bschematic shows the diagram relationship of the bet cutter ween fr th om e co cutting ordinate in to systems of the tool and the machine tool during the cutting process of the micro-textured cutter. It cutting out the workpiece is shown in Figure 4. Setting XYZ as the workpiece coordinate system and can be seen from the Figure 4 that the coordinate system of the micro-textured cutter changes with XcYcZc as the tool coordinate system, Figure 4a shows the process from cutting in to cutting out of the time during the process of cutting from point A to point B. Therefore, it is necessary to transform the micro-textured ball-end milling cutter, and Figure 4b shows the relationship between the coordinate milling force in the coordinate system of the machine tool to solve the force density function in the systems of the tool and the machine tool during the cutting process of the micro-textured cutter. It can coordinate system of the tool. According to the transformation relationship, its transformation matrix be seen from the Figure 4 that the coordinate system of the micro-textured cutter changes with time is during the process of cutting from point A to point B. Therefore, it is necessary to transform the milling force in the coordinate system of the machine tool to solve the force density function in the coordinate cos sin 0  system of the tool. According to the transformation relationship, its transformation matrix is  T sin cos 0 . (13)  2 3 6 cos sin 0 7 0 0 1 6 7  6 7 6 7 6 7 T = 6 sin cos 0 7. (13) 6 7 6 7 4 5 0 0 1 (a) (b) Figure 4. The schematic diagram of rotation period and coordinate system conversion diagram of Figure 4. The schematic diagram of rotation period and coordinate system conversion diagram of micro-textured cutter. (a) the process from cutting in to cutting out of the micro-textured ball-end micro-textured cutter. (a) the process from cutting in to cutting out of the micro-textured ball-end milling cutter; (b) the relationship between the coordinate systems of the cutter and coordinate system of the machine tool. Appl. Sci. 2020, 10, 818 10 of 20 According to the coordinate transformation of Equation (13), the force density function of the micro-textured cutter in the coordinate system of the cutter can be obtained as follows: 2 3 2 3 2 3 f f f cos + f sin 6 7 6 7 6 7 x x x y 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 f 7 = T 6 f 7 = 6 f sin + f cos 7, (14) y y x y 6 1 7 6 7 6 7 6 7 6 7 6 7 4 5 4 5 4 5 f f f z z z 0.5699 0.6664 0.5315 0.3119 f = 148.639(l 0.3174) l 0.4898 + 70.783(l 0.3174) l 0.4898 x w f w f 0.5699 0.6664 0.5315 0.3119 , (15) f = 85.817(l 0.3174) l 0.4898 122.599(l 0.3174) l 0.4898 y w f w f 0.8193 0.3175 f = 28.301(l 0.3174) l 0.4898 z w where = 150 . Similarly, the force density functions of the other eight texture density combination cutters and non-texture cutters were solved, and the force density functions are obtained as follows. The force density functions of a micro-textured cutter with a texture density combination of 0.09–0.07–0.05 are 0.5678 0.6458 0.5293 0.4005 f = 142.699(l 0.3108) l 0.4895 + 62.682(l 0.3108) l 0.4895 x w f w f 0.5678 0.6458 0.5293 0.4005 . (16) f = 82.388(l 0.3108) l 0.4895 108.568(l 0.3108) l 0.4895 y w f w f 0.8806 0.4382 f = 12.771(l 0.3108) l 0.4895 z w The force density functions of a micro-textured cutter with a texture density combination of 0.09–0.05–0.07 are 0.5739 0.685 0.4713 0.3893 f = 179.758(l 0.3233) l 0.4907 + 58.479(l 0.3233) l 0.4907 x w w f f 0.5739 0.685 0.4713 0.3893 . (17) f = 103.784(l 0.3233) l 0.4907 101.288(l 0.3233) l 0.4907 y w w f f 0.6767 0.4836 ( ) f = 61.105 l 0.3233 l 0.4907 z w f The force density functions of a micro-textured cutter with a texture density combination of 0.07–0.07–0.07 are 0.5214 0.7031 0.6146 0.1417 f = 167.426(l 0.4282) l 0.5122 + 79.135(l 0.4182) l 0.5122 x w w f f 0.5214 0.7031 0.6146 0.1417 . (18) f = 96.664(l 0.4282) l 0.5122 137.066(l 0.4182) l 0.5122 y w f w f 0.7283 0.4476 f = 34.777(l 0.4282) l 0.5122 z w f The force density functions of a micro-textured cutter with a texture density combination of 0.07–0.09–0.05 are 0.5129 0.7777 0.49 0.585 f = 246.387(l 0.4092) l 0.5117 + 21.275(l 0.4092) l 0.5117 x w f w f 0.5129 0.7777 0.49 0.585 . (19) ( ) ( ) f = 142.252 l 0.4092 l 0.5117 36.849 l 0.4092 l 0.5117 y w f w f 0.8316 0.6822 f = 12.029(l 0.4092) l 0.5117 z w f The force density functions of a micro-textured cutter with a texture density combination of 0.07–0.05–0.09 are 0.5157 0.7199 0.537 0.5536 ( ) ( ) f = 245.621 l 0.425 l 0.5163 + 40.356 l 0.425 l 0.5163 x w f w f 0.5157 0.7199 0.537 0.5536 . (20) f = 141.809(l 0.425) l 0.5163 69.898(l 0.425) l 0.5163 y w f w f 0.8101 0.644 f = 20.433(l 0.425) l 0.5163 z w f Appl. Sci. 2020, 10, 818 11 of 20 The force density functions of a micro-textured cutter with a texture density combination of 0.05–0.05–0.05 are 0.576 0.5698 0.574 0.5271 f = 177.396(l 0.5205) l 0.5268 + 108.216(l 0.5205) l 0.5268 x w w f f 0.576 0.5698 0.574 0.5271 ( ) ( ) . (21) f = 102.419 l 0.5205 l 0.5268 187.436 l 0.5205 l 0.5268 y w f w f 0.7086 0.8071 f = 20.039(l 0.5205) l 0.5268 z w f The force density functions of a micro-textured cutter with a texture density combination of 0.05–0.09–0.07 are 0.555 0.5445 0.5369 0.4862 ( ) ( ) f = 202.356 l 0.5389 l 0.5279 + 124.856 l 0.5389 l 0.5279 x w f w f 0.555 0.5445 0.5369 0.4862 . (22) f = 116.831(l 0.5389) l 0.5279 216.257(l 0.5389) l 0.5279 y w f w f 0.7014 0.8301 f = 15.432(l 0.5389) l 0.5279 z w f The force density functions of a micro-textured cutter with a texture density combination of 0.05–0.07–0.09 are 0.5072 0.504 0.5011 0.4508 f = 253.111(l 0.5139) l 0.5258 + 150.226(l 0.5139) l 0.5258 x w f w f 0.5072 0.504 0.5011 0.4508 . (23) f = 146.134(l 0.5139) l 0.5258 260.198(l 0.5139) l 0.5258 y w f w f 0.6886 0.7672 f = 19.46(l 0.5139) l 0.5258 z w The force density functions of the non-textured cutters are 0.608 0.6044 0.6117 0.5814 f = 147.123(l 0.6216) l 0.5468 + 86.922(l 0.6216) l 0.5468 x w f w f 0.608 0.6044 0.6117 0.5814 . (24) f = 84.942(l 0.6216) l 0.5468 150.553(l 0.6216) l 0.5468 y w f w f 0.7724 0.8193 f = 14.263(l 0.6216) l 0.5468 z w f 4. Stress Field Simulation of Variable Density Micro-Textured Ball-End Milling Cutter 4.1. Establishing the Tool Model Due to the limitation of conditions, it is impossible to measure the instantaneous stress ﬁeld of the cutter in real time by an experimental method. Therefore, in this paper, the ﬁnite element simulation method was used to study the distribution of the stress ﬁeld of the cutter during the titanium alloy cutting process. The instantaneous change of the stress ﬁeld at any point on the cutting tool was obtained by ﬁnite element simulation, which provided basic data for further optimizing the parameter design of the micro-textures. First, the cutter was modeled by SolidWorks, a micro-textured cutter with a texture density combination of 0.09–0.09–0.09 was taken as an example, and the model of the cutter is shown in Figure 5. The tool diameter is 20 mm and the micro-texture is placed in the cutter-chip compact contact area. The shape of the micro-texture is micro-pits with a diameter of 50 m and a depth of 35 m, and the distance from the cutting edge is 120 m. The micro-textures are uniformly distributed, and the center distance between adjacent textures is 150 m. The material parameters of the cutter are shown in Table 6. Appl. Sci. 2020, 10, 818 12 of 20 Appl. Sci. 2020, 10, 818 12 of 20 textures are uniformly distributed, and the center distance between adjacent textures is 150 μm. The Appl. Sci. 2020, 10, 818 12 of 20 material parameters of the cutter are shown in Table 6. textures are uniformly distributed, and the center distance between adjacent textures is 150 μm. The material parameters of the cutter are shown in Table 6. Figure 5. The blade model. Figure Figure5. 5. The b The blade lade m model. odel. Table 6. Constitutive parameters of the tool materials [33]. Table 6. Constitutive parameters of the tool materials [33]. Table 6. Constitutive parameters of the tool materials [33]. Specific Coefficient of Modulus Coecient of Thermal Heat Melting Boiling Thermal Modulus of Speciﬁc SpeciHeat fic Density Thermal of Poisson Density Thermal Poisson Melting Boiling Coefficient of Modulus Conductivity Capacity Point Point Conductivity Elasticity Capacity 3 Thermal Heat Melting Boiling kg/ kg m /m Expansion Expansion Elasticity Ratio Ratio Point ( C) Point ( C) Density (W/(mC)) Thermal E (Gpa) of Poisson C (J/(kgC)) (W/(m· C)) C (°C) (°C) 6 1 (10 C ) Conductivity −6 −1 Capacity Point Point α (× 10 C ) E (Gpa) kg/m Expansion Elasticity Ratio . (J/(kg C)) 14,700 (W/(m 75.4 · C)) 4.5 540 0.3 470 C 2780 (°C) 6000 (°C) −6 −1 α (× 10 C ) E (Gpa) 14,700 75.4 4.5 540 0.3 470 2780 6000 (J/(kg C)) 14,700 75.4 4.5 540 0.3 470 2780 6000 ANSYS Workbench 16.0 software (ANSYS company, Canonsburg, PA, USA) was used to simulate ANSYS Workbench 16.0 software (ANSYS company, Canonsburg, PA, USA) was used to and analyze the instantaneous stress ﬁeld of the cutter. A force distribution simulation of the simulate and analyze the instantaneous stress field of the cutter. A force distribution simulation of ANSYS Workbench 16.0 software (ANSYS company, Canonsburg, PA, USA) was used to micro-textured ball-end milling cutter was carried out, following the steps of inputting model, deﬁning the micro-textured ball-end milling cutter was carried out, following the steps of inputting model, simulate and analyze the instantaneous stress field of the cutter. A force distribution simulation of material attributes, partitioning meshes, deﬁning boundary conditions, solving the problem, and defining material attributes, partitioning meshes, defining boundary conditions, solving the problem, the micro-textured ball-end milling cutter was carried out, following the steps of inputting model, analyzing images. Meshing is very important, and the quality of meshing directly determines the and analyzing images. Meshing is very important, and the quality of meshing directly determines defining material attributes, partitioning meshes, defining boundary conditions, solving the problem, accuracy of simulation results. Therefore, it is necessary to reﬁne the grids of the cutter-chip contact the accuracy of simulation results. Therefore, it is necessary to refine the grids of the cutter-chip and analyzing images. Meshing is very important, and the quality of meshing directly determines area. Mesh optimization was performed using the ICEM CFD module in the ANSYS Workbench. contact area. Mesh optimization was performed using the ICEM CFD module in the ANSYS the accuracy of simulation results. Therefore, it is necessary to refine the grids of the cutter-chip Tetrahedral mesh is suitable for fast and ecient meshing of complex models, which is realized through Workbench. Tetrahedral mesh is suitable for fast and efficient meshing of complex models, which is contact area. Mesh optimization was performed using the ICEM CFD module in the ANSYS automatic mesh generation. Therefore, tetrahedral mesh was used in the mesh model. There are realized through automatic mesh generation. Therefore, tetrahedral mesh was used in the mesh Workbench. Tetrahedral mesh is suitable for fast and efficient meshing of complex models, which is 931,230 nodes in total and the minimum edge length is 2.5 10 m. The meshing of the cutting tool −8 model. There are 931,230 nodes in total and the minimum edge length is 2.5 × 10 m. The meshing of realized through automatic mesh generation. Therefore, tetrahedral mesh was used in the mesh is shown in Figure 6. The fewer the optimized mesh nodes, the accurate and faster the calculation. It the cutting tool is shown in Figure 6. The fewer the optimized mesh nodes, th− e 8 accurate and faster model. There are 931,230 nodes in total and the minimum edge length is 2.5 × 10 m. The meshing of turns out that the force distribution for the simulated micro-textured ball-end milling cutter is very the calculation. It turns out that the force distribution for the simulated micro-textured ball-end the cutting tool is shown in Figure 6. The fewer the optimized mesh nodes, the accurate and faster close to the force distribution in actual machining. milling cutter is very close to the force distribution in actual machining. the calculation. It turns out that the force distribution for the simulated micro-textured ball-end milling cutter is very close to the force distribution in actual machining. Figure 6. Mesh partition of the cutter. Appl. Sci. 2020, 10, 818 13 of 20 Appl. Sci. 2020, 10, 818 13 of 20 Figure 6. Mesh partition of the cutter. 4.2. Setting Boundary Conditions 4.2. Setting Boundary Conditions Boundary conditions and loads should be set on the model of the cutter before performing a Boundary conditions and loads should be set on the model of the cutter before performing a finite element simulation. In the actual machining process, the cutter was fixed to the cutter arbor by ﬁnite element simulation. In the actual machining process, the cutter was ﬁxed to the cutter arbor by screw, which limited the axial and radial translation of the cutter, and then the cutter arbor rotated screw, which limited the axial and radial translation of the cutter, and then the cutter arbor rotated with the spindle. Therefore, in the finite element model, the screw hole of the cutter was set to a fixed with the spindle. Therefore, in the ﬁnite element model, the screw hole of the cutter was set to a ﬁxed constraints to restrict the translational movement of the cutter in the axial and radial directions, as constraints to restrict the translational movement of the cutter in the axial and radial directions, as shown in Figure 7. During the cutting process, the cutting force on the cutter is mainly caused by the shown in Figure 7. During the cutting process, the cutting force on the cutter is mainly caused by the squeeze between the cutter and the workpiece and the friction between the front face of the cutter squeeze between the cutter and the workpiece and the friction between the front face of the cutter and the chip, and the cutting force is equivalent to a surface load on the cutter-chip contact area of and the chip, and the cutting force is equivalent to a surface load on the cutter-chip contact area of the the rake face of the cutter. However, the distributions of milling forces along the length and width of rake face of the cutter. However, the distributions of milling forces along the length and width of the the cutter-chip contact area are uneven, which is a function of time. Therefore, the force density cutter-chip contact area are uneven, which is a function of time. Therefore, the force density function function of the cutter calculated in the previous section was applied as a load to the cutter-chip of the cutter calculated in the previous section was applied as a load to the cutter-chip contact area of contact area of the cutter. the cutter. Figure 7. Boundary conditions of the simulation model. Figure 7. Boundary conditions of the simulation model. 4.3. Analysis of the Simulation Results 4.3. Analysis of the Simulation Results After setting the boundary conditions and loads, the stress ﬁeld of the micro-textured ball-end After setting the boundary conditions and loads, the stress field of the micro-textured ball-end milling cutter was simulated by ﬁnite element method. When the micro-textured ball-end milling cutter milling cutter was simulated by finite element method. When the micro-textured ball-end milling just cut into the workpiece as the initial time, the time to cut out the workpiece was 0.0036 s. Through cutter just cut into the workpiece as the initial time, the time to cut out the workpiece was 0.0036 s. simulation analysis, it can be concluded that the stress ﬁeld of the micro-textured ball-end milling cutter Through simulation analysis, it can be concluded that the stress field of the micro-textured ball-end reached the maximum value when the workpiece was in 0.002 s. The simulation results are shown in milling cutter reached the maximum value when the workpiece was in 0.002 s. The simulation results Table 7. From the simulation plots of the equivalent stress and equivalent displacement, it can be seen are shown in Table 7. From the simulation plots of the equivalent stress and equivalent displacement, that a stress concentration occurred in the contact area between the cutter and the chip on the rake face it can be seen that a stress concentration occurred in the contact area between the cutter and the chip of the non-textured cutter during the ﬁnishing process of titanium alloy. The reason is that, during on the rake face of the non-textured cutter during the finishing process of titanium alloy. The reason the ﬁnishing process of titanium alloy, the plastic deformation of the workpiece causes the extrusion is that, during the finishing process of titanium alloy, the plastic deformation of the workpiece causes of the cutter and the workpiece in the cutter-chip contact area, thereby changing the metallographic the extrusion of the cutter and the workpiece in the cutter-chip contact area, thereby changing the structure of the cutter-chip contact area and leading to the occurrence of stress concentration. During metallographic structure of the cutter-chip contact area and leading to the occurrence of stress the titanium alloy cutting process, the force and deformation of the micro-textured cutter are more concentration. During the titanium alloy cutting process, the force and deformation of the micro- uniform than those of the non-textured cutter, and the stress concentration is less. The maximum textured cutter are more uniform than those of the non-textured cutter, and the stress concentration deformation zone and the maximum stress value of the micro-textured cutter are smaller than those of is less. The maximum deformation zone and the maximum stress value of the micro-textured cutter the non-textured cutting cutter. The simulation results fully show that the micro-textures play a role in are smaller than those of the non-textured cutting cutter. The simulation results fully show that the reducing friction and wear on the rake face of the cutter. micro-textures play a role in reducing friction and wear on the rake face of the cutter. Table 7. Simulation results of stress field. Appl. Sci. 2020, 10, 818 14 of 20 Appl. Sci. 2020, 10, 818 14 of 20 Ap App pl. l. Sci. Sci. 2020 2020,, 10 10, , 8 81 18 8 14 14 of of 20 20 Appl. Sci. 2020, 10, 818 14 of 20 Appl. Sci. 2020, 10, 818 14 of 20 ApAp pl. p Sci. l. Sci. 2020 2020 , 10 , , 10 81 , 8 8 18 14 14 of of 20 20 Appl. Sci. 2020, 10, 818 14 of 20 App Ap l. Sci. pl. Sci. 2020 2020 , 10,, 10 81, 88 18 14 14 of of 20 20 Ap Ap pl. pSci. l. Sci. 2020 2020 , 10 , 10 , 8, 18 81 8 1414 of of 2020 Table 7. Simulation results of stress ﬁeld. Combinatio Combinatio Co Co mbinat mbinat ioio Combinatio Combinatio Combinatio Combinatio Combinatio Co Co Co mbinat mbinat mbinat ioio io n of Texture Equivalent Stress Equivalent Displacement n of Texture Equivalent Stress Equivalent Displacement n n ofof Texture Texture Eq Eq uiv uiv alent alent Str Str ess ess Eq Eq uiv uiv alent alent Di Di spsp lac lac ement ement n of Texture Equivalent Stress Equivalent Displacement Combination of Texture n of n of Texture Texture EqEq uiv uiv alent alent Str Str ess ess EqEq uiv uiv alent alent Di Di spsp lac lac ement ement n of n of Texture Texture EqEq uiv uiv alent alent Str Str ess ess EqEq uiv uiv alent alent Di Di splac splac ement ement n of n of Texture Texture Eq Eq uiv uiv alent alent Str Str ess ess Eq Eq uiv uiv alent alent Di Di spsp lac lac ement ement n of Texture Equivalent Equivalent Stress Stress Eq Equivalent uivalent Di Displacement splacement Density Density Den Densit sity y Density Density Den Den sitsit y y Density Den Den sity sit y Den Den sit sit y y 9 6 Maximum value: 3.9444 109 Maximum value: 4.1231 10 -6 9 9 - -6 6 Maximum value: 3.9444×10 9 Maximum value: 4.1231×10 -6 Maximu Maximum m v valu alue: e: 3 3..9444 9444××1 10 0 Maximu Maximum m v valu alue: e: 4 4..1231 1231××1 10 0 Maximum value: 3.9444×109 Maximum value: 4.1231×10-6 9 9 -6 -6 Maximum value: 3.9444×10 Maximum value: 4.1231×10 Maximu Maximu m m valu valu e: e: 3. 9444 3.9444×× 101 0 9 Maximu Maximu m m valu valu e: e: 4. 1231 4.1231×× 1010 -6 9 9 -6 -6 Maximum value: 3.9444×1 9 09 Maximum value: 4.1231×1 -60-6 Maximu Maximu m v m alu valu e: 3 e: .9444 3.9444 ×1× 0 1 0 Maximu Maximu m v m alu valu e: 4 e: .1231 4.1231 ×1× 0 1 0 Maximu Maximu mm valu valu e: e: 3. 9444 3.9444×× 101 0 Maximu Maximu mm valu valu e: e: 4. 1231 4.1231×× 1010 0.05-0.05-0.05 0.05-0.05-0.05 0. 0.05 05- -0. 0.05 05- -0 0..05 05 0.05-0.05-0.05 0.05-0.05-0.05 0.05 0.05 -0.-05 0.05 -0.-05 0.05 0.05-0.05-0.05 0.05 0.-05 0.05 -0.-05 0.05 -0. 05 0.05 0.05 -0. -05 0.05 -0- .05 0.05 9 6 9 -6 9 -6 Maximum Maximum value: value: 2.6527 2.6527× 1 10 0 9 9 Maximu Maximum m valu value: e: 3.3.887 887× 1010 -6 -6 Maximum value: 2.6527×10 Maximum value: 3.887×10 Maximu Maximu mm valu valu e: e: 2. 6527 2.6527×× 101 9 0 Maximu Maximu mm valu valu e: e: 3. 887 3.887×× 101 -60 9 -6 Maximum value: 2.6527×109 Maximum value: 3.887×10-6 9 -6 Maximu Maximu m m valu valu e: e: 2. 6527 2.6527×× 109 1 0 Maximu Maximu m m valu valu e: e: 3. 887 3.887×× 10-1 60 9 9 9 -6 --6 6 Maximu Maximu m m valu valu e: 2 e: .6527 2.6527 ×1× 0 1 0 Maximu Maximu m m valu valu e: 3 e: .887 3.887 ×1× 0 1 0 Maximu Maximu m m valu valu e: e: 2. 6527 2.6527×× 101 0 Maximu Maximu m m valu valu e: e: 3. 887 3.887×× 1010 Maximum value: 2.6527×10 Maximum value: 3.887×10 0.05-0.07-0.09 0.05-0.07-0.09 0.05-0.07-0.09 0.05 0.05 -0.-07 0.07 -0.-09 0.09 0.05-0.07-0.09 0.05-0.07-0.09 0.05-0.07-0.09 0.05-0.07-0.09 0.05-0.07-0.09 0.05 0. 0.05 05 -0. --07 0. 0.07 07 -0- .-09 0 0..09 09 9 -6 9 9 9 - -6 66 Maximum value: 3.6813×10 9 Maximum value: 4.0945×10 -6 Maximum value: 3.6813×10 Maximum value: 4.0945×10 Maximum Maximu Maximu mvalue: m valu valu e: 3.6813 e: 3. 6813 3.6813×× 10 101 9 0 Maximu Maximum Maximu mm vvalue: alu valu e: e: 4. 4.0945 0945 4.0945×× 1010 1 -60 9 9 -6 -6 Maximum value: 3.6813×10 Maximum value: 4.0945×10 Maximum value: 3.6813×10 9 Maximum value: 4.0945×10 -6 Maximum value: 3.6813×109 9 Maximum value: 4.0945×10-6 -6 Maximum value: 3.6813×1 9 09 Maximum value: 4.0945×1 -60-6 Maximum value: 3.6813×10 Maximum value: 4.0945×10 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 3. 6813 3 3..6813 6813××× 101 1 0 0 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 4. 0945 4 4..0945 0945××× 101 10 0 0.05-0.09-0.07 0. 0.05 05- -0. 0.09 09- -0 0..07 07 0.05-0.09-0.07 0.05-0.09-0.07 0.05-0.09-0.07 0.05 0.05 -0.-09 0.09 -0.-07 0.07 0.05-0.09-0.07 0.05 0.-05 0.09 -0.-09 0.07 -0. 07 0.05 0.05 -0. -09 0.09 -0- .07 0.07 9 -6 9 -6 9 9 -6 -6 Maximu Maximu m m valu valu e: e: 2. 849 2.849×× 101 0 Maximu Maximu m m valu valu e: e: 3. 5375 3.5375×× 1010 Maximum value: 2.849×1 9 90 Maximum value: 3.5375×1 -606 Maximum value: 2.849×10 Maximum value: 3.5375×10 9 9 -6 -6 Maximum Maximum value: value: 2.849 2.849× 1 10 0 Maximu Maximum m valu value: e: 3.5375 3.5375×1010 Maximu Maximu m m valu valu e: e: 2. 849 2.849×× 109 1 0 9 Maximu Maximu m m valu valu e: e: 3. 5375 3.5375×× 10-1 60 -6 9 9 -6 -6 Maximu Maximu m m valu valu e: 2 e: .849 2.849 ×1× 0 1 09 Maximu Maximu m m valu valu e: 3 e: .5375 3.5375 ×1× 0 1 0-6 Maximum value: 2.849×10 Maximum value: 3.5375×10 Maximu Maximu mm valu valu e: e: 2. 849 2.849×× 101 0 Maximu Maximu mm valu valu e: e: 3. 5375 3.5375×× 1010 0.07-0.07-0.07 0.07-0.07-0.07 0.07 0.07 -0.-07 0.07 -0.-07 0.07 0.07-0.07-0.07 0.07-0.07-0.07 0.07 0.07 -0.-07 0.07 -0.-07 0.07 0.07 0.-07 0.07 -0.-07 0.07 -0. 07 0.07 0.07 -0.-07 0.07 -0.-07 0.07 0.07-0.07-0.07 9 -6 9 9 - -6 6 Maximum value: 2.7749×10 9 Maximum value: 3.9043×10 -6 Maximum value: 2.7749×10 Maximum value: 3.9043×10 Maximu Maximu mm valu valu e: e: 2. 7749 2.7749×× 101 9 0 Maximu Maximu mm valu valu e: e: 3. 9043 3.9043×× 101 -60 9 9 9 -6 -66 Maximum value: 2.7749×10 Maximum value: 3.9043×10 Maximum value: 2.7749×10 9 Maximum value: 3.9043×10 -6 Maximum Maximum value: value: 2.7749 2.7749× 1 10 09 9 Maximu Maximum m valu value: e: 3.9043 3.9043×1010 -6 -6 Maximum value: 2.7749×1 9 09 Maximum value: 3.9043×1 -60-6 Maximum value: 2.7749×10 Maximum value: 3.9043×10 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 2. 7749 2 2..7749 7749××× 101 1 0 0 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 3. 9043 3 3..9043 9043××× 101 10 0 0.07-0.05-0.09 0. 0.07 07- -0. 0.05 05- -0 0..09 09 0.07-0.05-0.09 0.07-0.05-0.09 0.07 0.07 -0.-05 0.05 -0.-09 0.09 0.07-0.05-0.09 0.07-0.05-0.09 0.07 0.-07 0.05 -0.-05 0.09 -0. 09 0.07 0.07 -0. -05 0.05 -0- .09 0.09 9 9 -6 -6 9 -6 Maximum value: 2.6155×10 9 Maximum value: 3.7479×10 -6 Maximu Maximum m v valu alue: e: 2 2..6155 6155××1 10 0 Maximu Maximum m v valu alue: e: 3 3..7479 7479××1 10 0 Maximum value: 2.6155×109 Maximum value: 3.7479×10-6 9 9 -6 -6 Maximum value: 2.6155×10 9 Maximum value: 3.7479×10 6 Maximu Maximu m m valu valu e: e: 2. 6155 2.6155×× 109 1 0 9 Maximu Maximu m m valu valu e: e: 3. 7479 3.7479×× 10-1 60 -6 Maximum value: 2.6155 10 9 Maximum value: 3.7479 10 -6 Maximum value: 2.6155×1 9 09 Maximum value: 3.7479×1 -60-6 Maximu Maximu m v m alu valu e: 2 e: .6155 2.6155 ×1× 0 1 0 Maximu Maximu m v m alu valu e: 3 e: .7479 3.7479 ×1× 0 1 0 Maximu Maximu mm valu valu e: e: 2. 6155 2.6155×× 101 0 Maximu Maximu mm valu valu e: e: 3. 7479 3.7479×× 1010 0.07 0.07 -0.-09 0.09 -0.-05 0.05 0.07-0.09-0.05 0.07-0.09-0.05 0.07-0.09-0.05 0.07 0.07 -0.-09 0.09 -0.-05 0.05 0.07-0.09-0.05 0.07 0.-07 0.09 -0.-09 0.05 -0. 05 0.07-0.09-0.05 0.07 0.07 -0. -09 0.09 -0- .05 0.05 9 -6 9 -6 Maximum value: 2.1418×10 9 9 Maximum value: 2.891×10 -6 -6 Maximum value: 2.1418×10 Maximum value: 2.891×10 Maximu Maximu mm valu valu e: e: 2. 1418 2.1418×× 101 9 0 Maximu Maximu mm valu valu e: e: 2. 891 2.891×× 101 -60 9 -6 Maximum value: 2.1418×109 Maximum value: 2.891×10-6 Maximum value: 2.1418×10 9 Maximum value: 2.891×10 -6 Maximum value: 2.1418×109 Maximum value: 2.891×10-6 Maximum value: 2.1418×1 9 09 9 Maximum value: 2.891×1 -60--6 6 Maximum value: 2.1418×10 Maximum value: 2.891×10 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 2. 1418 2 2..1418 1418××× 101 1 0 0 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 2. 891 2 2..891 891××× 101 10 0 Appl. Sci. 2020, 10, 818 15 of 20 Table 7. Cont. Combination of Texture Equivalent Stress Equivalent Displacement Density Ap Ap pl. pSci. l. Sci. 2020 2020 , 10 , 10 , 8, 18 81 8 1515 of of 2020 Ap Ap pl. pSci. l. Sci. 2020 2020 , 10 , 10 , 8, 18 81 8 1515 of of 2020 Appl. Sci. 2020, 10, 818 15 of 20 Appl. Sci. 2020, 10, 818 15 of 20 Appl. Sci. 2020, 10, 818 15 of 20 Appl. Sci. 2020, 10, 818 15 of 20 9 6 Maximum value: 2.1418 10 Maximum value: 2.891 10 0.09 0.09 –0. –09 0.09 – – 0.09–0.09– 0.09–0.09– 0.09–0.09–0.09 0.09 0.09 –0. –09 0.09 – – 0.09 0.09 –0. –09 0.09 – – 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 9 6 9 9 -6 -6 Maximum value: 2.0607 109 9 Maximum value: 3.0588 10 -6 -6 Maximu Maximu mm valu valu e: e: 2. 0607 2.0607×× 101 9 09 Maximu Maximu mm valu valu e: e: 3. 0588 3.0588×× 101 -60 -6 Maximu Maximu mm valu valu e: e: 2. 0607 2.0607×× 101 0 Maximu Maximu mm valu valu e: e: 3. 0588 3.0588×× 1010 Maximum value: 2.0607×10 Maximum value: 3.0588×10 Maximum value: 2.0607×109 Maximum value: 3.0588×10-6 9 -6 Maximum value: 2.0607×10 Maximum value: 3.0588×10 Maximum value: 2.0607×10 Maximum value: 3.0588×10 0.09-0.05-0.07 0.09 0.09 -0.-05 0.05 -0.-07 0.07 0.09 0.09 -0.-05 0.05 -0.-07 0.07 0.09 0.09 -0.-05 0.05 -0.-07 0.07 0.09-0.05-0.07 0.09-0.05-0.07 9 9 9 -6 -66 9 -6 Maximum value: 1.7714×10 9 Maximum value: 2.7058×10 -6 Maximum Maximu Maximu m value: m valu valu e: 1.7714 e: 1. 7714 1.7714×× 1 10 01 9 09 Maximu Maximum Maximu m m valu value: valu e: e: 2. 7058 2.7058 2.7058×× 1010 1 -60 -6 Maximum value: 1.7714×10 Maximum value: 2.7058×10 Maximu Maximu mm valu valu e: e: 1. 7714 1.7714×× 101 0 Maximu Maximu mm valu valu e: e: 2. 7058 2.7058×× 1010 9 9 -6 -6 Maximu Maximu m m valu valu e: e: 1. 7714 1.7714×× 101 0 Maximu Maximu m m valu valu e: e: 2. 7058 2.7058×× 1010 0.09 0.09 -0.-07 0.07 -0.-05 0.05 0.09-0.07-0.05 0.09-0.07-0.05 0.09-0.07-0.05 0.09 0.09 -0.-07 0.07 -0.-05 0.05 0.09 0.09 -0.-07 0.07 -0.-05 0.05 9 9 -6 -6 9 9 -6 -6 Maximu Maximu mm valu valu e: e: 6. 14 6.14×× 101 09 Maximu Maximu mm valu valu e: e: 4. 2764 4.2764×× 1010 -6 Maximum value: 6.14×10 9 9 Maximum value: 4.2764×10 -6 6 Maximum value: 6.14×10 Maximum value: 4.2764×10 Maximu Maximu mm valu valu e: e: 6. 14 6.14×× 101 9 0 Maximu Maximu mm valu valu e: e: 4. 2764 4.2764×× 101 -60 Maximum value: 6.14 10 9 Maximum value: 4.2764 10-6 Maximu Maximu m m valu valu e: e: 6. 14 6.14×× 101 0 Maximu Maximu m m valu valu e: e: 4. 2764 4.2764×× 1010 Non- No No n- n- Non- No No n-n- No No n-n- Non-textur textu ed textu red red textu textu red red textured textured textured textured cutter cutter cutter cutter cutter cutter cutter cutter cutter As As shown shown in in Fi Fi gure gure 8, 8, duri duri ng ng th th e e prpr ocess ocess of of cutt cutt ing ing titan titan iuiu mm alloy alloy , Ori , Ori gin gin softwa softwa rere 2017 2017 As As shown shown in in Fi Fi gure gure 8, 8, duri duri ng ng th th e e prpr ocess ocess of of cutt cutt ing ing titan titan iuiu mm alloy alloy , Ori , Ori gin gin softwa softwa rere 2017 2017 As shown in Figure 8, during the process of cutting titanium alloy, Origin software 2017 As shown in Figure 8, during the process of cutting titanium alloy, Origin software 2017 As shown in Figure 8, during the process of cutting titanium alloy, Origin software 2017 As shown in Figure 8, during the process of cutting titanium alloy, Origin software 2017 (Originlab, Northampton, MA, USA) was used to plot and analyze the relationship between the (Ori (Ori ginlab, ginlab, Nort Nort hamp hamp ton to , nMA, , MA, US US A)A w ) as was used used to to pl pl ot ot and and analy analy zeze th th e re e l re atio latio nship nship bet bet wee wee n n thth e e (Originlab, Northampton, MA, USA) was used to plot and analyze the relationship between the (Ori (Ori ginlab, ginlab, NN ort ort hamp hamp toto n, nMA, , MA, US US AA ) w ) w asas used used to to pl pl otot and and analy analy zeze th th e e rere latio latio nship nship bet bet wee wee n n thth e e As shown in Figure 8, during the process of cutting titanium alloy, Origin software 2017 (Originlab, (Ori (Ori ginlab, ginlab, Nort Nort hamp hamp toto n, nMA, , MA, US US A) A w ) as was used used to to pl pl otot and and analy analy zeze th th e e rere latio latio nship nship bet bet wee wee n n thth e e equiva equiva lent lent stress stress and and th th e e e quiva equiva lent d lent d isp isp lala cem cem ent ent of of th th e var e var iaia ble d ble d ensity ensity micro micro -tex -tex tured tured cutt cutt ers ers and and equiva equiva lent lent stress stress and and th th e e e quiva equiva lent d lent d isp isp lala cem cem ent ent of of th th e var e var iaia ble d ble d ensity ensity micro micro -tex -tex tured tured cutt cutt ers ers and and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and Northampton, equiva MA, lent USA) stress a was nd th used e equiva to plot lent d and isplaanalyze cement of the ther var elationship iable density between micro-tex the tured equivalent cutters and str ess equivalent stress and the equivalent displacement of the variable density micro-textured cutters and the non-texture cutter. It can be seen from Figure 8 that, when the workpiece is cut in 0.002 s, the thth e non e non -tex -tex ture ture cutt cutt er. er. It It can can be be sese en en from from Fi g Fi ure gure 8 th 8 th at,at when , when th th e workp e workp iece iece is icut s cut in in 0.0 0.0 0202 s, s, th th e e the non-texture cutter. It can be seen from Figure 8 that, when the workpiece is cut in 0.002 s, the thth e e non non -tex -tex ture ture cutt cutt er. er. It It c an can be be sese en en from from Fi Fi gure gure 8 8 thth atat , when , when th th e e workp workp iece iece is icut s cut in in 0.0 0.0 0202 s, s, th th e e thth e non e non -tex -tex ture ture cutt cutt er. er. It It can can be be sese en en from from Fi Fi gure gure 8 th 8 th at,at when , when th th e workp e workp iece iece is icut s cut in in 0.0 0.0 0202 s, s, th th e e and the equivalent displacement of the variable density micro-textured cutters and the non-texture equiva equiva lent lent stress stress and and th th e e e quiva equiva lent d lent d isp isp lala cem cem ent ent of of th th e var e var iaia ble d ble d ensity ensity micro micro -tex -tex tured tured cutt cutt ers ers and and equiva equiva lent lent stress stress and and th th e e e quiva equiva lent d lent d isp isp lala cem cem ent ent of of th th e var e var iaia ble d ble d ensity ensity micro micro -tex -tex tured tured cutt cutt ers ers and and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and cutter. It can be seen from Figure 8 that, when the workpiece is cut in 0.002 s, the equivalent stress and the non-textured cutter reach the maximum value. The instantaneous stress and deformation in the thth e non e non -tex -tex tutu red red cutt cutt er er reac reac h th h th e m e axi maxi mum mum value value . Th . Th e in e stantane instantane ous ous stres stres s and s and deform deform ation ation in ith n th e e the non-textured cutter reach the maximum value. The instantaneous stress and deformation in the thth e e non non -tex -tex tutu red red cutt cutt er er rere acac h h thth e e mm axi axi mm um um value value . Th . Th e e inin stantane stantane ous ous stres stres s and s and deform deform ation ation in in thth e e thth e non e non -tex -tex tutu red red cutt cutt er er rere acac h h thth e m e m axi axi mm um um value value . Th . Th e in e in stantane stantane ous ous stres stres s and s and deform deform ation ation in in thth e e the equivalent non non - displacement tex -tex tured tured cutt cutt er er du of du rin the rin g variable g th th e pro e pro cess cess density o fo cutt f cutt ing micr ing titan titan o-textur ium ium alloy alloy ed are cutters are grea grea ter and ter th th an the an those tnon-textur hose in in thth e va e va ed ria ria bcutter le ble non non -tex -tex tured tured cutt cutt er er du du rin rin g g th th e pro e pro cess cess o fo cutt f cutt ing ing titan titan ium ium alloy alloy are are grea grea ter ter th th an an those those in in thth e va e va ria ria ble ble non non -tex -tex tured tured cutt cutt er er du du rin rin g g th th e pro e pro cess cess o fo cutt f cutt ing ing titan titan ium ium alloy alloy are are grea grea ter ter th th an an those those in in thth e va e va ria ria ble ble non-textured cutter during the process of cutting titanium alloy are greater than those in the variable non-textured cutter during the process of cutting titanium alloy are greater than those in the variable density density mm icro icro -tex -tex tured tured cutt cutt er. er. Due Due toto th th e change e change of oth f th e tex e tex ture ture dens dens ity ity in in thth e cutt e cutt erer -chip -chip clo clo se se coco ntnt act act density micro-textured cutter. Due to the change of the texture density in the cutter-chip close contact reach the maximum density m value. icro-tex The tured instantaneous cutter. Due to th str e change ess and of deformation the texture dens inity the in non-textur the cutter-chip ed clo cutte se co r during ntact density density mm icro icro -tex -tex tured tured cutt cutt er. er. Due Due toto th th e change e change of oth f th e tex e tex ture ture dens dens ity ity in in thth e cutt e cutt erer -chip -chip clo clo se se coco ntnt act act density density mm icro icro -tex -tex tured tured cutt cutt er. er. Due Due toto th th e change e change of o th f th e tex e tex ture ture dens dens ity ity in in thth e cutt e cutt erer -chip -chip clo clo se se coco ntnt act act arar eae , a th , th e “ e sec “sec ondary ondary cutt cutt inin g” g ph ” ph enom enom en en on on ofof th th e micr e micr o-o tex -tex tured tured cu cu tter tter du du ring ring th th e pro e pro cess cess of of cutt cutt ing ing arar eae , a th , th e “ e sec “sec ondary ondary cutt cutt inin g” g ph ” ph enom enom en en on on ofof th th e micr e micr o-o tex -tex tured tured cu cu tter tter du du ring ring th th e pro e pro cess cess of of cutt cutt ing ing arar eae , a th , th e “ e sec “sec ondary ondary cutt cutt inin g” g ph ” ph enom enom en en on on ofof th th e micr e micr o-o tex -tex tured tured cu cu tter tter du du ring ring th th e pro e pro cess cess of of cutt cutt ing ing the process of cutting titanium alloy are greater than those in the variable density micro-textured area, the “secondary cutting” phenomenon of the micro-textured cutter during the process of cutting area, the “secondary cutting” phenomenon of the micro-textured cutter during the process of cutting titaniu titaniu mm allo allo ys ys is is effect effect iviv ely ely red red uced uced . It . It can can be be see see n n from from th th e e s imul simul ation ation res res ulul ts ts th th atat th th e e micro micro - - titanium alloys is effectively reduced. It can be seen from the simulation results that the micro- titanium alloys is effectively reduced. It can be seen from the simulation results that the micro- titaniu titaniu mm allo allo ys ys is is effect effect iviv ely ely red red uced uced . It . It can can be be see see n n from from th th e e s imul simul ation ation res res ulul ts ts th th atat th th e e micro micro - - cutter. Duetitaniu to titaniu the mchange m allo allo ys ys is of is effect the effect iv textur iv ely ely red red euced density uced . It . It can in can the be be see cutter see n n from fr -chip om th th e close e si mul simul ation contact ation res res ul ar ul ts ea, ts th th at the at th “secondary th e e micro micro - - tex tex tured tured cutt cutt er er can can not not onl onl y y reduc reduc e fr e iction friction and and ww eaea r, r but , but also also imp imp rov rov e th e th e stres e stres s dis s dis tribution tribution of of thth e e tex tex tured tured cutt cutt er er can can not not onl onl y y reduc reduc e fr e iction friction and and ww eaea r, r but , but also also imp imp rov rov e th e th e stres e stres s dis s dis tribution tribution of of thth e e tex tex tured tured cutt cutt er er can can not not onl onl y y reduc reduc e fr e iction friction and and ww eaea r, r but , but also also imp imp rov rov e th e th e stres e stres s dis s dis tribution tribution of of thth e e textured cutter can not only reduce friction and wear, but also improve the stress distribution of the textured cutter can not only reduce friction and wear, but also improve the stress distribution of the cutting” phenomenon of the micro-textured cutter during the process of cutting titanium alloys is cutt cutt er. er. By By ch ch angi angi ng ng thth e e didi stribution stribution de de nsity nsity of of thth e e text text ure ure on on thth e e cutt cutt er, er, thth e e “seconda “seconda ry ry cu cu tting tting ” ” cutter. By changing the distribution density of the texture on the cutter, the “secondary cutting” cutter. By changing the distribution density of the texture on the cutter, the “secondary cutting” cutt cutt er. er. By By ch ch angi angi ng ng thth e e didi stribution stribution de de nsity nsity of of thth e e text text ure ure on on thth e e cutt cutt er, er, thth e e “seconda “seconda ry ry cu cu tting tting ” ” cutt cutt er. er. By By chch angi angi ng ng thth e e didi stribution stribution dede nsity nsity of of thth e e text text ure ure on on thth e e cutt cutt er, er, thth e e “seconda “seconda ry ry cucu tting tting ” ” eectively reduced. It can be seen from the simulation results that the micro-textured cutter can not ph ph ph enom enom enom enon enon enon dur dur dur ing ing ing th th th e e p e process rocess process o of f omic mic f mic ro roro --tex tex -tex tured tured tured c cutt utt cutt er er er mil mil mil li ling ng ling titaniu titaniu titaniu m m m allo allo allo y y y can can can be be be ef effe ef fect fe ctively ct ively ively phenomenon during the process of micro-textured cutter milling titanium alloy can be effectively ph ph enom enom enon enon dur dur ing ing th th e e process process of omic f mic roro -tex -tex tured tured cutt cutt er er mil mil ling ling titaniu titaniu m m allo allo y y can can be be efef fefe ctct ively ively ph ph enom enom enon enon dur dur ing ing th th e p e rocess process of omic f mic roro -tex -tex tured tured cutt cutt er er mil mil ling ling titaniu titaniu m m allo allo y y can can be be effe efct feively ctively reduced reduced . . only reduce reduced friction . and wear, but also improve the stress distribution of the cutter. By changing the reduced. reduced reduced . . reduced reduced . . distribution density of the texture on the cutter, the “secondary cutting” phenomenon during the process of micro-textured cutter milling titanium alloy can be eectively reduced. Appl. Sci. 2020, 10, 818 16 of 20 Appl. Sci. 2020, 10, 818 16 of 20 (a) (b) Figure 8. The curve of stress field and deformation of variable density micro-textured cutter with Figure 8. The curve of stress ﬁeld and deformation of variable density micro-textured cutter with respect to time. (a) equivalent stress changes with time; (b) equivalent displacement varies with time. respect to time. (a) equivalent stress changes with time; (b) equivalent displacement varies with time. 5. Optimization of Variable Density Distribution of Micro-Textured Cutter 5. Optimization of Variable Density Distribution of Micro-Textured Cutter Through the simulation of the stress ﬁeld in milling titanium alloy with variable density Through the simulation of the stress field in milling titanium alloy with variable density micro- micro-textured ball-end milling cutter, it is concluded that the instantaneous stress ﬁeld and the textured ball-end milling cutter, it is concluded that the instantaneous stress field and the maximum maximum stress value of the cutter are directly aected by the dierent texture distribution densities on stress value of the cutter are directly affected by the different texture distribution densities on the the rake face of the cutter. Therefore, it is necessary to establish the relationship between the dierent rake face of the cutter. Therefore, it is necessary to establish the relationship between the different distribution densities of the micro-textures and the instantaneous stress ﬁeld of the cutter, so as to distribution densities of the micro-textures and the instantaneous stress field of the cutter, so as to optimize the texture density in the cutter-chip compact contact area and to obtain the best combination optimize the texture density in the cutter-chip compact contact area and to obtain the best of texture distribution density, which provides a new concept for the design of micro-textured cutter. combination of texture distribution density, which provides a new concept for the design of micro- In this paper, a genetic algorithm was used to optimize the variable density distribution of textured cutter. micro-textured cutter. The instantaneous stress ﬁeld of the cutter was taken as the optimization In this paper, a genetic algorithm was used to optimize the variable density distribution of objective and the texture density X in the ﬁrst area, X in the second area, and X in the third area micro-textured cutter. The instantaneo 1 us stress field of 2 the cutter was taken as 3the optimization of the cutter-chip compact contact area were taken as the optimization variables. When the genetic objective and the texture density X1 in the first area, X2 in the second area, and X3 in the third area of algorithm was adopted for optimization, the objective function should be established ﬁrst. In this the cutter-chip compact contact area were taken as the optimization variables. When the genetic paper, the instantaneous stress ﬁeld of a micro-textured cutter with a variable density was taken as algorithm was adopted for optimization, the objective function should be established first. In this the optimization objective, so a prediction model of the instantaneous stress ﬁeld of the cutter was paper, the instantaneous stress field of a micro-textured cutter with a variable density was taken as established as the objective function of the optimization model. The mathematical model was used to the optimization objective, so a prediction model of the instantaneous stress field of the cutter was established as the objective function of the optimization model. The mathematical model was used to establish the instantaneous stress model of the variable density micro-textured cutter with respect to the variables X1, X2 and X3: Appl. Sci. 2020, 10, 818 17 of 20 establish the instantaneous stress model of the variable density micro-textured cutter with respect to the variables X , X and X : 1 2 3 1 2 3 = C X X X , (25) 1 2 3 where C denotes the correlation coecient of the prediction model and , , and denote the 1 2 3 undetermined indices of the related independent variables. The logarithm of the two sides of the Equation (25) is lg = lgC + lgX + lgX + lgX . (26) 1 1 2 2 3 3 If y = lg, = lgC, x = lgX , x = lgX , x = lgX , Equation (26) is transformed into a linear 0 1 1 2 2 3 3 equation as follows: y = + x + x + x . (27) 0 1 1 2 2 3 3 According to Equation (27) and the stress ﬁeld simulation data of the variable density micro-textured ball-end milling cutter, a multiple linear regression equation was established by the least-square method: y = + x + x + x + " 1 0 1 11 2 12 3 13 1 y = + x + x + x + " 2 0 1 21 2 22 3 23 2 , (28) :::::: y = + x + x + x + " 9 0 1 91 2 92 3 93 9 where " denotes a random error. The stress ﬁeld simulation data of the variable density micro-textured ball-end milling cutter was substituted into Equation (28). Then, MATLAB R2017b software was used to regress the experimental data through multiple linear regression, and the prediction model of the instantaneous stress ﬁeld of the variable density micro-textured ball-end milling cutter was obtained as follows: 8 0.88847 0.021204 0.1675 = 1.636 10 X X X . (29) 1 2 3 During the process of ﬁnishing titanium alloy with the micro-textured ball-end milling cutter, the instantaneous stress ﬁeld of the micro-textured cutter is aected by the texture density distribution in the ﬁrst, second and third regions where the cutter and chip are in close contact under the same cutting parameters. Therefore, in order to optimize the variable density distribution of the micro-textured cutters based on the stress ﬁeld, the constraints are that the texture density of all three regions where the cutter and chip are in close contact as 0.01 < X < 0.1 (i = 1, 2, 3). Taking the instantaneous stress ﬁeld of the micro-textured cutter as the evaluation standard and the above constraints as the boundary conditions, the genetic algorithm was used to optimize the variable density distribution of the micro-textured cutters. In order to ensure the accuracy of the optimization results, when the variable density distribution of the micro-textured cutters is optimized by the genetic algorithm, optimization parameters should be set in the genetic algorithm toolbox. The population size set in this paper is 300, the crossover probability is 0.95, and the mutation probability is 0.01. Finally, the genetic algorithm toolbox was used to solve the optimization model. The optimization results of the genetic algorithm are shown in Figure 9. The optimal solution of the variable density distribution of the micro-textured cutter in the cutter-chip compact contact area was obtained through the optimization solution. The texture distribution density X in the ﬁrst region, X in the second 1 2 region, and X in the third region are 0.0905, 0.0712, and 0.0493, respectively. 3 Appl. Sci. 2020, 10, 818 18 of 20 Appl. Sci. 2020, 10, 818 18 of 20 Figure 9. Optimization results of the genetic algorithm. Figure 9. Optimization results of the genetic algorithm. 6. Conclusions 6. Conclusions Aiming at the problem of “secondary cutting” during the process of ﬁnishing titanium alloy by Aiming at the problem of “secondary cutting” during the process of finishing titanium alloy by the micro-textured ball-end milling cutter, in this article, the mechanism of friction reduction and wear the micro-textured ball-end milling cutter, in this article, the mechanism of friction reduction and resistance of micro-textured cutters were studied in detail. By changing the distribution density of wear resistance of micro-textured cutters were studied in detail. By changing the distribution density the micro-texture on the cutter, the dynamic characteristics of the instantaneous stress ﬁeld during of the micro-texture on the cutter, the dynamic characteristics of the instantaneous stress field during the process of milling titanium alloy by the micro-textured cutter were studied, and the following the process of milling titanium alloy by the micro-textured cutter were studied, and the following conclusions were drawn: conclusions were drawn: (1) Through milling titanium alloy experiments, the milling force models and the cutter-chip (1) Through milling titanium alloy experiments, the milling force models and the cutter-chip contact area mathematical models of cutters with dierent micro-textured densities and non-texture contact area mathematical models of cutters with different micro-textured densities and non-texture were established. By solving the milling force model and the experimental formula of cutter-chip were established. By solving the milling force model and the experimental formula of cutter-chip contact area, the force density functions of the cutters with the dierent micro-texture densities and contact area, the force density functions of the cutters with the different micro-texture densities and non-texture were obtained. It provides a theoretical basis for studying the stress ﬁeld of the variable non-texture were obtained. It provides a theoretical basis for studying the stress field of the variable density micro-textured cutters. density micro-textured cutters. (2) The instantaneous stress ﬁelds of dierent density textured cutters and non-textured cutters (2) The instantaneous stress fields of different density textured cutters and non-textured cutters during the process of milling titanium alloy were simulated. The simulation results show that, during during the process of milling titanium alloy were simulated. The simulation results show that, during the process of milling titanium alloy, stress concentration will occur in the cutter-chip contact area of the process of milling titanium alloy, stress concentration will occur in the cutter-chip contact area of the rake face of the non-textured cutters. The force and deformation of the micro-textured cutters are the rake face of the non-textured cutters. The force and deformation of the micro-textured cutters are more uniform than those of the non-textured cutters, and there is less stress concentration, and the more uniform than those of the non-textured cutters, and there is less stress concentration, and the maximum deformation area and maximum stress value of the micro-textured cutters are smaller than maximum deformation area and maximum stress value of the micro-textured cutters are smaller than those of the non-textured cutters. those of the non-textured cutters. (3) Taking the instantaneous stress ﬁeld as the objective function, the genetic algorithm was used (3) Taking the instantaneous stress field as the objective function, the genetic algorithm was used to optimize the variable density distribution of the micro-textured cutters, and the optimal solution of to optimize the variable density distribution of the micro-textured cutters, and the optimal solution the variable density distribution of the micro-textured cutters in the cutter-chip compact contact area of the variable density distribution of the micro-textured cutters in the cutter-chip compact contact was obtained. The texture distribution density X in the ﬁrst region, X in the second region, and X in 1 2 3 area was obtained. The texture distribution density X1 in the first region, X2 in the second region, and the third region are 0.0905, 0.0712 and 0.0493, respectively. X3 in the third region are 0.0905, 0.0712 and 0.0493, respectively. Author Contributions: M.Z. and S.Y. conceived and designed the experiments. M.Z. and S.Y. analyzed the data Author Contributions: M.Z. and S.Y. conceived and designed the experiments. M.Z. and S.Y. analyzed the data and carried out ﬁnite element simulation analysis. C.H. performed the experiments and wrote the paper. All and carried out finite element simulation analysis. C.H. performed the experiments and wrote the paper. All authors have read and agreed to the published version of the manuscript. authors have read and agreed to the published version of the manuscript. Funding: This research was funded by [The National Natural Science Foundation of China] grant number [51875144]. And the APC was funded by [The National Natural Science Foundation of China and Construction of Funding: This research was funded by [The National Natural Science Foundation of China] grant number scientiﬁc research collaborative innovation platform-Advanced manufacturing intelligent technology]. [51875144]. 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Abstract

applied sciences Article Optimization of Texture Density Distribution of Carbide Alloy Micro-Textured Ball-End Milling Cutter Based on Stress Field Minli Zheng, Chunsheng He and Shucai Yang * Key Laboratory of Advanced Manufacturing and Intelligent Technology, Ministry of Education, Harbin University of Science and Technology, Harbin 150080, China; minli456456@163.com (M.Z.); hechunsheng0118@163.com (C.H.) * Correspondence: yangshucai@hrbust.edu.cn Received: 6 December 2019; Accepted: 20 January 2020; Published: 23 January 2020 Abstract: The insertion of micro-textures plays a role in reducing friction and increasing wear resistance of the cutters, which also has a certain impact on the stress ﬁeld of the cutter during milling. Therefore, in order to study the mechanisms of friction reduction and wear resistance of micro-textured cutters in high speed cutting of titanium alloys, the dynamic characteristics of the instantaneous stress ﬁeld during the machining of titanium alloys with micro-textured cutters were studied by changing the distribution density of the micro-textures on the cutter. First, the micro-texture insertion area of the ball-end milling cutter was theoretically analyzed. Then, variable density micro-textured ball-end milling cutters and non-texture cutters were used to cut titanium alloy, and the mathematical model of milling force and cutter-chip contact area was established. Then, the stress density functions of dierent micro-texture density cutters and non-texture cutters were established to simulate the stress ﬁelds of variable density micro-textured ball-end milling cutters and non-texture cutters. Finally, the genetic algorithm was used to optimize the variable density distribution of micro-textured cutters in which the instantaneous stress ﬁeld of the cutters was taken as the optimization objective. The optimal solution for the variable density distribution of the micro-textured cutter in the cutter-chip tight contact area was obtained as follows: the texture distribution densities in the ﬁrst, second, and third areas are second, and third areas are 0.0905, 0.0712, and 0.0493, respectively. Keywords: variable density; micro-textured ball-end milling cutter; high speed cutting; stress ﬁeld; genetic algorithm 1. Introduction In recent years, titanium alloy materials have been widely used in aerospace, shipbuilding, metallurgy, light industry, chemical industry, biomedical and other industries due to their excellent physical and chemical properties. However, the low thermal conductivity and high chemical activity of titanium alloys lead to severe tool wear and low cutting eciency, which are the main factors limiting the development of titanium alloys. In the ﬁeld of tribology, uneven surfaces have the function of reducing friction, and have received unprecedented attention. Therefore, the basic concept of surface texture is proposed. Preparing regularly arranged micro pits or grooves on smooth and susceptible surfaces can greatly reduce the friction and surface abrasion [1–3]. Micro-textures also play an active role in the ﬁeld of modern cutting tools. Milling titanium alloys is intermittent, and cutting process of the cutter is very complicated. The cutting force on the cutter is unevenly distributed during the milling process, and its size and direction change with time. The distribution of the milling force directly aects the stress distribution inside the Appl. Sci. 2020, 10, 818; doi:10.3390/app10030818 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 818 2 of 20 milling insert. Therefore, it is necessary to study the stress ﬁeld of the cutter during the cutting process in order to obtain the worst conditions of the cutter. Cheng and Li studied the stress density function and stress ﬁeld of the corrugated edge milling cutter and concluded that, during the cutting process of the corrugated edge milling cutters, the stress on the cutter is mainly distributed on the main cutting edge near the tip, and the stress is concentrated near the tip [4,5]. Fan et al. studied the cutting stress ﬁeld of ceramic tools with a gradient function by ﬁnite element analysis and obtained the optimal gradient distribution index by modeling the cutting stress ﬁeld under the same cutting load [6,7]. Li et al. carried out milling force prediction experiments on the titanium alloy TC21. The results show that, in the process of high-speed milling TC21 titanium alloy, the cutting depth and feed per tooth have a greater impact on the cutting force, while the cutting speed and radial cutting depth have no signiﬁcant eect on the cutting force [8,9]. Kim and Ehmann simulated the static and dynamic milling force in the face milling process. Based on the machine tool structure and ﬁxture design, a mathematical model of the scattered force components of the face milling cutter was established. Consistent results were obtained from cutting experiments on dierent milling cutters and workpiece materials [10]. Wertheim et al. studied the performance of spiral and serrated edge milling inserts in the cutting process. They believed that curved-edge milling inserts can improve the stability of machining, reduce milling forces and improve chip ﬂow [11]. Guo et al. numerically modeled and experimentally studied the micro-milling force of titanium alloy based on tool runout. The micro-milling force model was validated by analyzing the width of the steps on the edge of the groove [12,13]. Zhang simulated the stress ﬁeld of a ﬂat-faced milling cutter and a 3D complex groove milling cutter using the density function of the milling force as a boundary condition. It was found that a milling cutter with a rake angle and an edge inclination can fundamentally change the stress at the tool tip [14,15]. Sun et al. fabricated micro-grooves and micro-pits on the rake face of WC/Co tools, and then studied the cutting performance of the tools. The results show that the composite texture with micro-pits and micro-slots can be used as a micro-reservoir to continuously supplement lubricating oil, thus improving the cutting performance of the mixed micro-textured cutter [16–18]. Wei et al. conducted tribological and cutting experiments on aluminum alloy workpieces by sandblasting micro-materials and machining micro-geometric features of the rake face of the sapphire tools. The results show that, compared with traditional tools, the micro-textured tool edge has the lowest interfacial friction and the cutting force is signiﬁcantly reduced. Machining micro-textures on the rake face of the cutter can reduce the adhesion of the workpiece material [19]. Pang et al. prepared symmetric conical micro-grooves and parallel micro-grooves on carbide cutters, and then studied the friction performance of the cutters [20]. Lin et al. modeled the cutting force of the vertical milling cutter under the conditions of oblique cutting and proposed a mechanical model for predicting the cutting force of the vertical milling cutters [21]. Li et al. used a multi-level fuzzy comprehensive evaluation method based on multi-objective decision theory to evaluate the cutting performance of micro-textured cutters in titanium alloy processing [22]. Darshan studied the improvement of tribology and thermal environment of inconel-718 alloy by textured tools. The results reveal that the textured tools perform better, ensuring lower tool wear (VB), reduced cutting forces (Fc), lower surface roughness (Ra) and acceptable chip form [23,24]. In summary, placing micro-textures on the surface of a tool to improve the friction reduction and wear resistance of the tool has become a hot topic. However, in the process of milling titanium alloys, there is still a lack of theoretical research and experimental basis for in-depth study of the anti-wear and friction reduction mechanism of micro-textured cutters. Problems such as “secondary cutting” still exist during the cutting process of micro-textured cutters. Reasonable micro-texture arrangement can make the cutters have good anti-wear and anti-friction performance, and it can also solve the secondary wear problem of the micro-textured cutters, thereby improving the processing eciency. Therefore, in this paper, by changing the single density distribution of the micro-texture in the cutter-chip close contact area, the change of the tool stress ﬁeld during cutting titanium alloys with the variable density micro-textured cutter was studied. Based on the stress ﬁeld, the texture variable density distribution of the micro-textured ball-end milling cutters was optimized. Appl. Sci. 2020, 10, 818 3 of 20 Appl. Sci. 2020, 10, 818 3 of 20 2. Experiment of Milling Titanium Alloy with the Variable Density Micro-Textured Ball-End 2. Experiment of Milling Titanium Alloy with the Variable Density Micro-Textured Ball-End Milling Cutter Milling Cutter 2.1. Design and Fabrication of Variable Density Micro-Textures 2.1. Design and Fabrication of Variable Density Micro-Textures Previo Previous us stud studies ies ofof mic micr ro-t o-textur extureded cutt cutters ers used used a una iform uniform distribut distribution ion method method to prepto are pr micr epar oe - textures in the areas where the cutter-chips are in close contact [25,26]. However, from the tool wear micro-textures in the areas where the cutter-chips are in close contact [25,26]. However, from the tool diagr wearam diagram of the of micro the -micr textured o-textur cutt ed ers cutters after cutt after ing cutting titanium titanium alloy, ialloy t can , be it can seen be th seen at ththat e wear the of wear the tool along the contact length and width of the cutter-chip in the compact contact area of the rake face of the tool along the contact length and width of the cutter-chip in the compact contact area of the is rake irregul facear. is T irr he egular wear. ne The ar th wear e cutt ne ing ar the edge cutting is more edge severe is mor , and e, sever as the e,dis and, tance as fr the om distance the cuttin from g edge the gets longer, the wear on the tool becomes less and less [27]. There is also some wear in the direction cutting edge gets longer, the wear on the tool becomes less and less [27]. There is also some wear in the of dir chip ection outfl of chip ow. Th outﬂow is is bec . This ause is , d because, uring the during outflow the of outﬂow chips, of the chips, cutting thespee cutting d of speed the ball of-en the d ball-end milling cutter along the cutting edge is different, which leads to the transverse curl of the chip. As the cutting milling cutter along the cutting edge is dierent, which leads to the transverse curl of the chip. As the dept cutting h incre depth ases, incr theases, e flow the rate ﬂow at th rate e boat ttom the of bottom the chi of p the is dchip ifferent is di from erent flow from rateﬂow at thrate e top at , an the d top, the chip curls upward. Therefore, in the process of chip deformation, “secondary cutting” occurs at the and the chip curls upward. Therefore, in the process of chip deformation, “secondary cutting” occurs edges of the micro-texture, as shown in Figure 1. This phenomenon will cause secondary wear of at the edges of the micro-texture, as shown in Figure 1. This phenomenon will cause secondary wear micro-textured cutters. of micro-textured cutters. Figure 1. Diagram of “secondary cutting” for the micro-textured cutter. Figure 1. Diagram of “secondary cutting” for the micro-textured cutter. In In order order to to so solve lve th the e “ “secondary secondary cutt cutting” ing” ph phenomenon enomenon of of th the e micr micro o-textur -textured ed c cutter utter, , th the e reg region ion where the cutter-chip is in compact contact is divided into three regions according to the wear condition where the cutter-chip is in compact contact is divided into three regions according to the wear con of the dition cutter of, tnamely he cutter, the nﬁrst amely ar ea the Xfi,rst the are second a X1, th are ea secon X , and d arthe ea X thir 2, and d ar th eae X th,ir as d ar shown ea X3, in as Figur shown e 2 . 1 2 3 Studies have shown that pit texture can eectively reduce friction and wear [28,29]. Therefore, by in Figure 2. Studies have shown that pit texture can effectively reduce friction and wear [28,29]. Th changing erefore, the by density changing of micr the o-textur density e of inm each icro-rtex egion, ture the in dynamic each regievolution on, the dynamic of secondary evolution cutting of between micro-textured cutter and the chip was studied. Experiments have shown that a texture secondary cutting between micro-textured cutter and the chip was studied. Experiments have shown th distribution at a texture density distribution (the ratio density of the (thtotal e ratio area of of the the total pit area textur of eth to e the pit tex total ture area to of the the total micr aro-textur ea of the e preparation is deﬁned as the texture distribution density) between 0.05 and 0.1 can play a better role in micro-texture preparation is defined as the texture distribution density) between 0.05 and 0.1 can pla reducing y a better friction role in and reduc wear ing . The friction refor e, anthe d wea micr r. o-textur Therefore, e densities the micro in-tex theture cutter de-chip nsities contact in the ar cutt eaer of - the cemented carbide tool designed in this paper are 0.05, 0.07 and 0.09, respectively. By arranging chip contact area of the cemented carbide tool designed in this paper are 0.05, 0.07 and 0.09, respect and combining ively. By the arrang three ing textur and ecom densities bining in ththe e th cutter ree tex -chip ture compact densities contact in the ar cutt ea,er thr -chip ee uniformly compact distributed micro-textures and six variable density micro-textures were obtained. The distribution contact area, three uniformly distributed micro-textures and six variable density micro-textures were ob combination tained. Theof dithe stribution texturecom density bination is shown of the intex Table ture1 density . is shown in Table 1. Appl. Sci. 2020, 10, 818 4 of 20 Appl. Sci. 2020, 10, 818 4 of 20 Figure 2. Region segmentation of cutter-chip compact contact area of micro-textured cutter. Figure 2. Region segmentation of cutter-chip compact contact area of micro-textured cutter. Table 1. Distribution and combination of dierent density textures. Table 1. Distribution and combination of different density textures. Distribution of Arrangement and Combination of Micro-Texture Distribution of Micro-Texture Arrangement and Combination of Micro-Texture Micro-Texture Uniform distribution 0.05-0.05-0.05, 0.07-0.07-0.07, 0.09–0.09–0.09 Uniform distribution 0.05-0.05-0.05, 0.07-0.07-0.07, 0.09–0.09–0.09 0.05-0.07-0.09, 0.05-0.09-0.07, 0.07-0.05-0.09, Variable density distribution 0.05-0.07-0.09, 0.05-0.09-0.07, 0.07-0.05-0.09, 0.07-0.09-0.05, 0.09-0.07-0.05, 0.09-0.07-0.05. Variable density distribution 0.07-0.09-0.05, 0.09-0.07-0.05, 0.09-0.07-0.05. According to previous studies, when the diameter, depth and distance from the cutting edge of According to previous studies, when the diameter, depth and distance from the cutting edge of the micro-texture are 50 m, 35 m and 120 m, respectively, the micro-textured cutter can achieve the micro-texture are 50 μm, 35 μm and 120 μm, respectively, the micro-textured cutter can achieve better friction reduction and wear resistance [30]. Therefore, the diameter, depth and distance from the better friction reduction and wear resistance [30]. Therefore, the diameter, depth and distance from cutting edge of the micro-texture designed in this paper are 50 m, 35 m and 120 m, respectively. the cutting edge of the micro-texture designed in this paper are 50 μm, 35 μm and 120 μm, According to the three densities of 0.05, 0.07 and 0.09, the center spacing between the micro-textures are respectively. According to the three densities of 0.05, 0.07 and 0.09, the center spacing between the 190 m, 170 m and 150 m, respectively. The micro-textures were then prepared in three areas of the micro-textures are 190 μm, 170 μm and 150 μm, respectively. The micro-textures were then prepared cutter-chip compact contact by using a ﬁber laser. After processing, the melt around the micro-texture in three areas of the cutter-chip compact contact by using a fiber laser. After processing, the melt was cleaned by sandpaper and an ultrasonic cleaner. around the micro-texture was cleaned by sandpaper and an ultrasonic cleaner. 2.2. Design of Test Scheme and Test Equipment 2.2. Design of Test Scheme and Test Equipment 2.2.1. Design of Test Scheme 2.2.1. Design of Test Scheme In this paper, an orthogonal experiment was used to design the experiment of milling titanium In this paper, an orthogonal experiment was used to design the experiment of milling titanium alloy with a micro-textured ball-end milling cutter. By changing cutting parameters, the change of alloy with a micro-textured ball-end milling cutter. By changing cutting parameters, the change of milling force with time and the change of tool-chip contact length and width with the feed and cutting milling force with time and the change of tool-chip contact length and width with the feed and cutting depth were studied. The orthogonal test was designed to include three factors (cutting speed, cutting depth were studied. The orthogonal test was designed to include three factors (cutting speed, cutting depth and feed rate), which contained four levels, as shown in Table 2. L (4 ) was selected in the depth and feed rate), which contained four levels, as shown in Table 2. L16 (4 ) was selected in the orthogonal table for the milling test. orthogonal table for the milling test. Table 2. Cutting parameters for cutting titanium alloys. Table 2. Cutting parameters for cutting titanium alloys. Factor Cutting Depth Cutting Speed Feed per Tooth Factor Cutting Speed Cutting Depth Feed per Tooth a (mm) Level v (m/min) p f (mm/z) c z Level vc (m/min) ap (mm) fz (mm/z) 1 120 0.3 0.04 1 120 0.3 0.04 2 140 0.5 0.06 2 140 0.5 0.06 3 160 0.7 0.08 3 4 160 180 0.7 0.9 0.10 0.08 4 180 0.9 0.10 Appl. Sci. 2020, 10, 818 5 of 20 Appl. Sci. 2020, 10, 818 5 of 20 According to the arrangement and distribution of textures with different densities, nine combinations were obtained, corresponding to nine micro-texture cutters, and then a non-texture According to the arrangement and distribution of textures with dierent densities, nine cutter was used for comparative analysis. Milling titanium alloy test was carried out for each cutter combinations were obtained, corresponding to nine micro-texture cutters, and then a non-texture cutter according to Table 2. Each cutter was tested in 16 groups, and one layer was milled on the workpiece was used for comparative analysis. Milling titanium alloy test was carried out for each cutter according for each set of cutting parameters. Six points were averaged along the length of the workpiece, and a to Table 2. Each cutter was tested in 16 groups, and one layer was milled on the workpiece for each set set of cutting force values were measured at each point location. Then, by averaging six sets of data of cutting parameters. Six points were averaged along the length of the workpiece, and a set of cutting in each layer, the cutting force values in the X, Y, and Z directions for each set of cutting parameters force values were measured at each point location. Then, by averaging six sets of data in each layer, were calculated. This is the basic data for the next calculation of the cutting force test formula. At the the cutting force values in the X, Y, and Z directions for each set of cutting parameters were calculated. same time, the position of the center point was taken to measure the value of the milling force varying This is the basic data for the next calculation of the cutting force test formula. At the same time, the with time. position of the center point was taken to measure the value of the milling force varying with time. 2.2.2. Test Equipment 2.2.2. Test Equipment In this experiment, a VDL-1000E four-axis CNC milling machine (Dalian Machine Tool, Dalian, In this experiment, a VDL-1000E four-axis CNC milling machine (Dalian Machine Tool, Dalian, China) was used for milling titanium alloy test. The test material was titanium alloy TC4, and the China) was used for milling titanium alloy test. The test material was titanium alloy TC4, and the cutter was a micro-textured ball-end milling cutter. Sinusoidal tongs were used to clamp the cutter was a micro-textured ball-end milling cutter. Sinusoidal tongs were used to clamp the workpiece workpiece at an inclined angle of 15 degrees. In the case of planar milling, the tool bit always at an inclined angle of 15 degrees. In the case of planar milling, the tool bit always participates in participates in cutting, and the linear speed is always zero. This will accelerate the wear of the tool cutting, and the linear speed is always zero. This will accelerate the wear of the tool bit, reduce the bit, reduce the service life of the tool, and affect the quality of the machined surface of the workpiece. service life of the tool, and aect the quality of the machined surface of the workpiece. Some scholars Some scholars have found that when the processing angle of the workpiece is 15 degrees, the ball end have found that when the processing angle of the workpiece is 15 degrees, the ball end milling cutter milling cutter can achieve the best cutting performance [31,32]. The processing method adopted in can achieve the best cutting performance [31,32]. The processing method adopted in this paper was this paper was climb milling, and the established milling test platform is shown in Figure 3. The climb milling, and the established milling test platform is shown in Figure 3. The measurement of measurement of milling force was based on a Kistler 9257B dynamometer (Kistler, Winterthur, milling force was based on a Kistler 9257B dynamometer (Kistler, Winterthur, Switzerland) with a Switzerland) with a response frequency of 5000 Hz. The data acquisition system was the response frequency of 5000 Hz. The data acquisition system was the DH5922_1394 signal test and DH5922_1394 signal test and analysis system of Donghua testing company (Jingjiang, China). analysis system of Donghua testing company (Jingjiang, China). Figure 3. Test platform for milling titanium alloy with micro-textured cutter. Figure 3. Test platform for milling titanium alloy with micro-textured cutter. 2.3. Analysis of Milling Force Test Results 2.3. Analysis of Milling Force Test Results In the process of cutting titanium alloy by an orthogonal test, a dynamometer was used to In the process of cutting titanium alloy by an orthogonal test, a dynamometer was used to measure the change of cutting force of nine kinds of variable density micro-textured cutters and measure the change of cutting force of nine kinds of variable density micro-textured cutters and non- non-texture cutters with time. One of the micro-textured cutters with a texture density combination of texture cutters with time. One of the micro-textured cutters with a texture density combination of 0.09–0.09–0.09 is selected as an example. The cutting parameters are: n = 2729 r/min, a = 0.7 mm, f = p z 0.09–0.09–0.09 is selected as an example. The cutting parameters are: n = 2729 r/min, ap = 0.7 mm, fz = 0.08 mm/z, and the changes of the milling forces in the X, Y and Z directions of a milling cycle were 0.08 mm/z, and the changes of the milling forces in the X, Y and Z directions of a milling cycle were collected, as shown in Table 3. collected, as shown in Table 3. Appl. Sci. 2020, 10, 818 6 of 20 Table 3. Variation of milling force with time for micro-textured cutter. Milling Force in A Milling Cycle (s) the Three 0.0004 0.0008 0.0012 0.0016 0.002 0.0024 0.0028 0.0032 0.0036 Directions X(N) 3.15 50.46 122.33 235.85 305.37 226.94 78.26 9.34 0 Y(N) 14.92 77.98 156.15 220.8 284.28 229.1 156.22 12.44 0 Z(N) 17.87 65.51 103.94 136.53 147.88 126.03 79.28 10.63 0 A three-direction milling force data ﬁtting program was written with MATLAB software, and the equations of the three-direction milling force change over time were ﬁtted. The calculation results are 13 4 11 3 9 2 6 F = 7.106 10 t 5.567 10 t + 1.346 10 t 1.009 10 t + 231.1 13 4 11 3 8 2 5 F = 4.598 10 t + 3.656 10 t 8.69 10 t + 5.752 10 t 134.244 . (1) 13 4 11 3 8 2 5 F = 1.89 10 t 1.439 10 t + 3.075 10 t 1.329 10 t + 33.4 2.4. Analysis of Test Results of Cutter-Chip Contact Area Theoretically, the calculation of the contact area between the cutter and the chip is very complicated for the micro-textured ball-end milling cutter. Therefore, in the milling process, the contact diagram method was used to ﬁt the contact area between the ball-end milling cutter and the chip. After the milling, the titanium alloy, nine texture density combinations and non-texture cutters were observed through an ultra-depth microscopy, and the cutter-chip contact area on the front of the cutter was measured. The contact length and width of the cutter-chip contact were approximated by the contact diagram method. Taking a micro-textured cutter with a texture density combination of 0.09–0.09–0.09 as an example, the experimental data of the tool-chip contact length and width obtained by measuring and ﬁtting are shown in Table 4. Table 4. 0.09–0.09–0.09 contact length and width of micro-textured cutter. Cutting Parameters Cutting Depth Feed per Tooth Cutter-Chip Contact Cutter-Chip Contact a (mm) f (mm) Length l (mm) Number p Width l (mm) f z w 1 0.3 0.04 0.768 0.5302 2 0.3 0.06 0.775 0.5613 3 0.3 0.08 0.784 0.5888 4 0.3 0.1 0.788 0.6031 5 0.5 0.06 1.017 0.5691 6 0.5 0.04 1.008 0.5405 7 0.5 0.1 1.029 0.6124 8 0.5 0.08 1.021 0.5911 9 0.7 0.08 1.318 0.5928 10 0.7 0.1 1.327 0.6103 11 0.7 0.04 1.326 0.5445 12 0.7 0.06 1.315 0.5968 13 0.9 0.1 1.658 0.6179 14 0.9 0.08 1.651 0.5946 15 0.9 0.06 1.636 0.5675 16 0.9 0.04 1.628 0.5494 3. Force Density Function of Variable Density Micro-Texture Ball-End Milling Cutter 3.1. Milling Force Model of Micro-Textured Ball-End Milling Cutter The high-speed milling of titanium alloy by micro-textured ball-end milling cutter is intermittent cutting. With the change of the micro-textured cutter from cutting in to cutting out the workpiece, the magnitude and direction of the instantaneous milling force also change, which aects the stress ﬁeld distribution on the front of the cutter. Therefore, it is necessary to solve the milling cycle T, the angle Appl. Sci. 2020, 10, 818 7 of 20 of cutting into workpiece , the time of cutting into the workpiece t and the cutting time t of the in i 0 micro-textured ball-end milling cutter, respectively. The solution process is as follows: T = , (2) n z R a = 180 arccos , (3) in in t = T , (4) t = T t , (5) 0 i where n is the spindle speed (r/min), z is the number of teeth on the tool edge, and R is the tool edge radius. The main factors of cutting parameters aecting milling force are the cutting depth and feed per tooth. Therefore, an empirical formula model of milling force was established by using multiple linear regression method. The empirical formula model of the milling force is as follows: x x 1 2 F = C a f . (6) p z Taking the logarithm of both sides is lgF = lgC + x lga + x lg f . (7) p 2 z j 1 Let f = lgF , a = lgC, a = lga , a = lga , the linearization of Equation (7) is j 0 1 p 2 f f = a + a x + a x . (8) 0 1 1 2 2 The calculation and ﬁtting were performed using MATLAB software, and the milling force test data collected from the X, Y and Z directions of nine variable density combination cutters and non-textured cutters were substituted into the calculation. Taking a micro-textured cutter with a texture density combination of 0.09–0.09–0.09 as an example, the milling forces in the X, Y and Z directions measured by orthogonal tests are shown in Table 5. The experimental data in the table were substituted into MATLAB for calculation and solution, and the coecients and exponentials of the empirical formula for milling forces were obtained. The empirical formulae for the milling forces in three directions obtained by ﬁtting are 0.4685 0.4301 F = 1129.5 a f x p z 0.6881 0.3336 F = 866.99 a f . (9) y p z 0.6825 0.1807 F = 309.99 a f z p z Table 5. Test data and calculation results of milling force of micro-textured cutter. a f F F F p z x y z Number Lg(F ) lg(F ) lg(F ) lg(a ) lg(f ) x y z p z (mm) (mm/z) (N) (N) (N) 1 0.3 0.04 146.61 121.23 73.22 2.17 2.08 1.86 0.52 1.4 2 0.3 0.06 208.35 134.99 96.28 2.32 2.13 1.98 0.52 1.22 3 0.3 0.08 205.80 143.05 80.48 2.31 2.16 1.91 0.52 1.1 4 0.3 0.1 226.13 177.86 88.71 2.35 2.25 1.95 0.52 1 5 0.5 0.06 214.47 197.65 102.15 2.33 2.30 2.01 0.3 1.22 Appl. Sci. 2020, 10, 818 8 of 20 Table 5. Cont. a f F F F p z x y z Number Lg(F ) lg(F ) lg(F ) lg(a ) lg(f ) x y z p z (mm) (mm/z) (N) (N) (N) 6 0.5 0.04 230.43 227.16 139.25 2.36 2.36 2.14 0.3 1.4 7 0.5 0.1 416.26 389.46 135.73 2.62 2.59 2.13 0.3 1 8 0.5 0.08 222.35 216.19 99.25 2.35 2.33 2.00 0.3 1.1 9 0.7 0.08 305.37 284.28 147.88 2.48 2.45 2.17 0.15 1.1 10 0.7 0.1 408.36 296.41 162.39 2.61 2.47 2.21 0.15 1 11 0.7 0.04 238.45 208.29 110.56 2.38 2.32 2.04 0.15 1.4 12 0.7 0.06 348.95 315.82 164.58 2.54 2.50 2.22 0.15 1.22 13 0.9 0.1 355.73 333.41 196.27 2.55 2.52 2.29 0.05 1 14 0.9 0.08 328.63 304.18 200.08 2.52 2.48 2.30 0.05 1.1 15 0.9 0.06 293.05 302.13 178.88 2.47 2.48 2.25 0.05 1.22 16 0.9 0.04 280.62 293.06 152.83 2.45 2.47 2.18 0.05 1.4 3.2. Test Formula for Cutter-Chip Contact Area In the process of cutting titanium alloy with a micro-textured ball-end milling cutter, the milling force is distributed unevenly along the length and width of the cutter-chip contact, and the cutter-chip contact area directly aects the stress density function of the cutter surface. With the change of cutting parameters and texture density in the cutter-chip compact contact area, the cutter-chip contact area also changes. Therefore, it is necessary to solve the experimental formula of the cutter-chip contact area to determine the force density function of the variable density micro-textured ball-end milling cutter when milling titanium alloy. The experimental data of tool-chip contact length l and width l were ﬁtted and calculated by using MATLAB software. The relationships between l and feed per tooth f , as well as l and cutting depth a were linear functions. Taking a micro-textured cutter with a z w p texture density of 0.09–0.09–0.09 as an example, the obtained linear functions are f = 0.7808l 0.3824 z f . (10) a = 0.6872l 0.2181 p w Substituting Equation (10) into Equation (9), the milling forces for milling a titanium alloy using a micro-textured ball-end milling cutter with a texture density of 0.09–0.09–0.09 are 0.4301 0.4685 ( ) F = 1129.5 0.6872l 0.2181 0.7808l 0.3824 x w 0.3336 0.6881 . (11) F = 866.99 (0.6872l 0.2181) 0.7808l 0.3824 y w f 0.1807 0.6825 F = 309.99 (0.6872l 0.2181) 0.7808l 0.3824 z w 3.3. Establishment of Force Density Function for Variable Density Micro-Textured Cutter When micro-textured ball-end milling cutter cuts titanium alloy, the instantaneous milling forces in the three directions vary with time in the cutter-chip contact area, and the distributions along the cutter-chip contact length and width are uneven. Therefore, the second-order mixed partial derivative of the instantaneous milling force model was used to solve the force density function of the micro-textured ball-end milling cutter, and the instantaneous cutting force variation at a point on the cutter can be obtained by solving the force density function. By calculating the second-order mixed partial derivative of Equation (11), the force density functions of a micro-textured cutter with a texture density combination of 0.09–0.09–0.09 in the coordinate system of the machine tool can be obtained as follows: 0.5699 @F 0.5315 f = = 171.634(l 0.3174) l 0.4898 x w @l @l w f 0.6664 @F y 0.3119 f = = 141.565(l 0.3174) l 0.4898 , (12) y w @l @l w f 0.8193 @F 0.3175 f = = 28.301(l 0.3174) l 0.4898 z w @l @l w f Appl. Sci. 2020, 10, 818 9 of 20 l  1.072,1.929 l  0.5905, 0.6680     w f Appl. where Sci. 2020, 10, 818 , and . 9 of 20 The force density functions above of the micro-textured ball-end milling cutter are solved in the coordinate system of the machine tool. However, the magnitude and direction of the instantaneous where l 2 (1.072, 1.929), and l 2 (0.5905, 0.6680). w f cutting force of the micro-textured ball-end milling cutter change with the rotation of the cutter from The force density functions above of the micro-textured ball-end milling cutter are solved in the cutting in to cutting out the workpiece. The schematic diagram of the cutter from cutting in to cutting coordinate system of the machine tool. However, the magnitude and direction of the instantaneous out the workpiece is shown in Figure 4. Setting XYZ as the workpiece coordinate system and XcYcZc cutting force of the micro-textured ball-end milling cutter change with the rotation of the cutter as the tool coordinate system, Figure 4a shows the process from cutting in to cutting out of the micro- from tex cutting tured ba inll to -end cutting milliout ng cutt theer, workpiece. and Figure The 4bschematic shows the diagram relationship of the bet cutter ween fr th om e co cutting ordinate in to systems of the tool and the machine tool during the cutting process of the micro-textured cutter. It cutting out the workpiece is shown in Figure 4. Setting XYZ as the workpiece coordinate system and can be seen from the Figure 4 that the coordinate system of the micro-textured cutter changes with XcYcZc as the tool coordinate system, Figure 4a shows the process from cutting in to cutting out of the time during the process of cutting from point A to point B. Therefore, it is necessary to transform the micro-textured ball-end milling cutter, and Figure 4b shows the relationship between the coordinate milling force in the coordinate system of the machine tool to solve the force density function in the systems of the tool and the machine tool during the cutting process of the micro-textured cutter. It can coordinate system of the tool. According to the transformation relationship, its transformation matrix be seen from the Figure 4 that the coordinate system of the micro-textured cutter changes with time is during the process of cutting from point A to point B. Therefore, it is necessary to transform the milling force in the coordinate system of the machine tool to solve the force density function in the coordinate cos sin 0  system of the tool. According to the transformation relationship, its transformation matrix is  T sin cos 0 . (13)  2 3 6 cos sin 0 7 0 0 1 6 7  6 7 6 7 6 7 T = 6 sin cos 0 7. (13) 6 7 6 7 4 5 0 0 1 (a) (b) Figure 4. The schematic diagram of rotation period and coordinate system conversion diagram of Figure 4. The schematic diagram of rotation period and coordinate system conversion diagram of micro-textured cutter. (a) the process from cutting in to cutting out of the micro-textured ball-end micro-textured cutter. (a) the process from cutting in to cutting out of the micro-textured ball-end milling cutter; (b) the relationship between the coordinate systems of the cutter and coordinate system of the machine tool. Appl. Sci. 2020, 10, 818 10 of 20 According to the coordinate transformation of Equation (13), the force density function of the micro-textured cutter in the coordinate system of the cutter can be obtained as follows: 2 3 2 3 2 3 f f f cos + f sin 6 7 6 7 6 7 x x x y 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 f 7 = T 6 f 7 = 6 f sin + f cos 7, (14) y y x y 6 1 7 6 7 6 7 6 7 6 7 6 7 4 5 4 5 4 5 f f f z z z 0.5699 0.6664 0.5315 0.3119 f = 148.639(l 0.3174) l 0.4898 + 70.783(l 0.3174) l 0.4898 x w f w f 0.5699 0.6664 0.5315 0.3119 , (15) f = 85.817(l 0.3174) l 0.4898 122.599(l 0.3174) l 0.4898 y w f w f 0.8193 0.3175 f = 28.301(l 0.3174) l 0.4898 z w where = 150 . Similarly, the force density functions of the other eight texture density combination cutters and non-texture cutters were solved, and the force density functions are obtained as follows. The force density functions of a micro-textured cutter with a texture density combination of 0.09–0.07–0.05 are 0.5678 0.6458 0.5293 0.4005 f = 142.699(l 0.3108) l 0.4895 + 62.682(l 0.3108) l 0.4895 x w f w f 0.5678 0.6458 0.5293 0.4005 . (16) f = 82.388(l 0.3108) l 0.4895 108.568(l 0.3108) l 0.4895 y w f w f 0.8806 0.4382 f = 12.771(l 0.3108) l 0.4895 z w The force density functions of a micro-textured cutter with a texture density combination of 0.09–0.05–0.07 are 0.5739 0.685 0.4713 0.3893 f = 179.758(l 0.3233) l 0.4907 + 58.479(l 0.3233) l 0.4907 x w w f f 0.5739 0.685 0.4713 0.3893 . (17) f = 103.784(l 0.3233) l 0.4907 101.288(l 0.3233) l 0.4907 y w w f f 0.6767 0.4836 ( ) f = 61.105 l 0.3233 l 0.4907 z w f The force density functions of a micro-textured cutter with a texture density combination of 0.07–0.07–0.07 are 0.5214 0.7031 0.6146 0.1417 f = 167.426(l 0.4282) l 0.5122 + 79.135(l 0.4182) l 0.5122 x w w f f 0.5214 0.7031 0.6146 0.1417 . (18) f = 96.664(l 0.4282) l 0.5122 137.066(l 0.4182) l 0.5122 y w f w f 0.7283 0.4476 f = 34.777(l 0.4282) l 0.5122 z w f The force density functions of a micro-textured cutter with a texture density combination of 0.07–0.09–0.05 are 0.5129 0.7777 0.49 0.585 f = 246.387(l 0.4092) l 0.5117 + 21.275(l 0.4092) l 0.5117 x w f w f 0.5129 0.7777 0.49 0.585 . (19) ( ) ( ) f = 142.252 l 0.4092 l 0.5117 36.849 l 0.4092 l 0.5117 y w f w f 0.8316 0.6822 f = 12.029(l 0.4092) l 0.5117 z w f The force density functions of a micro-textured cutter with a texture density combination of 0.07–0.05–0.09 are 0.5157 0.7199 0.537 0.5536 ( ) ( ) f = 245.621 l 0.425 l 0.5163 + 40.356 l 0.425 l 0.5163 x w f w f 0.5157 0.7199 0.537 0.5536 . (20) f = 141.809(l 0.425) l 0.5163 69.898(l 0.425) l 0.5163 y w f w f 0.8101 0.644 f = 20.433(l 0.425) l 0.5163 z w f Appl. Sci. 2020, 10, 818 11 of 20 The force density functions of a micro-textured cutter with a texture density combination of 0.05–0.05–0.05 are 0.576 0.5698 0.574 0.5271 f = 177.396(l 0.5205) l 0.5268 + 108.216(l 0.5205) l 0.5268 x w w f f 0.576 0.5698 0.574 0.5271 ( ) ( ) . (21) f = 102.419 l 0.5205 l 0.5268 187.436 l 0.5205 l 0.5268 y w f w f 0.7086 0.8071 f = 20.039(l 0.5205) l 0.5268 z w f The force density functions of a micro-textured cutter with a texture density combination of 0.05–0.09–0.07 are 0.555 0.5445 0.5369 0.4862 ( ) ( ) f = 202.356 l 0.5389 l 0.5279 + 124.856 l 0.5389 l 0.5279 x w f w f 0.555 0.5445 0.5369 0.4862 . (22) f = 116.831(l 0.5389) l 0.5279 216.257(l 0.5389) l 0.5279 y w f w f 0.7014 0.8301 f = 15.432(l 0.5389) l 0.5279 z w f The force density functions of a micro-textured cutter with a texture density combination of 0.05–0.07–0.09 are 0.5072 0.504 0.5011 0.4508 f = 253.111(l 0.5139) l 0.5258 + 150.226(l 0.5139) l 0.5258 x w f w f 0.5072 0.504 0.5011 0.4508 . (23) f = 146.134(l 0.5139) l 0.5258 260.198(l 0.5139) l 0.5258 y w f w f 0.6886 0.7672 f = 19.46(l 0.5139) l 0.5258 z w The force density functions of the non-textured cutters are 0.608 0.6044 0.6117 0.5814 f = 147.123(l 0.6216) l 0.5468 + 86.922(l 0.6216) l 0.5468 x w f w f 0.608 0.6044 0.6117 0.5814 . (24) f = 84.942(l 0.6216) l 0.5468 150.553(l 0.6216) l 0.5468 y w f w f 0.7724 0.8193 f = 14.263(l 0.6216) l 0.5468 z w f 4. Stress Field Simulation of Variable Density Micro-Textured Ball-End Milling Cutter 4.1. Establishing the Tool Model Due to the limitation of conditions, it is impossible to measure the instantaneous stress ﬁeld of the cutter in real time by an experimental method. Therefore, in this paper, the ﬁnite element simulation method was used to study the distribution of the stress ﬁeld of the cutter during the titanium alloy cutting process. The instantaneous change of the stress ﬁeld at any point on the cutting tool was obtained by ﬁnite element simulation, which provided basic data for further optimizing the parameter design of the micro-textures. First, the cutter was modeled by SolidWorks, a micro-textured cutter with a texture density combination of 0.09–0.09–0.09 was taken as an example, and the model of the cutter is shown in Figure 5. The tool diameter is 20 mm and the micro-texture is placed in the cutter-chip compact contact area. The shape of the micro-texture is micro-pits with a diameter of 50 m and a depth of 35 m, and the distance from the cutting edge is 120 m. The micro-textures are uniformly distributed, and the center distance between adjacent textures is 150 m. The material parameters of the cutter are shown in Table 6. Appl. Sci. 2020, 10, 818 12 of 20 Appl. Sci. 2020, 10, 818 12 of 20 textures are uniformly distributed, and the center distance between adjacent textures is 150 μm. The Appl. Sci. 2020, 10, 818 12 of 20 material parameters of the cutter are shown in Table 6. textures are uniformly distributed, and the center distance between adjacent textures is 150 μm. The material parameters of the cutter are shown in Table 6. Figure 5. The blade model. Figure Figure5. 5. The b The blade lade m model. odel. Table 6. Constitutive parameters of the tool materials [33]. Table 6. Constitutive parameters of the tool materials [33]. Table 6. Constitutive parameters of the tool materials [33]. Specific Coefficient of Modulus Coecient of Thermal Heat Melting Boiling Thermal Modulus of Speciﬁc SpeciHeat fic Density Thermal of Poisson Density Thermal Poisson Melting Boiling Coefficient of Modulus Conductivity Capacity Point Point Conductivity Elasticity Capacity 3 Thermal Heat Melting Boiling kg/ kg m /m Expansion Expansion Elasticity Ratio Ratio Point ( C) Point ( C) Density (W/(mC)) Thermal E (Gpa) of Poisson C (J/(kgC)) (W/(m· C)) C (°C) (°C) 6 1 (10 C ) Conductivity −6 −1 Capacity Point Point α (× 10 C ) E (Gpa) kg/m Expansion Elasticity Ratio . (J/(kg C)) 14,700 (W/(m 75.4 · C)) 4.5 540 0.3 470 C 2780 (°C) 6000 (°C) −6 −1 α (× 10 C ) E (Gpa) 14,700 75.4 4.5 540 0.3 470 2780 6000 (J/(kg C)) 14,700 75.4 4.5 540 0.3 470 2780 6000 ANSYS Workbench 16.0 software (ANSYS company, Canonsburg, PA, USA) was used to simulate ANSYS Workbench 16.0 software (ANSYS company, Canonsburg, PA, USA) was used to and analyze the instantaneous stress ﬁeld of the cutter. A force distribution simulation of the simulate and analyze the instantaneous stress field of the cutter. A force distribution simulation of ANSYS Workbench 16.0 software (ANSYS company, Canonsburg, PA, USA) was used to micro-textured ball-end milling cutter was carried out, following the steps of inputting model, deﬁning the micro-textured ball-end milling cutter was carried out, following the steps of inputting model, simulate and analyze the instantaneous stress field of the cutter. A force distribution simulation of material attributes, partitioning meshes, deﬁning boundary conditions, solving the problem, and defining material attributes, partitioning meshes, defining boundary conditions, solving the problem, the micro-textured ball-end milling cutter was carried out, following the steps of inputting model, analyzing images. Meshing is very important, and the quality of meshing directly determines the and analyzing images. Meshing is very important, and the quality of meshing directly determines defining material attributes, partitioning meshes, defining boundary conditions, solving the problem, accuracy of simulation results. Therefore, it is necessary to reﬁne the grids of the cutter-chip contact the accuracy of simulation results. Therefore, it is necessary to refine the grids of the cutter-chip and analyzing images. Meshing is very important, and the quality of meshing directly determines area. Mesh optimization was performed using the ICEM CFD module in the ANSYS Workbench. contact area. Mesh optimization was performed using the ICEM CFD module in the ANSYS the accuracy of simulation results. Therefore, it is necessary to refine the grids of the cutter-chip Tetrahedral mesh is suitable for fast and ecient meshing of complex models, which is realized through Workbench. Tetrahedral mesh is suitable for fast and efficient meshing of complex models, which is contact area. Mesh optimization was performed using the ICEM CFD module in the ANSYS automatic mesh generation. Therefore, tetrahedral mesh was used in the mesh model. There are realized through automatic mesh generation. Therefore, tetrahedral mesh was used in the mesh Workbench. Tetrahedral mesh is suitable for fast and efficient meshing of complex models, which is 931,230 nodes in total and the minimum edge length is 2.5 10 m. The meshing of the cutting tool −8 model. There are 931,230 nodes in total and the minimum edge length is 2.5 × 10 m. The meshing of realized through automatic mesh generation. Therefore, tetrahedral mesh was used in the mesh is shown in Figure 6. The fewer the optimized mesh nodes, the accurate and faster the calculation. It the cutting tool is shown in Figure 6. The fewer the optimized mesh nodes, th− e 8 accurate and faster model. There are 931,230 nodes in total and the minimum edge length is 2.5 × 10 m. The meshing of turns out that the force distribution for the simulated micro-textured ball-end milling cutter is very the calculation. It turns out that the force distribution for the simulated micro-textured ball-end the cutting tool is shown in Figure 6. The fewer the optimized mesh nodes, the accurate and faster close to the force distribution in actual machining. milling cutter is very close to the force distribution in actual machining. the calculation. It turns out that the force distribution for the simulated micro-textured ball-end milling cutter is very close to the force distribution in actual machining. Figure 6. Mesh partition of the cutter. Appl. Sci. 2020, 10, 818 13 of 20 Appl. Sci. 2020, 10, 818 13 of 20 Figure 6. Mesh partition of the cutter. 4.2. Setting Boundary Conditions 4.2. Setting Boundary Conditions Boundary conditions and loads should be set on the model of the cutter before performing a Boundary conditions and loads should be set on the model of the cutter before performing a finite element simulation. In the actual machining process, the cutter was fixed to the cutter arbor by ﬁnite element simulation. In the actual machining process, the cutter was ﬁxed to the cutter arbor by screw, which limited the axial and radial translation of the cutter, and then the cutter arbor rotated screw, which limited the axial and radial translation of the cutter, and then the cutter arbor rotated with the spindle. Therefore, in the finite element model, the screw hole of the cutter was set to a fixed with the spindle. Therefore, in the ﬁnite element model, the screw hole of the cutter was set to a ﬁxed constraints to restrict the translational movement of the cutter in the axial and radial directions, as constraints to restrict the translational movement of the cutter in the axial and radial directions, as shown in Figure 7. During the cutting process, the cutting force on the cutter is mainly caused by the shown in Figure 7. During the cutting process, the cutting force on the cutter is mainly caused by the squeeze between the cutter and the workpiece and the friction between the front face of the cutter squeeze between the cutter and the workpiece and the friction between the front face of the cutter and the chip, and the cutting force is equivalent to a surface load on the cutter-chip contact area of and the chip, and the cutting force is equivalent to a surface load on the cutter-chip contact area of the the rake face of the cutter. However, the distributions of milling forces along the length and width of rake face of the cutter. However, the distributions of milling forces along the length and width of the the cutter-chip contact area are uneven, which is a function of time. Therefore, the force density cutter-chip contact area are uneven, which is a function of time. Therefore, the force density function function of the cutter calculated in the previous section was applied as a load to the cutter-chip of the cutter calculated in the previous section was applied as a load to the cutter-chip contact area of contact area of the cutter. the cutter. Figure 7. Boundary conditions of the simulation model. Figure 7. Boundary conditions of the simulation model. 4.3. Analysis of the Simulation Results 4.3. Analysis of the Simulation Results After setting the boundary conditions and loads, the stress ﬁeld of the micro-textured ball-end After setting the boundary conditions and loads, the stress field of the micro-textured ball-end milling cutter was simulated by ﬁnite element method. When the micro-textured ball-end milling cutter milling cutter was simulated by finite element method. When the micro-textured ball-end milling just cut into the workpiece as the initial time, the time to cut out the workpiece was 0.0036 s. Through cutter just cut into the workpiece as the initial time, the time to cut out the workpiece was 0.0036 s. simulation analysis, it can be concluded that the stress ﬁeld of the micro-textured ball-end milling cutter Through simulation analysis, it can be concluded that the stress field of the micro-textured ball-end reached the maximum value when the workpiece was in 0.002 s. The simulation results are shown in milling cutter reached the maximum value when the workpiece was in 0.002 s. The simulation results Table 7. From the simulation plots of the equivalent stress and equivalent displacement, it can be seen are shown in Table 7. From the simulation plots of the equivalent stress and equivalent displacement, that a stress concentration occurred in the contact area between the cutter and the chip on the rake face it can be seen that a stress concentration occurred in the contact area between the cutter and the chip of the non-textured cutter during the ﬁnishing process of titanium alloy. The reason is that, during on the rake face of the non-textured cutter during the finishing process of titanium alloy. The reason the ﬁnishing process of titanium alloy, the plastic deformation of the workpiece causes the extrusion is that, during the finishing process of titanium alloy, the plastic deformation of the workpiece causes of the cutter and the workpiece in the cutter-chip contact area, thereby changing the metallographic the extrusion of the cutter and the workpiece in the cutter-chip contact area, thereby changing the structure of the cutter-chip contact area and leading to the occurrence of stress concentration. During metallographic structure of the cutter-chip contact area and leading to the occurrence of stress the titanium alloy cutting process, the force and deformation of the micro-textured cutter are more concentration. During the titanium alloy cutting process, the force and deformation of the micro- uniform than those of the non-textured cutter, and the stress concentration is less. The maximum textured cutter are more uniform than those of the non-textured cutter, and the stress concentration deformation zone and the maximum stress value of the micro-textured cutter are smaller than those of is less. The maximum deformation zone and the maximum stress value of the micro-textured cutter the non-textured cutting cutter. The simulation results fully show that the micro-textures play a role in are smaller than those of the non-textured cutting cutter. The simulation results fully show that the reducing friction and wear on the rake face of the cutter. micro-textures play a role in reducing friction and wear on the rake face of the cutter. Table 7. Simulation results of stress field. Appl. Sci. 2020, 10, 818 14 of 20 Appl. Sci. 2020, 10, 818 14 of 20 Ap App pl. l. Sci. Sci. 2020 2020,, 10 10, , 8 81 18 8 14 14 of of 20 20 Appl. Sci. 2020, 10, 818 14 of 20 Appl. Sci. 2020, 10, 818 14 of 20 ApAp pl. p Sci. l. Sci. 2020 2020 , 10 , , 10 81 , 8 8 18 14 14 of of 20 20 Appl. Sci. 2020, 10, 818 14 of 20 App Ap l. Sci. pl. Sci. 2020 2020 , 10,, 10 81, 88 18 14 14 of of 20 20 Ap Ap pl. pSci. l. Sci. 2020 2020 , 10 , 10 , 8, 18 81 8 1414 of of 2020 Table 7. Simulation results of stress ﬁeld. Combinatio Combinatio Co Co mbinat mbinat ioio Combinatio Combinatio Combinatio Combinatio Combinatio Co Co Co mbinat mbinat mbinat ioio io n of Texture Equivalent Stress Equivalent Displacement n of Texture Equivalent Stress Equivalent Displacement n n ofof Texture Texture Eq Eq uiv uiv alent alent Str Str ess ess Eq Eq uiv uiv alent alent Di Di spsp lac lac ement ement n of Texture Equivalent Stress Equivalent Displacement Combination of Texture n of n of Texture Texture EqEq uiv uiv alent alent Str Str ess ess EqEq uiv uiv alent alent Di Di spsp lac lac ement ement n of n of Texture Texture EqEq uiv uiv alent alent Str Str ess ess EqEq uiv uiv alent alent Di Di splac splac ement ement n of n of Texture Texture Eq Eq uiv uiv alent alent Str Str ess ess Eq Eq uiv uiv alent alent Di Di spsp lac lac ement ement n of Texture Equivalent Equivalent Stress Stress Eq Equivalent uivalent Di Displacement splacement Density Density Den Densit sity y Density Density Den Den sitsit y y Density Den Den sity sit y Den Den sit sit y y 9 6 Maximum value: 3.9444 109 Maximum value: 4.1231 10 -6 9 9 - -6 6 Maximum value: 3.9444×10 9 Maximum value: 4.1231×10 -6 Maximu Maximum m v valu alue: e: 3 3..9444 9444××1 10 0 Maximu Maximum m v valu alue: e: 4 4..1231 1231××1 10 0 Maximum value: 3.9444×109 Maximum value: 4.1231×10-6 9 9 -6 -6 Maximum value: 3.9444×10 Maximum value: 4.1231×10 Maximu Maximu m m valu valu e: e: 3. 9444 3.9444×× 101 0 9 Maximu Maximu m m valu valu e: e: 4. 1231 4.1231×× 1010 -6 9 9 -6 -6 Maximum value: 3.9444×1 9 09 Maximum value: 4.1231×1 -60-6 Maximu Maximu m v m alu valu e: 3 e: .9444 3.9444 ×1× 0 1 0 Maximu Maximu m v m alu valu e: 4 e: .1231 4.1231 ×1× 0 1 0 Maximu Maximu mm valu valu e: e: 3. 9444 3.9444×× 101 0 Maximu Maximu mm valu valu e: e: 4. 1231 4.1231×× 1010 0.05-0.05-0.05 0.05-0.05-0.05 0. 0.05 05- -0. 0.05 05- -0 0..05 05 0.05-0.05-0.05 0.05-0.05-0.05 0.05 0.05 -0.-05 0.05 -0.-05 0.05 0.05-0.05-0.05 0.05 0.-05 0.05 -0.-05 0.05 -0. 05 0.05 0.05 -0. -05 0.05 -0- .05 0.05 9 6 9 -6 9 -6 Maximum Maximum value: value: 2.6527 2.6527× 1 10 0 9 9 Maximu Maximum m valu value: e: 3.3.887 887× 1010 -6 -6 Maximum value: 2.6527×10 Maximum value: 3.887×10 Maximu Maximu mm valu valu e: e: 2. 6527 2.6527×× 101 9 0 Maximu Maximu mm valu valu e: e: 3. 887 3.887×× 101 -60 9 -6 Maximum value: 2.6527×109 Maximum value: 3.887×10-6 9 -6 Maximu Maximu m m valu valu e: e: 2. 6527 2.6527×× 109 1 0 Maximu Maximu m m valu valu e: e: 3. 887 3.887×× 10-1 60 9 9 9 -6 --6 6 Maximu Maximu m m valu valu e: 2 e: .6527 2.6527 ×1× 0 1 0 Maximu Maximu m m valu valu e: 3 e: .887 3.887 ×1× 0 1 0 Maximu Maximu m m valu valu e: e: 2. 6527 2.6527×× 101 0 Maximu Maximu m m valu valu e: e: 3. 887 3.887×× 1010 Maximum value: 2.6527×10 Maximum value: 3.887×10 0.05-0.07-0.09 0.05-0.07-0.09 0.05-0.07-0.09 0.05 0.05 -0.-07 0.07 -0.-09 0.09 0.05-0.07-0.09 0.05-0.07-0.09 0.05-0.07-0.09 0.05-0.07-0.09 0.05-0.07-0.09 0.05 0. 0.05 05 -0. --07 0. 0.07 07 -0- .-09 0 0..09 09 9 -6 9 9 9 - -6 66 Maximum value: 3.6813×10 9 Maximum value: 4.0945×10 -6 Maximum value: 3.6813×10 Maximum value: 4.0945×10 Maximum Maximu Maximu mvalue: m valu valu e: 3.6813 e: 3. 6813 3.6813×× 10 101 9 0 Maximu Maximum Maximu mm vvalue: alu valu e: e: 4. 4.0945 0945 4.0945×× 1010 1 -60 9 9 -6 -6 Maximum value: 3.6813×10 Maximum value: 4.0945×10 Maximum value: 3.6813×10 9 Maximum value: 4.0945×10 -6 Maximum value: 3.6813×109 9 Maximum value: 4.0945×10-6 -6 Maximum value: 3.6813×1 9 09 Maximum value: 4.0945×1 -60-6 Maximum value: 3.6813×10 Maximum value: 4.0945×10 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 3. 6813 3 3..6813 6813××× 101 1 0 0 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 4. 0945 4 4..0945 0945××× 101 10 0 0.05-0.09-0.07 0. 0.05 05- -0. 0.09 09- -0 0..07 07 0.05-0.09-0.07 0.05-0.09-0.07 0.05-0.09-0.07 0.05 0.05 -0.-09 0.09 -0.-07 0.07 0.05-0.09-0.07 0.05 0.-05 0.09 -0.-09 0.07 -0. 07 0.05 0.05 -0. -09 0.09 -0- .07 0.07 9 -6 9 -6 9 9 -6 -6 Maximu Maximu m m valu valu e: e: 2. 849 2.849×× 101 0 Maximu Maximu m m valu valu e: e: 3. 5375 3.5375×× 1010 Maximum value: 2.849×1 9 90 Maximum value: 3.5375×1 -606 Maximum value: 2.849×10 Maximum value: 3.5375×10 9 9 -6 -6 Maximum Maximum value: value: 2.849 2.849× 1 10 0 Maximu Maximum m valu value: e: 3.5375 3.5375×1010 Maximu Maximu m m valu valu e: e: 2. 849 2.849×× 109 1 0 9 Maximu Maximu m m valu valu e: e: 3. 5375 3.5375×× 10-1 60 -6 9 9 -6 -6 Maximu Maximu m m valu valu e: 2 e: .849 2.849 ×1× 0 1 09 Maximu Maximu m m valu valu e: 3 e: .5375 3.5375 ×1× 0 1 0-6 Maximum value: 2.849×10 Maximum value: 3.5375×10 Maximu Maximu mm valu valu e: e: 2. 849 2.849×× 101 0 Maximu Maximu mm valu valu e: e: 3. 5375 3.5375×× 1010 0.07-0.07-0.07 0.07-0.07-0.07 0.07 0.07 -0.-07 0.07 -0.-07 0.07 0.07-0.07-0.07 0.07-0.07-0.07 0.07 0.07 -0.-07 0.07 -0.-07 0.07 0.07 0.-07 0.07 -0.-07 0.07 -0. 07 0.07 0.07 -0.-07 0.07 -0.-07 0.07 0.07-0.07-0.07 9 -6 9 9 - -6 6 Maximum value: 2.7749×10 9 Maximum value: 3.9043×10 -6 Maximum value: 2.7749×10 Maximum value: 3.9043×10 Maximu Maximu mm valu valu e: e: 2. 7749 2.7749×× 101 9 0 Maximu Maximu mm valu valu e: e: 3. 9043 3.9043×× 101 -60 9 9 9 -6 -66 Maximum value: 2.7749×10 Maximum value: 3.9043×10 Maximum value: 2.7749×10 9 Maximum value: 3.9043×10 -6 Maximum Maximum value: value: 2.7749 2.7749× 1 10 09 9 Maximu Maximum m valu value: e: 3.9043 3.9043×1010 -6 -6 Maximum value: 2.7749×1 9 09 Maximum value: 3.9043×1 -60-6 Maximum value: 2.7749×10 Maximum value: 3.9043×10 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 2. 7749 2 2..7749 7749××× 101 1 0 0 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 3. 9043 3 3..9043 9043××× 101 10 0 0.07-0.05-0.09 0. 0.07 07- -0. 0.05 05- -0 0..09 09 0.07-0.05-0.09 0.07-0.05-0.09 0.07 0.07 -0.-05 0.05 -0.-09 0.09 0.07-0.05-0.09 0.07-0.05-0.09 0.07 0.-07 0.05 -0.-05 0.09 -0. 09 0.07 0.07 -0. -05 0.05 -0- .09 0.09 9 9 -6 -6 9 -6 Maximum value: 2.6155×10 9 Maximum value: 3.7479×10 -6 Maximu Maximum m v valu alue: e: 2 2..6155 6155××1 10 0 Maximu Maximum m v valu alue: e: 3 3..7479 7479××1 10 0 Maximum value: 2.6155×109 Maximum value: 3.7479×10-6 9 9 -6 -6 Maximum value: 2.6155×10 9 Maximum value: 3.7479×10 6 Maximu Maximu m m valu valu e: e: 2. 6155 2.6155×× 109 1 0 9 Maximu Maximu m m valu valu e: e: 3. 7479 3.7479×× 10-1 60 -6 Maximum value: 2.6155 10 9 Maximum value: 3.7479 10 -6 Maximum value: 2.6155×1 9 09 Maximum value: 3.7479×1 -60-6 Maximu Maximu m v m alu valu e: 2 e: .6155 2.6155 ×1× 0 1 0 Maximu Maximu m v m alu valu e: 3 e: .7479 3.7479 ×1× 0 1 0 Maximu Maximu mm valu valu e: e: 2. 6155 2.6155×× 101 0 Maximu Maximu mm valu valu e: e: 3. 7479 3.7479×× 1010 0.07 0.07 -0.-09 0.09 -0.-05 0.05 0.07-0.09-0.05 0.07-0.09-0.05 0.07-0.09-0.05 0.07 0.07 -0.-09 0.09 -0.-05 0.05 0.07-0.09-0.05 0.07 0.-07 0.09 -0.-09 0.05 -0. 05 0.07-0.09-0.05 0.07 0.07 -0. -09 0.09 -0- .05 0.05 9 -6 9 -6 Maximum value: 2.1418×10 9 9 Maximum value: 2.891×10 -6 -6 Maximum value: 2.1418×10 Maximum value: 2.891×10 Maximu Maximu mm valu valu e: e: 2. 1418 2.1418×× 101 9 0 Maximu Maximu mm valu valu e: e: 2. 891 2.891×× 101 -60 9 -6 Maximum value: 2.1418×109 Maximum value: 2.891×10-6 Maximum value: 2.1418×10 9 Maximum value: 2.891×10 -6 Maximum value: 2.1418×109 Maximum value: 2.891×10-6 Maximum value: 2.1418×1 9 09 9 Maximum value: 2.891×1 -60--6 6 Maximum value: 2.1418×10 Maximum value: 2.891×10 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 2. 1418 2 2..1418 1418××× 101 1 0 0 Maximu Maximu Maximu mm m valu v valu alu e: e: e: 2. 891 2 2..891 891××× 101 10 0 Appl. Sci. 2020, 10, 818 15 of 20 Table 7. Cont. Combination of Texture Equivalent Stress Equivalent Displacement Density Ap Ap pl. pSci. l. Sci. 2020 2020 , 10 , 10 , 8, 18 81 8 1515 of of 2020 Ap Ap pl. pSci. l. Sci. 2020 2020 , 10 , 10 , 8, 18 81 8 1515 of of 2020 Appl. Sci. 2020, 10, 818 15 of 20 Appl. Sci. 2020, 10, 818 15 of 20 Appl. Sci. 2020, 10, 818 15 of 20 Appl. Sci. 2020, 10, 818 15 of 20 9 6 Maximum value: 2.1418 10 Maximum value: 2.891 10 0.09 0.09 –0. –09 0.09 – – 0.09–0.09– 0.09–0.09– 0.09–0.09–0.09 0.09 0.09 –0. –09 0.09 – – 0.09 0.09 –0. –09 0.09 – – 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 9 6 9 9 -6 -6 Maximum value: 2.0607 109 9 Maximum value: 3.0588 10 -6 -6 Maximu Maximu mm valu valu e: e: 2. 0607 2.0607×× 101 9 09 Maximu Maximu mm valu valu e: e: 3. 0588 3.0588×× 101 -60 -6 Maximu Maximu mm valu valu e: e: 2. 0607 2.0607×× 101 0 Maximu Maximu mm valu valu e: e: 3. 0588 3.0588×× 1010 Maximum value: 2.0607×10 Maximum value: 3.0588×10 Maximum value: 2.0607×109 Maximum value: 3.0588×10-6 9 -6 Maximum value: 2.0607×10 Maximum value: 3.0588×10 Maximum value: 2.0607×10 Maximum value: 3.0588×10 0.09-0.05-0.07 0.09 0.09 -0.-05 0.05 -0.-07 0.07 0.09 0.09 -0.-05 0.05 -0.-07 0.07 0.09 0.09 -0.-05 0.05 -0.-07 0.07 0.09-0.05-0.07 0.09-0.05-0.07 9 9 9 -6 -66 9 -6 Maximum value: 1.7714×10 9 Maximum value: 2.7058×10 -6 Maximum Maximu Maximu m value: m valu valu e: 1.7714 e: 1. 7714 1.7714×× 1 10 01 9 09 Maximu Maximum Maximu m m valu value: valu e: e: 2. 7058 2.7058 2.7058×× 1010 1 -60 -6 Maximum value: 1.7714×10 Maximum value: 2.7058×10 Maximu Maximu mm valu valu e: e: 1. 7714 1.7714×× 101 0 Maximu Maximu mm valu valu e: e: 2. 7058 2.7058×× 1010 9 9 -6 -6 Maximu Maximu m m valu valu e: e: 1. 7714 1.7714×× 101 0 Maximu Maximu m m valu valu e: e: 2. 7058 2.7058×× 1010 0.09 0.09 -0.-07 0.07 -0.-05 0.05 0.09-0.07-0.05 0.09-0.07-0.05 0.09-0.07-0.05 0.09 0.09 -0.-07 0.07 -0.-05 0.05 0.09 0.09 -0.-07 0.07 -0.-05 0.05 9 9 -6 -6 9 9 -6 -6 Maximu Maximu mm valu valu e: e: 6. 14 6.14×× 101 09 Maximu Maximu mm valu valu e: e: 4. 2764 4.2764×× 1010 -6 Maximum value: 6.14×10 9 9 Maximum value: 4.2764×10 -6 6 Maximum value: 6.14×10 Maximum value: 4.2764×10 Maximu Maximu mm valu valu e: e: 6. 14 6.14×× 101 9 0 Maximu Maximu mm valu valu e: e: 4. 2764 4.2764×× 101 -60 Maximum value: 6.14 10 9 Maximum value: 4.2764 10-6 Maximu Maximu m m valu valu e: e: 6. 14 6.14×× 101 0 Maximu Maximu m m valu valu e: e: 4. 2764 4.2764×× 1010 Non- No No n- n- Non- No No n-n- No No n-n- Non-textur textu ed textu red red textu textu red red textured textured textured textured cutter cutter cutter cutter cutter cutter cutter cutter cutter As As shown shown in in Fi Fi gure gure 8, 8, duri duri ng ng th th e e prpr ocess ocess of of cutt cutt ing ing titan titan iuiu mm alloy alloy , Ori , Ori gin gin softwa softwa rere 2017 2017 As As shown shown in in Fi Fi gure gure 8, 8, duri duri ng ng th th e e prpr ocess ocess of of cutt cutt ing ing titan titan iuiu mm alloy alloy , Ori , Ori gin gin softwa softwa rere 2017 2017 As shown in Figure 8, during the process of cutting titanium alloy, Origin software 2017 As shown in Figure 8, during the process of cutting titanium alloy, Origin software 2017 As shown in Figure 8, during the process of cutting titanium alloy, Origin software 2017 As shown in Figure 8, during the process of cutting titanium alloy, Origin software 2017 (Originlab, Northampton, MA, USA) was used to plot and analyze the relationship between the (Ori (Ori ginlab, ginlab, Nort Nort hamp hamp ton to , nMA, , MA, US US A)A w ) as was used used to to pl pl ot ot and and analy analy zeze th th e re e l re atio latio nship nship bet bet wee wee n n thth e e (Originlab, Northampton, MA, USA) was used to plot and analyze the relationship between the (Ori (Ori ginlab, ginlab, NN ort ort hamp hamp toto n, nMA, , MA, US US AA ) w ) w asas used used to to pl pl otot and and analy analy zeze th th e e rere latio latio nship nship bet bet wee wee n n thth e e As shown in Figure 8, during the process of cutting titanium alloy, Origin software 2017 (Originlab, (Ori (Ori ginlab, ginlab, Nort Nort hamp hamp toto n, nMA, , MA, US US A) A w ) as was used used to to pl pl otot and and analy analy zeze th th e e rere latio latio nship nship bet bet wee wee n n thth e e equiva equiva lent lent stress stress and and th th e e e quiva equiva lent d lent d isp isp lala cem cem ent ent of of th th e var e var iaia ble d ble d ensity ensity micro micro -tex -tex tured tured cutt cutt ers ers and and equiva equiva lent lent stress stress and and th th e e e quiva equiva lent d lent d isp isp lala cem cem ent ent of of th th e var e var iaia ble d ble d ensity ensity micro micro -tex -tex tured tured cutt cutt ers ers and and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and Northampton, equiva MA, lent USA) stress a was nd th used e equiva to plot lent d and isplaanalyze cement of the ther var elationship iable density between micro-tex the tured equivalent cutters and str ess equivalent stress and the equivalent displacement of the variable density micro-textured cutters and the non-texture cutter. It can be seen from Figure 8 that, when the workpiece is cut in 0.002 s, the thth e non e non -tex -tex ture ture cutt cutt er. er. It It can can be be sese en en from from Fi g Fi ure gure 8 th 8 th at,at when , when th th e workp e workp iece iece is icut s cut in in 0.0 0.0 0202 s, s, th th e e the non-texture cutter. It can be seen from Figure 8 that, when the workpiece is cut in 0.002 s, the thth e e non non -tex -tex ture ture cutt cutt er. er. It It c an can be be sese en en from from Fi Fi gure gure 8 8 thth atat , when , when th th e e workp workp iece iece is icut s cut in in 0.0 0.0 0202 s, s, th th e e thth e non e non -tex -tex ture ture cutt cutt er. er. It It can can be be sese en en from from Fi Fi gure gure 8 th 8 th at,at when , when th th e workp e workp iece iece is icut s cut in in 0.0 0.0 0202 s, s, th th e e and the equivalent displacement of the variable density micro-textured cutters and the non-texture equiva equiva lent lent stress stress and and th th e e e quiva equiva lent d lent d isp isp lala cem cem ent ent of of th th e var e var iaia ble d ble d ensity ensity micro micro -tex -tex tured tured cutt cutt ers ers and and equiva equiva lent lent stress stress and and th th e e e quiva equiva lent d lent d isp isp lala cem cem ent ent of of th th e var e var iaia ble d ble d ensity ensity micro micro -tex -tex tured tured cutt cutt ers ers and and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and equivalent stress and the equivalent displacement of the variable density micro-textured cutters and cutter. It can be seen from Figure 8 that, when the workpiece is cut in 0.002 s, the equivalent stress and the non-textured cutter reach the maximum value. The instantaneous stress and deformation in the thth e non e non -tex -tex tutu red red cutt cutt er er reac reac h th h th e m e axi maxi mum mum value value . Th . Th e in e stantane instantane ous ous stres stres s and s and deform deform ation ation in ith n th e e the non-textured cutter reach the maximum value. The instantaneous stress and deformation in the thth e e non non -tex -tex tutu red red cutt cutt er er rere acac h h thth e e mm axi axi mm um um value value . Th . Th e e inin stantane stantane ous ous stres stres s and s and deform deform ation ation in in thth e e thth e non e non -tex -tex tutu red red cutt cutt er er rere acac h h thth e m e m axi axi mm um um value value . Th . Th e in e in stantane stantane ous ous stres stres s and s and deform deform ation ation in in thth e e the equivalent non non - displacement tex -tex tured tured cutt cutt er er du of du rin the rin g variable g th th e pro e pro cess cess density o fo cutt f cutt ing micr ing titan titan o-textur ium ium alloy alloy ed are cutters are grea grea ter and ter th th an the an those tnon-textur hose in in thth e va e va ed ria ria bcutter le ble non non -tex -tex tured tured cutt cutt er er du du rin rin g g th th e pro e pro cess cess o fo cutt f cutt ing ing titan titan ium ium alloy alloy are are grea grea ter ter th th an an those those in in thth e va e va ria ria ble ble non non -tex -tex tured tured cutt cutt er er du du rin rin g g th th e pro e pro cess cess o fo cutt f cutt ing ing titan titan ium ium alloy alloy are are grea grea ter ter th th an an those those in in thth e va e va ria ria ble ble non-textured cutter during the process of cutting titanium alloy are greater than those in the variable non-textured cutter during the process of cutting titanium alloy are greater than those in the variable density density mm icro icro -tex -tex tured tured cutt cutt er. er. Due Due toto th th e change e change of oth f th e tex e tex ture ture dens dens ity ity in in thth e cutt e cutt erer -chip -chip clo clo se se coco ntnt act act density micro-textured cutter. Due to the change of the texture density in the cutter-chip close contact reach the maximum density m value. icro-tex The tured instantaneous cutter. Due to th str e change ess and of deformation the texture dens inity the in non-textur the cutter-chip ed clo cutte se co r during ntact density density mm icro icro -tex -tex tured tured cutt cutt er. er. Due Due toto th th e change e change of oth f th e tex e tex ture ture dens dens ity ity in in thth e cutt e cutt erer -chip -chip clo clo se se coco ntnt act act density density mm icro icro -tex -tex tured tured cutt cutt er. er. Due Due toto th th e change e change of o th f th e tex e tex ture ture dens dens ity ity in in thth e cutt e cutt erer -chip -chip clo clo se se coco ntnt act act arar eae , a th , th e “ e sec “sec ondary ondary cutt cutt inin g” g ph ” ph enom enom en en on on ofof th th e micr e micr o-o tex -tex tured tured cu cu tter tter du du ring ring th th e pro e pro cess cess of of cutt cutt ing ing arar eae , a th , th e “ e sec “sec ondary ondary cutt cutt inin g” g ph ” ph enom enom en en on on ofof th th e micr e micr o-o tex -tex tured tured cu cu tter tter du du ring ring th th e pro e pro cess cess of of cutt cutt ing ing arar eae , a th , th e “ e sec “sec ondary ondary cutt cutt inin g” g ph ” ph enom enom en en on on ofof th th e micr e micr o-o tex -tex tured tured cu cu tter tter du du ring ring th th e pro e pro cess cess of of cutt cutt ing ing the process of cutting titanium alloy are greater than those in the variable density micro-textured area, the “secondary cutting” phenomenon of the micro-textured cutter during the process of cutting area, the “secondary cutting” phenomenon of the micro-textured cutter during the process of cutting titaniu titaniu mm allo allo ys ys is is effect effect iviv ely ely red red uced uced . It . It can can be be see see n n from from th th e e s imul simul ation ation res res ulul ts ts th th atat th th e e micro micro - - titanium alloys is effectively reduced. It can be seen from the simulation results that the micro- titanium alloys is effectively reduced. It can be seen from the simulation results that the micro- titaniu titaniu mm allo allo ys ys is is effect effect iviv ely ely red red uced uced . It . It can can be be see see n n from from th th e e s imul simul ation ation res res ulul ts ts th th atat th th e e micro micro - - cutter. Duetitaniu to titaniu the mchange m allo allo ys ys is of is effect the effect iv textur iv ely ely red red euced density uced . It . It can in can the be be see cutter see n n from fr -chip om th th e close e si mul simul ation contact ation res res ul ar ul ts ea, ts th th at the at th “secondary th e e micro micro - - tex tex tured tured cutt cutt er er can can not not onl onl y y reduc reduc e fr e iction friction and and ww eaea r, r but , but also also imp imp rov rov e th e th e stres e stres s dis s dis tribution tribution of of thth e e tex tex tured tured cutt cutt er er can can not not onl onl y y reduc reduc e fr e iction friction and and ww eaea r, r but , but also also imp imp rov rov e th e th e stres e stres s dis s dis tribution tribution of of thth e e tex tex tured tured cutt cutt er er can can not not onl onl y y reduc reduc e fr e iction friction and and ww eaea r, r but , but also also imp imp rov rov e th e th e stres e stres s dis s dis tribution tribution of of thth e e textured cutter can not only reduce friction and wear, but also improve the stress distribution of the textured cutter can not only reduce friction and wear, but also improve the stress distribution of the cutting” phenomenon of the micro-textured cutter during the process of cutting titanium alloys is cutt cutt er. er. By By ch ch angi angi ng ng thth e e didi stribution stribution de de nsity nsity of of thth e e text text ure ure on on thth e e cutt cutt er, er, thth e e “seconda “seconda ry ry cu cu tting tting ” ” cutter. By changing the distribution density of the texture on the cutter, the “secondary cutting” cutter. By changing the distribution density of the texture on the cutter, the “secondary cutting” cutt cutt er. er. By By ch ch angi angi ng ng thth e e didi stribution stribution de de nsity nsity of of thth e e text text ure ure on on thth e e cutt cutt er, er, thth e e “seconda “seconda ry ry cu cu tting tting ” ” cutt cutt er. er. By By chch angi angi ng ng thth e e didi stribution stribution dede nsity nsity of of thth e e text text ure ure on on thth e e cutt cutt er, er, thth e e “seconda “seconda ry ry cucu tting tting ” ” eectively reduced. It can be seen from the simulation results that the micro-textured cutter can not ph ph ph enom enom enom enon enon enon dur dur dur ing ing ing th th th e e p e process rocess process o of f omic mic f mic ro roro --tex tex -tex tured tured tured c cutt utt cutt er er er mil mil mil li ling ng ling titaniu titaniu titaniu m m m allo allo allo y y y can can can be be be ef effe ef fect fe ctively ct ively ively phenomenon during the process of micro-textured cutter milling titanium alloy can be effectively ph ph enom enom enon enon dur dur ing ing th th e e process process of omic f mic roro -tex -tex tured tured cutt cutt er er mil mil ling ling titaniu titaniu m m allo allo y y can can be be efef fefe ctct ively ively ph ph enom enom enon enon dur dur ing ing th th e p e rocess process of omic f mic roro -tex -tex tured tured cutt cutt er er mil mil ling ling titaniu titaniu m m allo allo y y can can be be effe efct feively ctively reduced reduced . . only reduce reduced friction . and wear, but also improve the stress distribution of the cutter. By changing the reduced. reduced reduced . . reduced reduced . . distribution density of the texture on the cutter, the “secondary cutting” phenomenon during the process of micro-textured cutter milling titanium alloy can be eectively reduced. Appl. Sci. 2020, 10, 818 16 of 20 Appl. Sci. 2020, 10, 818 16 of 20 (a) (b) Figure 8. The curve of stress field and deformation of variable density micro-textured cutter with Figure 8. The curve of stress ﬁeld and deformation of variable density micro-textured cutter with respect to time. (a) equivalent stress changes with time; (b) equivalent displacement varies with time. respect to time. (a) equivalent stress changes with time; (b) equivalent displacement varies with time. 5. Optimization of Variable Density Distribution of Micro-Textured Cutter 5. Optimization of Variable Density Distribution of Micro-Textured Cutter Through the simulation of the stress ﬁeld in milling titanium alloy with variable density Through the simulation of the stress field in milling titanium alloy with variable density micro- micro-textured ball-end milling cutter, it is concluded that the instantaneous stress ﬁeld and the textured ball-end milling cutter, it is concluded that the instantaneous stress field and the maximum maximum stress value of the cutter are directly aected by the dierent texture distribution densities on stress value of the cutter are directly affected by the different texture distribution densities on the the rake face of the cutter. Therefore, it is necessary to establish the relationship between the dierent rake face of the cutter. Therefore, it is necessary to establish the relationship between the different distribution densities of the micro-textures and the instantaneous stress ﬁeld of the cutter, so as to distribution densities of the micro-textures and the instantaneous stress field of the cutter, so as to optimize the texture density in the cutter-chip compact contact area and to obtain the best combination optimize the texture density in the cutter-chip compact contact area and to obtain the best of texture distribution density, which provides a new concept for the design of micro-textured cutter. combination of texture distribution density, which provides a new concept for the design of micro- In this paper, a genetic algorithm was used to optimize the variable density distribution of textured cutter. micro-textured cutter. The instantaneous stress ﬁeld of the cutter was taken as the optimization In this paper, a genetic algorithm was used to optimize the variable density distribution of objective and the texture density X in the ﬁrst area, X in the second area, and X in the third area micro-textured cutter. The instantaneo 1 us stress field of 2 the cutter was taken as 3the optimization of the cutter-chip compact contact area were taken as the optimization variables. When the genetic objective and the texture density X1 in the first area, X2 in the second area, and X3 in the third area of algorithm was adopted for optimization, the objective function should be established ﬁrst. In this the cutter-chip compact contact area were taken as the optimization variables. When the genetic paper, the instantaneous stress ﬁeld of a micro-textured cutter with a variable density was taken as algorithm was adopted for optimization, the objective function should be established first. In this the optimization objective, so a prediction model of the instantaneous stress ﬁeld of the cutter was paper, the instantaneous stress field of a micro-textured cutter with a variable density was taken as established as the objective function of the optimization model. The mathematical model was used to the optimization objective, so a prediction model of the instantaneous stress field of the cutter was established as the objective function of the optimization model. The mathematical model was used to establish the instantaneous stress model of the variable density micro-textured cutter with respect to the variables X1, X2 and X3: Appl. Sci. 2020, 10, 818 17 of 20 establish the instantaneous stress model of the variable density micro-textured cutter with respect to the variables X , X and X : 1 2 3 1 2 3 = C X X X , (25) 1 2 3 where C denotes the correlation coecient of the prediction model and , , and denote the 1 2 3 undetermined indices of the related independent variables. The logarithm of the two sides of the Equation (25) is lg = lgC + lgX + lgX + lgX . (26) 1 1 2 2 3 3 If y = lg, = lgC, x = lgX , x = lgX , x = lgX , Equation (26) is transformed into a linear 0 1 1 2 2 3 3 equation as follows: y = + x + x + x . (27) 0 1 1 2 2 3 3 According to Equation (27) and the stress ﬁeld simulation data of the variable density micro-textured ball-end milling cutter, a multiple linear regression equation was established by the least-square method: y = + x + x + x + " 1 0 1 11 2 12 3 13 1 y = + x + x + x + " 2 0 1 21 2 22 3 23 2 , (28) :::::: y = + x + x + x + " 9 0 1 91 2 92 3 93 9 where " denotes a random error. The stress ﬁeld simulation data of the variable density micro-textured ball-end milling cutter was substituted into Equation (28). Then, MATLAB R2017b software was used to regress the experimental data through multiple linear regression, and the prediction model of the instantaneous stress ﬁeld of the variable density micro-textured ball-end milling cutter was obtained as follows: 8 0.88847 0.021204 0.1675 = 1.636 10 X X X . (29) 1 2 3 During the process of ﬁnishing titanium alloy with the micro-textured ball-end milling cutter, the instantaneous stress ﬁeld of the micro-textured cutter is aected by the texture density distribution in the ﬁrst, second and third regions where the cutter and chip are in close contact under the same cutting parameters. Therefore, in order to optimize the variable density distribution of the micro-textured cutters based on the stress ﬁeld, the constraints are that the texture density of all three regions where the cutter and chip are in close contact as 0.01 < X < 0.1 (i = 1, 2, 3). Taking the instantaneous stress ﬁeld of the micro-textured cutter as the evaluation standard and the above constraints as the boundary conditions, the genetic algorithm was used to optimize the variable density distribution of the micro-textured cutters. In order to ensure the accuracy of the optimization results, when the variable density distribution of the micro-textured cutters is optimized by the genetic algorithm, optimization parameters should be set in the genetic algorithm toolbox. The population size set in this paper is 300, the crossover probability is 0.95, and the mutation probability is 0.01. Finally, the genetic algorithm toolbox was used to solve the optimization model. The optimization results of the genetic algorithm are shown in Figure 9. The optimal solution of the variable density distribution of the micro-textured cutter in the cutter-chip compact contact area was obtained through the optimization solution. The texture distribution density X in the ﬁrst region, X in the second 1 2 region, and X in the third region are 0.0905, 0.0712, and 0.0493, respectively. 3 Appl. Sci. 2020, 10, 818 18 of 20 Appl. Sci. 2020, 10, 818 18 of 20 Figure 9. Optimization results of the genetic algorithm. Figure 9. Optimization results of the genetic algorithm. 6. Conclusions 6. Conclusions Aiming at the problem of “secondary cutting” during the process of ﬁnishing titanium alloy by Aiming at the problem of “secondary cutting” during the process of finishing titanium alloy by the micro-textured ball-end milling cutter, in this article, the mechanism of friction reduction and wear the micro-textured ball-end milling cutter, in this article, the mechanism of friction reduction and resistance of micro-textured cutters were studied in detail. By changing the distribution density of wear resistance of micro-textured cutters were studied in detail. By changing the distribution density the micro-texture on the cutter, the dynamic characteristics of the instantaneous stress ﬁeld during of the micro-texture on the cutter, the dynamic characteristics of the instantaneous stress field during the process of milling titanium alloy by the micro-textured cutter were studied, and the following the process of milling titanium alloy by the micro-textured cutter were studied, and the following conclusions were drawn: conclusions were drawn: (1) Through milling titanium alloy experiments, the milling force models and the cutter-chip (1) Through milling titanium alloy experiments, the milling force models and the cutter-chip contact area mathematical models of cutters with dierent micro-textured densities and non-texture contact area mathematical models of cutters with different micro-textured densities and non-texture were established. By solving the milling force model and the experimental formula of cutter-chip were established. By solving the milling force model and the experimental formula of cutter-chip contact area, the force density functions of the cutters with the dierent micro-texture densities and contact area, the force density functions of the cutters with the different micro-texture densities and non-texture were obtained. It provides a theoretical basis for studying the stress ﬁeld of the variable non-texture were obtained. It provides a theoretical basis for studying the stress field of the variable density micro-textured cutters. density micro-textured cutters. (2) The instantaneous stress ﬁelds of dierent density textured cutters and non-textured cutters (2) The instantaneous stress fields of different density textured cutters and non-textured cutters during the process of milling titanium alloy were simulated. The simulation results show that, during during the process of milling titanium alloy were simulated. The simulation results show that, during the process of milling titanium alloy, stress concentration will occur in the cutter-chip contact area of the process of milling titanium alloy, stress concentration will occur in the cutter-chip contact area of the rake face of the non-textured cutters. The force and deformation of the micro-textured cutters are the rake face of the non-textured cutters. The force and deformation of the micro-textured cutters are more uniform than those of the non-textured cutters, and there is less stress concentration, and the more uniform than those of the non-textured cutters, and there is less stress concentration, and the maximum deformation area and maximum stress value of the micro-textured cutters are smaller than maximum deformation area and maximum stress value of the micro-textured cutters are smaller than those of the non-textured cutters. those of the non-textured cutters. (3) Taking the instantaneous stress ﬁeld as the objective function, the genetic algorithm was used (3) Taking the instantaneous stress field as the objective function, the genetic algorithm was used to optimize the variable density distribution of the micro-textured cutters, and the optimal solution of to optimize the variable density distribution of the micro-textured cutters, and the optimal solution the variable density distribution of the micro-textured cutters in the cutter-chip compact contact area of the variable density distribution of the micro-textured cutters in the cutter-chip compact contact was obtained. The texture distribution density X in the ﬁrst region, X in the second region, and X in 1 2 3 area was obtained. The texture distribution density X1 in the first region, X2 in the second region, and the third region are 0.0905, 0.0712 and 0.0493, respectively. X3 in the third region are 0.0905, 0.0712 and 0.0493, respectively. Author Contributions: M.Z. and S.Y. conceived and designed the experiments. M.Z. and S.Y. analyzed the data Author Contributions: M.Z. and S.Y. conceived and designed the experiments. M.Z. and S.Y. analyzed the data and carried out ﬁnite element simulation analysis. C.H. performed the experiments and wrote the paper. All and carried out finite element simulation analysis. C.H. performed the experiments and wrote the paper. All authors have read and agreed to the published version of the manuscript. authors have read and agreed to the published version of the manuscript. Funding: This research was funded by [The National Natural Science Foundation of China] grant number [51875144]. And the APC was funded by [The National Natural Science Foundation of China and Construction of Funding: This research was funded by [The National Natural Science Foundation of China] grant number scientiﬁc research collaborative innovation platform-Advanced manufacturing intelligent technology]. [51875144]. 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Optimization of Texture Density Distribution of Carbide Alloy Micro-Textured Ball-End Milling Cutter Based on Stress Field

Optimization of Texture Density Distribution of Carbide Alloy Micro-Textured Ball-End Milling Cutter Based on Stress Field

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Optimization of Texture Density Distribution of Carbide Alloy Micro-Textured Ball-End Milling Cutter Based on Stress Field

Optimization of Texture Density Distribution of Carbide Alloy Micro-Textured Ball-End Milling Cutter Based on Stress Field

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