Academic Journal of Science and Technology ISSN: 2771-3032 | Vol. 8, No. 2, 2023 90 Simulation Analysis of Ti6Al4V Cutting Under Liquid Nitrogen Cryogenic Cooling Yongjie Xia1, Qi Zhang1, 2, * 1School of Mechanical Engineering, Sichuan University of Science & Engineering, Yibing 610300, China 2School of Intelligent Manufacturing, Panzhihua University, Panzhihua 617000, China * Corresponding author Abstract: Liquid nitrogen cryogenic cooling technology has great advantages in cutting machining. A thermodynamic finite element model of liquid nitrogen cryogenic cooling based on the plane strain assumption is established to observe the changes in cutting force and tool temperature corresponding to different cutting parameters (feed rate and cutting speed) under liquid nitrogen cryogenic cooling conditions. Existing tests verified the accuracy of the simulation model, and the prediction error of the simulation model was controlled within 10%. Analyzing the data obtained from the simulation model, it is found that a lower tool temperature is obtained when the cutting parameters are selected to be lower values; under the conditions of liquid nitrogen cryogenic cooling and dry cutting machining, the effect of the cutting speed on the cutting force is not obvious, while the effect of the feed volume on the cutting force is more significant; under the conditions of different cutting parameters, the tool temperature as well as the cutting force are lower under the conditions of liquid nitrogen cryogenic cooling compared to the dry cutting machining method. Keywords: Liquid nitrogen cryogenic cooling; Finite element; Cutting force; Tool temperature. 1. Introduction With the development of aerospace and medical industries, Ti6Al4V is more widely used, Ti6Al4V has excellent physical properties but also brings difficulties in processing [1]. Due to its poor thermal conductivity, the accumulation of heat generated during the cutting process accelerates the wear of the tool, the use of cutting fluid in the cutting process can reduce the cutting temperature to a certain extent, and improve the tool life, but the cutting fluid commonly used in the industry has a different degree of damage to the environment [2]. Liquid nitrogen cryogenic cooling is an environmentally friendly cooling technology [3], which can rapidly reduce the temperature of the cutting area with sufficient flow rate, and at the same time improve the tool- worker contact properties, which also plays an important role in reducing the cutting force and surface stress, and also improves the tool life and machining quality. Xu Zuodong et al [4] combined low-temperature micro- lubrication and vibratory cutting and found that the new cutting method demonstrated superior cutting performance. Hu Bo et al [5] analyzed the influencing factors of cutting force in low-speed orthogonal planing and found that the cutting parameters have more obvious influence than the tool geometry parameters. In order to improve the machining efficiency, Xu Qing et al [6] increased the milling feed under liquid nitrogen cryogenic cooling and found that the cryogenic cooling can reduce the cracking of the tool. Lu Jiafeng et al [7] investigated the effect of liquid nitrogen flow rate on the cutting performance of the tool by milling test. Zhao Di et al [8] designed a new toolholder configured with cryogenic cooling medium, which to a certain extent meets the needs of modern industry for cryogenic cooling cutting. Sahoo et al [9] investigated the spraying effect of different types of cooling medium nozzle equipment and comprehensively analyzed the changing law of cutting force under different tool coatings. Shokrani [10], in order to improve the life of the tool and the machining efficiency as much as possible, proposed A new hybrid cryogenic cooling method. In the research carried out on cutting Ti6Al4V under cryogenic cooling conditions, more experimental studies were used and less cryogenic cooling cutting models were established. Therefore, the Ti6Al4V liquid nitrogen cryogenic cutting model was established using the finite element method, and the orthogonal cutting process was analyzed using the material model proposed by Johnson- Cook, which comprehensively considered the material deformation and heat exchange in the cutting process, and investigated the effects of cutting parameters and cooling conditions on the cutting force and tool temperature. 2. Cutting Process of Ti6Al4V 2.1. Cutting process analysis The actual turning process is shown in Fig. 1(a) cutting motion process analysis diagram, in order to facilitate the analysis, the rotary motion of the workpiece is converted to linear motion as shown in Fig. 1(b). From the simplified cutting model, it can be seen that the workpiece is subjected to a uniform force perpendicular to the Y-axis, assuming that there is no deformation in the Y-axis direction, i.e., the strain in the Y-axis direction is zero. 1 ( ) 0 2xy u v y x         ， 1 ( ) 0 2zy w v y z         Substituting the above equation into Hooke's law gives: z( )y x    ＋ (1) Therefore, the constitutive equation of the Ti6Al4V cutting model under the plane strain assumption is: 91 21 ( ) 1x x zE          (2) 21 ( ) 1z z xE          (3) 1 2(1 ) xz xy xzG E      (4) Where, ε is strain, σ positive stress, τ shear stress, γ shear strain, μ Poisson's ratio, E elastic modulus, G shear modulus. Figure 1. Cutting Process Analysis 2.2. Heat exchange during cutting Titanium alloy due to its low thermal conductivity, the accumulation of heat in the cutting process aggravates the wear of the tool, so a reasonable analysis of heat transfer in cutting has an important impact on the accuracy of the model. There are mainly three forms of heat exchange in the cutting process, the heat mainly comes from the plastic deformation of the material occurring in the deformation zone, part of the heat flows to the tool or the cooling medium in the form of heat transfer, and the other part is taken away by the chips; the other part of the heat comes from the mutual friction between the tool and the workpiece, which is related to the friction of the tool-worker; the environmental impact on the cutting process of the heat through the convection heat transfer coefficient is calculated, and the heat transfer coefficient is set to 20℃ for the environment, and the convection heat transfer coefficient is set to 20℃ for the environment and 20 ℃ for the environment. The ambient temperature is set to 20℃, and the convective heat transfer coefficient is 20 2/W m K（ ）. Liquid nitrogen cryogenic cooling is mainly through changing the ambient temperature, convective heat transfer coefficient and friction effect on cutting, the tool - worker friction coefficient is 0.25, the ambient temperature is set to -196 ℃, the convection coefficient is related to the liquid nitrogen injection device and the flow rate, here take 20000 2/W m K（ ）. 3. Ti6Al4V Finite Element Model 3.1. Material model Here the isomorphic model proposed by Johnson-Cook is chosen to describe the effect of thermal changes in the material on the dynamic behavior of the processed material. The Johnson-Cook isomorphic equation is:   0 0 0 1 ln 1n p melt T T A B C T T                      (5) Where: A is the yield strength under quasi-static conditions; B is the hardening strain parameter; p is the equivalent plastic strain；n is the hardening index；C is the strain rate enhancement parameter； is the equivalent plastic strain rate； 0 is the reference strain rate of the material； 0T is room temperature； meltT is the melting point of the material； mis the thermal softening parameter。Here the parameters obtained by Seo [11] are chosen as：A, B, n, C, m, 0T , meltT in order ： 997.9,653.1,0.45,0.0198,0.7,20ºC,1605 ºC 。 Other thermodynamic parameters are shown in Table 1. Table 1. Material thermodynamic parameter materials Ti6Al4V WC densities 3( / )Kg m 4430 15700 Young's modulus ( )Gpa 113.8 650 Poisson's ratio 0.342 0.25 heat conductivity ( / )W m K 7.3 59 Expansion(K-1) 8.6×10-6 5.6×10-6 3.2. Cutting separation guidelines and contact behavior During metal cutting, the material reaches the failure criterion under the shearing and squeezing action of the tool, and then the material breaks and falls off, in order to accurately describe this process, Cockcroft and Latham [12] related the damage of the workpiece to the equivalent crack length: 0 Tid D     (6) Where  is the effective strain,  is the principal stress (MPa), TiD is the material constant. During the cutting process, the tool and the workpiece are mainly categorized into bonded and sliding contact. Özel et al [13] described bonded and sliding contact as: , , i f i i mk p mk p p mk         (7) where k is the shear yield stress of the working material, m is the shear friction coefficient, f is the friction stress, μ is the Coulomb friction coefficient, and ip is the interfacial pressure. Comprehensive analysis of the above, the use of DEFORM finite element calculation software, based on the assumption of plane strain, the establishment of two-dimensional finite element cutting model, the tool geometry parameters remain unchanged, the relevant parameters are shown in Table 2. In order to ensure the accuracy of the calculation, the tip of the tool and the cutting part of the local mesh as shown in Fig. 2, 92 the minimum mesh for the cutting depth of 1/20, the maximum mesh 0.1mm. to the tool- workpiece model to add motion constraints and thermal boundary conditions to ensure that the normal movement of the tool. Table 2. Cutting parameters and tool geometry batch number 1 cutting speed(m/min) 30m/min feed(mm/r) 0.06,0.28 Cutting length (mm) 2.5mm Rack angle (°) 15 Clearance angle (°) 2 Cutting edge radius (mm) 0.02 Figure 2. Ti6Al4V finite element model 4. Simulation Results and Discussion 4.1. Simulation model accuracy analysis Fig. 3 and Fig.4 show the trend graphs of cutting force changes and temperature distribution cloud graphs corresponding to different feeds at a cutting speed of 30m/min, from which it can be seen that an increase of 0.22mm/r in feed increases the cutting force by 291N and the cutting temperature by 60°C. Fig. 5 gives the experimental results of Ducobu[17] et al. The relevant cutting parameters are the same as the parameters in Table 2, and the comparison reveals that the main cutting force of the finite element model is basically the same as that of the test, and the errors under the feed of 0.06 mm/r and 0.28 mm/r are 4.76% and 4.3%, respectively. Figure 3. Feed (0.06mm/r) Figure 4. Feed f (0.28/mm) Figure 5. Comparison of test and simulation values for different feeds Fig.6 and Fig.7 show the trend graphs of cutting forces and temperature cloud graphs corresponding to dry cutting and liquid nitrogen cryogenic cooling under the conditions of 145 m/min cutting speed and 0.096 mm/r feed. From the graphs, it can be seen that liquid nitrogen cryogenic cooling exhibits lower cutting temperatures and the overall range of fluctuation of cutting forces is reduced for the same cutting speed and feed conditions. Figure 8 gives the test data of Jerold [18] et al. In his test, the cutting speed is 145m/min, the feed is 0.096mm/r, the tool material is PCBN tool, the tool is clamped by the ISO PCLNR 2020 K12 cage, and the same parameters are set, the simulation results obtained are shown in Fig. 8, and a comparison of the simulation values and the test values shows that the results are basically the same, liquid nitrogen cryogenic cooling exhibits a lower cutting temperature, and the overall fluctuation range of the cutting force is reduced. The simulation results are shown in Fig. 8, comparing the simulation values with the test values, the results are basically the same, the errors of liquid nitrogen cryogenic cooling and dry cutting are 7.8% and 5%, respectively. Figure 6. Dry cutting Figure 7. Cryogenic 93 Figure 8. Comparison of experimental and simulated values for different cooling methods 4.2. Cutting force influencing factor analysis Intercepting the average value of cutting efforts in both directions during the cutting stabilization phase. The cutting combined force is calculated as 2 2 X YF F F  。Fig. 9 and Fig. 10 show the cutting force values for different feeds at 30m/min and 145m/min cutting speeds, respectively, from which it can be found that the feeds affect the cutting force in a regular manner, and that cryogenic cooling with liquid nitrogen has the effect of reducing the cutting force. Comparison of Fig. 9 and Fig. 10 shows that no significant change is observed with the increase in cutting speed. Figure 9. Cutting force at 30m/min cutting speed Figure 10. Cutting force at a cutting speed of 145m/min 4.3. Analysis of tool temperature influencing factors Fig.11 and Fig.12 show the tool temperatures corresponding to different feeds and different cooling methods at 30m/min and 145m/min cutting speeds. As can be seen from the figures, the relationship between the influence of feed and cutting temperature, liquid nitrogen cryogenic cooling has a significant effect on reducing the tool temperature. Comparison of the two graphs shows that the cutting speed has a significant effect on the maximum tool temperature. Figure 11. Cutting Temperature at 30m/min Cutting Speed Figure 12. Cutting Temperature at 145m/min Cutting Speed 4.4. Influence of convective heat transfer coefficient on cutting force and tool temperature The boiling point of liquid nitrogen is -196℃, so the ambient temperature is often set to -196℃ when simulating liquid nitrogen cryogenic cooling. Under the effect of liquid nitrogen cryogenic cooling, the friction between the tool- worker and the heat dissipation relationship between the tool- worker model and the environment are changed, and the cooling effect is simulated by setting the friction coefficient, ambient temperature and convective heat transfer coefficient in the simulation model. As can be seen in Fig. 13, the effect of the convective heat transfer coefficient on the cutting force and cutting temperature in the -196°C environment, the cutting force was kept near 130N under three convective heat transfer coefficient gradients, and the tool temperature was about 300°C, and no significant changes were observed. Figure 13. Effect of convective heat transfer coefficient 0.06 0.096 0.28 0 50 100 150 200 250 300 350 400 450 cu tt in g fo rc e/ (N ) feed(mm/r) Cryogenic Dry cutting speed(30m/min) 0.06 0.096 0.28 0 50 100 150 200 250 300 350 400 cu tt in g fo rc e/ (N ) feed(mm/r) Cryogenic Dry cutting speed(145m/min) 0.06 0.096 0.28 0 50 100 150 200 250 T em pe ra tu re /( ℃ ) feed(mm/r) Cryogenic Dry cutting speed(30m/min) 0.06 0.096 0.28 0 100 200 300 400 500 600 T em pe ra tu re /( ℃ ) feed(mm/r) Cryogenic Dry cutting speed(145m/min) 10000 15000 20000 100 120 140 160 F T convective heat transfer coefficient cu tt in g fo rc e/ ( ) 280 300 320 340 360 T em pe ra tu re /( ℃ ) 94 4.5. Effect of coefficient of friction on cutting forces and tool temperature As can be seen from Fig. 14, the friction coefficient between the tool and the workpiece has a significant effect on the cutting force and cutting temperature at -196°C, and the smaller the friction coefficient, the better the cooling effect. Figure 14. Effect of coefficient of friction 5. Conclusion DEFORM finite element software was used to establish a Ti6Al4V cutting model based on the plane strain assumption, and the effects of the cutting parameters on the cutting force and the maximum tool temperature were analyzed under the condition of liquid nitrogen cryogenic cooling. The following conclusions were obtained: (1) The two-dimensional cutting model established is accurate and effective, and the error between the simulation value and the test value is within 10%. (2) The feed has a significant effect on cutting force and tool temperature, and the cutting speed has a greater effect on tool temperature and a smaller effect on cutting force. (3) Compared with dry cutting, the cutting force and tool temperature under liquid nitrogen cryogenic cooling machining are lower. (4) Liquid nitrogen cryogenic cooling technology mainly through the reduction of the cutting environment temperature and improve the tool - work friction relationship on the cutting process to have an effect. Acknowledgment Panzhihua Science and Technology Program (2021CY-G- 15). References [1] Schoop J, Falco Sales W, Jawahir I. High speed cryogenic finish machining of Ti - 6Al4V with polycrystalline diamond tools[J]. Journal of Materials Processing Technology, 2017, 250. [2] Sun S, Brandt M, Dargusch M S. Machining Ti–6Al–4V alloy with cryogenic compressed air cooling[J]. International Journal of Machine Tools and Manufacture, 2010, 50(11): 933–942. [3] Dhananchezian M, Pradeep Kumar M. Cryogenic turning of the Ti–6Al–4V alloy with modified cutting tool inserts[J]. Cryogenics, 2011, 51(1): 34–40. [4] Xu Zuodong, Dong Yueqing, Yang Xiaoyong. Cutting Analysis Of GH4169 Alloy Under Low Temperature Micro- Lubrication And Ultrasonic Elliptical Vibration[J].Modular Machine Tool﹠Automatic Manufacturing Technique, 2023(4): 125–127. [5] HU Bo，ZHAO Xianfeng，SHI Hongyan，et al. Research on the Influence of Cutting Parameters and Tool Parameters on Cutting Force Based on AdvantEdg[J]. Modular Machine Tool ＆ Automatic Manufacturing Technique, 2021(07): 128–132. [6] Xu Qing, Ren Fei, Zhao Wei, et al. Experimental Study on Tool Wear in Cryogenic High Feed Milling of Ti-6Al-4V[J], Tool Engineering, 2018, 52(5): 30–32. [7] Lu Jiafeng, Deng Xiaolin, Tang Jing, et al. Research on Cutting Force and Tool Wear of Ti5553 Titanium Alloy Milling with Liquid Nitrogen[J]. Tool Engineering,2023, 57(3): 44–48. [8] Zhao Di, Wang Yongqing, Liu Kuo, et al. Design And Experimental Study Of Cryogenic Medium Internal Cooling Toolholders. [J]. China Mechanical Engineering,2022, 33(5): 600–606. [9] Sahoo S P, Datta S, Roy T, et al. Machining performance of Ti6Al4V under dry environment, pressurized air supply and water-MQL: analysis of machining-induced vibration signals and captured thermographs[J]. Sādhanā, 2021, 46(4): 208. [10] Shokrani A, Al-Samarrai I, Newman S T. Hybrid cryogenic MQL for improving tool life in machining of Ti-6Al-4V titanium alloy[J]. Journal of Manufacturing Processes, 2019, 43: 229–243. [11] Seo S, Min O, Yang H. Constitutive equation for Ti–6Al–4V at high temperatures measured using the SHPB technique[J]. International Journal of Impact Engineering - INT J IMPACT ENG, 2005, 31: 735–754. [12] Kvačkaj T, Tiža J, Bacsó J, et al. Cockcroft-Latham Ductile Fracture Criteria for Non Ferrous Materials[J]. , 782. [13] Thepsonthi T, Özel T. 3-D finite element process simulation of micro-end milling Ti-6Al-4V titanium alloy: Experimental validations on chip flow and tool wear[J]. Journal of Materials Processing Technology, 2015, 221: 128–145. [14] Ducobu F, Rivière-Lorphèvre E, Filippi E. Experimental contribution to the study of the Ti6Al4V chip formation in orthogonal cutting on a milling machine[J]. International Journal of Material Forming, 2015, 8(3): 455–468. [15] Jerold B D, Kumar M P. The Influence of Cryogenic Coolants in Machining of Ti–6Al–4V[J]. Journal of Manufacturing Science and Engineering, 2013, 135(3): 031005. 0.15 0.25 0.35 125 130 135 140 145 F T coefficient of friction cu tt in g fo rc e/ ( ) 200 250 300 350 400 450 T em pe ra tu re /( ℃ )