Investigation of High-Speed Cryogenic Machining Based on Finite Element Approach 1

The simulation of cryogenic machining process because of using a three-dimensional model and high process duration time in the finite element method, have been studied rarely. In this study, to overcome this limitation, a 2.5D finite element model using the commercial finite element software ABAQUS has been developed for the cryogenic machining process and by considering more realistic assumptions, the chip formation procedure investigated. In the proposed method, the liquid nitrogen has been used as a coolant. At the modeling of friction during the interaction of tools – chip, the Coulomb law has been used. In order to simulate the behavior of plasticity and failure criterion, Johnson-Cook model was used, and unlike previous investigations, thermal and mechanical properties of materials as a function of temperature were applied to the software. After examining accuracy of the model with present experimental data, the effect of parameters such as rake angle and the cutting speed as well as dry machining of aluminum alloy by the use of coupled dynamic temperature solution has been studied. Results indicated that at the cutting velocity of 10 m/s, cryogenic cooling has caused into decreasing 60 percent of tools temperature in comparison with the dry cooling. Furthermore, a chip which has been made by cryogenic machining were connected and without fracture in contrast to dry machining.

Investigation of High-Speed Cryogenic Machining Based on Finite Element Approach

INTRODUCTION
In machining operations, mechanical energy, as a result of plastic deformation and friction is converting into thermal energy.This sudden increase in temperature results in a reduction of tool life, low quality of machined surfaces and additional charges.The cutting tools are an important factor in enhancing the efficiency of machining operations.Therefore, many researchers' have been done to Latin American Journal of Solids and Structures 14 (2017) 629-642 increase the life of cutting tools to meet industry requirements (Atlati et al. (2015), Buchkremer et al. (2015), Ducobu et al. (2015), Fu et al. (2016), Gao et al. (2015), Zhu et al. (2016)).Since experimental studies in the field of machining operation are costly, time-consuming and are limited so that, today researchers are using finite element methods as an efficient tool for their studies.
Most of the simulations aimed at obtaining the amount of residual stress and strain (Tounsi and El-Wardany (2015), Yang et al. (2016), Mahmoodi-k et al. (2014)), temperature distribution (Healy et al. (2015), Pittalà and Monno (2011)), and deformation of chip and predict the forces of machining (Khoshdarregi and Altintas (2013), Molnár et al. (2015), Wu et al. (2015).Yildiz et al. (2008), have been examined the studies in the field of cryogenic cooling method in machining processes and concluded that this approach can be used for various metals, including hard and soft metals, non-ferrous metals and non-metallic materials and composites.Zhan et al. (2011) simulated the formation of the chip and also examined the effect of cutting speed, the coefficient of friction and the rake angle by considering shear stress at the border area of chip and tool.Their results indicated that the cutting speed or higher feed rate is likely at the disruption of the chip.Cotterell and Byrne (2008), have studied the dynamics of chip formation in orthogonal machining of titanium alloy and demonstrated that disruption frequency of chip increased linearly with increasing cutting velocity.Pusavec (2012), has compared the machining of the tungsten of cryogenic method with the method of plastic injection and has considered its impact on some cutting parameters, cutting tool and the surface porosity.Then by using genetic algorithms has predicted values for the most optimal machining parameters.He also revealed that this method could be replaced by plastic injection method which has many environmental problems and physical hazards for the operator and will increase tools life and improve the performance of tools.Chen et al. (2004) have simulated the chip formation, cutting forces, stress, and strain and temperature distribution in orthogonal machining process by using a 2D finite element model.The Comparison of the obtained results in the case of cutting forces with the experimental results was satisfactory.
One of the biggest problems in machining processes is the generated temperature in material removal operations.This issue flares up at material discharges with high rigidity materials.The high temperature in machining can reduce tool life and dimensional accuracy and surface finish of the workpiece.An effective method to reduce machining temperatures is refrigeration cooling in which the liquid nitrogen is used as the coolant, usually.Various researchers by using the cryogenic method have examined the machining process in theory (Bajpai et al. 2015), Rana et al. (2016), Schoop et al. (2016), Umbrello et al. (2016)), and experiment (Biermann et al. (2015), Dinesh et al. (2016), Giasin et al. (2016), Gupta et al. (2016)).When cryogenic science is discussed, it is implied the use of refrigeration of fluids with lower temperatures than -150 .To create such temperatures some permanent gasses is being used such as helium, hydrogen, neon, nitrogen, oxygen, which the boiling point of such gasses is below -180℃ (Hocheng 20110).Gupta et al. (2016) in the cutting of AISI 1040 steel concluded that the refrigeration cooling reduces 55 percent of tool wear.Jun in his studies on machining of AISI 1018 steel and Ti6Al4V alloy indicated that refrigeration cooling reduces friction as much as 20 to 30 percent (Jun (2005)).Dhananchezian and Kumar (2011) have investigated the changes in temperature of cutting tool by tungsten carbide cutting tools, at Ti6Zl4V machining by the dry and cryogenic method.Their results indicate that refrigeration cooling can reduce cutting temperature to 60 percent in comparison to dry machining.On the other hand, geometric error in CNC machine tools can effect on machining process parameter, Pashaki and Pouya (2016) have developed volumetric error compensation in five-axis CNC machine tools to increase the accuracy of machined workpiece.
Examination of the further studies in recent years indicate that the cryogenic machining process diagonally so far has not been considered by researchers and parametric study on the effective parameters in this area is needed.Therefore, in this study, more realistic model of the simulation process is provided by the use of 2.5D finite element cryogenic machining based on Arbitrary Lagrangian-Eulerian (ALE) simulations.Johnson-Cook Plasticity Model for material plasticity model and failure criterion of Johnson-Cook is used to create the chip.Unlike conducted researches, in order to consider more realistic model, the finite element model has been provided more accurately and by taking into account the effect of temperature on mechanical properties of materials and using coupled dynamictemperature analyzes the cryogenic process has been simulated.After ensuring the accuracy of the results, the effect of present parameters on the cryogenic machining process and cutting forces as well as stress distribution, temperature and plastic deformation and residual stress are discussed.

THE NUMERICAL MODEL AND CONSTITUTIVE RELATIONS
In the current research, a 2.5D finite element model by using the ABAQUS has been created to simulate the cryogenic machining.The analysis is performed by Lagrangian formulation and as an explicit dynamic.Since the machining is being performed diagonally, the tool possesses the angle of inclination.Tool angles have been represented in Fig. 1-a.Work piece and tools were defined both as deformable.Latin American Journal of Solids and Structures 14 (2017) 629-642 2.1 Cryogenic Cooling In the present study cryogenic as spray cooling is examined.In this case, the cutting area particularly the contact surface of tool and chip with liquid nitrogen dispersion is being cooled by nozzles.At the finite element model, the cryogenic cooling impact on the workpiece is applied using convection heat transfer as follows: ( ) Where in, hcryo is the heat transfer coefficient, T is the surface temperature, and Troom is ambient temperature.Considering the aspects of heat transfer model, the temperature of the low surface and left side of workpiece same as an upper surface and right side of the cutting tools is considered equal to the ambient temperature Troom which is o 25 C .The upper surface and right side of the workpiece same as a lower surface and left the surface of removal material tools are under the influence of mandatory heat transfer.In Figure 1-a thermal boundary conditions have been represented.In the forced heat transfer surfaces by cryogenic cooling, the Troom temperature is to be considered o 196 C  due to the use of liquid nitrogen.Also, to consider more realistic assumptions of cryogenic cooling, more details of convective heat transfer is desired.For this purpose, according to the study Miranda (2013) heat transfer coefficient was considered as follows: 0.65 0.67 0.33 0.33 0.35 0.33 0.32 0.2 where e is the equivalent length, g gravity acceleration and other parameters are as follows: f V speed kg m ), f v dynamic viscosity ( Pa s ) and p c specific heat capacity ( According to equation ( 2) and taking into account the physical and thermal properties of liquid nitrogen, heat transfer coefficient is a function of temperature which is achieved as follows:

Plastic Criterion of Johnson-Cook
The material of tool and workpiece are considered steel aluminum respectively.To modeling of the plastic behavior of materials, Johnson-Cook Plasticity model is used.According to this model, the plastic behavior of materials is expressed as the below equation: In this regard, the first term represents the rate of strain hardening; the second term represents the flow of stress at high strain rates and in the third term is defined the softening rate of materials under material removal.Parameters A, B, c, n and m are material constants that have been extracted from the tables of Materials Engineering and have been represented in Table 1 (Davim and Ma-ranhão Latin American Journal of Solids and Structures 14 (2017) 629-642 2009).When Johnson-Cook model of dependent on the strain rate is being used the values of 0  and C should be determined.

Exhaustion Criterion of Johnson-Cook
For modeling of the chip formation, failure criterion of Johnson-Cook model is being used.Based on this test, deterioration parameter D in the equation ( 5) is defined which as should not exceed from number 1.
In the recent equation, pl f  is failure strain p is pressure and q is effective stress of Von-Mises.

Model of Coulomb Friction
The central concept of Coulomb friction pattern is the allowed maximum tangential friction (shear) on the length of the contact surface up to the contact pressure between the contact bodies.In this paper, the resistance model between the shared surface of the tool and the workpiece is defined by using Coulomb criterion.In this case, the frictional stress  is considered as proportional to the normal tension n  .Coulomb friction model is defined as follows: In which  is considered as the friction coefficient.

Meshing and Arbitrary Lagrangian-Eulerian (ALE) Simulations
In the chip formation process due to the high range of deformation, there is a lot of error associated with simple meshing process.In this study, the Adaptive Meshing method is used.The full name of the method is used; the Arbitrary Lagrangian-Eulerian method is conventional that it is more commonly referred to as ALE.According to the dynamic-temperature coupling analysis for meshing, 3D elements C3D8T that is an eight-node thermal coupled element is used.The surface of material removal with the depth of 1 mm with smaller features has meshed and other parts with larger elements.Boundary conditions and used meshing method is represented in Figure 1.

Mechanical and Thermal Properties of Used Materials
Respectively in Tables 1 and 2, variables of plasticity and failure of Johnson-Cook models are presented.As noted in this study, for taking into account more realistic assumptions, given that the Latin American Journal of Solids and Structures 14 (2017) 629-642 temperature of the workpiece during the machining process and tools increase extremely high, therefore, unlike the previous researches, mechanical and thermal properties of materials are considered as a function of temperature.The used thermal and mechanical properties for Al and AISI 316L at different temperatures are provided in Tables 3 and 4 respectively.Thermal conductivity (W m -1 K -1 ): Specific heat (J kg -1 K):

RESULTS AND DISCUSSION
In the present study the cryogenic machining of aluminum with the standard cutting tool are modeled and the impact of different parameters like cutting speed, rake angle and friction are examined.The first step is to verify the authenticity of the presented results, simulation results and Comparison of them to experimental results of Ref. (Günay, 2005).In Figure 2 the obtained cutting force values from simulation and experimental analysis are represented.As can be seen, the simulation outcomes have an acceptable agreement with experimental results presented in Ref. (Günay, 2005) and the maximum predicted error of the model is less than 8 percent.Although there are differences between experimental and numerical results, but the error rate due to the uncertainty of coefficients related to the behavior of the material, is acceptable.Afterward, by assuring the reliability of the conducted modeling, to evaluate the changes of any of the practical parameters, the length of the chip has been measured in ABAQUS software and according to this measure, the results were compared.

The Effect of Cryogenic Cooling
At first, for more considerations over the effects of the cryogenic process on the machining operations.In figure 3 the temperature distribution of the workpiece and cutting tool for rake angle of 32o and cutting edge inclination angle of 10o in machining with cutting speed of 10 m/s for both cooling, dry and cryogenic cooling is represented.Also in these figures, the effect of consideration of thermal stress on the geometrical shape of the chip and residual stress have been represented.By comparing Fig. 3a and 3-b it can be found that the dynamic resolution without considering the thermal tensions, first the length of the chip is lower and second less residual strain has been received.According to the results of the conducted analysis of machining, the coupled dynamic analysis of displacement-thermal should be used.
In Figures 4 and 5 temperatures distribution in the machining work piece and tool for both of the dry and cryogenic machining are compared at cutting speed of 10 m/s.As can be seen during machining, heat arises in the primary and secondary deformation areas, and the maximum temperature in the contact surfaces of tool and chip is created.Results indicated in cutting speed of 10m/s in cryogenic machining respectively causes in the reduction of 71.34 and 76.64 percent of the temperature of the chip and tool in comparison with dry machining.In Figure 6, the residual stress distribution in cutting speed of 10 m/s is represented for both dry and cryogenic machining.According to the figure 6, it is observed that the high created temperatures in thermal gradient creates a residual stress.Also, in the machining process by contact of the tip of the tool to the chip formation area these stress gradually become tensile stress.The results represent Latin American Journal of Solids and Structures 14 (2017) 629-642 that compressive and tensile residual stress of cryogenic machining in this case approximately is 20.12 and 24.39 percent lower than dry machining that the reason of it can be the low temperature of cryogenic machining and as a result, causes in low thermal stress.It is indicated that in both cases, the maximum compressive stress is at the contact zone of the tool and the workpiece and the area of the second shear due to high heat transfer and more thermal gradient, these stress are tensile.

The Effect of Rake Angle
According to released data by Materials Association of America, the chip angle of the tool at cutting aluminum alloys with the ability of low machining (grades C, D and E) is about 30 to 40 degrees.For this reason and to observe the effect of the angle of the chip in chip formation, machining process is considered with three different rake angles of 32, 38 and 42°.In this case the cutting speed is considered to be constant as 30 m/s, cutting depth 0.5 mm and the angle of inclination 10°. Figure 7 residual stress distribution of the piece is represented in dry and cryogenic for different angles of material removal.The results indicate that in dry machining for low rake angles, chip will be formed broken.At the angle of 32 o of the chip, the lengths of chip are averagely 23.4 mm and by increasing the angle of material removal, connected chip is formed.So for an angle of 42 o chip are created without a break.It should be noted that by increasing the rake angle the contact between the chip and tool is reduced and thus the generated compressive stress increases at the tip of the tool.It should be considered that the tensile stress is the highest amount for material removal tools with an angle of 38°.The main point should be noted is that, according to the figure 7, the difference between dry machining and cryogenic method is that, in cryogenic machining in contrast to dry machining the chip is formed connected.According to figure 8, the temperature distribution of the workpiece in cryogenic machining is indicated, it can be seen the temperature of the chip in the cryogenic machining decreases to 50% in comparison to the dry machining and rake angle 38 degrees more indicates the generated temperature.

The Cutting Speed Effect
Three various speeds of 10, 30 and 60 m/s have been studied to investigate the impact of cutting speed on chip features.The depth of cut and angle of inclination of tools is considered to be fixed and respectively equal to 0.5 mm and 10 degrees.In figure 9 the impact of cutting speed on the formation of the chip is represented in cryogenic machining process and different rake angles.The results represent that at low cutting speeds, the chip are conical and by speeding up the chip are more open and lose the conical shape.It can be said the most conical formation of the chip and disconnection of the newly formed chip with previous chip causes in increasing the length of the chip and reduces the break in them.According to figures also it is observed that at speeds of 10 and 30 m/s the increasing of the rake angle causes the reduction of residual plastic strains in the chip, but at higher speeds (60 m/s) the greatest strain occurs in the chip for the angle of 38 degrees.

CONCLUSION
In the machining process using cooling increases tool life, dimensional accuracy, and makes to better roughness which cause reduction of temperature and energy consumption and leads to improved productivity.Therefore, in this study, the finite element model is considered for oblique cutting with cryogenic cooling.To simulate material removal process and separation of chip, the plastics criterion materials as well as material damage, the Johnson-Cook model was used, and mechanical and thermal behavior of materials were applied as a function of temperature.After analyzing the simulated model by using coupled thermal-dynamic solutions model, the impact of parameters such as the speed of material removal, rake angle on residual stress and shape of the chip and also comparison of the results with dry and cryogenic machining have been considered.The results represent that applying thermal and mechanical loads in the workpiece during the machining process, in fluencies the residual stress and tensile stress distribution in the cryogenic process is more than dry machining and this fact on at residual stress on compression is vice versa.At the cutting speed of 10 m/s in cryogenic machining respectively causes in the reduction of 71.34 and 76.64 percent of temperature of the chip and tool in comparison to dry machining.It is observed that temperature of the chip in cryogenic machining is 50% reduces to dry machining and rake angle of 38 degrees shows more the generated temperature.The results also represent that the chip formed in cryogenic machining to be connected and without a fracture, unlike the dry machining.However, at speeds of less than 30 m/s shape of the chip are conical, and at high speeds has been created strips.Also, as the rake angle increases the conical shape of chip reduces.

Figure 1 :
Figure 1: (a) Meshing and thermal boundary conditions of cryogenic machining operations and (b) the angles of cutting tool.

Figure 2 :
Figure 2: Compares the obtained mechanical cutting force by the use of the presented model and the experimental results of Ref. (Günay, 2005).

Figure 3 :Figure 4 :Figure 5 :
Figure 3: Compares the residual strain distribution and chip shapes (a) dynamic analysis, (b) thermal-dynamic coupled analysis in dry machining and (c) thermal-dynamic coupled analysis in cryogenic machining.

Figure 6 :
Figure 6: The distribution of residual stress (Pa) in two modes (a) dry machining and (b) cryogenic machining.

Figure 7 :Figure 8 :
Figure 7: The distribution of residual stress (Pa) in (a) dry machining and (b) cryogenic machining in different rake angles in cutting speed of 30 m/s.

Figure 9 :
Figure 9: chip formation processes in the cryogenic machining for different rake angles in speeds of material removal for (a) 10 m/s, (b) 30 m/s and (c) 60 m/s.

Table 1 :
The values of variables of equation of Johnson-Cook Plasticity Model.

Table 2 :
The values the constant equation of Johnson-Cook failure model.

Table 3 :
(Yilbas et al. 2016hanical properties of the used aluminum in the simulation(Yilbas et al. 2016).

Table 4 :
The mechanical and thermal properties of used AISI 316L in simulation.