Chapter 4 Numerical Evaluation of Cutting Temperature and Chip
4.1 Temperature and chip formation modelling using FEM
In this research, an ALE FE model has been built to simulate the turning process of Ti-6Al-4V by carbide insert under various cooling conditions. From the actual machining viewpoint, the FE model is a restrictive approach that requires less computational time significantly and offers satisfactory results.
Workpiece and Tool Modeling: The 2D FE model comprises only a small segment of the workpiece and cutting tool which takes part in turning. A plane strain condition has been assumed because the feed rate value is generally very less as compared to the depth of cut.
In this study thermo-visco-plastic behavior of the workpiece has been expressed using the J-C constitutive material model. This model can be used to describe material behavior in the plastic regime over large strains, high strain rates and high temperatures [Duan et al., 2009]. The flow stress can be expressed as:
σ (A+B ) ……… (4.1) where,
ε = equivalent plastic strain
= strain rate normalized with a reference strain rate T = instantaneous temperature
TM = melting temperature TR = reference temperature
Here, the first bracketed term called elastoplastic term represents strain hardening of the yield stress that is given the stress as a function of strain. The next term (visco- plasticity term) models the increase in the yield stress at elevated strain rates and the final term is softening of the yield stress due to local thermal effects. The above yield strength portion of the J-C model has five material constants. A is the yield stress, B and n represent the effect of strain hardening determine . C is the strain rate constant. A, B, C, n and m are measured at TR or below TR.
Moreover, the J-C damage model was used for initializing the chip separation. This model is suitable for progressive damage to high strain rate deformation such as high- speed machining. According to the J-C damage criterion the expression for fracture strain is:
...(4.2) where,
D1= Initial fracture strain D2= Exponential factor D3= Triaxiality factor D4= Strain rate factor D5= Temperature factor
= Von-Mises equivalent stress
Here the first, mid and last bracketed term in the J-C damage model includes the effect of stress triaxiality, strain rate and local heating respectively. Damage initiation begins according to standard damage law,
... (4.3) where W is the damage parameter and ∆ε is the accumulated increment of equivalent plastic strain during an increment step. According to this model, damage initiation is followed by the damage evolution criterion which governs the propagation of plastic strain until an ultimate failure happens. For crack initiation, the fracture energy was used as damage evolution. In the following Table, Johnson-Cook model parameters and progressive damage model parameters for Ti-6Al-4V alloy have been presented.
Table 4.1 Johnson-Cook model and progressive damage parameters for Ti-6Al-4V [Wang and Liu, 2014]
Johnson-Cook model parameters Johnson-Cook progressive damage parameters
A (MPa) 862 D1 -0.09
B (MPa) 331 D2 0.25
C 0.012 D3 -0.5
n 0.34 D4 0.014
m 0.8 D5 3.87
Tmelt (°C) 1878 - -
The thermal and mechanical properties of Ti-6Al-4V, tungsten carbide and coating materials (TiN, TiCN, Al2O3) adopted in the numerical models are given in Table 7.2 and 7.3. In this research, multiple-layer coatings are represented by a composite single layer. ‗Equivalent‘ coating properties of the composite layer have been calculated according to the method utilized in a study by Yen et al. [2004] and defined as the coating properties.
Table 4.2 Material properties of Ti-6Al4V alloy [Wang and Liu, 2014]
Density, ρ
(Kg/m3) Elastic modulus, E
(GPa)
Poisson‘s
ratio, ν Thermal conductivity,
λ (W/m/°C) Specific heat, Cp (J/kg/°C)
4,430 109 (323 K) 0.34 6.8 (293 K) 611 (293 K)
91 (523 K) - 7.4 (373 K) 624 (373 K)
75 (723 K) - 9.8 (573 K) 674 (573 K)
- - 11.8 (773 K) 703 (773 K)
Table 4.3 Material properties of tool substrate and coatings [Fahad et al., 2011]
Materials Density, ρ (Kg/m3) Thermal conductivity, λ
(W/m/°C) Specific heat, Cp (J/kg/°C)
Tungsten Carbide 14700 100 203
21 (373 K) 702.6 (373 K)
TiN 5420 22 (573 K) 783.4 (573 K)
23 (773 K) 818.9 (773 K) 29 (373 K) 1030 (373 K)
TiCN 4180 30.6 (573 K) 1040 (573 K)
32 (773 K) 1120 (773 K)
17 (373 K) 903 (373 K)
Al2O3 3780 12.5 (573 K) 1089 (573 K)
7.75 (773 K) 1176 (773 K) 21.35 (373 K) 913.72 (373 K)
Composite layer 4268 18.46 (573 K) 1008.28 (573 K)
14.95 (773 K) 1082.18 (773 K) With the above mentioned properties, the material directory has been created for the analysis. The geometry of the workpiece and tool have been sketched considering the real dimension and the materials have been assigned. Then the geometry of the assembly was defined by creating instances of a part and positioned the instances relative to each other in a global coordinate system. Afterward, instances were merged to create a total metal cutting model. Fig.4.1 shows the assembly model of the work piece-tool.
Fig.4.1 Assembly model of work piece-tool
An intermediate layer known as the sacrificial layer has been considered in the workpiece. This layer defines the path of separation between the chip back surface and machined surface which is going to take place with the tool progression. The upper portion of this layer is equal to the uncut chip thickness or feed for the 2D simulation modeling. In this particular machining process, two edges of the tool are involved in cutting, such as the
Tool coating
Work piece Clearance
surface
Tool Sacrificial
Layer Damaged
Zone Rake surface
Un-deformed part
Feed
rake face and clearance face. At the two faces, a negative rake angle of 6o and a clearance angle of 6o were drawn as real geometry of the cutting tool. The applied mesh consisted of CPE4RT elements with plane strain conditions. CPE4RT means 4 node bilinear displacement and temperature, reduced integration with hourglass control. The tool is composed of the CPE4RT and some triangular elements, but of variable length. The mesh distribution of the assembly is shown in Fig.4.2, where the different densities can be seen.
Fig.4.2 Mesh structure of workpiece and tool
Interaction Modeling: Mechanical and thermal interaction between the tool and workpiece was modeled with a surface-to-surface contact. It consists of two surfaces expected to come into contact during the tool-workpiece interaction. These contact surfaces are designated by the master surface (edges of a tool) and node-based slave surface (node region of the top portion of the workpiece). Further, a self-contact was assigned to the top edge of the workpiece due to considering the possibility of the chips can be folded onto themselves during high deformation. Both types of contacts are shown in Fig.4.3. In this study, the contact areas have been modeled based on Coulomb‘s friction law, which is widely used in metal cutting simulations [Özel, 2006]. In the previous studies, friction coefficient 0.2 [Zhang et al., 2015], 0.3 [Shao et al., 2010], 0.5 [Sima and Özel, 2010], etc have been used when machining Ti-6Al-4V ally by carbide insert under dry condition. In this analysis, the friction coefficient has been selected within 0.2~0.5 for dry machining. Heat radiation and convection were neglected in the cutting model, as they are negligible compared to conduction. High speeds allow no time for heat transfer between integration points with which the process is treated as an adiabatic process. In this work, 100% of the frictional energy has been supposed to be transformed into heat and the fraction of heat distributed to the tool has been considered here as 0.75 for Ti-6Al-4V alloy machining by carbide tool, which is based on previous research. Tanveer et al. [2017]
showed that in machining Ti-6Al-4V alloy by carbide insert with 80 m/min, around 75%
heat is transferred to the tool. A wide range of thermal conductance between 20 ~104 W/m2/K at the tool-workpiece contact surface was utilized by different researchers [Sadeghifar et al., 2018]. Here, the thermal conductance value for turning Ti-6Al-4V alloy by coated and uncoated carbide inserts was used within this range. This conductance was imposed for the distance in the contact pair is less than 10-7 m.
(a) Surface to surface contact
(b) Self-contact
Fig.4.3 Contact model of workpiece and tool (a) Surface to surface contact and (b) Self- contact
In the case of MQL application with different coolants, the effect of the mist jet has been integrated into the model by a convective heat-transfer coefficient [Jamaluddin et al., 2017]. For this case, a surface film condition interaction in addition to thermal/ mechanical contact was generated and applied on the rake and flank surfaces of the cutting tool which are expected to come into contact with the workpiece during machining. The MQL effect was modeled by setting surface film conditions at the tool rake and flank surfaces. The
local temperature inside was set equal to 25 °C. The surfaces for the surface film interaction are highlighted in Fig.4.4.
Fig.4.4 Surface film condition for MQL at rake and flank surface of the tool The VG 68 cutting oil and hybrid nanofluid was used as an MQL fluid in this study. Fluids have been mixed with compressed air and applied as a fine mist into the interface. Therefore, to study the effect of MQL, mist with cutting oil and hybrid nano- fluid characteristics have been calculated considering 50:50 air and oil mixture. The necessary parameters to calculate the film coefficient of MQL mists are tabulated in Table 4.4 and 4.5. Here, the properties of nano-fluid have been calculated theoretically or experimentally determined.
Table 4.4 MQL fluid thermo-physical characteristics
Parameters VG 68 cutting
oil Hybrid nanofluid
(1 vol %) Air
Density ρ (kg/m3) 850 876.82 23.48
Dynamic Viscosity μ (N-s/m2) 0.061 0.09 1.81×10-5
Thermal conductivity λ (W/m/°C) 0.161 0.208 2.70×10-2
Specific heat, Cp (J/°C/kg) 1670 1677 1038
Table 4.5 MQL application parameters
Parameters Corresponding Value Diameter of the nozzle injector (mm) 1
Diameter of outlet nozzle (mm) 0.5
Pressure inside nozzle (bar) 20
Angle of the spray pattern 20o
Flow rate of cutting fluid (ml/hr) 50
Rake surface film
Flank surface film
Afterward, the film coefficient utilized for this interaction condition was calculated for the cutting oil mist and hybrid nanofluid mist. The traditional correlations for forced convection use a heat transfer co-efficient (film coefficient, h) of the form:
………...
(4.4) For cylindrical workpiece, the Reynolds number (Re), Prandtl number (Pr) and Nusselt number (Nu) are given below:………..…. (4.5)
………..…………... (4.6)
…….... (4.7)
………..……. (4.8)
Re depends on mist density (ρmist), dynamic viscosity (μmist), velocity (Vmist), and characteristics length (Lc). Lc is the distance between the nozzle and the target plane. Pr depends only on the dynamic viscosity (μ), specific heat (Cp) and thermal conductivity (k) of fluid. Pr number function (G(Pr)) can be calculated by using Eq. 4.7. Nu depends on G(Pr), Re and velocity gradient ( ). The dimensionless velocity gradient value =1.486 has been selected from previous literature [Liu et al., 1993]. After finding out the Nu value of the cutting oil and hybrid nanofluid mist, the heat convection coefficients and film coefficient values have been calculated by utilizing Eq. 4.4. All the characteristics values for both of the mists have been given in Table 4.6.
Table 4.6 MQL mist characteristics for different fluid
Parameters Base fluid mist Hybrid nanofluid mist
Density ρ (kg/m3) 436.74 450.15
Dynamic Viscosity μ (N-s/m2) 0.031 0.045
Thermal conductivity λ (W/m/°C) 0.094 0.1190
Specific heat, Cp (J/°C/kg) 1354 1357.5
Prandtl number (Pr) 4.39×102 5.20×102
Reynolds number (Re) 6.87 4.81
Average Nusselt number (Nu) 4.51 4.77
Heat convection coefficient, h 14.67 12.98
Film coefficient, G 168.70 192.87
Simulation environment and boundary conditions: The work-piece was modeled as an
elastic body. In this work, a FEM simulation model with an ALE scheme with pure Lagrangian boundaries is designed and kinematic penalty contact conditions between the tool and the workpiece are defined. This model allows a FEM simulation scheme to simulate the chip formation from the incipient to steady-state as it was proposed by the authors in reference [Özel and Zeren, 2005]. The boundary conditions for the 2D ALE Lagrangian base model along with the geometry of the system are shown in Fig.4.5. For the boundary conditions, ENCASTRE (fully built-in) applied to the workpiece at its left and bottom surfaces, restricting the workpiece in the X and Y direction, respectively. The tool is moved against the workpiece by applying constant cutting velocity. The tool moves in the–X-direction. The element deletion technique is used to allow element separation to form a chip.
Fig.4.5 Boundary conditions of workpiece and tool
The ALE adaptive meshing technique is used to reduce element distortion in cases of extreme deformation and applied at the top portion of the workpiece. So that, in this region the associated nodes move with the material in the direction normal to the material‘s surface and nodes are allowed to adapt (adjust their position) tangent to the free surface. The ALE re-mesh was used with a frequency of 2 and 1 re-meshing sweeps per increment. The adaptive mesh was controlled by a volume-based smoothing algorithm and the mesh motion was constrained to follow the underlying material.
Cutting speed
No displacement along Y
Feed
Fixed boundary