# Improved Cutting Force Modelling in Micro-Milling Aluminum Alloy LF 21 Considering Tool Wear
## 2 Prediction of Tool Wear Based on Simulation
### Material Parameters' Setting and Meshing  
Because the strength and stiffness of the micro-milling cutter are much higher than those of the workpiece, the cutter strain in processing can be ignored, so the micro-milling cutter is regarded as a rigid body; only friction and heat transfer are considered. The micro-milling cutter material is WC/Co, and the coating material is TiAlN. Call the database of material in DEFORM 3D and set the material parameters, as shown in Table 2. \begin{table}
\begin{tabular}{c c c} \hline
**Geometric Parameter** & **Symbol** & **Value** \\ \hline Tool head radius & r\({}_{\text{c}}\) (mm) & 0.3 \\ Shank radius & r\({}_{\text{s}}\) (mm) & 2 \\ Overall length & L (mm) & 45 \\ Extended Length & 1 (mm) & 15 \\ Cutting length & l\({}_{\text{c}}\) (mm) & 1.2 \\ Neck taper angle & \(\gamma\) & 12\({}^{\circ}\) \\ Helix angle & \(\beta\) & 30 \\ Rounded cutting edge radius & r (mm) & 0.002 \\ Number of flutes & — & 2 \\ \hline \end{tabular}
\end{table} 
Table 1: Geometric parameters of the micro-milling tool. Figure 3: Geometric model of workpiece. The meshing method of combining relative meshing and local encryption is used, which greatly improves the simulation speed on the premise of ensuring calculation accuracy. The mesh number of the cutter is 50,000, the ratio of the maximum mesh to the minimum mesh is set as 5:1, the local encryption size ratio of the blade is set as 10:1 and the coating thickness is set as 2 \(\upmu\)m. The meshing of the micro-milling cutter is shown in Figure 4.  
The workpiece material is aluminum alloy LF 21, which belongs to Al-Mn alloy, with low strength, low stiffness and good plasticity. The material parameters of the workpiece are shown in Table 3.  
Because of the characteristics of LF 21, the strain and strain rate of this material are both very high in the process of micro-milling. Therefore, to characterize the material properties and failure criteria of LF 21, the Johnson-Cook constitutive model and failure model are adopted. As shown in Equation (1), is the Johnson-Cook constitutive model [14]:  
\[\sigma=[A+B(\epsilon)^{n}][1+C\ln(\frac{\dot{\epsilon}}{\dot{\epsilon}_{0}}) ][1-(\frac{T-T_{room}}{T_{melt}-T_{room}})^{m}] \tag{1}\]  
where, \(\sigma\) is the stress; \(A\) is the yield strength of the material under the reference deformation temperature and the reference strain rate; \(B\) is the strain hardening parameter of the material; \(C\) is the strain rate coefficient of the material; n is the work hardening parameter of the material; m is the temperature softening parameter of the material; \(\dot{\epsilon}\) is the plastic strain \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Thermal** & **Coefficient of** & \multirow{2}{*}{**Modulus of** **Elasticity (Mpa)**} & **Heat** & \multirow{2}{*}{**Poisson’s** **Ratio**} & **Rockwell** \\  & **Conductivity** & & & & & **Analyticity (Mpa)** \\  & **(W/(m\({}^{\circ}\)C))** & & & & & **Analyticity (N/(mm\({}^{2,\circ}\)C))** & \\ \hline WC/Co (ISO K20) & 55 & 4.7 \(\times\) 10\({}^{-6}\) & 5.6 \(\times\) 10\({}^{5}\) & 15 & 0.25 & 65 \\ TiAlN & 12 & 9.4 \(\times\) 10\({}^{-6}\) & 6 \(\times\) 10\({}^{5}\) & 15 & 0.23 & 83 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material parameters of the micro-milling cutter. Figure 4: Meshing of the micro-milling cutter and partial enlargement of cutting edge. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Material**} & **Thermal** & **Coefficient of** **Thermal** & **Modulus of** **Elasticity (Mpa)** & **Heat** & \multirow{2}{*}{**Poisson’s** **Ratio**} & **Brinell** **Hardness** \\  & **Conductivity** & & & & & **Analyticity (N/(mm\({}^{2,\circ}\)C))** & \\  & **(W/(m\({}^{\circ}\)C))** & & & & & \\ \hline LF 21 & & & & & & \\ (GB/T3190-1996) & 180.2 & 2.2 \(\times\) 10\({}^{-5}\) & 6.86 \(\times\) 10\({}^{4}\) & 2.433 & 0.25 & 185 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Material parameters of the workpiece.