# Improved Cutting Force Modelling in Micro-Milling Aluminum Alloy LF 21 Considering Tool Wear
## 3 An Improved Cutting Force Model in Micro-Milling LF 21 Considering Tool Wear
### Parameter Identification of the Micro-Milling Force Model  
The minimum cutting thickness is used as a demarcation point to build the micro-milling force model. The research group has found that the micro-milling force increases significantly near the minimum cutting thickness. We conduct several experiments, and the experimental results are shown in Table 6. Based on the experimental results, we determine that the minimum cutting thickness of micro-milling aluminum alloy LF 21 is 0.45 \(\upmu\)m.  
There are altogether eleven coefficients in the cutting force model, as shown in Equations (10) and (22). Coefficient of shear effect indicates cutting force that the cutting edge infinitesimal withstands when cutting chip per unit cutting layer area. Ploughing effect coefficient indicates cutting force that the cutting edge infinitesimal withstands when there is unit interference volume between the cutting edge infinitesimal and machined surface. Cutting force coefficients are related to geometrical parameters of tools, materials of tools and materials of workpiece. For different tool materials and workpiece materials, cutting force coefficients are different, and thus, it is necessary to conduct parameter identification before utilizing cutting force prediction model. The cutting force coefficients are determined based on experiments. To determine the coefficients of micro-milling force model dominated by shear and plough effects, the authors refer to the research method of the literature [23]. By solving the cutting layer area and interference volume of the cutting edge at a certain tooth angle, combing the experimental force data and using the least square method, we obtain the coefficients of the force model. The cutting layer area corresponding to different tooth angles of the cutting edge involved in cutting is decomposed to the x - y coordinate axis. The simulation curve of the cutter rotation is shown in Figure 15. The simulation conditions are as follows: n = 40,000 rpm, \(a_{p}\) = 20 \(\upmu\)m and \(f_{z}\) = 0.8 \(\upmu\)m/z. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Number**} & **Spindle Speed** & **Axial Cutting** & **Feed per tooth \(f_{z}\)** & \multirow{2}{*}{\(\mathbf{F_{x}}\) (N)} & \multirow{2}{*}{\(\mathbf{F_{y}}\) (N)} & \multirow{2}{*}{\(\mathbf{F_{z}}\)**(N)} \\  & **n (rpm)** & **Depth \(a_{p}\) (\(\upmu\)m)** & **(\(\upmu\)m/z)** & & \\ \hline
1 & 40,000 & 50 & 0.25 & 0.0735 & 0.5045 & 0.2857 \\
2 & 40,000 & 50 & 0.35 & 0.0936 & 0.6645 & 0.2886 \\
3 & 40,000 & 50 & 0.45 & 0.1246 & 0.7894 & 0.3306 \\
4 & 40,000 & 50 & 0.55 & 0.1043 & 0.6275 & 0.2882 \\
5 & 40,000 & 50 & 0.65 & 0.1223 & 0.7293 & 0.3245 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experiments for determining the minimum cutting thickness. Figure 15 indicates that when the tooth angle at the bottom of the micro-milling cutter-edge line is 2.356 radians, the cutting layer area decomposed along the y axis reaches the maximum, corresponding to the peak of the cutting force in the y-direction. When the tooth angle at the bottom of the micro-milling cutter-edge line is \(1.571\) radians, the cutting layer area decomposed along the \(x\) axis reaches the peak. According to cutting forces prediction model of Formula (10), \(A_{c}\) and \(A_{s}\) corresponding to the tooth part involved in cutting at different tooth angles are solved. The simulation curve of cutter rotation is shown in Figure 16. The maximum cutting force in \(y\) direction corresponds to the tooth angle at the bottom of the blade at 2.356 radians. Where, \(A_{cy}=-3.0261\times 10^{-11}\)m\({}^{2}\), \(A_{sy}=3.1236\times 10^{-11}\)m\({}^{2}\). Similarly, the peak x-direction cutting force corresponds to the tooth angle at the bottom of the blade at 1.571 radians. Where, \(A_{cx}=2.5578\times 10^{-12}\)m\({}^{2}\), \(A_{sx}=5.8777\times 10^{-11}\)m\({}^{2}\). Figure 16: Decomposition of cutting layer area. Figure 15: Decomposition of cutting layer area to coordinate axes.