# Development of a Staggered PCD End Mill for Carbon Fiber Reinforced Plastic
## 4 Milling Experiment of CFRP
### Influence of Milling Parameters on Milling Force  
According to the results of the range analysis of milling force, the variation of milling forces with milling parameters is shown in Figure 8. It is seen that the milling force decreases with cutting speed, and the main cutting force varies significantly, as shown in Figure 8a. When \(\
u=100-150\) m/min, the main cutting force decreases rapidly. When \(\
u=150-200\) m/min, the main cutting force only has a little increase. This is because the actual shear angle of the cutter increases with the spindle rotation speed, resulting in a decrease in shear force. As the milling temperature increases with cutting speed [25], too high a cutting speed will aggravate tool wear and the cutting force will tend to increase. As shown in Figure 8b, the milling force has a little increase when \(a_{e}=0.5-1\) mm. When \(a_{e}\) exceeds 1 mm, the milling force increases significantly. However, when \(a_{e}\) exceeds 1.5 mm, the milling force decreases slightly. This is because the milling material volume per tooth increases with the increase of milling width, resulting in a rapid increasing of milling force. During down milling, the milling width increases results over a distance which in turn increases the distance of each tooth participating in the milling. Therefore, the milling force tends to be stable when the milling width increases to a certain extent. As shown in Figure 8c, the milling force increases as feed per tooth increases. Feed per tooth directly causes an increase in the milling width per tooth and the cutting area, which increases the deformation resistance and the friction force of the flank face. When \(f_{z}=0.01-0.02\) mm/z, the milling force increases slowly. When \(f_{z}=0.02-0.04\) mm/z, the milling force increases quickly. \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **A Cutting Speed \(\
u\)** & **B Milling Width \(a_{e}\)** & **C Feed per Tooth\(f_{z}\)** \\ \hline
1 & 257.73 & 121.30 & 127.58 \\
2 & 231.95 & 138.23 & 146.18 \\
3 & 151.05 & 273.75 & 238.65 \\
4 & 151.83 & 259.28 & 280.15 \\ R(Max. – Min.) & 106.68 & 152.45 & 152.58 \\ \hline \multicolumn{3}{c}{Rank of primary-secondary} & \multicolumn{2}{c}{C, B, A} \\ \hline \end{tabular}
\end{table} 
Table 6: Range table of \(F_{x}\)(N). \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **A Cutting Speed \(\
u\)** & **B Milling Width \(a_{e}\)** & **C Feed per Tooth\(f_{z}\)** \\ \hline
1 & 133.69 & 68.93 & 48.30 \\
2 & 117.45 & 72.38 & 61.61 \\
3 & 79.65 & 130.01 & 126.83 \\
4 & 62.51 & 121.99 & 156.56 \\ R(Max. – Min.) & 71.18 & 61.09 & 108.26 \\ \hline \multicolumn{3}{c}{Rank of primary-secondary} & \multicolumn{2}{c}{C, A, B} \\ \hline \end{tabular}
\end{table} 
Table 7: Range table of \(F_{y}\)(N). \[\mathrm{Y}=\mathrm{X}\beta+\mathrm{n} \tag{5}\]  
where  
\[\mathrm{Y}=\left[ \begin{array}{c}y_{1}\\ y_{2}\\ \ldots\\ y_{3}\end{array} \right];\mathrm{X}=\left[ \begin{array}{cccc}1&x_{11}&x_{12}&x_{ 13}\\ 1&x_{21}&x_{22}&x_{23}\\ \vdots&\vdots&\vdots&\vdots\\ 1&x_{16}&x_{16}&x_{16}&3\end{array} \right];\ \beta=\left[ \begin{array}{c}\beta_{0}\\ \beta_{1}\\ \beta_{2}\\ \beta_{3}\end{array} \right];\ \mathrm{n}=\left[ \begin{array}{c}n_{1}\\ n_{2}\\ \vdots\\ n_{3}\end{array} \right] \tag{6}\]  
Assuming that \(b_{0},\ b_{1},\ b_{2}\) and \(b_{3}\) are respectively the least square estimations of \(\beta_{0},\ \ \beta_{1},\ \ \beta_{2}\) and \(\beta_{3}\), then the regression equation is:  
\[\hat{y}=b_{0}+b_{1}x_{1}+b_{2}x_{2}+b_{3}x_{3} \tag{7}\]  
where \(\hat{y}\) is the statistical variable; \(b_{0},\ b_{1},\ b_{2}\)_and_\(b_{3}\) are the regression coefficients which can be calculated by:  
\[\mathrm{b}=\left(\mathrm{X}^{\prime}\mathrm{X}\right)^{-1}\mathrm{X}\mathrm{Y} \tag{8}\]  
Analyzing the test data by using multiple linear regression, the least square estimations of \(b_{0},\ b_{1},\ b_{2}\) and \(b_{3}\) can be done, and finally the linear regression model between milling forces and milling parameters is as follows:  
\[\left\{