## 2 Milling-Induced Residual Stress Experiment of 7075 Aluminum Alloy
### Test Results of Milling-Induced Residual Stress
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Test Piece Number**} & \(v_{c}\) & \(f_{z}\) & \(a_{p}\) & \(a_{e}\) & \(\sigma_{\text{e}all}\) & \(\sigma_{\text{e}all2}\) \\  & **(m/min)** & **(mm/z)** & **(mm)** & **(mm)** & **(MPa)** & **(MPa)** \\ \hline
1 & 125.6 & 0.01 & 15.00 & 0.20 & \(-31.32\) & \(-25.17\) \\
2 & 125.6 & 0.025 & 25.00 & 0.60 & \(-18.65\) & \(-12.17\) \\
3 & 125.6 & 0.05 & 35.00 & 1.00 & \(-10.69\) & \(-8.74\) \\
4 & 376.8 & 0.01 & 25.00 & 1.00 & \(-17.34\) & \(-10.40\) \\
5 & 376.8 & 0.025 & 35.00 & 0.20 & \(-21.57\) & \(-14.96\) \\
6 & 376.8 & 0.05 & 15.00 & 0.60 & \(-27.22\) & \(-16.17\) \\
7 & 628 & 0.01 & 35.00 & 0.60 & \(-34.04\) & \(-21.65\) \\
8 & 628 & 0.025 & 15.00 & 1.00 & \(-19.96\) & \(-18.86\) \\
9 & 628 & 0.05 & 25.00 & 0.20 & \(-11.18\) & \(-11.49\) \\ \hline \hline \end{tabular}
\end{table} 
Table 7: The equivalent results of the side milling-induced residual stress. \[\sigma_{end2}=-156.6478v_{c}^{-0.2277}f_{z}^{-0.2081}a_{p}^{-0.0383}a_{e}^{-0.269}, \tag{3}\]  
where \(\sigma_{end1}\), \(\sigma_{end2}\) denote the equivalent residual stress in the feed direction and vertical direction of feed of end milling, respectively; \(125.6\) m/min \(\leq v_{c}\leq 628\) m/min, \(0.01\) mm/z \(\leq f_{z}\leq 0.05\) mm/z, \(0.5\) mm \(\leq a_{p}\leq 1.5\) mm, \(10\) mm \(\leq a_{e}\leq 25\) mm. \[\sigma_{side1}=-11.8627v_{c}^{0.0577}f_{z}^{-0.3428}a_{p}^{-0.362}a_{e}^{-0.084 3}, \tag{4}\]  
\[\sigma_{side2}=-12.8353v_{c}^{0.0947}f_{z}^{-0.2419}a_{p}^{-0.449}a_{e}^{-0.162}, \tag{5}\]  
where \(\sigma_{side1}\), \(\sigma_{side2}\) denote the equivalent residual stress in the feed direction and vertical direction of feed of side milling, respectively; \(125.6\) m/min \(\leq v_{c}\leq 628\) m/min, \(0.01\) mm/z \(\leq f_{z}\leq 0.05\) mm/z, \(15\) mm \(\leq a_{p}\leq 35\) mm, \(0.2\) mm \(\leq a_{e}\leq 1\) mm. The four formulas indicate that the equivalent residual stress in milling is expressed as compressive stress. (1) The condition of end milling. According to Equations (2) and (3), the significance of the milling parameters to the residual stress in the feed direction is \(f_{z}>v_{c}>a_{e}>a_{p}\), and the significance of the parameters to the residual stress in the vertical direction of feed is \(a_{e}>v_{c}>f_{z}>a_{p}\). When \(v_{c}\) and \(f_{z}\) increase, the residual stress in the two directions exhibits a decreasing trend. When \(a_{p}\) and \(a_{e}\) increase, the residual stress in the feed direction increases, and the residual stress in the vertical direction of feed decreases. (2) The condition of side milling. According to Equations (4) and (5), the significance of the parameters to the residual stress in the two directions is \(a_{p}>f_{z}>a_{e}>v_{c}\). When \(n\) increases, the residual stress in the two directions increases. When \(f_{z}\), \(a_{p}\) and \(a_{e}\) increase, the residual stress in the two directions decreases. Note that, except for Equation (2), the \(p\)-values of the other three equations are all greater than \(0.05\). It shows that the regression effect is not significant. Thus, it is necessary to develop better analysis methods.