## 2 Milling-Induced Residual Stress Experiment of 7075 Aluminum Alloy
### Test Results of Milling-Induced Residual Stress  
The residual stress in the surface of the milled test pieces was measured by X-ray diffraction. The test instrument was a XSTRESS-3000 residual stress analyzer made in Finland, with an accuracy of \(\pm\)10 MPa. The parameters of the X-ray diffractometer are \begin{table}
\begin{tabular}{c c} \hline
**Parameters** & **Values** \\ \hline Stroke (mm) & X = 630, Y = 560, Z = 560 \\ B-axis swing angle (\({}^{\circ}\)) & \(-\)120\(\rightarrow\)+30 \\ Maximum spindle speed (r/min) & 12,000 \\ Maximum feed rate of linear axis (mm/min) & 30,000 \\ Positioning accuracy (mm) & 0.006 \\ Control system & Heidenhain iTNC530 \\ \hline \end{tabular}
\end{table} 
Table 1: The primary parameters of the five-axis machining center. Figure 1: The end milling and side milling: (**a**) the end milling; (**b**) the side milling. shown in Table 4. The residual stress of milling varied slightly with the milling position. The small ratio of the tool diameter to the spot diameter may affect measurement accuracy. To this end, we selected three test points on each machined surface of the test piece. In addition, the distance between two adjacent points was 25 mm, as shown in Figure 2. The residual stress average value at the three points was regarded as the milling-induced residual stress on the machined surface. An electrolytic polisher was used to polish the piece surface to obtain the residual stress distribution along the depth direction in the milled surface. The thickness of each polishing was 0.02 mm and the residual stress was measured layer by layer. A Kristall 650 electrolytic polishing machine mated in Germany was used for electrolytic polishing and the parameters are shown in Table 5. The residual stress distribution state corresponding to each milling parameter was obtained. We took the depth of the milling stress layer as the abscissa, and the residual stress value based on the experiment as the ordinate. Then, the spline function was employed for curve fitting in MATLAB. As a result, the residual stress distribution along the depth direction was obtained, as shown in Figures 3 and 4. The residual stress in the machined surface was the result of many factors. The experimental results showed that the end milling-  
Then, linear regression analysis was used to fit the empirical formula of the milling-induced residual stress of 7075 aluminum alloy. Through the orthogonal experiments, the exponential relationship between the residual stress and milling parameters was formulated as Equations (2)-(5). \[\sigma_{\text{equ}}=\int_{0}^{h}\sigma dh/H, \tag{1}\]  
where \(H\) is the depth of the milling-induced residual stress. \[\sigma_{\text{en}H}=-38.0195v_{c}^{-0.176}f_{z}^{-0.2827}a_{p}^{0.0108}a_{e}^{ 0.1732}, \tag{2}\] \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 & 0.50 & 10.00 & \(-84.77\) & \(-67.56\) \\
2 & 125.6 & 0.025 & 1.00 & 15.00 & \(-76.56\) & \(-61.18\) \\
3 & 125.6 & 0.05 & 1.50 & 20.00 & \(-60.34\) & \(-36.40\) \\
4 & 376.8 & 0.01 & 1.00 & 20.00 & \(-80.45\) & \(-58.48\) \\
5 & 376.8 & 0.025 & 1.50 & 10.00 & \(-52.16\) & \(-48.36\) \\
6 & 376.8 & 0.05 & 0.50 & 15.00 & \(-53.78\) & \(-39.35\) \\
7 & 628 & 0.01 & 1.50 & 15.00 & \(-77.18\) & \(-38.26\) \\
8 & 628 & 0.025 & 0.50 & 20.00 & \(-51.93\) & \(-31.72\) \\
9 & 628 & 0.05 & 1.00 & 10.00 & \(-41.43\) & \(-36.46\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The equivalent results of the end milling-induced residual stress. Figure 4: The residual stress distribution along the depth direction in the test piece surface of side milling: (**a**) the residual stress distribution in the feed direction; (**b**) the residual stress distribution in the vertical direction of feed.