# Influence of Ball-End Milling Strategy on the Accuracy and Roughness of Free Form Surfaces
## 3 Results
### Surface Texture  
The surfaces of the machined samples were examined using a VHX-5000 microscope (Keyence Corporation, Osaka, Japan). Three areas were selected on the test sample with a freeform surface: the planar area (1), the area on the inclined wall of the protrusion (2), and the area on the inclined toward to valley (3) (Figure 7). Photographs at \(200\times\) magnification were taken at these locations. The bottom and left sides of each photograph were oriented in the X-and \(Y\)-axis directions, respectively, which corresponded to the positions at which the samples were produced. The surface roughness was also measured at the locations where the microscope photographs were taken. Measurements were performed using a portable surface roughness tester Surf test SJ 410 (Mitutoyo Corporation, Headquarters: Takatsu-ku, Kawasaki City, Japan). During the measurement, the probe tip moved perpendicular to the direction of the tool paths at a given location. A cut-off value of \(0.8\) mm was selected, as recommended by the ISO 4287:1997 standard. Measurements were performed three times on each surface, and each presented value is the average of these three measurements. The values of parameters \(\mathrm{R_{a}}\) (arithmetical mean roughness), \(\mathrm{R_{z}}\) (mean roughness depth), \(\mathrm{R_{t}}\) (maximum height of the profile), and \(\mathrm{R_{q}}\) (root mean square of the surface roughness) were recorded. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Value**} & \multicolumn{3}{c}{**3-Axis Milling**} & \multicolumn{3}{c}{**5-Axis Milling**} \\ \cline{2-7}  & **Linear** & **Offset** & **Spiral** & **Linear** & **Offset** & **Spiral** \\ \hline Average & \(0.002\) & \(0.000\) & \(-0.004\) & \(-0.001\) & \(-0.005\) & \(-0.003\) \\ Negative deviation & \(-0.040\) & \(-0.042\) & \(-0.041\) & \(-0.031\) & \(-0.049\) & \(-0.024\) \\ Positive deviation & \(0.034\) & \(0.028\) & \(0.031\) & \(0.023\) & \(0.037\) & \(0.031\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Deviation values [mm] for samples made by 3-axis and 5-axis milling. Figure 6: Graph of the average deviation, maximum negative and positive deviation for each sample. Table 5 shows a surface image of the samples made using 3-axis milling. At location 1, there are clear traces of a tool, where, owing to its position relative to this surface element, the cutting speed near the tool's tip is equal to zero. The material was crushed or plowed in this location. In locations 2 and 3, the tool occupied a larger diameter of the hemispherical section, which is evidenced by the regularly arranged traces of the tool. Because of the larger foot radius at location 2, it can be concluded that in this area, the tool worked with a larger radius than that in location 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Strategy** & **Shooting Location No. 1** & **Shooting Location No. 2** & **Shooting Location No. 3** \\ \hline \hline \(\text{R}_{\text{a}}\) [\(\mu\)m] & 0.89 & 0.95 & 0.77 \\ \hline \(\text{R}_{\text{z}}\) [\(\mu\)m] & 4.76 & 3.93 & 3.56 \\ \hline \(\text{R}_{\text{t}}\) [\(\mu\)m] & 5.70 & 4.8 & 4.21 \\ \hline \(\text{R}_{\text{q}}\) [\(\mu\)m] & 1.06 & 1.16 & 0.92 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Surface texture and surface roughness in 3-axis milling. Figure 7: Sample with marked locations for microscopic scanning and surface roughness measurement. The table also lists the surface roughness values. The evaluation is presented in the following section. The surfaces of the samples made using 5-axis milling are shown in Table 6. A significant difference is observed in the planar parts of the samples. By tilting the tool, contact with the tool area with zero cutting speed was eliminated and traces of the tool were regular, similar to those of other sample areas.