## 3 Results and Discussion
### Cutting-Path Planning in Five-Axis CAM of Stents and Actual Stent Machining
#### 3.3.4 Arc Dimension Errors  
It was considered that the arc profile errors of the stent were inferred to be caused by PLA material rebound. PLA is a polymer material that exhibits elastic deformation under micromachining and may cause cutting errors [23; 24; 25]. Cutting at a microscopic scale further causes the rebound phenomenon of materials to manifest. Therefore, arc profile errors of the stent were inferred to be caused by PLA material rebound. To verify this inference, the Young's modulus \(E\) (2.8 GPa) and hardness \(H\) (0.2 GPa) of the PLA used in this study were substituted into the material rebound formula proposed by [PERSON] et al. [20], as depicted in (9) (where \(h\) is the theoretical depth of cut and \(h_{a}\) is the actual depth of cut) to calculate the rebound of PLA and compare the rationality of the arc shape:  
\[h_{a}/h=0.41498 logE/H-0.4224=0.41498 log2.8/0.2-0.4224=67\% \tag{9}\]  
The calculation results revealed that the actual to theoretical depth of cut ratio was 67%, implying a material rebound rate of 33%. However, because a ball end mill was used to cut the arc structure with 12 cuts, as shown in Figure 18a, the removed thickness values were inconsistent; thus, the thickest part was used for the rebound calculation. The rebound of the first cut was added to the second cut. For example, the removed thickness of the first cut was 6.64 \(\upmu\)m, which was multiplied by 33% and produced a rebound of 2.19 \(\upmu\)m; accordingly, the actual removed thickness was 4.45 \(\upmu\)m, and the profile of the first cut was moved horizontally 2.19 \(\upmu\)m (rebound) to the left. According to the first cut's rebound profile, the rebound profile of the second cut was calculated by multiplying its removed thickness of 10.28 \(\upmu\)m by 33% to produce a rebound of 3.39 \(\upmu\)m. Therefore, the removed thickness of each cutting must be summed to determine the ultimate arc shape with rebound considered. Table 3 presents the calculation results.  
Figure 18b presents an optical microscope (OM) image of the actual stent's cross-section after cutting. The dotted line represents the imagined profile without rebound and the solid line represents the imagined profile mapped according to the 33% rebound. The real stent arc profile after cutting was approximately close to the imagined profile with 33% rebound. This result confirmed that rebound occurred during cutting. The chain-dotted circle marked the thickest removed part during the cutting, where the greatest rebound and the deepest cutting depth occurred. However, the profile with 33% rebound considered was nearly identical to the actual arc profile of the stent. Figure 19 shows images of the completed stent product; the external diameter and tube wall thickness were 6 mm and 0.3 mm, respectively.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & **Theoretical Removed** & **Actual Removed** & **Removed Thickness with** \\
**of Cutting** & **Thickness** & **Thickness** & **Considering 33\% Rebound** \\ \hline
1 & 6.64 & 4.45 & 2.19 \\
2 & 10.28 & 6.88 & 3.40 \\
3 & 15.05 & 10.08 & 4.97 \\
4 & 15.45 & 10.35 & 5.10 \\
5 & 13.37 & 8.96 & 4.41 \\
6 & 11.33 & 7.59 & 3.74 \\
7 & 10.00 & 6.70 & 3.30 \\
8 & 7.63 & 5.11 & 2.52 \\
9 & 5.75 & 3.85 & 1.90 \\
10 & 4.08 & 2.73 & 1.35 \\
11 & 2.54 & 1.70 & 0.84 \\
12 & 0.83 & 0.56 & 0.27 \\ \hline \hline \end{tabular}  
Unit: \(\upmu\)m.  
\end{table}
Table 3: Removed thickness on the stent arc structure (12 cuts).