## 3 Results
### Application to Thin-Wall Components
In this way the output of the method is the \"desired\" machining allowance to be left on the workpiece stock to obtain an airfoil which respects the commanded tolerance in each portion. In the mentioned work, radial depth of cut was optimized to achieve a commanded tolerance (\(\pm\)0.02 mm) leading to a variable depth of cut. Indeed, since the blade presents significant differences in terms of local stiffness, in the thicker zones of the profile a higher depth of cut can be achieved, while in the critical points (e.g., trailing edge) a more conservative depth should be used. The resulting radial depth of cut is presented in Figure 7. As expected, the figure shows the minimum radial depth of cut (i.e., offset of the contour) at the trailing edge, the most flexible portion of the blade. The starting point was set on the stiffest portion and discontinuity on this point is found between the beginning and the end of the cycle. This result is caused by the fact that during the operation, the thickness of the blade changes, affecting the stiffness and hence the allowable radial depth of cut. Please refer to [12] for additional details on radial depth of cut computation. Figure 6: Blade 2D profile. To achieve the desired radial depth of cut during the finishing operation, the semi-finished stock should be computed based on the initial contour adding the defined radial depth of cut as a machining allowance. This procedure was carried out using the proposed algorithm, and results are shown in Figure 8. Results show that the proposed algorithm is able to perform the non-uniform offset of the blade contour, dealing with the discontinuity and returning the desired semi-finished profile. Since the blade application was dedicated to an external offset, generally easier to manage, an application to an internal offset in pocket 2.5 milling operations is also provided. The case study is a Pylon Bracket for aerospace application, such components often entail thin-wall structures and pocket milling. In our case, the pocket analyzed is the one in the middle, as highlighted in the 2D representation of Figure 9. The 2.5 milling of the investigated pocket is not affected by the flexibility of the workpiece (thin-wall structure) for most of the operation, except for one of the sides that is characterized by a very thin wall (3 mm). Therefore, in this portion a variable radial depth of cut could be profitable: constant and standard radial depth of cut should be used in the thick portions, while drastically reduced radial depth of cut must be adopted in the thin-wall portion. An example of such possible depth of cut variation is provided in Figure 10.  
Figure 8: Blade results: (**a**) Initial contour and proposed algorithm results (**b**) polygons of the proposed approach. Figure 7: Desired radial depth of cut for the blade, i.e., offset values to be applied. The desired radial depth of cut is applied through the developed offset algorithm to the initial contour to obtain the semi-finished pocket and results are shown in Figure 11. The algorithm produces what is required: a constant offset in the thick portions and a reduced offset in the critical one. Milling the resulting offset contour to obtain the initial contour will entail a high radial depth of cut in all the regions, except for the thin zone where such depth of cut will be more conservative, as desired. As already mentioned, it is worth pointing out that since the offset polyline should be obtained by a milling operation, sharp edges cannot be achieved, and the real machining allowance will depend on the tool geometry (i.e., diameter) used for the roughing operation. This consideration is valid in general, the offset algorithm could result in sharp edge contours if such a contour represents the semi-finished component. As in the applications provided in this section, the diameter of the tool will affect the actual machined contour. Figure 10: Desired radial depth of cut for the pocket, i.e., offset values to be applied.