## 3 Results
### Application to Thin-Wall Components  
In addition to the previous examples, which represent more theoretical applications rather than real case scenarios, more practical case studies are proposed. Indeed, the proposed algorithm is dedicated to contouring operations in 2.5 axis milling considering a flat endmill as the cutter. In this context, the proposed algorithm starting from the polyline, which represents the finished part of the contour, produces the shape of the machining allowance to be left on the part based on the offset values assigned to each point of the starting polyline (i.e., semi-finished contour). These offset values identify the amount of allowance to be left on each point of the finished contour. Then, the actual toolpath could be obtained by applying an offset algorithm to the semi-finished contour previously obtained using the same offset value (i.e., endmill radius) for each point. Therefore, in 2.5 axis milling contouring operations, the proposed algorithm creates a toolpath able to achieve a variable radial depth of cut along the part contour. These conditions are particularly interesting in contouring operations in which both the tool and the workpiece are characterized by low stiffness. This type of operation is referred to as thin-wall milling, and it is a challenging topic in the manufacturing field. In detail, thin-wall components are increasingly adopted in modern industries for their favorable stiffness to weight ratio, but precision milling on these components is still a complicated task because unstable vibrations and large surface errors are inevitable during the process, limiting productivity. To ensure the required surface quality without compromising productivity, it is important to identify the potential of each portion of the thin-wall component in terms of stiffness so that the most profitable cutting parameters, which each portion can handle, are selected. In this regard, two applications for the definition of the semi-finished part in 2.5 milling are provided. It must be noted that, in the context of milling operations, the proposed method does not create the actual toolpath, but the desired semi-finished contour, which must be offset uniformly by the tool radius to obtain the effective toolpath. As already mentioned above as well as in the introduction, one potential application of the proposed algorithm is the definition of a variable machining allowance on the finished thin wall part to achieve a variable radial depth of cut during the finishing operation. Indeed, the possibility to adopt a different radial depth of cut during the finishing cycle allows for removal of more material on the stiffer zones, reducing the actual material removal only in the critical portions of the part. As shown in [11], this allows an increase in productivity in comparison to the traditional constant engagement approach, in which the most conservative (i.e., minimum) radial depth of cut during the entire machining cycle must be used. Firstly, the proposed algorithm was applied to the case study proposed in [12]: 2.5 milling of a NACA 0005 airfoil profile 60 mm long and 20 mm high (Figure 6). In the cited work, the authors aimed at identifying, from a static point of view, the highest value of the radial depth of cut in each portion of the airfoil so that the form error caused by the static deflection of the tool-workpiece couple does not fail the commanded tolerance. Workpiece deflection is predicted, including the effect of the material removal through finite elements methods. In detail, the method proposed by the authors starts by finding the stiffest portion of the airfoil. It evaluates the highest radial depth of cut possible within the imposed constraints, it updates accordingly the airfoil stiffness in the analyzed portion, and, following this practice, it continues analyzing the rest of the airfoil profile in reverse order with respect to the classic milling cycle.