## 3 Case Study
### Determination of the Radius of Curvature  
Once the optimum land width and rake angle are selected, the next step is to determine a proper curvature that enables curling the chips without getting clogged. From the previous simulation in which no chip breaker was considered, with \(\alpha\) = 20\({}^{\circ}\) and a = 0.05 mm, the natural radius of curvature (R) obtained was 1.45 mm and the tool-chip contact length (L) was zero, measured from the land width (i.e., L = 0, see Figure 5). These two parameters are interrelated and, when adding the chip breaker, they will determine the tool-chip contact area. Regarding L, generally, the value of this parameter in the chip breaker design should be the same or lower than the natural tool-chip contact length, in order to increase chip curling. However, due to manufacturing issues, a minimum value of L should be stablished. Thus, although from simulation it was obtained that L = 0, on this stage of the chip breaker design, L was given a non-zero value, namely 0.05 mm, to ease manufacturing task. The radius (R) of the chip breaker must be selected bearing in mind the chip's natural shape in order to increase chip curling, for the chips breaking more readily. As the natural radius of curvature without chip breaker was 1.45 mm, R of the chip breaker must be lower. There is a threshold for R that is determined as, under this value, the chips are prone to get clogged and turning efforts are triggered. Figure 6 reveals how the chip curled for two different values of R, both of them lower than the natural curvature: 1.0 and 1.4 mm. Results show that the lowest one, that is R = 1 mm, was below the threshold value, as seen in Figure 6a. As the shearing angle was reduced, the chip thickness increased, and the chip tended to be relatively straight. Therefore, this is not an admissible solution. For R = 1.4 mm, the chip curled without clogging, this being a suitable solution. Thus, to machine the material considering the cutting parameters in Table 1, a radius greater than 1.0 and equal or lower than 1.4 mm is needed. Figure 5: Detail of the area close to the cutting edge for the selected design: \(\alpha\) = 20\({}^{\circ}\), a = 0.05 mm. Figure 6: Bending of the chip as a result of the radius of curvature with (**a**) R = 1 mm; (**b**) R = 1.4 mm. FEM simulation is a very powerful, reliable and cheap way of evaluating the cutting geometries. However, as modelling is a simplification of the reality, it is recommended that selected values for critical parameters of the design consider a security margin. Thus, as the gap between R being 1.0 mm or 1.4 mm is very small, instead of searching for an exact intermediate threshold value, the most conservative option was selected: R = 1.4 mm. Considering the dimensions of the diamond tip, geometrical constraints of the top surface of the original PCD insert have to be taken into consideration during the design phase. In fact, a limited groove width of 1 mm (see Figure 2) can be fabricated. Besides this, and due to limitation of laser manufacturing process, the depth of the groove should not be larger than 100 \(\upmu\)m. With \(\alpha\) = 20\({}^{\circ}\), a = 0.05 mm, L = 0.05 mm and R = 1.4 mm, these limits are slightly exceeded, so the design must be marginally modified to meet the requirements. From the FE simulation study in the first stage, it was concluded that minor modifications on the land width could drastically change the curling effect of the chip. Therefore, the land width (a) should not be modified. In the same way, regarding R, there was a small gap between the selected and the threshold value, so R will be maintained to avoid clogging. As for L, a minimum value of 0.05 mm was selected for manufacturing reasons, so it cannot be reduced. Thus, the only parameter suitable to be slightly modified is the rake angle. The new rake angle (which should be as similar as possible to 20\({}^{\circ}\)) which meets the requirements is \(\alpha\) = 17\({}^{\circ}\).