## 3 Results and Discussion
### Thrust Force and Optimization Process of Its Maximum Value  
Figure 4 illustrates the complete evolution of the thrust force during the drilling of a hole in a CFRP sample. The drilling process comprises three distinct stages, starting at point A and concluding at point D. At point A (first stage), the drill tip contacts the upper surface of the specimen, marking the beginning of the actual drilling operation. In this stage, the thrust force increases dramatically due to the tool's entry into the composite sample and the gradual increase in contact length between the composite laminate and the cutting edges of the tool. The duration of this stage is influenced by the drill tip geometry (\(h\) parameter) and the feed rate.  
At point B (second stage), drill tip thoroughly penetrates to a length of \(h\) corresponds to the height of the conical section of the tool. The maximum thrust force occurs at this stage, characterized by the full engagement of the drill chisel edge and cutting lips, oscillating around a constant mean. At point C (third stage), the drill tip contacts the bottom surface of the specimen and begins to exit. In this stage, the thrust force rapidly decreases as the drill chisel edge passes through the workpiece, reaching zero when the cutting lips cut through the last ply of the composite laminate's back (point D) [26]. Drilling parameters, the mechanical properties of the composite, and the drill geometry affect the drilling force. Minimizing the maximum thrust force is crucial to enhance drilling quality and reduce delamination in the drilling process [27].  
The ANOVA of the experimental data (Table 3) indicates that the quadratic model was significant, with a model \(Prob>F\) less than 0.05. Two main effects, the feed rate and rotational speed, along with their interaction effect on the maximum thrust force, were significant. The fitted equation in terms of actual factors for predicting the maximum thrust force was obtained as Equation (4) for each angle of layer types.  
Considering the significance of the interaction effect between the feed rate and rotational speed, the interaction, surface, and contour plots between these parameters were  
Figure 4: (**a**) Thrust force distribution for a complete drilling cycle, obtained using a rotational speed of 2400 mm/min, feed rate of 6000 rev/min, and angle of layers \(\pm\)45. (**b**) Parameter h in tool geometry.  
depicted to investigate the impact of independent variables on the response. As shown in Figure 5a-c, the minimum \(F_{max}\) value was obtained at lower and faster values of feed rate and rotational speed, respectively. By increasing the feed rate value, the chip cross-sectional area will be more significant, and consequently, the cutting resistance increases. This phenomenon results in an increasing thrust force value. In contrast, increasing the rotational speed increases the friction between the drill and the composite during the drilling process; consequently, softening of the composite will occur due to increasing the drilling temperature. As a result, the required cutting energy and its thrust force decreased. These results are in accordance with the literature [6; 16; 17; 18; 28; 29; 30]. According to Figure 5d, the angle of the layers did not affect the \(F_{max}\).  
\[F_{max}=\begin{cases}\text{{For }type 45}:&167.89+0.18(A)-0.03(B)-0.00001(A)(B)-4.19 \times 10^{-6}\big{(}A^{2}\big{)}+2\times 10^{-6}\big{(}B^{2}\big{)}\\ \text{{For }type 15}:&155.25+0.19(A)-0.03(B)-0.00001(A)(B)-4.19\times 10^{-6} \big{(}A^{2}\big{)}+2\times 10^{-6}\big{(}B^{2}\big{)}\end{cases} \tag{4}\]  
Figure 5: The effect of rotational speed and feed rate on the first response (\(F_{max}\)) (**a**) Contour plot. (**b**) 3D Surface plot. (**c**) Interaction plot, and (**d**) Main effect plot of the angle of layers.