## 3 Results and Discussion
### Response Surface Methodology
#### 3.2.2 Drilling Torque  
The relation between the analyzed factors, drill bit angle (\(X_{1}\)), tooth bite (\(X_{2}\)) and drill type (\(X_{3}\)), and drilling torque (\(Y_{2}\)) is described by a quadratic regression equation, which was also revealed by the Design Expert software. The coded form of the suggested mathematical model, which is significant at 1% (Table 7), is presented in Equation (15). This regression equation (in coded form) tells us that the most significant factor (from the analyzed ones) that affects the drilling torque during the drilling of plywood is the tooth bite (\(X_{2}\)). The next ones are the drill tip angle (\(X_{1}\)) and drill type (\(X_{3}\)) with almost the same influence (since both factors have a coefficient close to 0.30). The obtained results are almost identical with those obtained in the case of drilling prelaminated wood particleboard panels [16]. There is a significant interaction between the analyzed factors (\(X_{1}X_{2}\), \(X_{1}X_{3}\), \(X_{2}X_{3}\), \(X_{1}X_{2}X_{3}\)) on the drilling torque (\(Y_{2}\)). The most important interaction is between tooth bite (\(X_{2}\)) and drill type (\(X_{3}\)). The influence of drill tip angle (\(X_{1}\)) and tooth bite (\(X_{2}\)) on the drilling torque (\(Y_{2}\)) is presented in Figure 9. Equations (16) (in the case of a flat drill) and 17 (in case of a helical drill) could be used to predict the drilling torque during the drilling of plywood (\(Y_{2}\)) based on the drill tip angle (\(X_{1}\)) and tooth bite (\(X_{2}\)). The ANOVA results at 5% significance level are presented in Table 7.  
\[\hat{Y}_{2 coded}=1.26-0.31X_{1}+0.62X_{2}-0.30X_{3}-0.092X_{1}X_{2}+0.067X_{1}X _{3}-0.094X_{2}X_{3}+0.020X_{1}^{2}-0.032X_{2}^{2} \tag{15}\]  
\[-0.062X_{1}X_{2}X_{3}+0.0077X_{1}^{2}X_{3}+0.017X_{2}^{2}X_{3} \tag{16}\]  
\[\hat{Y}_{2 flat}=1.11-0.008X_{1}+2.97X_{2}-0.022X_{1}X_{2}+6.058e-006X_{1}^{2} -0.54X_{2}^{2} \tag{17}\]  
\[\hat{Y}_{2 helix}=0.37-0.0028X_{1}+2.73X_{2}-0.0113X_{1}X_{2}+1.373e-005X_{1}^{ 2}-0.164X_{2}^{2} \tag{18}\] \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Source** & **Sum of Squares** & **df** & **Mean Square** & **F-Value** & **\(p\)-Value** & **Observation** \\  & & & & & **Prob \textgreater{} F** & \\ \hline Model & 8.15 & 11 & 0.74 & 613.64 & \textless{}0.0001 & Significant \\ Drill tip angle (\(X_{1}\)) & 1.13 & 1 & 1.13 & 935.99 & \textless{}0.0001 & Significant \\ Tooth bite (\(X_{2}\)) & 4.59 & 1 & 4.59 & 3803.62 & \textless{}0.0001 & Significant \\ Drill type (\(X_{3}\)) & 1.04 & 1 & 1.04 & 862.460 & \textless{}0.0001 & Significant \\ \(X_{1}X_{2}\) & 0.067 & 1 & 0.067 & 55.79 & \textless{}0.0001 & Significant \\ \(X_{1}X_{3}\) & 0.054 & 1 & 0.054 & 44.52 & \textless{}0.0001 & Significant \\ \(X_{2}X_{3}\) & 0.11 & 1 & 0.11 & 88.57 & \textless{}0.0001 & Significant \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Results obtained during ANOVA analysis of the model selected to predict the drilling torque. Figure 8: The influence of the drill tip angle and tooth bite on the thrust force: flat drill (**a**) and helical drill (**b**). The optimum combinations of independent variables during the drilling of plywood in order to achieve both a lower thrust force and a lower drilling torque are presented in Table 8. In the case of the helical tool, the drill tip angle (\(X_{1}\)) should be equal to 30\({}^{\circ}\) and the tooth bite (\(X_{2}\)) equal to 0.1. The relative error, which was calculated using Equation (18), between predicted and experimental values is around 25% in the case of thrust force (\(Y_{1}\)) and around 5% in the case of drilling torque (\(Y_{2}\)). Regarding the flat tool, the minimum thrust force (\(Y_{1}\)) and drilling torque (\(Y_{2}\)) is obtained when the drill tip angle (\(X_{1}\)) is equal to 118\({}^{\circ}\) and the tooth bite (\(X_{2}\)) is adjusted at the minimum analyzed level (0.1 mm).