## 4 Results and Discussions
### The Chip-Evacuation Torque  
The continuous increasing trend of the chip-evacuation torque were taken out by applying a 8-point baseline technique, implemented in OriginLab(r) 2017 software (OriginLab Corporation, Northampton, Massachusetts, USA). The baseline data were then used to carry out the coefficient \(A\) of the model in Equation (6). Figure 4 depicts an example of the results.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **Value** & **Standard Error** & **Statistics Reduced Chi-Sqr** & **Statistics Adj. R-Square** \\ \hline C\_CD & 0.15475 & 0.00199 & 0.000027262 & 0.99869 \\ \hline C\_UAD & 0.12156 & 0.0012 & 1.48786 \(\times\) 10\({}^{-5}\) & 0.99863 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Calibrated results of the coefficient \(C\) in Equation (5).  
At first, the baseline of the real measured torque was made, as shown by the red line-diamond in Figure 4a. A regression process was then applied using the model in Equation (6) to calibrate the value of the coefficient \(A\). Figure 4b shows a result of the processes. Details of the calibration data are listed in Table 4.  
The coefficient \(A\) of the chip-evacuation torque model for each hole machined in CD and UAD will be compared in-pair; i.e., in the same cutting parameters. The paired \(t\)-test is useful for analyzing the same set of data that were obtained under two different conditions, differences between two treatments given to the same subject. In this study, the paired \(t\)-test was implemented by mean of Minitab(r) to check the hypothesis declared that the cutting torque in CD is higher than that in UAD. Using the paired \(t\)-test, from a limited number of experimental samples, we can predict the difference for the whole population of data. The results of the statistical test are shown in Table 5.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\#} & **Speed,** & **Feed,\(f\)** & **Coef. \(A\)** & **Coef. \(A\)** & **Coef. \(A\)** & **Ln(\(n\))** & **Ln(\(f\))** & **Ln(\(A_{CD}\))** & **Ln(\(A_{UAD}\))** \\  & \(n\) **(rpm)** & **(mm/rev)** & **(mm/rev)** & **(in CDs)** & **(in U  
At can be seen from Table 5, with a confident level is of 95% and the \(p\)-value less than 0.05, the coefficient \(A\) in the UAD population data is statistically confirmed to be smaller than that in CDs, at least 0.0952. For the exponential function with only one coefficient (see Equation (6)), the lower the exponential coefficient, the smaller the rate of the function increasing. Hence, at the same cutting conditions and depth \(z\), the chip evacuation torque in UAD is smaller than that in CD.  
In order to apply the prediction of the chip-evacuation torque at different cutting parameters, the \(A\) was expressed as a function of the spindle speed and the feed rate using the power law [8; 38], as shown in Equations (7) and (8). The results are depicted in Table 6.  
The model of the chip-evacuation torque, thus can be summarized as:  
\[T_{2}=A\left(e^{(A\cdot z)}-1\right) \tag{9}\] \[\text{forCDs}:\ln(A_{CD})=-13.7214+1.8805\ln(n)-4.9359\ln(f)+0.69 79\ln(n)\ln(f)\] \[\text{forUADs}:\ln(A_{UAD})=15.3907-2.2047\ln(n)+6.0016\ln(f)-0.8 265\ln(n)\ln(f)\]  
Using the approach to develop the model described, one can easily predict the chip evacuation torque for any deep drilling process and thus can determine the ability of the process and the tool to be used.