# Influence of Coolant Properties and Chip Former Geometry on Tool Life in Deep Drilling
## 5 Statistical Evaluation of the Impact of the Cooling Agent Parameters on the Gun Drill Life  
Mathematical statistics deals with mass phenomena and serves the purpose of objectively predicting their behavior, where statistical prediction is based on knowledge of the laws governing mass phenomena. On the basis of the data known about the previous course of development of a particular system, this will allow us to predict its future development to some extent.  
The first statistical evaluation is that of monitoring the life of the gun drill at different concentrations of cooling emulsion, namely 6%, 9%, 12%, and 15%, respectively, at 35 bar pressure. A plotted comparison of the tool life in terms of the cooling emulsion concentration is shown in Figure 13.  
From the value of the achieved level of significance of the Kruskal-Wallis scatter analysis (\(p=0.3522\)), it can be concluded that there is no significant relationship between the concentration of the cooling emulsion and the tool life at the level of significance of 5%, as shown in Table 2.  
Figure 12: Plotted representation of the drill bit’s life when geometry of the dipformer has been changed.  
Figure 13: Plotted comparison of the tool life in terms of the cooling emulsion concentration.  
The second statistical evaluation is that of monitoring the gun drill life at different concentrations of cooling emulsion, namely 6%, 9%, 12%, and 15%, respectively, at 35 bar pressure. A plotted comparison of the tool lie under the changed pressure of the cooling emulsion is shown in Figure 14.  
From the value of the achieved level of significance of the Kruskal-Wallis scatter analysis (\(p\) = 0.0005), it can be concluded that there is no significant relationship between the concentration of the cooling emulsion and the tool life at the level of significance of 5%, as shown in Table 3.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Kruskal–Wallis ANOVA by Ranks; Drill Life (Analysis) Independent (Grouping) Variable:** \\  & **Emoulsions of Cooling Liquid [\%]** \\  & **Kruskal–Wallis Test: H (3, N = 24) = 3.267349, \(p\) = 0.3522** \\ \hline
**Code** & **Valid N** & **Sum of Ranks** & **Mean Rank** \\ \hline
6\% & 1 & 6 & 49.50000 & 8.25000 \\
9\% & 2 & 6 & 75.00000 & 12.50000 \\
12\% & 3 & 6 & 89.00000 & 14.83333 \\
15\% & 4 & 6 & 86.50000 & 14.41667 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The result of the comparison of the tool life under different cooling emulsion concentrations.  
Figure 14: Plotted comparison of the tool life under changing cooling emulsion pressures.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Kruskal–Wallis ANOVA by Ranks. Tool Life (Analysis). Independent (Grouping)** \\  & **Variable: Coolant Pressure.** \\  & **Kruskal–Wallis Test: H (5, N = 36) = 22.07260, \(p\) = 0.0005** \\ \hline
**Code** & **Valid N** & **Sum of Ranks** & **Mean Rank** \\ \hline
20 bar & 1 & 6 & 34.5000 & 5.75000 \\
25 bar & 2 & 6 & 50.5000 & 8.41667 \\
30 bar & 3 & 6 & 126.5000 & 21.08333 \\
35 bar & 4 & 6 & 154.0000 & 25.66667 \\
40 bar & 5 &  
The last statistical evaluation is aimed at comparing the life of the drill bit under a changed chipformer geometry, which is shown in Figure 16.  
Based on the significance level achieved in the nonparametric Mann-Whitney test (\(p\) = 0.000183), it can be concluded that there is a significant difference in tool life between the standard and the reduced tool at the significance level of 5%. The graph shown in Figure 16 makes it clear that the reduced tool has a shorter life than the standard tool. The overall result of the tool life comparison in terms of the chipformer geometry is presented in Table 6.