# Cutting Force When Machining Hardened Steel and the Surface Roughness Achieved
## 3 Results
### Evaluation of Cutting Force Measurements with the Kistler Dynamometer  
The measurement data were converted to a.txt file and then graphical dependencies of the time course on the force load were created in Microsoft Excel. Due to the very small scatter of individual force values in virtually all graphs, these are sufficient as input data for the structural equation. The average values of the individual cutting forces at the specified cutting conditions are in Table 4.  
Figures 5-8 show the force load time histories for the selected samples, including the calculated total cutting force \(F\). For all machined samples, one pass and one measurement was performed on each sample. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Sample No.**} & \multirow{2}{*}{\begin{tabular}{c} \(v_{c}\) \\ (m\(\cdot\)min\({}^{-1}\)) \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} \(f\) \\ (mm\(\cdot\)rev\({}^{-1}\)) \\ \end{tabular} } & \multirow{2}{*}{\begin{tabular}{c} \(a_{p}\) \\ (mm) \\ \end{tabular} } & \multirow{2}{*}{**Force \(F_{c}\) (N)**} & \multirow{2}{*}{**Force \(F_{f}\) (N)**} & \multirow{2}{*}{\
\begin{tabular}{c} **Force \(F_{p}\)** \\ **(N)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Resulting** \\ **Force \(F\)** \\ **(N)** \\ \end{tabular} } \\ \hline
1 & & 0.05 & 0.2 & 121.4 & 49.0 & 71.0 & 148.9 \\
2 & & 0.05 & 0.35 & 165.6 & 99.7 & 114.1 & 224.5 \\
3 & & 0.1 & 0.2 & 167.9 & 64.8 & 112.8 & 212.4 \\
4 & & 0.1 & 0.35 & 224.9 & 117.4 & 175.5 & 308.5 \\ \hline
5 & & 0.05 & 0.2 & 133.6 & 54.8 & 72.3 & 161.5 \\
6 & & 0.05 & 0.35 & 153.9 & 106.6 & 115.3 & 219.9 \\
7 & & 0.1 & 0.2 & 171.7 & 59.5 & 97.3 & 206.2 \\
8 & & 0.1 & 0.35 & 206.1 & 128.3 & 175.5 & 299.6 \\ \hline
9 & & 0.05 & 0.2 & 119.0 & 47.1 & 68.7 & 145.3 \\
10 & & 0.05 & 0.35 & 147.5 & 87.7 & 103.3 & 199.0 \\
11 & & 0.1 & 0.2 & 152.1 & 62.2 & 123.2 & 205.5 \\
12 & & 0.1 & 0.35 & 199.1 & 118.6 & 197.4 & 304.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Average values of individual cutting forces. In order to determine the effect of the cutting parameters, the data obtained from the experimental measurements were analyzed by General Factorial Regression analysis using the DOE plan and Minitab software. Figure 8: Force load history of sample 12 (\(v_{c}\) = 180 m\(\cdot\)min\({}^{-1}\), \(f\) = 0.1 mm\(\cdot\)rev\({}^{-1}\), \(a_{p}\) = 0.35 mm). A basic analysis provided information on the combinations of factors and their effects and interactions. The results in Table 5 show that due to the low \(p\) value of 0.003, \(a_{p}\) and \(f\) are the main factors. Considering that the \(p\)-Value = 0.003, it can be concluded that these factors are significant with a reliability of 99.7%. Cutting speed, \(v_{c}\), is almost negligible in terms of the effect of the \(F_{c}\) and their interactions with \(a_{p}\). The interaction with \(f\) is moderate in terms of the significance level. The methodology for determining the specific form of the structural equation requires the following simplification. As shown in Table 5, the influence of the cutting speed is minimal, which implies the assumption of a very small value of the exponent \(z_{Fc}\) of about \(\pm\)0.05. Graphically, the interactions and dependencies are depicted in Figure 9. The low influence of \(v_{c}\) and the high influence of \(f\) and \(a_{p}\), due to the orthogonal distribution, are clearly visible. Figure 10 shows a contour plot of the effect of \(a_{p}\) and \(f\) on the cutting force \(F_{c}\). By referring to the contour representation, it is possible to observe the relationships and optimize the process, also the uniform distribution of the dependence for both \(f\) and \(a_{p}\) can be seen.