## 3 Results and Discussion
### Cutter Force  
The aim of this study was to compare the results of numerical simulations with the LCM test results obtained in a previous study [8]. Figure 15 shows the representative cutter forces obtained from the numerical simulation. The results show that the cutter forces obtained from the first cut were remarkably larger than those from the second cut. The first cut was made under a perfectly constrained condition, which is referred to as the unrelieved cutting mode, but the second cut was done under the relieved cutting mode. The results of cutter forces in numerical simulations were consistent with those from the previous studies [3; 26; 27; 28]; the cutting forces for the unrelieved cutting mode had higher values than those of the relieved cutting mode. Thus, the results indicated that the interaction between the adjacent cutters was well simulated by the numerical simulation. Therefore, in this study, the cutter forces obtained from the second cutting line were used for the analysis. This approach was also used in the experimental cutting tests. In the LCM test, the first cutting line represents the unrelieved cutting mode without any interaction between the adjacent cutting lines [28]. Thus, it is reasonable to exclude the cutter forces obtained from the first cutting line from further analysis. Table 4 summarizes the cutter forces determined by the numerical simulations of different penetration depths and cut spacings. The forces obtained during the cutting tests were averaged to give the mean cutter forces (\(F_{c\_mean}\), \(F_{n\_mean}\), and \(F_{s\_mean}\)). Among the three orthogonal force components, the side force acts in a direction orthogonal to the cutting force on the same plane, and it affected the balancing of the pick. In contrast to the normal and cutting force components, the magnitude of side force did not differ significantly for the unrelieved and the relieved cutting modes. Because the effect of the side force on the cutting performance of the pick was not significant when the skew angle was set to \(0^{\circ}\), the side force was not analyzed in the later part. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Penetration Depth, \(p\) (mm)**} & \multirow{2}{*}{**Cut Spacing, \(s\) (mm)**} & \multicolumn{3}{c}{**Mean Cutting Force**} & \multicolumn{3}{c}{**Mean Normal Force**} \\ \cline{3-8}  & & & **LCM * (kN)** & **Numerical** & **Relative** & **LCM * (kN)** & **Numerical** & **Relative** \\  & & & **(kN)** & **Error (\%)** & **(kN)** & **(kN)** & **Error (\%)** \\ \hline \multirow{4}{*}{\(5\)} & 5 & 3.23 & 2.84 & 12.1 & 3.63 & 2.94 & 19.0 \\  & 10 & 4.21 & 4.61 & 9.5 & 4.41 & 3.04 & 31.1 \\  & 15 & 5.19 & 4.80 & 7.5 & 5.29 & 4.31 & 18.5 \\  & 20 & 5.78 & 4.80 & 17.0 & 5.88 & 4.90 & 16.7 \\  & 25 & 6.37 & 5.00 & 21.5 & 6.47 & 5.10 & 21.2 \\ \hline \multirow{4}{*}{\(7\)} & 7 & 3.53 & 4.80 & 36.0 & 3.53 & 3.33 & 5.7 \\  & 14 & 5.10 & 5.78 & 13.3 & 5.10 & 4.41 & 13.5 \\ \cline{1-1}  & 21 & 6.17 & 6.66 & 7.9 & 6.86 & 5.00 & 27.1 \\ \cline{1-1}  & 28 & 6.96 & 6.57 & 5.6 & 7.25 & 4.80 & 33.8 \\ \cline{1-1}  & 35 & - & 7.06 & - & - & 5.39 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The results of cutter forces in the linear cutting machine (LCM) tests and numerical simulations. Figure 15: The representative cutter forces obtained from the numerical simulation. [PERSON] et al. [11] noted that the numerical forces are usually much lower than those of the experimental forces. They stated that this may be because that the crushing and grinding process between the cutter tip and rock is usually ignored in traditional FEM simulations. After the rock elements beneath the cutter tip are eliminated by the erosion, there are no contacts between the cutter tip and rock, which will result in zero values of the cutter forces [9; 11]. However, the crushed zone beneath the cutter tip plays an important role in transforming cutter forces to the side directions for chipping in real conditions.