## 4 Analysis of Calculation Results
### Crushing Efficiency of Arcing-Blade Cutters  
The specific energy (\(SE\)) refers to the energy required by the cutter to cut a unit volume of rock. A lower specific energy indicates a higher crushing efficiency of the cutter [25; 26; 27]. The calculation formula is as follows:  
\[SE=\frac{F_{\mathrm{R}}\cdot L}{V} \tag{1}\]  
where \(SE\) is the specific energy; \(F_{\mathrm{R}}\) is the rolling force; and \(V\) is the volume of the crushed rock.  
The variation in the specific energy with different cutting parameters when cutting the red sandstone is illustrated in Figure 15. Regardless of the type of penetration, the specific energy exhibited a decreasing trend followed by an increasing trend with an increase in the cutter spacing, and eventually stabilized. Notably, for the 4 mm and 6 mm penetrations, there was an optimal cutter spacing that yielded the lowest specific energy, referred to as the optimal cutter spacing, which corresponds to the highest crushing efficiency. For instance, with a 4 mm penetration, the specific energy decreased from 36.5 MJ/m\({}^{3}\) to 28.7 MJ/m\({}^{3}\) as the cutter spacing increased from 40 mm to 50 mm, reaching its minimum at a cutter spacing of 50 mm. Subsequently, the specific energy began to rise with further increases in the cutter spacing, stabilizing at the cutter spacing of 60 mm. Similarly, for a 6 mm penetration, the specific energy decreased from 32.1 MJ/m\({}^{3}\) to 20.5 MJ/m\({}^{3}\) as the cutter spacing increased from 40 mm to 60 mm, then increased to 93.1 MJ/m\({}^{3}\) at 70 mm, after which, it stabilized. In contrast, for a penetration of 2 mm, the specific energy remained stable at approximately 86 MJ/m\({}^{3}\) across various cutter spacings, without displaying the aforementioned trend.  
Figure 14: Statistics on crushed areas.  
Figure 15: Specific energy of rock crushing by arcing-blade cutter.  
This change trend can be explained by the crushing states under different cutting conditions. When the penetration was small, such as 2 mm, each arcing-blade cutter operated independently of the other, leading to a limited crushed area in the middle of the rock cross-section (Figure 14). Consequently, there was minimal change in the specific energy under different cutter spacings, resulting in a low rock-crushing efficiency. As the penetration increased to 4 mm, a synergy effect between the cutters was observed at cutter spacings of 40 mm and 50 mm (Figure 10a,b), with the synergy effect being stronger at 40 mm than at 50 mm. This resulted in excessive crushing of the rock ridges, subsequently leading to higher specific energy values at a 40 mm cutter spacing than those at a 50 mm cutter spacing. However, as the cutter spacing further increased, the synergy effect diminished and the rock ridges remained uncrushed (Figure 10c-e). This caused the specific energy to quickly reach a stable value, making the sequential cutting similar to a single cutting operation. Subsequently, with a further increase in penetration to 6 mm, a similar trend in specific energy as that with 4 mm penetration was observed. Notably, the specific energy reached its minimum value when the cutter spacing was 60 mm, signifying the highest crushing efficiency. This also indicates that, at cutter spacings 40 mm and 50 mm, the specific energy for 6 mm penetration was marginally higher than that for 4 mm penetration, owing to the excessive crushing of the rock ridges at these spacings. In summary, the most optimal cutter spacings under the conditions of 4 mm and 6 mm penetration were 50 mm and 60 mm, respectively. At these cutter spacings, the specific energy was the lowest, corresponding to the highest crushing efficiency.