# A Study on the Effects of Hob Temperature on the Rock-Breaking Characteristics of Sandstone Strata
## 4 The Establishment and Analysis of the Rock Breaking Model of Hobbing  
The primary contact parameters of the PFC\({}^{\text{3D}}\) particles were obtained by calibrating the basic mechanical experiments obtained from the previous physical experiments, as well as by exploring the effects of heat on thermodynamic experiments. The numerical modeling of the hob was carried out to study the influence of heat on the rock-breaking characteristics during the rock-breaking process. A 17-inch Robbins hob was used for the hob, and the three-dimensional model of the hob is shown in Figure 11 below. The outer ring height of the hob was 432 mm. The hob tip thickness was 20 mm and the total width of the hob was 80 mm. The hob was generated using the wall command of PFC\({}^{\text{3D}}\) based on the geometry and was imported into the model. A rigid wall was used as the boundary and the rock enclosure pressure was added to the surrounding wall. The rock-breaking model had a radius of 1 m and a thickness of 0.5 m. The implementation steps of the rock-breaking model are as follows. (1) Sandstone rock samples are generated inside the wall, according to the porosity. (2) Then, a FISH statement is given to apply the surrounding pressure and to give the previously calibrated mechanical parameters. (3) The particles are given calibrated thermodynamic parameters and the hob tip temperatures are set to 25 \({}^{\circ}\)C, 300 \({}^{\circ}\)C, 600 \({}^{\circ}\)C, and 900 \({}^{\circ}\)C, respectively. When the particles are in contact with the hob, the temperature is transferred from the hob to the particles, and the combined effect of the hob tip force and temperature damages the particles. The hob arrangement is shown in Figure 12.  
Figure 11: Diagram of the 17-inch Robbins hobber. Figure 10: Distribution of contact force and number of contacts at different temperatures. (**a**) Number of contacts and contact forces at 25 \({}^{\circ}\)C. (**b**) Number of contacts and contact forces at 300 \({}^{\circ}\)C. (**c**) Number of contacts and contact forces at 600 \({}^{\circ}\)C. (**d**) Number of contacts and contact forces at 900 \({}^{\circ}\)C.  
Because there are too many variable factors to study the rock-breaking effect, the following orthogonal experiments were established using orthogonal experiments to study the effects of heat, penetration (\(P\)), spacing (\(S\)), and surrounding pressure on rock breaking via hobbing. The details are shown in Table 6. Rock-breaking efficiency is determined by specific energy (\(SE\)); the larger the SE of the broken knife to break the rock, the greater the energy required and the poorer the rock breaking efficiency. Specific energy is mainly determined based on mean normal force (\(MNF\)), mean torque (\(MT\)), the angle of roll \(\theta\), and the depth of penetration \(h\). For the whole cutter, SE [27] can be expressed, as shown in Equation (5). \[\text{SE}=\frac{\text{HFcos}(\frac{\phi}{2})\sum\limits_{i=1}^{n}S_{i}^{\frac{ 1}{2}}+2\pi\text{F}\sin(\frac{\phi}{2})\sum\limits_{i=1}^{n}S_{i}^{\frac{1}{2} }\sum\limits_{\frac{1}{3}}^{\text{k}}S_{i}}{\pi R_{t}^{2}h} \tag{5}\]  
Multi-factor regression statistics analyzed the results of the orthogonal experimental data, and the mean of the orthogonal experimental data was taken in Figure 13 below. It can be seen from the figure that under the combined effect of heat and confining pressure, specific energy (SE) requires the largest specific energy for rock breaking at 60 mm and the lowest breaking efficiency, as well as the smallest specific energy for rock breaking at 70 mm and the highest breaking efficiency.