## 3 Results and Discussion
### Cutting Force and Specific Energy  
Normal contact force was directly measured by the testing apparatus in this study. Measured normal contact force at a steady phase was used to calculate the cutting force using Equation (2). The impact of cutting depth on cutting force at a constant back rake angle of 65\({}^{\circ}\) is reported in Figure 7, in which the cutting force clearly increases with cutting depth. It is evident, therefore, that the contact area between cutter surface and rock increases at a greater cutting depth. This means that more rock materials need to be removed during the cutting process. As a consequence, a greater cutting force is required from an energetic point of view. However, a simple linear fitting for the measured results reveals that the cutting force is not zero at zero cutting depth, which may be attributed to the friction force between cutter and rock [8].  
Figure 5: Variation of friction angle with back rake angle in dry condition and drilling fluid environment.  
Figure 6: Rock flow ahead of cutter at different back rake angle.  
In addition to cutting depth, the back rake angle is another significant parameter affecting cutting force. The changes of cutting force with a back rake angle at a constant cutting depth of 1 mm were evaluated and the results are presented in Figure 8. In both dry conditions and drilling fluid immersion, the cutting force was found to increase quickly, in line with the back rake angle. At the same back rake angle, a greater cutting force is required to cut the rock under the dry condition. 'Specific energy', the ratio of cutting force to the active cutting area of the cutter, describes the energy required to remove a unit volume of rock under a specific condition, and it is, therefore, a commonly investigated factor in evaluating a cutter's performance. Here, the active cutting areas of a PDC cutter at various back rake angles were determined, based on a simple geometrical calculation. The relationship between the resulting specific energy and the back rake angle is also shown in Figure 8, with hollow symbols as indicators. According to these results, specific energy is positively related to back rake angle in general. Similar to the results obtained for cutting force, specific energy is higher in dry conditions than in drilling fluid. A lower cutting force and specific energy are preferred when the cutting depth is the same, because less energy is then required to cut the same volume of rock. A higher cutting force and specific energy may, therefore, be possible reasons for the higher energy consumption observed in air drilling.  
Figure 8: Variation of cutting force and specific energy with back rake angle at a constant cutting depth of 1 mm. Solid symbols are cutting force results and hollow symbols stand for results of specific energy.  
Figure 7: Change of cutting force with cutting depth.  
Additives are commonly used to improve drilling performance [22] and glycol is a widely used additive for water-based fluids [23]. In this study, three types of PPG were added into the water-based drilling fluid and their impacts on the cutting force is presented in Figure 9. Neither PPG 200 nor PPG 400 showed any statistical influence on the cutting force. Measured cutting forces were noted to fluctuate significantly along the reference line, with 1 wt% to 10 wt% concentration. However, PPG 600 slightly reduced the cutting force by approximately 5% with additive concentrations of between 2 wt% and 10 wt%.