## 2 Experimental Details  
A testing apparatus was developed to measure the force acting on a PDC cutter during the rock cutting process. The structure of the apparatus is represented in Figure 1. The rock sample was fixed at the bottom of the apparatus while the PDC cutter was fixed to a holder. A force sensor was placed inside the holder to record the force acting on the PDC cutter during the cutting experiment. The rock sample was pre-treated with a hole at the center. The cutter was set to cut the inner surface of the rock in the experiments. The spatial position of the holder was adjustable, as was the PDC cutter, which was driven to rotate by a motor. Feeding was achieved by means of a linear actuator. In this study, the feeding rate was maintained at 0.04 mm/s, while the spindle speed was a constant 35 rpm. The sharp PDC cutters with a diameter of 19 mm used in this study were commercial products purchased from a domestic market in China. Rock samples of Jining limestone were obtained from the field. The physical properties of limestone used in this study are listed in Table 1. The PDC cutter and rock samples used are shown in Figure 2. Different back rake angles and cutting depths were achieved by adjusting the position of the cutter to evaluate their impact on the force response. Five back rake angles, of between 45\({}^{\circ}\) to 65\({}^{\circ}\) with incremental differences of 5\({}^{\circ}\), and four cutting depths, from 0.5 mm to 2 mm in increments of 0.5 mm, were applied. In order to compare the force response in both dry and drilling fluid conditions, force measurement was also performed when the cutter was immersed in drilling fluid, the formula for which is listed in Table 1. Furthermore, three types of PPG, namely PPG 200, PPG 400, and PPG 600, were added into the water-based drilling fluid in concentrations of 1 wt%, 2 wt%, 5 wt%, and 10 wt%. The numbers in the names indicate average molecular weight of the PPG polymers. The effects of the PPG additive on cutting force were investigated by the testing apparatus. Each experiment was repeated three times. Figure 1: Rock cutting testing facility. 1–Base, 2–Motor, 3–Linear actuator, 4–Motor controller, 5–Actuator controller, 6–DAQ unit, 7–Power adaptor, 8–Cutter holder, 9–Polycrystalline diamond compact (PDC) cutter, 10–Rock sample, 11–Rock holder. Figure 2: (**a**) PDC cutter and (**b**) rock samples. The force sensor in the apparatus was able to measure force normal to the cutter face. According to the force diagram, presented in Figure 3a, which is adjusted from [PERSON]'s model [7], the force directly measured in this study is the normal contact force. Normal contact force and tangent contact force are the two components of resultant force with respect to the cutter's surface. In order to evaluate cutting force, it is necessary to know another important parameter, namely friction angle \(\beta\), which is dependent on the back rake angle [7; 15]. A commercial tribometer, being able to measure normal force and cutting force, was used to evaluate the friction angle at different back rake angles. A schematic expression of the experiments conducted by the tribometer is shown in Figure 3c and compared with the schematic testing apparatus in Figure 3b. In the experiments to determine \(F_{n}\)/\(F_{c}\) using the tribometer, spindle speed and normal force were set at constants of 40 rpm and 20 N, for the test's duration of 30 min. The experiments were performed at -22 \({}^{\circ}\)C with relative humidity of 45-55%. The friction angle was subsequently calculated using the following formula:  
\[\beta=\text{arc}\ \tan(F_{n}/F_{c})\ -\ \alpha \tag{1}\]  
where, \(F_{n}\) and \(F_{c}\) stands for normal force and cutting force respectively, and \(\alpha\) is the back rake angle. Given the friction angle, back rake angle, and normal contact force, the cutting force in experiments conducted by the testing apparatus can be calculated as follows:  
\[\frac{F_  
30 N was applied and the speed was maintained at 40 rpm.