## 3 Results and Discussion
### Relationship between Resistance Torque and Roughness Height  
The roughness heights of the sidewalls, top and bottom walls, and armature also affect the torque resistance of the armature. To investigate the influence of the roughness height on the torque resistance, we simulated the torque resistance when the roughness heights of the sidewalls, top and bottom walls, and the armature varied at levels of 1 \(\times\) 10\({}^{-6}\), 1 \(\times\) 10\({}^{-5}\), 2.5 \(\times\) 10\({}^{-5}\), 5 \(\times\) 10\({}^{-5}\), and 1 \(\times\) 10\({}^{-4}\) m, as shown in Figure 12. The \"Sidewall\" subplot in Figure 12 depicts the changes in the torque resistance under different roughness heights of the sidewall when the roughness heights of the top and bottom walls and the armature are fixed at 1 \(\times\) 10\({}^{-5}\) m. The purple dots and yellow circles represent the torque resistance at an angular velocity of 57 and 40 \(\mathrm{rads/s}\), respectively. The graph shows that as the roughness height decreases, the torque resistance initially decreases and then stabilizes. At 57 \(\mathrm{rads/s}\), the torque resistance decreases by approximately 10.5%, whereas at 40 \(\mathrm{rads/s}\), it decreases by approximately 8%. Notably, the torque resistance does not necessarily decrease at lower roughness heights; instead, a critical roughness height exists. Below this threshold, the sidewall surface is effectively considered smooth, and torque resistance no longer decreases with decreasing roughness height. At an angular velocity of 57 \(\mathrm{rads/s}\), the critical roughness height is 1 \(\times\) 10\({}^{-5}\) m, whereas at 40 \(\mathrm{rads/s}\), it is 2.5 \(\times\) 10\({}^{-5}\) m. The critical roughness height is related to the angular velocity or rotational speed of the armature; higher speeds correspond to smaller critical roughness heights, a phenomenon that has also been verified by [PERSON] and [PERSON] (2018). The \"Top and bottom walls\" subplot in Figure 12 indicates a similar situation in which the torque resistance initially decreases and then stabilizes as the roughness height diminishes. At 57 \(\mathrm{rads/s}\), the resistance torque decreases by approximately 9.5%, whereas at 40 \(\mathrm{rads/s}\), it decreases by approximately 8.5%. Furthermore, a critical roughness height exists here as well, which decreases as the  
Figure 11: Cylindrical cross-section vorticity magnitude diagram, where (**a**) represents the vorticity diagram at a height of 1400 mm for a cylindrical cross-section with radius R = 3500 mm, and (**b**) represents the vorticity diagram at a height of 2200 mm for a cylindrical cross-section with radius R = 3500 mm. rotational speed increases. Consequently, when the rotational speed requirements for the supergravity centrifuge increase, to minimize the torque resistance as much as possible, the smoothness requirements of the sidewalls must be reduced, i.e., the roughness height must be reduced. Figure 12: Changes in torque resistance at various roughness heights of the sidewall, top and bottom walls, and arm. The \"Rotating arm\" subplot in Figure 12 illustrates the variation in torque resistance under different roughness heights of the armature when the roughness heights of the top and bottom walls and sidewalls are fixed at 5 \(\times\) 10\({}^{-5}\) m. The effect of the armature roughness height on the torque resistance is minimal compared with that of the roughness height of the sidewalls and top and bottom walls. At 57 rads/s, the torque resistance decreases by only 2.4%, and at 40 rads/s, it decreases by a mere 0.8%. This is primarily because, in the torque resistance components obtained from simulations, the shape (or pressure) component dominates the armature's contribution, accounting for over 96% of the total resistance, whereas the friction (or viscous) component constitutes less than 4%.