## 3 Results and Discussion
### The Effect of Bearing Rotating Speed  
As shown in Figure 6, the oil-gas two-phase distribution cloud images inside the bearing at different bearing rotating speeds are presented. The oil flow rate is 3 L/min, the oil viscosity is 0.0046 Pa-s, and the oil density is 938.6 kg/m\({}^{3}\). At different rotating speed conditions, the oil is mainly distributed near the outer ring of the bearing. With the increase of bearing rotating speed, the oil phase inside the bearing gradually decreases. Figure 7 shows the volume fraction of the oil phase inside the bearing along the circumference at different speeds. The oil exhibits periodic distribution in the bearing, with a period that is the same as the number of supply holes. The volume fraction of the oil phase is larger near the supply holes and smaller far away from them. With the bearing rotating speed increases, the rotating speed of the cage and ball also increases, resulting in a larger centrifugal force on the oil. The oil velocity inside the bearing becomes faster, making the oil distribution more uniform, but at the same time, the volume fraction of the oil phase decreases. Figure 8 shows the volume fraction of the oil phase inside the bearing along the radial direction at different rotating speeds. The oil mainly concentrates near the outer ring, which is consistent with the cloud image results shown in Figure 6. With the increase of the bearing rotating speed, the radial distribution of oil inside the bearing remains unchanged. Under the influence of increased bearing rotating speed, the centrifugal force on oil continues to increase. Under the guidance of the outer ring, it becomes easier for oil to be thrown to the outer ring rather than accumulate between the cage and inner ring, resulting in an increase in the volume fraction of the oil phase near the outer ring.  
Figure 4: Streamlines diagram.  
Figure 5: Oil distribution evolution inside the bearing with flow time.  
As shown in Figure 9, the volume fractions of the oil phase near the inner and outer rings of the bearing, as well as the average oil phase volume fraction inside the bearing, are presented at different bearing rotating speeds. With the increase of bearing rotating speed, both the volume fractions of the oil phase near the inner and outer rings of the bearing decrease, and the average oil phase volume fraction inside the bearing decreases approximately linearly. When the bearing rotating speed increases from 5000 rpm to 17,000 rpm, the volume fraction of the oil phase near the inner ring of the bearing decreases by 66%, the volume fraction near the outer ring decreases by 69%, and the average oil phase volume fraction inside the bearing decreases by 66%. It can be seen that when the bearing rotating speed increases, the oil supply should be increased to ensure lubrication and cooling in the bearing.  
Figure 8: Radial oil volume fraction at different bearing rotating speeds.  
Figure 6: Oil and gas distribution at different bearing rotating speeds.  
Figure 7: Circumferential oil volume fraction at different bearing rotating speeds.  
As shown in Figure 10, the ratio of oil phase volume fraction between the zone of outer and inner rings inside the bearing under different bearing rotating speeds is presented. With the increase of bearing rotating speed, the distribution difference of oil between the inner and outer rings decreases. When the bearing rotating speed is 5000 rpm, the volume fraction of the oil phase near the outer ring is approximately 4.59 times that near the inner ring. When the speed increases to 17,000 rpm, the volume fraction of the oil phase near the outer ring is 3.52 times that near the inner ring. This indicates that as the bearing rotating speed increases, the radial distribution of oil inside the bearing also tends to be more uniform.