## 3 The Numerical Simulation of the Floating Ring Rotor System
### Analysis of Floating Ring Fluid Torque and Rotation Speed  
When the system is started, the journal starts to accelerate and rotate. The rotation will drive the oil film in contact with the journal surface to start the shearing flow and finally drives the inner oil film to flow as a whole. At this time, there is a relative slippage between the fluid-solid contact wall of the inner oil film and the floating ring. There is no relative sliding motion at the fluid-structure interface between the outer membrane and the floating ring. Therefore, the relative sliding speed difference between the inner membrane and the outer membrane produces a viscous moment acting on the floating ring to make the floating ring start to rotate.  
The fluid torque change on the floating ring is shown in Figure 14. The maximum fluid torque produced by the inner oil film is 0.035 N\(\cdot\)m, which continuously decreases to 0.016 N\(\cdot\)m with time. The fluid torque of the outer oil film is initially 0 and continues to increase to 0.016 N\(\cdot\)m with time, which is a negative value. At this time, the inner and outer oil film fluid moments are in opposite directions. The total moment received decreases from 0.035 to 0 N\(\cdot\)m with time, and the force of the floating ring reaches a balanced state.  
Figure 13: The fluid load of the inner and outer layers of the oil film on the floating ring. (**a**) The fluid load of the inner of the floating ring 1; (**b**) the fluid load of the outer of the floating ring 1; (**c**) the fluid load of the inner of the floating ring 2; (**d**) the fluid load of the outer of the floating ring 2.  
The speed change of the floating ring is shown in Figure 15. Due to the net torque on the ring, it starts to accelerate axially, and the speed continues to increase. The subsequent rotation of the ring reduces the relative slip speed of the ring and the oil film. This result will lead to a decrease in the viscous force from the inner membrane and an increase in the viscous force from the outer membrane. The direction of the outer membrane torque and the inner membrane torque are opposite and cancel each other out. It can also be observed from the slope change of the ring velocity curve in Figure 15 that the net angular acceleration of the ring continuously decreases with the acceleration of the ring. Eventually, the floating ring will reach a stable rotation. When the torque of the outer membrane is equal and opposite, the net angular acceleration of the ring becomes zero. The force of the floating ring reaches a balanced state, and the fluid torque drops to 0. Then, the floating ring will keep rotating at this speed.  
Figure 14: The torque of the floating ring 1.  
Figure 15: The speed of the floating ring.  
Under the sub-working condition of 8000 rad/min, the floating ring 1 bears a greater load and the oil film squeezing effect is greater. As shown in Figure 15, the minimum oil film clearance is smaller and the viscous moment generated on the floating ring is greater, so the floating ring speed of ring 2 is higher than that of floating ring 1. The maximum angular velocity of floating ring 2 is 450 rad/min, the maximum rotating speed of floating ring 1 is 430 rad/min, and the rotating speed of floating ring 2 is slightly larger. The maximum angular acceleration of floating ring 2 is \(2.5\times 10^{4}\) (r/min\({}^{2}\)). Based on the working condition, the rotating speed ratio of the floating ring to the rotor is 5.6%. Compared with the rotor speed, the floating ring only rotates in the oil chamber at a very small speed.