## 5 Computational Analysis
### Confirmatory Experiment  
To verify the correctness of the unbalance response law for the SFD-containing rotor model proposed in this paper, and due to the high cost of actual rotors, an experimental test on unbalance response was conducted using a rotor test rig with SFD as shown in Figure 22.  
The test equipment was the B768 High-Speed Rotor Dynamic Test Rig, with the rotor adopting a 1-1-0 bearing support scheme. The front support point (compressor end) was equipped with a single-row ball bearing combined with an elastomeric support and squeeze film damping device, while the rear support point (turbine end) used a single-row roller bearing combined with the same damping system. The vacuum chamber pressure was maintained at \(\leq\)200 Pa. Two acceleration sensors (A\({}_{1}\) and A\({}_{2}\) at the compressor end, A\({}_{3}\) and A\({}_{4}\) at the turbine end) were installed on each support bracket to measure vertical and horizontal vibration accelerations, respectively: A\({}_{1}\) and A\({}_{3}\) were mounted vertically, while A\({}_{2}\) and A\({}_{4}\) were positioned horizontally. Additionally, one vibration velocity sensor (V\({}_{1}\) at the compressor end, V\({}_{2}\) at the turbine end) was installed in the vertical direction of each support bracket to measure vertical vibration velocities. Vibration displacement sensors D\({}_{1}\)-D\({}_{3}\) were placed on the turbine disk, the vicinity of the rear support bracket's rotor shaft, and the compressor disk to capture the rotor's vibration deflection. The SFD oil film force magnitude was adjusted by varying the supply oil pressure of the squeeze film dampers. Tests were conducted at speeds ranging from 0 to 35,000 r/min and supply oil pressures of 0.2 MPa, 0.4 MPa, and 0.6 MPa, measuring the vibration acceleration and vertical vibration velocity at both support brackets (as shown in Figure 23).  
Figure 21: Orbit for supports 1, 2, and 3 with 2 types of nonlinear forces applied.  
Figure 22: Test rotor and test platform.  
Increasing the supply oil pressure is equivalent to enhancing the SFD's nonlinear oil film force in simulation experiments. The experimental results show that as the oil pressure increases, the damping performance of the supports is enhanced, effectively suppressing the bi-stable phenomenon (Figure 23c, where the nonlinear jump disappears with increasing pressure). This observation aligns with the simulated results where the coupling of two nonlinear forces improved the damping performance of the supports and eliminated the bi-stable instability. The experiments validate the correctness of the unbalance response law in SFD-equipped rotor systems and confirm that the dynamic response mechanism proposed in this study can effectively control the vibration of modern aero-engine rotors. For instance, based on the identified influence law of SFD's nonlinear oil film force, adjusting parameters such as the oil supply pressure can suppress the rotor's nonlinear jumping behavior; furthermore, increased oil film force significantly reduces rotor vibration (Figure 23b), demonstrating the practical applicability of the proposed theory.  
Figure 23: Test result.