# Analysis on Influences of Squeeze Film Damper on Vibrations of Rotor System in Aeroengine
## 4 The Influence of SFD on the Vibration of the Rotor System
### The Unbalanced Vibration Response of Rotor System with SFD  
When the back fulcrum is set with SFD, it is known that the stiffness and damping of SFD have nonlinearity [3], and its typical stiffness and damping curves are shown in Figure 10.  
Figure 8: Response of high-pressure rotor at high speed. (**a**) time domain response; (**b**) frequency domain response.  
Figure 7: Orbits of high-pressure rotor at low speed.  
Figure 9: Orbit diagram of high-pressure rotor at high speed.  
Under the condition of high speed and large unbalanced mass, such as \(r_{n}=12,800\) r/min, which is higher than the second-order critical speed, \(m_{e}=4\times 10^{-4}\) kg\(\cdot\)m, the calculated rotor vibration response is shown in Figure 11.  
The unbalanced mass increases, namely \(m_{e}=4\times 10^{-3}\) kg\(\cdot\)m. Under the same high speed \(r_{n}=12,800\) r/min, the vibration response of the rotor system is calculated, as shown in Figure 12.  
When SFD is introduced into the back fulcrum, under the condition of high speed and large unbalance, the components in the time domain and frequency domain are complex,  
Figure 11: Vibration response under speed of \(r_{n}=12,800\) r/min and unbalanced mass of \(m_{e}=4\times 10^{-4}\) kg\(\cdot\)m. (**a**) time domain response; (**b**) frequency domain response; (**c**) displacement.  
Figure 12: Vibration response under speed of \(r_{n}=12,800\) r/min and unbalanced mass of \(m_{e}=4\times 10^{-3}\) kg\(\cdot\)m. (**a**) time domain response; (**b**) frequency domain response; (**c**) displacement.  
Figure 10: Typical stiffness and damping curves: (**a**) stiffness (**b**) damping.  
the orbit is complex, and the amplitude increases 4 times to about 24 \(\upmu\)m. When the unbalance is further increased, the orbit tends to be regular and approximately rectangular, with rounded corners, and the amplitude increases to about 40 \(\upmu\)m.  
By contrast, under the condition of high speed and small imbalance, the vibration is also stable. For example, when the unbalanced mass \(m_{e}\) = 4 \(\times\) 10\({}^{-5}\) kg\(\cdot\)m and the speed \(r_{n}\) = 12,800 r/min, the vibration response is shown in Figure 13.  
It can be seen from Figure 13 that under the conditions of high speed and small unbalance, the amplitude is only about 0.3 \(\upmu\)m, the time domain and frequency domain components are simple, the vibration is stable, and the orbit is a regular circle. By introducing SFD, in the high speed, after increasing the unbalance, the rotor vibration becomes more stable, which improves the stability of the rotor. After reducing the unbalance, the vibration response amplitude can be significantly decreased.  
Through qualitative comparative analysis with the relevant experiment results of the SFD-rotor system in Refs. [14,26], the stability of the SFD-rotor system can be improved by appropriately increasing the unbalance. This is essentially consistent with the simulation results in this paper, which verifies the correctness of the simulation model and analysis results. In subsequent research, we will use the to-be-built test rig to further carry out the experiments about vibration and stability of the SFD-rotor system.