# Analysis on Influences of Squeeze Film Damper on Vibrations of Rotor System in Aeroengine
## 1 Introduction  
Squeeze Film Damper (SFD) is frequently used for the vibration reduction of rotor systems in aeroengines. The principle of vibration reduction is that the bearing outer ring is installed in the bearing seat with a certain clearance, which is introduced to lubricating oil to form squeeze oil film. The vibration load caused by the rotor approaching or passing the critical speed or by the unbalanced force is transmitted from the rotor to the elastic support through the bearing. Under the transverse load of the rotor, the journal produces radial displacement and the vibration energy then is absorbed by the lubricating oil. The typical installation method of SFD in a bearing is shown in Figure 1.  
The influence of SFD on rotor systems is very significant, and it is an important vibration reduction element of many rotating machinery, such as aeroengines. Long-term theoretical and experimental research has been carried out by people. In the early stage, SFD was linearly equivalent to 8 coefficients (4 damping coefficients and 4 stiffness coefficients) [1]. However, the oil film force of SFD has obvious nonlinearity, and the linearization equivalent has shortcomings, causing many vibration phenomena which cannot be explained reasonably. The mechanism of nonlinear stiffness and damping of SFD is relatively clear now. Based on the assumption that the oil film is incompressible, the oil film distribution of SFD obtained by solving the Reynolds equation with a short bearing and a Sommerfeld oil film boundary condition is dependent on instantaneous displacement and velocity. In Refs. [2, 3], the fluid-structure coupling dynamics of SFD is analyzed by the finite difference method. The direct stiffness and damping coefficients and the cross stiffness and dampingcoefficients of SFD are obtained, which have the characteristics of hard nonlinearity. Theoretical and experimental studies also show that the introduction of SFD can improve the dynamic stability of the rotor system in a large speed range and the ability to bear serious unbalanced forces; however, there are nonlinear dynamic behaviors such as subharmonic, super harmonic, and torus orbit [4]. The nonlinearity of SFD has a significant influence on the dynamics of rotor systems. Professor [PERSON] [5; 6] pointed out that the nonlinear oil film force of SFD causes uncoordinated whirling of the rotor, and thought that the most obvious nonlinear behavior of the SFD-rotor system was a bistable phenomenon; that is, corresponding to the same speed ratio, the response will appear multivalue. Under certain conditions, the motion trajectory under large eccentricity may be unstable, and low-frequency precession and self-excitation vibration corresponding to higher critical speed and damping pressure may occur [7; 8]. [PERSON] [9] analyzed and simulated the SFD effect of sudden unbalanced excitation on a low-pressure rotor system with a large fan, revealing the way in which SFD affects the rotor passing through the unstable region. [PERSON]. [10] from Tianjin University established the dynamic model of the aeroengine rotor system considering the maneuver flight of the aircraft, in which the Coulomb friction force of the rotor rubbing and the SFD damping force based on the Reynolds equation was introduced, and the motion bifurcation diagram of the speed was obtained. The SFD played different roles in stability under different flight states and speeds. [PERSON] studied the effects of fluid inertia, unbalanced force, unidirectional load, stiffness of damper-centering spring on nonlinear vibration of a flexible rotor system, and the effects of oil pressure and bubble film cavitation [11; 12], in detail with harmonic balance method and prediction-correction algorithm. Many scholars also use the stability and bifurcation theory to comprehensively analyze the nonlinear dynamic, non-coordinated motion and periodic solution bifurcation and stability of the SFD rotor system [13].