# Dynamic Behavior of Twin-Spool Rotor-Bearing System with Pedestal Looseness and Rub Impact
## 1 Introduction  
### Dynamic Modeling for Two-Spool Rotor System  
Since the 1950s, axial and multiaxial rotor configurations such as twin-spool and triple-spool rotors have been increasingly used in turbojet and turbofan engines. However, there is limited literature available on the dynamic characteristics of multiaxial rotor systems. With the advancement of computer processing capacity in the early 21 st century, the complicated dynamic properties of the twin-rotor construction of aero-engines have garnered significant interest among scholars [1].  
On the basis of [PERSON] and [PERSON]'s work on rotor dynamics [2, 3], [PERSON] [4] constructed the dynamic equation of a twin-spool rotor model by utilizing Momentum Theory. [PERSON] model incorporates \"1-3-0\" and \"1-1-1\" configurations for the high- and low-pressure rotor supports. The bearings are simplified as springs with certain stiffness and damping properties. Additionally, the model accounts for the gyroscopic effect and the impact of the engine case. While the model can capture the reciprocal impact of vibration between high-pressure (HP) and low-pressure (LP) rotors, it has undergone significant simplification at the support. [PERSON] [5] utilized the transfer matrix method to create a twin-spool rotor-case model. The equivalent damping force at the bearings was determined by applying the Reynolds equation. The impact of this damping force on the system responsewas then analyzed. However, the above model derivation process is too complicated for rapid engineering analysis.  
In the 21 st century, as the finite element method has become more advanced and computer processing power has improved, scholars have developed more sophisticated models of the twin-spool rotor-bearing system. This refined model has allowed for a more comprehensive analysis of the dynamic characteristics.  
In modeling, [PERSON] and [PERSON] [6] employed the finite element method and the Timoshenko beam theory to develop the dynamic equations for the twin-spool rotor system. They also investigated the impact of support stiffness on the critical speed. This approach facilitated the derivation and analysis process, ensuring model accuracy. [PERSON] [7] examined the transient dynamics properties of a twin-spool rotor system during the acceleration phase. [PERSON] [8] conducted a study to examine the impact of speed ratio, radial clearance of inter-shaft bearing, and damping ratio on the hysteresis phenomena of a twin-spool rotor system. [PERSON] [9] examined the impact of unevenness, rotor bending deformation, and inertia load of the wheel disk on the dynamic load of the pivot point at various rotational velocities. [PERSON] [10] and [PERSON] [11] developed a robust finite element model for the twin-spool rotor system. They calculated the critical rotational speeds and Campbell diagrams, and the numerical values are in good agreement with the experimental results. Based on previous studies, more aero-engine components were considered in the numerical model. [PERSON] [12; 13] established a twin-spool rotor model with squeeze-film dampers and analyzed the effect of blade loss on the vibration response. The active magnetic bearings was used to control the vibration of a co-rotating twin-spool rotor system by [PERSON] [14].  
The dynamic model of a twin-spool rotor-bearing system now takes many elements into account, and it has become more sophisticated. Future modeling research should concentrate on achieving a better balance between the accuracy of the model and degrees of freedom, creating a more effective method for handling nonlinear elements, and progressively converting qualitative analysis to quantitative analysis [15; 16]. In this article, based on the previous modeling methods, the rotor-bearing system of aero-engine PW6000 is modeled with considering the transient effect and the rotational speed control strategy to improve the simulation accuracy and convergence.