مدل 5-DOF برای تجزیه و تحلیل سیستم دو روتور موتور هواپیما اسپیندل

This paper develops a five degrees of freedom (5-DOF) model for aeroengine spindle dual-rotor system dynamic analysis. In this system, the dual rotors are supported on two angular contact ball bearings and two deep groove ball bearings, one of the latter-mentioned bearings works as the inter-shaft bearing. Driven by respective motors, the dual rotors have different co-rotating speeds. The proposed model mathematically formulates the nonlinear displacements, elastic deflections and contact forces of bearings with consideration of 5-DOF and coupling of dual rotors. The nonlinear equations of motions of dual rotors with 5-DOF are solved using Runge-Kutta-Fehlberg algorithm. In order to investigate the effect of the introduced 5-DOF and nonlinear dynamic bearing model, we compare the proposed model with two models: the 3-DOF model of this system only considering three translational degrees of freedom (Gupta,1993, rotational freedom is neglected); the 5-DOF model where the deep groove ball bearings are simplified as linear elastic spring (Guskov, 2007). The simulation results verify Gupta's prediction (1993) and show that the rotational freedom of rotors and nonlinear dynamic model of bearings have great effect on the system dynamic simulation. The quantitative results are given as well.

The spindle dual-rotor system is very common in aerospace field. Because of complicated dynamics and coupling between dual rotors, the system features complicate nonlinear dynamics, which is crucial to stability of the aeroengine and plane. A spindle dual-rotor system is investigated in this paper. In this system, the dual rotors have co-rotating speeds and are connected by the intershaft bearing—a deep groove ball bearing. The intershaft bearing inner race is mounted on the low-pressure rotor while the outer race is mounted on the high-pressure rotor. The high-pressure rotor has higher rotational speed. Important progress has been made on studies of dynamics of dual-rotor system. Early in 1975, Hibner[1] put forward the application of the transfer matrix method in order to compute the critical speeds and nonlinearly damped response. In 1986, Li, et al.[2] analyzed the dynamics of the dual-rotor system which was connected by intershaft squeeze film damper. In 1993, Gupta, et al.[3] studied through experiment the critical speeds, mode shape and unbalanced response of the dual-rotor system whose rotors were connected by a deep groove ball bearing and developed theoretically an extend transfer matrix procedure in complex variable to obtain dynamic response. The experimental results were in reasonable agreement with theoretical results in the case of two degrees of freedom (2-DOF) model. In 1996, Ferraris, et al.[4] made theoretical research on dynamic behavior of non-symmetric coaxial co- or counter-rotating rotors. In his research, a 2-DOF model was built using finite element, and the natural frequency and mass unbalance responses were investigated. However, the displacements of rotors at the bearing points were assumed the same and calculation was simplified in his model (The equations can be solved by hand calculations). In 2007, Guskov, et al.[5] presented a numerical 4-DOF model to study unbalanced response of a dual-rotor test rig system where two coaxial shafts were supported on deep groove ball bearings and connected by an intershaft bearing. Basing on the above works, we numerically investigated a spindle dual-rotor system with five degrees of freedom (5-DOF) in this study. This work differs from the previous work[5] in two main aspects. Firstly, the bearing type is different. The rotors in Ref.[5] were supported on deep groove ball bearings, while the rotors in our work are supported on two angular contact ball bearings and two deep groove ball bearings. Therefore, besides translational degrees of freedom along x

(1) A 5-DOF model of aeroengine spindle dual-rotor system is proposed for dynamic analysis. The proposed model is compared with several previous models to investigate the effect of the introduced 5-DOF and nonlinear dynamic bearing models. (2) The simulation results of the proposed 5-DOF model accord with Gupta’s conclusions. In our proposed model, the involved rotational freedom of the rotors corresponds to the consideration of the rotary inertia. Our simulation results show the effects of dual rotors depend on their speeds. (3) The dual rotors of 5-DOF model have bigger simulation amplitudes than those of 3-DOF model. The introduced rotational freedom of the rotors also increases the simulation amplitudes deviation (lowered the stationarity). (4) The amplitudes of 5-DOF model and 3-DOF model show different changing trends as the initial clearance of intershaft bearing increases. In 3-DOF model, the amplitude of rotor a has decreasing trend while the amplitude of rotor b has increasing trend, and the dual rotors have stationary amplitudes when