低压转子初始弯曲双转子系统跨坐标系建模方法

针对航空发动机双转子系统中低压转子初始弯曲问题,考虑中介支点轴心位置偏移,提出一种跨坐标系的双转子系统建模方法,这种方法能够解决高低、压转子运动形式不同而不能在统一坐标系下建模的问题,进而可以较准确模拟中介支点轴心偏移对双转子系统动力学影响。基于高低压转子的耦合运动行为,分别在不同坐标系下建立高、低压转子有限元模型,通过Lagrange方程得到高、低压转子的运动微分方程。通过对中介轴承的内外环自由度坐标变换实现了高低压转子的跨坐标系自由度耦合。低压转子的初始弯曲将导致自身的质量偏心和角度偏置,这将引起对低压转子的附加离心载荷和附加陀螺力矩;由于中介支点轴心位置偏移,高压转子的运动微分方程中具有时变刚度和时变阻尼项,其附加的激励载荷也比较复杂;中介轴承由于连接不同坐标系通过坐标变换产生时变刚度。通过算例对该模型的稳态响应分析,并与传统模型进行了对比。结果表明:当接近低压转子激励临界转速时,该模型的响应幅值较传统模型明显增大。

Cross coordinate system modelling method for a dual-rotor system with initial bending of its low-pressure rotor

Aiming at the problem of initial bending of low-pressure rotor existing in a dual-rotor system of aero-engine, considering intermediate bearing offset, the cross coordinate system modeling method for a dual-rotor system was proposed.This method could solve the problem of different motion forms of high-pressure (HP) rotor and low-pressure (LP) one leading to their modeling being not able to be done in a unified coordinate system.Firstly, finite element models of HP and LP rotors were built in different coordinate systems based on their coupled motion behavior.Then, differential equations of motion for HP and LP rotors were obtained with Lagrange equation.The coordinate transformation of inner and outer rings’ DOFs of intermediate bearing was used to realize HP and LP rotors’ cross coordinate system DOF coupling.LP rotor’s initial bending caused its mass eccentricity and angle skewing to bring its additional centrifugal load and gyroscopic moment.Due to intermediate bearing’s position offset, HP rotor’s differential equations of motion had time-varying stiffness and time-varying damping terms, so its additional excitation load were more complex.Intermediate bearing connected different coordinate systems, so it produced time-varying stiffness after coordinate transformation.Finally, some computation examples were used to compare the proposed model’s steady state responses with those of the traditional one.The results showed that the response amplitude of the proposed model is obviously larger than that of the tradition one when LP rotor’s rotating speed is close to its critical speed.