周向均布拉杆柔性组合转子轴承系统的非线性动力特性

Nonlinear Dynamic Analysis of a Flexible Rod Fastening Rotor Bearing System

针对周向均布拉杆柔性转子轴承系统,应用哈密顿原理建立周向拉杆的动力学模型,得到了拉杆产生的附加刚度矩阵及由于拉杆预紧不均所产生附加广义力矩的一般形式,结果说明当拉杆数目大于等于3且拉杆均布时,拉杆产生的刚度矩阵保持各向同性;各根拉杆初始预紧不均的作用是产生一个以工作转速旋转的恒定广义附加力矩。结合对整体转轴应用计及轴向力的铁木辛格梁轴单元建立的有限元模型,得出了拉杆组合转子轴承系统的系统动力方程,进而采用自由界面系统缩减方法将系统中的线性自由度部分缩减,同时保留非线性自由度以方便非线性力的施加。运用打靶法结合Floquet稳定性分叉理论得到了系统稳态周期解的稳定性边界和分叉形式。数值结果表明,转子不平衡和拉杆预紧不均对系统周期解稳定性具有很大的影响,拉杆预紧不均将使得系统过一临界转速时周期解的倍周期分叉现象加剧。

For flexible rod-fastening rotor bearing system （FRRBS）,a dynamic model of tie rods distributed along the circumference is built by using Hamilton principle,and the general expressions of the additional stiffness matrix and additional generalized moment caused by n rods are obtained.The result shows that if the number of rods is greater than or equal to 3 and they are distributed uniformly along the circumference,the additional stiffness matrix caused by n rods keeps isotropy;and the unbalanced pre-tightening force of n rods leads to a constant generalized added-moment rotating at working speed.At the same time,the shaft is considered as an integral structure and is modeled by using Timoshenko beam-shaft element which can take the effects of axial load into consideration,so the whole dynamic model of FRRBS is obtained.Then the model is reduced by a component mode synthesis method,which can conveniently account for nonlinear oil film forces of the bearing.Afterward,the periodic motions and their stability margin are obtained by using shooting method and path-following technique,and the local stability and bifurcation behaviors of periodic motions are obtained by Floquet theory.The results indicate that mass eccentricity and unbalanced pre-tightening forces of tie rods have great influence on nonlinear stability and bifurcation of the T periodic motion of system,cause the spillover of system nonlinear dynamics and degradation of stability and bifurcation of T periodic motion.