Dynamic modeling of rotating blades system based on transfer matrix method of multibody system

Abstract

Due to the coupling between the stator and the blades, the vibration characteristics of rotating blades play an important role in the structural reliability of rotating machinery. The computational modeling challenge lies in achieving the coupling of the rotating bending-torsional blade with the stator. To perform rapid and accurate vibration characteristics analysis, the Transfer Matrix Method of Multibody System (MSTMM) is proposed to study the multibody dynamics models of single rotating beam and rotor-stator coupled system. The models are verified by comparison with finite element method (FEM) results. Using the beam model, rotating blades pure bending and torsion frequencies can be simply computed, these are the key parameters for establishing critical instability dynamic models, such as 2D aerofoil or blade flutter models. By computing the vibration characteristics with varying rotating speed, the influence of the blade rotation is illustrated. The computational results show that, the influence of rotation is greater on the frequencies associated with the bending rather than with the one of the torsion mode, hence the adjacent natural frequencies may intersect. At the veering point, the mode shape of bending-torsion coupling mode changes greatly, compared with that of other rotation speeds. In addition, asymmetric modes can be observed in the rotor-stator coupled model due to the coupling of elastic deformation and rigid body motion. The modeling process is simple and rapid, only assembling the transfer matrix of each element like building blocks. This proposed model can be applied to compute coupled/uncoupled bending-torsional frequencies of helicopter and wind turbine blades, and the results can provide useful guidance for the modeling of rotating machinery.