Dynamic model of coupled shaft torsional and blade bending deformations in rotors

A dynamic model for a typical elastic blade attached to a disk driven by a shaft which is flexible in torsion is presented. The shaft torsional flexibility is lumped in the form of flexible coupling that is usually employed in rotor systems. The Lagrangian approach in conjunction with the finite element method is employed in deriving the equations of motion, within the assumption of small deformation theory. All the dynamic coupling terms between the system reference rotational motion, shaft torsional deformations and blade bending deformations are accounted for. Furthermore, the effects of axial shortening due to blade bending deformations and rotational motions as well as the effects of gravity are included in the model. The resulting model and simulation results have shown strong dependence and energetic interaction between the shaft torsional deformations and blade bending deformations. The shown dynamic interaction between the coupling torsional flexibility and the blade flexibility might explain some practical aspects that appear in rotor vibrations when flexible blades are present in the system. In addition, the present study explored the necessity for including both the shaft torsional flexibility and the blade lead-lag deformations when a reliable model for either rotating blades or rotor torsional dynamics is needed.