Effect of Support Stiffness on the Stability of a Rotor System with Blade Flexibility

Abstract

A simple mathematical model describing the motion of a rotating flexible blade, rigid-disk, and flexible shaft assembly is derived. The model provides a fast parametric study for the dynamic behaviour of the proposed rotor system. The Lagrangian approach combined with the assumed mode method is used to derive the governing equations of motion for this system. The model consists of asymmetrical continuous shaft mounted on two isotropic supports; an end support, represented by two rotational and two translational springs, and an intermediate support, represented by two translational springs only. A rigid disk, with a number of flexible blades of uniformly distributed stiffness and mass, cantilevered to the disk, is attached to the free end of the shaft. The effect of support flexibility on the stability of the system is studied. Instability regions are presented for different system parameters. Coupling between flexible blades and shaft coordinates showed very little effect on the instability regions. The mathematical model results are similar to those found in the literature.