Stability Analysis for Unsymmetrical Shaft With Flexible Bladed-Disk

The governing equations of motion for a rotating flexible blade-rigid disk-flexible shaft system are derived. The bladed disk is attached at one end of an asymmetric shaft with uniformly distributed mass, mass moment of inertia, and stiffness. The shaft is held by two isotropic supports; one at the far end from the bladed disk, modeled by two translational and two rotational springs, and an intermediate support, modeled by two translational springs only. The effect of shaft asymmetry on the dynamics behavior of the rotating bladed disk shaft system is examined over a wide range of rotational speed, and for different combinations of springs’ stiffness, which determines the type of shaft supports. The cantilever, and the simply supported shaft with an over hang can be looked upon as special cases of the described above shaft configuration, since the former is obtained by assigning large stiffness for both translational and rotational springs at the end support, and zero spring stiffness at the intermediate one, whereas the latter is obtained by assigning large stiffness for the translational springs at both supports and zero stiffness for the rotational springs. Stability boundaries are calculated, and presented in terms of shaft asymmetry and rotor speed for given bearing stiffness.