Dynamic characteristics of a flexible bladed-rotor with Coulomb damping due to tip-rub

Starting with the basic dynamical equations for a rotating radial cantilever blade in a centrifugal force field, a system of equations are derived for a fully-bladed flexible rotor (shaft and disk) supported by a set of bearings at multiple locations. The dynamical equations include the effect of the rotary inertia and gyroscopic moments as a result of both shaft bending as well as staggered blades flexing in-and-out of the plane of the disk. The governing equations also account for internal material damping in the shaft and the external damping in the bearing. In addition to the unbalance load at the disk location, the shaft may be subjected to a torque and axial forces. In the analytical derivation, the blade tips are considered to be rubbing against the outer case introducing Coulomb damping in the system. Transient response of the rotor with the blades deforming due to rub during the acceleration and deceleration through the resonance is discussed. Numerical results are presented for this highly non-linear impact dynamics problem of hard rub with Coulomb friction. The effect of blade tip rub forces transmitted to the shaft are analyzed in terms of the dynamic stability of the rotor.