Effect of unbalanced rotor whirl on blade vibrations

In this paper, vibration of a bladed unbalanced flexible rotor is studied. The blade that is attached to the disk is considered as a fixed-free Euler–Bernoulli beam. Position of the blade with respect to the eccentric mass is taken into consideration. Coupled equations of the motion of unbalanced rotor and the blades are obtained through Lagrange equations. The dynamic equations have time variant periodic coefficients. Transient vibration analysis showed that rotor acceleration excites the blade vibration with its own natural frequency. While the rotor passes through its own natural frequency (critical speed) the blade vibration is again excited but this time with the rotor natural frequency. Modal behavior of the blades are different for subcritical, supercritical and for critical speed of the rotor. In the subcritical run of the rotor, blades located from 0° to 180° with respect to the eccentric mass are deflected in the negative direction while the rest are deflected in the positive direction. For supercritical run of the rotor, modal behavior of the blades is just the opposite. For critical speed of the rotor, blades located 90° to 270° from the eccentric mass are deflected in the positive direction while the rest of the blades are deflected in the negative direction. Blades have also different deflections. When the deflections of the blades are plotted with respect to their position angle, distribution of the blade deflections has a sinusoidal shape.