Numerical Analysis of Coupled Lateral and Torsional Vibrations of a Vertical Unbalanced Rotor

A model for the coupled lateral and torsional vibrations of a vertical unbalanced rotor is developed. The equation of motion is obtained using Lagrangian dynamics without considering the external actuating forces and torque. The equation showed coupling and nonlinear interaction between the rotor lateral and torsional vibrations. Most of the earlier work on coupled vibrations has been done for the horizontal rotor model. The coupled vibrations for a vertical rotor have not been reported in the past. An attempt is made to reveal dynamic characteristics of vertical rotor. The results of the simulation showed the coupled between torsional and lateral vibrations is induced by mass eccentricity. Coupled vibrations have appeared in the start period of the vibration. After a transient vibration process, the vibrations are not coupling. The lateral vibration becomes equal amplitude with shafting speed. And the torsional vibration keeps on attenuating until it stops. When the vibration is coupled, the coupling effect on which torsional vibration to lateral vibration is evident. But there's no coupling effect on the lateral to the torsional. It is also shown that for some operational parameters, the controlling action may excite large lateral vibrations due to coupling with the torsional motion.