NON-LINEAR VIBRATION ANALYSIS AND SUBHARMONIC WHIRL FREQUENCIES OF THE JEFFCOTT ROTOR MODEL

In this analysis, a Jeffcott rotor model is used which is a thin disk located on a flexible shaft which is simply supported at the ends. The non-linear dynamic equations of the rotor are obtained. A perturbation technique is used to obtain approximate linear equations for the non-linear equations. The non-linear equations and approximate linear equations are solved numerically and the solutions compared. The approximate linear equations correctly predict the non-linear vibration. It has been experimentally observed in many researches that in addition to the synchronous whirl, there exist subharmonic vibrations which may cause instability. This is generally attributed to the dry friction, non-linear or asymmetric stiffness, rubs, fluid-film bearing clearances. This study shows that there exist two subharmonic transient vibrations caused by the non-linearity of the system itself. The two subharmonic frequencies are equal to (ω+ωn) and (ω−ωn) and also the supersynchronous component of the vibration becomes unstable when the speed ratio ω/ωnis ⩾2.