Application of complex nonlinear modes to determine dry whip motion in a rubbing rotor system

Dry whip motion is an instability of rubbing rotor system and may cause catastrophic failures of rotating machinery. Up to now, the related mechanisms of the dry whip is still not well understood. This paper aims to build the relationship between the complex nonlinear modes and the dry whip motion, and propose an effective method to predict the response characteristics and existence boundary of the dry whip through complex nonlinear modes. For the first time, the paper discusses how to use the complex nonlinear modes to predict the dry whip systematically, and as a consequence, the mechanism of the relationship between the complex nonlinear mode and the dry whip is revealed. The results show that the Backward Whirl (BW) mode motion of the rubbing rotor system dominates the response characteristics and the existence boundary of dry whip. The whirl amplitude and whirl frequency of dry whip are equal to the modal amplitude and modal frequency of the BW mode at the jump up point where the modal damping is equal to zero. The existence boundary corresponds to the critical rotation speed where the minimum of the modal damping of the BW mode motion is exactly equal to zero. Moreover, the proposed nonlinear modal method in this article is very effective for the prediction of dry whip of the more complicated practical rotor system, which has been verified by applying the predicted method into a rubbing rotor test rig.