Nonlinear dynamic analysis using the complex nonlinear modes for a rotor system with an additional constraint due to rub-impact

A rub-impact can bring the impact load and friction force onto the rotor, and in the meantime, it can also produce the additional effect of changing the stiffness of the rotor system. Past analysis and numerical simulation work related to rub-impact problems primarily focus on the complicated nonlinear vibration responses caused by the rubbing force. However, the influence of the additional effect on the rotor's modal characteristics is rarely studied. The present study investigates the modal characteristic of the rotor system with the additional constraint and how it affects the rotor's responses. The governing equation for a modified Jeffcott rotor system with a rub-impact is established first. Next, the complex nonlinear modes concept is introduced, and the corresponding solution method is derived. Finally, the modal characteristics are analyzed in detail, such as the modal frequency, the modal damping, the stability and the interaction between the nonlinear mode motion and rotor's responses. The results show that the rubbing rotor system possesses both forward whirl mode motion and backward whirl mode motion. The magnitudes of the modal frequencies for both the forward whirl and backward whirl increase with an increase in the amplitude of the mode motion (modal amplitude). Nevertheless, the magnitudes are limited to an interval range, which can be approximately determined through the linear rotor without rub-impact and the coupled linear rotor/stator system. Differing from the forward whirl mode motion, the backward whirl mode motion can be unstable, since its modal damping may be less than zero in certain cases. Moreover, the instability of the backward whirl mode motion is only the primary physical mechanism for the partial rub transmitting into dry whip.