Nonlinear modal analysis and its application on prediction of resonance speed for a rotor–stator rubbing system

Abstract

In this article, the nonlinear dynamic characteristics of a rotor–stator rubbing system, which simultaneously considers the dynamical characteristics of rotor and stator as well as their coupled effect produced by rub-impact, are investigated from the perspective of the complex nonlinear modes. The solution method combining harmonic balance and trust region methods is built, based on which the modal characteristics of the rotor–stator rubbing system is obtained. The results show that the system possesses both the rotor-dominated and stator-dominated vibration modes. The coupling effect produced by rub-impact force can significantly change the modal frequencies and modal shapes of these two order modes. Despite that, the modal characteristics of this rubbing system have a feature of interval distribution and can be estimated by the two kinds of derived linear systems. The friction force of the rub-impact may lead to the instability of the backward whirl motions for these two order modes in some cases. Furthermore, the relationship of the nonlinear modes and resonance response of the rotor–stator rubbing system is studied for the first time, based on which a predicted method of the critical speed of the rubbing system is proposed. The method can obtain the critical speed interval of the rubbing system only through the linear modal analysis; therefore, it is very effective in the application of the actual engineering.