Harmonic Frequency Analysis of Asynchronous Motion in a Rubbing Rotor System with Flexible Casing Constraint

Rotor-flexible casing rubbing can induce strong nonlinear dynamics in rotor systems. This study investigates the harmonic frequency characteristics of a rubbing rotor system with a flexible casing constraint. A nonlinear rub-impact model combined with a finite element-based rotor–casing coupling framework is developed to evaluate system responses under concentric and eccentric configurations. The harmonic components of rotor and casing vibrations are analyzed over a range of rotational speeds. Results show that, under concentric conditions, harmonic frequencies originate from rubbing-induced asynchronous motion. The harmonic sub-frequencies observed in the spectrum correspond to lobed rotor orbits formed during the transition from synchronous to asynchronous motion under continuous rubbing forces. Under eccentric rotor–casing alignment, the vibration spectrum becomes more complex and exhibits frequency clustering. The results provide insight into harmonic generation mechanisms and highlight the role of casing flexibility in rubbing-induced asynchronous motion.