Frequency modulation of coupled lateral-torsional vibration of unbalanced rotor

In addition to introducing unbalance excitation to the rotor system, unbalance can also induce coupled lateral-torsional vibration under certain operating conditions, leading to frequency-modulated responses, combination resonance, and even instability, thereby posing a threat to system operational safety. To investigate the coupling mechanism of lateral and torsional vibration in unbalanced rotors and to develop a unified computational method for conducting modal analysis and response analysis, this paper first establishes the dynamic model of a rotor having an unbalanced disk at the midspan. Then the mechanism of frequency-modulated coupling of lateral and torsional vibrations is revealed from a kinematic perspective, and the closed-loop of this frequency modulation is highlighted. Subsequently, using the harmonic balance method, the modal characteristics of unbalanced rotor are analyzed, showing that a single mode of an unbalanced rotor comprises multiple asynchronous lateral and torsional components. The study further analyzes the impact of key parameters, such as rotational speed, eccentricity, and damping, on the coupled modes. The method for calculating the response of the unbalanced rotor under lateral or torsional external excitations based on the frequency is proposed, whose accuracy is validated through comparison with the numerical integration method. Finally, this paper presents a set of apparatus and methods for conducting coupled lateral-torsional vibration experiments on unbalanced rotor, which include instability testing and response experiments under lateral/torsional excitations, providing comprehensive validation of the theoretical findings.