A Vibration Response Prediction Model for Multi-Stage Assembled Rotors Based on Synchronous Excitation of Mass Eccentricity Error and Spigot Eccentricity Error

The precise prediction of vibration response is crucial for optimizing the assembly quality of multi-stage rotors. Existing models possess two key limitations: they neglect the geometric displacement excitation from spigot eccentricity error and oversimplify rotor behavior by not accounting for the excitation redistribution caused by significant dynamic deflection at high speeds, particularly near critical speeds. To overcome these shortcomings, this study establishes a novel dynamic model based on the synchronous excitation of both mass and spigot eccentricity errors, which simultaneously incorporates the coupling mechanism of dynamic deflection. System dynamics equations are developed using a finite element approach combined with Timoshenko beam theory and solved via the Newmark-β method. Simulations and experiments on a four-stage rotor demonstrate that the proposed model provides significantly improved accuracy. At sub-critical, first, and second critical speeds, it reduces the maximum prediction error for nodal displacement amplitudes by 6.1%, 9.2%, and 36.4%, respectively, compared to a model neglecting dynamic deflection. Furthermore, analysis confirms that the targeted assembly error excitation exists solely at the fundamental frequency. The developed model, which uniquely integrates dual eccentricity sources with dynamic deflection coupling, is essential for reliable high-speed vibration prediction and assembly optimization, especially for flexible rotors operating near critical speeds.