<p>The bearing-rotor system of a multi-shaft air separation centrifugal compressor becomes complex due to gear coupling interactions, necessitating the establishment of a dynamic characteristic analysis model that meets engineering practicality. This study focuses on an actual multi-shaft unit in an air separation system, constructing a bending vibration characteristics model for a complex multi-stage gear-bearing-rotor system. The model incorporates the effects of time-varying meshing stiffness, bearing stiffness, and unbalanced masses. Unbalanced response analyses of the rotor system were conducted under two conditions: with and without consideration of gear meshing stiffness. The actual unit’s vibration characteristics test bench was developed, and vibration and critical speed tests were performed. The results indicate the minimal influence of meshing stiffness on the rotor’s unbalanced response for the multi-shaft air separation system with a double-overhung gear-coupled rotor configuration. This is attributed to the fact that the gear meshing interface corresponds to the first-order bending mode, whose modal frequency lies outside the operational speed range. Critical speed test data closely align with numerical simulations, demonstrating that the proposed modeling methodology effectively characterizes the bending vibration behavior of the double-overhung multi-shaft gear-rotor system. These findings provide critical data support for the design and safe operation of complex multi-shaft units.</p>