<p>A nonlinear dynamic model is developed for an uncertain rotor-casing-pedestal coupled system under maneuvering flight. The model incorporates maneuver-induced inertial excitation, blade-casing rub-impact with circumferentially non-uniform clearance, squeeze-film-damper oil-film force, and bounded parameter uncertainties within a unified framework. An interval-based approach combined with Chebyshev polynomial approximation is employed as a computational tool to quantify the dispersion of nonlinear responses induced by parameter uncertainty. Based on the proposed model, the coupled effects of maneuvering motion, non-uniform clearance, and parameter uncertainty on the coupled system dynamics are investigated numerically. The results show that maneuvering flight significantly changes the nonlinear response characteristics of the coupled system, including the bifurcation distribution, transient displacement response, rub-impact force, and steady-state whirling orbit. Circumferentially non-uniform clearance strongly affects the spatial distribution and temporal characteristics of rub-impact, while increasing the number of non-uniform clearance sectors leads to more complex orbit patterns and more frequent contact events. Parameter uncertainty further enlarges the response range of the coupled system; among the considered uncertainties, disc unbalance eccentricity produces a relatively broad response interval over a wide speed range, whereas initial blade-tip clearance causes the most pronounced enlargement in the rub-impact-dominated region. Moreover, maneuver-induced nonlinearity increases the sensitivity of the response to clearance variation and parameter uncertainty. These results provide useful insight into the nonlinear vibration response and rub-impact risk of aero-engine rotor systems under uncertain maneuvering conditions.</p>