A Physics-Based Framework for Predicting Assembly-Induced Superharmonic Responses in Spline-Coupled Rotor–Casing Systems

Casing assembly deviations can disrupt aero-engine support alignment and induce abnormal vibration. However, the mechanism by which bearing-seat coaxiality errors generate superharmonic responses remains insufficiently understood. This study investigates how such deviations propagate through support misalignment and a spline coupling to influence the vibration response of a coupled rotor–casing system. A geometric relationship is formulated to transform the misalignment of the support into equivalent parallel and angular initial offsets at the spline coupling. An additional excitation model for the spline coupling, accounting for meshing stiffness, transmitted torque, tooth-side clearance, unilateral tooth contact, and relative whirl motion, is incorporated into a reduced-order whole-engine dynamic model. The integrated model is evaluated under a range of experimentally measured coaxiality conditions. Numerical simulations predict critical response regions near 16,000 and 23,000 r/min, along with subcritical resonance peaks at approximately 7800 and 12,500 r/min that are attributed to superharmonic excitation mechanisms rather than conventional mass unbalance alone. Experimental results indicate that the 0.234 mm coaxiality condition yields larger vibration amplitudes, additional low-speed resonance peaks, and more pronounced 2X–4X harmonic components compared with the 0.069 mm condition, thereby corroborating the proposed assembly deviation mechanism under cold-state structural dynamic conditions.