To gain a more comprehensive understanding of the rub-impact dynamics and failure mechanism between the high-speed rotor blade and static casing of an aero-engine, numerical simulations of the rubbing process and response characteristics of the rotor-disc-casing coupling system are conducted. These simulations are based on the harmonic equilibrium method, combining implicit-explicit analytical approaches from both theoretical and finite-element analysis perspectives. The simulation results are subsequently validated through comparison with experimental findings. Building upon this foundation, the factors influencing the rubbing response are further analysed, including variations in clearances between the rotor and stator, different stiffness ratios, and diverse rotational speeds. The conclusions drawn and the proposed methodology contribute to an enhanced understanding of the physical phenomena and principles of blade-casing rub-impact, thereby providing a valuable reference for the fault diagnosis of rubbing phenomena in engineering applications.