Inter-shaft bearings play a central role in connecting high-pressure (HP) and low-pressure (LP) rotors within aero-engines. Local defects in these bearings can lead to two distinct and complex vibration modes—paroxysmal or continuous impulse vibrations, which arise from the unique installation positions. This study offers a comprehensive exploration of the dynamic phenomena, the underlying physical mechanism, and the analytical conditions for the occurrence of paroxysmal impulse vibrations. The local defects of the inner ring are found to induce paroxysmal impulse vibrations when specific rotational speed ratios between HP and LP rotors are achieved. The dynamic differences and connections between paroxysmal and continuous impulse vibrations are contrasted. Three analytic and explicit prediction formulas are derived, enabling the direct calculation of the operating conditions for paroxysmal impulse vibrations. A summarized prediction flow for paroxysmal impulse vibrations is established. In addition, the proposed prediction formulas and flow allow for the prediction of the precise frequency components of paroxysmal impulse vibrations. In the validation of the simulation results, three experimental cases involving inter-shaft bearings with inner ring defects are conducted, confirming the existence of paroxysmal dynamic phenomena and validating the effectiveness of the proposed prediction formulas and prediction flow for paroxysmal impulse vibrations. Hence, this study offers a novel approach to understanding inter-bearing vibration fault mechanisms.