The two-section rotor needs to go through multiple critical speeds in the process of speed increase. When the rotor approaches the critical speed, its amplitude increases rapidly, easily causing collision damage. The auxiliary over-critical device cushions and protects the rotor through rubbing, which makes it pass the critical speed under the safe amplitude. In this paper, the influence of buffer stroke, the key structural parameter of the auxiliary over-critical device, on the dynamic response of the two-section rotor at the first-order bending critical speed is analyzed, the influence of its buffer stroke on the over-critical dynamic response of the rotor is calculated and analyzed, and the impact and friction force on the rotor is calculated. The design principles and results of the buffer stroke parameters of the auxiliary supercritical device are proposed.