The supercritical tail rotor drive shaft of a helicopter vibrates violently when driven through its critical speed. The hybrid damper is a specially-designed damper for the transcritical vibration reduction problem. The tail rotor drive shafts equipped with hybrid dampers are typical nonlinear system with friction and collision， and the dynamic characteristic is extremely complex. In order to uncover the underlying working mechanism and guide the design of the hybrid damper， a spring-mass-dashpot equivalent model with double-clearance structure has been established， the governing equations have been deduced and a systematic numerical simulation has been carried out. The results demonstrate that the working modes of the hybrid damper can be divided into 4 categories according to the unbalance quantity： no-effect mode， normal-damping mode， abnormal-damping mode， and hard-stopping mode.Among them， the hard-stopping mode can provide a temporary protection for a wounded tail rotor drive shaft. In addition， the influence of the initial gap， collision stiffness and the critical friction force on the working performance of the damper has been illustrated. There is an optimal critical friction force associated with each unbalance quantity. Besides， in the hard-stopping mode， the vibration amplitude can be reduced by increasing the collision stiffness between the rubbing ring and the base， which could also induce a greater impact. Moreover， prototypes of the hybrid damper are designed， manufactured and tested on a shaft test rig. The simulation results are well verified by the experiments.