A dynamic model of an asymmetric system is developed with limiter under heave conditions to explore the impact characteristics of a marine rotating machinery coupled airbag-floating raft-limiter systems. The steady-state response of the system is numerically solved using the Runge-Kutta theory. Nonlinear dynamic analysis methods, including energy trajectories and time-averaged energy diagrams, have been introduced to examine the influence of rotor speed, heaving amplitude, limiter clearance, and contact stiffness on the dynamic characteristics of the system. The results show that the amplitude of the heave increases, the system collides with the limiter, resulting in a significant reduction in amplitude. Meanwhile, the dynamic behavior of system transitions from quasi-periodic motion to chaotic state. After the impact, the energy of the system begins to concentrate in the region of impact, and the higher the time-averaged energy value, the more severe the impact of the system. The method proposed in this paper can provides an optimization scheme and theoretical reference for the impact problem of this system.