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In order to achieve stable operation of the free-piston engine generator, the forces status on the free-piston of the working process were analyzed. The results showed that the operation of the free-piston engine generator could be seen as a single degree of freedom damping system with forced excitations. Combining the energy conservation principle of the working process, the matching between the structure parameters and the performance parameters of free-piston engine generator was studied. Some necessary qualifications to achieve stable operation of the free-piston engine generator were obtained through coupling analysis calculation by using an energy equilibrium method. The analysis conclusion was validated on a prototype by simulation. The results showed that the movement of free-piston could reach stable operation approximately, and the coupling analysis method proposed was reasonable.