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In this study, a numerical model of a gamma-type free piston Stirling engine (γ-FPSE) with a nonlinear load is developed and verified experimentally. A dimensionless parameter  δ  is proposed to define the critical oscillation state of the FPSE. The influences of the average pressure, heating temperature, spring stiffness of displacer and power piston on the critical oscillation point are investigated. The results prove that when  δ  is equal to 1, the power that is generated by self-oscillation of nonlinear load equals the sum of power dissipated by linear damping of pistons, load, and the power dissipated by pressure drop of heater, regenerator and cooler, the FPSE reaches the state of critical oscillation. Besides, for the cases of critical oscillation, the ratio of displacement amplitudes  χ  decreases with average pressure and heating temperature, but does not change with spring stiffness of displacer and power piston. Increasing average pressure, heating temperature and power piston’s spring stiffness contribute to achieve oscillation. However, increasing displacer’s spring stiffness inhibits the oscillation, the maximum displacer’s spring stiffness that can ensure FPSE’s oscillation are identified. In addition, because of the influence of nonlinear load, the nonlinearity of power piston’s displacement amplitude is more evident than that of displacer.

Parametric analysis on the critical oscillation point of a free piston Stirling engine with a nonlinear load