The root locus method showed reasonable predictions with an operation criterion of the PP–DP phase angle of 90°. The 1-DOF vibration model was found to be simple and effective for predicting the operating frequency and charge pressure of FPSE. As a result, both prediction models showed good agreements with experimental results. We developed a test FPSE for verification of the dynamic models and conducted a series of experiments to measure the dynamic behaviors of PP and DP under varying charge pressures for various masses and stiffnesses of the PP. The dynamic models of FPSE we considered are the 1-DOF simple vibration model of each piston and the 2-DOF root locus model of coupled pistons.
The equations of motion of the FPSE are formulated as a 2-degree-of-freedom (DOF) vibration system of the power piston (PP) and displacer piston (DP), based on the state equation of ideal gas and the isothermal Stirling cycle model. This paper presents a linear dynamic analysis on operable charge pressure and working frequency of free-piston Stirling engines (FPSE) along with experimental verifications.
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