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This paper presents a linear dynamic analysis on operable charge pressure and working frequency of free-piston Stirling engines (FPSE) along with experimental verifications. 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. 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. 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. As a result, both prediction models showed good agreements with experimental results. The 1-DOF vibration model was found to be simple and effective for predicting the operating frequency and charge pressure of FPSE. The root locus method showed reasonable predictions with an operation criterion of the PP–DP phase angle of 90°. In addition, the FPSE was confirmed to operate in resonant oscillations when the DP–PP phase angle is 90°, based on analysis of the force vector diagram of the two pistons.

Linear Dynamic Analysis of Free-Piston Stirling Engines on Operable Charge Pressure and Working Frequency along with Experimental Verifications