Linear dynamics theory adequately describes the behavior of Free Piston Stirling Engines (FPSEs). The aim of this paper is to predict the conditions for stable operation of FPSEs and the modeling of FPSEs. The linearization technique of the dynamic balance equations proposed recently by F. de Monte and G. Benvenuto has been applied using RE-1000 of Sunpower Inc. for a typical well known FPSE. The equations of motion are solved analytically in terms of the stiffness and damping coefficients of the machine. Using the criterion of the stable engine cyclic steady operation a rigorous mathematical form is obtained for the main parameters of the engine. The proposed model gives results close to the data coming from the literature and can be used to predict the thermal performance, the piston stroke and the delivered power. Furthermore, using for reasons of simplicity Schmidt Analysis (Isothermal model) the indicated output power is obtained. In addition, a reference is given to some of the most important thermal losses in the engine decreasing the theoretical performance up to experimental level.

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