REFLECTIONS ON FREE-PISTON STIRLING ENGINES, PART 2 - STABLE OPERATION

In this paper a ne cv linearization technique of the dynamic balance e quations of a free-piston Stirling machine is developed. It takes acco unt of the nonlinear thermo-fluid-dynamic terms inherent in the machin e, while keeping the linearity of the differential dynamic equations. This allows the equations of motion to be solved analytically and, the refore, it allows the algebraic relations linking the various machine parameters, established in a companion paper, to be suitably used. The casing motion is also considered. The following advantages are relate d to the proposed linearization methodology: 1) It gives the correct i nterpretation of the machine response to variations in the operating c onditions because the considered nonlinear terms have a stabilizing ef fect that cannot be ignored; 2) it can be used to predict the machine performance not only with more accuracy than conventional linear dynam ic analyses that fully neglect the nonlinearities, but in a more exhau stive way, allowing the piston stroke and, therefore, the delivered po wer to be calculated; and 3) It enables the machine to be designed in the initial stages in such a way as to enhance its inherent stability. To illustrate these features,we have considered, as an example of a f ree-piston Stirling engine, the well-known Space Power Research Engine .