The effect of nonlinear thermo-fluid-dynamic terms on free-piston Stirling machine stability

In this work a new linearisation technique of the dynamic balance equations of a free-piston Stirling machine is developed. It takes into account the nonlinear thermo-fluid-dynamic terms inherent in the machine, although keeping the linearity of the differential dynamic equations. This allows the equations of motion to be solved analytically and, therefore, useful algebraic relations (already established by the authors in past studies) linking together the various machine parameters to be used. The advantages related to the proposed linearisation methodology are the following: it gives a right interpretation of the machine working when the operational parameters vary, because the considered nonlinear terms have a stabilizing effect; it can be used to predict the machine performance not only with more accuracy, but especially in a more exhaustive way, also allowing estimation of the piston stroke and, therefore, the delivered power; and it enables design of the machine in such a way as to enhance its stability, thus eliminating the necessity of power control systems.