A Linear Model of a Free-Piston Vuilleumier Machine Compared to Experimental Results of a Prototype

A linear model to predict the dynamics of a free-piston Vuilleumier machine will be presented. The model is based on the linear analysis of free-piston Stirling engines by Berchowitz /4/, where both the motion of the casing and the viscous coupling between the displacers are considered. Closed-form solutions are derived for the frequency, the phase angle and the amplitude ratio. In order to determine the accuracy of the results, they will be compared to the experimental data of a prototype.