Analysis of dynamic behavior and machine performance on a free-piston-type Vuilleumier cycle heat pump

A method used in analysis of dynamic behavior and machine performance on a free-piston-type Vuilleumier cycle (FPVM) machine is constructed as a nonlinear numerical model, because of a force acting on the surface of the moving part from a working gas and viscous damping due to the working gas flow. This model consists of three equations of motion for a hot displacer, a cold displacer and a casing, which are solved simultaneously by the Adams-Moulton method, and an equation of the instantaneous working gas pressure obtained on the supposition of an isothermal analysis on the Vuilleumier cycle machine. The cold displacer of the FPVM machine is combined with the hot displacer by a gas spring. A vibration model for those displacers is newly presented to verify a gas spring mechanism. In addition, self-excited vibration and forced vibration as to the FPVM heat pump are investigated.