A nonlinear model describing the dynamic, fluid dynamics and thermodynamics of a dynamically balanced Gifford-McMahon (G-M) cryorefrigerator was developed. The cryorefrigerator consists of two horizontally opposed first- and second-stage displacers, a first- and a second-stage thermal regenerator, and a rotary valve that cycles the compressor supply gas pressure. The model accurately describes the motion of the displacers and the refrigeration produced at the two stages of the cold head. The analytical model consists of a set of twelve first order nonlinear differential equations. The numerical solution of the system is presented in the form of pressure histories in each chamber, position and velocity histories of each displacer, and P-V diagrams of the two stages of the cold head. The performance of the cryorefrigerator is calculated under various conditions. It is clearly shown that the device can achieve non-impacting displacer motion with sufficient cooling capacities of the two stages. This non-impacting operation creates a very low vibration device, which is valuable in applications where low vibration is required, such as magnetic resonance imaging (MRI) systems. It was also shown that the cooling capacity of the device can be optimized over the operating frequency.

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