Investigation of magnetic spring stiffness characteristics in magnetic resonance linear compressors for pulse tube cryocoolers

Magnetic resonance linear compressors play a critical role in the miniaturization and reliability enhancement of miniature cryocoolers. In this study, a finite element analysis system is employed to investigate the mechanism of the magnetic spring effect in magnetic resonance linear compressors. Furthermore, the magnetic spring force of the linear compressor was measured through experimental testing. The experimental results are compared with simulation outcomes, validating the reliability of the simulation model. The magnetic spring effect caused by electromagnetic–mechanical coupling in magnetic resonance linear motors is studied through finite element simulation and experimental verification. The results reveal asymmetric stiffness characteristics, stroke dependence, and frequency independence in magnetic spring behavior. Quantitative analysis of stiffness nonlinearity across displacement ranges is conducted via static and dynamic magnetic spring tests. Experimental data demonstrate: under static conditions, magnetic spring stiffness increases from 28.9 N/mm to 37.4 N/mm (an increase of 29.4 %) during compression (0 to +7.4 mm), and from 21.5 N/mm to 34.1 N/mm (an increase of 58.6 %) during expansion (-15 mm to 0 mm). Dynamic conditions show resonant frequency increasing with stroke magnitude, validating displacement-dependent stiffness. At 7 mm stroke, the relative error between theoretical equivalent stiffness (24.6 N/mm) and frequency-scanned measured value (24.5 N/mm) is merely 0.58 %, confirming the feasibility of predicting dynamic stiffness using static test results. Furthermore, the integration of the magnetic resonance linear motor into the pulse tube cryocooler demonstrates the feasibility of applying magnetic resonance linear motors in miniature cryocoolers.