[APP2] Magnets, Electric power devices, Rotating machines

[APP2-06] Analytical Mechanics Approach to Motion Modeling on Actuator-driven Magnetic Refrigeration System

*Ryo Matsunaga¹, Shinnosuke Matsunaga^1,2, Kyohei Natsume², Koji Kamiya² (1. National Institute of Technology, Gifu College (Japan), 2. National Institute for Materials Science (Japan))

Keywords:

magnetic refrigeration,analytical mechanics

[Purpose]The magnetocaloric effect enables magnetic refrigeration, a next-generation cooling technology with low environmental impact and high efficiency. In active magnetic regenerative refrigerators, magnetic field variation is achieved by changing the distance between a magnetic material and a superconducting magnet. Accurate modeling requires coupling mechanics, heat transfer, and electromagnetic fields. This study applies analytical mechanics to develop a motion model for actuator-driven systems. [Method]We considered the motion of a magnetic body subject to forces from both a superconducting magnet and an actuator. The actuator force was designed as the sum of a canceling term for magnetic potential force and a divergent function inducing abrupt direction reversal at specified positions. Several candidate forms (polynomial, trigonometric, exponential) were tested, and an exponential form was chosen for sharpness and efficiency. The kinetic energy, magnetic potential energy, and actuator force were incorporated into a Lagrangian framework. The Euler–Lagrange equation was applied to derive equations of motion. Assuming negligible influence of the material on the field, the magnetic field B(z) was expressed analytically, leading to an actuator-driven formulation. [Results]The derived actuator force combines magnetic potential cancellation with a delta-like divergence function. The exponential form of the divergent function provided both sharp reversal and computational stability. The resulting motion model captures forced oscillatory behavior along the z-axis with controlled reversals. The formulation also enables comparison of different force functions and their influence on system dynamics. [Consideration]The model demonstrates the feasibility of constructing motion equations for actuator-driven magnetic refrigeration systems within the framework of analytical mechanics. While the current formulation neglects feedback from the magnetic material on the field, this assumption simplifies analysis and highlights actuator control. Further verification of derived equations and candidate function forms is ongoing, and parameter-specific studies will be pursued through numerical simulations. Incorporating the magnetocaloric effect will extend applicability to full magnetic refrigeration cycles. [Conclusion]An initial analytical mechanics model for actuator-driven magnetic refrigeration systems has been developed. The study evaluated force function candidates and identified an exponential divergent function as suitable for inducing sharp, position-controlled motion reversal. This approach provides a foundation for integrating magnetic, thermal, and mechanical interactions in future models and contributes to the development of efficient next-generation refrigeration systems.