Modular Study of a Force-Magnetic Coupling System

TL;DR

This paper presents a modular approach to analyzing a magnetic-mechanical oscillating system, combining theoretical modeling, experiments, and simulations to understand its dynamics and vibration modes.

Contribution

It introduces a modular modeling framework for complex magnetic-mechanical systems, simplifying analysis and facilitating educational applications.

Findings

The system exhibits normal mode behavior with two degrees of freedom.

Experimental and simulation results align well with theoretical predictions.

Vibration modes and energy transfer patterns are clearly characterized.

Abstract

A magnetic-mechanical oscillating system consists of two identical leaf springs, a non-magnetic base, and some magnets. The leaf springs are fixed at the bottom to the non-magnetic base, while the magnet is attached to the top of the leaf springs. This paper investigates the overall motion characteristics of the magnetic-mechanical oscillating system. Adopting the modular modeling concept, we simplify the system into three inter-coupled modules: the leaf springs, magnetic interactions, and the system's dissipation process. We conduct physical modeling and theoretical analysis on these modules and derived the system's dynamic equations. The research indicates that the system is a normal mode system with two degrees of freedom. In addition, we alter parameters and conduct multiple innovative experiments, obtaining intuitive vibration images that characterize the vibration modes and the periodic energy transfer. Furthermore, we employ the simulation software COMSOL Multiphysics simulation to substitute the theory for auxiliary validation, achieving a comprehensive research loop of theory-experiment-simulation. The experimental results show good consistency with the theoretical calculations and simulation results. This research provides a good teaching case for magnetic-coupling complex systems. This modular analysis and rather practical experimental design could solve the previous difficulty that the solution to such problem is too complex, and is conducive to the implementation of education.