A Coupled Magnetomechanical Model for Magnetostrictive Transducers and its Application to Villari-Effect Sensors

A coupled magnetomechanical model for the design and control of Villarieffect magnetostrictive sensors is presented. The model quantifies the magnetization changes that a magnetostrictive material undergoes when subjected to a dc excitation field and variable stresses. The magnetic behavior is characterized by considering the Jiles-Atherton mean field theory for ferromagnetic hysteresis. This theory is constructed from a thermodynamic balance between the energy available for magnetic moment rotation and the energy lost as domain walls attach to and detach from pinning sites. The effect of stress on magnetization is quantified through a law of approach to the anhysteretic magnetization. Elastic properties are incorporated by means of a wave equation that quantifies the strains and stresses which arise in magnetostrictive materials in response to moment rotations. This yields a nonlinear PDE system for the strains, stresses and magnetization state of a magnetostrictive transducer as it drives or is driven by external loads. Because the model addresses the magnetomechanical coupling, it is applicable to both magnetostrictive sensors and actuators. Properties of the model and approximation method are illustrated by comparison with experimental data collected from a Terfenol-D sensor.