A three dimensional rate equation model for the dynamical sensing effect of magnetostrictive Galfenol

Abstract

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Modeling a Galfenol based stress sensor capable of sensing up to three axial stresses

“…minimums in the free energy. 7,9,[14][15][16] The total magnetization of a material is the vector sum of the magnetic moments residing at each preferred orientation. The fraction of the total number of moments aligned with the ith preferred orientation will be denoted by n i , and referred to as the preferred orientation fraction, which will be treated in the Stoner-Wolfarth model.…”

“…The fraction of the total number of moments aligned with the ith preferred orientation will be denoted by n i , and referred to as the preferred orientation fraction, which will be treated in the Stoner-Wolfarth model. In this notation, the total magnetization in the system is then 14,15 …”

“…The moment vector is dependent on both magnetic field and stress because they modify the free energy surface and hence the location of the local minimums. 14,15 In order to find the time evolution of the total magnetization, one must first determine the time evolution of the magnetic moment fractions. In the rate equation model, 14,15 the rate of change of the ith preferred orientation fraction is given by…”

“…There exist a number of methods to do this. 7,[9][10][11][12][13][14][15] The rate equation model 14,15 is well suited to the task because it is three-dimensional, dynamic and requires fitting few parameters. In addition, it can model nonlinearity and hysteresis naturally and will therefore have the ability to model a larger range of stresses and frequencies, increasing the range of applicability of the device.…”

“…In the following work, the prototype system will be introduced first; then a previously developed 14,15 three dimensional rate equation model will be summarized. Next, it will be shown that, in principle, by applying a series of magnetic field biases and measuring all components of the resulting magnetization, one can determine all six stress components (axial and shear) acting on the material if they are periodic.…”