Abstract：Stacked giant magnetostrictive actuators (SGMAs) have been widely used due to their high energy density, fast response speed, and convenience in providing a stable bias magnetic field. Due to the very low relative magnetic permeability of permanent magnets and giant magnetostrictive materials, there is obvious spatial distribution inhomogeneity in the magnetic circuit, and the magneto-mechanical coupling makes its dynamics more complicated than that of conventional actuators. Existing studies typically use magnetic flux leakage coefficient and traditional single-degree-of-freedom model to describe magnetic leakage behavior and dynamic output characteristics, which cannot accurately calculate the magnetic field intensities nor characterize the uneven mechanical distribution characteristics of the SGMA. To address these issues, this paper built a multi-physics model considering magnetic flux leakage to predict the output characteristics of SGMA accurately. Firstly, an equivalent magnetic circuit (MEC) model is built based on the results of finite element simulation. The distribution of magnetic field lines inside the actuator can be analyzed and the types of flux transistors can be divided through the finite element simulation results, combining with the SGMA internal structure and related dimensional parameters, the relevant magnetoresistance in the MEC can be calculated completely, which completes the coupling of the electro-magnetic domain and characterize the inhomogeneity of the magnetic field inside the actuator fully. Secondly, the magnetization process is completely modeled with the classical Jiles-Atherton model, and the coupling of the magneto-mechanical domain is completed by the nonlinear constitutive model. Thirdly, based on the traditional single-degree-of-freedom model, the structural dynamics model considering distribution effects is established by rederiving the equivalent mass with the help of the kinetic energy theorem, which reflects the force and strain distribution caused by magneto-mechanical coupling of different GMM rods. Finally, with the assistance of Pspice circuit simulation software, a multi-physics coupling dynamics model of SGMA is established and the actuator output displacement is solved. In addition, an SGMA prototype is fabricated and an experimental platform for displacement measurement of SGMA is constructed. Compared with the experimental data and this purposed model results of the input-output characteristics of the SGMA at different frequencies, the calculated results of the model were in good agreement with the experimental results, the maximum absolute error of the output displacement at the maximum excitation current is 0.54 μm, and the relative error is about 9.3%, suggesting that the proposed multi-physics dynamic model can accurately predict the tracking behaviors of the SGMA prototype to the excitation signals and describe its dynamic output characteristics, and fully characterize the attenuation and hysteresis variation trend of actuator output displacement effectively. Through further discussion of this purposed model, the influence of magnetic flux leakage and strain distribution on the output displacement of the SGMA is analyzed, and the necessity and accuracy of the magnetic flux leakage modeling and the dynamic model considering the mechanical distribution characteristics in this paper are verified. The following conclusions can be drawn from the discussion above: compared with the traditional multi-physics coupling model of the actuators, the proposed model in this paper can more accurately analyze the magnetic flux leakage behavior in the magnetic circuit and reflect the mechanical distribution characteristics caused by the non-uniform magnetic field.
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2023, Vol. 38 
