Effect of Grain Size on Magnetic Loss of Nanocrystalline Alloy Under High-Frequency Non-Sinusoidal Excitation

Abstract

To investigate the effects of internal microstructure and high-frequency non-sinusoidal excitation on the magnetic loss of nanocrystalline alloy, a three-dimensional mesoscopic model based on G. Herzer’s theory of random anisotropy is developed. First, the AC test platform is used to measure the loss value of the nanocrystalline alloy under sinusoidal excitation, and then the model is subjected to the same excitation to obtain its loss value. These values are compared to verify the model’s accuracy. Using the micromagnetic model provided by OOMMF software, we investigate the microscopic effect of grain size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> on the high-frequency magnetic loss <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> of nanocrystalline alloys. Next, we apply non-sinusoidal alternating magnetic fields (square wave, trapezoidal wave, and triangular wave) to the model to explore <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> under non-sinusoidal excitation. The results show that as the grain size <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> of the nanocrystalline alloy increases, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> also increases. Additionally, when <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">d</i> and the frequency <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> are held constant, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">v</sub> is greatest under triangular wave excitation, followed by trapezoidal wave excitation, and smallest under square wave excitation. This conclusion is due to the fact that the equivalent frequency <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eq</sub> , which contains the rate of change of magnetic flux density (d <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> /d <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> ), can replace <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> in the Original Steinmetz Formula when the excitation source is non-sinusoidal. Our calculations indicate that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">f</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eq</sub> is smaller under square wave excitation than under triangular wave excitation.