To improve the modeling and design accuracy of electromagnetic devices made from nanocrystalline materials under varying temperature conditions

this paper proposes a Steinmetz loss prediction model for nanocrystalline materials under varying temperature conditions. Initially

a temperature-variable magnetic property testing system

consisting of a thermostatic chamber and a BROCKHAUS soft magnetic measuring instrument

was set up to measure the magnetic properties of nanocrystalline materials in a frequency range from 1 kHz to 20 kHz and temperatures from 25 ℃ to 125 ℃. The results indicate that the saturation magnetic flux density of nanocrystalline materials is linearly negatively correlated with temperature; the linear fitting equations between saturation magnetic flux density and temperature across different frequency ranges have the same slope of −0.001

indicating no coupling relationship between frequency and temperature. The loss corresponding to saturation magnetic flux density points has a nonlinear relationship with temperature

decreasing as temperature increases. Furthermore

the magnetic flux density term in the classical Steinmetz formula was modified from a constant to a variable linearly changing with temperature

and a quadratic temperature correction term was derived to represent the nonlinear relationship between loss and temperature

and a Steinmetz loss prediction model applicable to the saturation stage of nanocrystalline materials was established. Finally

the parameters of the improved Steinmetz loss prediction model and the classical Steinmetz formula were fitted using the trust-region-reflective optimization algorithm. The proposed loss prediction model can achieve an average prediction error of 0.62% and a maximum prediction error of 2.66%

compared to the classical Steinmetz loss model's average prediction error of 5.26% and maximum error of 14.85%. The results validate the high-precision prediction capability of the proposed model under varying temperature conditions

providing a theoretical basis and data support for saturation control and design optimization of electromagnetic equipment.