## 3 Results of Magnetic Measurements and Discussion
### AC Properties
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Total (W/kg)** & **Hysteresis (W/kg)** & **Eddy (W/kg)** & **Excess (W/kg)** \\ \hline Annealed, 1 T & 8.17 & 0.95 & 6.26 & 0.96 \\ Unannealed, 1 T & 14.17 & 3.65 & 7.85 & 2.67 \\ Annealed, 1.5 T & 83.7 & 2.81 & 74.3 & 6.59 \\ Unannealed, 1.5 T & 47.3 & 7.18 & 37.6 & 2.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Segregated iron losses at 50 Hz. Figure 9: Total iron losses as a function of magnetization of both the annealed and unannealed toroid in the magnetization range of \(\sim\)0.9–1.5 T: (**a**) 1 Hz, (**b**) 10 Hz and (**c**) 50 Hz. The hysteresis loss reduction after annealing is well documented [28; 30] and can mostly be attributed to the material grain growth and the relief of internal stress. The segregated losses confirm the reduction of hysteresis losses after the annealing process: dropping by 74% at 1T and 61% at 1.5 T. In general, the classical eddy current losses are shown to increase after annealing [31]. In this study the eddy current losses however decreased by 20% at 1 T and approximately doubled in magnitude at 1.5 T after the annealing process. The authors propose the effect of nonlinear saturation losses to explain for this phenomenon. Presently, formation of eddy currents in silicon steel has widely been studied and modelled mostly for laminated structures and for non-saturated conditions, complicating comparisons with an analytical model (such as the Bertotti model) [32]. In deep saturation, a new loss component of nonlinear saturation losses should be considered in addition to the classical loss components of hysteresis, classical Foucault eddy current and excess eddy current losses [33; 34; 35; 36]. This loss component would help to explain the decrease in eddy current loss at 1 T (annealed sample not saturated) and the increase at 1.5 T (both saturated, but the annealed sample magnetized at 1.5 T at considerably higher magnetic field strength) after the annealing process. Excess losses can be related to the microscopic eddy currents arising from the domain wall motion, and they have been shown to increase with domain (also grain) size [37]. In this study, as the segregated excess losses were not calculated separately, they incorporate the eddy and hysteresis losses calculation error as well. The classical eddy current error of calculation can mostly be the result of inhomogeneous resistivity of the material due to internal cracking and porosities, which complicates accurate estimation of the eddy current generation in the entirety of the toroid in the FEM simulation. The proportion of the post-annealed excess loss can be considerably more from the estimation, due to extensive grain growth and underestimated resistivity of the cross-section of the toroid (due to porosities and cracks present in the printed material). Despite limitations however, the segregation process gave a rough estimation on the magnitude and contribution of each of the loss type on the total losses, confirmed by extensive Foucault eddy current losses in the printed bulk material and suggesting next steps for the reduction of iron losses in the printed material. Additionally, the determination of the behavior of each loss component in saturated state is planned as future work due to its significant impact on 3D printed material performance, especially with the potential material oversaturation due to the reduced filling factor in partitioned material designs discussed in the next chapter.