# Energy Consumption Characteristics for Design Parameters of Permanent Magnet-Based Al Billet Heater
## 4 Heating Characteristic Effects on Design Parameters
### Heating Effect for Billet Assemble Eccentricity  
In this section, the characteristics of the eccentricity of the billet heater using permanent magnets that can occur as the billet rotates were analyzed. To that end, numerical analysis models were configured by changing the clearance between the billet center and the billet heater center. The eccentric distances were applied at 0.5 mm intervals in the range of 0-2 mm in consideration of the internal air gaps. The billet heating characteris  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **Case01** & **Case02** & **Case03** & **Case04** & **Case05** & **Case06** \\ \hline Outer Radius [mm] & 46.60 & 46.93 & 47.26 & 47.60 & 47.93 & 48.27 \\ \hline Inner Radius [mm] & 30.50 & 31.00 & 31.50 & 32.00 & 32.50 & 33.00 \\ \hline Clearance [mm] & 0.50 & 1.00 & 1.50 & 2.00 & 2.50 & 3.00 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Configuration clearance and radius dimension for construction model.  
Figure 12: Analysis result with different clearances—torque, heating time, and energy consumption graphs for case model.  
tics were analyzed by applying the arrangement of 4 and 12 permanent magnets to the tangential model.  
When the rotary induction heating system was driven with eccentricity given to the billet and the heating object, the trend of flux linkage was changed due to a change in the flux density of the air gap. A change in the flux linkage changed the trend of loss by magnetic flux density, current density, and eddy current. The change in the magnetic flux density as a result of the electromagnetic-thermal analysis according to different eccentric distances is shown in Figure 13. As shown in Figure 13, the maximum current density in static eccentricity was 7.36 \(\times\) 10\({}^{7}\) A/m\({}^{2}\); however, as the eccentric distance was increased by 0.5 mm, the maximum current density was increased to 7.45 \(\times\) 10\({}^{7}\), 8.17 \(\times\) 10\({}^{7}\), 8.28 \(\times\) 10\({}^{7}\), and 8.89 \(\times\) 10\({}^{7}\) A/m\({}^{2}\), respectively. A higher current density asymmetrically occurred on one surface owing to the change in the clearance between the permanent magnet and billet caused by the eccentricity of the rotation of the billet.  
The increase in the current density inside the billet also affected the power loss. To analyze the power loss in the billet, the mean power losses in the billet are shown in Table 6. The power losses in the billet in static eccentricity (eccentricity of 0 mm) where the stator and rotor rotate coaxially were 3.23 and 3.49 kW and those in the dynamic eccentricity (eccentricity of 2.0 mm) were 3.29 and 3.90 kW, respectively. That is, it was confirmed that the power loss increased by about 1.79% in the four permanent magnets to the tangential model, and increased by about 10.51% in the 12 permanent magnets to the tangential model when an eccentricity of 2 mm was applied at a clearance of 2.5 mm.  
Since eccentricity can increase the power loss by decreasing the clearance, the heating efficiency was improved. However, as shown in Table 6 and Figure 14, the size of the ripple increased due to the asymmetry of magnetic force, and there was a risk of mechanical vibration and noise.