# From Modeling to Failure Prognosis of Permanent Magnet Synchronous Machine
## 4 Aging of PMM's Components
### Aging of the Magnet
\begin{table}
\begin{tabular}{c c c} \hline
**Time (year)** & **Brnew (Tesla)** & **Hcnew (A/m)** \\ \hline
1 & 0.92728 & 419,161 \\
5 & 0.5644 & 280,540.8 \\
10 & 0.1108 & 107,265.6 \\
14 & \(-\)0.25208 & \(-\)31,354.6 \\ \hline \end{tabular}
\end{table} 
Table 7: Effect of magnet aging on its Br and Hc (150 \({}^{\circ}\)C). In the end of this section, we conclude that tracking the aging of the dynamic and sensitive components inside the machine is not of big interest during normal operation because the life cycle of these components is much greater than that of the electric machine itself. However, studying and considering this aging, when a fault occurs, is very important because this will largely influence the machine's health operation. 5 Estimation Strategy of RUL Calculation Using Thermal FEM in the Case of Turn-to-Turn Short Circuit  
As explained previously, the aging and performance of critical components in the PMM are highly affected by temperature. The aging equation for the coil insulation is noted. The phases of the magnet function of temperature are noted. In this section, we will take advantage of the detailed knowledge of the machine's thermal aspect and its well-developed thermal FEM, combine it with the aging equations, and elaborate the appropriate RUL for the insulation and magnet phase in the case of turn-to-turn short circuit. The proposed strategy will solve and answer two questions: what is the remaining useful life of insulation? And, in which slot will the next turn-to-turn short circuit fault occur? In other words, at the end of this analysis we will get the time we still have before insulation, in specific areas, deteriorates and causes a new turn-to-turn short circuit fault. A block diagram presenting the steps of this strategy is illustrated in Figure 26.  
An illustrative example clarifying the prognostic approach and the RUL calculation in the case of turn-to-turn short circuit will be presented in Figure 27. The sensor's data will be collected. The prognostic approach (HMM) will investigate this data and elaborate the state of the machine. If a turn-to-turn short circuit is detected in the electric machine, the thermal FEM will be conducted, where the phase of the magnet and the remaining useful life of the insulation are elaborated. The location of the next turn-to-turn short circuit that will occur in the machine will be identified also. The thermal FEM is capable of determining temperature in the whole machine. As stated in the previous section, the critical machine elements whose performance is directly related to the operating temperature are the magnet and the stator coil. Hence, when a turn-to-turn short circuit fault occurs, the higher temperature at the magnet and coil level is noted. The RUL of insulation is calculated using insulation aging Equation (11) from the previous section. The new 'Br' of the magnet due to the increase of its temperature is calculated using the aging magnet Equations (12) and (13). Figure 25: The change in air gap flux density with magnet aging (150 \({}^{\circ}\)C). _Appl. Sci._**2020**, _10_, 691  
Figure 26: RUL calculation in the case of turn-to-turn short circuit.