# From Modeling to Failure Prognosis of Permanent Magnet Synchronous Machine
## 4 Aging of PMM's Components
### Aging of the Magnet  
Several factors affect the stability and performance of magnets: temperature, change in reluctance, external magnetic fields, radiation, and vibration. The magnet used in our machine is neodymium iron boron (NdFeB). The most common temperature related parameters for NdFeB are mentioned in Table 5, [35]. NdFeB loses approximately 0.11% of its remanence 'Br' and 0.4% of its coercive force 'Hc' for every degree Celsius above 20 \({}^{\circ}\)C. Rare earth magnets may face three types of losses; each type moves the magnet to a specific phase [36]. Reversible losses: They can be defined as temporary loss of the magnet's magnetic force. These losses can be reversed when the magnet returns to its normal original temperature. Reversible losses are expressed by the reversible temperature coefficient, -%Br/\({}^{\circ}\)C.  
Irreversible losses: These losses are defined as a partial demagnetization of the magnet due to exposure to high or low temperatures or other demagnetizing simuluses. These losses are only recoverable by re-magnetization and are not recovered when the temperature returns to its original value. This occurs when the magnets are operating at temperatures higher than the identified \"maximum operating temperature\" or when the operating temperature of the magnet reaches a minimal value. Permanent losses: They occur when magnets are exposed to extremely high temperatures that are usually as high as the initial heat treatment when they were manufactured. This is called the magnet's Curie temperature. In this case, the magnetic properties are not recoverable to its initial state even after re-magnetization. The effect of time on modern permanent magnets is minimal. Figure 24 shows the percentage decrease of Br function of time when the maximum operating temperature of the magnet is 100 \({}^{\circ}\)C and 150 \({}^{\circ}\)C.  
Figure 23: Aging graph of windings insulation. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **NdFeB** \\ \hline \(\alpha\), Temperature coefficient Br \%/\({}^{\circ}\)C & 0.11\% \\ \(\beta\), Temperature coefficient Hc \%/\({}^{\circ}\)C & 0.4\% \\ Maximum operating temperature \({}^{\circ}\)C & 180 \\ Tc \({}^{\circ}\)C & 300–400 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: NdFeB temperature related parameters. There is no aging equation for magnet relating its remanence flux density 'Br' to its temperature and operating time. However, an approximate analytical equation can be deduced from experimental graphs like the one in Figure 24. The curves are approximately a straight line. At 100 \({}^{\circ}\)C, the equation of the curve is expressed in (21); at 150 \({}^{\circ}\)C, the equation of the curve is expressed in (22) [37]. \[\%Br=-0.0002\;t(hours)-1 \tag{21}\]  
\[\%\;Br\;loss=-0.0035\times time-1 \tag{22}\]  
Table 6 shows the effect of magnet aging on Br and Hc, under healthy conditions. Table 7 shows the effect of magnet aging at 150 \({}^{\circ}\)C.  
As we can see, at 100 \({}^{\circ}\)C, there is small remarked degradation of Hc and Br with time. The degradation worsens if the temperature at the magnet level increases. The numbers in Table 6 detect a pace acceleration in Br and Hc. The negative values indicate a complete deterioration of the magnet. The air gap flux density of the machine function of aging, in the faulty case, is illustrated in Figure 25. As we can see, the air gap flux density degrades radically at 150 \({}^{\circ}\)C. This will greatly affect the performance of the machine since the machine's torque is directly proportional to the average air gap flux density. \begin{table}
\begin{tabular}{c c c} \hline
**Time (year)** & **Brnew (Tesla)** & **Hcnew (A/m)** \\ \hline
1 & 1.1052048 & 646,594.592 \\
5 & 1.086024 & 635,372.96 \\
10 & 1.062048 & 621,345.92 \\
14 & 1.0428672 & 610,124.288 \\ \hline \end{tabular}
\end{table} 
Table 6: Effect of magnet aging on its Br and Hc (100 \({}^{\circ}\)C). Figure 24: Magnet’s flux loss versus time at different temperatures [38].