## 6 Simulation
The fatigue tool uses Miner's rule to calculate the cumulative damage from vibration-induced stresses, factoring in both the amplitude of the stresses and the number of cycles that the component undergoes. The following are what these values represent:  
* **Expected life** indicates how many cycles the component is expected to endure before failure, given the applied vibration conditions;
* **Damage factor** shows how much cumulative damage has occurred on the component. A value of 1 means that the component is expected to fail, while values below 1 suggest that it is still within safe operating limits. Figure 8 illustrates that bond wires experience higher stress levels than other parts of the module, particularly at the knee points of the bond wires. A closer view in Figure 9 highlights that the minimum lifetime under these conditions is around \(2.14\times 10^{12}\) cycles. To convert the number of cycles to failure into real lifetime, the frequency of vibrations to which the IGBT module is subjected needs to be specified. The operational lifetime in seconds is then calculated using the following equation:  
\[Time\ to\ Failure=\frac{Cycles\ to\ failure}{Vibration\ frequency\ (\mathrm{Hz})} \tag{5}\]  
As outlined in Section 4, the maximum vibration frequency is due to the gearbox mesh at 1000 Hz. As a result, the calculated time to failure based on Equation (5) is \(2.14\times 10^{9}\) s, which is equivalent to 67.4 years. This suggests that the effect of vibration on the IGBT module lifetime is relatively minimal. However, it is important to note that, in real-world conditions, vibration is not the only stressor affecting the IGBT module lifetime. Factors such as thermal stress, electrical load cycling, and the 3 aging of the IGBT's internal components--like the semiconductor material and bonding--are likely to contribute much more significantly to its failure than vibration alone. In addition, environmental influences, including temperature fluctuations, humidity, and electrical current spikes, often play a more substantial role in the degradation of the IGBT module. Figures 10 and 11 present the damage distribution. These outputs show how the damage varies spatially within the IGBT module. This helps to identify which areas of the module are more prone to failure based on the applied cyclic loads. These figures indicate that the highest concentrations are observed at the knee points of the bond wires. The maximum damage factor is \(4.67\times 10^{-13}\simeq 0\), much lower than 1, indicating that vibration has an almost negligible effect on the IGBT module's overall lifetime. This suggests that the module is highly reliable under the simulated vibration conditions. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Deformation** & **1\(\sigma\) (68.27\%)** & **3\(\sigma\) (99.73\%)** \\ \hline Minimum (mm) & 0 & 0 \\ \hline Maximum (mm) & 9.74 \(\times 10^{-7}\) & 2.92 \(\times 10^{-6}\) \\ \hline Average (mm) & 3.02 \(\times 10^{-7}\) & 9.07 \(\times 10^{-8}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Minimum, maximum, and average deformation values for 1\(\sigma\) and 3\(\sigma\) studies. Figure 8: Lifetime distribution on the IGBT module. Figure 10: Damage distribution on the IGBT module. Figure 7: Deformation pattern of the IGBT module bond wire under vibration conditions. Figure 9: Knee points of the bond wires exhibiting the minimum lifetime (2.14 \(\times 10^{12}\) cycles).