### Overview

In order to prevent mechanical problems during high-speed rotation, it is necessary to realize a highly accurate design considering the tradeoff between the centrifugal force at high-speed rotation and torque. For this, FEA is essential for accuracy, and it is recommended to use a genetic algorithm as a tool to deal with the trade-off.

In this example, presented where a rotor geometry is designed by a multi-objective genetic algorithm with objective functions for torque characteristics (5,000 r/min) and for the stress due to the centrifugal force at high-speed rotation (10,000 r/min).

### Optimization Conditions

Fig. 1 shows the design variables, and Table 1 shows their ranges and evaluation items. Six design variables are chosen for the rotor geometry design variables. The position of the magnet, the geometry of the magnet, and the geometry of the flux barrier are considered to have a large influence on von Mises stress and torque, and are parameterized.

In this analysis the goal is to achieve high torque at 5,000 r/min and low von Mises stress in the rotor at 10,000 r/min. Therefore, the performance vs. rotor geometry is evaluated using the two evaluation items.

### Optimization Results

Fig. 2 shows the results of a multi-objective optimization using a genetic algorithm with the von Mises stress maximum value and average torque used for objective functions. When comparing the first and tenth generations, a performance improvement can be confirmed. In the 10th generation, it can be seen that there is a trade-off between von Mises stress and torque.

In the first generation, pay attention to case (1) having the smallest von Mises stress and case (2) having the largest average torque. Cases A and B, tenth generation cases having the maximum average torque for approximately the same maximum von Mises stress as cases (1) and (2) respectively, are shown in Table 2. Although the maximum von Mises stress is approximately the same value, it can be seen that the average torque improves by about 36 % between (1) and A, and by about 15 % between (2) and B.