223 – Multi-Objective Optimization of IPM Motors Considering Stress at High Rotation

Application Note / Model Data


In an IPM motor, a permanent magnet is embedded in the rotor along with a flux barrier. The purpose of the flux barrier is to prevent the magnetic flux of a magnet from penetrating the magnetic poles of adjacent magnets and to efficiently convert the magnetic force into torque. Therefore, in order to increase the magnetic resistance of the magnetic path to the adjacent poles, it is desirable when trying to improve the torque to make the bridge portions thin. However, when designing with priority given to torque, problems with the strength of the bridges, which is not apparent at low-speed rotation, may appear such as breakage with high centrifugal force during high-speed rotation.
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.

Von Mises Stress Distribution

Fig. 3 shows the von Mises stress distribution for the geometries A and B in Fig. 2. With a thin bridge (B), it can be confirmed that the stress on the bridge tends to be high. Conversely, with the thick bridge (A), the von Mises stress is kept low, so it can be seen that maintaining the thickness of the bridge is effective in suppressing von Mises stress.

Magnetic Flux Flow in the Rotor

Fig. 4 shows the magnetic flux density distribution and magnetic flux lines for each geometry. For the thick bridge (A), it is thought that the magnetic flux flows through the bridge to the adjacent magnetic pole, causing a decrease in torque. On the other hand, for a thin slit (B), since the magnetic flux short-circuited inside the rotor is suppressed and flows to the stator, a high torque value is obtained.

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