As so to prevent mechanical issues from occurring during high-speed rotation for IPM motors, it is necessary to realize highly accurate designs accounting for the trade-off between torque and the stress that generates from centrifugal force at high-speed rotations. The phase at which maximum torque can be obtained will also change alongside changes to geometry, and it is necessary that optimization calculations account for this. FEA is essential for accuracy in these circumstances, and the use of genetic algorithms is recommended as a tool for handling the issues in this trade-off relationship.
In this example, the optimum current phase that achieves high torque per each geometry is obtained, and the torque characteristics (1,000 r/min) and stress due to centrifugal force at high-speed rotation (10,000 r/min) obtained with that optimum phase are both taken as objective functions for a multi-objective genetic algorithm used to carry out the optimization of rotor geometry.
Design variables in Fig. 1 are displayed in Table 1. 6 rotor shape design variables are selected. Magnet positions, magnet geometry, and flux barrier geometry that are considered to have a large influence on von Mises stress and torque are parameterized.
This time obtains geometry with high torque at 1,000 r/min and low von Mises stress within the rotor during rotations at 10,000 r/min. In accordance with this, 2 evaluation items shown in Table 1 are used and the performance of rotor geometry is evaluated.
Fig. 2 shows the result of multi-objective optimization using genetic algorithms with the maximum value of von Mises stress and average torque objective functions. Performance improvements can be confirmed from a comparison of all individuals from the initial and 10th generations. It can also be observed that von Mises stress and torque are in a trade-off relationship in the 10th generation.
The case with the lowest von Mises stress (1) and the case with the highest average torque (2) in the initial generation are emphasized. Cases A and B are 10th generation cases with the maximum average torque for approximately the same maximum von Mises stress as cases (1) and (2) respectively, and are shown in Table 2. While each have approximately the same maximum von Mises stress, it can be confirmed that average torque improves between (1) and A by 93 %, and by 16 % between (2) and B.
Selecting Rotor Phase
Fig. 3 shows a graph of the phase of each geography and torque. From the maximum phase geometry obtained from the torque formula, it is understood that the phase showing maximum torque differs. The phase showing the maximum torque value is shown in red.
Rotor Interior Magnetic Flux Flow
The magnetic flux density distribution and magnetic flux lines of each geometry are shown in Fig. 4. For thick-bridge geometry (A), it is thought that the magnetic flux flows through the bridge to the adjacent magnetic pole, causing a decrease in torque. Conversely, for thin-bridge geometry (B), a high torque value is obtained because the short-circuited rotor interior magnetic flux is suppressed and flows to the stator.
Von Mises Stress Distribution
The von Mises stress distribution of geometry A and B shown in Fig. 5. It can be confirmed that for thin-bridge geometry (B), there is a tendency for stress to be higher at those locations, while von Mises stress remains low for thick-bridge geometry (A). From this it can be observed that maintaining bridge thickness is effective in controlling von Mises stress.
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