268 – SPM Motor Teeth Geometry Topology Optimization

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Model Data

Overview

Basic policies for motor design are the maximization of torque and low oscillation. The smaller the torque ripple, the lower the vibrations of the motor. Torque ripple is generally affected by stator teeth geometry. Due to the complexity of the magnetic flux distribution in gap vicinities, expressing detailed teeth geometry with magnetic equivalent circuits can prove to be of considerable difficulty.
Performing optimization that uses FEA capable of analyses based on actual geometry can be effective in satisfying these requirements. Optimization results can be obtained with a high degree of freedom because topology optimization additionally performs searches that are not dependent on initial geometry.
In this example, the on / off method is used to search for stator teeth geometry that maximizes average torque and minimizes torque ripple with the entire areas of stator teeth tips as the design region.

Optimization Conditions

Fig. 1 shows the design region, and Table 1 shows the evaluation items and objective functions.
As shown in Fig. 1, the design region is the stator teeth parts, which are considered to have a large influence on torque and torque ripple.

Optimization Results

Fig. 2 shows a correlative diagram between torque average value and torque ripple rate, and Fig. 3 shows a larger view of the range for the maximum torque and minimum torque ripple from Fig. 2. In Fig. 3, the maximum torque average value is shown at point A as the best case, and the minimum torque ripple rate is shown at point B.
Topology optimization geometries for best cases A and B are shown in Fig. 4 and Fig. 5 respectively.
For best case A which has the largest torque, materal inside the teeth consists entirely of magnetic steel sheets. The presence of slot opening parts can also be observed. Conversely, for best case B which has the lowest torque ripple, air regions are included inside the teeth. Teeth are additionally connected around the entire arc, and there are no slot opening parts.

Sensitivity Analysis

In order to confirm the influence of teeth geometry on characteristics, sensitivity analysis is performed for each best case.
Consider best case A, which has the largest average torque. Analysis patterns are shown in Table 2, and analysis results are shown from Fig. 6 to Fig. 8. For the model featured in this document, it is understood that teeth geometry has no effect on torque. Rather, only the width of the slot opening part has an effect on torque.
Consider best case B, which has the lowest torque ripple rate. Analysis patterns are shown in Table 3, and analysis results are shown from Fig. 9 to Fig. 11. It is understood that the presence or absence of teeth part air regions has an effect on the torque ripple rate.

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