Figure 1 shows the flow of topology optimization by genetic algorithm. Here, the coding format is coding with a normalized Gaussian function network [2] and the genetic algorithm is simplex crossover [3].

The objective function is defined as follows

The first term is the objective function to minimize the mass, and the second term is a penalty function to ensure that the average torque is greater than or equal to the target torque. If the average torque is lower than the target torque, the penalty is added linearly.

Figure 2 shows a cross-sectional view of the IEEJ D model [4]. The IEEJ D model is used as the base model. The red area in Figure 3 indicates the design region. The target torque τ_des is the average torque of the base model, and the structure of the rotor core in the design region is optimized.

Figure 4 shows the mass and average torque of the rotor core for each gain K. Figure 5 shows the rotor geometry for each gain K. When the gain K is small, the rotor core is almost nonexistent and the average torque is small compared to the target torque. For small gain K, the rotor core is almost nonexistent and the average torque is small compared to the target torque. On the other hand, when the gain K is sufficiently large, a lightweight structure with an average torque near the target torque is obtained. From this, it can be said that this method can obtain the target shape if the gain K is sufficiently large, although the gain K must be set by the designer.

For the lightweight design of electromagnetic motors capable of outputting a designer-independent target torque, we proposed an optimization that explicitly includes mass in the objective function and average torque in the constraints as a penalty function. Optimization for the rotor core resulted in a lightweight rotor core structure with an average torque equivalent to the target torque.

In this study, we have previously worked on weight reduction [3] using topology optimization of the IPMSM rotor core by the ON/OFF method using NGnet, using the IEEJ D model [2], a 3-phase, 4-pole, 24-slot IPMSM, as the comparison target. In this effort, it was noted that if the optimization results were not modified, the core would be difficult to machine as a component. Table 1 shows the specific issues and possible solutions. In this presentation, we describe the smoothing of contours and the addition of necessary parts. First, the contour is extracted as a node from an image of a rotor shape using the image processing library OpenCV. The Ramer-Douglas-Peucker algorithm [4][5] is applied to the extracted nodes to smooth the contours. Nodes set along the circumference of the shaft are then added, and the necessary components are added by applying the algorithm [6] to create a contour that encompasses the point cloud.

Figures 1-4 show the original shape, the result of smoothing, the result of adding necessary members, and the result of smoothing + addition of necessary members, respectively. From these figures, it can be confirmed that the proposed method succeeded in smoothing and adding the necessary members. Figures 5~7 show the results of comparing the average torque, torque ripple, and rotor core mass before and after approximation. These figures show that the average torque and torque ripple remain almost the same as before approximation. On the other hand, the mass of the rotor core has increased.

In this presentation, we propose a method to approximate the shape of the IPMSM rotor core using image processing techniques to solve the problems of fine irregularities in the contour of the rotor core and the separation of the motor shaft and the rotor core, respectively. The proposed method was applied to the optimization results of the IPMSM rotor core obtained in this study, and the performance after shape approximation was analyzed and compared with that before approximation. The results confirm the effectiveness of the proposed method.