The lightweighting of electromagnetic motors can lead to increased torque and higher power density, thereby contributing to overall improved performance. Historically, efforts to achieve lightweighting have centered on structural optimization [1], the use of lightweight materials [2], and even initiatives to move away from electromagnetic motors entirely [3]. In this study, our attention is drawn to the optimization in the pursuit of further reducing the weight of traditional electromagnetic motors. Topology optimization allows for the highest level of design freedom when it comes to shape optimization. Due to the extensive computational costs associated with such optimization, past research efforts have been confined to specific components, with studies focusing solely on the rotor [4] or just the stator [5]. In this presentation, our focus is on the stator. While previous research [5] had only optimized the shape and form of the stator's core, we propose a method that extends the optimization to include the windings. The effectiveness of this approach is validated through actual optimization results.

• Objective Function: The aim is to reduce the mass, with a constraint that τave ≥ τdes​ (i.e., the average torque should be greater than or equal to the target torque). In practice, this constraint is incorporated into the optimization problem as a penalty function. 

• Optimization Algorithm: (μ/μw, λ)-CMA-ES 

• Design Variables and Decoding Method: Method based on the Normalized Gaussian Network.

Figure 2 illustrates the concept. By determining whether the values from the two Normalized Gaussian Networks are greater than a certain threshold, we can differentiate between three states (represented in the figure as yellow, blue, and white).

Figure 4 shows the results when applied. The number of individuals in CMA-ES and the magnitude of the penalty function gain were taken as parameters, and the results of three runs for each are shown. These parameters influence the performance of the optimization, but they don't affect the physical design outcome of the optimization. By looking at the shape, it's clear that we obtained a design unlike any before. Furthermore, in terms of weight, we've managed to reduce it by 50% for the lighter designs and by about 30% even for the heavier ones. Also, as targeted, we can see that the performance hasn't changed.

In this study, we tackled motor weight reduction using topology optimization. In this presentation, we focused on the stator and proposed a method to optimize not only the shape but also the form of the winding without changing the winding area. The actual design results demonstrate its effectiveness. The weight was reduced to about half of the conventional one, while performance was maintained. Generating such "shapes beyond the imagination of traditional engineers" is the true beauty of entrusting design to computers. Moving forward, we aim to fully automate the entire motor design process.

[1] Zhang, X., et al., Mass Optimization Method of a Surface-Mounted Permanent Magnet Synchronous Motor Based on a Lightweight Structure, IEEE Access (2020).

[2] Rallabandi, et al., Coreless Multidisc Axial Flux PM Machine with Carbon Nanotube Windings, IEEE Transactions on Magnetics (2017).

[3] Sakai, K., et al., Ultralightweight motor design using electromagnetic resonance coupling, IEEE-ECCE (2016).

[4] Sato, T., et al., Multi-material Topology Optimization of Electric Machines Based on Normalized Gaussian Network, IEEE Transactions on Magnetics (2015).

[5] Choi, J. S., et al., Topology Optimization of the Stator for Minimizing Cogging Torque of IPM Motors, IEEE Transactions on Magnetics (2011). 

Through topology optimization, the enhancement of electromagnetic motors has been achieved. However, the designed shapes are based on the optimization mesh, resulting in many uneven and protruding parts, making them unsuitable for mechanical processing. Therefore, in previous studies [1][2], the obtained shapes have been manually adjusted and modified by engineers to be more suitable for machining. As a result, the discretion of the engineers interferes, undermining the benefits of using optimization in design. In this research, we are challenging this issue by algorithmically making these shape corrections, aiming to prototype and manufacture motors without the intervention of engineers.

In this presentation, we focus on the protruding and narrow areas. Figure 1 shows the shape obtained by topology optimization. As can be seen from the figure, the shape is obtained based on the mesh used in finite element analysis. In reality, the motor core is processed by press working, so sharp protrusions and thin bridge parts cannot be processed. Therefore, we proposed an algorithm to detect and correct these issues.

In this context, if the closed loop in which the line segment and node exist doesn't match, it can be identified as a narrow section. In this case, by adding points, we can create a sufficiently large difference. On the other hand, if they do match, it can be identified as a protrusion. In this scenario, by deleting beyond the point identified as narrow, we can eliminate the protrusion.

Figure 3 shows an example of the application to the results of topology optimization obtained from another project in our lab. On the left is the pre-application, and on the right is the post-application. As indicated by the blue circles, because it exists in a different closed loop, it's determined to be a narrow section, and we can see that the bridge part has become thicker. Moreover, the areas indicated by the red circles exist in the same closed loop and are thus determined to be protrusions and have been removed. From these results, we can confirm that the desired behavior is achieved, and it's demonstrated that this can be applied to real-world problems.

[1] 佐藤孝洋，五十嵐一，高橋慎矢，内山翔，松尾圭祐，松橋大器，“トポロジー最適化による埋込磁石同期モータの回転子形状最適化”，電気学会論文誌D（産業応用部門誌）,  Vol.135-3, pp.291–298, 2015. 

[2] 坂本宏紀，阿部崇史，“回転機のトポロジー最適化”，明電時報, vol.364, pp.42–46, 2019. 

Elementary Multidisciplinary Optimization of Workspace and Driving Mechanism to Reduce Weight of Industrial Robots

　In this research, the minimum link lengths and types of motors and reducers required to achieve the purpose of use are selected by considering the purpose of use from the design stage. We believe that this will enable us to design a lean manipulator and reduce the number of resources and energy required, and we will work on the optimal design of serial link manipulators. In doing so, we describe the method and results of optimizing the relative position of the manipulator to the target trajectory, link lengths, and types of motors and reducers, with the aim of reducing the overall mass of the manipulator by using multidisciplinary design optimization [1].

The optimization structure in this paper consists of a system-level optimizer for overall optimization and two sub-optimizers for region-specific optimization, as shown in Figure 1.

　The system-level optimizer outputs the length of the link that results in the optimal design by calculating and evaluating the mass based on the results of the two sub-optimizers, with the aim of reducing the overall weight of the manipulator. The objective function f(A) is defined as follows.

Suboptimizer 1 (geometric region) analyzes the trajectory based on the link lengths set by the system-level optimizer and outputs the relative position of the manipulator to the target trajectory using the degree of manipulability as a decision. The objective function f_1 (A_1 ) is defined as follows.

In sub-optimizer 2 (the dynamic region), dynamics calculations are performed using the link lengths and the results of sub-optimizer 1. The calculation results output the lightest combination of motor and reducer that satisfies the torque required to move on the target trajectory. The objective function f₂ (A₂) is defined as follows.

Table 3 shows the results of overall manipulator optimization by the system-level optimizer.

　A square trajectory was given as the target trajectory, and optimization was performed for each square side length and travel time. The larger the orbit size, the larger the overall system structure, and thus the mass tends to increase. In addition, the shorter the travel time, the greater the required drive speed and acceleration, and thus the greater the required torque, and the greater the mass of the drive mechanism to meet these requirements. Since the Co-bot that operates near humans without fences operates at low speed, the optimization result with a travel time of 2.0 s shows that the robot is lighter than a conventional general-purpose machine that weighs 40~50 kg.

This paper aims to select the link length and motor/reducer with the minimum mass that satisfies the target trajectory by using a multidisciplinary design optimization method to reduce the weight of manipulators.By comparing the optimization results with those of conventional products, it is shown that manipulators designed for human cooperation can be expected to be lighter than current designs.

[1] Mykel J.Kochenderfer, Tim A.Wheeler, 岸本祥吾, 島田直樹, 清水翔司, 田中大毅, 原田耕平, 松岡勇気, “最適化アルゴリズム”, 共立出版, pp.345–363, 2022.

In order to achieve the lightweight design of collaborative robots, efforts have been made to reduce the weight of electromagnetic motors, one of their constituent elements. In our research so far, we have been engaged in the optimal design by applying topology optimization with the objective of reducing the weight of the rotor of the IPMSM. Genmoto et al.'s study [1] introduced a multi-objective optimization method into the objective function of topology optimization, using an objective function that combines a function to minimize mass with a function to maximize average torque using a weighted sum. Furthermore, Genmoto et al.'s study [2] proposed treating the average torque as a penalty function while having a single objective for mass. As a result of these optimizations, a lightweight structure was obtained while maintaining the average torque. On the other hand, the challenge was that torque ripple increased.

In this paper, we propose a method to also achieve low torque ripple. We design the shape of the electromagnetic steel sheet of the rotor of the IPMSM using topology optimization so that it achieves the target torque while being lightweight and having low torque ripple.

In this paper, we use the Normalized Gaussian Network (NGnet) as a method for topology optimization [1][3]. Figure 1 shows the flowchart of topology optimization using NGnet in this study.

The objective function is defined as follows. The first term is the objective function to minimize mass, the second term is the objective function to minimize torque ripple rate, and the third term is a penalty function to ensure that the average torque is greater than or equal to the target torque. This is an objective function that introduces weight w for multi-objective optimization to minimize both mass and torque ripple, while considering average torque using a penalty function. Figure 2 shows the general shape of the Institute of Electrical Engineers D model [4], which serves as the base model for optimization. Also, Figure 3 indicates the optimization target in this study. We aim to optimize the structure of the rotor iron core represented in red.

Table 1 shows the rotor iron core shape, average torque, rotor iron core mass, and torque ripple rate in the optimized results of this study, previous research [1][2], and the base model. Additionally, Figure 4 illustrates the torque for each mechanical angle in the optimized results of this study, previous research, and the base model. As a result of the optimization in this study, the torque ripple rate, which was over 50% in previous research, has been reduced to less than 10%. The average torque is equivalent to that of previous research. On the other hand, the mass of the rotor iron core has increased by about 20g compared to previous research. However, this increase rate is small compared to the reduction rate of the torque ripple. Compared to the base model, both weight reduction and a decrease in torque ripple rate have been achieved.

In this study, we tackled the challenge of reconciling rotor iron core weight reduction for IPMSMs, which are used in collaborative human robots, with the torque ripple reduction, which was identified as an issue in previous research. By adding a term to minimize torque ripple to the objective function, we were able to obtain a lightweight structure while suppressing torque ripple.

[1] 源元颯人, 遠藤央, 中村裕司, 田中真平, 野口孝浩, “軽量化のためのトポロジー最適化を用いた電磁モータにおける回転子鉄心の最適設計”, ロボティクス・メカトロニクス講演会講演概要集, vol.2022 ,2022.

[2] 源元颯人, 遠藤央, 中村裕司, 田中真平, 野口孝浩, “平均トルクを制約条件に持つトポロジー最適化を用いた電磁モータ回転子鉄心の軽量設計”, 第23 回システムインテグレーション部門講演会, 2022.

[3] 佐藤孝洋, 五十嵐一, 高橋慎矢, 内山翔, 松尾圭祐, 松橋大器, “トポロジー最適化による埋込磁石同期モータの回転子形状最適化”, 電気学会論文誌D（産業応用部門誌）, vol. 135, no. 3, pp. 291–298,2015.

[4] 電気学会回転機のバーチャルエンジニアリングのための電磁界解析技術調査専門委員会, “回転機のバーチャルエンジニアリングのための電磁界解析技術”, 電気学会技術報告, no. 776, pp. 1–58, 2000.