Estimation of electrical resistivity of CNT yarn for use as motor windings using 3D resistive network model

Taichi Ueyanagi, Mitsuru Endo, Hiroshi Nakamura, Yukio Tsutsui, Yijun Qu, Shimpei Tanaka, Shinsuke Mori

第66回フラーレン・ナノチューブ・グラフェン総合シンポジウム

The 66th Fullerenes-Nanotubes-Graphene General Symposium

2P-16

Nagoya University, March 6-8, 2024.

背景 – Background

CNT糸は銅線に代わる導線の材料として注目されている．従来のCNT糸を用いたモータ設計では代表値をCNT糸の電気抵抗率として決定している[1]．しかし，CNT糸の電気抵抗率は，糸を構成するCNTと糸自体の寸法や構造によって異なるため，実用的なモータ設計を想定すると，CNT糸の仕様に基づき電気抵抗率を決定する必要がある．そこで本研究では，CNT糸の仕様に基づく電気抵抗率の推定手法の提案を目的とする．CNT糸をモデル化するために3次元抵抗ネットワークを採用した．

CNT yarn has attracted attention as a conductive material that could replace copper wire. In conventional motor designs using CNT yarn, a representative value is typically used as the electrical resistivity of the CNT yarn [1]. However, the electrical resistivity of CNT yarn varies depending on the CNTs that make up the yarn, as well as the yarn’s dimensions and structure. Therefore, for practical motor design, it is necessary to determine the electrical resistivity based on the specifications of the CNT yarn. In this study, we aim to propose a method for estimating the electrical resistivity based on the specifications of CNT yarn. To model the CNT yarn, we employ a three-dimensional resistance network.

手法 – Method

モデリングを実現するために，”ネットワーク生成”，”方程式の立式”，”ネットワーク分析 “の3つのプロセスを採用した．ネットワーク生成では，CNT糸を微小領域に分割し，その領域内にCNTを配置することでネットワークを作成する．領域内に配置されるCNTの数はCNT糸の空隙率に基づいて決定する．CNTはわずかな配向角度でランダムに配置する．CNT間の交点は，CNTの最短距離に基づいて計算され，節点としてリスト化する．方程式の立式では，キルヒホッフの法則を用いて，各節点の電位を変数とする方程式を立式する．ネットワーク分析では，立式された方程式をヤコビ法により解く．そして，計算された各節点の電位を用いてCNT糸の電気抵抗率を計算する．

To implement the modeling, we adopted three processes: “network generation,” “equation formulation,” and “network analysis.”

In the network generation process, the CNT yarn is divided into microscopic regions, and CNTs are arranged within these regions to form a network. The number of CNTs placed in each region is determined based on the porosity of the CNT yarn. CNTs are randomly arranged with slight orientation angles. The intersections between CNTs are calculated based on their shortest distances and listed as nodes.

In the equation formulation process, Kirchhoff’s laws are used to establish equations with the potential at each node as variables.

In the network analysis process, the formulated equations are solved using the Jacobi method. The electrical resistivity of the CNT yarn is then calculated using the computed potential values at each node.

model

結果 – Result

提案モデルは，サンプルの実験結果，先行研究[2]の実験結果を用いて検証する．図1～3に提案モデルに基づいて推定した電気抵抗率（黒線）と実験結果の電気抵抗率（赤い点，青い×印）を示す．赤い点に示す実験結果によりモデルを校正している．図1～3より推定結果と実験結果は概ね一致しており，提案モデルにより各空隙率における電気抵抗率が推定可能であると考える．

The proposed model is validated using experimental results from our samples and previous research [2]. Figures 1–3 show the estimated electrical resistivity based on the proposed model (black line) alongside the experimental results (red dots and blue × marks). The model is calibrated using the experimental results indicated by the red dots.

As shown in Figures 1–3, the estimated values generally agree with the experimental results, suggesting that the proposed model can predict the electrical resistivity for different porosities.

fig1

図1 サンプル群Aによる検証 / Validation using Sample Group A

fig1

図2 サンプル群Bによる検証 / Validation using Sample Group B

fig1

図3 先行研究[2]の実験結果による検証 / Validation using Experimental Results from Previous Research [2]

結論 – Conclusion

本研究では実用的なモータ設計を想定し，CNT糸の仕様に基づく電気抵抗率の推定手法を提案した．3次元抵抗ネットワークによりCNT糸をモデル化し，CNT糸の仕様に基づく電気抵抗率を推定した．実験結果と比較することでモデルを検証し，提案モデルにより各空隙率における電気抵抗率を推定できることを確認した．したがって，糸を構成するCNTと糸自体の寸法，構造，電気抵抗率が既知のCNT糸があれば，空隙率の異なるCNT糸の電気抵抗率が推定可能であるといえる．さらに提案モデルを使用することで，CNT糸の仕様に基づいたモータ設計が可能となる．

In this study, we proposed a method for estimating the electrical resistivity of CNT yarn based on its specifications, considering practical motor design applications. The CNT yarn was modeled using a three-dimensional resistance network, and its electrical resistivity was estimated based on its specifications. The proposed model was validated by comparing the estimated values with experimental results, confirming that it can predict the electrical resistivity for different porosities.

Therefore, if the CNTs that make up the yarn, as well as the yarn’s dimensions, structure, and electrical resistivity, are known, the electrical resistivity of CNT yarn with different porosities can be estimated. Furthermore, by using the proposed model, motor design based on the specifications of CNT yarn becomes feasible.

参考文献 - Reference

[1] Vandana Rallabandi, Narges Taran, and Dan M. Ionel, Multilayer Concentrated Windings for Axial Flux PM Machines, IEEE TRANSACTIONS ON MAGNETICS, Vol.53, No.6, 2017, https://doi.org/10.1109/TMAG.2017.2661312.

[2] Menghe Miao, Electrical conductivity of pure carbon nanotube yarns, Carbon, Vol.49, No.12, pp.3755-3761, 2011, https://doi.org/10.1016/j.carbon.2011.05.008.

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