Torque Maximization of Induction Motor with CNT Yarn Applied Secondary Conductor using Size Optimization

Seiya Zaima, Mitsuru Endo, Yukio Tsutsui

2025 The 8th Jc-IFToMM International Symposium The 8th Jc-IFToMM

Session VI: Actuators and Applications

**This presentation was selected as an award finalist. **

Background

Induction motors are widely used for their simplicity, robustness, and cost-effectiveness. However, their efficiency decreases at high temperatures because common metallic conductors have a positive temperature coefficient of resistance (TCR), which increases electrical resistance as temperature rises.

Carbon nanotube (CNT) yarn, a novel conductor material, has a negative TCR[1]. This property offer the potential to improve efficiency in high-temperature environments. Although CNT yarn has the advantage, it has lower electrical conductivity, leading to decreased maximum torque when used in the rotor’s secondary conductor.

Previous work[2] confirmed this trade-off. While CNT yarn-based motors showed improved efficiency at elevated temperatures, they suffered from reduced torque output. To address this limitation, this study focuses on maximizing the torque of an induction motor with CNT yarn applied to its secondary conductor by optimizing the rotor structure.

Method

1. Optimization Problem

The optimization target is based on the IEEJ K-model[3], a benchmark three-phase, four-pole squirrel-cage induction motor. The rotor design is parameterized using two variables:

$\alpha$: half of the angular width of the secondary conductor
$r_{si}$: radial length of the secondary conductor

These variables define the cross-sectional shape of each slot’s conductor. The number of slots and stator dimensions are fixed, and only the rotor geometry is modified.

The objective is to maximize the maximum torque $T_{i \max}$. The optimization problem is formulated as:

\[\underset{\alpha, r_{si}}{\mathrm{maximize}} \quad T_{i, \max}\]

This problem is solved using the DIRECT (DIvided RECTangle) method[4], which theoretically converges to the global minimum. It divides the design space into rectangles, explores globally, and refines locally, making it suitable for highly nonlinear problems such as the torque of induction motor.

2. Torque Computation using JMAG

Torque cannot be expressed analytically due to nonlinearities such as the skin effect, proximity effect, and magnetic saturation. Therefore, torque is computed using Finite Element Method (FEM) simulations in JMAG-Designer 23.02.

For each candidate geometry generated by the optimization algorithm, JMAG is used to evaluate the torque-slip curve. The peak value of this curve is extracted as $T_{i, \max}$ and used as the objective function value.

Results

Torque Improvement by Optimization

Optimization was conducted to maximize the maximum torque by modifying the shape of the secondary conductor. The result is shown below.

	Pre-optimized Model	Post-optimized Model
Rotor structure
Maximum Torque [Nm]	2.51	2.92
Area of secondary conductor [mm²]	16.9	44.9
Resistance of secondary conductor [μΩ]	249	84.7
Weight of motor [kg]	3.45	3.20

As shown in the table, the optimized model achieved a 17.9% increase in maximum torque.
This improvement was achieved by increasing the cross-sectional area of the secondary conductor by 2.66 times, which also reduced its electrical resistance.
In addition, the total motor weight slightly decreased due to the lightweight properties of CNT yarn.

Conclusion

This study demonstrated that by applying size optimization to the rotor of an induction motor with CNT yarn as the secondary conductor, the torque reduction issue can be mitigated. The optimized geometry increased maximum torque by 17.9 percent.

Future work includes expanding the search range, incorporating stator-side design variables, and validating results using experimental prototypes. The methodology can also be extended to other motor types.

References

[1] C. D. Hernandez et al., “Multifunctional characteristics of carbon nanotube (CNT) yarn composites,” n Proc. MN2006: Multifunctional Nanocomposites, 2006

[2] T. Tezuka et al., “Performance Comparison of Induction Motors at High Temperatures with Different Secondary Conductor Material” in The Papers of Joint Technical Meeting on Static Apparatus and Rotating Machinery 2024

[3] Technical Committee for Investigating Electromagnetic Field Analysis Technology for Virtual Engineering of Rotating Machines, Electromagnetic Field Analysis Technology for Virtual Engineering of Rotating Machines, IEEE Japan, 2000 (IN JAPANESE)

[4] Jones, D.R et al. The DIRECT algorithm: 25 years Later. J Glob Optim 79, 2021

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