Optimal Design of a Coaxial Magnetic Gear Pole Combination Considering an Overhang
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper proposed an coaxial magnetic gear (CMG) pole combination considering overhang, which increases the torque density of CMG.
1.
In line 119, the statement that the torque density increases with the increase of the outer diameter in both schemes is incorrect. In practice, it should be that as the outer diameter increases and the outer diameters of each component also increase accordingly, the torque density first increases and then decreases. Because as the outer diameter increases, the increase rate of the output torque is lower than that of volume.
2.
It is suggested that the radii of the main parts on rotors 1, 2, and 3 should be provided in table. 1, as CMG can only achieve a large output torque when the radial thickness of each component reach the optimal thicknesses. Moreover, the radial thickness of the back iron of the rotor 3 in Figure 1 is obviously too large, which is of no benefit to increasing the output torque of CMG and will only reduce its torque density.
3.
Lines 337-340 suggest that the paper has discovered that three-dimensional simulation can capture magnetic leakage phenomena, that cannot be seen in two-dimensional simulations. This is a fact, but it has long been revealed by experts and serves as the basis for evaluating magnetic leakage or end effects at the ends of CMG. In fact, the overhang of the permanent magnet outside the body does make up for part of the torque loss caused by the leakage of magnetic flux at the end. However, the actual leakage of magnetic flux at the end doesn’t decrease but increases, because the magnetic field of the extended permanent magnet is not fully utilized in the radial direction.
4. In lines 423 and 424, it is recommended that the unit of stress be MPa instead of N/m ².
5.
The overhang structure of the permanent magnet is relatively safe for a fixed rotor 3. But for the rotor 1 that rotates at high speed, it will generate a large centrifugal force, which increases with the rise in speed and may cause the permanent magnets to break. How should the structure be compensated for?
6.
Lines 136 to 141 indicate that when the transmission ratio of CMG is an integer, the torque ripple will be relatively larger. This is indeed the case. However, in reality, when the number of pole pairs on the permanent magnets of the two rotor 1 and 3 is an integer multiple, the torque ripple is also relatively large, and the design result is the best when it is a decimal multiple.
Author Response
Responses to the Associate Editor’s and Reviewers’ Comments
07 August, 2025
Dear reviewers and editor in Applied Sciences
We are sincerely grateful for your thorough consideration and scrutiny of our manuscript, “Optimal Design of Coaxial Magnetic Gear Pole Combination Considering Overhang”. Through the accurate comments made by the reviewers, we better understand the critical issues in this paper.
We have revised the manuscript according to the Reviewer’s suggestions. We hope that our revised manuscript will be considered and accepted for publication in the Applied Sciences.
The changes within the revised manuscript were highlighted (blue). Point-by-point responses to the reviewers’ comments are provided below.
[Reviewer #1]
Q1. In line 119, the statement that the torque density increases with the increase of the outer diameter in both schemes is incorrect. In practice, it should be that as the outer diameter increases and the outer diameters of each component also increase accordingly, the torque density first increases and then decreases. Because as the outer diameter increases, the increase rate of the output torque is lower than that of volume.
A1. We appreciate the reviewer’s comment. Considering the relationship between torque and volume, it cannot be concluded that torque density unconditionally increases. Therefore, reflecting the feedback, the content on line 119 was revised. ‘In both configurations, VTD generally tends to increase with the outer radius. While axial-flux CMGs exhibit a faster VTD increase than radial-flux CMGs, axial-flux CMGs tend to generate asymmetric axial magnetic forces, which can lead to structural imbalances.
Q2. It is suggested that the radii of the main parts on rotors 1, 2, and 3 should be provided in table. 1, as CMG can only achieve a large output torque when the radial thickness of each component reach the optimal thicknesses. Moreover, the radial thickness of the back iron of the rotor 3 in Figure 1 is obviously too large, which is of no benefit to increasing the output torque of CMG and will only reduce its torque density.
A2. We appreciate the reviewer’s comment. We appreciate the reviewer’s comment. Table 1 was revised based on reviewer’s comments. We are also aware of the issue of the excessive radial thickness of the back iron of Rotor 3. As the reviewer mentioned, we were able to confirm that the radial thickness of the back iron appears to be a structural waste of electromagnetic energy through the magnetic flux density distribution. This clearly results in a loss in the overall torque density calculation per volume.
We plan to develop a module combining the CMG and the axial motor in the future. Therefore, the outer radial portion of the CMG back iron will have holes drilled for mounting. We appreciate your understanding that the mechanical dimensions of the CMG were designed with structural margins in mind. In other words, this study developed an optimal model under limited conditions. In future research, we plan to improve torque density by considering (reducing) the thickness of the back iron.
Q3. Lines 337-340 suggest that the paper has discovered that three-dimensional simulation can capture magnetic leakage phenomena, that cannot be seen in two-dimensional simulations. This is a fact, but it has long been revealed by experts and serves as the basis for evaluating magnetic leakage or end effects at the ends of CMG. In fact, the overhang of the permanent magnet outside the body does make up for part of the torque loss caused by the leakage of magnetic flux at the end. However, the actual leakage of magnetic flux at the end doesn’t decrease but increases, because the magnetic field of the extended permanent magnet is not fully utilized in the radial direction.
A3. We appreciate the reviewer's comments. We also agree with the reviewer's observation that the actual flux leakage at the tip does not decrease but rather increases because the magnetic field of the extended permanent magnets is not fully utilized in the radial direction.
We selected design variables that considered realistic dimensions when increasing the overhang height. In this paper, we confirmed that the permanent magnet overhang improves the flux leakage. Furthermore, considering the electrical angle of the permanent magnets as an optimal design variable, we hypothesized that in the optimal model, the magnets are separated by an electrical angle of 164 degrees, which reduces mutual interference flux, concentrates the flux, and increases torque. The results of this torque increase are presented in Section 4.1 and Table 9.
Q4. In lines 423 and 424, it is recommended that the unit of stress be MPa instead of N/m ².
A4. We appreciate the reviewer’s kind comment. The stress unit was corrected to MPa.
Q5. The overhang structure of the permanent magnet is relatively safe for a fixed rotor 3. But for the rotor 1 that rotates at high speed, it will generate a large centrifugal force, which increases with the rise in speed and may cause the permanent magnets to break. How should the structure be compensated for?
A5. We appreciate the reviewer’s comment. As explained in Section 4.2 of this paper, we conducted a structural analysis to verify the structural stability of the optimal model's permanent magnets when rotor 1 was rotated at 1,000 rpm under the established analysis conditions. As a result, we confirmed that the yield stress was not reached.
Furthermore, we plan to apply a non-magnetic structure to protect the permanent magnets from external influences. While there is a concern that the increased air gap length will reduce torque, we are considering a practical design that also considers structural stability as a future research area.
Ultimately, we plan to develop a module that combines a CMG and an axial motor. Therefore, we plan to conduct future research to verify an optimal design that considers both electromagnetic characteristics and structural stability.
Q6. Lines 136 to 141 indicate that when the transmission ratio of CMG is an integer, the torque ripple will be relatively larger. This is indeed the case. However, in reality, when the number of pole pairs on the permanent magnets of the two rotor 1 and 3 is an integer multiple, the torque ripple is also relatively large, and the design result is the best when it is a decimal multiple.
A6. We appreciate the reviewer’s comment. Thank you for your insight. We confirmed through references that non-integer gear ratios are better, and accordingly, in this paper, we utilized non-integer gear ratios in the relationship between Rotors 1 and 3, as shown in Table 2 in Section 2.2.
We revised the description to emphasize that torque ripple increases not only when the gear ratio is an integer, but also when the number of pole pairs of Rotors 1 and 3 is an integer multiple. The added sentence is as follows:
The torque ripple of a CMG is affected by the gear ratio, which is an important consideration during the design process. When the gear ratio is an integer, torque ripple tends to increase while torque density decreases.
Conversely, non-integer gear ratios generally reduce torque ripple and improve torque density. Therefore, implementing a non-integer gear ratio is an effective strategy for minimizing torque ripple [12].
Torque ripples tend to be greater when the gear ratio is an integer or when the pole pair numbers of Rotor 1 and Rotor 3 form an integer multiple relationship. Minimizing ripple is often achieved through fractional or decimal gear ratios and pole pair combinations.
Reviewer 2 Report
Comments and Suggestions for AuthorsThis paper presents a comprehensive design approach for optimizing the pole configuration of a coaxial magnetic gear (CMG) structure with an overhang. The proposed method utilized an optimal Latin hypercube sampling method to generate experimental points and constructed a kriging-based metamodel. The results show overall improvement of the proposed mode over the existing one.
The paper is overall well-written and interesting. It is also detailed and the structure of the paper is decent. I consider that there are improvements of the proposed model in this paper relevant for today. Topic is also relevant for today. Their main motivation is to capture the influence of the axial leakage flux, which I consider also important. This also represents an important gap that this research addresses. Figures and Tables are clear and visible. I do not find some major limitations of the paper. I do have few questions for the authors:
1. Highlight a bit more contributions of this paper in the Introduction.
2. Add a paper outline in the Introduction.
3. Are you satisfied with your objective function? Would you consider some other parameters besides maximizing torque in the future, and create some multi-objective optimization?
4. Would it be possible to make a prototype of this motor?
5. Are there any disadvantages of this model?
6. Elaborate more if there are any significant differences between initial and optimal model in Figure 9.
Author Response
Responses to the Associate Editor’s and Reviewers’ Comments
07 August, 2025
Dear reviewers and editor in Applied Sciences
We are sincerely grateful for your thorough consideration and scrutiny of our manuscript, “Optimal Design of Coaxial Magnetic Gear Pole Combination Considering Overhang”. Through the accurate comments made by the reviewers, we better understand the critical issues in this paper.
We have revised the manuscript according to the Reviewer’s suggestions. We hope that our revised manuscript will be considered and accepted for publication in the Applied Sciences.
The changes within the revised manuscript were highlighted (blue). Point-by-point responses to the reviewers’ comments are provided below.
[Reviewer #2 ]
Q1. Highlight a bit more contributions of this paper in the Introduction.
A1. Thank you for your review comments. We wrote that phrase at the end of the introduction:
The resulting optimal CMG design was validated through electromagnetic field analysis, air-gap magnetic flux density evaluation, and structural analysis. It was confirmed that torque characteristics differ depending on the difference in gear ratio within the same specification CMG, and that torque performance is improved through the overhang structure. The 3D FEM analysis results enabled us to effectively analyze magnetic flux leakage, and we expect that this type of magnetic gear can be used for connection with other power sources, including motors.
Q2. Add a paper outline in the Introduction.
A2. Thanks for the reviewer's feedback. We've added it to the paper outline.
The remainder of this paper is organized as follows.
Section 2 presents the fundamental principles of magnetic gears and the initial de-sign of the coaxial magnetic gear CMG, including various pole-pair combinations and gear ratio analysis.
Section 3 describes the optimization methodology, including the design variables, optimal Latin hypercube sampling, metamodel construction, and optimization results.
Section 4 validates the optimal design through electromagnetic analysis, fast Fourier transform of air-gap flux density, and structural stress analysis.
Section 5 summarizes the key findings and contributions of the study and discusses directions for future work.
Q3. Are you satisfied with your objective function? Would you consider some other parameters besides maximizing torque in the future, and create some multi-objective optimization?
A3. Thank you for your feedback. We achieved satisfactory results by satisfying the objective function and constraints for improving CMG torque performance within the same dimension. We plan to consider increasing torque density as an additional objective function in the future. To this end, we plan to implement an optimal model through analysis utilizing multiphysics optimization, including electromagnetic, thermal, and structural analyses, under the same dimensions and conditions.
Q4. Would it be possible to make a prototype of this motor?
A4. As indicated in answer 3 above, we plan to build an optimal CMG model through multiphysics optimization, including electromagnetic, thermal, and structural optimization. Then, we will build a prototype through analytical verification.
We particularly agree with the reviewers' concerns about the excessive thickness of the back iron. Considering this, we plan to conduct an optimal design that considers structural stability.
The next step is to research a module that combines the CMG and the axial motor. We will incorporate your valuable feedback into our review process and present improved research results. Thank you.
Q5. Are there any disadvantages of this model?
A5. Thanks for reviewer’s question. A disadvantage of the optimal model presented in this paper is the excessively large thickness of the back iron.
This was not considered as an optimal design variable. In future research, we plan to adjust the back iron thickness to an appropriate size that prevents magnetic flux saturation while considering increased torque density. Of course, if the dimensions of the back iron can be reduced without affecting the output torque, the torque density of the CMG will be improved.
Q6. Elaborate more if there are any significant differences between initial and optimal model in Figure 9.
A6. Thank you for your valuable comments. Figures 9 and 10 show the magnetic flux density distributions of the initial and optimal CMG models. Unlike the initial model, which configured the permanent magnets with an electrical angle of 180 degrees, the optimal model, which uses the optimal solution of 164 degrees, reduces the magnetic flux interference caused by the magnets being in contact and concentrates the magnetic flux. Furthermore, the magnetic flux leakage in the axial direction is compensated for by the permanent magnet overhang.
Round 2
Reviewer 2 Report
Comments and Suggestions for AuthorsAll comments are answered by the Authors.
