MEC-Based Modeling and Design of Permanent Magnet Synchronous Machines with Axial–Radial Rotor Extensions Using Yoke and Rotor-Side Spaces

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors proposed a design method that utilizes unused space in the motor—specifically, the areas around the stator end windings and the stator yoke—to enhance torque. However, the reviewer believes the paper has numerous issues and requires substantial revision and improvement.

1. The authors need to provide a magnetic flux line diagram based on the 3D model in Figure 1, rather than a hand-drawn version, to verify the correctness of the flux paths. Labels for each component in Figure 2 should also be added. Does Figure 3 not include a feedback correction loop?
2. The main text directly lists equations (1) to (33), many of which lack any textual explanation. The authors need to clarify why these equations are introduced, how they are derived, and the logical relationships between them. The entire equation system is highly disorganized and requires careful revision. For instance, in the description of "Axial overhang (Equation 41)", Equation 41 cannot be found.
3. The authors only provided a second-level heading "2.1", but no "2.2". If there is no Section 2.2, is Section 2.1 necessary? Ending the paper with "Discussion" is unreasonable; a "Conclusions" section must be included. The first- and second-level headings are overly broad and vague, failing to precisely define the content covered. While not technically wrong, this naming style does not conform to conventional academic practice.
4. What exactly does "axial rotor" refer to? Do Figure 2(b) and Equation (6) describe the same concept?
5. What is the basis for the values of \( h_a \), \( l_{mai} \), and \( l_{mao} \) in Table 2? And why are they all integers? Is this a coincidence?
6. The validation only focuses on static performance (static torque, no-load back-EMF). Other crucial motor performance indicators—such as torque ripple, core losses, and power factor—are neither mentioned nor validated. The authors need to supplement these parameters. Given the addition of extra axial magnets and rotor iron, how do the iron losses and efficiency of the new structure compare to the conventional one? Is there relevant simulation data?
7. The paper presents optimization results at 1A current. Why was 1A chosen? Can the optimized structure maintain its "Torque/PM" advantage at rated or higher currents?
8. The paper emphasizes that its innovation lies in utilizing the "yoke side" space. Can the authors provide a comparison between a model that does not use the "yoke side" and one that does? What is the contribution percentage of the new flux path added by placing magnets on the "yoke side" to the total torque?
9. The mathematical model is very confusing, especially Equations (4) and (5). The use of the min function in Equation (5) is perplexing both mathematically and physically. Distributed parameter reluctances (Equations (10) and (15)) are directly used as lumped parameters without necessary explanation or integration.
10. The paper claims the proposed structure outperforms conventional ones under the "same PM volume" constraint (Fig. 9). However, the "Conventional Overhang" and "Non-Overhang" baseline models used for comparison are not detailed. The reviewer questions how these benchmark models were redesigned based on the "same PM volume" constraint.

Author Response

 

Original Manuscript ID: actuators-3860146

Original Article Title: “MEC-Based Modeling and Design of Permanent Magnet Synchronous Machines with Axial–Radial Rotor Extensions Using Yoke and Rotor-Side Spaces”

 

 

To: Actuators Editor

Re: Response to reviewers

Editor-in-chief/Associate Editor

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The authors would like to sincerely thank the Editor-in-chief /Associate Editor for the opportunity of revising and resubmitting the paper. We have carefully replied to all comments of the Reviewers as detailed in the next pages of this response letter. Also, the paper has been revised according to the comments. All the new round revisions are indicated by blue color in the revised paper for quick reference. We hope that our replies and revisions can address the comments of the Reviewers.

-------------------------------------------------------------------------------------------------------

 

Dear Editor,

 

Thank you for allowing the resubmission of our manuscript, with an opportunity to address the reviewers’ comments.

We are uploading (a) our point-by-point response to the comments (response letter (reviewer1.docx)), (b) an updated manuscript with changes shown in red font, and (c) a clean updated manuscript without highlights (main document).

 

Best regards,

Majid Mehrasa, Assistant professor, University of New Orleans

Soheil Yousefnejad, PhD candidate, University of New Orleans

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The paper proposes an interesting way to increase the electromagnetic torque generated in the machine by using two additional rotors with an axial structure located in the area of the end connections. The authors conclude that the magnetic flux produced by magnets placed on additional rotors (according to Table 2) increases the induced electromotive force and electromagnetic torque produced in the machine.

After a thorough analysis of the article, many doubts and questions arise:

1. A method of equivalent magnetic circuit was proposed for the analysis of the magnetic circuit and the determination of the main flux and the flux produced by additional axial rotors.
2. The proposed equivalent circuit, apart from minor modifications, are not original, i.e. they are presented in the literature [16] and [21].
3. Why the proposed equivalent circuits do not take into account the magnetomotive force generated by the winding?
4. The analytical model is presented in a non-transparent way. A ready-made substitute scheme is given, without explaining which sections of the magnetic circuit are affected by individual reluctances. In addition, many designations have not been clarified (m.in example, the designations distinguished by the index ' and '' – dependencies (21)-(33))
5. The designations F1, F2, F3 depending on (21) are not explained. This also applies to the notations F in equation (31). F symbols are not present in equivalent circuits.
6. It is not explained how the following parameters were calculated on the basis of the presented analytical model: a) EMF and electromagnetic torque given in Table 2. The lack of a complete model undermines the reliability of the calculations.
7. The graphic illustration of the idea (Fig. 2) is illegible and insufficient. It would be advisable to show the structure of the machine with additional axial rotors in cross-sections and to indicate the magnetic flux paths on them. It would be important to indicate the directions of the magnetization vectors of individual magnets. This will make it much easier to understand the idea of the Authors.
8. Similarly, the explanations of the idea of how the motor works given in Chapter 2 are, in my opinion, insufficient.
9. In the paragraph before Chapter 3. Results is a reference to the formula (41) – there is no such formula in the article.
10. 9. I have not found an explanation of what the phrase "conventional overhang" means. No parameters defining such a structure are provided.
11. 9. If the volume of magnets changes, doesn't this cause a change in the dimensions of the magnetic circuit? Changes in dimensions can lead to a change in the electromagnetic moment. There is no proper explanation here.
12. The finite element method was used for verification calculations. So why was the magnetic flux associated with the phase windings not calculated with FE and thus shown the effect of additional rotors on the magnetic flux in the machine?
13. The proposed MEC method was also not used to calculate the flux associated with the winding)
14. In Chapter 4. Discussion concluded that "The results confirm that incorporating the axial-assist PM rotor in a dual-stator PM machine increases the average airgap magnetic field ...". It is difficult to agree with this conclusion, since magnets placed in additional rotors increase the flux only in the stator core. By saturating the teeth, this can even lead to a reduction in the magnetic flux in the working gap.
15. The article does not contain information on the impact of power losses from eddy currents induced in magnets and the core of additional rotors on the operation and efficiency of the motor.

For the above reasons, in my opinion, the article does not meet the requirements set by the editors and therefore I do not recommend it for publication.

Author Response

Original Manuscript ID: actuators-3860146

Original Article Title: “MEC-Based Modeling and Design of Permanent Magnet Synchronous Machines with Axial–Radial Rotor Extensions Using Yoke and Rotor-Side Spaces”

 

 

To: Actuators Editor

Re: Response to reviewers

Editor-in-chief/Associate Editor

-------------------------------------------------------------------------------------------------------

The authors would like to sincerely thank the Editor-in-chief /Associate Editor for the opportunity of revising and resubmitting the paper. We have carefully replied to all comments of the Reviewers as detailed in the next pages of this response letter. Also, the paper has been revised according to the comments. All the new round revisions are indicated by blue color in the revised paper for quick reference. We hope that our replies and revisions can address the comments of the Reviewers.

-------------------------------------------------------------------------------------------------------

 

Dear Editor,

 

Thank you for allowing the resubmission of our manuscript, with an opportunity to address the reviewers’ comments.

We are uploading (a) our point-by-point response to the comments (response letter (reviewer2.docx)), (b) an updated manuscript with changes shown in red font, and (c) a clean updated manuscript without highlights (main document).

 

Best regards,

Majid Mehrasa, Assistant professor, University of New Orleans

Soheil Yousefnejad, PhD candidate, University of New Orleans

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

• Classic theory (from the last century) shows that by increasing the rotor core with 5% enables the increase of the torque through stator’s end-windings flux recovery. By simply considering a magnet increase, without the rotor iron below the PM, not only reduces the overall torque (which is proportional to inertial weight), but also increases the flux leakage at PM level, isn’t it? Please comment this aspect.
• From Fig.4 is not sure how the flux lines flow within the active part of the proposed structure… The air-gap g0 seems to be too large to facilitate flux transit and torque production… Only one air-gap length is indicated in table 1… The authors need to provide all geometrical data of the structure within Table one and to show the field lines plots (obtained through FEM) in order to prove and evaluate the transfer of the flux towards the lateral rotor part, especially at stator level.
• Personally, I suspect that the reported increased torque is not due to the active interaction between the stator and supplementary rotor field, but though the increase of the volume of the rotor. Please comment on that.
• The authors need to carefully define the operating point. One can see in table 2 and Fig.9 values of torque of 0.6Nm, while in Fig.7 values between (13150—14550)Nm/m3 are depicted. Next, in Fig.8 one can see values of torque of 10 or 50 times bigger than the initial values, and a range of torque density between (75500—77000)Nm/m3. This is really confusing.
• In table 2 the authors indicated some FEM RMS value for the emf. We would like to see the plotted curves from the 3D analysis.
• If the authors have detailed a MEC model, we should see in table 2 also the comparison of torque obtained though analytical and numerical approach.
• For Fig.6, please avoid double use of the word model. The caption for this figure could be “The MEC model of the proposed configuration in the axial rotor structure”.
• For fig.7 the torque values are not visible for the ”outer PM width=1mm”, like in the case of 2mm. Please add the torque/PM_volume values on the left plot too.
• In Fig. 8, the y label should be Torque/PM volume.
• In fig.8a, the so called “knee point at 25A” is not at all visible…
• The first paragraph of the paper emphasizes the torque ripple issue raised by PM topologies and one would expect that the authors will focus part of their scientific effort in investigating the torque ripple issue for the proposed structure, in comparison with the ones for common or ordinary topologies. What is the torque ripple level for the proposed structure? Due to the fact that the PM volume has increased, the torque ripple level should increase too, isn’t it? Please add results and supplementary information related to this aspect.
• Since there is no experimental validation in this work, the authors need to add extra results from FEM analysis (i.e., the emf, the torque variation the iron losses within the active parts etc.) in order to increase the scientific value of their paper.

Author Response

Original Manuscript ID: actuators-3860146

Original Article Title: “MEC-Based Modeling and Design of Permanent Magnet Synchronous Machines with Axial–Radial Rotor Extensions Using Yoke and Rotor-Side Spaces”

 

 

To: Actuators Editor

Re: Response to reviewers

Editor-in-chief/Associate Editor

-------------------------------------------------------------------------------------------------------

The authors would like to sincerely thank the Editor-in-chief /Associate Editor for the opportunity of revising and resubmitting the paper. We have carefully replied to all comments of the Reviewers as detailed in the next pages of this response letter. Also, the paper has been revised according to the comments. All the new round revisions are indicated by blue color in the revised paper for quick reference. We hope that our replies and revisions can address the comments of the Reviewers.

-------------------------------------------------------------------------------------------------------

 

Dear Editor,

 

Thank you for allowing the resubmission of our manuscript, with an opportunity to address the reviewers’ comments.

We are uploading (a) our point-by-point response to the comments (response letter (reviewer3.docx)), (b) an updated manuscript with changes shown in red font, and (c) a clean updated manuscript without highlights (main document).

 

Best regards,

Majid Mehrasa, Assistant professor, University of New Orleans

Soheil Yousefnejad, PhD candidate, University of New Orleans

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

This paper is acceptable.

Reviewer 2 Report

Comments and Suggestions for Authors

In my opinion, due to the explanations provided, the amendments and additions made, the article satisfactorily meets the requirements of the journal and can be published in an up-to-date form.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have addressed all the questions and remarks. Even if the analytical and numerical comparison of the torque was not added into the final manuscript (and I accept the authors argumentation), sufficient numerical (FEM based) results have been added and the scientific quality of the paper has significantly increased. For these reasons I do agree for the acceptance of this manuscript.