Analytical Model for the Design of Axial Flux Induction Motors with Maximum Torque Density

Round 1

Reviewer 1 Report

Dear authors,

As for the content page, the work is acceptable.

My recommendations:

• Please, use the Microsoft Word template or LaTeX template to adjustment your manuscript (https://www.mdpi.com/journal/wevj/instructions).
• The abstract could be extended about the methods: briefly describe the main methods. The abstract should be an objective representation of the article.
• Complete the chapter "2. Materials and Methods". Materials and Methods should be described with sufficient details to allow others to replicate and build on the published results. New methods and protocols should be described in detail, while well-established methods can be briefly described and appropriately cited.
• In chapter "3. Results", if it is possible about, it would be advisable to create the algorithm (figure) of the proposed solution so that the reader from another professional area is easier to orient when studying the paper and results.
• Complete the chapter "4 Discussion" about a description of your solution's scientific and practical contribution. Authors should discuss the results and how they can be interpreted from previous studies and the working hypotheses. The findings and their implications should be discussed in the broadest context possible. Future research directions may also be highlighted.
• The conclusion could be extended about the possibility of a next specific application of the proposed solution in practice.
• In the manuscript, please emphasize the novelty of your approach.

 

Overall, however, the article is interesting. I wish you good luck in further research.

 

Kind regards

Reviewer

Author Response

We thank the Anonymous Referee for his\her efforts on reviewing our manuscript and fruitful suggestions.

>>As for the content page, the work is acceptable.

Thank you for warm acceptance of our paper. Please, find our answers below.

>>Please, use the Microsoft Word template or LaTeX template to adjustment your manuscript

Thank you for this suggestion. We used LaTex template in this resubmission.

>>The abstract could be extended about the methods: briefly describe the main methods. The abstract should be an objective representation of the article.

Thank you for this recommendation. The abstract was completely rewritten in the revised manuscript.

>>Complete the chapter "2. Materials and Methods". Materials and Methods should be described with sufficient details to allow others to replicate and build on the published results. New methods and protocols should be described in detail, while well-established methods can be briefly described and appropriately cited.

Thank you for thoughtful reading. The section 2 has been revised in accordance with this comments. Besides, we believe that the new methods and protocols are described in sufficient detail. Our mathematical calculations were performed automatedly using MATLAB Symbolic Toolbox thus they are not much readable for a human reader. Nevertheless, we revised the References list and works [21] - [23] were added.

>>In chapter "3. Results", if it is possible about, it would be advisable to create the algorithm (figure) of the proposed solution so that the reader from another professional area is easier to orient when studying the paper and results.

Thank you for this advice. Since our development is a mathematical model, not an algorithm, we barely believe that any scheme will have an explanatory effect here.

>>Complete the chapter "4 Discussion" about a description of your solution's scientific and practical contribution. Authors should discuss the results and how they can be interpreted from previous studies and the working hypotheses. The findings and their implications should be discussed in the broadest context possible. Future research directions may also be highlighted.

Thank you for this suggestion. We added the Discussion Section in the revised manuscript accordingly.

>>The conclusion could be extended about the possibility of a next specific application of the proposed solution in practice.

Thank you for this recommendation. We expanded the Conclusions with possible future applications of our solution

>>In the manuscript, please emphasize the novelty of your approach.

Thank you for this question. The main contribution of our study is a novel motor design procedure aimed for torque density optimization. As far as authors know, such design techniques are not known from literature. We added some explanations to the Section 1 of the revised manuscript.

>> Overall, however, the article is interesting. I wish you good luck in further research.

Thank you one more time for time and efforts put in reviewing our manuscript. We sincerely hope, that the revised manuscript will better meet the expectations of the Referees.

Reviewer 2 Report

The manuscript proposed a mathematical model of an axial flux induction motor to optimize the electromagnetic torque density of motors. Although the manuscript has carried on the very detailed mathematical model of electromagnetic torque derivation, but the foothold point and the innovation are insufficient. The author is suggested to modify according to the following comments：

1. First of all, the author mentioned in the introduction and conclusion that the research purpose of this manuscript is to reduce the iterative process of motor optimization design. The method studied by the author is to complete the optimization process of one-step iteration through the unified expression of torque, and set the optimization variables to two (stator core and air gap flux density). However, has the author considered that in addition to electromagnetic torque, the motor has other design requirements and design goals, for example, what if the optimal torque design point does not meet the thermal load/max current requirements? What if the motor efficiency is too low? On the other hand, is it reasonable to optimize the design of a motor by relying only on two design variables? Therefore, from this point of view, the author's research foothold is not sufficient
2. In the introduction, the author only describes the relevant research on motor optimization. However, the research topic of this paper is axial induction motor, so the author should add relevant research literature in this respect.
3. Is the ‘mataheuristic’ a misspelling? Whether it should be the ‘metaheuristic’.
4. Is it appropriate to call the section 2 ‘Results’?
5. In Table 1, inner diameter is not given; the names of B_c1,B_c2 and B_t1 are wrong； the unit of qa1 is wrong. And what does km mean? It is not mentioned in the paper. Please examine Table 1 carefully.
6. In 2.3.2, the author mentions 'It should be noted that the values of the parametric factor (16) and generalized coefficient (17) do not depend on these variables. I.e. extremes of electromagnetic torque are at the same points as extremes of the expression of functional factor (18).'. This view is wrong. When the air gap magnetic density changes, the stator/rotor structure (slot areas) changes, then the stator/rotor resistance/inductances value in (16) must change. Therefore, it is difficult to show that the optimum point in Fig. 4 is the maximum torque point. On the other hand, even if the air-gap magnetic density is taken as the optimization/design variable, its change will affect the change of parametric factor F, so it is difficult for the method proposed in this paper to realize one-step iteration.
7. Section 2.3.3 is too simple. Please provide detailed comparison results, error analysis and conclusion. Secondly, the electromagnetic torque in Fig. 6 is not stable, so the simulation period should be increased.
8. In the manuscript, some motor technical terms need to be unified, like’ electromagnetic torque’ and ‘electromagnetic moment’, ’Flux density in the air gap’ and ‘induction in the air gap’.
9. In general, the derivation of the electromagnetic torque of axial flux induction motor in the manuscript is very detailed and valuable for reference,, but it can not be used as a reasonable mathematical model for the design of a AFIM, because the model considers too few factors and is not completely correct (thermal load, efficiency, saturation, etc.)..

Author Response

We are thankful to the Referee for his insightful review and useful suggestions. Please, find our answers (A) below.

1. First of all, the author mentioned in the introduction and conclusion that the research purpose of this manuscript is to reduce the iterative process of motor optimization design. The method studied by the author is to complete the optimization process of one-step iteration through the unified expression of torque, and set the optimization variables to two (stator core and air gap flux density). However, has the author considered that in addition to electromagnetic torque, the motor has other design requirements and design goals, for example, what if the optimal torque design point does not meet the thermal load/max current requirements? What if the motor efficiency is too low? On the other hand, is it reasonable to optimize the design of a motor by relying only on two design variables? Therefore, from this point of view, the author's research foothold is not sufficient.

А: Thank you for this important question. Indeed, there are some simplifying assumptions in our model. Let us clarify it further. In our algorithm, the main variable for optimization is the relative length of the stator stack. In Section 2, we provide a thorough illustration of such a technique. Optimization for magnetic induction in the air gap follows from the obtained mathematical description. Note that, apparently, we present such a view of the motor design procedure for the first time: it is not proposed in any of the publications we know. In its current state, our design method is dedicated to finding the basic dimensions of the motor allowing to achieve a single design goal – optimal torque density. Despite the limitedness of this task, this solution can be practically used in present form. If the motor design obtained with our approach does not satisfy the criterion of maximum current, it is necessary to change the winding parameters  and recalculate the design. Also, an experienced engineer can use this design as a sketch and modify it manually without significant loss of torque density, but meeting other important criteria. In our further work, our model will be extended to meet a number of design goals including current limitations, temperature conditions, weight, and so on.

2. In the introduction, the author only describes the relevant research on motor optimization. However, the research topic of this paper is axial induction motor, so the author should add relevant research literature in this respect.

А: Thank you for this remark. We added references [21]-[23] in the revised manuscript.

3. Is the ‘mataheuristic’ a misspelling? Whether it should be the ‘metaheuristic’.

А: Thank you for careful reading. We fixed this issue in the revised manuscript.

4. Is it appropriate to call the section 2 ‘Results’?

А: Thank you for this question. Section 2 is now "Materials and Methods".

5. In Table 1, inner diameter is not given; the names of Bc1,Bc2 and Bt1 are wrong； the unit of qa1 is wrong. And what does km mean? It is not mentioned in the paper. Please examine Table 1 carefully.

А: Thank you for this comments. The value Km is the overload capability (the ratio of break-down torque to rated torque). This parameter is required to calculate the factor F. We edited the Table 1 accordingly.

6. In 2.3.2, the author mentions 'It should be noted that the values of the parametric factor (16) and generalized coefficient (17) do not depend on these variables. I.e. extremes of electromagnetic torque are at the same points as extremes of the expression of functional factor (18).'. This view is wrong. When the air gap magnetic density changes, the stator/rotor structure (slot areas) changes, then the stator/rotor resistance/inductances value in (16) must change. Therefore, it is difficult to show that the optimum point in Fig. 4 is the maximum torque point. On the other hand, even if the air-gap magnetic density is taken as the optimization/design variable, its change will affect the change of parametric factor F, so it is difficult for the method proposed in this paper to realize one-step iteration.

А: Thank you for this important remark. Unfortunately we cannot present all of calculations in order to keep description of the mathematical model as compact as possible. We used automated symbolic calculations to obtain the model, thus the whole underlying math is not adapted to human reader. The main purpose of our paperis to demonstrate the fundamental basis of the developed method and, particularly, the possibility for searching for the optimal ratio between the stator and the rotor in a limited volume according to the criterion of the maximum torque density which demonstrates the functional factor. As for the parametric factor, it can be shown that at values of sn = 0.005-0.05 and km = 2-2.5, it can be considered as constant.

7. Section 2.3.3 is too simple. Please provide detailed comparison results, error analysis and conclusion. Secondly, the electromagnetic torque in Fig. 6 is not stable, so the simulation period should be increased.

А: Thank you for this recommendation. We added some textual explanations on obtained results to subsection 2.3.3. Speaking of Figure 6, it will not be stable at any simulation period, since it illustrates the rotation of the motor, and the transient process is already on it.

8. In the manuscript, some motor technical terms need to be unified, like’ electromagnetic torque’ and ‘electromagnetic moment’, ’Flux density in the air gap’ and ‘induction in the air gap’.

А: Thank you very much for this suggestion. We did our best to unify the technical terms throughout the manuscript.

9. In general, the derivation of the electromagnetic torque of axial flux induction motor in the manuscript is very detailed and valuable for reference, but it can not be used as a reasonable mathematical model for the design of a AFIM, because the model considers too few factors and is not completely correct (thermal load, efficiency, saturation, etc.)..

А: We highly appreciate the opinion of the Referee, but cannot agree at this point. Indeed, in its current form, the proposed model is not a complete mathematical model for the AFIM design, and we do not claim it as complete in this work. But the proposed model is relevant while solving a practical engineering problem outlined in our article. The model is not complete, but still sufficient for intermediate design purposes. Nevertheless, we agree that the introduction of additional factors into the model will improve the design quality, and we are going to continue working in this direction right after publishing this first necessary milestone paper.

We thank the Reviewer for a fruitful discussion and rigorous review and sincerely hope that we managed to address all the questions properly and meet all the expectations.

Round 2

Reviewer 1 Report

Dear authors,

Thank you for your comment and adjustment.

The paper demonstrates an adequate understanding of the relevant literature in the field and cites an appropriate range of literature sources. No significant work is ignored. The Conclusion and Discussion tie adequately together with the other elements of the paper.

The paper is very interesting and meets all the requirements for a good scientific publication. The paper contains new and significant information adequate to justify publication.

I have no further comments. I suggest acceptance in the present form.

I wish you good luck in further research.

Kind regards
Reviewer

Reviewer 2 Report

This paper has been modified according to the reviewer's suggestion, and there are no other suggestions for modification.