Methodology for Shape Optimization of Magnetic Designs: Magnetic Spring Characteristic Tailored to Application Needs

Round 1

Reviewer 1 Report

The magnet shape optimization through Fourier decomposition, breaking conventional design symmetry and spline techniques is presented in this paper. The paper is well written and the results are pretty impressive. However, the reviewer would like to see some minor additional details.

1) The free shaping can give very good results however they would have practical limitations. How would you address those constraints. I mean how those complex shapes can be practically prepared?

2) Kindly define abbreviations such as NOMAD and PMSM where they are used first time such as on page 4 and 5 etc.

3) Kindly explain parameter space optimization based on smart guesses in a bit more detail. Isn't it like this that although It can converge to the final solution faster but there are equal chances of divergence as well. I mean how the gausses are not random.

4) Kindly include some kind of comparison table of all techniques under investigation. This table may include prose and ones of each technique particularly the complexity such as simulation time etc.

Author Response

Dear Reviewer,

Thank you for your kind review of our article. We believe it helped to improve its quality by pointing out some parts that could use a better / deeper explanation.

1. We partly address these points in the text - section 4. Discussion and Outlook- we are aware of metal injection molding (MIM) and 3D printing of magnets as a high potential technology to achieve free shaped magnets with. After your comment we added a small addition to highlight this and clear out that there are still limitations to 3D printing and MIM such as minimum feature size, maximum part size, non-containing shapes etc.

2. the full names of terms PMSM, IM-PMSM, LM-PMSM and NOMAD are added when first introduced in the text. 

3. I presume that you meant to say "how the guesses aren't random". To address this we add the following paragraph: "Initialization could alternatively be done as fully symmetric or even random. In both cases we see that our initial guess can outperform them...." We also return to this point in section 3. Results where the initial guesses are present for each design problem, and obviously show a better than random guess. 

4. Due to the short length of the review time we were able to add a rather simple pro/con table for one of the exemplary design requirements.

We hope the updates described above are sufficiently addressing this request from the reviewer.

Kind regards,

Branimir Mrak

Author Response File: Author Response.pdf

Reviewer 2 Report

The authors provide a study of the magnetic spring shape design with four optimization approaches at full length, especially for the first two approaches: extended parametric optimization and parametric shape optimization. The manuscript is very instructive. However, since there are too many contents in the manuscript, the authors have not finished the regulation. It is better to make a revision before the publication.

Here are some examples:

1. The format of the references are not uniform.

2. There are a lot of abbreviations which are lacking of descriptions (I give a list and possible description here):

FEM: finite element method

PMSM: permanent magnet synchron motor

BH product: I suppose it mean the energy product in magnetic material

FE SW:?

HPC:?

RMS: root mean square

3. There are some typo and grammar errors in the text:

Page 2 Line 47 “An exhaustive explanation of which …”, what do the authors want to interpret the “which” here?

Page 4 Line 92 “Difficulty of capture …” I suppose it should be “Difficulty of capturing …”.

Page 5 two lines after Line 154 “… in order to …, a series of 2D magneto static model of the geometry is calculated,….” I suppose here “model” should be used in plural form.

Page 6 Line 169 “… we limit ourselves to braking symmetry in …” I suppose here “braking” is a typo, it should be “breaking”.

And I would like to ask some questions about the detail content:

1. Page 7 Line 184 to 185, the authors state that the parameter space is allocated according to the biggest possible parameter vector dimension, so how to determine the biggest possible parameter vector here?

2. Page 8 Line 192, what do the authors mean by “points” in the sentence “in the other designs, other points could be used.”?

3. Page 8 Line 204, for the free shape optimization, what are the criteria of the blackbox optimization here?

4. Page 10 Line 260, according to the result in Figure 7, doest that mean the cam-follower is more suitable for optimization in this approach?

Author Response

Dear Reviewer,

Thank you for your kind review of our article. We believe it helped to improve its quality by sharply spotting some of the typos/ grammar mistakes, but also pointing out the parts that could use a better / deeper explanation.

The typos have been addressed accordingly, for the detailed questions, below are some in depth comments:

1. Page 7 Line 184 to 185, the authors state that the parameter space is allocated according to the biggest possible parameter vector dimension, so how to determine the biggest possible parameter vector here? - paragraph added

More specifically, the length of parameter vector is determined based on the number of attractors N_A and repellers N_R in the torque characteristic requirements and parameters per magnet as described in the table 1, where number of magnets on stator Ns and rotor Nr are calculated as follows:

Ns=Nr= (Na+Nr)

In specific cases where magnet segmentation is desired, leading to more than one magnets per magnetic pole, the user still needs to override this allocation.

2. Page 8 Line 192, what do the authors mean by “points” in the sentence “in the other designs, other points could be used.”? - sentence expanded to explain more clearly that the curve (and its points) to be shaped is chosen for this specific problem by the motor/ magnetic spring designer, while on another problem, the best choice of curve might be a different one.

3. Page 8 Line 204, for the free shape optimization, what are the criteria of the blackbox optimization here? The criteria for the blackbox optimization are the same as before: min. normalized RMS error, however in this case the deformations are applied to a nominal geometry. Therefore we are searching for an optimal operator, instead of an optimal parameter set. In our work we also tried to use a form of a "topological derivative" such as mentioned in reference [10] to take a step away from blackbox optimizers, which should've lead to improved convergence time. However, we encountered convexity problems with such formulations when applied to magnetic spring optimization, and abandoned the white-box approach.

If the reviewer thinks this info is critical for the reader, we could add it to the article.

4. Page 10 Line 260, according to the result in Figure 7, does that mean the cam-follower is more suitable for optimization in this approach?

• That is a possible conclusion to make, even though it's hard to substantiate it with more information on why. This is the main reason why we avoid drawing such a "conclusion".  Instead, we added the following comment: "The limitations of this problem formulation are clearly visible when trying to perfectly match the requirement in fig. 6. On the other hand, even though the requirement in fig. 7 shows a greater deviation from a single order sine profile, the approach is more successful at matching the requirement here with normalized RMS error of 4.39% as opposed to 11.31%, in former case".

Kind regards,

Branimir Mrak

Author Response File: Author Response.pdf