Coupled Numerical Model of Vibration-Based Harvester

Round 1

Reviewer 1 Report

1. On the page 3 I would suggest to add for electric charge density "free electric charge density"
2.  I think that the equation (3) is not correct. It should be B=µ.H=µ_oH+µ_oM=µ_oµ_rH. If I am not right, the authors should it comment and explain in more detail.
3. The generation of equation (12) using expressions (5) to (11) is not correct. It requires a little bit more comment and explanation. Especially the right side of equation (12).

Author Response

1. On the page 3 I would suggest to add for electric charge density "free electric charge density"

Authors:

This comment was taken into account, indeed for the model under consideration and its numerical analysis, the effects with the distribution of the electric charge on the parts of the coupled MG model were not considered.

 2. I think that the equation (3) is not correct. It should be B=µ.H=µ_oH+µ_oM=µ_oµ_rH. If I am not right, the authors should it comment and explain in more detail.

Authors:

This comment was taken into account, indeed there was an error in the given relation (3) and thus the transcription of the corresponding FEM relations / equations resulted in a mismatch. Wrong spots in the text of the post have been corrected and marked with a highlighter.

3. The generation of equation (12) using expressions (5) to (11) is not correct. It requires a little bit more comment and explanation. Especially the right side of equation (12).

Authors:

Permanent magnets with magnetization of M relation (13), damping elements based on magnetic field with application of permanent magnets, relation (12) are used as a source of magnetic field. Therefore, in the model (12), (13), there is a right side including magnetization M with corrected (previously misspelled) permeability. Furthermore, in subsequent FEM model relations, this fact is taken into account and incorrect transcription is corrected.

Reviewer 2 Report

Opinioned paper is the example how the scientific works should not be reported. 

1. There is no geometry of analyzed device - fig.1 is very unclear, it is impossible to find position of the coil where the EMF is induced. The arrows present in this picture show nothing - their heads point the air. The next figure 2 also does not explain anything, besides, it contains non-english captions. Fig.6 gives the overal impression but without dimensions and description where is coil and magnets.
2. Authors use the low frequency form of Maxwell equations but simultaneously the separate electric field due to electric charge  is present in the part of device equations - compare (3a) and (17). Connecting (6) and (6a) we have that electric current in metal depends on electric permittivity. Finally, what is solved elliptic or hiperbolic 2nd order differential problem?
3. Authors copy the well known fundamental 3D equations of finite elements method - lines from 240 up to 400  and finally solve 2D problem without explanation what it is steady harmonic state or transient as one may suppose from the earlier theory.
4. The results of solution of coupled mechanical-electromagnetic problem are not reported.
5. It can be suspected that coil is fixed and magnets are moving. Therefore, eq.(107) does not contain the force of electromagnetic nature, the component f0 is not defined.
6. Experimental results shown in fig.8 contain power P_RMS. What is it?

Author Response

1. There is no geometry of analyzed device - fig.1 is very unclear, it is impossible to find position of the coil where the EMF is induced. The arrows present in this picture show nothing - their heads point the air. The next figure 2 also does not explain anything, besides, it contains non-english captions. Fig.6 gives the overal impression but without dimensions and description where is coil and magnets.

Authors:

The original figure 2 was replaced by the final geometric design of the MG with the description of the basic parts further specified in Figure 7, the description of Figure 1 was added and the functional parts, motion parts and magnetic elements of the MG concept were differentiated. It is just a diagram to illustrate the function and the context, not a drawing or capturing the details of the MG core. Fig. 2, Fig. 6 (newly Fig. 7) were supplemented with descriptions, supplemented with basic dimensional data and data on essential parts and critical points of MG. New picture (Fig.6) of original concept of vibrating MG with magnetic bearings and shock was added.

2. Authors use the low frequency form of Maxwell equations but simultaneously the separate electric field due to electric charge  is present in the part of device equations - compare (3a) and (17). Connecting (6) and (6a) we have that electric current in metal depends on electric permittivity. Finally, what is solved elliptic or hiperbolic 2nd order differential problem?

Authors:

The commentary on the choice of the numerical model (reduced MAxwell equations and shapes of stationary, quasi-stationary formulations, etc.) has been consistently commented in the text. The proposed FEM model was originally used in parallel to model other types and variants of MG with a different range of resonant frequencies of the source of vibration and transformation principles (piezo effects, etc.). These variants and their analyzes are not the subject of the paper. Therefore, the authors added a comment on the conditions under which the associated FEM model was applied to the harvester with the specified parameters using the transformation based on Faraday's law.

3. Authors copy the well known fundamental 3D equations of finite elements method - lines from 240 up to 400  and finally solve 2D problem without explanation what it is steady harmonic state or transient as one may suppose from the earlier theory.

Authors:

  The proposed FEM model (3D, tetrahedron, pentahedron, hexahedron) was originally used in parallel to model other types and variants of MG-harvesters, with a different range of resonant frequencies of the vibration source and transformation principles (piezo effects, etc.).

The associated 3D structure model, as described in the text, was modeled according to the numerical FEM solution described, but at the same time the auxiliary verification of parts of the MG function or the design estimates of the MG magnetic circuit were made using simpler 2D models.

4. The results of solution of coupled mechanical-electromagnetic problem are not reported.

Authors:
  From a number of analyzes and visualization of EMG field distribution, mechanical displacements and deformations, temperature field and other parameters for clarity, the authors only selected examples of critical critical sections / parts, which proved to be a fundamental distribution of magnetic field in MG core and its spatial "gradients" and time changes. Figure 8c) shows the result of the modeled voltage at the MG winding output.

5. It can be suspected that coil is fixed and magnets are moving. Therefore, eq.(107) does not contain the force of electromagnetic nature, the component f0 is not defined.

Authors:

Regarding the design of the MG, the winding of the MG is relatively rigidly mounted and movable relative to the coil is a source of magnetic field (permanent magnets with magnification M in the rocker arm). The relative movement causes the voltage U to be induced in the generator windings. However, both the arm and the fixed part of the MG are in the gravitational field of the earth g, therefore a non-zero static load f₀ is considered.

6. Experimental results shown in fig.8 contain power P_RMS. What is it?

Authors:

In the original figure 8, the quantities in root mean square (RMS) are given. It is true that this fact was not mentioned in the text.

Reviewer 3 Report

The authors studied the Coupled numerical model of the vibration-based harvester. This paper contains good information and it can be accepted after minor revision:

1. Please improve the methodology you have used in this study. More referencing needed and the gap should be explained.
2. Figure 2 is not needed as it does not include any important information. Instead, more explanation about using FEM software should be included.
3. The formulas have used in the paper need more explanation. All parameters should be defined. Making the table is recommended.
4. The discussion part can be improved.

Author Response

1. Please improve the methodology you have used in this study. More referencing needed and the gap should be explained.

Authors:

The methodology was briefly explained in the introductory sections, and in the corresponding chapters the text was extended with reference to the methodology of the design of the final harvester.

2. Figure 2 is not needed as it does not include any important information. Instead, more explanation about using FEM software should be included.

Authors:

Figure 2 - an example of an analytical and parametric solver has been replaced by the corresponding MG design and dimensions of the final harvester.

3. The formulas have used in the paper need more explanation. All parameters should be defined. Making the table is recommended.

Authors:

Derivation of the FEM numerical model was supplemented by the necessary commentary and link to the geometric model and the MG concept. Modified comments on relevancy of model parts, corrected transcription errors.

4. The discussion part can be improved.

Authors:

The conclusion was supplemented by evaluation of methodology and choice of methods of design principles of MG, geometry and approach to quick gaining experience with the associated harvester model.

Changes in the text are highlighted for comparison with the original text.