Calculating the Load Distribution and Contact Stress of the Disposable Harmonic Drive under Full Load

Round 1

Reviewer 1 Report

Overview and general consideration

The article shows an analytical model to calculate the contact stress and contact stiffness  of disposable harmonic drive (HD). Contact stress and load distribution results from such analytical model are compared with a HD modelled using finite element method.

The topic covered in the manuscript is very interesting in harmonic drive research community, however, the novelty of the article is not well described. There are also some major comments that should be considered.

Major comments

The following major comments should be addressed in the manuscript:

• 1. The need for the introduction of the fractal contact stiffness is not well described. Is it really necessary to reach the objective of the research work? What is the contribution of using such model instead of classical Hertz contact models? I will consider not including section 4 in the manuscript.
• Section 1. Introduction.
  1. It is not clear the references related with the research covered in the manuscript and the associated novelty. For instance, several references are within gear research but the relation with the present work is not clearly stated.
  2. When showing different works in HD literature, it should be highlighted what is still not done and will be covered in this work.
  3. References related to the effect of the total length (l) and teeth width (L) are missing. If there is not any work covering such effect, it should be considered to include in this work the effect of different “l/L” ratios, not only l/L = 3.5 (conventional HD) and l/L = 1 (disposable HD).
• Section 2 and 3. Analytical model.
  1. The whole analytical model should consider together (i.e. sections 2 and 3).
  2. Why only radial deformation is considered in disposable HD should be discussed.
  3. Please give the detail of the steps followed to achieve the equations and give references of other works.
  4. Figures – results. Please before introducing the results, specify the values of the variables used to obtain them
  5. Figure 4, which values are used to get such plots. Please specify.
  6. Figure 5, please describe what each line represents (i.e. dashed line, dash-dot line, solid line…). Figure caption should be self-explaining. Please use variables already explained in the text.
  7. Figure 6. Why is the minimum value of the backlash minimized if the radial deformation is the same in both HD-s? Which values are used to get such backlash? Which is the manufacturing profile shift used in both cases?
  8. Figure 7 is not well described. Moreover, it should be referenced before in the text.
  9. Figure 9.
     1. The deformation energy (the areas of both curves) seem to be different, how could it be explained? Does it make any sense? Is there any mistake in the formulation when only radial deformation is considered?
     2. The teeth in contact (i.e. \psi angle) shown in Fig. 6 differ from Fig. 9. Which one is correct? In Figure 6, the conventional HD have larger angle than disposable HD (-25º to 50º vs -25º to 40º) while in Figure 9 the values are different (respectively, -20º to 25º vs -23º to 22º)?

• The asymmetry of the curves should be explained.

11. Figure 11.
    9. Although the angles are in accordance with Fig. 9 (not Fig 6), the shape of the curve is not related with Fig. 9. How could it be explained?

• Section 5. Finite element model.
  1. The finite element model should be better explained.
  2. Geometry and mesh.
     1. The mesh of the tooth root should be better shown and described since it has influence in the results.
     2. Have you done any mesh sensitive analysis?
     3. Root and/or tip modifications were considered?
  3. The mesh seems to be quite large to represent Hertz contact area and therefore compute contact stresses correctly.
  4. Figure 19 shows that the contact along the teeth width is not uniform. Why? Which value is shown in Fig. 20?

1.  

Minor comments

• English should be revised.
• Consistency in notation. For instance,
  1. w0* and w0, both are used (w0 in eq. 11 is the same as in the previous equations);
  2. \mu is used for different variables (\mu in eq.5 and Fig.5 vs. \mu in eq. 37)
  3. X1 and xk1 in eq. 12, 13 and 14 are the same? If not, the meaning of xk1 should be introduced.
• Table 1.
  1. It is not clear why those geometries were selected for the study. It should be clearly specified the reason to choose those geometries.
  2. The transmission ratio is not described in the text. Is it somehow relevant?
  3. The variables of the parameters should be included.
• Is the email of the corresponding author correct? The * mark is written in Yuefeng Li, while the email is referring to [email protected], it seems that it is the second author (Guanglin Wang).

 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

This paper addresses an interesting engineering problem regarding the disposable harmonic gears. To sum up, it is a nice paper, and can be accepted for publication. If below things are added, the paper quality could be enhanced more.

1) To improve overall readability, a nomenclature may be needed.

2) The quality of finite element mesh needs to be further explained。

3）Please further explain the numerical calculation method.

4) The following literature may help the authors understand the harmonic gears more clearly. “Deformation analysis of the flexspline of harmonic drive gears considering the driving speed effect using laser sensors”.

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

The manuscript 1505688, entitled “Calculating the contact stress and normal contact stiffness of the disposable harmonic drive under full load” by Yuxin Zhang et al., has been carefully reviewed. And some problems make me confuse:

1. The introduction is poorly organized that I don’t know exactly what problem this paper concentrates on. And there are too many unnecessary abbreviations such as VFIFE, HCR, TRG and so on, which introduce trouble for reading.
2. What is the novel idea in this paper?
3. The fractal parameters including fractal dimensions and fractal roughness are introduced to discuss their influence laws on contact stiffness in Section 4. Do these fractal parameters have more intuitive physical meanings? And what is their influence law helpful to understand or solve something problems about contact stiffness of disposable HD?

4. This paper neither illustrates how long exactly the disposable HD need to work under high load, nor discusses how long the disposable HD could opera normally with the analyzed stress conditions. How to come out the conclusion that “The disposable harmonic drive can be used for short-time operation under high load”? 

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Please find the following comments to authors’ responses:

Response 1

If it is important, it should be highlighted in any results with and without considering fractal contact stiffness. The conclusion outlined from the fractal analysis that “it is possible to improve the contact performance of the disposable HD by enhancing the tooth surface quality” is well known in machine design and it is considered by gear sizing standards. It is not related with the contact stress calculation and later with the verification done with finite element analysis.

Response 2(3)

Even if you are only analyzing and comparing two cases, conventional (l/L = 3.5) vs. disposable (l/L = 1), it is important to highlight its influence. Some questions, just to give some ideas to improve your work, not only to answer them:

• Which is the range of L/l studied in literature?
• When reducing this l/L ratio, and approaching to l/L 1, is the trend of the results in agreement with the findings of your research. It is important to discuss if your findings are in agreement with literature.

Response 3(1)

The section and subsections should be more clearly defined.

Response 3(2)

It can be observed in Figure 4 that the radial deformation is the same in conventional and disposable HD. Is it correct? Shouldn’t it be higher than

For instance, in order to verify such hypothesis would the results of l/L = 1 be similar to l/L = 1.05?

Response 3(3)

Although the description of the procedure included is correct, the required details and references were related to equations in section 2.1.

Response 3(4)

Ok. Even if the selection of the variables could be confidential, they should be justified.

Response 3(6)

Figure caption should be self-explanatory. Please add some descriptions to the figure captions.

Response 3(7)

Ok, but the question “which is the manufacturing profile shift used in both cases?” was not answered.

Response 3(8)

Now the figure is better described.

However, as already seen in figure 6, the range for conventional HD is -25º to 50º and therefore, the analysis should consider up to 50º.

Response 3(9)1

Please specify the revision done in the flexibility matrix that have changed the results.

Response 3(10)

Not fully answered.

Response 3(11)

Yes Figure 13, sorry for the mistake. Anyway, what do you mean by algebraic operation?

Response 4(1)

The finite element model is better described. Anyway, there are some points that should be clarified:

• It is not clear why dynamic solver was used. Are the inertial effects considered? If so, what velocity curve was imposed?
• The boundary conditions should be better explained and include in Fig. 17.

Response 4(2)

Figure 20 is not well described. Moreover, x and y axis are not labeled.

Response 4(3)

Are there any difference with previous results with the new refined mesh?

Response 4(4)

Not answered. It seems that only 5 elements are used in the facewidth (L) and according to figure 21, the contact stress values are not homogenous along the facewidth. Which values were used in figure 22?

Final remark:

• Does it make any sense that the contact stress results for disposable HD are lower than for conventional HD? If that was the case, why do not all HD have “l/L = 1” relation?

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 3 Report

The manuscript 1505688, entitled “Calculating the contact stress and normal contact stiffness of the disposable harmonic drive under full load” by Yuxin Zhang et al, has been carefully reviewed again.

I think the authors' response is convincing and the revision of the manuscript is satisfactory. To the current revision, the authors have answered all my queries and I have no further comments. The paper can be accepted.

Author Response

We are very grateful for the high approvals on our work, and thanks a lot for all your meaningful and instructive comments.