Review Reports - Hermite Quartic Splines for Smoothing and Sampling a Roughing Curvilinear Spiral Toolpath

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript presents a new method to construct a curvilinear spiral toolpath using a thermical model. The new method has been verified in terms of speed and time by implementing it into software. A minimum of 10% of the time can be reduced by the new method. The result is promising and a revision is recommended by the reviewer. Please see below for comments to further improve the manuscript.

- The reviewer understands that software can be used to simulate the milling process and calculate the speed and time. However, simulations can't replace the experiments as many factors will alter the processing speed and time. Moreover, there is a 10% time reduction for some conditions, and sometimes the variance between the simulation and experiments may exceed this value. So the reviewer is wondering if the authors have performed the actual experiments to further validate the developed method.

- In the case study, the authors selected two patterns, BIG pocket, and HUG pocket. What are the reasons for selecting those particular patterns? Some explanations are needed.

- For figure 12, it is better to add a legend instead of using arrows to point out each method.

Comments on the Quality of English Language

N/A

Author Response

This manuscript presents a new method to construct a curvilinear spiral toolpath using a thermical model. The new method has been verified in terms of speed and time by implementing it into software. A minimum of 10% of the time can be reduced by the new method. The result is promising and a revision is recommended by the reviewer. Please see below for comments to further improve the manuscript.

The authors would like to thank the reviewer for reading their article and for the constructive comments they received.

The reviewer understands that software can be used to simulate the milling process and calculate the speed and time. However, simulations can't replace the experiments as many factors will alter the processing speed and time. Moreover, there is a 10% time reduction for some conditions, and sometimes the variance between the simulation and experiments may exceed this value. So the reviewer is wondering if the authors have performed the actual experiments to further validate the developed method.

The main focus of the paper is the generation of smooth spiral trajectories suitable for any pocket geometry. The quality of trajectories is assessed by using indicators such as the curvature radius. The results have been validated numerically using an alreday established and published tools VPOp (see [3] and [18]). The authors agree that discrepancies can arise between experiments and simulations, however, we feel confident that the relative gains will remain similar with those estiated from simulation. An experimental plan will be investigate futher in a near future on a CNC machine.

In the case study, the authors selected two patterns, BIG pocket, and HUG pocket. What are the reasons for selecting those particular patterns? Some explanations are needed.

As mentioned in the article (lines 186 and 240), the BIG pocket is the pocket used by Bieterman and Sandström in their article. It allows us to compare the aspect of the trajectory we obtain with theirs. Furthermore, its geometry contains a wide variety of curvatures (small, large, positive and negative) and tangent inclinations, so the robustness of our algorithm could be tested. As for the HUG pocket, it constitutes, above all, a geometry for which the method of Bieterman and Sandström is not functional. We can thus show that our method can generalize an existing method for shapes that are not globally convex. A reformulation of the text has been done for better understanding.

For figure 12, it is better to add a legend instead of using arrows to point out each method.

The requested changes have been made in the specified figure.

Reviewer 2 Report

Comments and Suggestions for Authors

1. I think the Figure 4 may be improved. For example, the main investigation methodologies used in each step can be marked in this figure.

2. Why the authors choose two case studies? What is the main difference between two cases? Is it just the shape difference?

3. Why not consider the role of filter ?

4. The scientific merits and the main innovations should be highlighted in Abstract and Conclusion.

5. Conclusion should be rewritten for better understanding.

Author Response

1. I think the Figure 4 may be improved. For example, the main investigation methodologies used in each step can be marked in this figure.

The authors would like to thank the reviewer for reading their article and for the constructive comments they received. The requested changes have been made in the specified figure.

2. Why the authors choose two case studies? What is the main difference between two cases? Is it just the shape difference?

As mentionned for answering question 3 from reviewer 1, the BIG pocket is the pocket used by Bieterman and Sandström in their article. It allows us to compare the aspect of the trajectory we obtain with theirs. Furthermore, its geometry contains a wide variety of curvatures (small, large, positive and negative) and tangent inclinations, so the robustness of our algorithm could be tested. As for the HUG pocket, it constitutes, above all, a geometry for which the method of Bieterman and Sandström is not functional. We can thus show that our method can generalize an existing method for shapes that are not globally convex. A reformulation of the sentence has been done for better understanding (lines 185 and 240 of article).

3. Why not consider the role of filter ?

FIR filter is just use as a comparison point. Our goal is to enhance the average tool speed by a work on continuity of structure curves (C²). Moreover, the use of FIR filter may cause machining of non appropriate zone (overcut) which is not the case with our method .

4. The scientific merits and the main innovations should be highlighted in Abstract and Conclusion.

Thank you for the comment, modifications have been done in the manuscript and highlighted in red.

5. Conclusion should be rewritten for better understanding.

Thank you for the comment, modifications have been made in the manuscript and highlighted in red.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have investigated the machine tool through connecting the points and trajectory. The suggestions have been issued through suggesting to enhance the continuity level of the toolpath by rebuilding structure curves with set of Hermite quartic spline patches connected in tangency and curvature. This study is interesting however there are some drawbacks that the authors should address them to improve this study.

In the abstract, the authors must rewrite this part according to the scientific writing mode. Especially, let’s remove the common phrase “Thanks to this” in this abstract.
In the introduction, the authors must indicate clearly the novelty points that the authors have contributed on the mining techniques in this study.
The research gap must be implemented in this study through outlining the recent studies and comparing with proposed method through establishing the table based on the years.
The nomenclature and abbreviation should be added at the beginning of this study.
In the results, the authors must indicate and analyze clearly the priority points of proposed method through evaluating the different toolpath locations.
The acknowledgement should be implemented in this study.

Comments on the Quality of English Language

The English writing in this paper must be polished.

Author Response

1. In the abstract, the authors must rewrite this part according to the scientific writing mode. Especially, let’s remove the common phrase “Thanks to this” in this abstract.

The authors would like to thank the reviewer for reading their article and for the constructive comments they received. The "thanks to" formulation has been removed.

2. In the introduction, the authors must indicate clearly the novelty points that the authors have contributed on the mining techniques in this study.

The introduction has been update to stress on those points, mainly after table 3 that has been added to answer the next comment.

3. The research gap must be implemented in this study through outlining the recent studies and comparing with proposed method through establishing the table based on the years.

The main research gap is the possibility to generate smooth sprial-like trajectories for pocket milling, adapted to any geometries (even non-convex one). Table 3 have been added to summarize the state of the art, the paper has been updated to stress out the research gap more clearly.

4. The nomenclature and abbreviation should be added at the beginning of this study.

A table of nomenclatures and a table of abbreviations have been added at the beginning of the article.

5. In the results, the authors must indicate and analyze clearly the priority points of proposed method through evaluating the different toolpath locations.

The proposed method aims to optimize the trajectories for pocket milling, The primary indicator is simulated time, and the secondary indicator is curvature measurement. Modifications have been made in the manuscript to stress on those points.

6. The acknowledgement should be implemented in this study.

This work is self-funded. The authors' contribution note has been completed.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have addressed all of my comments. The manuscript is ready for publication.

Author Response

Authors thank you for your review.

Reviewer 3 Report

Comments and Suggestions for Authors

The authors have addressed some comments of this reviewer in this revised manuscript. However, there are some drawbacks that the authors should address them to improve this study.

The English writing mode in scientific working must be improved in this study. The authors must recheck totally carefully all sentences in the main text.
In the collected results, the authors must analyze and indicate clearly the significance of these results in curvilinear spiral toolpath.
The acknowledgement should be implemented in this study.

Comments on the Quality of English Language

The English writing mode must be polished.

Author Response

1. The English writing mode in scientific working must be improved in this study. The authors must recheck totally carefully all sentences in the main text.

Authors would like to thank the reviewer for comments.

Many sentences (colored in blue) from the main text have been reworded to be in line with the scientific writing style.

2. In the collected results, the authors must analyze and indicate clearly the significance of these results in curvilinear spiral toolpath.

As the tangency discontinuities challenge the acceleration capabilities of the machine tool, curvature distribution is a good indicator of geometric quality of a toolpath: the more the curvature is high, the more the speed decreases. Moreover, curvature can be quickly calculated and can be easily inserted in a optimization loop. Lines 60 to 65 and Paragraph 3 (lines 165 to 190) have been modified to improve analysis results understanding.

3. The acknowledgement should be implemented in this study.

Acknowlegements have been added.