CAD-Integrated Automatic Gearbox Design with Evolutionary Algorithm Gear-Pair Dimensioning and Multi-Objective Genetic Algorithm-Driven Bearing Selection

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1.Figure numbering and citations are inconsistent: Figure 3 is not explicitly referenced in the text, while Figures 6 and 7 contain duplicate content (both labeled “Finished gear pair model”).
2.Reference formatting is inconsistent: Some references lack titles or page numbers; standardization is recommended.
3.References are outdated: Most are from before 2010, with insufficient citations of relevant research from the past five years, failing to adequately reflect current research frontiers.
4.Lack of experimental validation: No simulation verification, or comparison with relevant similar designs.
5.Although KissSys is mentioned, no quantitative comparison of performance or efficiency was conducted under identical design tasks. For instance, it remains unclear whether its ten-minute modeling speed consistently outperforms other software.

Author Response

1. Figure numbering and citations are inconsistent: Figure 3 is not explicitly referenced in the text, while Figures 6 and 7 contain duplicate content (both labeled “Finished gear pair model”).

Response 1: Figure 3 has been replaced with a different one due to quality and licensing issues and is now also referenced in the text. The titles of Figures 6 and 7 have been changed.

2. Reference formatting is inconsistent: Some references lack titles or page numbers; standardization is recommended.

Response 2: All known information has been added, and the formatting has been improved.

3. References are outdated: Most are from before 2010, with insufficient citations of relevant research from the past five years, failing to adequately reflect current research frontiers.

Response 3: Several more recent papers have been added to the literature review.

4.Lack of experimental validation: No simulation verification, or comparison with relevant similar designs.

Response 4: Full experimental validation is outside the scope of this work, as manufacturing and testing physical prototypes is not feasible here. However, the optimization method was verified through multiple computational tests with different input settings, and in all cases the solver satisfied the constraints and produced feasible designs. This provides confidence in the correctness of the approach, and the limitation is now stated clearly in the conclusion chapter of the manuscript.

5.Although KissSys is mentioned, no quantitative comparison of performance or efficiency was conducted under identical design tasks. For instance, it remains unclear whether its ten-minute modeling speed consistently outperforms other software.

Response 5: I understand the remark. It was not correct to mention Kisssys software. The goal was to compare the classical calculation and automated approach with this novel methodology. The paragraph has been updated.

Reviewer 2 Report

Comments and Suggestions for Authors

1. Text states: “The base circle is … usually larger than the pitch circle.” It is wrong. For involute gears, the base circle is always smaller than or equal to the pitch circle (never larger), because, , and . Pls clarify.
2. You write:
   This is actually the transverse pitch diameter of a helical gear, not the base circle diameter. The correct base circle diameter is:
   where = transverse pressure angle. Calling it “crown circle” is unusual; standard terminology = addendum circle. “Ensures sufficient clearance” is misleading—clearance depends on dedendum depth, not addendum circle.
3. Addendum = m × ha*, where ha* is standardized (usually 1.0), not 1 mm. Addendum in mm depends on the module. Writing “ha normally equals 1 mm” is incorrect and dimensionally wrong. You used:
   ➝ This is describing root circle, but the sign is reversed. Root circle < pitch circle.
   
   
4. Pitch circle calculation “last” is conceptually wrong. Pitch diameter is primary geometry, not last. Addendum and root circle depend on pitch circle, not vice-versa. Mass of gear using crown circle cylinder is crude and physically wrong. Mass ≠ mass of solid cylinder of addendum diameter. Real gears have hollow root region, tooth gaps, and geometry. This leads to large overestimation and is unscientific for an optimization problem.
5. Incorrect mechanical power–torque equation. Mk​=P​/ 2πn ➝ Wrong by a factor of 60,000. Correct:
   or
    for P in W. Also, Minimum shaft diameter formula incorrect

Dimensionally wrong: τ³ has wrong units; shaft diameter cannot depend on τ³.

6. Force formulas incorrect,

• 
  It should be
• Axial force:
  Should be:

Gear tooth angle α is not defined; they probably mean pressure angle, but text says, “tooth angle”.

7. Bearing life equation looks incorrect. Pls address:

But standard ISO formula is:

8. Fe depends on P = XFr + YFa, not Co (static rating). You mix Fa/Fr and Fa/Co, resulting in conceptual confusion. “Choice of X and Y is based on Fa/Co” — Wrong. Should be Fa/Fr compared with “e”. Reduced stress formula looks incorrect.

It is stated:

Torque stress and bending stress cannot be algebraically added as σo + σt, but von Mises stress:

9. Incorrect bending stress formula.

You use:
But actual bending moment = Fo × a, so
Not d². Incorrect torque stress formula

You use:
This is not torque stress; torque stress uses torsion modulus, not a force.

10. Objective function is inconsistently defined. You minimize gear weight using “two cylinders of crown circle diameter”; physically unrealistic. Multi-objective weighting (70-20-10) chosen arbitrarily without validation or sensitivity analysis. Constraint table is inconsistent. Constraint 5: “Allowed stress from Bach formula <110 MPa” — reversed.
    Should be actualstress < allowed stress.
11. Empirical constraints applied without justification. Width constraints are cited but not linked to specific standards. Pareto front description copied from textbook. Not applied to actual results, no illustration of real Pareto points. Table 1 unreadable. X and Y table printed incorrectly → mixing rows. No validation of optimization output. No comparison with catalog gears or bearings. No check against standard gear design (ISO 6336). Significant CAD–Python integration section irrelevant. Adds length but provides no scientific insight. What programme used? Write it. Entire gear design ignores ISO/AGMA standards. No use of standard tooth strength, pitting resistance, safety factors, etc.
12. Shaft stress and bearing load based on wrong forces and torque. Therefore, stress constraints meaningless. Optimization results meaningless. Because inputs to optimization are physically wrong. Claiming the algorithm “could substitute the work of a human engineer” is unscientific and unvalidated; no benchmarking, expert evaluation, or real-world cases are provided. No comparative metrics vs. expert-designed gear pairs are shown (quality, weight, safety margins, cost, manufacturability). Stating that “normal PC completes design in 10 minutes” but providing no hardware specifications, algorithm complexity, or batch test results undermines scientific credibility.
13. Gear boundaries (e.g., <300 teeth, module <30, width <100 mm) are stated with no technical rationale or references. These limits contradict real gear design ranges; modules up to 30 are extremely large, used only in heavy-duty machines. You mention the algorithm “very often leads to failure of the whole automatic process.” No frequency, reasons, error logs, or examples are provided. This is a major scientific gap. Mentions RL and Text2CAD without feasibility analysis or linkage to present work.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

The English language needs improvement.

Author Response

Please, see the file attached. I was not possible to insert the answers into the web interface with the correct format. 

 

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The paper explores the use of global optimization and AI to automate gearbox design, from selecting gear and shaft parameters to generating a full CAD model in Siemens NX. It shows that combining Ipopt and NSGA-II enables fast, optimized designs, delivering a complete CAD assembly in about ten minutes, far quicker than traditional manual methods. Although the topic is certainly interesting and relevant, there are several major issues that need to be addressed, as listed below.

 

• The statement “exceeding the ability of a human designer” appears overly strong in its current form; such claims should be moderated unless supported by clear evidence.
• The introduction is very brief, and typically the literature review is integrated within it to contextualize the work, highlight the novelty, and clarify the scientific contribution of the article.
• All technical statements should be properly supported with references, including those related to algorithms, artificial intelligence, and general methodological claims.
• Although the paper deals with optimization, the focus of the introduction should remain on gearboxes, as this is the central subject. The current structure shifts the attention too much toward optimization methods; the literature review is useful but should be integrated into a more gearbox-focused introduction.
• The description of the proposed methodology is not entirely clear, and the novelty of the work should be stated more explicitly and convincingly.
• The literature review is very broad, and in places it drifts away from the specific problem of gear design, which weakens the focus of the article.
• The pseudocode shown in Figure 1 is visually unrefined; improving its clarity and presentation would significantly enhance readability.
• The expression “The calculation is taken from [18]” should be accompanied by a clearer explanation, especially since the referenced source is not in English, which raises concerns for an international audience.
• The definition of bounds might be better presented in a table rather than in a simple list, improving organization and readability.
• The sentence regarding real-world considerations for gear-tooth width (wear resistance, strength, stress distribution) is appropriate, but it should be supported with relevant references.
• Reference [18] appears repeatedly throughout the text, the reviewer thinks its is a typo
• While a simplified design method may be appropriate for a preliminary study, it should be clearly acknowledged that this does not represent an industrially viable workflow. Only macro-geometry is considered, while micro-geometry effects, well documented in the literature (e.g., [1], [2]), are neglected. This is a major limitation that should be openly discussed. Furthermore, the claim that the proposed method outperforms a human designer should be avoided, as it is not supported.
• The choice of the Ipopt algorithm is not sufficiently justified. Have alternative solvers been tested? The explanation provided is too brief and relies excessively on references; in its current form, the dedicated paragraph adds little value.
• The statement “The preparation of the correct and broad set of bearings… is not necessary for the scientific paper” is not convincing. A scientific paper may be theoretical or industrially oriented, but the current compromise achieves neither. As presented, the algorithm finds only a first-attempt design and does not represent a rigorously optimized industrial solution, so it should not be compared to manual design practices.
• Figure 3 is of poor visual quality; it could be reproduced more clearly with minimal effort.
• Including a schematic overview of the entire optimization workflow (showing both logical and coding steps) would help readers understand the process more easily.
• The trend shown in Figure 5 appears to simply demonstrate that the cost function decreases; its purpose in supporting the scientific narrative should be better explained.
• The case study is described in a rather concise manner, lacking the depth necessary to properly validate the proposed methodology.
• It would be helpful to show how the optimized solution compares to the rounded design. Moreover, the assumption that rounding an unconstrained optimum yields a near-optimal discrete solution is not self-evident; this should either be demonstrated or discussed critically.

References:

[1] https://doi.org/10.1016/j.mechmachtheory.2025.106118

[2] https://doi.org/10.1016/j.mechmachtheory.2024.105752

Comments on the Quality of English Language

The English writing would benefit from refinement to make the style more formal and scientific, as some expressions currently sound informal.

Author Response

The paper explores the use of global optimization and AI to automate gearbox design, from selecting gear and shaft parameters to generating a full CAD model in Siemens NX. It shows that combining Ipopt and NSGA-II enables fast, optimized designs, delivering a complete CAD assembly in about ten minutes, far quicker than traditional manual methods. Although the topic is certainly interesting and relevant, there are several major issues that need to be addressed, as listed below.

1. The statement “exceeding the ability of a human designer”appears overly strong in its current form; such claims should be moderated unless supported by clear evidence.

Response 1: Changed in the manuscript

2. The introduction is very brief, and typically the literature review is integrated within it to contextualize the work, highlight the novelty, and clarify the scientific contribution of the article.

Response 2: Thank you for your comment. The introduction has been updated to address this and other remarks.

3. All technical statements should be properly supported with references, including those related to algorithms, artificial intelligence, and general methodological claims.

Response 3: More references have been added to the text. I have focused especially on the introduction and methodology chapters.

4. Although the paper deals with optimization, the focus of the introduction should remain on gearboxes, as this is the central subject. The current structure shifts the attention too much toward optimization methods; the literature review is useful but should be integrated into a more gearbox-focused introduction.

Response 4: Thank you for your comment. The introduction has been updated to address this remark. I still feel that the literature review should have somehow its own chapter. It is now part of the introduction as a subchapter. Clearer connection to the rest of the introduction has been added. The introduction now also clearly states the aims of the paper.

The aim of the paper is not the optimization of a gearbox as such. My goal was to show a novel approach to the design process. Creation of a gearbox was just chosen as an example. I tried to add a clear explanation of the aim to the introduction.

5.The description of the proposed methodology is not entirely clear, and the novelty of the work should be stated more explicitly and convincingly.

Response 5: The first part of the methodology has been updated to emphasize the novelty of the work. It highlights the integration of evolutionary algorithms with CAD modelling, which enables faster and more efficient design iterations. The literature review is very broad, and in places it drifts away from the specific problem of gear design, which weakens the focus of the article.

The focus of the paper is on the novel designing method and a direct combination of optimization methods with CAD modelling. The gearbox design was originally chosen just as an example to demonstrate the approach. The literature review had to be broad, because there are very few examples similar to our current research. It is also important to say that the method could be applied to basically any engineering task. However, I accept that the Introduction and Literature review could underline the aim of the research more clearly. My revision has tried to address this remark.

6. The pseudocode shown in Figure 1 is visually unrefined; improving its clarity and presentation would significantly enhance readability.

Response 6: Agreed. The pseudocode has been updated.

7. The expression “The calculation is taken from [18]”should be accompanied by a clearer explanation, especially since the referenced source is not in English, which raises concerns for an international audience.

Response 7: I agree with this feedback. The sentence has been updated and English-language reference has been added. The calculations are the same, however, I do understand the concern.

8. The definition of bounds might be better presented in a table rather than in a simple list, improving organization and readability.

Response 8: Bounds are calculation constraints stated in Table 2 for the first calculation and in Table 3 for the second one. I agree that the paragraph in 3.1 could be confusing for the reader. The explanation reference to the tables has been added.

9. The sentence regarding real-world considerations for gear-tooth width (wear resistance, strength, stress distribution) is appropriate, but it should be supported with relevant references.

Response 9: I have added appropriate references supporting the influence of gear-tooth width on wear resistance, strength, and stress distribution. There are many possible ways to address in detail those considerations. The uploaded reference states more than the basic calculation.

10. Reference [18] appears repeatedly throughout the text, the reviewer thinks its is a typo

Response 10: This is not a typo. The basic calculation is taken from reference [18] (after adding some more references it is 22) I was not really sure if I needed to cite every single equation. I just wanted to have it absolutely clear. The reference remained, however, I can delete it if necessary.

11. While a simplified design method may be appropriate for a preliminary study, it should be clearly acknowledged that this does not represent an industrially viable workflow. Only macro-geometry is considered, while micro-geometry effects, well documented in the literature (e.g., [1], [2]), are neglected. This is a major limitation that should be openly discussed. Furthermore, the claim that the proposed method outperforms a human designer should be avoided, as it is not supported.

Response 11: I agree with the remark. The text of the conclusion has been updated accordingly. The use of the basic designing approach is now clearly stated in the conclusion.

The comparison with a human designer has been deleted.

12. The choice of the Ipopt algorithm is not sufficiently justified. Have alternative solvers been tested? The explanation provided is too brief and relies excessively on references; in its current form, the dedicated paragraph adds little value.

Response 12: The paragraph has been revised. Ipopt gives computational stability and fast convergence even for problems with nonconvex constraints and large numbers of continuous variables. It is part of the Ipopt library and is thoroughly tested.

13. The statement “The preparation of the correct and broad set of bearings… is not necessary for the scientific paper”is not convincing. A scientific paper may be theoretical or industrially oriented, but the current compromise achieves neither. As presented, the algorithm finds only a first-attempt design and does not represent a rigorously optimized industrial solution, so it should not be compared to manual design practices.

Response 13: Agreed. The statement has been deleted.

14. Figure 3 is of poor visual quality; it could be reproduced more clearly with minimal effort.

Response 14: Figure 3 has been updated due to the quality and licencing.

15. Including a schematic overview of the entire optimization workflow (showing both logical and coding steps) would help readers understand the process more easily.

Response 15: Figure 9 has been added to the end of the conclusion to summarise the whole creation process. It is basically a graphical form of a pseudocode.

16. The trend shown in Figure 5 appears to simply demonstrate that the cost function decreases; its purpose in supporting the scientific narrative should be better explained.

Response 16: An explanatory sentence has been added.

17. The case study is described in a rather concise manner, lacking the depth necessary to properly validate the proposed methodology.

Response 17: The aim of the case study was to show the possibility of the connection between evolutionary optimization algorithms and the CAD designing process. The author tested the software’s ability using the broad spectrum of the input parameters. Both optimization and CAD models are stable and feasible for creating the preliminary design models and suggesting the main parameters to the designer. I understand that the case study was not described properly. The input parameters and results have been added to the given paragraph in the conclusion. The main results are also clearly stated now.

18. It would be helpful to show how the optimized solution compares to the rounded design. Moreover, the assumption that rounding an unconstrained optimum yields a near-optimal discrete solution is not self-evident; this should either be demonstrated or discussed critically.

Response 18: The rounding of the modulus and an explanation are mentioned in the text. The difference is 3%, which is insignificant for a preliminary design.

 

References:

[1] https://doi.org/10.1016/j.mechmachtheory.2025.106118

[2] https://doi.org/10.1016/j.mechmachtheory.2024.105752

 

 

 

 

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The paper can be accepted now. Authors have addressed the concerns.

Comments on the Quality of English Language

The English language needs improvement.