Manufacturing of Rotational Toroidal Shells in Coin Minting

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Reviewer comments

 

Manuscript ID: eng-3706505

Title: Manufacturing of Rotational Toroidal Shells in Coin Minting

Journal: Eng.

The paper presents a forming process for manufacturing collector coins with rotating toroidal shells. The authors propose a single-stage (or double-stage) tube-forming operation to create hollow toroidal shells that allow a coin blank (disk) to rotate freely. The authors combine finite element modeling with experimental validation to analyze the mechanics of deformation, critical process parameters, and operational limits.

It is stated that the paper falls within the scope of the journal, but some points need to be corrected:

1- The abstract is too long and somewhat redundant. It should be shortened and focused on the main results and contributions.

2- The paper states that deformation is driven by bending and circumferential stretching but lacks detailed discussion of the mechanics (e.g., strain paths, local thinning, stress distribution) in the results and conclusion sections. A more in-depth mechanical analysis would improve the scientific rigor.

3- Lines 124–126: The authors state that “…different convergence analyses for adequate modelling of the distribution of the field variables and force-displacement evolutions.” However, no supporting data is provided. A proper mesh sensitivity analysis should be presented, illustrating for example the evolution of key variables such as plastic strain and stress distributions with different mesh sizes.

4- While references are included, the introduction could better situate the work within the broader context of joining by forming, tube inversion processes, and applications in other industries (beyond coin minting). This would increase the relevance of the paper for a wider audience. Add more references on tube forming processes.

5- A table illustrating the mechanical properties of the Silver (Ag925) should be included.

6- In the simulation, it appears that the authors only considered isotropic hardening. What about kinematic hardening or combined isotropic-kinematic hardening to more accurately predict the behavior of the sheet material after the forming process?

7- The paper contains many grammatical errors, awkward phrasing, and inconsistent sentence structures:

• “… is employed to produce a rotating element in collector coins to introduce new aesthetic effects and functionalities to the current coin market.” Rephrase to avoid repetition of “to” : “...is employed to produce a rotating element in collector coins, introducing new aesthetic effects and functionalities to the current coin market.”
• “ The forming process is related to the conventional external inversion of tube ends with some modifications that result in different deformation mechanics from those of conventional tube forming.” Replace by “...that result in deformation mechanics distinct from those of conventional tube forming.”
• “so that to provide the incorporation of advanced security features...” Incorrect construction ("so that to"). Correct form: “...to enable the incorporation of advanced security features...”
• Lines 23-27: Reformulate the sentence to avoid lengthiness.
• “Although coin minting is an old metal-forming process that has been studied for many years...” replace by “Although coin minting is a long-established metal-forming process that has been extensively studied...”
• “…extending tool life and therefore reducing the production costs” Remove “the”: “...reducing production costs.”
• “…the axis of the rotation ” replace by “…the axis of rotation”
• “To avoid smashing the tube ends against the disk...” replace by “To avoid crushing the tube ends against the disk...”
• “...which facilitate the quality assessment of the newly manufactured coins having rotating elements.” Replace by “...which facilitates quality assessment of the newly manufactured coins with rotating elements.”
• “allow to understand the mechanics of deformation” should be “allow us to understand...”

The manuscript would benefit from major revision, as suggested by the reviewer. Additionally, it is advisable for the authors to conduct a thorough proofreading of the article to eliminate any typographical and grammatical errors, and to improve clarity by avoiding overly long sentences.

Author Response

Comments 1: The abstract is too long and somewhat redundant. It should be shortened and focused on the main results and contributions.

 

Response 1: Thank you for highlighting this point. We fully agree with your observation. As a result, we have rewritten the abstract to be more concise, focusing on the key results and contributions.

 

Comments 2: The paper states that deformation is driven by bending and circumferential stretching but lacks detailed discussion of the mechanics (e.g., strain paths, local thinning, stress distribution) in the results and conclusion sections. A more in-depth mechanical analysis would improve the scientific rigor.

 

Response 2: Agree. A more comprehensive analysis of the deformation mechanics has been incorporated into the Results and Conclusions sections.

With regard to the strain paths, they range from a tensile strain state,  to a near plane strain state, , corresponding to elements located at the extremity and at the midsection of the torus cross-section, respectively.

The effective stress varies from a minimum of 195 MPa near the middle of the central section to a maximum of 485 MPa at the inner surface and where it contacts the die. This can be seen in the image on the right side of the strain path diagram.

Concerning the thickness variation, it remains approximately equal to the initial thickness at the midsection, increases from 0.5 mm to a maximum of 0.6 mm near the first quarter of the cross-section, and subsequently decreases to a minimum at the extremity of the torus cross-section. These previous statements can be observed in the new Figure 9. These changes can be found on page number 9, lines (275-290) and page 12, lines (344-347).

 

Comments 3: Lines 124–126: The authors state that “…different convergence analyses for adequate modelling of the distribution of the field variables and force-displacement evolutions.” However, no supporting data is provided. A proper mesh sensitivity analysis should be presented, illustrating for example the evolution of key variables such as plastic strain and stress distributions with different mesh sizes.

 

Response 3: Thank you very much for your comment, with which we fully agree. A mesh sensitivity study was indeed carried out using a quarter of the number of elements, as shown in Figure1 (a) below. Since neither the field variables Figure1 (a) and (b) nor the force – displacement evolution Figure (2), changed significantly, we chose to use the finer mesh due to its higher geometric accuracy, and therefore did not highlight this study in the manuscript.

In fact, the case (b) of Figure 1, runs in only 2 minutes on a personal computer equipped with an Intel(R) Core i7-8565U CPU at 1.99 GHz and 16.0 GB of RAM, making the computation time negligible. This information has been included in the text on page 4, lines (125-133).

 

• (b)                                     

Figure 1 – Effective strain field corresponding to discretizations with (a) 75 and (b) 300 elements, respectively.

Figure 2 – Force–displacement response for finite element models with 75 and 300 elements.

 

Comments 4: While references are included, the introduction could better situate the work within the broader context of joining by forming, tube inversion processes, and applications in other industries (beyond coin minting). This would increase the relevance of the paper for a wider audience. Add more references on tube forming processes.

 

Response 4: Thank you for your valuable feedback. We agree that the introduction could better contextualize the work within the broader field of joining by forming and its relevance to other industries beyond coin minting. In response, we have expanded the literature review by incorporating two new references related to tube forming processes on joining, as suggested. This information has been included in the text on page 1, lines (30-31).

 

Comments 5: A table illustrating the mechanical properties of the Silver (Ag925) should be included.

 

Response 5: Thank you for your suggestion. A table detailing the main mechanical properties of 925 silver (Ag925) has been included in the document on page 3, lines (79-81).

 

Comments 6: In the simulation, it appears that the authors only considered isotropic hardening. What about kinematic hardening or combined isotropic-kinematic hardening to more accurately predict the behavior of the sheet material after the forming process?

 

Response 6: Thank you for your valuable feedback. The press speed for shaping the silver tubes was 10 mm/min. Given the tube height, the process can be considered quasi-static. The strain rate is on the order of 1 s⁻¹, as shown in Figure 3. At these strain rates, for this material, there is no significant influence on the stress response, and therefore, kinematic hardening was not taken into account. This information can be found on page 4, lines (115-117).

Figure 3. - Effective strain rate distribution

 

Comments 7: The paper contains many grammatical errors, awkward phrasing, and inconsistent sentence structures:

 

Response 7: Thank you for your valuable feedback. The suggested revisions have been made, and we appreciate your input in improving the clarity and coherence of the paper.

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

The manuscript presents an innovative forming process capable of shaping thin-walled tubes into toroidal shells in a single-stage operation, applied to the design of rotating elements in collector coins. The proposed approach introduces novel aesthetic and functional dimensions to coin manufacturing. The study is well-structured, the methodology is clearly described and technically sound, and the results demonstrate both academic significance and practical applicability in engineering contexts. However, certain aspects of the work would benefit from further clarification. Specifically, more detailed explanations regarding the control of the end-forming process, the mechanics of the rotational interaction between the toroidal shell and the coin blank, and the tolerance requirements for ensuring consistent rotation would enhance the overall clarity and robustness of the study.

1. When performing axisymmetric modeling, the specific basis for mesh division (such as element size and convergence tests) is not explained.

2.The paper only uses Vickers hardness and stress-strain curves to illustrate the material differences between the tube and the disk, but does not analyze the influence of the anisotropy of the silver alloy on forming.

3.The selection basis for the specific tested values of key parameters in the forming process (such as flaring radius R and initial tube height h₀) is not clarified, and it is recommended to supplement the explanation.

 4.Figure 9 only shows the force-displacement curve of the non-circular cross-section, and does not provide a comparison of the circular cross-section under different h₀. A reasonable basis for not considering this influencing factor should be given.

5. In section 4, it reveals a noticeable deviation between the FE model and the experimental results in terms of lateral displacement. However, the manuscript merely attributes this discrepancy to "experimental data errors" without providing a thorough analysis. It is recommended that the authors explore additional contributing factors, such as simplifications in boundary conditions, material nonlinearity, fracture principle or residual stress. For reference, a more detailed discussion can be found in similar studies (e.g., DOI: 10.1061/JSENDH.STENG-13418).
6. Section 4.1 mentions that "the surface of the forming tool in contact with the silver tube and disk should have a low friction level to avoid appearance defects or material flow defects." Please explain how this requirement is achieved in the test and simulation processes.
7. Regarding the "clearance set between the tubular preform and the mandrel" mentioned in Figure 6b, how is 0.75 mm determined as the limit value?
8. The differences between the test and finite element results in Figure 9 need to be reasonably explained.

Author Response

 

Comments 1: When performing axisymmetric modeling, the specific basis for mesh division (such as element size and convergence tests) is not explained.

 

Response 1: Thank you very much for your comment, with which we fully agree. A mesh sensitivity study was indeed carried out using a quarter of the number of elements, as shown in Figure1 (a) below. Since neither the field variables Figure1 (a) and (b) nor the force – displacement evolution Figure (2), changed significantly, we chose to use the finer mesh due to its higher geometric accuracy, and therefore did not highlight this study in the manuscript.

In fact, case (b) of Figure 1, runs in only 2 minutes on a personal computer equipped with an Intel(R) Core i7-8565U CPU at 1.99 GHz and 16.0 GB of RAM, making the computation time negligible. This information has been included in the text on page 4, lines (125-133).

•                                (b)                                     

Figure 1 – Effective strain field corresponding to discretizations with (a) 75 and (b) 300 elements, respectively.

Figure 2 – Force–displacement response for finite element models with 75 and 300 elements.

 

Comments 2: The paper only uses Vickers hardness and stress-strain curves to illustrate the material differences between the tube and the disk, but does not analyze the influence of the anisotropy of the silver alloy on forming.

 

Response 2: Thank you for highlighting this point. Yes, anisotropy was not taken into account for this study. The criterion of plasticity used was the von Mises criterion, which is applied for isotropic materials. In fact, given the small dimensions of the tube, 7.5 mm in diameter and 0.5 mm in thickness, it becomes extremely difficult to manufacture specimens in all three directions that would allow the determination of anisotropy coefficients. On the other hand, the good correlation between the experimental values and those obtained by FEM, both in terms of force evolution and the final dimensions of the toroidal shell, confirms that the anisotropy can be considered negligible. This information can be found on page 4, line 124 and Figure 10, page 11, lines (308-309).

 

Comments 3: The selection basis for the specific tested values of key parameters in the forming process (such as flaring radius R and initial tube height h₀) is not clarified, and it is recommended to supplement the explanation.

 

Response 3: Thank you very much for the question. The radius must range from 0.5 to 1 mm due to geometric constraints, with a specific value of R=0.75 mm chosen based on the coin design, as it represents a good compromise, as seen in the evolution shown in Figure 8 (a). The initial tube height (h₀) was determined through trials in FEM. This information is on page 9, lines (247-249) and (257-260).

 

Comments 4: Figure 9 only shows the force-displacement curve of the non-circular cross-section, and does not provide a comparison of the circular cross-section under different h₀. A reasonable basis for not considering this influencing factor should be given.

 

Response 4: Thank you very much for your comment, which we fully agree with. The initially intended geometry for the cross-section was circular. However, during the development of the project, the design team opted for a non-circular cross-section for aesthetic reasons. In fact, the circular cross-section produced coins that were excessively thick, making them aesthetically unappealing to collectors. Therefore, the authors focused solely on the study of the C-shaped cross-section, as it was deemed the most suitable for the desired design and functionality. This information is on page 8, lines (211-214).

 

Comments 5: In section 4, it reveals a noticeable deviation between the FE model and the experimental results in terms of lateral displacement. However, the manuscript merely attributes this discrepancy to "experimental data errors" without providing a thorough analysis. It is recommended that the authors explore additional contributing factors, such as simplifications in boundary conditions, material nonlinearity, fracture principle or residual stress. For reference, a more detailed discussion can be found in similar studies (e.g., DOI: 10.1061/JSENDH.STENG-13418).

 

Response 5: Thank you for your valuable feedback. The authors carefully reviewed Section 4 of the manuscript and did not find discrepancies in terms of lateral displacement. Indeed, divergences between the experimental results and the FEM can be observed in the correlation between force evolution and displacement. However, the authors consider these divergences acceptable, as the maximum load difference between the experimental and numerical values (2.47 kN and 2.80 kN) is less than 12%. The authors appreciate your reference to similar studies and have revised the manuscript to address potential factors contributing to the discrepancy on results, including simplifications in boundary conditions, material characterization, fracture mechanics, and friction factor between others. This information is on page 11, lines (293-297).

 

Comments 6: Section 4.1 mentions that "the surface of the forming tool in contact with the silver tube and disk should have a low friction level to avoid appearance defects or material flow defects." Please explain how this requirement is achieved in the test and simulation processes.

 

Response 6: Thank you very much for your comment. Experimentally, a fine polishing process was carried out to ensure that the formed surface of the torus was free from visible scratches or surface defects. Numerically, a friction factor of 0.1 was applied to the contact interfaces between the dies and objects, which provided the most compatible results between the predicted numerical forces and the experimental data. This information is on page 5, lines (137-139).

 

Comments 7: Regarding the "clearance set between the tubular preform and the mandrel" mentioned in Figure 6b, how is 0.75 mm determined as the limit value?

 

Response 7: Thank you very much for your comment. Gap values smaller than 0.75 result in an external inversion, while values greater than 0.75 lead to an internal inversion. Gap values very close to 0.75 initiate contact between the tube end and the flaring dies near the top and bottom of the flaring radius of the dies, which induces a plastic instability, as shown in Figure 6(b). Therefore, the maximum clearance value of 0.75 corresponds to the flaring radius.

 

Comments 8: The differences between the test and finite element results in Figure 9 need to be reasonably explained

 

Response 8: Thank you very much for your comment. This comment was previously responded in the Response 5.

 

Thank you for your valuable feedback. The suggested revisions have been made, and we appreciate your input in improving the clarity and coherence of the paper.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

All questions have been addressed and concisely revised by the authors. Following these revisions, the manuscript may be considered acceptable in its current form.

Reviewer 2 Report

Comments and Suggestions for Authors

The author resolved the mentioned issues, and now the research paper can be accepted from my side.