Evaluation of the Adaptive Behavior of a Shell-Type Elastic Element of a Drilling Shock Absorber with Increasing External Load Amplitude
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis work may be a research report rather than a paper because the manuscript does not compare with previous data in any journals. How can readers trust the results just generated from the commercial code without any validation ? First of all, native English speaker should check all contents and improve the quality of the manuscript.
Precise comments are :
-Original English speaker should assist all contents to improve the quality of this work. In addition, just check the typo errors. Ex) Line 26 , line 540 etc.
-Title should be enhanced to clear understanding the issue of this work.
Ex)...Elastic Element of for a....
What is the meaning of ‘with Increasing External Load Amplitude’ ?
-All sections need reorganization. Ex) Line 114~130 should be reorganized. Some part may be suitable in the first portion of ‘Introduction’ and the other parts should be moved in other sections or conclusion.
-Paper should not include specific numerical data in the Conclusion because the content is not for a research report.
-Why not non-dimensionlization of the mathematical model for more generalization of the results ?
-Why not include the Refs in sections ? Ex) Section 2. Check all other sections.
-Illustrations of Figs are incomplete. And redraw Figs for more precisely rather than the Figs in the manuscript which are just the copy of the commercial code. Check all Figs.
-Too many data are just the results of parametric studies without any validations from the data using commercial codes.
-Titles of all sections and subsections should be precisely improved.
-Conclusion should not be the summery of numerical results.
Comments on the Quality of English LanguageRefer to the comment.
Author Response
Comments and Suggestions for Authors
This work may be a research report rather than a paper because the manuscript does not compare with previous data in any journals. How can readers trust the results just generated from the commercial code without any validation ? First of all, native English speaker should check all contents and improve the quality of the manuscript.
General Response
Thank you for the careful read and for sharing these broader concerns.
On the nature of the submission.
This manuscript is a research article, not a report. Its purpose is to introduce and evaluate a new load-bearing shell element within a drilling shock absorber and to elucidate its adaptive regime under progressively increasing external loads. The paper follows the MDPI structure for research articles (focused background; methods and modeling framework; results that extract qualitative trends and decision-level quantitative markers; concise conclusions that also state limitations). The contribution is conceptual and mechanistic: it proposes a specific construction and modeling framework and demonstrates how contact growth redistributes stresses and pressures – insight that is actionable for design.
On “trust” and the role of a commercial solver.
The solver is an instrument, not the result. Ideas on which the research is based, new design, geometry, boundary conditions, contact law, friction, loading protocol, and interpretation are author-defined and documented. We verified the solutions internally (mesh-refinement checks, stability with respect to contact and step parameters, balance consistency) and observed that the spatial patterns and extrema locations are robust, while peak magnitudes vary only marginally. The reported trends are consistent with classical mechanics expectations and with our prior analytical and experimental publications on related devices. Where exact legacy datasets do not exist – because the element and regime are new – we provide systematic parameter sweeps to establish monotonicity and sensitivity, which is the appropriate validation pathway for a new construction evaluated numerically.
On language quality.
We agree that clear English helps the reader. Occasional slips happen even in professionally edited texts; we therefore re-checked the full manuscript with a native speaker and corrected minor typographical issues. These copyedits do not alter the technical content.
Comments 1.
-Original English speaker should assist all contents to improve the quality of this work. In addition, just check the typo errors. Ex) Line 26 , line 540 etc.
Response to Comment 1
Thank you for the careful reading. Occasional typographical slips are a common occurrence even in texts reviewed by professional linguists. We have re-checked the manuscript in full with the assistance of a native English speaker and corrected minor typographical issues. These copyedits did not affect the technical content, figures, or conclusions.
Comments 2.
-Title should be enhanced to clear understanding the issue of this work.
Ex)...Elastic Element of for a....
What is the meaning of ‘with Increasing External Load Amplitude’ ?
Response to Comment 2
We appreciate the attention to the title. The phrase “with Increasing External Load Amplitude” is intentional: in deep drilling the precise upper bound of external loads is difficult to forecast a priori, and the device’s adaptive response is best assessed under a parametrically increasing load envelope, beyond nominal conditions. The current title transparently signals:
- the evaluation study;
- the adaptive behavior of a shell-type elastic element;
- its functional context in a drilling shock absorber, and
- the load-increase scenario that reveals the adaptive regime.
If the reviewer wishes to suggest a specific alternative wording, we would be glad to consider it; otherwise we respectfully prefer to retain the present title because it aligns with the manuscript’s scope and findings.
Comments 3.
-All sections need reorganization. Ex) Line 114~130 should be reorganized. Some part may be suitable in the first portion of ‘Introduction’ and the other parts should be moved in other sections or conclusion.
-Paper should not include specific numerical data in the Conclusion because the content is not for a research report.
Response to Comment 3
From the outset we structured the manuscript to follow the MDPI conventions for research articles. The current organization is:
Abstract
- Introduction (context, motivation, novelty and aim)
- Materials and Methods with subsections
2.1 Design features of the adaptive shock absorber
2.2 Calculation scheme of the shell elastic element
2.3 Finite-element model and contact formulation
- Results with subsections
3.1 Normal mode (clearance open)
3.2 Emergency/adaptive mode (clearance closure)
- Conclusions (principal findings and limitations)
Standard back matter (Funding, Data Availability, Conflicts, References)
This structure mirrors the flow recommended for MDPI journals and reflects the logical progression from motivation to model, from model to results, and finally to distilled takeaways. If a specific clause between the cited lines is believed to belong elsewhere, we would appreciate a precise pointer; absent a concrete requirement, we prefer to keep the current sequencing because it maintains continuity for the reader. Regarding the Conclusions: we include only brief, decision-level quantitative markers (for example, thresholds and qualitative trends) to make the practical implications explicit; this is a standard, concise summary rather than a repetition of derivations or datasets. For transparency, the conclusions also state the model’s limitations.
If the editor ultimately prefers any stylistic adjustment, we will of course comply, but we believe the manuscript in its present form already satisfies the journal’s organization standards and communicates the study’s purpose and findings clearly.
Comments 4. -Why not non-dimensionlization of the mathematical model for more generalization of the results ?
Response to Comment 4
Thank you for raising this point. In this article we intentionally report results in dimensional form because the study is aimed at direct engineering use in deep-drilling applications, where designers and operators work with physical units for sizing and decision-making. Non-dimensional presentations are a valuable complementary lens; we have used them in our prior publications (for example, the work cited as Ref. [18]) and in other contributions that include both analytical and experimental perspectives. In the present paper, however, the research instrument is a numerical model focused on evaluating an adaptive shell-type element across practical load envelopes. The dimensional reporting chosen here best serves that applied intent, while the generality is conveyed through systematic parameter sweeps already included in the study.
Comments 5. -Why not include the Refs in sections ? Ex) Section 2. Check all other sections.
Response to Comment 5
The manuscript follows a conventional research-article flow: a focused literature review in Section 1 establishes the state of the art and the gap, and the subsequent sections present our original shock absorber design, and our original model, results, and interpretation. We intentionally keep Methods and Results uncluttered by background citations so that the new material reads clearly and linearly. All essential prior art is already covered in the Introduction; if there is a specific source the reviewer believes is strictly necessary within a particular subsection, we would appreciate a precise pointer for consideration.
Comments 6. -Illustrations of Figs are incomplete. And redraw Figs for more precisely rather than the Figs in the manuscript which are just the copy of the commercial code. Check all Figs.
Response to Comment 6
We respectfully note that Fig. 1 depicts an original shock-absorber concept and its shell-type elastic element; the underlying prototypes are protected by national patents. Fig. 2 shows our original mechanical model of the principal assembly. Figures 6, 7, 8, 12, and 13 are author-generated analyses and do not constitute “copies of a commercial code.” While we use ANSYS as a computational and post-processing tool, ideas on which the research is based, the geometry, modeling assumptions, contact formulation, loading protocol, and the way results are composed and annotated are entirely our own. The chosen renderings prioritize engineering readability and consistency across panels, which is why we retain the current figure set.
Comments 7. -Too many data are just the results of parametric studies without any validations from the data using commercial codes.
Response to Comment 7
Parametric exploration is central to this contribution because the paper develops a new construction and a new numerical model to reveal its adaptive regime and to extract actionable design guidance. The solver is merely a means; the novelty lies in the concept, the modeling framework, and the interpretation that leads to concrete recommendations. As standard numerical quality checks, the study includes internal verification such as mesh-sensitivity assessment and balance checks, and its trends are consistent with our prior analytical and experimental work published elsewhere. Given the objectives here, additional experimental replication is outside the present article’s scope and is not required for the conclusions we draw.
Comments 8. -Titles of all sections and subsections should be precisely improved.
Response to Comment 8
We appreciate the suggestion. The current headings were crafted to align with the journal’s structure and to map one-to-one to the content of each section, maintaining continuity from motivation through methods to results and conclusions. If the reviewer has a concrete alternative for any specific title, we are happy to consider it; otherwise we prefer to keep the existing wording, which the editorial guidelines also accommodate.
Comments 9. -Conclusion should not be the summery of numerical results.
Response to Comment 9
We drafted the Conclusions – indeed, the manuscript as a whole – in line with MDPI’s guidance for research articles, which asks authors to provide a concise synthesis of the principal findings. In research articles, conclusions are expected to distill the main findings – both qualitative trends and the essential quantitative markers that make the results actionable. Our Conclusions do precisely that: they summarize the principal observations from the study at decision-making granularity and, for transparency, state the model’s limitations. They are not a reproduction of derivations or raw datasets, and therefore are appropriate as written.
We appreciate the reviewer’s time and careful attention.
Reviewer 2 Report
Comments and Suggestions for AuthorsDear authors,
I found the article interesting and very readable. However, I have some comments and suggestions in the interesting of improving the article.
Minor detail, but I would propose to make the coordinate system in Fig. 4 more conspicuous. When it is printed in black and white, the letters may be hard to see.
You did not discuss the cut gap in the text or caption during describing the system to be studied—although it is visible in the cross section, A-A, in Fig. 2. For clarity to the reader that physical element should be part of the description, in both text and caption.
What is the meaning of the 10 s time in Fig. 4, i.e. with respect to the loading parameter, t/T? Please, discuss that in the text.
The displacement distribution shown on Fig. 4.b is very symmetric along the z-axis, spatially speaking. The color distribution gives such an impression. Could there be an artifact introduced by the FEA code? Do you see changes in the spatial distribution if you change the grid size? Let me explain the issue about the symmetry that I observe. If you take -34.72mm as the middle point. The relative difference between the max and min is the same, an absolute value of 27.79mm. I don’t consider the max of 0.02255 mm, because I don’t see that color in the diagram—by the way, why is that color not shown? I personally would not expect the displacements to be symmetric. To make the article more complete I suggest that you elaborate on that point, perhaps right there and then add a summary in the conclusions.
I propose to add the corresponding back view of 4.a, for the viewer to judge the color distribution overall. This is an extension of my comment above about 4.b. Perhaps someone can see something I don’t at the moment, similar to what is discussed for 4.b above.
I would propose to use a different color for the housing in 4.b, as is done in 4.a. Unless there is a good reason to keep the color red, in which case a note to that effect should be included.
Figures 9 and 10 would display more clearly if shown unfolded, indicating the azimuthal component and the coordinate along the z-axis—and referring back to Fig. 2 cross section A-A, to highlight to the reader the location of the gap. You could keep as an inset the views presently displayed. Besides, such a representation would assist your description along section 3.2.
My understanding is that you deal with the tangential stress as a sliding-type zone—not explicitly spelled, buy I infer so—and the geometry of stress distribution observed could well be an artifact of the boundary conditions. I made a comment along these lines above, though less explicitly. Some comment from your side, for the reader, would round up your article real well. Your research in the past has dealt with other geometries of the gap or cut but that detail has not been clearly discussed there, in my opinion.
Good luck with the publication process.
Comments on the Quality of English LanguageThe article is very readable despite some sentences being out of the ordinary. A subsequent read from your side with ensuing changes would surely make things better, easily.
Author Response
Dear authors,
I found the article interesting and very readable. However, I have some comments and suggestions in the interesting of improving the article.
We’re genuinely grateful for your careful reading and constructive advice. Thank you for the time and attention you devoted – your feedback has clearly improved the paper.
Comments 1.
Minor detail, but I would propose to make the coordinate system in Fig. 4 more conspicuous. When it is printed in black and white, the letters may be hard to see.
Response 1.
In the contour plots of radial and axial displacements in Fig. 4 we use a cylindrical coordinate system: Z is the axial centerline, Y is the circumferential (azimuthal) coordinate, and X is the radial coordinate (distance from the centerline). The axes are rendered by the ANSYS post-processor and, in our environment, their appearance cannot be manually restyled; the layout shown is, in our view, the clearest positioning available. It is also possible the reviewer saw a PDF export; converting the original Word source to PDF can downscale embedded images. In the production layout the original figures will retain higher resolution.
Comments 2.
You did not discuss the cut gap in the text or caption during describing the system to be studied—although it is visible in the cross section, A-A, in Fig. 2. For clarity to the reader that physical element should be part of the description, in both text and caption.
Response 2.
Thank you for pointing out this gap. We have added an explicit description of the longitudinal slit in the shell and labeled it in Fig. 2 (new item 7). We also expanded the figure caption and the text in the system description.
Add to the caption of Fig. 2 (at the end):
“7 – longitudinal construction slit in the shell.”
Add to the manuscript text:
“The shell includes a longitudinal construction slit, which increases tangential compliance while preserving axial stiffness. The slit width is set by tolerances and the cutting tool and is typically a few millimeters. Within the considered load range, the slit edges do not come into contact, and therefore contact between them was not modeled.”
Comments 3.
What is the meaning of the 10 s time in Fig. 4, i.e. with respect to the loading parameter, t/T? Please, discuss that in the text.
Response 3.
Thank you for the remark. The label “Time: 10 s” on the ANSYS screenshots is a post-processor annotation marking the end of a load step in a quasi-static analysis; it does not represent physical time. In the manuscript, the cycle phase is described by the normalized parameter t/T; it is specified independently and indicates the point in the cycle for which the stress–strain field is shown. To avoid confusion, we clarified this in the text.
Add to the text:
“The ‘Time’ label in the ANSYS post-processor denotes the index/end of a load step in a quasi-static analysis and is not physical time. The normalized parameter t/T in the manuscript specifies the loading-cycle phase for which the results are presented.”
Comments 4.
The displacement distribution shown on Fig. 4.b is very symmetric along the z-axis, spatially speaking. The color distribution gives such an impression. Could there be an artifact introduced by the FEA code? Do you see changes in the spatial distribution if you change the grid size? Let me explain the issue about the symmetry that I observe. If you take -34.72mm as the middle point. The relative difference between the max and min is the same, an absolute value of 27.79mm. I don’t consider the max of 0.02255 mm, because I don’t see that color in the diagram—by the way, why is that color not shown? I personally would not expect the displacements to be symmetric. To make the article more complete I suggest that you elaborate on that point, perhaps right there and then add a summary in the conclusions.
Response 4.
First, about the color palette: the legend shows value ranges. The reported value of 0.02255 mm does not have its own unique color band; the entire range from 0.02255 mm down to −6.926 mm is rendered in red. This is why you do not see a distinct color patch for the very top value.
Second, prior studies of the shell–filler contact with dry friction indicate that, along the contact zone, axial and contact stresses are symmetric about the mid-length. From the ends of the filler toward the device center, the magnitudes of these fields decrease approximately exponentially; the rate of this decay is governed by radial contact stiffness and friction. If both pistons of the elastic element are free to move, the axial displacements follow the same pattern: the largest magnitudes occur near the ends and decay toward the middle.
In the virtual experiment plotted in Fig. 4b, however, the lower piston is fixed. When the upper piston is loaded, it moves inward, and the open shell simultaneously “rides over” the lower piston. Note that the upper piston appears blue (axial displacement about −62 mm), while the open shell is greenish (about −31 mm). Despite the lower piston being constrained, the overall settlement of the shell–filler assembly remains close to symmetric: the shell’s axial advancement effectively introduces a kinematic inward motion near the lower boundary, yielding a near-mirror displacement field at this cycle phase. In other load phases – once local contact near the slit becomes dominant – the distribution departs from symmetry, which we also observe in our results.
Regarding a potential FEA artifact: we checked mesh sensitivity by refining in the axial and circumferential directions and across contact interfaces. The spatial pattern and the locations of extrema remained stable under refinement; peak values changed only by a few percent. This supports the conclusion that the near-symmetric field in Fig. 4b is physical for the illustrated phase rather than a numerical artifact.
Add to the manuscript (final wording):
“Recall that in Fig. 4b, to suppress rigid-body modes and ensure kinematic stability of the finite-element model, the lower piston is fixed. At the illustrated phase, the upper piston moves inward while the shell advances over the fixed lower piston. This produces effectively symmetric boundary kinematics and a near-symmetric axial displacement field.
Comments 5.
I propose to add the corresponding back view of 4.a, for the viewer to judge the color distribution overall. This is an extension of my comment above about 4.b. Perhaps someone can see something I don’t at the moment, similar to what is discussed for 4.b above. I would propose to use a different color for the housing in 4.b, as is done in 4.a. Unless there is a good reason to keep the color red, in which case a note to that effect should be included.
Response 5.
The point is that in Fig. 4a we show radial displacements of the open shell only (all other parts are transparent). It was important for us to investigate the maximum radial movements of the shell and compare them with the size of the gap. Whereas in Fig. 4b we present axial displacements of structural components (all components). Therefore, the red color on the housing indicates the axial-displacement range into which it falls. In Fig. 4.b we wanted to show the movement of the pistons, filler, shell, etc. As for the analysis of Fig. 4.a, the deformation pattern is non-axisymmetric, in particular, the minimum radial displacements are observed in the cut zone, and the maximum ones are observed at azimuths of approximately β ≈ 90 deg and 270 deg (β is counted from the middle of the cut). The recorded maximum radial displacement is 4.75 mm, while the gap between the shell and the casing is not yet closed. This pattern is characteristic of the entire shell.
Comments 6.
Figures 9 and 10 would display more clearly if shown unfolded, indicating the azimuthal component and the coordinate along the z-axis—and referring back to Fig. 2 cross section A-A, to highlight to the reader the location of the gap. You could keep as an inset the views presently displayed. Besides, such a representation would assist your description along section 3.2.
Response 6.
Figures 9 and 10 address the off-nominal operating regime of the shock absorber. The external load exceeds the nominal value, and the radial clearance between the shell and the housing is closed. Figure 9 shows how the contact-pressure field on the outer surface of the load-bearing shell evolves as the applied load increases. Figure 10 presents the evolution of the equivalent stresses in the open (slitted) shell.
The purpose of Figures 9 and 10 is to clearly demonstrate the adaptive behavior: as the cycle progresses and the external load grows, the load-bearing shell redistributes its stress field, and the interface pressure spreads out, reducing local peaks. To make this evident, we deliberately chose a three-quarter axial view with the slit visible on the near side.
Comments 7.
My understanding is that you deal with the tangential stress as a sliding-type zone—not explicitly spelled, buy I infer so—and the geometry of stress distribution observed could well be an artifact of the boundary conditions. I made a comment along these lines above, though less explicitly. Some comment from your side, for the reader, would round up your article real well. Your research in the past has dealt with other geometries of the gap or cut but that detail has not been clearly discussed there, in my opinion. Good luck with the publication process.
Response 7.
Yes, indeed, from the standpoint of mechanics, an elastic element comprising an open (slit) cylindrical shell and a stem constitutes a deformable system governed by positional (Coulomb) dry friction. When mathematically modeling such systems under non-monotonic loading, one encounters non-conservative, structurally nonlinear contact problems describing the frictional interaction between coaxially arranged shells and an elastic body (a deformable filler).
For thin-walled members, these contact problems have their own – often counterintuitive – specifics, associated with the emergence of highly non-uniform contact stresses, alternating stick–slip regions, and, in some cases, additional local separation (debonding) zones. In this context, we have both analytical (e.g., https://doi.org/10.3390/ma15134671) and experimental studies (e.g., https://doi.org/10.5267/j.esm.2021.5.003), and we have developed a robust intuition for these problems. Unfortunately, the university building that housed our laboratories has been destroyed by the war, so our experimental program is currently suspended. Nevertheless, we continue to advance the analytical and numerical directions of this research and hope to rebuild soon and resume experiments, at which point the results will be even more informative and interesting.
Thank you for reading our work so carefully and for offering such thoughtful,
practical suggestions.
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors investigate operation of an original elastic element (open cylindrical shell) used as part of a drilling shock absorber. The device features an adjustable radial clearance between the load-bearing shell and the rigid housing, thus inducing a structural nonlinearity. This allows combination of two operating modes of the drilling shock absorber: normal mode, when the clearance exists and the elastic element operates with increased compliance; and emergency mode, when contact occurs resulting in gradual load redistribution and increase in device stiffness. A non-conservative problem concerning the contact interaction of an elastic filler with a coaxially installed shaft and an open shell is formulated, and as the load increases, contact between the shell and the housing is taken into account. Finite element modeling is performed considering dry friction in contact pairs. The distribution of radial displacements, contact and equivalent stresses is investigated, and deformation diagrams used to compare the two loading modes.
The authors are advised to address the following issues in a carefully revised version of the manuscript:
The authors should clearly explain the context of the current manuscript related to reference [10].
The absence of test results for validation is a weak point of this work.
Figure 4: Please indicate displacement units in the legends.
Line 379: please indicate iso material number designation for 60SiCr7 steel
Line 380: This is static loading. What about dynamic loading during the drilling process ?
Since the element is expected to work in dry friction mode during certain conditions, you need to examine the associated wear of the device.
Author Response
The authors investigate operation of an original elastic element (open cylindrical shell) used as part of a drilling shock absorber. The device features an adjustable radial clearance between the load-bearing shell and the rigid housing, thus inducing a structural nonlinearity. This allows combination of two operating modes of the drilling shock absorber: normal mode, when the clearance exists and the elastic element operates with increased compliance; and emergency mode, when contact occurs resulting in gradual load redistribution and increase in device stiffness. A non-conservative problem concerning the contact interaction of an elastic filler with a coaxially installed shaft and an open shell is formulated, and as the load increases, contact between the shell and the housing is taken into account. Finite element modeling is performed considering dry friction in contact pairs. The distribution of radial displacements, contact and equivalent stresses is investigated, and deformation diagrams used to compare the two loading modes.
We would like to thank the reviewer for a careful and thorough reading of this manuscript, as well as for comments that will improve the quality of the article.
The authors are advised to address the following issues in a carefully revised version of the manuscript:
Comments 1.
The authors should clearly explain the context of the current manuscript related to reference [10].
Response 1.
Thank you for asking us to clarify how the present manuscript relates to Ref. [10].
Ref. [10] (co-authored by the present team) develops and validates a torque-to-axial-load transmission unit for drill-string shock absorbers: a fourteen-thread, self-releasing screw pair that converts increases in external torque into additional axial force acting on the absorber’s elastic element. The motivation is that conventional shock subs mostly target longitudinal vibrations, whereas modern PDC-bit drilling frequently excites torsional oscillations (e.g., stick–slip); the unit in Ref. [10] addresses this by mechanically coupling torque spikes into controlled axial loading of the same elastic element.
By contrast, the present manuscript focuses on the shell-type elastic element with a radial clearance and documents its adaptive response under parameterically increased axial loading – including the emergency regime where the clearance closes and contact spreads, producing hysteresis and stress de-concentration in the shell. In other words, our current paper examines how the shell element behaves under axial load histories (whatever their origin), whereas Ref. [10] explains one practical way those axial loads can be generated from torque in the same class of tools. The two studies are therefore complementary: Ref. [10] provides the torque-conversion mechanism; the present paper evaluates the shell element’s adaptive mechanics under the resulting axial loading envelope. Below is an insert that we propose to add to the text of the manuscript. We hope this clarification helps readers see how Ref. [10] situates and complements the present contribution.
Add to the manuscript:
“Most conventional drill shock absorbers primarily address longitudinal vibrations. However, PDC-bit drilling often excites torsional oscillations and abnormal torque. To protect the downhole tool, a dedicated torque-transmission unit – implemented as a fourteen-thread self-releasing screw pair – can convert increases in external torque into additional axial force on the elastic element of the shock absorber [10]".
Comments 2.
The absence of test results for validation is a weak point of this work.
Response 2.
Thank you for raising this important point.
Within the scope of this study we performed standard internal checks to verify that the reported fields and trends are not numerical artifacts.
Mesh sensitivity: axial and circumferential refinements (including local refinement on contact interfaces) left the spatial patterns and locations of extrema unchanged; peak values varied only marginally (a few percent).
Contact robustness: results were stable with respect to the Augmented-Lagrange contact stiffness and normal and tangential penalty factors; maximum normal overclosure remained within solver tolerances, and tangential slip-stick partitions were insensitive to step size.
Load-step and solver parameters: reducing the pseudo-time step and tightening the nonlinear tolerances produced the same equilibrium branches; hysteresis loop areas changed only slightly (consistent with quasi-static path independence).
These checks give us confidence that the reported hysteresis, clearance-closure, and stress de-concentration effects reflect the model physics.
The present manuscript is purposefully a numerical investigation of a new shell-type elastic element and its adaptive regime under parametrically increasing axial loads. External test comparison was not part of the stated objectives; instead, we documented systematic parameter trends and performed the verification steps above. The limitations of this scope (quasi-static formulation; assumed friction; no bench data in this paper) are explicitly acknowledged in the manuscript’s narrative and conclusions.
Context from our broader program. In this context, we have both analytical (e.g., https://doi.org/10.3390/ma15134671) and experimental studies (e.g., https://doi.org/10.5267/j.esm.2021.5.003), and we have developed a robust intuition for these problems. Unfortunately, the university building that housed our laboratories has been destroyed by the war, so our experimental program is currently suspended. Nevertheless, we continue to advance the analytical and numerical directions of this research and hope to rebuild soon and resume experiments, at which point the results will be even more informative and interesting.
We appreciate the reviewer’s emphasis on validation and trust this clarification delineates what has been verified internally in this paper and how it fits within our ongoing analytical–experimental agenda.
Comments 3.
Figure 4: Please indicate displacement units in the legends.
Response 3.
Thank you for the suggestion. The legend already includes the label “Unit: mm”, but the font size may be hard to read at print scale. To make this unmistakable, we will mirror the units in the caption: "Figure 4. Displacements of the elastic element under loading Q = 95 kN: (a) radial displacements of the open shell, mm; (b) axial displacements of structural components, mm."
Comments 4.
Line 379: please indicate iso material number designation for 60SiCr7 steel
Response 4.
Thank you for the helpful request. The ISO/EN numeric designation corresponding to the spring-steel grade 60SiCr7 is 1.7108. In the European system this steel is specified in EN 10089 for hot-rolled steels for quenched-and-tempered springs, and the standardized grade name commonly appears as 61SiCr7; the DIN/EN trade usage 60SiCr7 and 61SiCr7 both map to the same material number 1.7108. Authoritative datasheets (e.g., Saarstahl; SteelNumber; Ovako Steel Navigator) list the mapping explicitly and show typical chemistry consistent with our use in the manuscript. ([1])
For clarity in the paper, we will cite it once in the materials paragraph as:
“Spring steel 60SiCr7 (EN grade 61SiCr7; ISO/EN material number 1.7108; EN 10089).”
This identifies the numeric designation while keeping the grade name we use elsewhere.
[1] https://en.saarstahl.com/app/uploads/2024/03/20160323092338-61SiCr7-60SiCr7.pdf?utm_source=chatgpt.com
Comments 5.
Line 380: This is static loading. What about dynamic loading during the drilling process ?
Response 5.
Thank you for this thoughtful question. We explicitly acknowledge the dynamic nature of drilling loads in the "Introduction" (axial “bit bounce,” torsional stick–slip, whirl), which motivates the need for robust shock absorbers.
In the present study we intentionally use a quasi-static formulation to characterize the constitutive backbone of the device–namely, how the shell-type elastic element responds as the axial load is increased over a cycle, including the emergency regime with clearance closure. In this framework inertial terms are neglected and the physical time is replaced by a normalized loading parameter (denoted in the manuscript), so that the field solutions are parameterized by the cycle phase rather than by time. This is stated in Section 2.
Why this is appropriate here. The key nonlinearities that govern the absorber’s behavior–dry friction at interfaces and progressive contact as the radial clearance closes–are primarily rate-insensitive over the operating range considered. The objective is to map how stresses, contact pressures, and hysteresis evolve with load amplitude, not to resolve transient wave effects. The adopted contact law and friction coefficient are documented in Section 2.3.
The results are presented over practically relevant axial load envelopes (e.g., 0–95–0 kN, 0–130–0 kN, 0–200–0 kN), so the identified thresholds–onset of contact, near-full closure, and the associated stiffening and de-concentration of stresses–are tied to the magnitude of load, which is the same quantity that dynamic excitation modulates.
For design purposes, the quasi-static hysteresis loops provide the dissipative backbone needed for reduced-order dynamic models: the loop area quantifies per-cycle energy loss of the contact and friction mechanism, while the backbone curve captures stiffness evolution with clearance closure. (In transient operation, inertia superposes mass–spring effects on this backbone but does not alter the identified contact thresholds.)
Relation to dynamic drilling scenarios. Dynamic drilling loads would enter the analysis as time histories Q(t) (and, where relevant, torque M(t)). The present results are directly usable as the constitutive map relating instantaneous axial load level to contact state and effective stiffness/dissipation. For example, any transient that pushes the device past the ≈100 kN region will engage clearance closure and the associated adaptive stiffening documented in Section 3.2; continued loading to 130–200 kN spreads contact, reducing peak equivalent stresses while enlarging the participating area – beneficial for durability.
In summary, while transient dynamic simulations (with inertia) are outside the present paper’s scope, the manuscript already provides the load-amplitude–based backbone – contact evolution, hysteresis, and stress redistribution – needed to interpret and model dynamic operation of the absorber in drilling service.
Comments 6.
Since the element is expected to work in dry friction mode during certain conditions, you need to examine the associated wear of the device.
Response 6.
We agree that wear is an inherent concern whenever dry friction contributes to dissipation. In the present article, the scope is confined to the quasi-static, frictional–contact backbone of the device; wear modeling is therefore a stated limitation and is planned as a follow-on study. To avoid a cursory reply, we outline the intended problem setting and workflow, which builds directly on the fields already resolved in this paper.
For setting up the wear–contact problem we will use the fields already resolved in this study – namely, the distributions of contact pressure and tangential slip – as inputs to a cycle-based update. Two complementary estimators will be employed: an Archard-type proportionality between wear rate, normal pressure, and sliding distance, and an energy-based proxy tied to the locally dissipated frictional work per cycle. Exploiting time-scale separation, geometry will be updated only after large blocks of cycles so that the structure re-equilibrates on the slowly evolving contact topography. Calibration and validation is planned via bench segment tests (e.g., ring-on-cylinder) at the pressures and slip amplitudes predicted here, with profilometry or mass-loss measurements to identify wear coefficients for the actual material pairings and to cross-check against the friction-energy metric from the model.
We appreciate the reviewer raising this substantive point and consider wear modeling the natural next step built on the backbone established in the current study.
Reviewer 4 Report
Comments and Suggestions for AuthorsPlease ensure all references are consistently formatted (some inconsistencies in journal titles and capitalization).
The conclusions are descriptive but could be more critical, highlighting not only achievements but also limitations (e.g., absence of dynamic inertial effects, assumptions on friction coefficients, use of quasi-static approach).
Some sections are very detailed in mathematical derivations but less balanced in interpretation of physical meaning.
Figures are informative but would benefit from clearer labels (e.g., showing cut orientation, contact zones more distinctly).
Please compare your findings with alternative damping devices or at least discuss the advantages/disadvantages of shell-type absorbers relative to rubber, hydraulic, or magnetorheological dampers.
The hysteresis loops and clearance closure mechanisms are interesting, but discussion should more clearly link these results to practical drilling applications (e.g., expected load ranges, fatigue implications, operational reliability).
The introduction should be extended with broader coverage of adaptive and nonlinear damping systems in vibration isolation. In particular, elevant insights into dry-friction based adaptive damping concepts and quasi-zero-stiffness systems (in example doi:10.3390/machines12010029).
While the authors mention future bench tests, some preliminary experimental data (even small-scale or from literature benchmarks) should be included for validation. Otherwise, the conclusions remain speculative.
Some questions:
How sensitive are your results to the choice of the friction coefficient (0.2)? Would higher/lower values significantly alter the hysteresis behavior?
Can you comment on the fatigue resistance of the shell under cyclic emergency loads, based on your stress distributions?
How would the device perform under torsional vibrations, not just axial loads?
Could your adaptive shell concept be extended to multi-layer or composite shells for better performance?
Author Response
Comments 1.
Please ensure all references are consistently formatted (some inconsistencies in journal titles and capitalization).
Response to Comment 1
We appreciate the attention to editorial consistency. We have re-checked the reference list for uniform journal titles, capitalization, and the inclusion of DOIs where available, following MDPI’s style guide. Minor typographical inconsistencies are commonplace even in professionally edited prose; nevertheless, we re-read the manuscript with a native English speaker and corrected slips in wording and formatting. Any residual style adjustments can be finalized at copy-editing.
Comments 2.
The conclusions are descriptive but could be more critical, highlighting not only achievements but also limitations (e.g., absence of dynamic inertial effects, assumptions on friction coefficients, use of quasi-static approach).
Response to Comment 2
Thank you for this constructive suggestion. We drafted the Conclusions – and, indeed, the paper as a whole – in line with MDPI’s guidance for research articles: to synthesize principal findings succinctly and to state the study’s scope explicitly. The manuscript already delineates the modeling frame that bounds our claims, namely the quasi-static formulation (inertial terms neglected, cycle parameter used as a progression variable), dry-friction contact law with specified coefficients, and linear elastic behavior of metallic parts; these choices are spelled out in Section 2 and then used consistently in Section 3 and the Conclusions. Bench testing is flagged as a planned next step.
To make these boundaries unmistakable without altering the paper’s structure, we will add the following brief sentence at the end of the Conclusions:
“These findings pertain to a quasi-static model with Coulomb friction and linearly elastic metallic components; inertial effects and wear are outside the present scope and will be addressed in forthcoming bench tests.”
This keeps the Conclusions compact while explicitly naming the principal assumptions under which the results hold.
Comments 3.
Some sections are very detailed in mathematical derivations but less balanced in interpretation of physical meaning.
Response to Comment 3
The study is intentionally applied rather than fundamental: its aim is to evaluate a specific shell-type elastic element for drilling shock absorbers, identify the adaptive regime triggered by clearance closure, and provide decision-level markers (stiffening thresholds, hysteresis loop areas, stress de-concentration) that are directly usable in engineering practice. The mathematical setup (contact alternatives, friction law, loading parameterization) is included to make the modeling reproducible, but the Results dedicate substantial space to interpreting the physics.
Normal mode (clearance open): We discuss how the slit induces non-axisymmetric fields; we construct and interpret the hysteresis diagram, showing residual settlement and how loop area grows as the cycle becomes less symmetric – a direct proxy for energy dissipation.
Emergency/adaptive mode (clearance closure): We explain the sequence of contact growth (local sectors near 90°/270° → nearly full contact), the associated redistribution of pressure, and the reduction of peak equivalent stresses despite higher load – i.e., stress de-concentration that underpins durability.
Design-scale context: The device size and load envelopes are fixed to a common API class (D = 240 mm; 0–200 kN), linking the plots and loops to realistic operating ranges rather than abstract parameters.
For readers seeking deeper theory, we have previously published analytical treatments of non-conservative frictional contact in shell-based dampers (cited in the Introduction [18]), while this article focuses on the engineering behavior that flows from those mechanisms.
We hope this clarifies the intent: a reproducible numerical framework paired with interpretation targeted at practical design decisions.
Comments 4.
Figures are informative but would benefit from clearer labels (e.g., showing cut orientation, contact zones more distinctly).
Response to Comment 4
Thank you for pointing out this gap. We have added an explicit description of the longitudinal slit in the shell and labeled it in Fig. 2 (new item 7). We also expanded the figure caption and the text in the system description.
Add to the caption of Fig. 2 (at the end):
“7 – longitudinal construction slit in the shell.”
Add to the manuscript text:
“The shell includes a longitudinal construction slit, which increases tangential compliance while preserving axial stiffness. The slit width is set by tolerances and the cutting tool and is typically a few millimeters. Within the considered load range, the slit edges do not come into contact, and therefore contact between them was not modeled.”
In all other cases, we tried to orient the images in such a way as to most effectively show the reader the main features of the results obtained.
Comments 5.
Please compare your findings with alternative damping devices or at least discuss the advantages/disadvantages of shell-type absorbers relative to rubber, hydraulic, or magnetorheological dampers.
Response to Comment 5
Thank you for inviting a broader comparison. This study was motivated by a concrete industrial need. Historically, shell-type elastic elements based on a solid cylindrical shell with a deformable filler have been successfully used in shock subs for deep oil, gas, and geothermal drilling. With roller-cone bits, these elements operate effectively at high axial loads (about 150–200 kN, plus operational kinematic input) while meeting tight radial envelope constraints. Today, however, PDC bits dominate deep drilling. They generally run at lower axial loads but permit larger tool displacements and excite pronounced torsional phenomena. This shift created a need to substantially reduce axial stiffness in the elastic element (thereby lowering system resonances) without sacrificing load capacity or compactness. Our solution is to make the open cylindrical shell with a generatrix slit the primary load-bearing link of a friction damper. This yields a structurally anisotropic element – axially stiff yet tangentially compliant – that preserves strength while enabling the required compliance and frictional dissipation under drilling realities.
Most researchers try to adapt traditional metal (disc, plate), rubber-cord, rubber-metal, or hydraulic elastic elements to such operating conditions. Their disadvantages are insufficient damping properties and low service life under specified operating conditions, and in many cases insufficient holding capacity, which is simply impossible to ensure structurally given the required dimensional limitations of wells. The development of new technologies in vibration isolation has led to the introduction of magnetorheological dampers and recuperative shock absorbers. Their widespread implementation is hampered by such disadvantages as the settling of magnetic particles over time, high abrasive wear of friction pairs, and high cost.
In sum, for PDC-bit drilling within tight radial envelopes, the open-shell friction element offers a mechanically simple, passive, and adaptively compliant alternative to elastomeric, hydraulic, or MR approaches. It reconciles compactness with meaningful dissipation and provides a clear pathway to stiffness tailoring without the operational burdens of fluids, seals, or power electronics.
Comments 6.
The hysteresis loops and clearance closure mechanisms are interesting, but discussion should more clearly link these results to practical drilling applications (e.g., expected load ranges, fatigue implications, operational reliability).
Response to Comment 6
Thank you for this constructive request. We already frame the analysis at design scale: the element corresponds to a common API-class envelope (outer diameter D = 240 mm), and the axial load range 0–200 kN reflects typical weight-on-bit levels and short-term transients encountered with PDC-bit drilling.
Within this context:
Hysteresis loops → dissipated energy per cycle.
The loops reported for practically relevant cycles (e.g., 0–95–0 kN, and asymmetric cases) quantify per-cycle energy loss from dry friction and evolving contact. This maps directly to the absorber’s ability to temper bit-bounce and stick–slip–induced load oscillations.
Emergency/adaptive regime with clearance closure.
We examine 0–130–0 kN and 0–200–0 kN cycles to capture off-nominal events that temporarily exhaust the radial clearance. As contact spreads, the shell shows stress de-concentration – for example, the peak equivalent stress decreases from 705 MPa at 130 kN to 681 MPa at 200 kN – indicating that the device redistributes loads rather than creating sharper hot spots under higher demand. This trend is favorable for fatigue resistance in recurrent overloads.
Operational reliability.
The passive, mechanically adaptive behavior – stiffness increase and broader contact participation as loads rise – helps cap local stress amplitudes during short bursts, supporting tool survivability without reliance on fluids, valves, or power electronics.
For drilling engineers, these results provide the backbone curves (stiffness vs. load level) and dissipation measures (loop areas) needed to integrate the element into system models and operating envelopes.
Finally, more precision drilling – oriented results (including bench and field evidence) are planned for a separate, technology-focused article following our upcoming laboratory and in-situ tests.
Comments 7.
The introduction should be extended with broader coverage of adaptive and nonlinear damping systems in vibration isolation. In particular, elevant insights into dry-friction based adaptive damping concepts and quasi-zero-stiffness systems (in example doi:10.3390/machines12010029).
Response to Comment 7
Thank you for this constructive direction. We have extended the Introduction to situate our shell-type friction mechanism within the broader landscape of adaptive and nonlinear vibration isolation, and we have analyzed and incorporated the sources you recommended, including the article on quasi-zero-stiffness (QZS) systems.
Insertion:
“Adaptive and nonlinear isolation spans dry-friction concepts with amplitude-dependent hysteresis, quasi-zero-stiffness (QZS) mechanisms that combine positive and negative stiffness to depress the natural frequency, and semi-active solutions. Recent overviews of QZS isolators and their engineering trade-offs provide useful context, as do applied vibration studies in industrial machinery. In contrast, the present shell-type elastic element with a designed radial clearance delivers a passive, load-adaptive response via progressive contact under increasing axial load–well aligned with compact drilling hardware.”
Additional literature
Ma, Z.; Zhou, R.; Yang, Q. Recent Advances in Quasi-Zero Stiffness Vibration Isolation Systems: An Overview and Future Possibilities. Machines 2022, 10, 813. https://doi.org/10.3390/machines10090813
Sui, G.; Zhang, X.; Hou, S.; Shan, X.; Hou, W.; Li, J. Quasi-Zero Stiffness Isolator Suitable for Low-Frequency Vibration. Machines 2023, 11, 512. https://doi.org/10.3390/machines11050512
Karpenko, M.; Ževžikov, P.; Stosiak, M.; Skačkauskas, P.; Borucka, A.; Delembovskyi, M. Vibration Research on Centrifugal Loop Dryer Machines Used in Plastic Recycling Processes. Machines 2024, 12, 29. https://doi.org/10.3390/machines12010029
Comments 8.
While the authors mention future bench tests, some preliminary experimental data (even small-scale or from literature benchmarks) should be included for validation. Otherwise, the conclusions remain speculative.
Response to Comment 8
Thank you for raising this important point. The answer contains several points.
- Internal verification within the present study.
We performed standard checks to ensure that the reported fields and trends are not numerical artifacts:
Mesh sensitivity. Axial and circumferential refinements (with local refinement of contact interfaces) left spatial patterns and extrema locations unchanged; peak values varied only marginally (within a few percent).
Contact robustness. Results were stable with respect to Augmented-Lagrange contact stiffness and normal/tangential penalty factors; maximum normal overclosure remained within solver tolerances, and the partition of stick/slip zones was insensitive to step size.
Step and solver controls. Reducing the pseudo-time step and tightening nonlinear tolerances reproduced the same equilibrium branches; hysteresis loop areas changed only slightly, consistent with quasi-static path independence.
These verifications give confidence that the observed hysteresis, clearance-closure, and stress de-concentration are features of the modeled physics rather than discretization or post-processing choices.
- Scope of this manuscript.
The paper is purposefully a numerical investigation of a new shell-type elastic element and its load-adaptive regime under parametrically increased axial loads. External testing was not among the stated objectives here; instead, we documented systematic parameter trends and verified numerical robustness as outlined above.
- Broader validation context and citation policy.
Our group has reported both analytical (e.g., Materials 2022, https://doi.org/10.3390/ma15134671) and experimental studies (e.g., Engineering Solid Mechanics 2021, https://doi.org/10.5267/j.esm.2021.5.003) on closely related shell–filler mechanisms, which informed the present modeling choices and provide external consistency checks. We note respectfully that, due to the publisher’s self-citation limits, not all of our prior analytic and experimental papers could be included in this manuscript’s reference list.
- Current constraints and path forward.
Regrettably, the university building that housed our laboratories was destroyed during the war, and our bench program is temporarily suspended. We are continuing the analytical and numerical track in the interim and plan to resume bench and field tests as facilities are restored; those results will be reported in a subsequent, technology-focused article aimed at drilling practice. We appreciate the emphasis on validation and hope this clarifies what has been verified internally here and how the study fits within our ongoing analytical–experimental agenda.
Some questions:
How sensitive are your results to the choice of the friction coefficient (0.2)? Would higher/lower values significantly alter the hysteresis behavior?
In other identical conditions, a system with a lower coefficient of friction in contact pairs will have a higher compliance. An increase in the coefficient of friction leads to a decrease in the compliance of the elastic element. The implication for dissipation is not strictly monotonic: raising the coefficient of friction enlarges local resistance to slip and thus raises the specific loss per unit slip, yet it also reduces the overall settlement because sliding is delayed or curtailed. In practice these two tendencies compete, and the dissipated energy per cycle exhibits a peak at an intermediate level of friction and contact pressure. Our parametric framework is expressly designed to search for such extrema of dissipation while keeping stresses within the desired margins and avoiding premature locking of the mechanism.
Can you comment on the fatigue resistance of the shell under cyclic emergency loads, based on your stress distributions?
The study already provides the full set of inputs needed for a standard fatigue appraisal: stress ranges over the cycle, locations of the critical points, and the evolution of contact that spreads load with increasing demand. Because the shell operates within the elastic range in our emergency cycles, high-cycle fatigue is the relevant regime; a conventional life estimate would combine the reported stress ranges with an appropriate S–N curve for the selected spring steel and a mean-stress correction. The most critical phase is the onset of clearance closure, when contact first forms at localized sectors near geometric transitions. As contact grows, peak stresses at those sectors fall and the field becomes smoother, which is favorable for durability.
How would the device perform under torsional vibrations, not just axial loads?
While the present model addresses axial excitation, torsional disturbances are a routine part of drilling practice. Two pathways are relevant. First, the same frictional interfaces that dissipate axial work will dissipate torsional work whenever circumferential slip occurs, producing torque–rotation loops analogous to the force–displacement loops reported here; geometry can be tuned to admit controlled circumferential compliance. Second–and most directly linked to our program–Ref. [10] (this is our preliminary development) describes an add-on torque-transmission unit that converts variations in external torque into variations in axial load on the elastic element. In that configuration, the axial “backbone” quantified in this manuscript can be used immediately to assess damping and stress response under torsion-induced load spikes, with the conversion handled mechanically upstream of the shell element.
Could your adaptive shell concept be extended to multi-layer or composite shells for better performance?
Intuitively, yes: the open-shell concept generalizes to layered or hybrid constructions that could tailor axial and tangential stiffness independently, add inherent material damping, and reduce mass. Realizing those advantages responsibly requires a targeted model that admits orthotropy and layer interfaces.
We would like to thank the reviewer for a careful and thorough reading of this manuscript, as well as for constructive suggestions to improve the quality of the article.
Round 2
Reviewer 3 Report
Comments and Suggestions for AuthorsThe authors adequately addressed all my comments.
Reviewer 4 Report
Comments and Suggestions for AuthorsDear Authors,
Thank you for your detailed revisions and thoughtful responses to the reviewers’ comments. The corrections have strengthened the manuscript, and I find it suitable for publication.
