Fatigue Analysis for Shaft of Inland River Ship Under Ice Load

Round 1

Reviewer 1 Report (Previous Reviewer 1)

Comments and Suggestions for Authors

This paper studies how to calculate the natural frequency of free torsional vibration of the system, then use Newmark integral programming to calculate the maximum torsional stress of shaft system under ice load at resonance speed. Low cycle stress and high cycle stress are studied according to fatigue analysis theory. The method of determining S-N Curve and Ice load Torsional Stress Cycle Curve is given, the cumulative damage degree is calculated based on Palmgren Miner linear cumulative damage theory. Although my previous comments have been incorporated in the revised version by the authors, I have few minor suggestions/comments.

1)     In my opinion, the title of the manuscript is not appropriate.

2)     Some abbreviations are used without defining them first, e.g., “CCISR” in line 25.

3)     The statement made in lines 33-37: "The innovation and purpose of ….." need to be rephrased.

4)     Structural arrangement of the introduction section is not need up to the standard.

a.      Authors should first present the problem the want to tackle.

b.     Followed by presenting the studies from the literature in way to build case for the novelty of their work.

c.      Once identifying the shortcomings in the literature, the authors should state the objective/novelty of their work.

d.     At the end of the introduction section, add a paragraph describing the organization of the manuscript.

5)     Description provided for figure 1 needs more elaboration.

6)     Figure 3 & 4 are still blur. Furthermore, text within these figures of different formatting.

7)     In Figure 5, some text is provided in non-English form. These need to be corrected.

Author Response

The authors would like to thank the reviewers for the carefully reading of this manuscript and for the constructive comments which help to improve the quality of this manuscript. The corrections are marked in revised Manuscript. Please see below for our responses to the reviewers’ comments.

1. In my opinion, the title of the manuscript is not appropriate.

Response: Thanks for your comments. The title of the manuscript has been changed to Fatigue Analysis for Shaft of Inland River Ship under Ice Load.

2. Some abbreviations are used without defining them first, e.g., “CCISR” in line 25.

Response: Thanks for your comments. The abbreviation has been changed to RCIWSS in line 24 of the revised manuscript, and the full name has been defined in Reference [1].

3. The statement made in lines 33-37: "The innovation and purpose of ….." need to be rephrased.

Response: Thanks for your comments. The innovation and purpose has been rephrased in lines 33 to 37 of the revised manuscript.

4. Structural arrangement of the introduction section is not need up to the standard.                  a.Authors should first present the problem the want to tackle.                                                    b.Followed by presenting the studies from the literature in way to build case for the novelty of their work.

         c.Once identifying the shortcomings in the literature, the authors should state the objective/novelty of their work.

        d.At the end of the introduction section, add a paragraph describing the organization of the manuscript.

Response: Thanks for your comments. The introduction section of the revised manuscript has been rewritten according to your comments.

5. Description provided for figure 1 needs more elaboration.

Response: Thanks for your comments. The Description for figure 1 has been provided in lines 123 to 124 of the revised manuscript.

6. Figure 3 & 4 are still blur. Furthermore, text within these figures of different formatting.

Response: Thanks for your comments. Figures 3 and 4 of the revised manuscript have been replaced with clearer images.

7. In Figure 5, some text is provided in non-English form. These need to be corrected.

Response: Thanks for your comments. Figure 5 of the revised manuscript has been corrected in English form.

Reviewer 2 Report (Previous Reviewer 2)

Comments and Suggestions for Authors

I see some improvements are made, but a resubmitted manuscript still has formatting mistakes:

the phrases "This paper.." is repeated 8 times

" .. between my paper and previous papers..." line 36

"Wu S used ABAQUS.." in line 64

line 287 "Drawing the Ice load Torsional Stress Cycle Curve according to formula (29). "- here is no drawing. I see "Drawing the Ice load Torsional Stress Cycle Curve in Figure 16"  (line 386)

in "References" some scholars are in Capital letters (lines 498-501, 518, 526, etc.).

In the chapter "Discussion" there is no comparison with other scholars results.

Author Response

The authors would like to thank the reviewers for the carefully reading of this manuscript and for the constructive comments which help to improve the quality of this manuscript. The corrections are marked in revised Manuscript. Please see below for our responses to the reviewers’ comments.

1. he phrases "This paper.." is repeated 8 times.

Response: Thanks for your comments. The phrases "This paper.." have been replaced by other phrases in the whole paper.

2. " .. between my paperand previous papers..." line 36

Response: Thanks for your comments. The innovation and purpose has been rephrased in lines 33 to 37 of the revised manuscript, there is no "my paper" phrase.

3. "Wu Sused ABAQUS.." in line 64.

Response: Thanks for your comments. It has been changed to "Wu used ABAQUS." in line 64 of the revised manuscript.

4. line 287 "Drawing the Ice load Torsional Stress Cycle Curve according to formula (29). "- here is no drawing. I see "Drawing the Ice load Torsional Stress Cycle Curve in Figure 16" (line 386)

Response: Thanks for your comments. In line 297 of the revised manuscript, only the method of drawing the Ice load Stress Spectrum is described, and line 394 is the actual Stress Spectrum drawn based on the calculation example.

5. in "References" some scholars are in Capital letters (lines 498-501, 518, 526, etc.).

Response: Thanks for your comments. All scholars in the "References" of the revised manuscript have been replaced with Lowercase letters.

6. In the chapter "Discussion" there is no comparison with other scholars results.

Response: Thanks for your comments. It has supplemented comparisons with other scholars' results in lines 446-449 of the revised manuscript

Reviewer 3 Report (Previous Reviewer 3)

Comments and Suggestions for Authors

The reviewer misses a proper reply to the author's comments.
Regarding comment 1, the reviewer misses still the justification for emphasizing river ships in the title and text.
Regarding comment 2, the scientific depth of the paper is still very low, although the authors claim that their findings are important for science. The reviewer still has the impression that existing procedures and assumptions in classification rules are solely applied.
Regarding comment 3, the paper is still unclear in several details, as the further comments below show.
Regarding comment 4, attempts have been made to improve the issues mentioned, but without much success, as the new comment 7) below shows.
Regarding comment 5, the English grammar and wording are still poor, as many comments listed below show. A native speaker and/or interpreter is recommended to help the authors.
The paper is still close to be rejected, nevertheless the additional comments are listed here as the authors and/or editors are obviously willing to publish the paper:
1. Fig. 1: Upper and lower figures do not match with each other regarding numbering and systems shown!
2. Why are there different equivalent systems in Fig. 1 and 2?
3. Line 122: What is sharpness method? Explain!
4. End of line 133: Explain lambda in equation!
5. Eq. (1) - (4): The explanation is poor and has to be improved.
6. Line 246: Sentence unclear. Do you mean a certein point of the S-N curve at 10,000 cycles? Dto. in the following!
7. Section 6, first para: The explanation is obviously wrong. The curve, as shown later in the paper, displays obviously the CUMULATIVE number of stress cycles, i.e. showing for a certain stress amplitude or range the number of cycles EXCEEDING this value! And the fatigue life cannot be checked by simply comaring the curve with the S-N curve at certain stress levels! This requires still a damage accumulation rule like the Palmgren-Miner rule. The text has to be revised accordingly! Furthermore: 'stress cycle curve' is misleading! Usual terms are 'stress spectrum' (although mathematically somewhat unprecise) or 'cumulative distribution of stress amplitude (or range)'.
8. Table 2: Explain 'Cly'! Has the system six gears? Unbelievable!
9. Fig. 6ff: Delete duplicate explanation in figures!
10. Line 276: what is 'propellers bow first operation? Explain!
11. Fig. 10: This is a very strange S-N curve, having several knuckles. Maybe further explanations are necessary, why this is the case.
12. Fig. 11: The reviewer wonders if the service time has been mentioned, for which the number of cycles are plotted.
13. Table 9: Why are the stresses for two ice thicknesses exactly the same?

Comments on the Quality of English Language

The English grammar and wording are still poor, as the following examples show:

- Line 27: by ice blocks, they cause ...; line 31: are => is. Line 36: 'my'? (two authors).
- Line 47: Check grammar/wording of sentence! Same in line 50 (can get?). Line 53ff: Explain Pro/E. Line 71: introduces => introduce. Line 79: Author not in upper case letters. Line 85: Give reference for Soderberg.
- Line 109: calculation method.
- Line 124: frequencies and mode shapes.
- Line 196: An show => A plot.
- Line 252; while => for (?).
- Line 261/262: Check structure of the sentence.
- Line 271: What is meant by 'it'?
- Line 289: degree => ratio (use internationally agreed terms!). Also in following text!
- Line 304: ... dimensions ... are (also in caption of Fig. 3 and in line 334).
- Table 6: Mpa => MPa.
- Line 341: What is meant by 'it'?
- Line 346: The drawing --- is shown... (same in line 383).
- Line 353: Check grammar of the sentence (not understandable)!
- Check reference list regarding words completely in upper case letters.

Author Response

The authors would like to thank the reviewers for the carefully reading of this manuscript and for the constructive comments which help to improve the quality of this manuscript. The corrections are marked in revised Manuscript. Please see below for our responses to the reviewers’ comments.

Comments and Suggestions for Authors

 Fig. 1: Upper and lower figures do not match with each other regarding numbering and systems shown!

Response: Thanks for your comments. The relevant explanations for Figure 1 have been provided in lines 123 to 124 of the revised manuscript.

2. Why are there different equivalent systems in Fig. 1 and 2?

Response: The relationship between Figure 1 and Figure 2 has been explained in lines 123 to 129 of the revised manuscript.

3. Line 122: What is sharpness method? Explain!

Response: Thanks for your comments. The English error for the sharpness method has been corrected to Rayleigh's method in line 135 of the revised manuscript. Rayleigh's method is a method used to determine the natural frequency of free torsional vibration of a shaft system. This method was proposed by Lord Rayleigh, which is based on the principle of energy and approximates the natural frequency of a system by assuming a specific vibration mode. In the context of free torsional vibration of the shaft system, Rayleigh's method can be used to estimate the fatigue characteristics caused by the transient torsional stress generated by the impact of ice on the shaft system.

4. End of line 133: Explain lambda in equation.

Response: Thanks for your comments. The explanation for lambda has been provided in lines 145 to 146 of the revised manuscript.

5. Eq. (1) - (4): The explanation is poor and has to be improved.

Response: Thanks for your comments. It has explained all parameters for formulas (1) to (4) in lines 164 to 168 of the revised manuscript.

6. Line 246: Sentence unclear. Do you mean a certein point of the S-N curve at 10,000 cycles? Dto. in the following!

Response: Thanks for your comments. Yes, τ_vLC is a certein point of the S-N curve at 10,000 cycles. It explains how to calculate τ_vLC with Formula (23).

7. Section 6, first para: The explanation is obviously wrong. The curve, as shown later in the paper, displays obviously the CUMULATIVE number of stress cycles, i.e. showing for a certain stress amplitude or range the number of cycles EXCEEDING this value! And the fatigue life cannot be checked by simply comaring the curve with the S-N curve at certain stress levels! This requires still a damage accumulation rule like the Palmgren-Miner rule. The text has to be revised accordingly! Furthermore: 'stress cycle curve' is misleading! Usual terms are 'stress spectrum' (although mathematically somewhat unprecise) or 'cumulative distribution of stress amplitude (or range)'.

Response: Thanks for your comments. The comparative relationship between the two curves is to compare whether the stress amplitude in the Ice load Stress Spectrum exceeds that of the S-N Curve under the same cycles. This has been explained in lines 369-370 of the revised manuscript. . Ice load torsional stress cycle curve has been changed to Ice load Stress Spectrum throughout the revised manuscript.

8. Table 2: Explain 'Cly'! Has the system six gears? Unbelievable!

Response: Thanks for your comments. The Cly in Table 2 represents different crankshafts of the diesel engine, as it has 6 cylinders and therefore 6 crankshafts.

9. Fig. 6ff: Delete duplicate explanation in figures!

Response: Thanks for your comments. The relevant explanation for Figure 5 in the revised manuscript has been removed.

10. Line 276: what is 'propellers bow first operation? Explain!

Response: Thanks for your comments. It has changed to 'propeller located on the centerline' in line 286 of the revised manuscript.

11. Fig. 10: This is a very strange S-N curve, having several knuckles. Maybe further explanations are necessary, why this is the case.

Response: Thanks for your comments. Figure 10 shows the double slope S-N curve, with two points determined by τ_vLC and τ_vHC. The remaining curve is determined by formulas (25) and (26) based on the number of cycles, and the curve is drawn smoothly according to the coordinate values corresponding to different cycles in the formula. Due to the limited number of selected coordinate points, the smoothness is not perfect, resulting in many knuckles.

12. Fig. 11: The reviewer wonders if the service time has been mentioned, for which the number of cycles are plotted.

Response: Thanks for your comments. The rotation angles under different cases in Table 1 represent the service time.

13. Table 9: Why are the stresses for two ice thicknesses exactly the same?

Response: Thanks for your comments. The explanation has been provided in lines 403 to 407 of the revised manuscript.

Comments on the Quality of English Language

1. Line 27: by ice blocks, they cause ...; line 31: are => is. Line 36: 'my'? (two authors).

Response: Thanks for your comments. Corresponding modifications have been made to lines 27, 31, and 36 of the revised manuscript.

2. Line 47: Check grammar/wording of sentence! Same in line 50 (can get?). Line 53ff: Explain Pro/E. Line 71: introduces => introduce. Line 79: Author not in upper case letters. Line 85: Give reference for Soderberg.

Response: Thanks for your comments. Corresponding modifications have been made to lines 50, 54, 71, and 79 of the revised manuscript. The Soderberg method is a calculation method and is not a reference for the relevant scholar.

3. Line 109: calculation method.

Response: Thanks for your comments. Corresponding modification has been made to line 109 of the revised manuscript.

4. Line 124: frequencies and mode shapes.

Response: Thanks for your comments. Corresponding modifications have been made to lines 136 to 137 of the revised manuscript.

5. Line 196: An show => A plot.

Response: Thanks for your comments. Corresponding modification has been made to line 208 of the revised manuscript.

6. Line 252; while => for (?).

Response: Thanks for your comments. Corresponding modification has been made to line 262 of the revised manuscript.

7. Line 261/262: Check structure of the sentence.

Response: Thanks for your comments. The sentence structure has been reorganized from lines 271 to 272 of the revised manuscript.

8. Line 271: What is meant by 'it'?

Response: Thanks for your comments. The term 'it' in the text refers to 'this paper' in line 281 of the revised manuscript.

9. Line 289: degree => ratio (use internationally agreed terms!). Also in following text!

Response: Thanks for your comments. It have changed cumulative damage degree to cumulative damage ratio of the whole revised manuscript.

10. Line 304: ... dimensions ... are (also in caption of Fig. 3 and in line 334).

Response: Thanks for your comments. The content of lines 313 and 343 and the caption of Figure 5 of the revised manuscript have been modified.

11. Table 6: Mpa => MPa.

Response: Thanks for your comments. Corresponding modification has been made to Table 6 in the revised manuscript.

12. Line 341: What is meant by 'it'?

Response: Thanks for your comments. In the paper, 'it' represents the S-N Curve in line 350 of the revised manuscript.

13. Line 346: The drawing --- is shown... (same in line 383).

Response: Thanks for your comments. Corresponding modifications have been made to lines 355 and 392 of the revised manuscript.

14. Line 353: Check grammar of the sentence (not understandable)!

Response: Thanks for your comments. The sentence structure has been revised in lines 362 to 363 of the revised manuscript.

15. Check reference list regarding words completely in upper case letters

Response: Thanks for your comments. The full names with upper case letters of all scholars in reference of the revised manuscript have been changed.

Round 2

Reviewer 3 Report (Previous Reviewer 3)

Comments and Suggestions for Authors

The following numbering corresponds to the comments by the reviewer and replies by the authors:

1. The different numbering in the upper and lower figure is still not understood. Please clarify or remove/modify numbers.
2. Fig. 2 and the explanation puzzle more than clarify! Proposal: Delete Fig. 2.
3. Ok
4. Lambda is still not explained.
5. There are still some variables not explained, e.g. [C], [J] etc. Also the dots above x are displaced.
6. Maybe it is more clear when replacing 'with' by 'for' in lines 256 and 259.
7. Ok
8. Add below Table 2 'Cly = Cylinder' (by the way, there are six cranks, not crankshafts). Table 2 contains 'Gear 1 - Gear 6'. Again: Are there six gears?
9. Figs. 6ff means 'and following', i.e. Fig. 6 - 16 still include duplicate information (given in the caption and in the figure). Please delete, also the frame should be deleted.
10. Ok
11. The response is not understood. The S-N curve seems to be a six-slope curve. Please redraw the figure to avoid confusion!
12. The rotation angles represent the service time? The reviewer cannot see any operation time nor number of cycles in Table 1. Please make this point clear! If you calculate a stress spectrum, the total number of cycles must be somehow predicted! By the way, the horizontal axis in Fig. 11 is unclear (where are exactly the given numbers?).
13. Ok

Regarding the comments given in my first review, there is no reply, e.g. regarding the question about specialties of inland vessels compared to sea-going vessels.

Comments on the Quality of English Language

The numbers correspond to the replies by the authors:

8. 'This paper calculates???'
12. The explanation is superfluous and can be deleted (of course is the same S-N curve used for different load levels!).
14. Add 'is' behind 'thickness'!
15. Why are titles and Journal names still in upper case letters?

Author Response

The authors would like to thank the reviewer for the carefully reading of this manuscript and for the constructive comments which help to improve the quality of this manuscript. The corrections are marked in revised Manuscript. Please see below for our responses to the reviewer’s comments.

The following numbering corresponds to the comments by the reviewer and replies by the authors:

1. The different numbering in the upper and lower figure is still not understood. Please clarify or remove/modify numbers.

Response: Thanks for your comments. Figure 2 has been removed from the revised manuscript, and other figures have been rearranged.

2. Fig. 2 and the explanation puzzle more than clarify! Proposal: Delete Fig. 2.

Response: Thanks for your comments. Figure 2 has been removed from the revised manuscript, and other figures have been rearranged.

4. Lambda is still not explained.

Response: Thanks for your comments. λ is the eigenvalue in equation  (H-λE)A=0, λ=ω_n², and ω_n is the nth natural frequency of the system. Explanations have been provided in lines 140 to 142 of the revised manuscript.

5. There are still some variables not explained, e.g. [C], [J] etc. Also the dots above x are displaced.

Response: Thanks for your comments. The explanation of [C] and [J] et al. have been added in lines 160 to 161 of the revised manuscript, the dots above x are corrected.

6. Maybe it is more clear when replacing 'with' by 'for' in lines 256 and 259.

Response: Thanks for your comments. It have replaced 'with' by 'for' in lines 253 and 256 of the revised manuscript.

8. Add below Table 2 'Cly = Cylinder' (by the way, there are six cranks, not crankshafts). Table 2 contains 'Gear 1 - Gear 6'. Again: Are there six gears?

Response: Thanks for your comments. Cly has been changed to Cylinder in Table 2 of the revised manuscript, there are six gears of the gearbox.

9. Figs. 6ff means 'and following', i.e. Fig. 6 - 16 still include duplicate information (given in the caption and in the figure). Please delete, also the frame should be deleted.

Response: Thanks for your comments. Figures 5 to 15 in the revised manuscript have been modified according to the comments.

11. The response is not understood. The S-N curve seems to be a six-slope curve. Please redraw the figure to avoid confusion!

Response: Thanks for your comments. Figure 9 in the revised manuscript has been modified according to the comments.

12. The rotation angles represent the service time? The reviewer cannot see any operation time nor number of cycles in Table 1. Please make this point clear! If you calculate a stress spectrum, the total number of cycles must be somehow predicted! By the way, the horizontal axis in Fig. 11 is unclear (where are exactly the given numbers?)

Response: Thanks for your comments. It has clarified the relationship between the number of cycles and stress amplitude by formula (29) of the revised manuscript.

Regarding the comments given in my first review, there is no reply, e.g. regarding the question about specialties of inland vessels compared to sea-going vessels.

Response: Thanks for your comments. There are significant differences between inland and sea-going vessels, primarily reflected in the following aspects:

1.Ice Load Characteristics

Inland Vessels: Inland river ice is typically thin and highly fragmented, resulting in relatively short-duration impacts with moderate force.

Sea-Going Vessels: Sea ice is relatively thick, and instances of multiple floating ice blocks acting together significantly increase the complexity and impact force of ice loads.

2.Fatigue Analysis Methods

Inland Vessels: They require more sensitive fatigue analysis methods, including dynamic stress analysis and transient response analysis, due to the rapid changes and localized nature of ice loads.

Sea-Going Vessels: They require more comprehensive fatigue analysis techniques, such as multi-axis fatigue assessment and nonlinear fatigue analysis, to account for the complex and sustained nature of sea ice loads.

3.Structural Design and Material Selection

Inland Vessels: They focus on optimizing structural layout and improving material strength to mitigate the effects of ice loads on the propulsion shaft system.

Sea-Going Vessels: They emphasize enhancing overall structural strength and stiffness to improve ice resistance. Special considerations are also given to the unique requirements of navigating in ice-infested areas, such as ice-breaking capabilities.

4.Response Measures

Inland Vessels: They adopt measures such as strengthening channel maintenance and enhancing ship maneuverability to reduce the impact of ice loads on the propulsion shaft system.

Sea-Going Vessels: They respond the challenges posed by ice loads by strengthening ship structural strength and improving the ice resistance of propulsion shafts. These measures are aimed at ensuring the safe, stable, and reliable operation of vessels in icy conditions.

Comments on the Quality of English Language

8. 'This paper calculates???'

Response: Thanks for your comments. 'It' refers to reference [27], which has been clearly stated in lines 278-280 of the revised manuscript.

12. The explanation is superfluous and can be deleted (of course is the same S-N curve used for different load levels!)

Response: Thanks for your comments. The explanation has been removed from line 347 of the revised manuscript.

14. Add 'is' behind 'thickness'!

Response: Thanks for your comments. It has added 'is' on line 358 of the revised manuscript.

15. Why are titles and Journal names still in upper case letters?

Response: Thanks for your comments. The original versions of some reference have been downloaded from the internet, with full names of titles in upper case letters and some journal names in upper case letters.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper investigates the inland river vessel navigating in ice area by presenting how to calculate the natural frequency of free torsional vibration of the system and calculated the maximum torsional stress of shaft system under ice load at resonance speed. Low cycle stress and high cycle stress are studied according to fatigue analysis theory. A major revision of the manuscript is required before it can be considered for publication. Applying the following comments and suggestions will improve the quality of paper.

1)     Title of the manuscript need to be revised.

2)     The abstract is written poorly.

3)     In my opinion the introduction section needs to be merged with the research status section.

4)     It is very uncommon use the title of the reference while citing it within text as is done in line 21. It is recommended to use the standard method of citation.

5)     Overall the introduction section (literature review) is very weak. Literature covered is very limited. Only a single study from the last five years has been included. It is recommended to expand the literature review by incorporating more recent relevant studies.

6)     Novelty of the study in terms of shortcomings in the literature needs to be established, which is currently missing form the manuscript.  

7)     It is recommended to add a Figure depicting the actual system before introducing the equivalent system of shaft (Fig. 1).

8)     Not even a single parameter/variable shown in Fig. 1 has been defined within the text.

9)     It is highly recommended to first introduce different possible approaches to study the free vibration of the study before deciding to use the field matrix method.

10) Square brackets are used to present the equations "lines 82-84". Square brackets are also used for the citation. This might cause confusion. It is recommended to use a different method of representation for equations.

11) It is claimed that the upon collision with the ice, the propeller will experience a huge torsional excitation of shaft system. A justification is required for this claim.

12) Any specific reason for the selection of stepwise integration method?

13) What are the main loads that cause the instantaneous torsional vibration of shaft system?

14) How did the authors incorporate the duration interaction between the propeller blades and ice?

15) Figure 2 is very blur. It is very difficult to read the text within the figure.

16) In Figs. 4-1, use different line type for each data.

17) Detailed quantitative and comparative representation of the results will further strengthen the result and discussion section.

Author Response

1. Title of the manuscript need to be revised.

Response: Thanks for your comments. The title of the manuscript has been changed to Research on Shaft Fatigue Evaluation Method of Inland River Ship under Ice Load.

2. The abstract is written poorly.

Response: Thanks for your comments. The abstract has been rewritten and some content has been added.

3. In my opinion the introduction section needs to be merged with the research status section.

Response: Thanks for your comments. The introduction section and the research status section have been merged and more research status have been added.

4. It is very uncommon use the title of the reference while citing it within text as is done in line 21. It is recommended to use the standard method of citation.

Response: Thanks for your comments. The citation has been replaced by abbreviation in line 25 of revised manuscript.

5. Overall the introduction section (literature review) is very weak. Literature covered is very limited. Only a single study from the last five years has been included. It is recommended to expand the literature review by incorporating more recent relevant studies.

Response: Thanks for your comments. The references from the past five years have been added. Reference [3], [19], [20], [21], [22] of revised manuscript are new.

6. Novelty of the study in terms of shortcomings in the literature needs to be established, which is currently missing form the manuscript.

Response: Thanks for your comments. The researches in terms of shortcomings were added in line 23-25 of revised manuscript.

7. It is recommended to add a Figure depicting the actual system before introducing the equivalent system of shaft (Fig. 1).

Response: Thanks for your comments. The Figure depicting the actual system has been added by Figure 1 of revised manuscript.

8. Not even a single parameter/variable shown in Fig. 1 has been defined within the text.

Response: Thanks for your comments. The definitions of variable have been added to line 117 to 119 in Figure 2 of the revised manuscript.

9. It is highly recommended to first introduce different possible approaches to study the free vibration of the study before deciding to use the field matrix method.

Response: Thanks for your comments. Different methods for studying free vibration have been introduced in line 122 to 132 of the revised manuscript.

10. Square brackets are used to present the equations "lines 82-84". Square brackets are also used for the citation. This might cause confusion. It is recommended to use a different method of representation for equations.

Response: Thanks for your comments. The square brackets in the original manuscript represent matrix symbols, which have been replaced with matrix symbols in line 133 to 135 of the revised manuscript.

11. It is claimed that the upon collision with the ice, the propeller will experience a huge torsional excitation of shaft system. A justification is required for this claim.

Response: Thanks for your comments. The original meaning was that ice hit the propeller, it caused significant torsional stress on the shaft system. Correction on line 139 of the revised manuscript was done.

12. Any specific reason for the selection of stepwise integration method?

Response: Thanks for your comments. The calculation of instantaneous torsional stress can only be represented by transient time stress, and cannot be represented by steady-state frequency stress.

13. What are the main loads that cause the instantaneous torsional vibration of shaft system?

Response: Thanks for your comments. The torque formula (9) for diesel engines and the torque formula (11) for ice loads of the revised manuscript are the main loads.

14. How did the authors incorporate the duration interaction between the propeller blades and ice?

Response: Thanks for your comments. It can corporate the duration interaction between the propeller blades and ice by formula (11), in the formula: α_i is duration of interaction between propeller blades and ice measured by rotation angle. Because the propeller speed remains constant, the rotation angle represents the rotation time. α_i can be obtained in Table 1.

15. Figure 2 is very blur. It is very difficult to read the text within the figure.

Response: Thanks for your comments. Figure 2 has been decomposed into two parts, Figure 3 and Figure 4, in the revised manuscript for clear expression.

16. In Figs. 4-1, use different line type for each data.

Response: Thanks for your comments. All the line type of Figures have been changed in the revised manuscript for clear expression.

17. Detailed quantitative and comparative representation of the results will further strengthen the result and discussion section.

Response: Thanks for your comments. Relevant comparisons have been added in line 359 to 361 of the revised manuscript.

Reviewer 2 Report

Comments and Suggestions for Authors

The study of the fatigue strength of the shaft system under different working conditions of ice load excitation is presented in the manuscript.

The subject of the paper is typical and of interest to the readership of the journal. However, I have some concerns about the novelty of present format of the manuscript the authors are encouraged to address.

Comments and Suggestions for Authors

To enhance the review, it’s crucial to critically assess and articulate the novelty and scientific significance of the research presented by the authors. The shortage of previous investigation and the innovation of this work should be highlighted in the introduction section. The last sentence of introduction should be moved to "Conclusions" or "Abstract". Most importantly, introduction does not clearly demonstrate the innovation and contribution of the present work. What is the main purpose of the article? The difference between your paper with the previous papers (mentioned in "Research Status") is not clear.

The scientific impact of the manuscript is average - the limitations of research are not mentioned. The manuscript findings and their implications should be discussed in the chapter "Discussion" before "Conclusions". There is no comparison with other scholars results. Future research directions may also be highlighted. Please consider the implications of the research for future scientific inquiries. Does the study open new avenues for investigation? How can it influence future research directions?

 Formatting

The quality of Fig.3 is not good.

A lot of typing and formatting mistakes are noticed - for example Line 21 “RULES FOR CONTRUCTION OF INLAND RIVER STEEL SHIPS”- it has and typing error and formatting (Capital letters), same errors are seen in "References" .

The manuscript text (Diesel engine parameters are shown in Table 3 (line 234). Propeller parameters are shown in Table 4 (line 235) should be above Tables 3 and 4.

Some manuscript text should be placed between Figures 4, 5, 6 and 9,10,11.

Author Response

1. To enhance the review, it’s crucial to critically assess and articulate the novelty and scientific significance of the research presented by the authors. The shortage of previous investigation and the innovation of this work should be highlighted in the introduction section. The last sentence of introduction should be moved to "Conclusions" or "Abstract". Most importantly, introduction does not clearly demonstrate the innovation and contribution of the present work. What is the main purpose of the article? The difference between your paper with the previous papers (mentioned in "Research Status") is not clear.

Response: Thanks for your comments. The last sentence of the introduction has been moved to the abstract, and lines 23 to 25 and 33 to 37 of the revised manuscript have been supplemented with innovations and contributions, as well as the purpose of the paper.

2. The scientific impact of the manuscript is average - the limitations of research are not mentioned. The manuscript findings and their implications should be discussed in the chapter "Discussion" before "Conclusions". There is no comparison with other scholars results. Future research directions may also be highlighted. Please consider the implications of the research for future scientific inquiries. Does the study open new avenues for investigation? How can it influence future research directions?

Response: Thanks for your comments. Chapter 9 has been added to the revised manuscript to explain the impact of this research on future scientific investigations.

3. The quality of Fig.3 is not good.

Response: Thanks for your comments. Clear drawing has been replaced in Figure 5 of the revised manuscript.

4. A lot of typing and formatting mistakes are noticed - for example Line 21 “RULES FOR CONTRUCTION OF INLAND RIVER STEEL SHIPS”- it has and typing error and formatting (Capital letters), same errors are seen in "References".

Response: Thanks for your comments. The citation has been replaced by abbreviation in line 25 and reference of revised manuscript.

5. The manuscript text (Diesel engine parameters are shown in Table 3 (line 234). Propeller parameters are shown in Table 4 (line 235) should be above Tables 3 and 4.

Response: Thanks for your comments. Line 299 to 301 of the revised manuscript have been changed to the comments.

6. Some manuscript text should be placed between Figures 4, 5, 6 and 9,10,11.

Response: Thanks for your comments. All Figures of the revised manuscript have been changed to the comments.

Reviewer 3 Report

Comments and Suggestions for Authors

The paper is rejected for the following reasons:
1. The authors claim to describe research on fatigue of Inland Waterway Vessel propulsion shaft under ice load and say in the introduction that no calculation method nor analysis procedures on this topic exist. However, there is principally no difference between inland waterway and seagoing vessels is this respect. Seagoing vessels are sailing in calm waters when these are covered with ice - the same situation as for inland waterway vessels. Also the mechanical models of the shaft system are the same, as the calculation model in the paper shows. The authors do not mention any special characteristic of inland waterway navigation which can justify their claim.
2. No research was found by the reviewer in the paper. Instead, the authors seem to reproduce the procedure of ship classification societies with a great number of analytical and empirical formulae given in the rules - in several cases without clearly describing the variables and the origin of the formulae. This is far from research.
3. The description and explanations are partly unclear, e.g. the time of exposure to certain ice thicknesses. It is not always winter. And how are the number of cycles counted, e.g. considering Rainflow-method in view of the changing mean stress? Sometimes the reader is completely lost, e.g. what means Will distribution? Do the authors mean Weibull?
4. The representation contains errors. For example, Figs. 8 and 13 contain S-N curves (with a very strange course) and Weibull distributions, having per se different horizontal axes, S-N curves the cycles to failure, and Weibull distributions the cumulative cycles of exceedence.
5. The English grammar, wording and sentence structures are poor.
There could be several other comments by the reviewer, as the Chinese-dominated reference list.

Comments on the Quality of English Language

No details are given in view of the great number. A native speaker of interpreter would be needed

Author Response

1. The authors claim to describe research on fatigue of Inland Waterway Vessel propulsion shaft under ice load and say in the introduction that no calculation method nor analysis procedures on this topic exist. However, there is principally no difference between inland waterway and seagoing vessels is this respect. Seagoing vessels are sailing in calm waters when these are covered with ice - the same situation as for inland waterway vessels. Also the mechanical models of the shaft system are the same, as the calculation model in the paper shows. The authors do not mention any special characteristic of inland waterway navigation which can justify their claim.

Response: Thanks for your comments. Inland shipping has its unique characteristics that may affect the fatigue research of propulsion shafts. For example:

Ship type and size: Inland vessels usually differ from sea vessels in terms of type, size, and structure. These differences may affect the design, materials, and stress distribution of the propulsion shaft, thereby affecting its fatigue performance.

Differences in ice conditions: The ice conditions in inland rivers may be more complex and varied, including special phenomena such as ice accretion, ice dams, and ice jams, which may have different effects on the propulsion axis. Relevant references [18] and [30] on inland river ice have been added to the revised manuscript.

2. No research was found by the reviewer in the paper. Instead, the authors seem to reproduce the procedure of ship classification societies with a great number of analytical and empirical formulae given in the rules - in several cases without clearly describing the variables and the origin of the formulae. This is far from research.

Response: Thanks for your comments. This research is based on a deep understanding of the procedures of classification societies, and conducts in-depth analysis and exploration of the fatigue characteristics of inland waterway ship propulsion shafts under specific ice load conditions. In the paper, fatigue research utilizes classification society formulas, but the study of instantaneous torsional stress uses time-domain Newmark integration. This paper combines programming calculations with classification society formulas. The parameters of this research are novel

Some reference [26] was added to the sources of formulas in the revised manuscript.

3. The description and explanations are partly unclear, e.g. the time of exposure to certain ice thicknesses. It is not always winter. And how are the number of cycles counted, e.g. considering Rainflow-method in view of the changing mean stress? Sometimes the reader is completely lost, e.g. what means Will distribution? Do the authors mean Weibull?

Response: Thanks for your comments. The ice thickness was selected based on the characteristics of ice blocks in the Heilongjiang River system, and corresponding reference [30] has been added to the revised manuscript.

The Will distribution in the original manuscript was named incorrectly and it has been changed to Ice load Torsional Stress Cycle Curve in line 263 of the revised manuscript. The meaning of this curve is explained in line 264 to 266 of the revised manuscript.

4. The representation contains errors. For example, Figs. 8 and 13 contain S-N curves (with a very strange course) and Weibull distributions, having per se different horizontal axes, S-N curves the cycles to failure, and Weibull distributions the cumulative cycles of exceedance.

Response: Thanks for your comments. The two types of curves have been separated into two curves, S-N Curve and Ice load Torsional Stress Cycle Curve in the revised manuscript, as shown in Figures 10 and 11.

It can explain the relationship between the two curves in line 266 to 270 of the revised manuscript, and explain how to use the two curves to study the fatigue characteristics of the shaft system under ice load excitation in line 359 to 360 of the revised manuscript.

5. The English grammar, wording and sentence structures are poor.

Response: Thanks for your comments. English writing skill has been improved in all contents of the revised manuscript.