Influence of Wheel-Rail Contact Algorithms on Running Safety Assessment of Trains under Earthquakes

Round 1

Reviewer 1 Report

General comments

The paper is interesting and of high theoretical and practical value. The authors study influence of different wheel-rail contact approaches on running safety assessment of high-speed railway vehicles in view of their possible motion under earthquakes. They differentiate between the algorithms that take account of single- and multi-point contact, of vertical and normal penetration as a base for the normal compression amount and of empirical and theoretical formulae for normal contact stiffness determination. The authors take account of both the geometry and forces of contact. Finally they consider and compare four coupled track-vehicle dynamical models. These models correspond to real CRH2 train and CRTS II slab balastless track. In addition the track lateral irregularities for the earthquake conditions, based on those measured, are adopted as the excitation during the analysis. The study is based on calculations obtained as numerical simulation of the mechanical systems (models) as just characterized. During the comparisons the following quantities are analysed and make the effect of the study: vertical wheel-rail force, lateral wheel-rail force, normal contact stiffness, normal compression amount, wheel-rail contact state (in terms of multi-point contact), normal contact force in different contact regions, and wheel jump amount. Besides the maximum left wheel-rail and right wheel-rail vertical and lateral forces were determine and used in comparisons, as well as the running safety indices. The letter are: derailment coefficient (Q/Y), wheel unloading rate (∆P/P), and wheelset lateral force (∑Q). They are used to finally assess the running safety conditions. The results are clearly summarized and presented while the original practical recommendations for use of the particular contact approaches, taking account of the errors generated by them, are formulated at the same time.

Summarizing previous paragraph, this reviewer assesses formulation of the study, tools used, and analyses performed as staying in accordance with contemporary knowledge of rail vehicle dynamics. This combined with valuable results causes that present paper deserves publication for sure.

 Arrangement of the paper, level of the language, and general clarity of the paper are more than good and appropriately correspond with the quality of the journal. That is why no general comments needing corrections are formulated by this reviewer. Just detailed comments are formulated below.

 

Detailed comments

Page 1. Line 36.

It is suggested to replace “… contact and wheel jumping directly impacting …” with “… contact and wheel jumping occur directly impacting …”.

 

Page 2. Line 51.

It is suggested to replace “… a unique contact point …” with “… a single contact point …” or “… a individual contact point …”.

 

Page 2. Lines 68-70.

The formulation is unclear and needs some intervention. The reliability of solution of normal compression is stated “under all conditions”. If it is so, it means under earthquakes, too. Thus, why it needs to be further clarified is not obvious.

 

Page 2. Line 77.

It is suggested to replace “… clarified in under seismic …” with “… clarified for seismic …”, please.

 

Page 2. Line 82.

It seems that for benefits of the readers that “EL-Centro wave excitation” needs some reference to literature or regulation or eventually some explanation. What in fact these waves are and what is their origin?

 

Page 3. Line 95.

This reviewer does not accept the notion “direction vectors” in this line.  Quantities lx, ly, and lz are not vectors in terms of mathematics! They are elements of direction cosine matrix between the co-ordinate systems, to this reviewer. If you agree, specify which co-ordinate systems you mean.

 

Page 3. Line 95 and Fig. 1.

The notion “wheelset central line” seems awkward the context it appears. Isn’t it simply “wheelset’s axis of revolution” or “wheelset’s geometrical axis”?

 

Page 3. Line 96.

It seems that name “rotation angle” is wrong for angle фw. Should not it be “rolling angle” (the rotation angle around longitudinal axis Ox)?

 

Page 5. Line 150.

The authors mention “two calculation formulae” in this lin. Say immediately, please, which two formulae you mean.

 

Page 5. Lines 167 and 168.

Please, replace word “number” with “indicator” and word “amount” with “number” in these lines. Note, that “amount” refers to non-countable, while “number” to countable nouns only.

 

Page 6. Line 173.

This reviewer suggests more elegant and formal formulation of the section title. For example it could be “Train-track coupling system for the analysis at earthquake conditions”.

 

Page 6. Line 185.

Number of the subchapter is 2.2 while subchapter 2.1 is missed.

 

Page 6. Line 190.

It is suggested to replace “… to the four degrees of …” for “… to the former four degrees of …”.

 

Page 6. Fig. 6.

The “CA mortar layer” is between rail and track slab in this figure. In Fig. 8, however, the “AC mortar layer” is differently between “track plate” (slab?) and “base plate”. Are both figures correct?

 

Page 7. Line 202.

In this line the “CRTS II slab track” is mentioned. Say a few words about this structure. Say at least who elaborated it and who exploits it. Is it used in China, for example?

 

Page 7. Lines 204-205.

The formulation “… for the modeling, beam element, shell element, and spring damping element were adopted” is not clear. Explain, please, which elements in Fig. 8 correspond to beam, shell, and damping elements.

 

Page 7. Line 21.

It seems that “schematic” should be replaced with “scheme”, please.

 

Page 8. Equation (17).

Explain very shortly, please, size of Fwj vector. Namely, the number 31 is not obvious. The reviewer was able to easily count as much as 28 forces, while you specify more, namely 31.

 

Page 11. Line 276.

The formulation “… were compared under seismic conditions first” seems to be better than proposed by the authors.

 

Page 11. Lines 289-290.

Please consider “Considering single point contact only, will …” instead of the original formulation.

 

Page 12. Lines 298-299.

Should not it be “Next, models 2 and 3 are compared as shown in Fig. 16. Both wheel-tread …. are adopted for wheel-rail ….”?

 

Page 12. Paragraph 1 (Lines 298-312).

It seems to this reviewer that comparisons and results discussed in this paragraph are not general in time and refer to t=3,80 s again. If yes, be helpful to the readers and say it explicitly in the text.

 

Page 12. Line 308.

For clarity and friendly attitude to readers the notion “wheel jump” should be explained prior to further discussions. Is it simply wheel abrupt vertical displacement.

 

Page 17. Point 2. (Lines 402-406).

It seems to this reviewer that something is wrongly formulated in this point. It looks point 2. Concerns models 1 and 2. As stated earlier both these models have the same effect. They overestimate the running safety and underestimate the safety margin. Correct it, please, or if this reviewer is wrong then explain the matter better.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

The paper presents a theoretical analysis aiming to describe the behavior of wheel-rail contact under earthquake conditions. For this purpose, different algorithms are introduced to calculate the normal compression amount, the normal contact stiffness and the number of contact points which are important parameters in wheel-rail space contact modeling.

Among other, detailed models are presented for the calculation of wheel-rail contact geometry and wheel-rail contact force. In addition, appropriate equations are introduced for the coupling of train and truck subsystems.

Application of different submodels under seismic conditions leads to a series of highly interesting conclusions which support the model validity.

The discussion and explanations provided by the authors about the findings are quite analytical and sufficient, stand in the appropriate level and do not extend into useless details. Quality of presentation is quite good and the reader of the paper obtains easily and quickly an overview of the findings of the investigation performed. The subject of this investigation is very important and offers several fundamental conclusions concerning the behavior of wheel-rail system during an earthquake which is a critical factor for system safety

Comparison of model results with relevant experimental data (if available) is highly recommended to the authors, in order to increase the validity of theoretical model findings.

Author Response

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Author Response File: Author Response.pdf

Reviewer 3 Report

Dear Authors, Thank you for your research.

Please explain:

1. "To solve the geometric relationship between wheel and rail contact in this study, the contact trace method [25] was used..."     why did you choose (apply) this method?

2. Why don't you use other research methods?

3. "Table 1. Settings of various wheel-rail contact models."     necessarily!!! explain and describe all four models.

4. "3. Comparison of different wheel-rail contact models" correct the numbering (2.1. Comparison under normal conditions. ets ).

5. In my opinion, it is necessary to finalize Fig. 5.

my recommendation "Reconsider after major revision"

Best regards,

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

dear Authors, my recommendation

"Accept in present form"