Venkatarami Reddy Thesis (PDF 2MB) - QUT ePrints

Queensland University of Technology School of Engineering Systems

DEVELOPMENT OF AN INTEGRATED MODEL FOR

ASSESSMENT OF OPERATIONAL RISKS IN

RAIL TRACK

Venkatarami Reddy

Master of Applied Science (Research and Thesis)

Master of Information Technology

Principal supervisor:

A/Prof. Gopinath Chattopadhyay

Associate Supervisor:

Prof. Doug Hargreaves

Submitted to

Queensland University of Technology for the degree of

DOCTOR OF PHILOSOPHY

2007

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ABSTRACT In recent years there has been continuous increase of axle loads, tonnage, train speed,

and train length which has increased both the productivity in the rail sector and the

risk of rail breaks and derailments. Rail operating risks have been increasing due to

the increased number of axle passes, sharper curves, wear-out of rails and wheels,

inadequate rail-wheel grinding and poor lubrication and maintenance. Rolling contact

fatigue (RCF) and wear are significant problems for railway companies. In 2000, the

Hatfield accident in the UK killed 4 people, injured 34 people and led to the cost of £

733 million (AUD$ 1.73 billion) for repairs and compensation. In 1977, the Granville

train disaster in Australia killed 83 people and injured 213 people. These accidents

were related to rolling contact fatigue, wear and poor maintenance.

Studies on rail wear and lubrication, rolling contact fatigue and inspection and rail

grinding analyse and assess the asset condition to take corrective and preventive

measures for maintaining reliability and safety of rail track. Such measures can reduce

the operational risks and the costs by early detection and prevention of rail failures,

rail breaks and derailments. Studies have so far been carried out in isolation and have

failed to provide a practical solution to a complex problem such as rail-wheel wear-

fatigue-lubrication-grinding-inspection for cost effective maintenance decisions.

Therefore, there is a need to develop integrated economic models to predict expected

total cost and operational risks and to make informed decisions on rail track

maintenance.

The major challenges to rail infrastructure and rolling stock operators are to:

1. keep rolling contact fatigue and rail-wheel wear under controllable limits,

2. strike a balance between rail grinding and rail lubrication, and

3. take commercial decisions on grinding intervals, inspection intervals, lubrication

placements, preventive maintenance and rail replacements.

This research addresses the development and analysis of an integrated model for

assessment of operational risks in rail track. Most significantly, it deals with problems

associated with higher axle loads; wear; rolling contact fatigue; rail defects leading to

early rail replacements; and rail breaks and derailments. The contribution of this

research includes the development of:

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� failure models with non-homogenous Poisson process and estimation of

parameters.

� economic models and analysis of costs due to grinding, risks, downtime,

inspection and replacement of rails for 23, 12, 18 and 9 Million Gross Tonnes

(MGT) of traffic through curve radius 0-300, 300-450, 450-600 and 600-800 m;

and application of results from this investigation to maintenance and replacement

decisions of rails. Cost savings per meter per year are:

• 4.58% with 12 MGT intervals compared to 23 MGT intervals for 0-300 m



• 12.29% with 12 MGT intervals compared to 23 MGT intervals for 600-800 m.

� a lubrication model for optimal lubrication strategies. It includes modelling and

economic analysis of rail wear, rail-wheel lubrication for various types of

lubricators. Cost effectiveness of the lubricator is modelled, considering the

number of curves and the total length of curves it lubricates. Cost saving per

lubricator per year for the same curve length and under the same curve radius is:

• 17% for solar wayside lubricators compared to standard wayside lubricators.

� simulation model for analysis of lubrication effectiveness. Cost savings per meter

per year for:

• 12 MGT grinding interval is 3 times for 0-450 m and 2 times for 450-600 m

curve radius with lubrication compared to without lubrication.

• 23 MGT grinding interval is 7 times for 0-450 m and 4 times for 450-600 m

curve radius with lubrication compared to without lubrication.

� a relative performance model, total curve and segment model.

� an inspection model for cost effective rail inspection intervals. Cost savings per

year for same track length, curves and MGT of traffic:

• 27% of total maintenance costs with two inspections, compared to one

inspection considering risk due to rail breaks and derailments.

� a risk priority number by combining probability of occurrence, probability of

detection and consequences due to rail defects, rail breaks and derailments.

� integrated model combining decisions on grinding interval, lubrication strategies,

inspection intervals, rectification strategies and replacement of rails.

Cost saving per meter per year for 12 MGT is:

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• 5.41% of total maintenance costs with two inspections, compared to one


• 45.06% of total maintenance costs with lubrication for two inspections,

compared to without lubrication.

Cost saving per meter per year for 23 MGT is:

• 5.61% of total maintenance costs with two inspections, compared to one


• 68.68% of total maintenance costs with lubrication for two inspections, per

year compared to no lubrication.

The thesis concludes with a brief summary of the contributions that it makes to this

field and the scope for future research in wear-fatigue-lubrication-grinding-inspection

for maintenance of rail infrastructure.

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ACKNOWLEDGEMENT The preparation of a substantial piece of work such as this thesis is not possible

without the assistance and support of a large number of people. I would like to take

this opportunity to acknowledge all those people who have contributed to the

completion of this project.

• My principal supervisor, A/Prof. Gopinath Chattopadhyay for his sincere

constant and determined support, encouragement, and guidance throughout

this research project. He spent his valuable time in discussing various

solutions related to the problems of the research project. I am indebted to him

for his patience during discussions and detailed examination of this

manuscript. His critical insight and valuable suggestions have contributed to a

great extent to the final form of this dissertation.

• My associate supervisor, Professor Doug John Hargreaves, Head of School,

School of Engineering Systems, for his valuable assistance, direction and

support for my research work and for providing valuable financial support,

without which it would have been impossible for me to continue this research.

• Dr. Per-Olof Larsson, Banverket, Swedish National Rail Administration, for

providing his support and valuable time for providing data and for helping me

in analysing the data.

• Professor Joseph Mathew, Chief Executive Officer, CIEAM and Associate

Professor Lin Ma, Faculty of Built Environment of Engineering for providing

financial support.

• Professor John Bell, Director and Assistant Dean of Research, for giving me

this opportunity and providing financial support.

• Mr. John Powell and Mr. Nicholas Wheatley, Queensland Rail, for their

support in providing data and analysis of models.

• Dr. Lance Wilson, Research Assistant for providing his support in analysing

data and analysis of the integrated model.

• Professor Uday Kumar, Head of Division of Operation and Maintenance

Engineering, Lulea University of Technology, Lulea, Sweden for providing

financial support during research in Sweden and presentation at the

COMADEM 2006 Conference.

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• Prof. Dinesh Kumar, Indian Institute of Management, Bangalore, India, for

proving his support in analysis of models during my candidature.

• Dr. Aditya Parida, Lecturer, Division of Operation and Maintenance

Engineering, Lulea University of Technology, Lulea, Sweden for providing

support during the exchange programme in 2006.

• Mr. Anisur Rahman, Mr. Praveen Posinaseeti and Mr. Ajay Desai, Mr.

Saurabh Kumar, Mr. Ambika Patra for helping me from time to time in

preparation of this thesis and in analysis of models.

• Finally, I express my heart felt appreciation to my wife Suneetha and my

Parents (Samba Shiva Reddy and Subbalaxmamma) and my sister’s family

(Sri Laxmi, Ramasubba Reddy, Surendranath Reddy and Sumathnath Reddy)

for their love, support, sacrifice and continuous encouragement throughout

this doctoral program.

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STATEMENT OF ORIGINALITY

I declare that to the best of my knowledge the work presented in this thesis is original

except as acknowledged in the text, and that the material has not been submitted,

either in whole or in part, for another degree at this or any other university.

Signed:………………………………Venkatarami Reddy

Date:

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LIST OF RESEARCH PUBLICATIONS PUBLICATIONS RESULTING FROM THIS THESIS Refereed international journal Papers (Published):

1. Reddy V., Chattopadhyay G., Hargreaves D. and Larsson P. O. (2007) “Modelling and Analysis of Rail Maintenance Cost”, International Journal of Production Economics, 105, 475-482, Feb 2007 (Chapter 4).

2. Chattopadhyay G., Reddy V. and Larsson P. O. (2005) “Decision on

Economical Rail Grinding Interval for Controlling Rolling Contact Fatigue”, International Transactions in Operational Research, 12.6, 545-558, Nov 2005 (Chapter 4).

3. Chattopadhyay G., Reddy V., Hargreaves D. and Larsson P. O. (2004)

“Assessment of Risks and Cost Benefit Analysis of Various Lubrication Strategies for Rail Tracks Under Different Operating Conditions”, Published in TRIBOLOGIA – Finnish Journal of Tribology, 1 – 2 Vol. 23/2004, Norway, 32-40, ISSN 0780-2285 (Chapter 5).

Refereed international Conference and Journal Papers (under review/in process):

4. Reddy V. Chattopadhyay G., Hargreaves D. (2007). “Modelling & Analysis of Operational Risks due to Rail defects”, in process for IEEE Transactions on Reliability (Chapter 6).

5. Reddy V., Chattopadhyay G., Hargreaves D., (2007). “Analysis of

Lubrication Effectiveness for Different Rail Materials”, in process for International Journal of Tribology (Chapter 5).

6. Reddy V., Chattopadhyay G., Hargreaves D. (2007). “Rail-Wheel

Lubrication: An Overview”, in process for International Journal of Wear (Chapter 5).

Refereed international conference papers (Published):

7. Chattopadhyay G., Reddy V. (2007) “Cost-Benefit Model for Rail Inspection Decision Using Limited and Incomplete Data”, 20th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2007), 13th – 15th June, 2007, Faro, Portugal (Chapter 6).

8. Reddy V., Chattopadhyay G., Hargreaves D. (2006) “Analysis of Rail Wear

Data For Evaluation of Lubrication Performance”, 7th International Tribology Conference to be held in Australia and the 3rd in Brisbane AUSTRIB 2006 (Chapter 5).

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9. Chattopadhyay G., Reddy V., Hargreaves D. (2006) “Development of Framework for Benchmarking Rail-Wheel Lubrication”, 7th International Tribology Conference to be held in Australia and the 3rd in Brisbane AUSTRIB 2006 (Chapter 5).

10. Reddy V., Chattopadhyay G., Hargreaves D. and Larsson-Kråik P. O. (2006)

“Techniques in Developing Economic Decision Model Combining Above Rail and Below Rail Assets”, 1st World Congress on Engineering Asset Management (WCEAM 2006), Gold Coast, Australia, Paper 58, ISBN 1-84628-583-6.

11. Reddy V., Chattopadhyay G., Hargreaves D. and Larsson-Kråik P. O. (2006)

“Development of Wear-Fatigue-Lubrication-Interaction Model for Cost Effective Rail Maintenance Decisions”, 1st World Congress on Engineering Asset Management (WCEAM 2006), Gold Coast, Australia, Paper 59, ISBN 1-84628-583-6 (Chapter 7).

12. Reddy V., Chattopadhyay G., Larsson-Kråik P. O. and Hargreaves D. (2006)

“Analysis of field data to develop rail wear prediction model”, 19th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2006), Lulea, Sweden, 585-594, ISBN 978-91-631-8806-0 (Chapter 5).

13. Chattopadhyay G., Reddy V., Larsson-Kråik P. O., Hargreaves D. (2006)

“Rail-wheel lubrication practice: framework for lubrication effectiveness”, 19th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2006), Lulea, Sweden, 595-604, ISBN 978-91-631-8806-0 (Chapter 5).

14. Reddy V., Chattopadhyay G., Hargreaves D. and Larsson-Kråik P. O.

(ICORAID-2005-ORSI) “Analysis of Lubrication Effectiveness For Different Rail Materials”, International Conference on Operations Research Applications in Infrastructure Development in Conjunction with the 2005 Annual convention of Operation Research Society of India (ORSI) 27 - 29, December 2005 NSSC Auditorium, IISc, Bangalore, India (Chapter 5).

15. Chattopadhyay G., Reddy V., Pannu H. S. and Dinesh Kumar U. (ICORAID-

2005-ORSI) “Modelling and Analysis of Wear limit for Economic Rail Replacements”, International Conference on Operations Research Applications in Infrastructure Development in Conjunction with the 2005 Annual convention of Operation Research Society of India (ORSI) 27 - 29, December 2005 NSSC Auditorium, IISc, Bangalore, India.

16. Larsson-Kråik P. O., Chattopadhyay G., Powell J., Wheatley N., Hargreaves

D., and Reddy V. (ICORAID-2005-ORSI) “Rail-Wheel Lubrication: A Conceptual Decision Model”, International Conference on Operations Research Applications in Infrastructure Development in Conjunction with the 2005 Annual convention of Operational Research Society of India (ORSI) 27 - 29, December 2005, NSSC Auditorium, IISc, Bangalore, India.

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17. Larsson P. O., Chattopadhyay G., Reddy V. and Hargreaves D. (2005) “Effectiveness of Rail-Wheel Lubrication in Practice”, 18th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management, (COMADEM 2005) Cranfield University, UK, 453-462, ISBN 1871315913.

18. Chattopadhyay G., Reddy V., Hargreaves D. and Larsson P. O. (2004)

“Comparative Evaluation of Various Rail-Wheel Lubrication Strategies”, 17th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management, (COMADEM 2004) The Robinson College, Cambridge, UK, 52-61, ISBN 0-954 1307-1-5.

19. Reddy V., Chattopadhyay, G. and Larsson, P. O. (2004) “Technical vs.

Economical decisions: A case study on preventive rail grinding”. The Fifth Asia-Pacific Industrial Engineering And Management Systems Conference 2004 (APIEMS 2004). 12-15 December 2004, Gold coast, Australia, ISBN 0-9596291-8-1 (Chapter 4).

20. Reddy V., Chattopadhyay G. and Ong P. K. (2004) “Modelling & analysis of

risks due to broken rails & rail defects”. VETOMAC-3 & ACSIM-2004 Conference, 6th – 9th December 2004, New Delhi, India (Chapter 6).

Refereed international symposium

21. Reddy V. (ISRS 2004) “Development of Framework for Integrated Prediction Models for Analysis of Operational Risks due to Rolling Contact Fatigue (RCF) and Rail/Wheel Wear”, International Symposium for Research Students on Materials Science and Engineering, December 20th - 22nd, 2004, IIT Madras, India.

OTHER PUBLICATIONS

22. Chattopadhyay G., Soenarjo M., Powell J. and Reddy V. (2007) “Study and Analysis of Risks at Railway Level Crossings”, Second World Congress on Engineering Asset Management and the Fourth International Conference on Condition Monitoring (WCEAM CM 2007), 11-14th June, 2007, Harrogate, UK.

23. Kumar S, Chattopadhyay G., Reddy V. and Kumar U. (2006) “Issues and

Challenges with Logistics of rail Maintenance”, International Intelligent Logistics Systems Conference 2006 (IILS 2006), Brisbane, Australia, 16.1-16.9, ISBN 0-9596291-9-X.

24. Chattopadhyay G., Reddy V., Ong T. K. and Hayne M. (COMADEM 2004)

“Development of a Low Cost Data Acquisition System for Condition Monitoring of Rail Tracks”, 17th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management, (COMADEM 2004) The Robinson College, Cambridge, UK, 62-69, ISBN 0-954 1307-1-5.

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25. Chattopadhyay G., Reddy V., Hargreaves D. and Larsson P. O. (2004) “Integrated Rail & Wheel Maintenance Model for Cost sharing by Rail Players”, VETOMAC-3 & ACSIM-2004 Conference, 6th – 9th December 2004, New Delhi, India.

26. Chattopadhyay G., Reddy V. and Larsson P. O. (2003) “Integrated Model for

Assessment of Risks in Rail Tracks under Various Operating Conditions”, International Journal of Reliability and Applications, 4.3, 113-120.

27. Chattopadhyay G., Reddy V. and Larsson P. O. (2003) “Mathematical

Modelling for Optimal Rail Grinding Decisions in Maintenance of Rails”, 16th International Congress and Exhibition on Condition Monitoring and Diagnostic Engineering Management (COMADEM 2003), Växjö, Sweden, Pg 565-572, ISBN 91-7636-376-7.

28. Chattopadhyay G., Reddy V., Larsson P. O. and Hargreaves D. (2003)

“Development of Optimal Rail Track Maintenance Strategies based on Rolling Contact Fatigue (RCF), Traffic Wear, Lubrication and Weather Condition”, 5th Operations Research Conference on Operation Research in the 21st Century, the Australian Society of Operations Research ASOR (Qld), Sunshine coast, Australia, 9-10 May, 2003, 54-66.

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NOMENCLATURE

a Expected cost per derailment [AUD]

Ac Critical railhead area when rail replacement is recommended [mm2]

Ai Cross sectional rail profile area ith interval [mm2]

AGWj Cross sectional area loss due to grinding in period j [mm2]

ATWj Cross sectional area loss due to traffic wear in period j [mm2]

A0 Cross sectional profile area of a new rail [mm2]

AH Hertzian contact area [m2]

AGWq Cross sectional area loss due to grinding in period [mm2]

ATWq Cross sectional area losses due to traffic wear in period q [mm2]

Alub Area below lubricated wear rate for high rail [mm2]

Anon-lub Area above non-lubricated wear rate for high rail [mm2]

% AHL percentage of reduction in area head loss [mm2/MGT]

A Dimension of table wear [mm2/MGT]

B Dimension of side wear [mm2/MGT]

Cr Cost per rectification of rail breaks on emergency basis [AUD]

cs Particular curve section under consideration [m]

c Expected cost of each rail break repair on emergency basis [AUD]

cd Down time cost [AUD/year]

cg Grinding cost [AUD/year]

ci Inspection cost [AUD/year]

cr Risk cost [AUD]

cre Replacement cost [AUD/year]

lc Lubrication cost [AUD/year]

totc Total cost [AUD/year]

mirsC Cost of maintenance during the failure of ith lubricator [AUD/year]

'mirsC Cost of emergency repair during the failure of ith lubricator [AUD/year]

'pirsC Cost of personnel involved in maintenance of ith lubricator [AUD/year]

rmC Cost of rail material per kg [AUD]

C0 Cost of each service on site [AUD]

Cdl Cost of each service pf lubricator in depot [AUD]

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0C Expected cost of each service on site [AUD]

dlC Expected Cost of each service pf lubricator in depot [AUD]

EC Total cost for electric lubricators [AUD]

mtC Maintenance cost for each lubricator in time t. [AUD]

reC Cost to replace rail [AUD]

trebC Benefit due difference between lubricated and non-lubricated rail [AUD]

CNDT Total expected cost for NDT inspection interval [AUD]

wC Total cost for wayside lubricators [AUD]

sC Total cost for solar wayside lubricators [AUD]

scC Setup cost for each lubricator lubricator [AUD]

jC Cost per unit time for running each train in period j [AUD]

d Expected cost of down time due to traffic loss [AUD/h]

da/dN Crack propagation rate [ - ]

da/dn Crack propagation rate [ - ]

D Sliding distance [m]

E Energy dissipation [J/m]

E [Mi+1, Mi] Expected number of failures over Mi and Mi+1 [ - ]

Ej [Mi+1, Mi] Expected number of failures over Mi and Mi+1 for jth strategy [ - ]

tE Electric consumption cost in time t [kWh]

Fx ,Fy Creep forces in x and y direction [N]

Fn(m) [fn(m)] Rail failure distribution [density] function [ - ]

Fj(m) [fj(m)] Rail failure distribution [density] function for jth strategy [ - ]

f2 = f(rlub) = f2(R) is the function of curve radius for the lubricated curve [mm2]

f2(R) = ( ) 1=Rφ , this is the traffic wear rate for Lubricated high rails [MGT/mm2]

f1 = f(rnon-lub) = f1 (R) the function of curve radius for the non-lubricated curve [mm2]

f1 (R) = ( ) 0=Rφ , the traffic wear rate for non-lubricated high rail [MGT/mm2]

f tangential friction force [ - ]

G Cost of grinding per pass per m [AUD/pass/m]

G(c) Distribution function of cost of each rail break repair [ - ]

jGD Wear Depth due to rail grinding after period j [mm]

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GDq Grinding Depth due to grinding after period q [mm]

GW Rail side (gauge) wear [mm2]

h Vertical central wear on the railhead [mm]

hDT Expected downtime due to each grinding pass [h]

H Material hardness [Pa]

H Weighted side- and height wear [mm]

Hlimit Critical H when the rail must be replaced [mm]

I Cost in investment of rail for segment L [AUD]

If Inspection frequency in Millions of Gross Tonnes (MGT) [ - ]

I Index [ - ]

ic Cost of each inspection [AUD]

j Index [ - ]

j Lubrication strategy [ - ]

k Cost of rectification of potential rail breaks based on NDT [AUD]

K wear coefficient of Archard equation [-]

∆K the range of the stress intensity factor [-]

L Length of rail segment under consideration [m]

L% Percent rail length under consideration [ - ]

m Millions of Gross Tonnes [kg.106]

mj MGT in period j [ - ]

mq MGT in period q [kg.106]

Mi Total accumulated MGT of the section studied up to decision I [kg.106]

jM Total accumulated MGT for the section studied up to decision j [kg.106]

MN Total accumulated MGT for rail life up to end of period N [kg.106]

MΦ Spin moment [Nm]

n The number of failures [ - ]

nw total number of wheels passing through the curve section [ - ]

nAj Number of accidents in period j [ - ]

nGPi Number of grinding passes for ith grinding [ - ]

nNDTj Number of detected potential rail breaks using NDT [ - ]

nRBj Number of rail brakes in between two NDT inspections [ - ]

nAq Number of accidents in period q [ - ]

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nGPij Number of grinding pass for ith grinding in jth strategy [ - ]

nNDTq Number of NDT detected potential rail breaks in period q [ - ]

nRBq Number of rail breaks in between two NDT inspections in period q [ - ]

N Normal load [N]

N(Mi+1,Mi) Number of failures over Mi and Mi+1 [ - ]

NI Number of inspection over rail life [ - ]

Nj Total number of periods up to safety limit for renewal for strategy j [ - ]

Nj(Mi+1,Mi) Number of failures over Mi and Mi+1 as per strategy j [ - ]

P[.] Probability [ - ]

Pi(A) Probability of undetected potential rail breaks leading to derailment [ - ]

Pi(B) Probability of detecting potential rail breaks using NDT [ - ]

EP Purchase price of electric lubricator [AUD]

wP Purchase price of wayside lubricator [AUD]

sP Purchase price of solar wayside lubricator [AUD]

spP Purchase price of the solar panel and its maintenance [AUD]

Rev Revenue per MGT [AUD]

q Index [ - ]

r Discounting rate between preventive rail grindings [%]

ri Discounting rate between inspections using NDT [%]

ry Annual discounting factor [ - ]

R Track circular curve radii [m]

RCw Estimated Rail Crown wear width [mm]

RGw Estimated Rail Gauge wear width [mm]

s Flange wear [mm]

S Speed of train [km/h]

Suj Supply of the year j [ - ]

T Tangential force [N]

icslTC Total cost of differential wear loss for particular curve section [AUD]

icsWTC Total cost of differential wear loss for particular curve section [AUD]

TDj Wear Depth due to traffic after period j [mm]

TDq Traffic Depth due to wear after period q [mm]

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TW Table (crown) wear [mm2]

VW Wear volume [m3]

WOLi Worn out level of rail after ith grinding [%]

wz Normal applied load [ - ]

Wt Weighted wear rate [ - ]

icsW Differential wear loss [mm2/MGT]

Wagonv Wagon capacity [ - ]

x the inspection intervals per year for a rail corridor under consideration [ - ]

γ Creepage [m/m]

γ’ slide/roll ratio [ - ]

γx , γy Creepage in x and y direction [ - ]

Φ Spin [-]

jY = Decision variable for lubrication strategy [ - ]

= 0 for no or continuous lubrication [ - ]

= 1 for stop/start lubrication [ - ]

y rail life in years [ - ]

α Miniprof degrees [o]

β, ( Weibull parameters [ - ]

Λ(m) Failure intensity function associated with m [ - ]

βj, λj Weibull parameters for failures in jth strategy [ - ]

Λj(m) Failure intensity function associated with m in jth strategy [ - ]

µ Coefficient of friction with film parameter Λ [ - ]

φ = Traffic wear rate [MGT/mm2]

Twear = Total wear rate between lubricated and non-lubricated curves [MGT/mm2]

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CONTENTS

ABSTRACT…………………………………………………………………………..2

ACKNOWLEDGEMENT ………………………………………………..…………..5

Statement of Originality……………………………………………………..….……..7

LIST OF PUBLICATIONS……………………………………………..………….....8

NOMENCLATURE………………………………………………………………….12

LIST OF TABLES.......................................................................................................21

LIST OF FIGURES .....................................................................................................24

CHAPTER 1

SCOPE AND OUTLINE OF THESIS ........................................................................29

1.1 Introduction.........................................................................................................29 1.2 Scope of the research study.................................................................................31 1.3 Aims and Objectives ...........................................................................................31 1.4 Thesis Outline .....................................................................................................32

CHAPTER 2

OVERVIEW OF RAIL TRACK STRUCTURE, DEFECTS AND

MAINTENANCE STRATEGIES ...............................................................................34

2.1 Introduction.........................................................................................................34 2.2 Railway Track Structure .....................................................................................34 2.3 Rails ....................................................................................................................35 2.4 Fastening System ................................................................................................35 2.5 Sleeper (Tie)........................................................................................................36 2.6 Ballast..................................................................................................................37 2.7 Subballast ............................................................................................................38 2.8 Subgrade..............................................................................................................38 2.9 Track Component Characteristics .......................................................................38 2.10 Rail Degradation ...............................................................................................38 2.11 Rolling Contact Fatigue (RCF) and Grinding Strategies ..................................39 2.12 Rail Wear and Lubrication Strategies ...............................................................45 2.13 Inspection Frequency and Techniques ..............................................................50 2.14 Maintenance Strategies .....................................................................................54 2.15 Rail transposition ..............................................................................................55 2.16 Rail straightening ..............................................................................................55 2.17 Rail replacement ...............................................................................................55 2.18 Sleeper replacement ..........................................................................................55 2.19 Ballast maintenance ..........................................................................................56 2.20 Tamping ............................................................................................................56 2.21 Subgrade stabilisation .......................................................................................56 2.22 Operational Conditions .....................................................................................56 2.23 Summary ...........................................................................................................57

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CHAPTER 3

STUDY OF RAIL WEAR, ROLLING CONTACT FATIGUE AND RAIL MAINTENANCE MODELS.......................................................................................58

3.1. Introduction........................................................................................................58 3.2 Rail Wear and Rolling Contact Fatigue Models .................................................58 3.3 Rail Maintenance Models ...................................................................................70 3.4 NSW State Railway Authority’s Wheel-Rail Management Model ....................70 3.5 Railways of Australia (ROA) Rail Selection Module.........................................71 3.6 Railways of Australia (ROA) Rail Grinding Model ...........................................71 3.7 Railways of Australia (ROA) Wheel/Rail Management Model .........................71 3.8 ECOTRACK .......................................................................................................71 3.9 TOSMA...............................................................................................................72 3.10 Mini-MARPAS .................................................................................................73 3.11 AMP98 Cost Model ..........................................................................................73 3.12 Track Maintenance Cost Models (TMCOST) ..................................................73 3.13 Swedish Track Degradation Cost Model ..........................................................73 3.14 An Austrian Track Maintenance Cost Model ...................................................74 3.15 The UNIFE Life Cycle Costing ........................................................................74 3.16 Track Degradation Model .................................................................................74 3.17 Track Maintenance Planning Model (TMPM)..................................................75 3.18 Survey of Lubrication Practice .........................................................................75 3.19 Summary ...........................................................................................................85

CHAPTER 4

MODELLING AND ANALYSIS OF RAIL DEGRADATION AND RAIL GRINDING DECISIONS............................................................................................86

4.1 Introduction.........................................................................................................86 4.2. System Approach and Modelling.......................................................................86 4.3 Modelling Rail Breaks ........................................................................................87 4.4 Modelling Rail Degradation (Rail Section Loss)................................................90 4.5 Economic Grinding Model for Optimal Grinding Decisions..............................94

4.5.1 Modelling preventive rail grinding cost ....................................................98 4.5.2 Modelling down time cost due to rail grinding (loss of traffic) ................99 4.5.3 Modelling inspection cost..........................................................................99 4.5.4 Modelling risk cost of rail breaks and derailment ..................................100 4.5.5 Modelling Replacement Costs of Worn-Out Unreliable Rails ................101 4.5.6 Modelling Total Cost of Rail Maintenance .............................................101

4.6 Estimation of cost and life data.........................................................................102 4.6.1 Analysis of results....................................................................................102 4.6.2 Grinding cost ...........................................................................................102 4.6.3 Grinding cost/m.......................................................................................103 4.6.4 Grinding cost/MGT/m .............................................................................104 4.6.5 Risk cost/m...............................................................................................105 4.6.6 Risk cost/MGT/m .....................................................................................105 4.6.7 Down time cost/m ....................................................................................105 4.6.8 Down time cost/MGT/m...........................................................................106

4.7 Annuity Cost/m .................................................................................................107 4.7.1 Annuity cost/m for grinding.....................................................................107 4.7.2 Annuity cost/m for risk.............................................................................108

19

4.7.3 Annuity cost/m for down time..................................................................108 4.7.4 Annuity cost/m for inspection ..................................................................109 4.7.5 Annuity cost/m for replacement...............................................................110 4.7.6 Total annuity cost/m ................................................................................111

4.8 Annuity cost/m assessment for each MGT .......................................................111 4.8.1 Annuity cost/m for 23 MGT .....................................................................111 4.8.2 Annuity cost/m for 12 MGT .....................................................................112 4.8.3 Annuity cost/m for 18 MGT .....................................................................113 4.8.4 Annuity cost/m for 9 MGT .......................................................................114

4.9 Summary ...........................................................................................................115

CHAPTER 5

MODELLING AND ANALYSIS OF WEAR AND LUBRICATION DECISIONS………………………………………………………………………...117

5.1 Introduction.......................................................................................................117 5.2 Assessment of lubricator’s performance...........................................................119 5.3 Lubrication decision model...............................................................................122 5.4 Modelling rail wear ...........................................................................................127

5.4.1 Modelling Rail Wear Limits ....................................................................131 5.4.2 Modelling Rail Lubrication .....................................................................136 5.4.3 Modelling Repair Cost of Applicator due to Breakdowns.......................138 5.4.4 Modelling Replacement Cost of Applicator ............................................138 5.4.5 Cost for various Lubricator Maintenance Strategies..............................138 5.4.6 Modelling Lubricant Cost........................................................................139 5.4.7 Modelling Benefits of Lubricators by Reducing Rail Wear Cost ............139 5.4.8 COST-BENEFIT Analysis of Applicators and Various Lubricants.........140 5.4.9 Failure of Lubricators .............................................................................141 5.4.10 Cost for Fixing Breakdowns..................................................................141 5.4.11 Cost to Maintain Lubricators ................................................................141 5.4.12 Cost-Benefit Analysis of Lubricators.....................................................141 5.4.13 Cost of Lubricants .................................................................................142

5.5 Modelling Failures ............................................................................................142 Renewal Process...............................................................................................144

5.6 Framework for Benchmarking Lubrication ......................................................147 5.7 Modelling Annuity Cost of Lubricators............................................................148 5.8 Collection and Analysis of Data .......................................................................150

5.8.1 Estimation of Area Head Loss (AHL)......................................................151 5.8.2 Analysis of Wear for Curves radii 0-300 m.............................................152 5.8.3 Analysis of Wear for Curves radii 301-450 m.........................................159 5.8.4 Analysis of Wear for Curves radii 451-600 m.........................................164

5.9 Analysis of Annuity Costs ................................................................................170 5.9.1 Numerical Example .................................................................................173

5.10 Summary .........................................................................................................177

CHAPTER 6

MODELLING AND ANALYSIS OF INSPECTION FOR INSPECTION DECISIONS...............................................................................................................179

6.1 Introduction.......................................................................................................179 6.2 Modelling Inspection ........................................................................................179

20

6.2.1 Modelling Rail Breaks.............................................................................180 6.2.2 Modelling Replacement Costs of Worn-out Unreliable Rails .................181 6.2.3 Modelling Cost Benefit Analysis .............................................................181

6.3 Failure Mode and Effect Analysis (FMEA)......................................................182 6.3.1 Occurrence of Failure .............................................................................183 6.3.2 Detectability of Failure ...........................................................................184 6.3.3 Severity of Failure ...................................................................................186 6.3.4 Risk Priority Number Ranking (RPN) .....................................................188

6.4 Collection and Analysis of Rail Failure Data ...................................................190 6.4.1 Rail Defect Initiation ...............................................................................190 6.4.2 Rail Failures from Defect Initiation ........................................................192 6.4.3 Cost-Benefit Analysis of Inspection Frequency.......................................193 6.4.4 Analysis of cost data................................................................................195 6.4.5 Analysis of selected defect, rail break and derailment............................196 6.4.6 Limitations of data...................................................................................198

6.5 Total cost of rail inspection and rectification....................................................199 6.6 Limitations of Detecting Rail Breaks................................................................201 6.7 Effect of Seasonal Conditions on Rail Defect Initiation...................................202 6.8 Summary ...........................................................................................................203

CHAPTER 7

DEVELOPMENT OF AN INTEGRATED MODEL FOR ESTIMATION OF EXPECTED TOTAL COSTS ...................................................................................204

7.1 Introduction.......................................................................................................204 7.2 Development of the Integrated Model ..............................................................204 7.3 Analysis of Results............................................................................................207

7.3.1 Annuity costs/m for 12 MGT....................................................................209 7.3.2 Annuity costs/m for 23 MGT....................................................................210 7.3.3 Annuity costs/m for 12 MGT & 23 MGT.................................................212 7.3.4 Estimation of Annuity costs/m .................................................................214

7.4. Summary ..........................................................................................................229

CHAPTER 8

CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH ..................231

8.1 Introduction.......................................................................................................231 8.2 Contribution of This Thesis ..............................................................................231 8.3 Scope for Future Research ................................................................................234

REFERENCES ..........................................................................................................235

APPENDICES ...........................................................................................................250

Appendix - A .....................................................................................................250 Appendix – B.....................................................................................................258 Mechanism of Way-side Lubricators (Mechanical) .........................................276 Mechanism of Hydraulic Lubricators ..............................................................277 Visual Inspection ..............................................................................................278 Rail head temperature rise method ..................................................................278 Tribometer ........................................................................................................279

21

LIST OF TABLES

Table 3.1: Cost of Lubrication strategies.....................................................................77

Table 3.2: Lubrication costs to rail players..................................................................77

Table 3.3: Lubricators used in Sweden, 2004..............................................................80

Table 3.4: Lubricators used in UK...............................................................................81

Table 3.5: Lubricators used in Spoornet ......................................................................81

Table 4.1: Measurements of grinding ..........................................................................92

Table 4.2: Safety limit for Malmbanan........................................................................94

Table 4.3: The ideal grinding for heavy-haul ..............................................................95

Table 4.4: Track path divided into sections .................................................................97

Table 4.5: Estimated costs and area safety limits ......................................................102

Table 4.6: Grinding cost/m for 0 to 800 m curves .....................................................103

Table 4.7: Grinding cost/MGT/m for 0 to 800 m curves ...........................................104

Table 4.8: Risk cost/m for 0 to 800 m curves ............................................................105

Table 4.9: Risk cost/MGT/m for 0 to 800 m curves ..................................................105

Table 4.10: Down time cost/m for 0 to 800 m curves ...............................................106

Table 4.11: Down time cost/MGT/m for 0 to 800 m curves .....................................106

Table 4.12: Annuity cost/m for grinding 0 to 800 m curves......................................107

Table 4.13: Annuity cost/m for risk in 0 to 800 m curves .........................................108

Table 4.14: Annuity cost/m for down time in 0 to 800 m curves ..............................109

Table 4.15: Annuity cost/m for inspection in 0 to 800 m curves...............................109

Table 4.16: Annuity cost/m for replacement in 0 to 800 m curves............................110

Table 4.17: Total annuity cost/m for 0 to 800 m curves ............................................111

Table 4.18: Annuity cost/m for 23 MGT in 0 to 800 m curves .................................112



22

Table 4.21: Annuity cost/m for 9 MGT in 0 to 800 m curves ...................................114

Table 5.1: Cost of Trackside Lubrication ..................................................................120

Table 5.2: ‘Where to lubricate’ and ‘not to lubricate’ ...............................................124

Table 5.3: Expert Chart of Lubrication Effectiveness ...............................................125

Table 5.4 Traffic for Section A to B during period from 1998 to 2004 ....................150

Table 5.5: Area head loss (mm2/MGT) for 300 m curve...........................................153

Table 5.6: Costs of Wayside Lubricator ....................................................................171

Table 5.7: Estimated rail lives in heavy-haul track....................................................172

Table 5.8: Savings achieved ......................................................................................177

Table 6.1: Causes of Defective Rails.........................................................................183

Table 6.2: Causes of Broken Rails.............................................................................183

Table 6.3: Ranking of Failure Occurrence.................................................................184

Table 6.4: Ranking of Detectability...........................................................................185

Table 6.5: Train Accidents Jan 2000 - Dec 2003.......................................................186

Table 6.6: Severity Ranking of Failure......................................................................187

Table 6.7: Risk Priority Number (RPN) ratings ........................................................188

Table 6.8: Cost Benefit Analysis ...............................................................................200

Table 7.1: Examined cases with the integrated model...............................................208

Table 7.2: Annuity costs/m for 12 MGT with lubrication .........................................209

Table 7.3: Annuity costs/m for 12 MGT without lubrication....................................210

Table 7.4: Annuity costs/m for 23 MGT with lubrication .........................................211

Table 7.5: Annuity costs/m for 23 MGT without lubrication....................................212

Table 7.6: Analysis of total annuity costs/m for 12 MGT .........................................213

Table 7.7: Analysis of total annuity costs/m for 23 MGT .........................................213

Table 7.8: Annuity costs/m for 12 MGT with lubrication for one inspection ...........214

Table 7.9: Annuity costs/m for 12 MGT without lubrication, one inspection...........215

23

Table 7.10: Annuity costs/m for 23 MGT with lubrication for one inspection .........216

Table 7.11: Annuity costs/m for 23 MGT without lubrication for one inspection ....217

Table 7.12: Annuity costs/m for 12 MGT with lubrication for two inspections .......218

Table 7.13: Annuity costs/m for 12 MGT without lubrication for two inspections ..219

Table 7.14: Annuity costs/m for 23 MGT with lubrication for two inspections .......220

Table 7.15: Annuity costs/m for 23 MGT without lubrication for two inspections ..221

Table 7.15: Annuity costs/m for 12 MGT with lubrication for three inspections .....222

Table 7.17: Annuity costs/m for 12 MGT without lubrication for three inspections 223

Table 7.18: Annuity costs/m for 23 MGT with lubrication for three inspections .....224

Table 7.19: Annuity costs/m for 23 MGT without lubrication for three inspections 225

Table 7.20: Total annuity costs/m for 12 and 23 MGT with lubrication...................226

Table 7.21: Total annuity costs/m for 12 and 23 MGT without lubrication..............227

Table 7.22: Findings from examined cases................................................................230

Table B1: Mean temperature rise...............................................................................278

Table B2: Friction Coefficients based on Tribometer ...............................................279

24

LIST OF FIGURES

Figure 1.1: Factors behind the problems......................................................................30

Figure 2.1: Cross sectional view of rail track structure ...............................................34

Figure 2.2: Profile of rail head.....................................................................................35

Figure 2.3: Spikes, Rail Anchors and Elastic Fastening System .................................35

Figure 2.4: Concrete and Wooden Sleepers and Fasteners..........................................36

Figure 2.5: RCF, Shelling and Gauge Corner Cracking ..............................................39

Figure 2.6: Flaking problems.......................................................................................41

Figure 2.7: Influence of rail wear from lubrication .....................................................47

Figure 2.8: Rail area worn off with and without lubrication .......................................47

Figure 2.9: Ultrasonic and induction techniques .........................................................51

Figure 2.10: Improved ultrasonic test vehicle system .................................................53

Figure 2.11: Automated re-railing machine.................................................................55

Figure 3.1: Synergy of rail metallurgy & track engineering........................................61

Figure 3.2 Phases of crack life using curve of da/dn and length .................................62

Figure 3.3 Truncation of a shallow angled crack.........................................................63

Figure 3.4 Life line due to wear and fatigue................................................................63

Figure 3.5: Head check (HC) and transverse rail fracture ...........................................66

Figure 3.6: Factors influencing rail/wheel degradation ...............................................69

Figure 3.7: Lubrication systems...................................................................................75

Figure 3.8: Lubricators are full of ice and snow in track.............................................79

Figure 3.9: Rail and wheel lubricators.........................................................................82

Figure 3.10: Bleeding from the blade ..........................................................................83

Figure 3.11: Short wave corrugation ...........................................................................84

Figure 3.12: Grease leakage and environmental hazard ..............................................84

Figure 4.1: Integrated system approach for modelling and analysis ...........................87

25

Figure 4.2: Rail profile measurement using MINIPROF.............................................91

Figure 4.3: Central vertical wear and side wear ..........................................................92

Figure 4.4: Measurement of rail wear..........................................................................93

Figure 4.5: Flow chart of the track monitored base model ..........................................96

Figure 4.6: Probabilities of failures ...........................................................................101

Figure 4.7: Grinding cost estimation method ............................................................103

Figure 4.8: Grinding cost/m for 0 to 800 m curves....................................................104

Figure 4.9: Grinding cost/MGT/m for 0 to 800 m curves..........................................104

Figure 4.10: Down time cost/m for 0 to 800 m curves ..............................................106

Figure 4.11: Down time cost/MGT/m for 0 to 800 m curves ....................................107

Figure 4.12: Annuity cost/m for grinding 0 to 800 m curves ....................................107

Figure 4.13: Annuity cost/m for risk in 0 to 800 m curves........................................108

Figure 4.14: Annuity cost/m for down time in 0 to 800 m curves.............................109

Figure 4.15: Annuity cost/m for inspection in 0 to 800 m curves .............................110

Figure 4.16: Annuity cost/m for replacement in 0 to 800 m curves ..........................110

Figure 4.17: Total annuity cost/m for replacement of 0 to 800 m curves..................111

Figure 4.18: Annuity cost/m for 23 MGT in 0 to 800 m curves................................112



Figure 4.21: Annuity cost/m for 9 MGT in 0 to 800 m curves..................................114

Figure 5.1: Flowchart for the modelling and analysis of lubrication decisions.........118

Figure 5.2: A well lubricated rail wear face in a Spoornet curve ..............................119

Figure 5.3: Lubrication decision model .....................................................................123

Figure 5.4: Coefficient of friction..............................................................................124

Figure 5.5: Dry rail condition ....................................................................................125

Figure 5.6: Aggressive wear ......................................................................................126

26

Figure 5.7: Lubricated rail-wheel interface ...............................................................126

Figure 5.8: Rail with minimal wear ...........................................................................126

Figure 5.9: Simulation model to estimate total costs due to wear .............................130

Figure 5.10: Wear limit for rail head cross sectional area .........................................131

Figure 5.11: Traffic wear rates for high rail ..............................................................134

Figure 5.12: Rail wear limits for mainline, rail type 20 kg/m ...................................135

Figure 5.13: Lubrication influencing rail life ............................................................140

Figure 5.14: Wayside lubrication...............................................................................142

Figure 5.15: Framework for benchmarking lubrication.............................................147

Figure 5.16 Curve distribution for A-B corridor .......................................................150

Figure 5.17: Table wear and side wear measurements ..............................................151

Figure 5.18: Wear for curves radii 0-300 m from 1998-2001 ...................................153

Figure 5.19: Wear for curves radii 0-300 m from 2001-2004 ...................................154

Figure 5.20: Rail wear for four different curves ........................................................154

Figure 5.21: Curve fitting analysis for curve radius 300 m .......................................155

Figure 5.22: Gaussian distribution of the RMSE for 0-300 m curves .......................156

Figure 5.23: Area head loss comparison for 47 kg rail..............................................157

Figure 5.24: Area head loss comparison for 50 kg ....................................................158

Figure 5.25: Wear for curve radius 300 m.................................................................158

Figure 5.26: Wear for curve radius 245 m.................................................................159

Figure 5.27: Wear for curves radii 301-450 m from 1998-2001 ...............................159

Figure 5.28: Wear for curves radii 301-450 m from 2001-2004 ...............................160

Figure 5.29: Rail wear for different radii for accumulated MGT..............................160

Figure 5.30: Curve fitting for curve radius 415 m.....................................................161

Figure 5.31: Gaussian distribution of the RMSE for curve radii 301-450 m ............162

Figure 5.32: Area head loss for 50 kg rail .................................................................163

27


Figure 5.34: Wear data for curves radii 451-600 m from 1998-2001........................164

Figure 5.35: Wear data for curves radii 451-600 m from 2001-2004........................165

Figure 5.36: Rail wear for curves with different radii ...............................................165

Figure 5.37: Curve fitting for curve radius 500 m.....................................................166

Figure 5.38: Gaussian distribution of the RMSE for curves radii 451-600 m...........167

Figure 5.39: Area head loss for 47 kg........................................................................168


Figure 5.41: Area head loss curve radius 500 m........................................................169

Figure 5.42: Analysis of lubrication costs .................................................................174

Figure 5.43: Wear progression for curve radius 236.7 m from 1997-2004 ...............176

Figure 6.1: Rail defects occurrence ...........................................................................188

Figure 6.2: Rail defects detectability .........................................................................189

Figure 6.3: Rail defects severity ................................................................................189

Figure 6.4: Proposed model for risk mitigation of rail defects ..................................189

Figure 6.5: Rolling contact fatigue defects ................................................................191

Figure 6.6: Error in ultrasonic (NDT) inspection ......................................................192

Figure 6.7: Analysis of NDT and visual inspection of rail ........................................193

Figure 6.8: Process map of rail inspection................................................................195

Figure 6.9: Block diagram of inspection and detection .............................................197

Figure 6.10: Venn diagram of inspection ..................................................................198

Figure 6.11: Pie chart for preventive, corrective (rail breaks) ...................................199

Figure 6.12: Pie chart for detected rail breaks and derailment ..................................199

Figure 6.13: Detecting rail breaks using signalling system .......................................202

Figure 7.1: Integrated model for rail grinding-lubrication-inspection.......................205

Figure 7.2: Annuity costs/m for 12 MGT with lubrication........................................209

28

Figure 7.3: Annuity costs/m for 12 MGT without lubrication...................................210

Figure 7.4: Annuity costs/m for 23 MGT with lubrication........................................211

Figure 7.5: Annuity costs/m for 23 MGT without lubrication...................................212

Figure 7.6: Total annuity costs/m for 12 MGT..........................................................213

Figure 7.7: Total annuity costs/m for 23 MGT..........................................................214

Figure 7.8: Annuity costs/m for 12 MGT with lubrication for one inspection..........215

Figure 7.9: Annuity costs/m for 12 MGT without lubrication for one inspection.....216

Figure 7.10: Annuity costs/m for 23 MGT with lubrication for one inspection........217

Figure 7.11: Annuity costs/m for 23 MGT without lubrication for one inspection...218

Figure 7.12: Annuity cost/m for 12 MGT with lubrication for two inspections........219

Figure 7.13: Annuity costs/m for 12 MGT without lubrication for two inspections.220

Figure 7.14: Annuity costs/m for 23 MGT with lubrication for two inspections ......221

Figure 7.15: Annuity costs/m for 23 MGT without lubrication for two inspections.222

Figure 7.16: Annuity costs/m for 12 MGT with lubrication for three inspections ....223

Figure 7.17: Annuity costs/m for 12 MGT without lubrication for three inspection 224

Figure 7.18: Annuity costs/m for 23 MGT with lubrication for three inspections ....225

Figure 7.19: Annuity costs/m for 23 MGT without lubrication for three inspection 226

Figure 7.20: Total annuity costs/m for 12 & 23 MGT with lubrication ....................227

Figure 7.21: Total annuity costs/m for 12 & 23 MGT without lubrication ...............228

Figure B1: Mechanical lubricators.............................................................................276

Figure B2: Plunger mechanism..................................................................................277

Figure B3: Smear Test ...............................................................................................278

Figure B4: Tribometer at the gauge face ...................................................................279

29

CHAPTER 1

SCOPE AND OUTLINE OF THESIS

1.1 Introduction

Rails play a significant role in transport of passengers and freight movements. In 2003

the rail industry contributed AUD $ 5.3 billion in value to the Australian economy

(Australasian Railway Association Inc, 2004). In the past five years, railroads have

purchased approximately 500,000 tonnes of replacement rails per year at an estimated

total cost of US $1.25 billion (AUD $ 1.37 billion). Even a small improvement in rail

performance has significant economical benefits to rail industry (Kristan, 2004). In

2000, the Hatfield accident in UK was caused due to rolling contact fatigue. It killed 4

people and injured 34 people and led to the cost of £ 733 million (AUD $ 1.73 billion)

for repairs and compensation payments. In 1977, the Granville train disaster in

Australia killed 83 people and injured 213 people. These accidents were mainly due to

wear, rolling contact fatigue (RCF) and poor maintenance.

Increasing traffic density, axle loads, accumulated tonnages (Million Gross Tonnes

(MGT)), train speed and longer trains have increased productivity but with an

increased risk of rail breaks and derailments. Rail wear and rolling contact fatigue

(RCF) are inevitable due to rail wheel interaction. These problems have increased the

maintenance and replacement costs. If undetected, these problems can cause

derailment causing huge loss of revenue, disruption of service, resulting damage of

assets, and loss of lives. RCF alone costs European railways around € 300 million

(AUD$ 485 million) per year and these defects account for about 15% of the total

costs. The total costs of all defects are about € 2 billion (AUD$ 3.23 billion) per year

(Cannon et al., 2003). The American Association of Railroads (AAR) estimated that

the wear and friction occurring at the wheel/rail interface of trains due to ineffective

lubrication, costs American Railways in excess of US $ 2 billion each year (Sid and

Wolf, 2002). The Office for Research and Experiments (ORE) of the International

Union of Railways (UIC) has noted that maintenance costs increases directly (60–65

per cent) with increase in traffic, train speed and axle load. These costs are greater

when the quality of the track is poor (ORR, 1999).

30

In rail transport, operational risks are defined as risks of rail breaks and derailments

that occur during the rail-wheel interaction. During the rail-wheel interaction, some of

these unwanted events occur due to lack of maintenance, rail-wheel wear and rolling

contact fatigue (RCF) cracks. These are influenced by various operating conditions

such as traffic density, freight, rail material type, size, hardness, bogie type, speed

limit, temperature, curve radius and environmental factors. Risks have been

increasing due to increased number of axle passes, steeper curve radius, worn-out rail-

wheel profile in the system and inadequate material hardness, unfavourable rail/wheel

interaction, inappropriate rail-wheel grinding, poor lubrication and poor maintenance.

Modelling and analysis of operating risks require failure time data, probability of

detection and consequences of failures. Interpretation of various rail defects and

broken rails and their consequences is extremely important for developing these

models. Preventive rail grinding and lubrication is used to control surface fatigue

defects and to reduce wear and noise. However, knowledge of surface fatigue cracks,

rail-wheel wear, rail grinding and lubrication is limited.

Figure 1.1: Factors behind the problems

Some of the factors behind the problems are shown in Figure 1.1. It is important to

study the interaction of rail-wheel degradation and influencing factors, monitor those

factors and find cost effective technological solutions to eliminate or reduce those

problems. Therefore, there is a need to develop an integrated model to predict

operational risks, and take appropriate economic decisions to reduce maintenance

costs and improve reliability and safety of rail operation.

31

This chapter begins with a brief introduction of the research problem in Section 1.1.

This is followed by the scope of this research work in Section 1.2. Aims and

objectives are presented in Section 1.3. Finally an outline of the thesis is presented in

Section 1.4.

1.2 Scope of the research study

Research shows that most of the existing models for predicting rail degradation and

operational risks are based on Million Gross tonnes (MGT). They have not considered

other possible influential factors. This research is a comprehensive study of rail wear,

rolling contact fatigue (RCF), lubrication, rail grinding, inspection, rectification and

rail replacements. It develops stochastic models and economic models, and integrate

those models for grinding, lubrication, inspection, rail maintenance and replacement

decisions. These models will be useful for informed strategic decisions based on

operating conditions.

1.3 Aims and Objectives

This research addresses the development and analysis of an integrated model for

assessment of operational risks in rail track. The main focus of this research is

problems associated with higher axle loads, wear, early rail replacements, rail defects

leading to rail breaks and derailments.

The specific aims of this research project are to develop:

• Knowledge based models for analysis and assessment of operational risks

associated with rail-wheel degradation due to wear, lubrication, rolling contact

fatigue (RCF), rail grinding, inspection, replacement and operating conditions.

• Integrated economic models for decision support systems that investigate risk

and economical impact analysis with “what if” scenarios for maintenance

strategies.

The main objectives of this research are:

• Collection and analysis of data on rail failures, rail breaks and related costs of

lubrication, grinding, inspection, rectification and replacement of rails.

• Development of failure models and estimation of parameters, considering

operational and environmental conditions.

• Development of grinding models for optimal grinding decisions, linking

cumulative MGT, axle load, curve radius and operating conditions.

32

• Development of lubrication models for optimal lubrication strategies.

• Development of inspection models for optimal inspection decisions, considering

detected and undetected defects, using non destructive ultrasonic testing methods.

• Development of an integrated model for managerial decisions based on costs and

risks.

1.4 Thesis Outline

Outline of the thesis is as follows:

Chapter 1 defines the scope and outline of this research. It clearly defines the

background of the problem and the need for the development of an integrated model

to predict operational risks and maintenance costs.

Chapter 2 provides a brief overview of the literature on rail track structure, rail

defects, rail wear, rail-wheel lubrication, rail grinding, inspection, replacement of rails

and maintenance strategies.

Chapter 3 provides models for rail wear, rolling contact fatigue (RCF), and rail

maintenance. It analyses the gaps in the existing models and proposed solutions to

eliminate/ reduce these gaps for increased safety and reliability of rail operation.

Chapter 4 deals with modelling and analysis of rail degradation and rail grinding

costs. Real life data are collected and analysed for developing these models.

Economic models are developed and analysed. Illustrative numerical examples are

used for application to industry.

Chapter 5 deals with the development of lubrication models for optimal lubrication

strategies. It includes modelling and economic analysis of rail wear and rail-wheel

lubrication, based on various types of lubricators and curve radius.

Chapter 6 deals with development of inspection models for optimal inspection

decisions, considering detected and undetected defects, using non destructive

ultrasonic testing.

33

Chapter 7 deals with development of an integrated model for managerial decisions

related to lubrication, grinding, inspection and replacements, based on costs and risks.

It includes development of decision support systems and user friendly software.

Finally, Chapter 8 provides a summary of this thesis, the contribution of the thesis to

this field of research, and a discussion of the potential extensions and topics for future

research.

34

CHAPTER 2

OVERVIEW OF RAIL TRACK STRUCTURE, DEFECTS AND

MAINTENANCE STRATEGIES

2.1 Introduction

Rail transport makes a significant contribution to the Australian economy,

representing a sizeable gross domestic product (GDP) and providing passenger,

freight, and heavy haul services. However, rail infrastructure owners are lagging

behind best practice in monitoring, controlling and predicting rail defects and

maintenance strategies to reduce operational risks. Railways have a history of two

hundred years of steel wheels on steel rails, still there are more unknown than known

features of their interaction. Rail degradation depends on rail track structure, rail

condition and maintenance strategies for reliable and safe operation.

This chapter provides an overview of rail structure, rail defects and existing models

for predicting wear, rolling contact fatigue, inspection, lubrication and grinding

decisions for rail maintenance strategies.

2.2 Railway Track Structure

Rail tracks are important for carrying passengers and moving freight. The main

components of rail track structure (Esveld, 2001) are shown in Figure 2.1.

Figure 2.1: Cross sectional view of rail track structure (Esveld, 2001)

halla

This figure is not available online. Please consult the hardcopy thesis available from the QUT Library

35

2.3 Rails

Rails operate under harsh environment, heavy axle loads, accumulated tonnage,

million gross tonnes (MGT), longer trains, increased traffic density and increased

train speeds. As a part of track structure, they have no redundancy, thus their defects

and failures can lead to rail breaks and result in derailments causing huge loss of

property, revenue and lives. Rails are major capital investments and incur a huge

amount of maintenance cost for infrastructure owners. Rail steels are usually joined

together, either bolted or welded. There are complexities in the replacement of

defective and broken rails due to temperature changes, cost of materials, transposing

decisions and laying techniques (Cope, 1993). A profile of rail head is as shown in

Figure 2.2.

Figure 2.2: Profile of rail head

2.4 Fastening System

The purpose of the fastening system is to retain the rails against the sleepers and resist

vertical, lateral, longitudinal and overturning movements of the rail.

Figure 2.3: Spikes, Rail Anchors and Elastic Fastening System (PANDROL)

Gauge Corner

Rail Head

Web

Foot

Gauge Corner

Rail Head

Web

Foot

36

These movements are caused by force systems from the wheels and temperature

changes in the rails. Various types of fasteners used in railtrack systems are shown in

Figure 2.3:

(a) Spikes

(b) Rail anchors

(c) Elastic fastening system

The selection of appropriate fasteners depends on railtrack structure (rail type and

size, sleeper type and size, track curvature and superelevation), traffic conditions (axle

loads, train speeds and annual tonnage), maintenance requirements and economic

restraints (Zhang, 2000).

2.5 Sleeper (Tie)

Sleepers hold the rails to the correct the gauge and transmit loads on the rails to the

ballast. Sleepers or ties have several important functions (Esveld, 2001). These are to:

1. receive the load from the rail and distribute it over the supporting ballast at an

acceptable ballast pressure level;

2. hold the fastening system to maintain the proper track gauge;

3. restrain the lateral, longitudinal and vertical rail movement by anchorage of

the superstructure in the ballast; and

4. provide support to the rails to help develop proper rail/wheel contact.

Various types of sleepers used in the railtrack system are: timber, concrete and steel.

Timber sleepers are the most commonly used in the railway system. The reasons for

choosing timber are its cost effectiveness, resilience, corrosion resistance,

workability, ease of handling, potential re-use and insulation. The life of timber

sleepers can vary from 8 to 30 years depending on quality and density of traffic,

position in the track, climate and maintenance. Some species may even have a life of

50 years (McAlpine, 1991). Figure 2.4 shows concrete and wooden sleepers and

fasteners.

Figure 2.4: Concrete and Wooden Sleepers and Fasteners (PANDROL)

37

Concrete sleepers are generally considered more economical than timber sleepers for

heavy haul tracks. Concrete sleepers have much longer life than timber sleepers, with

an anticipated life of 50 years. Prestressed concrete sleepers were first used in

Australia in 1940 and are now widely used since the 1980s (Muller, 1985). Tracks

constructed with concrete sleepers also have higher buckling resistance, lower

maintenance requirements and uniform specifications. However, due to heavy weight

of more than 300 kg each, they need special laying machines for installation. They

also need special considerations in specifying design loads to prevent cracking, and

need rail pads to reduce vibrations (McAlpine, 1991). Concrete sleepers are very

sensitive to impact loads (Riessberger, 1984). Therefore, rail top irregularities need to

be controlled to avoid impact loads.

Steel sleepers are used because of sleeper life advantages over timber sleepers and

resistance to insect attack (Brodie et al., 1977). They also provide greater lateral and

longitudinal track resistance than timber sleepers (Birks et al., 1989). However, due to

their special cross shape, they require more tamping after initial installation. Special

attention must also be paid to rail fastening selection and insulation. Steel sleepers

have been used for many years, particularly in countries where termites are a problem.

Research is being undertaken in this area by British Steel Corporation for techno-

economic evaluation (BSC) (Cope, 1993).

2.6 Ballast

Ballast is the selected, crushed granular material placed as the top layer of the

substructure in which the sleepers are embedded. The functions of ballast are to:

• resist vertical, uplift lateral and longitudinal forces applied to the sleepers to

retain track in its required position;

• provide some of the resiliency and energy absorption for the track;

• provide large voids for storage of fouling material in the ballast, and

movements of particles through the ballast;

• facilitate maintenance surfacing and lining operations (to adjust track

geometry) by the ability to rearrange ballast particles with tamping;

• provide immediate drainage of water falling onto the track; and

• reduce pressures from the sleeper bearing area to acceptable stress levels for

the underlying material (Esveld, 2001).

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2.7 Subballast

The layer between the ballast and the subgrade is the subballast. The functions of

subballast are to:

• prevent upward migration of fine material emanating from the subgrade;

• prevent interpenetration of the subgrade and the ballast; and

• prevent subgrade attribution by the ballast, which in the presence of water,

leads to slurry formation. [This is a particular problem if subgrade is hard

(Ernest and John, 1994)].

2.8 Subgrade

The subgrade is the platform upon which the track structure is mounted. It is also

referred to as formation (Zhang, 2000). Its main function is to provide a stable

foundation for the subballast and ballast layers. The subgrade is an important

substructure component which can have a significant influence on track performance

and maintenance. It acts as superstructure support resiliency, and contributes

substantially to the elastic deflection of the rail under wheel loading. Its stiffness

magnitude influences ballast, rail and sleeper deterioration (Esveld, 2001).

2.9 Track Component Characteristics

The railtrack is composed of several components with specific functions. The rail

tracks experience vertical, horizontal and longitudinal forces that can be static,

dynamic and thermodynamic (Zhang, 2000). These forces influence the functions of

the basic components in the track which, in turn, affect degradation and the failure

process. The failure of each component has an effect on the function of other

components in the rail track system. It is, therefore, important to analyse the

characteristics of each component to be able to measure the defects and failures to

prevent catastrophic failures. This research focuses mainly on the rails.

2.10 Rail Degradation

Rail degradation is a major economic burden for rail infrastructure owners around the

world. It costs approximately € 2 billion per year in the European Union alone

(Cannon et al., 2003). Failures include:

� rail manufacturing defects

� defects or damage caused by inappropriate handling, installation and use

39

� exhaustion of rail steel’s inherent resistance to the fatigue damage.

2.11 Rolling Contact Fatigue (RCF) and Grinding Strategies

Head checks, gauge-corner cracks, squats and shelling (as shown in Figure 2.5) are

forms of rolling contact fatigue. They are caused by a combination of high, normal

and tangential forces between rail and wheel.

Figure 2.5: RCF, Shelling and Gauge Corner Cracking (QR, 2005)

The initiation of crack occurs due to accumulation of shear deformation due to

repeated rolling-sliding contact loading. The plastic deformation caused by large

contact stresses has a great influence on crack initiation. The microscopic crack

produced, propagates through the heavily deformed material until it reaches a depth

where the steel fails to retain its original isotropic properties. At this stage the crack is

a few millimetres deep and may lead to spalling of material from the rail surface

(Ishida et al., 2003). However, isolated cracks can turn down into the rail and, if not

detected, can cause the rail to break. These events appear to be rare, but are highly

dangerous since RCF cracks tend to grow almost continuously at a given site. Fracture

at one crack increases stress in the nearby rail, increasing the risk of further breaks

and disintegration of the rail Cannon et al., (2003). Bower and Johnson (1991) and

Bogdanski et al., (1997) found that shallow angle crack propagation, is encouraged by

fluid entrapment that leads to crack pressurization. To reduce crack face friction, it

allows relative shear of the crack faces. The direction of growth of the crack beneath

the rail surface and the direction of the crack mouth on the rail surface, are both a

guide to the predominant direction of traction causing the crack. Generally, large

numbers of head checks can form on high rail (especially on steep curves) and deep

transverse head checks may be developed from some of them. The squat defect is a

similar form of fatigue damage that tends to occur more randomly on very shallow

curves and tangent track. These forms of surface-initiated RCF pose special

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inspection problems. For both head checks and squats, the development of a

downward-turning fatigue crack leads to final rail failure.

This research found that limitations exist in accurately predicting rolling contact

fatigue (RCF) and initiation of cracks which lead to rail breaks. The stages of fatigue

crack as outlined by Milker (1997) are follows:

• Stage 1: shear stress driven initiation at the surface

• Stage 2: transient crack growth behaviour

• Stage 3: subsequent tensile and/or shear driven crack growth

Bannantine et al., (1991) and Suresh (1998) identified two types of approaches that

may be used to analyse crack initiation. They are:

• The defect-tolerant approaches

• The total-life approaches

The defect-tolerant approaches rely on the resistance to crack growth in materials that

are inherently flawed by small cracks. These approaches use fracture mechanics to

calculate the number of cycles required to propagate a crack to a critical size. There

are, however, some disadvantages related to these approaches: (a) it is difficult to

establish by tests the material parameters and crack growth data mechanically for

small cracks, (b) the results are sensitive to the choice of initial crack and defect size

and (c) it is has been difficult to establish approaches that are applicable to

engineering calculations, in particular, for elastic–plastic conditions (Ringsberg,

2001).

The total-life approaches estimate the resistance to fatigue crack initiation based on

nominally defect-free materials and components. These approaches attempt to analyse

the total fatigue life to failure (initiation); they are divided into stress-based and

strain-based approaches. The stress-based approach is characterised in terms of low

cyclic stress ranges that are designed against fatigue crack initiation (high-cycle

fatigue failures). The strain-based approach (also called the strain-life approach)

involves the fatigue life prediction of crack initiation according to which the strain

range characterises the fatigue life. The stresses in this approach are high enough to

cause plastic deformations that govern fatigue failure (low-cycle fatigue failures). A

drawback to the total-life approaches is that the definition of fatigue failure (or

41

initiation) is ambiguous. Tests should therefore be carried out to define fatigue failure

and the size of the initiated crack at this point (Ringsberg, 2001).

Yokoyama et al., (2002) investigated rolling contact behaviour for the materials of

standard carbon rail steel with Vickers hardness of 270 (270 HV), a head hardened

premium pearlitic rail steel with 390 HV, a bainitic rail steel of 270 HV and a high

strength bainitic rail steel of 420 HV. The carbon contents of pearlitic steels are in the

range from 0.65 to 0.80 mass %, which are almost double those of the bainitic steels.

Bainitic steels contain large amounts of chromium, molybdenum, niobium and

vanadium to obtain the desired strength using less carbon.

Figure 2.6: Flaking problems (Yokoyama et al., 2002)

Results show that bainitic steel has much better flaking (as shown in Figure 2.6)

resistance than pearlitic rail steels of the same tensile strength level. The initiation

time for RCF damage decreases with an increase in the angle of attack for all the

steels tested. Bainitic rail steels showed better RCF damage resistance than pearlitic

rail steels at any angle of attack.

Sawley and Kristan (2003) conducted small and full scale tests to investigate potential

resistance of rolling contact fatigue damage. They found that wear performance of

bainitic rail steel depends considerably on test conditions; however, the indication was

that bainitic steel rails can have significantly better rolling contact fatigue

performance compared to pearlitic rails. There is a need for better understanding of

fatigue performance.

Garnham and Beynon (1991) analysed rolling-sliding contact fatigue behaviour of rail

steels. They described a new wear machine which is capable of testing large, standard

cyclic discs at high contact with accurate control of low creepages. An eddy current

method is used for the detection of the initiation and propagation of cracks during

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RCF test. They examined the relationship between rolling-sliding contact fatigue,

contact stress, creepage, microstructure and surface events for a range of pearlitic rail

steels. Magel and Kalousek (2002) examined the influence of rail wheel profiles.

Performance of profile for a given application is measured in terms of:

• resistance to wear

• resistance to fatigue

• resistance to corrugation development

• minimisation of lateral and truck forces

• maximisation of stability

• minimisation of noise

Rail grinding is used for removing the surface defects due to RCF and maintaining

favourable rail profiles. The appropriate rail-grinding interval depends on the rail

metallurgy, track curvature, axle loads and fasteners. Magel and Kalousek (2002)

recommended an interval of 8-12 MGT (280-300 BHN standard carbon rail) and 12-

25 MGT (360-380 BHN premium rail) for sharp curves (<500 m). Rail players around

the world take grinding decisions based on Visual Qualitative Checks (VQC), Non

Destructive Testing (NDT) report, assumed Million Gross Tonnes (MGT) and Traffic

Density (TD). This is a slow, time consuming and costly process for decision making,

leading to a risky operating condition between inspections.

Kalousek and Magel (1997) introduced the concept of a magic wear based on

boundary between sufficient and insufficient wear – the optimal, or “magic”, wear

rate –a trade-off in which the development of fatigue is arrested by wear/ metal

removal. The magic wear rate is achieved when the surface material wears just

enough to prevent surface fatigue cracks from propagating. A combination of

lubrication and light, but frequent profile grinding is recommended. Every wheel/rail

system has a magic wear rate. It changes with the hardness of the materials, the

average contact stress, the wheelset-steering performance, coefficient of friction and

the effectiveness of the lubrication. Ishida et al., (2003) carried out a detailed study on

rail grinding. He recommended a scientific determination of grinding interval (how

frequently the grinding should be conducted) and grinding depth (how much surface

material should be removed) based on rail signature. This knowledge is important for

improving the efficiency of grinding work and reducing the track maintenance cost

and risk.

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Kapoor et al., (2002) studied plastic deformation at asperities (unevenness of surface)

between wheel and rail and its effect on the shakedown process. Shakedown process

is used as a basis for design of railway track and bearings. When the load increases

above the ‘elastic limit’, the contact stresses exceed the yield and the rail material

flows plastically. Upon unloading, material develops residual stresses. These stresses

reduce the tendency of plastic flow in the subsequent passes of the wheel. This,

together with any effect of strain hardening, enables the rail material to support loads

which are much higher than its elastic limit. This is called the shakedown process.

The maximum contact pressure which is carried purely elastically in the steady state

is known as ‘shakedown limit’. For frictionless rolling/sliding, this shakedown limit is

four times the shear yield stress of the rail material. With increasing friction the limit

drops, initially gently and then rapidly, at a friction coefficient of about 1/3. It is

found in the observations that substantial plastic deformation in a sub-surface layer of

thickness 15-20 µm, is generally found in cross sections of rails. Ishida et al., (1998)

confirm that the plastic flow is confined to a thin surface layer where material fails

and leads to initiation of squat cracks. Removing this layer by preventive grinding,

reduces the chances of cracks initiating and developing squats. Magel et al., (2003)

examined rail grinding, corrugations and lubrication from theoretical modelling based

on lab based experiments and field trails.

Johnson (1989) studied plastic deformation due to repeated transmission of wheel

load to the rail through a tiny contact area under high contact stresses. He found that

the depth of the plastic flow depends on the hardness of rail and sharpness of curves.

Due to sliding in the contact area, significant wear occurs for poorly lubricated

conditions of wheel-rail contact (Olofsson et al., 2000). The wear affects the form of

contacting surfaces of a rolling-sliding contact. Contact pressure, the size of the

sliding component, lubrication, microstructure and hardness are influencing factors

behind the wear rate (Garnham and Beynon, (1992), and Muster et al., (1996).

Ishida et al., (2003) studied wheel rail interface problems resulting from rolling

contact fatigue (RCF), squat defects and corrugations. The study covers grinding and

lubrication of Japanese Railways (JR). In Japan, grinding started in the 1970s with

100 km of track per year. Since 1995 more than 1000 km of track per year is subject

to grinding (Tada, 1999). It is found that the number of squats has been steadily

44

decreasing as a result of grinding. The target has been a grinding thickness of 0.08

mm/pass and a grinding interval of 40 MGT.

Grohmann and Schoech (2002) studied contact geometry for minimising the risk of

head check formation. German Railways (DBAG) experimented with target profile

for appropriate tolerances in rail grinding to limit or prevent head checks. This

research revealed that optimal grinding strategies should aim at correct profiling and

minimal metal removal.

The potential failures of a single component or multi-component system indicates that

complacency must not set in because an accident has not occurred in the past, / its

probability of occurrence is low, or its past consequences were not severe. Rail Track

was blamed for the train accident at Ladbroke Grove, Paddington, UK (1999) because

Rail Track had taken inadequate action following earlier incidents at the same site.

There was inadequate analysis of what else might happen and, equally importantly, of

potential rather than actual consequences. When resources needed to be added for

thousands of locations across a complex network, the choices become more complex.

The solution was automatic train protection (ATP). Four years earlier, when Rail

Track was government owned, the government decided not to proceed with ATP, as it

was too costly compared to safety priorities. The Ladbroke Grove accident led to 31

fatalities and many serious injuries. Safety decisions, taking into account technical,

political and economic aspects, become more complex.

Ringsberg (2001) developed a strategy for life prediction of rolling contact fatigue

and crack initiation. It comprises elastic-plastic finite element analysis, multiaxial

fatigue assessment of life to fatigue initiation, and comparison of results with lab tests

and field observations.

Field data showed that at loads of 10 tons per wheel and at 200 km/h speed, the

dynamic load increases the static load per wheel by 6 tons. This means that the rail

deteriorates at a faster rate with the combination of higher axle loads and train speeds.

After the Hatfield accident, extensive investigation was carried out all over Britain’s

rail network. The number of broken rails on the network increased sharply from 656

in 1995-96, to 949 in 1999-2000. Larsson et al., (2003) developed an integrated

approach to modelling rail track degradation for deciding optimal maintenance

45

strategies. Chattopadhyay et al., (2003) developed an integrated model for assessment

of risk in rail tracks under various operating conditions.

Besuner et al., (1978) revealed limitations of rail life prediction models using MGT

because they do not differentiate between the following cases:

1. a certain number (say m) of heavy wheel loads of magnitude P and

2. twice this number (2m) of smaller wheel loads of magnitude P/2.

For fatigue crack initiation and propagation, the heavier wheel load of Case 1 is more

damaging to the rail compared to the larger number of lighter loads of Case 2.

Johnson and Besuner (1977) proposed that the crack propagation rate da/dN is

proportional approximately to the 4th power of stress, leading to an effective usage

parameter, MGT-Effective given by

4/1

1

4)(

=− ∑

=

n

i

MGTEffectiveMGT (2.1)

where n = total number of wheels passing through the curve section.

The usage for an accurate prediction model should consider axle load, gross tonnage,

speed and curvature such that the damage level is estimated based on wear, RCF,

defects, failure rate, rail grinding and maintenance including lubrication, rectification

and replacements.

2.12 Rail Wear and Lubrication Strategies

Wear is the loss of material from the contacting surface due to rail-wheel interaction.

Rail operators currently use executive judgement and take decisions based on

experience and historical data to mitigate wear. Rail area head loss and rail wear

depend on train speed, axle load, rail-wheel material type, size and profile, track

construction, characteristics of bogie type, Million Gross Tonnes (MGT), curvature,

traffic type, lubrication, rail grinding, weather and environmental conditions. There is

no international standard available for rail-wheel lubrication and grinding, capable of

accurately predicting rail-wheel wear for monitoring and control. It is important to

study the factors behind these and develop a model for predicting rail area loss under

wear-lubrication-fatigue-grinding interaction.

Dearden (1954) found that wear on the top of running surface of rail in straight track

is predominantly a corrosion problem. Clayton and Allery (1982) found, from the

46

very different rail surface appearance and lower wear rates of modern rails, that the

situation had changed. It was described as severe metallic wear, following the

terminology of Archard and Hirst (1956). Beagley (1976) used an Amsler machine to

determine patterns of wear. He found that, at a certain contact pressure, wear changed

from mild wear to severe wear. Under severe wear conditions the wear rate was found

to be a function of contact pressure. The experimental approach of Beagley was

criticized by Bolton et al. (1982) on the basis that, even in the severe wear regime,

copious quantities of oxide were produced. This problem was overcome, in a practical

sense, by continually brushing the roller surfaces with a wire brush. The second

feature of the experimental technique to come under scrutiny was the very short time

intervals over which the wear loss was measured for a given set of operating

conditions. It was noted that this approach could lead to much of the wear data

representing break-in rather than steady state conditions. In the rail-wheel contact,

three wear regimes are defined by Nilsson (2005). They are mild, severe and

catastrophic wear. The mild and severe wear was studied by Jendel, (1999). The

changeover from mild to severe wear is found to be governed by a combination of

sliding velocity, contact pressure and temperature in the contact region. In the mild

wear it was observed that the wear process is slow, similar to oxidation. In the severe

wear it occurs much faster, similar to adhesive wear, as observed in curves under dry

conditions. Mild wear is observed at the wheel tread and rail crown. Severe wear is

observed at the wheel flange and gauge face. The catastrophic wear is one in which

the wear rate is extremely high and is unacceptable due to safety requirements (Bolton

and Clayton, 1984).

The Stockholm local network studied the lubricated and non-lubricated rails for UIC

900A and UIC 1100 grade rail steel under various seasons. The study found that the

contact situation in terms of pressure and sliding between rail and wheel, strongly

influences the wear. When the surfaces are worn, the contact situation changes due to

changed geometries. The changed geometries can lead to altered conditions regarding

sliding and pressure distribution between the surfaces. The curve radius of the track

has significant influence on wear behaviour. It is found that the wear rate increases

exponentially for decreasing curve radius. Sharper curves lead to increased track

guiding forces on the wheels, leading to increased creep and increased wear. The

study shows that new rails have higher wear rate than old rails. It was also found that

47

the wear rate is approximately four times higher for new rails compared to the rails

that already had been in the system (Nilsson, 2005). Track side lubrication reduces

rail wear significantly. Figure 2.7 shows the lubrication benefit as a factor of 9 for

small radius curves (300 m). For 600 - 800 m radius curve the lubrication benefit

varied from 2 to 4 compared to non-lubricated curves. An increase in the temperature

of the rail leads to increased rate of wear. This may be because of the high

temperatures causing the lubricant to become more liquefied, thus resulting in

inadequate lubrication at the wheel-rail contact area. It can also be due to the fact that

the oil in the grease evaporates, which results in reduced effect of the lubricant.

Figure 2.7: Influence of rail wear from lubrication (Nilsson, 2005)

The properties of steel and surface treatment can have a significant impact on the

behaviour of wear. The effect is shown in Figure 2.8 for high rails with steel grade

900A and UIC 1100, compared to non-lubricated surface in 300 m curve.

Figure 2.8: Rail area worn off with and without lubrication (Nilsson, 2005)

For the non-lubricated curve, the ratio of rail wear rate for the 900A grade rail

compared to that of 1100 grade rail, is approximately 2. This ratio for lubricated

conditions is approximately 9 (Nilsson, 2005).

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The wear is proportional to the normal load and inversely proportional to hardness of

the softer material. In the wheel/rail interaction, the coefficient of friction and the

degree of lubrication greatly influence the size of creep forces in the contact area and

therefore influence wear. Increase of train speeds has a significant impact on wear

rate. Archard’s wear model (1953) for sliding adhesive wear is as follows:

H

NK

D

Vw •= (2.2)

Where WV = Wear volume [m3]

D = Sliding distance [m]

N = Normal load [N]

H = Material hardness [Pa]

K = Wear coefficient of Archard’s equation that can be interpreted as the probability

that a wear particle is formed due to shear effect when a local contact is broken.

The energy dissipation model indicates that wear is proportional to the work done by

forces in sliding contact. Jendel (1999) expressed the wear coefficient with sliding

velocity on the horizontal axis and contact pressure on the vertical axis. Wear model,

using energy dissipation per running distance, can be expressed as wear index, as

follows:

φγγ φMFFE yyxx ++= (2.3)

Where xxF γ = Product of creep forces and creepages in x direction, yyF γ = Product of

creep forces and creepages in y direction, φ = Spin and φM = Spin moment. The

energy dissipation E is defined as the product of the creep forces and creepages, spin

moment and spin, and is proportional to the amount of wear. Relations between the

energy dissipation and material worn off are used for prediction of absolute wear.

Step-like behaviour of the wear rate is modelled by assigning different constants for

different levels of energy dissipation.

The energy approach is adopted in the rail/wheel analysis to study the relationship

between wear rate and contact conditions. This is done to comply with a wear model

from the non-linear curving (Elkins and Gostling, 1977). Bolton and Clayton (1984)

modelled wear rate as a linear function of tangential force (T) times slide/roll ratio (γ),

divided by Hertzian contact area (AH) for a narrow range of materials. McEwen and

49

Harvey (1988) applied this to a full-scale laboratory test. Tγ/AH parameter (wear

parameter) calculated from the curving model was used to predict wear performance

as a function of suspension characteristics and wheel-rail profiles. Martland and

Auzmendi (1990) modified wear parameter to fit railroad practice. It is difficult to

accurately describe wear using existing predictive models because of the stochastic

process involved in rail wear. Therefore, there is a need for an integrated approach

where a wear model, combined with updated track field measurement, is able to

predict rail wear based on rail signature. The complexity of the problem indicates that

empirical models, combined with continuously updated field test data, might be a

realistic way of predicting and controlling the wear at different parts of the track. This

would be useful to railway players in planning cost effective maintenance of rail

infrastructure.

A survey of heavy haul railways in the mid 1990s indicated rail lives varying between

about 1500 million gross tonnes (MGT) of traffic in straight track and about 300

MGT in highly curved track. This life also depends on axle load, traffic density, track

formation, bogie type and railway track maintenance practices. Rail area loss includes

the material removed by wear, grinding to maintain the rail profile to remove surface

cracks, and spalls caused by rolling contact fatigue (RCF). It is found in one set of

Association of American Railroads studies that rail material removed by grinding

exceeded that removed by natural wear. The ratio of ground/worn rail material

removed varied from 1.4 to 3.1 for high rails and from 2.1 to 9.8 for low rails, in

curves varying from 240 to 540 m in radius (Sawley and Kristan, 2003).

Fletcher and Beynon (2000) conducted twin-disc simulation tests to investigate the

influence of contact pressure variation on rail steel fatigue life using colloidal

suspension of molybdenum disulphide in an oil carrier fluid (similar to commercial

flange lubrication product) and water as lubricants. It was found that the reduction of

1500 to 900 MPa of the maximum Hertzian contact pressure (at which a

molybdenum-disulphide-lubricated and previously worn rail sample was tested)

extended the fatigue life of the rail steel by over five times. Water lubrication

produced only a marginal increase in fatigue life.

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Reiff and Gage (1999) found lubrication increases wheel and rail life; reduces energy

consumption of trains; and reduces lateral curving loads and noise emissions.

However, improper application of lubrication may have a negative impact on truck

curving, train handling, and rail fatigue.

Franklin et al., (2005) conducted twin-disc tests (using two laser-cladded coated rails

numbered 222 and 508) to determine rolling contact fatigue (RCF) performance in the

laboratory. The result showed that 222 had high fatigue resistance at the lower

pressure, but that 508 was found to be susceptible to surface crack initiation during

prolonged (15000 cycles) unlubricated testing. They found that lubrication after a

long period of dry testing had accelerated crack propagation.

2.13 Inspection Frequency and Techniques

Inspection methods commonly used are (Cope, 1993).

1. Visual inspection

2. Dye penetrant inspection and magnetic particle inspection

3. Eddy current testing

4. Radiography

5. Ultrasonic

Visual inspection is often carried out by track maintenance staff and pedestrian

operators of ultrasonic equipment.

Dye penetrant inspection works on the principle that liquid is drawn into a “clean”

crack due to a capillary action. After a certain dwell time, the excess penetrant is

removed. A developer is then applied which acts like a “blotter” and draws the

penetrant from within the cracks. This method, however, relies on a clean surface and

thorough removal of the excess penetrant so as not to yield misleading indications and

can only be used on non ferro-magnetic materials. The magnetic particle inspection

technique is used on ferro-magnetic materials. Contrast paint is applied to the rail,

followed by the magnetic particle coating. The inspection is carried out in two

directions at very slow speed. This technique uses the principle that a flaw is detected

by the distorted flux. If a surface defect (or one that is close to the surface) is present

within the magnetic field when a magnet is applied to a ferro-magnetic material, the

location of the flaw can be determined from “flux leakage”. The effectiveness of the

51

method depends on flaw depth and type of flaw. Surface irregularities and scratches

can give misleading indications and, therefore, extensive surface preparation is

required before testing.

The eddy current testing method uses electromagnetic technique. This technique uses

an energised coil in close proximity to the surface, which induces eddy currents in the

specimen. These eddy currents create a magnetic field opposite to that which caused it

and, therefore, affect the impedance of the coil. This change in impedance is

measured to detect flaws.

Rail Testing really became a regular inspection activity entity in the late 1920s when

Dr Elmer Sperry, driven by the needs of the US railroad industry, developed the

induction method for testing railroad rail (Allison, 1968). Over the years, this

technique was refined in the US and then, in the 1950s, ultrasonic testing emerged and

started to become the method for rail testing. Some exceptions to this have been

Sperry in the US, where the idea of ‘complementary testing techniques’ has been

developed, and in Russia where the magnetic induction technique is used.

Figure 2.9: Ultrasonic and induction techniques (Clark, 2004)

The report prepared by the Transportation Technology Center, Inc. (TTCI) for the

Office of the Rail Regulator in October 2000 provides much useful background on the

global rail testing industry (Sawley and Reiff, 2000). Figure 2.9 shows the technology

deployed on the US railroads. The system brings together the complementary

ultrasonic and induction testing techniques on a hi-rail platform. This provides the

railroad with high quality testing and increased flexibility of deployment. In the past,

induction was not possible on a rail bound vehicle because of the large size of the

plant needed to generate the high currents injected into the rails. With developments

in power supply technology, the production of a hi-rail based vehicle has become

feasible (Clark et al., 2000). These vehicles operate at speeds of up to 32 km/h,

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although with the ‘stop and confirm’ testing requirements in North America, there is

always an operational trade-off between going forward faster and the risk of longer

reversing moves when a confirmation is required.

In North America, the most common and problematical defects are transverse defects,

weld defects and vertical split head defects. These defects constitute around 55% of

the yearly detected defects. They also constitute 75% of the notified failures. A

notified failure is an instance where a rail has broken and the company has been

informed of the occurrence. In many cases, an investigation is performed to identify

the cause of the failure. The possible causes are many—each situation presenting a

source of further learning. On many occasions the defect is classified as undetectable

at the time of test because it has been too small or the surface condition of the rail

may have presented additional ‘noise’ that masked the defect. The cause of the broken

rail can also be a wheel flat. In these instances, a latent defect likely to be found at the

next test may become a catastrophic failure due to the impact of a wheel flat. Sawley

and Reiff (2000) found that broken rails are the result of the following major factors:

• Poor inspection procedures (This may be due to poor operator training, out-of

calibration equipment.)

• Surface conditions interfering with the ultrasonic signal (It is known that

surface damage, such as cracks, spalls, and flakes can hinder ultrasonic

inspection by affecting transmission of ultrasound signals.)

• Defects that are inherently difficult to detect using existing technologies

(Ultrasonic signals enter the head of rail and, though they travel down the web

section, they are not able to find defects in the outer edges of the foot. Cracks

towards the outer edges of the head are difficult to locate, similar to

vertical/transverse cracks found in thermite welds.)

• Inspection intervals that are longer than optimum (If the inspection interval is

too long, defects can grow from non-detectable to critical sizes between

inspections.)

There are three aspects to rail inspection: (1) technology used, (2) frequency of

inspection, and (3) actions specified when a defect is detected. Inspection is important

for reducing rail breaks. Inspection is generally based on line speed, track conditions,

traffic tonnage, axle load and traffic type. German Railways uses intervals from 4 to

24 months; Japanese Railways uses frequency from once in every year to once in 5

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years depending on the MGT per year in the route; SNFC rail uses frequency from 3

times a year to once in 5 years depending on the track classification. Most of the

large freight railways in North America now use risk management to schedule

ultrasonic inspections. A 40 million gross tonnes (MGT) per year freight line is

inspected two or three times annually, and lines over 140 million tones per year are

inspected every 30 days. Inspection intervals can be as frequent as every 7 days, as in

Australia on 37 tonnes axle load lines (Cannon et al., 2003).

In railway applications, the rails are regularly inspected by ultrasonic techniques using

inspection vehicles followed by manual walking stick for verification. Inspection

vehicles operate up to speed of 40 - 50 km per hour and have a much higher number

of ultrasonic transducers than manual systems. Manual systems are more sensitive to

defects than test vehicles but the results are influenced by the sensitivity of the

operator.

The detection vehicle shown in Figure 2.10 was tested on special test track (the Rail

Detection Test Facility – RDTF) at the Transportation Technology Centre (TTCI),

Pueblo, Colorado. It indicates a possible false alarm rate of 2.4% and a missed defect

rate of 3.6%. The vehicle was also able to detect head checks in gauge corners

previously not possible to detect with conventional systems. Small defects in welds

are also detectable with a false alarm rate of 16.7% and a missed defect rate of 6.3%.

Figure 2.10: Improved ultrasonic test vehicle system (Cannon et al., 2003)

Cannon at el., (2003) noted that, although the NDT techniques mentioned above have

been able to detect defects, there is a need to improve current techniques for

consistent and accurate detection. Some of the techniques currently being evaluated

are:

� Inspection using ultrasonic waves generated by electromagnetic acoustic

transducers (EMAT)

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� Low-frequency eddy-current sensors to locate deeply buried defects

� Neural network analysis of signals to improve defect detection and

identification

� Longitudinal guided waves (for example, to potentially allow locomotives to

scan the track head)

� Laser generation and reception of ultrasonic waves to enable non-contacting

inspection

� Improved ultrasonic probe combinations and arrangements in vehicle-based

systems

� Higher speed ultrasonic testing

� Non-destructive measurements of residual stresses and rail neutral temperature

Granström and Kumar., (2004) studied the punctuality of the transportation system

that can be improved by applying condition monitoring technology. This

methodology was identified to evaluate different condition monitoring applications in

relation to punctuality problems.

2.14 Maintenance Strategies

Maintenance is one of the major issues in a railway track system. It is very important

to detect the possible problems in advance and to find cost effective solutions to

prevent them (Simson, 1999).

The majority of Amtrak railway train accidents since 1993 have been found to be due

to train de-railing. Proper maintenance of railway tracks can prevent similar accidents.

Exceeding the life spans and limits of rail track components can result in failure to

perform the intended function, thereby affecting the rail operation. Various types of

maintenance methods currently used are (Cope, 1993):

• Rail grinding

• Lubrication of rails

• Rail transposition

• Rail straightening

• Rail replacement

• Sleeper replacement

• Ballast maintenance

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• Tamping

• Subgrade stabilization

2.15 Rail transposition

Transposition is carried out on tight curves where wear on the high rail is the main

cause of rail replacement. Rail from the high rail is changed to the low rail of the

curve. Rail transposition requires rail grinding of the rail profile to reduce problems of

tight contacts, high contact stresses and poor lubrication. Otherwise, it is likely to

have higher wear rates, high wheel squeal noise and gauge corner shelling.

2.16 Rail straightening

Welded rail joints are straightened by stretching the joint. Rail straightening is

performed on previously mechanically jointed track that has been upgraded by rail

welding. Even though the rail ends of mechanical joints are cropped before rail

welding, a certain amount of rail misalignment can occur.

2.17 Rail replacement

Rail replacement is often done in conjunction with other major maintenance activities

such as sleeper replacements (Figure 2.11). Rail and the rail fasteners are replaced to

fix problems of rail wear, fatigue defects or derailment damage causing notches or

bends.

Figure 2.11: Automated re-railing machine (Simson, 1999)

2.18 Sleeper replacement

Sleeper replacement is done either mechanically or manually. The need and

productivity of re-sleepering is greatly influenced by the density of the defective

sleepers to be replaced.

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2.19 Ballast maintenance

Ballast rehabilitation or stone blowing cleans the fines from the ballast with high-

pressure air. Ballast rehabilitation or undercutting involves automated machinery that

uses chains or mechanical arms to pull through the ballast bed for removing ballast

fines (Wenty, 1996). Ballast undercutters scoop up the ballast and pass it over the

strainer. The fines are removed and the rest of the ballast is returned to the track. At

least 30% of the ballast bed is removed by a ballast rehabilitator/undercutter. As a

result, extra ballast is added to maintain the depth of the ballast after undercutting.

2.20 Tamping

Tamping is used for correcting the rail-sleeper geometry faults. The tampers used by

British Rail (BR) typically combine the functions of correcting top, cross level and

line on the one machine and all corrections are carried out during one pass. Chirsmer

and Clark (1998) discuss the economics of continuous tamping over spot tamping,

along with lift tamping compared to conventional tamping. In conventional tamping,

the track is lifted to return it to the design track profile and alignment. In design lift

tamping, the track is lifted to a mirror image to allow for the rapid settling of the track

profile following tamping. This means the track has a much flatter profile after

stabilising than it would have with conventional tamping.

2.21 Subgrade stabilisation

Reactive soils or clay patches are major problems in track maintenance, causing a

whole range of defects. Lime slurry injection stabilises reactive soils that harden to

cement for filling soil voids. Lime slurry is injected into the sub-grade through a

nozzle lowered through the ballast. Slurry injection will only affect the upper layers of

the subgrade and sometimes several applications may be required to stabilise the

subgrade.

2.22 Operational Conditions

Operational conditions are influenced by train speed, track construction,

characteristics of bogie type, the available adhesion between the wheel and the rail

(based on environmental conditions), tonnage, axle load, curvature and traffic type.

Other factors include rail material and rail type and size, sleepers and fasteners.

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Operating conditions have significant influence on reliability and safety of rail

operation.

Weather (precipitation) creates a natural lubricating layer of water in the wheel/rail

contact. It is found that the decreased wear rate at low temperatures (below 00 C) can

occur due to the condensation on the rail surface. Lower bulk temperature can reduce

the temperature in the contact area and hence reduce the wear rate. Water, snow or

ice, alters the friction coefficient of wheel and rail. Other elements such as organic

debris from trees and fields, and non-organic debris in contact with water/moisture,

worn metallic debris from rails and silicon debris from the concrete sleepers/ballast

can also influence contact conditions. Air temperature and exposure to sun are other

factors influencing evaporation and condensation to the rail surface (Nilsson, 2002).

Track and wheel discontinuities can cause high dynamic forces depending on the

speed and geometry. Rail stresses depend on the amount of wear and the track

structure (including sleeper, ballast and subgrade condition).

2.23 Summary

In this chapter, an overview of rail track structure, defects and maintenance strategies

is presented. It explores the principle structure of rail track, and the functions of its

components, to establish a comprehensive background understanding of the whole

track system. Rolling contact fatigue, rail wear, rail grinding, rail-wheel lubrication,

inspection techniques, and maintenance strategies are also discussed. The major issues

arising from these influencing factors and models will be addressed in Chapter 3. The

major focus of this research will be maintenance of rails. Cost and risk models will be

developed in this thesis for managerial decisions. Development of economic models

on rolling contact fatigue and rail grinding, lubrication and inspection, for optimal

maintenance decisions will be presented the Chapters 4, 5 and 6.

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CHAPTER 3

STUDY OF RAIL WEAR, ROLLING CONTACT FATIGUE AND RAIL

MAINTENANCE MODELS

3.1. Introduction

An overview of rail track structure, defects and maintenance strategies are discussed

in Chapter 2. Grounded theories on rail wear, rolling contact fatigue (RCF) and rail

maintenance models will be discussed in this chapter. The gaps in the existing models

are analysed. Risk based economic models for grinding, lubrication and inspection are

proposed and the need for an integrated model is assessed.

The outline of this chapter is as follows: a review of existing rail wear and rolling

contact fatigue models is carried out in Section 3.2; Section 3.3 presents existing rail

maintenance models; a survey of lubrication practice in Australia and around the

world is discussed in Section 3.4; finally, a summary of this chapter is presented in

Section 3.5.

3.2 Rail Wear and Rolling Contact Fatigue Models

Elkins and Gostling (1977) studied a general quasi-static curving theory for railway

vehicles. They developed a non-linear and vehicle curving model which can be used

to analyse wear behaviour and estimate wear rate. An energy approach is developed to

analyse the relationship between wear rate and contact conditions. That is, wear rate

(expressed as weight loss per meter per rolling per unit of Hertzian contact area) is a

linear function of (tangential force T × slide/roll ratio γ’)/hertzian contact area AH,

considering different relationships for each case. Subsequent work by McEwen and

Harvey (1985) showed that this approach was equally applicable to full-scale

laboratory tests and field. Lyon and Weeks (1983) used this approach to estimate

anticipated improvements in wear by changing the suspension design of confined

rolling stock. Danks and Clayton (1987) studied the wear process for eutectoid rail

steels, using field and laboratory tests. The results are compared with those from a

similar study of the wear surfaces of rail steel specimens, tested in both a pin-on-disk

and a twin-disk rolling contact wear testing device. It is found that, provided the test

conditions are chosen carefully, an adequate simulation can be produced.

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Devanathan and Clayton (1991) conducted rolling-sliding wear tests on three bainitic

steels with 0.04, 0.10 and 0.52 wt% C. The contact conditions employed simulate the

most severe wear situation encountered by wheels and rails in curved track. The

results confirm the potential of bainitic steels for wear resistance, particularly at high

contact pressures. The wear behavior of the bainitic steels has been examined in

relation to microstructure and the surface damage experienced by the worn rollers.

Tyfour and Beynon (1994) studied the effect of different single and multiple rolling

direction reversal (RDR) regimes on wear rate and mechanism. Changes in structure

deformation morphology and accumulated plastic strain are analysed. Results

obtained under the test conditions used show that RDR has a beneficial effect on the

wear rate of pearlitic rail steel. Multiple short RDR resulted in the lowest wear rate,

less than half the unidirectional value.

Clayton (1995) analysed the existing academic models (described as general wear

models) developed by Archard (1953), Quinn (1967), Sub (1973) and Zum Gahr

(1987). The approaches used for these models to predict wear over a wide range of

operating conditions for any material, have small practical significance. Rail

infrastructure owners raised questions about the applicability of the Martland and

Auzmendi (1990) model to heavy haul rail road applications. Bolton and Clayton

(1984) investigated wear behaviour of several rail steels in rolling-sliding contact with

a wheel steel in the laboratory, using an Amsler wear testing machine. Three wear

regimes were identified and metallurgical examinations to determine the characteristic

wear modes within these regimes are described. These were defined as Type I, II and

III, and occur in ascending order of contact pressure and slide/roll ratio. Type I

involves a combination of two modes of wear, resulting in debris containing oxide

and metal particles leading to oxidative wear. Type II involves complete metallic

wear debris, the occurrence of ripples on the roller surface and some metal transfer.

Type III involves an initial break-in period that leads to the production of large pieces

of wear debris. Laboratory work by Danks and Clayton (1987) suggests that Type III

wear simulates unlubricated gauge face wear. Although Type I relations are used to

model wear on the top of the rail, there has been no research to justify this. Finally,

Clayton et al., (1988), Devanathan and Clayton (1991), suggested that specific

relation between wear rate and contact parameters is a function of material properties;

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this model is based on work with relatively soft rail steel. Martland and Auzmendi

(1990) selected the work of Bolton and Clayton (1984) to develop a simplified model

for rail wear for use in track maintenance planning. The wear parameters were

modified to make them fit better with those normally used in rail road operations.

They retained the relations between wear rate and contact parameters derived from the

small scale tests (Clayton, 1995). Clayton (1995) conducted a study on rail and wheel

wear over many years and had concluded that general wear models are unlikely to

yield any real practical benefits. The number of operating variables is overwhelmingly

large and the basic understanding of wear phenomena still limited. The use of models

with very restricted application can prove more useful. The relationships derived from

laboratory tests have been successfully applied to developing new materials and

assessing the benefits of vehicle suspension changes. Such an approach is particularly

applicable to the railroad situation because the cost of access, downtime and materials

for replacement are relatively low. While the general model approach (favoured by

academics) has had little practical impact, it serves to keep in focus the limitations of

existing knowledge and understanding.

Tyfour et al., (1995) conducted a study on the steady state wear behaviour of pearlitic

rail steel. The results show that steady state wear rate prevails after a certain number

of rolling-sliding cycles. It was found that the start of the steady state wear rate

coincides with the termination of plastic strain accumulation and additional strain

hardening.

Alp et al., (1996) developed a standardised method to measure the railroad gauge side

lubricant performance. This method correlates the amount of energy saved to

lubricant breakdown and stabilisation points, and lubricant breakdown duration to

lubricant performance. A vertical pin-on-disk system was modified and used as a

bench-top friction and wear test machine, available at Argonne National Laboratory.

A series of experiments were conducted to evaluate the effectiveness of each

lubricant, in terms of friction, wear and amount of energy saved. It is observed that

lubricants which provided a considerable amount of reduction friction energy

dissipation, resulted in a greater savings in energy. This can be considered as a

measure of effectiveness of lubricant. Hiensch and Smulders (1999) studied rolling

contact fatigue propagation after initiation. The study shows that head checks are a

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potential hazard and can cause rail failure. A critical limit value at which vertical

propagation suddenly occurs was identified. Lubrication of rails appears to encourage

vertical propagation.

Magel and Kalousek (2002) developed a pummelling model at The NRC Center for

Surface Technology to quantify the performance of rail profiles when loaded with a

large number of measured new and worn wheels. Contact mechanics principles are

further discussed on several aspects of rail grinding, including surface roughness, rail

gauge width and rail grinding interval. The IRSID group developed an analytical

model to examine the life of rails experiencing rolling contact fatigue. Corus (2004)

has further developed this model in combination with other analytical techniques to

form the Corus Track System Suite of Model (TSM). This model consist of

� a vehicle dynamics model using Adams Rail Software

� a global track model using Abaqus FE software

� a detailed wheel-rail contact model using Abaqus FE software

� analytical fatigue and fracture models, and

� a detailed component model, including the pad and fastening system

The model produces a “time to crack” initiation which enables the high speed grinder,

or other preventive maintenance procedures, to run over the line to prevent the

development of cracks. This process of fatigue management allows the track engineer

to carry out predictive maintenance well in advance (Jaiswal, 2004).

Figure 3.1: Synergy of rail metallurgy & track engineering (Jaiswal, 2005)

Jaiswal (2005) mentions that appropriate and timely maintenance is an integral part of

the system approach that needs to be adopted by railways if they are to meet the

demanding challenges they face. The synergy of optimum rail metallurgy, good track

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engineering and non-destructive high-speed grinding is explained in Figure 3.1. On

17th October 2000 an inter-city train was derailed at 188 km/h by a broken rail near

Hatfield on Britain’s East Cost main line. The cause was gauge corner cracking

(GCC) or head checking, which are forms of rolling contact fatigue (RCF), and the

rail broke into many small pieces. This is not only confined to Britain; it caused a

collision in Switzerland in 1998 and SNCF views surface defects resulting from RCF

as a serious concern. Substantial problems have also been reported from Germany and

Queensland. Kapoor et al., (2002) indicate that interaction between wear and rolling

contact fatigue is the key issue in managing the wheel/rail interface for optimum rail

life. Four main phases in crack life using curve of (da/dn) against crack length are

discussed and shown in Figure 3.2. They are:

� Crack initiated and driven by ratchetting in the plastically deformed layer

(Curve R)

� Contact stress greatly influencing on the crack as it becomes longer and deeper

(the propagation rate increases because the stress intensity rises with

increasing crack length [Curve Ss]

� Decrease in the crack propagation rate as it becomes longer still and a critical

crack length has been reached. (At this point, the crack tip moves away from

the region with high contact stress and the stress intensity drops. In the

descending part of the curve SL, (da/dn) changes are determined by the shape

of the ∆K curve for long cracks and the crack growth.)

Figure 3.2 Phases of crack life using curve of da/dn and length (Kapoor, 2002)

� The effect of the contact stresses diminishing at certain crack depth, and the

crack driven by the bending, residual and continuously-welded rail stresses in

the rail (Curve B).

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Kapoor et al., (2002) modelled wear using several different approaches. They used

experimentally determined Archard wear and coefficient to link the wear process with

all phases of crack propagation.

Figure 3.3 Truncation of a shallow angled crack (Kapoor et al., 2002)

Figure 3.3 illustrates the effect of wear on crack propagation. As the running surface

wears, the crack mouth is truncated. The effect is most rapid for shallow crack angles.

From the results of this model it is possible to identify strategies for maintaining the

rail/wheel interface to a better standard, and for optimising rail life and safety. Kapoor

et al., (2002) developed a whole life model in a collaborative project with AEAT Rail.

Statistical variations in traffic, axle loads, and vehicle and traffic dynamic

characteristics, determine crack initiation, propagation and wear. To correct crack

growth at the marginal and high risk sites, rail track has reintroduced preventive

grinding and has ordered new rail grinding trains to cope with the workloads, but the

rail life remains a balance between wear and fatigue. Figure 3.4 shows rail life line

due to wear and fatigue.

Figure 3.4 Life line due to wear and fatigue (Kapoor et al., 2002)

If total rail head wear is limited to T, and the rate of removal is ∆T per million gross

tonnes, both by grinding and traffic wear, then the life is T/∆T. At higher wear rates,

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rail must be replaced frequently. For fatigue crack growth, increasing the material

removal rate increases rail life because cracks are truncated before they can move

deep into the rail head. Maximum rail life occurs where two life curves intersect. A

successful strategy (employed by North American and Australian railways) is to use

grinding in conjunction with low wear rate rail steel, to achieve an appropriate

material removal rate to ensure the operation in the region of controlled by wear

Kapoor et al., (2002).

Ekberg et al., (2002) developed an engineering model for prediction of rolling contact

fatigue of railway wheels. Three well-known types of fatigue in wheels considered for

this model are: surface-initiated fatigue, subsurface-initiated fatigue and fatigue

initiated at deep material defects. The model can be integrated in a multibody

dynamics code without significantly increasing computational demands.

Jendel (2002) developed a wheel profile wear prediction tool and applied it to a

vehicle operating the commuter rail network in Stockholm. The methodology is based

on a load collective concept where time-domain simulations are performed, based on

actual track data, measured rail profiles, and pertinent operating conditions. The

vehicle model is built in the GENSYS MBS software utilising validated suspension

models. The contact between wheel and rail is modelled with Hertzian theory and

Kalker’s simplified theory (FASTSIM). The wear modelling is based on Archard’s

wear model and the implementation, including laboratory measurements, is performed

in cooperation with tribology experts at KTH Machine Elements. Comparisons

between simulated and measured wheel profiles, including four scalar wear measures

(flange thickness, flange height, flange inclination and area worn off), are explained.

Yoshida et al., (2002) discussed the influence of elastic modulus of a plated layer on

the contact pressure and the subsurface stresses. It is found that the failure mode of all

metal to metal contact surfaces (spalling/flaking) was caused by subsurface cracking.

The rolling contact fatigue strength of soft surface modified metals is higher than that

of non-coated ones. This is due to smaller contact pressure and smaller subsurface

stresses by the small elasticity, as well as the conformity of the surface modified

elements.

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Magel et al., (2003) discussed modern rail grinding practices, but these discussions

were largely based on a combination of field experience and intuitive speculation.

Many theories related to crack initiation and growth have been proposed through the

decades, and those concepts have been cleverly extended to the field of rail grinding

to form the basis of the practice known as 'preventive grinding'. However, only

recently have practical models emerged from the laboratory and theoretical

environment and been applied to the process of rail grinding. These models are

substantiating the past practices and providing a pathway towards the development of

improved predictive tools for rail fatigue and profile deterioration. While there have

been many advances in rail grinding over the last four decades, there is still much

work to do. The practical importance of surface roughness is still not well understood.

Franklin et al., (2003) developed a computer model which simulates the ratchetting

wear of a ductile material subject to repeated loading. Variation of material properties

is a feature of the model, failure by ductility exhaustion occurring at isolated points or

extending regions of failure. Such regions form crack-like features. Mechanisms for

removal of weakened material from the surface as wear debris, are described. The

wear process causes a degree of surface roughness. The simplicity of the model

enables simulation of millions of load cycles in only a few hours' computer time. The

computer model is used to study the effect of partial slip on wear rate. When creepage

is relatively low, the wear rate increases sharply with creepage. When creepage is

relatively high, the wear rate is largely insensitive to the creepage.

Cannon et al., (2003) studied an overview of rail defects. This review covers many

topics relating to railway rail failures. The emergence of surface-initiated rail RCF as

a major cause of premature rail removal is of great concern as it indicates that

operating conditions are taking the rail to and beyond its natural endurance limit. This

review indicates that current research and modelling activity are very much focussed

on this issue, but the problem is complex and much still must be done. It is likely that

a major step in rail/wheel technology will be required to solve the RCF problem.

Figure 3.5 shows some forms of RCF defects.

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Figure 3.5: Head check (HC) and transverse rail fracture (Railtrack plc., 2001)

Despite major improvements in rail making and inspection, rail breaks still occur: for

example, in the UK the annual number of broken rails remained almost constant at

about 770 per year between 1969 and 2000. The costs of reducing rail failures have to

be balanced against reduced costs from death and injury, penalty payments, train

disruption, increased customer satisfaction, and better planning of track maintenance

and renewal.

Ringsberg and Bergkvist (2003) developed a finite element model to predict short

crack growth conditions for rolling contact fatigue (RCF) loading. This model is used

for linear-elastic and elastic–plastic FE calculations of short crack propagation,

together with fracture mechanics theory. The crack length and orientation, crack face

friction, and coefficient of surface friction near the contact load are varied.

Comparison of results from linear-elastic and elastic–plastic FE calculations, shows

that the former cannot describe short RCF crack behaviour properly, in particular,

0.1–0.2 mm long (head check) cracks with a shallow angle; elastic–plastic analysis is

required instead.

Fletcher et al., (2003) conducted image analysis to reveal crack development, using a

computer simulation of wear and rolling contact fatigue. The simulation allows

simultaneous investigation of wear, crack initiation and propagation. The model

reveals the interaction of wear with crack development, processes which are linked

because wear truncates surface-breaking cracks, and can completely remove small

surface-breaking cracks.

Andersson (2003) developed modelling and simulation of train-track interaction,

including wear prediction. The proposed train-track interaction model, together with a

wear model, constitutes a frame within which the effects of the compound

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longitudinal, lateral and vertical dynamics on rail corrugation growth can be

investigated.

Olofsson and Telliskivi (2003) conducted full-scale tests and laboratory study for

wear, plastic deformation and friction of two rail steels. This investigation was to

study the development of these damage mechanisms on new and 3-year-old rails in a

commuter track over a period of 2 years. The experimental results from the

measurements show that there was a significant change in rail profile due to wear, as

well as to plastic deformation. Plastic deformation and wear was a continuing process,

even for rail that had been in service for 5 years. The plastic deformation mechanism

was plastic ratchetting. Material tests were performed on two different testing

machines: a two-roller and a pin-on-disk machine. On the basis of results from the

material testing, a simple wear map was constructed. In the wear map, the wear

coefficient is presented as a function of sliding velocity and contact pressure. The

results from laboratory tests showed that wear coefficient depended strongly on

sliding velocity. The increase in the wear coefficient when increasing sliding velocity,

was due to a change of wear mechanism from mild wear to severe wear.

Telliskivi and Olofsson (2004) developed a wheel–rail wear simulation. The normal

load was validated for two cases by comparison with results obtained from FEM

analysis. The result show that the wear expressed, as mass loss per distance slid, can

be up to 2.5 times higher when using an elastic–plastic material model compared with

a linear-elastic material model. Also, the form change for a typical two-point contact

in a low radius curve was analysed and discussed.

Chattopadhyay et al., (2005) studied decisions on economical rail grinding intervals

for controlling rolling contact fatigue. The complexity of deciding the optimal rail

grinding intervals for improving the reliability and safety of rails is due to insufficient

understanding of the various factors involved in the crack initiation and propagation

process. They identified the factors influencing rail degradation, analysing the costs of

various grinding intervals for economic decision making. They developed a total cost

model for rail maintenance considering rail grinding, downtime, inspection, rail

failures and derailment, and replacement of worn-out rails.

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Nolsson (2005) studied wear in sliding and rolling contacts such as the wheel-rail

contact for rail roads and the roller-washer contact for roller bearings. Wear and

surface cracks on rails have been observed for a period of three years. They compared

the wear depth with the crack length and equilibrium between these two damage

mechanisms was found for lubricated rail. They found that, by using lubricant with

friction modifiers, the stresses were low enough to prevent crack propagation; also,

rail was hard enough to reduce wear rate.

Lee and Polycarpou (2005) studied wear of conventional pearlitic and improved

bainitic rail steels that were tested in an actual wheel/rail track. Micro-Vickers and

Rockwell C hardness measurements at different length scales were conducted to

investigate the cause of their wear behavior. It was found that the initially softer

pearlitic rail steel was work hardened more than the initially harder bainitic rail steel

as in-service stresses accumulated on the rails, and thus the better wear performance.

Pure sliding laboratory experiments were performed, using both pearlitic and bainitic

samples. These simpler laboratory experiments confirmed that, indeed, pearlitic steel

work hardens more with tribological contact testing and exhibits less wear compared

to J6 bainitic steel, and supported the rail track findings. It is, therefore, important to

consider the in-service work microhardening behavior of rail steels as the initial

hardness cannot reliably predict rail wear and rail life.

Viáfara et al., (2005) conducted sliding wear tests, in a pin-on-disk device to study the

behavior of AISI 1070 pearlitic and AISI 15B30 bainitic pins sliding against AISI

1085 pearlitic disks. The sliding speed was 1 ms−1 for all the tests, and normal loads

of 10, 30 and 50 N were used. The wear resistance was related to the mass loss

measured after the tests and the worn surfaces - as well as particle debris - were

analyzed by optical and scanning electron microscopy. Micro-hardness profiles were

also obtained to analyze strain hardening effects beneath the contact surfaces. The

pearlitic steel showed higher sliding wear resistance than bainitic steel, due to the

excellent strain hardening of pearlite compared to bainite. Oxidative wear regimes

were observed in the pearlitic steel, while in the bainitic one, adhesive wear was the

main removal mechanism, leading to a much more accentuated damage of the surface.

In fact, the wear regime for bainitic samples was always severe, even for the lower

loads applied.

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Franklin et al., (2005) conducted twin disc tests using specimens claded with the same

coatings to determine rolling contact performance in the laboratory. The effects of

lubrication, applied load and coating thickness were studied. An eddy current probe

was used for crack detection. Both materials survived 200,000 cycles of water-

lubricated twin-disc testing without crack formation, in contrast to UIC (260 grade)

900A base material which showed severe cracking after only 4000 cycles.

Metallurgical investigations show excellent RCF resistance, although one coating

developed cracks quickly during water-lubricated testing (after 15,000 dry cycles) and

bonding of the tested coatings (delamination occurred at the bonding interface of one

coating during high-pressure tests). Donzella et al., (2005) developed a model to study

the competitive role of wear and surface origin RCF, predicting their occurrence in

rolling contact as a function of material properties and working conditions. The

presence of the quiescent zone and the exceeding of the elastic shakedown limit were

evaluated in order to predict crack initiation. In rolling/sliding tests, wear is important,

producing large thin metallic flakes and removing surface micro-cracks. From the

preliminary results on wear behaviour under very low creepage conditions, wear rate

seems to be almost constant up to a high number of cycles and dependent on contact

pressure. Figure 3.6 shows the number of factors influencing rail-wheel degradation.

Figure 3.6: Factors influencing rail/wheel degradation

Lewis and Dwyer-Joyce, (2006) studied wear rates and mechanisms of rail and wheel

wear as a result of sand application. This research found that sand causes severe

surface damage. A semi-empirical model has been developed to predict wear of rail

steel caused by sand.

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Jiang and Dwight (2006) conducted a study to investigate the possibility of using

wheel-rail noise as a real-time indicator of wheel-rail lubrication condition. It has

been found that both wheel flanging noise level and the flanging distance increase as

the interface lubrication deteriorates.

Kumar et al., (2006) studied issues and challenges with logistics of rail maintenance

to reduce costs and risk related to rail operations. It is found that rail operation is

influenced by effective logistics decisions related to rail inspection, grinding,

lubrications, rectifications and rail replacements.

The study demonstrated an extensive literature of existing models of wear and rolling

contact fatigue defects. Gaps were identified and it was found that existing models

related to wear and fatigue are not satisfactory for rail infrastructure owners. This is

mainly due to limited knowledge of the consequences of various influencing factors

between rail-wheel interactions under different operating conditions. There is more

work needed to better understand and to increase safety and reliability of rail

operation and reduce maintenance costs. Concerns are growing for rail owners due to

increasing demand for axle loads, traffic, freight and heavy haul services. Therefore, it

is important to develop an integrated economic model for maintenance decisions

considering rail wear, lubrication, rolling contact fatigue, rail grinding, and inspection

and replacement strategies.

3.3 Rail Maintenance Models

A considerable number of different maintenance planning systems have been

developed by American and European railways. Different approaches and methods

have been used on these systems. But these systems face challenges due to increase of

axle loads, high speed and growing traffic densities. To overcome these problems, rail

players have changed the intervals of inspection and maintenance.

3.4 NSW State Railway Authority’s Wheel-Rail Management Model

A wheel/rail management computer model has been developed for the State Rail

Authority of New South Wales, Hunter Valley Coal Operations. The model can be

used to determine cost effective procedures for wheel machining, rail grinding and

lubrication (Soeleiman et al., 1991). This model focuses on wear related rail failure.

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This allows large amounts of condition data pertaining to alignment. Non-rail

components are ignored and a more detailed examination of wear data is carried out.

3.5 Railways of Australia (ROA) Rail Selection Module

A technical and economic Rail Selection Module covering 31, 41, 47, 50, 53, 60

kg/m, and 60 lbs /yd rail sections has been developed for the Railway of Australia

(ROA), (Twiddle et al., 1991). The model utilises system specific operating

conditions such as axle load, gauge, track stiffness, annual tonnage, curve radius,

wheel/rail contact position, vehicle speed and superelevation. The model provides an

output which indicates allowable head wear limits, rail life, rail costs, corrugation and

defect warnings for various rail sections. It aids the design of new railway track and

the selection of rails for replacement of worn and damaged rails.

3.6 Railways of Australia (ROA) Rail Grinding Model

Rail profile grinding can result in improved curving performance (wheel/rail

interaction) and reduced propagation of surface cracks due to RCF. It is necessary to

quantify the major cost factors influenced by the engineering phenomena associated

with wheel rail interaction. The rail-grinding model can be used to determine an

optimal grinding cycle, together with the cost sensitivity to variations (Soeleiman and

Rucinski, 1991).

3.7 Railways of Australia (ROA) Wheel/Rail Management Model

This is a wheel and rail deterioration computer model (WRDM) for the railways of

Australia (ROA), using a quasi-expert systems approach. It is a simple model that

uses general track link data to determine what maintenance practices should be

applied and what upgrading of track structure can minimise on going track

maintenance costs (Soeleiman and Mutton, 1993).

3.8 ECOTRACK

European Railway Research Institute (ERRI) has developed ECOTRACK.

ECOTRACK plans track maintenance based on forecasts of track conditions for the

next five years. It enables track maintenance to be optimised in terms of cost, time

scale and maintenance crew resources, or consumable resources. The most important

use is a decision support tool. Savings of up to 5% ~ 10% on track maintenance are

expected following evaluation trials (Leeuwen, 1997; Korpanec, 1998).

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ECOTRACK assesses homogeneous track sections as small as 200 meters at a time. It

considers rail replacement, tamping, rail grinding and ballast rehabilitation, and

sleeper and fastener renewal maintenance activities. The system relies on user input to

select the best maintenance activity and an expert system to select the timing of

maintenance scheduling. ECOTRACK is designed as a modular system with an

interface to use the existing database of the individual railway. ECOTRACK is

dependent on the accuracy and extent of an existing track condition database. The

database required to achieve the full potential of ECOTRACK is well beyond that

which is available within the majority of railway systems (Leeuwen, 1997; Korpanec,

1998).

The ECOTRACK system has already been implemented by European railway for

(SNCB) 5000-km of track. The prototype of the system was tested on 10 European

railways since 1995. The system is highly complicated and requires expert staff to

run. ECOTRACK is the leading technology in the field of railway maintenance

planning. It is flexible and can be modified to suit any railway operation, having an

existing, detailed, historical track condition database (Leeuwen, 1997; Korpanec,

1998).

3.9 TOSMA

TOSMA is the new track maintenance system of Central Japanese Railways (JR).

This is a highly specialised system that has been developed for a high speed rail

operation, specifically, the Tokyo to Osaka route, with 11 passenger trains an hour

operating at speeds of up to 270 km/hr (Ohtake and Sato, 1998). Such operating

conditions clearly require more care than typical freight operations.

The key to the TOSMA is the data collection from JR Central’s high speed track

recording car that records track geometry every 10 days on the entire high speed

system. Geometry data is for a 10 m versine and is recorded at every track meter. Any

irregularities showing rapid growth are identified immediately. The work priorities

and volumes in track sections are calculated and interpolated into the feature for the

whole line. TOSMA allows the planner to identify problem locations that may require

sub-grade or formation work. It identifies any rapid deterioration problems before

they become a hazard to traffic. It also allows the track engineer to program work

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volumes into the feature for tamping and ballast renewal operations (Ohtake and Sato,

1998).

3.10 Mini-MARPAS

Mini-MARPAS is a Maintenance and Renewal Planning Aid System which was

developed by BR Research (Grimes and Kay, 2002). There are seven basic track

damage sub-models (Booz-Allen & Hamilton, 1999):

� Rail Maintenance

� Rail Life

� Sleeper Life

� Track Geometry Maintenance

� Ballast Life

� Switch & Crossing Model

� Track Inspection Model

Mini-MARPAS has also been further developed to a Track Usage Cost Model which

is used by Railtrack to establish track usage charge. However, there are a number of

limitations in both the Mini-MARPAS and the Track Usage Cost Model (Booz-Allen

& Hamilton, 1999; Railtrack, 2001; Thanh, 2003).

3.11 AMP98 Cost Model

Asset Management Plan 98 (AMP 98) is a cost model developed to estimate the cost

of rail track maintenance and renewal for a 10 year planning cycle with different

scenarios of traffic (passenger and freight) growth (Sultan, 1999; Atkins, 1999;

Thanh, 2003).

3.12 Track Maintenance Cost Models (TMCOST)

Hargrove (1985) developed an aggregate model to estimate maintenance costs for

given standards of track components (Andersson, 2002). The model uses separate

deterioration models for rail wear as a function of traffic load, rail fatigue as a

function of repeated loading cycles, and ballast and sleepers as a function of loading

(Thanh, 2003).

3.13 Swedish Track Degradation Cost Model

Swedish Railway developed an economic model for track degradation to estimate

maintenance costs due to increasing axle loads from 25 to 30 tonnes (on heavy haul

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lines) and from 22.5 to 25 tonnes (on normal lines). This model considers track

length, quality, friction and superelevation; axle loads; coefficients for wear and

fatigue; speed profile as function of curvature and height to centre of gravity; and

traffic (annual MGT per vehicle set) (Paulsson, 1998; Andersson, 2002; Thanh,

2003).

Patra and Kumar (2006) studied methods to determine life period of the track, proper

scheduling of preventive maintenance/overhauling, man power allocation for

maintenance and spare parts quantity determination for all the major parts of the

railway track system.

3.14 An Austrian Track Maintenance Cost Model

To achieve an economic track strategy in Austria, a model was developed for

evaluating track maintenance (Veit, 1997). This model considers track type

(continuous welded or bolted track), type of rails, sleeper fastening and ballast,

subgrade condition and traffic density. It also covers investment and operation costs

of machinery and equipment and materials used for maintenance of track. The model

is based on life cycle costing and calculates the cash flow (NPV, IRR) and the annuity

(Thanh, 2003).

3.15 The UNIFE Life Cycle Costing

The Union of the European Railway Industries Life Cycle Cost (LCC) Working

Group (UNIFE LCC) has developed software for collection and exchange of LCC

data. The main focus of this model is on rolling stock and train operation and

maintenance. Economic analysis of the whole system is not covered in this model

(Thanh, 2003).

3.16 Track Degradation Model

Zhang (2000) has developed the integrated track degradation model (ITDM) to

predict future track condition. This model contains four interrelated sub models for

rails, sleepers, ballast and subgrade, and track modulus. The rail sub model is for rail

wear analysis and the sleeper sub model is for timber sleeper damage prediction.

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3.17 Track Maintenance Planning Model (TMPM)

Simson et al., (1999) hava developed the Track Maintenance Planning Model

(TMPM) to simulate the costs of maintaining rail track. This model is capable of

calculating the costs of track maintenance and train operations when traffic or track

conditions are changed. The model links track condition obtained from the ITDM

(Zhang, 2000) track degradation model, to train delays and other operating costs. The

TMPM model did not include rail grinding, ballast undercutting and ballast blowing

maintenance activities.

The above literature shows that, even though there are a number of existing rail

maintenance models, most of them are generic and not specific. None of these models

has considered the integration of rail grinding, lubrication, inspection, rectification

and rail replacement maintenance activities. This research developed an integrated

approach for the assessment of operational risks in rail track. Models for rail grinding,

lubrication, inspection, rectification and replacement of rails are developed in this

research thesis to evaluate risks and costs.

3.18 Survey of Lubrication Practice

Lubrication at the wheel flange and rail gauge face on sharp curves has been accepted

as an effective solution to reduce rail and wheel wear and noise. Three methods of

lubrication are used: Track-side (way-side), Onboard and Hi-rail (shown in Figure

3.7).

Figure 3.7: Lubrication systems (Chattopadhyay et al., 2004)

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In the wayside lubrication system, grease is applied to track when the lubricator is

activated either mechanically or electronically by passing wheels. For the on board

lubrication system, the lubricator is mounted on the locomotive and the lubricant is

applied using a spray system to the locomotive wheel flanges. Hi-rail lubrication

systems use a specially designed mobile truck for grease application from the nozzle,

as a thin bead along the rail gauge face. By using one or a combination of the above

systems, railroads can achieve significant savings in fuel and cost of wheel/track

maintenance. However, there are some harmful effects of using excessive lubricant.

These are wastage, loss of locomotive traction due to presence of lubricant on the top

of rail, and environmental concerns of underground water contamination (Pandey et.

al., 2000).

Railway flange lubrication is used to reduce wear of the rail and wheel which is

particularly severe at curves. However, fluid lubricants may contribute to the

development of rolling contact fatigue (RCF) cracks by mechanisms; for example,

crack face friction modification and fluid entrapment. The possibility therefore exists

that, while application of a fluid lubricant may reduce rail and wheel wear, the

lubricant may contribute to rail RCF failures. Dry, solid lubricants have some

advantage in avoiding this problem (Fletcher and Beynon, 2000). The American

Association of Railroads (AAR) estimated that the wear and friction occurring at the

wheel/rail interface of trains due to ineffective lubrication, costs American Railways

in excess of US $ 2 billion each year. Currently, the largest expenditure faced by the

railroad industry is rail maintenance and replacement. Application of lubricants at the

wheel rail interface dramatically reduces the rail track degradation and fuel

consumption (Sid and Wolf, 2002). Rail life has been increased by a factor of two and

wheel life by a factor of five (Queensland Rail, Australia), using appropriate

lubrication. Spoornet (South Africa) has reported that rail life was increased from 27

MGT to up to 350 MGT, depending on curve radius. Canadian Pacific (CP) rail

indicated that rail life improved by 110%, using effective lubrication. Experiments on

the Olympic Park loop, NSW (Australia) on a 200 m radius curve, indicated that

flange wear rate is reduced from 0.36 mm/day (life of 0.2 year) to 0.006 mm/day (life

3.5 years). HKMTRC (Hong Kong) reported a cost saving of £ 783,000 per year on

wheel and rail maintenance on the solid lubricant lines. Eurostar conservatively

estimates that effective lubrication saves £ 1,000,000 per year on maintenance and

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wheel replacement costs (Larke, 2002). ERL/Malaysia has recorded data on

lubrication shown in Table 3.1.

Table 3.1: Cost of Lubrication strategies (Larke, 2002)

Track/Vehicle

condition

Wheel life in km Wheel life in weeks

Typical lubricant costs in the UK are between £ 2.50/kg to £ 6/kg. In the field

measurement, Norfolk Southern, the electric lubricators achieved 107% improvement

in lubricant dispersion along the track, a 67% reduction in lubricant usage and a 57%

reduction in wastage (Larke, 2002). Typical grease usage data, lubricant costs and

maintenance costs are shown in Table 3.2.

Table 3.2: Lubrication costs to rail players (Larke, 2002)

Railway Quantity

(tonnes/yr)

Lubricator

(AUD$/yr)

Three types of lubrication strategies are considered in this research:

• No lubrication: Cost of lubricant is zero. Rail wear increases for sharp curves and

the replacement of rails occurs more frequently. Wheel wear is rapid and causes

damage to rail and wheels and increases wheel replacement costs.

• Continuous lubrication: Lubrication is applied over rail and wheel throughout

the year (especially in dry areas where temperature is between 20 to 40 degrees

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This table is not available online. Please consult the hardcopy thesis available from the QUT Library

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0C) and lubrication cost per MGT is reasonably high. However, research shows

that continuous lubrication extends rail and wheel life; improves vehicle/track

interaction and reduces wear in rail and wheel; reduces fuel costs and also

prevents derailments to some extent.

• Stop/Start lubrication: This lubrication strategy is applied in cold countries

where temperature is below 4 degrees 0C. In the cold countries like Europe, North

America and Scandinavia, lubrication is stopped in the winter and starts operating

again in spring and dry seasons. In this strategy, lubrication cost is less compared

to continuous lubrication. However, there is the cost of switching stop/start

mechanisms and increased wear during winter compared to lubrication periods.

For “no lubrication”, the cost of lubrication is nil. However, field experiments in

Scandinavia show that the wear rate at non-lubricated sharp curves for 300 to 400 m

radius is ten times higher than for lubricated curves. For curve radius 600 m and

above, the wear rate is about two to five times higher than lubricated curves (Jendel,

2002). In start/stop lubrication, lubrication is activated periodically according to need.

Field experiments show that the wear rate during the autumn, winter and spring is

higher than the wear rate during the fall. This has aesthetic (and possibly economic)

appeal but it is not a common option by rail players in the world (Nilsson, 2002). In

continuous lubrication, lubricant between wheel and rail reduces (i) squeal, (ii) wheel

flange vertical wear and (iii) rail gauge face wear. It is also used to prevent low rail

corrugations at sharp curves (Ishida et al., 2003). On the other hand, lubrication of the

rail crown has some risk of wheel sliding. Therefore, advantages and risks need to be

balanced by choosing reliable lubrication methods and a lubricant with a suitable

friction coefficient. Railway companies are looking for the appropriate lubricant that

can enhance the efficiency of operation, along with reliability and safety.

Transportation Test Centre (TTC) in Pueblo Colorado USA recommends that research

efforts should be aimed at developing and testing lubricants to meet the different

needs that the railroads have in different countries. There is a need to work towards

an international standard.

Nilsson (2002) discusses important factors influencing rail wear such as friction

coefficient (based on humidity, temperature, surface texture); type of lubrication

equipment (on board or wayside); grease contamination from dust, leaves, worn away

metal particles, water and rail and wheel profile rectification. Other influential factors

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are track irregularities (vertical, lateral, cant, gauge), curve radius, magnitude of creep

in wheel/rail contact, traction braking and acceleration. Rail players in Canada have

found that lubrication is effective in some areas and inadequate in others. The reason

for this is not clear, but lubrication may not be working effectively. Reasons might be

that they are running out of lubricant or that they need to monitor the method of

lubrication and improve standard maintenance activities (Judge, 2000). The trackside

lubrication system in Spoornet had problems of labour intensive maintenance and hi-

rail lubrication was substituted. The subsequent investigation found that some curves

were poorly lubricated and the schedule of hi-rail lubrication operation was increased,

with resultant increased maintenance costs (Koker, 2003). In Sweden, curves with

radius less than 600 m are routinely lubricated with stationary (wayside, Clicomatic)

applicators. Around 3000 such units are currently in use in Sweden. Figure 3.8 shows

the conditions in winter.

Figure 3.8: Lubricators are full of ice and snow in track (Larsson et al., 2005)

In the 1970s Swedish State Railways (SJ) experienced a heavy increase in wear on

rail curves and wheel flanges. Conventional lubricators did not work satisfactorily.

Clicomatic LP has been developed by SRS in cooperation with SJ Track division to

address this problem. In 1995 the SRS Clicomatic EC was designed and developed

out of LP-version. Clicomatic FC operates under to 220V/50Hz (alt, 110V/60Hz) and

has a transparent, exchangeable grease container. SJ Track division observed that rail

wear in steep curves has been reduced by up to 98% with a small amount of grease

(17 grams (0.06 oz.)/1000 wheels). It also showed that the wear on wheel flanges

decreased up to 50% after installation of lubricators. From 1978 to 1996 more than

2500 lubricators of the Clicomatic type were placed in Scandinavian rail track. Trains

create vibrations in the track which are detected by the vibratory sensor in the grease

gun housing. The electronic control unit receives a signal from the vibratory sensor

and opens the solenoid valve at preset intervals, activating the grease gun. The grease

is then ejected through a four-hole nozzle, hitting the rail flange with four spots of

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grease; the intervals between the impulses can be preset for different time intervals.

This means that, while the sensor is registering vibrations, either one or several grease

shots can be released during a train passage, depending on the preset time interval.

Table 3.3: Lubricators used in Sweden, 2004 (Larsson et al., 2005)

Type

Installation and

setup cost (AUD

$)

Maintenance cost

per annum (AUD $)

All costs (in Table 3.3) are determined in a yearly agreement with the subcontractor.

Field measurements in the USA have shown that rail and wheel flange lubrication

reduces rolling resistance of up to 50% around curves and up to 30% on straight and

tangent track compared to the unlubricated track. The efficiency of the lubricant film

between the rail and wheel greatly affects the improvement of rail and wheel life.

In the UK a number of QHi Rail lubricators are used to lubricate the track. Both

mechanical and electric powered rail lubricators are used to cater for high/low speed

lines, low and high radius curves and running /check rail. There are upgrade kits for

QHi and Portec units. The system is a simple mechanical design that is easy to install

and suits all rail types (Network Rail approved Cert. No. PA05/459). The pump is a

positive displacement pump that produces a consistent volume of grease flow. The

plunger only requires minimal movement to apply the amount of grease on to the rail.

Grease used is standard grease and it is suitable for high and low speed traffic. The

modular distribution blade applicator (GDU) has a controller for grease flow. The

grease reservoir is a robust durable aluminium construction that can contain 35 or 70

kg. Network rail has 8 000-10 000 mechanical QHi units and London Underground

Ltd has 200 units (figures updated up to 2001). Lubricators that are mounted directly

on rail need to be dismounted and remounted when rail grinding or other work (such

as tamping) is performed. Network Rail also has 20 top of rail lubricators (Portec

protector IV). Uneven rail wear and very high rail wear rate was found in certain

sections at sharp curves at London Underground, even though the line had been fitted

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with a number of lubricators. A special team investigated the lubricators at the

London Underground in December 2000 and found that not all the lubricators were

working properly (they were not dispensing sufficient grease). In some cases this

resulted in the replacement of rail every 18 months instead of 18 years. Consequently,

this has increased maintenance costs. It is also important to achieve the critical

balance between over-greasing and under-greasing – a bit of black art (Briginshaw,

2004). All costs (in Table 3.4) are estimated in SEK and maintenance cost is from

yearly agreement with the subcontractor.

Table 3.4: Lubricators used in UK (Larsson et al., 2005)

Type

Installation

and setup

cost (AUD $)

Maintenance cost

(AUD $) per annum

Locomotive wheel life of 35000 km and less, and rail life of less than 25 million gross

tonnes have been recorded on unlubricated Spoornet track (South Africa). The

economic implications of these high wear rates are exorbitant, as the cost of new rail

is more than $AUD 65.20 per m, excluding replacement costs. Spoornet has achieved

a seven to tenfold increase in rail life with rail and flange lubrication. On the Richards

Bay Coal line (South Africa), high-tensile rail under high axle-loading conditions has

provided an expected life of more than 1500 million gross tonnes (MGT) with

lubrication (Koker, 2003), compared to rail life of 25 million gross tonnes without

lubrication.

Spoornet has 3 000 lubricators manufactured by RailQuip and another 500 (reservoir

of 120 kg capacity) hydraulic lubricators manufactured by Moore & Steel. There is

maintenance cost data but no technical data available. All costs (in Table 3.5) are

estimated in SEK and maintenance cost is from yearly agreement with the

subcontractor.

Table 3.5: Lubricators used in Spoornet (Larsson et al., 2005)

Type

Installation

and setup

cost

Maintenance cost

(AUD $) per annum

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In the Canadian rail track, the Top-of-rail coefficient of friction was difficult to

achieve with wayside lubricators. Running trains in the westbound direction, then in

the eastbound direction, leads to drying of the top of the rail a few miles from

lubricators, and iron oxide particles from the top of the rail begin to accumulate on the

ties. Lubricators were turned to pump more grease to wheels, leading to wastage,

environmental problems, high maintenance (filling of grease) and potential slips for

locomotives (Judge, 2000). Other types of lubricators are widely used by rail players

around the world. Figure 3.9 illustrate examples from Protec and Lubritech.

In Australia, a self-contained, stand-up unit with choice of AC or DC (with/without

solar panel) power supply, as well as sensor or adjustable pre-set timing for lubricant

flow to suit varied traffic patterns, is used by rail players. These are designed for train

and tramway systems for rail and wheel lubrication. Top of rail Lubricators and

Gauge Face Lubricators:

• Increase rail and wheel life and reduce fuel consumption

• Minimize derailment potential, abate noise and reduce lateral forces in track

Figure 3.9: Rail and wheel lubricators (Chattopadhyay et al., 2004)

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These are central lubrication systems operated by compressed air, which

intermittently spray the minimum possible amount of lubricant in exact quantities on

to the friction points.

The problems associated with wheel and track lubrication in the Australian system are

different from those of the Scandinavian system in many ways: clogging; cleaning

intervals; temperature; pumpability problems in hot seasons; placing the lubricant in

the correct position on the rail head for a mixed traffic line; and oil/thickener

separation problems. However, most of the rail players have common problems in

planning and maintaining way-side lubricators. Such problems could include: long

distances between lubricators, environmental problems, cleaning the ballast of grease,

and unpleasant working conditions (with potential health risks of maintenance crews

in handling grease and lubricants).

Figure 3.10: Bleeding from the blade (QR, 2005)

Wayside lubricators are found to be highly reliable with low maintenance cost.

However, Piston is heavy (a mechanical/hydraulic device to pull the plunger could be

helpful) and actuating block clamp screw is not user friendly. Grease contamination

(as shown in Figure 3.10) has been observed on lubricated sites due to dust, leaves,

worn metal particles, water, and rail and wheel profile rectification. Corrosion found

on the rail head due to the oxidation of metals results in vibration, noise and uneven

wear of rail. Field tests and literature show that preventive rail grinding and top of

rail lubrication and friction modifiers can be used to overcome corrugation.

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Figure 3.11: Short wave corrugation (QR, 2005)

It was found that (as shown in Figure 3.11) insufficient lubrication at curve sections

results in higher flanging noise. This may be due to improper application of lubricant

from blades across the curves. This also has a negative effect on truck curving and

train handling, rail fatigue and energy savings. Excessive amounts of lubrication can

cause numerous problems ranging from operating conditions to environmental impact.

Too much lubrication (as shown in Figure 3.12) causes wheel slippage and increases

the train braking distance. This is an important safety issue for the rail administrators.

Excessive lubrication can also cause locomotive adhesion problems that may result in

increased wheel and rail wear.

Figure 3.12: Grease leakage and environmental hazard (QR, 2005)

Lubricants spread easily and have a tendency to migrate to the top-of-rail even if

applied at the gauge face of rail. However, from the literature and observation, it is

found that there are a limited number of lubrication programs to accurately and

effectively measure and maintain the effectiveness of lubrication on the rail. Routine

maintenance of lubricators and tolerable numbers of lubricant application can be

achieved only if adequate monitoring methods are available.

Questions have been recently raised by rail players as to how much lubricant is

appropriate and effective for a particular curve section under various operating

Shortwave Corrugation

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conditions. Research is being carried out to investigate the amount of lubricant and

its effectiveness for a particular curve. There is a need to develop a performance

evaluator of lubricators for achieving desirable benefits and savings.

3.19 Summary

Extensive literature on existing models of rail wear and rolling contact fatigue, rail

grinding and lubrication are discussed in this chapter. A survey of lubrication practice

in Australia and around the world is presented. It is found that there are several

existing models available to predict rail wear, rolling contact fatigue and rail track

maintenance. However, there is a need for an integrated model to predict and assess

operational risks and costs. The model includes rail grinding, lubrication, inspection

for grinding, NDT inspection, rectification and replacement of worn-out rails and

risks due to rail breaks and derailments. These models are discussed in subsequent

chapters. Failure and cost models will be developed for optimal grinding decisions in

Chapter 4.

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CHAPTER 4

MODELLING AND ANALYSIS OF RAIL DEGRADATION AND RAIL

GRINDING DECISIONS

4.1 Introduction

Grounded theory of rail wear, rolling contact fatigue (RCF), rail track maintenance

models and survey of rail lubrications were discussed in Chapter 3. This chapter will

focus on modelling and analysis of rail degradation and rail grinding costs. Real life

data is collected and analysed for developing these models. Economic models are

developed, analysed for the risks and costs due to rolling contact fatigue and optimal

rail grinding. Illustrative numerical examples are used to assist industry with informed

strategic decisions in rail grinding.

The outline of this Chapter is as follows: In Section 4.2, a system approach to

modelling is discussed; in Section 4.3, modelling rail breaks and rail degradation are

explained; Section 4.3 deals with economic models for optimal grinding decisions;

numerical examples are provided in Section 4.4; simulation results are analysed and

interpreted in Section 4.5, and an analysis of annuity cost/m per MGT is discussed in

Section 4.6; in the concluding section, results are summarised and contributions are

discussed.

4.2. System Approach and Modelling

Rail failures can be modelled using a system approach, as shown in Figure 4.1.

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Figure 4.1: Integrated system approach for modelling and analysis

Rail defects and rail wear occur due to accumulated tonnage (Million Gross Tonnage)

on rail track from traffic and freight movements and heavy haul services. In real life,

the asset life is at risk due to continuous usage, initiation and propagation of defects,

loss of material due to rail-wheel interaction and increased axle loads and train

speeds.

4.3 Modelling Rail Breaks

Chattopadhyay et al. (2002) developed models for optimal maintenance of high

volume infrastructure components. Kalousek and Magel (1997) proposed a ‘magic’

Collection and analysis of rail wear, rail breaks, derailments, lubrication, inspection, grinding data from the rail industry and lab experiments

Identification of causes and characterisation of problems

System characterisation depending on operating conditions

Stochastic modelling and development of integrated models

Risk (cost-benefit) analysis to minimise the probability of occurrence, detectability and severity of rail defects.

Parameter estimation of developed models

Testing and validation of these models using real life data

Application and implementation of these models in real life industry

Optimisation of model

Collection and analysis of rail wear, rail breaks, derailments, lubrication, inspection, grinding data from the rail industry and lab experiments

Identification of causes and characterisation of problems

System characterisation depending on operating conditions

Stochastic modelling and development of integrated models

Risk (cost-benefit) analysis to minimise the probability of occurrence, detectability and severity of rail defects.

Parameter estimation of developed models

Testing and validation of these models using real life data

Application and implementation of these models in real life industry

Optimisation of model

88

wear rate in the maintenance of railway tracks. They applied contact mechanics to rail

profile design and rail grinding. Ringsberg (2001) developed models of life prediction

in rolling contact fatigue crack initiation. Jendel (2002) developed prediction models

for wheel profile wear and compared the predictions with field measurements.

Kalousek et al., (1989) proposed the use of Preventive Rail Grinding Strategy. This

process is applicable to both standard and head hardened rails. Grinding cycles are

used to remove small initiating surface cracks early and frequently with light

grinding, rather than applying heavy grinding based on the surface appearance of the

rail. It was argued that longer rail grinding intervals require a disproportionately

greater amount of metal removal, since it is necessary to remove longer cracks that

are propagating more rapidly than short cracks. [Also, continuously restoring

favourable profiles to control the rail stress, creepage and rail surface roughness

minimises both the rates of initiation and propagation]. Canadian Pacific Railway

(CPR) experimented with the idea, grinding up to 6 times per year (i.e. 10-MGT

intervals) on 'typical rail with cracks'. Field tests on Canadian Pacific Railway (CPR)

and British Columbia Rail (BCR) proved that this method would control cracks and

was, in fact, a considerably more economical technique for grinding rail, permitting

single pass grinding where multiple passes had been required before. Canadian

National and Burlington Northern had similar findings and adopted a frequent

grinding cycle in their high tonnage regions.

In the preventive mode, rail grinding is a process of controlled artificial wear and,

through fine-tuning, can be applied to restore the desired profiles and achieve the

required depth of metal removal, with minimal grinding effort and steel wastage.

'Fine-tuning' means both determining and applying the 'Magic Wear Rate'– that is, the

combined amount of natural and artificial wear required to just remove the existing

and incipient cracks that are contained within a thin skin of metal at the surface.

CPR's Magic Wear Rate in sharp curves has, over time, evolved to be about 0.025

mm (0.001 in) per MGT of traffic, providing approximately 750 MGT wear life,

based on 19 mm (0.75 in) of allowable wear. At a 25 MGT grinding interval, this

translates into about 0.6 mm of vertical wear each cycle, of which about 0.2–0.3 mm

is typically removed during grinding – the rest being natural wear.

89

The model proposed here is based on a total cost of rail maintenance. Cost data

collected from infrastructure players are: inspection cost, grinding cost, down time

cost due to rail grinding (loss of traffic), replacement of worn-out rails, rectification,

and associated cost of rail breaks and derailment.

Counting Process

In the integrated approach, failures can be modelled as a point process. A point

process { }0),( ≥ttN is a counting process where N(t) represents the total number of

failures that have occurred up to time t. It must satisfy:

1. 0)( ≥tN

2. N (s, t] is integer valued random variable, counting the number of failures that

occur in the time interval (s, t]. It includes both the number of failures

occurring in (s, t] and the times when they occur.

3. If s < t, then )()( tNsN ≤

4. For s < t, { })()( sNtN − equals the number of events that have occurred in the

interval (s, t].

Λ(m) is an intensity function, where m represents Millions of Gross Tonnes (MGT)

and Λ(m) is increasing function of m, indicating that the number of failures in a

statistical sense increases with MGT. Fn(m) denotes the cumulative rail failure

distribution, modelled as Weibull distribution (Crowder et al., 1995) given by:

))(exp(1)( βλmmFn −−= (4.1)

)(1)( mFmS n−= (4.2)

where S(m) is survivor function.

Then the density function is expressed as:

dt

mdS

dt

mdFmf n

)()()( −== (4.3)

Then intensity function, Λ(m) is given by:

)(1

)()(

mF

mfm

n

n

−=Λ (4.4)

11

)())(exp(1(1

))(exp()(

)(1

)()( −

−

=−−−

−=

−=Λ β

β

ββ

λλβλ

λλλβm

m

mm

mF

mfm

n

n (4.5)

1)()( −=Λ βλλβ mm (4.6)

90

with the parameters β > 1 (shape parameter) and λ > 0 (scale parameter [characteristic

life]). This is an increasing function of m. The probability of failure rate is higher in

case of aged (old) rails with the increase of accumulated MGT passed through this

section. Note that this corresponds to the failure rate of two-parameter Weibull

distribution. As a result, ),( 1 ii MMN + the number of failures over 1+iM and iM are a

function of MGT and random variable. With condition on N(Mi+1, Mi) = n, the

probability is given by:

∫

∫Λ−

Λ==++

+

1

1

!/

)(

})({});1

({i

M

iM

iM

iM

n

dmm

endmmni

Mi

MNP (4.7)

This type of characterisation is considered appropriate because rail track is made

operational through repair or replacement of the failed segment and no action is taken

with regards to the remaining length. Since the length of failed segment replaced at

each failure is very small relative to the whole track, the rectification action can be

viewed as having negligible impact on the failure rate of the track as a whole. Then

the expected number of failures over 1+iM and iM is given by:

))()(()],([ 11βββλ iiii MMMMNE −= ++ (4.8)

where the total accumulated MGT, Mi, is given by:

∑=

=i

i

ii mM0

(4.9)

where im is MGT in period i.

4.4 Modelling Rail Degradation (Rail Section Loss)

MINIPROF (Greenwood Engineering) is a standard system used for the determination

of rail profiles in the field. The sensing element consists of a magnetic wheel 12 mm

in diameter, attached to two joint extensions. When the magnetic wheel is moved

manually over the rail surface, two angles are measured and stored in a computer. The

profile is then transformed to Cartesian co-ordinates. Marks on the edge of the rail are

used to ensure that the measurements were performed at the same location each time.

The accuracy of the MINIPROF system is of the order ± 0.015 mm for similar

profiles. Figure 4.2 shows rail profile measurement using MINIPROF.

91

Figure 4.2: Rail profile measurement using MINIPROF (Greenwood, Denmark)

From profile measurement data, a stochastic rail model is developed, using effect of

traffic wear and grinding wear. The area after ith period is modelled as:

( )∑=

+++−=i

oj

jwwjwwi GDRGRCTDRGRCAA )()(0 [TD0, GD0 = i] (4.10)

where A0 is the cross sectional profile area of a new rail, RCw is Rail Crown wear

width, RGw is Rail Gauge wear width, TD is the wear Depth from Traffic, GD is the

Grinding Depth due to grinding. It can be expressed as:

∑=

+−=i

j

GWTWi jjAAAA

00 ][ ci AA ≥ (4.11)

where jTW

A is the cross-sectional area loss due to traffic wear in period j and jGW

A is

the cross-sectional area loss due to grinding wear in period j.

( ) jWwTW TDRGRCAJ

+= (4.12)

( ) jWWGW GDRGRCAi

+= (4.13)

The % worn out level of rail after ith period is given by:

c

ii

AA

AAWOL

−

−∗=

0

0100 (4.14)

where Ac is the critical railhead for rail replacement, based on safety

recommendations. Ai is the cross sectional rail profile area at ith interval. The rail

industry from Scandinavia used the MINIPROF Rail profile system to measure the

profiles just before and after rail grindings (Åhrén et al. 2003). Transverse profiles are

measured for outer and inner rails at 60 positions on Malmbanan line in Sweden. The

rate of metal removal by rail grinding is about 0.2 mm across the railhead for every 23

MGT. It considers two measurements for railhead wear (Regulations BVF 524.1,

92

1998). The vertical wear on the railhead h and the flange wear s, 14 mm down from

the top of a new rail profile (Figure 4.3) is explained in Equation 4.15.

Figure 4.3: Central vertical wear and side wear (Chattopadhyay et al., 2005)

2BV

BVBV

ShH += (4.15)

The mean wear per year and amount of material removal per year due to grinding is

presented in Table 4.1.

Table 4.1: Measurements of grinding (Chattopadhyay et al., 2005)

12 months of traffic, (MGT) 23 [106 kg]

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Figure 4.4: Measurement of rail wear (Åhrén et al. 2003)

Figure 4.4 shows measurement of wear for 23 MGT Malmbanan. Using the relation

between measured s and h, one can determine Ac, the critical railhead area. The

Malmbanan line shows the annual h/s from traffic wear 0.16/0.24 mm and that from

grinding wear 0.48/0.42 mm per year for 23 MGT intervals at curve radii R<800 m.

The relation between s and h to H (equation 4.15) is as follows:

For traffic wear: TBVTBVTBVTraffic hhhH 75.1*2*16.0

24.0=+= (4.16)

For grinding wear: GBVGBVGBVGrinding hhhhH 44.116

23*

2*48.0

42.0≈=+= (4.17)

Total wear: )()()( 1.52*2*64.0

66.0GBVTBVGBVTBVGBVTBVTotal hhhH +++ ≈+= (4.18)

The safety wear limit Hlimit is set to 11 mm for the 50-kg/m BV50-rail profiles in

Malmbanan line. Ac can be calculated as function of hBV and is given by:

WWc RGsRChA ** += (4.19)

where RCw is the estimated Rail Crown wear width and RGw is the estimated Rail

Gauge wear width. Results are shown in Table 4.2.

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Table 4.2: Safety limit for Malmbanan (Åhrén et al. 2003)

s Traffic

The critical area that corresponds to the safety limit of 11 mm (BV50) is 440 mm2 and

for UIC 60 is estimated to be 560 mm2. For a theoretical 80 kg/m rail, 1000 mm2 wear

area is used (Åhrén et al. 2003).

4.5 Economic Grinding Model for Optimal Grinding Decisions

A huge share of the operational budget is spent on maintenance and replacement of

rails and wheels. Although many factors contribute to degradation, the influence of

wheel/rail contact conditions, the magnitude of friction coefficient and the rail wheel

condition are extremely important. The possible reasons for the increase in broken

rails through the 1990s include:

• Falling levels of rail renewals over the last 30 years

• Increased reliance on manual ultrasonic rail inspection

• A worsening of track quality and a possible increase in wheel irregularities

and higher dynamic forces

• Increased traffic which has not been followed up by increased inspections, and

revised minimum action criteria for defect removal, and

• Acceleration of rolling contact fatigue as a result of the introduction of bogies

with higher wheelset yaw stiffness.

Burlington Northern Santa Fe (BNSF) followed hybrid grinding procedure with a

corrective grinding practice, and faced poor surface condition and increasing defect

counts and was seeking a method to get back to the preventive grinding practice from

which they had regressed several years earlier. Canadian Pacific Railway (CPR)

successfully extended their previous 18 MGT to 25 MGT intervals on their timber-

sleepered track while retaining the single pass grinding strategy. This step removed

full grinding cycle, saving 440 000 US dollars annually in rail grinding costs without

compromising rail life.

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Table 4.3: The ideal grinding for heavy-haul (Magel & Kalousek, 2002)

Grinding depth [mm]

Magel and Kalousek (2002) identified the favourable “wear rate”, as shown in Table

4.3. The vertical crack rate is estimated to be 0.05 to 0.15 mm/ 10 MGT. The

preventive rail grinding is used to control the vertical crack propagation rate with

removal of railhead material as proposed in Figure 4.5.

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Figure 4.5: Flow chart of the track monitored base model

It is important to develop effective maintenance strategies combining technology and

safety methods for optimal rail grinding in controlling RCF and wear. Some of the

associated costs are:

START

Track segment and inspection

input: initial track data; wear

from grinding and traffic data,

lubrication data and period of

analysis (MGT -step)

Statistical Input Data

Distribution of: rail break,

derailment, detected cracks,

grinding passes, traffic wear,

grinding “wear”

Calculate wear

rate distribution

due to Traffic

Calculate wear

rate distribution

due to Grinding

Calculate

distribution of No. of

Grinding passes

Current values of

track costs and

track conditionsCalculate distribution of

rail breaks, detected

cracks and derailments

UpdateNext increment

in traffic MGT

Generate a new

expected value of

rail profile

Calculate total

cost to reach

optimal safety life

Is safety limit

reached?

Display total

cost/MGT

Economic Input Data

Cost for inspection, rail

breaks, derailment, down

time (loss of traffic),

grinding cost, lubrication

cost and replacement of

worn-out rails

Yes

No

START










grinding “wear”

Calculate wear

rate distribution

due to traffic

Calculate wear

rate distribution

due to grinding

Calculate


grinding passes

Current values of

track costs and





in traffic MGT

Generate a new

expected value of

rail profile

Calculate total

cost to reach

optimal safety life

Is safety limit

reached?

Display total

cost/MGT

Economic Input Data






worn-out rails

Yes

No

START










grinding “wear”

Calculate wear

rate distribution

due to Traffic

Calculate wear

rate distribution

due to Grinding

Calculate


Grinding passes

Current values of

track costs and





in traffic MGT

Generate a new

expected value of

rail profile

Calculate total

cost to reach

optimal safety life

Is safety limit

reached?

Display total

cost/MGT

Economic Input Data






worn-out rails

Yes

No

START










grinding “wear”

Calculate wear

rate distribution

due to traffic

Calculate wear

rate distribution

due to grinding

Calculate


grinding passes

Current values of

track costs and





in traffic MGT

Generate a new

expected value of

rail profile

Calculate total

cost to reach

optimal safety life

Is safety limit

reached?

Display total

cost/MGT

Economic Input Data






worn-out rails

Yes

No

97

• Restricted track access while grinding

• Rail grinding cost per m

• Replacement of worn-out rails

• Derailment and damage of track, train, property, life and down time

• Repairing rail breaks in terms of material, labour, equipment and down time

• Inspecting rail tracks in terms of material, labour, equipment and down time.

The grinding at Malmbanan has been an increasing problem. In 2001 a new ore

carrier was introduced with 30 tonne axle loads. This rise in axle load from 25 tonnes

resulted in RCF damage. Scandinavian rail industry carried out rail profile

measurements before and after grinding activities for analysis of its effectiveness in

controlling rolling contact fatigue (RCF) (Åhrén et al., 2003). The grinding campaign

is analysed in Table 4.4.

Table 4.4: Track path divided into sections (Larsson et al., 2003)

Sections

In spite of aggressive grinding programs and frequent, onboard, non-destructive

measurements, rail breaks happen. Other factors such as weld joints, rail geometry

and corrugation contribute to the risk. The cost of these unplanned replacements is

treated as risk cost. For an infrastructure player, it is essential to measure and manage

these risks by implementing cost effective traffic and maintenance management

strategies (Larsson et al., 2003). Questions commonly posed are:

• How much is the current risk of derailment on a specific track section?

• Will the current risk change with changed maintenance strategies in the

future? and

• What is the cost/benefit ratio of various strategies in terms of maintenance

costs and risk costs?

The total cost of maintaining any segment of rail is modelled as the sum of costs for:

rail grinding; down time due to rail grinding (loss of traffic); rectification and

associated costs of rail breaks and derailment; and inspection and replacement of

worn-out rails. The present value of rail maintenance associated costs is discounted at

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98

annuity rate. (For example, the present value of $1 to be received t periods in the

future at a discount rate of r, (PV = $1 × [1/(1+r)t)] = $1/(1+r)t), where r is discount

rate and t is number of periods.)

Results from the analysis show that different sections have different technical life for

high rail and low rail. This analysis did not consider changes in the technology of

steel making for rail material. Using the statistical data on derailments, rail breaks and

rectifications initiated by routine inspections, the expected costs are estimated.

Finally, the total costs for different traffic situations and grinding strategies are

analysed using an annuity method.

4.5.1 Modelling preventive rail grinding cost

Let G be the cost of grinding per pass per m and ni be the number of grinding pass for

ith grinding; L be the length of rail segments (0-300, 300-450, 450-600, 600-800 m of

curve radius sections) under consideration; N be the total number of periods up to

safety limit for renewal; and r be the discounting rate per period. It is assumed that

payments are made to subcontractors after each of the (N-1) grinding.

Then, total grinding cost in present value =

( )∑

−

= +

1

1 1

N

ii

i

r

G (4.20)

The total present value of grinding cost is spread in equal amounts each year of those

N periods. Then the annuity cost is (G) for each period and total annual grinding cost

can be given by:

( )∑= +

y

ii

yrG

1 1

1 (4.21)

where y is expected life in years and ry is yearly discounting factor. Discounting

factor for grinding interval, r, is given by (ry*i/12) where i is months interval between

grindings.

Results of 4.20 and 4.21 equation are the same.

( )∑= +

Y

ii

yrG

1 1

1 =

( )∑−

= +

1

1 1

N

ii

i

r

G (4.22)

Then annuity cost can be derived from equation 4.22:

99

Annuity cost G = ( )

( )∑

∑

=

−

=

+

+Y

ii

y

N

ii

i

r

r

G

1

1

1

1

1

1 (4.23)

Equation 4.21 can also be expressed as:

Total cost = ( ) ( ) ( ) ( )Yyyyy r

G

r

G

r

G

r

G

+++

++

++

+ 1...............

111 321 (4.24)

After simplification,

Annuity cost G = ( )

( )

+−

+∑

−

=

Y

Y

yN

ii

i

r

r

r

G

1

11

*1

1

1

(4.25)

Therefore, the annuity cost for rail grinding is given by:

)))1/(1(1/(*})1/()**({1

1

y

yy

iN

i

ig rrrLnGc +−+= ∑−

=

(4.26)

4.5.2 Modelling down time cost due to rail grinding (loss of traffic)

Let hDT be the expected downtime due to each grinding pass, nGPi be the number of

grinding pass for ith grinding and d be the expected cost of down time per hour. Then

down time cost due to rail grinding leading to loss of traffic is given by:

)))1/(1(1/(*})1/({1

1

y

yy

iN

i

DTGPd rrrdhnci

+−+∗∗= ∑−

=

(4.27)

Congestion costs and delay costs are not considered in this research.

4.5.3 Modelling inspection cost

Let If be the inspection per MGT and ic be the cost of one inspection. Then annual

spread, over inspection cost, over the rail life, is given by:

)))1/(1(1/(*})1/(({1

y

yy

j

i

N

j

ci rrricI

+−+= ∑=

(4.28)

where

][f

N

II

MIntegerN = (4.29)

and ri is discounting rate associated with interval of Non Destructive Testing (NDT).

100

4.5.4 Modelling risk cost of rail breaks and derailment

Let cost per rectification of rail breaks on emergency basis, Cr be modelled through

G(c), and is given by

][)( cCPcG r ≤= (4.30)

For example, if G(c) follows exponential distribution (Crowder et al, 1995), then it is

given by

cecG ρ−−= 1)( (4.31)

where c denotes the expected cost of each rail break repair on emergency basis and is

given by:

]/1[ ρ=c (4.32)

Let k be the expected cost of repairing potential rail breaks based on NDT in a

planned way and a be the expected cost per derailment; then k and a could be

modelled in a similar manner.

The risk cost associated with rail break and derailment is based on the probability of

NDT detecting potential rail breaks, rail breaks not detected by NDT, derailments and

associated costs.

Let Pi(B) be the probability of detecting potential rail break in NDT; Pi(A) be the

probability of undetected potential rail breaks leading to derailments; nNDTj be the

number of NDT detected potential rail breaks; nRBj be the number of rail breakes in

between two NDT inspections and nAj be the number of accidents in a period. Then

the risk cost is given by:

)))1/(1(1/()1(*)))1/(1(1(*})1(

/]*))(1(*)((*))(1(*)([)],([{0

1

y

yyy

i

N

i

iiiiiir

rrrr

cAPaAPBPkBPMMNEc

+−++−+

−+−+∗= ∑=

+(4.33)

where Pi(B) and Pi(A) could be estimated based on nNDTj the number of NDT detected

potential rail breaks; nRBj the number of rail breakes in between two NDT inspections;

and nAj be the number of accidents in between two NDT inspections over j periods.

Figure 4.6 shows probability of failures.

101

Probability of failures

Pi(A),

2%

Pi(B),

92%

1-Pi(A),

6%

Figure 4.6: Probabilities of failures

4.5.5 Modelling Replacement Costs of Worn-Out Unreliable Rails

Let cre be the expected cost of replacement for segment L and consist of labour,

material, and equipment, consumable and down time cost for rail replacement. Let I

be the cost of current investment in new rail. In this model, the cost of replacement is

assumed to be occurring at the beginning of each year and is simplified as the annual

spread over of investment of new rail. Then cre is given by:

)))1/(1(1/()))1/(1(1(* y

yre rrIc +−+−= (4.34)

4.5.6 Modelling Total Cost of Rail Maintenance

Costs associated with rail maintenance are estimated separately for low rail, high rail

and curve radius and added up to obtain total cost of maintenance. Therefore, the total

cost of maintaining a segment of rail is equal to the sum of cost for: Preventive rail

grinding cost (cg); down time cost due to rail grinding (loss of traffic) (cd); inspection

costs (NDT) (ci); risk cost of rectification based on NDT, rail breaks and derailment

(cr) and replacement cost of worn-out unreliable rails (cre). It is the given by:

reridgtot cccccC ++++= (4.35)

This is analytically intractable and so a simulation needs to be used to arrive at train

speed, inspection frequency and MGT interval for preventive rail grinding. Rail

breaks generally occur from fatigue initiated surface cracks (shells/squats/head

checks) and transverse defects. Other rail defects can be due to manufacturing

problems, wear, welding problems (Railtrack plc. 2001) and other factors such as

heavy axle loads, high speed and many other factors such as wheel burn. There is risk

involved due to these undetected defects that lead to rail breaks, rail failures and

102

derailments, loss of lives, revenue and property. This, in turn, increases maintenance

costs and risks to safety and reliability.

4.6 Estimation of cost and life data

Data was collected from field observations and, in these calculations, Weibull

distribution is used with the parameters β = 3.6 and 1250/12350 << λ (Besuner et

al., 1978), to estimate the rail breaks and derailments. In this case, the grinding speed

is set to 10 km/h with 3 passes (Table 4.1) to a total cost of 2 AUD/ m/pass. Other

costs are given in Table 4.5. Discounting factor is used, assuming 10% per year.

Table 4.5: Estimated costs and area safety limits (Chattopadhyay et al., 2005)

Cost of grinding per pass per m 2.00 [AUD/pass/m]

(For detailed data, see Appendix B.)

4.6.1 Analysis of results

Data is used in simulation model developed and analysed using Mat lab and Microsoft

Excel, and results are shown in sections 4.6.2 to 4.8.

4.6.2 Grinding cost

Grinding cost is estimated using the grinding cost/m/pass data ($AUD 2.00/m/pass)

and the average number of passes per section (minimum 2 and maximum 5 passes per

section). Grinding cost estimation method is shown in Figure 4.7.

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Figure 4.7: Grinding cost estimation method (Chattopadhyay et al., 2005)

4.6.3 Grinding cost/m

Analysis of grinding cost/m for 23, 12, 18 and 9 MGT intervals are compared for

curve radius from 0 to 800 m. Results are given in Table 4.6.

Table 4.6: Grinding cost/m for 0 to 800 m curves

MGT Interval 23 12 18 9

Length (m) Radius (ms) Grinding cost/m ($AUD) 1318 0-300 10 20 18 36

1384 300-450 16 12 22 40 36524 450-600 16 16 26 30 33235 600-800 6 8 32 22

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Grinding cost/meter

0

10

20

30

40

50

0-300 300-450 450-600 600-800

Curve radius (meters)

Cost ($AUD)

23 MGT

12 MGT

18 MGT

9 MGT

Figure 4.8: Grinding cost/m for 0 to 800 m curves

Figure 4.8 shows the analysis of grinding cost/m for 23, 12, 18, and 9 MGT intervals

of curve radius from 0 to 800 m. It is observed that cost is higher for smaller grinding

intervals. The costs for lower curve radius 0-300 m are in general more compared to

higher curve (300-450 or more) sections of rail segment. This indicates more rolling

contact fatigue (RCF) in tighter curves.

4.6.4 Grinding cost/MGT/m

Analysis of grinding cost/MGT/m for 23, 12, 18 and 9 MGT intervals are compared

for curve radius from 0 to 800 m. Results are given in Table 4.7.

Table 4.7: Grinding cost/MGT/m for 0 to 800 m curves


Length (ms) Radius (ms) Grinding cost/MGT/m ($AUD) 1318 0-300 0.43 1.67 1 4

1384 300-450 0.7 1 1.22 4.44 36524 450-600 0.7 1.33 1.44 3.33 33235 600-800 0.26 0.67 1.78 2.44

Grinding cost/MGT/meter

0

1

2

3

4

5

0-300 300-450 450-600 600-800


Cost ($AUD)

23 MGT

12 MGT

18 MGT

9 MGT

Figure 4.9: Grinding cost/MGT/m for 0 to 800 m curves

105

Figure 4.9 shows the analysis of grinding cost/MGT/m for 23, 12, 18, and 9 MGT

intervals of curve radius from 0 to 800 m. It is observed that cost/MGT/m trend is

similar to per m costs.

4.6.5 Risk cost/m

Analysis of risk cost/m for 23, 12, 18 and 9 MGT intervals are compared for curve

radius from 0 to 800 m. Results are given in Table 4.8.

Table 4.8: Risk cost/m for 0 to 800 m curves


Length (ms) Radius (ms) Risk cost/m ($AUD) 1318 0-300 0.00004 0.0000076 0.00002 0.0000013 1384 300-450 0.00003 0.0000080 0.00001 0.0000012 36524 450-600 0.00000 0.0000003 0.00000 0.0000000

33235 600-800 0.00000 0.0000003 0.00000 0.0000000

4.6.6 Risk cost/MGT/m

Analysis of risk cost/MGT/m for 23, 12, 18 and 9 MGT intervals are compared for


Table 4.9: Risk cost/MGT/m for 0 to 800 m curves


Length (ms) Radius (ms) Risk cost/MGT/m ($AUD) 1318 0-300 0.000002 0.000001 0.000001 0.000000

1384 300-450 0.000002 0.000001 0.000001 0.000000 36524 450-600 0.000000 0.000000 0.000000 0.000000 33235 600-800 0.000000 0.000000 0.000000 0.000000

From the above Tables 4.8 and 4.9, it is observed that risk cost is negligible in these

sections. This is due to the fact that rail operators work in a conservative manner

related to rail replacements and rail repairs. It may be also due to the fact that many of

the failure and accident data are not reported so as to avoid public criticism.

4.6.7 Down time cost/m

Analysis of down time cost/m for 23, 12, 18 and 9 MGT intervals are compared for


106

Table 4.10: Down time cost/m for 0 to 800 m curves


Length (ms) Radius (ms) Down time cost/m ($AUD) 1318 0-300 1.57 3.14 2.82 5.64 1384 300-450 2.51 1.88 3.45 6.27 36524 450-600 2.51 2.51 4.08 4.7

33235 600-800 0.94 1.25 5.02 3.45

Down time cost/meter

0

2

4

6

8

0-300 300-450 450-600 600-800


Cost ($AUD)

23 MGT

12 MGT

18 MGT

9 MGT

Figure 4.10: Down time cost/m for 0 to 800 m curves

Figure 4.10 shows the analysis of down time cost/m for 23, 12, 18, and 9 MGT

intervals of curve radius from 0 to 800 m. It is observed that cost is higher for 9 MGT

interval, compared to 23, 12 and 18 MGT intervals. This is due to increased number

of set ups for lower MGT intervals. Costs are higher for steeper curves, compared to

other sections of rail segment. This may be due to increase in grinding passes due to

more rolling contact fatigue (RCF) in sharper curves.

4.6.8 Down time cost/MGT/m

Analysis of down time cost/MGT/m for 23, 12, 18 and 9 MGT intervals are compared

for curve radius from 0 to 800 m. Results are given in Table 4.11.

Table 4.11: Down time cost/MGT/m for 0 to 800 m curves


Length (ms) Radius (ms) Down time cost/MGT/m ($AUD) 1318 0-300 1.57 3.14 2.82 5.64 1384 300-450 2.51 1.88 3.45 6.27

36524 450-600 2.51 2.51 4.08 4.7 33235 600-800 0.94 1.25 5.02 3.45

Figure 4.11 shows the analysis of down time cost/MGT/m for 23, 12, 18, and 9 MGT

intervals of curve radius from 0 to 800 m. It is observed that cost/MGT/m trends are

similar to per m costs.

107

Down time cost/MGT/meter

0

0.2

0.4

0.6

0.8

0-300 300-450 450-600 600-800


Cost ($AUD)

23 MGT

12 MGT

18 MGT

9 MGT

Figure 4.11: Down time cost/MGT/m for 0 to 800 m curves

4.7 Annuity Cost/m

Annuity cost/m for 23, 12, 18 and 9 MGT intervals are estimated. Results are

compared for each MGT and for different curves. Annuity costs/m for grinding, risk,

down time, inspection and replacement are estimated using the mathematical model.

4.7.1 Annuity cost/m for grinding

Analysis of annuity cost/m for grinding 23, 12, 18 and 9 MGT intervals are compared

for curve radius from 0 to 800 m. Results are shown in Table 4.12.

Table 4.12: Annuity cost/m for grinding 0 to 800 m curves


Length (ms) Radius (ms) Annuity cost/m for grinding ($AUD) 1318 0-300 5.42 6.82 11.41 14.00 1384 300-450 5.95 6.08 11.00 12.00

36524 450-600 6.00 7.12 11.00 10.00 33235 600-800 5.88 6.86 12.00 11.00

Annuity cost/meter for Grinding

0.00

4.00

8.00

12.00

16.00

0<R<300 300<R<450 450<R<600 600<R<800


Cost ($AUD)

23 MGT

12 MGT

18MGT

9 MGT

Figure 4.12: Annuity cost/m for grinding 0 to 800 m curves

108

Figure 4.12 shows the analysis of annuity cost/m for grinding 23, 12, 18, and 9 MGT

intervals of curve radius 0 to 800 m. It is observed that annuity cost/m for grinding is

higher for 9 and 18 MGT. This is due to excessive grinding in these intervals.

4.7.2 Annuity cost/m for risk

Analysis of annuity cost/m for risk 23, 12, 18 and 9 MGT intervals are compared for

curve radius from 0 to 800 m. Results are shown in Table 4.13.

Table 4.13: Annuity cost/m for risk in 0 to 800 m curves


Length (ms) Radius (ms) Annuity cost/m for risk ($AUD) 1318 0-300 0.0016 0.0002 0.0011 0.0000 1384 300-450 0.0018 0.0004 0.0002 0.0000 36524 450-600 0.0001 0.0000 0.0000 0.0000

33235 600-800 0.0001 0.0000 0.0000 0.0000

Annuity cost/meter for Risk

0.0000

0.0005

0.0010

0.0015

0.0020

0<R<300 300<R<450 450<R<600 600<R<800


Cost ($AUD)

23 MGT

12 MGT

18MGT

9 MGT

Figure 4.13: Annuity cost/m for risk in 0 to 800 m curves

Figure 4.13 shows the analysis of annuity cost/m for risk 23, 12, 18 and 9 MGT

intervals of curve radius from 0 to 800 m. It is observed that annuity cost/m for risk

trend is similar to cost/MGT/m of grinding. The data on risk cost is based on a very

small number of derailment incidents and there is enough scope for estimating actual

risk cost based on real life derailment data.

4.7.3 Annuity cost/m for down time

Analysis of annuity cost/m for down time 23, 12, 18 and 9 MGT intervals are

compared for curve radius from 0 to 800 m. Results are shown in Table 4.14.

109

Table 4.14: Annuity cost/m for down time in 0 to 800 m curves


Length (ms) Radius (ms) Annuity cost/m for down time ($AUD) 1318 0-300 0.85 1.07 1.79 2.14 1384 300-450 0.93 0.95 1.56 1.85 36524 450-600 0.94 1.12 1.77 1.57

33235 600-800 0.92 1.08 1.83 1.74

Annuity cost/meter for Down time

0

1

2

3

0<R<300 300<R<450 450<R<600 600<R<800


Cost ($AUD)

23 MGT

12 MGT

18MGT

9 MGT

Figure 4.14: Annuity cost/m for down time in 0 to 800 m curves

Figure 4.14 shows the analysis of annuity cost/m for down time 23, 12, 18 and 9

MGT intervals of curve radius from 0 to 800 m. It is observed that annuity cost/m for

down time trend is similar to annuity cost/m of grinding.

4.7.4 Annuity cost/m for inspection

Analysis of annuity cost/m for inspection 23, 12, 18 and 9 MGT intervals are


Table 4.15: Annuity cost/m for inspection in 0 to 800 m curves


Length (ms) Radius (ms) Annuity cost/m for inspection ($AUD) 1318 0-300 0.044 0.023 0.035 0.017

1384 300-450 0.044 0.023 0.033 0.017 36524 450-600 0.044 0.023 0.030 0.016 33235 600-800 0.044 0.023 0.031 0.018

110

Annuity cost/meter for Inspection

0.00

0.01

0.02

0.03

0.04

0.05

0<R<300 300<R<450 450<R<600 600<R<800


Cost ($AUD)

23 MGT

12 MGT

18MGT

9 MGT

Figure 4.15: Annuity cost/m for inspection in 0 to 800 m curves

Figure 4.15 shows the analysis of annuity cost/m for inspection 23, 12, 18 and 23

MGT intervals for curve radius 0 to 800 m. It is observed that the cost for inspection

is slightly higher for 23 and 18 MGT intervals compared to 9 and 12 MGT intervals.

This is due to increased life and number of inspections.

4.7.5 Annuity cost/m for replacement

Analysis of annuity cost/m for replacement 23, 12, 18 and 9 MGT intervals are


Table 4.16: Annuity cost/m for replacement in 0 to 800 m curves


Length (ms) Radius (ms) Annuity cost/m for replacement ($AUD) 1318 0-300 17.65 15.00 16.00 20.62 1384 300-450 15.17 13.10 24.00 25.00 36524 450-600 16.06 11.63 32.00 28.00 33235 600-800 15.00 11.49 21.00 28.00

Annuity cost/meter for Replacement

0

10

20

30

40

0<R<300 300<R<450 450<R<600 600<R<800


Cost ($AUD)

23 MGT

12 MGT

18MGT

9 MGT

Figure 4.16: Annuity cost/m for replacement in 0 to 800 m curves

Figure 4.16 shows the analysis of annuity cost/m for replacement 23, 12, 18 and 9

MGT intervals of curve radius from 0 to 800 m. It is observed that cost for

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replacement is higher for 9 and 18 MGT intervals compared to 23 and 12 MGT

intervals. This may be due to more replacements and excessive grinding in higher

MGT intervals.

4.7.6 Total annuity cost/m

Analysis of total annuity cost/m for 23, 12, 18 and 9 MGT is compared for curve

radius 0 to 800 m. Results are shown in Table 4.17.

Table 4.17: Total annuity cost/m for 0 to 800 m curves


Length (ms) Radius (ms) Total annuity cost/m ($AUD) 1318 0-300 23.96 22.91 29.24 36.78 1384 300-450 22.09 20.15 36.59 38.87 36524 450-600 23.04 19.89 44.80 39.59

33235 600-800 21.84 19.45 37.86 40.76

Total annuity cost/meter

0.00

10.00

20.00

30.00

40.00

50.00

0-300 300-450 450-600 600-800


Cost ($AUD)

23 MGT

12 MGT

18 MGT

9 MGT

Figure 4.17: Total annuity cost/m for replacement of 0 to 800 m curves

Figure 4.17 shows the analysis of total annuity cost/m for 23, 12, 18 and 9 MGT

intervals of curve radius from 0 to 800 m. From the analysis, it is observed that cost is

higher for 18 and 9 MGT intervals. This may be mainly due to more rail replacements

due to excessive grinding for lower MGT intervals.

4.8 Annuity cost/m assessment for each MGT

4.8.1 Annuity cost/m for 23 MGT

Analysis of annuity cost/m of grinding, risk, down time, inspection and replacement

for 23 MGT interval of curve radius from 0 to 800 m is compared. Results are shown

in Table 4.18.

112

Table 4.18: Annuity cost/m for 23 MGT in 0 to 800 m curves

Radius (m) 0-300 300-450 450-600 600-800

Length (m) 1318 1384 36524 33235 Maintenance costs Annuity cost/m ($AUD)

Grinding 5.42 5.95 6.00 5.88

Risk 0.00 0.00 0.00 0.00 Down time 0.85 0.93 0.94 0.92 Inspection 0.04 0.04 0.04 0.04

Replacement 17.65 15.17 16.06 15.00 Total cost 23.96 22.09 23.04 21.84

Annuity cost/meter for 23 MGT

Inspection0%

Risk0%

Down time4%

Grinding23%

Replacement73%

Figure 4.18: Annuity cost/m for 23 MGT in 0 to 800 m curves

Figure 4.18 shows the analysis of annuity cost/m for 23 MGT of curve radius from 0

to 800 m. It is observed that replacement and grinding costs are higher compared to

other costs. It is found that total costs for tighter curves (radii 0-300 m) are higher

compared to radii of 301 - 800 m curves.



for 12 MGT of curve radius from 0 to 800 m is compared. Results are shown in Table

4.19.


Radius (m) 0-300 300-450 450-600 600-800

Length (m) 1318 1384 36524 33235

Maintenance costs Annuity cost/m ($AUD) Grinding 6.82 6.08 7.12 6.86 Risk 0.00 0.00 0.00 0.00

Down time 1.07 0.95 1.12 1.08 Inspection 0.02 0.02 0.02 0.02 Replacement 15.00 13.10 11.63 11.49

Total costs 22.91 20.15 19.89 19.45

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Annuity cost/meter 12 MGT

Grinding30%

Risk0%

Down time5%

Inspection0%

Replacement65%



to 800 m. It is observed that the cost is higher for replacement and grinding. It is

found that total costs for tighter curves (radii 0-300 m) are higher, compared to radii

of 301 - 800 m curves.




4.20.


Radius (m) 0-300 300-450 450-600 600-800


Grinding 11.41 11.00 11.00 12.00


Replacement 16.00 24.00 32.00 24.00 Total costs 29.23 36.59 44.8 37.86

Annuity cost/meter for 18 MGTGrinding39%

Risk

0% Down time

6%

Inspection0%

Replacement55%


114


to 800 m. It is observed that the cost for replacement and grinding are higher

compared to other costs.




4.21.


Radius (m) 0-300 300-450 450-600 600-800


Grinding 14.00 12.00 10.00 11.00


Replacement 20.62 25.00 28.00 28.00 Total Costs 36.78 38.87 39.59 40.76

Annuity cost/meter for 9 MGT

Inspection

0%

Down time7%

Risk0%

Replacement

44%

Grinding49%


Figure 4.21 shows the analysis of annuity cost/m for 9 MGT of curve radius from 0 to

800 m. It is observed that grinding cost is higher compared to other costs. In this

research, risk is defined as the percentage of defects occurrence, annual rate of

undetected defects, rail breaks and derailments. Track segments are used as per the

database of rail replacements and ageing is estimated by assuming 23 MGT per year

of traffic flow.

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4.9 Summary

This chapter proposed a systematic approach to developing cost models for rail

grinding decisions. Field data from rail industry have been used for developing

models and estimation of parameters. In this research work failures are modelled with

non-homogenous Poisson process. Results from this investigation can be used for

maintenance and replacement decisions about rails. The annuity cost/m for grinding,

risk, down time, inspection and replacement are analysed. Results for 23, 12, 18 and 9

MGT of curve radius from 0 to 300, 300-450, 450-600 and 600-800 m are discussed.

Summary of the findings are:

• Analysis shows that total annuity cost/m for 0-300 ms for 23 MGT AUD $ is

23.96; for 12 MGT is AUD $ 22.91; for 18 MGT is AUD $ 29.24; for 9 MGT

is AUD $ 36.78. It shows that rail players can save 4.58% of costs with 12

MGT intervals, compared to 23 MGT intervals.

• Analysis shows that total annuity cost/m for 300-450 ms for 23 MGT AUD $

is 22.09; for 12 MGT is AUD $ 20.15; for 18 MGT is AUD $ 36.59; for 9

MGT is AUD $ 38.87. This shows that rail network providers can save 9.63%

of costs with 12 MGT intervals, compared to 23 MGT intervals.



MGT is AUD $ 39.59. This shows that rail players can save 15.80% of costs

with 12 MGT intervals, compared to 23 MGT intervals.



MGT is AUD $ 40.76. This shows that rail players can save 12.29% of costs

with 12 MGT intervals, compared to 23 MGT intervals.

In steep curves, rail replacement is more due to rolling contact fatigue (RCF),

compared to curves with higher radius. It is found that rail players can save with 12

MGT intervals compared to 23 MGT intervals. Analysis suggests that 23 MGT (or

longer) grinding intervals demand much heavier grinding each cycle, or the use of

heavy relief in curves to control fatigue. Both of these measures can result in large

wear rates, reduced rail life and ineffective use of the grinding budget. Therefore, it is

recommended that 12 MGT grinding interval is economical to achieve optimal wear

and to control surface fatigue cracks. There is enormous scope to extend these models

116

for optimal maintenance decisions concerning rail-wheel lubrication. Modelling and

analysis of lubrication strategies will be discussed in Chapter 5.

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CHAPTER 5

MODELLING AND ANALYSIS OF WEAR AND LUBRICATION

DECISIONS

5.1 Introduction

Cost models on rail grinding for optimal rail grinding decisions are developed in

Chapter 4. The annuity cost/m for grinding, risks, down time, inspection, replacement

and lubrication are analysed. This chapter focuses on modelling and analysis of

lubrication strategies. Data collected from rail industry is used for illustration.

Rail wear is an important element for budgeting rail replacements and reducing

operational risks. It acts as a performance indicator for rail-wheel lubrication.

Currently, rail players are making executive decisions based on experience. There are

no international standards for rail lubrication. It is important to study the factors

behind wear and develop lubrication models for lubrication decisions.

The outline of this chapter is as follows: in Section 5.2, there is an assessment of

lubricators’ performance; modelling of rail wear and rail wear limits are discussed in

Section 5.3; modelling for rail lubrication decisions is explained in Section 5.4;

Section 5.5 deals with modelling failures of lubricators using renewal process;

framework for benchmarking lubrication is discussed in Section 5.6; in Section 5.7,

annuity costs of lubricators are modelled; collection and analysis of data is explained

in Section 5.8; cost-benefit analysis is discussed in Section 5.9; finally, the

conclusions, summary and contributions are discussed in Section 5.10.

Rail infrastructure owners have been working around the world to improve

performance of lubrication. Three types of lubrication (way-side lubricators, on-board

lubrication, and hi-rail lubrication) are generally used. It is a great challenge for rail

infrastructure owners to decide whether a lubrication system is economical under

different operating conditions. Wayside lubrication has problems of wastage of

lubricant, nozzle clogging, empty reservoirs and oil separation. For the Hi-rail

lubrication system, the track availability is a challenge to rail infrastructure owners.

On-board lubrication systems have problems of maintenance linked to reliability and

safety. It is important to analyse and identify the costs and benefits of these systems

118

and develop a model for comparison of performance. Variables affecting the lubricant

transfer at the wheel-rail interface can be grouped into the following categories:

� Application method that is wayside, on-board, hi-rail

� Parameters of the lubricant, such as viscosity and its variation with temperature,

separation rates and base oil attributes

� Geographic issues such as grade, curvature (expressed as degrees of central

angle), location of wayside lubricators (temperature difference), rail contour, and

wheel contour

� Operating issues such as train length, gross weight, and speed

� The initial state of the lubrication, including surface roughness

� Temperature generated due to rail-wheel interaction

Generally, the three types of track mounted lubricator systems used are:

� Hydraulic lubricator (eg. PORTEC M&S 761, HL1, PW Series, PORTEC MC3)

� Mechanical lubricator (eg. P&M – Model C4, M6, RTE 25)

� Electric lubricator (eg. SYSCOM)

It is important for track practitioners to identify the types of lubricator when

conducting maintenance activities, to record the condition of the lubricators, position

of the lubricator, identification of spare parts, and skills required to trouble shoot

different types of lubricators. (For more details, see Appendix B). Figure 5.1 shows

the flowchart for the modelling and analysis of lubrication decisions.

Figure 5.1: Flowchart for the modelling and analysis of lubrication decisions

Framework for Lubrication Effectiveness

Assessment of lubricators performance

Modelling

� rail wear, wear limit

� rail lubrication

� applicators

� lubricant

� benefits of lubricators

� failures

� cost-benefit analysis

� annuity cost of lubricators

Collection and analysis of data

Estimation of annuity costs

Numerical example

Evaluation of

Lubrication

Decisions

119

5.2 Assessment of lubricator’s performance

In the UK it has been estimated that only 25% of the 8000-10000 conventional

lubricators are adequately maintained. This is not only due to the requirement to refill

frequently (small capacity reservoirs) or frequent adjustment of wearing parts, but

also due to the lack of dedicated teams of experienced and trained personnel. Track

side lubricators can be effective only if they are positioned correctly and maintained

properly. Way-side lubrication is more effective in sharper curves (for example, 200

m).

Figure 5.2: A well lubricated rail wear face in a Spoornet curve (Koker, 2004)

Recent experience and measurements on Spoornet track suggests that the wear

induced in one month of poor or no lubrication on sharp curves (radius less than 300

m) is equal to that of sixty months (five years) of a well lubricated curve. For medium

curves between 300 and 800 m radius, the figure gradually reduces to 30 times. Figure

5.2 shows a well lubricated rail wear face in a Spoornet curve (Koker, 2004). Koker

(2004) has discussed the problems in track side lubrication systems on Richard Bay

Coal Line. The trackside lubrication system was labour intensive due to lower grease

capacity and inadequately trained maintenance staff. As an interim measure,

electronic, gas-operated lubricators, mounted on inspection trolleys, were used. This

system failed because of leakage in the gas lines and the mechanical unreliability of

the trolleys. A decision was taken to use trackside, small capacity lubricators. Table

5.1 shows the costs of track side lubrication on Richard Bay Coal Line. A monitoring

system was implemented for measuring the efficiency of the lubrication. The

positioning of the machines was optimized. Staff members were trained for

maintenance of lubricators. Grease consumption and availability data were recorded

and analysed.

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120

Table 5.1: Cost of Trackside Lubrication Koker (2004)

Item Cost ($ AUD) Percentage of Total

Thelen and Lovette (1996) identified factors that can significantly affect the

effectiveness of wayside lubricator:

• The location of the lubricator in regard to the curve

• The viscosity of the grease at different temperatures

• The grease output adjustment

• The level of maintenance of lubricators

On-board lubrication systems mainly use a liquid or solid lubricant applied to the

wheel flange or directly to the rail. These systems are maintained in the depot during

routine maintenance operations. It was found that, due to negligible migration of the

lubricant to the top-of-rail in dry tunnels without natural lubrication, this type of

lubricant leaves the top-of-rail totally unlubricated, leading to excessive wheel wear

problems. Liquid spray systems that incorporate control systems to spray according to

various set parameters are more expensive to install compared to solid lubricant

systems, but lubricant costs are likely to be lower. Excessive dosage rates can cause

contamination problems. Solid lubricant systems are applied continuously, are

cheaper to install, and the system is less likely to produce contamination.

Hi-rail lubrication systems have been cost effective for many rail players around the

world. They can be controlled with a limited of application of lubricant through beads

directed to the rail gauge face on the track. The hi-rail equipment improves the

maintenance procedures as the equipment is regularly returned to workshops. It helps

in improved train handling, reduced train noise, bogie hunting and development of rail

corrugation. Koker (2003) found that, on Richards Bay Coal Line (South Africa), hi-

rail grease application on curves was sufficient and most curves were always well

lubricated. Some curves were poorly lubricated because they were situated at the

beginning of momentum gradients. Some of the problems with hi-rail lubrication

exposed by the study are:

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121

� Increased risk of over-lubrication (This causes wastage, rail/wheel damage

through slippage, interference with ultrasonic testing, fouling of ballast, and

environmental pollution.)

� Increased risk of rail flaking (The pumping of lubricant into micro-cracks may

lead to fatigue cracking or flaking at the gauge corner.)

� Increased risk of rail damage if not correctly supervised (Lubrication on the rail

head, coupled with sanding for traction, may produce a grinding paste which

increases head wear.)

� Relatively high capital cost and

� Accumulation of lubricant on vehicle bogie and bodies.

Some of the factors influencing economic analysis are:

� resources to run and maintain lubricators

� reservoir capacity of lubricators

� location and position of the lubricator and grease coverage

� skilled personnel and their time for maintenance and repair of lubricators

� grease travel on rail track

� availability of spare parts

� replacement of aging lubricators and product support

� training in fitting, fault diagnosis and maintenance

� refilling interval of reservoirs

� inspection and maintenance intervals.

Assessment of lubricators and lubricants is important to examine overall

effectiveness. The configuration of lubrication systems may vary for the following

reasons (Tew and Mutton, 1991):

� Proportion of tangent and curved track

� Constraint introduced by track availability

� Maintenance requirements

Tew and Mutton (1991) found that effectiveness of lubrication depended on the

following factors:

� Application method

� Lubricants

� Frequency of application

� Rate of application (dose)

� Lubricator components (pump, container, nozzle and hose system)

122

� Grease consumption based on various axle loads (tonnes)

Performance of lubrication systems can be analysed based on visual inspection,

scientific method and readings from a tribometer.

5.3 Lubrication decision model

Determination of the effectiveness of a lubricator is possible by using finger testing at

the gauge face after a week or two of operation. The grease film should be seen on the

gauge face of the curve. Change of position of the lubricators can improve the

distance the lubricant is carried. Any visible, excessive grease on the top of the rail

indicates that the ramp or wiping bars should be lowered. Insufficient grease is

possible in some areas, even though the lubricators are functioning properly. The

insufficiency of the grease indicates that the ramp or wiping bars should be raised.

Temperature changes indicate requirements for adjusting the ramp settings to achieve

consistency and lubrication propagation (Larsson et al., 2005). At high temperature,

lower ramp allows the lubricant to stay at the same level on the gauge face. High

temperature reduces the grease viscosity and can cause problems due to grease

migrating on the top of the rail. Cold temperature increases the viscosity and can

cause clogging of the distribution hole. Therefore, higher ramp settings are

recommended during the cold season. Heeler (1979) suggested that rail lubricator

maintainers need to consider the following points before installation and maintenance

of lubricators:

� Positioning of the lubricator should be close to where the wheel flange intacts

with the high rail. Indication of improper installation of lubricator is evidenced by

thick beads of lubricant visible on distribution bars. The train passage can cause

fling off of the grease, leading to a messy environment. Positioning of the

lubricator should be near the curve. In addition, the pump should be set low on

fast lines and high on slow lines.

� Refilling activity should be scheduled frequently rather than waiting for the

lubricators to be empty.

� The number of lubricators and maintenance intervals should be determined by

lubricator effectiveness.

� Grease plates need to be adjusted to the desired height for an even distribution of

lubricant over the gauge face.

123

The key roles and responsibilities of the lubricator maintainer are to (QR, 2005):

� understand basic principles of tribology ( friction and wear)

� understand benefits of lubricating the rail/wheel

� understand rail/wheel interaction at various curves

� recognize usefulness of different types of lubricators

� adjust the position of the lubricator

� record important information related to improving lubricator performance and

lubricant effectiveness.

� conduct analysis for effectiveness of lubricants and lubricators

� address the environmental issues

Figure 5.3: Lubrication decision model

Figure 5.3 shows the lubrication decision model. Table 5.2 shows ‘Where to place’

and ‘Where not to place’.

Issues in lubrication decision� type of Lubricator� on-site or depot service� plan for maintenance activity� selection of resources and skilled personnel� type of inspection using lubricator manual

Inspection,Maintenance, Servicing

Checking during inspection� tank� plunger condition, air locks� leaks at hose connection � replace gaskets if necessary� check pumps are working properly� grease leaks and loose bolts� bent plungers must be replaced� position and location of lubricator

Measures of lubrication effectiveness� rail head temperature rise method� visual inspection� tribometer measurements

Analysis of data� estimation of energy dissipation� continuous and uniform lubrication� relative performance of different lubricants� relative performance for different curves� lubricant type� position, location and operation of lubricator

Maintenance/Service decision� minimal repair� overhaul� planned or preventive� corrective � condition based

Review of Lubrication Decision� Review of lubricator location and position� distance covered by each lubricator� type of application� type of lubricant� maintenance intervals

Issues in lubrication decision� type of Lubricator� on-site or depot service� plan for maintenance activity� selection of resources and skilled personnel� type of inspection using lubricator manual

Inspection,Maintenance, Servicing

Checking during inspection� tank� plunger condition, air locks� leaks at hose connection � replace gaskets if necessary� check pumps are working properly� grease leaks and loose bolts� bent plungers must be replaced� position and location of lubricator

Measures of lubrication effectiveness� rail head temperature rise method� visual inspection� tribometer measurements

Analysis of data� estimation of energy dissipation� continuous and uniform lubrication� relative performance of different lubricants� relative performance for different curves� lubricant type� position, location and operation of lubricator

Maintenance/Service decision� minimal repair� overhaul� planned or preventive� corrective � condition based

Review of Lubrication Decision� Review of lubricator location and position� distance covered by each lubricator� type of application� type of lubricant� maintenance intervals

124

Table 5.2: ‘Where to lubricate’ and ‘not to lubricate’ (CETS, 2004)

Position for placing lubricator Position for not placing lubricator

It is important to evaluate the gauge face friction before positioning the lubricators, in

order to determine the point of contact when physical interaction occurs between rail

and the wheel. Coefficient of friction means the classification of the surface

roughness. Smoothness of the surface means a reduction of wear. The coefficient of

friction µ as a function of film parameter λ is shown in Figure 5.4. The coefficient of

friction is defined as:

µ = f/w z (5.1)

where f is tangential friction force and w z is the normal applied load.

Figure 5.4: Coefficient of friction (Hamrock and Dowson, 1981)

Wheel and rail interaction operates in various lubrication regimes. The film thickness

parameter λ, is related to the coefficient of the friction, µ and depends on the mode of

lubrication. International Heavy Haul Association (IHHA) recommends “Expert

Eyeball Chart” as replacement of tribometer to cut down the cost of labour and time

when assessing lubricated curves. Expert Eyeball Chart estimates the coefficient of

friction of the rail gauge surfaces. Table 5.3 shows expert chart of lubrication

effectiveness from International Heavy Haul Standards.

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Table 5.3: Expert Chart of Lubrication Effectiveness (IHHA, 2001)

Observed Conditions of Rail Gauge Face Surface Evaluation of the Coefficient

of Friction

Figure 5.5: Dry rail condition

Figure 5.5 shows the microscopic view when rail/wheel interface without lubrication.

It is observed that wear rates increase dramatically. When two surface roughnesses

are in contact, abrasive wear occurs. This is also known as ‘Snowing’. If lubrication is

not taken seriously, coefficient of friction can reach up to 0.6, where it is considered

aggressive wear. Figure 5.6 shows the aggressive wear with coefficient of friction

approximately 0.6.

Unlubricated Wheel/Rail Interaction

� Dry Rail Condition Coefficient of friction, µ = 0.45 to 0.6

� Propagate wear at both wheel flange and rail gauge

Microscopic view of surface roughness if not separated by lubricant film thickness (boundary lubrication)

Steel particles known as ‘Snowing’ drops on the foot of the rail

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Figure 5.6: Aggressive wear (Powell and Wheatley, 2004)

Figure 5.7: Lubricated rail-wheel interface

Figure 5.7 shows the effectiveness of lubrication at rail-wheel interface. It was

analysed earlier that 1 mm2 of material loss for rail 50 kg SC is AUD $ 6.93 and

increases the lifespan of rail from 30 years to 50 years, provided that proper

maintenance of lubricators are conducted. Coefficient of friction of 0.15 to 0.2 is

desirable, not only to reduce wear but also to obtain optimum wear rate which can

also solve defects issues as well. It is important to know that lubrication does not

mean 100% benefit.

Figure 5.8: Rail with minimal wear (Powell and Wheatley, 2004)

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Figure 5.8 shows rail that has undergone minimal wear with effective lubrication and

coefficient of friction. Excessive lubrication can lead to other problems such as

lubricants wastage, environmental concern, wheel slip and traction problems.

5.4 Modelling rail wear

The rail life is determined by rail area head loss limit, which is a relative measure of

the ratio of a worn rail head to the area of a new rail head (Zhang, 2000). Clayton

(1996) concluded that general wear models are unlikely to produce the practical

benefits in the field. The existing models are restricted to particular application under

limited conditions.

Rail area head loss can be estimated using rail table (crown) wear (TW) and rail side

(gauge) wear (GW), based on current Civil Engineering Track Standards (CETS).

Then the % of reduction in area head loss (%AHL) is given by

+

=B

GW

A

TWAverageredAHL% (5.2)

where A and B are dimensions of table and side of rail. For example, wear loss for

period from j to j+1 can then be expressed as:

jj TWTW AAjjWearloss −=++1

)1,( (5.3)

Wear rate for period j due to traffic wear can be expressed as

( )j

j

jMGT

mmHLreductionAWearrate

2

= in MGTmm /2 (5.4)

It is assumed that the track is used by mixed traffic; for example, passenger, freight

and heavy hauls such as rock, ore and coal. It is also assumed that the pattern of

traffic distribution (% of each category) and the wear factor (wear rate conversion

compared to normal traffic category; for example, passenger traffic in city area) of

each category is known. Let At be the wear loss after tth period and modelled as:

ttt WNPA = (5.5)

where NPt is the total axle passes in tth period and Wt is the weighted wear rate (say

the average of 5% heavy haul, 10% freight and 85% passenger train mix) for the

period. Assuming the traffic, forecast up to the N period (which is the mean life of the

lubricator or the contract duration) is known by using forecasting techniques.

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Lubrication cost can be estimated assuming cost of lubricant (Cl) selected for

application of particular curve section (cs) of rail segment under known weather and

environmental conditions. Let Cmirs be the cost of maintenance of each lubricator. It

includes lubricator servicing, checking and filling of lubricator tanks, evaluating the

performance of lubricators and checking the blades and plungers for each lubricator.

'micsC = cost of emergency repair during the failure of ith lubricator or lubricant leak

or spilling of lubricant.

Cpics = cost of the personnel involved in maintenance of ith lubricator.

The wear loss can be analysed as a differential wear loss and given by:

Differential Wear loss (Wics ) = Total rail wear before lubrication – Loss of material

after lubrication for ith lubricator of curve section r of rail segment s. (5.6)

Where i is the index.

Cr = Cost of rail material per m per kg

Therefore, the total cost of differential wear loss for a particular curve section (r) of

rail segment (s) can be expressed as

csicsW CWTCics

∗= (5.7)

Total cost of lubrication for ith lubricator at curve section (cs) and rail segment can be

expressed as

picsmicsmicsLicsl CCCCTC +++= ' (5.8)

IficsWicsl TCTC ≤ (5.9)

then the lubrication is effective.

This is a comparison of total cost of each lubricator and total wear cost for particular

curve section (cs) and rail segment. For some places, it is difficult to compare these

costs due to different curve radius and rail size, age and condition of rail. The results

will be more appropriate if we consider average total cost of n number of lubricators

for curve section for a rail segment. Therefore, the total average cost of n number of

lubricators for curve section (cs) and rail segment can be expressed as:

∑=

=n

iicslnlcs TCTC

1

(5.10)

The total average wear cost for n lubricators of curve section (cs) and rail segment can

be expressed as:

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∑=

=n

iicsWwncs TCTC

1

(5.11)

The ratio of Equation (5.10) and (5.11) can be used to determine the percentage of

average costs of wear and lubrication for particular curve section at a rail segment

under consideration. Therefore, the ratio can be expressed as,

% of average costs = 100×wncs

nlcs

TC

TC (5.12)

The average costs can be compared to determine the effectiveness of lubrication and

differential wear costs. The ratio of these costs could be used to determine the

percentage of savings in terms of lubrication costs and also for evaluation of the

lubricator’s performance. Then the total cost of maintaining n lubricators for

particular curve section (csi) of rail segment per year can be shown as:

∑=

=n

iirsClc TT

1

(5.13)

Figure 5.9 shows the logic for a simulation model for statistical analysis, prediction,

estimation and evaluation of rail wear costs, with lubrication and without lubrication.

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Figure 5.9: Simulation model to estimate total costs due to wear

Lubrication effectiveness can be analysed using a simulation model and identifying

the influencing factors such as

� Curve radius

� Curve length

� Number of curves lubricated

� Rail material, size, profile, and hardness

� Rail wear with and without lubrication

Measuring factors for effectiveness of lubrication

� Cost savings in rail wear

� Cost of lubricator maintenance

� Effectiveness of lubricator (performance)

� Financial model for the analysis of effectiveness of lubrication

�

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5.4.1 Modelling Rail Wear Limits

Wear limit is considered as one of the main criteria for rail replacements. It monitors

and controls the risks associated with rail operation based on axle load, train speed,

rail type, Million Gross Tonne (MGT) and curve radius. Wear is the loss or

displacement of a material from a contacting surface. Material loss may be in the form

of debris. Material displacement may occur by transfer of material from one surface to

another by adhesion or by local plastic deformation.

The existing standards of wear limits are very generic and are conservative in many

situations. Conversely, in some cases, the existing limits may no longer be suitable

due to the increased traffic loads that have been introduced to existing lines. Most of

the rail wear limits specify side, table and combined wear for specific rail sizes.

However, they do not allow any significant differentiation between specific traffic and

track variables such as axle loads, track modulus and curve radii. Figure 5.10 shows

rail profile with wear limit for rail head cross sectional area section.

Figure 5.10: Wear limit for rail head cross sectional area (Larsson, 2003)

The Stockholm local network studied the lubricated and non-lubricated rails for two

different rail hardness grades (standard UIC 900A grade rail steel and the harder UIC

1100 grade rail steel) under various seasons. The study found that the contact

situation, in terms of pressure and sliding between rail and wheel, strongly influences

the wear. When the surfaces are worn, the contact situation changes due to changed

geometries. The changed geometries can lead to altered conditions regarding sliding

and pressure distribution between the surfaces. The curve radius of the track has a

strong influence on the vehicles and their behaviour. It is found that the wear rate

increases exponentially for decreasing curve radius. Sharper curves lead to increased

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track guiding forces acting on the wheels, which can lead to increased creep and,

hence, increased wear. The study shows that new rails have higher wear rate than old

rails that already have been run in. In the test, it was found that the wear rate is

approximately four times higher for new rails compared to the rails that already had

been worn, for UIC 900A grade rails. This is mainly due to alteration in the contact

geometry (Nilsson, 2005).

The Volpe Center (USA) conducted research on estimation of wear limits based on

rail strength. Rail-wear limits were assumed based on fracture strength of the internal

transverse defect (detail fracture) of the existing rail (Jeong et al., 1998). The study

shows that, for safe operation on railroad tracks, allowable rail-wear limits should be

estimated on the basis of fracture strength. The research considered only lightest rail

sections and limits for allowable wear were estimated as 1.27 cm (0.5 inch) head-

height loss or 1.52 cm (0.6 inch) gauge-face loss, under the assumption that the rail is

inspected for internal defects every 20 million gross tons (MGT). This research has

limitations for estimation of wear limits, considering accumulated MGT and axle load

for different rail size and materials and also above rail parameters. There is huge

scope for research in this area to consider the above rail parameters and different

curve radii sections.

Setting a lower wear limit for rail replacements means throwing away effective use of

life before it should be replaced; this ultimately affects the cost of maintaining

infrastructure. On the other hand, higher wear limit means additional operating life of

the rail in the track which poses higher risk of accidents/derailments. Therefore, a

trade off is required, based on rail signature for reducing operating costs and risks of

accident/derailments. CN's (Canadian National) SPC 3200 (Standard Practice

Circular) indicates that, for 100-pound (45.45 kg) rail with standard joint bars, the

vertical rail wear limit is 7 mm (¼ inch), while the sum of vertical and gauge side

lateral wear limit is 3/8 inch (10 mm). The accident in 2002 at Dartmouth Yard, Nova

Scotia, Canada, found that the combined vertical and lateral rail wear measurements

were a maximum of 14 mm (9/16 inch). The maximum vertical wear was 10 mm (3/8

inch), and was found near the point of derailment. The measurements of both the

vertical wear and the combined vertical and lateral wear exceeded SPC 3200 limits.

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When the rail wear exceeds these limits, the rail must be removed from the main

track.

The rail wear rate decreases with increase in curve radius for both high and low rails.

The wear rate ratio between non-lubricated and lubricated sites decreases for the

curves with higher radius. There is a need to analyse wear rate for the operating point

of a line to identify “good”, “acceptable with possible improvements”, or “poor”

lubrication segments. The area below (Alub) in the Figure 5.18 - the lubricated high

rail curve - is considered as a safe region where rail life is enhanced due to low wear

rate. The area above (Anon-lub) in the Figure 5.18 - the non-lubricated curve - is

considered as operating with high wear rates, where rail is required to be replaced

earlier than planned due to excessive wear. Each track segment - depending on traffic

type, tonnage, lubrication strategy, history of maintenance and weather conditions -

will operate with its own typical values. It is therefore essential to establish a finger

print and a status of the rail lubrication on each line segment. When that is done, it is

possible to compare each curve with itself or with other curves on that segment over

time. It is also possible to detect curves with a “good” lubrication and identify causes

when lubrication starts to fail. An operating value, or a Lubrication Key Performance

Indicator (LubKey), can be defined by assuming that the actual measured operating

point for a curve lies between the points A and B in the Figure 5.11, and is different

for different curves and curve radii. It varies with lubrication performance and

depends on curve radii and environmental and operating conditions.

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Figure 5.11: Traffic wear rates for high rail (Reddy, 2004)

The wear rate [mm2]/MGT can be used to measure, indicate and determine if a track

is operated close to the upper curve, f1(R), - “poor”, non-lubricated high wear scenario

- or close to the lower curve, f2(R) - “good” effective lubrication, compared to the

actual operating point. If such value is more than 1, then the rail is operated with a

high wear rate.

Let ( ) ( )( )RfRf 21 ≥ and let α (R) be the range between 1f and 2f for curve radius

R=500 m between points A and B. The operating point range, from a non-lubricated

curve of rail, is given by:

( ) ( )( )

( )Rf

RfRfR

1

21 )(−=α

(5.14)

This α is a measure of how wide the range is between the best lubricated situation and

the poorly lubricated (non-lubricated) situation. High ranges between lubricated and

non-lubricated curves, with same radii, give high α value and indicate good

possibilities of improvements in lubrication. Low α value indicates low range

between lubricated and non-lubricated curves with same radii; that is, there is a small

operational difference. However, different α values for a specific line do not indicate

if the studied line is better or worse compared to other lines. The value is an

operational indicator for curves with high wear rates, compared to other curves on the

same line. α - value can pinpoint curves not operating, as well as other simular curves

on the same line. An example of defining a LubKey-Line-Performer value is given

below.

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Let β(R) be the range between 1f and 2f for a specific curve radius R. The studied

track section or track lines operating mean point is expressed as:

( ) ( )( )2

)(21 RfRfR

+=β (5.15)

The β value is used for comparing the same type of lines with another line that

operates under similar conditions. The number of parameters involved and the

uncertainty and complexity of the wear problem, suggest that each infrastructure

player needs to develop their own best practice plots of “good” and “poor”

lubrication. Indicators such as β and α are useful tools for internal benchmarking and

continuous improvements.

A typical rail maintenance plan includes activities such as yearly preventive grinding,

rail head re-profiling and extensive rail lubrication. Maintenance supportability for

these activities can be different for different lines. For example, it can be achieved by

giving responsibility for the lubrication program to in-house or out-sourced

contractors.

There is a need to define drivers for lubrication improvements such as loss of

lubricants into the environment, long or short term asset costs, safety, noise reduction,

wear reduction and energy consumption. Figure 5.12 shows rail wear limits for

mainline track of rail type 20 kg/m.

Figure 5.12: Rail wear limits for mainline, rail type 20 kg/m (Larsson, 2005)

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The rail wear limits are: Dimension A is the Table wear in mm: Dimension B is the

Side wear in mm; and Combined Wear Dimension A’ and B’ are shown in Figure

5.19. Dimensions B and B’ are to be measured 16 mm below the original top of the

rail. When any of the linear measurements A, B, A’ or B’, or the percentage reduction

in area are exceeded, the rail is ready for replacement. Four different examples of

measurements of A and B are plotted together with the limits for rail renewal and

shown in Figure 5.19. Knowing the average traffic tonnage per month, it is now

possible to estimate the average wear rate of A and B in mm /10 MGT/month. Hence,

it is possible to estimate when the wear rate line is expected to cross the maximum

wear limit.

The maintenance and strategic planner, together with the budget and economic

strategies for the company, need budget forecast and estimate of when, in the

planning period, these replacements might occur. Instead of using the outer limit of A

and B, it is possible to use plan and budget lines for A and B. For example, if the

planning period for rail renewal is two years, one needs to find a two year forecast

limit line for A and B. Those maintenance planning limit constraints are then plotted.

When the measurements of A and B crosses that planning line, it signals the need for

renewal of this section in the next plan.

5.4.2 Modelling Rail Lubrication

Investigations in Sweden using a tribometer (by measuring friction) found that a

single wayside lubricator can cover 1-1.5 km of track (say +/- 750 from the lubricator

for bidirectional traffic). It also found that the friction is reduced up to a distance +/-

100 m from the applicator.

The failure rate on the applicator, rail wear and consumption of lubricant, are

modelled, based on time of the year, traffic volume in terms of Million Gross Tonnes,

number of axle passes and weather conditions. In this model, applicator failures are

modelled as a point process with an intensity function Λ(p), where p represents the

number of axle pass. Λ(p) is an increasing function of p, indicating that the number of

failures in a statistical sense increases with the number of axle passes. Let Fi(p)

denote the cumulative rail failure distribution for ith type of applicator modelled as

Weibull distribution, given by:

137

))(exp(1)( βλppFi −−= (5.16)

with the parameters β > 1 and λ > 0.

Then the expected number of failures over period t and (t+1) can be obtained from

failure intensity, Λ(p). Then Λ(p) is given by:

11

)())(exp(1(1

))(exp()(

)(1

)()( −

−

=−−−

−=

−=Λ β

β

ββ

λλβλ

λλλβp

p

pp

pF

pfp

i

i (5.17)

with the parameters β > 1 and λ > 0. Then the expected number of failures over

period t and (t+1) is given by:

))()(()],([ 11βββλ tttt PPPPNE −= ++ (5.18)

where Pt is the total number of axle passes up to tth period.

Modelling lubrication can be based on lubricant, application equipment (whether

wayside or on board) and lubrication strategy whether it is continuous or stop/ start

lubrication based on weather condition. Therefore, if the applicator and lubricants are

selected, there are three possibilities:

• No lubrication: the wear occurs more in sharp curves and the replacement of

rails occurs too frequently.

• Lubrication is continuous: per MGT cost of lubrication in curves is more;

however, there is no cost of switching for stop/start mechanism. There may be

environmental cost due to lubrication contaminating ground water.

• Start/ Stop Lubrication: per MGT cost of lubrication is less; it can reduce RCF

to some extent. However, there is the cost of switching stop/start mechanism

and also some risk of spalling. There may be reduced impact on environmental

damage.

)))1/(1(1/(*})1/()({1

j

j

j

y

yy

N

i

i

sjjjl rrrcYMcc +−++= ∑=

(5.19)

As already mentioned

j = 1 means lubricated

= 0 means no lubrication

In no lubrication, cost of lubrication is nil. In this case, rail replacement cost may rise.

From the field experiments, it is found that the wear rate at non-lubricated sharp

curves for 300 to 400 meters radius is ten times higher than the lubricated curves. For

curve radius 600 meters and above, the wear rate is about two to five times higher

than lubricated curves (Jendel, 2002).

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In start/stop lubrication, lubrication is effective periodically according to the

requirement. This method may have aesthetic and economic appeal but it is not a

valid option, particularly in areas with high moisture. From the field experiments, it is

found that the wear rate during the autumn, winter and spring is higher than the wear

rate during the fall. It is also found that, if the average daily precipitation is about 1.4

millimeters then the wear rate may reach to 35 - 50 mm2/MGT in dry conditions. With

the continuous lubrication it is possible to reach the wear rate between 7 to 10

mm2/MGT. Precipitation and air temperature are important parameters that influence

the rail wear rate under non-lubricated conditions. Increased precipitation reduces the

rail wear rate at non-lubricated conditions and increased air temperature increases the

wear rate. High rail temperature may cause lubrication to become more liquified and

vanish more easily from wheel-rail contact zone. It may also cause the lubrication to

dry up to reduce the effect of the lubrication.

5.4.3 Modelling Repair Cost of Applicator due to Breakdowns.

Let c be the expected cost of each repair, then cost of repair (Cs, t) for each year could

be obtained by multiplying c with the expected number of failures for any particular

year.

where Cs, t is given by:

))()(( 1,βββλ −−= ttts PPcC (5.20)

5.4.4 Modelling Replacement Cost of Applicator

Let I be the expected cost of replacement for applicator and consist of labour,

material, equipment, consumables and down time cost of replacement. This can be

estimated based on historical data.

5.4.5 Cost for various Lubricator Maintenance Strategies

• On site service: Extra time is taken due to train passing and lack of tools to

perform proper service quickly. However, there is no cost for keeping extra

lubricator. However, there is risk of down time of applicator and trains passing

during that time, causing additional wear and contamination of ballast and ground

water.

• In depot service: Efficiency and quality of service in depot reduces time and cost

of maintenance. This also reduces the risk of ballast and ground water

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contamination. However, there is a need to keep spare units for quick

replacements in the track.

Let C0 be the cost of each service on site and Cd be the cost of each service in depot

which considers the elements as mentioned above. These are random variables. Let

0C and dC be the expected cost for service on site and in depot respectively. The

number of services required is based on service interval and is estimated by

combining failure intensity of applicators, capacity of tank for lubricant and traffic

flow. Let Cm,t be the cost for service for maintenance strategy m in period t, based on

number of services ns. Then the cost for each service for a particular maintenance

strategy can be estimated by using cost per service, based on servicing strategy and

number of services.

• m = 1 maintenance and service on site

• m = 0 replacement on site and maintenance of non-conforming lubricators in

depot

5.4.6 Modelling Lubricant Cost

Let Cl be the cost of lubricant per kg and q be the amount of lubricant used in kg per

axle pass. Then cost of lubricant for the period t can be obtained by using the number

of passes based on traffic flow, quantity per pass and cost per kg.

5.4.7 Modelling Benefits of Lubricators by Reducing Rail Wear Cost

Let Ac be the critical area for replacing rail. If A0 is the area for new rail, then the

allowable wear is (A0 -Ac). Let cost to replace rail be Cre, then cost in period t due to

rail wear can be obtained, based on pro-rata life loss of rail. The difference between

lubricated and non lubricated rail is the benefit of lubrication and is given bytrebC .

Figure 5.13 shows the lubrication effect over rail life for different curve radii.

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Figure 5.13: Lubrication influencing rail life (Larsson et al., 2005)

This benefit in terms of rail life varies from lubricant to lubricant and type of

applicator.

5.4.8 COST-BENEFIT Analysis of Applicators and Various Lubricants

For no lubrication, the cost of lubrication is nil. In this case, rail replacement costs

may rise. The wear rate for non lubricated rail is higher than lubricated curves (Jendel,

2002). Wear rate for various lubricants can be estimated from laboratory tests and

field data. This can be used to calculate the cost due to rail wear.

Net Present Value (NPV) of lubrication decision in any particular curve can be given

by:

NPV = Ir

CCCCttltmts

N

ttreb −

+−−−∑

= )1(

1*)( ,,,

1

(5.21)

where r is the discounting rate.

This model is able to determine economic lubrication, lubricator and maintenance

policies based on the following variables:

i = curve segment for particular radius

j = lubrication strategy = 1 means lubricated and 0 means non-lubricated

curves

u = applicator type and make

l = lubricant type based on product and supplier

m = lubricator maintenance strategy= 1 means on site maintenance and 0

means replacement on site

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5.4.9 Failure of Lubricators

The lubricators in Scandanavia generally fail due to nozzle clogging. Static pre

pressure of the grease container causes the oil to be separated from the grease. The

graphite and soap thickener clogs the nozzle and stops the system working properly. It

then needs to be cleaned thoroughly. In Australia, during summer seasons with high

temperature, if the applicator is not used for a long time, the nozzles start clogging.

This leads to improper functioning of the lubrication system.

5.4.10 Cost for Fixing Breakdowns

It takes two persons one and a half to two hours in the Scandinavian system to clean

up wayside applicators (Clicomatic). If it is done on site, it costs AUD $480 /service

(2 personnel x 2 hours and one car for transportation). If it is done at the depot, the

cost could be different.

5.4.11 Cost to Maintain Lubricators

The cost to maintain lubricator in Scandinavia is around AUD $1200 - $2000

/year/apparatus (only six months operation of applicators per year due to no

lubrication during winter) to fill up applicators and maintain the lubricators.

5.4.12 Cost-Benefit Analysis of Lubricators

Generally, to service a lubricator, the total number of hours used at lubrication site, is

approximately 2.5. The service cost includes total vehicle cost (Cv), total travelling

cost (Ct), total repair cost (Cr) and total labour cost (CL). The service cost also

depends on the number of services (n) per year, cost per service (Csi) and unplanned

maintenance cost (Cum) resulting from failures. Then, the expected total service cost

per year (Cs) is expressed as:

( )∑=

++++=n

i

umLrtvis CCCCCCsC

1

)(* (5.22)

where unplanned maintenance cost (UMc) is expressed as:

))((1

tNECCn

i

umium ∗= ∑=

(5.23)

where i is index for unplanned maintenance for each event

n is the number of unplanned maintenance per year

Cumi is unplanned maintenance cost for each maintenance

142

E(N(t)) is expected number of failures per each service of the lubricator

Cumi

∑=

+++=n

i

Lrtvumi CCCCC

1

)( (5.24)

Then expected total maintenance cost of each lubricator per year is expressed as

∑=

++=n

i

lumsmt CCCC

1

)( (5.25)

where Cl is the cost of lubricant per year.

5.4.13 Cost of Lubricants

Cost of lubricant varies in the range of AUD $ 3.20 to AUD $ 4.80 /kg and usage of

15 kg /year per applicator in Scandinavian rail, with no lubrication during winter.

Figure 5.14: Wayside lubrication (Larsson, 2004)

As can be seen in Figure 5.14, the lubricated area shows 30% less in terms of the

lateral wear of the rail head. This means that infrastructure owners can save at least

30% in wear losses by using an appropriate lubrication and maintenance strategy

(Larsson, 2004).

5.5 Modelling Failures

A system failure (either complete or partial) is due to the failure of one or more of its

components (Blischke and Murthy, 2000). Failures over the lifetime can be modelled

either at component level or at the system level. The component level models are

sometimes appropriate for certain policies but the difficulty with these models is that

they require data at component level. Often, companies do not keep records of those

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data at component level, but system level models require aggregated data which are

usually available from the data base.

Age Policy can be followed in this case. Age Policy is used for components that

degrade with age. When the degradation is due to usage (rather than age), then this

policy is used with T representing a measure of usage.

We assume that T<t. The time required for a corrective maintenance action (replacing

a failed component by a new one) and preventive maintenance action (replacing a

non-failed component of age T by new one) are sufficiently small so that they can be

ignored. The costs of each corrective and preventive maintenance action are Cc and Cp

(<Cc), respectively.

Let iX~denote the age of Item I when it is replaced (either under preventive or

corrective maintenance). Then it is easily seen that

{ IX

TiX =~

TifX

TifX

i

i

≥

<

(5.26)

where iX is the time to failure.

Failure of each component can be modelled separately. The modelling of the first

failure needs to be treated differently from that of subsequent failures. It depends on

(i) whether the component is repairable or not, (ii) the type of rectification and (iii) the

type of component (new or used) used as replacement. MTTF of the first failure can

be modelled by a probability distribution function. Subsequent failure can be

modelled either by ordinary renewal process (when every failure results in a

replacement by a new product and the replacement times are negligible) or a delayed

renewal process or point process (when all failures are repaired with negligible repair

time and with a specified intensity function) (Blischke and Murthy, 1994). When the

rectification involves either repair or replacement by a used or cloned part, then the

modelling is more complex and can be formulated by the modified renewal process

(Kijima 1989).

Modelling first failure for one dimensional formulation – Black Box approach

Let X1 denote the usage of an item at its first failure. This is also called time to first

failure. Let F(m) and R(m) denote the cumulative distribution function and reliability

144

function (the probability that the first failure does not occur prior to x) for the first

time to failure respectively. Then f(x) is the density function for this case and is given

by

f(m) = dF(m)/dx. (5.27)

Here we have,

( ) { }mXPmF ≤= 1 and (5.28)

( ) ( ) { }mXPmFmR >=−= 11 (5.29)

The conditional probability of item failure in the interval [m, m + t], given that it has

not failed before m, is given by

( ) ( ) ( )[ ] ( )mRmFmtFmtF −+=

(5.30)

The failure rate associated with a distribution function F(m) is defined as

( )( ) ( )

( )mR

mf

t

mtFmr

t==

→0lim

(5.31)

For Exponential distribution, the density function, f(m), and failure rate, r(m), are given by

( ) ( )memf λλ −= , for 0 ≤ m < ∝, and λ > 0 (5.32)

( ) λ=mr (5.33)

where λ is the failure intensity.

For Gamma distribution, the density function and failure rate are given by

( )( )β

λ λββ

Γ=

−− memmf

1

, for 0 ≤ m < ∝, λ > 0 and β > 0 (5.34)

( ) ( )11 −

∞−−

−

= ∫m

mt dtem

tmr λ

β

(5.35)

For Weibull distribution, the distribution function and failure rate are given by

( ) ( )[ ]βλmemF −−= 1 , for 0 ≤ m < ∝, λ > 0, and β > 0 (5.36)

( ) ( ) 11

1

1 −−−

− =×

== ββ

ββ

β

ηβ

ηηβ

λβλ mxmmr

(5.37)

Renewal Process

Let us consider the renewal process for a lubricator whose lifetime is independent and

identically distributed. Generally, preventive maintenance is scheduled twice in every

145

month. For example, if there is a failure found in the lubricator, then as per the

renewal process Xi is the renewal at time i, let

S0 = 0, ∑=

=n

i

in XS1 , 1≥n

(5.38)

That is, S1 = X1 is the time of the first renewal; S2 = X1 + X2 is the renewal until the

first renewal, plus the time between the first and second renewal; that is, S2 is the time

of the second renewal. In general, Sn = denotes the time of the nth renewal. Under

these conditions, ( ){ }0,,, ≥tmtmN is a renewal process when N(m, t) represents the

number of items that failed by usage m and time t. The distribution of N(m, t) can be

obtained with the number of renewals by time t is greater than or equal to n if, and

only if, the nth renewal occurs before or at time t. That is,

( ) tSntN n ≤⇔≥ (5.39)

( ){ } ( ){ } ( ){ }1+≥−≥== ntNPntNPntNP

= { } { }tSPtSP nn ≤−≤ +1 (5.40)

We can apply an ordinary renewal process (Cox, 1962) as follows:

Let the number of renewals over the usage m [0, m), be M(m), and this is given by

( ) ( )[ ] ( ){ }∑

∞

=

==0n

mNnPmNEmM

(5.41)

where E[N(m)] is the expected number of renewals during the usage m of the item,

and n is the number of failures, and n =0, 1, 2, …….

Conditioned on X1(the time to first failure), M(m) can be expressed by

( ) ( )[ ] ( )xdFxXmNEmM ∫∞

==0 1 (5.42)

According to the renewal property, the following expression is valid:

( )[ ]( )

≤−+

⟨==

mxifxmM

mxifxXmNE

,1

,01

(5.43)

If the first failure occurs at x ≤ m, then the number of renewals over (m – x) occur

according to an identical renewal process, and hence, the expected number of

renewals over the period is M(m - x). Therefore, we have

146

( ) ( ) ( ) ( )dxxfxmMmFmML

∫ −+=0 (5.44)

where, F(m) and f(x) represent cumulative failures during usage period and

probability distribution function respectively. Therefore, the total cost over the usage

of the item is given by

( ) ( ) ( ) ( )

−+= ∫

L

ii dxxfxmMmFcmC0 (5.45)

where, ci is the cost of each failure replacement.

Let the new failure distribution be given by G(x), which is different from the failure

distribution of the new item F(x). This situation represents the delayed renewal

process (Cox, 1962).

A counting process {N(t), t ≥ 0} is a delayed renewal process if

1. N(0) = 0

2. X1, the time to first renewal, is a non negative random variable with

distribution function F(x).

3. Xj, j ≥ 2, the time interval between jth and (j-1)th repair, are independent and

identically distributed random variables with distribution function G(x), which

is different from F(x).

4. N(t) = sup{n; Sn ≤ t}, where S0 = 0 and, for n ≥ 1.

∑=

=n

j

jn XS1 (5.46)

Let Md(m) denote the expected number of renewals over the lifetime [0, m) for the

delayed renewal process. Then, in line with Ross (1970), we can rewrite the following

expressions for products sold with lifetime warranties:

( ) ( )[ ] ( )[ ] ( )xdFxXmNEmNEmML

d ∫ ===0 1 (5.47)

An expression for this can easily be obtained using the conditional expectation

approach used for obtaining M(m) for the ordinary renewal process. Conditioning on

T1, the time to first renewal, we have

( )[ ] ( )

≤−+

>==

mxifxmM

mxifxXmNE

g1

,01

(5.48)

147

where, Mg(m) is the renewal function associated with the distribution function G(m).

This follows from the fact that, if the first repair occurs at x ≤ m, then over the interval

(x, m), the repairs occur according to a renewal process with distribution G. Hence,

Md(m) is given by

( ) ( ) ( ) ( )dxxfxmMmFmML

gd −+= ∫0 (5.49) And the total cost is given by

( ) ( ) ( )

−+= ∫ dxxfxmMmFcC

L

gjj 0 (5.50) where cj is the average cost of all repairs.

5.6 Framework for Benchmarking Lubrication

The framework for benchmarking lubrication effectiveness with what-if scenario for

integrated economic lubrication strategies is shown in Figure 5.15. The model can be

used to analyse annuity costs of maintenance and replacement of different types of

lubricators.

Figure 5.15: Framework for benchmarking lubrication (Larsson, 2004)

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148

The following measures are proposed for assessing lubrication effectiveness and

improving performance:

• Relative performance model: The absolute values of effectiveness of lubrication

may not provide accurate results for assessment of lubricator performance [for

example, if lubricator is placed near 300 m, 400 m and 2000 m curve radius for

three locations]. The assessment of lubrication effectiveness of three curves is

based on rail head temperature rise and acoustic emission and tribometer

measurements. The relative performance of these curves with the same application

strategy under different operating conditions can be an appropriate measure for

the assessment of lubrication effectiveness.

• Total curve and segment model: It is important to determine the length and

radius of curve to determine the plunger adjustment and to provide adequate

lubrication along the curve.

• Above rail and below rail model: This model is to consider known wear of

rolling stock related to rail head wear and uses head wear data for assessing the

effectiveness of lubrication, considering both above rail and below rail.

5.7 Modelling Annuity Cost of Lubricators

Let P be the purchase price of lubricator and Csc be the cost of investment for each

lubricator (it includes set up cost of each lubricator), r be the discount rate assumed

for the estimation of present value of each lubricator in use.

For electric lubricator, let

=EP Purchase price of electric lubricator

=tE Electric consumption cost in time t

=EC Total cost for electric lubricators

=mtC Maintenance cost for each lubricator in time t. This includes lubricant cost,

cost for purchasing and replacing spare parts, vehicle cost, labour cost for each

lubricator.

Total cost of each lubricator investment can be estimated using the following

equations.

Cost for one electric lubricator is given by

)( mttEscE CEPCC +++= (5.51)

Therefore, the annuity cost of electric lubricator is given by

149

( )∑= +−

×+

+++=

n

iy

y

y

imttEsc

Er

r

r

CEPCC

1 )))1/(1(1(1

)( (5.52)

where r is discount rate per year

i is number of years and

n is number of maintenance periods per year and

y is expected life of lubricator in number of years.

Cost for standard way-side lubricator is given by

Cw = purchase price of lubricator + setup cost + maintenance cost

mtscww CCPC ++= (5.53)

Therefore, the annuity cost of standard way-side lubricator is given by

( )( ) ( )( )( )y

y

yn

ii

mtscww

r

r

r

CCPC

+−×

+

++= ∑

= 1/1111

(5.54)

Cost for solar lubricator is given by

Cs = purchase price of lubricator + setup cost + maintenance cost + purchase price of

solar panel and its maintenance.

spmtsscs PCPCC +++= (5.55)

Therefore, annuity of solar lubricator is given by

( )( ) ( )( )( )y

y

yn

ii

mtspssc

sr

r

r

CPPCC

+−×

+

+++= ∑

= 1/1111 (5.56)

Failure of lubricator depends on various factors which include:

� poor maintenance

� poor support from lubricator’s manufacturer

� problems with lubricator’s service

� aging of lubricators

� inefficient delivery of grease

� problems in finding correct blade and pump

� inappropriate plungers

� clogging of grease

� distribution units and

� reliability and environmental conditions.

150

5.8 Collection and Analysis of Data

Data collected from rail industry is used to analyse lubrication effectiveness, to

estimate costs and predict risks due to rail wear and lubrication. Most rail

infrastructure owners are spending millions of dollars to control rail wear and to

achieve effective rail-wheel lubrication. This has been costly and ineffective due to a

lack of preventive maintenance of lubricators, lack of technology and ad-hoc

maintenance procedures. Therefore, it is important to analyse the field data and

estimate the costs involved to predict associated risks and achieve effective

lubrication maintenance to reduce costs and maximise savings, enhance rail-wheel life

and increase safety of rail operation.

Data for sections A and B was collected from 1998 to 2004 in Australia. The curve

distribution of the corridor is shown in Figure 5.16. Table 5.4 shows traffic for

Section A to B during the period 1998 to 2004.

Curve Distribution

17%

7%

18%

22%

8%

28%

0-300m

301-450m

451-600m

601-800m

801-1500m

1501-6000m

Figure 5.16 Curve distribution for A-B corridor

Table 5.4 Traffic for Section A to B during period from 1998 to 2004

Traffic from Year 1998-2004 in A to B Corridor

Year 1998 1999 2000 2001 2002 2003 2004

Traffic (MGT) 8.576 9.233 9.101 9.586 9.438 9.496 9.478

(For detailed data see Appendix B.) Rails are the most expensive component in the railway tracks and cost approximately

AUD $ 180 per m, accounting for millions of dollars annually in the rail industry

budget. It is advantageous for rail owners to be able to identify when to replace worn

rail, not only for budgeting purposes, but also for regular maintenance of rail for safe

and reliable rail operation with increased axle loads, speed and million gross tonnes

151

(MGT) which accelerate rail wear and rail degradation, leading to rail breaks and

derailments. In this research, rail table (head) wear and rail gauge side wear are

considered to estimate area head loss (AHL) in mm2, % area head loss and wear rate.

Due to inconsistency in data, statistical distribution was used to analyse the data and

results are presented in the following sections. Figure 5.17 shows rail table wear and

side wear measurements.

Figure 5.17: Table wear and side wear measurements (Grassie, 2005)

5.8.1 Estimation of Area Head Loss (AHL)

Let A be the total area head loss allowable, A0 be the rail new area and AL be the area

head limit for rail to renewal or replacement of rail. Therefore, the total allowable area

head loss is given by

A = (A0 - AL) MGT/Year (5.57)

If i is index, then area head loss for ith period for million gross tonnes (MGT) Mi is

given by

=i

i

M

A MGT/year (5.58)

AK is the critical area head loss for remaining life = (A0 – AK)

% of error = Actual area head loss – Predicted area head loss/Actual *100

% remaining life =

−

−

L

a

AA

AA

0

0 (5.59)

% per year difference from normal distribution = µ

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152

No of years on average = µ

LK AA − (5.60)

According to international standards, rail wear can be predicted, based on statistical

studies of rail wear; that is, current wear level measured in the curve divided by the

accumulated tonnage since new.

The analysis of lubrication effectiveness performed for curve radius is in a scale of

� 0 – 300 m

� 301 – 450 m

� 451 – 600 m

� 601 – 800 m

� 801 – 1500 m

� 1501 – 6000 m

The main focus of the study is between 0-800 m curve radii. Curves below this radius

wear off significantly faster than curves with longer radii. A significant amount of

lubrication is used for these sections to control severe wear. Furthermore, this is the

main focus of rail players to reduce maintenance costs to control wear and enhance

rail life, with minimum maintenance of lubricators and rails.

5.8.2 Analysis of Wear for Curves radii 0-300 m

Data collected was investigated and extracted for analysis. Data was reliable and was

used for analysis since the results will help to predict the models and to make better

maintenance decisions which reduce costs. Data was collected between 0-6000 m

curve radius for different rail size (47, 50, 53 and 60 kg) during the years 1998 to

2004. The data is filtered with separation of curves that have no replacement over this

period. In this case, there was a reduction of 25% of overall data. This is considered

mainly due to the fact that new rail wears much less than old rails. Statistical

distribution is used to estimate area head loss for every year and wear rate, due to

inconsistency in the data. The amount of wear and rate indicated performance and

effectiveness of lubrication for particular curve in a particular period. Table 5.5 shows

a sample of the amount of area head loss per MGT for a curve radius 300 m of section

from 88.028 to 88.076.

153

Table 5.5: Area head loss (mm2/MGT) for 300 m curve (QR, 2005)

Area head loss (mm^2) for curve radius 300 m from 88.028 to 88.076 section

Wear can be estimated as follows:

� Wear (1998-1999) = (22.847 – 16.183) mm2/MGT = 6.665 mm2/MGT

� Wear (1999-2000) = (23.179 – 22.847) mm2/MGT = 0.331 mm2/MGT

� Wear (2000-2001) = (29.534 – 23.179) mm2/MGT = 6.356 mm2/MGT

� Wear (2001-2002) = (29.997 – 29.534) mm2/MGT = 0.463 mm2/MGT

� Wear (2002-2003) = (36.829 – 29.997) mm2/MGT = 6.832 mm2/MGT

� Wear (2003-2004) = (36.889 – 36.829) mm2/MGT = 0.070 mm2/MGT

Wear (mm^2/MGT) for curves radii 0-300 m

-30

-20

-10

0

10

20

30

0 5 10 15 20 25 30

Curve Section

Wear (m

m^2/MGT)

1998-99

1999-00

2000-01

Figure 5.18: Wear for curves radii 0-300 m from 1998-2001

Wear data collected and analysed as shown in Figure 5.18. The data lies between ± 30

mm^2/MGT. The positive (+ve) values show the rate of increase of wear every year,

with accumulated tonnage at different sections. The negative (-ve) values show the

rate of decrease of wear every year. Analysis found that:

� Decrease of wear is mainly due to better performance of lubricators at some

sections of curve radii

� Measurement error in estimation of area head loss has significant influence in

determining the wear rate and performance of lubricators

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154

� Accurate results can be obtained by comparing analysis of data for mixed

traffic under various operating and environmental conditions

Figure 5.19 shows the wear data analysis for curve radii 0-300 m from year 2001 to

2004. The analysis shows the increase of area head loss in 2001 to 2004 compared to

area head loss during 1998-2001. However, there is only a small percentage of

increase of wear during this period. This may be due to the effectiveness of

lubrication or replacement of new rail.

Wear (mm^2/MGT) for curve radii 0-300 m

-30

-20

-10

0

10

20

30

0 5 10 15 20 25 30

Curve Section

Wear (m

m^2/MGT)

2001-02

2002-03

2003-04


Wear data for curve radius 0 to 300 m were further analysed. Figure 5.20 shows wear

for various curves radii between 0-300 m for accumulated MGT.

Rail Wear (mm^2/MGT)

0

20

40

60

80

100

8.576 9.233 9.101 9.586 9.438 9.496 9.478

MGT

Wear (m

m^2/MGT)

194.9

231

256

300

Figure 5.20: Rail wear for four different curves

155

It is observed that wear has increased constantly with accumulated MGT. It shows

that wear for curves radii 300 and 194.9 m is higher, compared to curves with radii

231 and 256 m. For curves 231 and 256 m, wear has increased for the first few years

and then stable for all other years; however, for curves 300 and 194.9 m, wear has

been increasing continuously. This shows that the effectiveness of lubrication is better

at curves radii 231 and 256 m, compared to curves with radii 300 and 194.9 m

respectively.

Data is analysed for the better prediction and estimation of wear rate for various

curves. Weibull and Gamma distributions have been explored for analysis and R-

square and Root mean square error (RMSE) were not acceptable. Due to the variation

in the data, curve fitting methods and Gaussian (Normal) distribution have been

applied for better accuracy of results. Figure 5.21 shows a sample of curve fitting of

actual and predicted data for accumulated MGT of a 300 m curve radius for a

particular location (Section 88.028 to 88.076).

0 20 40 60 80 100 1200

20

40

60

80

100

120

140

160

180

Fit w

ith 9

5%

pre

d b

ounds

Analysis of fit "fit 1" for dataset "ahl8 vs. mgt"

fit 1

95% prediction bounds

ahl8 vs. mgt

Figure 5.21: Curve fitting analysis for curve radius 300 m

The analysis found that general Gaussian (Normal) distribution is best suited to fit this

continuous data.

( ) ( )( ) ( )( )( )22 2/2exp*21/1exp*1 cbxacbxaxf −−+−−= (5.61)

where x is normalized by mean 44.47 and standard deviation 39.46

Coefficients (with 95% confidence bounds):

MGT

156

a1 = -7247 (-1.398e+009, 1.398e+009)

b1 = 1.602 (-1425, 1429)

c1 = 1.749 (-1489, 1492)

a2 = 7386 (-1.398e+009, 1.398e+009)

b2 = 1.617 (-1448, 1451)

c2 = 1.765 (-1498, 1501)

Goodness of fit: Sum of Squared Errors (SSE): 443.4, R-square: 0.9865 Adjusted R-

square: 0.9813, (Root Mean Square Error) RMSE: 5.84. Analysis found that R2 is

closer to 1 which indicates the best fit. These results were further analysed using a

distribution fitting tool to find out mean, variance and standard deviation for better

prediction of the wear rate. Data is best fitted with Gaussian (Normal) distribution and

results shown in Figure 5.22.

2 4 6 8 10 12 140

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

Data

Density

ahl9 data

fit 1

Figure 5.22: Gaussian distribution of the RMSE for 0-300 m curves

Therefore Mean of RMSE = 6.58104, Variance: 8.56982, Standard Deviation =

2.92743. Analysis shows that Mean of RMSE is considered as wear rate for

estimation of rail life and to analyse lubrication effectiveness. For 0 to 300 m curve

radii for accumulated MGT is 6.58 mm2/ MGT.

Estimation of rail life is as follows: CETS limit for 47 kg rail size = 684 mm2

Measurement of area head loss for a curve section 63.920 to 63.945 for a radius 300

m in year 2004 = 390 mm2

Wear rate = 6.58 mm2/MGT

Estimated actual rail life = 684 mm2/ 6.58 mm2/MGT = 104 MGT

157

Estimated rail life left = (684-390) mm2/ 6.58 mm2/MGT = 45 MGT

The analysis of comparison of area head loss (mm2) for 47 kg rail is shown in Figure

5.23. The analysis shows that, continuous increase of wear for 220 m and 300 m.

Area Head Loss (mm^2) for 47 kg rail from 0-300 m

0

200

400

600

800

1998(8.576)

1999(9.233)

2000(9.101)

2001(9.586)

2002(9.438)

2003(9.496)

2004(9.478)

Year(MGT)

Area Head Loss (mm^2)

300 (RS1)

300 (RS2)

Wear Limit

220

Figure 5.23: Area head loss comparison for 47 kg rail

The wear rates for curves radii 300 m at different locations are analysed and

compared in the Figure 5.23. Wear is higher for curve radius 300 m of rail segment 1

(RS1), compared to that for curve radius 300 m of rail segment 2 (RS2) at different

locations. Analysis found that effective lubrication at the RS2 has significantly

reduced wear compared to RS1. This is due to poor performance and maintenance of

lubricators in the RS1 section.

The analysis shows that, according to the CETS standard, the estimated rail life for 47

kg size rail is approximately 104 MGT. Analysis shows that, for the section 63.920 to

63.945 of curve radius 300 m, the rail life left after 2004 is 45 MGT. It is found in the

investigation of actual data and predicted data, rail has 4 years life left, if on an

average 10 MGT every year. This may change with effectiveness of lubrication and

traffic density and operating conditions.


m in year 2004 = 733 mm2

Wear rate in 5 years from 2000 to 2004 is 31 mm2/ MGT.

CETS limit for 50 kg rail size = 866 mm2

Estimated actual rail life = 866 mm2/ 31 mm2/MGT = 28 MGT

Estimated rail life left = (866-733) mm2/ 31 mm2/MGT = 4 MGT

158

Area Head Loss (mm^2) for 50kg rail curves radii 0-300 m

0

150

300

450

600

750

900

1998(8.576)

1999(9.233)

2000(9.101)

2001(9.586)

2002(9.438)

2003(9.496)

2004(9.478)

Year(MGT)


195

241

300

300

Wear Limit

Figure 5.24: Area head loss comparison for 50 kg


5.24. This shows that, according to the CETS standard, estimated new rail life for 50

kg size rail is approximately 28 MGT. Analysis shows that, for the curve radius 300

m, the rail life left over after 2004 is 4 MGT. It is found in the investigation of actual

data and predicted data, that rail needs to be replaced immediately. It shows poor

performance of lubrication in this section. Rail condition may be improved with

improved effectiveness of lubrication and operating conditions (which are more

economical than replacing with new rail), but it has involved higher risk of rail breaks

or derailments. Figure 5.25 shows that the wear of section 87.641 to 88.020 is 5 times

higher, compared to the section 63.920 to 63.945 for same curve radius 300 m in the

last five years.

Wear (mm^2/MGT) for 300 m

0

10

20

30

40

1998-2002 1999-2003 2000-2004

Year

Wear (mm^2/MGT)

Wear at 63.920-63.945

Wear at 87.641-88.020

Figure 5.25: Wear for curve radius 300 m

159

The analysis of lubrication effectiveness needs to be carried out for accurate

prediction and estimation of rail life, to reduce and prevent risk of rail breaks and

derailments. Figure 5.26 shows the analysis of wear for a section from 93.341 to

93.596 of curve radius 245 m. A considerable decrease of wear is observed in this

section. For years 2000 to 2004, wear has decreased approximately at 15 (mm2/MGT)

per year. This shows that lubrication performance is effective and has extended rail

life in this section.

Wear (mm^2/MGT) for 245 m

-20

-10

0

10

20

1998-2002 1999-2003 2000-2004

Years

Wear (mm̂2/MGT)

Wear for 93.341-93.596

Figure 5.26: Wear for curve radius 245 m


Collected data was analysed for curves radii 301-450 m for different locations. Figure

5.27 shows the wear for curves radii of 301-450 m. It is observed that scattered wear

data has fallen between ±30 mm2/MGT. Analysis shows that wear rate of increase

(that is, +ve values) is higher than the wear rate of decrease (that is, –ve values). This

may be an indication of poor performance and effectiveness of lubrication in these

sections.

Wear (mm^2/MGT) for curves radii 301-450 meters

-30

-20

-10

0

10

20

30

0 5 10 15 20 25 30 35 40

Curve Section

Wear (mm^2/MGT)

1998-99

1999-00

2000-01


160

Figure 5.28 shows the wear for curves radii of 301-450 m from year 2001-2004. It is

observed that scattered wear data has fallen between ±30 mm2/MGT. Analysis shows

that wear rate of increase (that is, +ve values) is higher than the wear rate of decrease

(that is, –ve values). It also shows that wear has increased at a slower rate and is close

to X-axis. This may indicate good performance and effectiveness of lubrication in

these sections.

Wear (mm^2/MGT) for curves radii 301-450 meters

-30

-20

-10

0

10

20

30

0 5 10 15 20 25 30 35 40

Curve Section

Wear (mm^2/MGT)

2001-02

2002-03

2003-04


Figure 5.29 shows that rail wear has increased constantly with accumulated MGT. It

shows that wear for curves radii 400 and 388 m is higher, compared to curves with

radii 320 and 425 m. Analysis shows that wear has decreased for both curves after

first 8.576 MGT, and then wear rate has increased constantly at a slower rate.

Rail Wear (mm^2/MGT)

0

20

40

60

80

8.576 9.233 9.101 9.586 9.438 9.496 9.478

MGT

Wear (m

m^2/M

GT)

320

388

400

425

Figure 5.29: Rail wear for different radii for accumulated MGT

161

Analysis shows the effectiveness of lubrication is better for curves with radii 320 and

425 m. Further data is analysed for all the section between curves of radius 301 to 450

m, using the Gaussian (Normal) distribution for better and accurate prediction of wear

rate and to estimate rail life. Curve fitting tools have been used to find R2 and RMSE

for curves radius 301 to 450 m. Figure 5.30 shows a sample of curve fitting for actual

and predicted data for accumulated MGT of a curve radius 415 m for a particular

location (Section 135.283 to 135.512).

0 20 40 60 80 100 12055

60

65

70

75

80

85

90

95

Fit w

ith 9

5%

pre

d b

ounds


fit 1


ahl8 vs. mgt

Figure 5.30: Curve fitting for curve radius 415 m

Data is best fitted with Normal (Gaussian) distribution

( ) ( )( ) ( )( )( )22 2/2exp*21/1exp*1 cbxacbxaxf −−+−−= where x is normalized by

mean 44.47 and standard deviation 39.46

Coefficients (with 95% confidence bounds):

a1 = 101.3 (-336.4, 539.1)

b1 = 4.594 (-65.05, 74.24)

c1 = 7.006 (-72.7, 86.71)

a2 = 9.834 (-121.8, 141.5)

b2 = -0.6955 (-4.211, 2.82)

c2 = 0.8351 (-4.239, 5.909)

Goodness of fit: Sum of Squared Errors (SSE): 104.1, R2: 0.9139, Adjusted R2:

0.8808, Root Mean Square Error (RMSE): 2.83.

MGT

162

These results were further analysed using the distribution fitting tool to find out mean,

variance and standard deviation for better prediction of the wear rate. Data is best

fitted with Gaussian (Normal) distribution and results shown in Figure 5.31.

0 5 10 15 20 25 300

0.05

0.1

0.15

Data

Density

q data

fit 1

Figure 5.31: Gaussian distribution of the RMSE for curve radii 301-450 m

Therefore Mean of RMSE 8.37691, Variance is 29.9521, Standard Deviation is

5.47285

Mean of RMSE is considered as wear rate for estimation of rail life and to analyse

lubrication effectiveness. For 301 to 450 m curve radii, accumulated MGT is 8.38

mm2/ MGT.

Estimation of rail life is as follows:


Measurement of area head loss for a particular curve section 101.424 to 101.671, for a

radius 410 m in year 2004 = 733 mm2

Wear rate = 8.38 mm2/ MGT



The analysis of comparison of area head loss (mm2) for different rail curve sections is

shown in Figure 5.32.

163

Area Head Loss (mm^2) for 50kg Rail

0

150

300

450

600

750

900

1998(8.576)

1999(9.233)

2000(9.101)

2001(9.586)

2002(9.438)

2003(9.496)

2004(9.478)

Year(MGT)


301.3

345

400.2

410

Wear Limit

Figure 5.32: Area head loss for 50 kg rail

This shows that, according to the CETS standard, actual estimated rail life for 50 kg

size rail between 301-450 m curve radius is approximately 103 MGT. Analysis shows

that, for the section 101.424 to 101.671 of curve radius 410 m, the rail life left after

2004 is 16 MGT. It is found in the investigation of actual data and predicted data that

rail has only 2 years life left, if on an average 8 MGT every year. This may indicate

changes with effectiveness of lubrication and traffic density and operating conditions.


m in year 2004, is 693 mm2. From the actual data, wear rate in 5 years from 2000 to

2004, is 12 mm2/ MGT. CETS limit for 47 kg rail size = 684 mm2

Estimated actual rail life = 684 mm2/ 12 mm2/MGT = 57 MGT

Estimated rail life left = (684-693) mm2/ 12 mm2/MGT = -0.75 MGT

Results show that rail wear has reached critical wear limit. Immediate replacement or

repair of rail is essential to avoid rail break or derailment.

Area Head Loss (mm^2) for 47kg Rail

0

200

400

600

800

1998(8.576)

1999(9.233)

2000(9.101)

2001(9.586)

2002(9.438)

2003(9.496)

2004(9.478)

Year(MGT)


303

320

400

415

Wear Limit


164




98.775 of curve radius 400 m, the rail should be replaced immediately. Figure 5.33

shows that it has crossed the wear limit and there is a high risk of rail break or

derailment involved. It shows poor performance of lubrication in this section. Rail

condition can be improved with effectiveness of lubrication and operating conditions.

It is more economical to replace with new rail, rather than overhauling old rail and

increasing risk of rail break and derailments.


Collected data was analysed for curves radii 451 to 600 m in different locations.

Figure 5.34 shows the wear for curves radii of 451-600 m. It is observed that scattered

wear data has fallen between ±30 mm2/MGT. Analysis shows that wear rate of

increase (i.e. +ve values) is higher than the wear rate of decrease (i.e –ve values). This

may be an indication of poor performance and effectiveness of lubrication in these

sections.

Wear (mm^2/MGT) for 451-600 m from 1998-01

-30

-20

-10

0

10

20

30

0 5 10 15 20 25 30 35

Curve Section

Wear (m

m^2/M

GT)

1998-99

1999-00

2000-01

Figure 5.34: Wear data for curves radii 451-600 m from 1998-2001

Figure 5.35 shows the wear for curves radii of 301-450 m, from year 2001-2004. It is

observed that scattered wear data has fallen between +30 and -10 mm2/MGT.

Analysis shows that wear rate of increase (i.e. +ve values) is higher than the wear rate

of decrease (i.e –ve values).

165

Wear (mm^2/MGT) for 451-600 m from 2001-04

-30

-20

-10

0

10

20

30

0 5 10 15 20 25 30 35

Curve Section

Wear (m

m^2/M

GT)

2001-02

2002-03

2003-04

Figure 5.35: Wear data for curves radii 451-600 m from 2001-2004

It also shows that wear has increased at a slower rate and most of the data fell close to

X-axis. This may be an indication of good performance and effectiveness of

lubrication in these sections. Figure 5.36 shows that rail wear has increased constantly

with accumulated MGT. It shows that wear for curves radii 600.2 and 500 m is

higher, compared to curves with radii 465.5 and 550 m. Analysis shows that wear has

decreased for 465.5 m curve after the first 8.576 MGT, then increased constantly at a

slower rate, and suddenly increased in the last accumulated MGT. This shows the

effectiveness of lubrication is better for curves with radii 550 and 465.5 m

respectively.

Rail Wear (mm^2/MGT) for accumulated MGT

0

20

40

60

80

8.576 9.233 9.101 9.586 9.438 9.496 9.478

MGT

Wear (mm

2̂/MGT)

465.5

500

550

600.2

Figure 5.36: Rail wear for curves with different radii

Further data is analysed for all the section between curves of radius 451 to 600 m,

using the Gaussian (Normal) distribution for better and accurate prediction of wear

rate and to estimate rail life. Curve fitting tools have been used to find our R2 and

166

RMSE for curves radius 451 to 600 m. Figure 5.37 shows a sample of curve fitting

analysis of actual and predicted data for accumulated MGT of a curve radius 500 m

for a particular location.

0 20 40 60 80 100 1200

50

100

150

200

250

300

Fit w

ith 9

5%

pre

d b

ounds


fit 1


ahl8 vs. mgt

Figure 5.37: Curve fitting for curve radius 500 m

Data is best fitted with Normal (Gaussian) distribution (Gauss2)

( ) ( )( ) ( )( )( )22 2/2exp*21/1exp*1 cbxacbxaxf −−+−−= where x is normalized by

mean 44.47 and std 39.46, Coefficients (with 95% confidence bounds):

a1 = 391 (-2922, 3704)

b1 = 3.332 (-29.04, 35.7)

c1 = 2.213 (-32.5, 36.93)

a2 = 20.85 (-1591, 1632)

b2 = 0.2542 (-21.21, 21.72)

c2 = 1.265 (-20.41, 22.94)

Goodness of fit: SSE: 323.8, R2: 0.9971, Adjusted R2: 0.996, Root Mean Square Error

(RMSE) 4.991. These results were further analysed using the distribution fitting tool

to find mean, variance and standard deviation for better prediction of the wear rate.

Data is best fitted with Gaussian (Normal) distribution and results are shown in Figure

5.38.

MGT

167

0 2 4 6 8 10 12 14 16 180

0.02

0.04

0.06

0.08

0.1

0.12

Data

Density

q data

fit 1

Figure 5.38: Gaussian distribution of the RMSE for curves radii 451-600 m

Therefore Mean of RMSE = 5.49596, Variance = 9.58875, Standard Deviation =

3.09657

Mean of RMSE is considered as wear rate for estimation of rail life and to analyse

lubrication effectiveness. For 451-600 m curve radii for accumulated MGT is 5.50

mm2/ MGT.

Estimation of rail life is as follows:


Measurement of area head loss for a particular curve section 66.265 to 67.004 for a

radius 600.20 m in year 2004 = 693 mm2

Wear rate = 5.50 mm2/MGT


Estimated rail life left = (684-693) mm2/ 5.50 mm2/MGT = -1.63 MGT

168

Area Head Loss (mm^2) for 47 kg Rail

0

150

300

450

600

750

1998(8.576)

1999(9.233)

2000(9.101)

2001(9.586)

2002(9.438)

2003(9.496)

2004(9.478)

Year(MGT)


506.5

553.2

600.2

Wear Limit

Figure 5.39: Area head loss for 47 kg




67.004 of curve radius 600.20 m, the rail should be replaced immediately. Figure 5.24

shows it has crossed the wear limit and there is a high risk of rail break and

derailment involved. It shows poor performance and effectiveness of lubrication in

this section. It is also found that wear rate is constant for curve radius 553.2 m. This

may be an indication of good performance of lubrication in this section. For the curve

radius 506.50 m, wear rate has been increasing constantly, but at slower rate. Rail

condition can be improved with effectiveness of lubrication and operating conditions.

It is more economical to replace with new rail rather than overhauling old rail and

increasing risk of rail break and derailments.


Measurement of area head loss for a particular curve section 89.648 to 89.819 for a

radius 500 m in year 2004 = 638 mm2

Wear rate for last five year (2001-2004) = 16.73 mm2/MGT



Analysis shows that, for the section 89.648 to 89.819 of curve radius 500 m, the rail

should be replaced immediately. Figure 5.38 shows it is close to wear limit and can

tolerate one more year with an average of 10 MGT under effective lubrication

performance and suitable operating conditions. It is more economical to replace with

169

new rail rather than overhauling old rail and increasing risk of rail break and

derailments.


Estimated actual rail life for 50 kg rail = 866 mm2/ 5.50 mm2/MGT = 157 MGT

Area Head Loss (mm^2) for 50 kg Rail

0

150

300

450

600

750

900

1998(8.576)

1999(9.233)

2000(9.101)

2001(9.586)

2002(9.438)

2003(9.496)

2004(9.478)

Year(MGT)

Area Head Loss (mm̂

2)

500

550

597

Wear Limit


Figure 5.40 shows the analysis of comparison of area head loss (mm2) for 50 kg rail

of different rail curve sections. According to the CETS standard, actual estimated rail

life for 50 kg size rail between 451-600 m curve radius is approximately 157 MGT. It

was found in the investigation that wear of actual and predicted data of rail curve with

radius 597 m is constant for an accumulated MGT. This may be due to superior

performance and effectiveness of lubrication in this section. For the curves radii 500

and 550 m, wear has constantly increasing with accumulated MGT. This may be due

to poor performance and effectiveness of lubrication. Rail life improved in these

sections with continuous monitoring of lubricator performance and rail condition

under effective operating conditions.

Area Head Loss (mm^2) for 500 m Radius

0

150

300

450

600

750

900

1998(8.576)

1999(9.233)

2000(9.101)

2001(9.586)

2002(9.438)

2003(9.496)

2004(9.478)

Year(MGT)


47 kg rail

50 kg rail

Wear limit 47 kg rail

Wear limit 50 kg rail

Figure 5.41: Area head loss curve radius 500 m

170

Figure 5.41 shows the analysis of area head loss of 500 m curve radius for different

rail size of 47 and 50 kg. It is observed that, in both rail size 47 and 50 kg, rail wear

has been constantly increasing at a lower rate and is significantly below the wear

limit. This shows that there is high quality of lubrication performance in these

sections. It was found in the recent research that rail degradation or loss of rail

material increases risk of rail breaks and derailments. This, in turn, increases cost of

rail maintenance to rail infrastructure owners. However, it is important to study and

understand the severity of damage and measure the risk due to these defects before

planning maintenance schedules. These defects may lead to increased rail and wheel

repair costs and increased risk of rail breaks and derailments. Reduction of rail side

and table wear with effective performance of lubrication and preventive grinding

maintenance methods, extends rail life. It is found that, with proper lubrication, it

would take at least two years to remove the amount of rail material that is removed in

one week of dry running (Kalousek, 1997). Excessive grinding maintenance intervals

reduce rail life and increase rail maintenance costs. It is important to achieve proper

effective lubrication strategies with optimal grinding intervals to reduce maintenance

cost and annual rail replacement costs, to enhance rail and wheel life and increase

safety of rail operation.

5.9 Analysis of Annuity Costs

Data was collected from survey and field observations to estimate the maintenance

cost of lubricator and rail wear costs. In this case, the cost and analysis is calculated

for wayside lubricators. Discounting factor is used, assuming 10% per year. Table 5.6

shows the costs of wayside lubricator.

171

Table 5.6: Costs of Wayside Lubricator

Item Cost (AUD $)

Purchase cost of Standard Wayside

Lubricator (37.5 kg)

AUD $ 4200

Solar Lubricator (including the overhead

cost and installing, excluding 2 solar

panels)

AUD$ 15968.50

Standard setup cost (labour cost) per hour AUD $ 50

Standard hours to set up lubricator 2 hours

Personnel required to set up lubricator 2

Grease per drum (One drum of lubricant

for a month is expected to lubricate

approximately 1600 m of track length.)

AUD $ 132.85

Lubricant cost per m (AUD$ 132.85/1600

m)

AUD$ 0.08303

Lubricant cost for 313 m track curve

length

AUD$ 25.98

Lubricant cost for 313 m track curve

length per year

311.86/year

Lubricant cost per kg AUD $ 4.5

Labour cost per hour for unplanned

maintenance

AUD $ 50

Vehicle cost per hour for unplanned

maintenance of lubricator

AUD $ 45

(For detailed data see Appendix B.) Activities involved and approximate time required to maintain lubricators are:

� Adjusting plunger/remove plunger (0.6 hours)

� Removing or positioning lubricator (2 Hours)

� Filling (0.6 hours)

� Tightening & retightening plunger (0.6 hours – 0.75 hours )

� Removing servicing pump & cleaning filter, nozzles (2 Hours)

� Travelling (Average 0.3125 hours for single way; total time is 0.625)

172

Generally, rail life of up to 10 years can be expected with effective lubrication and

proper maintenance. Worn-out rails are replaced at shorter intervals - approximately 5

to 6 years in sharp curves - due to lack of proper lubrication and maintenance. For

example, some sections of London Underground Rail have been replaced every 18

months instead of 18 years, even though lubricators are working properly

(Briginshaw, 2004). Effective lubrication can extend rail life up to 50% under optimal

operating conditions (Tuzik, 1996). Effective wayside and/or hi-rail lubrication

reduces gauge face wear substantially. Table 5.7 gives estimated rail life in heavy

haul, straight, and curved track (Cannon et al., 2003).

Table 5.7: Estimated rail lives in heavy-haul track (Cannon et al., 2003)

Curve Radius

Estimated rail life (MGT traffic)

Generally removal and installation of rails is costly and influenced by:

� Rail cost escalation rate (% per annum)

� Maintenance cost escalation rate (% per annum)

� Non –inflated discount rate (% per annum)

� Inflation rate (% per annum)

� Track maintenance cost ($AUD per track km)

� Track Grinding Cost ($AUD per track km)

� Rail Installation Cost ($AUD per rail km)

� Risk Cost/MGT/m ($ AUD)

� Down time cost/m ($AUD)

Data from industry show that

60 kg Rail for 110 m (HH) -----------------------------------AUD $7805.40

50 kg Rail for 110 m (SC) ----------------------------------- AUD $6592.40

Cost for installing or removing rail is approximately = AUD $ 175 per m

halla


173

5.9.1 Numerical Example

Analysis of Standard Wayside Lubricator

Time to travel from depot to site and time to service the wayside lubricator = 2.3

hours. Curve radius of 236.7 m of a 50 kg rail (SC) for curve length of 313 m for

passenger traffic is considered for estimation of rail costs and benefits, with

lubrication and without lubrication.

Costs with Lubrication

50 kg Rail (SC) for one m = (6592.40/110) = AUD $ 60 per m

Cost for 313 m curve length of rail = (60*313) = AUD $ 18780

To install or remove rail for 313 m of curve length of 50 kg SC rail = (175*313) =

AUD $ 54775. Therefore, total cost of rail for 313 m of rail curve length =

(18780+54775) = AUD $ 73555. Then, the annuity cost of rail for 313 m rail curve

length for 10 years = AUD $ 66868.18. The annuity cost per m for rail = AUD $

213.64

Generally, lubricator maintenance takes place twice a month. Then, the total cost per

service = AUD $ 267.

The total unplanned maintenance cost per each failure = AUD $ 190

Total expected cost of service per year Cs = AUD $ 3202

Total standard setup cost Csc = AUD $ 400

Estimation of total cost of lubrication for 7 years = Investment of a lubricator +

Maintenance cost of lubricator + Lubricant consumption

Using equation 5.55, the annuity cost of lubricator to lubricate 313 m of rail section =

AUD $ 5665

Then, the annuity cost per m for 313 m curve length = AUD $ 18.10

Then, total annuity cost of rail with lubrication per m = (213.64+18.10) = AUD $

231.74

Costs without Lubrication

It is assumed that rail life without lubrication is 5 years and needs immediate

replacement. Total cost to replace 313 m of curve length of 50 kg SC rail for 5 years =

(18780+54775) = AUD $ 73555. Figure 5.42 shows analysis of lubrication and rail

replacement costs.

174

Figure 5.42: Analysis of lubrication costs

The annuity of rail without lubrication for 313 m of curve length of 50 kg SC rail for

10 years = AUD $ 99240.34

The annuity cost rail per m without lubrication for 313 m curve length of 50 kg SC =

AUD $ 317.06

The savings per m for rail of curve length 313 m of curve radius 236.7 m of 50 kg SC

with and without lubrication = AUD $ ( 317.06 – 231.74) = AUD $ 85.32 per m.

There is a huge difference between the costs of rail with lubrication and without

lubrication. The analysis shows that lubricating rails below 500 m curve radius

throughout the year can reduce rail replacement costs. It is also found that rail

replacement cost is much higher without lubrication and it affects the total rail

maintenance costs and also wheel maintenance costs.

Analysis of Solar Wayside Lubricator

Time to travel from depot to site and time to service the solar lubricator = one hour.

Analysis of solar wayside lubricator for curve radius of 236.7 m of a 50 kg rail (SC)

for curve length of 313 m for passenger traffic is considered for estimation of rail

costs and benefits with lubrication and without lubrication.

Costs with Lubrication

50 kg Rail (SC) for one m = (6592.40/110) = AUD $ 60 per m

Cost for 313 m curve length of rail = (60*313) = AUD $ 18780

Wear rate [mm2/MGT]

300 600 900 1200

Bad lubrication, un-lubricated

Good lubrication, lubricated

Increased rail life – saving costs

Investm

ent in lubrication (AUD$)

73555

147110

220665

275831

Wear rate [mm2/MGT]

300 600 900 1200

Bad lubrication, un-lubricated

Good lubrication, lubricated

Increased rail life – saving costs

Investm

ent in lubrication (AUD$)

73555

147110

220665

275831

175

To install or remove rail for 313 m of curve length of 50 kg SC rail = (175*313) =

AUD $ 54775. Therefore, total cost of rail for 313 m of rail curve length =

(18780+54775) = AUD $ 73555. Then, the annuity cost of rail for 313 m rail curve

length for 10 years = AUD $ 66868.18. The annuity cost per m for rail = AUD $

213.64

Generally, lubricator maintenance takes place twice a month. Then, the total expected

cost of service = AUD $ 145

The total unplanned maintenance cost per each failure = AUD $ 190

Total expected cost of service per year Cs = AUD $ 1740

Total standard setup cost Csc = AUD $ 400

Estimation of total cost of lubrication for 7 years = Investment of a lubricator +

Maintenance cost of lubricator + Lubricant consumption

Using equation 5.55, the annuity cost of lubricator to lubricate 313 m of rail section =

AUD $ 3429.47

Then, the annuity cost per m for 313 m curve length = AUD $ 10.96

Then, total annuity cost of rail with lubrication per m = (213.64+10.96) = AUD $ 224.

60.

Costs without Lubrication

It is assumed that rail life without lubrication is 5 years and needs immediate

replacement. Total cost to replace 313 m of curve length of 50 kg SC rail for 5 years =

(18780+54775) = AUD $ 73555.

The annuity of rail without lubrication for 313 m of curve length of 50 kg SC rail for

10 years = AUD $ 9240.34

The annuity cost rail per m without lubrication for 313 m curve length of 50 kg SC =

AUD $ 317.06

The savings per m for rail of curve length 313 m of curve radius 236.7 m of 50 kg SC

with and without lubrication = AUD $ ( 317.06 – 224.60 ) = AUD $ 92.46 per m. The

analysis shows more savings with solar lubricator than standard wayside lubricator.

This may vary with number of failures and operating and environmental conditions.

Is lubrication cheaper than wear?

It is important to determine the cost of area head loss of the rail to assist the track

practitioner to measure annual budget costs.

176

For 50 kg rail SC, the percentage of area head loss allowable is 32 % (or 866

mm2)from the total area of head which is 2680 mm2. It is mentioned that the cost to

purchase 50 kg Standard Carbon rail of 110 m length is AUD $6592.40. In this case,

curve radius length and size affected the cost of area head wear. Figure 5.43 shows

wear progression for curve radius 236.7 m, from 1997 to 2004.

Area Head Loss for curve radius 236.7 meter (97 - 04)

0

150

300

450

600

750

900

1997 1998 1999 2000 2001 2002 2003 2004

Year (MGT)


Limit of Rail Head Wear 857.6 mm 2̂ 50 kg SC

Figure 5.43: Wear progression for curve radius 236.7 m from 1997-2004

Civil Engineering Track Standard (CETS) noted that 50 kg SC rail was allowed to

wear 32% of total area head (2680 mm2), which is 866 mm2. That is:

% Reduction Area Head Loss x Cost Rail Length = 32% x 18777.00 = AUD $6008.64

Total Area Head Loss for 50 kg SC rail (866 mm2) is AUD$ 6008.64

Cost of Area Loss per mm2 = AUD $ 6008.64 ÷ 866 mm2 = AUD $6.93/ mm2

Figure 5.50 shows that there is 2% of increment in area head loss for an average of

7.9 MGT per year. Then, 2% of total area head loss of 50 kg SC 313 m length = 0.02

x 2680 = 53.6 mm2

Therefore, the total cost of losing 53.6 mm2 = 53.6 mm2 x AUD $6.93/ mm2 = AUD

$371.448. The cost for accumulated area head loss for 7 years = AUD$ 371.448 x 7

= AUD $2600.136

Therefore, savings can be calculated by subtracting Total Area Head Loss for 50 kg

SC rail (866mm2) is AUD$ 6008.64 to Total Area Head Loss for 50 kg SC rail in 7

years (AUD $2600.136) which is AUD $ 3408.504. The analysis found that the

annuity cost of 37.5 kg standard wayside lubricator is AUD $ 10562.98 for the curve

radius of 236.7 m radius. According to the CETS standards, the curve is only allowed

to wear at 32% from the total area head which is 866 mm2. The total cost of 32% wear

177

limit is AUD $6008.64 for that curve length of 313m. However, questions arise from

this analysis:

� Can savings be made if the wayside lubricator could lubricate more than one

curve?

� What is the distance the grease travels and what is the cause of this mobility?

� How does the wheel profile affect the savings?

� Can maintenance of the lubricators ensure savings?

For solar lubricator, savings can be achieved if the lubricator can lubricate more than

3 curves. The annuity cost solar lubricator is AUD $ 6091.228 and to achieve savings,

it has to lubricate effectively at least 5 curves (of 313m length) because, for every 313

m length of curve, the limit rail cost AUD $ 6008.64.

This analysis shows that lubrication is cheaper than wear but it depends on the cost of

the lubricator, maintenance activity and number of curves requiring lubrication to

cover the purchase cost, setup cost and maintenance cost. Maintenance cost can be

reduced by using the solar lubricators. Table 5.8 shows savings that can be achieved.

Table 5.8: Savings achieved

Lubricator Type Radius Curve No of Curves to Achieve

Savings

Standard Wayside

lubricator (37.5 kg)

< 500 m 2

Solar Wayside lubricator <500 m More than 5

On Board <500 m Unknown

Hi Rail <500 m Unknown

Due to the limitation of the data, standard wayside lubricator and solar wayside

lubricator costs and benefits were analysed. It was found that solar lubricators are

more economical than standard wayside lubricators. These savings vary with

environmental and operating conditions.

5.10 Summary

Modelling and analysis of rail wear, rail wear limit and lubrication are discussed.

Economic models are developed for lubrication decisions. A framework for

benchmarking lubrication effectiveness is proposed in this chapter. Data collected

178

from rail industry is used for illustration. Modelling of failures and renewal of

lubricators is carried out. A simulation model for analysis of lubrication effectiveness

is developed. Cost-benefit analyses of lubricators and annuity costs of lubricators are

estimated for managerial decisions. The analysis shows that cost effectiveness of the

lubricator depends on the numbers of curves it lubricates and the length of curve. It

also provides guidelines for installation and maintenance of lubricators. Rail area head

loss and rail wear data are analysed to determine rail life and evaluate the

effectiveness of lubrication decisions. Real life rail wear data was collected from

industry for analysis of 0-600 m curves. For better prediction and estimation of wear

rate for various curves, Gaussian (Normal) distribution and curve fitting methods have

been used. Prediction of rail life and lubrication effectiveness is analysed. The

specific outcomes of this chapter are:

� Lubricator failures are modelled with non-homogenous Poisson process

� Data analysis found that higher wear in 50 kg rails for curve radii from 0 – 300

m and need immediate replacement or repair to avoid risk of rail break or

derailment

� Cost-benefit analysis of lubricators for standard wayside lubricator and solar

wayside lubricator were estimated. The analysis found that solar wayside

lubricators are economical and more effective than standard wayside

lubricators. It is found that solar lubricators save 17% more than standard

wayside lubricators.

� A simulation model for analysis of lubrication effectiveness estimation of

wear and lubrication costs is proposed

� A relative performance model, total curve segment model and above rail and

below rail model are proposed

Modelling of inspection intervals for rail testing methods are discussed in Chapter 6.

Integration of rail grinding, lubrication and inspection models considering operational

risks will be discussed in the subsequent chapters.

179

CHAPTER 6

MODELLING AND ANALYSIS OF INSPECTION FOR INSPECTION

DECISIONS

6.1 Introduction

Modelling and analysis of wear, lubrication decisions and a framework for

benchmarking lubrication effectiveness are discussed in Chapter 5. This chapter

focuses on the development of an inspection model, analysis of rail failure data and

reliability of inspection technology for optimal inspection decisions. Real life data are

collected from industry for analysis. Ultrasonic rail inspection including manual

verification, costs around € 70 million per year for 0.5 million kilometre track system

(Cannon et al., 2003). These costs do not include derailment costs. There is a need to

develop models and analyse costs for inspection to reduce economic pressure due to

the number of broken and defective rails and derailments.

The outline of this chapter is as follows: Modelling of inspection, rail breaks,

replacement costs of worn-out unreliable rails and cost benefit analysis are discussed

in Section 6.2; modelling and analysis of rail defects using failure mode and effect

analysis (FMEA) and risk priority number (RPN) are presented in Section 6.3;

collection and analysis of rail failure data, rail defect initiation, rail failures, cost-

benefit analysis of inspection and derailment are discussed in Section 6.4; Section 6.5

discusses the total cost of rail inspection and rectification; limitation of detecting rail

breaks by signalling system is discussed in Section 6.6; the effect of seasonal

conditions is discussed in Section 6.7; finally, summary, conclusion and results are

presented in Section 6.8

6.2 Modelling Inspection

Inspection is carried out at predetermined intervals. An inspection cost model is

developed using MGT interval. Let If be the inspection per MGT and ic be the cost of

each inspection. Then, annual inspection cost over the rail life is given by:

( )

+−

∗

+= ∑

=

N

N

j

j

i

c

i

r

r

r

iC

I

1

11

11

(6.1)

180

where

=

f

NI

I

MIntegerN and ri is discounting rate associated with interval of non

destructive testing (NDT).

Let c denote the expected cost of each rail break repair on an emergency basis. Let k

be the expected cost of repairing potential rail breaks based on railhead area, RCF and

speed of train. Let a be the expected cost per derailment. The risk cost associated with

rail break and derailment is based on railhead area, RCF and speed of train. Let Pi(A,

Fatigue, s) be the probability of undetected potential rail breaks leading to

derailments based on rail head area, RCF and speed of train. Pi(B) is the probability of

detecting potential rail breaks based on rail head area, fatigue and speed of train.

Rolling contact fatigue (RCF) is given by Million Gross Tonnes (MGT). Railhead

area is determined by wear and preventive rail grinding, based on MGT. When

expected number of failures are modelled as Non Homogeneous Poisson process and

is given by E[N(Mi+1, Mi), then the risk cost is given by:

( )[ ] ( ) ( )( ) ( ) ( )( )( )[ ]( )

( )

+−

∗

+

−+∗∗−+∗∗= ∑

=+

N

N

ii

iiii

iir

r

r

r

cSFatigueAPaSFatigueAPBPkBPMMNEC

1

11

1

,,1,,1,

01

(6.2)

6.2.1 Modelling Rail Breaks

In this study, failures are modelled as a point process with an intensity function Λ(m),

where m represents Millions of Gross Tonnes (MGT) and Λ(m) is an increasing

function of m, indicating that the number of failures in a statistical sense increases

with MGT. That means that older rails with higher cumulative MGT passed through

the section, are expected to have more probability of initiating defects and, if

undetected, then further passing of traffic can lead to rail failures. As a result, N(Mi+1,

Mi), the number of failures over Mi and Mi+1, is a function of MGT, m, and is a

random variable. Let cumulative MGT of rail till inspection by NDT car, m, be

known, and Fn(m) denote the cumulative rail failure distribution, modelled as Weibull

distribution given by:

))(exp(1)( βλmmFn −−= (6.3)

with the parameters β (known as shape parameter of the distribution) > 1 and λ

(known as inverse of characteristic function for the distribution)> 0

181

When β is greater that 1 it indicated that there is increasing failure rate of the item

under study and ageing is predominant in failure mechanism (Chattopadhyay et. al.,

2003). Then failure intensity function Λ(m) is derived from (1) and is given

by 1)( −βλλβ m . Rail track is normally made operational through repair or replacement

of the failed segment and no action is taken with regards to the remaining length of

the whole track in case of detected defects and rail breaks. Since the length of failed

segment replaced at each failure is very small relative to the whole track, the

rectification action can be viewed as having negligible impact on the failure rate of

the track as a whole. Then the expected number of failures over period i and (i+1) is

given by:

))()(()],([ 11βββλ iiii MMMMNE −= ++ (6.4)

where the total accumulated MGT up to ith inspection, Mi, is given by:

∑=

=i

j

ji mM0

(6.5)

6.2.2 Modelling Replacement Costs of Worn-out Unreliable Rails

Let cre be the expected cost of replacement for segment L and consist of labour,

material, equipment, consumables and down time cost for rail replacement. Let I be

the cost of current investment in new rail. Cost of replacement is assumed to be

occurring at the beginning of each year and is simplified as the annual cost of

investment for new rails. Then cre is given by:

( )

( )

+−

+∗

=

N

re

r

r

rI

C

1

11

1 (6.6)

6.2.3 Modelling Cost Benefit Analysis

Cost benefit analysis is modelled based on demand and supply for the year j. Revenue

of the organisation depends on supply Suj and the operating condition of the rail head

area, fatigue, and speed of the train. When travel time (t) is variable and based on

speed s, then t is given by t = L/s

Supply is given by Suj = min {Dj, (Fj/t) * Wagonv * n} (6.7)

Then, net present value (NPV) over rail life is given by

182

( ) tot

N

jj

jv

j Ci

Cs

L

nWagonv

SuNPV −

+

∗

∗

−

∗= ∑=1 1

.

1Re

(6.8)

6.3 Failure Mode and Effect Analysis (FMEA)

Failure mode and effect analysis (FMEA) enables the recording and monitoring of

information regarding actual and potential failures, failure causes and effects. A Risk

Priority Number (RPN) for each rail defect is analysed based on assessment of

severity of failures, frequency of occurrence, probability of detection of failures. A

higher RPN indicates that the defect is more critical. Data from Railtrack (UK), SNCF

(French Railways), HSPC (North American High Speed Passenger Corridor), NS

(Netherlands Railways), EJR (Japanese Railways), Banverket North Region

(Sweden), Spoornet (South Africa), HH1 and HH2 (North America Heavy Haul) are

analysed in this paper (Sawley and Reiff, 2000). Rolling Contact Fatigue defects

(squats, shells, head checks, horizontal and vertical head split, wheel burns)

associated with increased axle load (transverse defects and broken base) and defects

associated with welding (thermite weld and flash weld defects) are analysed. Some of

the limitations of the current data are:

1. Track mileage is not always known accurately.

2. Each railway track classification system and method of collecting traffic data is

different.

3. Railways may use different definitions for “defects” and “breaks” and reporting

may be more or less accurate. Railways have different types of traffic and thus

have different types of defects. This is especially the case for the heavy haul

railroads, which run more slowly (typically 30 to 60 mph) and much heavier

traffic (often 286,000-pound cars) compared to passenger lines.

4. Railways have many different populations of rail age (i.e. a newer railway with

higher renewal frequency ought to have fewer defects and breaks than an older

established railway).

Due to problems in comparing the performance of railways with different types of

traffic and methods of quantifying, the data is summarized largely on the basis of the

numbers of defects and rail breaks per track mile. Tables 6.1 & 6.2 explain the

183

common causes of rail defects and rail breaks of various railway networks around the

world.

Table 6.1: Causes of Defective Rails (Sawley and Reiff, 2000)

Railway First Second Third Fourth

Table 6.2: Causes of Broken Rails (Sawley and Reiff, 2000)

Railway First Second Third Fourth

6.3.1 Occurrence of Failure

The estimation of likelihood of occurrence of potential failure is graded on a scale of

“1-10”. The lowest number in the scale indicates the lowest probability of occurrence.

The analysis shows that RCF and Thermite weld problems are contributing at a higher

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percentage, leading to the probability of a high risk of rail breaks and derailments.

The defects are ranked according to Hasting (2000), revised using executive

judgement, and presented in Table 6.3.

100*%soccurrenceofnumberTotal

defectforoccurrenceOccurrence=

(6.9)

Table 6.3: Ranking of Failure Occurrence (Reddy et al., 2004)

Probability of failure Defects Occurrence of

each defect

%

occurrence

Table 6.3 shows the analysis of rail defect occurrence. The ranking of these defects

can be used to estimate the likelihood of occurrence of those potential failures which

cause risk of rail breaks and derailments. The analysis enables the inspection crew to

estimate the frequency of occurrence of each failure and to decide upon the optimal

maintenance solution. The probable solution may be speed restriction, and temporary

or permanent repair to avoid the risk of heavy revenue losses.

6.3.2 Detectability of Failure

Detectability of failure establishes the cause/mechanism/weakness of actual or

potential failure which can be graded on a scale of “1-10”. The lowest number in the

scale indicates high probability of detecting a failure. The ratio of broken to defective

rails is a measure of the efficiency of ultrasonic inspection. A low ratio implies that

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defects are being found and removed before rail breaks. The analysis shows that

thermite welds and broken base have a high ratio and are least able to be detected by

inspection. These defects are ranked according to detectability of the failure rating

table (Leitch, 1995), revised in line with the technique mentioned earlier in the

occurrence section, and shown in Table 6.3. Table 6.4 shows the detectability ranking

of failure, with broken base having the highest rank; this indicates least detectability

of defects by ultrasonic inspection. Rail players need to increase frequent visual

inspection to avoid undetected broken base defects.

100*det

%ratioectabilityTotal

defecteachofratioityDetectabilityDetectabil = (6.10)

Table 6.4: Ranking of Detectability (Reddy et al., 2004)

Detection Chance that failure mode will

be detected by control Defect

Detection

ratio Rank

Recent research in the UK shows that the current technology can detect rail defects of

20% to 25% size with high reliability. After a section of track has been inspected, it is

likely that some defects above the 25% size will remain undetected on the track and

continue to grow. If the next inspection does not occur in a reasonable time, the

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likelihood of a break is high (Sawley and Reiff, 2000). The increase of inspection

frequency increases the likelihood of detection of undetected defects and can prevent

the risk of rail breaks and derailments.

6.3.3 Severity of Failure

The severity of failure is the assessment of the seriousness of the defect of the actual

and potential failure mode if it occurs. Severity is estimated on a “1-10” scale with the

lowest number of the scale indicating minor concerns. The classification of severity

level is a subjective value and it needs to take into account the system failure mode,

the possible degree of damage and financial loss, and the risk of injury or maybe even

death to the operator and other personnel (Leitch, 1995). Table 6.5 shows train

accident data from Federal Railroad Administration (FRA) (USA) from 2001 to 2003

and the number of derailment by each defect type. For the ranking of the severity

level, it is assumed that the casualty (people killed is ranked higher compared to

injured) has been caused by the defect derailment. If there is no casualty reported,

then the ranking is done based on the number of derailments caused by the defect

type.

Table 6.5: Train Accidents Jan 2000 - Dec 2003 (Orringer, et al., 1999)

Total Type of Accident Damage Casualty

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Table 6.6: Severity Ranking of Failure (Reddy et al., 2004)

Total Type of accident Casualty

Table 6.6 shows the analysis of severity of failure ranking. Thermite fissure, RCF,

horizontal split head and weld defects and bolt holes are ranked with high severity. It

also indicates that severity of rail defects varies from location to location.

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6.3.4 Risk Priority Number Ranking (RPN)

RPN is the product of severity, occurrence and detection, as shown in Table 6.7.

Analysis shows that thermite weld, transverse defects, shells/squats/head checks and

broken base are in the top four ranking for critical failures. Identification of critical

failures provides the probability of occurrence, detectability and severity to analyse

the consequences of each defect.

Table 6.7: Risk Priority Number (RPN) ratings

Rank Defects Occurrence Detectability Severity RPN (O x D x S)

1 Thermite weld 9 2 9 162

2 Transverse defects 8 2 10 160

3 Shells/Squats/Head Checks 8 2 9 144

4 Broken base 4 5 7 140

5 Bolt hole defects 6 2 9 108

6 Horizontal split head 8 1 9 72

7 Vertically split head 8 1 7 56

8 Head/web defects 6 1 9 54

9 Wheel burn 6 2 4 48

10 Flash weld 5 1 9 45

11 Rail manufacture 4 2 4 32

Total 1021

Figure 6.1: Rail defects occurrence

Figure 6.1 shows the analysis of rail defects occurrence. It indicates that 27% of risks

of occurrence of rail breaks or derailments are due to thermite welds, 25% due to

transverse defects, RCF, horizontal split head and vertical split head.

Rail defect occurrence using RPN

TW27%

TD, RCF, HSH, VSH25%

BH, WB, HWD19%

BB, RM13%

FW16%

189

Figure 6.2: Rail defects detectability

Figure 6.2 shows the analysis of rail defects detectability. It indicates the high

probability of risk due to undetected rail defects (such as broken base) during the

inspection. Figure 6.3 shows the analysis of severity of rail defects. It indicates the

high probability of risk due to severity of undetected defects such as thermite welds

and RCF during the inspection.

Figure 6.3: Rail defects severity

Figure 6.4: Proposed model for risk mitigation of rail defects

Reduce risk of rail breaks and derailments, downtimes, loss of lives, property and revenue

Reduce occurrence of rail defects

Increase of Detectability of rail defects

Reduce intensity of severity of rail defects

Detectability of rail defects using RPN

BB62%

HSH, VSH, HWD, FW13%

TW, TD, RCF, BH, WB, RM

25%

Severity of rail defects using RPN

TW34%

WB, RM13%

BB, VSH23%

TD, RCF, BH, HSH, HWD, FW30%

190

Figure 6.4 shows the proposed model for risk mitigation of rail defects. This method

can be used for corrective and preventive measures, based on continual analysis. The

magnitude of the defect, length of defect, time phase of defect propagation, and

mitigating factors (such as consequences of derailment/accident due to each defect)

need to be considered for detailed analysis.

6.4 Collection and Analysis of Rail Failure Data

Here we assume rails are inspected by means of non destructive testing. Data

collected from the industry is from NDT inspections and followed by handheld

inspection for validation. The probability of detectable defects developed in the rail

for known MGT at inspection and accumulated MGT before next inspection, is

determined and analysed. Rail breaks are detected by signalling system and inspection

and derailment data are analysed for known MGT.

In spite of preventive grinding programs and frequent onboard non-destructive

measurements, rail breaks happen. Factors such as weld joints, rail geometry, wheel

burns, and corrugation contribute to the risk. The cost of unplanned replacements due

to these problems is considered as a risk cost. For an infrastructure player, it is

essential to monitor and control these risks by implementing cost effective traffic and

maintenance management strategies. Questions commonly asked are:

• How much is the current risk of derailment in a specific track section?

• Will it change with changed operating, traffic and maintenance activities?

• What is the cost/benefit ratio of these factors?

6.4.1 Rail Defect Initiation

In last few years there has been a tremendous increase in annual traffic volumes. This

has influenced the significant increase in number of defects on existing railways.

Figure 6.5 shows the increase of rolling contact fatigue related defects (such as

horizontal head crack and tache ovale) due to the increase of traffic and axle loads and

million gross tonnes (MGT) (Marais and Mistry, 2003). Data analysis shows that

horizontal head crack defects are severe compared to tache ovale.

191

Figure 6.5: Rolling contact fatigue defects (Marais and Mistry, 2003)

Detectability of initiation, size and depth of sub surface initiated defects, depends on

the orientation and location of the defect, reliability of the inspection equipment and

processes and skill of the inspection personnel. The determination of crack length and

crack growth rate of defect depends on the ultrasonic testing method used, rail and

probe temperature, the efficiency of sound transmission of the couplant between the

ultrasonic probe and the rail, and even the stress level in the rail. Initiation of sub

surface defects depend on the rail degradation, rail material condition, age of the rail,

size of the rail, accumulated tonnage and axle loads passed though the rail

(Chattopadhyay and Reddy., 2007). The analysis includes:

� Initiation and occurrence of rail defect

� Progression to critical stage resulting in rail breaks due to traffic loading

� Expected number of critical defects between inspections

� Expected number of detections of probable defects using ultrasonic testing cars

and subsequent validation by hand held device

� Expected number of undetected defects for various inspection strategies

� Expected cost of rectifications, rail breaks and derailments for various alternative

strategies.

� Estimation of ageing in terms of MGT of traffic passed through the line

� Analysis of effect of grinding campaign by comparing the data before 1997 and

after 1997

It was found in the research that probable errors in ultrasonic detection are:

� Rail area scanned by 0º probe

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� Rail area scanned by transverse 45º probe

� Rail area scanned by 70º probe

� Rail area scanned by 35 - 45º probe

(a) (b)

(c) (d)

Figure 6.6: Error in ultrasonic (NDT) inspection (Chattopadhyay et al., 2005)

Figure 6.6 shows error in ultrasonic non destructive (NDT) inspection. As ageing

takes place in the line, due to tonnage accumulation on track resulting from traffic

movement. Rail defects are developed due to the steel, axle load, maintenance of rail

and wheel and contact fatigue. The number of defects expected for a given rail and

MGT till inspection with a predictable MGT before next inspection due to traffic flow

is modelled using Weibull distribution.

6.4.2 Rail Failures from Defect Initiation

It is realistic to assume that initiated defect left in the system will continue to grow in

size with increase in cumulative MGT. This research estimates the expected number

of undetected defects in the system with probability for rail breaks. With increased

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inspections per year, the expected number of undetected defects with high probability

of resulting failure leading to rail breaks and derailments, are reduced. A model for

cost benefit analysis is developed to examinine the effectiveness of various inspection

frequencies in reducing risk and cost. Figure 6.7 shows the analysis of NDT and

visual inspection of rail.

Figure 6.7: Analysis of NDT and visual inspection of rail

6.4.3 Cost-Benefit Analysis of Inspection Frequency

Currently, inspection is done annually by most rail owners. In cold countries such as

Scandinavia, inspection is carried out twice per year, especially in cold climatic

places. These tests do not take into account the ageing of rail, type of the rail and

defect history. The detectable defect data and rail failure data can be used for Weibull

parameter estimation. Data analysed from Scandinavian countries, showed that failure

rate is higher in winter compared to that in summer. Maximum allowable defect size

was analysed by experienced ultrasonic testing personnel for defect validation based

on test car data and, subsequently, by Hand Held ultrasonic equipment analysis of the

locations identified by test cars.

Rail defects�Shells/Squats/Head Checks

� Thermite weld

� Transverse defects (HSH, VSH)

� Broken base

� Bolt hole defects and Head/web defects

Inspection of Rail

-

Non destructive testing (NDT)

Handheld equipment

Defect is critical Defect is not critical Defect is minor

1 2 3

Either

rectify or

repair

Cost depends

repair and

operating

conditions

No need for immediate

replacement

Need to estimate the

time length for criticality

Rail break

Derailment

Risks

Minor break

Costs

Major break

Minimal Huge cost (millions)

Damage depend on

Speed axle load, MGT

Huge cost (in millions)

Loss of lives

Down time

Property Damage

Service DisruptionImmediate repair or

replacement

-

This involves huge cost

Ineffective

� Lubrication

� Grinding

� Inspection

� Maintenance

Strategies

� How to prevent rail breaks and derailments?

� How to reduce costs due to these defects?

Detected

Not detected

Rail defects�Shells/Squats/Head Checks

� Thermite weld

� Transverse defects (HSH, VSH)

� Broken base

� Bolt hole defects and Head/web defects

Inspection of Rail

-

Non destructive testing (NDT)

Handheld equipment

Defect is critical Defect is not critical Defect is minor

1 2 3

Either

rectify or

repair

Cost depends

repair and

operating

conditions

No need for immediate

replacement

Need to estimate the

time length for criticality

Rail break

Derailment

Risks

Minor break

Costs

Major break

Minimal Huge cost (millions)

Damage depend on

Speed axle load, MGT

Huge cost (in millions)

Loss of lives

Down time

Property Damage

Service DisruptionImmediate repair or

replacement

-

This involves huge cost

Ineffective

� Lubrication

� Grinding

� Inspection

� Maintenance

Strategies

� How to prevent rail breaks and derailments?

� How to reduce costs due to these defects?

Detected

Not detected

194

• Rail Defect History Data (NDT testing Car and Service Defects)

• Location

• Type

• Date Found

• Rail Replacement History

• Location

• Date Installed, date manufactured

• Size (Kilogram per Metre), Steel Grade

• Ageing in terms of MGT

• Annual MGT assumed is 23 on average and is multiplied by the number of

years that portion of rail is in operation since last replacement

• Number of NDT car inspections per year (1, 2 or 3)

Rail segments were based on rail replacement data from rail industry in Scandinavia.

The expected number of defect initiation and failures are estimated using the model.

Current practice is documented and a process map is developed after data collection

and interviews with inspection and maintenance personnel (Chattopadhyay et al.,

2005).

1. Measurement cars for rail geometry and surface quality

2. Non Destructive Testing (NDT) cars for ultrasound inspection, measuring

internal cracks and probable rail breaks

3. Hand held ultrasound testing to verify identified weak spots by NDT cars

4. Rectification of identified defects by cutting rail segment and welding a new

rail segment using a preventive maintenance programme. In winter, a

temporary rectification is carried out first, using fish plate concept and is

inspected every two weeks to monitor and control risk. The segment is

permanently welded at the end of the winter.

5. Undetected cracks and probable rail breaks can lead to rail breaks

6. Some of the railbreaks are detected through signalling systems. Emergency

rectification is carried out following the procedure explained in Step 4.

7. Some of the rail breaks undetected by signalling system, cracks and probable

rail breaks, are detected by visual inspection. These are picked up by drivers,

passers-by and rail inspectors.

195

8. Undetected rail breaks by NDT, visual and signalling systems, can lead to

derailments. Emergency rectification is carried out following the procedure

explained in Step 4.

Figure 6.8: Process map of rail inspection (Chattopadhyay et al., 2005)

Figure 6.8 shows the process map of rail inspection and rectification. PM=Preventive

Maintenance, CM=Corrective Maintenance, HH=Inspection using Hand Held

ultrasound testing device.

6.4.4 Analysis of cost data

Relevant costs for this analysis are taken from the rail industry in Scandinavia and

other published documents (Chattopadhyay et al., 2005):

• Cost of ultrasonic inspection (u): For 130 km = AUD $ 12,375

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• Cost of hand held inspection (h) test to run is AUD $ 1320 /day. (Can inspect 7 to

10 detected cracks per day, depending on travel time and access to track)

• Cost of physical visual inspection (v) AUD $ 1320 /day

• Cost of planned repair (k) AUD $ 4,950 /break

• Cost of emergency unscheduled repair (b) is Subcontracting price - Emergency

rail break rectification is AUD $ 990 + permanent fixed cost AUD $ 4950 +

maintenance control of the emergency rectification AUD $ 743 in total AUD $

6683 /rail break

• Cost of regular inspection of temporary repairs (d) AUD $ 743 /break per site for

the winter

• Cost of temporary repair and full repair at convenient time (w), done in two stages

6683 + 743 for regular inspection = AUD $ 7,425 for emergency

• Cost of derailment (a); [The average cost is between AUD $ 428,980 to AUD $

577,472 depending on time of year (more expensive in winter) and how many

wheels and wagons are damaged. Need to estimate average and variance based on

historical data, including life loss and injuries. It could approximate AUD $

2,474,880, including human loss and injuries.]

6.4.5 Analysis of selected defect, rail break and derailment

Data on detection of rail defects using ultrasonic system, hand held device, signalling

system, visual inspection, rail breaks and derailments linked to cracks, are collected

for analysis. Data from detected defects using Hand Held Devices are analysed to

estimate the probability of detecting defect with potential for failure before next

inspection. Defect developed later, or undetected during inspection, can result in rail

break. Some rail breaks are detected by signalling system. Some undetected breaks

are detected by visual checks. Balance of undetected rail breaks can result in

derailment (Chattopadhyay et al., 2003). Probability of rail break between inspections

depends on the probability that the detectable defect was present at the time of

inspection but remained undetected; the developed defect then grows into rail break

before the next inspection. Expected detectable defects with potential for rail breaks

in between MGT for various inspection frequencies, are estimated. Cost Benefit

Analysis of those inspection frequencies for one, two and three per year is carried out

(Chattopadhyay et al., 2005).

197

Data for incidents (1999-2004)

Item Numbers

Derailments 2

Detected through Ultrasonic NDT inspection 27

Detected through signalling 23

Detected through NDT HH 474

Rail break data and detected defects (using NDT Hand Held for incidents with

information on last replacements) are used for MGT. Time between incidents and

year of last replacements is multiplied by 23 MGT per year for analysis. Figure 6.9

shows a block diagram of rail inspection and detection. Figure 6.10 is a Venn diagram

of inspection, rail breaks and derailment (For detailed data, see Appendix B).

Figure 6.9: Block diagram of inspection and detection (Chattopadhyay et al.,

2005)

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Figure 6.10: Venn diagram of inspection (Chattopadhyay et al., 2005)

6.4.6 Limitations of data

Accurate data for NDT car, calibrations and confirmation by Hand Held, is used for

analysis (Chattopadhyay et al., 2005). Technology has limitations and some defects

remain undetected due to location and orientation in the rail. Estimation can be

possible by destructive testing of replaced rails.

α = error of NDT not detecting defects where there is a defect

NDefcal = Number of defects correctly picked up in calibration

NDeftot = Total number of defects in the test rail

−=

tot

cal

NDef

NDef1α = 11.5% to 19.2%

During the inspection, 3 out of 26 tests in calibration were not detected and 2 more

defects (close to other defects) were detected as one defect. Without considering the

second category, the total number of defects not detected accurately by NDT car in

calibration is 3 out of 26 known defects. Considering the second category, 5 out of 26

known defects were not picked up accurately.

Φ = error of NDT car finding defects where there is no defect

NDefHH = Number of defects verified by Hand Held

NDeftot (NDT car) = Number of Defects identified by NDT Car

( )

−=Φ

NDTcartot

HH

NDef

NDef1 = 30.2%

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There is inconsistency in data of defects detected by NDT car and validated by Hand

Held NDT equipment for the years 1999 - 2004. However, 2002 data appears to be

reasonably consistent with other rails around the world and is considered for analysis.

It is found in the analysis that the total number of defects detected by NDT car is 119,

and the number of defects validated by NDT Hand Held equipment is 83


6.5 Total cost of rail inspection and rectification

Costs associated with rail inspection and rectifications are estimated. The total cost of

inspection and rectification of rail is equal to the sum of costs for: ultrasonic

inspections using non destructive testing (NDT) cars; Hand Held NDT verification;

rectifications based on NDT (planned rectification cost); repair of rail breaks detected

by signalling and inspection; inspections detecting rail breaks undetected by

signalling system, inspection of temporary rectifications during winter; rectification of

defects temporarily in winter and finally in summer; and derailments. Figure 6.11

shows the pie-chart for preventive and corrective rail breaks. Figure 6.12 shows the

pie chart for detected rail breaks and derailment (Chattopadhyay et al., 2005).

Percentage of rectification (1999-2004)

Corrective Rail

break, 10.36%

Deraiment,

0.38%

Preventive,

89.27%

Figure 6.11: Pie chart for preventive, corrective (rail breaks)

Detection of rail breaks

Signaling

system

40%Visual

Inspection

56%

Deraiment

4%

Figure 6.12: Pie chart for detected rail breaks and derailment

200

Table 6.8: Cost Benefit Analysis (Chattopadhyay et al., 2005)

Inspection Frequency per year

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Table 6.8 shows the cost benefit analysis for inspection intervals. Total risk costs

considering different derailment costs, and for one, two three inspection intervals, are

estimated. These costs include inspection of non destructive testing (NDT) by car and

inspection of non destructive (NDT) Hand Held (HH) equipment. Probability of

derailment, probability of detection by signalling and probability of visual inspection

are modelled with non homogenous poisons process. Failures are found with Weibull

distribution. The analysis shows that two NDT runs per year is cost effective and

economical for the rail segment under consideration. The difference of probability of

undetected defects with two inspection intervals, compared to the probability of

undetected defects with three inspection intervals, is negligible. There is a need to

integrate data management to extract more meaningful information about risk and

cost associated with inspection, maintenance and rail replacements. There is huge

scope to carry out this analysis for all other segments of rail track, to minimise risks

and costs associated with inspection, maintenance, and rail replacements


6.6 Limitations of Detecting Rail Breaks

The purpose of a track signalling system is primarily to detect if there is a train

positioned on an isolated section of the track. One rail is labelled as S-rail and the

other rail is called I-rail. The I-rail is incoherent and is isolated in parts to ensure that

the section is divided into sub-sections along the track. S-rail is coherent and is acting

as the continuous rail for feeding back the power current from the electric

locomotives. The S-rail is a continuous welded rail with no isolation cuts for

sectioning, and the S-rail is also connected to the contact wire pole foundation and,

hence, connected to a zero electric potential regarding ground. The S-rial will then

close the electric current to the electric power for the locomotive engine. The I-rail

has also a 6 volt electric potential compared to the S-rail and hence, in each isolated

section of the track, there will be a 6 volt difference between rails. The two rails are

connected via an intermediate rely and the relay is then closes 6 volt circuit of two

rails. As long as the relay has a 6 volt potential difference, the adjoining section’s

signalling system is set to green (OK to pass) between the sections. If the circuit is

closed by a train, the adjoining section’s signalling system is set to red. This indicates

no passing between the sections. When the circuit is not completely closed, that is,

there exists a rail break on the I-rail, the relay changes its value and the signalling

202

system for the adjoining section is set to red. This indicates that you are not allowed

to pass on to the next adjoining section; the train then stops. However, if there exists a

rail break in S-rail, this rail is connected to ground, the circuit might be closed via the

ground and the rely will then "believe" that the circuit is not broken. Hence, the signal

is in green with a rail break in S-rail (Chattopadhyay et al., 2005). Figure 6.13 shows

detection of rail breaks using the signalling system.

Figure 6.13: Detecting rail breaks using signalling system (Chattopadhyay et al.,

2005)

6.7 Effect of Seasonal Conditions on Rail Defect Initiation

Failures and defect identifications can be analysed separately for estimating the effect

of seasonal conditions (summer and winter) on rail defect initiation and failures for a

known MGT of ageing and traffic movement before next inspection.

Rail Industry from Scandinavia believes that the number of detected failures in May

due to the impact of winter (when no lubrication and grinding campaign can operate),

is greater than that detected in September (when defects are generated by summer

traffic flow and both grinding and lubrication campaigns operate).

y

halla


203

6.8 Summary

Modelling and analysis of inspection models and analysis of rail failure data for

optimal inspection decisions, are discussed in this chapter. Real life data was collected

from industry for analysis. Probability models are developed to reduce unplanned

maintenance due to rail breaks. The specific outcomes of this chapter are:

� Analysis found that two NDT inspections per year are more cost effective than

one and three inspections

� Rail owners can save 27% on total maintenance costs with two inspections per

year over one inspection per year

� Risk priority number is used to analyse risks due to rolling contact fatigue and

rail defects

� Analysis found that there is high probability of failure due to the severity of

undetected defects such as thermite welds and rolling contact fatigue related

defects

There is a need to integrate these models. Integration of grinding, lubrication,

inspection and rectification models will be discussed in Chapter 7. Results,

conclusions, contributions, and scope for future work will be presented in Chapter 8.

204

CHAPTER 7

DEVELOPMENT OF AN INTEGRATED MODEL FOR ESTIMATION OF

EXPECTED TOTAL COSTS

7.1 Introduction

Probabilistic models are developed for optimal inspections to reduce unplanned

maintenance due to rail breaks and undetected defects in Chapter 6. This chapter

focuses on development of an integrated model for estimating expected total cost of

grinding, lubrication, inspection, rectification and replacement decisions, and

associated risks of derailments.

The outline of this chapter is as follows: In Section 7.2 development of the integrated

model is presented. In Section 7.3, the integrated model is proposed for wear-fatigue-

lubrication interaction. It proposes a cost model for effective maintenance decisions.

The concluding section presents the summary and scope for future work.

7.2 Development of the Integrated Model

This research has focused on the development of economic models for rail grinding,

lubrication, inspection, rectification and replacement. A simulation model is

developed to integrate grinding, lubrication, inspection, rectification and replacement

models. The integrated model can be used:

� to predict and assess operational risks due to rail defects in the track for

informed managerial decisions to improve reliability and safety of rail

operation,

� to estimate the expected total annuity costs for grinding, lubrication,

inspection and replacement of rails,

� for cost-benefit analysis and making managerial decisions on risk based

approach on grinding, lubrication and inspection intervals,

� to estimate relative performance of lubricators, total curve and segment, above

rail and below rail for assessing effectiveness of lubrication strategies and

� to estimate the savings with grinding, inspection intervals, lubrication, rail

replacement and rectification decisions.

Figure 7.1 shows the proposed integrated model for economic evaluation, based on

cost-benefit analysis and risk based approach for managerial decisions.

205

Figure 7.1: Integrated model for rail grinding-lubrication-inspection

The Integrated Model consists of grinding, lubrication and inspection models to

estimate total annuity costs of maintenance of rail segment under consideration.

Therefore, the total cost of maintaining a segment of rail is equal to the sum of cost

for: Preventive rail grinding cost (cg); down time cost due to rail grinding (loss of

traffic) (cd); inspection costs for rail grinding (ci); risk cost of rectification based on

NDT; rail breaks and derailment (cr); and replacement cost of worn-out, unreliable

rails (cre); lubrication (cl); and NDT inspection cost (Ultrasonic NDT car, NDT hand

held equipment). Then the total annuity cost/m can be modelled as:

Start: InputExperimental dataRail and wheel discs, curve radius

steel grade, axle load, speed and lubricant

Integrated wear-fatigue-lubrication model

Lubrication model

(Chapter 5)

Change the conditions and variables

Industry dataRail data (year installed, material, size (kg), profile,

age), curve radius, MGT, rail grinding, wear and

lubrication, rail inspection, rail rectification and

replacement, weather and environmental conditions

Current condition and usage of rail

�Measurement of wear rate

�with and without lubrication

� Compare wear rate

with existing wear standards,

�experiment,

� field, environmental and

�weather conditions

� Inspection of rail for

� RCF defects by NDT

� Signaling system and

� Visual inspection

� Inspection of lubricators

Interpretation of RCF

defects, Wear and

Lubrication interaction

Grinding model

(Chapter 4)Inspection model

(Chapter 6)

� Rail lubricant

� Applicator performance

� Lubricator position

� Condition of lubricator,

� axle loads, traffic types and

speed

� curve length, radius and

number curves and

� Environmental conditions

Rectification and Replacement

(Chapter 4, 5, 6)

� Detection of RCF cracks

� Rail profile measurements,

� Rail grinding interval

� Selection of rail segment

� Grinding depth

� Rectification of RCF defects

� Determining wear limit

� Correction of rail profile

� Lubricator maintenance

� weather and environmental

conditions

Decisions on

Cost of replacing rail

segment

Maintenance of lubricators

Risk of rail breaksDecisions on

whether to grind or not?

what is grinding depth and frequency?

Operational risks and costs due to

undetected defects

Accuracy of detection technology

Appropriate maintenance activity

Decisions on lubricant

type, lubricator position,

and performance

risk of fluid entrapment

Start: InputExperimental dataRail and wheel discs, curve radius

steel grade, axle load, speed and lubricant

Integrated wear-fatigue-lubrication model

Lubrication model

(Chapter 5)

Change the conditions and variables

Industry dataRail data (year installed, material, size (kg), profile,

age), curve radius, MGT, rail grinding, wear and

lubrication, rail inspection, rail rectification and

replacement, weather and environmental conditions

Current condition and usage of rail

�Measurement of wear rate

�with and without lubrication

� Compare wear rate

with existing wear standards,

�experiment,

� field, environmental and

�weather conditions

� Inspection of rail for

� RCF defects by NDT

� Signaling system and

� Visual inspection

� Inspection of lubricators

Interpretation of RCF

defects, Wear and

Lubrication interaction

Grinding model

(Chapter 4)Inspection model

(Chapter 6)

� Rail lubricant

� Applicator performance

� Lubricator position

� Condition of lubricator,

� axle loads, traffic types and

speed

� curve length, radius and

number curves and

� Environmental conditions

Rectification and Replacement

(Chapter 4, 5, 6)

� Detection of RCF cracks

� Rail profile measurements,

� Rail grinding interval

� Selection of rail segment

� Grinding depth

� Rectification of RCF defects

� Determining wear limit

� Correction of rail profile

� Lubricator maintenance

� weather and environmental

conditions

Decisions on


segment


Risk of rail breaks

Decisions on


segment


Risk of rail breaksDecisions on




undetected defects



Decisions on




undetected defects





and performance




and performance


206

NDT

y

yy

N

i

i

sjjj

y

y

y

yyy

i

N

i

xixixixixixi

y

x

y

yy

j

i

N

j

c

y

yy

iN

i

DTGP

y

yy

iN

i

itot

xCrrrcYMc

rrI

rrrr

cAPaAPBPkBPMMNE

rrri

rrrdhn

rrrLnGC

j

j

I

i

++−++

++−+−

++−++−+

−+−+∗

++−+

++−+∗∗

++−+=

∑

∑∑

∑

∑

∑

=

=+++

=

=

−

=

−

=

))1/(1(1/(*})1/()({

)))1/(1(1/()))1/(1(1(*

)))1/(1(1/()1(*)))1/(1(1(*})1(

/]*))(1(*)((*))(1(*)([)],([{

)))1/(1(1/(*})1/(({

)))1/(1(1/(*})1/({

)))1/(1(1/(*})1/()**({

1

0,,,,1

0

1

1

1

1

1

(7.1)

where ( )BP xi, is probability of detecting potential rail breaks in non destructive

testing (NDT) for x number of inspections per year; ( )AP xi, is probability of

undetected potential rail breaks leading to derailments for x number of inspections per

year, in a planned way; and a is the expected cost per derailment. NDTxC is the cost

for non destructive testing for x number of inspections per year.

( ) α=BPi 1, (7.2)

where ( )BPi 1, is probability of detecting potential rail breaks in non destructive testing

(NDT) for one inspection per year, and α is % of defects detected in NDT.

( ) ( ){ }( )( )

+

−+−−=

==

==

2,1,

2,1,2,

111

xixi

xixi

iNN

NNBP

αα (7.3)

where ( )BPi 2, is probability of detecting potential rail breaks in non destructive

testing (NDT) for two inspections per year. The Ni is number of rail defects found

during x number of inspections per year.

( ) ( ){ }( )( ) ( )α

αα−

++

+−+−−=

===

=== 111

13,2,1,

3,2,1,3,

xixixi

xixixi

iNNN

NNNBP (7.4)

where ( )BPi 3, is probability of detecting potential rail breaks in non destructive

testing (NDT) for two inspections per year.

G is the cost of grinding cost per pass per m, ni number of grinding pass for ith

grinding and L is the length of rail segments under consideration; N be the total

207

number of periods up to safety limit for renewal, and r is the discounting rate per

period.

x is the inspection intervals per year for a rail corridor under consideration,

CNDT is total expected cost for NDT inspection interval,

hDT is the expected downtime due to each grinding pass and d is the expected cost of

down time per hour.

ci is the cost of inspection before and after rail grinding

c is the expected cost of each rail break repair on emergency basis

I is cost of investment in new rail

sc is switching cost for stop/start lubrication

jY is the decision variable for lubrication strategy (dimensionless), 0 for no or

continuous lubrication (dimensionless), and 1 for stop/start lubrication

(dimensionless).

The integrated model can be used for effective maintenance decisions on grinding

interval, application of lubrication and inspection intervals. It can also be used to

estimate the relative performance of lubricators, total curve and segment model,

above rail and below rail model for assessing effectiveness of lubrication strategies

and to evaluate the performance of lubricators.

7.3 Analysis of Results

Heavy haul data was used for analysis of the model, for prediction, and to estimate

total annuity costs. Table 7.1 shows all the cases examined with the integrated model.

208

Table 7.1: Examined cases with the integrated model

Case Studies Sections

Total annuity cost for 12 MGT with lubrication Section 7.3.1

Total annuity cost for 12 MGT without lubrication Section 7.3.1

Total annuity cost for 23 MGT with lubrication Section 7.3.2

Total annuity cost for 23 MGT without lubrication Section 7.3.2

Total annuity cost for 12 MGT with and without lubrication Section 7.3.3

Total annuity cost for 23 MGT with and without lubrication Section 7.3.3

EAC/m for 12 MGT with lubrication for one NDT inspection/year (Case 1) Section 7.3.4

EAC/m for 12 MGT without lubrication for one NDT inspection interval/

annum (Case 1)

Section 7.3.4

EAC/m for 23 MGT with lubrication for one NDT inspection

interval/annum (Case 1)

Section 7.3.4

EAC/m for 23 MGT without lubrication for one NDT inspection

interval/annum (Case 1)

Section 7.3.4

EAC/m for 12 MGT with lubrication for two NDT inspection/ annum

(Case 2)

Section 7.3.4

EAC/m for 12 MGT without lubrication for two NDT inspection/ annum

(Case 2)

Section 7.3.4

EAC/m for 23 MGT with lubrication for two NDT inspection/ annum

(Case 2)

Section 7.3.4

EAC/m for 23 MGT without lubrication for two NDT inspection/ annum

(Case 2)

Section 7.3.4

EAC/m for 12 MGT with lubrication for three NDT inspection/ annum

(Case 3)

Section 7.3.4

EAC/m for 12 MGT without lubrication for three NDT inspection/ annum

(Case 3)

Section 7.3.4

EAC/m for 23 MGT with lubrication for three NDT inspection/ annum

(Case 3)

Section 7.3.4

EAC/m for 23 MGT without lubrication for three NDT inspection/ annum

(Case 3)

Section 7.3.4

EAC/m for 12 & 23 MGT with and without lubrication Section 7.3.4

* EAC- Estimated Annuity Cost/m

209

7.3.1 Annuity costs/m for 12 MGT

Analysis of annuity costs/m of grinding, risk, down time, inspection and replacement

for 12 MGT of curve radius 0 to 600 m are compared. Results are shown in Table 7.2.

Table 7.2: Annuity costs/m for 12 MGT with lubrication

Radius (ms) 0-300 300-450 450-600 Length in ms (Percentage) 1318 (0.0101) 1384 (0.0106) 36524 (0.2798)

Annuity costs of rail maintenance Annuity costs/m ($AUD) Grinding 6.82 6.08 7.12 Risk 0.0002 0.0004 0.00011

Down time 1.07 0.95 1.12 Inspection 0.02 0.02 0.02 Replacement 15.48 13.10 11.63 Lubrication 0.67 0.46 0.34

Total Annuity Cost/m 24.06 20.02 20.23 Figure 7.2 shows the analysis of annuity costs/m for 12 MGT of curve radius 0 to 600

m with lubrication. It is observed that the replacement and grinding costs are higher

compared to risk, inspection and down time cost.

Annuity costs/meter for 12 MGT with Lub

0

5

10

15

20

Grinding Risk Downtime Inspection Replacement Lubrication

Maintenance Costs

Cost/meter ($ AUD)

0-300

300-450

450-600

Figure 7.2: Annuity costs/m for 12 MGT with lubrication

Table 7.3 shows the annuity costs/m for 12 MGT without lubrication.

210

Table 7.3: Annuity costs/m for 12 MGT without lubrication

Radius (m) 0-300 300-450 450-600 Length in m (Percentage) 1318 (0.0101) 1384 (0.0106) 36524 (0.2798)


Down time 0.96 0.64 0.8936 Inspection 0.0232 0.02 0.0238 Replacement 66 53.16 46.99

Total Annuity Cost/m 73 60 54

Figure 7.3 shows the analysis of annuity costs/m for 12 MGT of curve radius 0 to 600

m without lubrication. It is observed that replacement and grinding costs are higher

compared to downtime, inspection and risk costs. This is mainly due to early

replacement of rails at steeper curves with no lubrication.

Annuity costs/meter for 12 MGT No Lub

0

20

40

60

80

Grinding Inspection Risk Downtime Replacement

Maintenance Costs

Cost/meter ($ AUD)

0-300

300-450

450-600

Figure 7.3: Annuity costs/m for 12 MGT without lubrication

7.3.2 Annuity costs/m for 23 MGT

Analysis of annuity costs/m of grinding, risk, down time, inspection and replacement

costs with lubrication for 23 MGT of curve radius 0 to 600 m are compared. Annuity

costs/m for 23 MGT are shown in Table 7.4.

211

Table 7.4: Annuity costs/m for 23 MGT with lubrication

Radius (m) 0-300 300-450 450-600 Length in m (Percentages) 1318 (0.0101) 1384 (0.0106) 36524 (0.2798)


Down time 0.85 0.93 0.94 Inspection 0.04 0.04 0.04 Replacement 17.65 15.17 16.06 Lubrication 0.68 0.46 0.33

Total Annuity Cost/m 24.64 22.55 23.37 Figure 7.4 shows the analysis of annuity costs/m for 23 MGT of curve radius 0 to 600

m. It is observed that replacement and grinding costs are higher compared to other

maintenance costs.

Annuity costs/meter for 23 MGT with Lub

0

4

8

12

16

20

Grinding Inspection Risk Downtime Replacement Lubrication

Maintenance Costs

Cost/meter ($ AUD)

0-300

300-450

450-600

Figure 7.4: Annuity costs/m for 23 MGT with lubrication

Table 7.5 shows annuity costs/m for 23 MGT without lubrication. Annuity cost/m of

grinding, risk, down time, inspection and replacement costs without lubrication for 23

MGT of curve radius from 0 to 600 m are compared and estimated.

212

Table 7.5: Annuity costs/m for 23 MGT without lubrication

Radius (m) 0-300 300-450 450-600 Length in m (Percentage) 1318 (0.0101) 1384 (0.0106) 36524 (0.2798)

Annuity costs of rail maintenance Annuity costs/m ($AUD) Grinding 16.02 13.61 6.3074

Risk 0.044 0.04 0.04

Down time 0.0014 0.0018 0.0001

Inspection 2.51 2.13 0.99

Replacement 152 152 79.41

Total Annuity Cost/m 171 168 87

Figure 7.5 shows the analysis of annuity costs/m for 23 MGT of curve radius 0 to 600

m without lubrication. It is observed that the cost is higher for replacement compared

to other maintenance costs. Rails develop wear and rolling contact fatigue cracks in

between longer grinding and inspection intervals. In many heavy haul lines rails are

mainly removed due to rail wear and rolling contact fatigue cracks. The rate of

replacement of rails is much higher for curves without lubrication than with

lubrication.

Annuity costs/meter for 23 MGT No Lub

0

40

80

120

160

Grinding Inspectiont Risk Downtime Replacement

Maintenance Costs

Cost/meter ($ AUD)

0-300

300-450

450-600

Figure 7.5: Annuity costs/m for 23 MGT without lubrication

7.3.3 Annuity costs/m for 12 MGT & 23 MGT

Table 7.6 shows total annuity costs/m for 12 MGT with and without lubrication for

curve radius 0-600 m.

213

Table 7.6: Analysis of total annuity costs/m for 12 MGT

Radius (m) With Lubrication Without Lubrication Length in m (Percentage) Total Annuity costs/m ($AUD) for 12 MGT

0-300 24.06 73

301-450 20.62 60

451-600 20.23 54

Figure 7.6 shows the total annuity costs/m for 12 MGT with and without lubrication.

The analysis found that the total annuity costs/m for without lubrication is 3 times

higher compared to with lubrication for 0-600 m curve radius.

Total Annuity Costs for 12 MGT

0

20

40

60

80

0-300 301-450 451-600

Curve Radius (meters)

Costs/meter ($ AUD)

With Lubrication

Without Lubrication

Figure 7.6: Total annuity costs/m for 12 MGT

Table 7.7 shows total annuity costs/m for 23 MGT with and without lubrication for

curve radius 0-600 m.

Table 7.7: Analysis of total annuity costs/m for 23 MGT

Radius (m) With Lubrication Without Lubrication Length in m (Percentage) Total Annuity costs/m ($AUD) for 23 MGT

0-300 24.64 171

301-450 22.55 168

451-600 23.25 87 Figure 7.7 shows the total annuity costs/m for 23 MGT with and without lubrication.

The analysis found that the total annuity costs/m for without lubrication is 7 times

higher for 0-450 m curve radius and 4 times higher for curves 451-600 m curve radius

compared to with lubrication.

214

Total Annuity costs for 23 MGT

0

40

80

120

160

200

0-300 301-450 451-600

Curve Radius (meters)

Total Annuity Costs

($AUD)

With Lubrication

Without Lubrication

Figure 7.7: Total annuity costs/m for 23 MGT

7.3.4 Estimation of Annuity costs/m

The total annuity costs/m for risk and inspection are further analysed considering the

expected number of failures under various inspection scenarios.

Case 1 – One Inspection per year

Data collected from industry for one inspection interval using ultrasonic (non

destructive testing) NDT and verified with handheld equipment. Table 7.8 shows the

total annuity costs/m of rail grinding, inspection for grinding, risk, downtime and

replacement, lubrication and NDT inspection costs for 12 MGT with lubrication for

one inspection interval.

Table 7.8: Annuity costs/m for 12 MGT with lubrication for one inspection

Radius (m) 0-300

Length (m) (Percentage) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)

Grinding 6.82

Inspection for grinding 0.02

Risk 36.31

Down time 1.07

Replacement 15.48

Lubrication 0.67

NDT Inspection 1.60

Total Annuity cost 61.97

215

Annuity costs/m for 12 MGT with Lub, One Ins

Lubrication,

0.67, 1%

Replacement,

15.48, 25%

Inspection for

rail grinding,

0.02, 0%

Downtime,

1.07, 2%

Risk, 36.31,

58%

Grinding, 6.82,

11%

NDT Inspection

, 1.60, 3%

Figure 7.8: Annuity costs/m for 12 MGT with lubrication for one inspection

Figure 7.8 shows annuity costs/m for 12 MGT of curve radius 0 to 300 m with

lubrication for one inspection interval. It is found that risk cost is higher compared to

replacement and grinding costs. This is mainly due to higher number of detected

defects with NDT during the year. These failures have a significant influence on the

risk of rail breaks and derailments. The risk and inspection cost has a great influence

on total maintenance and it is much higher without lubrication. Table 7.9 shows the

total annuity costs/m for rail grinding, inspection, risk, downtime, replacement and

NDT inspection for 12 MGT without lubrication for one inspection interval.

Table 7.9: Annuity costs/m for 12 MGT without lubrication, one inspection

Radius (m) 0-300


Grinding 6.12 Inspection for grinding 0.000024

Risk 36.31

Down time 0.0232

Replacement 66

NDT Inspection 1.60

Total Annuity cost 110

216

Annuity costs/m for 12 MGT without Lub One Ins

Grinding, 6.12,

6%

Risk, 36.31,

33%

Downtime,

0.0232, 0%

Inspection for

rail grinding,

0.000024, 0%

Replacement,

66, 60%

NDT Inspection

, 1.60, 1%

Figure 7.9: Annuity costs/m for 12 MGT without lubrication for one inspection

Figure 7.9 shows annuity costs/m for 12 MGT of curve radius 0 to 300 m without

lubrication for one inspection interval. It is observed that replacement cost is higher

compared to all other costs. This is mainly due to early replacement of rails and a

higher number of defects detected with NDT during the year with no lubrication.

Lubrication has significant influence on rail defects which increase risk of rail breaks

and derailments. Table 7.10 shows the total annuity costs/m for rail grinding,

inspection, risk, downtime, replacement, NDT inspection for 23 MGT with

lubrication for one inspection interval.

Table 7.10: Annuity costs/m for 23 MGT with lubrication for one inspection

Radius (m) 0-300

Length in m (Percentages) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)

Grinding 5.42

Inspection for rail grinding 0.00

Risk 43.32

Down time 0.04

Replacement 14.03

Lubrication 0.68

NDT Inspection 3.82

Total Annuity Cost/m 70.93


lubrication for one inspection interval. The analysis shows that the risk cost is higher

compared to other costs. This is mainly due to the higher number of failures found in

one inspection for 23 MGT. The analysis shows that higher MGT grinding intervals

have increased the risk of rail break and derailment costs.

217

Annuity costs/m for 23 MGT with Lub One Ins

Replacement,

17.65, 25%

Risk, 43.32, 61%Downtime, 0.04,

0%

Inspection for rail

grinding, 0, 0%

Lubrication,

0.68, 1%

NDT Inspection,

3.82, 5%Grinding, 5.42,

8%

Figure 7.10: Annuity costs/m for 23 MGT with lubrication for one inspection

Table 7.11 shows the total annuity costs/m for rail grinding, inspection, risk,

downtime, replacement, NDT inspection for 23 MGT without lubrication for one

inspection interval.

Table 7.11: Annuity costs/m for 23 MGT without lubrication for one inspection

Radius (m) 0-300

Length in m (Percentages) 1318 (0.0101) Rail maintenance Annuity costs/m ($AUD)

Grinding 16.02


Risk 43.32

Down time 2.51

Replacement 152

NDT Inspection 3.82

Total Annuity Cost/m 218


lubrication for one inspection interval. The analysis shows that the replacement cost is

higher compared to other costs. This is mainly due to early replacement of rails and a

higher number of defects detected with NDT during the year with no lubrication.

218

Annuity costs/m for 23 MGT without Lub One Ins

Grinding,

16.02, 7%

NDT

Inspection,

3.82, 2%

Inspection for

rail grinding,

0.044, 0%

Downtime,

2.51, 1%

Risk, 43.32,

20%

Replacement,

152, 70%

Figure 7.11: Annuity costs/m for 23 MGT without lubrication for one inspection

Case 2 – Two inspections per year

The expected number of failures estimated with stochastic models in two inspection

intervals per year is 55.79508. Table 7.12 shows the annuity costs/m of rail grinding,

inspection for grinding, risk, and downtime, replacement, lubrication and NDT

inspection for 12 MGT with two inspections intervals.

Table 7.12: Annuity costs/m for 12 MGT with lubrication for two inspections

Radius (m) 0-300


Grinding 6.82


Risk 32.93

Down time 1.07

Replacement 15.48

Lubrication 0.67

NDT inspection 1.63


Figure 7.12 shows annuity costs/m for 12 MGT of curve radius from 0 to 600 m with

lubrication for two inspection intervals per year. The analysis shows that risk cost and

replacement costs are higher compared to other costs. It is observed that the NDT

inspection cost for two inspection intervals is higher compared to one inspection

interval per year.

219

Annuity costs/m for 12 MGT with Lub, Two Ins

Replacement,

15.48, 26%

NDT Inspection

, 1.63, 3%Grinding, 6.82,

12%

Lubrication,

0.67, 1%

Inspection for

rail grinding,

0.02, 0%

Downtime,

1.07, 2%

Risk, 32.93,

56%

Figure 7.12: Annuity cost/m for 12 MGT with lubrication for two inspections

Table 7.13 shows the annuity costs/m of rail grinding, inspection for grinding, risk,

and downtime, replacement and NDT inspection for 12 MGT without lubrication for

two inspection intervals per year.

Table 7.13: Annuity costs/m for 12 MGT without lubrication for two inspections

Radius (m) 0-300


Grinding 6.12


Risk 32.93

Down time 0.0232

Replacement 66

NDT inspection 1.63


Figure 7.13 shows annuity costs/m for 12 MGT of curve radius from 0 to 600 m

without lubrication for two inspection intervals per year. The analysis shows that the

replacement cost is higher compared to other costs. This is mainly due to early

replacement of rails and a higher number of defects detected with NDT during the

year with no lubrication.

220

Annuity costs/m for 12 MGT without Lub Two Ins

NDT Inspection

, 1.63, 2%

Replacement,

66, 61% Inspection for

rail grinding,

0.000024, 0%

Downtime,

0.0232, 0%

Risk, 32.93,

31%

Grinding, 6.12,

6%

Figure 7.13: Annuity costs/m for 12 MGT without lubrication for two inspections

Table 7.14 shows the annuity costs/m for rail grinding, inspection for rail grinding,

risk, downtime and replacement, lubrication and NDT inspection for 23 MGT with

lubrication for two inspection intervals per year.

Table 7.14: Annuity costs/m for 23 MGT with lubrication for two inspections

Radius (m) 0-300


Grinding 5.42

Inspection 0.00

Risk 39.29

Down time 0.04

Replacement 17.65

Lubrication 0.68

NDT inspection 3.87



lubrication for two inspection intervals per year. The analysis shows that the risk and

replacement costs are higher, compared to other costs. Higher NDT inspection cost is

observed for two inspection intervals, compared to one inspection interval per year.

221

Annuity costs/m for 23 MGT with Lub Two Ins

Grinding,

5.42, 8%

NDT

Inspection,

3.87, 6%Lubrication,

0.68, 1%

Inspection for

rail grinding,

0, 0%

Downtime,

0.04, 0%

Risk, 39.29,

59%

Replacement,

17.65, 26%

Figure 7.14: Annuity costs/m for 23 MGT with lubrication for two inspections

Table 7.15 shows the annuity costs/m for rail grinding, inspection for rail grinding,

risk, downtime and replacement and NDT inspection for 23 MGT without lubrication

for two inspection intervals per year.

Table 7.15: Annuity costs/m for 23 MGT without lubrication for two inspections

Radius (m) 0-300


Grinding 16.02


Risk 39.29

Down time 2.51

Replacement 152

NDT inspection 3.87



without lubrication for two inspection intervals per year. The analysis shows that the

replacement and risk costs are higher compared to other costs.

222

Annuity costs/m for 23 MGT without Lub Two Ins

Replacement,

152, 72%

Risk,

39.28879671,

18%

Downtime,

2.51, 1%

Inspection for

rail grinding,

0.044, 0%

NDT

Inspection,

3.87, 2%

Grinding,

16.02, 7%

Figure 7.15: Annuity costs/m for 23 MGT without lubrication for two inspections

Case 3 – Three inspections per year

The expected number of failures estimated with stochastic models in three inspection

intervals per year is 27.47331. Table 7.16 shows the annuity costs/m of rail grinding,

inspection for grinding, risk, downtime and replacement, lubrication and NDT

inspection for 12 MGT with lubrication for three inspection intervals per year.

Table 7.15: Annuity costs/m for 12 MGT with lubrication for three inspections

Radius (m) 0-300


Grinding 6.82


Risk 31.58

Down time 1.07

Replacement 15.48

Lubrication 0.67

NDT Inspection 1.68



lubrication for three inspection intervals per year. The analysis shows that risk and

replacement costs are higher compared to other costs. It is observed that the NDT

inspection cost for three inspection intervals is higher compared to one and two

inspection intervals per year.

223

Annuity costs/m for 12 MGT with Lub, Three Ins

Replacement,

15.48, 27%

Risk, 31.58,

55%Downtime,

1.07, 2%

Inspection for

rail grinding,

0.02, 0%

Lubrication,

0.67, 1% Grinding, 6.82,

12%

NDT Inspection

, 1.68, 3%

Figure 7.16: Annuity costs/m for 12 MGT with lubrication for three inspections

Table 7.17 shows the annuity costs/m of rail grinding, inspection for grinding, risk,

downtime and replacement and NDT inspection for 12 MGT without lubrication for

three inspection intervals per year.

Table 7.17: Annuity costs/m for 12 MGT without lubrication for three

inspections

Radius (m) 0-300


Grinding 6.12


Risk 31.58

Down time 0.232

Replacement 66

Lubrication 0.67

NDT Inspection 1.68



lubrication for three inspection intervals per year. The analysis shows that

replacement and risk costs are higher compared to other costs. It is observed that the

NDT inspection cost for three inspection intervals is higher compared to one and two

inspection intervals per year.

224

Annuity costs/m for 12 MGT without Lub Three Ins

Grinding,

6.12, 6%

Risk, 31.58,

30%

Downtime,

0.0232, 0%

Inspection for

rail grinding,

0.000024, 0%

Replacement,

66, 62%

NDT

Inspection ,

1.68, 2%

Figure 7.17: Annuity costs/m for 12 MGT without lubrication for three inspections

Table 7.18 shows the annuity costs/m for rail grinding, inspection for grinding, risk,

downtime, replacement, lubrication and NDT inspection for 23 MGT with lubrication

for three inspection intervals per year.

Table 7.18: Annuity costs/m for 23 MGT with lubrication for three inspections

Radius (m) 0-300


Grinding 5.42


Risk 37.68

Down time 0.04

Replacement 17.65

Lubrication 0.68

NDT inspection 4.00



lubrication for three inspection intervals per year. The analysis shows that the risk and

replacement cost are higher compared to other costs. Higher NDT inspection cost is

observed for three inspection intervals, compared to one and two inspection intervals

per year.

225

Annuity costs/m for 23 MGT with Lub Three Ins

Replacement,

17.65, 27%

Risk,

37.68386716,

58%Downtime,

0.04, 0%

Inspection for

rail grinding, 0,

0%

Lubrication,

0.68, 1%

NDT

Inspection,

4.00, 6%Grinding, 5.42,

8%

Figure 7.18: Annuity costs/m for 23 MGT with lubrication for three inspections

Table 7.19 shows the annuity costs/m for rail grinding, inspection for grinding, risk,

downtime, replacement, lubrication and NDT inspection for 23 MGT without

lubrication for three inspection intervals per year.

Table 7.19: Annuity costs/m for 23 MGT without lubrication for three

inspections

Radius (m) 0-300


Grinding 16.02


Risk 37.68

Down time 2.51

Replacement 152

NDT inspection 4.00



without lubrication for three inspection intervals per year. The analysis shows that the

replacement and risk costs are higher compared to other costs.

226

Annuity costs/m for 23 MGT without Lub Three Ins

Grinding,

16.02, 8%NDT

Inspection,

4.00, 2%

Inspection for

rail grinding,

0.044, 0%

Downtime,

2.51, 1%

Risk, 37.68,

18%

Replacement,

152, 71%

Figure 7.19: Annuity costs/m for 23 MGT without lubrication for three inspections

The analysis shows that the annuity costs/m of inspection has been increased with

increase of inspection intervals per year. However, the risk cost and total cost are

lower for three inspection intervals, compared to two and one inspection intervals per

year. Three inspection intervals per year have a significant influence on the

probability of detecting a number of rail defects and rail breaks. This has significant

influence on risk and total maintenance cost. Table 7.20 shows the comparison of

total annuity costs/m of 0-300 m curve radius for 12 and 23 MGT with lubrication.

Table 7.20: Total annuity costs/m for 12 and 23 MGT with lubrication

Radius (m) 0-300

Length (m) (Percentage) Total annuity costs/m ($AUD) Rail maintenance 12 MGT 23 MGT One Inspection 61.97 70.93

Two Inspection 58.62 66.95

Three Inspection 57.32 65.47

Figure 7.20 shows total annuity costs/m for 12 and 23 MGT of curve radius 0 to 300

m with lubrication for one, two and three inspection intervals per year. The analysis

shows that total annuity costs/m for one inspection interval is 5.41% higher with

lubrication for 12 MGT and 5.61% higher with lubrication for 23 MGT, compared to

two inspection intervals per year. It is also observed that total costs/m for 23 MGT is

higher, compared to 12 MGT grinding interval.

227

Total Annuity Costs/m with Lubrication

0

20

40

60

80

One Two Three

Inspections/year

Costs/m ($ AUD)

12 MGT

23 MGT

Figure 7.20: Total annuity costs/m for 12 & 23 MGT with lubrication

Table 7.21 shows the comparison of total annuity costs/m of 0-300 m curve radius for

12 and 23 MGT without lubrication.

Table 7.21: Total annuity costs/m for 12 and 23 MGT without lubrication

Radius (m) 0-300

Length (m) (Percentage) Total annuity costs/m ($AUD) Rail maintenance 12 MGT 23 MGT One Inspection 110 218

Two Inspection 107 214

Three Inspection 105 212

Figure 7.21 shows total annuity costs/m for 12 and 23 MGT of curve radius 0 to 300

m without lubrication for one, two and three inspection intervals per year. The

analysis shows that total costs/m for one inspection interval is higher, compared to

two and three inspection intervals per year. It is also observed that total costs/m for 23

MGT is higher, compared to 12 MGT grinding interval. It is found that total costs/m

without lubrication inspection intervals are higher, compared to lubrication inspection

intervals.

228

Total Annuity Costs/m without Lubrication

0

40

80

120

160

200

240

One Two Three

Inspections/year

Costs/m

($ AUD)

12 MGT

23 MGT

Figure 7.21: Total annuity costs/m for 12 & 23 MGT without lubrication

Therefore, the analysis found that two inspection intervals with lubrication is

economical, compared to one inspection and three inspection intervals per year.

The existing models have not considered the integration of all the maintenance

activities to assess operational risks and to estimate total annuity costs. The integrated

model developed in this research considers:

� Rail grinding: Increase of axle loads, accumulated tonnage (Million Gross

Tonnes), axle passes, curve radius, grinding wear, traffic wear, detected cracks

and derailments

� Lubrication: Total annuity costs were estimated considering lubrication and non-

lubrication, wayside lubricators, lubricator maintenance, rail wear and area head

loss, and rail maintenance

� Inspection: Non destructive testing (NDT) ultrasonic, NDT hand held, signalling

and visual inspection.

� Rectification and replacement: Rectification of rails due to worn-out rails,

undetected rail defects, rail breaks and derailments.

The integrated model considered relative cost of maintenance for various curves. The

relative performance of these curves, with the same lubrication strategy under

different operating conditions, can provide accurate results for assessment of

lubrication effectiveness. The integrated model can be used for managerial decisions

on rail grinding, rail lubrication, rail inspection intervals and rectification and

replacement of rails. It is important to consider increase of axle load, gross tonnage,

and speed such that the damage level based is on wear, RCF, defects, failures. It also

229

includes rail grinding and maintenance including lubrication, inspection, rectification

and replacements for accurate prediction of risks due to rail breaks and derailments.

Currently, research is being carried out by Larsson D (2004), Lee and Chiu (2005)

and Leong (2006) in the area of increase of axle loads and their impact on existing rail

tracks. The difference of axle loads (including dynamic load) could be included in this

model for the analysis of risk and, therefore, the effect on total cost. The productivity

increase due to increased axle loads from 26 tonnes to 30 tonnes, is 15.5 %. The cost

effectiveness due to this increase can be based on increased damage. The Office for

Research and Experiments (ORE) of the Union International des Chemins de Fer

(UIC) has noted that maintenance costs vary directly (60–65 per cent) with change in

axle load. It is found from the failure data analysis that 25% of the total failures occur

as a result of rolling contact fatigue defects. The multiplying factor for 30 tonne axle

load compared to 26 tonne axle load for failures can be (0.25*0.60) - a 15% increase

in failures. This is around 25% of 60% increase in maintenance problems and a 15%

increase in costs.

7.4. Summary

An integrated model is developed for grinding interval, lubrication decisions,

inspection intervals, rectification and replacement decisions. Total annuity costs

(TAC) are estimated, using an integrated wear-fatigue-lubrication-grinding-

inspection-rectification and replacement decision model. The analysis also shows that

inspection cost is higher for three inspection intervals per year, but the total

maintenance cost is lower, compared to one inspection interval and two inspection

intervals per year. It is found that two inspection intervals are more economical and

can reduce risk of rail breaks and derailment costs. Table 7.22 shows all the cases

examined with the integrated model and their findings. The conclusion and summary

of this thesis and a outline of the scope for future research are included in Chapter 8.

230

Table 7.22: Findings from examined cases

Case Studies Sections Conclusions

TAC/m for 12 MGT with

and without lubrication

Section

7.3.1

TAC for 0-600 m is 3 times higher without

lubrication compared to with lubrication.


and without lubrication

Section

7.3.2

TAC for 0-450 m is 7 times and 450-600 m

is 4 times higher without lubrication

compared to with lubrication.


and without lubrication for

one NDT inspection/yr

Section

7.3.3

Case 1

TAC/m for 0-300 m without lubrication for

one inspection is 43.69% higher compared

to with lubrication for 12 MGT



one NDT inspection/ annum

Section

7.3.3

Case 1


one inspection is 67.40% higher compared




two NDT inspection/ annum

Section

7.3.3

Case 2


two inspection is 45.06% higher compared




two NDT inspection/ annum

Section

7.3.3

Case 2

TAC/m without lubrication for 0-300 m for

two inspection is 68.68% higher compared



and without lubrication, for

three NDT inspection/

annum

Section

7.3.3

Case 3


three inspection is 45.62% higher compared




three NDT inspection/

annum

Section

7.3.3

Case 3


three inspection is 69.15% higher compared



lubrication for one and two

NDT inspections/ annum

Section

7.3.3

Cost savings per meter for 12 MGT is

5.41% with two inspections compared to

one inspection


lubrication for one and two

NDT inspections/ annum

Section

7.3.3

Cost savings per meter per year for 23

MGT is 5.61% with two inspections

compared to one inspection

231

CHAPTER 8

CONCLUSIONS AND SUGGESTIONS FOR FUTURE RESEARCH

8.1 Introduction

In recent years there has been a continuous increase of axle loads, tonnage, train

speed, and train length which has increased the productivity in the rail sector and

increased the risk of rail breaks and derailments. Rail operating risks have been

increasing due to increasing number of axle passes, steeper curves, wear-out of rails

and wheels, inadequate rail-wheel grinding, poor lubrication and reduced

maintenance. Rolling contact fatigue (RCF) and wear are significant problems for

railway companies. In 2000, the Hatfield accident in UK killed 4 people and injured

34 people and has lead to the cost of £ 733 million (AUD$ 1.73 billion) for repairs

and compensations. In 1977, the Granville train disaster in Australia killed 83 people

and injured 213 people. These accidents were related to rolling contact fatigue, wear

and poor maintenance.

The scope of this research was to develop models for rail grinding, wear and

lubrication, inspection and replacement of rails. Integration of these models is applied

for economic analysis of costs and operational risks. This chapter summarises the

contributions of this thesis and discusses scope for future research. The main

contributions of this thesis are development of (i) failure models and estimation of

parameters, considering operational and environmental conditions, (ii) grinding

models for optimal grinding decisions under various operating conditions, (iii)

lubrication models for optimal lubrication strategies, (iv) inspection models for

optimal inspection decisions, considering detected and undetected defects using non

destructive ultrasonic testing methods and (v) integrated models for estimating costs

and operating risks. A summary of the contributions are provided in Sections 8.2.

Scope for future research work is discussed in Section 8.3.

8.2 Contribution of This Thesis

Chapter 1 of this thesis provides the scope and outline of this research. It discusses the

background of the problems associated with rail degradation, influencing factors, and

the need for development of integrated models to predict and monitor maintenance

costs and operational risks.

232

In Chapter 2, a brief overview of the literature on rail track structure, rail defects, rail

wear, rail-wheel lubrication, rail grinding, inspection, replacement of rails and

maintenance strategies was provided as background for this research.

In Chapter 3, grounded theory of rail wear models, rolling contact fatigue (RCF) and

rail maintenance models are discussed. An extensive literature review identified the

gaps in the existing models and the approach needed to reduce the gaps for increased

safety and reliability of rail operation.

In Chapter 4, failure models are developed and parameters, considering operational

and environmental conditions, are estimated. Failures are modelled with non-

homogenous Poisson process and economic models are developed to analyse the

costs due to grinding, risks, downtime, inspection and replacement of rail. Costs for

23, 12, 18 and 9 MGT of curve radius from 0 to 300, 300-450, 450-600 and 600-800

m are estimated. Cost savings per meter per year are:





Analysis shows that rail players can save with 12 MGT intervals, compared to 23

MGT intervals under conditions outlined in this research.

In Chapter 5 a lubrication model is developed for optimal lubrication strategies. It

includes modelling and economic analysis of rail wear, rail-wheel lubrication, and

various types of lubricators. Cost-benefit analyses and annuity costs of lubricators are

estimated for managerial decisions. The analysis shows that cost effectiveness of

lubricator depends on the numbers of curves and length of curve it lubricates. The

Specific Outcomes of this chapter are:

Cost savings per lubricator per year for same curve length and under same curve

radius is:

• 17% for solar lubricators, compared to standard wayside lubricators.

Cost savings per meter per year are:

• 3 times for 0-450 m and 2 times for 450-600 m curve radius with lubrication

compared to without lubrication for 12 MGT grinding interval

233

• 7 times for 0-450 m and 4 times for 450-600 m curve radius with lubrication

compared to without lubrication for 23 MGT grinding interval

A relative performance model, a total curve and segment model and a simulation

model are developed for analysis of lubrication effectiveness.

In Chapter 6, a model is developed for rail inspection. Modelling and analysis

includes failure mode and effect analysis (FMEA) and risk priority number (RPN).

Collection and analysis of rail failure data, rail defect initiation and cost-benefit

analysis for inspection frequency are discussed. Probabilistic models are developed to

reduce unplanned maintenance due to rail breaks. The specific outcomes of this

chapter are the development of:

� an inspection model for cost effective rail inspection intervals

� a risk priority number by combining probability of occurrence, probability of

detection and consequences due to rail defects, rail breaks and derailments

Cost savings per year for same track length, curves and MGT of traffic:

• 27% on total maintenance costs with two inspections, compared to one


Analysis found:

• a high probability due to severity of undetected defects such as thermite welds

and rolling contact fatigue related defects

• that two NDT inspection intervals per year is cost effective, compared to one

inspection interval per year of the rail track under consideration

In Chapter 7 an integrated model is developed for costs and risks. It combines

decisions on grinding interval, lubrication strategies, inspection intervals, rectification

strategies and replacement of rails. Total annuity costs (TAC) are estimated using this

integrated wear-fatigue-lubrication-grinding-inspection-rectification and replacement

decision model.

Cost savings per meter per year for 12 MGT are:

• 5.41% on total maintenance costs with two inspections compared to one

inspection, considering risk due to rail breaks and derailment

• 45.06% on total maintenance costs with lubrication for two inspections,

compared to without lubrication

Cost savings per meter per year for 23 MGT are:

234

• 5.61% with two inspections, compared to one inspection, considering risk due

to rail breaks and derailments.

• 68.68% with lubrication for two inspections per year, compared to without

lubrication.

In summary, the main contributions of this research thesis include the development

of:

• failure models and estimation of parameters, considering operational and

environmental conditions

• economic models for rail grinding decisions linking cumulative MGT, axle load,

curve radius and operating conditions

• cost models for optimal lubrication strategies

• a risk based cost benefit model for optimal inspection decisions, considering

detected and undetected defects using non destructive ultrasonic testing

• integrated models for estimation of expected total cost and associated risks for

grinding, lubrication, inspection, rectification and replacement decisions.

8.3 Scope for Future Research

There is huge scope for future research in this area. Some suggestions are:

1. Assessment of operating risks due to rolling contact fatigue (RCF) and rail

grinding under various environmental conditions

2. Modelling and analysis of rolling contact fatigue crack initiation and growth rate,

considering passenger and mixed traffic under various operating conditions

3. Modelling and analysis of rail-wheel wear and rolling contact fatigue cracks for

higher axle loads and tonnage

4. Development of an international standard for rail-wheel lubrication

5. Development of an international standard for wear limit

6. Analysis of inspection technologies for better detection and to reduce undetected

defects leading to rail breaks and derailments

7. Development of extended models on rail grinding, lubrication and inspection

considering rail-wheel profile, material, hardness and size of rail under

deregulated environment

8. Development of a penalty pricing model, considering a deregulated environment

9. Detailed data collection for analysis to develop and predict more accurate and

appropriate models

235

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185. Zum Gahr K-H., (1987) “Microstructure and wear of materials”, Tribologv

Series, 10, 137-165, Elsevier, 1987.

186. www.hocking.com/applications/rail/ rail_inspection_appnote.pdf

187. http://safetydata.fra.dot.gov/officeofsafety/

250

APPENDICES

Appendix - A

% This Simulation program is calculating the .... % clear % Clear the working memory % % Set number of data that you will study, in the DAT file there is 720 data that you can use % %ndata = 100; % ndata is set % %load Inputdata.dat; % This is to Import the wear data for different curve sections %Inputdata=10*Inputdata; %This is to convert to 10MGT for each wearrate step %dummy=Inputdata; %dummy(1:8,2)=(Inputdata(1:8,1)+Inputdata(1:8,3))/2;% Manipulate 900A-Hi Rail %dummy(1:8,8)=(Inputdata(1:8,7)+Inputdata(1:8,9))/2;% Manipulate 1100-Hi Rail %dummy(1:8,2)=Inputdata(1:8,2).*0.85; %dummy(1:8,3)=Inputdata(1:8,3).*0.80; % The column 3 is moved to Colum 2 due to wrong input file set up %dummy(1:8,3)=Inputdata(1:8,2); %Inputdata=dummy; % % Create a radius vector starting at R=150, with a step of 10 ends at 801 % R = 200:25:800; % % Indata for wear rates, two different values, max wear rate high rail and % min wear rate for high rail. Data from KTH and litterature findings. Data % from south of Stockholm. % % General equation is: Wear(R)=A^(B*R+C)+D , dim (mm2/MGT) % % High Rail no lubrication % Hinolub=[1.6 -0.01 8 0]; % Based on BV findings of wear rates % [1.6 -0.01 8 0] is the nominal values % High Rail with lubrication % Hilub=[1.2 -0.01 4 0]; % Based on BV findings of wear rates % [1.2 -0.01 4 0] is the nominal values % % HilubOpt=[1.4 -0.01 6 0]; % for i =1:max(size(R)); HinonlubWear(i)=Hinolub(1)^(Hinolub(2)*R(i)+Hinolub(3))+Hinolub(4); HilubWear(i)=Hilub(1)^(Hilub(2)*R(i)+Hilub(3))+Hilub(4); % HilubOptWear=HilubOpt(1)^(HilubOpt(2)*R(i)+HilubOpt(3))+HilubOpt(4); end; %

251

% rUIC60_900A = 800; % This is replacement [SEK] cost per meter of one Rail % for segment L due to worn out regulation (I AUD % = 5.21 SEK) %rUIC60_1100 = 900; % rBV50_900A = 800*49/60; % This is replacement cost [SEK] per meter of BV50 Rail for one rail % for segment L due to worn out regulation. %rBV50_1100 = 900*50/60; % % Calculation of the total life as function of curve radii for the two % different wear rate functions, Hinonlubwear and Hilubwear. % BV50arealoss = 585; % Total critical area that can be used before renewal for 50 kg/m rail UIC60arealoss = 745; % Total critical area that can be used before renewal for 60 kg/m rail % % % Calculate total no of MTG before renewal % for i =1:max(size(R)); TotalMGTBV50(i,1)=BV50arealoss./HinonlubWear(i); % Index 1 is for Non lubrication TotalMGTBV50(i,2)=BV50arealoss./HilubWear(i); % Index 2 is for lubrication TotalMGTUIC60(i,1)=UIC60arealoss./HinonlubWear(i); % Index 1 is for Non lubrication TotalMGTUIC60(i,2)=UIC60arealoss./HilubWear(i); % Index 2 is for lubrication end; % % Calculate the annuity cost for rail replacement per meter for the % four different scenarios, UIC, BV, Lub, NonLub % Discount = 0.04; % MGT = 24; % To get No years, set MGT to a value of 24 for studied track of Malmbanan at BV % % Calculate present value and life for the unlubricated and lubricated curves % sumation1 = 0.; clear m k; for m=1:max(size(R)); % Non lubrication curves BV 50 profile for k=1:(max(TotalMGTBV50(m,1)./MGT)) sumation1(k,m) = rBV50_900A./(1+Discount)^(k); end; end; % sumation2 = 0.; clear m k; for m=1:max(size(R)); % Lubricated curves BV 50 profile for k=1:(max(TotalMGTBV50(m,2)./MGT)) sumation2(k,m) = rBV50_900A./(1+Discount)^(k);

252

end; end; % dummy1=sum(sumation1); % sum up the total values for Non lubrication curves BV 50 profile dummy2=sum(sumation2); % sum up the total values for lubrication curves BV 50 profile % for i=1:max(size(R)); sumpv_RailBV50(i,1) = dummy1(i); % Transpose back sumpv_RailBV50(i,2) = dummy2(i); % Transpose back end; % % Calculate the sum pv values for UIC60 % % Totalpv = 0.; clear m k; for m=1:max(size(R)); % Non lubrication curves for k=1:(max(TotalMGTUIC60(m,1)./MGT)); Totalpv(k,m) = rUIC60_900A./(1+Discount)^(k); end; end; % sumation4 = 0.; clear m k; for m=1:max(size(R)); % Lubricated curves for k=1:(max(TotalMGTUIC60(m,2)./MGT)) sumation4(k,m) = rUIC60_900A./(1+Discount)^(k); end; end; % dummy3=sum(Totalpv); dummy4=sum(sumation4); % % for i=1:max(size(R)); sumpv_RailUIC60(i,1) = dummy3(i); % Transpose back sumpv_RailUIC60(i,2) = dummy4(i); % Transpose back end; % % % Calculare the annuity cost for lub and un-lub curves % % for p=1:max(size(R)); Noyears60(p,1) = (TotalMGTUIC60(p,1)./MGT); % Calculate the no years for different radii Noyears60(p,2) = (TotalMGTUIC60(p,2)./MGT); Noyears50(p,1) = (TotalMGTBV50(p,1)./MGT); % Calculate the no years for different radii Noyears50(p,2) = (TotalMGTBV50(p,2)./MGT); end; % for w=1:max(size(R));; % Calculate the annuity cost for # no years annuUIC60(w,1)= sumpv_RailUIC60(p,1).*Discount./(1-(1./(1+Discount))^Noyears60(w,1)); annuUIC60(w,2)= sumpv_RailUIC60(p,2).*Discount./(1-(1./(1+Discount))^Noyears60(w,2)); annuBV50(w,1)= sumpv_RailBV50(p,1).*Discount./(1-(1./(1+Discount))^Noyears50(w,1));

253

annuBV50(w,2)= sumpv_RailBV50(p,2).*Discount./(1-(1./(1+Discount))^Noyears50(w,2)); end; % % % Calculate the savings per meter rail, i.e. difference between the lubricated and the unlubricated case. % Saving = anuity_Rail???(i,1) - anuity_Rail???(i,2) % savingBV50 = annuBV50(1:max(size(R)),1)-annuBV50(1:max(size(R)),2); savingUIC60 = annuUIC60(1:max(size(R)),1) - annuUIC60(1:max(size(R)),2); % % % Calculate cost for one lubricator according to BV data findings % % Maintenance cost (Service, Inspection and repair costs) % MainCostLub=6000; % mc=5800 to 6300 (Sek) per lubricator per year (12 months) % Independent of Tonnage 30 MGT per year (12 months) % Technical life of lubricator is 15 years LifeLub=15; % Discount rate = 4% Discount=0.04; % The purchase price of lubricator=26600 Sek PurchpriceLub=26000; % Lubricator Setup cost at the site = 5000 Sek LubSetCost=5000; % There are three types of lubricators (Electric (A), Gas(B) and Solar cell(C)) % Additional purchase cost for A = (50000-26600)=23400 Sek PurchpriceLubElecA=PurchpriceLub+23400; % Additional maintenance cost for B = (5800+1360)=7160Sek MainCostLubGasB=MainCostLub+1360; % Additional Purchase cost for C = (5000+26600)=31600Sek (Cost is for ten years) PurchpriceLubSolarC=PurchpriceLub+5000; % % Cost_inv_Lub = Cost of investments of Lubricators % Cost_inv_Lub(1)=(LubSetCost+PurchpriceLub); %Investments cost for one standard Lubricator Cost_inv_Lub(2)=(LubSetCost+PurchpriceLubElecA); %Investments cost for a El lub Cost_inv_Lub(3)=(LubSetCost+PurchpriceLub); %Investments cost for Gas Lub Cost_inv_Lub(4)=(LubSetCost+PurchpriceLubSolarC); %Investments cost Solar Lube % % Cost_main_Lub = Cost of investments of Lubricators % Cost_main_Lub(1)=(MainCostLub);%Maintenance cost for standard lubricator Cost_main_Lub(2)=(MainCostLub);%Maintenance cost for Type A Elc lubricator Cost_main_Lub(3)=(MainCostLub+MainCostLubGasB);%Maintenance cost for Type B Gas lubricator Cost_main_Lub(4)=(MainCostLub);%Maintenance cost for Type C Solar lubricator

254

% pv_LubMaint(1) = (Cost_main_Lub(1));% Lubricator maintenance cost is assumed same every year. Discount rate is constant over % period of time. Standard pv_LubInv(1) = (Cost_inv_Lub(1)).*Discount./(1+Discount);% Standard pv_LubMaint(2) = (Cost_main_Lub(2)); % Electrical pv_LubInv(2) = (Cost_inv_Lub(2)).*Discount./(1+Discount)^(15);% Electrical pv_LubMaint(3) = Cost_main_Lub(3);% ./(1+Discount)^(15);% Gas pv_LubInv(3) = Cost_inv_Lub(3).*Discount./(1+Discount)^(15);% Gas pv_LubMaint(4) = Cost_main_Lub(4);% ./(1+Discount)^(15);% Maint + Standard inv + Solar for 10 years pv_LubInv(4) = Cost_inv_Lub(4).*Discount./(1+Discount);% PV of Solar Lub % pv_LubSolPanel = (Cost_inv_Lub(4)-LubSetCost).*Discount./(1+Discount);% Solar panel life % % % % Calculate the Annuity cot for the four differnt Lubricators. Lubricator 4 % has solar panel that have 10 y life % anuity_LubMaint=pv_LubMaint; % for i=1:3 anuity_LubInv(i)=pv_LubInv(i)./(1-(1/(1+Discount))^15); end; anuity_LubInv(4)=pv_LubInv(4)./(1-(1/(1+Discount))^15)+pv_LubSolPanel./(1-(1/(1+Discount))^10); % anuity_Lub=anuity_LubMaint+anuity_LubInv; % % MGTL is a dummy for making plots with MGT step on x-axis % MGTL = MGT:MGT:1500; length = 1:1:max(size(R)); % % Calculate the BEP for each lubricator, each curve radii for each profile % for j=1:max(size(R)); for k=1:max(size(R)); saveMGTBV50(j,k)=savingBV50(j).*length(k); saveMGTUIC60(j,k)=savingUIC60(j).*length(k); end; end; % % %if saveMGTBV50(j,k)<=anuity_Lub(1) % BEP(j)=K %elseif saveMGTBV50(j,k)>=anuity_Lub(1) % statements2 %else % statements3 %end; % % Plot the total accumulated MGT v.s. curve radii for the choosen wear rates

255

% for i=1:max(size(R)); output(i,1)=R(i); output(i,2)=TotalMGTUIC60(i,1); output(i,3)=TotalMGTUIC60(i,2); output(i,4)=TotalMGTBV50(i,1); output(i,5)=TotalMGTBV50(i,2); output(i,6)=sumpv_RailUIC60(i,1); output(i,7)=sumpv_RailUIC60(i,2); output(i,8)=sumpv_RailBV50(i,1); output(i,9)=sumpv_RailBV50(i,2); output(i,10)=annuUIC60(i,1); output(i,11)=annuUIC60(i,2); output(i,12)=annuBV50(i,1); output(i,13)=annuBV50(i,2); output(i,14)=savingUIC60(i); output(i,15)=savingBV50(i); end; % save Case1 -ascii -double output;

Hinolub=[1.6 -0.01 8 0] With Lub No Lub With Lub No Lub With Lub No Lub With Lub No Lub

Hilub=[1.2 -0.01 4 0] Case 1 Case 1 Case 2 Case 2 Case 3 Case 3 Case 4 Case 4

A 1.2 1.6 1.2 1.6 1.2 1.5 1.2 1.8

B -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01 -0.01

C 4 8 4 8 4 8 4 8

D 0 0 0 2 0 0 0 0

Replacement [SEK] cost per m UIC60 800 SEK

Replacement [SEK] cost per m BV50 653 SEK

Total critical area loss UIC60 745 mm2

Total critical area loss BV50 585 mm2

Discount rate 0.04

MGT/year 24

Annuity cost for 4 lubricators 8.68E+

03 8.72E+03 1.49E+

04 1.28E+04

Output

TotalMGTBV50 v.s. Radii

TotalMGTUIC60 v.s. Radii

Failure data MGT Interval

13.13 13.16

17.28 17.72

17.72 18.29

29.05 29.73

30.25 31.00

31.68 32.46

32.46 32.49

256

257

10.00 100.00

1.00

5.00

10.00

50.00

90.00

99.00

ReliaSoft's Weibull++ 6.0 - www.Weibull.com

Probability - Weibull

Million Gross Tonnes (MGT)

Unre

liability, F(t)

2/03/2007 16:14LUTChattopa

WeibullData 1

W2 RRX - RRM MED

F=7 / S=0CB[FM]@95.00%2-Sided-B [T2]

β=3.0983, η=27.6176, ρ=0.9456

258

Appendix – B

Data for 23 MGT from curve radius 0 to 300 meters

5.74 27.57 7 67 1 0

Low Rail

MGT Traffic wear Grinding wear No of passes Detected cracks Rail brakes Derailments

23.00 5.43 21.10 4.00 62.00 0.00 0.00

46.00 5.93 23.15 2.00 48.00 3.00 0.00

69.00 6.66 25.47 3.00 52.00 1.00 0.00

92.00 6.79 29.43 7.00 48.00 3.00 0.00

115.00 6.77 23.02 4.00 60.00 2.00 1.00

138.00 6.96 23.04 2.00 59.00 3.00 0.00

161.00 5.83 21.20 5.00 51.00 1.00 0.00

184.00 5.77 25.69 4.00 50.00 2.00 0.00

207.00 5.40 26.88 7.00 50.00 3.00 0.00

230.00 6.38 16.84 3.00 50.00 2.00 0.00

253.00 6.00 24.92 3.00 61.00 2.00 0.00

276.00 6.70 25.94 4.00 50.00 1.00 0.00

299.00 7.24 22.56 2.00 63.00 0.00 1.00

322.00 6.66 17.63 5.00 49.00 2.00 0.00

345.00 5.64 16.71 2.00 66.00 3.00 0.00

368.00 7.29 23.04 4.00 53.00 0.00 0.00

391.00 5.45 19.46 2.00 49.00 0.00 0.00

414.00 6.65 29.65 3.00 59.00 3.00 0.00

437.00 6.91 22.13 4.00 64.00 3.00 0.00

460.00 6.80 27.21 2.00 51.00 0.00 0.00

7.31 33.19 5 80 3 0

High Rail

Traffic wear Grinding wear No of passes Detected cracks Rail brakes Derailments

6.87 27.42 2.00 84.00 1.00 0.00

8.75 31.40 1.00 79.00 3.00 1.00

8.35 26.87 1.00 83.00 3.00 0.00

9.08 33.25 5.00 83.00 0.00 0.00

8.53 23.48 2.00 82.00 3.00 0.00

7.24 33.28 1.00 89.00 3.00 0.00

8.36 20.91 3.00 80.00 3.00 0.00

8.42 32.04 2.00 80.00 1.00 0.00

7.41 19.11 5.00 90.00 3.00 0.00

7.83 24.91 1.00 78.00 1.00 0.00

8.47 25.27 2.00 80.00 3.00 0.00

8.77 29.96 2.00 86.00 2.00 0.00

8.96 29.56 1.00 89.00 3.00 0.00

9.16 26.72 2.00 83.00 1.00 0.00

6.97 27.28 1.00 79.00 2.00 0.00

7.71 18.02 2.00 82.00 2.00 1.00

7.47 19.03 1.00 82.00 2.00 0.00

7.21 33.48 2.00 81.00 3.00 0.00

8.52 26.75 2.00 79.00 3.00 0.00

8.23 18.82 1.00 83.00 2.00 0.00

259

Estimation of total annuity cost for grinding, inspection, risk, down time,

replacement

Cost ofgrinding per passper meter($AUD)

2 Section Curve radii [m]

Length [m] Percentage Length [m]

Grinding production speed

10 1 0<R<300

1318 1.01% 51791

Cost ofreplacement of one rail for segment Ldue toworn outregulation ($AUD)

152 2 300<R<450

1384 1.06% 30526

Expected costs ofrepairing rail brakes($AUD)

1700 3 450<R<600

36524 27.98% 48220

Expected cost perderailment (accident) ($AUD)

3000000 4 600<R<800

33235 25.46% 130537

Expected cost ofdown timeper hour($AUD)

3136 5 800<R<1500

4569 3.50%

Inspection cost ($AUD)

0.0043 6 1500<R<9 999

4569 3.50%

New railcross sectional area

2960 7 10 000<R 718 0.55%

Critical area forreplacement decision

2520 8 Tangential track

16073 36.94%

Discount rate

0.1 Total length

130537 100.00%

Weibull constants Beta

3.6

4.5$AUD per

Kg

Weibull constants Lambda

0.001

1.36Kg per MGT

Pi(A) Probability of failure to detect the undetected potential rail breaks leading to

derailment during the NDT

(1-Pi(A)) is the probability of detecting the undetected potential rail breaks during

the NDT leading to derailment are repaired in an emergency.

Lubrication consumption

Pi(B) is the probability of detecting potential rail breaks during the NDT and

repairing immediately

(1-Pi(B)) is the probability of undetected potential rail breaks during the NDT

leading to derailment

Lubrication Cost The costs vary with quality of the

lubrication oil.

Discount rate is 10% is taken as flatrate for 23 MGT

Radius<800

Radius>800

Tangential track

260

Data for 23 MGT of curve radius from 0 to 300 meters low rail

23 Low RailYear MGT Comment Traffic

wearGrinding wear

No of passes

Detected cracks

Rail brakes

Derailments

1 23 6 25.92 3 50 1 02 46 5.38 23.16 3 60 3 03 69 7.09 26.92 4 67 3 04 92 7.27 16.85 5 64 1 05 115 5.9 16.71 4 50 3 06 138 6.98 18.11 4 61 3 07 161 6.8 27.35 3 65 1 08 184 7.21 20.54 4 64 3 09 207 7.17 28.82 4 49 2 010 230 6.87 17.03 5 51 1 011 253 6.76 22.09 4 54 3 012 276 7.23 26.24 2 62 2 013 299 7.2 19.63 5 61 2 014 322 6.56 26.4 5 60 3 015 345 7.1 18.85 5 51 3 116 368 6.53 24.56 5 52 2 017 391 No

grinding6.79 26.62 2 52 1 0

18 414 Replaced 5.4 30.32 5 49 3 0 Estimation of annuity cost for grinding low rail Grinding cost

Present value

Total PV at

Replacement

Annuity cost

Annuity cost/Meter

Annuity cost/MGT

Annuity cost/MGT/Meter

7910.54 7191.47910.54 6537.6410547.39 7924.4113184.24 9005.0110547.39 6549.110547.39 5953.737910.54 4059.3610547.39 4920.4410547.39 4473.1213184.24 5083.0910547.39 3696.85273.69 1680.3613184.24 381913184.24 3471.8213184.24 3156.213184.24 2869.27

80390.76 9110.77 6.91 396.12 0.3

261

Data for 23 MGT of curve radius from 0-300 meters high rail

23 High Rail

Year MGT Comment Traffic wear

Grinding wear

No of passes

Detected cracks

Rail brakes

Derailments

1 23 8.76 20.16 2 83 1 02 46 7.89 28.44 2 83 1 03 69 8.66 32.41 2 80 1 04 92 9.02 29.15 3 84 3 15 115 9.29 23.42 2 79 2 06 138 8.16 19.61 2 80 0 17 161 8.41 23.32 1 79 3 08 184 8.97 29.7 2 80 1 09 207 7.27 24.88 2 79 1 010 230 7.22 18.36 4 79 2 011 253 6.83 26.01 2 85 2 012 276 7.12 32.88 1 87 1 013 299 9.29 25.27 4 89 2 114 322 8.25 33.75 4 82 2 015 345 No

grinding7.71 23.49 4 79 3 0

16 368 Replaced 7.32 22.77 3 79 3 0 Estimation of annuity cost for grinding high rail Grinding cost

Present value

Total PV at

Replacement

Annuity cost

Annuity cost/Meter

Annuity cost/MGT


5273.69 4794.275273.69 4358.435273.69 3962.27910.54 5403.015273.69 3274.555273.69 2976.862636.85 1353.125273.69 2460.225273.69 2236.5610547.39 4066.485273.69 1848.42636.85 840.1810547.39 3055.210547.39 2777.46

43406.93 5188.07 3.94 225.57 0.17

262

Average annuity cost for grinding of high rail and low rail for practical purpose Annuity cost

Annuity cost/Meter

Annuity cost/MGT


Grinding cost/Meter

Grinding cost/MGT/Meter

10 0.4310 0.4312 0.5216 0.712 0.5212 0.528 0.3512 0.5212 0.5218 0.7812 0.526 0.2618 0.7818 0.7810 0.4310 0.43

7149.42 5.42 310.84 0.24 Data for accumulated area loss for low rail and high rail

Low Rail High Rail

Accumulated Area Loss [mm2]

Worn out level %

Area loss/MGT

Accumulated Grinding Passes

Accumulated Area Loss [mm2]

Worn out level %

Area loss/MGT

Accumulated Grinding Passes

E(M j+1 ; M j)

31.91 7.25% 1.39 3 28.92 6.57% 1.26 2 060.45 13.74% 1.31 3 65.25 14.83% 1.42 4 0.000194.46 21.47% 1.37 7 106.32 24.16% 1.54 6 0.0001118.58 26.95% 1.29 12 144.5 32.84% 1.57 9 0.0002141.18 32.09% 1.23 16 177.2 40.27% 1.54 11 0.0004166.27 37.79% 1.2 20 204.97 46.58% 1.49 13 0.0006200.41 45.55% 1.24 23 236.7 53.79% 1.47 14 0.0009228.17 51.86% 1.24 27 275.36 62.58% 1.5 16 0.0012264.16 60.04% 1.28 31 307.51 69.89% 1.49 18 0.0016288.05 65.47% 1.25 36 333.08 75.70% 1.45 22 0.0021316.91 72.03% 1.25 40 365.92 83.16% 1.45 24 0.0026350.38 79.63% 1.27 42 405.92 92.25% 1.47 25 0.0032377.2 85.73% 1.26 47 0 0.00% 0 0 0.004410.16 93.22% 1.27 52 42 9.55% 0.13 4 0.0048436.11 99.12% 1.26 57 73.21 16.64% 0.21 8 0.00570 0.00% 0 0 103.3 23.48% 0.28 11 0.0067

33.42 7.59% 0.09 2 137.56 31.26% 0.35 12 0.007869.14 15.71% 0.17 7 164.87 37.47% 0.4 15 0.00998.36 22.35% 0.23 10 199.87 45.42% 0.46 17 -0.0508

263

Estimation of probabilities and annuity cost for risk of low rail

Low rail

Pi(B) (1-Pi(B)) Pi(A) (1-Pi(A)) Risk cost PV Risk cost

Total present value

Annuity Risk cost

Annuity Risk

cost/Meter

Annuity Risk

cost/MGT

Annuity Risk

cost/MGT/Meter

0.9804 0.0196 0 0.0196 0.024 0.02180.9524 0.0476 0 0.0476 0.087 0.07190.9571 0.0429 0 0.0429 0.2058 0.15460.9846 0.0154 0 0.0154 0.3912 0.26720.9434 0.0566 0 0.0566 0.6627 0.41150.9531 0.0469 0 0.0469 1.0195 0.57550.9848 0.0152 0 0.0152 1.4682 0.75340.9552 0.0448 0 0.0448 2.0435 0.95330.9608 0.0392 0 0.0392 2.7245 1.15540.9808 0.0192 0 0.0192 3.519 1.35670.9474 0.0526 0 0.0526 4.4864 1.57250.9688 0.0313 0 0.0313 5.5479 1.76770.9683 0.0317 0 0.0317 6.7764 1.96290.9524 0.0476 0 0.0476 8.1847 2.15530.9273 0.0545 0.0182 0.0364 26.235 6.28040.963 0.037 0 0.037 11.4265 2.48670.9811 0.0189 0 0.0189 21.8531 2.4766 0.0019 0.1077 0.0001

Probabilities of Low rail Risk cost calculations for low rail

Estimation of probabilities and annuity cost for risk for high rail

Pi(B) (1-Pi(B)) Pi(A) (1-Pi(A)) Risk cost PV Risk cost

Total present value

Annuity Risk cost

Annuity Risk

cost/Meter

Annuity Risk

cost/MGT

Annuity Risk

cost/MGT/Meter

0.9881 0.0119 0 0.0119 0.024 0.02180.9881 0.0119 0 0.0119 0.0864 0.07140.9877 0.0123 0 0.0123 0.2045 0.15370.9545 0.0341 0.0114 0.0227 0.6495 0.44360.9753 0.0247 0 0.0247 0.6585 0.40890.9877 0 0.0123 -0.0123 0.9826 0.55460.9634 0.0366 0 0.0366 1.4745 0.75660.9877 0.0123 0 0.0123 2.0304 0.94720.9875 0.0125 0 0.0125 2.71 1.14930.9753 0.0247 0 0.0247 3.5228 1.35820.977 0.023 0 0.023 4.4601 1.56320.9886 0.0114 0 0.0114 5.5259 1.76070.9674 0.0217 0.0109 0.0109 9.4098 2.72570.9762 0.0238 0 0.0238 8.1461 2.14510.9634 0.0366 0 0.0366 14.06 1.6805 0.0013 0.0731 0.0001

Probability calculations for High rail Risk cost calculations for High rail

264

Average annuity cost for risk of high rail and low rail for practical purpose Annuity cost

Annuity cost/Meter

Annuity cost/MGT


Risk cost/Meter

Risk cost/MGT/Meter

0 00.0001 00.0003 00.0008 00.001 00.0015 0.00010.0022 0.00010.0031 0.00010.0041 0.00020.0053 0.00020.0068 0.00030.0084 0.00040.0123 0.00050.0124 0.00050.0199 0.00090.0087 0.0004

2.0786 0.0016 0.0904 0.0001 Estimation of annuity cost for down time of low rail Down time cost

PV of Down time cost

Total PV Annuity cost

Annuity cost/Meter

Annuity cost/MGT


1240 11281240 10251654 12432067 14121654 10271654 9341240 6371654 7721654 7012067 7971654 580827 2632067 5992067 5442067 4952067 450827 164 12605 1429 1.08 62.11 0.05

265

Estimation of annuity cost for down time of high rail Down time cost

PV of Down time cost


Annuity cost/Meter

Annuity cost/MGT


827 752827 683827 6211240 847827 513827 467413 212827 386827 3511654 638827 290413 1321654 4791654 4361654 396 6806 813 1 35 0.03

Average annuity cost for down time of high rail and low rail for practical purpose Annuity cost

Annuity cost/Meter

Annuity cost/MGT


Down time cost/Meter

Down time cost/MGT/Meter

1.57 0.06821.57 0.06821.88 0.08182.51 0.10911.88 0.08181.88 0.08181.25 0.05451.88 0.08181.88 0.08182.82 0.12271.88 0.08180.94 0.04092.82 0.12272.82 0.12272.82 0.12272.51 0.1091

1121 0.85 48.74 0.04

266

Average annuity cost for inspection of High rail and low rail for practical purpose Inspection cost

PV of Inspection


Annuity cost/Meter

Annuity cost/MGT


Inspection cost/Meter

65 59 0.04965 54 0.04965 49 0.04965 45 0.04965 40 0.04965 37 0.04965 33 0.04965 30 0.04965 28 0.04965 25 0.04965 23 0.04965 21 0.04965 19 0.04965 17 0.04965 16 0.04965 14 0.04965 13 510 58 0.04 2.51 0

Estimation of annuity cost for replacement of Low rail Replacement cost

PV Total PV Annuity cost

Annuity cost/Meter

Annuity cost/MGT


199873 1998730 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00 0 199873 22652 17 985 1

267

Estimation of annuity cost for replacement of High rail Replacement cost


Annuity cost/Meter

Annuity cost/MGT


199873 19987300000000000000 199873 23889 18 1039 1

Average annuity cost for replacement of high rail and low rail for practical purpose

Annuity cost Annuity cost/Meter Annuity cost/MGT Annuity cost/MGT/Meter

23270 17.65 1011.76 0.77

268

Estimation of annuity cost for lubrication of high rail Lubrication cost

Present value

Total PV at Replacement

Annuity cost

Annuity cost/Meter

Annuity cost/MGT


985 896985 814985 740985 673985 612985 556985 506985 460985 418985 380985 345985 314985 285985 259985 236

7494 896 0.68 39 0.0295 Estimation of average annuity cost for lubrication of low rail and high rail for practical purpose Lubricatio

n cost/Meter

Lubrication

cost/Meter/MGT

Total annuity cost/meter up to

replacement

Total annuity cost/meter with

lubrication

0.75 0.030.75 0.060.75 0.10.75 0.130.75 0.160.75 0.190.75 0.230.75 0.260.75 0.290.75 0.320.75 0.360.75 0.390.75 0.420.75 0.450.75 0.490.75 0

23.97 24.65

269

Inspection data Conversion rate (AUD) 6.0892

Total track length (m) considered for analysis 130537

Insp cost NDT Car 75000 150000 225000

NDT HH 76921.60 76005.99073 76660.955

Planned 2884560.00 2850224.65 2874785.8

Risk with 3500000 Derailment cost 35622036.21 31229236.78 29953537

Total Cost 38658517.81 34305467.43 33129983

Total NDT inspection cost 3036481.60 3076230.643 3176446.77

Risk cost/meter SEK 272.89 239.24 229.46

Total Insp cost /meter SEK 23.26 23.57 24.33

Risk cost/meter AUD 44.82 39.29 37.68

Total Insp cost /meter AUD 3.82 3.87 4.00

270

Lubrication Data Data to estimate total annuity cost for Way Lubricator COST

Item $ AUD Purchase cost of lubricator 4200

Standard set up (Installation cost) per hour is $AUD 50 (2 hours*2 personnel*$AUD 50)

400

Lubricant cost per meter (Club)(AUD$132.85/1600 m) 0.08303

Vehicle cost per hour is AUD $ 45 ( for example 2.3 hours) 104

Travelling cost AUD $ 35 (for example 2.3 hours) 0 Labour and repair cost (generally 2 people) per hour AUD $ 50 (for example 2.3 hours) 163

Number Services per month 2

Expected total cost of per service 267

Expected total cost of per service per month 534 Expected total number of failures per year (for example in year 2006 failures was 5) per each lubricator 2 Unplanned Maintenance cost per failure maintenance $ AUD 190 Expected total cost of unplanned maintenance per year $ AUD 380

Expected total cost of service per year $ AUD 6403

Expected life of Lubricator (y) on an average 30

Cost of lubricant for 313 meters 25.98839

Lubricant cost per year for 313 meter rail 311.86068

Expected total cost of maintenance activity per each lubricator (Cmt) $ AUD 6905

Discount rate 0.1

Inflation every year 0.025

271

Years

Traffic during the year (Million gross tonnes, MGT)

Total number of failures every year

Expected total Unplanned maintenace cost

Expected total cost of service per year

Cost of Lubricant per year pe meter

Expected total cost of lubricant per year

Total Maintenace cost

Present Value

1998 8.576 1.00 190 6403 0.08 0.9964 6905.06 6277.33

1999 9.233 1.00 190 6403 0.08 0.9964 6905.06 5706.66

2000 9.101 1.00 190 6403 0.08 0.9964 6905.06 5187.87

2001 9.586 1.00 190 6403 0.08 0.9964 6905.06 4716.25

2002 9.438 1.00 190 6403 0.08 0.9964 6905.06 4287.50

2003 9.496 1.00 190 6403 0.08 0.9964 6905.06 3897.73

2004 9.478 1.00 190 6403 0.08 0.9964 6905.06 3543.39

Total Present Value at replacement

Annuity cost for each lubricator

Annuity cost for each lubricator per meter

Rail material cost

Rail installation cost

Total cost of rail material and installation


Annuity cost per meter

18780 54775 73555 66868.18

73555 60789.26

73555 55262.96

73555 50239.05

73555 45671.87

73555 41519.88

33616.73 10563 33.75 73555 37745.35

73555 34313.95

73555 31194.5

73555 28358.64 451963.6 66868 213.64

Total cost/m with lubrication 247.38

272

Rail material cost

Rail installation cost

Total cost of rail material and installation

PV Total PV

Annuity cost

Annuity cost per meter

18780 54775 73555 73555 66868.18

73555 60789.26

73555 55262.96

73555 50239.05

147110 91343.74

147110 83039.76

147110 75490.69

147110 68627.9

147110 62389

147110 56717.27 670767.

8 99240.34 317.0618

Savings/m 69.6779

Savings for 313 m per year 21809.18

Savings for 313 m for 10 years 347582.2

AA35*(1-1/(1+0.1)^10)/0.1*(1.1)^10

Curve length Cost of rail per meter

313 60 300 73555 6886

Rail installation cost 175 600 147110 6886

0.99636 311.86068 800 220665 6886

207 1000 294220 6886

273

Wear Data 47 kg Rail

Area Head Loss from 0-300 meters Data for Rails which are replaced are eliminated for better prediction

1998 Reduction in Reduction in

CURVE DETAILS CHANGED RAIL SIZE Area of Head Area Head loss

FROM TO RADIUS YES/NO IN KG mm^2 mm^2/MGT

72.466 72.484 220.00 No 47 57 6.65

163.146 163.296 231.00 No 47 500 58.28

97.312 97.394 256.00 No 47 360 41.92

100.386 100.522 295.00 No 47 193 22.50

63.920 63.945 300.00 No 47 250 29.14

64.673 64.698 300.00 No 47 219 25.56

160.626 160.651 300.00 No 47 136 15.85

177.792 177.813 300.00 No 47 0 0.00

192.327 192.352 300.00 No 47 136 15.85

193.100 193.125 300.00 No 47 26 3.07

47 kg Rail





72.466 72.484 220.00 No 47 57 6.17

163.146 163.296 231.00 No 47 526 56.99

97.312 97.394 256.00 No 47 443 47.96

100.386 100.522 295.00 No 47 193 20.89

63.920 63.945 300.00 No 47 250 27.07

64.673 64.698 300.00 No 47 219 23.74

160.626 160.651 300.00 No 47 136 14.72

177.792 177.813 300.00 No 47 0 0.00

192.327 192.352 300.00 No 47 136 14.72

193.100 193.125 300.00 No 47 26 2.85

274

47 kg Rail





72.466 72.484 220.00 No 47 228 25.05

163.146 163.296 231.00 No 47 552 60.70

97.312 97.394 256.00 No 47 640 70.34

100.386 100.522 295.00 No 47 224 24.57

63.920 63.945 300.00 No 47 307 33.72

64.673 64.698 300.00 No 47 0 0.00

160.626 160.651 300.00 No 47 136 14.93

177.792 177.813 300.00 No 47 83 9.15

192.327 192.352 300.00 No 47 0 0.00

193.100 193.125 300.00 No 47 0 0.00

47 kg Rail





72.466 72.484 220.00 No 47 228 23.78

163.146 163.296 231.00 No 47 552 57.63

97.312 97.394 256.00 No 47 640 66.78

100.386 100.522 295.00 No 47 281 29.27

63.920 63.945 300.00 No 47 333 34.76

64.673 64.698 300.00 No 47 189 19.67

160.626 160.651 300.00 No 47 162 16.92

177.792 177.813 300.00 No 47 83 8.69

192.327 192.352 300.00 No 47 0 0.00

193.100 193.125 300.00 No 47 0 0.00

275

47 kg Rail





72.466 72.484 220.00 No 47 228 24.16

163.146 163.296 231.00 No 47 609 64.58

97.312 97.394 256.00 No 47 666 70.61

100.386 100.522 295.00 No 47 281 29.73

63.920 63.945 300.00 No 47 333 35.31

64.673 64.698 300.00 No 47 189 19.98

160.626 160.651 300.00 No 47 162 17.19

177.792 177.813 300.00 No 47 83 8.83

192.327 192.352 300.00 No 47 0 0.00

193.100 193.125 300.00 No 47 0 0.00

47 kg Rail





72.466 72.484 220.00 No 47 254 26.78

163.146 163.296 231.00 No 47 609 64.18

97.312 97.394 256.00 No 47 579 60.95

100.386 100.522 295.00 No 47 307 32.32

63.920 63.945 300.00 No 47 333 35.09

64.673 64.698 300.00 No 47 246 25.86

160.626 160.651 300.00 No 47 162 17.08

177.792 177.813 300.00 No 47 83 8.77

192.327 192.352 300.00 No 47 193 20.32

193.100 193.125 300.00 No 47 57 6.00

276

47 kg Rail





72.466 72.484 220.00 No 47 254 26.83

163.146 163.296 231.00 No 47 609 64.30

97.312 97.394 256.00 No 47 579 61.06

100.386 100.522 295.00 No 47 307 32.38

63.920 63.945 300.00 No 47 390 41.17

64.673 64.698 300.00 No 47 272 28.68

160.626 160.651 300.00 No 47 219 23.13

177.792 177.813 300.00 No 47 83 8.79

192.327 192.352 300.00 No 47 364 38.40

193.100 193.125 300.00 No 47 83 8.79

Mechanism of Way-side Lubricators (Mechanical)

Figure B1: Mechanical lubricators (QR, 2005)

Figure B1 shows an example of a mechanical lubricator. It was found that mechanical

lubricators have been widely used because of simple, effective mechanical design and

high performance in reducing wheel and rail wear. However, evolving cutting edge

technology such as hydraulic and electric lubricators have replaced mechanical

lubricators to adapt to changes in operating and environmental conditions.

The basic components of a Mechanical Lubricator are:

(A) Grease Container: Contains a piston attached to the springs which supplies the

energy to deliver the grease to the hose to be picked up by the wheel flange. In

addition, it contains a valve to ensure safe filling of the tank and provide

protection to the operation (as it is operating in high pressure). Selection of

the tank is based on the volume of traffic which passes the lubricator. The

lubricator comes with a range of tank capacity from 9 kg to 75 kg.

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277

(B) Grease Pump: The grease pump is clamped or bolted outside of the rail for the

wheel tread to push the grease pump to create pressure in the grease container.

(C) Grease Distribution Unit: A pair of blades/wiping bars are clamped or bolted

at gauge face of the rail. Grease is distributed evenly on and along the length

of the wiping bars. The length of the wiping bars varies from 400 mm to 600

mm depending on the model.

(D) Grease Hose System: The larger diameter of the grease hose system enables

the grease to travel to the delivery hose and be distributed evenly on the

wiping bars. The position of the grease container on the ballast must be

carefully taken into consideration as the vibration from the traffic may

damage the mechanical operation of the lubricator.

(E) Grease Delivery Hose System: The hose acts as a transport medium between

the tank and the distribution unit. The hoses are long and smaller in diameter

than the feed hose. The grease travelling in the hose will be under high

internal pressure. The lubricator maintainer has to ensure that the hose does

not leak. In addition, the placement of the hose under the rail must be given

tolerance to avoid pressure drop (which can break the hose) and squashing.

Positive Displacement Pump

Displacement moves the liquid from one place to another place. As the plunger moves

toward the inside of the cylinder, liquid is displaced. The plunger displacement is

positive and the volume displaced is equal to the volume of the plunger in the

cylinder. Therefore, grease pump that displaces constant volume of grease is defined

as positive displacement pump (as shown in Figure B2).

Figure B2: Plunger mechanism (QR, 2005)

Mechanism of Hydraulic Lubricators

Hydraulic lubricators are widely used on track for rail flange lubrication. However,

maintenance of these lubricators shall not be neglected. These lubricators are designed

for:

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� Effective lubrication

� Economic solution to lubrication

� Minimum maintenance

� Use under any operating condition (eg. Tracks, MGT, temperature etc)

� Improvement of grease distribution

� Ease and convenience (for example, simple operation and easy adjustments

when tank filling)

The lubricator is designed in 3 different sizes: 12.5 kg, 25 kg and 37.5kg.

Visual Inspection

Visual inspection is commonly used by rail players to assess the effectiveness of the

lubricators and lubricants. Finger or “smear test” on the gauge faces helps to assess

lubricant distribution (as shown in Figure B3). This is useful to understand the need

for adjusting plunger height and blade position (Reiff, 1991).

Figure B3: Smear Test (Powell and Wheatley, 2004)

Rail head temperature rise method

Rail head temperature rise method is used to indicate the effectiveness of lubrication.

For energy, a Type K thermocouple is placed at the lower corner of the gauge side. To

avoid/compensate for noise effects, another thermocouple is located on a dummy rail

section. In order to accommodate longer operations, photo – voltaic arrays is used to

maintain battery power in remote locations.

Table B1: Mean temperature rise (Tew and Mutton, 1991)

Condition Mean Temperature Rise (°C)

Fully Lubricated 0 – 0.5°C

Dry 2 – 3 °C

Non Lubricated 5°C

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Table B1 shows mean temperature rise, indicating the condition of the lubricated rail

track under metropolitan transit conditions. Tew and Mutton (1991) found that this

method is applicable for heavy haul conditions where higher temperature rise occurs.

Tribometer

Use of the tribometer overcomes limitations of visual and scientific methods. It

provides data on limiting co-efficient of friction for both rail top and gauge faces. The

tribometer is able to measure friction as a function of distance from trackside

lubricator, lubricants and application rates (dose amount and frequency). Table B2

shows friction coefficients based on tribometer measurements.

Table B2: Friction Coefficients based on Tribometer (Tew and Mutton, 1991)

Condition Friction Coefficient

Fully Effective Lubrication 0.1 – 0.15

Dry 0.35 – 0.45

Unlubricated > 0.45

Advantages of The tribometer:

� accurate assessment of friction as an indicator of wear

� objective comparison over a wide range of track locations and conditions

� provision of friction data for service conditions and rail profiles

Figure B4: Tribometer at the gauge face (Powell and Wheatley, 2004)

Figure B4 shows the application of the tribometer for measuring friction. However,

the tribometer is not equipped with high storage facilities required for inspecting large

track section.

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