t549 report final

Research Programme

EngineeringDevelopment of a wheel wear and rolling contact fatigue

model

A Review of Wheel Wear and Rolling Contact Fatigue

UK Proprietary 05-009 John Tunna, TTCI(UK), Ltd.

John Sinclair, Interfleet Technology Ltd.

Javier Perez, Rail Technology Unit of

Manchester Metropolitan University

1 February 2006

©RSSB copyright 2006. This research report, excluding any logos, may be reproduced free of charge

in any format or medium for research, private study or for internal circulation within an organization.

This is subject to it being reproduced accurately and not used in a misleading context. The material

must be acknowledged as Rail Safety & Standards Board copyright and the title of the publication

specified. Disclaimer: This report was prepared for members of the Rail Safety & Standards Board by TTCI(UK) Ltd., a subsidiary of the Transportation Technology Center, Inc. (TTCI) Pueblo, Colorado, USA. It is based on investigations conducted by TTCI(UK) Ltd. with the direct participation of the members of the Rail Safety & Standards Board to criteria approved by them. The contents of this report imply no endorsements whatsoever by TTCI(UK) Ltd. of products, services or procedures, nor are they intended to suggest the applicability of the test results under circumstances other than those described in this report. The results and findings contained in this report are the sole property of the Rail Safety & Standards Board. The contents of this report may not be released by anyone to any party other than the Rail Safety & Standards Board without the written permission of the Rail Safety & Standards Board. TTCI(UK) Ltd. is not a source of information with respect to this report, nor is it a source of copies of this report. TTCI(UK) Ltd. makes no representations or warranties, either expressed or implied, with respect to this report or its contents. TTCI(UK) Ltd. assumes no liability to anyone for special, collateral, exemplary, indirect, incidental, consequential, or any other kind of damages resulting from the use or application of this report or its contents.

Prepared by TTCI(UK) Ltd. 1 February 2006 Page i

EXECUTIVE SUMMARY

Task T549 is a Rail Safety & Standards Board project to develop a wheel wear and rolling contact fatigue (RCF) model. TTCI(UK) Ltd. is leading this project with help from Interfleet Technology Ltd. and the Rail Technology Unit of Manchester Metropolitan University.

The project begins with this report, which covers current best practices in wheel wear and RCF.

Shear stresses at and just below the surface are shown to be driven by forces generated during steady-state curving.

Repeated applications of plastic shear stresses causes shear deformation of the material at and just below the wheel’s surface. This can eventually lead to the formation and growth of surface cracks.

Depending on the contact conditions, the surface cracks can develop into either wear or RCF. Tangential and normal forces, contact pressure, creepage, and the presence of fluid are important factors in determining the amount of wear and RCF.

High strength wheel steels have been developed to withstand severe service loads. New materials and treatments are being developed to extend wheel life.

Currently, train operators in the UK are managing wheels affected by RCF by reducing wheel profiling intervals. Braking characteristics and alternative wheel materials are also being investigated.

The references quoted in this report show that RCF and wear of rails and wheels have been the subject of investigation for over 25 years. Several well-developed models exist for predicting wheel and rail wear. New models are emerging for rail RCF. These need to be further developed to be applicable to wheels.

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Table of Contents 1 Introduction......................................................................................................................1 2 Load environment............................................................................................................2

2.1 Wheel/Rail Curving Forces ...............................................................................2 2.2 Contact Conditions............................................................................................7 2.3 Traction & Braking Forces...............................................................................10

3 Wheel Materials.............................................................................................................11 3.1 Wheel Steels Currently Used on Network Rail ................................................11 3.2 Other Wheel Materials ....................................................................................12 3.3 Microstructure .................................................................................................14 3.4 Shakedown .....................................................................................................15

4 Wheel Wear...................................................................................................................18 4.1 Wear Mechanisms ..........................................................................................18 4.2 Wear Models...................................................................................................19

4.2.1 Energy transfer wear models..............................................................20 4.2.2 Sliding wear models ...........................................................................23

4.3 Effect of Fluid on Wear....................................................................................25 4.4 Effects of Metallurgy on Wear .........................................................................25 4.5 Effects of Change in Direction on Wear ..........................................................26

5 Wheel Rolling Contact Fatigue ......................................................................................27 5.1 RCF Mechanism .............................................................................................27 5.2 RCF Models ....................................................................................................33 5.3 Effect of Metallurgy on RCF ............................................................................37 5.4 Effects of Change in Direction on RCF............................................................38 5.5 Interaction between RCF and Wear ................................................................39

6 Wheel Asset Management ............................................................................................40 7 Conclusions...................................................................................................................41 References ............................................................................................................................42 Appendix – Notations & Definitions ........................................................................................45

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A Review of Wheel Wear & Rolling Contact Fatigue

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1 INTRODUCTION Task T549 is a Rail Safety & Standards Board project to develop a wheel wear and rolling contact fatigue (RCF) model. TTCI(UK) Ltd. is leading this project with help from Interfleet Technology Ltd. and the Rail Technology Unit of Manchester Metropolitan University.

The project begins with this report, which covers current best practices in wheel wear and RCF, addressing the following subject areas:

• Description of the load environment experienced by wheels in service. The derivation of surface and sub-surface stresses in the wheel from fundamental principles of wheel/rail interaction is described.

• Materials that have been developed to withstand service stresses. Information is given on the microstructure of wheel steels and the changes that occur to the material properties in service.

• Descriptions of two main failure modes of wheels in service – wear and RCF. Mechanisms of failure are described and the current state-of-the-art of modelling failure is given.

• Information on current practice in managing the wheel asset in operation on Network Rail controlled infrastructure is provided.

• A list of notations and some important definitions, including a figure showing nomenclature for the parts of a wheel, are provided in the appendix.



2 LOAD ENVIRONMENT 2.1 Wheel/Rail Curving Forces An unconstrained wheelset steers in a curve by generating a rolling radius difference between the wheel on the outside rail and the wheel on the inside rail. The rolling radius difference results from a lateral shift of the wheelset and the coned profiles of the wheels, as Figure 1 illustrates.

Figure 1. Effect of Lateral Shift on Coned Wheels

When the unconstrained wheelset negotiates a curve and maintains a radial orientation, there are no tangential forces between the wheels and the rails. In this orientation, creep, which is defined as the velocity of the wheel relative to the rail, is zero at both contact points.

When wheelsets are combined in a bogie, they are no longer unconstrained. Each wheelset is prevented from aligning itself radially in the curve by its connection (usually through the bogie frame) to the other wheelset. The constraining forces between wheelsets are reacted by longitudinal forces between the wheels and rails. These wheel/rail forces are generated by longitudinal creep that results from a lateral shift of the wheelset from its unconstrained rolling line. Figure 2 shows a bogie in a typical position during curving. In this example, the curve radius is 1000m, the cant is 100mm and the vehicle is travelling at the balance speed of 92km/hour. The vehicle in the example is a typical multiple unit with primary yaw stiffness of 16MNm/rad. Wheel and rail profiles are conformal giving a relatively high conicity. The coefficient of friction at all wheel/rail contact points is 0.4.



Figure 2. Typical Wheelset Positions when Curving

Figure 2 shows that the leading wheelset has moved laterally outside the equilibrium rolling line and developed a positive angle-of-attack (AOA) to the rail. The trailing wheelset has stayed close to the equilibrium rolling line and has developed a negative AOA that has a smaller magnitude than that for the leading wheelset.

The AOA (the yaw rotation of the wheelsets relative to the radius of the curve) causes lateral creep between the wheels and rails and results in lateral creep forces. In addition, spin creep arises from the angular rotation of the wheelset resolved perpendicular to the plane of contact. Figure 3 shows the magnitude and direction of the creepages for the example used in Figure 2. Creepage (also called creep ratio) is creep divided by the forward velocity of the wheelset.



Figure 3. Typical Creepages when Curving

Figure 3 shows that the lateral displacement of the leading wheelset has produced almost equal and opposite longitudinal creepages at the wheels. Because the trailing wheelset is close to the equilibrium rolling line, it does not produce significant longitudinal creepages. The AOA of the leading wheelset has produced lateral creepages at both wheels. Because the AOA for the trailing axle is smaller and in the opposite direction, the creepages there are smaller and in the opposite direction to those at the leading wheelset.

The forces that arise from the creepages between wheel and rail depend on the shape of the contact patch and the wheel and rail material properties. They are usually calculated using creep coefficients derived by Kalker.1 Figure 4 shows typical forces acting on the wheels of a bogie for the same example used in Figure 2.



Figure 4. Typical Forces on the Wheels when Curving

Figure 4 shows that the longitudinal creepages on the leading wheelset result in equal and opposite longitudinal creep forces. Although the lateral creepages are the same for both wheels on the leading wheelset, the lateral creep forces are not equal. This is because the lateral creep forces shown in Figure 4 are in the plane of the contact patch. The angle of the contact plane to the horizontal plane is different for each contact point (see Figure 5). Because the vehicle is running round the curve at balance speed, the resultant of the lateral creep forces and the normal forces in the horizontal plane from all contact points should be zero.



Figure 5. Typical Contact Angles and Forces on the Leading Wheelset when Curving

The example given above is one of fairly moderate curving. Larger displacements, creepages, and forces can readily be produced. Significant factors affecting curving performance include (in no particular order):

• Curve radius

• Wheel and rail profiles

• Cant deficiency

• Wheelset yaw stiffness

• Bogie wheelbase

• Axleload

• Coefficient of friction between wheel and rail



2.2 Contact Conditions Wheel/rail contact is typically assumed to be Hertzian, in which case the shape of the contact patch on the wheel and rail is elliptical and the contact pressure is distributed elliptically over the contact area. The length and width of the ellipse are similar in magnitude when contact occurs on the tread of the wheel. For contact on the flange of the wheel, the ellipse tends to become long and thin, with the longest axis oriented along the rail.

Figure 6 shows the maximum contact pressure, contact patch area, and contact position for each contact point in the example used in Figure 2. The contact position, d, is relative to the tread datum (positive towards the flange, negative towards the rim).

Figure 6. Typical Contact Pressures, Areas, and Positions when Curving

Johnson shows how the surface and sub-surface stresses are distributed in the material in and around the contact patch for the relatively simple case of a cylinder sliding on a plane surface.2 Figure 7 shows how the shear and longitudinal surface stresses vary under tangential traction q0 acting from right to left. In this example the coefficient of friction μ = 0.4. The distribution of direct stress in the longitudinal direction (normalised by the contact pressure) is shown by the solid line. The dashed line shows the distribution of shear stress



(normalised by the tangential traction). The leading edge of the contact patch is at +1 and the trailing edge is at -1 on the x-axis.

It can be seen that the maximum tensile longitudinal stress occurs at the leading edge of the contact patch. Maximum compressive longitudinal surface stress occurs at the trailing edge of the contact patch. The shear stress varies elliptically over the contact area. Thus, a piece of material at the surface of a wheel sees a reversal in longitudinal stress, superimposed on a changing shear stress, as it comes into contact, passes through and then leaves the contact patch.

-1.5

-1

-0.5

0

0.5

1

-3 -2 -1 0 1 2 3

x/a

σ x /p 0

τxz /q 0

τxz

σ x

LeadTrail

Compression

Tension

Figure 7. Surface Stress Distributions under Sliding Line Contact (μ = 0.4)

Below the surface, the stress distributions are more complicated. The maximum principal shear stress tends to occur below the surface when the ratio of tangential traction to contact pressure is low. Its depth below the surface depends on this ratio. A piece of material below the surface of the wheel will generally experience compressive direct principal stresses and rotating principal shear stresses as the wheel rotates.

Sliding between two surfaces (which is the case in Figure 7) happens when the ratio of tangential to normal force reaches the coefficient of friction. It is an extreme condition that does not usually occur in wheel/rail contact. For typical creepages slip occurs over the trailing part of the contact patch, while the wheel and the rail stick over the leading part of the contact patch. The distribution of tangential traction over the contact patch is modified from



the sliding case, as Figure 8 shows. The dashed line represents the sliding case. The solid line is the distribution with stick and slip in the contact patch. The leading edge of the contact patch is at +1 and the trailing edge is at -1 on the x-axis. In this example, the coefficient of friction μ = 0.4 and the ratio of tangential force (Qx) to normal force (P) is 0.25.

0

0.05

0.1

0.15

0.2

0.25

0.3

-1 -0.5 0 0.5 1

x/a

StickSlip

LeadTrail

Figure 8. Distribution of Tangential Traction for Line Contact (μ = 0.4, Qx/P = 0.25)

Because contact between wheel and rail is three dimensional, the distribution of forces and stresses is more complicated than the line contact example used above. To derive the surface stresses, the contact patch is often divided into thin strips, parallel to the rolling direction. The two dimensional solution is applied to each strip with the constraint that stick/slip boundaries are continuous across strips. Net creepages can then be derived by summing across the elements. Figure 9 shows typical results from this type of analysis.



Figure 9. Example of Contact Conditions Analyzed in Strips and Elements (from W. Kik)

2.3 Traction & Braking Forces Typical braking and acceleration rates for passenger vehicles are 0.8m/s2 (corresponding to 9% g). Assuming a four axle vehicle has a mass of 45,000kg gives a wheel/rail longitudinal force of 4.5kN during braking and acceleration. As shown in the example in Section 2.1, Figure 4, this is significantly less than the tangential forces that are typically generated when a vehicle travels through a curve.

Modern vehicles have wheel spin and slide control systems that optimise traction and braking performance. With these systems, the wheels in a train do not necessarily carry the same traction and braking effort. Levels of creepage on some wheels can be very high (up to 20%). This is thought to be a possible cause of raised amounts of RCF on the leading wheels of some trains.

The most severe contact conditions on the wheel no doubt arise when curving at the same time as braking with high creepage. Section 3 describes wheel materials that have been developed to withstand the severe contact conditions described here.



3 WHEEL MATERIALS This section begins with a description of the current wheel steels in use on Network Rail controlled infrastructure. It then describes several new types of wheel steel that are being investigated. The microstructure of wheel steels is described. The change in microstructure and other material property changes that occur during loading are also discussed.

3.1 Wheel Steels Currently Used on Network Rail Railway Group Standard GM/RT2466 specifies the approved material grades for monobloc wheels used on Network Rail controlled infrastructure.3 This requires particular BS 5892 part 3 wheel material grades to be used for particular vehicle applications,4 as Table 1 shows.

Table 1. Wheel Material Grades

Wheel Type Wheel Material Grade (BS 5892 Part 3 and UIC812-3)

Freight, integral brake disc wheel R7E Freight, cheek mounted brake disc wheel R8E Other freight wheels R7T or R8T All passenger vehicle and other wheels R8T

The material grade specifies the chemical composition and the heat treatment condition of the wheel. The first two alphanumeric characters define the chemical composition (Table 2) and the third character describes the heat treatment. “T” corresponds to “rim chilled”. This heat treatment hardens the tread and flange of the wheel to improve wear resistance. It also creates large compressive residual stresses that restrict fatigue and thermal crack growth. “E” corresponds to immersion quenched and tempered. This treatment improves the integrity of the wheel’s web.

Table 2. Chemical Composition of Standard Wheel Steels (% by weight)

Cast Composition

Class D (typical)

Grade R7 (max.)

Grade R8 (max.)

C 0.61 0.52 0.56 Si 0.33 0.40 0.40 Mn 0.70 0.80 0.80 P 0.027 0.04 0.04 S 0.022 0.04 0.04 Cr 0.30 0.30 0.30 Cu 0.30 0.30 Mo 0.05 0.08 0.08 Ni 0.20 0.30 0.30 V 0.05 0.05

Cr+Mo+Ni 0.60 0.60



There have been significant improvements in wheel manufacturing processes and inspection techniques in the last 30 years.5 These have improved steel cleanness, consistency, and quality. The advances include the change from ingot to continuously cast steel and the setting of compositional limits on the wheel chemistries. Previously British Rail Research wheel specifications controlled the mechanical properties and limited only the sulphur and phosphorus levels for chemical control. Typically, wheel chemistries were 0.60 to 0.65% carbon and 0.7 to 0.9% manganese (see Table 2). Hence, the introduction of BS 5892 grade materials has resulted in lower carbon content and an increased resistance to thermal-induced RCF damage.

Modern wheels are made from vacuum argon degassed steel. This limits the hydrogen content to less than two parts per million and reduces the likelihood of hydrogen cracking. The controls on chemical composition limit the number of non-metallic inclusions, which can act as stress concentrators and potential crack initiation sites. Any macroscopic defects in the material should be detected by ultrasonic inspections in the final part of the manufacturing process.

Certain mechanical properties of wheel material grades are specified in BS5892 part 3.4 As Table 3 shows, there are significant overlaps between the properties of the grades. Table 3 shows typical properties for the older Class D wheel steel for comparison.

Table 3. Mechanical Properties of UK Wheel Steels

Wheel Material Grade

Tensile Strength

(MPa) Minimum

Elongation Brinell Hardness

Range (HB)

R7T 820 to 940 14% 241 to 277 R7E 780 to 940 14% 229 to 277 R8T 860 to 980 13% 255 to 285 R8E 820 to 980 13% 241 to 285

Class D 960 20% n/a

3.2 Other Wheel Materials The choice of wheel material is based on the balance between cost, wear resistance, and strength (RCF resistance). Cast wheels have a lower cost and have hardened treads by chills in the mould. The webs can be peened to produce compressive residual stresses to improve their fatigue resistance. Some recently developed wheel steels are claimed to have superior resistance to surface damage. For example, martensite-resistant wheel materials may be used to resist thermally included RCF formation. Higher strength ductile materials can be used to reduce the plastic flow and suppress mechanically induced RCF formation. Table 4 is a summary of the chemical compositions of candidate wheel materials.



Banitic wheel steels contain low carbon (0.08%) but have higher manganese, chromium, molybdenum, and boron than pearlitic steels.5 Rapid cooling produces a ductile material that is claimed to be more resistant to RCF and shelling. The wear rates are expected to be higher than standard pearlitic wheel steels due to the lower carbon content. Imacro steel wheels have a relatively ductile martensitic structure that is obtained from water quenching.5 This is claimed to reduce tread damage and maintain the wear resistance. Kymenite wheels are made from a cast bainitic–austenitic ductile iron.5 This steel is claimed to reduce wear and tread damage. Its chemical analysis is not provided in the reference.

Ekberg and Sotkovski describe a wheel steel with a fine grained ferrite-pearlite structure and an improved control of material defects.6 Tests have indicated that it has an increased strength without a decrease in ductility. It also has improved impact toughness at low temperatures. The sulphur and phosphorus contents are controlled to reduce the size of inclusions. Calcium is added to encourage the manganese sulphides to form small spherical inclusions with a lower stress concentration and a reduced probability of becoming crack initiation sites. A fine-grained pearlitic structure is recommended to increase the wear resistance. The chromium content increases the steel’s hardening capacity and encourages the production of carbides.

The “WT superior steel” manufactured by Lucchini is claimed to mitigate RCF damage.7 The steel is compliant with BS 5892 part 3 apart from the silicon and manganese content. The steel has a raised level of silicon that should reduce its susceptibility to thermal damage and an increased manganese content to control the hardness. This wheel steel may be trialled on the Class 175.

Table 4. Chemical Composition of New Wheel Steels (% by weight)

Cast composition Bainitic5 Imacro5 Ekberg6 Lucchini WT

superior7 C 0.08 0.55 0.52 0.54 Si 0.26 0.25 0.27 0.905 Mn 1.62 0.80 0.90 0.995 P 0.013 0.03 max 0.017 0.006 S 0.024 0.025 max 0.014 0.006 Cr 1.40 4.20 0.25 0.05 Mo 0.46 -- 0.06 0.01 Ni 0.23 -- 0.30 0.035 B 0.002 -- -- --

Nb -- 0.05 -- 0.001



3.3 Microstructure The BS 5892 wheel materials have a ferrite-pearlite microstructure. This mainly consists of mixture of ferrite (the “alpha” body centre cubic form of iron with a very small amount of carbon) and pearlite (lamella of cementite and ferrite). Cementite is iron carbide (Fe3C) and is hard and brittle. Ferrite is relatively soft. The hardness of pearlitic steels increases as the lamellae spacing becomes finer. This can be encouraged with alloying elements such as chromium, molybdenum, and vanadium. The typical lamellae spacing for R7 material is 0.14 to 0.19μm. Walther & Eifler show how microstructure varies from the tread to the flange and with depth.8

The wheel’s microstructure is influenced by shear deformation from surface tangential traction. As Figure 10 shows, the deformation typically extends to 1mm below the surface. The shear deformation at the surface causes the brittle cementite to break and allows the softer ferrite to be worn away.8 This results in a concentration of iron carbides at the surface and a significant increase in the surface hardness (to more than 600 HB). The changed surface material is called the “white phase” and is typically 20 to 50μm deep.

Figure 10. Microstructure of Pearlitic Steel



A change in the wheel’s microstructure can be caused by thermal inputs.5 During a wheel slide, for example, the tread surface can be locally heated above 730oC and then rapidly cooled by conduction into the bulk of the wheel. In this process, the wheel steel will transform from austenite (the “gamma” face centre-cubic form of iron) to martensite. Martensite can be considered to be a supersaturated solid solution of carbon in body-centred tetragonal iron and has hard, brittle properties. Martensite formation occurs more readily in wheel materials with high carbon content. The depth of martensite depends on the thermal conditions and typically varies between 0.2 and 2mm.

3.4 Shakedown If the stresses produced in the wheel under contact with the rail are below the elastic limit of the wheel material, no permanent deformation will take place. However, in practice, the stresses usually exceed the elastic limit causing plastic flow and residual stress changes near the surface. Plastic flow raises the elastic limit for steel materials. Residual stress makes plastic flow less likely during subsequent loading cycles. The combined effect is known as “shakedown” or “work hardening”.9

There is a limit — known as the “shakedown limit” — to the increase in hardening that the wheel material can achieve. If the stresses are above this limit then permanent plastic deformation will occur for each subsequent wheel revolution. If this continues, the plastic strain limit for the material will be exceeded and surface cracking will occur. This process is known as “ratchetting”.

Figure 11 is an example of a shakedown diagram that is commonly used to compare contact conditions with the shakedown limit.10 In Figure 11, po is the maximum contact pressure (MPa), Ke is the shear yield strength of the material (MPa), Q is the tangential force in the contact patch (N), and P is the normal force (N). The traction coefficient should not be confused with the coefficient of friction. It is limited by the coefficient of friction and is sometimes called the utilised coefficient of friction.



0

1

2

3

4

5

6

0 0.1 0.2 0.3 0.4 0.5 0.6

Traction Coefficient (Q/P )

Load

Fac

tor

(po/K

e)

Shakedown Limit

Surface and sub-surface flow

Surface flowElastic shakedown

Elastic

Sub-surface flow

Figure 11. Example Shakedown Diagram

The maximum contact pressure, po, is often estimated as 1.5P/A where A is the contact area (mm2). Shear yield strength can be calculated from a material’s yield strength in direct tension, Ky, using the Von Mises criterion, as Equation 1 shows. Ky can be estimated from the material’s tensile strength, Kt, as Equation 2 show.

3y

e

KK ≈ (1)

3t

yKK ≈ (2)

Table 5 shows the results of this estimation for the wheel steels listed in Table 3, except Class D.

Table 5. Estimated Values of Shear Yield Strength

Wheel Material Grade

Tensile Strength (N/mm2)

Estimated Yield Stress

(N/mm2)

Estimated Shear Yield Strength

(N/mm2) R7T 820 to 940 473 to 543 273 to 313 R7E 780 to 940 450 to 543 260 to 313 R8T 860 to 980 497 to 566 287 to 327 R8E 820 to 980 473 to 566 273 to 327



For the lead wheel on the low rail in the examples shown in Figures 4 and 6, the load factor is 4.5 (assuming the low end of the range for R8T steel), and the traction coefficient is 0.3. Thus, the contact conditions are close to the shakedown limit. This shows that surface damage can be expected on wheels under quite moderate curving conditions.

The limits shown in Figure 11 are based on laboratory tests under ideal conditions of line contact. Empirical limits, based on comparisons with observations in the field, are often used.11

The shakedown diagram shows that surface flow can happen when the traction coefficient is high. This type of surface damage can occur in the flange root of wheels when the coefficient of friction is high. It is not discussed further in this report. The next two sections describe two other important types of surface damage; i.e., wear and rolling contact fatigue.



4 WHEEL WEAR 4.1 Wear Mechanisms Of the many types of wear described in the literature on contact mechanics, only two appear to be dominant in wheel/rail contact: adhesive and delamination.12

Adhesive wear is relatively mild. Thin flakes are produced on the surface over a large number of cycles. Figure 12 shows a scanning electron micrograph produced by Bolton from the surface of a disk that experienced mild wear.13 It is possible that the thin flakes break away from the surface when they adhere to asperities in the rail surface. Bolton found the mild wear debris to be a mixture of iron oxide (Fe2O3 and Fe3O4) and metallic iron. From scanning electron micrographs, he found the flakes are typically 100μm long and less than 10μm thick. Their thinness implies they come from the transformed white phase at the wheel’s surface. Wheel and rail surfaces remain shiny under adhesive wear.

Figure 12. Surface Resulting from Mild Wear (from Bolton13)

Delamination wear is more severe than adhesive wear. It is characterised by light

grey wear debris that is entirely metallic. Delamination wear begins when a crack is initiated at the surface. The crack propagates under the surface until it turns up and breaks through the surface, allowing a flake of material to become detached.14 Delamination wear produces a rougher surface than adhesive wear. The surface contains ripples with smooth peaks and troughs with a pitted appearance.



The debris from delamination wear is in the form of flakes that show a smaller mean size but a wider range of sizes than for adhesive wear.13 Bolton produced the scanning electron micrograph shown in Figure 13 from debris collected from the gauge corner of a rail in service. The flakes are of the order of 400μm long and more than 20μm thick. This suggests the crack that caused the delamination may have progressed through the white phase.

Figure 13. Debris Collected from a Side-wearing Rail in Service (from Bolton13)

Wear rates are typically quantified using twin-disk and small-scale roller rigs in the

laboratory.13,15 It is recognised that there is a scale effect with non-linear plastic deformation and laboratory tests do not usually include dynamic wheel/rail interaction loads.16 Laboratory tests do not faithfully reproduce the atmosphere and contamination found in railway service. Twin-disk tests simulate only line contact and do not include lateral and spin creepage. However, results from these tests are commonly used to develop and calibrate the wear models described below.

4.2 Wear Models Two basic types of wear models are described in the literature on wheel/rail interaction17:

1. Energy transfer models, which assume the material loss to be a function of the energy dissipated in the contact patch.

2. Sliding models where the material loss depends on combinations of sliding distance, normal force, and material hardness.



4.2.1 Energy transfer wear models BR Research carried out pioneering work to understand and model wheel/rail wear behaviour.18 They concluded that the wheel wear rate could be related to the frictional energy expended through creepage in each wheel/rail contact. This can be shown to be the sum of the products of the individual creep forces, T, and creepages, γ, in the longitudinal and lateral directions. In most cases, the contribution from the spin term is assumed to be small and is ignored.

Wear Number = yyxx TTT γγγ += (3)

Applying Equation 3 to the examples shown in Figures 2 to 4 would give a wear number of 49.5N on the tread of the leading wheel on the high rail. Including the spin term would raise the wear number to 52.3N. For larger contact angles, the spin term can be more significant.

In un-lubricated tests, McEwen and Harvey observed a mild wear regime (probably adhesive wear) if the wear number was less than 200N. A severe wear regime (probably delamination wear) was found for wear numbers greater than 400N. For wear numbers between 200 and 400N, either type of wear could occur.18

In tests lubricated with water, mild wear was found to occur for wear numbers up to 500N, beyond which severe wear was found.

Equations were developed to describe the wear behaviour (see Table 6). Because the wear rate is expressed as profile area loss per distance rolled, the wheel diameter (D mm) needs to be considered in the equations. Note that for un-lubricated wear numbers between 200N and 400N, where either type of wear may occur, the formulae in Table 6 assume severe wear takes place.

Table 6. Wear Rates from BR Research18

Friction Regime Tγ (N)

Wear Rate (mm2/km rolled)

Dry Mild < 100 0.25Tγ/D Dry Mild Plateau > 100 and < 200 25.0/D Dry Severe > 200 (1.19Tγ - 154)/D

Lubricated Mild < 500 3.0/D Lubricated Severe > 500 (1.19Tγ - 154)/D

Because the equations in Table 6 were based on laboratory tests, they are thought to generally overestimate wear rates in service. The equations were developed for the wheel steel (Class D) and rail steel (BS11) that were in use at the time. They most likely will need to be adjusted for alternative wheel and rail steels.



The BR Research results showed that severe wear took place only when the combined creepage level reached 1%.18 This occurs normally when the flange of the wheel makes contact with the gauge face of the rail. This implies that severe wear is only significant for this type of wheel/rail contact.

BR Research found that the rate of severe wear could be modelled more accurately by plotting the results against the Wear Index, defined as Tγ/A, where A is the contact patch area. Lewis et al. used the same parameter to obtain wear rates from twin-disk tests with R8T wheel steel on UIC60 900A rail steel.14 Their results are summarised in Table 7. Note that the units of wear rate here are mg/mm2/km rolled. When multiplied by the contact patch area, the units of wear rate become mg/km rolled.

Table 7. Wear Rate Results from Lewis et al.14

Regime Tγ/A (N/mm2) Wear Rate

(mg/mm2/km rolled)

Oxidative (adhesive) < 10.4 5.3Tγ/A Delamination > 10.4 and < 77.2 55.0

Metallic > 77.2 61.9Tγ/A

These results introduce a new wear regime called “metallic” in which cracks were seen to form below the surface of the wheel. The high creepage and small contact area required to experience this type of wear are very unlikely to arise for wheel/rail contact in practice.

Kik et al. use the vector sum of the longitudinal and lateral components, rather than the arithmetic sum in Equation 3, to derive a contact patch energy dissipation wear number19:

( ) ( )22yyxxg TTE γγ += (4)

Enblom and Berg show that this can be converted to an energy flow density as follows17:

AvEE gd =& (5)

where v is the vehicle speed (m/s), and that two distinct wear regimes exist separated by a value of dE& = 4.0 Nm/s/mm2.

The three alternative friction energy damage models described above can be compared for the contact conditions on the low rail and leading axle of the example given in Figures 2 to 4. For the BR Research model, Tγ = 37.9N, which is in the region of mild wear. Assuming a wheel diameter of 850mm gives an area loss rate from the profile of



0.011mm2/km rolled. Assuming a density for steel of 7.85kg/litre gives a material loss rate from the wheel of 0.234g/km rolled.

For the model of Lewis et al., Tγ/A = 0.550N/mm2, which is also in the mildest wear regime. 14 The material loss rate would be 2.915 mg/mm2/km. Multiplying by the contact patch area of 68.9mm2 gives a material loss rate of 0.201g/km, which is similar to that calculated by the BR Research model.

The wear damage parameter from the model of Kik et al. would be Eg = 32.0N.19 Assuming a vehicle speed of 44.4m/s (160 km/hour) gives dE& = 20.6Nm/s/mm2, which is in the severe wear regime.

Two of the wear models (BR Research and Lewis et al.) predict the contact conditions to give rise to mild wear, which is what would be expected on the tread of a wheel during normal curving. They also agree in the material loss rate.

Assuming a typical contact patch area of 15mm2 for wheel flange/rail gauge face contact, the boundary between the Lewis et al. mild and severe wear regimes would occur at a Tγ = 156N.14 This is less than the BR Research value of 200N required for severe wear. For both models to predict the same boundary between mild and severe wear would require a contact patch area of 19.2mm2. This is towards the upper end for contact on the flange of a wheel in practice. Thus, the Lewis et al. model will nearly always predict the onset of severe wear before the BR Research model.

A vehicle speed of approximately 0.4 m/s (1.4km/hour) would be required for the Lewis et al. and the Kik et al. models to give the same break point between mild and severe wear. Because this is very slow, the Kik et al. model will nearly always predict the onset of severe wear before the Lewis et al. model.

Energy transfer wear models differ in the way the net creep forces are calculated for the contact area. This may be a reason why the models give different results. In the BR Research model, the wear number and wear index are calculated using the total tangential forces and creepages. In the Lewis et al. and Kik et al. models, the contact area is divided into small elements. Wear damage is calculated for each element. Total wear is then calculated as the sum from all elements.



4.2.2 Sliding wear models The Archard wear model is widely used in the tribology community for modelling wear due to rolling and sliding contact.20 The model predicts the volume of material removed based on the normal and the tangential forces, sliding distance and the material properties, as Equation 6 shows.

HPskVwear = (6)

where wearV is the volume of wear (m3), s is the sliding distance (m), P is the normal force (N), H is the hardness of the softer material (N/m2) and k is a wear coefficient.

The Archard wear model has been calibrated for use with wheel and rail steels and has been applied by several European railway administrations to study wheel wear. Examples of the use and validation of this model are provided by Enblom and Berg.17 Together with vehicle dynamics simulation using the GENSYS software package, it has been successfully used to predict wheel and rail profile change due to wear by the Royal Institute of Technology (KTH) in Stockholm for Banverket.20 The method uses a modified wear coefficient that allows the effect of contamination, lubrication and environmental factors to be accounted for in the analysis.

The Archard wear model has recently been used by the Rail Technology Unit at Manchester Metropolitan University together with VAMPIRE® to predict wear of wheel profiles on UK railways for RSSB.21 This work required recalibration of the Archard wear coefficient (k in Equation 6) for UK wheel and rail steels (see Figure 14). Figure 14 also shows the normal regions for tread and flange contact. Figure 15 shows an example of the predicted and measured wheel profile change from this study.

Figure 14. Wear Chart with Archard Wear Coefficients21



-800 -790 -780 -770 -760 -750 -740 -730 -720 -710 -700 -690-40

-30

-20

-10

0

10(m

m)

Simulated Distance 54210km

SimulatedMeasuredNew

-800 -790 -780 -770 -760 -750 -740 -730 -720 -710 -700 -690-0.5

0

0.5

1

1.5

2

(mm)

Wea

r D

istri

butio

n(m

m)

SimulatedMeasured

Figure 15. Simulated and Measured Wear of Profile21

(upper plot shows profile, lower plot shows wear all mm)

Figure 15 shows that good comparisons between measured and predicted wheel

profiles were achieved. This allowed a theoretical study of alternative wheel profiles to be performed.21

In common with some of the energy transfer wear models, the Archard sliding wear model separates the contact patch area into small elements. Total wear is the sum of the wear calculated for each element.

Enbolm and Berg reported a comparison between the Archard sliding model, the BR Research, and the Lewis et al. energy transfer models.17 They concluded that the Archard and the BR Research wear models agreed remarkably well for many of the contact conditions they studied, despite their totally different tribological approaches.

Since the BR Research wear model uses a damage parameter, Tγ, which is readily derived from computer simulations of vehicles, it can be used to give a first approximation of wheel wear. Only if a more detailed analysis of the wear distribution across the tread of the wheel is required would it be necessary to use the Archard wear model.

Kapoor and Franklin developed a model for predicting delamination wear that separates the near-surface material affected by contact into thin layers.22 Strain accumulation



in each layer is calculated from the shear stress at the appropriate depth. Work hardening is also accounted for. When the accumulated shear strain in the layer at the surface exceeds the critical shear strain to failure, that layer is removed, bringing the layer below to the surface. The model successfully predicts the general variation in wear rate with number of cycles and the general effect of increasing material hardness observed in practice.

4.3 Effect of Fluid on Wear Oil and grease from flange lubrication not only reduce the coefficient of friction but also change the wear mechanism. In laboratory tests, effective lubrication reduced the wear rate by a factor between 200 and 1,000.18 In service, this factor is expected to be less due to the effects of background contamination and the weather. Effective lubrication in service conditions can produce wear rates that are ten times less than the wear rate associated with the dry, mild wear process.

Water provides a degree of lubrication and can reduce the wear rate by between 10 and 100 times. The wear rate with water under severe contact conditions becomes similar to that for dry, mild wear. It is possible that water provides surface protection by encouraging the development of an oxide film.

4.4 Effects of Metallurgy on Wear Benson performed a literature review of wheel and rail wear tests to assess the effect of material hardness on wear rates.23 She found that in laboratory tests, increasing the hardness of one component in a two-body wearing system generally decreases the wear of that component. The wear of the other component is either unaffected or also decreases depending on the metallurgy and hardness of the second component. The service tests reviewed generally supported this observation. However, service results showed increasing the rail hardness caused a slight increase in wheel wear rate.23

Table 8 summarises wheel and rail wear trends under heavy haul conditions.23

Table 8. Summary of Wheel/rail Wear Trends23

Effect on: Wheel Hardness

Rail Hardness Rail wear rate Wheel wear rate

Constant Increasing Decreases Rail < 360 HB – decreases Rail > 360 HB – increases

Increasing Constant Standard carbon rails – increases Heat treated rails – decreases Decreases



Several of the authors researched by Benson published results that showed logarithmic relationships between wheel wear and material hardness (see Equation 7).

Weight Loss cHBk

= (7)

where HB is the Brinell hardness, and k and c are constants.

4.5 Effects of Change in Direction on Wear The wear models described above make the assumption that the loading on a wheel is unidirectional. It might be argued that the tangential direction of wheel loading changes with traction/braking applications and also when the wheel runs from the high to the low rail on curved track.

Un-lubricated, twin-disk laboratory tests by Tyfour and Benyon indicated that direction reversals can decrease the severe wear rate.24 The largest decrease in rail wear rate occurred with frequent direction reversals. This rate was less than half the unidirectional rail wear rate.

Benson has shown that reversals in direction have a significant effect on wear if the specimens receive water lubrication.25 Reversing the running direction of the wheel every 10,000 cycles increased the wheel wear rate by a factor of three. The effect of reversals was small for the un-lubricated tests, which disagrees with Tyfour’s results.24

Care needs to be taken when applying these laboratory results to the real world. As Figure 6 shows, the contact point on the wheel on the high rail of the leading axle is towards the flange of the tread. The example shows that the contact is at 27mm from the centre of the tread. When this wheel runs in the opposite direction, the contact point moves closer to the centre of the tread by 15mm, which is more than the width of the contact patch. Thus, the material that was experiencing the worst contact conditions in one direction no longer sees those conditions when the direction changes. Contact positions on the wheel will change with curve radius. Thus, in practice, only some parts of the wheel’s profile may see reversed loading.



5 WHEEL ROLLING CONTACT FATIGUE RCF is the damage to the wheel at and close to its surface from cracks that propagate by changes in mechanically induced stress that occur when the wheel rotates. Thermally induced RCF that initiates from martensite produced from a wheel slide is a special case and will not be discussed here.

The type of RCF discussed here is initiated by mechanical changes to the microstructure resulting from normal and tangential forces in the contact patch.

5.1 RCF Mechanism RCF failure of a wheel can be separated into four phases:

1. Crack initiation

2. Early crack growth

3. Extended crack growth

4. Separation of a piece of material from the surface and the formation of a cavity

In the final two stages, the crack grows below the surface at a shallow angle to the surface until it joins with another crack and allows the piece of material above the crack to become detached. The following discussion concerns the first two stages. After stage two, a wheel should show a band of surface cracks around its circumference that are visible to the naked eye.

Initiation can occur at the surface, just below the surface (say up to 10mm below the surface) or deep below the surface.26 Deep initiation requires a large material defect, such as a void or inclusion, to be present to produce a stress concentration. It is assumed that these defects are not a significant problem in wheels manufactured to modern standards.27

Surface initiation of RCF is from the same mechanism that causes delamination wear. Repeated plastic deformation of the surface layer eventually leads to the material reaching its plastic strain limit and a crack being initiated. If the contact conditions are severe, then wear by delamination will take place. If the contact conditions are less severe, but are still above a certain threshold, then the cracks may propagate to form RCF, and the effect of fluid on crack propagation becomes important.

Figure 16 shows a RCF crack in section from a wheel. This figure shows that the crack is longer and deeper than in the case of delamination wear.



0.5 mm0.5 mm

Figure 16. RCF Crack in a Wheel

There is evidence to show that that a relatively low viscosity fluid (e.g. oil lubricant or

water) is required to produce RCF.28 This can be explained by analysing the stress field in the surface layer of the wheel. If there are tangential and normal wheel/rail forces, the pattern of stresses will be similar to those shown in Figure 7. A piece of material in the surface layer of the wheel will see a shear stress reversal superimposed on a mainly compressive stress field. With no fluid present, the compressive stresses will hold the crack surfaces together and prevent the crack from growing. The effect of fluid on RCF is the subject of much research and testing. What follows is a consolidation of the emerging theories.28

Figure 17a shows a crack in the driven surface of a rail immediately ahead of a driving wheel. The crack is pulled open by the tensile longitudinal stress acting at the surface. If a fluid of sufficiently low viscosity is present, it will enter the crack. Figure 17b shows the crack as it moves farther under the wheel. The normal force from the wheel has closed the tip of the crack and trapped a volume of fluid in the crack cavity. As the wheel continues to move forward, the fluid is forced towards the tip of the crack, as Figure 17c shows. Assuming the fluid is incompressible, large stress will be applied to the material around the trapped fluid. These stresses will help the crack to grow in Mode I (see Figure 18). Eventually the pressure in the trapped lubricant may be sufficient to force the crack to open (Figure 17d). The crack surfaces are now held apart under a shear stress, which can cause the crack to grow in Mode II (see Figure 18).



Figure 17. The Fluid Entrapment Mechanism (after Bower28)

Figure 18. Modes of Fatigue Crack Growth



Figure 19 shows the sequence of events for a fatigue crack in the wheel, which is the driving surface. As the crack approaches the contact patch, it is under a compressive stress. The crack is closed, and it is not possible for fluid to enter (see Figure 19a). The tip is the first part of the crack to experience the contact stresses. Thus, any fluid trapped in the crack may be squeezed out. When the crack on the wheel is in the contact region (see Figure 19b), there is no tensile stress to produce Mode I growth. The crack faces are held together and friction prevents the shear stresses giving Mode II growth.

Figure 19. The Fluid Expulsion Mechanism

The effect of lubrication can be seen to help propagate cracks in the driven surface.

In the typical curving situation shown in Figure 3, the driven surface for the high rail is the rail. For the low rail, the driven surface is the wheel. This can also be explained by calculating longitudinal creepage at the two interfaces. On the high rail, the creepage is given approximately by:

( )0

01 r

rr highhigh

−≈γ (8)

where r0 is the nominal radius of the wheels, rhigh is the rolling radius on the high rail and rlow is the rolling radius on the low rail.

On the low rail the creepage is approximately:

( )0

01 r

rr lowlow

−≈γ (9)



Recognising that the rhigh is greater than r0 and rlow is less than r0, it can be seen that the sign of the creepage at the high rail is opposite to that at the low rail.

As Figure 20 shows, this explains why RCF is often observed on the high rail of curves, and it leads to the hypothesis that RCF damage to wheels is caused when the wheel is leading on the low rail.29

Figure 20. Reciprocity of RCF Damage on Wheel and Rail (after Kalousek29)

Figure 4 shows the direction of the longitudinal and lateral tangential forces acting on

the leading wheel on the low rail. In this example, these forces combine to give a resultant at 20 degrees to the longitudinal direction. RCF cracks can be expected to appear on the tread of the wheel perpendicular to the direction of this force. When the wheel is viewed from above, the direction of the cracks will appear to be rotated through 90 degrees, as Figure 21 shows.



Qlong

Qlat

Qlong

Qlat

Figure 21. Example of Tangential Forces Producing RCF on a Leading,

Low Rail Wheel (top view)

When a bogie runs in both directions through left- and right-hand curves, all four

wheels take turns at leading and being on the low rail. Thus, the pattern of wheel RCF shown in Figure 21 can be expected to be repeated for each wheel. When viewed from above, the wheel RCF cracks on the tread should point towards the centre of the bogie, as Figure 22 shows. When the top of the wheel tread is rubbed from the outside of the bogie to the other axle (from left to right in Figure 21), it should feel rough.

Figure 22. Pattern of RCF on Wheels of a Bogie (top view)



5.2 RCF Models The models described here cover wheel RCF initiation and propagation to a point where they should be visible on the surface (e.g., Figure 21). Some of these models were developed to predict RCF on rails. With suitable adjustment for material properties, the effects of heat treatment, residual stresses and loading they should be applicable to RCF on wheels.

Some researchers have attempted to model RCF crack growth using linear elastic fracture mechanics.30 Finite element models are used to determine the stress intensity factors for the different modes of crack growth. However, as explained by Beynon and Kapoor, this is a challenging task since the loading is multi-axial and the direction of the principal stresses changes.31

Franklin et al. have extended the layer model used to predict delamination wear to also handle RCF initiation. 32 They divided each subsurface layer into small elements referred to as bricks. Material properties are assumed to be randomly distributed. The cumulative plastic strain and work hardening are calculated in each brick. A brick is said to have lost its integrity when the shear strain limit has been reached. If a failed brick is unsupported by neighbouring healthy bricks, it detaches and forms wear debris. Bricks that fail but are supported by healthy bricks can join to create micro-cracks and possible sites for RCF initiation. The brick model predicts sub-surface material deformation similar to that observed in practice. It needs further development to be able to predict early RCF propagation by fluid entrapment.

Shakedown theory provides a popular model for RCF initiation. If contact conditions are plotted on a shakedown diagram and they lie above the shakedown limit, then RCF or some other form of surface damage can be expected. If, on the other hand, the contact conditions are below the shakedown limit, then repeated loading cycles should not cause material failure. Ekberg et al. propose a surface initiated RCF index of the form:33

QAK

FI esurf 3

2−′= μ (10)

Where Q is the vector sum of the lateral and longitudinal tangential forces (Equation 11) and μ′ is the utilised friction coefficient (Equation 12).

22yx QQQ += (11)

PQ

=′μ (12)

The damage index can be rearranged to give:

0pK

PQFI e

surf −= (13)



RCF is assumed to occur when FIsurf > 0.

The relationship 0p

KPQ e= is the curved part of the shakedown limit. Thus, when

shown on a shakedown diagram, FIsurf can be seen to be the horizontal distance from the

contact condition to the shakedown limit when 25.0>PQ (see Figure 23). For 25.0<

PQ , a

negative value of FIsurf could still mean sub-surface damage may occur.

0

1

2

3

4

5

6

7

0 0.1 0.2 0.3 0.4 0.5 0.6

Traction Coefficient (Q/P )

Load

Fac

tor

(po/K

e)

Shakedown Limit

Q/P=K e /p 0

FI surf

Figure 23. Shakedown Diagram Showing Surface Fatigue Index (after Ekberg33)

A disadvantage of the Ekberg RCF surface damage index is that it does not take

account of wear. There are likely to be contact conditions that produce a large FIsurf but do not result in RCF appearing because material is worn away too quickly.

Hill and Clayton developed a RCF prediction model from RCF crack initiation tests on small scale wheel and rail steel specimens.34 Known contact stresses and creepages were applied to class D wheel steel running against various pearlitic rail steels. It was not possible to produce RCF without applying fluid to the interface between wheel and rail specimens, which supports the theory of fluid entrapment described above. The test was configured so that the wheel was the driving surface. As expected, RCF cracking was observed only on the rail steel specimens (the driven surface). RCF life was defined as the number of rolling cycles to the time when the surface of the wheel disk was rough enough to cause measurable vibration of the test rig.



For a fixed contact pressure of 1500MPa and lubrication with water, the shortest life occurred at a creepage of 0.3 percent. Creepages less than or greater than 0.3% produced longer lives to RCF failure.

For a fixed creepage and lubrication with water, RCF life was found to be inversely dependent on the contact pressure. The relationships shown in Table 9 were developed. In these relationships the coefficient of proportionality varies with creepage.

Table 9. RCF Life Relationships from Hill & Clayton34

Creepage

RCF life 8.1

0−∝ p

0.3%

RCF life 0.3

0−∝ p

2.0%

RCF life 2.4

0−∝ p

5.0% and 10.0%

The increase in RCF life at high creepages may be due to an increase in wear. Thus, in a limited way, the Hill and Clayton model combines both RCF and wear associated with lubricated surfaces.

Much work has been performed at Chalmers University of Technology, Sweden, to develop a RCF model from engineering principles. The model that evolved was called WLIFE™, and it was based on stress-life relationships. In this type of model, an effective stress in the material is calculated and compared to a fatigue limit. If the stress is above the limit, then the number of cycles to failure can be calculated from equations that are derived from test results. A key to the success of this type of model is the choice of effective stress. In the case of wheel RCF, where the stresses are multi-axial and the principal stresses rotate, the choice is very important. Ekberg chooses the Dang Van criterion because it handles rotating principal stresses, does not assume any particular shear plane, and uses the values of shear and direct stress as they vary with time.35

The Dang Van effective stresses are given by:

( ) ( )( ) ( )tat

tat

DVeq

DVeq

σττ

σττ

−=

+=

2

1 (14)

where τ(t) and σ(t) are measures of shear and direct stress amplitudes at time t, and aDV is a dimensionless material parameter.



τeq1 and τeq2 are compared to the fatigue limit of the material in shear, τe. The diagram in Figure 24 shows the stress regions where RCF damage is predicted to occur. A typical cycle of stress in the wheel is shown. In this example damage accumulates between time t1 and t2.

Figure 24. Damage Regions for the Dang Van Stress Criteria (after Ekberg & Bjarnehed35)

Ekberg later extended the stress/life model to take into account material defects and the anisotropy of the wheel material caused by the manufacturing process.6 Ekberg performed a few comparisons between the WLIFE predictions and wheel lives with limited success.36

The last type of RCF model discussed here uses energy transfer through the contact patch in a similar way to some wear models. As part of work funded and managed by RSSB, Burstow has developed a RCF damage model for rails that uses Tγ. 37 T is the same tangential traction referred to as Q earlier in this report. The model was developed by calculating accumulated damage on strips across the head of the rail and comparing the totals with RCF damage observed in practice. Figure 25 shows the resulting model.



-15

-10

-5

0

5

10

15

0 50 100 150 200 250

Tγ (N)

RCF

Dam

age

(10

-6/a

xle)

Figure 25. Rail RCF Damage Model (after Burstow37)

The model combines the effects of wear and RCF. For Tγ < 15N, there is no surface damage on the rail. For 15N < Tγ < 65N, there is RCF that increases linearly with Tγ. For Tγ > 65N, wear starts to counteract RCF damage. For Tγ > 175N, there is only wear since the wear rate exceeds the rate of propagation of RCF. The y-axis gives damage per axle. For example, if Tγ = 65N the damage per axle = 10-5, and 100,000 axles are required to produce RCF on the rail. It should be noted that the values quoted here come from a calibration with a particular type of rail material in service on Network Rail controlled infrastructure. Recalibration would probably be required for the model to be useful in other types of operations.

A benefit of the rail RCF model based on Tγ is that it handles the effect of wear on RCF. It is anticipated that, with appropriate re-calibration, this model will be suitable for predicting wheel RCF.

5.3 Effect of Metallurgy on RCF One solution to wheel and rail RCF problems is to use steel with better material properties than standard wheel and rail steels. Table 10 compares typical material properties for standard and premium (head hardened) rail steels. The shear yield strengths have been estimated from the tensile strength using Equations 1 and 2.

Table 10. Material Properties of Various Rail Steels

Normal Grade Grade A Heat Treated Surface Hardness 220 – 260 HB 260 – 300 HB 350 – 390 HB Tensile Strength 680MPa 880MPa 1180MPa Estimated Yield Strength 393MPa 508MPa 681MPa Estimated Shear Yield Strength 227MPa 293MPa 393MPa



From Table 10 and the example in Figure 6, it can be seen that for the high rail maximum contact pressure of 1510MPa, the load factor on the shakedown diagram (see Figure 11) would be 5.2 for the Grade A rail steel and 3.8 for the premium, heat-treated rail steel. Thus, contact conditions would be above the shakedown limit for the Grade A rail steel and below it for the premium rail steel. Improvements by a factor of three on rail wear and RCF initiation have been measured in service trials with premium rail steels.38

Material properties also affect the damage parameter developed by Burstow.37 For a typical shear yield strength of 300MPa and a contact patch area of 60mm2 (high rail in Figure 6), the shear force required to cause plastic deformation T = 18.0kN. From Hill and Clayton, the maximum RCF damage occurs at a creepage γ = 0.3%. Thus, Tγ = 18,000 × 0.3/100 = 54N for maximum fatigue damage. 34 This is close to the value of 65N in the Burstow RCF damage model for rail (see Figure 25). Assuming upper and lower bounds on creepage to cause RCF of 0.1 percent and 1.0 percent, respectively, gives support to the upper and lower limits on RCF shown in Figure 25.37

Applying these observations to wheel materials, it might be expected that higher strength wheel steels would result in smaller load factors on the shakedown diagram and a raised threshold for Tγ on the energy transfer damage model. The alternative wheel materials described in Section 3.2 do not necessarily have a higher strength than conventional wheel steels. They promise to improve RCF life by subtle changes to the steel’s microstructure.

5.4 Effects of Change in Direction on RCF Tyfour and Beynon, in addition to wear tests,24 measured the effect of reversing direction on RCF initiation and propagation.39 They noted that reversing the direction of rolling always increased RCF life. The increase was greatest when the reversal factor (cycles between reversals/cycles to failure) was around 1/3. The smallest reversal factor of 0.053 (a reversal every 2000 cycles with a life to failure with no reversals of 37422 cycles) gave an increase in life of 47 percent.

The crack changed direction as it grew through the material when the smallest reversal factor was applied. It was suggested that the increase in life may result from the arrest of Mode II (see Figure 18) propagation when the direction of the crack is opposite to the direction of loading.39

In service, a wheel on a rail might have a reversal factor of 2/40000 = 0.0005 (a reversal every curve of 2km length in a life of 40,000km). This is much smaller than in any tests performed by Tyfour and Beynon, but by extrapolating their results, it could give a 20 percent increase in RCF life over unidirectional loading.

As with the discussion on wear, it should be noted that the contact point on the wheel that experiences the most RCF damage does not necessarily experience the same damage



when the direction of travel is reversed. Thus, the benefits of reversed loading observed in the laboratory tests may not be realised in service.

5.5 Interaction between RCF and Wear As described above, the mechanism for initiating RCF and delamination wear is the same. In both cases repeated plastic deformation in the surface and near surface layers of the driven surface produces micro-cracks between ferrite lamellae. The following paragraphs provide a hypothesis for determining the mode of damage that follows the formation of micro-cracks.

If the contact conditions are mild (energy transfer, load factor, and traction coefficient are all low such that there is no ratcheting) and there is lubrication (e.g., oil or water), wear at a very low rate will occur. If the lubrication is removed, the traction coefficient may increase enough to cause ratcheting and the mild wear regime will dominate. RCF is unlikely since it is generally accepted that some form of fluid is necessary for the cracks to grow.

For moderate contact conditions, such as may occur across the tread of the wheel, and no lubrication, the mild wear regime is still expected to dominate with an increase in wear rate. Adding a sufficiently low viscosity fluid will reduce the wear rate and encourage the propagation of RCF cracks.

Under severe contact conditions, such as may occur on the flange of the wheel, with no lubrication, the severe wear regime will dominate. Small cracks will branch to the surface before they grow too deep. Delamination occurs and a new, un-cracked surface is exposed to contact. Material is worn away quicker than the cracks can grow to produce RCF. The presence of a fluid may change the wear regime to mild wear, but the material loss rate is still likely to be sufficient to prevent RCF appearing.

Thus, different modes of surface damage can be expected across the spectrum of contact conditions, as Table 11 shows.

Table 11. Damage Modes and Contact Conditions

Contact Conditions (energy transfer, load

factor, traction coefficient)

Fluid Present Damage Mode

Yes Very low wear Mild No Mild wear

No Moderate wear Moderate

Yes RCF and/or mild wear No Severe wear

Severe Yes Moderate wear



The interaction between wear and RCF in the region of moderate contact conditions with fluid present requires further investigation.

6 WHEEL ASSET MANAGEMENT This section provides an overview of wheel wear and RCF lives for a range of vehicles in operation on NR controlled infrastructure. The information comes from unpublished reports by train operators, manufacturers, and the depots where the vehicles are stabled and maintained. The range of vehicles includes modern and older designs of multiple units, and loco hauled coaches. The vehicles operate over routes that range from straight to curvy. Typically, these vehicles run for 200,000 miles each year. Average operating speeds vary from 50 to 100 miles/hour.

Radial tread wear rates have been estimated by comparing wheel profile measurements on the same wheel after a period in service. Typical values fall in the range 2.0×10-6 to 7.0×10-5 mm/mile.

The rate at which the depth of RCF cracks increases can be estimated from the amount of material that must be turned from a wheel to remove the cracks divided by the distance travelled since there were no cracks on the surface. This analysis has been performed using wheel lathe records for a few types of vehicle. Radial RCF growth rates in the range 3.5×10-5 to 9.0×10-5 mm/mile have been estimated.

The life of a wheel before the onset of RCF has often been observed. Typical values lie in the range 75,000 to 300,000 miles. For some vehicles, RCF has never been reported as a problem. Some reports show that powered axles have a shorter life (1/3 less) to RCF initiation than unpowered axles on the same vehicle. Other reports show the first and last axles in a multiple unit have half the life to RCF initiation of the other axles in the same train.

Railway Group Standard GM/RT2466 specifies limits on wheel wear and general crack conditions that may be found on the tread of a wheel.3 Where there are multiple cracks (see Figure 21) and one of the cracks exceeds 40mm long, the wheelset must be withdrawn from service within 24 hours. Where an isolated crack longer than 30mm is found, the vehicle must be withdrawn from service immediately. Where an isolated crack longer than 20mm but shorter than 30mm is found, the wheelset must be withdrawn from service within 24 hours.

If the RCF should develop to form cavities in the tread of the wheel GM/RT2466 sets limits on the maximum size of cavity. The wheelset must be withdrawn from service if any single cavity is greater than 15mm long circumferentially around the wheel or any two cavities separated by less than 50mm have a total length greater than 15mm.

It is common practice for train operators to re-profile wheels at short enough intervals to avoid either of the crack length or cavity length limits being reached. The reprofiling



intervals are adjusted for the different RCF initiation lives on powered axles and the first and last axles in a multiple unit. While preventive wheel turning has been successful in reducing wheel RCF problems, it reduces vehicle availability.

Where effective inspection and preventive turning regimes are not in place, wheels that have suffered severe RCF are usually identified by wheel impact load detectors and scheduled for maintenance.

7 CONCLUSIONS The references quoted in this report show that RCF and wear of rails and wheels have been the subject of investigation for over 25 years. The high stresses in the material near the contact patch in both the wheel and the rail mean that some type of surface damage is almost inevitable in normal operation.

With high strength steels, lubrication and bogies that steer well, it is possible to limit the surface damage on wheels and rails to mild wear. If the contact conditions exceed the material’s ability to support them and a relatively low viscosity fluid is present the wheel and rail will probably suffer RCF. In general, RCF can be expected on the high rail of curves and the wheels running on the low rail in curves. If the fluid is removed, the RCF is replaced by wear.

The state-of-the-art in modelling is more advanced for wear than it is for RCF. The Archard wear model has shown good agreement between predictions and measured wear on wheels. A simpler model based on net energy transfer in the contact patch has been shown to give similar results to the Archard wear model.

There has been more work performed on developing RCF models for rails than for wheels. The most promising rail RCF models take account of the interaction between wear and RCF. The objective of T549 project is to develop these models for use in predicting wear and RCF on railway wheels.

Train operators faced with wheel RCF are currently managing the problem by turning wheels at relatively frequent intervals. They are trying several solutions including alternative wheel profiles and materials. The variation of RCF between the different wheels in a trainset indicates that traction and braking forces may combine with steering forces to give a worst case. Tests with alternative braking arrangements are also being proposed.



REFERENCES

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30. Ringsberg, J. W., 2005, Shear mode growth of short surface-breaking RCF cracks, Wear, Vol. 258, pp 955-963, Elsevier

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APPENDIX – NOTATIONS & DEFINITIONS

Symbol Definition Units aDV Dang Van material constant A Contact patch area mm2 c Constant g Acceleration due to gravity m/s2

HB Brinell hardness k Constant

Ke Yield strength in shear N/mm2 Kt Ultimate tensile strength N/mm2 Ky Yield strength in tension N/mm2 l0 Semi spacing between rail m μ Coefficient of friction p0 Maximum contact pressure N/mm2 q0 Tangential traction N/mm2 Q Tangential force N Qx Longitudinal tangential force N Qy Lateral tangential force N P Normal force N

rhigh Rolling radius of high wheel m rlow Rolling radius of low wheel m ro Nominal rolling radius m rr Rolling radius of right wheel m R Curve radius m t Time s T Tangential force N y0 Lateral displacement of wheel relative to track m γ1high Longitudinal creepage on high rail γ1low Longitudinal creepage on low rail μ’ Utilised coefficient of friction σ Direct stress amplitude N/mm2 τ Shear stress amplitude N/mm2 τe Fatigue limit for material in shear N/mm2

τeq1, τeq2 Dang Van effective stresses N/mm2



Figure A1. Parts of a Wheel (from GM/RT24663)

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