Wear 265 (2008) 1266–1272

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Problems with wheel and rail profiles selection and optimization

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Sergey Zakharova,∗, Irina Goryachevab, Victor BogdIlya Zharova, Vladislav Yazykovc, Elena Torskayab,a All-Russian Railway Research Institute, 10, 3d Mytishchinskaya, 129851, Moscow, Russb Institute for Problems in Mechanics of the Russian Academy of Sciences, 101 Prospectc Bryansk State Technical University, 241035, Bryansk, Russia

a r t i c l e i n f o

Article history:Accepted 18 March 2008Available online 9 June 2008

Keywords:WheelRailProfileSimulationOptimization

a b s t r a c t

Serious problems with whger traffic exists on the linpolicies and real practicesA scientific approach to pSome aspects of profile moptimization based on com

1. Introduction

There is a wide spectrum of conditions and environment char-acteristics that has an impact on traffic operation. These are

associated with dedicated lines, mixed (combined) passenger andfreight traffic, differences in traffic density, terrain conditions, ratioof curves to tangent track, etc.

It is one task when wheel and rail profiles are to be selectedfor dedicated lines, e.g. heavy haul line, or high speed line. It ismuch more difficult to solve the problem of profile selection whencombined freight and passenger traffic exists on the line on whichdifferent type of rolling stock operate or this task should be solvedon a network scale. Such a problem exists for the Russian Railways,that have about 86,000 km route length and about 124,000 km tracklength, with several climatic regions, terrain features, and differ-ence in wheel profiles for locomotive, freight, passenger cars andelectric trains. Profile policies and approaches to profile selectionand optimization are discussed.

2. Profile policies and practice

A short review of profile policies and practices is given.Rail and wheel profile design for heavy haul lines approachhave been proposed by Tournay [1]. The approach is based

∗ Corresponding author.E-mail addresses: zakharov@vniizht.ru (S. Zakharov), goryache@ipmnet.ru (I.

Goryacheva), pogorelov@tu-bryansk.ru (D. Pogorelov).

0043-1648/$ – see front matter © 2008 Sergey Zakharov. Published by Elsevier B.V. All rigdoi:10.1016/j.wear.2008.03.026

ova, Dmitry Pogorelovc,gey Soshenkovb

skogo, 119526, Moscow, Russia

d rail profile design arise particularly when combined freight and passen-his task should be solved on a big railway network scale. Profile selectionescribed. An example of practical approach to profile evaluation is given.

s evolution and optimization is described and some results are presented.ement and control are presented. An approach to profiles evaluation andd scientific and practical methods is described.

© 2008 Sergey Zakharov. Published by Elsevier B.V. All rights reserved.

on the consideration that three functional zones exist inwheel/rail contact and that recommendations should be for-mulated for each zone. In particular it is considered thatconformal flange contact is an optimum condition for non-steeringvehicle.

In Guidelines to Best Practices for Heavy Haul Railway Operation[2] it is recommended to apply a system approach to optimizingwheel/rail performance. This involves a number of recommenda-

tions, in particular, regularly reprofiling rails to shapes that conformto the worn wheel to reduce high stress contact and avoid wheeltread hollowing through reprofiling.

A description of quasi-static curving program PUMEL [2,3], thatevaluates contact pressure for measured wheel profiles (from threedifferent North American Railways) and is used to practically eval-uate the performance of rail profiles, is given. According to Mageland Kalousek the optimized wheel and rail profiles from the contactmechanics aspects should satisfy the following criteria [3]: avoidcontact stresses greater than three times the strength of materialin shear; avoid closely conformal contact; design appropriate steer-ing capability; ensure effective conicity that are within the conicitywindow of the truck; arrange for as many contact points across thewheel tread. Rail grinding with “optimal” intervals is considered asa practical and economical technique for maintaining favorable railprofile.

In [4] an optimal design of wheel profile for railway vehicleis based on the rolling radius difference (RRD) function vs. thelateral displacement of a wheelset, optimization procedure withtarget function as mean RRD function or modified RRD functionand dynamic analysis of optimized variants.

hts reserved.

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m)

S. Zakharov et al. / W

Table 1Locomotive wheels profiles used on the line

Profiles Type Flange

Thickness (mm) Height (m

Standard New 33 30Integral New 29 30Standard Repair 29 30Var.2 Repair 30 28Var.3 Repair 29 32

Professor Yoshihiko Sato gave profound historical study of JRShinkansen the wheel and rail profiles development and recom-mendations [5]. On JR-line conical and arc wheel profiles arecompared for curving performance and hunting stability [6]. Inworks of Ishida et al. [7] based on laboratory study and field testsconical and arc profiles wheels are compared based on their wearperformance and conclusion was made that arc wheel profiles areconsiderably better. In Sawley’s works [8,9], the influence of wheelhollowing on wheel/rail rolling resistance, gauge spread forces,rolling radius difference, the angle of wheel/rail attack, vehicle sta-bility in straight track, economic effects of hollow wheel removalhave been investigated and recommendation are given.

Ushkalov and Zhechev [10] suggested performing a complexmodernization of the conventional three-piece bogie 18100 typeused for freight cars in Ukraine (and other countries of the for-mer USSR). This modernization comprises the utilization of Stuckiroller assisted constant-contact side bearings, polyurethane padsfor friction wedges and the bolster wedge pockets together withnon linear “one-point” contact type of wheel profile. Runningtests for 3 years (about 190,000 km.) have shown that this mod-ernization resulted in increase of the critical velocity of emptycars by 30–40 km, decrease the wheel flange wear by two timesand some other benefits. The Ukrainian Railways is now perform-ing above-mentioned modernization of several hundred freightcars.

TTCI (Pueblo, USA) has developed wheel/rail profile tolerancesoftware (WRTOL) using a database of measured wheel profiles thatevaluates the interaction characteristics of the wheel set typicallypassing over rails and identifies rail and wheel profiles that pro-duce high stresses or induce high lateral forces or have excessivewheel hollowing thus enabling to improve rail and wheel profilemaintenance [11].

SBB (R. Muller) has developed an approach to the wheel/railprofile design, in particular applied to the line between Switzer-land and Italy [12]. This line has very sharp (up to 45 m radius)curves and different rail cants (1:20, 1:40). Appropriate profiles areselected based on continuous measurement and contact geome-try assessment methods including plotting radius difference andeffective conicity vs. gauge clearance functions. Recommendationson profiles selection are to avoid two-point contact in sharp curvesand matched profiles by use of so called stabilized (worn) wheelprofiles and appropriate rail profiles.

In UIC/WEC Joint Research Project-2 compared world experi-ence of wheel/rail profiles design [13]. The design and maintenanceof profile involves seeking a balance to obtain the lowest contactstresses in all areas of wheel/rail contact and the lowest appro-priate conicity for the prevailing curve radii and required huntingstability threshold. From the stress point of view, the desired con-tact between the rail and the wheel will occur under the followingconditions [13]:

- If the radii of the surfaces of the contacting bodies are as large aspossible to insure the largest area of the contact patch.

5 (2008) 1266–1272 1267

Fillet (mm) Central part of the tread

Angle (◦)

70 13.5 1:2065 1570 13.5 1:20

Curved65 13.6 Curved + 1:12

- When the two contacting bodies, particularly in the regions of therail head gauge corner and wheel flange throat, have conformalshapes.

- There exists an optimal conformal profile that provides for theminimal pressure distribution at given wear rate or minimal wearrate at given limitation on the contact pressure.

- To avoid conditions when the prevailing contact takes place at theedges of the contacting bodies and plastic flow may be expectedon the field side of the wheel and the rail.

- A single point non-conformal contact is the most damaging tothe rail as the high contact stresses occurring under high creepconditions result in rolling contact fatigue of breakage of the railgauge corner.

It was suggested that the following balance should be achieved:

• Contact in the area of the edges may not be allowed as experiencehas shown the materials cannot accommodate under prevailingaxle load and lateral creepage.

• Contact is aligned with prevailing rail side wear, rail gauge andwheel flange wear limits.

• Contact as conformal as possible to reduce forces; no appreciableradius differential is generated by conformity.

• A limit of hollow wear is set to reduce stresses in false flangecontact and to reduce the loss of radius differential generated ina curve.

3. Example of the practical approach

It was assumed that by measuring worn profiles of locomotivewheels before turning, operating on long distance section with a

large number of diverse radius curves, after certain time the profileis formed that reflects an accumulated wear action of rails withgiven ratio of curves and tangent sections, adopted periodicity ofturning and difference in initial profiles. The MiniProf system ofGreenwood Engineering was used for profile measurements [14].

Two section and three section electric locomotives are operatingon more that 2000 km length track section in the terrain with highgrades (up to 11‰) and a considerable number of 650 m radius andless curves. Locomotive tire multiple wear wheels are used for theselocomotives. Two types of new profiles and three types of “repair”profiles are allowed to be used for locomotive wheels at this line(Table 1).

To characterize the profiles several numeric geometric char-acteristics of the contact were calculated using a program of theincremental displacement. Geometric characteristics of the contactare angles of tangents in the contact points of the wheel with therail, radius difference between contact points and effective conic-ity. Profiles of new Russian rail R65 type were used to calculatethese characteristics. After some time of locomotives operation,they return to depots, in particular for wheel sets turning. Wheelset profiles of locomotives have been measured before turning.

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Table 2Change of an average geometric characteristic of the contact and effective conicityof locomotive wheels

Types of profiles ˛1 ˛2 �r (mm) � (rad)

Standard var.1 Init. 2.5 70.0 12.5 0.05Worn 4.2 72.0 12.4 0.06

Var2 Init. 8.0 * 2.9 0.12Worn 70.8 10.7 0.13

Var.3 Init. 12.1 65.6 9.2 0.17Worn 6.5 71.5 11.9 0.10

where, ˛1: angle of tangent in the area of tread contact, ˛2: angle of tangent in thearea of flange contact, �r: radius difference between contact points, �: effectiveconicity.

Average results of data treatment and calculation of the geomet-rical characteristics of contacts for three studied profiles are shownin Table 2. If conformal contact occurred, the contact point may shiftalong the profile. This case is marked in the table by an asterisk.

The following conclusions could be made from this study:

- Profiles of worn locomotive wheels in the area of wheel flangefillet are close to the average wheel profile corresponding to theaverage rail profile on the line and is about 15 mm.

- The maximal angle of flange of the average worn wheel profile is

about 72◦.

- Average effective conicity of worn profiles that have been initiallyturned under three above-mentioned profiles after locomotiveruns before turning became not more than 0.13.

From Table 2 it follows that the influence of the initial profile onthe flange wear rate is considerable. Another factor is the share oflocomotives with one type of profiles. In Table 3 change in the flangewear rate in the process of the introduction of locomotives withanother type of wheel profile is shown. This resulted in increase ofthe flange wear rate of all wheels in operation. Depending on thequantity of locomotives with new profile not less than 3 months arerequired to adapt wheel–rail system under study to new profile.

4. Scientific approach to profile design and optimization

4.1. Some definitions

Indices for the evaluation of wheel–rail profiles could be localand integral. Local indices are related to the contact area, forinstance, to the maximal contact pressure or the minimal wear

Table 3Change in the flange wear rate in process of introduction of locomotives with another typ

Year, month Profile var.2

Locomotives Flange wear (mm/104 k

2000 18.7 0.3201.2001 16 0.3202.2001 24 0.3403.2001 21 0.3004.2001 25 0.3005.2001 23 0.3606.2001 54 0.3407.2001 52 0.3808.2001 70 0.4009.2001 44 0.4210.200111.200112.200101.20022002, av.2003, av2004, av

5 (2008) 1266–1272

rate. Integral indices are functionals that could be found dur-ing vehicle–track interaction on a representative rail section, forinstance, the total wear of the wheel and the rail, or safety indices.The integral indices are those that are found for period of wheeland rail life. Wheel/rail profiles are considered as the concurrent ifintegral indices are within acceptable range. Wheel/rail profiles areconsidered as the optimal if one of the indices reaches extreme. Forinstance, the profiles that provide for the minimal wear rate, underlimitation on derailment safety criteria, hunting stability, contactpressure. A separate task is a demonstration of the possibility toreach the optimum and the algorithm of optimization. It requiresparameterizing the profile description and demonstrating that theoptimal profile is within this range.

4.2. Examples of scientific approaches

In previous work [15] a model of mutual wheel/rail wearunder conformal contact conditions was suggested along with anapproach to profile optimization.

The suggested approach is based on the following assumptions:

- for particular conditions the steady-state profile exists and

depends on the initial wheel/rail profiles and on tribological prop-erties of materials,

- there exists an optimal, upon selected criteria, profile providingfor the minimum wear rate or the minimum pressure distribution,

- the optimal profiles are selected for a family of wheel flange/railhead conformal profiles; to find optimal profiles, the condition ofthe constant ratio of wear rate of contacting bodies at the contactarea is set the vertical and the lateral forces as well as the angle ofwheel to rail attack are known from calculation of the quasi-staticmovement of a bogie in a curve,

- the dependence of the wear rate from the contact parameters isderived from the laboratory simulation of wheel flange/rail headwear.

Equations derived in this study [15] enable the identificationof the optimal wheel flange/rail head profiles which provides forthe minimal total wear rate of wheel traveling along the selectedtrack section, provided that the lateral forces and the angle of attackand the wear model are known and that an adequate wear modelis obtained from experiments (Fig. 1). Using these equations it ispossible to evaluate the wear rate for other than optimal profiles.

e of wheel profile

Profile var.3

m) Locomotives Flange wear (mm/104 km)

– –

6 0.2317 0.2423 0.2417 0.2524 0.2873 0.4160 0.4264 0.4060 0.3752.5 0.3881.2 0.3785.6 0.37

S. Zakharov et al. / Wear 26

Fig. 1. Unit load, contact pressure distribution obtained for the optimal profile [15].(1) Function of profile, (2) function of load P and (3) function of contact pressure p,and y and z are coordinates.

4.3. Using tribodynamic simulation model for profile optimization

Many studies have been performed on wheel or rail or both pro-files evolution and prediction using numerical methods based ondynamical models of vehicle/track interaction, contact mechanicsand tribology consideration. These studies enable the evolution of

profiles for a particular track and rolling stock and to evaluate theinfluence of essential factors. Work in the direction of integrationmodels of wheel/rail frictional interaction into vehicle dynamic hasactively been performed in many organizations.

In particular, VNIIZhT together with the IPM of Russian Academyof Sciences, worked in that direction from 1995–1996. However, thiswork has not been completed with the program complex enablingto solve jointly dynamics of rail vehicles and tribological problemsof wear and contact fatigue accumulation considering feedback ofwear on dynamic characteristics. At the same time during the lastdecade similar modeling tool had been created in Hungary, Sweden[16,17], Germany, Japan and some other countries.

The task of creating tribodynamic model (Fig. 2) has beenaccomplished in 2005 as a result of joint efforts of All RussianRailway Research Institute (VNIIZhT), Bryansk State Technical Uni-versity (BSTU) and Institute of Problems in Mechanics of the RussianAcademy of Sciences. The base for this work was the program com-plex (code UM Loco) developed by the BSTU [18].

Wheel profile simulation due to wear was performed as mul-tiversion calculation procedure in which external conditions arechanging at the end of the procedure. In our case external condi-

Fig. 2. Scheme of tribodynamic model of a vehicle/track interaction.

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Table 4Data for multiversion calculations

Curve radius (m) Share of curves andtangent (%)

Super-elevation(cm)

Velocity (m/c)

300 5 12 12500 7.5 9 16700 11 7 201000 8 4 20∞ 68.5 0 20

tions are wheel profile that is changing due to wheel/rail interactionon selected line and tribological model of wear.

Let F = {Fi}, i = 1 . . .. NF is a quantity of families in multiversioncalculations. Each family {Fi} is the calculation of vehicle dynamicsat various speeds under given external conditions that are trackplan (tangent, curves of particular radiuses), track irregularities, leftand right rail profiles. For example, if there are three families, F = {F1,F2, F3} where F1—vehicle movement in tangent and F2, F3—vehiclemovement in curves, i.e. R = 300,600 m. Thus NF = 3 and a quantity ofvelocities (in m/c) that are F1 = {15,20,25}, F2 = {13}, F3 = {15,18,21}.

For each family of multiversion calculation weight coefficients˛i, i = 1, . . ., NF defining the share of external conditions on theparticular railway line are introduced. The weight coefficient ˛i isa share of external conditions corresponding to Fi family on therailway line under study and is defined as

˛i = si

s,

NF∑

i=1

˛i = 1,

where s is the length of track section, si is the total of track sectioncorresponding to Fi (including transition part of curves).

For each family Fi weight coefficients of velocity defining vehi-cle speed distribution should be assigned. Beta-spline is used forsmoothing the wear distribution. Applied algorithm provides fordoubled smoothing of worn profile: on a phase of wear distribution

diagram and on a phase of take off of worn material.

Electric locomotive BL10 wheel profiles evolution during loco-motive run on the tested line with weight coefficients wasmeasured. Simulated worn profile with weight coefficients given inTable 4, are found to be close to the average between worn profiles.

From the practical point of view, to better evaluate the influenceof different initial profiles on the wheel profile evolution simulationdue to wear after the same distance of the locomotive operation,the minimal turning depth was calculated (Table 5). That is howmuch depth of metal should be machined under parallel shift ofthe profile to restore the profile.

Simulation of the freight car wheel profile of the vehicle run-ning over the line, characterized by the weigh coefficients given inTable 4, has been also performed. Evolution of the first wheel profileafter 50 and 100 steps of the material removal is shown in Fig. 3.

4.4. Contact fatigue and wear

The position of contact points, normal and tangential forces act-ing in these points as well as step-wise wheel profile evolution areobtained from the tribodynamic model. This information is used

Table 5Minimal dimensionless turning depth

Curve radius (m) Profile variants

Var. 1 13 mm, 70◦ Var. 2 19 mm, 65◦ Var. 3 25 mm, 60◦

00 1.2 1.7 2.5500 0.6 1.1 1.6

700 0.4 0.65 0.95

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Fig. 3. Freight car wheel profile evolution due to wear, (1) initial profile, (2) profileafter 50 steps of calculation and (3) after 100 steps of calculation.

by the program of the accumulation of the contact fatigue dam-age [19]. The function Q(y, z) of the accumulation of contact fatiguedamages is assumed as

Q (y, z) =N∑

1

c�m(y, z, n) + Q0(y, z),

where y – coordinates from the center of wheel tread, m, z – coor-dinates in the direction of wheel depth, cm, Q0 – is initial damage,which for initial calculation is assumed as zero, � – is the maxi-mal tangential stress that is considered responsible for the damageaccumulation and m and c – coefficients, that for calculation wereaccepted as m = 4 and c = 1.1 × 10−24.

Calculations were performed for a tangent track and simulatedvehicle operation corresponding to 5 × 107 cycles. Results of calcu-lations for different stages of wear for profile 1(70◦ and 13 mm) areshown in Fig. 4. Damage function has three local maxima: two onthe surface in the boundaries to the worn area and one subsurface.Such forms of functions are because of hollow form of tread wear

and traction forces less than 0.3.

Maximal values of dimensionless damage function are shownin Table 6. It should be noted that at the tread wear rate more than0.3 mm/104 km the limiting damage Q = 1 was not achieved.

Studies of wear and damage accumulation on wheel tread sur-face as competing mechanisms have been performed for two otherprofiles mentioned above. Studies of the influence of these pro-files on the tread surface damage under uniform wear of thetread area have shown that their damage accumulation functionis very close. Accelerated tread damage accumulated for pro-file 01 type. The major influence on the damage accumulationfunction show the wear rate. When the wear rate is increas-ing, the subsurface damage maximum is decreasing and movingcloser to the surface. Using a scientific approach makes it pos-sible to evaluate various profiles for both wear and contactfatigue damage. These are necessary steps in profile optimiza-tion.

In principal, for every profile it is possible to find the optimalwear rate and try to achieve it.

Table 6Maximal dimensionless damage function

Area Iterations corresponding to vehicle operation

50 100 150 200

On the surface 0.16 0.25 0.43 0.54Subsurface 0.15 0.305 0.33 0.46

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5. Some notes to profile management

The wear rate may be controlled by introducing wheels possess-ing variable wear resistance over entire profile. Depending on theobjectives, the wear resistance may be increased or decreased.

There are still some myths about wheel/rail hardness and theirdifference that influence wheel and rail wear and profile formation.

5.1. Influence of wheel/rail hardness and their difference

Laboratory tests in rolling/lateral sliding conditions have shownthat the influence of hardness on the wheel–rail wear depends onwear mode and on the wheel rail hardness level:

• at hardness levels less than HB 250 increase of one componenthardness does not influence the total wear of rail/wheel rollers,

• at hardness level HB 250-450 an increase of one component hard-ness resulted in decrease of the total wear of wheel/rail rollers,

• at hardness levels greater than HB 450 an increase in hardnessof one component resulted in considerable decrease of the totalwheel/rail rollers wear and decrease of wear of the second com-ponent as well.

Field simulated tests confirmed by the laboratory study in therange of rail to wheel hardness ratios (HR/Hw) of 0.7 to 1.6, showedthat there is no optimal rail to wheel hardness ratio providing forminimal total wear of both wheels and rails. The wear rate of eachasset is inversely proportional to its hardness by the relation n = 4–6,that is I ≈ (HR/Hw)n. Increasing the hardness of either the rail or thewheel (higher than HB 250) resulted in a decrease of the total wearrate.

There exist direct and indirect methods of profile control (man-agement). Direct methods are wheel turning in depots and railgrinding in the field. Indirect methods are those that promote form-ing favorable profile during operation.

Technology of wear control is suggested that comprise param-eters that characterize profiles, goals to be achieved and means ofcontrol. It is assumed that the average stable profile exists which isformed on all wheels and rails if wheels and rails are not changedduring operation. Goal of the profile management is to achieve ten-dency of rails and wheels to the average profile and the averageprofile to the optimal one.

6. Combining scientific and practical approaches to profilesselection

The best result could be achieved if scientific and practicalapproaches are used together. This is because it is very time con-suming and expensive to perform measurements of profiles andvehicle/track interaction tests on a network scale. Besides many fac-tors are impossible to reproduce. For instance weather conditions,rail cant variation, profiles variants, etc. Experiments are essentialto validate computer models and models are to be used for findingthe concurrent and then optimal profiles.

Generally speaking, the majority of recent approaches to wheeland rail profile design combine scientific and practical approaches.

When selecting profiles for mixed traffic operation and on dis-tributed railway network one should remember that:

- it requires a system approach as wheel profiles influence rail pro-files, that are dependent on wheel profiles of all types of vehiclesin operation, rail cant, gauge clearance, superelevation in curvesand vehicle dynamics;

S. Zakharov et al. / Wear 265 (2008) 1266–1272 1271

Fig. 4. Worn profiles (a–c) and damage function

- it is a multiobjective task as profile should provide for minimumderailment risk, vehicle hunting stability, limited assets wear rateand contact pressure, rolling resistance.

The following combination of scientific and practical approachesis suggested to find concurrent (optimal) profiles for variousvehicles working on the Russian Railways network: usage of tribo-dynamic model described above, tests of vehicle/track interactionand wheel/rail profile measurements.

Assumptions:

- because in combined traffic rail profiles are formed by hundredsof thousands of freight cars wheels the task of profile selectionfor freight car could be solved separately. When selecting wheel

(d–f) on different stages of wear process.

profiles for other types of vehicles rail profile variation may beconsidered as given;

- because wear and damage accumulations do not depend on asequence of wheel/rail interactions, then distribution of the curvelength and tangent of the network could be used for simulation;

- various wheel and rail worn profiles in operation are modeled bythe set of worn profiles obtained with the help of tribodynamicmodel.

The process of finding desired profiles should comprise:

(1) Using tribodynamic model multiversion calculations for therepresentative railway line or for a major part of the railwaynetwork. Weighting coefficients representing a share of major

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[8] K. Sawley, Huimin Wu, The formation of hollow-worn wheels and

1272 S. Zakharov et al. / W

curve radiuses and tangent track for both variants are takenfrom a central database. Track irregularities are taken frommeasured data, which are used for comparative calculationsof vehicles. Weight coefficients of train velocities are selectedfrom a statistical data.

(2) Definition of rail profiles. Left and right rail profiles are definedfor a range of curves accepted for multiversion calculationsand for a range of worn profiles. Rail renewal should also beconsidered. Foundation for the above definition of profiles ismeasuring of rail profiles in selected range of curve radiuseswith divers passed tonnage.

(3) Profiles’ evaluation. Using tribodynamic model, different pro-files were evaluated for the wear rate in characteristic profilezones (flange, fillet, tread), rolling resistance, critical speed andother criteria.

(4) Comparing modelled and measured profiles. Wheel profiles inselected depots are measured. By a statistical treatment thestable profile is defined. Modeling of profiles evolution for con-ditions mentioned above is performed. Measured and modeledprofiles are compared and if necessary input data are corrected.

(5) Finding dynamic parameters of vehicle/track and wheel/railinteraction. The critical speeds of hunting stability and param-eters of vehicle/track interaction for profiles under study andassociated truck characteristics are measured experimentallyand calculated by means of modeling. Functions of wheel treaddamage accumulation when moving along selected track line ormodel network for different profiles under study are calculatedconsidering tread wear.

(6) Minimal wheel turning depth for worn profiles at different ini-tial profiles are calculated.

(7) Summarizing of the influence of initial profiles by all criteria.

Evaluation of economical indices, such as predicted wheel life,rolling resistance, minimal turning depth by studied initial pro-files.

(8) Evaluation of the influence of rail grinding profiles on econom-ical indices by means of modeling.

(9) Attempt to optimize wheel/rail profile in the following way:• criteria of optimization and limitations (critical speeds, etc.)

are selected,• parametric description of wheel profiles is performed,• effective conicity of wheel–rail system is calculated,• dependence of criteria of optimization from profile parame-

ters are calculated; limitation are considered,• dependence of economical indices from profile parameters

are plotted,• all the above results are analyzed and attempt is made to find

parameters of optimal profile.

7. Conclusions

1. Decisions of profile design should be based on combined scien-tific and practical approaches. It is suggested that a scientific

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5 (2008) 1266–1272

approach should be based on tribodynamic model of vehicletrack interaction that enables to find profiles evolution due towear and defect damage accumulation. The model should bevalidated by the experiments.

2. When comparing either the wheel or the rail profiles perfor-mance it is necessary to consider their evolution during all periodof their life.

3. An approach to the solution of the problem of selection of theconcurrent and the optimal profiles for mixed traffic conditionsand large scale network is suggested.

Acknowledgement

Part of the work presented in this paper has been done underfinancial support of the Russian Fund of Fundamental Studies(Grant 06-08-01105).

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