Simulation of Rail-wheel Contact Force

Simulation of wheelrail contact forces

S. IWNICKIManchester Metropolitan University, Chester Street, Manchester M1 5GD, UK

Received in final form 4 August 2003

A B S T R A C T This paper summarizes the forces that develop in the contact patch between the wheeland rail in a railway vehicle. The ways that these forces govern the behaviour of a vehiclerunning on straight and curved track are explained and the methods commonly used tocalculate and utilize the forces summarized. As an illustration, the results from a computersimulation of a typical UK passenger train are presented and certain aspects examined.

Keywords contact forces; profiles; railway vehicle dynamics; vehicle dynamics; wheelrail interaction.

N O M E N C L A T U R E a, b = the contact ellipse semi-axesC11, C22, C23, C33 = constants calculated from approximate formulae given by Kalker5

E = Youngs modulus for the material in the contact patchY l, Y r, Y w = lateral forces at left, right wheel contact patch, lateral force on

wheelsetFx, Fy, Mz = longitudinal and lateral force and spin moment at contact patch

Fx, Fy = forces at the contact patch (as above) modified by Johnson andVermeulen4

f 11, f 22, f 23, f 33 = linear creep coefficients defined by Kalker5I = inertia of the wheelset about a central vertical axis

l0 = half the gaugem = mass of the wheelset

N l, N r = normal force at left, right wheel contact patchP0 = vertical force at the wheel due to static vehicle load

P1, P2 = dynamic vertical force response peaks at the wheel after a verticalirregularity

Ql, Qr, Qw = vertical forces at left, right wheel contact patch, vertical force onwheelset

rl, rr, = wheel radius at left, right wheelr0 = wheel radius with wheelset in central positionR = curve radiusv = forward velocity of the wheelset

U1, U2, 3 = actual velocity at the contact patch in lateral, longitudinal and spindirections

U 1, U2,

3 = velocity at the contact patch (as above) calculated from wheel

motionW = wheelset weight

y, y = wheelset lateral displacement, velocity 1, 2, 3 = lateral, longitudinal and spin creepage

l, r, = conicity of wheel, left, right, effective

Correspondence: S. Iwnicki. E-mail: [email protected]

c 2003 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 26, 887900 887

888 S. IWNICK I

= coefficient of friction at the contact patch, = roll angle of wheelset, angular velocity of wheelset rolling about

axle, = yaw angle, yaw velocity of wheelset

= angular frequency of the kinematic oscillation of the rollingwheelset

I N T R O D U C T I O N

All the forces supporting and guiding a railway vehiclemust be transmitted through the contact patches betweenthe wheels and the rails. An understanding of the way thatthese forces are generated and the effect that they have onthe behaviour of the vehicle has developed from trial anderror in the early days to the use of computers to solvethe complex equations developed in the 1960s and hasresulted in the powerful computer packages currently inuse. An understanding of the geometry of the wheel andrail are the foundations of this understanding.

T H E G E O M E T R Y

The forces between railway wheels and rails are governedby the geometry of the wheel and the rail. In particularthe geometry of a vertical cross section of the rail and aradial cross section of the wheel are critical.

Wheel and rail profiles

The earliest railway wheels were cylindrical and ran onflanged rails. They were usually fitted to an axle so that

Fig. 1 Trevithicks tram engine in 1804 running on flanged rails at the Pen-y-Darren plateway. Painted by Terence Cuneo. Reproducedwith the kind permission of the Cuneo Estate.

both wheels could rotate independently. A good exampleof this is shown in Fig. 1 with probably the first locomotivein the world, built by Richard Trevithick, pulling truckson the plate way at the Pen-y-Darren iron works in Walesin 1804. Fitting the flanges to the wheels instead of therails must have made a considerable saving of material andprobably allowed better guidance of the vehicle althoughit had the disadvantage of preventing the vehicles fromrunning on the road. Adding a small amount of conicityto the wheels would have enhanced this guidance and themodern wheelset was formed when the two wheels werejoined to the axle and fixed to the vehicle body throughbearings in axleboxes.

If a rolling wheelset moves away from the centre of thetrack the conicity at the wheels means that it will havea larger rolling radius on one side than on the other. Asthe wheels are stiffly linked in torsion they have to havethe same rotational speed and the wheelset is forced toyaw about the vertical axis. This yaw angle tends to pointthe wheelset back towards the central rolling line and thewheelset will then naturally roll back to the centre of thetrack.

In a curve the wheelset will tend to move outwards un-til the rolling radius difference between the two wheels

c 2003 Blackwell Publishing Ltd. Fatigue Fract Engng Mater Struct 26, 887900

S IMULATION OF WHEELRAIL CONTACT FORCES 889

Fig. 2 An idealized wheelset displaced laterally.

matches the yaw velocity needed for the curve (Fig. 2).This lateral displacement is known as the rolling line off-set and the wheelset will curve perfectly as long as thereis sufficient clearance for the required lateral movement.If the flangeway clearance is exceeded before the rollingline offset is reached then perfect curving will not bepossible.

The following equation links the lateral displacement, y,and the curve radius R:r0 yr0 + y =

R l0R + l0 , (1)

and the rolling line offset is therefore:

y = r0l0R

, (2)

where r0 is the radius at the contact point when thewheelset is central, l0 represents half the gauge, R the ra-dius of the curve and is the effective conicity.

In fact the wheelset will tend to overshoot its equi-librium position (due to the developed yaw angle) andan oscillation known as the kinematic oscillation will beset up. This kinematic oscillation is also observed onstraight track after any deviation from the natural rollingline.

This oscillation was observed by George Stephenson in1827 and analyzed by Klingel1 in 1873. The angular fre-quency of the kinematic oscillation can be found by as-suming the motion to be sinusoidal:

= v

r0l0, (3)

where v is the forward velocity of the wheelset.The greater the conicity of the wheelset, the smaller the

curve radius for which perfect curving will be possiblegiven a particular flangeway clearance. The other side ofthis engineering compromise is that the greater the conic-ity, the lower the rolling speed at which the wheelset be-comes unstable. This instability is caused by the wheelsetovershooting the equilibrium rolling line and is knownas hunting. Hunting will be limited by flange contact but

can lead to derailment. The speed at which hunting oc-curs is known as the critical speed and vehicle designersmust ensure that the critical speed is above the maximumrunning speed. In fact the kinematic behaviour is usuallymoderated by the creep forces, which are discussed below.

Most railway organizations cant the rails inwards by asmall angle and this usually matches the conicity of thewheel so that the normal force with the wheelset in thecentral position is directed along the web of the rail. Inthe United Kingdom this is 1 in 20 but 1 in 30 (for ex-ample in Sweden) and 1 in 40 (many countries includingGermany) are also common.

Wear at the wheel will tend to change the wheel treadfrom a cone to a more complex concave shape. Many rail-way organizations have designed worn profiles, which areintended to maintain a constant geometry as the wheelwears. In the United Kingdom the P8 profile was con-structed from an average measured worn profile and isshown in Fig. 3.

In use the wheel and rail will wear and the profiles mustbe measured to obtain accurate geometrical information.This can be done with reasonable accuracy using me-chanical or laser devices and Fig. 4 shows a typical mea-sured wheel and rail profile from the MiniProf measuringdevice.

T H E C O N TA C T

At the point or points where the wheel contacts the rail acontact patch develops. The size and shape of this contactpatch can be calculated from the normal force, the materialproperties and the geometry of the wheel and the rail inthis region. As the wheel and the rail are both bodies ofrevolution it is possible to describe this geometry by usingthe radii of curvature in the direction of rolling and forthe cross sectional geometry.

In predicting the contact, the theory of Hertz based onuniform elastic properties of contacting bodies of revolu-tion is often used giving an elliptical contact patch withsemiaxes that can be calculated. Although this is an ap-proximation based on full elasticity it is widely used andgenerally gives acceptable results. An alternative is to splitthe contact patch up into strips and to evaluate the con-tact conditions and the contact stress for each strip finallyensuring a balance between the wheel load and the totalnormal force at the contact patch.

T H E F O R C E S

The forces acting in the contact patch can be split intonormal and tangential components. The tangential forceis usually split further into longitudinal (in the directionof the rail axis) and lateral (in the plane normal to therail axis). The normal force and the lateral force can be


890 S. IWNICK I

Fig. 3 The P8 worn profile.

Fig. 4 Wheel and rail profiles as measured by a miniprof device.

replaced with a vertical and lateral force where the verti-cal force is truly vertical and the lateral force acts in thehorizontal plane. These are known as V (or Q)verticaland L (or Y)lateral and the ratio L/V or Y/Q is oftenused as an indicator of the nearness to derailment.

Gravitational stiffness force

As the wheelset moves laterally the direction of the normalforce between the wheel and rail changes and a componentof this force is directed towards the track centreline and

helps to centre the wheelset. This effect is known as thegravitational stiffness and the force depends on the lateraldisplacement and the roll angle of the wheelset.

When the lateral displacement is small the gravitationalstiffness force can be calculated ignoring differences inconicity across the wheels:

Referring to Fig. 5

Yl = Nl sin(l ),Yr = Nr sin(r + ),

(4)



Fig. 5 An idealized wheelset.

where Y l, Y r are the lateral forces, N l, N r are the normalforces, lr represent the conicity at left and right wheeland roll angle of wheelsetequating vertical forces

Nl cos(l ) = Ql,Nr cos(r + ) = Qr,

(5)

so the total lateral force

Yw = Yr Yl = [Ql tan(l ) Qr tan(r + )] , (6)for small angles this can be simplified to:

Yw = W,where W = Ql + Qr = the total vertical load acting onwheelset.

But = rr rl2l0

= yl0

, (7)

so finally Yw = Wyl0 . (8)

Creep forces

When a railway wheel deviates from pure rolling, that isduring acceleration, braking or curving or when subjectto lateral forces through the suspension, forces tangentialto the normal force are transmitted to the rail at the con-tact patch. These are called creep forces and are due tomicroslippage or creepage in the area of contact.

If a cylindrical wheel rolls along a straight, flat rail with notangential force being transmitted between the wheel andthe rail the horizontal distance covered in one revolutionof the wheel will be exactly equal to its circumference.If, however, a torque is applied to the axle to acceleleratethe wheel then it will be found that in one revoultion thehorizontal movement is less than the circumference ofthe wheel. This is due to the material behaviour within thecontact patch as material is compressed at entry before asection where adhesion takes place then a section wherethe material slips out of compression and finally exits intension.

Carter2 was the first to study creep in railway wheels andhe looked to the earlier work of Reynolds in belt drives.He considered the wheel to be a thick cylinder rollingon a flat plate and only examined creepage in the lon-gitudinal direction. He assumed without proof that thearea of adhesion was at the leading edge of the contactpatch. This was extended to the three-dimensional caseof two rolling spheres in contact by Johnson3 who in-cluded consideration of lateral and longitudinal creepage.He assumed elliptical Hertzian contact and predicted anelliptical adhesion region within this. Slip only occurredin the area between the two regions. As a result of ex-perimental work by Johnson and Vermeulen4 this theorywas extended for non-spherical bodies and calculated tan-gential creep forces with an error consistently less than25%.

In a railway wheel the creepage can be calculated fromthe attitude of the wheelset and the resulting creep forcesmay then be evaluated. The relationship between creepageand creep force has been studied thoroughly by Kalker5

and his equations are used in almost all simulations.The theory of wheel rail creepage was only truly con-

sidered in three dimensions for the first time by Johnson3

who included spin of the wheel about a vertical axis inhis theory. Kalker then developed a numerical method ofpredicting creep forces for arbitrary creepage and spin,the first available for predicting these forces. This wassubsequently verified experimentally by Brickle6 who alsolooked at the result of having a narrow contact ellipse asis the case during flange contact. From this work Kalkerhas produced an exact numerical theory and a linear the-ory for use when creepage and spin are small. He hasalso made available several computer programs to predictcreep forces for given creepages and spin.

Creepage occurs in all three directions in which relativemotion can occur and it is defined as follows:

Longitudinal creepage 1 = v1 v1

v, (9a)

Lateral creepage 2 = v2 v2

v, (9b)

Spin creepage 3 =3 3

v, (9c)

where v1, v2 and 3 are the actual velocities of the wheel;v1, v

2 and

3 are the pure rolling velocities (velocity when

no creep occurs at the same forward velocity) calculatedfrom the wheel motion and v is the forward velocity of thewheelset.

The creepage can be calculated from the attitude of thewheelset using equations based on the geometry and de-rived by Wickens.7

The velocities at each wheel can then be derived in termsof the lateral displacement of the wheelset centre of gravity


892 S. IWNICK I

and the yaw angle of the wheelset, both with respect tothe track centreline:

for the right-hand wheel : for the left-hand wheel :

v1r = v rrr0 v1l = vrlr0

v2r = y + v v2l = y + vv3r = 0 v3l = 03r = + 3r = +

(10)

for the right-hand rail : for the left-hand rail :

v1r = v2l02R

l0 v1l = v2l02R

+ l0v2r = 0 v2l = 0v3r = 0 v3l = 03r = 0 3l = 0where y, y are the lateral displacement and velocity of thewheelset, , are the yaw angle and yaw velocity of thewheelset and is the angular velocity of wheelset rolling(=V /ro)

Note: If the track is considered to be flexible rather thanrigid there may be a lateral component of track velocityto consider.

These velocities can then be used in the previous equa-tions to give the creepages for both wheels:

1r = l0v yr0

l0R

1l = + l0v +yr0

+ l0R

21r = yv 21l =yv

3r = r0

v3l = r0

v.

(11)

After determining the creepages it is necessary to find therelated creep forces. At small values of creepage the re-lationship can be considered to be linear and linear coef-ficients can be used in calculations. However, at largervalues of creepage, for example during flange contact,the relationship becomes highly non-linear and the creepforce approaches a limiting value determined by the nor-mal force and the coefficient of friction in the contactarea. When working in this region it is necessary to use adifferent calculation method.

It may be appropriate to use one of the programs basedon the Kalker theory described above (e.g. Duvorol, Con-tact and Fastsim) but a simpler method based on the cu-bic saturation theory of Johnson and Vermeulen can alsobe used with generally good results. This is a heuristicmethod and involves calculating the creep force expectedfrom the linear coefficient and modifying it by a factor de-rived from this value divided by the limiting creep force.The inaccuracy of this method has been shown by Shen,Hedrick and Elkins8 to be less than 10% when compared

with Duvorol at low values of spin creepage and less than18% at all values of spin creepage.

The creepage creep/force relationship is further com-plicated by the fact that the three creepages do not actindependantly. Kalker5 has shown that the creep forcesdepend on the creepages as follows:

F x = f111,F y = f222 f233,Mz = f232 f333,

(12)

where f 11, f 22, f 23 and f 33 are the linear creep coefficients.The equations of Johnson and Vermeulen then modify

the tangential forces:

F x = F xFs

[FsN

13

(FsN

)2+ 1

27

(FsN

)3]N

(for Fs 3N), (13)

and F x = N F xFs

(for Fs > 3N),

where Fs = (F x2 + F y2) 12 , is the coefficient of friction at the contact patch and Nis the normal force at the contact patch and similarly forFY from FY .

The linear creep coefficients are calculated as follows:

f11 = E(a, b)C11,f22 = E(a, b)C22,f23 = E(a, b)3/2C23,f33 = E(a, b)2C33,

(14)

where E is the Youngs modulus, a, b represent the con-tact ellipse semi-axes and C11, C22, C23, C33 are constantscalculated from approximate formulae given by Kalker.5

The creep forces thus arrived at for the lateral and longi-tudinal direction at each wheel are then combined to givea lateral force and a yaw torque acting on each wheelset:

Yw = 2 f22(

yv

)

f23 v

Mw = 2 f23(

yv

)

2 f33 v 2 f11l20

v 2 f11l0y

r0.

(15)

This equation can be seen to explain the observed motionof the wheelset described earlier. The lateral creep forceis proportional to the yaw angle of the wheelset and theyaw torque acting on the wheelset about a vertical axis isproportional to its lateral displacement. The effect of thisis to steer the wheelset towards the centre of the track indecaying oscillations at all speeds up to a critical speedat which the oscillations continue laterally and in yaw. Athigher speed the behaviour is unstable and the oscillationsincrease until limited by flange contact.



The equations for creep force and gravitational stiff-ness derived above can now be combined with the in-ertia force terms for a wheelset to give a general equationof motion. The wheelset is taken as having the two de-grees of freedom of lateral translation motion and yawrotation

my + 2 f22(

yv

)

+ f23 v +Wy

l0= 0

Iz 2 f23(

yv

)

+ 2 f33 v +2 f11l20

v+ 2 f11l0y

r0= 0.(16)

These equations are used in simulations of completerailway vehicles.

A note on approximations

Some approximations are made due to the Hertz con-tact (mentioned in Section 3), due to the longitudinalshift of the contact patch and the change in the angleof the contact plane. It is also possible for multiple con-tact to occur between the wheel and the rail for somewheel rail profile combinations. These may be signifi-cant in flange contact and a fuller treatment is given byBrickle.6

The Kalker methods are widely used within computersimulation packages but they tend to be complicatedand a new heueristic model has been proposed by Shenet al.8 which is much simpler to evaluate and is becomingmore popular. Figure 6 shows a comparison of the Shenet al.8 heuristic model with Kalkers Duvorol and simpli-fied Fastsim predictions.

Fig. 6 Comparison of creep force models(from Ref. [8]).

Vertical forces

The vertical forces that develop between the wheel andrail are made up of a force that supports the static load ofthe vehicle and a dynamically varying force in response tothe vehicle motion along track with irregularities. Theseforces are usually referred to asP0 force: the static load on the wheelP1 force: the high frequency dynamic force where the

wheel vibrates on the contact stiffnessP2 force: the lower frequency dynamic force caused by

the wheel and rail vibrating on the substruc-ture stiffness (pad, sleeper, ballast)

Figure 7 shows an example of these forces as a vehicleruns over a vertical dip (such as a fishplated joint betweenrails).

Fig. 7 Vertical forces after a dipped rail joint.


894 S. IWNICK I

The frequency of the P1 force is influenced by the un-sprung mass (wheel and associated axle mass, bearings andbrake gear) and the Hertzian stiffness at the contact patch.The P1 force can be excited by a rail irregularity or defector a wheel flat and its peak value occurs at around 1 msafter the disturbance.

The P2 force peak occurs at around 10 ms and is in-fluenced by the rail and sleeper mass as well as theunsprung mass and the stiffness of the rail pads andsubstructure.

F O R C E L I M I T S

Railway organizations around the world have set limits onthe various forces existing between the wheel and the rail.Some brief comments on the main limits are given belowto provide a context for the force levels.

Vertical

In the vertical direction high forces can cause damage tothe rails and supporting structures and can cause rollingcontact fatigue when combined with high tangential forcessuch as occur during traction, braking or curving.

In the United Kingdom a limit of 322 kN is set forthe P2 force (based on the maximum load measured fora Deltic locomotive running at maximum speed over adipped rail joint). UIC 5189 sets a maximum static load of112.5 kN per wheel and a maximum dynamic vertical forceper wheel of between 160 kN and 200 kN, depending onmaximum speed (provided this values does not exceed thestatic wheel load plus 90 kN).

In small radius curves (less than 600 m) UIC 518 sets alimit of 145 kN for the quasi-static vertical force.

Lateral

In the lateral direction high forces can cause distortionof the track on the bed of ballast. This is normally pro-tected against by using the simple but widely establishedPrudHomme limit for the track shifting force at onewheelset, which can be calculated from the static load(P0 force):

Y


discrete events representing, for example, dipped joints orswitches, or can be measured values from a real section oftrack taken from a recording vehicle. In the United King-dom the High Speed Track Recording Coach (HSTRC)runs over the whole network collecting track data at reg-ular intervals. Additional forces may be specified such aswind loading or powered actuators (e.g. in tilting mech-anisms). Depending on the purpose of the simulation awide range of outputs for example displacements, accel-erations, forces at any point can be extracted.

C A S E S T U DY

In order to demonstrate the nature and effect of the forcesdescribed above a short case study is presented here. Com-puter models of a locomotive and a passenger coach havebeen set up using the computer package ADAMS/Rail.The Class 43 power car and the Mk.3 passenger coach arechosen as making up the widely used HST train runningon UK main lines. Various results from the two vehiclemodels are then presented as examples of what can be ob-tained from simulations such as these. Figure 8 shows theMk.3 coach model in ADAMS/Rail format.

Fig. 8 The computer model of the Mk3 passenger coach in ADAMS/Rail.

Class 43 power car

The Class 43 HST power car is a four-axle, two-bogiediesel engine locomotive. The main characteristics are:

Axle load 171.67 kNTotal weight 70 000 kgUnsprung mass per axle 2175 kgBogie wheelbase 2.6 mBogie pivot spacing 10.3 mMaximum operating speed 125 mphTractive effort at 125 mph 1368 kW

The primary suspension includes (per axle):

4 coil springs2 vertical dampers4 traction links with end bushes2 vertical bumpstops

The secondary suspension includes (per bogie):

4 coil springs1 traction centre equivalent bush2 vertical dampers


896 S. IWNICK I

2 lateral dampers2 yaw dampers2 lateral bumpstops2 vertical bumpstops

Measured worn wheel profiles from a typical vehicle areused and left and right profiles are different.

Mark 3 passenger coach

The Mark 3 coach is often coupled with the Class43 power car and is modelled here in the ladenconfiguration:

Axle load 101.2 kNTotal weight 41 281 kgUnsprung mass per axle 1595 kgBogie wheelbase 2.6 mBogie pivot spacing 16.0 mMaximum operating speed 125.0 mph

The primary suspension includes (per axle):

2 trailing arm bushes2 vertical coil springs2 vertical viscous damper1 bush to represent the panhard link

The secondary suspension includes (per bogie):

2 spring elements to represent the airspring + spring planksystem1 traction centre equivalent bush + damping

Fig. 9 Simulated lateral forces on the rail at the front bogie of a Class 43 locomotive running around a 760 m radius curve.

1 anti roll bar equivalent bush2 vertical viscous dampers1 lateral viscous damper2 vertical bump-stops + rebound-stops2 lateral bump-stops2 yaw friction elements to represent the friction pads.

The wheel profiles used in the model are new P8 profiles.The vehicle models have been validated against mea-

sured track data provided by Corus Rail Technologies.These data were in the form of forces at the rail head de-rived from strain gauges on the rail web at a number of testsites where the Class 43 locomotive and Mk3 passengercoach was running. More details of this work are given inJaiswal.12

Results

The vehicles have been run on a range of track configu-rations and the behaviour in steady state curves as well asthe dynamic response to track forces simulated. The trackirregularities are taken from track recording coach datafor the particular site.

Figure 9 shows the lateral forces for the locomotive run-ning into and around the 760 m radius curve at Aycliffeand Fig. 10 shows the position of the contact patch on thewheel and the rail for the same curve.

The tables in Figs 11 and 12 present a summary of thedisplacements and forces acting on the rail as the two ve-hicles run in curves of 700 m and 1500 m at differentspeeds and with varying coefficients of friction. The speed



Fig. 10 Simulation results showing contact position on rail and wheel for the Class 43 locomotive running around a 760 m radius curve.

Fig. 11 Curving behaviour of the Mk3 passenger coach 700 m radius curve with varying friction and cant deficiency.

differences are shown as cant deficienciesdeviations inthe height difference across the rails from a balancingspeed at which the lateral components of the centrifu-gal and gravitational forces balance. It can be seen thatthe lateral displacement of the leading wheelset does not

change greatly as the vehicles are running close to flangecontact in all cases. The second wheelset moves outwardswith increasing cant deficiency and on the coach this ismore pronounced at the lower value of the coefficientof friction. The high stresses, sometimes evident on the


898 S. IWNICK I

Fig. 12 Curving behaviour of the Class 43 locomotive in a 1500 m radius curve with varying friction and cant deficiency.

Fig. 13 Predicted contact stress against position on the rail headfor the Class 43 locomotive in 700 m to 1800 m radius curves.

inside rail, are probably not as damaging as those on theoutside wheel in the curve as the creep force is generallymuch lower at the inside contact. The highest stress oc-curs at the flange contact in the locomotive when the areacan drop as low as 10 mm2.

Figure 13 shows how the contact stress at the high (out-side) rail varies with the position on the rail head for theClass 43 locomotive on a range of curves. The trend ofincreasing contact stress as the contact moves towards theflange can clearly be seen.

Finally, Fig. 14 shows the frequency distribution ofthe contact position for the two vehicles on straightand curved track. Observed running bands are super-imposed on these plots and can be seen to match rea-sonably well with the tread contact of the vehicles (onthe right rail). Flange contact (on the cess rail) is muchmore variable and is influenced greatly by the dynamicbehaviour.

C O N C L U S I O N S

The forces acting between the wheel and rail in a rail-way vehicle have been analyzed and can be simulated withmodern computer packages to simulate the behaviour ofthe vehicle on any track configuration. A wealth of infor-mation about the vehicle motions and forces within thesuspension and on the rails can be obtained from thesesimulations.

Acknowledgements

The author thanks Yann Bezin and the rest of theRail Technology Unit team for the computer mod-els of the Class 43 locomotive and the Mk3 passen-ger coach. Thanks also to Jay Jaiswal, Andy Stephens,Stephen Blair and Tom Kay at Corus Rail Technologiesfor the wheel and rail profiles and the trackside measure-ments used to validate the models; and Network Rail



Fig. 14 Frequency of predicted contact positions and observed running band for the class 43 locomotive in a 760 m radius curve.

Fig. 15 Frequency of predicted contact positions and observed position of the running band for the Mk3 coach on straight track.


900 S. IWNICK I

for their support for the Corus Rail Technologies andMMU work.

R E F E R E N C E S

1 Klingel (1883) Uber den Lauf der Eisenbahnwagen auf geraderBahn. Organ Fortsch. Eisenb-wes 38, 113123.

2 Carter, F. W. (1926) On the action of a locomotive drivingwheel. Proc. R. Soc. A 1125, 151157.

3 Johnson, K. L. (1958) The effect of spin upon the rollingmotion of an elastic sphere upon a plane. J. Appl. Mech. 25,332338.

4 Johnson, K. L. and Vermeulen, P. J. (1964) Contact ofnonspherical bodies transmitting tangential forces. J. Appl.Mech. 31, 338340.

5 Kalker, J. J. (1979) The computation of three dimensionalrolling contact with dry friction. Int. J. Numer. Methods Eng. 14,12931307.

6 Brickle, B. V. (1973) The steady state forces and moments on arailway wheelset including flange contact conditions. Doctoral

Thesis, Loughborough University 1973.7 Wickens, A. H. (1965) The dynamic stability of a railway

vehicle wheelset and bogies having profiled wheels. Int. J. SolidsStruct. 1, 319341.

8 Shen, Z. Y., Hedrick, J. K. and Elkins, J. A. (1989) Acomparison of alternative creep force models for rail vehicledynamic analysis. In: Proceedings of the 8th IAVSD SymposiumCambridge U.K. Swets and Zeitlinger B.V. Lisse 1989.

9 UIC. (1999) Leaflet 518 (draft). Test and approval of railwayvehicles from the points of view of dynamic behaviour, safety,track fatigue and ride quality. International Union of RailwaysJanuary 1999.

10 Nadal, M. J. (1908) Locomotives a Vapeur. CollectionEncyclopedie Scientific, Biblioteque de Mechanique Appliquee etGenie, 186 (Paris).

11 Iwnicki, S. D. (1999) The Manchester Benchmarks for RailVehicle Simulation. Suppl. Veh. Syst. Dyn. 31.

12 Jaiswal, J., Blair, S., Stevens, A., Iwnicki, S. and Bezin, Y. (2002)A systems approach to evaluating rail life. In: RailwayEngineering 2002 (Edited by M. Forde). Glasgow University,London.


Simulation of Rail-wheel Contact Force

Documents

lateral forces

vertical forces

right wheel contact

contact patchfx

contact patchy

e t r ythe forces

wheel radius

wheel andrail