modern track 2

iWocle117 i?a/Iwa!/ TI ack 2 WPEEL-RAIL INTE~~FAcE I i

2 WHEEL-RAIL INTERFACE ~ ?"' 1- I 2,1 Ylhea3-rail guidance

r i- A rail vehicle basically consists of a body supported by secondary suspension on bogles in which the

wheelsets are mounted and damped by means of primary suspension. Track guidance of the wheel IS

achieved in pr~nciple by making the following two provisions: ip""

L - The tires are conical ~nstead of cylindrical which means that in straight track a centering force is

exerted on the wheelset if there is slight lateral displacement. The centering effect promotes a bet- ter radial adjustment of the wheelset in curves. This leads to more rolling. less slipping and hence less wear.

i - The tires have flanges on the ~nside of the track to prevent derailment. In case of more considera-

ble lateral displacement both in curves and on sw~tches, the lateral clearance between wheelset and track is often no longer sufficient to restrict lateral displacements adequately by means of the

restor~ng mechanism previously discussed Should the wheel flange touch the rail head face, this [ can result In high lateral forces and wear

2.2 Wheelset and track dimensions I@' &

Generally the track gauge is used as a distance measured between the two rails. more specifically the distance between the inslde of the railheads measured 14 mm below the surface of the rail. By choosing 14 mm the measurement IS less influenced by llpping or lateral wear on the rail head and by ihe radius r = 13 mm of the rail head face. On normal track the gauge is 1435"O-~ mm with a maxi- mum grsdient of 1 :300 For new track. however, NS apply the following standards-

- Mean gauge per 200 m. 1435+", mm

- Standard deviation within a 200 m section less than 1 mm

F Figure 2 1 llustrates the definition of the track gaiige as well as some other commonly used dimen- b sions such as.

- , Mean wheel c~rcle

i B I Y

F h

h,

Figrire 2 1 Wheeisef and track dimensions foi straight normal gauge track F i

1R 1

Y

_J

' 1 2 WHEEL-RAIL INTERFACE Modern Ra~iway Track

A I I

7 - Track width: distance between the po~nts of contact of the mean wheel circles with the rails, having \ a nominal value of 1500 rnm. This d~mension is important for calculations and should not be con-

fused w~th gauge nor track distance.

- Track distance: distance between lines of adjacent tracks I

For the wheelset the following dimensions are used:

, - Flange gauge: distance across the wheel flanges. measured 10 rnrn below the rail surface (wheel- set in the centred position) on standard track is 1426+'-,~ mrn.

- Inside gauge: distance between the insides of the wheels, on standard track is 1360'~.~ rnm.

- Flangeway clearance: clearance between wheelset and track, i.e, the distance the wheelset can

I w+d be displaced laterally. This is not the same as the difference between track gauge and flange gauge.

ri eori

It should be mentioned that a specific method of design process applies to switches and crossings. I

I The following summary gives some values for narrow gauge, standard gauge, and broad gauge. I

- Narrow gauge: d

750 mm. parts of Indonesia

Y 1000 m m parts of Switzerland, tram lines etc.

m 1067 mm: (3%') (Cape gauge), South Africa, Japan, Indonesia, etc.

d - Standard gauge:

F"i 1435 mm: (4' 8%") Gauge used by George Stephenson in 1825 based on existing mail d coaches. Most commonly used nowadays.

9 - Broad gauge:

Y 1524 mm: (5'). Russia, Finland

R d 1665 mm: Portugal

1667 mrn: Spain

S

2.3 Conicity

Orig~nally conical tire profiles w~th an inclination of 1:20 were used. Since a centrally applied load on the railhead is desired, a rail inclination of 1:20, as shown In Figure 2.1, was also selected; this for lnstance st111 applies to NS proflie NP 46. UIC 54 rail usually has an ~nclination of 140 . This inclination matches the S 1002 worn wheel profile which is in general use In Europe. During manufacturing the tires are given a profile which matches the average shape caused by wear. In contrast to the straight conical profile this has a hollow form.

I

PRI

L

r- iLlodein Railway Tack 2 WEEEL-RAlL II\lTERFACE

L

- I h ~ s means that the lateral movement takes on a completely d~fferent behav~ocrr whlch IS known as 1 iHz] r C hunrlng. As shown In the draw~ng in Flgure 2.5 the movement changes from a harmonlc to a zrg-zag shape The wavelength becomes shorter and the frequency Increases q~llckly untrl ~t IS In the crltical

C range for the rolling stock and resonance occurs.

p.il I

Thls phenomenon IS shown In Figure 2.6 The L bogre design, as far as con~clty and flangeway - clearance are concerned. must be such that stable v

i""!

running rs always guaranteed for the speed range sl In whlch the veh~cle IS to be used. I

I PP bllb

! - - - I < / I I ! r ' * V

F~gure 2 6 Increase in amplitude and frequency with speed and the dekelopment of instability

F luii

2.5 Equivalent conicity F IiSk

It IS clear that regarding a worn profile the conic~ty depends on the actual shape of the rail head and trre, rnclud~ng any wear, track gauge. and rarl rncl~nation, Likewise, elast~c deformatlon of the wheelset and rarl iastenlngs plays a role. Fe

W

Generally, the effectlve or equivalent conlcity IS defined as:

A r IT - f-2 y = %-- = 1/2- Y Y (2 8) m

Here r, - r2 IS the Instantaneous difference in roll- f Ar = r, - r2

IW

rng radrus of the wheel treads; generally speaking this IS a non-lrnear function of the lateral displace- ment y of the wheelset wlth respect to the central i posrt~on The difference between conical and worn Worn profile

profiles IS glven In F~gure 2.7. To enable numerrcal 1 comparisons ./, IS determined at a certain lateral displacement y = y . I

II C*ri

I

I With a conlcal proflle the conrcity IS constant and Conic ~ ro f l l e I

7, I (2.8) becomes (see also): L ', Y

= 1/2& = 1/2X(r+ YY) - ( r - YY) = y (2.9) Y

P Y $e*i

In the next paragraph the effects resulting from F4 progressive non-l~near behavlour of the effective coniclty and t s influence on the rirnnrng stab~lity of ! ~ l a n ~ e w a ; clearance L - vehlc!es and rzrl \blear are dealt w ~ t h In greater deta~l. I I P irPi

Flgiire 2 7 y-Ar curves Difference between conical and worn wheel profiles

2 WHEEL-RAIL INTERFACE Modern Railway Track

2.6 Worn wheel profiles

A perfectly conrcal wheel profile IS unstable as far as its shape is concerned, but will take on a shape that is y AS

stable as the effect of wear In additron, conrcal profiles have the disadvantage that a substantial lateral movement will, because of the two-pornt contact, lead directly to an impact. If the profile of the r a~ l and wheel tire at the point of contact is assumed to be circular, it can be deduced from Figure 2.8 that in the case of lateral displacement y of the wheelset with respect to the track, the contact point on the rail w~ l l over a distance translate to:

P r A s = - Y (2.10) P w - Pr

Moreover, rf the value of y is small compared to the radir, the followrng relationship holds true: Figure 2.8 Displacement of contact point on rail due

to wheelset displacement

P w A r = tan$-2y = y,2y (2.11)

P w - Pr 6

In the case of ccnlcal profiles the radius is infinite and therefore the contact point on the rail does not move.

4 Thrs means that rail wear is very much concentrated on one pornt.

An interesting case arrses rf the radii of the wheel t ~ r e 2

and rail are almost equal. If there is slrght lateral dis- placement of the axle, the contact point jumps which

Y tmml results in less passenger comfort. In the y-Ar graph

2 4 6 this man~fests itself as a jump.

Confirmation of this is given in the y-Ar curve in Figure 2 9 Y-Jrcun1e fo ra theoretical S1002~rof i Ie in comSination with a UIC 54 rail 1 40 gauge 1434 m

Figure 2 9, wh~ch IS derived from the theoretical S 1002 wheel profile in combinat~on wrth UIC 54 r a ~ l and track gauge 1434 mm.

Practical research has shown that over a period of ,( Equ~valent con~c~ty ye

time wheel profiles stabilise wrth wear at an equiva- lent conic~ty of 0.2 to 0.3. With regards to running sta- bil~ty, the equivalent conicity must remain below 0.4 and to ensure the centering effect it must be greater excursion = 3 75 rnm than 0.1. - nornlnal gauge

\

Figure 2.10 gives a summary of equivalent conicity values for the S 1002 profile In comb~nation with UIC 60 r a ~ l for different track gauges and rail inclinations. ra~ i ~nchnat~on T h ~ s rnformation shows that, apart from a rail ~nclina- t ~on of 1:20, the conic~ty increases as track gauge decreases and rarl inclination becomes steeper. With ,;120

a rail inctll-3tion of 1:20 the coniclty IS very small and 1428 1432 1436 1440 gauge Imml IS independent of the track gauge 1430 1434 1438

Figure 2 10 Eq~iivalent conicity for S 1002 on UIC 60

3 3

L

Modern Ra~lway Track f- -

2 WHEEL-RA IL INTERE4 CE L-

r e 2 O W a measurement result of both n e w and w o n w h e e p o l e s whlcl; the wear is quantified In z o n e s a s spec~f ied ~2351.

2.7.3 Single and two-point contact between wheel and rail ~ r I

In the case of srngle-polnt contact, according to Figure 2.13, heel load and lateral force act on the L

same point. This siruation occurs when uslng worn wheel proflles. In the case of two-point contact, shown in Flgcire 2.14, the applicatron pornts do not coincide. F

I h

Figure 2 13 Single

F contact po i~ i t Figure 2 14 Double contact point Forces on rails in case of

b lateral slip in curves

a

Thrs two-point contact situation arises rn curves where the wheelset lacks the freedom to positron Lu

irself radlally The flrst wheelset of the vehicle that enters the curve makes an ang!e of attack produc- ing a flange force on the high rail This flange force forces both wheels to slip In the drrectron of the II

~nslde of the curve causing fr~ction forces on the rarls as indicated In Flgure 2.14 and Flgure 2.17 b

Accord~ng to Sectlon 2.7.1 the contact force is the resultant of a stress distribution whlch acts on the contact area. Flgure 2 15 and Figure 2.16 show plctures of both contact situations which -were obtarned by means of photo-elastic measurements. The calculation of the stress distriburion within the rail head will be drscussed In Section 5.6.4.

n Y1

Flgiire 2 15 Internal cross sectlon st/-ess distribution ln Figlire 2 16 lnternal cross section stress distr~biition in the ra11 heacl due to one-point contact the rail head due to two-po~nt contact r"i

L

--. . 7

,rai 1

a I

; ?I 2 WHEEL-RAIL INTERFACE Modern Railway Track

' 7 2.7.4 Spreading forces J

In order to satisfy equilibrium, the hori- zontal component of the flange force ' d equals the sum of the horizontal friction forces. It can be concluded that under these circumstances both rail heads are I

I

pushed apart.

Figure 2.18 gives another explanation of t h~s phenomenon based on the rolling and creep movements to be discussed in the following sections. This figure, which by the way IS viewed from the top 1 (not a perspective view), shows the situ- ation of a moving wheelset making lat-

&L _ - - - _ . _ - - -

era1 contact with the high rail (a). 7 Y 4 t - y y i I X

The rotation vector of the wheelset can I

be resolved in a lateral component (roll- m I ing) and a longitudinal component i (creep). These movements cause forces

to act on the wheelset as drawn (b) m

I which also includes the lateral flange d force From this, the resultant forces can

be derived that act on the rail (c) Appar- P ently, the lateral forces on the railheads

d are identified as spreading forces. F~gure 2 17 Contact between wheel flange and railhead

m Thls observation leads to some impor-

d tant effects. First the track components I

1 I

are loaded by this mechanism It should

w be noted that we deal here wlth internal forces. I

d If there are also external I I forces, for instance due to runnrng d~rectron

7 non-compensated acceler- Lid ations, the resulting flange I I 4@' force can be considerably t. ,so higher 7 \" yng

I livri '\ -

Secondly, as a result of the creep \ '\ I

7 striking angle the flange contact point is located at \/?' ,

2 7 of attack a I kf some distance in front of \, a .\ b

1 the contact point on the '\, $2, \/ ', rrra

I runnlng surface. This

y induces a sliding velocity *c3Lp5/2 vF ,/*' -& - \

\ / / /- -in the vertical direction ,' , I

between the flange and I

I the railhead In combina- S

''On with the Figure 2 18 Orig,n of spreading forces this effect creates a friction force on the wheel which pushes the wheel upward If th~s force is high enough to surmount the vertical force on the wheel. the wheel may climb up the railhead followed by a derailment A simple model for dera~lment risk IS dis- cussed In the next section ~

3 --

r" ;P

1

r--

Modern Railway Track 2 WHEEL-RAIL INTERFACE ,

2.7.5 Wheel-rail creep r I i I

According to the Hertz theory the contact area is elliptic and the inside pressure distribution is also ellipbc. In the case of perfectly smooth surfaces the highest pressure I L

occurs at the centre. In real~ty, the surfaces show a cer- tain roughness resulting in an irregular pressure distribu- far

I

tion with high local peak values. At these spots, the high LuL

pressure may lead to plastic deformation of the material causing loose particles and thus wear. (nar

Also, the pressure distribution will be changed in such a - - - - - - - - - - - - -

way that the maximum is moved a bit in the forward LL

direction Consider for instance the pulled wheel situa- tion in Figure 2 I 9 (see other possibilities in Figure 2.25).

F h

Because the resultant of the pressure is also moved for- ward, a moment will be created in combination with the wheel load This moment should be surmounted during

7 lvrrl

the movement and is called rolling resistance. The small asymmetry of the pressure distribution, ca 0.5 mm, IS in practice not taken into consideration.

Pr U1

The tangential force. which must be transmitted in the Figure 2 19 ~symmetr icai pressure dlnr~bution

contact area. is based on friction and can be quite sub- stantial, e g with driving wheels or a braking operation

Alrf It seems logical that for each particle of the contact area the maximum shear force to be transmitted is T equal to the product of the friction coefficient and the local current pressure. This assumes that all points wheel are about to glide at the same time However, this is not the case because the shear forces create elastic ++ - - - - . w X

deformations of the material of both wheel and rail. *

ra~l - + + + + 1 - pos /neg

Therefore, gliding will sooner occur at the rear of the contact ellipse than at the front. (Figure 2.20). stra~n 2

normal For small values of the transmitted friction force, the RT prmsure

P Y

elast~c effects are dominant and the force will increase with the magnitude of the apparent slip This shear

apparent slip or 'creep' arises if part of the surfaces of stress wheel and rail are not gliding but are deformed elasti- cally As the transmitted force becomes higher, glid- ing will take place over a constantly increasing part of slipped lociied the contact area until the whole contact area takes region part in gliding The total transmitted force is then obviously equal to the friction coefficient p times the total transmitted normal force The slip is defined as relative quantity. For practical

C purposes a simplified form is used.

Flgure 2 20 Explanation of creep phenomenon PI

wheel/rall lrrYi

- v- w r E x - -

v (2.14)

P hi The theoretical path of the friction force as a function of the creep or slip is drawn in Figure 2 21

For low values of the creep the behaviour is dominated by elastic deformations and there is an almost n linear relation For larger values, the slip zone expands and the curve becomes more and more flat- I

tened unt~l finally it runs horizontal when slip occurs in t h ~ whole contact area,

2 &HEEL-RAIL 1NTEFFr4CE Modern Railway Tack

T,IQ t ' a11 71

I

111i J

I I y r lu

R

I Ex

"19 Figure 2 21 Relative longit~iclinal friction force Figiire 2 22 Actiiai lateral friction force vei-sus slip veisus slip

psn

hi In the precedrng consideration it was more or less assumed that the frrctron force and slrp act in the longrtudinal drrectlon. A complete analogue mechanrsm acts in the lateral direction wrth the same

i"k.l, functronal relationship between the force Ty and the slip, the latter defined by:

bid

- "/ate,a/ ve~ootv EY - (2.15)

T" l i V

wr3 The displayed functlon of the creeping force IS theoretical. In reality, once full glidrng occurs, the force 1

will decrease in accordance with the increasrng slip (Figure 2.22). The descendrng part of the curve, m

I combined \ ~ i t h the elasticity of the material of wheel and rail and one of the own value mode shapes dl of the wheel body, produces a phenomenon called stick-slrp. Thrs mechanism IS the cause of the well-

I known squealing of wheels in curves. E Because of the presence of the attack angle of the wheel whlch causes the flange to push agarnst the

I

W inside of the rarlhead, a lateral slip in the running surface exrsts and conseqciently a lateral slip force I wrll be developed. The negatrve relation between thrs force and the slrp wrll not grve a stable equrlib-

I

1-4 num, but will instead rnduce a highly frequent jumping to and fro between t \ ~ o points on the curve U.

I 2.7.33 Spin

7 1 bit

Apart from slrp In the longitudrnal and lat- I era1 drrectlon a thlrd quantrty also exlsts: I Rotation Vector "

' m the so-called spin which also partlclpates Force on R a ~ l

lu in transmrttrng the frlctron force. Spln or

3 rotational slip arises if the small contact i +

Running direction area between wheel and rail IS not parallel rs S p l n m i to the rctation axrs of the wheelset. The rotation vector of the wheelset can then be '$f Force on Wheel

decomposed rn a component parallel to the contact area (this is pure rolling), and a Fig~ire 2 23 Effect of spin

component perpendicular to it, which is the rotational slip or spin as indicated in

I ! Figure 2.23 6'

The spin IS def~ned as:

o s i n y - s l n y ( b = - - - (2.1 6) v r

I

;~ It should be noted that the spin (b has a dimension [ l lm].

Pj '7 0

- lo*:

Modern Ra~lway Track

i"! 6 2.8 Train resistances

I I

A 2.8.1 Types of resistances u A tram must overcome several traln reslstances to start moving or to continue movlng. Instead of the t ra~n reslstance itself, denoted by W, mostly the relat~ve value is given with respect to the tram we~ght as rndlcated by the symbol w. The relat~ve value 1s ~ndependent of the train weight and ~ t s un~ t is NIkN or, more customary, ?ho. The most important train reslstances are:

- R ~ ~ n n l n g resistance, consrst~ng prlmarlly of the rolllng res~stance between wheel and ra~ l and the journal fr~ction (see F~gure 2.25).The order of magn~tude of the runnlng res~stance 1s 1.5 to 2 %o, wh~ch is much lower than In the case of road vehrcles (10 to 30 ?Lo);

- Air resistance, whlch depends on the dimensrons and the cross section shape of the roll~ng stock The arr reslstance 1s proport~onal to the square of the speed wh~le a possible headwind should also

?! be taken ~ n t o account; V

'7 c. * i I

2 I\ = in( l 6 g I , g = r n~n (a / ' b ,b ;a ) , In4 = 1 386, u. Po~sson's ratlo '

I pna The analyt~cal forms involv~ng !\are accurate for very small g only

Table 2 2 Creepage and spin coeffioents

n/Iocle~i~ Railway Track r 2 WHEEi-R,IIL INTERFACE i-

As the pullng force is the sum of all adhes~on iorcss. the following result c-n be obtained by using r (2.23) I

F = 1 T < f 7 Q,,,, i f Wad, i

where: fld

I

I

Wad,, is the total adhesion weight of the traln in case of pulled vehicles, the adhesion weight IS the k

we~ght of the locomotive