EVALUATION OF DEGRADED ADHESION IN THE WSPHOMOLOGATION TESTS

Gianluca Cocci1, Paolo Presciani1, Alessandro De Rosa1

Paolo Toni2, Benedetto Allotta2, Alessandro Pugi2

1 FS – Trenitalia – Unità Tecnologie Materiale RotabileDirezione Tecnica – SperimentazioneProve Meccaniche e Sistemi Frenanti

Viale Spartaco Lavagnini 58 – 50129 Firenze – ItalyPhone +39 055 2353166, fax +39 055 473864

e-mail cocci@asamrt.interbusiness.it

2 Department of Energetics “Sergio Stecco”,University of Florence

Via di S. Marta n. 3, 50139 Firenze – Italy

SUMMARYEstimation of the degraded adhesion between wheel and rail artificially obtained during thehomologation track tests of the wheel slide prevention devices

INTRODUCTIONThe homologation of the wheel slide prevention devices is currently regulated by the UICleaflet UIC 541-05.This norm prescribes the execution of some series of track tests using a single trailer vehicle(slip tests). During these tests the adhesion between wheels and rails is artificially reducedspraying a solution of water and soap on the surface of the rail, near the point of contact of thewheels of the first axle.The correct degradation of the adhesion is based on the dilution of a specific liquid soap inwater in concentration of 1%.The verification of the correct level of adhesion is obtained by the estimation of the adhesionfactor at the beginning of the braking, when all the axles of the vehicle start slidingcontemporarily.The adhesion value demanded at this moment is:

08.006.0 ÷=f [1]

This value is deduced from the vehicle acceleration (negative) in simple way using thefollowing relation, without taking into account the rolling resistances and considering thegravitational acceleration equal to 10 m/s2:

≅ 10

dtdVf T [2]

where:VT : velocity of the vehicle,

insofar the equivalent deceleration demanded at the first sliding is:

8.06.0 ÷=dt

dVT m/s2 [3]

We realise that this criterion, only taking into account the beginning of the braking, is ratherapproximate.As confirmation, in many tests carried out in the past we found manifold inconveniences indetermination of the adhesion level achieved, due mainly to external factors capable toinfluence sensibly the results, as air humidity, contamination of the rail and pollution, surfacecondition of the wheels and the rail and many others.

PURPOSE OF THE STUDYIn this paper is explained the work that leads us to the determination of a method permittingto reduce the problems related to the application of the homologation prescription.More than a radical changing with an alternative method, we try to integrate the actualcriterion with an another permitting to evaluate the adhesion condition achieved during thecomplete braking, using the information coming from the measuring parameters already usedin the homologation tests, without introducing others.It is important to specify that a such method can not strictly define the characteristic of one ormore parameters involved in the braking (eg: cylinder pressure), because in this case we riskto evaluate the ability of the WSP in a specific condition that does not cover all thepossibilities that we find in the operating conditions, moreover we also risk to determinedesign requirements instead of a verification method.

ANALYSIS OF THE ADHESION BETWEEN WHEEL AND RAILThe first step of the study was to numerically determine the adhesion level demanded duringthe whole braking, using as base the results of some test series already performed withhomologated WSP.The considered tests were performed at initial speeds of 120 and 160 km/h.The adhesion between wheel and rail is obtained by the formula:

dtd

rIfZ

rr

PdtdIrfZrP f

fωµωµ +=⋅⇒=⋅−⋅ [4]

where:P : application force transmitted from the pad to the disc (per axle),µ : friction factor between pads and disc,Z : vertical load acting on the wheels of the axle,rf : brake disc application radius,r : wheel radius,I : moment of inertia of the wheel-set,ω : angular speed of the wheels,

from which, we obtain the term f :

Zdtd

rI

rr

Pf

f ωµ −⋅= [5]

The terms appearing in [5] are calculated as follows:

P: perpendicular application force transmitted from the pad to the disc (peraxle)The expression that link pcf with the force P it is the following:

441

2 ⋅η⋅

λλ

⋅−⋅=⋅= lmollacfi )FAp(PP [6]

where:Pi : application force transmitted from the pad to the disc for the axle i,pcf : brake cylinder pressure,A : bake cylinder area,Fmolla : reaction force of the spring in the brake cylinder,λ2/λ1: amplification ratio of the calipers,ηl : mechanical efficiency of the calipers.

µ: friction factor between pads and discThe friction factor is obtained by the results of the tests performed in completeadhesion (dry rail), in which the brake force applied in the interface wheel-rail isgiven by the following formula:

dtd

rI

rr

PF ff

ωµ −⋅= [7]

In these tests the braking force, applied by mean of the wheels, can be considered thesame for all axles, so the Ff in the [7] can be expressed as it follows:

4

Rdt

dVmF

T

f

−⋅= [8]

than, replacing [8] into the [7], the friction coefficient can be obtained by thefollowing expression:

rr

P

dtd

rIR

dtdVm

rr

P

dtd

rIF

f

T

f

f

⋅

+−

=⋅

+

=

ωω

µ

4

[9]

Applying the formula [9] to the results provided by the tests in complete adhesion,we find, for speed above 60 km/h, a value of µ varying between 0.30 ÷ 0.34 (see fig.1). For speed below 60 km/h the friction coefficient increases with a differentbehaviour from test to test.

10 20 30 40 50 60 70 80 90 1000.32

0.33

0.34

0.35

0.36

0.37

0.38

Test n.84

velocity [km/h]

Pad/

disc

- fri

ctio

n fa

ctor

Figure 1 - friction factor calculated in one test with initial speed of 120 km/h in complete adhesioncondition

The values of µ calculated for the tests carried out at the initial speed of 120 km/h,compared with the ones calculated for the tests carried out at the initial speed of 160km/h, show a different increasing at low speed (see fig. 2 and fig. 3). It seems thatthe increasing at low speed of the friction factor can depend on the heat accumulatedfrom the pads, proportionally to the dissipated energy.So, it is drawn a relation to take into account this variability, setting the expression ofµ in this way:

( )DTVCBA

++=µ [10]

where the constants A, B, C and D were determined by means of the experimentalresults. The selected values lead to the following expression:

TV++=

07.015.029.0µ [11]

10 20 30 40 50 60 70 80 900.28

0.3

0.32

0.34

0.36

0.38

0.4

Tests on complete adhesion condition – initial speed 120 km/h

velocity [km/h]

Pad

/dis

c -

frict

ion

fact

or

Figure 2 - tests at initial speed of 120 km/h, friction factor drawn by the tests (blue curves) andcalculated by the [11] (red curve)

20 40 60 80 100 120 140

0.28

0.3

0.32

0.34

0.36

0.38

0.4

0.42

Tests on complete adhesion condition – initial speed 160 km/h

velocity [km/h]

Pad

-dis

c –

frict

ion

fact

or

Figure 3 - tests at initial speed of 160 km/h, friction factor drawn by the tests (blue curve) andcalculated by the [11] (red curve)

In the test in degraded adhesion it was ascertained that the friction factor µ wasgenerally higher (with a numerical difference of about 0,03) compared to the onefound in the tests in complete adhesion; that probably depends on the reduced levelof average specific pressure on the pads.So, for the tests in degraded adhesion the following expression was adopted:

TV++=

07.015.032.0µ [12]

ω

dtd

rI : force of inertia applied on the surface of the wheel

In case of complete adhesion condition, the angular acceleration of the axles is linkedto the longitudinal acceleration of the vehicle, insofar, compared to the amount of thebrake force, the term

dtd

rI ω

assumes a negligible value (in the tests in complete adhesion it is generally nothigher than 5% of the brake force).Contrarily when the wheel slide the above consideration is not valid anymore,because the wheel can assume accelerations not related to the ones of the vehicle andit can develop the a

dtd

rI ω

comparable with the one generated by the brake action.In the figure 4 the values

rr

P f⋅µ [*] and dtd

rI ω [**]

calculated in one test carried out in degraded adhesion are shown.

25 30 35 40 45 50 55

-2

0

2

4

6

8

10

12

14

16Test n. 29

Time [s]

[kN

]

Pµ rp/rI/r (dω/dt)Ff

Figure 4 - comparison between the values µµµµP*(rf/r) (blue curve), (I/r)*(dωωωω/dt) (green curve), and the brakeforce resulting by their difference (red curve)

Calculation of the demanded adhesionApplying the values calculated as described in the [5] we obtain the values of the adhesiondemanded in the tests carried out in degraded condition.As confirmation of the correctness of the applied method, the acceleration calculated usingthe following expression:

m

Rmgf

dtdV i

iT

+

⋅

=∑=

4

1 4[13]

where:fi : demanded adhesion of the axle i,m : vehicle mass,g : gravitational acceleration,R : rolling resistance,

was compared with the one measured during the tests. In the figure 5 an example of thiscomparison is shown.

20 25 30 35 40 45 50 55 60-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8Test n.29

time [s]

dece

lera

tion

[m/s

]

Measured decelerationCalculated deceleration

Figure 5 - comparison between measured deceleration (green) and calculated deceleration (red)

As we can see in the figure 5, there is a very good correspondence between the measured andthe calculated acceleration (we have only a small difference at very low speed).So, for each test the numerical values of the demanded adhesion are stored in a threedimensional function depending on the absolute sliding and on the actual speed.An example is shown in figure 6.

2040

6080

1001200

2

4

6

80

0.02

0.04

0.06

0.08

0.1

0.12

velocity [km/h]

Test n.31 - Axle 1

absolute slide [km/h]

adhe

sion

Figure 6 - three dimensional function representative the demanded adhesion during one slip test indegraded adhesion condition

Although the result so obtained are not sufficient to give information about the available levelof adhesion, they have a statistical value that permitting us to define a criterion to evaluate theconformity of each tests.Nevertheless the method above described still involves some complexities owed to thecalculation of the demanded adhesion during the braking, so we tried to develop a new type ofanalysis to let us have a simplification of the method.

ELABORATION OF A METHOD TO EVALUATE THE LEVEL OF THEDEGRADED ADHESION BASED ON THE ANALYSIS OF THE RELATIVESLIDING OF THE AXLESWith the purpose to simplify the method for the evaluation of the correctness of the adhesionlevel achieved during the slip tests, we tried to deduce the necessary information by means ofthe evaluation of the amount of the axles sliding.

Conceptual elements for the formulation of the methodThe expression of the relative slide is:

TVW=ν where: W = VT - VR (VR: axle speed)

this expression changes its value between two extreme states:ν = 0 ⇒ rolling in complete adhesionν = 1 ⇒ wheel lockedIn all intermediate states we have the wheel slide.Some experimental researches in these last two decades have allowed to draw a relationbetween the adhesion and the relative slide, as represented by the curve of figure 7.

Figure 7 - adhesion/relative slide curve(ref. Boiteux Michel – «Le problème de l’adhérence en freinage»)

When a braking moment is applied on the wheel, the demanded adhesion increases up to thepoint α, corresponding to a very small ν value (ν = 0.01÷0.02).The phase ανν ÷= 0 is called creeping and the little mutual sliding between the wheel andthe rail are owed more to the elastic phenomenon in the point of contact rather than to realsliding effect; so the values between 0 and αν are defined as micro-slide.Increasing the braking moment on the wheel, the adhesion decreases to the point A, and thengoes up to the point B (ν = 0.05÷0.20). On the right of point B the adhesion stronglydecreases to reach, with ν = 1, a value equivalent to the dynamic friction factor.In reality the shape of the curve )(νff = is more indefinite, but we it can be consideredqualitatively reliable.It is important to notice that WSPs are calibrated to control the slide around of ν0 (point B),because the regulation near the point α is very difficult to achieve and also because, inparticular conditions of degraded adhesion, the point α becomes less and less evident, up tobe practically indistinguishable. For this reason ν0 is usually defined as optimal slide and theWSPs able to reach the best available adhesion value between the wheel and the rail, has toregulate the axle slide in proximity of this zone.It is also important to specify that the curve )(νff = is not the same in all the conditions ofdegraded adhesion but it changes as shown in the figure 8, and the value of the optimal slideincreases with the increasing of the adhesion degradation.

Adhesiondegradation

Figure 8 – adhesion/relative slide curves, variation due to the different degradation level

Analysis of the amount of the axle slide measured in the slip tests executed in degradedadhesion conditions

An accurate analysis of the slides measured during the tests leads us to divide the braking inthree different phases:

- Transitory initial phase (from the beginning of the braking up to about 85% of initialtest speed), the deceleration increases progressively following the increasing of thebrake application force. In this phase, the tests performed in different degradedadhesion condition show a quite similar behaviour than the slides with a differentdeceleration increasing. As example, in figure 9 the deceleration and the relative slide(of the first axle of the vehicle) measured in the tests 96 (adhesion degraded with wateronly) and 87 (adhesion degraded with solution with soap concentration of 1%) arerepresented.

- Intermediate phase (between the 85% of the initial speed one and 50 km/h): in thisphase the WSP performance can be considered stabilised and the sliding values aremostly indicative on the adhesion level on the rail.

- Final phase (between 50 km/h – 0 km/h): when speed is low (see fig. 9, test 89) thelittle variations of the absolute term(VT – VR)determine a great variability of the relative term( )

−

T

RT

VVV

in this last phase the WSP operating can cause a great oscillations of the relative slide,independently of the adhesion level on the rail. So this phase can not be taken intoaccount in the evaluation of the adhesion level.

01020304050607080901001101200

0.2

0.4

0.6

0.8

1

1.2

1.4

Velocity [km/h]

Dec

eler

atio

n [m

/s2 ]

Test 96Test 87

01020304050607080901001101200

20

40

60

80

Axle 1

Rel

ativ

e sl

ide

[%]

Velocity [km/h]

Test 96 - axle 1Test 87 - axle 1

1° phase 2° phase 3° phase

Figure 9 - comparison of the deceleration and the relative slide measured in two tests executed underdifferent degraded adhesion condition

We also noticed how in the tests performed at the initial nominal speed of 160 km/h, theslides are generally lower compared to those related to the tests performed at speed of 120km/h.The study of the slides has also highlighted that for insufficient values of degraded adhesion,the amount of the axle slide is an useful index, but for values of degraded adhesion too higherthan the right one, the slide can not return a reliable information about the real value of theadhesion.A simple explanation can be given by means of the figure 10, where it is possible to evaluatethat the optimal fields of intervention of the WSP have an intersection zone that increaseproportionally with the increasing of the adhesion degradation.

not sufficient degradation

correct degradation

excessive degradation

Figure 10 – adhesion/relative slide curves, variation of the optimal slide range

It suggests that a method based on the examination of wheel slides could be useful toestimate if the adhesion level has not been sufficient, but it does not permit to establish if ithas been excessive.Nevertheless, the simple evaluation of the average of the slides does not let us establish theadhesion level on the rail with a satisfactory precision.In fact, the typical regulation of the WSPs determines a continuos alternation between brakingand release, and it generates some oscillations during the development of the slides. Theseoscillations, ideally around a zone of optimal sliding, sometimes can become so great tocompromise the stopping in the prescribed distance, even if the average slide is equivalent asthe one measured in other tests with acceptable stopping distances.The slide variation range is characteristic of the WSP operational precision and it can not beadopted like index of the adhesion level.For these reasons we thought to elaborate a method based on a numerical reference for theslide; in that way it is possible to consider the adhesion degraded insufficiently in those testswhere the slide level is below this conventional limit.

Research of the minimum slide limitSome studies in the past have shown that, in the same environmental conditions, the optimalslide vary with the speed with a certain trend. It is clear, that a method based on a minimalfixed slide limit loses its effectiveness in the speed intervals where the optimal slide issensibly different by such limit.In figure11 the variability of the optimal absolute slide depending on the slide energy isshown.

Figure 11 – optimal absolute slide versus the slide energy and depending on the vehicle speed(ref. DT ORE 257 B 164)

80 100 120 140 160 180 200 220 24010

12

14

16

18

20

22

24

26

28

30

Velocity [km/h]

Abso

lute

slid

e W

o [km

/h]

Es =800 kJEs =600 kJEs =400 kJ

Es =300 kJEs =200 kJEs =100 kJ

Figure 12 – optimal absolute slide versus the vehicle speed and depending on the slide energy

Transferring the data of figure 11 on a graphic with the vehicle speed on the abscissas(fig.12) and approaching the numerical data, we draw that, up to 80 km/h, the optimalabsolute slide Wo linearly depends on the vehicle speed:

BVAW T +⋅=o [15]

with the constants A e B depending on the slide energy.Dividing the expression [15] by VT we have the link between the relative optimal slide νo andthe speed:

TVBA +=oν [16]

We can notice how this relation has an hyperbolic behaviour (see fig. 13).

80 100 120 140 160 180 200 220 24010

11

12

13

14

15

16

17

18

19

Velocity [km/h]

Rel

ativ

e sl

ide

[%]

Es=800 kJEs=600 kJEs=400 kJEs=300 kJEs=200 kJEs=100 kJ

Figure 13 - optimal relative slide versus the vehicle speed and depending on the slide energy

By mean of the results of the slip tests carried out in correct condition of degraded adhesion,we can approximately found a slide behaviour close to the one indicated in the [16] (seefig.14), also for speed lower than 80 km/h.It follows that if we use a minimum fixed slide limit, established in the zone where thehyperbolic curve is approximately constant, the method loses his validity only incorrespondence of the last part of the braking.This drawback can be avoided reducing the application field to a certain speed value.Following an accurate evaluation of the slide behaviour, compared with the trend of thetheoretical curve, we decided to fix this speed value at 60 km/h.

Time [s]

Velo

city

[km

/h] –

rela

tive

slid

e [%

]

Optimal relative slide rangeVehicle speedTip axle speedRelative slide

Test 89 – axle 4

Figure 14 – calculated optimal relative slide range

“Minimum slide” criterionConsidering what expressed until now, it was decided to analyse the relative slide measuredin each test for each axle, according to the following rules:a) domain of analysis: time,b) for each axle, calculation of the total time during which the relative slide was higher than

the specified level (10%, 15%, 20 %), in the period comprises between the beginning ofthe braking and the vehicle speed of 60 km/h (see fig. 16),

c) calculation of the percentage of the total time above indicated in comparison with the timecomprises between the beginning o\f the braking and the vehicle speed of 60 km/h (seefig. 16).

Time [s]

Test 89 – axle 4

Vel

ocity

[km

/h] –

rela

tive

slid

e [%

]

Vehicle speedTip axle speedRelative slide

Figure 15 – zone of analysis of the relative slide

Relative slide 15%

t2

(km/h)

(sec)t3

30 40

20

60

40

120

100

80

20

Axle velocity

Vehicle velocity

t1

T

b) t1 + t2 + t3 = total time during which the relative slide is higher than the specified level (15%), in the period comprises between the beginning of the braking and thevehicle speed of 60 km/h

c) [(t1 + t2 + t3)/ T] * 100 = percentage of the total time (t1 + t2 + t3) above indicated in comparison to the time comprises between the beginning of the braking and thevehicle speed of 60 km/h (T)

Figure 16 – example of application of the “minimum slide” criterion on one axle

As final result of the analysis one criterion, named “Minimum slide” was established.This criterion has to be applied in each test.

The criterion is achieved and the adhesion degradation is sufficient when, inside an intervalbetween the beginning of the braking and the vehicle speed of 60 km/h, at least 50 % of theaxles of the vehicle shows a relative slide higher than 15 % for a time equal or higher than

B(*)% of the total time of the interval.

(*) B =35 % for tests at initial speed of 120 km/hB =20 % for tests at initial speed of 160 km/h

We note that a similar criterion does not permit to establish if the adhesion degradation isexcessive.But, if we combine this information with the stopping distance we can define a generalmethod to evaluate the conformity of each test to the prescription regarding the adhesiondegradation.The application of this method let us avoid considering the external parameters capable toinfluence the level of adhesion between wheel and rail (air and rail temperatures, railpollution, ecc.),

METHOD TO EVALUATE THE CONFORMITY OF THE WSP HOMOLOGATIONSLIP TESTS

For each test, taking into account the “minimum sliding” criterion and the stopping distancewe obtain one of the following solutions:

A. If the “minimum sliding” criterion is not achieved and the stopping distance is longerthan the prescribed limit, we can estimate that the WSP is not capable to give asatisfactory performance, because it impose a level of relative sliding too small (on theleft side of the point B on the curve adhesion/relative sliding, fig. 7),

B. If the “minimum sliding” criterion is not achieved and the stopping distance is shorteror equal than the prescribed limit, we can estimate that the adhesion is not degradedenough, so the test is not significant for the evaluation of the WSP,

C. If the “minimum sliding” criterion is achieved and the stopping distance is longer thanthe prescribed limit, we can do the following two hypothesis:- The WSP is not able to regulate the sliding of the axles in a correct way, because it

permits an excessive level of sliding (on the right side of the point B on the curveadhesion/relative sliding, fig. 7),

Or:- The adhesion is excessively degraded,so, considering that it is not possible to determine what is the correct hypothesis, the testhas to be considered not significant,

D. If the “minimum sliding” criterion is achieved and the stopping distance is shorter orequal than the prescribed limit, we can estimate that the test is significant and theperformance of the WSP is satisfactory.

The method can be represented with the following flow chart:

Test Results

Minimum slidingcriterion achieved ?

Stopping distanceshorter than

prescribed limit ?

Reduce soapconcentration in

solution

Stopping distanceshorter than

prescribed limit ?

Increase soapconcentration in

solution

Start

AWSP

performancenot satisfactory

no

no

noyes

yes

yes

BTest not

significant

CTest not

significant

DWSP

performancesatisfactory

BIBLIOGRAPHY

Office de Recherches et d’Essais de l’Union Internationale des Chemins de Fer – «Adhérenceen freinage et anti-enrayeurs Rapport n. 1 – Synthèse des connaissance actuelles surl’adhérence » - Utrecht, Septembre 1985

Office de Recherches et d’Essais de l’Union Internationale des Chemins de Fer – «Synthèsedes connaissance théoriques et pratiques relatives à l’adhérence dégradée et acquises depuisla parution du RP 2 du comité ORE B 164» - Utrecht, Juillet 1992

Boiteux Michel – «Le problème de l’adhérence en freinage», Revue générale des chemins defer - Février, 1986