543 on minimizing derailment risks and … minimizing derailment risks and consequences ......

543

On minimizing derailment risks and consequencesfor passenger trains at higher speedsD Brabie∗ and E AnderssonDepartment of Aeronautical and Vehicle Engineering, Royal Institute of Technology (KTH), Stockholm, Sweden

The manuscript was received on 12 January 2009 and was accepted after revision for publication on 13 May 2009.

DOI: 10.1243/09544097JRRT271

Abstract: The first part of this article deals with the possibility of preventing wheel climbingderailments after an axle journal failure by implementing mechanical restrictions between thewheelsets and the bogie. A multi-body system (MBS) computer model is developed to account forsuch an axle failure condition, which is successfully validated by comparing the pre-derailmentsequence of events with two authentic cases. An extensive parameter analysis on the maximumvertical and longitudinal play between the wheelset and the bogie, required to prevent a high-speed power or trailer car to derail, is performed for various combinations of running conditionsin curves.

Once an actual derailment has occurred on conventional passenger trains at 200 km/h, exten-sive MBS simulations are performed on the feasibility of utilizing alternative substitute guidancemechanisms, such as low-reaching parts of bogie frame, axle box, or brake disc, as means of min-imizing the lateral deviation. Results are presented in terms of geometrical parameters that leadto a successful engagement with the rail for a total of 12 different derailment scenarios. These arecaused by an axle journal failure, an impact with a small object on the track, or a high rail fail-ure. Minimizing the lateral deviation is also investigated by means of restraining the maximumcoupler yaw angle and altering the bogie yaw stiffness. Time-domain simulations are also per-formed in terms of lateral track forces and derailment ratio when negotiating a tight horizontal‘S-curve’. Further, the articulated train concept is investigated in terms of the post-derailmentvehicle behaviour after derailments on tangent and curved track at a speed of 200 km/h. In thisrespect, a trainset consisting of one power car and four articulated passenger trailer cars is mod-elled in the MBS software. Results in terms of lateral deviation and maximum carbody roll angleare presented as a function of different inter-carbody damper characteristics and running gearfeatures. The feasibility of these damper characteristics is also tested in terms of lateral trackforces and derailment ratio when negotiating a tight horizontal S-curve.

Keywords: railway, safety, derailment, guidance, lateral deviation, bogie, vehicle model, multi-body system simulation

1 INTRODUCTION

Despite being one of the safest modes of transporta-tion, railway accidents and incidents still occur, some-times with derailments as an attendant phenomenon.A multitude of factors may bring high-speed passen-ger rail vehicles into a derailed condition such as

∗Corresponding author: Department of Aeronautical and Vehicle,

Royal Institute of Technology (KTH), Teknikringen 8, Stockholm 100

44, Sweden.

email: [email protected]

mechanical failures in the wheelset–track interface(wheel, axle, rail failure, etc.), impact with objectson the track, earthquakes, etc. Depending on vari-ous aggravating factors (track geometry, switches andcrossings, etc.), the derailed wheelsets may start todeviate laterally. In such situations, the risk of catas-trophic outcomes can be diminished by minimizingthe consequences.

‘Robust safety systems for trains’, in short RSST, isthe name of a project that started at the Division ofRailVehicles of the Royal Institute of Technology (KTH)with the aim of studying various means of minimiz-ing serious consequences resulting from mechanical

JRRT271 Proc. IMechE Vol. 223 Part F: J. Rail and Rapid Transit

544 D Brabie and E Andersson

failures at high speeds on rail vehicles or the track. Thisstudy is performed in close cooperation with Swedishrailway authorities as well as rail operators, rail vehiclesuppliers, and consultants.

A previous technical report [1], supported as wellas an initial study [2] within the RSST project, indi-cated that mechanical restrictions limiting a wheelset’smovements relative to its bogie frame might be ben-eficial in cases of axle failure on the outside of thewheel, at the journal bearing. This insight emanatedfrom empirical observations involving the Swedishhigh-speed tilting train X 2000, which limited the con-sequences to a minimum after a couple of axle failureincidents. Out of four such incidents, only one caseled to a derailment with fairly modest consequences.Furthermore, empirical evidence from Sweden andabroad [2] suggested, among others, the possibility ofutilizing alternative substitute guidance mechanismsas a means for reducing the potentially very danger-ous lateral deviation of the running gear from the trackcentre line. In addition, the articulated design concepthas been suggested to have positive effects on the out-come of a derailment, mainly based on a number ofobservations on the French TGV.

The first part of the current article evaluates the pos-sibility of reducing derailment risks after axle journalfailures. This is presented in section 2 together with thevalidation of the proposed MBS model representingaxle journal failures. Means of minimizing conse-quences once a derailment has occurred because ofthree different reasons is assessed in section 3. In thissection also a description of the post-derailment com-putation methodology is presented briefly. Generalconclusions and some outlooks for future work arepresented in section 4.

2 MINIMIZING DERAILMENT RISK DUE TO AXLEJOURNAL FAILURE

Although not the most frequent cause of derailmentin general, axle failures at the journal bearing possesan imminent danger to vehicle safety, as the affectedwheel becomes unloaded. To the best of the authors’knowledge, pre-derailment multi-body system (MBS)simulations and analysis of rail vehicles after an axlefailure were first reported in reference [3]. The MBS

vehicle model, especially the part dealing with theaxle failure interface, has since then been refined. It istherefore imperative for such a new model to undergoa validation process.

2.1 Axle failure computer model validation

2.1.1 The validation cases and general simulationconsiderations

Two Swedish incidents, the Tierp [4] and Gnesta [5]cases, have been chosen for the purpose of validatingthe proposed axle failure computer model. The axlefailed at the same location in the bogie in both cases,the tube side of the wheelset opposite to the gear onan X 2000 power car. In the current context, valuablefactual information can be found in Table 1.

The vehicle and the track is modelled in the generalpurpose MBS analysis tool GENSYS [6]. The GENSYScode is used in Sweden and abroad for simulatingdynamic track–vehicle interaction. Simulation resultshave on numerous occasions been validated by com-parisons with measured quantities as well as withresults obtained with other software; see for examplereferences [7] and [8].

The vehicle model consists of seven rigid bodies: onecarbody and two bogies with six degrees of freedom(DoF) each, and four wheelsets with five DoF each (thepitch DoF is constrained). The primary suspension, i.e.the suspension between wheelsets and bogie frame, ismodelled by linear springs in parallel with linear andnon-linear dampers acting in the longitudinal, lateral,and vertical directions. The secondary suspension, i.e.the suspension between bogie frame and carbody,consists of non-linear springs acting in the longitu-dinal, lateral, and vertical directions in parallel withnon-linear viscous dampers. Each bogie includes a rollbar element to produce a linear roll stiffness betweencarbody and bogie frames as well as non-linear viscousdampers acting primarily in the longitudinal directionon each side of the bogie to provide a yaw damp-ing between carbody and bogie frame. The modelalso includes bumpstops that restrict carbody to bogieframe lateral and vertical motions.

The wheel–rail contact element is described by alinearized stiffness in parallel with a linear viscous

Table 1 Factual information for the two AJF validation cases

CaseSpeed(km/h) Failure location Consequences Track info Weather info

Tierp 200 Wheelset 2, left-hand (high)wheel on rear-end power car

Wheelset 1 derails in a circularcurve over the low rail

R = 1805 m Daylight, dry conditions, lightcloudiness, T = 16 ◦C

Contact with fist sleeper at11 m from start of circularsection

D = 110 mm

Gnesta 180 Wheelset 3, right-hand side onfront-end power car

No derailment S-shaped curves,R = 998 m,D = 140 mm

Daylight, light rain, hazy,T = 12–13 ◦C

Proc. IMechE Vol. 223 Part F: J. Rail and Rapid Transit JRRT271

On minimizing derailment risks and consequences for passenger trains at higher speeds 545

damper, which only produces compressive forces.Accordingly, wheel–rail separation is possible aswheels are allowed to lift.

A three DoF track model is implemented, based ona so-called ‘moving track piece’, which follows undereach wheelset and incorporates two rigid bodies: tworails joined together by a track piece and a fixedground. The two rails and the track piece are con-nected with the ground by linear springs in parallelwith linear dampers, with values corresponding to astandard track. For validation purposes, the imple-mented track curvature and geometrical irregularitiesdescribe the actual conditions at the incident sitesof Tierp and Gnesta. They were obtained by Banver-ket’s measurement vehicle STRIX at 80 and 73 days,respectively, prior to the incidents’ date.

All simulations use nominal UIC/ORE S1002 wheelprofiles running on UIC 60 rails according to Swedishstandards, i.e. inclined at 1:30 with a 1435 mm nomi-nal gauge.

For regular dynamic simulations under normaloperating conditions, the model described above isconsidered sufficient. However, for the purpose of sim-ulating an axle journal failure (AJF) in combinationwith an eventual pre-derailment sequence of events,additional ‘semi-flexible’ restrictions are required, seeTable 2. The restrictions are implemented as piece-wise linear stiffnesses, with no effect unless certainpre-defined displacement limits are reached. Exceed-ing these limits, whose values could be obtained bymeasurements, a high stiffness value is set corre-sponding to an approximate structural stiffness of aneventual metallic contact. Special attention is paid tothe first two mechanical restrictions in Table 2. Foran X 2000 powered bogie, they represent the maxi-mum play movement of the axle relative to the tubedrive system. Because of their location in the bogie, itwas difficult to measure these limits exactly; however,plausible ranges for the vertical (�zt) and longitudinal(�xt) plays on the tube side (opposite to the gear) areapproximately 40–60 and 40–50 mm, respectively. Onthe gear side of the wheelset, the value of these limitsis known [1] and set in both directions to �xg = �zg =50 mm. In the computer model, these restrictions are

Fig. 1 Wheelset ‘semi-flexible’ mechanical restrictions(max. play) relative to the bogie frame

located at a distance of ±0.52 m on both sides of thewheelset centre-line (Fig. 1).

The actual AJF is simulated by removing the longi-tudinal and vertical primary suspension elements atthe involved axle side at a specified location alongthe track. The lateral stiffness is maintained as longas the wheelset is pushed towards the decoupled axlejournal. Additionally, linear longitudinal and verti-cal viscous dampers are activated at the interface ofthe failed axle in order to approximately describe thecontact between the broken side of the axle journalwith the wheelset. The damping coefficient is set to10 kNs/m for both longitudinal and vertical directions.

Once the axle journal has failed, the surface of therotating axle may come into contact with stationaryparts of the tube drive system, hereby producing aforce that opposes the rotation of the wheelset. In thecomputer model, this is approximately accounted forby applying a set of longitudinal and vertical forces toboth wheelset and bogie frame.

The magnitude of these forces are calculated byrecording the force values emerging from the longitu-dinal and vertical ‘semi-flexible’ restrictions betweenthe axle and tube, respectively, and scaling them by anarbitrarily chosen friction coefficient, μa-t.

Not all parameters are known. Because of theseuncertainties simulations are performed with threeconditional parameters having varying values. Thethree defined conditional parameters are:

(a) location of axle failure along the track;(b) wheel–rail friction;(c) axle–tube friction.

Table 2 Implemented ‘semi-flexible’ restrictions in the MBS vehicle model

No. Connecting bodies Limiting relative movements Direction

Total No. inone vehiclemodel

1 Wheelset and bogie Axle and tube drive Vertical 82 Wheelset and bogie Axle and tube drive Longitudinal 83 Wheelset and bogie Axle box and bogie frame Vertical 84 Wheelset and bogie Axle box and bogie frame Longitudinal 85 Wheelset and bogie Wheel running surface and brake shoe Longitudinal 86 Bogie and carbody Bogie frame and carbody underframe; prevents

abnormal bogie roll and pitch anglesVertical 8

7 Bogie and carbody Yaw damper attachment points on bogie frame andcarbody: prevent abnormal bogie yaw angles

Longitudinal 4



Simulation results therefore have a spread depend-ing on the actual values of conditional parametercombinations. Conditional parameter values are setas below.

The input track geometry for the Tierp validationsimulation set is shown in Fig. 2(a). The first dam-aged sleeper was located 11 m from the start of thecircular curve section. Accordingly, three possible axlefailure locations are included in the simulation set:25 m before the start of the transition curve (Tfp1), alter-natively 5 m (Tfp2) and 55 m (Tfp3) from the start of thetransition curve. Based on the meteorological infor-mation at the time of the incident, three wheel–railfriction coefficients are tested, μ = 0.3, 0.4, and 0.5.Currently, an empirical value for the coefficient of fric-tion as the rotating failed axle comes into contact withstationary parts of the tube drive system cannot beassessed. An attempt to minimize this uncertainty isby testing two values, μa-t = 0.1 and 0.3.

For the Gnesta case, the input track geometryis shown in Fig. 2(b). Since no actual derailmentoccurred, the exact location of the AJF along thetrack is even more difficult to determine. However,the incident report indicates that full braking wasautomatically applied by the ATP system (in Swedencalled ATC) at approximately 137 m from the startof the second circular curve section. It can there-fore be assumed that at least from that locationand further on, the journal side detached completelyfrom the rest of the axle. Four different possible axlefailure locations have been included in the simula-tion set: 30 m before the start of the first transitioncurve (Gfp1), 100 m from the start of the first tran-sition curve (Gfp2), 400 m from the start of the firstcircular curve section (Gfp3), and at the end of thesecond transition curve (Gfp4). The meteorologicalinformation for the Gnesta case indicated wet con-ditions. Accordingly, lower wheel–rail coefficients offriction are tested, μ = 0.15, 0.25, and 0.35. For theaxle to tube interface, the same coefficients of fric-tion are tested as in the Tierp case, namely μa-t = 0.1and 0.3.

2.1.2 Validation results

The vehicle and axle failure model is validated as belowby comparing the tendency of derailment resultingfrom combinations of all the conditional parame-ters described above with the authentic sequence ofevents. Two additional, partially unknown, parame-ters are included in the validation simulation sets forboth Tierp and Gnesta: the ‘semi-flexible’ mechanicalrestrictions (elements 1 and 2 in Table 2 and Fig. 1)in the range for the vertical play of 10 100 mm andlongitudinal play of 40–60 mm, both in steps of 10 mm.

The validation simulation set for the Tierp case issummarized in Figs 3(a) and (b) for the two testedvalues μa-t = 0.1 and 0.3, respectively, representingthe uncertain friction coefficient between the axleand stationary parts of the tube. This so-called derail-ment maps indicate the lowest (from all simulationswith different conditional parameters) vertical play fordifferent longitudinal play at which the leading andtrailing wheelset derail as a result of an axle failure onthe trailing wheelset above the high (outer) rail. Thefigures also indicate as a shaded rectangle the plausi-ble range of vertical and longitudinal plays found in anactual X 2000 power car bogie.

The computer simulations clearly show that forcertain conditional parameters in combination withcertain vertical and longitudinal plays, the leadingwheelset of the vehicle derails towards the low (inner)rail in the curve. Furthermore, these simulations suc-cessfully predict that the leading wheelset leaves therails within a few metres from the entrance in the cir-cular curved section (not shown here), in accordancewith observations from the first damaged sleepersfrom the authentic case. The explanation for suchbehaviour is not obvious. As a result of the failure, thevertical force on the trailing (high) wheel is dimin-ished, thus the creep forces on this wheel are lost,hereby allowing the trailing wheelset to be laterallydisplaced towards the high rail of the curve. The highwheel flange of the trailing wheelset is occasionallyrunning above the high rail. The vertical force of

Fig. 2 Curvature and cant data for (a) Tierp and (b) Gnesta validation simulation sets



Fig. 3 Summary of results for the Tierp validation set; the lowest vertical play (�zt) for differentlongitudinal play (�xt), which leads to a derailment of the leading and trailing wheelsetfor (a) axle–tube friction μa-t = 0.1 and (b) μa-t = 0.3. Shaded areas show possible play inauthentic incident

the low wheel on the leading wheelset is now alsogreatly diminished, because it is diagonally locatedwith respect to the axle failure. The new occasionallarge wheelset yaw angle steers the leading wheelsettowards the low rail, ultimately leading to a flangeclimbing derailment of the low wheel.

At the same time, certain combinations of condi-tional parameters and mechanical restrictions mayalso lead to a derailment of the trailing wheelset, unlikethe sequence of events of the authentic case. Thisespecially applies to the cases where a higher frictioncoefficient μa-t was tested (Fig. 3(b)), where the trailingwheelset derailment line passes through the region ofplausible vertical and longitudinal mechanical restric-tions.

The summary of results for the Gnesta validationsimulation set is presented in Figs 4(a) and (b) forthe two tested friction coefficient values μa-t = 0.1 and0.3, respectively. The results are presented in a similarmanner as for the Tierp case described above; how-ever, as no derailment occurs in the authentic case,

no distinction is made as to which wheelset is derail-ing. Moreover, each derailment line corresponds tothe lowest vertical play for different longitudinal playsfor each of the tested wheel–rail friction coefficients.The simulation results agree with the outcome of theauthentic case, where no derailment occurred as aresult of an axle failure on the leading wheelset in theX 2000 power car trailing bogie. However, a derailmentmay occur in the plausible mechanical restrictionrange for certain conditional parameter combinationsincluding relatively high axle–tube and wheel–railfriction coefficients, see Fig. 4(b) for μa-t = 0.3 andμ = 0.35. Nevertheless, as meteorological informationvalid at the incident site indicates wet running condi-tions, it is reasonable to presume that, in general, lowerfriction coefficients should better correspond with theauthentic case.

Comparing the results of the two validation caseswith each other for the same axle–tube friction coef-ficient μa-t, it appears quite clear that the chain ofevents at Tierp was less favourable than in the Gnesta

Fig. 4 Summary of results for the Gnesta validation set; the lowest vertical play (�zt) for differentlongitudinal play (�xt), which leads to a derailment of the leading or trailing wheelsetfor (a) axle–tube friction μa-t = 0.1 and (b) μa-t = 0.3. Shaded areas show possible play inauthentic incident



incident. Despite a considerably lower lateral trackplane acceleration, only one curved track section, anda, presumably, less dangerous axle failure location,the bogie was more prone to derail at Tierp. Onedifference, however, between the two cases is the posi-tion of the braking shoe relative to the failed axle. AtTierp, the rotating axle in contact with the stationarytube part pulls the failed side of the wheelset awayfrom the brake shoe. At Gnesta, the opposite takesplace: the failed part of the axle is pulled towards thebrake shoe, which then acts as a tighter longitudi-nal mechanical restriction. This, in combination witha lower wheel–rail friction coefficient most probablyhindered a derailment at Gnesta.

In comparison with the previous work [3], the cur-rent axle failure model has lowered the vertical playrequired for a derailment not to occur, implying a bet-ter agreement with the chain of events in the authenticcases.

2.2 Axle-bogie frame mechanical restrictions

2.2.1 Vehicle and track modelling

Two coupled X 2000 vehicles are considered: onepower car followed by one tilting trailer car. A sim-ilar vehicle model, as used for the validation casesin section 2.1.1, is implemented in the MBS softwareGENSYS. For the power car, however, the ‘semi-flexible’ restriction representing the brake shoe con-tact with the wheel’s running surface (Table 2, element5) is removed, for a better assessment of the verticaland longitudinal mechanical restrictions between theaxle and the bogie frame (Table 2, elements 1 and 2).Moreover, no further differentiation is made betweenthe tube and gear side of the wheelset, in terms ofmaximal relative play of the mechanical restrictions(�zt = �zg = �z) and (�xt = �xg = �x). An equiva-lent set of ‘semi-flexible’ restrictions as for the powercar (Table 2, without element 5) is also implementedin the trailer car, based on measurements.

It is presumed that axle failure in a curve would cor-respond to a worst case scenario. Two authentic tracksections with geometrical irregularities are tested, cor-responding to the validation cases of Tierp and Gnesta,see Figs 2(a) and (b), respectively. The vehicle speedis held constant at 200 and 180 km/h along the twotested track sections, implying a lateral track planeacceleration of ∼1.0 and 1.6 m/s2, respectively. Onlyone axle failure location along the track is chosen, Tfp1

and Gfp1, 25 and 30 m before the start of the transi-tion curve, respectively. Moreover, for the Gnesta track,the simulation is terminated at the end of the secondtransition curve.

2.2.2 Axle failure location

In order to obtain a better general understanding ofderailments caused by axle failures on the outsideof the wheel, specifically means of minimizing theconsequences in curves by implementing mechani-cal restrictions, a parameter analysis is performed foralternative axle failure locations. It is assumed that afailure may occur on each of the four axle journalsof the leading bogie of the power and trailer cars.The following friction coefficients in wheel–rail andaxle–tube surfaces are considered: μ = 0.2, 0.35, 0.5and μa-t = 0.1, 0.3, respectively. The tested range forthe vertical mechanical restriction (vertical play ) liesbetween 10 and 100 mm in steps of 10 mm and forthe longitudinal mechanical restrictions (longitudinalplay ) five values were chosen: 10, 20, 40, 60, and80 mm.

The simulation results are summarized in derail-ment maps for the power car (Figs 5(a) and (b)) andtrailer car (Figs 6(a) and (b)), for the two tested μa-t val-ues. Each line corresponds to the location of the axlefailure, denoted relative to the closest wheel’s positionin the bogie and in the curve, and indicates the lowestvertical play �z for different longitudinal play �x atwhich a derailment occurs. Each derailment line is

Fig. 5 Derailment map for an X 2000 power car at different axle failure locations; the lowest verticalplay (�zt) for different longitudinal play (�xt), which leads to a derailment for (a) axle–tubefriction μa-t = 0.1 and (b) μa-t = 0.3



Fig. 6 Derailment map for an X 2000 trailer car at different axle failure locations; the lowest verticalplay (�zt) for different longitudinal play (�xt), which leads to a derailment for (a) axle–tubefriction μa-t = 0.1 and (b) μa-t = 0.3

a result of 300 MBS computer simulations, includingvariation of conditional parameters.

As expected, a higher wheel–rail friction coefficient(not shown specifically in the diagrams) increasesthe tendency of derailment, as all lines in the resultsdiagrams belong to the simulated cases of high fric-tion. Moreover, the bogie seems to be most sensibleto derailment at an axle failure affecting the leadingwheelset; this case also requires tighter mechani-cal restrictions to avoid derailment. Failure on thehigh (outer) side requires slightly less tight mechan-ical restrictions. A feasible explanation is found byanalysing the time domain simulations: the bogieframe drops towards the failure corner on the out-side in the curve, hereby preventing the correspondingwheel to climb over the high rail. Moreover, the trailercar bogie allows larger vertical mechanical restrictionas an average before derailment, in comparison withthe powered bogie. This is due to the fact that the bear-ings on the trailer bogie are closer to the wheel, thusa smaller bending moment is produced by the journalvertical load on the axle side opposite to the failed one,which in turn will cause a reduced wheel lift effect onthe failed side.

As previously remarked in the two validation simula-tion sets, a larger axle–tube friction coefficient impliesa greater tendency of derailment. For a power car bogiewith a fixed longitudinal play �x = 20 mm, a verticalplay �z below 50 mm would be considered sufficientto stop a derailment to occur if a relatively low axle–tube friction coefficient is considered. Under similarconditions, a trailer car bogie would require a verticalplay value just below 80 mm. On the other hand, therequired vertical play values drop considerably once arelatively high μa-t is considered, to 20 and 40 mm forthe power and trailer car, respectively. Additionally, asmaller vertical play is also required as the longitudinalplay increases.

Removing the brake shoe in the power car modelin combination with a higher wheel–rail friction

coefficient requires rather tight mechanical restric-tions in order to avoid derailments. This can be clearlyseen by comparing the results of the current section(Figs 5(a) and (b)) with the Gnesta validation results(Figs 4(a) and (b)). At Gnesta, the wheel closest tothe failed axle journal can be labelled both ‘Leadinglow’ and ‘Leading high’, as the vehicle negotiated an‘S-shaped’ curved track section.

3 MINIMIZING CONSEQUENCES AFTERDERAILMENTS

If a derailment, after all, does occur it is most desirablethat the lateral deviation of the wheels is very limited,allowing the whole vehicle to stay aligned close to thetrack centre-line, thus reducing risks of colliding withtrains on adjacent tracks or with other obstacles as wellas reducing the risks of vehicle turn over.

After a derailment has occurred at least some of thewheels will run and bounce on top of the sleepers.Such a cause of events is not usually embraced byordinary vehicle–track models and computer codes;thus a specialized post-derailment module must bedeveloped and included in the simulation software.This is described in section 3.1. In section 3.2 thedefined derailment scenarios and other assumptionsare presented.

In subsequent sections 3.3–3.5 the simulated effectsof different means to limit lateral deviation after derail-ments are described, both for conventional four-axlebogie vehicles and partly also for an articulated trainconfiguration.

3.1 Post-derailment wheelset–track interaction

The current work utilizes a validated post-derailmentMBS module [9] that applies pre-calculated forceresultants on the wheel as a function of the initial



impact state condition defined by the following fiveparameters:

1. the vertical distance from the wheel’s lowestpoint, i.e. on the flange, to the upper sleepersurface (hz);

2–4. the wheel’s longitudinal, lateral, and verticalvelocities (vx, vy, and vz);

5. the wheelset’s yaw angle relative to the sleeper(ψ).

The force resultants are calculated using the MBSsoftware GENSYS (see section 2.1.1) through linearinterpolation based on a pre-defined look-up table.The table is previously constructed through numer-ous finite-element (FE) wheel-concrete sleeper impactsimulations utilizing the commercially available FEsoftware LS-DYNA [10] and it contains the longitudi-nal, lateral, and vertical force variations on the wheelas a function of time. The data in the current pre-defined table are valid for an unworn UIC/ORE S1002wheel impacting an A9P type monoblock concretesleeper, frequently used for Swedish railway lines. Thesleeper top surfaces are positioned 10 mm under therails, implying a total vertical distance from the topof the rail (ToR) UIC60 to the sleeper of 182 mm. Thevertical variation of the upper sleeper surface as afunction of the lateral position is also captured in theMBS module.

In order to approach situations close to a ‘worstcase’ in terms of the derailed wheelset’s rebound-ing tendency, a relatively high compressive strengthof f ′

c = 80 MPa is set, corresponding to an aged con-crete sleeper. Likewise, the parameters describing thevertical track stiffness are equivalent to a ‘stiff’ bal-lasted track defined by the following values, valid forhalf a sleeper: stiffness kztg = 200 MN/m and damp-ing cztg = 300 kNs/m. Any possible wheel to ballastcontact is not taken into account. For cases in whichthe derailed wheels do not exceed the sleepers’ lateralboundary, the assumed simplification is considered

reasonable. Likewise, the simplification is consideredas being acceptable in terms of the ballast’s possi-bility to support the wheel vertically. However, if awheel goes outside the sleeper end special attentionshould be paid to the possibility of relatively high lon-gitudinal and lateral force resultants on the wheel forcases where the wheel sinks considerably under thesleepers’ upper surface.Where applicable, the implica-tions of such simplifications will be commented in theforthcoming results sections. Furthermore, the wheelmay not return back onto the sleepers once the flangeleaves the sleeper surface laterally.

In the initial derailment phase, wheels may alsocome into contact with the rail fastening system. Arecent upgrade of the post-derailment module [11]enables such circumstances to be taken into accountfor a Pandrol fastening system type.

Briefly, the post-derailment module has been cali-brated and successfully validated in three stages.

1. FE model versus Authentic derailment 1: FE impactsimulations were performed and compared withthe indentation marks in three consecutive sleep-ers [9].

2. FE model versus MBS model: a wheel’s trajec-tory over 24 consecutive sleepers was comparedbetween FE and MBS model [9].

3. MBS model versus Authentic derailment 2: MBSsimulations of a derailing vehicle were performedand compared with on-site measurements over 10consecutively damaged sleepers [11], see also Fig. 7.

The MBS post-derailment module is valid under thefollowing premises:

(a) derailment on ballasted track with equally spacedundamaged concrete sleepers of constant proper-ties;

(b) constant post-derailment train speed (no appliedbraking);

(c) wheel to ballast contact is not considered;

Fig. 7 Simulated wheel trajectory versus measured sleeper damage used for the third validationstage of the post-derailment module: (a) wheal tread vertical position relative to sleeperupper surface and (b) flange lateral position relative to rail foot



(d) impact with rail fastening system of Pandrol type;currently valid only for situations where the fas-tening system orientation and the train’s directionof travel coincide in such a manner that the frontarch of the clip is pushed out of the centre leg uponimpact;

(e) wheel-fastener impact model can only predict thevertical force, and accordingly longitudinal andlateral forces arising during contact are not takeninto consideration;

(f) additional impact with other infrastructure partssuch as switches and crossings, signalling devices,etc. are currently not considered;

(g) various mechanical restrictions between bodies incontact are assumed to have sufficient strengthto withstand impact forces at contact, withoutfracture or permanent deformation of significantimportance for the cause of events.

3.2 Derailment scenarios and vehicle formation

Three different causes of derailment in combinationwith various track geometry parameters comprise aset of six derailment scenarios, see further Table 3.

The MBS model of an AJF has been validated insection 2.1. The failure of the journal, located on theoutside of a trailing wheelset, affects the leading bogieof an intermediate passenger car. As a result, the lead-ing wheelset starts to deviate laterally due to flangeclimbing on the high rail of a circular curve section.

Another derailment scenario is a hypothetical ‘wheelflange on rail’ (WFOR) condition as initiated on theleading wheelset of a leading driving trailer car byan initial lateral displacement of 80 mm in combi-nation with a yaw angle of 1.58◦. The leading bogieand carbody midpoints are also displaced laterally 40and 20 mm, with yaw angles of 1.58 and 0.13◦, respec-tively. No defects, neither to the leading vehicle norto the track, are considered. This derailment scenariomight correspond to a sequence of events subsequentto the train encountering relatively small objects onthe track.

Furthermore, two cases are considered by varyingthe track geometry. In one case, the track ahead ofthe point of derailment consists of a transition curve

(150 m long) in the opposite direction as the derailedwheelset, i.e. the leading wheelset is set to derailtowards the left side of the track, while the transi-tion curve is modelled towards the right. In the secondcase, the track is tangent and the rail fasteners are notconsidered, as this situation is believed to correspondbetter to sequence of events approaching a ‘worst-case’ scenario. A high rail failure (HRF) in a curve isautomatically a treacherous situation as the wheelsetslose all lateral guidance. Such a failure is modelled byremoving subsequently the lateral and vertical wheel–rail contact elements once the train passes the start ofa circular curve section.

The rail vehicle formations employed in derailmentsimulations consist of three conventionally coupledand one articulated vehicle configuration accordingto Table 4.

In the conventional design (C1–C3 in Table 4), eachvehicle consists of one carbody, two bogie frames, andfour wheelsets. In the articulated design (A1 in Table 4),adjacent carbody ends share the same bogie.

The axle loads for the power, trailer, and interme-diate passenger cars in configuration C1–C3 are 180,148, and 131 kN, respectively. The axle load of the

Table 4 Train configurations employed in the MBSderailment simulations for vehicle derail-ment-worthiness studies

Abbreviation Train configurationFirst derailingwheelset

C1 Powercar + intermediatepassenger car

Wheelset 1 inintermediatepassenger car

C2 Drivingtrailer+intermediatepassenger car

Wheelset 1 indriving trailer

C3 Three intermediatepassenger cars

Wheelset 1in secondintermediatepassenger car

A1 Power car+semi-articulatedpassenger car+2articulated pas-senger cars+1semi-articulatedpassenger car; seefurther Fig. 20

Wheelset 1 of thesecond medianbogie (fifth bogiein the trainset);see further Fig. 20

Table 3 Overview of implemented derailment simulation scenarios

No. Abbreviation Derailment causeSpeed(km/h)

Curveradius (m)

Cant(mm)

Cantdeficiency(mm)

Lateraltrack-planeacceleration(m/s2)

1 AJF-16 AJF on circular curve 200 1200 150 245 1.62 AJF-10 2580 30 153 1.03 WFOR-10 Impact with objects on track or

others2120 70 153 1.0

4 WFOR-00 ∞ 0 0 0.05 HRF-16 HRF on circular curve 1200 150 245 1.66 HRF-10 2580 30 153 1.0



median bogie in the articulated section of the train(configuration A1) is 169 kN.

The vehicles are modelled in the MBS software fol-lowing the general description found in section 2.1.1.

3.3 Substitute guidance mechanisms

3.3.1 General considerations

The concept of utilizing substitute guidance mecha-nisms is not new. For instance, on the Swedish networkit is common practice to install two additional railsin-between the running rails, on track sections wherea lateral deviation following an accident would havedisastrous effects. Such enhanced passive safety com-ponents can currently be found on viaducts, bridges,at certain distances prior to tunnel openings, as wellas in tunnels. The concept is that, in a derailed con-dition, the lateral deviation of the wheelset would beprevented by means of these additional rails.

The guidance mechanisms studied in this article areconnected to the vehicle. They could be divided intotwo groups, depending on to which vehicle part theyare attached:

(a) on the sprung mass, as low-reaching bogie frameparts, see Fig. 8(a);

(b) on the unsprung mass, as low-reaching brake discsor axle journal boxes, see Fig. 9(a).

For both groups, their intended purpose is to guidelaterally and stabilize a derailed running gear by sim-ply engaging with the appropriate running rail. Thisprinciple is shown in Fig. 8(b) for a bogie frame andFig. 9(b) for a brake disc and an axle journal box.

Fig. 10 Additional simulation set, subcase I–IV; fourdifferent longitudinal start locations of thewheelset that will derail first relative to the tracksleepers

All these substitute guidance mechanisms have beenfound to prevent lateral deviation of the running gearin authentic cases of derailment at different railwaysystems around the world; see reference [2].

In order to initiate as well as to maintain a successfullateral guidance, geometrical and strength require-ments need to be fulfilled. In addition, mechanismsshould be able to cope with track discontinuities, i.e.traversing switches and crossings, in a derailed condi-tion so that a further aggravating situation is avoided.The latter issues are not, however, dealt with in thisarticle.

Fig. 8 Guidance mechanism attached to the sprung mass: (a) geometrical feasibility parametersunder study and (b) the intended sequence of events in derailed condition

Fig. 9 Guidance mechanism attached to the unsprung mass: (a) geometrical feasibility parametersunder study and (b) the intended sequence of events in derailed condition



In this article, the study has been mainly focusedon the geometrical feasibility requirements. In thisrespect, the mechanism should be positioned suffi-ciently low relative to ToRs as to overcome the verticaldynamic movements induced by the derailed runninggear bouncing on the sleepers, in combination with asufficient lateral gap to accommodate the width of therail. Moreover, the positioning of the guidance mech-anisms should not interfere with applicable gaugingstandards for low-reaching parts. In Sweden, featuresplaced on the wheelset (except the wheels themselves)may not be lower than 80 mm above ToR, including apossible minimum wheel wear of 30 mm. For featuresplaced on the bogie frame, one also needs to considerthe maximum vertical deflection of the primary sus-pension, usually in the order of 30 mm, implying alimit of ∼110 mm in nominal position. The interopera-ble European gauging standard, as in UIC leaflet 505 orthe provisional EN 15 273, dictates a more conservativevertical limit, raising the above-mentioned values with∼30 mm implying a minimum vertical distance to ToRof 110 and 140 mm for features on the wheelset andbogie frame, respectively. For the considered lateralgap values between 80 and 290 mm, the Swedish andthe interoperable European gauging standards shouldnot impose any limitations.

Out of all five parameters that make up the initialimpact state condition described in section 3.1, fourof them are inherent in the derailment scenarios. Thefifth, non-deterministic parameter that has a directeffect on the derailed wheelset’s dynamical behaviouris the vertical distance from the lowest point of thewheel to the upper sleeper surface, hz. At the instant ofinitial contact with sleepers, hz is varied by shifting the

initial longitudinal location of the sleeper in relationto the wheelset that derails first, see Fig. 10. This shift-ing is performed for all derailment cases described insection 3.2 and Table 3. For instance, in subcase I, thetrack’s sleepers are laid in the model in such a mannerthat the first derailing wheelset is located with its cen-tre exactly above a sleeper at the start of the simulation.Accordingly, subcases II, III, and IV imply a subsequentlongitudinal shifting of the sleepers by 0.1625 m, i.e. aquarter of the assumed constant sleeper spacing of0.65 m.

3.3.2 Guidance mechanisms computer modelling

The guidance mechanisms are modelled in the MBSsoftware GENSYS by a specially designed contact ele-ment, ‘derailm_1’ (Fig. 11). It consists of vertical andhorizontal boundaries that can define two distinctrigid planar features that may come into contact ifany of the boundaries approach each other. In suchcircumstances, a linear stiffness and damper in par-allel will obstruct the bodies’ motion towards eachother, according to the following parameters: kGM-y =kGM-z = 80 MN/m (lateral and vertical stiffness forguidance mechanism to rail contact, respectively) andcGM-y = cGM-z = 100 kNs/m (lateral and vertical damp-ing for guidance mechanisms to rail contact, respec-tively). The feature corresponding to the guidancemechanism is rigidly connected to ‘Body 1’, which inthe current work represents either wheelsets or bogieframes. The rails are distinguished by the featuresconnected to ‘Body 2’, which stands for the track pieceintroduced in section 2.2.

Fig. 11 Principal appearance of the ‘derailm_1’ contact element in GENSYS used for modelling theinteraction between substitute guidance mechanisms and rails



Furthermore, the UIC60 rail profile is modelledas a rectangle of width br = 72 mm and height hr =158 mm. The maximum height of an unworn rail is172 mm to the ToR. However, the considered rail widthand height correspond to a location where the almostvertical surfaces of the rail head turn into radii of13 mm, at ∼14 mm below the ToR. For reasons ofpossible vertical wear and additional safety margins,the curved surface of the rail is therefore omitted.Longitudinal, lateral, and vertical frictional forces areapplied to the bodies based on the magnitude of theimpact forces arising at the contact between guidancemechanisms and rail, scaled by a friction coefficientμb1-b2 = 0.4.

In the longitudinal direction, the brake discs andaxle journal boxes are located at the centre of thewheelsets, while the guiding parts of the bogie frameare located 0.7 m fore and aft of the centre-line(Fig. 12).

3.3.3 Geometrical feasibility results

Computer simulations are performed for curved trackas well as tangent track, at speeds of 100 and 200 km/h.In this article only results at 200 km/h are presented.The intension is to show principles rather than pre-senting all possible cases.

All combinations of the geometrical parameters insteps of 5 mm are investigated. For each derailmentscenario, four simulations are performed (subcase I–IVin Fig. 10). The highest vertical distance (h, H , or Hajb)according to Fig. 8(a) is registered at different lateralgap values (b, B, or Bajb), which leads to a successfulengagement with the rail. The results are presented asthe averaged vertical distance, computed among thefour simulations, as a function of the tested lateral gapvalues.

Whether the studied guidance mechanisms havemanaged to successfully retain the running gear’s

Fig. 12 The studied guidance mechanisms and theirlongitudinal location in the derailing bogie

lateral deviation, this is evaluated once the firstderailed wheelset has rolled on the track for a dis-tance of about 150 m. Furthermore, only a successfulengagement with the rail of guidance mechanismsadjacent to the leading wheelset, in the derailing bogie(Fig. 12), is considered. In some situations, the com-puter simulation results indicate a laterally stabilizedrunning gear by the guidance mechanism adjacentto the trailing wheelset. Depending on other runninggear design parameters, e.g. mechanical stops in theyaw dampers that limit large carbody to bogie yawangles, such sequence of events may also be beneficial.As mentioned earlier, such successful engagementsare not accounted for here.

The geometrical feasibility results for a low-reachingbogie frame, or its attached parts, are presented inFig. 13. Each line in the six diagrams represents dif-ferent derailment scenarios and corresponds to theaveraged highest vertical distance H at different lateralgap B for which a successful engagement with the railis obtained. Consequently, a low-reaching bogie framewith geometrical parameter combinations located onor on the right hand of the line would stop and stabi-lize the lateral deviation of the bogie, on the average.Some specific geometrical combinations located onthe right-hand side of the lines might also lead toa non-guiding condition. In this context it is worthrecalling that the MBS simulations are preformedfor certain ‘worst-case’ conditions, such as an exces-sive rail wear and new wheels, among others. It cantherefore be assumed that a successful guidance con-dition is obtained for most of the cases of geometricalcombinations found in the proximity of the lines.

The diagrams also indicate the approximate low-est possible vertical distance according to Swedish(110 mm) and the stricter interoperable European(140 mm) gauging standards. The latter considerablylimits the amount of feasible geometrical parametercombinations, although successful guiding should stillbe possible in most real cases. Another important lim-iting factor is associated with cases of relatively smalllateral gaps B, which require small vertical distancesH , violating the permissible gauging standards. Par-tially, this is caused by the Pandrol fastening systemthat obstructs the wheelset in the vertical direction andconsequently the low-reaching bogie frame from sink-ing sufficiently below the ToR. Furthermore, smallerlateral gaps B, in combination with large initial post-derailment vertical bouncing, increases the risk of theguidance mechanism to slide over the rail.

In general, derailment scenarios corresponding tohigher lateral track plane acceleration (cant defi-ciency) and consequently higher post-derailmentwheelset lateral velocity would require a smaller ver-tical distance H for a successful engagement withthe rail. Once again, the explanation can be foundin the correlation between the rate at which the railis approached by the guidance mechanisms and its



Fig. 13 Low-reaching bogie frame geometrical feasibility results for derailments at 200 km/h;scenario WFOR-00 is on the tangent track, all others are on the curved track; see Tables 3and 4

vertical displacement as the wheelset initially bounceson sleepers along the track, the amplitude of which isirrespective of the lateral track plane acceleration (cantdeficiency). In addition, a high cant deficiency impliesa higher roll angle on the bogie, which lifts the partsof the bogie frame running towards the inside of thecurve.

For derailments caused by HRF with lateral gaps ofat least 200–240 mm, it is in most real cases, e.g. mod-erate lateral acceleration, possible to prevent lateraldeviations even for interoperable European gaugingcases. However, for cases according to the interopera-ble European gauging standard, a low-reaching bogieframe is unable to limit the lateral deviation for eventscorresponding to high cant deficiency. In addition, thelow-reaching bogie frame cannot provide the expectedlateral guidance for smaller lateral gaps. This is dueto large vertical motion of the guidance mechanismarising from the wheelsets’ bounce on sleepers in com-bination with larger bogie pitch and bounce motionbecause of the nature of the derailment.

The geometrical feasibility results for a low-reachingbrake disc (Fig. 14) and low-reaching axle journal box(Fig. 15) are presented in a similar manner as in theprevious subsection. In the brake disc case, the HRFderailment case has not been closely investigated,

since the brake disc is located on the inside of thefailed rail and is therefore not able to limit the lateraldeviation.

Clearly, derailments on tangent track (WFOR-00)lead to the least dangerous situations among thederailment scenarios considered. The tested guid-ance mechanisms can stabilize the derailed bogieeven at smaller lateral gaps in combination withrather large vertical distances. However, the brake discrequires a smaller vertical distance h for a larger lat-eral gap b, on tangent track than on the transitioncurve that leads to lateral track plane accelerationay = 1.0 m/s2 (compare WFOR-10 with WFOR-00 inFig. 14). The explanation is related to the dynam-ics of the whole running gear at the instant of thebrake disc to rail lateral contact. In the derailmentscenario on the curved track (WFOR-10), the trailingwheelset derails before the brake disc reaches the rail.This is not true for the tangent track case (WFOR-00),where the derailing trailing wheelset induces addi-tional vertical movement on the leading wheelsetbrake disc just at the instant of lateral contact withthe rail.

Unlike the bogie frame, the low-reaching axle jour-nal box can cope better with an HRF derailmentscenario, even for vertical distances Hajb well above



Fig. 14 Low-reaching brake disc geometrical feasibility results for derailments at 200 km/h;scenario WFOR-00 is on tangent track, all others are on the curved track; see Tables 3and 4

Fig. 15 Low-reaching axle journal box geometrical feasibility results for derailments at 200 km/h;scenario WFOR-00 is on the tangent track, all others are on the curved track; see Tables 3and 4

the stricter limit of interoperable European gaugingstandard, see Fig. 15.

3.4 Vehicle coupler and additional bogie designfeatures

The current section attempts to quantify the effectson the vehicle lateral deviation tendency after a

derailment in relationship with the maximum coupleryaw angle and bogie yaw stiffness.

3.4.1 Restrained coupler and vehicle modelling

Three coupled intermediate passenger cars (seeTable 4)are modelled in the MBS software GENSYS, followingthe general description found in section 2.1.1.



The inter-connection between two adjacent vehi-cles consists of a semi-permanent centre coupler witha principal appearance for one carbody end accord-ing to Fig. 16. At each carbody end, a lateral damperconnects the buffer beam with the coupler bar. Inthe computer simulation model, the vehicle coupleris modelled as a rigid beam with six DoF, connectedat each end with the respective carbody at the pivotcentre. The coupler–carbody connection flexibility atthe pivot centre is taken into account by a three-dimensional elastic spring. In the longitudinal direc-tion the stiffness corresponds to deformations of therubber springs in the draw gear followed by stiff metal-lic contact. Material failure is not anticipated, implyingthat coupler–carbody separation cannot occur.

The assumed intermediate car centre coupler in its‘standard’ configuration permits approximately ±13and ±4◦ yaw and pitch rotation, respectively, at the

pivot centre relative to the carbody. Once the couplerexceeds these limits, as may happen after derailments,the coupler bar and draw gear assembly might startto deform until the coupler makes contact with thebuffer beam. In the MBS model, the coupler’s yawand pitch motion limits, relative to the carbody, arerepresented by stiff elastic springs at the level of thebuffer beam acting in the lateral and vertical direc-tions, respectively. In the lateral direction, the stiff-ness characteristic, describing the deformation stagesmentioned above, for the assumed coupler configu-ration is shown in Fig. 17(a), and labelled ‘Std’ as in‘standard’.

In order to minimize vehicle lateral deviation afterderailments, two additional coupler configurationsare tested with lateral restraints corresponding to theforce–displacement diagrams labelled ‘R1’ and ‘R2’in Fig. 17(a). The coupler configurations adopted in

Fig. 16 Planar sketch (top view) of the assumed semi-permanent coupler at one carbody end

Fig. 17 Force–displacement diagrams representing: (a) lateral and (b) vertical contact ele-ment between coupler to buffer beam for the standard (Std) and restrained (R1, R2)configurations



the current study imply a maximum inter-carbodylateral deflection, i.e. stiff metallic contact, at 0.65,0.26, and 0.23 m for configuration ‘Std’, ‘R1’, and ‘R2’, respectively.

In the vertical direction, no additional variation ismade between the tested configurations. The force–displacement diagram for the coupler to buffer beamvertical contact is shown in Fig. 17(b).

An important feature that might influence the post-derailment sequence of events involving relativelylarge lateral deviations from the track centre-line is thetransversal beam attached to the bogie. Depending onits vertical position in the bogie frame, the transversalbeam may come into contact with the rail either imme-diately after a derailment or once the wheels lose thevertical support of sleepers. Accordingly, if properlyplaced, the transversal beam may act as a substi-tute guidance mechanism in the vertical direction.For the current simulation set, the vertical distancebogie transversal beam to ToR is set to htb = 170 mmin nominal position, see Fig. 18.

The transversal beam is modelled in the MBScode through the contact element ‘derailm_1’, seesection 3.3.2, consisting of vertical and horizontalboundaries that can define two distinct planar fea-tures. Two transversal beams are modelled for eachbogie, symmetrically located at a longitudinal dis-tance from the bogie centre of 0.7 m. In the assumedtransversal beam configuration, lateral contact withthe rail may not occur. Longitudinal and lateral fric-tional forces are applied to the bodies based on themagnitude of the impact forces between the transver-sal beam and rail which arise at contact, with anassumed friction coefficient μtb-r = 0.4.

Another bogie feature studied in combination withcoupler restrictions is the bogie to carbody yaw stiff-ness. Three levels are studied: ‘std’, ‘std −30 per cent’,and ‘std +30 per cent’, where ‘std’ has a yaw stiffnessof 650 kNm/rad.

Low-reaching features in the running gear such asbogie frame parts, brake discs, etc. that may act aslateral substitute guidance mechanisms are not con-sidered in combination with coupler restrictions and

Fig. 18 Principal arrangement of the contact elementused for modelling the bogie transversal beam

here mentioned bogie features so as not to interferewith the purpose of this particular part of the study.

3.4.2 Feasibility analysis of the restrained coupler

The main aim of a laterally movable coupler betweencars is to assure that the bogies can follow a curvedtrack without infringing safety with regard to lateraltrack forces and derailment. In particular this is rel-evant for ‘S-shaped’ curve combinations with shorttransitions between the reversed curve directions, forexample in crossovers between two parallel tracks. Toorestrictive coupler motions are not feasible for real railoperations.

In the following, a feasibility analysis on the possibil-ity of restraining the couplers as intended is performedin terms of permissible lateral track shift forces andderailment criteria according to UIC 518 [12] and EN14363 [13]. In this respect, the ‘worst case’ track geom-etry that a trainset is required to negotiate safely inSweden [14] consists of a ‘so-called’ ‘S-curve’ con-taining two circular sections with radii RS = 190 m inopposite directions with no intermediate section.

For each restrained coupler configuration, MBStime-domain computer simulations are performedwith three intermediate passenger cars at a trainspeed of V = 40 km/h and wheel–rail friction coeffi-cient μ = 0.4 running through the above-mentionedS-curve. The modelled track geometry might corre-spond with a real-life operational situation of runningthrough a crossover on a double-track section with anapproximate lateral spacing of 4.47 m.

The maximum obtained lateral track shift force, �Y ,over a distance of 2 m and its 99.85 percentile, on anywheelset of Car 2 or Car 3, for the current ‘Std’ as well asthe tested restrained coupler configurations ‘R1’ and‘R2’ are plotted in Fig. 19(a). The limit value accord-ing to EN 14 363 and equation (1) for these vehiclesis also plotted in the diagram. It should be noted thatthere is no formal requirement that these limits shallbe applied to this type of crossovers, but anyhow itis possible to indicate whether safety problems wouldarise or not.

For coupler configuration ‘R2’, the evaluated �Yvalue tangents the limit, while the other two wouldnot represent any concern in terms of the permissi-ble track shift forces. The permissible Y /Q ratio, i.e.derailment ratio between lateral and vertical wheel–rail forces, according to EN 14363 and equation (2),is presented in Fig. 19(b). It clearly appears that therestrained coupler does not have any significant effecton the derailment risk compared to the assumed ‘Std’configuration

�Y20 Hz,2 m,mean,99.85% �(

10 + 2Q0

3

)(kN) (1)

(YQ

)20 Hz,2 m,mean,99.85%

� 0.8 (2)



Fig. 19 Influence of different centre coupler restrictions on maximum obtained: (a) track shiftforce �Y and (b) derailment ratio Y /Q on two passenger trailer cars when negotiating atight S-curve (flexible wheelset guidance)

3.4.3 Results on derailing bogie lateral displacement

Time-domain MBS simulations for two derailmentscenarios are performed and evaluated in terms ofthe maximum lateral displacement of the derailingwheelsets as a function of the coupler restrictionconfiguration and variation of the bogie yaw stiffness.

Despite zero cant deficiency in the tangent trackderailment scenario ‘WFOR-00’, the derailing leadingwheelset, and subsequently even the trailing wheelset,continue to deviate laterally until the carbody reachesthe limits imposed by the coupler. Once the wheelsleave the sleeper surface, the bogie transversal beammay act as a substitute vertical support mechanism,preventing further sinking of the wheels into the bal-last. The maximum registered lateral displacementfrom the track centre-line of the leading and trailingwheelset is shown in Figs 20(a) and (b) as a function ofcoupler restriction configurations and bogie rotationalstiffness variation.

All values above the horizontal limit line implythat the wheel’s flange has left the sleepers’ surface,corresponding to a sleeper length of 2.53 m. Thisoccurs with both wheelsets with the coupler config-uration ‘Std’. However, the wheels continue to roll onthe relatively ‘safe’ sleeper surface for almost all theother tested restrained coupler configurations ‘R1 and‘R2’. An increased bogie yaw stiffness tends to fur-ther limit the maximum lateral displacement of thederailed wheelsets. However, these changes are notsignificant.

It should also be noted that, as the wheel’s flangereaches the edge of the sleeper, the risk of concretefracture increases. In addition, the FE model mightoverestimate the concrete’s ability to resist the impactforces of the wheel in the proximity of the sleeper’s lat-eral edge. Accordingly, a certain safety margin shouldbe kept from the sleeper’s edge. In this respect, tightercoupler lateral restrictions are beneficiary, as for exam-ple configuration ‘R2’.

Fig. 20 Influence of different centre coupler restrictions and bogie yaw stiffness on maximumlateral displacement of (a) the leading and (b) trailing wheelsets in the derailing bogie onthe tangent track (WFOR-00 #4, see Table 3 and train configuration C3, see Table 4)



The results for derailment situations in curves thatexert an additional centrifugal force on vehicles, as forthe ‘AJF-10’ scenario, are presented in Fig. 21. Undersuch conditions, only coupler configuration ‘R2’ and‘+30 per cent’ bogie yaw resistance can maintain thewheel of the leading wheelset to roll on the sleeper sur-face. However, still the low-reaching transverse beamin the bogie would prevent wheel to sink into theballast, as no vehicle turnover is indicated.

3.5 Longitudinal inter-vehicle dampers

Trains with an articulated configuration, i.e. car-body ends sharing the same bogie, as found on theTGV, Eurostar, etc., have gained a reputation synony-mous with safety after being involved in a couple ofderailments at speeds up to 300 km/h with limitedconsequences [2]. The articulated concept is oftenaccounted for such favourable behaviour. In order toassess this assumption as well as for comparison pur-poses with previous results involving a two-bogie vehi-cle configuration, an articulated train based essentiallyon the previous conventional vehicle characteristics ismodelled and derailment simulations are performed.

As in the previous section, the lateral deviation andvehicle overturning tendency are of primary interest,which are evaluated after derailments, as a function ofvarious inter-carbody longitudinal damper character-istics and of vertical distance htb of bogie transversalbeam above ToR.

3.5.1 MBS vehicle modelling of the articulatedconfiguration

A trainset carrying five carbodies with an articulatedconfiguration according to Fig. 22 is modelled in theMBS software GENSYS. The articulated configurationis based on the ‘3-point’ principle. This implies thateach intermediate trailer rests on a median bogie atone end with two support points, i.e. the ‘carryingend’, which in turn supports the end of the adjacenttrailer with one support point, i.e. the ‘supported end’.In a conventional design (4-point principle), each car-body end rests on the bogie at two support points.The choice of carbody support points in the articulatedtrainset modelled here can also be seen in Fig. 22.

The leading vehicle, ‘Car 1’, represents a conven-tional power car with an axle load of 180 kN. The

Fig. 21 Influence of different centre coupler restrictions and bogie yaw stiffness on maximumlateral displacement of (a) the leading and (b) trailing wheelsets in the derailing bogie onthe curved track (AJF-10 #2, see Table 3 and train configuration C3, see Table 4)

Fig. 22 Sketch of the modelled articulated trainset



standard centre coupler configuration ‘Std’, describedin more detail in section 3.4.1, links the power carwith the leading intermediate passenger car. The restof the carbodies in the articulated sections are inter-connected at the median bogie level by means of aball-and-socket joint with 6 DoF and structural flex-ibility incorporated in the longitudinal, lateral, andvertical directions. The assembly rests on the upperbolster of the median bogie, which in addition con-sists of one bogie frame, one lower bolster, and twowheelsets. The upper bolster is locked to the bogieframe in the lateral, vertical, and roll directions. Thelower bolster is locked to the bogie frame in all otherdirections but yaw motion.

The primary suspension consists of linear springs inparallel with linear and non-linear dampers acting inthe longitudinal, lateral, and vertical directions. Theirproperties are chosen to represent a relatively flexi-ble guidance. The secondary suspension consists ofnon-linear springs acting in the longitudinal, lateral,and vertical directions in parallel with non-linear lat-eral and vertical viscous dampers. In addition, eachbogie includes one anti-roll bar and two yaw dampersconnected to the carbody. For median bogies, theabove-mentioned elements are connected to the car-body at its carrying end. Furthermore, the carbodiesare inter-connected by one anti-roll damper actingprimarily in the lateral direction and positioned in themiddle of the upper corners of the carbodies as well asby four longitudinal dampers, located at each carbodycorner.

A ‘standard’ inter-carbody damper is assumed andlabelled ‘Std’, with characteristics according to Fig. 23.The effects of various longitudinal damper propertiesare the subject of a parameters analysis in the sectionsto follow.

The suspension elements characteristics of themedian bogies as well as the other coupling ele-ments are essentially based on the previously mod-elled conventional intermediate passenger cars andmodified proportionally to the amount of increased

Fig. 23 Tested inter-vehicle damper characteristics inthe articulated trainset

mass. The axle load of the modelled median bogie inthe articulated train configuration is 169 kN.

3.5.2 Feasibility analysis of longitudinal damperscharacteristic

Inter-carbody longitudinal damper characteristicsaffect the general vehicle running performance, andin accordance with the focus of this article it mayalso influence the post-derailment vehicle behaviour.Strong longitudinal dampers are expected to have abeneficiary effect by stabilizing and minimizing thelateral deviation of the articulated section after aderailment. At the same time, large inter-carbody lon-gitudinal forces arising once the carbody ends moverelative to each other, i.e. in tight curves, may alsohave a negative effect on the track shift forces orthe derailment ratio. In order to assess these matters,according to UIC 518 [12] and EN 14363 [13], com-puter simulations are performed. The articulated trainwas set to negotiate an S-curve of radius Rs = 190 mat a speed of V = 40 km/h with no intermediate tan-gent section, as described earlier in section 3.4.2.Three additional longitudinal damper configurationsare tested by increasing the forced response by 50, 100,and 150 per cent from the assumed standard value‘Std’(Fig. 23), linearly.

The maximum obtained track shift forces �Y , overa distance of 2 m and its 99.85 percentile, on anywheelset of Car 2, 3, or 4 are plotted in Fig. 24atogether with the limit value according to equation (1).The permissible derailment ratio Y /Q according toequation (2) is presented in Fig. 24(b). All results arekept well within the permissible values for all testedparameters.

3.5.3 Results on derailing vehicle lateraldisplacement and overturning tendency

The articulated train is brought into a derailed con-dition on tangent and curved track by implementingsimilar scenarios as described in section 3.2 with trackgeometry and speed according to Table 3. However,the derailing bogie is now located under Car 3 and Car4, accordingly the fifth bogie in the trainset (Fig. 22).Although the derailment has a direct effect on bothCar 3 and Car 4, the consequence in terms of over-turning tendencies is more prominent for Car 3, as thenon-derailing front end of this carbody, ‘the supportedend’, is only attached at one support point.

The simulations in the current section comprise aparameter analysis of the longitudinal inter-carbodydamper characteristics, which are varied from nodampers to +150 per cent relative to the assumedstandard value ‘Std’ according to Fig. 23. A secondparameter analysis includes three different values ofthe vertical distance from the bogie transversal beamto ToR, htb = 170, 270, and 370 mm.



Fig. 24 Influence on tested inter-carbody damper configuration on maximum obtained: (a) trackshift forces �Y and (b) derailment ratio Y /Q on any wheelset or wheel belonging to Car 2,Car 3, and Car 4 when negotiating a tight S-curve

The maximum carbody roll angle towards the out-side of the track on Car 3 obtained after derailment ontangent track, ‘WFOR-00’, as a function of the above-mentioned parameters is presented in Fig. 25(a). Incase that no dampers are present, the carbody over-turns irrespective of the chosen vertical transversalbeam position in the bogie frame. In such cases thederailing median bogie together with the trailing endof Car 3 and leading end of Car 4 are relatively ‘free’to deviate laterally. Once the wheels leave the sleeperarea, the bogie starts to gain a considerable roll angle.As a direct consequence and because of the fact theleading end of Car 3 is only attached at one sup-port point, this vehicle overturns. For stronger inter-carbody damper configurations than the assumed‘Std’ value, the carbody roll angle is kept to a mini-mum as the wheels of the derailing bogie remain onsleepers. This is shown in Fig. 25(b) in terms of theleading wheelset maximum lateral deviation. As thereis no significant difference between the leading and

trailing wheelsets in terms of lateral deviation, resultsfor the latter are omitted here. It appears clear thatthe inter-carbody dampers play an important roll inminimizing derailment consequences by providing aresistance against lateral deviation.

In a similar manner to the above, the resultsobtained after a derailment on curved track with cantdeficiency ‘AJF-10’ are presented in Figs 26(a) and(b) in terms of the maximum obtained carbody rollangle and maximum lateral deviation of the lead-ing wheelset, respectively. The dampers alone cannotcope with the relatively constant centrifugal force,and consequently one side of the derailing bogiefalls into the ballast for all the tested cases. However,the assumed standard (‘Std’) as well as the strongerdamper configurations are all able to avoid carbodyoverturning with maximum carbody roll angles pro-portional to the amount of inter-carbody dampingand vertical distance of the transversal beam in thebogie.

Fig. 25 Articulated trainset results after a tangent track (‘WFOR-00’) derailment scenario as afunction of inter-carbody damper configuration and vertical distance of bogie transversalbeam: (a) maximum carbody roll angle towards the outside of the track on Car 3 and (b)maximum lateral displacement of the leading wheelset of the derailing bogie



Fig. 26 Articulated trainset results after a curved track (‘AJF-10’) derailment scenario as a functionof inter-carbody damper configuration and vertical distance of bogie transversal beam: (a)maximum carbody roll angle towards the outside of the track on Car 3 and (b) maximumlateral displacement of leading wheelset of the derailing bogie

It should be noted that an articulated configura-tion alone does not prevent vehicles from turning overaccording to this analysis; the decisive feature is thelongitudinal dampers. Longitudinal dampers couldpossibly be fitted also to conventional vehicles withsimilar advantages at derailment incidents. From thederailment overview presented in reference [2], at leastfive such incidents can be found in which such a hypo-thetical configuration could have positively affectedthe derailment outcome: Sävsjö, Upplands Väsby -Antuna, Nodaway, Upplands Väsby, and Lochloosa.

At this point, it should be further emphasized thatthe employed MBS post-derailment module does nottake into account the possible interaction occurringbetween ballast and parts of the running gear. In theconventional configuration, this limitation might beneglected for the studied derailment scenarios, as thecoupler provides most of the vertical support oncewheels deviate outside the sleeper area. Due to thenature of the articulated configuration, the derailingmedian bogie is expected to sink deeper in the bal-last. For such situations, the ballast might, however,provide some vertical support. In this respect, themaximum carbody roll angle results might be over-estimated. The general trend, however, should still bevalid.

4 CONCLUSIONS AND FUTURE WORK

It should be emphasized that the present study is per-formed under the assumption of a number of vehicleand design parameters as well as derailment scenariosthat might not be generally applicable. For a correctassessment of the post-derailment vehicle behaviour,a detailed MBS model of the vehicle under investiga-tion is necessary, including a correct description of alllow-reaching features in the running gear. However,

the principal influence of a number of vehicle designparameters can still be evaluated, from which basicconclusions, which may ultimately lead to a morederailment-resistant design, can be drawn.

4.1 Mechanical restriction wheelset to bogie frame

In order to perform a more systematic investigationof the maximum longitudinal and vertical play of themechanical restrictions in combination with variousrunning condition parameters, an MBS vehicle modelhas been developed to account for the pre-derailmentsequence of events after an axle failure. The proposedvehicle computer model has successfully been vali-dated for two Swedish axle journal failures cases, bothin curves. In one case, at Tierp, the model can cor-rectly predict the derailment of the leading wheelsettowards the lower side in a curve with a lateral trackplane acceleration of 1 m/s2 (cant deficiency 153 mm)as a result of a failure on the trailing wheelset at thehigh wheel. In connection with this phenomenon aplausible explanation can be found. In the secondauthentic case, at Gnesta, no derailment occurreddespite a higher lateral track plane acceleration of1.6 m/s2 (cant deficiency 243 mm). Indeed, the com-puter simulations also indicate that the affected bogieis less prone to derail for the tested running conditions.For both validation simulations, the maximum verticaland longitudinal mechanical restrictions, in combina-tion with various running condition parameters, havea strong influence on the derailment tendency. Cor-relating authentic derailment observations with MBScomputer simulations appears as a feasible approachfor validating the computer model.

An axle failure on the leading wheelset’s inner sidein a curve appears to be the most sensitive locationin a bogie for both X 2000 power and trailing cars. Atsuch a location, a vertical mechanical restriction just



below 50 mm (power car) and 60 mm (trailer car) isconsidered sufficient to avoid a derailment for a lon-gitudinal mechanical restriction corresponding to amaximum wheelset to bogie frame yaw angle of 1.1◦

at static conditions.

4.2 Substitute guidance mechanisms

In this study three types of substitute guidance mech-anisms are studied, namely (1) low-reaching part ofbogie frame, (2) low-reaching axle-mounted brakediscs, and (3) low-reaching axle-boxes. The numer-ical results obtained support the favourable effectsobserved in a number of authentic derailment eventsinvolving these substitute guidance mechanisms. Fur-thermore, it is worth mentioning that in this articlethe guidance mechanisms were tested independentlyof each other. It is quite possible that the mechanismscould complement each other, thus amounting to afurther increase of the beneficial effects.

In the vertical direction, guidance mechanismsshould generally be located as close as possible to theToR level, without obstructing the permissible gaug-ing standards. The interoperable European gaugingstandard limits the amount of possible geometricalpositioning configurations for a guidance mechanismplaced on the sprung bogie frame. This is principallyalso the case for mechanisms placed on the unsprungaxles, either between or on the outside of the rails,although practically to a less extent. Further, the guid-ance mechanisms should be located at an appropriatelateral distance from the respective adjacent wheel.

For the studied derailment scenarios, the largestflexibility in terms of feasible geometrical parame-ters can be obtained by utilizing a low-reaching axlejournal box.

The topic dealing with vehicles running throughswitches and crossings in a derailed condition, in par-ticular for running gears equipped with low-reachingguidance mechanisms, should deserve special atten-tion in further studies, together with strength feasi-bility assessments. In addition, computer simulationsshould continue with other types of rail fasteners aswell as different rail vehicle design configurations. Fur-ther, the exact parameter values obtained in termsof feasible geometrical positioning of substitute guid-ance mechanisms may not be generally applicable toall rail vehicle designs.

4.3 Restricted coupler on conventional traindesign

Utilizing three coupled conventional passenger carswith two bogies each, MBS computer simulations haverevealed the possibility of reducing the maximum per-missible coupler yaw angle relative to the carbody byapproximately 60 per cent compared to an assumedstandard configuration of a trailer car centre coupler.

According to numerical simulations, such restrictionsare feasible in terms of maximum track shift forces andderailment ratio for vehicles equipped with both flexi-ble and stiff wheelset guidance, when running througha ‘worst-case’ track geometry that train units need tonegotiate in Swedish rail operations.

For a derailment scenario on tangent track at a speedof 200 km/h, such coupler restrictions limit the lat-eral deviation of the bogie so that all wheels remainon the relatively ‘safe’ sleeper surface. On a curvedtrack with relatively high cant deficiency, the largestdeviation obtained with the least restraining coupleris ∼0.7 m from the track centre-line, implying that thewheel is no longer rolling on sleepers, assuming a stan-dard sleeper length of 2.53 m. In such situations, alow-reaching bogie transversal beam is beneficial, asit provides a vertical support mechanism so that thewheel will have limited contact with ballast.

4.4 Inter-carbody dampers on articulated trainconfiguration

An initial study was performed on the post-derailmentbehaviour of articulated trainsets as a function ofthe inter-carbody longitudinal damper characteris-tics and vertical positioning of a transversal beam inthe bogie. Assuming a standard inter-carbody dampercharacteristic, an increase up to 150 per cent appearsfeasible in terms of track shift forces and derailmentratio even for a stiff wheelset guidance negotiating anS-curve with radius 190 m.

For the studied derailment scenarios, on tangentand curved track, the articulated configuration withno inter-carbody longitudinal dampers behaves ratherpoorly in terms of lateral deviation and overturningtendency in comparison with a two-bogie conven-tional configuration. In a conventional configuration,the ultimate barrier against large inter-carbody lateraldeviations after a derailment relies on the centre cou-pler, if sufficiently robust, and the assurance that theadjacent vehicle is safely rolling on rails. Evidently,the articulated configuration with two carbody endsresting on the same bogie cannot utilize the adjacentvehicle in the same manner.

However, the study has pointed out the inter-carbody longitudinal dampers as the most importantsingle feature capable of minimizing the lateral devi-ation and consequently avoiding catastrophic conse-quences for trains with an articulated configuration.For such a configuration, the ultimate barrier is there-fore provided by incorporating a certain resistanceagainst adjacent carbodies’ relative yaw motion.

ACKNOWLEDGEMENT

The authors would like to express their gratitude forthe financial support obtained from Vinnova (Swedish



Governmental Agency of Innovation Systems), Ban-verket (Swedish National Rail Administration) as wellas the Railway Group of KTH. Furthermore, Mr Inge-mar Persson of DEsolver AB deserves special thanksfor the initial MBS train articulated model as wellas the continuous help with the software GENSYS.The authors are also most grateful to SJ AB, Inter-fleet Technology AB, and Bombardier Transportationfor all assistance regarding investigation reports anddifferent rail vehicle specifications.

© Authors 2009

REFERENCES

1 Tolérus, U. Consequence analysis of axle failure on X2(in Swedish: Konsekvensanalys av axelbrott på X2). MTM98-06, 1998 SJ Maskindivisionen Teknikenheten (notpublic), Sweden.

2 Brabie, D. and Andersson, E. An overview of some high-speed train derailments: means of minimizing conse-quences based on empirical observations. Proc. IMechE,Part F: J. Rail and Rapid Transit, 2008, 222(F4), 441–463.DOI: 10.1243/09544097JRRT149.

3 Brabie, D. and Andersson, E. Robust safety systems fortrains – can running gear prevent catastrophic derail-ments? In Proceedings of the 6th International Confer-ence on Railway bogies and running gears, Budapest,13–16 September 2004, pp 325–334.

4 SJ Investigation Report. Derailment on the tierp – orrskogsection 2001-09-08 (in Swedish: Urspårning på sträckanTierp – Orrskog 2001-09-08), SJ AB Trafiksäkerhet,Sweden, 2001.

5 SJ Investigation Report. Axle failure on the Mölnbo –Gnesta section 2001-09-10 on train 437 (in Swedish: Axel-brott på sträckan Mölnbo – Gnesta 2001-09-10 i tåg 437),SJ AB Trafiksäkerhet, Sweden, 2001.

6 Persson, I. Using GENSYS.0603, DEsolver, Östersund,2006.

7 Iwnicki, S. The Manchester benchmarks for rail vehiclesimulations, vol. 131, 1999 (Swets & Zeitlinger B.V. Lisse).

8 Kufver, B. Optimization of horizontal alignments for rail-ways – procedures involving evaluation of dynamic vehi-cle response. Doctoral thesis, TRITA-FKT report 2000:47,KTH Railway Technology, Stockholm, 2000.

9 Brabie, D. Wheel–sleeper impact model in rail vehicleanalysis. J. Syst. Des. Dyn., 2007, 1(3), 468–480.

10 Whirley, R. G. and Hallquist, O. A nonlinear explicitthree-dimensional finite element code for solid andstructural mechanics. User Manual, Report UCRL-MA-107254, LLNL, Livermore, CA, USA, 1991.

11 Brabie, D. and Andersson, E. Post-derailment dynamicsimulations of rail vehicles – methodology and applica-tions. Veh. Syst, Dyn., 2008, 46(S1 & 2), 289–300.

12 UIC. Testing and approval of railway vehicles from thepoint of view of their dynamic behaviour – safety, trackfatigue, ride quality. Code 518 OR, 3rd edition, Paris,October 2005.

13 CEN. Railway applications – testing for the acceptanceof running characteristics of railway vehicles – testing

of running behaviour and stationary tests. EN 14363,Brussels, June 2005.

14 von Bahr, H. Smallest curve radii for SJ AB vehicles (inSwedish: Minsta kurvradie för SJ AB fordon). TS1271-1037-01-RES, Interfleet Technology Sweden, 2006.

APPENDIX

Notation

ay unbalanced lateral track planeacceleration (m/s2)

b, B, Bajb lateral gap between guidancemechanism and its adjacent wheel(mm)

br rail width (mm)cGM-y,GM-z lateral and vertical damping for

guidance mechanism to rail contact(Ns/m)

cztg vertical track damping used in the FEmodel (Ns/m)

D cant (mm)f ′

c concrete compressive strength (Pa)Gfp1, Gfp2, axle failure locations considered for

Gfp3, Gfp4 the Gnesta track (m)h, H , Hajb vertical distance between the lowest

point on the guidance mechanismand ToR (mm)

hr height of the rail that the guidancemechanisms might encounter (mm)

htb vertical distance bogie transversalbeam to top of rail (mm)

hz vertical distance from the lowestpoint of the wheel to the sleeper’supper surface (mm)

kGM-y,GM-z lateral and vertical stiffness forguidance mechanism to rail contact(N/m)

kztg vertical track stiffness used in the FEmodel (N/m)

Q, Q0 vertical wheel–rail force (N)R, Rs curve radius (m)Tfp1, Tfp2, axle failure locations considered for

Tfp3 the Tierp track (m)vx,y,z the wheel’s longitudinal, lateral, and

vertical velocity at the instant ofimpact with the sleeper (m/s)

V train speed (km/h)Y lateral wheel–rail force (N)Y /Q flange climbing derailment ratio

(dimensionless)

�xg, �xt longitudinal play wheelset axle tobogie frame at the gear or tube side(mm)

�zg, �zt vertical play wheelset axle to bogieframe at the gear or tube side (mm)



μ wheel–rail friction coefficient(dimensionless)

μa-t friction coefficient between the axlesurface and stationary bogie frameparts (dimensionless)

μb1-b2 friction coefficient between the twobodies used in contact element‘derailm_1’ (dimensionless)

μtb-r friction coefficient between bogietransversal beam and rail(dimensionless)

�Y track shift force (N)ψ wheelset’s yaw angle relative to the

sleeper at the instant of impact (◦)

Abbreviation

AJF axle journal failureATC automatic train control (the swedish

automatic train protection system)Banverket swedish national rail administrationDoF degrees of freedomHRF high rail failureMBS multi-body systemRSST robust safety system for trainsSJ AB swedish railwaysTGV French high-speed trainToR top of railWFOR wheel flange on rail


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