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PLEASE SCROLL DOWN FOR ARTICLE This article was downloaded by: [Purdue University] On: 5 December 2010 Access details: Access Details: [subscription number 917342650] Publisher Taylor & Francis Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37- 41 Mortimer Street, London W1T 3JH, UK Vehicle System Dynamics Publication details, including instructions for authors and subscription information: http://www.informaworld.com/smpp/title~content=t713659010 Measurements and simulations of rail vehicle dynamics with respect to overturning risk Dirk Thomas a ; Mats Berg a ; Sebastian Stichel b a Department of Aeronautical and Vehicle Engineering, Centre for ECO 2 Vehicle Design, Royal Institute of Technology (KTH), Stockholm, Sweden b Bombardier Transportation, Specialist Engineering, Västerås, Sweden Online publication date: 21 January 2010 To cite this Article Thomas, Dirk , Berg, Mats and Stichel, Sebastian(2010) 'Measurements and simulations of rail vehicle dynamics with respect to overturning risk', Vehicle System Dynamics, 48: 1, 97 — 112 To link to this Article: DOI: 10.1080/00423110903243216 URL: http://dx.doi.org/10.1080/00423110903243216 Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.

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Page 1: Vehicle System Dynamics Measurements and simulations of ... · PDF fileRail vehicles in everyday operation are often exposed to ... simulation of rail vehicle dynamics is therefore

PLEASE SCROLL DOWN FOR ARTICLE

This article was downloaded by: [Purdue University]On: 5 December 2010Access details: Access Details: [subscription number 917342650]Publisher Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK

Vehicle System DynamicsPublication details, including instructions for authors and subscription information:http://www.informaworld.com/smpp/title~content=t713659010

Measurements and simulations of rail vehicle dynamics with respect tooverturning riskDirk Thomasa; Mats Berga; Sebastian Stichelb

a Department of Aeronautical and Vehicle Engineering, Centre for ECO2 Vehicle Design, RoyalInstitute of Technology (KTH), Stockholm, Sweden b Bombardier Transportation, SpecialistEngineering, Västerås, Sweden

Online publication date: 21 January 2010

To cite this Article Thomas, Dirk , Berg, Mats and Stichel, Sebastian(2010) 'Measurements and simulations of rail vehicledynamics with respect to overturning risk', Vehicle System Dynamics, 48: 1, 97 — 112To link to this Article: DOI: 10.1080/00423110903243216URL: http://dx.doi.org/10.1080/00423110903243216

Full terms and conditions of use: http://www.informaworld.com/terms-and-conditions-of-access.pdf

This article may be used for research, teaching and private study purposes. Any substantial orsystematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply ordistribution in any form to anyone is expressly forbidden.

The publisher does not give any warranty express or implied or make any representation that the contentswill be complete or accurate or up to date. The accuracy of any instructions, formulae and drug dosesshould be independently verified with primary sources. The publisher shall not be liable for any loss,actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directlyor indirectly in connection with or arising out of the use of this material.

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Vehicle System DynamicsVol. 48, No. 1, January 2010, 97–112

Measurements and simulations of rail vehicle dynamicswith respect to overturning risk

Dirk Thomasa*, Mats Berga and Sebastian Stichelb

aDepartment of Aeronautical and Vehicle Engineering, Centre for ECO2 Vehicle Design,Royal Institute of Technology (KTH), 10044 Stockholm, Sweden; bBombardier Transportation,

Specialist Engineering, 72173 Västerås, Sweden

(Received 19 December 2008; final version received 25 July 2009 )

Rail vehicles are exposed to strong lateral influences through curves, track imperfections and crosswindleading to large deflections of the vehicle suspension systems and carbody displacements. In turn, thisincreases the risk of vehicle overturning. In the present work, multibody simulations are performedin order to study the motion in the secondary suspension. Suspension deflection measurements on afast test train were carried out and used for validation of the simulations. The simulations show goodagreement with the measurements and represent a good tool to predict the motion in the secondarysuspension.

Keywords: rail vehicle dynamics; overturning risk; crosswind; suspension modelling; multibodysimulations; field measurements

1. Introduction

Rail vehicles in everyday operation are often exposed to strong lateral influences due tocurves and imperfections of the track. These influences depend in particular on operationalspeed, curve layout and magnitudes of the track imperfections. As a consequence, vehicles canreact with large lateral suspension deflections and lateral displacement of the vehicle carbodyrelative to the centre of the track.

In recent years, an increased interest in building lighter rail vehicles can be observed aimingat less energy consumption and track deterioration. However, by just decreasing the vehicleweight these advantages come along with the disadvantage of increased vehicle sensitivity tocrosswind. Thus, in addition to the lateral influences above, the crosswind can lead to evenlarger lateral carbody displacement and hereby to a higher risk of the vehicle overturning.High crosswinds therefore represent a safety issue. The crosswind stability has been a wideresearch area in recent years, in particular, in the field of aerodynamics. Examples on researchcarried out are seen in [1–7]. However, research results on the crosswind stability within thefield of rail vehicle dynamics are more rare [8–11].

*Corresponding author. Email: [email protected]

ISSN 0042-3114 print/ISSN 1744-5159 online© 2010 Taylor & FrancisDOI: 10.1080/00423110903243216http://www.informaworld.com

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98 D. Thomas et al.

During the last decades, overturning accidents of rail vehicles mainly caused by the cross-wind have in fact occurred [12]. It is hence desirable to be able to predict the overturningrisk of a vehicle. For this purpose, knowledge of the lateral dynamics of rail vehicles withlarge deflections, in particular in the secondary suspension, is required. However, full-scalefield experiments using a rail vehicle at overturning risk are not practicable due to safety andeconomical reasons. Also, a reproducible crosswind situation in field is hard to create. Thesimulation of rail vehicle dynamics is therefore a necessary and important tool. Nevertheless,it is preferable to validate such simulations with measurements. As mentioned earlier, it isnot practicable to measure on a vehicle at overturning risk. But relatively large suspensiondeflections are also reachable due to the lateral influences of curves and track irregularitieswithout an immediate overturning risk for the vehicle. Hence, a verification for large suspen-sion deflections due to lateral influences without the crosswind is possible. If a fair agreementbetween simulated and measured suspension deflections is achieved, simulations can representa powerful tool to predict overturning risk of rail vehicles.

During the summer of 2008, deflection measurements of the secondary suspension wereperformed on a fast test train running on several tracks in Sweden. These measurementsincluded suspension deflections due to curves and track imperfections. A risk for overturningwas not present during the measurements. The measurement results are here used as inputs,and validation for multibody simulations performed according to the measurement conditions.

However, accurate vehicle modelling is crucial to gain feasible simulation results. Nowa-days, the secondary suspension of rail vehicles, in particular, for modern high-speed trains,often contains air springs that bring additional effects of nonlinearity to the simulations. In themultibody simulations performed in this study, effects of different input data for an air springmodel are investigated. The simulations are carried out quasi-statically in 2D and dynamicallyin 3D. The simulation model is further exposed to a calculated dynamic wind gust. This loadis taken from a calculation using computational fluid dynamics (CFD).

2. Problem description and definitions

This section describes the problem case the work is dealing with and introduces some necessarydefinitions.

2.1. Vehicle configuration and track design geometry

Figure 1(a) shows a schematic side view of a bogie rail vehicle used in this study. The vehiclesuspension, which is only indicated here, consists of the primary suspension connecting thewheelsets to the bogie frames as well as the secondary suspension between the bogie framesand the carbody. The suspensions consist of a combination of physical springs and dampers aswell as bumpstops delimiting the suspension deflection in vertical and lateral directions. Thesecondary suspension also contains anti-roll bars counteracting roll movement of the carbody.Forces in longitudinal direction between the bogie frames and the carbody are transferred bytraction rods.

Figure 1(b) shows the rear view of a rail vehicle negotiating a right-hand curve of radius R

and track cant angle ϕt at (high) speed v. The carbody and the bogie frame are displaced andtilted outwards of the curve mainly related to large suspension deflections between the bogieframe and the carbody. Regarding overturning risk of the vehicle, the position of the centre ofmass of the carbody is crucial. It is hence necessary to gain information about the displacementmagnitudes of the bogie frame and the carbody.

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Figure 1. (a) Schematic side view of a bogie rail vehicle, (b) rear view of a rail vehicle negotiating a right-handcurve of radius R and cant angle ϕt at speed v.

2.2. Lateral accelerations

The vehicle shown in Figure 1(b) is exposed to the horizontal centrifugal acceleration v2/R.Furthermore, the acceleration of gravity, g, must be considered. The lateral acceleration onthe vehicle in the track plane can thus be explained by

ay = v2

R· cos ϕt − g · sin ϕt . (1)

Due to horizontal centrifugal forces, the bogie frames and the carbody are displaced laterallytowards the outer side of the curve and also roll angles between the track plane and the bogieframe as well as the carbody appear. By defining these roll angles by ϕb and ϕc, respectively, thelateral acceleration in the bogie frame plane ayb and the carbody plane ayc can be described by

ayb = v2

R· cos(ϕt + ϕb) − g · sin(ϕt + ϕb), (2)

ayc = v2

R· cos(ϕt + ϕc) − g · sin(ϕt + ϕc). (3)

Note that in Figure 1(b), both angles ϕb and ϕc are negative.

2.3. Air springs

For the secondary suspension of high-speed trains, air springs have almost become standardcomponents. They are also more and more introduced into regional trains. Figure 2 showsthe principal assembly of an air spring system on rail vehicles [13]. The air bellow of thespring is provided with air by an air container coupled with a compressor. An additional airreservoir increases the total air volume of the spring to achieve a softer spring and a higherride comfort. If the spring is deflected beyond a certain level in vertical direction, for example,due to additional load caused by passengers entering the train, a levelling valve comes intoplay and opens the connection to the air container, which leads to an inflation of the air bellow.Air springs on rail vehicles also transfer forces in longitudinal and lateral directions, whichmostly is not the case for air springs installed on road vehicles.

Modelling of air springs for rail vehicles has been the subject for several researchers.Examples for existing models for air springs are found in [13–16]. The models presented

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100 D. Thomas et al.

Figure 2. Air spring system of rail vehicle. 1, carbody; 2, Bogie frame; 3, air bellow; 4, auxiliary spring; 5, surgepipe; 6, orifice; 7, surge reservoir; 8, levelling valve; 9, air container; 10, compressor [13].

Figure 3. Mechanical model of air spring. Note that friction forces Ff are considered. (a) vertical direction,(b) horizontal direction (axisymmetry with respect to vertical axis assumed).

in [14,15] take the thermodynamic properties of the air spring including auxiliary volumeinto account. Besides this model, the multibody code SIMPACK includes a spring modelthat considers thermodynamic properties [16]. The difference between the thermodynamicmodels [14–16] consists in the modelling of the air pipe connecting the bellow of the air springand the auxiliary volume. Here damping effects of an orifice can be taken into account [14].The flow in the air pipe is modelled as a dynamic motion of a constant mass [16] or as amass flow [14,15]. The model presented in [13] represents a mechanical substitution model.A comparison between different modelling approaches is given by [17]. Within this studythe mechanical substitution model [13] is chosen. However, the input data to this model arevaried in order to study the influence of suspension modelling effects on simulation results.Figure 3(a) and (b) shows the general setup of the present air spring model.

The model consists of an elastic, a viscous and a friction part both in the vertical directionand in the horizontal plane. In vertical direction, the viscous part contains nonlinear viscousdamping and a mass effect to consider the air flow between the air bellow and the air reservoir.

2.4. Overturning risk

The risk of overturning of a rail vehicle can be defined by different methods. An overview isgiven for example in [9]. Three methods are summarised below.

2.4.1. Wheel unloading

The criterion of wheel unloading uses the vertical wheel-rail force on the windward (inner) railto define an overturning risk. The instantaneous vertical wheel-rail force Q may, for example,

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not be less than 10% of the static vertical wheel-rail force Q0, thus

Q

Q0≥ 0.1. (4)

This method is used by different rail operators [18], standards [19] and has been used for severalstudies, for example [8,11]. But the quotient of the forces is usually low-pass filtered by 2or 1.5 Hz to eliminate high-frequent influences from track irregularities [9,18,19]. However,there are also standards that do not take dynamic input of the track into account [19].

2.4.2. Moment method

The moment method calculates the moment equilibrium about the leeward (outer) rail. Itcompares the centrifugal forces and the aerodynamic forces due to crosswind on the vehiclewith the gravity forces of the vehicle. If the moments produced by these forces are equal,the vehicle starts to overturn. The method is used in aerodynamic studies, for example [1,2].Usually, this method does not take dynamic influences due to track imperfections and transitioncurve passage into account. Andersson et al. [20] describe a moment method taking dynamiceffects into account.

2.4.3. Intercept method

The intercept method takes only vertical and (indirectly) lateral wheel-rail forces into accountin order to calculate an overturning risk. The resultant force of the wheel-rail forces is calcu-lated. The location of the point of attack in the track plane, bt , relative to the centre of track isdetermined and compared with the distance b0 between the wheel-rail contact point and thetrack centre. The quotient of these values can be used as a safety measure:

nR,int = bt

b0= �bogie | Ql − Qr |

�bogie(Ql + Qr), (5)

where Ql and Qr are the vertical wheel-rail forces on the left and right side, respectively.Usually, a quotient value between 0.8 and 1 is used as limit. The intercept method takesdynamic influences of the track and curve passage into account. However, the forces have tobe low-pass filtered to consider the low-frequent overturning process. For detailed information,see for example [9,21].

3. Displacement measurements

As mentioned earlier, displacement measurements of the secondary suspension have beenperformed on one vehicle of a test train during the summer of 2008. The train ran on severalrailway tracks in Sweden comprising a wide range of curve radii. The measurements recordedthe relative lateral displacement in the secondary suspension on each bogie. Furthermore,two transducers were installed on both sides of one bogie measuring bogie–carbody verticaldisplacements in order to get information about the relative roll movement. An angular trans-ducer (gyro) installed on the carbody floor was also used to measure the absolute carbody rollmovement. Figure 4(a) and (b) show schematically the positions of the installed transducers.

The transducers measuring the relative lateral and vertical displacements were placed in thelongitudinal middle of each bogie frame to avoid influences of yaw motion of the bogie frame

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102 D. Thomas et al.

Figure 4. Transducer setup on test train. (a) side view, (b) rear view. Relative displacements �y and �z. Carbodyroll φc . Lateral accelerations ayb and ayc .

relative to the carbody. The measurement plane of the lateral transducers shown in Figure 4(b)is underneath the bogie frame due to lack of space between the carbody and the bogie.

In addition to the quantities above the lateral accelerations of one axle box, both bogie framesand the carbody were measured. These signals were recorded in the plane of the respectivebody and include effects of gravity. Two measuring wheelsets were also installed on the train tomeasure lateral and vertical track forces.All signals were recorded at a sampling rate of 300 Hzexcept the vertical wheel–rail forces, which were recorded at a sampling rate of 1200 Hz.General wind conditions on the days of testing were recorded on several meteorologicalmeasurement stations in the test regions. It was judged that the crosswind effectswere minor.

Figure 5(a) and (b) shows unfiltered measurement results of a curve negotiation at arunning speed of v = 261 km/h. The circular curve part has a radius of R = 3046 m and

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01020304050

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Δz

[mm

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Leading bogieTrailing bogie

Outer sideInner side

(a)

(b)

Figure 5. Example of measured relative carbody–bogie displacements. v = 261 km/h, R = 3046 m andϕt = 2.67◦. Unfiltered signals. (a) lateral displacement �y at both bogies, (b) vertical displacement �z at bothsides of trailing bogie.

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Vehicle System Dynamics 103

a track cant angle of ϕt = 2.67◦, which with the given speed results in a track planeacceleration of ay = 1.27 m/s2. Figure 5(a) represents the relative lateral displacementsmeasured between the carbody and both bogies, whereas Figure 5(b) shows the relativevertical displacements, which in this curve are measured between the carbody and thetrailing bogie. A mean relative displacement of 0 mm represents the train running on tan-gent track, whereas an offset in the measurement signals describes a curve negotiation.The train first enters a transition curve followed by a circular curve. Here, the overalllateral displacement remains on a constant non-zero level in the circular curve part andthe oscillations in the signals are caused by track irregularities. During the circular curvenegotiation, the carbody has contact with the lateral bumpstops, which delimit the lateralcarbody–bogie displacements. The measurement results of Figure 5 will be further discussedin Section 5.

4. Multibody simulations

Multibody simulations are now performed for various track curve negotiations using the com-mercial MBS-code SIMPACK [16]. The simulations are carried out in both 2D and 3D space.The vehicle bodies within the simulation models are treated as rigid bodies.

4.1. Quasi-static simulations in 2D

The multibody simulations in 2D space are performed as quasi-static using a half-vehiclemodel containing one body with three degrees of freedom.

Figure 6 shows schematically the setup of the simulation model including the bogie frame,air springs, the anti-roll bar and half-carbody. The model further contains bumpstops in lateraldirection, which are not indicated in Figure 6.

Since the measurements described in Section 3 focus on the relative motion between the car-body and the bogie, it is chosen here to treat the bogie frame as fixed and ignore the primarysuspension, the wheelsets and the wheel-rail contacts. The carbody can move in the y–z-planeonly with three degrees of freedom (lateral, vertical and roll) and is exposed to the horizontalcentrifugal acceleration, v2/R, and the acceleration of gravity, g. The secondary suspensionmodel consists of linear elastic shear springs without any energy dissipation from friction orviscous damping. The same applies to the torsional stiffness of the anti-roll bar. The bump-stops are modelled as progressive springs with a certain clearance. The fixed bogie frame

Figure 6. Schematic setup of the simulation model used for quasi-static simulations in 2D. Horizontal centrifugalforce mv2/R, gravitational force mg and bogie frame angle (ϕt + ϕb).

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104 D. Thomas et al.

angle (ϕt + ϕb) with respect to the horizontal plane is determined from

ϕt + ϕb ≈ 1

g·(

v2

R− ayb

), (6)

where the quasi-static lateral acceleration ayb is gained from negotiation of constant radiuscurves of sufficient length to allow the vehicle bodies to oscillate about a quasi-static positions.The acceleration as input for the simulations is then calculated by taking the mean valueof the lateral bogie acceleration. Using this bogie frame roll angle, the carbody centre ofgravity is then subjected to a lateral force corresponding to the centrifugal force generatedby the curve radius and the running speed during the measurements as well as the half-carbody weight. Here v and R are taken from the measurements. At equilibrium, the resultingrelative displacements are determined from positions identical to the transducer setup of thedisplacement measurements.

4.2. Dynamic simulations in 3D

The multibody simulations in 3D space are carried out as dynamic simulations. Here a modelwith a total of 46 bodies and 124 degrees of freedom representing a full vehicle is used.It contains all wheelsets, including nonlinear wheel-rail contacts, primary suspension andsecondary suspension. The carbody and the bogie frames have six degrees of freedom each.The primary suspension is build up of linear dampers and springs as well as bumpstops in threedirections. The secondary suspension contains linear dampers in vertical and lateral direction,air springs, anti-roll bars and bumpstops. Some suspension elements are coupled with rubberbushings to the respective bodies. The air springs are generally modelled according to [13].The wheel-rail forces are modelled using the FASTSIM algorithm by Kalker [22].

The vehicle operational conditions are taken from the measurements. The inputs for the sim-ulations are the running speed v and the track geometry including the actual track irregularities.The relative displacements are also determined from positions identical to the measurementsetup. Further, all other measurement parameters mentioned in Section 3 are gained from thesimulations.

5. Comparison measurements – simulations

This section presents comparisons of the displacement measurements and the multibodysimulations.

Figure 7 shows the lateral carbody–bogie displacement as a function of time for bothmeasurements and 3D simulation for negotiation of a curve with a radius of R = 3046 mat a running speed of v = 261 km/h. The signals are unfiltered and represent the same casepresented in Figure 5.

It can be seen that the simulation shows good agreement with the measurements. The highlateral track plane acceleration of ay = 1.27 m/s2 leads to bumpstop contacts in the secondarysuspension during circular curve negotiation. This is also visible as both measurement andsimulation signals stay about the same level and oscillations are relatively small.

It is thus interesting to investigate a case where bumpstop contacts do not occur. Figure 8shows such an example, with ay now limited to 0.59 m/s2. The simulations show goodagreement with the measurements, at least for the leading bogie.

However, it can be seen that the measured displacement at the trailing bogie does not reachthe same level as for the leading bogie and the simulations. In this case, the trailing bogie

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Vehicle System Dynamics 105

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ativ

ela

tera

ldispl

acem

ent,

Δy

[mm

]

Simulation 3D

Leading bogieTrailing bogie

Leading bogieTrailing bogie

(a)

(b)

Figure 7. Lateral carbody–bogie displacement �y during curve negotiation. v = 261 km/h, R = 3046 m andϕt = 2.67◦ (ay = 1.27 m/s2). Unfiltered signals (a) measurement (b) simulation 3D.

0 5 10 15 20 25 30−10

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ela

tera

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acem

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Leading bogieTrailing bogie

Leading bogieTrailing bogie

(a)

(b)

Figure 8. Lateral carbody–bogie displacement �y during curve negotiation. v = 201 km/h, R = 2800 m andϕt = 3.06◦ (ay = 0.59 m/s2). Unfiltered signals (a) measurement (b) simulation 3D.

is located next to an additional car of the test train, a car not considered in the simulations.During circular curve negotiation, larger oscillations can be observed compared with Figure 7.

Figure 9 shows the relative roll angle between the carbody and the bogie frame of the trailingbogie as a function of time for the same case shown in Figure 7. The signals are derived fromthe relative vertical carbody–bogie displacements, cf. Figure 4. Here an interesting effect canbe noticed. While both signals reach a similar level at the beginning of the circular curve,the measured relative roll angle then decreases whereas the simulated value stays about the

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106 D. Thomas et al.

0 5 10 15 20 25 30−0.2

0

0.2

0.4

0.6

0.8

1

1.2

Time [s]

Rel

ativ

ero

llan

gle,

Δϕ

[◦]

MeasurementSimulation 3D

Figure 9. Carbody–bogie roll angle �ϕ during curve negotiation. v = 261 km/h, R = 3046 m and ϕt = 2.67◦(ay = 1.27 m/s2). Unfiltered signals.

initial level. This process can be explained by the levelling mechanism of the air springs,see Section 2.3. In this case, the air springs on the outer side of the vehicle in the curveare compressed, and the levelling valve is activated increasing the air pressure and springstiffness. Since this mechanism is not included in the model, the simulation does not showthis behaviour.

Figure 10 shows the relative roll angle for the case introduced in Figure 8 where bumpstopcontacts do not occur. The simulations now agree well with the measurements in the circularcurve. The effect of a decreasing relative roll angle during circular curve negotiation is hardlyvisible in the measurement signal. The outer air springs are thus not compressed enough toactivate the levelling valve.

0 5 10 15 20 25 30−0.2

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0.3

0.4

0.5

0.6

Time [s]

Rel

ativ

ero

llan

gle,

Δϕ

[◦]

MeasurementSimulation 3D

Figure 10. Carbody–bogie roll angle �ϕ during curve negotiation. v = 201 km/h, R = 2800 m and ϕt = 3.06◦(ay = 0.59 m/s2). Unfiltered signals.

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Vehicle System Dynamics 107

The measured and simulated parameters above are dependent on the running speed andthe track geometry. In order to compare several curve negotiations, the lateral bogie frameacceleration ayb is used, compare Section 4. This acceleration is recorded in all measurementsand can also be simulated easily in 3D. To compare the different curves, the circular curve partwhere the vehicle bodies oscillate about quasi-static positions are studied in particular. Here,the signals are low-pass filtered by 0.5 Hz followed by taking the mean value of measuredand simulated parameters to compare different curve lengths. Note that despite this low-passfiltering the simulated parameters in 3D are gained from dynamic simulations.

Figure 11 shows the lateral carbody–bogie displacement as a function of the lateral bogieplane acceleration for the negotiation of 26 track curves with a radius span of R = 600–5000 m.The measured and simulated (3D) values are taken from both bogies. The measured valuesshow a tendency of variation for similar acceleration levels. Note that the lateral bogie frameacceleration depends on operational conditions like the running speed and the curve radius.This can result in similar acceleration levels for different operational conditions. Furthermore,wind effects, the position of the bogies on the train with respect to the travelling directionand the next car of the train influence the measurement results. Neither effect is modelledin the 3D simulations since the wind effects are not included and the simulation model onlyconsists of one car. In addition, track irregularities in the circular curves can yield variancesfor similar acceleration levels in both measurements and 3D simulations. A reduced increasein lateral displacement for higher lateral accelerations can be observed for acceleration valuesabove approximately 1 m/s2. This is due to lateral bumpstop contacts in the secondary sus-pension. Apart from the scatter and the bumpstop contacts, the measured values follow mainlya straight line.

The simulations in 3D show good agreement with the measurements, mainly following astraight line as well. Beside not simulated effects named above the differences between mea-surements and simulations can occur since the vehicle speed during a curve negotiation maynot be perfectly constant but vary slightly which could not be simulated. The displacementsgained from 2D simulations get a bit larger than within 3D simulations, which mainly should beexplained by the lack of air spring friction in the 2D simulation. It can be noticed from Figure 11

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Lateral bogie frame acceleration, ayb [m/s2]

Rel

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MeasurementSimulation 3DSimulation 2D

Figure 11. Lateral carbody–bogie displacement �y in circular curve as a function of lateral bogie frame accelerationayb . For measurement and 3D simulation both signals are first 0.5 Hz low-pass filtered and then mean values are taken.26 track curves are studied.

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108 D. Thomas et al.

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Lateral bogie frame acceleration, ayb [m/s2]

Rel

ativ

ero

llan

gle,

Δϕ[◦

]

MeasurementSimulation 3D

Figure 12. Carbody–bogie roll angle �ϕ in circular curve as a function of lateral bogie frame acceleration ayb .For measurement and 3D simulation, both signals are first 0.5 Hz low-pass filtered and then mean values are taken.Twenty-six track curves are studied.

that the simulated 2D values, apart from the effect of the bumpstop, are located on a straightline, which is due to the linear characteristics of the air spring model used in 2D simulations.

Figure 12 shows the relative roll angle as a function of the lateral bogie frame accelerationfor the negotiation of the 26 track curves. Note that only one value per curve is representedsince the vertical carbody–bogie displacements were only recorded on one bogie. It can beseen that the 3D simulations mostly overestimate the roll angle. In particular, for higheracceleration levels the measured values are lower. This can be explained by the effect shownin Figure 9. If the levelling valve of the outer air springs is activated and thus the roll angledecreases during the negotiation of the circular curve, the mean value of the roll angle getslower. The impact of the lateral bumpstop in the secondary suspension is not visible but thesimulation results essentially follow a straight line. The measurements follow a similar straightline for lower acceleration levels, but for accelerations above a level of approximately 0.6 m/s2

this straight line shows another inclination. Again, this can be explained by the effect shownin Figure 9.

The simulations carried out show good agreement with the displacement measurements.Some effects affecting the measurement results are not represented in the simulations due tolack of modelling. Besides the impact of the bumpstops, the measurements and simulationsshow a tendency of following a straight line for lateral carbody–bogie displacements. Evenif this appears globally to be a linear behaviour, the nonlinear friction part in the air springmodel of the 3D simulations is important.

6. Introduction of transient crosswind

This section presents results of a curve negotiation case including transient crosswind. Wheelunloading is compared with the simulation cases above and the lateral displacement of thecarbody centre of gravity for the crosswind case and a non-crosswind case is calculated.

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Vehicle System Dynamics 109

As mentioned in Section 1, full-scale tests using a vehicle at overturning risk are not prac-ticable due to economical and safety reasons. However, using simulations it is possible toexpose the vehicle model to crosswind in order to study the vehicle reactions.

This is done using the 3D vehicle model for the negotiation of a curve with a radius ofR = 3300 m at a speed of v = 200 km/h. The level of lateral track plane acceleration isshown in Figure 13(a), leading to a value of ay = 0.52 m/s2 in the circular curve. A windscenario is introduced where the vehicle is loaded with a mean crosswind at a wind speed ofvmean = 7.8 m/s at the curve entrance and during transition curve negotiation, see Figure 13(b).As soon the vehicle enters the circular curve, it is exposed to a wind gust with a gust speed ofvgust = 23.6 m/s. The crosswind is perpendicular to the track.

In Section 2, three methods are presented to define the risk of overturning of a rail vehicle.Figure 14 shows the wheel-unloading on both bogies of the vehicle as a function of thelateral bogie frame acceleration for the 26 curves studied in Section 5 and one curve includingthe crosswind scenario described above. The values for wheel-unloading represent simulatedvalues and are calculated by low-pass filtering the vertical wheel-rail forces and then takingthe minimum of the mean value of wheel-unloading for both wheelsets on one bogie. Thepresented values include the curve negotiation case with the crosswind as well as all curvespresented above.

It can be seen in Figure 14 that the 26 curves studied in Section 5 do not represent anoverturning risk. The simulated values for wheel-unloading are mainly located on a straightline and all above the ratio 0.6. Little variance can be observed, which can be explained bythe influence of track irregularities. However, the presence of transient crosswind worsens thewheel-unloading up to a critical level for the leading bogie.

The lateral displacement of the carbody centre of gravity relative to the track centre is crucialregarding overturning risk. However, this parameter cannot be obtained by measurements. Thedisplacement information can be used for the moment method presented in Section 2.4.2if aerodynamic loads on the train are available. Figure 15 presents the simulated lateraldisplacement of the carbody centre of gravity relative to the track centre ycg during the

0 2 4 6 8 10 12 14 16 180

0.2

0.4

0.6

0.8

1

Lat

.tra

ckpl

ane

acc.

,ay

[m/s

2]

0 2 4 6 8 10 12 14 16 180

5

10

15

20

25

30

Time [s]

Win

dsp

eed

[m/s

]

(a)

(b)

Figure 13. The crosswind scenario during curve negotiation. v = 200 km/h, R = 3300 m. (a) lateral track planeacceleration ay (b) wind speed.

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110 D. Thomas et al.

0 0.5 1 1.50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

Lateral bogie plane acceleration, ayb [m/s2]

ΣQ

/(2Q

0)

Leading bogieTrailing bogie

Transient crosswind

Figure 14. Wheel unloading �Q/(2Q0) as a function of lateral bogie frame acceleration ayb . The wheel unloadingvalues are first 2 Hz low-pass filtered and then mean values for both wheelsets of one bogie are taken. The lateralbogie plane acceleration is first 0.5 Hz low-pass filtered and then mean values are taken. Twenty-seven curves studied.

0 2 4 6 8 10 12 14 16 180

20

40

60

80

100

120

140

160

Time [s]

Lat

.di

spla

cem

ent

ofca

rbod

yce

ntre

ofgr

avity

rela

tive

totr

ack

cent

er,y

cg

[mm

]

no wind loadcrosswind

Figure 15. Lateral displacement of the carbody centre of gravity relative to track center ycg during curve negotiation.v = 200 km/h, R = 3300 m. Unfiltered, simulated signals.

curve negotiation of the crosswind case. Furthermore, the signal is presented for a negotiationof the same curve without impact from the crosswind. It can be observed that the meancrosswind leads to an initial displacement of the centre of gravity already in the beginningof the curve. The difference between the wind-loaded and the non wind-loaded vehicle staysrelatively constant through the transition curve. The wind gust then leads to a three timeslarger lateral displacement of the carbody centre of gravity in the circular than for the nonwind-loaded vehicle.

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Vehicle System Dynamics 111

7. Conclusions and future work

In this work, multibody simulations in 2D and 3D are performed to study the lateral dis-placement and roll angle between the bogie frames and the carbody of a railway vehicle.The simulations include different input data for the suspension modelling and are validatedwith displacement measurements performed on a fast test train. The simulations show goodagreement with the measurements and represent a good tool to estimate the relative motionsin the secondary suspension.

Furthermore, transient crosswind is introduced to the 3D simulation model during a curvenegotiation. The vehicle reacts in large displacements for the carbody centre of gravity andcritical wheel-unloading.

Future work should investigate the influence of transient crosswind on the vehicle reactions.Furthermore, the modelling of effects which are not included in the simulations above shouldbe considered to study their influence.

Acknowledgements

This study is supported by the VINNOVA Centre of Excellence for ECO2 Vehicle Design as part of the project‘Crosswind stabilty and unsteady aerodynamics in vehicle design’. The displacement measurements were carried outon the test train of the Swedish project ‘Gröna Tåget’ by Interfleet Technology AB. General wind data were deliveredby the Swedish Meteorological and Hydrological Institute (SMHI). CFD data were provided by Ben Diedrichs withinthe VINNOVA Centre of Excellence for ECO2 Vehicle Design.

References

[1] B. Diedrichs, On computational fluid dynamics modelling of crosswind stability for high-speed rolling stock,Proc. Inst. Mech. Eng. F, J. Rail Rapid Transit 217 F3 (2003), pp. 203–226.

[2] B. Diedrichs, M. Sima, A. Orellano, and H. Tengstrand, Crosswind stability of a high-speed train on a highembankment, Proc. Inst. Mech. Eng. F, J. Rail Rapid Transit 221 F2 (2007), pp. 205–225.

[3] B. Schulte-Werning, R. Grégoire, A. Malfatti, and G. Matschke (eds.), TRANSAERO – A European Initia-tive on Transient Aerodynamics for Railway System Optimisation, Notes on Numerical Fluid Mechanics andMultidisciplinary Design Vol. 79, Springer, Berlin, Germany, 2002. ISBN 3-540-43316-3.

[4] C. Baker, Ground vehicles in high cross winds - part I: Steady aerodynamic forces, J. Fluid Struct. 5 (1991),pp. 69–90.

[5] C. Baker, Ground vehicles in high cross winds - part II: Unsteady aerodynamic forces, J. Fluid Struct. 5 (1991),pp. 91–111.

[6] C. Baker, Train aerodynamic forces and moments from moving model experiments, J. Wind Eng. Ind. Aerodyn.24 (1986), pp. 227–251.

[7] C. Baker, Measurements of the cross wind forces on trains, J. Wind Eng. Ind. Aerodyn. 92 (2004), pp. 547–563.[8] A. Carrarini, Reliability based analysis of the crosswind stability of railway vehicles, Ph.D. thesis, Technische

Universität Berlin, Shaker Verlag, Aachen, Germany, 2006. ISBN 3-8322-5232-0.[9] S. Lippert, On side wind stability of trains, TRITA-FKT Report 1999:38, Department of Vehicle Engineering,

Royal Institute of Technology (KTH), Stockholm, Sweden, 1999.[10] B. Diedrichs, M. Ekequist, S. Stichel, and H. Tengstrand, Quasi-static modelling of wheel-rail reactions due to

crosswind effects for various types of high-speed rolling stock, Proc. Inst. Mech. Eng. F, J. Rail Rapid Transit218 F2 (2004), pp. 133–148.

[11] C. Wetzel and C. Proppe, On the crosswind stability of high speed railway vehicles, Proc. Appl. Math. Mech. 6(2006), pp. 341–342.

[12] B. Diedrichs, Computational methods for crosswind stability of railway trains - A literature survey, TRITA-AVEReport 2005:27, Department of Aeronautical and Vehicle Engineering, Royal Institute of Technology (KTH),Stockholm, Sweden, 2005.

[13] M. Berg, A three-dimensional airspring model with friction and orifice damping, in The Dynamics of Vehicles onRoads and Tracks, Proceedings of the 16th IAVSD Symposium, Pretoria, South Africa, 30 August–3 September1999, Swets & Zeitlinger, Lisse, The Netherlands, 2000, pp. 528–539. ISBN 90-265-1629-0.

[14] O. Krettek and J. Grajnert, Die Modelldarstellung pneumatischer Fahrzeugfederungen und die Vorauswahl derModellparameter, ZEV DET Glas. Ann. 115(5) (1991), pp. 142–153.

[15] G. Quaglia and M. Sorli, Air suspension dimensionless analysis and design procedure, Veh. Syst. Dyn. 35(6)(2001), pp. 443–475.

Downloaded By: [Purdue University] At: 15:53 5 December 2010

Page 17: Vehicle System Dynamics Measurements and simulations of ... · PDF fileRail vehicles in everyday operation are often exposed to ... simulation of rail vehicle dynamics is therefore

112 D. Thomas et al.

[16] Intec GmbH, SIMPACK Reference Guide – SIMPACK Release 8.8, 2006; software available athttp://www.simpack.de.

[17] N. Docquier, P. Fisette, and H. Jeanmart, Multiphysic modelling of railway vehicles equipped with pneumaticsuspensions, Veh. Syst. Dyn. 45(6) (2007), pp. 505–524.

[18] DB Netz AG, Ausgewählte Maßnahmen und Anforderungen an das Gesamtsystem Fahrweg/Fahrzeug -Aerodynamik/Seitenwind, RIL 80704, 2006.

[19] European Rail Agency, Technical specification for interoperability (TSI) - rolling stock subsystem, 96/48/EC,2008.

[20] E. Andersson and M. Berg, Railway systems and rail vehicles (in Swedish: Spårtrafiksystem och Spårfor-don), Textbook, Department of Aeronautical and Vehicle Engineering, Royal Institute of Technology (KTH),Stockholm, Sweden, 2007. ISBN 978-91-7178-743-9.

[21] E.Andersson, M. Berg, and S. Stichel, RailVehicle Dynamics, Textbook, Department ofAeronautical andVehicleEngineering, Royal Institute of Technology (KTH), Stockholm, Sweden, 2007. ISBN 978-91-7415-272-2.

[22] J.J. Kalker, A fast algorithm for the simplified theory of rolling contact, Veh. Syst. Dyn. 11 (1982), pp 1–13.

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