tool SIMPACK, [1], a computer programme with a very wide ... · tool SIMPACK, [1], a computer programme with a very wide range of applica-tion (vehicles, aircraft landing gears, robots

Investigation of running behaviour and

derailment criteria for freight cars by dynamic

simulation

G. Schupp, A. Jaschinski

DLR-Institute for Robotics and System Dynamics,

D-82234 Wessling, Germany

Abstract

Using the simulation software SIMPACK, the mechanical model of a freight cartrain running along a s-shaped track under high longitudinal pressure forces ispresented. With the aid of simulation the freight car in the centre of the trainshould be judged with respect to several derailment criteria. The results are veri-fied by comparison with measurements.

1 Introduction

Simulation of the dynamic behaviour becomes more and more significant foranalysis, design and development of railroad systems. Recently, the simulationtool SIMPACK, [1], a computer programme with a very wide range of applica-tion (vehicles, aircraft landing gears, robots and space structures) has beenenhanced by analysis and design features for railway vehicles, [2], [3]. With theaid of this tool, it is demonstrated in this paper that many experimental investi-gations in the field of freight car operation can be replaced by computer simula-tions.

The experiments deal with formations of freight cars, undergoing longitudi-nal forces between 100 kN up to about 400 kN during passing a s-shaped curvewith a speed of about 2 m/s. The experimental track with measurement device islocated at DB AG Minden, where numerous experiments have been performedin order to determine the maximum longitudinal force which a particular type offreight car can tolerate without violating various derailment criteria, as forinstance the maximum amount of wheel lift or the maximum lateral force actingbetween wheel and rail.

Transactions on the Built Environment vol 18, © 1996 WIT Press, www.witpress.com, ISSN 1743-3509

14 Computers in Railways

These experiments and measurements, performed by the DB AG at Mindenand partially supported by the European Rail Research Institute (ERRI), areelaborate, time consuming and expensive. Therefore DLR has been selected tofurther develop the simulation tool for replacing such kind of experiments par-tially by simulation. However, it is required that experiments and simulationresults are in good agreement which has to be judged by comparing the simula-tion results with measurements. Therefore, digitized measurement results havebeen made available by the DB AG in order to verify SIMPACK for this specialapplication.

In the following sections the simulation task and the simulation model willbe described as well as the most important features and development steps of thesimulation tool are mentioned. Finally, some selected simulation results will becompared with measurements and discussed.

2 The simulation model of three freight cars passing a

s-shaped curve

The simulations are all performed using the simulation tool SIMPACK. In thesequel, a short description of this tool is given, concentrating mainly on features,necessary for the simulations described in this paper. A deeper insight into SIM-PACK and its possible applications is given for example in [1] and [2]. Afterthat, the developed model of a train consisting of three different types of freightcars is described including the chosen implementation of the track.

2.1 The modelling and simulation toolThe software tool SIMPACK is designed for the simulation of general multibodysystems (MBS). It includes all steps from the modelling of the MBS via generat-ing the equations of motion automatically and analysing as well as evaluatingthem up to the visualisation of the results. The complete simulation task isdivided into several steps and is controlled and performed very comfortably bythe user with the help of a graphical user interface. The main steps are:

1. Pre-processing: Essentially, the user has to set up the MBS-model byabstraction of the real system (mathematical modelling).

2. Calculations: Herein, the automatically generated equations of motion canbe evaluated by different methods, like time integration, static and kine-matic analysis, linear systems analysis, parametric analysis etc.

3. Post-processing: Most important features are 3D-animation and visualiz-ing of the results by arbitrarily definable 2D-plots.

The MBS-model can consist of nearly any number of rigid or elastic bod-ies', each interconnected with others by different kinds of joints and force ele-ments. Joints and force elements can be chosen from extensive libraries or, forspecific applications they may be user-defined. Joints restrict the relative move-ment between two bodies. Predefined are translational and rotational joints from


Computers in Railways 15

zero up to six degrees of freedom and special joints like wheel-rail jointsdescribing the movement of wheelsets or single wheels on an arbitrary track.Force elements represent applied forces and torques. The library offers forexample linear and nonlinear spring and damper elements in series or parallel,tyre models for road vehicles as well as wheel- ail creep forces.

The MBS setup is supported by a graphical, three dimensional representa-tion of the model, that can be created by the user to a sensible extend simultane-ously. Thus, it provides him with the possibility of checking nearly every inputgraphically Then, during animation - for instance after time integration - thisgraphical model can be used to give a realistic overview of the reaction of thesimulated overall system.

As an additional information, which is not considered for the task describedin this paper, it is worthwhile to mention that SIMPACK may not only be usedfor pure simulation. This software is also applicable as an integrated systemdesign and optimization tool, performed by an extensively automated parameter-variation. Here the user only has to choose the parameters to be varied, the out-put values and eventually some output filters. With these instructions, SIM-PACK performs the complete parameter variation automatically. In order tocouple the modelling with the design procedure, an interface to CAD softwarehas been developed. The implementation of elastic bodies is provided by aninterface to FEM software.

2.2 Brief description of the simulation model

2.2.1 The experimental task A characterisation of the experiments can bedescribed as follows. The freight car of consideration is placed between twoother freight cars, the so-called frame-cars. This three-waggon formation isthen placed between two heavy loaded freight cars. Each of these heavy loadedcars is coupled with a locomotive, in order to control the buffer forces and thespeed. The frame cars are of the following types: The first car in the direction ofmotion is a Tdgs930 and the second frame car is a bogie freight car of typeRs680. For experimental investigations to determine the tolerable long&aWmalforce, tfcrce types of freight cars have been considered between the previouslymentioned fmme cars: two types of two-axled freight cars, a Hbbins306 and aKls442 and o*e bogie freight car of the type Sgns #4.

The complete formation starts on tangent track, the longitudinal fa*oe isapphed fry $ke *wo kmamwiw* amd (fee speed is set to 2 m/s before readMtf «feF *a#gdaarve. Derii* #**ma* Ae curve, speed, buffer forces, buffer strokes, aswell as a&e lateral buffer deviations and the vertical and lateral forces between*#*ek #md mat* are measured at Ac car of consideration. For the measuremeatof *e m*a*l tail forces *** &**&* car is equipped with special wheelsets byapplying ***** gauge technique*. Additionally, the vertical distance betweenwtacl #a#d am* mil is •uaaamnii $adescribe the wheel lift.



2.2.2 The model of the freight car train In order to simulate the previouslymentioned experiments, a mechanical model of a freight car formation consist-ing of two frame cars and the freight car of consideration (for this example aKls442) between them has been established as shown in figure 1. Table 1 putstogether the mass and inertia data of the three waggons.

Table 1. Mass and inertia data of the car bodies

data

car

RS680

Kls442

Tdgs930

mass [kg]

36840

9020

70000

moment

4

35500

14310

59200

s of inertia

4198000

162800

1570000

i [kgm ]

/,

200000

177900

1620000

Kls442 TDGS930

LJRS6809 L2

13.0 m19.9 m

—(

«

;5 - - d8.0 m

13.86 m

S (

6

\ (\6.0 m9.64 m

)

V = 2 m/SP

Figure 1: Examined train built of three freight cars on a s-shaped track; thecentre car of consideration is a Kls442.

It has to be taken into account that for the centre freight car the modellingshould be more detailed as for the frame cars, since the behaviour of these cars isonly important with respect to the correct buffer forces applied to the centre car.The necessary grade of modelling has been tested by establishing a rather exten-sive model where the complete three-waggon formation was modelled as exactas possible, concerning

• the wheel-rail contact, taking into consideration Kalker's Theory of Roll-ing Contact, [4], as well as a linear elastic contact forces between the con-tact points of wheel and rail,

• the buffer contact, taking into account three dimensional contact of thespherical buffer heads with dry friction,

• the suspensions, mostly leaf springs with hysteresis caused by dry friction,



• the torsional elasticity of the car body and the bogie frames,

# the track model, using measured values of the curvatures.

Investigations with this complex model revealed that the modelling of theframe cars can be simplified by ignoring the wheel-rail contact mechanics andthe torsional elasticity of the car bodies. Therefore a simpler model was definedwhere the frame cars are modelled as rigid bodies with regular suspended wheel-sets, but the wheelsets are kinematically coupled to the track, i.e. the wheelsetsof the frame cars are assumed to follow the track without any deviation.

The centre car of this simpler model has to be modelled taking into consid-eration wheel-rail contact mechanics as well as car body elasticity. However, itis sufficient to take into account only rotational elasticity about the longitudinalaxis and to simplify it to the first eigenmode of an elastic, free-free mountedbeam. The chosen rotational stiffness is taken from measurements.

The velocity along the track remains nearly constant, if the leading car isguided kinematically along the track. The leaf springs, building the primary sus-pensions and connecting car bodies with wheelsets and bogies with wheelsets,respectively, are modelled as nonlinear springs with damping hysteresis toreproduce the dry friction. The spring characteristics are piecewise linear andapproximate the measured characteristics pretty well. The bearing between thecar body and the bogies of the RS680 is a one-dimensional, rotational joint, rela-tive rotation is only possible after a certain amount of frictional torque isexceeded.

The buffers between the cars are modelled again as rigid bodies, connectedto the car bodies using one dimensional force elements with a piecewise linearspring characteristic including hysteresis. This characteristic is once againbrought into line with measurement data. For the interaction between two buff-ers two different contact descriptions are used: In order to calculate the potentialpoints of contact, the ideally spherical buffers are supposed to be rigid. Then thepoints of contact can be found by solving a pure geometrical problem.

Unlike this rigid description, the contact forces are found by taking intoconsideration the elasticity of the buffer heads due to Hertzian contact like it isshown principally in figure 2 while equation (1) collects the mathematical for-mulations of the contact forces. Herein three different states of interaction arepossible:

1. No contact: There is no interaction between the buffers at all.

2. Stick: Contact between buffers, but there is no relative displacement.

3. Slip: Contact between buffers with relative displacement.

The normal forces F^ result from a linear spring-damper characteristic withvery high stiffness and damping coefficients (c, d) acting normal to the sphericalbuffer surfaces in the point of contact. The tangential forces F? are calculatedaccording to dry Coulomb friction where the inherent discontinuity is avoidedby applying a linear damper law with a very high damping coefficient. Thisdamper law is defined by introducing the parameter v^ which can be interpreted



as the limit of micro slip. When this limit is reached, the buffers begin to slide. Acharacteristic value of v% for the simulations presented in this paper isVg = 0.001 m/s. The tangential forces act in the plane tangential to the sphericalbuffer surfaces at the points of contact and antiparallel to their relative velocityVf projected to this plane.

Fifure 2: Scfaematk; representation of interaction between buffer heads as wella* force law for slip forces.

= c

<0, M > Vg => ¥# = c • e + d • e,

(no contact)

j (stick)

(slip)

In principle, Ac contact between wheels and rail for each wheelset isapproximated in tfce #amc way. After calculating the potential contact pointsiMMig a m#d naatart feacriptkm, the normal forces are calculated again byapplying a *ttff rpriiq; iiMpri ktw between the contact points of wheel and rail

t). tie #me#m $mmgemdal) forces result from Kalker's Simpli-m, [4].

en simulation and measurement as good: models are ao* sufficient. Therefore theas meASurod with a resolution of 2.5 m.

t #n Ais data, SiMPACK generates a good

in comparison with

i a*e compared witfc Digitized results of measure-•abie by OS AG at Mmden. However, from the



extensive material only a small selection of the significant quantities can be pre-sented in this paper.

Two of the most important quantities relevant to security are the sum of lat-eral forces ZY per wheelset and the quotient Y/Q of the lateral and the verticalforce per wheel. Additionally, in this special case the wheel lift dz itself is a cri-terion for security against derailment. For these three quantities the comparisonbetween the results generated with the simulation software SIMPACK and theexperimental measurements is discussed in the sequel. As applied longitudinalpressure force FL = 195 kN is chosen. Since the measurements have been per-formed only over a track length of 80 m, the comparison is restricted to thislength.

3.2 Comparison of important quantities

An important safety criterion against lateral displacement of the rail (and elasticor even plastic deformation) is the maximum value of the sum of lateral forcesZY acting between each wheelset and the track. The allowed limit of this force,responsible for the stress of the rails, is defined in the draft of DIN 5550, [5]. Thediagrams of figure 3 represent these forces for the front (wheelset 1) and the rear(wheelset 2) wheelset in comparison with measured values.

Measurement75.0

Simulation with SIMPACK40.0

' -25.0 -80.00.0 20.0 40.0 60.0 80.0arc length on track [m]

0.0 20.0 40.0 60.0 80.0arc length on track [m]

Figure 3: Sum of lateral forces acting at wheelset 1 and wheelset 2 of a Kls442-waggon at a longitudinal pressure force of FL = 195 kN.

The diagrams denote that experiment and simulation agree rather well. Dif-ferences in the force histories can be explained by the simplified track modelwhich is assumed to be rigid. However, the real track of course has a lateral elas-ticity but this quality is neither easy to be described physically nor are its param-eters easy to determine by measurements. Therefore, the rigid track has to beconsidered as a compromise yielding slightly larger forces. But as long as thelateral forces calculated by simulation are slightly larger then the measurements



represent, there is no danger of underestimating the influence of the amount oflongitudinal force applied on the formation of freight cars.

When the formation passes the experimental track, wheel lift occurs at bothwheelsets. At first, the left wheel of wheelset 1 loses contact when the train haspassed a distance of about 40 m. Here, the wheel lift takes place only for a shortperiod, see figure 4 at left. Presented is the vertical distance between the liftingwheel and the rail - the so-called wheel lift dz - generated by simulation andmeasured within an experiment. After covering a distance of about 55 m, theright wheel of wheelset 2 begins to lift and remains out of contact for nearly15 m travel distance, see figure 4 at right.

Measurement40.0

30.0

20.0

10.0

- 0.0 ---------

-10.0




Figure 4: Vertical wheel lift distance at wheelset 1 left and wheelset 2 right of aKls442-waggon at a longitudinal pressure force of FL = 195 kN.

The wheel lift is caused by sticking buffers in combination with contactbetween the flange of wheels and the rails (flange contact). In the wheel lift situ-ation of wheelset 1 flange contact occurs at the front right and at the rear leftwheel. This is due to a diagonal buffer contact with stick at the front buffers atright and the rear buffers at left (the location of the buffers is always given withrespect to the centre car). The other buffers are out of contact. However, whenthe second wheelset loses contact at the right wheel, both left wheels showflange contact while both right buffers are in contact and sticking.

As criterion against derailment the maximum value of the wheel lift is used.As long as it is lower than 50 mm it is supposed, that there is no danger of derail-ment to be expected.

Figure 4 indicates very good agreement between measured and simulatedvalues of the wheel lift distance for the rear wheelset, but at wheelset 1 the sim-ulated value is about 20 mm whereas the measurement yields 35 mm. However,the wheel lift reacts very sensitive on slight changes of several parameters, as forinstance the torsional stiffness c* of the centre car body, the friction coefficients



between the buffers, the longitudinal characteristic of the buffer spring etc. Theexperimental results reveal this extreme sensitiveness of the wheel lift, too. Forexample a statistical variation of about 20 mm occurs, even if the same longitu-dinal forces are applied and all other experimental parameters remain as good aspossible unchanged.

A very critical situation for a waggon with respect to derailment is flangecontact followed by wheel climb (i.e. a wheel climbs up via its flange upon therail). As usual criterion of security against this derailment scenario the quotientY/Q of the lateral force Yy and the vertical force Qy between each wheel ij andthe track is used (i = 1/2: front/rear wheelset, j = 1/2: right/left wheel). Withinthe already mentioned DIN 5550, see [5], it is recommended, that the maximumvalue of Y/Q must not exceed 1.2 if quasi static conditions are supposed. Figure5 displays the values of Y/Q for all four wheels of the Kls442-waggon.


Measurement1.50

-0.500.0 20.0 40.0 60.0 80.0arc length on track [m]




Figure 5: Quotient Y/Q of lateral and vertical forces of each wheel of a Kls442-waggon at a longitudinal pressure force of FL = 195 kN.



It is demonstrated, that Y/Q becomes large for a wheel during flange con-tact while its opposite wheel lifts off the rail. For the lifting wheel, since there isno contact, Y = 0 and Q = 0 is valid, hence also Y/Q = 0 holds. But for such sit-uations the measurement fails. However, the simulation yields the correct valuesof Y/Q: A maximum of Y/Q at 40 m for wheel 11 corresponds with Y/Q = 0 forwheel 12. The same relation appears for wheel 22 and wheel 21 at about 55 m.

4 Conclusions

The simulation of a freight car train passing a s-shaped track with the aid of themultibody simulation tool SIMPACK generates results, for which a generallygood agreement with experiments could be stated. Two of the main critenons forthe judgement of freight cars with respect to derailment caused by growing lon-gitudinal pressure forces are, according to DIN 5550, the sum of lateral forcesbetween wheel and rail per wheelset and the quotient of the lateral and verticalforces per wheel. The simulation reflects these two criterions in a satisfactoryway.

For the third examined criterion concerning security against derailment, thewheel lift, the correspondence between simulation and measurement is usuallynot as good. The problem with this criterion is, as experiments and various sim-ulations have demonstrated, its strong dependence on slight parameter changes.

During the integration process itself, especially if high longitudinal pressureforces are applied, one distinct situation may cause numerical problems, result-ing in a questionable reliability: Diagonal buffer contact in combination withdiagonal flange contact at both wheelsets and wheel lift. Here, along with thewheel lift, additional research and modelling improvements are necessary.

5 References

1. Rulka, W. & Eichberger, A. SIMPACK - An Analysis and Design Tool forMechanical Systems, Multibody Computer Codes in Vehicle System Dynam-ics, Supplement to Vehicle System Dynamics, 22, 1993.

2. Rulka, W., Haigermoser, A., Mauer, L. & Netter, H. Anwendung modernerAuslegungesstrategien fur Schienenfahrzeuge durch Einsatz des Simulations-programms SIMPACK, VDI-Bericht 1219, Munchen, 1995.

3. Kortum, W., Rulka, W. & Eichberger, A. Recent Enhancements of SIM-PACK and Vehicle Applications, European Mechanics Colloquium, EURO-MECH 320, Prague, Czech Republic, June 6-8 1994.

4. Kalker, J. J. Three Dimensional Elastic Bodies in Rolling Contact, KluwerAcademic Publishers, Dordrecht, 1990.

5. DIN 5550, part 1-5 (draft) Fahrtechnische Prufung und Zulassung vonSchienenfahrzeugen, Beuth, Berlin, 1992.


Documents

tool SIMPACK, [1], a computer programme with a very wide ... · tool SIMPACK, [1], a computer programme with a very wide range of applica-tion (vehicles, aircraft landing gears, robots