A 3D Simulation Model of Train Dynamics for Testing ...

A 3D Simulation Model of Train Dynamics for Testing Odometry Algorithms Luca Pugi1,2, Alessandro Ridolfi1,2, Benedetto Allotta1,2, Monica Malvezzi3, Gregorio Vettori1,2, Fabrizio Cuppini4, Filippo Salotti4 1 Mechatronics and Dynamic Modelling Lab (MDM Lab), University of Florence @Pistoia, Italy 2 Dept. of Energy Engineering, University of Florence, Italy 3 Dept. of Information Engineering, University of Siena, Italy 4 ECM S.p.a., Pistoia, Italy 1 INTRODUCTION Automatic Train Protection systems (ATP) are planned to increase the railway running security as they are able to react to the engine driver’s conduct mistakes, which might cause accidents and they can stop automatically the train in these situations. The European Rail Traffic Management System (ERTMS) [1] [2] [3] [4] represents an advanced ATP, which are provided three different levels for: ERTMS of Level 2 and 3 setting aside the existence of a traditional type of a railway signalling system and ERTMS of Level 1 requiring, on the contrary, a traditional system of semaphore signalling. Odometry [5] is basically important for the rail running security as it has the aim to estimate the instantaneous speed of the train and the distance the train covers (train position); all these data are fundamental for the correct behaviour of the protection functions of the ATP system (and consequently for the safety and efficiency of the automatic train protection and control system). Within the estimation of the complete motion of a vehicle the term odometry refers to the use of data fusion techniques of measures that generally are provided by a set of different types of sensors. For instance, the odometric algorithm inside SCMT (Italian acronym for “Sistema Controllo Marcia Treno”) uses two tachometers which are put on two independent axles [5]; one if its developments integrates the information of the two GITs (Italian acronym for “Generatore di Impulsi Tachimetrici”: Tachometric Impulse Generator), with the acceleration measurement given by a longitudinal accelerometer [6]. Other chances are the use of a Doppler Radar sensor combined with the two GITs [7] or, considering present and future developments too, the use of Inertial Navigation Systems (INS) based on inertial sensors (MEMS accelerometers and gyroscopes) which can be integrated with magnetometers and/or GPS, GNSS-GALILEO or like location systems [8]. The common aim of the different systems is to get a more and more precise and reliable odometric estimate; currently the research of more accurate solution is leading to the introduction of different types of sensors and in particular the integration of INS (Inertial Navigation System) devices in the traditional odometric system seems to be a promising solution. In particular INS may be used to improve speed estimations of the algorithms, in particular working conditions in which the information of some sensors are not available or the correlation between the sensor measurements and the vehicle longitudinal motion is in some way “weak”. For example, in case of traction or braking manoeuvres with degraded adhesion conditions the measurements of the axle speed are deeply influenced by the behaviour of WSP (Wheel Slide Protection) and Anti-Skid systems. Anyway as a general rule, to exceed the restrictions of any single sensor typology, sensor fusion techniques of redundant measures that are got from the train sensor set can be used. The development and prototyping of odometry algorithms involve the simulation of realistic environmental conditions which are usually produced using recorded experimental data and synthetic results from simulation models [9] which may be also used for the development of HIL testing devices such as the Trenitalia MI-6 Test rig of Firenze Romito [10]. Even when experimental data are available from previous activities, the use of synthetic inputs from dynamic simulation models is recommendable in order to simulate the wide variety of different working conditions that have to be verified to assure the respect of performance, safety and reliability specifications of the tested algorithms. Furthermore such types of tests are completely reproducible and the operative conditions are fully controllable, even critical conditions can be safely be performed (for example, extremely degraded wheel/rail adhesion conditions). To test and calibrate correctly the odometry algorithms it is therefore necessary to reproduce in a simulation environment the train sensor outputs, that is 3D rail kinematics measurements, which have to be consistent the one with the other; simulated signals vary

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according to the kind of measurements needed as inputs by the tested algorithms: typically redundant measurements of two axle tachometers (GITs), but also the estimation of vehicle longitudinal speed through Doppler Radar sensors or the acceleration measures. There are some troubles both using experimental data, in the event they are available (as often they do not fill the whole sensor set which is necessary for these applications), and to yield results with two-dimensional simulation models (the development of inertial navigation systems involves the use of accelerometer and gyroscopic sensors whose response is sensitive to the three-dimensional behaviour of the vehicle). As a consequence, simplified planar models of railway vehicles that have been widely used for example for Hardware in the Loop testing of SCMT odometry algorithms [9] are not suitable to develop this innovative solutions. In addition to 3D nature of kinematics outputs to produce it also needs to simulate complex interactions between the mechatronics on board rail subsystems (for instance anti-skid and WSP) and the dynamics of rail vehicle itself; in order to correctly test the odometric algorithm, extremely different railway tracks and running conditions have also to be enquired. Then the authors chose, rather using traditional multibody modelling programs, preferred to carry out a series of “ad hoc” simulations with a TM TM railway vehicle multibody model, developed using Matlab-Simulink (tool SimMechanics ). An accurate simulation of degraded adhesion conditions according to applicable norms [11] with corresponding interactions with on board subsystems is also quite difficult to be performed using conventional or commercial multibody codes (degraded adhesion conditions are critical in the location algorithm testing). In order to avoid these limitations a complete three-dimensional multibody model of a railway vehicle has been developed using Matlab-Simulink™ including an efficient contact model [12] which has been further modified in order to simulate degraded adhesion conditions: a wide variety of on board subsystems (for example WSP, anti-slip devices) is available and, as a consequence, the model can simulate various running conditions, with arbitrary tracks, including conditions that may stress the sensor behaviour, like i.e. low adhesion between the wheels and the TM rails, track irregularities, curves, line gradient, etc.. The use of Matlab-Simulink allows testing easily the on board components with real-time implementation; for instance, considering the WSP subsystem as a safety relevant component for railway running and a device affecting directly the rotational dynamics of axles (and consequently GIT measurements), you can carry out HIL tests TM (Hardware in the loop) on suitable test rigs [10], using Matlab-Simulink as a real-time simulation software. On this point you can find current regulations [13] [11] including all the requirements to respect in the simulation environment in order to make valid HIL tests, in a partial or full substitution of the corresponding trials on the real railway line. In addition to WSP systems, you can also test ATP/ATC systems, odometry boards, anti-skid systems, etc.. 2 RAILWAY VEHICLE MULTIBODY MODEL The correct evaluation of the performances of an odometric algorithm requires the simulation of extremely different railway tracks and running conditions. In order to make a series of significant simulations for the location algorithm test, the authors have developed a complete 3D multibody TM TM model of a high speed train using SimMechanics tool inside Matlab-Simulink . For commercial/industrial policy reasons authors have not used data of a known high speed train; however data used are quite realistic and obtained introducing light modification on values taken from some well-known existing high speed applications. The aim of the 3D mechanical model used for the simulations is to reproduce kinematics outputs which are necessary for the algorithm test (outputs corresponding to on board sensor set measurements): coach accelerations and angular velocities (3D inertial sensor outputs), axle angular velocities (GITs), coach longitudinal speed (radar-Doppler), etc.. The rail vehicle multibody model has to be supported by a well-run 3D contact model, reproducing the real forces exchanged between wheel and rail; the wheel-rail contact force has been calculated through an algorithm developed during other research activities [12], which has been implemented TM with Matlab-Simulink too. This model, based on the Hertzian contact theory and on the Kalker nonlinear one (with saturation), can calculate multiple points of contact (up-to 4 points for every single wheel). Inside this model an accurate law of degraded adhesion, allowing the reproduction of a series of running conditions which are critical for the working of the different algorithms, has been implemented; in degraded adhesion conditions on board mechatronics devices are activated (i.e. WSP, traction control), affecting the dynamic behaviour of the whole system and consequently the location algorithm estimation too. Besides the authors used a track model allowing a high flexibility in the creation of the railway line with the possibility of planning, in a parametric way and as a function of the covered space, straights/curves, slopes, cant angles, connection tracks, etc.. This way you can “stress” the different sensors and enquire efficiency of location algorithms as a function of the different parameters of interest.

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2.1 RAIL TRACK MODEL The parametric track model allows getting the required geometries of the rail lines: particularly straight stretches, curves (with the corresponding connection tracks and cant angles), rail line slopes (altimetry with the corresponding connection tracks), introducing a series of actions (of inertial type too) which may affect the measurements of the on board sensor set (i.e. inertial sensors such as accelerometers and gyroscopes). Some patterns of irregularities of the rail line (rail gauge irregularities, cant, etc.) have even been planned; the irregularities in the track (put inside at the wheel-rail contact model) are useful for the analysis of the sensor response if disturbances occur: i.e. you can excite accelerometers and gyroscopes to estimate their sensitivity (analysis of the influence of possible irregularities, which may be present on the rail line, on the inertial sensors) or to impose some secondary motions, caused by irregularities, for the analysis of the Doppler-Radar response (the accuracy of its measure also depends on the assembly tolerance of the Doppler-Radar sensor on the rail vehicle). Depending on the covered space you can also set the desired adhesion pattern and other significant features, such as, for instance the availability or unavailability of the signal of the GPS system (for example while crossing a tunnel) and the state of the reflective surface (scattering): this last parameter is basically important for the correct behaviour of the Doppler-Radar type speed sensor, whose efficiency significantly depends on the state of the surface it directs towards (with reference to studies about this subject [14] [15]). 2.2 MECHANICAL MODEL OF THE RAIL VEHICLE The coach motion of the first rail vehicle (with its own 3D motion dynamics), where the sensors of the location system are set up, was simulated and estimated. The authors chose to model a single unit composed of a coach attached to two bogies (Figure 1). This rail vehicle has been modelled with a multibody approach; the system was divided in the following rigid bodies: one coach, two bogie frames, eight axle boxes (four for each bogie), and four wheelsets (two for each bogie). Each component was modelled with geometrical and inertial properties whose values are very close to the real typical values of the actual high-speed trains. The rail vehicle characteristics can be easily TM changed in a parametric way (customizable and flexible model). The model used in Matlab-Simulink is a rail vehicle with wheel-and-axle set Bo-Bo (2 engine axles for every bogie, with independent traction control).

Figure 1 – Rail vehicle bogie model

The main features of the rail vehicle that has been employed for simulations are the following (Table 1):

Total Mass

About 56000 kg

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Coach Mass Wheel-and-axle set Bogie wheelbase Bogie distance Wheel diameter Primary suspension own frequency Secondary suspension own frequency Wheel-rail profiles

About 42000 kg Bo-Bo 2.42 m 16.9 m 0.92 m About 4.5 Hz About 0.8 Hz ISO-ORE 1002 Rail UIC60 with 1/20 pose

Table 1 – Characteristics of the rail vehicle

The coach is held by a rear and front bogie with a two-stage suspension system. Particularly the rail vehicle is provided with a double suspension stage (vertical and lateral) between the coach, the bogies and the axles, damping devices (vertical, lateral, anti-yaw dampers) with non-linear characteristics, anti-roll bar and bump-stop plugs to reduce souplesse and other coach motions (in order to respect in every condition the rules concerning the loading gauge of the rail vehicle). The bodies are supposed to be rigid and the degrees of freedom of each body is defined by joints connecting each component to the other, reproducing the available movement of the real parts of the train. The primary suspension system, comparatively hard, links the axles to the bogie frame, while the secondary one, typically softer for comfort reasons, is interposed between bogie and coach and supports the weight of the latter. The transmission of the longitudinal efforts between coach and bogies takes place through elastic elements simulating the effect of the main solutions that are utilized for traction vehicles and carriages (for instance push-pull bar, Watt’s quadrilateral, etc.). The force elements (i.e. the two suspension stages and the bump-stop) have been modelled by means of force elements such as springs and dampers, with opportunely defined non-linear characteristics (due to this the default Simscape elements have been modified introducing lookup tables with real component behaviours). The primary suspension stage is constituted by an axle box with one of its oscillating arms attached to the bogie frame by means of a rubber element (sutuco) while the other arm is linked to the frame with a damper oriented vertically. The upper part of the axlebox is the base for a shear spring, which represents the elastic element of the primary suspension. The secondary suspension stage consists of a pair of air spring: usage of air spring permits better performances in terms of comfort and the possibility to control spring characteristics by means of the pneumatic system acting on it. Concerning motion resistance, the authors considered the contribution of the rolling resistance (a strongly limited value) through the contact model that has been employed and the resistant contribution due to the track slope directly from the combination of the Multibody model and track generation. Estimating some further resistant contributions such as the cushion friction and the aerodynamic resistance, a longitudinal force has been applied at the centre of mass of the coach. The overall resistance is modelled according to a second order polynomial function of the longitudinal speed (the resistant forces have a quadratic trend as to the rail vehicle velocity): the coefficients of this polynomial are estimated under the data available in literature [15] [17]. In order to carry out some straight stretch tests, the motion resistances corresponding to the presence of towed vehicles can be modelled in a completely similar way, so you can just spare the Multibody modelling of the whole train. The relative resistant concentrated force is applied just next to the driving hook which is located in the rear of the front rail vehicle: this way the longitudinal dynamics of a whole train is rebuilt, with the consequent locomotive pitch phenomena (coach load transfer and bogie load transfer). Briefly the front rail vehicle is modelled as a Multibody vehicle, while the remaining part of the train and the motion resistances of the front rail vehicle are modelled with a concentrated longitudinal force (lumped system). 2.3 BRAKING SYSTEM AND WSP Since the necessary sensor set for the rail vehicle location implementations is typically located in the front vehicle cab (rail vehicle modelled in Multibody environment), during a braking manoeuver simulation the typical braking delays which are connected to the train length can be neglected (the train vehicles get the starting braking signal with a delay which is nearly proportional to the distance from the front locomotive). This remark stands both in consideration of an electro-pneumatic braking plant [18] and in case of a pneumatic plant [19]. The braking plant modelled in Matlab-Simulink is just of pneumatic type. Moreover the authors have modelled a WSP system intervening if the axle slips increase too much; the locomotive is usually in front of the train and consequently its wheels find a rail

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which is statistically dirtier than the one which is found by the towed rail vehicles and therefore the available adhesion is lower. In the pneumatic plant (you can see its elementary layout in Figure 2) there are two electromagnetic valves directly modulating the pressure in the brake cylinder: the electromagnetic bleed valve EVS causes a pressure decrease in the brake cylinder, connecting it to the atmosphere through a calibrated orifice, the electromagnetic back pressure valve EVR causes the increase of the braking pressure connecting the brake cylinder to the distributor through a calibrated orifice.

Figure 2 – Simplified scheme of the pneumatic braking plant

WSP system dynamically modulates the braking torque that is applied on each axle with the aim of avoiding the axle skid and using the available adhesion as much as possible. In order to estimate the adhesion loss state during the braking manoeuver the vehicle longitudinal velocity, called reference velocity is needed; the logic of the anti-skid system used offers the chance to plan a periodic brake release of one of the four axles to guarantee that at least one of the four linear velocities of the axles is nearly close on the effective longitudinal speed of the vehicle. Usually adhesion losses are estimated by comparing recorded axle speeds and accelerations with the corresponding reference values; the system tries to keep the slip of each axle in an optimized interval that is variable according to the speed value. In the simulation environment four braking axles and a pair of EVR/EVS valves for every axle were modelled. The working logic of the implemented WSP system causes the activation of the two electromagnetic valves EVR and EVS according to three possible stages: the pressure increase in the brake cylinder (braking), the pressure preservation (tube plug) or the pressure decrease (loosing pressure). Two different time constants have been planned for the description of the dynamics response of EVR and EVS electromagnetic valves. Besides the distributor has a different timing response according to its filling or emptying. Both the distributor and the EVR and EVS valves are modelled as first order systems, characterized by two different time constants (which fix the typical dynamic response of a pneumatic system): one at the pressure increase stage and the other one at the pressure decrease stage. The series of these dynamics causes the law of the brake cylinder filling/emptying and consequently the effective braking (as shown in the simplified diagram in Figure 3).

Figure 3 – Working logic of the pneumatic plant and of the implemented WSP system

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In the scheme in figure 3, is the control pressure at the bottom of the pneumatic distributor, and are the time constants of the distributor, respectively in course of pressure increase (loading) and decrease (unloading) stage, is the distributor output pressure, the logic state 1 represents the activation of the electropneumatic valve, is the reference pressure, and are the time constants of the electromagnetic back pressure valve EVR and of the bleed valve EVS and at last is the effective pressure of the braking cylinder which sets out the mechanical braking action. For further explanations you can also see [20]. Moreover a variable clamping effort as a function of the rail vehicle velocity can be set out, an effort depending on the typology of the considered braking gaskets (characterized by the trend friction factor-velocity) [21]. 2.4 TRACTION AND ANTI-SKID SYSTEM Concerning the traction plant modelling, the following simplifying hypotheses are considered: the torsional dynamics of the transmission system is omitted, the electrical time constants of the system are considered much smaller compared to the mechanical ones, the rotational inertia of the engine is reduced to the axle. Simulations are carried out considering that the vehicle axles (with wheel-andaxle set Bo-Bo) are independent both from the mechanical point of view and the electrical one; practically you consider four power independent groups formed by electrical driving gear-mechanical transmission-axle (previous researches were carried out in order to study the effects of the mutual interaction of parallel connected induction motors [22]). The torque is therefore directly applied to the axles: the inertia of the single axle is properly increased to consider the reduced inertia value of the transmission system (engine, reduction gear, etc.). The group engine-reduction gear-axle can be studied referring to the only axle velocity, introducing the inertia equivalent value (reduced inertia); for instance to calculate the engine reduced inertia related to the axle rotation axis, the following kinetic energy equivalence relation is used: (1) where J is the moment of inertia of the engine, represents the reduction ratio, that is the ratio between the engine angular velocity and the axle one . The torque value applied to every single axle is properly modulated by the on board anti-skid subsystem, limiting the axle creepages under low adhesion conditions. Obviously the wheel-rail contact is characterized by rather low adhesion coefficients. Moreover as the electric locomotive is the first carriage (at the head of the train), the locomotive wheels find a rail which is statistically dirtier than the one which is found by the drawn carriage, and in case of dirty contact surfaces the available adhesion is obviously lower. The anti-skid aim is to regulate in real time the braking torque in order to keep the slips within tolerable limits, avoiding high axle slips and consequently wear and overheating of the rolling surfaces. The anti-skid system calculates the rail vehicle longitudinal velocity (reference speed) and on the basis of this one it modulates the engine torque, whenever the axle creepage is identified: the evaluation of the slip stage occurs according to an accelerometric principle and a tachometric one (in a few words, comparing the reference values with the one the sensors placed on the axles have measured). The traction torque is taken away, in case of slip, and afterwards given back, when the slip stops, according to suitable laws. 2.5 ABOUT ADHESION Testing and calibrating location algorithms involve the simulation of degraded adhesion conditions. The contact forces were calculated using a wheel-rail contact model developed during previous researches [12]. In this model, forces are calculated according to Kalker non-linear theory: the creep forces were saturated using the modified Johnson-Vermeulen formulation suggested by [23]. As regards tests made in degraded adhesion conditions the authors implemented, inside the contact model, an adhesion law with the addition of an hysteretic cycle to the classical friction law of Coulomb’s model (with a transition from the static adhesion coefficient to the kinematics one). More specifically, when low adhesion conditions occur, longitudinal and lateral contact forces coming from Kalker’s non-linear theory are corrected (according to (2)) with a multiplicative coefficient that is a function of the relative creepage .

√

} 6

(

)

(2)

where

is the total creep force. The creep relative slip

(3) is defined as:

√

}

( )

(3)

where and are respectively actual and pure rolling forward velocities, and and are actual and pure rolling lateral velocities. The correction factor , which realizes the transition between static and kinematical friction factor, is defined according to (4): ̇

{ (4) ̇

(

)

Where is the value of corresponding to the maximum adhesion value, is the kinematical friction reduction factor, is an exponential slope factor, is the force saturation coefficient used inside Kalker non-linear theory (according to [23]) and dt is the integration interval. In order to reproduce a hysteretic behaviour of the adhesion, the dependence from creep time derivative has been added. Figure 4 shows the corresponding behaviour of the contact force , during a typical cycle due to a loss and subsequent recover of adhesion.

Figure 4 – Contact force behaviour during a loss and subsequent recover of adhesion

The exact estimation of the effective state of the adhesion coefficient is quite difficult, because of its dependence on several parameters; particularly the interaction of the two contact rolling surfaces is influenced by the presence and the nature of the contamination between them: it is just the contamination which causes conditions of low adhesion. Substantially there is a lack of a stable theoretical background for high degraded adhesion conditions; that’s why the authors have followed heuristic models based on experimental results and common sense engineering considerations [10] [24] [25] [26] [27] [28] [29]. These studies show how the available adhesion during a loss phase is different from the subsequent recover phase. In the original contact model [12] the saturation proposed by [23] is applied only to creep forces, as spin torques are considered near to negligible terms; in case of heavily degraded adhesion conditions an unsaturated calculation of the spin torques will lead to results that are quite unrealistic since computed spin torques become equal or higher than creep forces which are limited by the saturation coefficient. In real conditions when macro-slip occurs, the spin torque is expected to be null or negligible. Since the proposed model was devoted to the simulation of much degraded adhesion conditions the spin torques have been neglected. 3 ACHIEVED RESULTS As regards the generation of synthetic signals, a family of relatively short simulations has been detected in order to make computation on more workstations and processors faster and easier. The intention is to carry out tests about relatively short tracks, but they have to be individually significant (in order to reproduce typical running situations), to build some “modules” which can be settled the one with the other (assisted if necessary by an appropriate interpolation and filtering) to form the desired course. Some arbitrarily elaborate tracks (as regards length, characteristics of the track drawing, adhesion and running conditions) can consequently be produced by combining the results corresponding to the “elementary” track simulations; this operation can be directly made in a post-

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processing stage. This way time consumption is reduced since the computational effort is distributed on a limited set of shorter simulations; the combination of the different elementary simulations enables anyway to get the desired rail track geometry and the desired real conditions. Figure 5 shows the results of a braking simulation in degraded adhesion conditions on a straight and level rail track, without any irregularity; the vehicle has initially a longitudinal speed and after a brief stretch of coasting it’s braked up to a complete stop. Because of the conditions of degraded adhesion the profiles of the peripheral speed of the axles don’t match the speed profile of the rail vehicle (the axles creep). The WSP system sets a limit for the axle slips, avoiding their locking (down to low speeds); the relative slips are kept around values.

Figure 5 – Longitudinal speed profiles of a braking simulation in degraded adhesion conditions

Hereunder figure 6 shows the corresponding odometric results got through SCMT algorithm (that is using only 2 GITs as sensors) [5]. In figure 6 the velocity error is shown, which is defined according to (5): (5) where

is the estimated speed of the train and

is the real speed (measured on the coach).

60

3

2

Velocity error [m/s]

Longitudinal speed [m/s]

50 40 30 20 10 0 -10 0

True Velocity Wheel Velocity Axle 2 Wheel Velocity Axle 3 SCMT

500

1000

1500

1

0

-1

-2

2000

2500

-3 0

3000

ERTMS Requirement SCMT 500

1000

1500

2000

2500

3000

Space [m]

Space [m]

Figure 6 – Vehicle speed, GITs measurements and corresponding SCMT speed estimation. Velocity error calculated by SCMT odometry algorithm compared with corresponding ERTMS specifications

The reconstruction of the speed profile, and consequently the evaluation of the train position, suffers from errors that are rather high: these errors are caused by the low adhesion conditions (critical conditions for GITs). You can get definitely better results with location inertial-type algorithms using a 3D sensor set (accelerometers and gyroscopes). So the modelling of the only longitudinal dynamics of the rail vehicle (two-dimensional dynamic models), traditionally employed for a first setting-up of some odometric systems [6], is not enough anymore. On the contrary, for testing correctly these advanced algorithms, modelling in a complete way the 3D dynamics of the rail vehicle is important, in order to reproduce in a simulation the typical outputs of the 3D sensor set which has been employed. For instance, running a curve, the lateral accelerometer will measure the so-called non-compensated acceleration (given by the difference between the centrifugal effect and the gravitational one linked to the superelevation of the rail line [30]). The planned curve has, at a steady state, a 1800 curve

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radius and a superelevation ; in the connection tracks of the curve input-output these values change linearly (clothoid line). The rail vehicle runs the curve with a longitudinal speed. Figure 7 shows in red the lateral non-compensated acceleration, which is the lateral accelerometer output; this result is obtained in a simulation test thanks to the 3D multibody model of the rail vehicle (described on paragraph 2.2). The track is superelevated so that, in the plane of the track, the component of gravity (generated by the rail cant) will provide some fraction of the so-called “centrifugal lateral acceleration”; the resultant non-compensated lateral acceleration on the vehicle is given by (6): (6) Where is the running speed [ the track gauge [ ].

],

is the curve radius [ ],

Figure 7 – Lateral acceleration of a curve simulation with

is the superelevation [

] and s is

longitudinal speed

The theoretical value of the “centrifugal lateral acceleration” is about (this value represents the non-compensated lateral acceleration for the curve without cant). The theoretical value of the resultant non-compensated lateral acceleration is about . The difference between this theoretical value and the result of the simulation (that’s about ) has to be given to the carbody roll towards the outside of the curve (souplesse), tending to reduce the gravitational effect of compensation. As it’s shown in Figure 7, the lateral “non-compensated” acceleration value is positive and physically that means the passenger feels to be pushed towards the outside of the curve. As further example of the 3D simulation model, Figures 8-10 show the results obtained starting from the previous braking trial and applying some irregularity patterns to the track. Irregularities are applied as imposed displacements on the track. The authors considered the following types of irregularities:    

lateral irregularities: both rails have a lateral displacement perpendicularly to the original railway track; vertical irregularities: both rails of the track have vertical displacement; gauge irregularities: one rail is moved perpendicularly to the original railway track; cant irregularities: a superelevation is set rotating the track plane respect to an axis oriented along the track.

In Figure 8 you can see the reference path of lateral irregularity which has been employed: among the planned irregularities, the lateral ones have the highest size and lead to high values of imposed acceleration measured on the coach.

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Figure 8 – Lateral irregularity applied on the railway track

In simulations the referring irregularity patterns ( long) have been carried out in a periodic way for the whole length of the simulation. Figures 9 and 10 show the trends of the longitudinal and lateral acceleration in presence of irregularities. 0.3

0.2

Lateral acceleration [m/s2]

Longitudinal acceleration [m/s2]

0.4

without irregularities with irregularities

0 -0.2 -0.4 -0.6 -0.8 -1 0

20

40

60

80

0.2 0.1 0 -0.1 -0.2

-0.4 0

100

without irregularities with irregularities

-0.3

20

40

60

80

100

Time [s]

Time [s]

Figure 9 - Longitudinal acceleration of a braking simulation in degraded adhesion conditions (with and without irregularities)

Figure 10 - Lateral acceleration of a braking simulation in degraded adhesion conditions (with and without irregularities)

The longitudinal acceleration profile is affected by “noise” in the rail stretches that are interested to irregularities. The lateral acceleration trend is the one which more differs from the trend of the trial in absence of irregularities, coherently with the imposed irregularity patterns: the lateral accelerometer will be subject to “disturbances” just next to the irregularity stretches. The 3D rail vehicle modelling allowed testing the INS-type location algorithm [31] by getting results which are definitely better compared to SCMT. In figure 11 the results of the braking test (previously analyzed with SCMT algorithm) are shown: it should be noted that the speed estimated error is decidedly lower and this brings advantages as regards the train localization and consequently for the railway safety. 60

2 1.5 1

Velocity error [m/s]

Longitudinal speed [m/s]

50 40 30 20 10

True Velocity Wheel Velocity Axle 3 INS/GIT

0 -0.5 -1 -1.5

0 -10 0

0.5

ERTMS Requirement INS/GIT

-2 500

1000

1500

2000

2500

-2.5 0

3000

Space [m]

500

1000

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Space [m]

Figure 11 - Vehicle speed, GIT measurement and corresponding INS localization algorithm speed estimation. Velocity error calculated by INS localization algorithm compared with corresponding ERTMS specifications

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Lastly Figure 12 shows the results obtained analyzing with SCMT and INS location algorithm a more complex rail track: a straight railway which is about long, with slope and descent stretches with a ±30/1000 gradient, characterized by mixed adhesion conditions (good adhesion stretches alternated to degraded adhesion ones). 60

6 5

ERTMS Requirement SCMT INS-ODO

4

Velocity error [m/s]

Longitudinal speed [m/s]

50 40 30 20 10

True Velocity Wheel Velocity SCMT INS-ODO

0 -10 0

0.5

1

Space [m]

3 2 1 0 -1 -2 -3

1.5

-4 0

2

0.5

1

Space [m]

4

x 10

1.5

2 4

x 10

Figure 12 - Vehicle speed, GIT measurement and corresponding SCMT and INS algorithm speed estimation. Velocity error calculated by SCMT and INS algorithm compared with corresponding ERTMS specifications

The results obtained with INS localization algorithm respect, more than satisfactorily, ERTMS requirements [1] [2] [3] [4]. CONCLUSIONS AND FUTURE DEVELOPMENTS The availability of a complete three-dimensional model able to reproduce complex interactions among on board safety relevant subsystems is an important instrument for the preliminary design and calibration of innovative odometry and localization algorithms. The application of this kind of models can be extended to HIL testing of safety relevant on board subsystems: reliable offline testing of train position and speed estimation methods by means of 3D real-time train dynamic simulation may significantly reduce time and cost of the development and tuning of new on board systems. Further activities will be carried out in order to improve the following aspects:  

Real-time implementation on a multiprocessor system for the development of an HIL testing platform; Further improvement and validation of wheel-rail adhesion models.

REFERENCES [1] [2] [3] [4] [5] [6]

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