RAILWAY VEHICLE RESPONSE UNDER RANDOM … · 2018. 7. 30. · the equivalent conicity is shown in...

http://iaeme.com/Home/journal/IJMET 944 [email protected]

International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 7, July 2018, pp. 944 956, Article ID: IJMET_09_07_101 –Available online at http://iaeme.com/Home/issue/IJMET?Volume=9&Issue=7 ISSN Print: 0976-6340 and ISSN Online: 0976-6359

© IAEME Publication Indexed Scopus

RAILWAY VEHICLE RESPONSE UNDER RANDOM IRREGULARITIES ON A TANGENT

TRACK NONLINEAR 3D MULTI-BODY –MODELLING

Mohammed TOUATI, Nouzha LAMDOUAR and Azzeddine BOUYAHYAOUI GC Laboratory, Mohammadia Engineering School,

Mohammed V University, Rabat, Morocco

ABSTRACT Safety and ride comfort are the main issues in railway industry that have to be

harnessed and well controlled, especially when the operating speed is increasing continuously. Actually, many studies are performed in that matter in order to assess

the risks of derailment of a railway vehicle and determine the level of exposure of passengers to the mechanical vibrations. However, the assumptions made turned out to be often inadequate, especially when it comes to consider that the lateral movement of the wheel-axle set adhere perfectly to the transversal track irregularities.

Our study is presenting the results of a dynamic 3D-modelling of a full railway vehicle, and comparing its response when exposed to the track disturbances with real measurements performed in each part of it.

To that end, 27 degrees of freedom are describing the vibration of each part of the vehicle. The simulation is carried out by Matlab. Regarding the rail/wheel contact

issue, we have needed to adopt the linear theory of rolling contact developed by Kalker to estimate the creep forces. Moreover, the rail/wheel contact geometry is

evaluated according to UIC 519 leaflet which gives an approach that allows us to summarize the contact area to a conical wheel on a knife-edged rail. The angle of such wheel is named equivalent conicity and depends on the rail profile, the wheel profile, the rail cant, the track gage and the initial lateral displacement. A computer

based-program is developed with Matlab to determine this parameter and it’s validated according to the recommendations of the leaflet mentioned earlier.

On the other hand, track irregularities are measured using an inertial measurement unit (IMU) which has the advantage to provide the accurate track

parameters defined in the standard EN 13848-1. This system was validated according to the recommendations of the standard 13848-2.

Finally, the results are compared in the frequency domain to the vibrations measured on a vehicle travelling over the track considered in our simulation and show the effectiveness of the proposed model.

Railway Vehicle Response under Random Irregularities on A Tangent Track Nonlinear 3d –

Multi-Body Modelling


Key words: Railway Vehicle, Dynamic 3D-Modelling, Equivalent Conicity, KALKER Theory, Track Irregularities, Train Vibrations.

Cite this Article: Mohammed TOUATI, Nouzha LAMDOUAR and Azzeddine BOUYAHYAOUI, Railway Vehicle Response Under Random Irregularities on a Tangent Track Nonlinear 3D Multi-Body Modelling, – International Journal of Mechanical Engineering and Technology 9(7), 2018, pp. 944 956. –

http://iaeme.com/Home/issue/IJMET?Volume=9&Issue=7

1. INTRODUCTION Various researches have been performed in order to predict the effect of track irregularities on the behavior of a railway vehicle. However, the focus has mostly been given to the vertical

response as long as it’s mainly related to the loads communicated to the substructure. Therefore, the one-dimensional modelling of the system was widely used.

Kouroussis and Verlinden [1] discussed the vertical behavior of French railway vehicles under empiric track unevenness spectrum. The wheel/rail contact problem was resumed to a Hertzian spring assembling these two bodies in the vertical direction. Lee and Cheng [2] took

into account the lateral displacement by using a truck model of 10 degrees of freedom, including the linear creep model. However, they assumed that lateral displacement of the

wheel adhere to the transversal unevenness of the track and that creep factors remains constant despite of the variation of the wheel/rail contact area according to the wheel-axle set lateral displacement. Sezer and Atalay [3] studied a 54 degrees of freedom model of a Turkish locomotive using the same assumptions as Lee and Cheng. Xu and Zhai [4] developed a 3D model of the train/track system including the Hertzian elastic contact in the normal direction,

and creep forces in the tangential direction calculated by the use of Kalker’s linear theory. Still, wheel/rail contact geometry wasn’t taken into account.

This paper aims to highlight the lateral behavior of a wheel-axle set governed by the wheel/rail contact geometry and creep forces on a perfect tangent track. Then, the full

dynamic behavior of a railway vehicle under recorded track irregularities will be discussed and compared to experimental data.

2. WHE -AXLE SET BEHAVIOR ON A TANGENT TRACK EL The main purpose of this section is to develop an analytical model of the wheel-axle set

(fig.1) where the equations of its motion will be presented. Certainly, the creep forces will be involved as well as the geometry of rail/wheel contact which depends on their profiles.

Figure 1 Wheel-axle set characteristics

The wheel and rail profiles (wide-spread in Moroccan substructure) used in this simulation are 54E1 (fig.2) and S1002 (fig.3), respectively. These profiles are defined in the standards EN 13674-1 and EN 13715+A1.

Mohammed TOUATI, Nouzha LAMDOUAR and Azzeddine BOUYAHYAOUI


Figure 2 54E1 Rail profile from EN 13674-1 S1002 Wheel profile from EN 13715+A1 Figure 3

We assume that vertical movements of the wheel-axle set adhere perfectly to the vertical track irregularities. Therefore, 3 degrees of freedom are taken into account in that study which is the lateral displacement y, the roll angle Φ, and the yaw angle ψ.

2 Linear Theory .1. Kalker’s

Kalker’s linear creep theory [5] is widely used in railway vehicle dynamics as far as it concerns determining the lateral stability. It’s based on assuming that the contact area, whose

shape and size are defined by Hertz’s static solution, is covered by the entire zone of adhesion. Therefore, the creep forces are given by

Where ζx, ζy , and ζsp are longitudinal, lateral and spin creepages, respectively. They are

given by

That is

Where V is the speed of the wheel-axle set and Ω is the angular velocity of the wheel.

The creep coefficients f11, f12, f22 and f33 are defined by Kalker as

Where a and b are the semi axis of the Hertz’s contact ellipse in rolling direction and lateral direction, respectively. G is the modulus of rigidity. Finally, Cij are creepage and spin coefficients which depend mainly on Poisson’s ratio and the ratio a/b.




Obviously, the creep forces vary on each step of lateral and longitudinal displacements as long as the size of Hertz’s ellipse depends on the rail and wheel profiles at the contact point, and the normal force that fluctuate due to track geometry in the vertical direction. Therefore, creep forces have to be computed on each problem resolution step.

2.2. Wheel-Axle S Equations of Motion et Under creep forces, the weight of the wheel-axle set and by using the position vectors, the simplified lateral, roll and yaw equations of motion of the wheel-axle set could be written as

Where e is the half distance between the rail/wheel contact points.

The rail/wheel contact angles and radiuses are nonlinear functions of the lateral displacement y. Therefore, the wheel-axle set equations are also nonlinear. The figures below show the variation of these angles and radiuses at nominal track gage and nominal rail cant (which are equal to 1435 mm and 2.86°, respectively, in Morocco) when the wheel-axle set is moving laterally.

Figure 5 Rail/wheel contact points according to lateral displacements y



Figure 6 Normalized rolling radiuses difference between left and right contact points according to lateral displacement y

Figure 7 Contact angles according to lateral displacement y

The UIC 519 leaflet propose an approach where the rail/wheel contact geometry can be simplified to a conical wheel on a knife-edged rail in tangent tracks. The angle of that wheel is called equivalent conicity.

In that matter, a computer based-program is developed with Matlab to calculate this parameter. The UIC 519 leaflet recommend also to validate the method of calculation applied by using reference profiles of rail and wheel. The results of calculations have to be within the tolerances defined in the leaflet.

The following figures show the results of that program validation.

Figure 8 Figure 9 Equivalent conicity program validation test 1– Equivalent conicity program validation test 2 –




Figure 10 Figure Equivalent conicity program validation test 3 – 11 Equivalent conicity program validation test 4 –

Figure Figure 12 Equivalent conicity program validation test 5 – 13 Equivalent conicity program validation test 6 –

Figure 14 Equivalent conicity program validation test 7 Equivalent conicity program validation test 8 – Figure 15 –

Figure 16 Equivalent conicity program validation test 9 –

It’s clear that the computer based-program satisfy entirely the recommendations of UIC 519 leaflet.



We assume, for numerical applications, the wheel-axle set characteristics listed in the table below.

Table 1 Characteristics of Wheel-axle set V (km/h) r0 (m) mw (kg) Iwx (kg.m²) Iwy (kg.m²) Iwz (kg.m²) e (m) 160 km/h 0.445 2000 980 84 980 1.5

In the case of rail and wheel profiles taken into account in this study and defined earlier, the equivalent conicity is shown in the figure below (fig. 17) for nominal track gage and track cant.

Figure 17 Equivalent conicity program validation test 9 –

Table 2 Equivalent conicity according to lateral displacements for S1002 wheel and 54E1 rail profiles y (mm) Eq. conicity y (mm) Eq. conicity y (mm) Eq. conicity y (mm) Eq. conicity

0 0 1.6 0.009530205 3.2 0.010196578 4.8 0.010979198 0.2 0.008735159 1.8 0.009681145 3.4 0.010295043 5 0.011095375 0.4 0.009319714 2 0.009917 191 3.6 0.010448651 5.2 0.019561548 0.6 0.00942403 2.2 0.009999693 3.8 0.01053617 5.4 0.039177002 0.8 0.009459827 2.4 0.010051295 4 0.010610161 5.6 0.053426332 1 0.009479378 2.6 0.010090878 4.2 0.010678528 5.8 0.097229848

1.2 0.009495318 2.8 0.010126125 4.4 0.010744808 6 0.138239707 1.4 0.009511739 3 0.010160719 4.6 0.010810919 6.2 0.173454302

As a consequence to that simulation, we get

Figure 18 Conical wheel-axle set on a knife-edged rail

We also assume that, for small lateral displacements, the creep coefficients may be written as

Therefore, the wheel-axle set equations of motion could be simplified to




The resolution of these equations shows that wheel-axle set movement is sinusoidal if it’s excited by a lateral initial displacement even if it’s travelling on a perfect tangent track, and

may derail if creep forces are taken into account.

The derailment is estimated through the ratio Y/Q where Y is the sum of lateral loads, and Q is the sum of vertical loads. Therefore, the derailment occur when that ration exceeds 1.

The figures below show the wheel-axle set behaviour under an initial lateral displacement equal to 5 mm.

Figure 19 Figure Wheel-axle set lateral response Null creep forces – 20 Wheel-axle set lateral response under creep forces

3. TRACK IRREGULARITIES AND VEHICLE MODEL After establishing the equations of movement of a wheel- te axle set, it’s proposed to incorporathem in the full vehicle behaviour system of equations by modelling it as a multibody system, and taking into account the source excitation represented by track geometry.

3.1. Track Irregularities Description Track unevenness is recorded in Morocco through a measuring car named EM120 (fig.21).

Since 2014, It has been equipped by an IMU (Inertial Measuring Unit) system that may provide an accurate recorded track geometry if it fills the recommendations of EN 13848-1 and EN 13848-2 standards. This technic of geometry measuring replaced the 5m-5m chord

based track measuring system whose transfer function modify the real track geometry. It’s given by

Where λ is the track defect wavelength, L is the chord length and α is indicating the position of measuring point.

In the opposite, the gain of the IMU transfer function is equal to 1 and the signal can be filtered in any wavelength range. The figure below (fig.23) compare 5m-5m measuring chord transfer function with IMU transfer function in the wavelength range [3m 25m]. –



Figure Figure 21 Moroccan geometry measuring car EM120 22 Inertial measuring unit (IMU)

Figure 23 Transfer functions of IMU and 5m-5m measuring systems

The parameters taken into account in this study are shown in the figure below.

Figure 24 Geometry track parameters Figure 25 Recorded geometry signals

If track gage impacts equivalent conicity parameter and wheel vertical displacement adhere perfectly to track levelment as it was assumed before, superelevation and alignment will be involved in the lateral dimension of vehicle equations of motion.

In this study, the track recorded and taken into account is located between Casablanca and Settat (53+250/55+000). The alignment and levelment signals are filtered in the wavelength range [3m 70m – ].

3.2. Railway Vehicle Model The railway vehicle used in this study is named Corail with an Y32 wheel-axle set. The model consists on one car body, two bogies and a total of four wheel-axles set.




Figure 26 Railway vehicle model

3.3. Position of Accelerometers in the Vehicle (Experimental Measurement) In order to validate the model, an experimental measurement was realized to determine the accelerations in several positions of the vehicle. In this study, we will consider the recorded

data of the accelerometers placed in the wheel-axle set (left wheel), bogie and the compartment located in the middle of the car body.

Figure Figure 26 Corail car acceleration sensors positions : 26 Wheel-axle set and bogie implemented by sensors

The speed of the vehicle measured in the area (53+250 / 55+000) is constant and equal to 114 km/h. However, the track profile isn’t a perfect alignment. Thanks to high rates of

radiuses in that area, we may consider that curves are similar to very long wavelength defects. As a consequence, an important spectral density will be noticed in very low frequencies of

experimental data that will be ignored in this study as long as the track measurement is limited to 70m wavelength.

Figure 27 Vehicle speed in experimental acquisition data



4. RESULTS AND DISCUSSI ON The aim of this chapter is to validate the model described earlier through comparing the

results of the simulation with experimental data. To that end, we assume that the rail and the wheel profiles are similar to the theoretical profiles described earlier.

As long as the sampling frequency isn’t the same as far as it concerns experimental and

calculated data, this comparison will be restricted to spectral density of the signals. Both signals will be filtered according to a low-pass filter with a cut-off frequency equal to 10 Hz.

4.1. Lateral Movement of the Vehicle Components 4.1.1. Wheel-Axle Set Lateral Movement

We can easily notice 2 peaks in the experimental data spectral density corresponding to 1.05Hz and 4.93Hz, respectively. If we don’t take into account the first frequency caused by

high wavelength defects as mentioned earlier, the second frequency is almost equal to the one corresponding to the peak of calculated signal (4.38Hz).

Figure 28 Figure 29 Lateral wheel-axle set movement experimental data – Lateral wheel-axle set movement model results –

In other words, the behaviour of the wheel-axle set is near harmonic. This behaviour has been observed in a video recording of wheel-axle set motion. 4.1.2. Bogie Lateral Movement

Similarly to the wheel-axle set, the bogie shows also a near harmonic behaviour at a frequencies equal to 4.30Hz and 4.67Hz for model results and experimental data respectively (we don’t consider low frequencies corresponding to high wavelength track defects).

Figure Figure 30 Lateral bogie movement experimental data – 31 Lateral bogie movement model results –

4.1.3. Car body Lateral Movement For the car body, the lateral movement is impacted by suspensions shape. Therefore, the peak in the spectral density noticed for low frequencies is directly related to stiffness and damping values taken into account.




Figure Figure 31 Lateral car body movement experimental data – 32 Lateral car body movement model results –

4.2. ical Movement of the V Components Vert ehicle If we assume that the wheel-axle set movement adhere perfectly to the track levelment

defects, the bogie and car body behaviours depend on the suspensions shape. 4.2.1. Bogie Vertical Movement

Figure Figure 3231 Vertical bogie movement experimental data – Vertical bogie movement model results –

We can clearly notice a peak at 4.78Hz and 4.30Hz in in experimental data and model results, respectively. Therefore, the stiffness and damping values taken into account in our study can also be validated. 4.2.2. Car Body Vertical Movement

Figure 31 Vertical car body movement experimental data Vertical car body movement model results – Figure 32 –

Similarly, a spectral density peak is spotted at 1.26Hz and 1.10Hz for experimental data and model results respectively, which validate the suspensions model adopted in this study.

5. CONCLUSIONS Based on the results of experimental data and the model analysis studied in order to determine the behaviour of a railway vehicle in each part of its components, the following conclusions can be drawn



The lateral movement of wheel-axle set can’t be resumed to a perfect adherence with track

lateral defects as long as it’s massively influenced by the creep forces and the wheel/rail geometry contact. As a result, not only track alignment should be taken into account, but also rail and wheel profiles, track gage, track superelevation and rail cant parameters ;

Equivalent conicity parameter was involved in our study to simplify the model of wheel/rail contact geometry to a conical wheel on a knife-edged rail. A Matlab based program was

developed in that matter and was validated according to the recommendations of UIC 519 leaflet. The results of lateral movement validate the effectiveness of that model ;

The effectiveness of the model depends on reliable measured parameters as far as it concerns track geometry. In our study, track defects measured wavelengths was limited to 70m as long as the speed is limited to 114km/h. However, if the speed increases (especially for high speed tracks), the wavelength range of recorded track geometry should be larger.

This model can be applied in order to evaluate the ride comfort, to quantify the railway traffic loads, or to check a vehicle safety particularly if it’s rolling over a bridge shacked by an earthquake.

REFERENCES

[1] G. Kouroussis, O. Verlinden, Prediction of railway ground vibrations: accuracy of a coupled lumped mass model for representing the track/soil interaction, Soil Dynamics and Earthquake Engineering 69 (2015) 220-226.

[2] S. Lee, Y. Cheng, Hunting stability analysis of high speed railway vehicle trucks on tangent tracks, Journal of Sound and Vibration 2828 (2005) 881-898.

[3] S. Sezer, A. E. Atalay, Dynamic modelling and fuzzy logic control of vibrations of a railway vehicle for different track irregularities, Simulation Modelling Practice and

Theory 19 (2011) 1873-1894.

[4] L. Xu, W. Zhai, A novel model for determining the amplitude-wavelength limits of track irregularities accompanied by reliability assessment in railway vehicle-train dynamics,

Mechanical Systems and Signal Processing 86 (2017) 260-277.

[5] Kalker, Simplified theory of rolling contact, Mechanical and Aeronautical Engineering and Ship Building (1973) 1-10.

RAILWAY VEHICLE RESPONSE UNDER RANDOM … · 2018. 7. 30. · the equivalent conicity is shown in...

Documents

Transcript of RAILWAY VEHICLE RESPONSE UNDER RANDOM … · 2018. 7. 30. · the equivalent conicity is shown in...