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Simulation of vehicle–track interaction with flexible wheelsets, moving track models and field tests a

Nizar Chaar & Mats Berg

a

a

Division of Railway Technology, Royal Institute of Technology , Stockholm, Sweden Published online: 04 Apr 2007.

To cite this article: Nizar Chaar & Mats Berg (2006) Simulation of vehicle–track interaction with flexible wheelsets, moving track models and field tests, Vehicle System Dynamics: International Journal of Vehicle Mechanics and Mobility, 44:sup1, 921-931, DOI: 10.1080/00423110600907667 To link to this article: http://dx.doi.org/10.1080/00423110600907667

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Vehicle System Dynamics Vol. 44, Supplement, 2006, 921–931


Simulation of vehicle–track interaction with flexible wheelsets, moving track models and field tests NIZAR CHAAR* and MATS BERG Division of Railway Technology, Royal Institute of Technology, Stockholm, Sweden Vehicle–track dynamic interaction emerged as a key multi-aspect subject following the development in high-speed and high axle-load trains. In this context, wheelset structural flexibility and track flexibility are the two main factors that contribute to high frequency content of the wheel–rail forces and influence the vehicle–track damage. Appropriate wheelset and track flexibility models are hence of great importance in pertinent numerical simulations. The present study comprises vehicle–track dynamic simulations considering wheelset structural flexibility and advanced moving track models. Simulated wheel–rail forces are then validated against measured data. The effects of the wheelset structural flexibility and track flexibility on the wheel–rail forces are investigated in the frequency range 0–150 Hz. The influence of track modelling and pertinent data on the simulation results is particularly assessed through a set of moving track models. Measured track data, i.e. irregularities, roughness and flexibility support the simulations. It is confirmed that track flexibility with appropriate modelling and data is important when examining the vehicle–track interaction. In the present case study, the influence of wheelset structural flexibility on the lateral wheel–rail forces is quite significant too. Keywords: Vehicle–track interaction; Wheelset structural flexibility; Track flexibility; Wheel–rail forces; Measurements; Simulations

1.

Introduction

The recent decades witnessed major changes in the railway sector marked by the development of high-speed and high axle-load trains, as a result of which trains became an attractive and effective means of transportation. In return, ride comfort and stability, wheel–rail wear and fatigue and other phenomena originating from the vehicle–track dynamic interaction were affected by these changes. Although numerical simulations evolved as a fast and inexpensive tool for investigating the main sources and causes of the vehicle–track dynamic interaction, on-track measurements are still considered as most reliable for approval of vehicles under various ride conditions. Relevant standards, e.g. UIC518 [1], are formulated to regulate and monitor these measurements. Yet, these standards present some questionable topics requiring continuous and further review. The cut-off frequency of the low-pass filtered track forces and the wavelength interval for track irregularities are among these issues. In fact, the suggested wavelength interval in ref. [1] *Corresponding author. Email: [email protected]

Vehicle System Dynamics ISSN 0042-3114 print/ISSN 1744-5159 online © 2006 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/00423110600907667


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Figure 1.

N. Chaar and M. Berg

Measured dynamic vertical force at a wheel, low-pass filtered by 100 Hz (left) and by 20 Hz (right), [3].

is 3–25 m and the recommended cut-off frequency is 20 Hz which in turn cancels the high frequency content of the track forces (figure 1), and thus may be too forgiving with respect to wheel and rail damage. In this context, the wheelset structural flexibility significantly influences the vehicle–track interaction [2–7], and is contributing to high frequency content of the wheel–rail forces. The effects of the wheelset structural flexibility are usually investigated through numerical simulations using wheelset eigenmodes. Track flexibility and pertinent modelling play an important role [6, 8]. Although continuous track models, e.g. rails regarded as beams, are quite common, these models are complicated, have a large number of degrees of freedom (dof) and are hence time consuming. In contrast, the so-called moving track models have limited number of dof, are rather convenient for simulating long travel distances and are quite appropriate for a frequency range up to, say, 200 Hz. Vertical static track preloads can also be introduced in these models as well as the sleeper passing frequency effects. Moving track models are situated under each wheelset and follow the vehicle with the same speed. Examples of such models are described in section 4. The present study comprises vehicle–track simulations considering the effects of wheelset structural flexibility and advanced moving track models. Simulated wheel–rail forces are validated against measured ones in the frequency range 0–150 Hz. The influence of track modelling and pertinent data is particularly assessed through a set of moving track models. The credibility of this work is enhanced by using measured track data, i.e. irregularities, roughness and flexibility to support the simulations.

2. Vehicle and track under study 2.1 Vehicle The vehicle under study is a Swedish Rc7 locomotive (figure 2). It has two two-axle powered bogies; the primary suspensions consist of chevron springs and primary dampers are not included. The secondary suspensions consist of coil springs located between bolster beams and the carbody. Vertical and lateral dampers are also present as well as yaw dampers linking the carbody to the bogie frames. The total mass of the locomotive is 78 tonnes and its axle load is thus 19.5 tonnes. The top speed of the locomotive is 180 km/h.


Simulation of vehicle–track interaction

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Figure 2. Rc7 locomotive under study (left) and track under investigation (right).

2.2

Track

The track under investigation is a 780 long tangent track section which is located 5–6 km east of Sala. The rail is a Swedish BV50 (50 kg/m) with an inclination 1/30. The rails are mounted through Hambo fastenings to concrete sleepers while plastic rail pads, 4–5 mm in thickness, are fixed between the rails and the sleepers (figure 2). The sleeper distance is 0.65 m. The locomotive running speed on this track is 140 km/h, (39 m/s).

3. Track flexibility measurements 3.1 Aim and procedure A track section above a sleeper (figure 3) was selected along the tangent track and its dynamic properties were investigated. The measurements, which were carried out in late March 2005, aimed at investigating the vertical and lateral stiffnesses (flexibility) of the track section under different combinations of vertical static loads and vertical or lateral harmonic loads in the frequency range 0–200 Hz. Despite the fact that the dynamic behaviour of the track may vary between track sections, these measurements provide a general idea on the dynamic properties of the selected tangent track which in turn will serve as an input in the numerical modelling and simulations.

Figure 3. TLV undercarriage (left) and experimental set-up (right).

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The measurements were carried out using Banverket’s (Swedish National Rail Administration) track loading vehicle (TLV). The TLV is equipped with three hydraulic shakers: two acting vertically and one laterally (figure 3, left); each cylinder having a possible maximum force of 150 kN. The vertical static load on each of the rail heads (Fstat ) is superposed by a dynamic load acting either vertically on each rail head (Fzdyn ) or laterally on one rail (Fydyn ). The total vertical and lateral loads are expressed by equations (1a) and (1b). Fz (t) = Fstat + Fzdyn (t) = Fstat + Fzamp sin(2πf t)

(1a)

Fy (t) = Fydyn (t) = Fyamp (1 − cos(2πf t))

(1b)

Here, the dynamic load amplitudes (Fzamp , Fyamp ) depend on the excitation frequency (f ) and are chosen with respect to the shakers’ limitation. Two vertical static preloads of 50 and 90 kN per track side were selected. For each vertical preloading, two harmonic excitations with different amplitudes were applied either vertically or laterally. The dynamic amplitudes for the vertical excitations, expressed as the percentage of the maximum capacity of the shakers, were 90% and 50%, whereas for the lateral excitation the dynamic amplitudes were 25% and 45%. The track response was measured through accelerometers placed on the rail heads and also on the sleeper for the lateral excitations (figure 3, right). In total, eight accelerometers were placed to measure the vertical and lateral accelerations on both rail heads and the lateral acceleration at one sleeper end. 3.2 Vertical and lateral receptances By also double-integrating the accelerations above, we arrive at the quantities illustrated in figure 4. The dynamic behaviour of the track is then described in terms of track receptance. Vertical and lateral track receptance or flexibility per rail side (αz , αy ) are defined by equations (2a) and (2b). αz (f ) =

z(f ) Fzdyn (f )

(2a)

αy (f ) =

y(f ) Fydyn (f )

(2b)

where f is the frequency in Hz and z(f ) and y(f ) represent the vertical and lateral rail head displacements, respectively. Figure 5 shows examples of vertical receptance. The dynamic vertical stiffness is increasing with frequency and a resonance peak is noticed at around 90 Hz. Because of the nonlinear relationship between load and deflection, the track receptances are also dependent on the preload and on the dynamic loading amplitude. The preload effect is exemplified in figure 5a. For a given amplitude, the magnitude of the vertical track receptance decreases, i.e. the track stiffness increases, with higher preload. In contrast, the influence of

Figure 4.

Quantities for calculating vertical and lateral receptances.



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Figure 5. Vertical receptance per track side: preload dependence (left); dynamic load amplitude dependence (right).

Figure 6.

Lateral track receptance: preload dependence (left); dynamic load amplitude dependence (right).

dynamic amplitude on the vertical receptance is small in this case (figure 5b). The static vertical stiffness under 90 kN preload per track side and 50% amplitude is around 110 MN/m per side. The lateral receptance increases (i.e. the track stiffness decreases) in the frequency range 0–100 Hz, but is almost unaffected by the preload (figure 6, left). However, at the resonance frequency around 95 Hz the track is laterally stiffer under lower preload. The influence of dynamic amplitude on the lateral receptance is shown at frequencies above 110 Hz (figure 6, right). The lateral static stiffness at the rail head is around 65 MN/m. As for the lateral receptance at the sleeper, it is smaller for higher static preload and much smaller than rail head receptance (i.e. more stiff); the lateral static stiffness at the sleeper is around 250 MN/m. Furthermore, the lateral receptance at sleeper also shows a peak at 95 Hz which is relatively more damped (not shown here).

4. Track flexibility modelling 4.1

Moving track models

As explained in the introduction, moving track models are simplified track models with few dof and are convenient for simulating long travel distances. The track is situated under each wheelset and follows the vehicle (figure 7, left). The track is modelled as rigid bodies and its flexibility is introduced through linear springs and dampers. A set of moving track models,


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Figure 7.


Principle of moving track model under each wheelset (left); track model A based on ref. [9] (right).

which differs in terms of complexity and number of dof, was generated. Three different moving track models are described in this study (figure 7, right and figure 8). Track model A is based on the so-called ‘pe1’ model in ref. [9]. It has three masses and five dof, (figure 7, right), whereas track model B [10] and C comprise five masses and have seven and nine dof, respectively (figure 8). 4.2 Vertical and lateral receptances The track model data above are chosen by comparing the calculated vertical and lateral receptances, both magnitude and phase, to the measured ones in section 3. It is important to note that the masses and stiffnesses, etc. generally do not represent any physical correspondence in terms of track components; the given data in table 1 are selected so that the calculated receptances give a best match to the measured ones. The data selection of the track models was performed in two steps: first, the parameters influencing the lateral receptance were selected and kept constant while in the second step, the track vertical dynamics was studied. The parameters ky12 and ky2 represent static lateral stiffnesses measured at the rail and sleeper, respectively. The masses m1 and m2 and the damping values cy12 and cy2 are then selected to give a good match with measurements. In the vertical direction, the static stiffness kz12 is set

Figure 8. Track model B (left) [10]; track model C (right).

Simulation of vehicle–track interaction Table 1.


Model A Model B Model C

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Selected track data.

ky12 , cy12 (MN/m, kNs/m)

ky2 , cy2 (MN/m, kNs/m)

kz12 , cz12 (MN/m, kNs/m)



m1 (kg)

m2 (kg)

m3 (kg)

J (kgm2 )

75, 15 75, 15 75, 15

270, 40 270, 40 270, 40

110, 1700 – 1700, 100

– 115, 1700 100, 120

– 5600, 2000 5600, 5000

20 20 20

690 690 690

– 15000 15000

– 300 300

in model A then the damping value cz12 is selected. In models B and C, a new mass ‘level’ is introduced and the vertical stiffness and damping are split into two and three stiffnesses in series, respectively. In this way, improved vertical receptance can be obtained. Up to 80 Hz, the magnitude of the vertical receptance from model A agrees quite well with the measured one (figure 9, left). However, this model cannot capture the peak at 90 Hz. Vertical receptance from models B and C agrees fairly well with the measured one in the frequency up to 120 Hz. Above 120 Hz, model C yields better agreement with measurement. The calculated lateral receptances for the three track models are identical and agree well with the measured one (figure 10). The frequency spectrum is marked by a peak at 95 Hz.

Figure 9.

Calculated and measured vertical receptance: magnitude (left), phase (right).

Figure 10.

Calculated and measured lateral receptance: magnitude (left), phase (right).

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5. Track irregularities and roughness Track irregularity measurements were performed in September 2001 using Banverket’s measurements coach STRIX. The irregularity data were sampled for each 0.25 m. The selected wavelength interval for the vertical and lateral misalignments is 0.5–100 m. The short wavelengths were filtered through an eighth-order Butterworth filter. Cant and gauge misalignments are also included. Roughness measurements through axle-box vertical accelerations were carried out in October 2002. These data were sampled for each 0.01 m. The measured data were then filtered using special transfer functions in order to remove the effects of the wheelset and track flexibility. The wavelength interval considered in this study is 0.25–0.5 m. Hence, at a speed of 140 km/h, the maximum excitation frequency is about 150 Hz.

6.

On-track simulations and comparison with measurements

6.1 Introduction On-track simulations of the present case study were performed using the multi-body dynamics code GENSYS [9]. In the simulations, the carbody, bogie frames and bolster beams were modelled as rigid bodies with six dof each. The primary and secondary suspensions were modelled as springs and dampers connecting the wheelset to the bogie and the carbody to the bogie frames and bolster beams [3]. The wheelset structural flexibility was introduced at the wheelsets (of the leading bogie) through eigenmodes derived from a finite element model and validated against measurements [11]. The wheel–rail contacts are modelled as single contact points [3, 9]. The wheel–rail friction coefficient is set to 0.4. The sleeper passing is a function of the sleeper distance (l). In the moving track models, the sleeper passing effect is represented by decreasing the vertical stiffness and damping and the lateral stiffness when a wheelset is passing between any two sleepers according to equations (3a) and (3b):

a 2π s k = k0 1 − 1 − cos 2 l a 2π s c = c0 1 − 1 − cos 2 l

(3a) (3b)

where k0 is the vertical or lateral stiffness and c0 is the vertical damping at a sleeper, a is stiffness variations relative amplitude and s is the wheelset longitudinal position (with s = 0, l, 2l, . . . at sleepers). In this work, the vertical track stiffness and damping between two sleepers are assumed to be 70% of the track stiffness at sleeper (a = 0.3). The lateral stiffness between two sleepers is 80% of the stiffness at sleeper (a = 0.2). 6.2

New track flexibility data

The importance of track flexibility is highlighted by comparing simulated wheel–rail forces, using two sets of track data, to measured ones. The first set of data, ‘old data’, has been used in ref. [3], and was derived from common experience in this field, whereas ‘new data’ refers to the data obtained from measurements of section 3. Figure 11 shows the power spectral density (PSD) of the vertical (Q) and lateral (Y ) forces of the left leading wheel. The PSDs of



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Figure 11. Measured and simulated PSDs of Q-force (left) and Y -force (right) of the left leading wheel with old [3] and new data, using track model A.

the measured Q- and Y -forces (in black) are marked by a peak at 60 Hz, which corresponds to the sleeper passing frequency. For the Y -force, the measured PSD is marked by two more peaks at 80 and 130 Hz. The last peak which coincides with the first wheelset umbrella mode is exaggerated because of measurements errors. The introduction of the ‘new data’ (dark grey line) has led to a major improvement in simulated results for virtually the whole frequency range studied as compared to the ‘old data’ (light grey line). For the Y -force, the improvement in the simulated results is mainly noticed for the frequencies above 60 Hz where the simulated PSD holds, beside the sleeper passing frequency, the peaks at 80 and 135 Hz.

6.3

New moving track models

The importance of the track modelling is investigated here. Figures 11 (left) and 12 show the simulated PSDs of Q-force using track models A, B and C with ‘new data’. The level of the simulated Q-force using model B is somewhat larger in the frequency range 100–150 Hz (as compared to model A). Model C shows a fairly good agreement with the measurements and also the sleeper passing effect is well represented.

Figure 12.

Measured and simulated PSDs of Q-force of the left leading wheel using models B and C, ‘new data’.


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Figure 13. Measured and simulated PSDs of Q-force of the left leading wheel using models A and C, with ‘new data’ and including track roughness.

6.4 Inclusion of track roughness The inclusion of the track roughness increases the frequency content of the Q-force; hence, the corresponding PSD is larger for higher frequencies. Figure 13 shows PSDs of the measured and simulated Q-force using track models A and C and considering the track roughness. Simulated results using both modelsA and C now show very good agreement with the measured wheel–rail forces.

7.

Influence of the wheelset structural flexibility

The influence of the wheelset structural flexibility is assessed by comparing simulated results, using flexible and rigid wheelset models, to measured wheel–rail forces. The effect of this flexibility on the Q-force is not so significant in this case (not shown here). However, this effect is quite prominent in the Y -force. The simulated PSD of the Y -force agrees better with the measured one provided that the wheelset flexibility is included (figure 14). The introduction of the wheelset structural flexibility reduces the level of the PSD in the frequency range 20–40 Hz while it increases this level in the frequency range 60–100 Hz.

Figure 14. Measured and simulated PSDs of Y -force of the left leading wheel using model C; flexible (left) and rigid wheelset (right).



8.

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Conclusions and future work

This study examined the effects of the wheelset and track flexibility on the wheel–rail forces in the frequency range 0–150 Hz. The track flexibility influences the frequency content of the wheel–rail forces significantly. Hence, reliable track data and pertinent track modelling are two important factors when simulating and investigating different aspects of the vehicle–track dynamic interaction. Track roughness contributes to high frequency content of the vertical track force and its inclusion in the simulations is important when predicting various damage mechanisms. The wheelset structural flexibility influences the Y -force significantly, whereas its effect on the Q-force is small for this case study. Further work should include additional track flexibility measurements, also between two sleepers, to further reinforce the track modelling. Also the influence of wheelset and track flexibility on vehicle ride stability should be investigated. Dynamic studies of other vehicles and tracks in this context would be desirable. Acknowledgements The authors would like to express their gratitude for the financial support and the assistance they received from Banverket (Swedish National Rail Administration), Interfleet Technology, Bombardier Transportation, Green Cargo, SJ AB and SL (Stockholm Transport). They also thank Banverket for their help during the track stiffness measurements and Mr Ingemar Persson (DEsolver) for his appreciated assistance with the software GENSYS. References [1] UIC, April 2003, Testing and approval of railway vehicles from the point of view of their dynamic behaviour – Safety – Track fatigue-ride quality, UIC Code 518, (2nd edn). [2] Chaar, N., 2002, Structural flexibility models of wheelsets for rail vehicle dynamics analysis – a pilot study, Report TRITA-FKT 2002:23, ISSN 1103-470X, Division of Railway Technology, Department of Vehicle Engineering, Royal Institute of Technology (KTH), Stockholm. [3] Chaar, N. and Berg, M., Vehicle-track dynamic simulations of a loco considering wheelset structural flexibility and comparison with measurements, Journal of Rail and Rapid Transit, in press. [4] Bruni, S., Collina, A., Diana, G. and Vanolo, P., 1999, Lateral dynamics of a railway vehicle in tangent track and curve: tests and simulations. Vehicle System Dynamics Supplement, 33, 464–477. [5] Popp, K., Kruse, H. and Kaiser, I., 1999, Vehicle-track dynamics in the mid-frequency range. Vehicle System Dynamics, 31, 423–463. [6] Ripke, B., and Knothe, K., 1995, Simulation of high-frequency vehicle–track interactions. Vehicle System Dynamics Supplement, 24, 72–85. [7] Szolc, T., 1998, Simulation of bending-torsional-lateral vibrations of the railway wheelset-track system in the medium frequency range. Vehicle System Dynamics, 30, 473–508. [8] Andersson, C., 2003, Modelling and simulation of train-track interaction including wear prediction, PhD Thesis, ISSN 0346-718X, Department of Applied Mechanics, Chalmers University of Technology, Göteborg, Sweden. [9] DEsolver: GENSYS User’s manual, 2005. Available online at www.gensys.se. [10] Claesson, S., 2005, Modelling of track flexibility for rail vehicle dynamics simulations, Master of Science Thesis, TRITA AVE 2005:26, ISSN 1651-7660, Division of Railway Technology, Department of Aeronautical and Vehicle Engineering, Royal Institute of Technology (KTH), Stockholm. [11] Chaar, N. and Berg, M., 2004, Experimental and numerical modal analyses of a loco wheelset. Paper presented of the Proceedings of the 18th IAVSD Symposium on Dynamics of Vehicles on Roads and on Tracks, Vehicle System Dynamics Supplement, 41, 597–606.