SOME PRELIMINARY RESULTS IN SIMULATION OF INTERACTION BETWEEN A PUSHED TRAIN AND A TURNOUT 1
Nico Burgelman1, Zili Li1 and Rolf Dollevoet2 Railway Engineering, Faculty of Civil Engineering and Geosciences Delft University of Technology Stevinweg 1, 2628 CN Delft, the Netherlands 2 Asset Management Railsystems, Department of Civil Technology B4.09, ProRail, P.O. Box 2038, 3500 GA Utrecht, The Netherlands
[email protected]
Abstract When a train runs through a turnout very high lateral forces or high impact forces between the wheels and the switch blade or the frog may occur. This study examines the dynamic behavior of a train when it runs through a turnout. Traction does not only change the dynamic behavior of the wheelset on which it is applied but the dynamics of the whole train. Lateral forces in the coupler cause higher lateral wheel-rail.
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BACKGROUND
The interaction between trains and tracks is most violent at turnouts due to the complex geometry and structure. Improperly designed or maintained turnouts can cause discomfort to passengers, damage to cargo, or even derailment. Maintenance and reparation of turnouts are a major cost drive for many railways. In Switzerland approximately 25% of the annual maintenance budget goes to turnouts, which is about 1 billion Swiss Francs (730 million EUR) [1]. The costs for the maintenance of one turnout equal those of 300 to 500 m of plain track. Lateral train-track interaction force is high in turnouts due to the small curve radii. When a train consisting of a number of vehicles is pushed through a turnout, the couplers transfer lateral force between the vehicles. This may significantly increase lateral wheel-rail force. The high lateral force may lead to deformation of the control mechanism of switch, and lateral shift of the whole track. A deformed stretch bar of the control mechanism may lead to wrong positioning of switch blades. All these may result in malfunctioning of turnouts, causing wheel climb and subsequent derailment. Wear and head checking are the other common consequences of high wheelrail contact forces. There is a clear need for mathematical modeling of the dynamic interaction between trains and turnouts. Such model should be accurate enough to assess the contact forces, their consequences on turnout components and the associated derailment risk in order to achieve optimal design of turnouts and running gears of rolling stock. Such a model may also be employed to establish quantitative relationships between responses of train-turnout interaction and parameters of the train-turnout system, so that new and better methods for condition monitoring of turnouts can be developed by measurement of dynamic responses of trains or turnouts. This will facilitate preventive and predictive maintenance of turnouts. Mennsen and Kik [2] were among the first to deal with the numerical simulation of a rail vehicle passing through a turnout. Some of the most recent works in vehicle-turnout interaction has been done by Kassa and Nielsen [3] and Alfi and Bruni [4]. They simulated one vehicle coasting through a turnout and compared the results with measured data. Kassa and Nielsen modeled the turnout with flexible bodies; the vehicle was modeled as a bogie with linear primary suspension without secondary suspension. The loads on the bogie are derived from a simulation with GENSYS with limited track flexibility, with 5 degrees of freedom moving along with each wheelset. To the knowledge of the authors all the models in the literature have so far included only one vehicle coasting through a turnout. Work in train-turnout interaction seems still lacking. These may particularly be relevant when trains are pushed so that lateral wheel-rail forces increase. Grassie and Elkins [5] concluded that applying traction or braking has a significant influence on the curving behavior of the wheelsets on which the traction is applied. This paper presents some preliminary results of an investigation in modeling of train-turnout interaction. The focus will be on the effect of traction on the lateral wheel-rail force and on the effect of lateral coupler force on the curving behavior of the bogie. A train will be simulated numerically when it is pushed through a turnout. The model includes flexible turnout components such as the rail, the railpad and the ballast. An attempt will be made to identify the wheelsets that experience the highest contact force. For comparison the train will also be simulated when it coasts through the same turnout.
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MODEL
A double deck passenger car that is used nowadays on the Dutch rail network, and a UIC1:15 turnout with a radius of 725 m are modeled. Changing profiles of the switch blade and the crossing are accounted for. 2.1 Flexible turnout model The rails are modeled as flexible body. The eigenmodes are computed with a finite element software package and are imported into the model. Modes under 500 Hz in lateral and vertical bending and in torsion about the longitudinal axis are considered. The guiding rails are modeled as rigid bodies with a flexible connection to the stock rail. Sleepers are assumed to behave as rigid bodies that are allowed to move in vertical and lateral direction and rotate around an axis parallel with the track. The ballast and the sleeper pads are modeled as spring/dampers. The properties of the railpad and ballast are taken from [6]. 2.2 Vehicle model Each vehicle has 42 degrees of freedoms (dof): 6 dof for each of the wheelsets, the bogie frames and the car bodies. All major nonlinearities are considered in the primary and secondary suspension, including the friction dampers, the bump stops and the airsprings. The model has been validated by comparing the hunting wavelength obtained from simulations with wavelengths observed from wear patterns on the rail [7]. For the wheel-rail contact the FASTSIM algorithm is used. 2.3 Coupling of the coaches The VIRM vehicles are coupled with a Scharfenberg coupler. This kind of coupler does not transfer any yaw moment. It is modeled as a spring in series with a damper. Constant Backwards Differentiation Formula (C-BDF) is used with a timestep of 1 ms.
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SIMULATIONS
3.1 Single vehicle Figure 1 shows the total lateral force on the outer wheel of the first wheelset of a vehicle coasting through a flexible turnout. It is the sum of the lateral components of the creep force and of the normal contact force. When there is more than one contact points the force is summed over all of them. In Figure 2 the wavelet scalogram [8] shows the frequency content of the force in Figure 1.
Figure 1. lateral wheel-rail force on the outer wheel of the first wheelset of a vehicle coasting at 20 m/s through a flexible turnout
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Figure 2. Wavelet scalogram of the lateral wheel-rail force of the first wheel of the vehicle coasting at 20 m/s through a turnout. The vehicle starts on a rigid straight track, all forces are steady as there is no perturbation. From ten meters before the beginning of the switch blade on the track is modeled as being flexible. When the vehicle reaches the flexible part some transient phenomena take place due to the transition from rigid to flexible track. Because of the flexibility of the rail the wheelsets sink a bit between sleepers; this motion causes oscillations in the wheelrail contact force, see Fig. 1 and 2. The effect is the largest for the vertical contact force but due to the contact angle the oscillations have also a component in the lateral direction. This oscillation is visible throughout the whole turnout, its frequency can be read from Fig. 2: 33 Hz with the vehicle speed of 20 m/s; this corresponds to a wavelength of 0.6 m, which is the sleeper span. When a wheelset reaches the switch blade two-point contact takes place; with this the contact point changes from the tread to the flange. Once in the turnout the flange contact continues to counteract the lateral forces and negotiate the curve . At the frog there is a clear impact leading to high forces. Figures 3 shows the lateral forces on all the wheelsets of a vehicle coasting through a turnout. With the rigid model in Fig. 3(a) the impact of the wheelset on the frog is absorbed only by the Hertzian wheel-rail contact; this leads to very high contact forces, also in the lateral direction. A flexible track model, in Fig. 3(b), seems more realistic to obtain the impact force as the lateral wheel-rail impact force is half the force obtained with a rigid track. For the lateral forces on the switch blade and in the turnout shown in figure 4 the story is more complicated. The lateral wheel-rail force on the first wheel of the front bogie is slightly higher for the flexible track and the force on the second wheel lower. The opposite is the case for the rear bogie.
(a) Rigid track (b) flexible track Figure 3. Lateral force on the wheelsets of a vehicle running through a turnout at 20 m/s)
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(a) Front bogie
(b) Rear bogie Figure 4 Lateral force on the wheelsets of a vehicle coasting through a turnout at 20 m/s 3.2 Two couches Figures 5 and 6 show the lateral forces on all the wheelsets of a two-coach train pushed through a turnout. Traction is applied on the wheelsets of the rear bogie of the last vehicle with 4000 Nm per wheelset, equivalent to a forward longitudinal force of 17.4 kN. This causes a peak dynamic pushing force of 11.2 kN in the coupler. Due to curving the lateral component of coupler force is 1450 N, this force influences the curving behavior. In figure 5 it can be seen that the extra force due to the pushing of the rear coach is largest for the fourth wheelset of the first coach and the second wheelset of the second coach, compare which curve if Fig. 5(a) with which curve of Fig. 5(b). In Figure 6 it can be seen that applying traction deteriorate curving behavior of the bogie – the contact forces are increased; this is in agreement with the conclusions by Grassie and Elkins [5].
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(a) Rear bogie of the pushed coach (b) Front bogie of the pushing coach Figure 5 Lateral wheel-rail forces for a coasting train and for a train with traction on the wheelsets of the rear bogie of the second coach
Figure 6 Lateral wheel-rail forces of the rear bogie of the second coach with and without traction on that wheelsets
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COMPARISON WITH MEASUREMENT
Measured lateral axle box accelerations (ABA) of a measurement vehicle on straight track show a dominant wavelength corresponding with the hunting wavelength of 4 m; this wavelength is used to tune the vehicle model so that the simulated wavelength corresponds to the measured wavelength. The lateral ABA measured in a 1:9 turnout is then compared with simulation results in Figure 7. In the measurements a negative acceleration can be seen just before the turnout; this might be due to lateral track shift. The impact at the frog can be seen in the simulated ABA but not in the measurements; this could be because in the simulation the angle of attack of the wheelset or the turnout geometry is not realistic at the frog. The angle of attack might be different because of a difference in the vehicle characteristics or because the phase of the hunting movement initiated at the switch blade is not simulated accurately. A preliminary simulation has been done with an adapted turnout geometry. Around the beginning of the switch blade the track was shifted outwards 10 mm for a length of 3 m, using a sine function. At the frog the outer rail was shifted outwards 10 mm for 2 m. The new geometry causes a negative acceleration just before the beginning of the switch, this is compensated by a higher acceleration just after the switch. At the frog the modified geometry causes the lateral impact to be lower. These indicates that by parameter variation the real track geometry could be identified and ABA might be a method to detect geometry irregularities in turnouts. More work needs to be done in this regards.
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Figure 7 Lateral acceleration of the axle box measured at a turnout close Eindhoven station, low-pass filtered at 30 Hz (vehicle speed: 11 m/s)
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FUTURE WORK
Improvements to the model may include rail bending in the lateral-vertical plane and adding sleeper flexibility to the model. Also the restriction that the sleeper/rail cannot move in longitudinal direction should be closely examined. In order to determine the impact forces at the frog more accurately it will be necessary to consider the wheelset as being flexible. The wheel-rail contact was modeled using FASTSIM; in the future the effect of more advanced methods should be investigated . More work is needed to correlate ABA and parameters of the model. Further more complex situations can be studied such as a long train (6-12 coaches) pushed through a series of sharper turnouts (1:9), as this often happens at shunting yards or stations, so that the effect of vehicle length and the critical number of vehicles, traction force, speed and curvature can be determined.
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CONCLUSIONS
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Pushing a train of two coaches through a turnout increases the lateral forces on the first wheelset of the rear bogie of the pushed coach and the first wheelset of the pushing coach significantly. Flexible track is more realistic in calculating the impact force at frog. Modeling the track as flexible instead of rigid seems to has only a small effect on the overall vehicle dynamics.
References [1] W-J Zwanenburg: Modelling degradation processes of switches & crossings for maintenance & renewal planning on the Swiss railway network. PhD thesis at EPFL (no 4176), 2009. [2] R. Menssen and W. Kik: Running through a Switch - Simulation and Test, Vehicle Dynamics, Vol. 23, pp. 378-389, 1994. [3] E. Kassa and J. Nielsen: Dynamic interaction between train and rail-turnout: full-scale field test and validation of simulation model, Vehicle System Dynamics, Vol. 46, 1, pp. 521-534, 2008. [4] S. Alfi and S. Bruni: Mathematical modelling of train-turnout interaction. Vehicle System Dynamics. Vol. 47, pp. 551-574, 2009. [5] L. Grassie and J. Elkins: Traction and curving behaviour of a railway bogie, Vehicle System Dynamics. Vol. 44: S1, 883-981, 2006 [6] Z. Li, X. Zhao, C. Esveld, R. Dollevoet and M. Molodova: An investigation into the causes of squats— Correlation analysis and numerical modeling, Wear, Vol. 265, pp. 1349-1355, 2008. [7] O. Arias-Cuevas, Z. Li, and C. Esveld: Simulation of the lateral dynamics of a railway vehicle and its validationbased on rail wear measurements, Proceedings of the ECCOMAS Thematic Conference on Multibody, Politecnico di Milano, 2007. [8] G. Bachman, L. Narici and E. Beckenstein: Fourier and wavelet analysis, ISBN 0-387-9889-8, 2000. 6
