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264 Runge Kutta scheme is that it is self starting and forwardsolving. This simplifies the starting of the simulation and reduces number of initial conditions that need to be set. III. INTERACTION OF LONGITUDINAL TRAIN AND LATERAL/VERTICAL WAGON DYNAMICS Traditionally, the study oflongitudinal train dynamics has considered wagons as single degree of freedom masses connected with either spring–damper units or nonlinear wagon connection models. Theinputs to the system are arranged and applied to the modelinthe longitudinal direction, i.e., locomotive forces, grade forces, and resistanceforces. Similarly, the study of wagon dynamics has focused on lateral and vertical wagon dynamics with the inputs being from the track geometry. Depending on the way arail system develops, there could becases where the interaction of train and wagon dynamics should be considered. Interaction has the potential to become aproblem when freight train lengths become large, giving rise to both larger steady and impact forces. Impacts can be reduced by reducing coupling slack. Largersteady forces can be reduced by adopting distributed power configurations and appropriate control techniques. It should not be assumed that adopting distributed power alone will reduce all in-train forces. The discussion in Section VI shows that inappropriate use of distributed power can lead to very high in-train forces and pull-aparts. Another key factor is the rate at which rail infrastructure development matches the rollingstock development. When the rail infrastructure is driven by high-speed passenger train requirements, mild curvatures will tend to ensure that lateral components of in-train forces are minimal. Three modes of train–wagon interaction can be considered: † Wheel unloading on curves due to lateral components ofcoupler forces. † Wagon body pitch due to coupler impact forces. † Bogie pitch due to coupler impact forces. A . W HEEL U NLOADING ON C URVES DUE TO L ATERAL C OMPONENTS OF C OUPLER F ORCES The published work usually referred to in this area is that of El-Sibaie, 4 which presented experimental data and simulation of wheel unloading due to lateral force components incurves. Wheel unloading was shown toincrease for: increased in-train forces, decreased curve radius and long–short wagon combinations (i.e., the effect of differing wagon body lengths and bogie overhang distances). The usual method of analysis is to complete alongitudinal train simulation to obtain coupler force data. Coupler angles are then calculated allowing lateral components of coupler forces to be calculated. The lateral force components are then applied to afully detailed wagon dynamics model tostudy the resulting wheel unloading and lateral/vertical wheel force ratios. B . W AGON B ODY P ITCH DUE TO C OUPLER I MPACT F ORCES Handbook of Railway Vehicle Dynamics Wagon body pitch can occur in response to alongitudinal impact force and is due to the centre of mass of the wagon being higher than the line of action of the coupler. As this is the mechanism, body pitch is most likely in loaded wagons. Body pitch is unlikely in empty wagons as the centre of mass is usually close to coupler level. Simulation studies using various models and packages were published byMcClanachan et al. 5 Asample result from this paper is shown in Figure 9.37. The longitudinal force of , 380 kN results in body pitch and at least 10% wheel unloading. © 2006 by Taylor & Francis Group, LLC
Longitudinal Train Dynamics 265 Longitudinal Force, kN Inter-wagon Distance, m 400 200 0 - 200 Front Rear Sum - 400 15.5 15.7 15.9 16.1 Time,s 0.08 0.06 0.04 0.02 0 Front Rear - 0.02 15.5 15.7 15.9 16.1 Time,s C . B OGIE P ITCH DUE TO C OUPLER I MPACT F ORCES - 30 15.5 15.7 15.9 16.1 Time,s Similarly, coupler impacts can be sufficient to accelerate or deceleratethe wagon so rapidly that the bogies will pitch. This behaviour is most likelytooccur in empty wagons. When awagon is empty, the line of action of the coupling forceisclose to the same level as the wagon body centre of mass. Wagon Acceleration, m/s/s Vertical Axle Force, % 30 20 10 0 - 10 - 20 20 15 10 5 0 - 5 - 10 Axle 1 2 3 4 - 15 15.5 15.7 15.9 16.1 Time,s FIGURE 9.37 Wagon body pitch —loaded in aloaded unit train. 5 Source: From McClanachan M., Cole C., Roach D., and Scown B., The Dynamics of Vehicles on Roads and on Tracks-Vehicle Systems Dynamics Supplement 33, Swets &Zeitlinger, Amsterdam, pp. 374–385, 1999. With permission. Longitudinal Force, kN Inter-wagon Distance, m 400 200 0 - 200 Front Rear Sum - 400 15.5 15.7 15.9 16.1 0.08 0.06 0.04 0.02 0 Time,s Front Rear - 0.02 15.5 15.7 15.9 16.1 Time,s Wagon Acceleration, m/s/s Vertical Axle Force, % 30 20 10 0 - 10 - 20 - 30 15.5 15.7 15.9 16.1 20 15 10 5 0 - 5 - 10 Axle Time,s 1 2 3 4 - 15 15.5 15.7 15.9 16.1 Time,s FIGURE 9.38 Bogie pitch —empty wagon in empty unit train. 5 Source: From McClanachan M., Cole C., Roach D., and Scown B., The Dynamics of Vehicles on Roads and on Tracks-Vehicle Systems Dynamics Supplement 33, Swets &Zeitlinger, Amsterdam, pp. 374–385, 1999. With permission. © 2006 by Taylor & Francis Group, LLC
Page 1 and 2: 9 CONTENTS Longitudinal Train Dynam
Page 3 and 4: Longitudinal Train Dynamics 241 ass
Page 5 and 6: Longitudinal Train Dynamics 243 By
Page 7 and 8: Longitudinal Train Dynamics 245 Pol
Page 9 and 10: Longitudinal Train Dynamics 247 For
Page 11 and 12: Longitudinal Train Dynamics 249 If
Page 13 and 14: Longitudinal Train Dynamics 251 var
Page 15 and 16: Longitudinal Train Dynamics 253 For
Page 17 and 18: Longitudinal Train Dynamics 255 Com
Page 19 and 20: Longitudinal Train Dynamics 257 Tra
Page 21 and 22: Longitudinal Train Dynamics 259 Bra
Page 23 and 24: Longitudinal Train Dynamics 261 The
Page 25: Longitudinal Train Dynamics 263 G .
Page 29 and 30: Longitudinal Train Dynamics 267 FIG
Page 31 and 32: Longitudinal Train Dynamics 269 tak
Page 33 and 34: Longitudinal Train Dynamics 271 “
Page 35 and 36: Longitudinal Train Dynamics 273 Res
Page 37 and 38: Longitudinal Train Dynamics 275 ope
Page 39: Longitudinal Train Dynamics 277 V f

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