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252 asingle look up table representing the two draft gear springs in series and then tuning draft gear modelparameters to suit adraft gear pair.The slack element can be added either in the look up table or added in series.Different parameterscan be chosenfor loading and unloadingcurves. The small kick in the unloading curve is observed in some test data. The dynamicist can also implement slightly different values of, f , V f , m s and m k for the unloading curve if required toobtain agood fit to the experimental data. There is always room for debate as to whether acomplex model asdescribed here is justified whencomparedtothe simpler yetdetailed work by Duncan and Webb. 1 Theuser may decide on the complexity of the model according to the purpose and accuracy required for the simulation studies being completed. While the wedge friction model adjusts for different impact conditions, its use is really justified for simulations where these conditions are expected to vary. The use of the wedge model for the unloading curve is an area where asimple lookup table may suffice, as it is only the loading curve data that shows large variations in stiffness. The following figures show the response of the model with sine wave inputs with frequencies of 0.1, 1.0, and 10.0 Hz. This frequencyrange covers both normal train operation and loose shunt impact conditions, Figures 9.19 to 9.21, inclusive. These results were obtained byapplying the friction wedge model only to the loading curve. 9 Train simulations using this model are given in Figure 9.22 and Figure 9.23. Force and acceleration traces are plotted for train positions: first and last connected couplers and wagons positioned at intervals of 20% of train length. Both simulations are for adistributed powertrain for which athrottle disturbance is added at time ¼ 38 sec. The first result showing sinusoidal locked behaviourhas the train situated on acrest with the top of the crest situated in the first wagon group. The second result uses exactly the same control input on flat track. It will be noted inFigure 9.22 that while longitudinal forces behave sinusoidally between time ¼ 40 sec and time ¼ 100 sec, wagon accelerations are steady demonstrating locked draft gear behaviour. This is contrasted with the oscillatory nature of wagons longitudinal behaviour for the sameperiod and control input on flat track, Figure 9.23. The difference between what Duncan and Webb referred to as sustained longitudinal vibration and cycle vibration can be identified in Figure 9.22 and Figure 9.23, respectively. Force, kN 2500 2000 1500 1000 500 0 - 500 - 1000 - 1500 - 2000 Model Output Full Drop Test Data Friction Wedge model - 2500 - 200 - 150 - 100 - 50 0 50 100 150 200 Deflection, Incl, Slack, mm Handbook of Railway Vehicle Dynamics FIGURE 9.19 Draft gear model response —slow loading (0.1 Hz). 9 Source:From Cole, C., Improvements to wagon connection modelling for longitudinal train simulation, Conference on Railway Engineering, Rockhampton, Institution of Engineers, Australia, pp. 187–194, 1998. With permission. © 2006 by Taylor & Francis Group, LLC
Longitudinal Train Dynamics 253 Force, kN 2500 2000 1500 1000 500 0 - 500 - 1000 - 1500 - 2000 Model Output Full Drop Test Data Friction Wedge model - 2500 - 200 - 150 - 100 - 50 0 50 100 150 200 Deflection, Incl, Slack, mm FIGURE 9.21 Draft gear model response —shunt impact (10 Hz). 9 Source: From Cole, C., Improvements to wagon connection modelling for longitudianl train simulation, Conference on Railway Engineering, Rockhampton, Institution of Engineers, Australia, pp. 187–194, 1998. With permission. Coupler Force, kN Force, kN 2500 2000 1500 1000 500 800 700 600 500 400 300 200 100 0 - 100 0 20 40 60 80 100 0 - 500 - 1000 - 1500 - 2000 Time,s Model Output Full Drop Test Data Friction Wedge model - 2500 - 200 - 150 - 100 - 50 0 50 100 150 200 Deflection, Incl, Slack, mm FIGURE 9.20 Draft gear model response — mild impact loading (1 Hz). 9 Source: From Cole, C., Improvements to wagon connection modelling for longitudianl train simulation, Conference on Railway Engineering, Rockhampton, Institution of Engineers, Australia, pp. 187–194, 1998. With permission. Wagon Acceleration, m/s/s 2.5 2 1.5 1 0.5 0 - 0.5 - 1 - 1.5 - 2 - 2.5 0 20 40 60 80 100 Time, s FIGURE 9.22 Simulation results showing “locked” draft gear behaviour —crest track. © 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: Longitudinal Train Dynamics 251 var
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 and 26: Longitudinal Train Dynamics 263 G .
Page 27 and 28: Longitudinal Train Dynamics 265 Lon
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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