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Longitudinal Train Dynamics 259
Braking Force, kN
250
200
150
100
50
0
0 20 40 60 80 100 120
Velocity, kph
FIGURE 9.31 Dynamic brake characteristics —electric locomotives.
see characteristics on the right hand side of Figure 9.30 and both characteristics inFigure 9.31. In
these cases acombination of look up tables and mathematical functions will be required.
D . P NEUMATIC B RAKE M ODELS
0
0 20 40 60 80 100 120
The modelling of the brake system requires the simulation of afluid dynamic system that must
run in parallel with the train simulation. The output from the brake pipe simulation is the brake
cylinder force, which is converted bymeans of rigging factors and shoe friction coefficients into
aretardation force that is one term of the sum of retardation forces F r .
Modelling of the brake pipe and triple valvesystems is asubject in itselfand therefore will not
be treated in this chapter beyond characterising the forces that can be expected and the effect of
these forces on train dynamics. The majority of freight rollingstock still utilises brake pipe-based
control of the brake system. The North Americansystem differs in design from the Australian/U.K.
systems, but both apply brakes sequentially starting from the point where the brake pipe is
exhausted. Both systems depend on the fail-safe feature whereby the opening of the brake valve in
the locomotive, or the facture of the brake pipe allowing loss of brake pipe pressure, results in the
application of brakes in the train.
The implications for train dynamics is that the application of brakes can be accompanied by
severe slack action as the brakes nearest the lead of the train, closest to the brake control, apply
brakes first.For brakes applied at the leadofagroup of wagons 700 mlong, the initiationofbraking
at the last wagon typically lags the lead application by , 5sec, Figure 9.32. The brake system
shown in Figure 9.32 benefits from distributed locomotives allowing the release ofair at the lead
and mid train positions. The response at the mid point of the first wagon group (Vehicle 26) is faster
Brake Pipe Pressure, kPa
600
500
400
300
200
100
0
40 60 80 100
Time,s
Brake Cylinder Pressure,kPa
600
500
400
300
200
100
Braking Force, kN
250
200
150
100
50
Velocity, kph
0
40 60 80 100
Time,s
FIGURE 9.32 Brake pipe and cylinder responses —emergency application.
© 2006 by Taylor & Francis Group, LLC
Vehicle 3
Vehicle 26
Vehicle 77
Vehicle 105