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Longitudinal Train Dynamics 255
Combined Draft
Gear Model
Limiting Stiffness or
'locked stiffness'
FIGURE 9.25 Wagon connection model —drawbar coupled wagon.
conventional autocouplers at either end. Drawbar connections, which connect toenergy absorbing
draft gear, have the advantage of retaining full capability to absorb impact energy. Modelling
drawbarswith energy absorbing draft gear units is simplyamatter of removing mostofthe coupler
slack from the model, Figure 9.25.
C . L OCOMOTIVE T RACTION AND D YNAMIC B RAKING
When developing atrain model it is logical to treat tractive effort and dynamics braking in the same
mathematical model, as both introduce forces to the train via the locomotive–wagon connections.
The modelling oflocomotive traction/dynamic brake systems is asubject in itself. The complexity
of the model required will depend on the particular aspect(s) of locomotive performance that are
important for analysis and/or how complex the installed locomotive control systems are. Modern
locomotive design has incorporated many performance improvement features. For afully detailed
model, the following may need consideration:
† Torque derating due to thermal effects.
† Limited power application control (pollution control).
† Adhesion limit.
† Traction slip controls.
† Steerable traction bogies.
† Extended range dynamic braking.
Minimal
Coupler Slack
The traction control,knownasthrottle notch, is used to set acurrent reference. Typically, diesel
electric locomotives have eight notches or levels of throttle adjustment. Fully electric haulage
locomotives may have differing control systems, e.g., in Australia there are electric locomotives in
service with 31 notches (i.e., 32 control positions, 2 5 ). At low speeds the traction system is limited
by current so tractive effort is applied proportionally to throttle notch levels. Tractive force
delivered in this region may be independent of speed, or reduce with speed, depending on
the locomotive characteristics and control. At higher speeds the system is limited by power so
the tractive effort available decreases at increased speeds according to force velocity product
P ¼ F t = dbv : An example ofatypical locomotive performance curve is given in Figure 9.26. Itwill
also be noticed that because the control is acurrent reference, the powercurve is proportional to the
square of the throttle notch.
Atypical equation set for modelling tractive effort would be:
© 2006 by Taylor & Francis Group, LLC
For F t = dbv , ð N 2 = 64Þ P max F t = db ¼ðN = 8 Þ Te max 2 k f v ð 9 : 18Þ