22-12-2012, 05:11 PM
Tractive effort, acceleration and braking
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Context
For a railway to operate efficiently and safely, its locomotives should be powerful
enough to accelerate their trains rapidly to the maximum allowed line speed, and the
braking systems must be able to bring a train reliably to a standstill at a station or
signal, even on an adverse gradient. Railway operators need to calculate train
accelerations and decelerations in order to plan their timetables, and signals must be
sited so as to allow adequate stopping distances for all the various passenger and
goods services that they are required to control.
In practice there are many different and complex considerations that must be included
in a realistic model of railway operation. Here, just some of the simpler main issues
are identified and examined, in order to show how mathematical analysis can be used
to provide an indication of expected performance. The data values used in the
examples (from [1]) do not refer to any specific operating company, locomotive or
rolling stock, but are chosen to give realistic illustrations of how practical equipment
might behave.
Drag
Inevitably, a moving train exerts a drag on the locomotive propelling it. This force,
which opposes the motion, comes from a variety of sources, the most important being
friction in the axle bearings, air resistance, and resistance from the rail as the wheels
roll along it. Railway operators estimate drag from experiments which measure the
force needed to keep a train moving at a constant speed. Polynomials can again be
used to approximate the variation of drag with speed, and it is generally agreed in the
railway industry that a quadratic function often suffices over the full range, although
the coefficients used will vary from railway to railway and with train type.
Time spent accelerating to required speed
Each stop that a train makes during its journey involves three phases: braking to a
standstill, remaining stationary to set down and pick up passengers, and accelerating to
the required line speed. An appropriate allowance for the time taken for each of these
phases, as well as other braking and acceleration manoeuvres (e.g. to traverse a set of
points) must be included when drawing up realistic timetables. The previous section
considered time taken for braking; calculation of the time taken in acceleration is
similar, but somewhat more involved because of the piecewise-linear approximation
to the variation of tractive effort with speed.
Diesel and electric locomotives
For a diesel-electric locomotive or electric locomotive, starting tractive effort
can be calculated from the stall torque of the traction motors (the turning force
it can produce while at a dead stop), the gearing, and the wheel diameter. For a
diesel-hydraulic locomotive the starting tractive effort depends on the stall
torque of the torque converter.
In general, it is more common for heavy freight trains (such as Class 59, Class
60 and Class 66 locomotives) to have a high maximum tractive effort due to
the mass which they haul. Passenger trains (such as Class 43/Intercity High
Speed Train locomotives) usually have much lower maximum tractive efforts
due to the higher gear ratio required for a higher top speed.
Stall torque
Stall torque is the torque which is produced by a device when the output
rotational speed is zero, it may also mean the torque load that causes the output
rotational speed of a device to become zero - i.e. to cause stalling
Devices such as electric motors, steam engines and hydrodynamic
transmissions produce torque under these conditions.
Electric motors continue to provide torque when stalled. However, electric
motors left in a stalled condition are prone to overheating and possible damage
since the current flowing is maximum under these conditions.
The maximum torque an electric motor can produce in the long term when
stalled without causing damage is called the maximum continuous stall
torque.
Torque converter
A torque converter is a modified form of fluid coupling that is used to transfer
rotating power from a prime mover, such as an internal combustion engine or
electric motor, to a rotating driven load. Like a basic fluid coupling, the torque
converter normally takes the place of a mechanical clutch, allowing the load to
be separated from the power source. As a more advanced form of fluid
coupling, however, a torque converter is able to multiply torque when there is a
substantial difference between input and output rotational speed, thus providing
the equivalent of a reduction gear.
Function
Torque converter elements
A fluid coupling is a two element drive that is incapable of multiplying torque,
while a torque converter has at least one extra element—the stator—which
alters the drive's characteristics during periods of high slippage, producing an
increase in output torque.
In a torque converter there are at least three rotating elements: the pump, which
is mechanically driven by the prime mover; the turbine, which drives the load;
and the stator, which is interposed between the pump and turbine so that it can
alter oil flow returning from the turbine to the pump. The classic torque
converter design dictates that the stator be prevented from rotating under any
condition, hence the term stator.