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Torque Speed CurveGeneral CurveUsing the induction machine power
and torque equations it is possible to produce thetorque speed
curve shown below.
The torque speed curve is approximately symmetric about
synchronous speed. (Themagnitude of the peak negative torque is
larger than the positive torque, thedifference being a function of
stator resistance)Operating RegionsThe torque speed curve brakes
down into three operating regions!
". #raking, n m < 0, s > 1Torque is positive whilst speed
is negative. $onsidering the power conversionequation
it can be seen that if the power converted is negative (from P =
) then theairgap power is positive. i.e. the power is flowing from
the stator to the rotorand also into the rotor from the mechanical
system. This operations is alsocalled plugging .This mode of
operation can be used to quickly stop a machine. %f a motor
istravelling forwards it can be stopped by interchanging the
connections to two
of the three phases. &witching two phases has the result of
changing thedirection of motion of the stator magnetic field,
effectively putting the machineinto braking mode in the opposite
direction.
'. otoring, 0 < n m < n s , 1 > s > 0 Torque and
motion are in the same direction. This is the most common modeof
operation.
. *enerating, n m > n s , s < 0 %n this mode, again torque
is positive whilst speed is negative. +owever, unlikeplugging,
"
http://www.ece.ualberta.ca/~knight/electrical_machines/induction/basics/pandt.htmlhttp://www.ece.ualberta.ca/~knight/electrical_machines/induction/basics/pandt.html
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Using the above equation, the variation of torque with slip can
be plotted directly .ote that if power or efficiency calculations
are needed, the full equivalent circuitmodel should be used (not
the Thevenin version).
Motoring Torque CharacteristicThe motoring region of the
induction machine torque speed curve is the region ofgreatest
interest. The plots below show a number of different torque speed
curves,due to differences in the motor designs. $ommon features of
interest are noted anddiscussed below.
rated . The rated torque of the machine. This is the design
operating point. start . The start torque of the machine, when the
machine is at standstill. max or po . The maximum torque or pull
out torque. -nce a machine has
reached rated operating point, this is the maximum torque that
can be appliedwithout stopping the machine (pulling out). %n
reality, since this torque issignificantly more than the design
rated torque, operation at maximum torqueis not possible due to
thermal heating issues. ($urrents will be above rated
values, I 2
R losses will be excessive.)
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pu . The pull up torque of the machine. %n some machines, the
lowest point onthe torque speed curve between starting and pullout
is not the start torque. %nthis case it is important to know the
pull up torque. This is the minimum torquethat the motor can
accelerate up to the desired operating speed.
%n steady state operation, an induction motor will operate at
the speed where themechanical load torque equals the torque
developed by the motor. t low speeds,the difference between the
motor torque and the load torque accelerates themachine. ormal
operation is to the right of the maximum torque. %n this region,
anincrease in the load torque will cause the motor to slow,
increasing the motor torqueuntil an equilibrium is reached. To the
left of the pullout torque, no such equilibriumcan be reached.
echanically,
where J is the rotational inertia of the mechanical system.
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