
 Does anyone have, or know where to find an explanation of
 the relationship between back emf and the mechanical power
 at the shaft of an AC electric motor other than I Eb. I'm
 referring to the theory that the mechanical power at the
 shaft is due to the electrical power expended against the
 back emf or back current. TIA

 Bill W.

Bill, I think you might have your wires crossed a little.
Let me have a go at explaining.
I will use a DC motor as an example because it is easier to get your head
around, but the same thing applies to AC motors as well ( well kinda, at
least )
An electric motor can only deliver power against a mechanical load. If you
take away the mechanical load the motor will spin at it's unloaded speed,
drawing very little power.
Counter Electro Motive Force ( CEMF ) is a voltage generated by the
armature of a motor turning inside the magnetic flux of it's field. (
voltage is proportional to RPM and Flux density, along with a couple of
constants)
Consider the simplist case of an unloaded DC motor, initially at standstill,
powered by a battery, with a separately excited field (Shunt field ). At the
instant the armature circuit is closed, the armature CEMF is zero because
the motor is stationary. the only effective resistance in the circuit is the
resistance of the armature. THe current that will flow in the armature
circuit is simply the battery voltage divided by the resistance of the motor
armature, I armature = V battery / R armature
this current will be realtively large and the resulting torque produced by
the armature windings will start to accelerate the armature.
Once the armature starts to turn, you have a winding rotating in a magnetic
field. This motion will start to produce a voltage, Which just happens to
be of the opposite polarity as that of the battery, ( Thus COUNTER EMF )
Now our calculation of current has to take into account , this voltage
subtracting from the battery voltage. Thus
I armature = (V battery  V cemf) / R armature.
considering the CEMF opposes the battery voltage, the net circuit voltage
will be less then it was before, Thus the current will start to fall as the
motor accelerates.
Once the motor reaches it's full no load speed, the generated counter EMF
will almost match the battery voltage, thus the net voltage will be very
small and the current flowing will be small. Basically a balance is reached
where windage and friction of the unloaded motor slows the motor to a speed
where the difference in voltage between the battery voltage and the CEMF is
enough to have the right amount of current ( read force) to overcome these
losses.
This is called the "No Load Current"
Lets assume we have the equipment to apply an infinitely variable load to
this motor. If we apply some load to the motor shaft, The balance of forces
would be upset because the total load would be greater then the force, the
"No Load current" can provide. The result is the motor slows a little.
With this slowing , comes a reduction in the motor CEMF. The net result is
the diffrernce between the battery voltage and the CEMF is greater, and
thus the armature current will increase.
This Increased current, results in increased torque ( read force) and at
some stage a new balance is reached where again the torque produced by the
motor armature current. matches the torque of the mechanical load. So
effectively the motor has slowed. however the torque has increased to match
the torque of the load. ( the amount the motor slows is referred to as the
"droop" )
If we continue to increase the load on the motor , the speed will continue
to fall, until such times as the "Full load current" is flowing.
If the applied Armature voltage is set at the "Motor rated voltage", and the
voltage on the field is set to "motor rated field", The power delivered at
this speed and torque is said to be "Rated power" of the motor, and the
speed of the motor is said to be at "Rated Speed" .
These values are normally specified for a particular motor design and are
stamped on the motor "Name Plate"
If the mechanical load was suddenly removed, the motor would quickly
accelelrate back up to it's "No Load Speed" and sit there with " No Load
curnent" flowing.
As long as we leave the terminal volts constant the behaviour under varying
loads will be that the motor speed changes up or down until the current
flowing produces enough torque to match what ever load is applied.
If the load is increased beyond motor rated, Nothing magical happens, The
motor simply slows down even further and the current increases until the net
motor torque matches the torque demanded by the mechanical load.
This is termed as "over loading the motor" , and if sustained for any length
of time will result in the internal temperature rising to an excessive
level. This excessive temperature will result in premature failure of the
winding insulation, or in more common terms " Motor Burned out"
Now typically we employ control systems to keep the motor at some desired
speed, independant of load, To do this, the "Battery voltage", so to speak,
is increased as a function of load, instead of letting the motor slow, so
that the desired armature current or torque is acheived without the
armature speed (or CEMF) decreasing.
The Back EMF is a funtion of the motor speed and the field current ONLY.
The actual speed the motor goes for any given load can vary depending on the
control system employed.
Translating this to AC motor theory, is not so simple, but basically the
field of an AC Induction motor is produced by current in the Squirrel cage
winding, which itself is a function of the slip between the stator and the
rotor. Counter EMF is still dependent on the motor speed ( which does not
change a lot in the normal operating range) and the field flux, which is
dependent on how much the motor slows for a given load.
Again the input voltage is fixed by virtue of the fixed line voltage. supply
frequency is normally fixed so, as in the example above, the only thing
the motor can do to respond to an increasing load is to slow down.
As it slows, the slip between the stator and the rotor increases, causing
the field (or excitation current) to increase.
The net result of the slowing motor speed and the increasing Field flux is a
net reduction in Motor CEMF. Lower CEMF with fixed supply ( as above) will
result in more Armature ( read LINE) current thus more torque.
Again A balance is reached where the torque produced by the combination of
increased field, and increased line curent, matches the torque demanded by
whatever the mechanical load is.
The counter EMF in this case is still the direct function of the motor speed
and the motor excitation Flux. NOT directly related to mechanical load, but
effected by it in any case.
Well That is my attempt,
I know it is a little long but maybe it made sense
Good Luck
Tom Grayson
10 Nov 2003