Machine terminology problem.
Machine terminology problem.
(OP)
Having difficulty understanding a bit of machine terminology and I’m hoping you chaps might be able to help…
The main field of an alternator can be thought of as a single phase winding, producing one field travelling in one direction and another field travelling in the opposite direction.
Discuss?!?!
The main field of an alternator can be thought of as a single phase winding, producing one field travelling in one direction and another field travelling in the opposite direction.
Discuss?!?!






RE: Machine terminology problem.
A field oscillating along a linear axis is roughly equivalent to sum of a forward and backward rotating field.
The proof is shown as follows:
Forward rotating wave is
Forward = cos(w*t + p*theta)
Applying cos(a+b) = cos(a)cos(b)-sin(a)sin(b) we have
Foward = cos(w*t)cos(p*theta) -sin(w*t)sin(p*theta)
Backward rotating wave is
Backward = cos(w*t - p*theta)
Applying cos(a-b) = cos(a)cos(b)+sin(a)sin(b) we have
Backward = cos(w*t)cos(p*theta) +sin(w*t)sin(p*theta)
Add the forward and the backward waves
Forward + Backward = 2 * cos(w*t)cos(p*theta)
This result have a shape in space which is fixed over time (cos(p*theta)). At any point it varies sinusoidally. It is a stationary variation, not a rotating variation.
What was the question?
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RE: Machine terminology problem.
For three phase motors, each phase has forward and reverse rotating phase. But when you add the three phases together, the forward components add and the reverse components cancel so the stationary stator winding is capable of generating a true rotating field (without those extra starting gadgets).
Notice I focus on the field associated with the stator. If you add the rotor field into your question, clearly it is rotating.
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RE: Machine terminology problem.
cos(a)cos(b) = 0.5*[cos(a+b)+cos(a-b)]
This leads directly to:
cos(w*t)cos(p*theta) = 0.5* [cos(w*t+theta) + cos(w*t-theta)
LHS does not rotate.
RHS is sum of forward and backward rotating field.
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RE: Machine terminology problem.
Pete has demonstrated that a single phase sinewave generates two rotating fields with opposing directions. I guess that the next question is "how can two opposing fields generate torque in a rotor?"
To make things simple, consider the rotor of an induction machine having a resistance and an inductance. The magnetic field induces a current in the rotor and the current is proportional to frequency divided by rotor winding impedance (Ir = k*f/sqrt(R^2 + X^2) or Ir = k*f/sqrt(R^2 + (2*pi*f*L)^2)
Torque is the result of magnetic field times rotor current (Ir) times cosine(alpha), where alpha is the phase-shift between magnet field and Ir.
Looking at the two rotating fields and the Ir induced in the rotor, you will see two identical currents that produce identical, but opposing, torques. So the net torque is zero.
If the rotor is set in motion in one direction, the Ir frequency corresponding to that direction decreases and so does the phase shift. The current magnitudes remain approximately constant as long as X >> R. The result is a net torque working in the same direction as the rotation, and the motor accelerates.
When it gets up in speed, the X part goes down even more and the phase shift between field and rotor current gets close to zero. At the same time, the opposing current stays nearly constant (double frequency makes R very small compared to X and the opposing current is given by k*f/(2*pi*f*L) or k/(2*pi*L) with a 90 degree phase shift.
This means that the "constructive" torque is proportional to slip and that "destructive" torque is essentially zero - or very close to.
This is the (quite verbose, admitted) explanation to how a single-phase induction motor (with or without an auxiliary winding) works. If it has an auxiliary winding, it can be switched off once the motor is running.
Gunnar Englund
www.gke.org
RE: Machine terminology problem.
I note a paradox in the equations. I think I know the answer but I'd rather call it a quiz for you guys:
Ir = k*f/sqrt(R^2 + (2*pi*f*L)^2) where f is slip frequency.
This suggests that rotor current is lowest at low slip and steadily increases as slip increases until it flattens out at very high slip at max value k / (2*Pi*L). So we would conclude that the reverse current at full speed (slip = 2) would be as high or higher than the current during starting (slip = 1).
Can you spot the flaw in this argument?
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RE: Machine terminology problem.
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RE: Machine terminology problem.
Thanks again
RE: Machine terminology problem.
Gunnar Englund
www.gke.org
RE: Machine terminology problem.
I am trying to put together a picture of how large is that reverse current.
During initial start I have LRC. That includes a forward component and a reverse component. There is no symmetry which favors forward or reverse at the moment of start so I assume the forward and reverse components of rotor current each cause approx LRC/2 worth of stator current (neglecting magnetizing current which is typically much less than LRC... at least based on my experience with 3-phase motors... never worked with 1-phase much).
So now let's say I start the motor and get to full speed and run the motor unloaded. My reverse rotor current is still as high or higher than during start (as discussed above approaches k / (2*Pi*L)). So do we see stator no-load current of single-phase motors approaching LRC/2?
I don't know but I don't think so. I must be missing something. I realized single-phase motors were less efficient for a variety of reasons but I didn't realize they had that large of a reverse current.
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